  We report on our discovery of the radio pulsar, PSR J2016$+$3711, in
supernova remnant (SNR) CTB 87, with a $\sim10.8\sigma$ significance of pulses,
which confirms the compact nature of the X-ray point source in CTB 87. It is
the first pulsar discovered in SNRs using Five-hundred-meter Aperture Spherical
radio Telescope (FAST). Its integrated radio pulse profile can be well
described by a single component, with a width at 50% of the peak flux density
of about 28.1$^\circ$ and an effective width of about 32.2$^\circ$. The mean
flux density at 1.25 GHz is estimated to be about 15.5$\mu$Jy. Combined with
the non-detection of the radio pulse at lower frequencies, the radio spectral
index of the pulsar is constrained to be $\lesssim 2.3$. We also present the
timing solution based on 28 follow-up FAST observations. Our results reveal a
period of 50.81 ms, period derivative of $7.2\times 10^{-14}$ s s$^{-1}$, and
dispersion measure of 428 pc cm$^{-3}$. The strength of the equatorial surface
magnetic dipole magnetic field is inferred to be about $1.9\times10^{12}$ G.
Using the ephemeris obtained from the radio observations, we searched Fermi-LAT
data for gamma-ray pulsations but detected no pulsed signal. We also searched
for radio pulses with FAST toward the X-ray counterpart of the gamma-ray binary
HESS J1832$-$093 proximate to SNR G22.7$-$00.2 but found no signal.


  There exists a minimum integer $N$ such that any 2-coloring of
$\{1,2,...,N\}$ admits a monochromatic solution to $x+y+kz =\ell w$ for $k,\ell
\in \mathbb{Z}^+$, where $N$ depends on $k$ and $\ell$. We determine $N$ when
$\ell-k \in \{0,1,2,3,4,5\}$, for all $k,\ell$ for which
${1/2}((\ell-k)^2-2)(\ell-k+1)\leq k \leq \ell-4$, as well as for arbitrary $k$
when $\ell=2$.


  We study stochastic heat equations in the sense of Walsh defined by fractal
Laplacians on Cantor-like sets. For this purpose, we first investigate the
corresponding heat kernels. Then, we prove existence and uniqueness of mild
solutions to stochastic heat equations provided some Lipschitz and linear
growth conditions. We establish H\"older continuity in space and time and
compute the H\"older exponents. Moreover, we address the question of weak
intermittency.


  Event Shape Data from $e^+e^-$ annihilation into hadrons collected by the
JADE experiment at centre-of-mass energies between 14 GeV and 44 GeV are used
to determine the strong coupling $\alpha_S$. QCD predictions complete to
next-to-next-to-leading order (NNLO), alternatively combined with resummed
next-to-leading-log-approximation (NNLO+NLLA) calculations, are used. The
combined value from six different event shape observables at the six JADE
centre-of-mass energies using the NNLO calculations is
  $\alpha_S(M_Z)$= 0.1210 +/- 0.0007(stat.) +/- 0.0021(expt.) +/- 0.0044(had.)
+/- 0.0036(theo.) and with the NNLO+NLLA calculations the combined value is
$\alpha_S$= 0.1172 +/- 0.0006(stat.) +/- 0.0020(expt.) +/- 0.0035(had.) +/-
0.0030(theo.) . The stability of the NNLO and NNLO+NLLA results with respect to
missing higher order contributions, studied by variations of the
renormalisation scale, is improved compared to previous results obtained with
NLO+NLLA or with NLO predictions only. The observed energy dependence of
$\alpha_S$ agrees with the QCD prediction of asymptotic freedom and excludes
absence of running with 99% confidence level.


  Elastic nucleon scattering from the 3He and 3H mirror nuclei is examined as a
test of charge symmetry violation. The differential cross-sections are
calculated at 500 MeV using a microsopic, momentum-space optical potential
including the full coupling of two spin 1/2 particles and an exact treatment of
the Coulomb force. The charge-symmetry-breaking effects investigated arise from
a violation within the nuclear structure, from the p-nucleus Coulomb force, and
from the mass-differences of the charge symmetric states. Measurements likely
to reveal reliable information are noted.


  Noether's theorem is one of the fundamental laws in physics, relating the
symmetry of a physical system to its constant of motion and conservation law.
On the other hand, there exist a variety of non-Hermitian parity-time
(PT)-symmetric systems, which exhibit novel quantum properties and have
attracted increasing interest. In this work, we extend Noether's theorem to a
class of significant PT -symmetric systems for which the eigenvalues of the
PT-symmetric Hamiltonian H change from purely real numbers to purely imaginary
numbers,and introduce a generalized expectation value of an operator based on
biorthogonal quantum mechanics. We find that the generalized expectation value
of a time-independent operator is a constant of motion when the operator
presents a standard symmetry in the PT -symmetry unbroken regime, or a chiral
symmetry in the PT-symmetry broken regime. In addition, we experimentally
investigate the extended Noether's theorem in PT -symmetric single-qubit and
two-qubit systems using an optical setup. Our experiment demonstrates the
existence of the constant of motion and reveals how this constant of motion can
be used to judge whether the PT -symmetry of a system is broken. Furthermore, a
novel phenomenon of masking quantum information is first observed in a PT
-symmetric two-qubit system. This study not only contributes to full
understanding of the relation between symmetry and conservation law in PT
-symmetric physics, but also has potential applications in quantum information
theory and quantum communication protocols.


  The NTRU lattice is a promising candidate to construct practical
cryptosystems, in particular key encapsulation mechanism (KEM), resistant to
quantum computing attacks. Nevertheless, there are still some inherent
obstacles to NTRU-based KEM schemes in having integrated performance, taking
security, bandwidth, error probability, and computational efficiency \emph{as a
whole}, that is as good as and even better than their \{R,M\}LWE-based
counterparts. In this work, we solve this problem by presenting a new family of
NTRU-based KEM schemes, referred to as CTRU and CNTR. By bridging
low-dimensional lattice codes and high-dimensional NTRU-lattice-based
cryptography with careful design and analysis, to the best of our knowledge
CTRU and CNTR are the first NTRU-based KEM schemes with scalable ciphertext
compression via only one \emph{single} ciphertext polynomial, and are the first
that could outperform \{R,M\}LWE-based KEM schemes in integrated performance.
For instance, compared to Kyber that is currently the only standardized KEM by
NIST, on the recommended parameter set CNTR-768 has about $12\%$ smaller
ciphertext size while encapsulating 384-bit keys compared to the fixed 256-bit
key size of Kyber, security strengthened by $(8,7)$ bits for classical and
quantum security respectively, and significantly lower error probability
($2^{-230}$ of CNTR-768 vs. $2^{-164}$ of Kyber-768). In comparison with the
state-of-the-art AVX2 implementation of Kyber-768, CNTR-768 is faster by 1.9X
in KeyGen, 2.6X in Encaps, and 1.2X in Decaps, respectively. When compared to
the NIST Round 3 finalist NTRU-HRSS, our CNTR-768 has about $15\%$ smaller
ciphertext size, and the security is strengthened by $(55,49)$ bits for
classical and quantum security respectively. As for the AVX2 implementation,
CNTR-768 is faster than NTRU-HRSS by 19X in KeyGen, 2.3X in Encaps, and 1.6X in
Decaps, respectively.


  Few Shot Class Incremental Learning (FSCIL) with few examples per class for
each incremental session is the realistic setting of continual learning since
obtaining large number of annotated samples is not feasible and cost effective.
We present the framework MASIL as a step towards learning the maximal separable
classifier. It addresses the common problem i.e forgetting of old classes and
over-fitting to novel classes by learning the classifier weights to be
maximally separable between classes forming a simplex Equiangular Tight Frame.
We propose the idea of concept factorization explaining the collapsed features
for base session classes in terms of concept basis and use these to induce
classifier simplex for few shot classes. We further adds fine tuning to reduce
any error occurred during factorization and train the classifier jointly on
base and novel classes without retaining any base class samples in memory.
Experimental results on miniImageNet, CIFAR-100 and CUB-200 demonstrate that
MASIL outperforms all the benchmarks.


  The elliptic 3-manifolds are the closed 3-manifolds that admit a Riemannian
metric of constant positive curvature, that is, those that have finite
fundamental group. The (Generalized) Smale Conjecture asserts that for any
elliptic 3-manifold M, the inclusion from the isometry group of M to the
diffeomorphism group of M is a homotopy equivalence.
  The original Smale Conjecture, for the 3-sphere, was proven by J. Cerf and A.
Hatcher, and N. Ivanov proved the generalized conjecture for many of the
elliptic 3-manifolds that contain a geometrically incompressible Klein bottle.
Our main results are
  1. The Smale Conjecture holds for all elliptic 3-manifolds containing
geometrically incompressible Klein bottles. These include all quaternionic and
prism manifolds.
  2. The Smale Conjecture holds for all lens spaces L(m,q) with m at least 3.
  These results complete the Smale Conjecture for all cases except the
3-dimensional real projective space and those admitting a Seifert fibering over
the 2-sphere with three exceptional fibers of types (2,3,3), (2,3,4), or
(2,3,5).
  The technical work needed for these results includes the result that if V is
a Haken Seifert-fibered 3-manifold, then apart from a small list of known
exceptions, the inclusion from the space of fiber-preserving diffeomorphisms of
V to the full diffeomorphism group is a homotopy equivalence. This has as a
consequence:
  3. The space of Seifert fiberings of V has contractible components, and apart
from a small list of known exceptions, is contractible.
  Considerable foundational and background material on diffeomorphism groups is
included.


  Progress in simulating QCD at nonzero baryon density requires, amongst
others, substantial numerical effort. Here we propose two different expansions
to all orders in the hopping parameter, preserving the full Yang-Mills action,
which are much cheaper to simulate. We carry out simulations using complex
Langevin dynamics, both in the hopping expansions and in the full theory, for
two flavours of Wilson fermions, and agreement is seen at sufficiently high
order in the expansion. These results provide support for the use of complex
Langevin dynamics to study QCD at nonzero density, both in the full and the
expanded theory, and for the convergence of the latter.


  That shared features between train and test data are required for
generalisation in artificial neural networks has been a common assumption of
both proponents and critics of these models. Here, we show that convolutional
architectures avoid this limitation by applying them to two well known
challenges, based on learning the identity function and learning rules
governing sequences of words. In each case, successful performance on the test
set requires generalising to features that were not present in the training
data, which is typically not feasible for standard connectionist models.
However, our experiments demonstrate that neural networks can succeed on such
problems when they incorporate the weight sharing employed by convolutional
architectures. In the image processing domain, such architectures are intended
to reflect the symmetry under spatial translations of the natural world that
such images depict. We discuss the role of symmetry in the two tasks and its
connection to generalisation.


  We analyse the equilibrium pile-up configurations of infinite periodic walls
of edge dislocations which are forced against an impenetrable obstacle by a
constant applied shear stress. Numerically generated density distributions
exhibit two distinct regions, for each of which we provide an interpretation
and an analytical prediction. Near the obstacle, the influence of neighbouring
slip planes may be neglected and the classical solution for a single slip plane
applies. At a larger distance a linear decay is obtained. The characteristic
length scales of the two parts of the pile-up are shown to depend differently
on the parameters of the problem.


  We present high resolution simulations of two-fluid (ion-neutral) MHD
turbulence with resolutions as large as 512^3. The simulations are supersonic
and mildly sub-Alfvenic, in keeping with the conditions present in molecular
clouds. Such turbulence is thought to influence star formation processes in
molecular clouds because typical cores form on length scales that are
comparable to the dissipation scales of this turbulence in the ions. The
simulations are motivated by the fact that recent studies of isophotologue
lines in molecular clouds have found significant differences in the
linewidth-size relationship for neutral and ion species. The goals of this
paper are to explain those observations using simulations and analytic theory,
present a new set of density-based diagnostics by drawing on similar
diagnostics that have been obtained by studying single-fluid turbulence, and
show that our two-fluid simulations play a vital role in reconciling
alternative models of star formation. The velocity-dependent diagnostics
display a complementarity with the density-dependent diagnostics. We find that
the linewidth-size relationships show a prominent difference between ions and
neutrals when the line of sight is orthogonal to the mean field. This is
because the MHD waves in the ions differ from hydrodynamic waves in the
neutrals. We also find that the density probability distribution functions
(PDFs) show prominent differences between the ions and neutrals when the line
of sight is parallel to the mean field. This is because the velocity
fluctuations in the ions tend to produce column density fluctuations along
field lines. When the magnetic field makes an angle to the line of sight, both
observable differences should be visible. These diagnostics should be easy for
observers to test. This analysis assumes optically thin lines and a mean
magnetic field that is uniform in direction within a cloud.


  Observation of ferroelectricity among non-d0 systems, which was believed for
a long time an unrealistic concept, led to various proposals for the mechanisms
to explain the same (i.e. magnetically induced ferroelectricity) during last
decade. Here, we provide support for ferroelectricity of a displacive-type
possibly involving magnetic ions due to short-range magnetic correlations
within a spin-chain, through the demonstration of magnetoelectric coupling in a
Haldane spin-chain compound Er2BaNiO5 well above its N\'eel temperature of
(TN=) 32K. There is a distinct evidence for electric polarization setting in
near 60 K around which there is an evidence for short-range magnetic
correlations from other experimental methods. Raman studies also establish a
softening of phonon modes in the same temperature (T) range and T-dependent
x-ray diffraction (XRD) patterns also reveal lattice parameters anomalies.
Density-functional theory based calculations establish a displacive component
(similar to d0-ness) as the root-cause of ferroelectricity from (magnetic) NiO6
chain, thereby offering a new route to search for similar materials near room
temperature to enable applications.


  Reformulating constitutive relation in terms of gradient dynamics (being
derivative of a dissipation potential) brings additional information on
stability, metastability and instability of the dynamics with respect to
perturbations of the constitutive relation, called CR-stability. CR-instability
is connected to the loss of convexity of the dissipation potential, which makes
the Legendre-conjugate dissipation potential multivalued and causes dissipative
phase transitions, that are not induced by non-convexity of free energy, but by
non-convexity of the dissipation potential. CR-stability of the constitutive
relation with respect to perturbations is then manifested by constructing
evolution equations for the perturbations in a thermodynamically sound way. As
a result, interesting experimental observations of behavior of complex fluids
under shear flow and supercritical boiling curve can be explained.


  We present multiwavelength investigation of morphology, physical-environment,
stellar contents and star formation activity in the vicinity of star-forming
region Sh 2-100. It is found that the Sh 2-100 region contains seven HII
regions of ultracompact and compact nature. The present estimation of distance
for three HII regions, along with the kinematic distance for others, suggests
that all of them belong to the same molecular cloud complex. Using NIR
photometry, we identified the most probable ionizing sources of six HII
regions. Their approximate photometric spectral type estimates suggest that
they are massive early-B to mid-O ZAMS stars and agree well with radio
continuum observations at 1280 MHz. The morphology of the complex shows a
non-uniform distribution of warm and hot dust, well mixed with the ionized gas,
which correlates well with the variation of average visual extinction (~ 4.2 -
97 mag) across the region. We estimated the physical parameters of ionized gas
with the help of radio continuum observations. We detected an optically visible
compact nebula located to the south of the 850 micron emission associated with
one of the HII regions and the diagnostic of the optical emission line ratios
gives electron density and electron temperature of ~ 0.67 x 10^3 cm^-3 and ~
10^4 K, respectively. The physical parameters suggest that all the HII regions
are in different stages of evolution, which correlate well with the probable
ages in the range ~ 0.01 - 2 Myr of the ionizing sources. The positions of IR
excess stars, ultracompact and compact HII regions at the periphery of an HI
shell, possibly created by a WR star, indicate that star formation in Sh 2-100
region might have been induced by an expanding HI shell.


  Using the Grothendieck-Lefschetz theory (see \cite{[SGA2]}) we prove a
criterion to deduce that certain subvarieties of $\mathbb P^n$ of dimension
$\geq 2$ are not set-theoretic complete intersections (see Theorem 1 of the
Introduction). As applications we give a number of relevant examples. In the
last part of the paper we prove that the arithmetic rank of a rational normal
$d$-dimensional scroll $S_{n_1,...,n_d}$ in $\mathbb P^N$ is $N-2$, by
producing an explicit set of $N-2$ homogeneous equations which define these
scrolls set-theoretically (see Theorem 2 of the Introduction).


  We report new single dish CO J=6--5 line observations for the archetypal
Ultra Luminous Infrared Galaxy (ULIRG) Arp 220 with the James Clerk Maxwell
Telescope atop Mauna Kea in Hawaii. The J=6--5 line is found to be faint, with
brightness temperature ratios (6--5)/(1--0), (6--5)/(3--2) of R_{65/10} =
0.080+/-0.017 and R_{65/32} = 0.082+/-0.019, suggesting very low excitation
conditions that cannot be reconciled with the warm and very dense molecular gas
present in one of the most extreme starbursts in the local Universe. We find
that an optically thick dust continuum, with tau(f>350 GHz)>=1 for the bulk of
the warm dust and gas in Arp 220, submerges this line to an almost black body
curve, reducing its flux, and {\it affecting its CO Spectral Line Energy
Distribution (SLED) at high frequencies}. This also resolves the CII line
deficiency in this object, first observed by {\it ISO}: the near absence of
that line is a dust optical depth effect, not a dense Photodissociation Region
(PDR) phenomenon. Finally we briefly comment on the possibility of such extreme
ISM states in other ULIRGs in the distant Universe, and its consequences for
the diagnostic utility of high frequency molecular and atomic ISM lines in such
systems. In the case of Arp 220 we anticipate that the now spaceborne Herschel
Space Observatory will find faint high-J CO lines at f>=690 GHz that would
appear as sub-thermally excited with respect to the low-J ones as a result of
the effects of dust absorption.


  We present some "in silico" experiments to design combined chemo- and
immunotherapy treatment schedules. We introduce a new framework by combining
flatness-based control, which is a model-based setting, along with model-free
control. The flatness property of the used mathematical model yields
straightforward reference trajectories. They provide us with the nominal
open-loop control inputs. Closing the loop via model-free control allows to
deal with the uncertainties on the injected drug doses. Several numerical
simulations illustrating different case studies are displayed. We show in
particular that the considered health indicators are driven to the safe region,
even for critical initial conditions. Furthermore, in some specific cases there
is no need to inject chemotherapeutic agents.


  Open-set domain adaptation (OSDA) considers that the target domain contains
samples from novel categories unobserved in external source domain.
Unfortunately, existing OSDA methods always ignore the demand for the
information of unseen categories and simply recognize them as "unknown" set
without further explanation. This motivates us to understand the unknown
categories more specifically by exploring the underlying structures and
recovering their interpretable semantic attributes. In this paper, we propose a
novel framework to accurately identify the seen categories in target domain,
and effectively recover the semantic attributes for unseen categories.
Specifically, structure preserving partial alignment is developed to recognize
the seen categories through domain-invariant feature learning. Attribute
propagation over visual graph is designed to smoothly transit attributes from
seen to unseen categories via visual-semantic mapping. Moreover, two new
cross-main benchmarks are constructed to evaluate the proposed framework in the
novel and practical challenge. Experimental results on open-set recognition and
semantic recovery demonstrate the superiority of the proposed method over other
compared baselines.


  This is a report for reproducibility challenge of NeurlIPS 2019 on the paper
Competitive Gradient Descent (Schafer et al., 2019). The paper introduces a
novel algorithm for the numerical computation of Nash equilibria of competitive
two-player games. It avoids oscillatory and divergent behaviours seen in
alternating gradient descent. The purpose of this report is to critically
examine the reproducibility of the work by (Schafer et al., 2019), within the
framework of the NeurIPS 2019 Reproducibility Challenge. The experiments
replicated in this report confirms the results of the original study. Moreover,
this project offers a Python (Pytorch based) implementation of the proposed CGD
algorithm which can be found at the following public git repository:
(https://github.com/GopiKishan14/Reproducibility_Challenge_NeurIPS_2019)


  We report on a metal-insulator transition (MIT) that is observed in an
electron system at the SmTiO3/SrTiO3 interface. This MIT is characterized by an
abrupt transition at a critical temperature, below which the resistance changes
by more than an order of magnitude. The temperature of the transition
systematically depends on the carrier density, which is tuned from ~ 1x10^14
cm^-2 to 3x10^14 cm^-2 by changing the SmTiO3 thickness. Analysis of the
transport properties shows non-Fermi liquid behavior and mass enhancement as
the carrier density is lowered. We compare the MIT characteristics with those
of known MITs in other materials systems and show that they are distinctly
different in several aspects. We tentatively conclude that both long range
Coulomb interactions and the fixed charge at the polar interface are likely to
play a role in this MIT. The strong dependence on the carrier density makes
this MIT of interest for field-tunable devices.


  Focusing on the grand-canonical extension of the ordinary restricted
Boltzmann machine, we suggest an energy-based model for feature extraction that
uses a layer of hidden units with varying size. By an appropriate choice of the
chemical potential and given a sufficiently large number of hidden resources
the generative model is able to efficiently deduce the optimal number of hidden
units required to learn the target data with exceedingly small generalization
error. The formal simplicity of the grand-canonical ensemble combined with a
rapidly converging ansatz in mean-field theory enable us to recycle
well-established numerical algothhtims during training, like contrastive
divergence, with only minor changes. As a proof of principle and to demonstrate
the novel features of grand-canonical Boltzmann machines, we train our
generative models on data from the Ising theory and MNIST.


  We introduce a framework to dynamically combine heterogeneous models called
\texttt{DYCHEM}, which forecasts a set of time series that are related through
an aggregation hierarchy. Different types of forecasting models can be employed
as individual ``experts'' so that each model is tailored to the nature of the
corresponding time series. \texttt{DYCHEM} learns hierarchical structures
during the training stage to help generalize better across all the time series
being modeled and also mitigates coherency issues that arise due to constraints
imposed by the hierarchy. To improve the reliability of forecasts, we construct
quantile estimations based on the point forecasts obtained from combined
heterogeneous models. The resulting quantile forecasts are coherent and
independent of the choice of forecasting models. We conduct a comprehensive
evaluation of both point and quantile forecasts for hierarchical time series
(HTS), including public data and user records from a large financial software
company. In general, our method is robust, adaptive to datasets with different
properties, and highly configurable and efficient for large-scale forecasting
pipelines.


  A microfabricated Fabry-Perot optical resonator has been used for atom
detection and photon production with less than 1 atom on average in the cavity
mode. Our cavity design combines the intrinsic scalability of microfabrication
processes with direct coupling of the cavity field to single-mode optical
waveguides or fibers. The presence of the atom is seen through changes in both
the intensity and the noise characteristics of probe light reflected from the
cavity input mirror. An excitation laser passing transversely through the
cavity triggers photon emission into the cavity mode and hence into the
single-mode fiber. These are first steps towards building an optical
microcavity network on an atom chip for applications in quantum information
processing.


  Data race, a category of insidious software concurrency bugs, is often
challenging and resource-intensive to detect and debug. Existing dynamic race
detection tools incur significant execution time and memory overhead while
exhibiting high false positives. This paper proposes HMTRace, a novel Armv8.5-A
memory tag extension (MTE) based dynamic data race detection framework,
emphasizing low compute and memory requirements while maintaining high accuracy
and precision. HMTRace supports race detection in userspace OpenMP- and
Pthread-based multi-threaded C applications. HMTRace showcases a combined
f1-score of 0.86 while incurring a mean execution time overhead of 4.01% and
peak memory (RSS) overhead of 54.31%. HMTRace also does not report false
positives, asserting all reported races.


  We investigated the radio wavefront of cosmic-ray air showers with LOPES
measurements and CoREAS simulations: the wavefront is of approximately
hyperbolic shape and its steepness is sensitive to the shower maximum. For this
study we used 316 events with an energy above 0.1 EeV and zenith angles below
$45^\circ$ measured by the LOPES experiment. LOPES was a digital radio
interferometer consisting of up to 30 antennas on an area of approximately 200
m x 200 m at an altitude of 110 m above sea level. Triggered by KASCADE-Grande,
LOPES measured the radio emission between 43 and 74 MHz, and our analysis might
strictly hold only for such conditions. Moreover, we used CoREAS simulations
made for each event, which show much clearer results than the measurements
suffering from high background. A detailed description of our result is
available in our recent paper published in JCAP09(2014)025. The present
proceeding contains a summary and focuses on some additional aspects, e.g., the
asymmetry of the wavefront: According to the CoREAS simulations the wavefront
is slightly asymmetric, but on a much weaker level than the lateral
distribution of the radio amplitude.


  In this paper, we consider the advective unstable Cahn-Hilliard equation in
2D with shear flow: \begin{equation*}
  \begin{cases} u_t+Av_1(y) \partial_x u+\varepsilon \Delta^2 u= \Delta(a u^3+
b u^2) \quad & \quad \textrm{on} \quad \mathbb T^2; \\ \\ u \ \textrm{periodic}
\quad & \quad \textrm{on} \quad \partial \mathbb T^2, \end{cases}
\end{equation*} with an initial data $u_0 \in H_0^2(\mathbb T^2)$, where
$\mathbb T^2$ is the two-dimensional torus, $A, \varepsilon>0$, $a<0$, $b \in
\mathbb R$. Under the assumption that the shear has a finite number of critical
points and there are linearly growing modes only in the direction of the shear,
we show the $L^2$-energy of the solutions to such problems converges
expotentially to zero, if in addition, both $|a|$ and $\left\| \int_{\mathbb T}
u_0(x, \cdot ) dx \right\|_{L_y^2}$ are sufficiently small.


  Motivated by the potential connection between metric-affine gravity and
linear Generalized Uncertainty Principle (GUP) in the phase space, we develop a
covariant form of linear GUP and an associated modified Poincar\'e algebra,
which exhibits distinctive behavior, nearing nullity at the minimal length
scale proposed by linear GUP. We use 3-torus geometry to visually represent
linear GUP within a covariant framework. The 3-torus area provides an exact
geometric representation of Bekenstein's universal bound. We depart from
Bousso's approach, which adapts Bekenstein's bound by substituting the
Schwarzschild radius ($r_s$) with the radius ($R$) of the smallest sphere
enclosing the physical system, thereby basing the covariant entropy bound on
the sphere's area. Instead, our revised covariant entropy bound is described by
the area of a 3-torus, determined by both the inner radius $r_s$ and outer
radius $R$ where $r_s\leq R $ due to gravitational stability. This approach
results in a more precise geometric representation of Bekenstein's bound,
notably for larger systems where Bousso's bound is typically much larger than
Bekensetin's universal bound. Furthermore, we derive an equation that turns the
standard uncertainty inequality into an equation when considering the
contribution of the 3-torus covariant entropy bound, suggesting a new avenue of
quantum gravity.


  This review provides an overview of many recent advances in detector
technologies for particle physics experiments. Challenges for new technologies
include increasing spatial and temporal sensitivity, speed, and radiation
hardness while minimizing power and cost. Applications are directed at several
future collider experiments, including the Large Hadron Collider luminosity
upgrade (sLHC), the linear collider, and the super high luminosity B factory,
as well as neutrino and other fixed target experiments, and direct dark matter
searches. Furthermore, particle physics has moved into space, with significant
contributions of detector technology, and new challenges for future efforts.


  We prove that the Zarisky closure of the monodromy group of the polynomial $
x^2 y^2(1-x-y) $ is the symplectic group $Sp(4,\mathbb C)$. This shows that
some previous results about this monodromy representation are wrong.


  Economic withholding in electricity markets refers to generators bidding
higher than their true marginal fuel cost, and is a typical approach to
exercising market power. However, existing market designs require storage to
design bids strategically based on their own future price predictions,
motivating storage to conduct economic withholding without assuming market
power. As energy storage takes up more significant roles in wholesale
electricity markets, understanding its motivations for economic withholding and
the consequent effects on social welfare becomes increasingly vital. This paper
derives a theoretical framework to study the economic capacity withholding
behavior of storage participating in competitive electricity markets and
validate our results in simulations based on the ISO New England system. We
demonstrate that storage bids can reach unbounded high levels under conditions
where future price predictions show bounded expectations but unbounded
deviations. Conversely, in scenarios with peak price limitations, we show the
upper bounds of storage bids are grounded in bounded price expectations. Most
importantly, we show that storage capacity withholding can potentially lower
the overall system cost when price models account for system uncertainties. Our
paper reveals energy storage is not a market manipulator but an honest player
contributing to the social welfare. It helps electricity market researchers and
operators better understand the economic withholding behavior of storage and
reform market policies to maximize storage contributing to a cost-efficient
decolonization.


  Searching for gamma rays from dwarf spheroidal galaxies (dSphs) is a
promising approach to detect dark matter (DM) due to the high DM densities and
low baryon components in dSphs. The Fermi-LAT observations from dSphs have set
stringent constraints on the velocity independent annihilation cross section.
However, the constraints from dSphs may change in velocity dependent
annihilation scenarios because of the different velocity dispersions in
galaxies. In this work, we study how to set constraints on the velocity
dependent annihilation cross section from the combined Fermi-LAT observations
of dSphs with the kinematic data. In order to calculate the gamma ray flux from
the dSph, the correlation between the DM density profile and velocity
dispersion at each position should be taken into account. We study such
correlation and the relevant uncertainty from kinematic observations by
performing a Jeans analysis. Using the observational results of three
ultrafaint dSphs with large J-factors, including Willman 1, Reticulum II, and
Triangulum II, we set constraints on the p-wave annihilation cross section in
the Galaxy as an example.


  Hub location problems have multiple applications in logistic systems, airways
industry, supply chain network design, and telecommunication. In the hub
location problem, a number of nodes should be selected as the hub nodes to act
as the main distributors and other nodes are connected together by these hubs.
The input flow to the hub nodes is very large so more often we face the
congestion in the hub nodes that causes disturbances in the whole system. Also,
we have different service rates which is another cause of disturbance and
should be addressed by the models. This paper addresses these issues by
providing a model that prevents congestion in the system. We incorporated
queuing system in the p-median hub location problem by considering multiple
server options and different service rates. CAB dataset (contains 25 US cities)
was used in the implementation and our findings show the big impact of
considering congestion on the hub location network design.


  Many physical and biological systems rely on the progression of material
through multiple independent stages. In viral replication, for example, virions
enter a cell to undergo a complex process comprising several disparate stages
before the eventual accumulation and release of replicated virions. While such
systems may have some control over the internal dynamics that make up this
progression, a challenge for many is to regulate behaviour under what are often
highly variable external environments acting as system inputs. In this work, we
study a simple analogue of this problem through a linear multicompartment model
subject to a stochastic input in the form of a mean-reverting
Ornstein-Uhlenbeck process, a type of Gaussian process. By expressing the
system as a multidimensional Gaussian process, we derive several closed-form
analytical results relating to the covariances and autocorrelations of the
system, quantifying the smoothing effect discrete compartments afford
multicompartment systems. Semi-analytical results demonstrate that feedback and
feedforward loops can enhance system robustness, and simulation results probe
the intractable problem of the first passage time distribution, which has
specific relevance to eventual cell lysis in the viral replication cycle.
Finally, we demonstrate that the smoothing seen in the process is a consequence
of the discreteness of the system, and does not manifest in system with
continuous transport. While we make progress through analysis of a simple
linear problem, many of our insights are applicable more generally, and our
work enables future analysis into multicompartment processes subject to
stochastic inputs.


  A sample of quasars has been recently assembled to investigate the non-linear
relation between their monochromatic luminosities at 2500{\AA}, and 2 keV and
to exploit quasars as a new class of standardized candles. The use of this
technique for cosmological purposes relies on the non-evolution with redshift
of the UV-optical spectral properties of quasars, as well as on the absence of
possible contaminants such as dust extinction and host-galaxy contribution. We
address these possible issues by analysing the spectral properties of our
cosmological quasar sample. We produced composite spectra in different bins of
redshift and accretion parameters (black hole mass, bolometric luminosity), to
investigate any possible evolution of the spectral properties of the continuum
of the composites with these parameters. We found a remarkable similarity
amongst the various stacked spectra. The overall shape of the continuum does
not show any statistically significant trend with the accretion parameters nor
with the redshift. The composite spectrum of our quasar sample is consistent
with negligible levels of both intrinsic reddening (with a colour excess
E(B-V)< 0.01) and host-galaxy emission (less than 10%) in the optical. We
tested whether unaccounted dust extinction could explain the discrepancy
between our cosmographic fit of the Hubble-Lemaitre diagram and the concordance
{\Lambda}CDM model. The average colour excess required to solve the tension
should increase with redshift up to unphysically high values (E(B-V)=0.1 at
z>3) that would imply that the intrinsic emission of quasars is much bluer and
more luminous than ever reported in observed spectra. The similarity of quasar
spectra across the parameter space excludes a significant evolution of the
average continuum properties with any of the explored parameters, confirming
the reliability of our sample for cosmological applications.


  Large Multi-modal Models (LMMs) have made impressive progress in many
vision-language tasks. Nevertheless, the performance of general LMMs in
specific domains is still far from satisfactory. This paper proposes FoodLMM, a
versatile food assistant based on LMMs with various capabilities, including
food recognition, ingredient recognition, recipe generation, nutrition
estimation, food segmentation and multi-round conversation. To facilitate
FoodLMM to deal with tasks beyond pure text output, we introduce a series of
novel task-specific tokens and heads, enabling the model to predict food
nutritional values and multiple segmentation masks. We adopt a two-stage
training strategy. In the first stage, we utilize multiple public food
benchmarks for multi-task learning by leveraging the instruct-following
paradigm. In the second stage, we construct a multi-round conversation dataset
and a reasoning segmentation dataset to fine-tune the model, enabling it to
conduct professional dialogues and generate segmentation masks based on complex
reasoning in the food domain. Our fine-tuned FoodLMM achieves state-of-the-art
results across several food benchmarks. We will make our code, models and
datasets publicly available.


  The fundamental question of how Bose-Einstein condensates tunnel into a
barrier is addressed. The cubic nonlinear Schrodinger equation with a finite
square well potential, which models a Bose-Einstein condensate in a
quasi-one-dimensional trap of finite depth, is solved for the complete set of
localized and partially localized stationary states, which the former evolve
into when the nonlinearity is increased. An immediate application of these
different solution types is tunable tunneling. Magnetically tunable Feshbach
resonances can change the scattering length of certain Bose-condensed atoms,
such as $^{85}$Rb, by several orders of magnitude, including the sign, and
thereby also change the mean field nonlinearity term of the equation and the
tunneling of the wavefunction. We find both linear-type localized solutions and
uniquely nonlinear partially localized solutions where the tails of the
wavefunction become nonzero at infinity when the nonlinearity increases. The
tunneling of the wavefunction into the non-classical regime and thus its
localization therefore becomes an external experimentally controllable
parameter.


  This paper has two parts. The first part surveys Euler's work on the constant
gamma=0.57721... bearing his name, together with some of his related work on
the gamma function, values of the zeta function and divergent series. The
second part describes various mathematical developments involving Euler's
constant, as well as another constant, the Euler-Gompertz constant. These
developments include connections with arithmetic functions and the Riemann
hypothesis, and with sieve methods, random permutations and random matrix
products. It includes recent results on Diophantine approximation and
transcendence related to Euler's constant.


  A local phenomenological model that reduces to a non-local gravitational
theory giving dark energy is proposed. The non-local gravity action is known to
fit the data as well as $\Lambda$-CDM thereby demanding a more fundamental
local treatment. It is seen that the scale-invariant higher-derivative
scalar-tensor theory of gravity, which is known to be ultraviolet perturbative
renormalizable to all loops and where ghosts become innocuous, generates
non-locality at low energies. The local action comprises of two real scalar
fields coupled non-minimally with the higher-derivative gravity action. When
one of the scalar acquiring the Vacuum Expectation Value (VEV) induces
Einstein--Hilbert gravity, generates mass for fields, and gets decoupled from
system, it leaves behind a residual theory which in turn leads to a non-local
gravity generating dark energy effects.


  We study aging in a colloidal suspension consisting of micron-sized particles
in a liquid. This system is made glassy by increasing the particle
concentration. We observe samples composed of particles of two sizes, with a
size ratio of 1:2.1 and a volume fraction ratio 1:6, using fast laser scanning
confocal microscopy. This technique yields real-time, three-dimensional movies
deep inside the colloidal glass. Specifically, we look at how the size, motion
and structural organization of the particles relate to the overall aging of the
glass. Particles move in spatially heterogeneous cooperative groups. These
mobile regions tend to be richer in small particles, and these small particles
facilitate the motion of nearby particles of both sizes.


  In \cite{BR1}, \cite{BR2}, a parabolic determinant line bundle on a moduli
space of stable parabolic bundles was constructed, along with a Hermitian
structure on it. The construction of the Hermitian structure was indirect: The
parabolic determinant line bundle was identified with the pullback of the
determinant line bundle on a moduli space of usual vector bundles over a
covering curve. The Hermitian structure on the parabolic determinant bundle was
taken to be the pullback of the Quillen metric on the determinant line bundle
on the moduli space of usual vector bundles. Here a direct construction of the
Hermitian structure is given. For that we need to establish a version of the
correspondence between the stable parabolic bundles and the Hermitian--Einstein
connections in the context of conical metrics. Also, a recently obtained
parabolic analog of Faltings' criterion of semistability plays a crucial role.


  Intelligent systems designed for play-based interactions should be
contextually aware of the users and their surroundings. Spoken Dialogue Systems
(SDS) are critical for these interactive agents to carry out effective
goal-oriented communication with users in real-time. For the real-world (i.e.,
in-the-wild) deployment of such conversational agents, improving the Natural
Language Understanding (NLU) module of the goal-oriented SDS pipeline is
crucial, especially with limited task-specific datasets. This study explores
the potential benefits of a recently proposed transformer-based multi-task NLU
architecture, mainly to perform Intent Recognition on small-size
domain-specific educational game datasets. The evaluation datasets were
collected from children practicing basic math concepts via play-based
interactions in game-based learning settings. We investigate the NLU
performances on the initial proof-of-concept game datasets versus the
real-world deployment datasets and observe anticipated performance drops
in-the-wild. We have shown that compared to the more straightforward baseline
approaches, Dual Intent and Entity Transformer (DIET) architecture is robust
enough to handle real-world data to a large extent for the Intent Recognition
task on these domain-specific in-the-wild game datasets.


  We introduce an $\ell$-adic analogue of Gauss's hypergeometric function
arising from the Galois action on the fundamental torsor of the projective line
minus three points. Its definition is motivated by a relation between the
KZ-equation and the hypergeometric differential equation in the complex case.
We show two basic properties, analogues of Gauss's hypergeometric theorem and
of Euler's transformation formula for our $\ell$-adic function. We prove them
by detecting a connection of a certain two-by-two matrix specialization of even
unitary associators with the associated gamma function, which extends the
result of Ohno and Zagier.


  The HII complex N159 in the Large Magellanic Cloud (LMC) is used to study
massive star formation in different environments, as it contains three giant
molecular clouds (GMCs) that have similar sizes and masses but exhibit
different intensities of star formation. We identify candidate massive young
stellar objects (YSOs) using infrared photometry, and model their SEDs to
constrain mass and evolutionary state. Good fits are obtained for less evolved
Type I, I/II, and II sources. Our analysis suggests that there are massive
embedded YSOs in N159B, a maser source, and several ultracompact HII regions.
Massive O-type YSOs are found in GMCs N159-E and N159-W, which are associated
with ionized gas, i.e., where massive stars formed a few Myr ago. The third
GMC, N159-S, has neither O-type YSOs nor evidence of previous massive star
formation. This correlation between current and antecedent formation of massive
stars suggests that energy feedback is relevant. We present evidence that
N159-W is forming YSOs spontaneously, while collapse in N159-E may be
triggered. Finally, we compare star formation rates determined from YSO counts
with those from integrated H-alpha and 24 micron luminosities and expected from
gas surface densities. Detailed dissection of extragalactic GMCs like the one
presented here is key to revealing the physics underlying commonly used star
formation scaling laws.


  Let $X = \mathbb{P}(E_1) \times_C \mathbb{P}(E_2)$ where $C$ is a smooth
curve and let $E_1$, $E_2$ be vector bundles over $C$. In this paper, we extend
the results in \cite{K-M-R} by computing the nef cone of $X$ without
restriction on the rank or semistability of $E_1$ and $E_2$. We also study the
Seshadri constants of ample line bundles on $X$. We calculate the Seshadri
constants in some cases and give bounds in some of the remaining cases.


  In this paper we describe the operation and performance of the HERA-B Outer
Tracker, a 112674 channel system of planar drift tube layers. The performance
of the HERA-B Outer Tracker system fullfilled all requirements for stable and
efficient operation in a hadronic environment, thus confirming the adequacy of
the honeycomb drift tube technology and of the front-end readout system. The
detector was stably operated with a gas gain of 30000 in an Ar/CF4/CO2
(65:30:5) gas mixture, yielding a good efficiency for triggering and track
reconstruction, larger than 95 % for tracks with momenta above 5 GeV/c. The hit
resolution of the drift cells was 300 to 320 micrometers and the relative
momentum resolution can be described as: sigma(p)/p (in %) = (1.61 +- 0.02) +
(0.0051 +- 0.0006) p. At the end of the HERA-B running no aging effects in the
Outer Tracker cells were observed.


  The Ricci curvature of the Bergman metric on a bounded domain $D\subset
\mathbb{C}^n$ is strictly bounded above by $n+1$ and consequently $\log
(K_D^{n+1}g_{B,D})$, where $K_D$ is the Bergman kernel for $D$ on the diagonal
and $g_{B, D}$ is the Riemannian volume element of the Bergman metric on $D$,
is the potential for a K\"ahler metric on $D$ known as the Kobayashi--Fuks
metric. In this note we study the localization of this metric near holomorphic
peak points and also show that this metric shares several properties with the
Bergman metric on strongly pseudoconvex domains.


  Sparse linear models are one of several core tools for interpretable machine
learning, a field of emerging importance as predictive models permeate
decision-making in many domains. Unfortunately, sparse linear models are far
less flexible as functions of their input features than black-box models like
deep neural networks. With this capability gap in mind, we study a not-uncommon
situation where the input features dichotomize into two groups: explanatory
features, which are candidates for inclusion as variables in an interpretable
model, and contextual features, which select from the candidate variables and
determine their effects. This dichotomy leads us to the contextual lasso, a new
statistical estimator that fits a sparse linear model to the explanatory
features such that the sparsity pattern and coefficients vary as a function of
the contextual features. The fitting process learns this function
nonparametrically via a deep neural network. To attain sparse coefficients, we
train the network with a novel lasso regularizer in the form of a projection
layer that maps the network's output onto the space of $\ell_1$-constrained
linear models. An extensive suite of experiments on real and synthetic data
suggests that the learned models, which remain highly transparent, can be
sparser than the regular lasso without sacrificing the predictive power of a
standard deep neural network.


  Electron spin resonance (ESR) is a useful tool to investigate properties of
materials in magnetic fields where high spin polarization of target electron
spins is required in order to obtain high sensitivity. However, the smaller
magnetic fields becomes, the more difficult high polarization is passively
obtained by thermalization. Here, we propose to employ a superconducting flux
qubit (FQ) to polarize electron spins actively. We have to overcome a large
energy difference between the FQ and electron spins for efficient energy
transfer among them. For this purpose, we adopt a spin-lock technique on the FQ
where the Rabi frequency associated with the spin-locking can match the
resonance (Larmor) one of the electron spins. We find that adding dephasing on
the spins is beneficial to obtain high polarization of them, because otherwise
the electron spins are trapped in dark states that cannot be coupled with the
FQ. We show that our scheme can achieve high polarization of electron spins in
realistic experimental conditions.


  These lectures review the progress made in our present understanding of $B$
decays. The emphasis here is on applications of QCD to $B$ decays and the
attendant perturbative and non-perturbative uncertainties, which limit present
theoretical precision in some cases but the overall picture that emerges is
consistent with the standard model (SM). This is illustrated by quantitatively
analyzing some of the key measurements in $B$ physics.


  We study string propagation in a spacetime with positive cosmological
constant, which includes a circle whose radius approaches a finite value as
|t|\to\infty, and goes to zero at t=0. Near this cosmological singularity, the
spacetime looks like R^{1,1}/Z. In string theory, this spacetime must be
extended by including four additional regions, two of which are compact. The
other two introduce new asymptotic regions, corresponding to early and late
times, respectively. States of quantum fields in this spacetime are defined in
the tensor product of the two Hilbert spaces corresponding to the early time
asymptotic regions, and the S-matrix describes the evolution of such states to
states in the tensor product of the two late time asymptotic regions. We show
that string theory provides a unique continuation of wavefunctions past the
cosmological singularities, and allows one to compute the S-matrix. The
incoming vacuum evolves into an outgoing state with particles. We also discuss
instabilities of asymptotically timelike linear dilaton spacetimes, and the
question of holography in such spaces. Finally, we briefly comment on the
relation of our results to recent discussions of de Sitter space.


  Graph products of groups were introduced by Green in her thesis. They have an
operator algebraic counterpart introduced and explored by Fima and the
first-named author. In this paper we prove Khintchine type inequalities for
general C$^{\ast}$-algebraic graph products which generalize results by Ricard
and Xu on free products of C$^{\ast}$-algebras. We apply these inequalities in
the context of (right-angled) Hecke C$^{\ast}$-algebras, which are deformations
of the group algebra of Coxeter groups. For these we deduce a Haagerup
inequality. We further use this to study the simplicity and trace uniqueness of
(right-angled) Hecke C$^{\ast}$-algebras. Lastly we characterize exactness and
nuclearity of general Hecke C$^{\ast}$-algebras.


  The optical spectroscopy of a single InAs quantum dot doped with a single Mn
atom is studied using a model Hamiltonian that includes the exchange
interactions between the spins of the quantum dot electron-hole pair, the Mn
atom and the acceptor hole. Our model permits to link the photoluminescence
spectra to the Mn spin states after photon emission. We focus on the relation
between the charge state of the Mn, $A^0$ or $A^-$, and the different spectra
which result through either band-to-band or band-to-acceptor transitions. We
consider both neutral and negatively charged dots. Our model is able to account
for recent experimental results on single Mn doped InAs PL spectra and can be
used to account for future experiments in GaAs quantum dots. Similarities and
differences with the case of single Mn doped CdTe quantum dots are discussed.


  The objective of this article is to provide for the reader a basic
description of all the steps involved in the COM object life-cycle process. COM
is a software technology and process performer. The first section briefly
introduces the Component Object Model (COM), considering the process of the COM
object life cycle as the baseline of all COM issues. The second part describes
in detail the basic steps of the process - client request, server location,
object creation, interaction, and disconnection. A brief description is given
for the components involved in each step. Finally, the third section provides a
brief conclusion summarizing all the process steps.


  Shannon entropy, a cornerstone of information theory, statistical physics and
inference methods, is uniquely identified by the Shannon-Khinchin or
Shore-Johnson axioms. Generalizations of Shannon entropy, motivated by the
study of non-extensive or non-ergodic systems, relax some of these axioms and
lead to entropy families indexed by certain `entropic' parameters. In general,
the selection of these parameters requires pre-knowledge of the system or
encounters inconsistencies. Here we introduce a simple axiom for any entropy
family: namely, that no entropic parameter can be inferred from a completely
uninformative (uniform) probability distribution. When applied to the
Uffink-Jizba-Korbel and Hanel-Thurner entropies, the axiom selects only R\'enyi
entropy as viable. It also extends consistency with the Maximum Likelihood
principle, which can then be generalized to estimate the entropic parameter
purely from data, as we confirm numerically. Remarkably, in a generalized
maximum-entropy framework the axiom implies that the maximized log-likelihood
always equals minus Shannon entropy, even if the inferred probability
distribution maximizes a generalized entropy and not Shannon's, solving a
series of problems encountered in previous approaches.


  We experimentally study the nonlinear fluid damping of a rigid but
elastically mounted pitching wing in the absence of a freestream flow. The
dynamics of the elastic mount are simulated using a cyber-physical system. We
perturb the wing and measure the fluid damping coefficient from damped
oscillations over a large range of pitching frequencies, pitching amplitudes,
pivot locations and sweep angles. A universal fluid damping scaling is proposed
to incorporate all these parameters. Flow fields obtained using particle image
velocimetry are analyzed to explain the nonlinear behaviors of the fluid
damping.


  We present a quantitative method, utilising a highly sensitive quantum
sensor, that extends applicability of magnetorelaxometry to biological samples
at physiological temperature. The observed magnetic fields allow for
non-invasive determination of physical properties of magnetic materials and
their surrounding environment inside the specimen. The method is applied to
American cockroaches and reveals magnetic deposits with strikingly different
behaviour in alive and dead insects. We discuss consequences of this finding to
cockroach magneto-reception. To our knowledge, this work represents the first
characterisation of the magnetisation dynamics in live insects and helps to
connect results from behavioural experiments on insects in magnetic fields with
characterisation of magnetic materials in their corpses.


  Facial Expression Recognition from static images is a challenging problem in
computer vision applications. Convolutional Neural Network (CNN), the
state-of-the-art method for various computer vision tasks, has had limited
success in predicting expressions from faces having extreme poses,
illumination, and occlusion conditions. To mitigate this issue, CNNs are often
accompanied by techniques like transfer, multi-task, or ensemble learning that
often provide high accuracy at the cost of increased computational complexity.
In this work, we propose a Part-based Ensemble Transfer Learning network that
models how humans recognize facial expressions by correlating the spatial
orientation pattern of the facial features with a specific expression. It
consists of 5 sub-networks, and each sub-network performs transfer learning
from one of the five subsets of facial landmarks: eyebrows, eyes, nose, mouth,
or jaw to expression classification. We show that our proposed ensemble network
uses visual patterns emanating from facial muscles' motor movements to predict
expressions and demonstrate the usefulness of transfer learning from Facial
Landmark Localization to Facial Expression Recognition. We test the proposed
network on the CK+, JAFFE, and SFEW datasets, and it outperforms the benchmark
for CK+ and JAFFE datasets by 0.51% and 5.34%, respectively. Additionally, the
proposed ensemble network consists of only 1.65M model parameters, ensuring
computational efficiency during training and real-time deployment. Grad-CAM
visualizations of our proposed ensemble highlight the complementary nature of
its sub-networks, a key design parameter of an effective ensemble network.
Lastly, cross-dataset evaluation results reveal that our proposed ensemble has
a high generalization capacity, making it suitable for real-world usage.


  We study matrices whose entries are free or exchangeable noncommutative
elements in some tracial $W^*$-probability space. More precisely, we consider
operator-valued Wigner and Wishart matrices and prove quantitative convergence
to operator-valued semicircular elements over some subalgebra in terms of
Cauchy transforms. As direct applications, we obtain explicit rates of
convergence for a large class of random block matrices with independent or
correlated blocks. Our approach relies on a noncommutative extension of the
Lindeberg method and operator-valued Gaussian interpolation techniques.


  We introduce RAMP, an open-source robotics benchmark inspired by real-world
industrial assembly tasks. RAMP consists of beams that a robot must assemble
into specified goal configurations using pegs as fasteners. As such, it
assesses planning and execution capabilities, and poses challenges in
perception, reasoning, manipulation, diagnostics, fault recovery, and goal
parsing. RAMP has been designed to be accessible and extensible. Parts are
either 3D printed or otherwise constructed from materials that are readily
obtainable. The design of parts and detailed instructions are publicly
available. In order to broaden community engagement, RAMP incorporates fixtures
such as April Tags which enable researchers to focus on individual sub-tasks of
the assembly challenge if desired. We provide a full digital twin as well as
rudimentary baselines to enable rapid progress. Our vision is for RAMP to form
the substrate for a community-driven endeavour that evolves as capability
matures.


  J. Pevtsova and the author constructed a ``universal $p$-nilpotent operator"
for an infinitesimal group scheme $G$ over a field $k$ of characteristic $p >
0$ which led to coherent sheaves on the scheme of 1-parameter subgroups of $G$
associated to a $G$-module $M$. Of special interest is the fact that these
coherent sheaves are vector bundles if $M$ is of constant Jordan type. In this
paper, we provide similar invariants for a finite group $\tau$ which recover
the invariants earlier obtained for elementary abelian $p$-groups. To do this,
we replace the analogue of 1-parameter subgroups by a refined version of
equivalence classes of $\pi$-points for $k\tau$. More generally, we provide a
construction of vector bundles for the semi-direct product $G\rtimes \tau$ of
an infinitesimal group scheme $G$ and a finite group $\tau$.
  A major motivation for this study is to further our understanding of the
relationship between representations of $\mathbb G(\mathbb F_p)$ and $\mathbb
G_{(r)}$ associated to a finite dimensional rational $\mathbb G$-module $M$,
where $\mathbb G$ is a reductive group with $r$-th Fobenius kernel $\mathbb
G_{(r)}$. Using vector bundles, we extend and sharpen earlier results comparing
support varieties.


  High sidelobe level is a major disadvantage of the Capon beamforming. To
suppress the sidelobe, this paper introduces a mainlobe to sidelobe power ratio
constraint to the Capon beamforming. it minimizes the sidelobe power while
keeping the mainlobe power constant. Simulations show that the obtained
beamformer outperforms the Capon beamformer.


  Barlowite Cu$_4$(OH)$_6$FBr shows three-dimensional (3D) long-range
antiferromagnetism, which is fully suppressed in Cu$_3$Zn(OH)$_6$FBr with a
kagome quantum spin liquid ground state. Here we report systematic studies on
the evolution of magnetism in the Cu$_{4-x}$Zn$_x$(OH)$_{6}$FBr system as a
function of $x$ to bridge the two limits of Cu$_4$(OH)$_6$FBr ($x$=0) and
Cu$_3$Zn(OH)$_6$FBr ($x$=1). Neutron-diffraction measurements reveal a
hexagonal-to-orthorhombic structural change with decreasing temperature in the
$x$ = 0 sample. While confirming the 3D antiferromagnetic nature of
low-temperature magnetism, the magnetic moments on some Cu$^{2+}$ sites on the
kagome planes are found to be vanishingly small, suggesting strong frustration
already exists in barlowite. Substitution of interlayer Cu$^{2+}$ with
Zn$^{2+}$ with gradually increasing $x$ completely suppresses the bulk magnetic
order at around $x$ = 0.4, but leaves a local secondary magnetic order up to
$x\sim 0.8$ with a slight decrease in its transition temperature. The
high-temperature magnetic susceptibility and specific heat measurements further
suggest that the intrinsic magnetic properties of kagome spin liquid planes may
already appear from $x>0.3$ samples. Our results reveal that the
Cu$_{4-x}$Zn$_x$(OH)$_6$FBr may be the long-thought experimental playground for
the systematic investigations of the quantum phase transition from a long-range
antiferromagnet to a topologically ordered quantum spin liquid.


  This paper concerns the large deviations of a system of interacting particles
on a random graph. There is no stochasticity, and the only sources of disorder
are the random graph connections, and the initial condition. The average number
of afferent edges on any particular vertex must diverge to infinity as $N\to
\infty$, but can do so at an arbitrarily slow rate. These results are thus
accurate for both sparse and dense random graphs. A particular application to
sparse Erdos-Renyi graphs is provided. The theorem is proved by pushing forward
a Large Deviation Principle for a `nested empirical measure' generated by the
initial conditions to the dynamics. The nested empirical measure can be thought
of as the density of the density of edge connections: the associated weak
topology is more coarse than the topology generated by the graph cut norm, and
thus there is a broader range of application.


  We performed numerical simulations of a homogeneous swarm of bubbles rising
at large Reynolds number, Re = 760 with volume fractions ranging from 1% to
10%. We consider a simplified model in which the interfaces are not resolved,
but which allows us to simulate flows with a large number of bubbles and to
emphasize the interactions between bubble wakes. The liquid phase is described
by solving, on an Eulerian grid, the Navier-Stokes equations, including sources
of momentum which model the effect of the bubbles. The dynamics of each bubble
is determined within the Lagrangian framework by solving an equation of motion
involving the hydrodynamic forces exerted by the fluid accounting for the
correction of the fictitious self-interaction of a bubble with its own wake.
The comparison with experiments shows that this coarse-grained simulations
approach can reliably describe the dynamics of the resolved flow scales. We use
conditional averaging to characterize the mean bubble wakes and obtain in
particular the typical shear imposed by the rising bubbles. On the basis of the
spectral decomposition of the energy budget, we observe that the flow is
dominated by production at large scales and by dissipation at small scales and
we rule out the presence of an intermediate range in which the production and
dissipation are locally in balance. We propose that the k-3 subrange of the
energy spectra results from the mean shear rate imposed by the bubbles, which
controls the rate of return to isotropy.


  Predicting user preferences and sequential dependencies based on historical
behavior is the core goal of sequential recommendation. Although
attention-based models have shown effectiveness in this field, they often
struggle with inference inefficiency due to the quadratic computational
complexity inherent in attention mechanisms, especially with long-range
behavior sequences. Drawing inspiration from the recent advancements of state
space models (SSMs) in control theory, which provide a robust framework for
modeling and controlling dynamic systems, we introduce EchoMamba4Rec. Control
theory emphasizes the use of SSMs for managing long-range dependencies and
maintaining inferential efficiency through structured state matrices.
EchoMamba4Rec leverages these control relationships in sequential
recommendation and integrates bi-directional processing with frequency-domain
filtering to capture complex patterns and dependencies in user interaction data
more effectively. Our model benefits from the ability of state space models
(SSMs) to learn and perform parallel computations, significantly enhancing
computational efficiency and scalability. It features a bi-directional Mamba
module that incorporates both forward and reverse Mamba components, leveraging
information from both past and future interactions. Additionally, a filter
layer operates in the frequency domain using learnable Fast Fourier Transform
(FFT) and learnable filters, followed by an inverse FFT to refine item
embeddings and reduce noise. We also integrate Gate Linear Units (GLU) to
dynamically control information flow, enhancing the model's expressiveness and
training stability. Experimental results demonstrate that EchoMamba
significantly outperforms existing models, providing more accurate and
personalized recommendations.


  Deformation theory for 2-dimensional dynamical triangulations with N vertices
is discussed by exploiting the geometry of the moduli space of Euclidean
polygons. Such an analysis provides an explicit connection among Regge
surfaces, dynamical triangulations and the Witten-Kontsevich model. We show
that a natural set of Regge measures and a triangulation counting of relevance
for dynamical triangulations are directly connected with intersection theory
over the compactified moduli space of genus g Riemann surfaces with N
punctures.The Regge measures in question provide volumes of the open strata in
moduli space. It is also argued that the arguments presented here offer
evidence of a form of topological S-duality between Regge calculus and DT
theory.


  Let $\vec C_m$ and $\vec C_n$ be directed cycles of length $m$ and $n$, with
$m,n \ge 3$, and let $P(\vec C_m \mathbin{\Box} \vec C_n)$ be the digraph that
is obtained from the Cartesian product $\vec C_m \mathbin{\Box} \vec C_n$ by
choosing a vertex $v$, and reversing the orientation of all four directed edges
that are incident with $v$. (This operation is called "pushing" at the vertex
$v$.) By applying a special case of unpublished work of S.X.Wu, we find
elementary number-theoretic necessary and sufficient conditions for the
existence of a hamiltonian cycle in $P(\vec C_m \mathbin{\Box} \vec C_n)$.
  A consequence is that if $P(\vec C_m \mathbin{\Box} \vec C_n)$ is
hamiltonian, then $\gcd(m,n) = 1$, which implies that $\vec C_m \mathbin{\Box}
\vec C_n$ is not hamiltonian. This final conclusion verifies a conjecture of
J.B.Klerlein and E.C.Carr.


  Friction modeling has always been a challenging problem due to the complexity
of real physical systems. Although a few state-of-the-art structured
data-driven methods show their efficiency in nonlinear system modeling,
deterministic passivity as one of the significant characteristics of friction
is rarely considered in these methods. To address this issue, we propose a
Gaussian Process based model that preserves the inherent structural properties
such as passivity. A matrix-vector physical structure is considered in our
approaches to ensure physical consistency, in particular, enabling a guarantee
of positive semi-definiteness of the damping matrix. An aircraft benchmark
simulation is employed to demonstrate the efficacy of our methodology.
Estimation accuracy and data efficiency are increased substantially by
considering and enforcing more structured physical knowledge. Also, the
fulfillment of the dissipative nature of the aerodynamics is validated
numerically.


  We study a graph based version of the Ohta-Kawasaki functional, which was
originally introduced in a continuum setting to model pattern formation in
diblock copolymer melts and has been studied extensively as a paradigmatic
example of a variational model for pattern formation.
  Graph based problems inspired by partial differential equations (PDEs) and
varational methods have been the subject of many recent papers in the
mathematical literature, because of their applications in areas such as image
processing and data classification. This paper extends the area of PDE inspired
graph based problems to pattern forming models, while continuing in the
tradition of recent papers in the field.
  We introduce a mass conserving Merriman-Bence-Osher (MBO) scheme for
minimizing the graph Ohta-Kawasaki functional with a mass constraint. We
present three main results: (1) the Lyapunov functionals associated with this
MBO scheme $\Gamma$-converge to the Ohta-Kawasaki functional (which includes
the standard graph based MBO scheme and total variation as a special case); (2)
there is a class of graphs on which the Ohta-Kawasaki MBO scheme corresponds to
a standard MBO scheme on a transformed graph and for which generalized
comparison principles hold; (3) this MBO scheme allows for the numerical
computation of (approximate) minimizers of the graph Ohta-Kawasaki functional
with a mass constraint.


  Excited states (ESs) of two- and three-dimensional (2D and 3D) solitons of
the semivortex (SV) and mixed-mode (MM) types, supported by the interplay of
the spin-orbit coupling (SOC) and local nonlinearity in binary Bose-Einstein
condensates, are unstable, on the contrary to the stability of the SV and MM
solitons in their fundamental states. We propose a stabilization strategy for
these states in 3D, combining SOC and long-range Rydberg-Rydberg interactions
(RRI), in the presence of a spatially-periodic potential, that may include a
parity-time (PT)-symmetric component. ESs of the SV solitons, which carry
integer vorticities S and S+1 in their two components, exhibit robustness up to
S= 4. ESs of MM solitons feature an interwoven necklace-like structure, with
the components carrying opposite fractional values of the orbital angular
momentum. Regions of the effective stability of the 3D solitons of the SV and
MM types (both fundamental ones and ESs), are identified as functions of the
imaginary component of the PT-symmetric potential and strengths of the SOC and
RRI terms.


  In this paper we describe a generalisation and adaptation of Kedlaya's
algorithm for computing the zeta function of a hyperelliptic curve over a
finite field of odd characteristic that the author used for the implementation
of the algorithm in the Magma library. We generalise the algorithm to the case
of an even degree model. We also analyse the adaptation of working with the
$x^idx/y^3$ rather than the $x^idx/y$ differential basis. This basis has the
computational advantage of always leading to an integral transformation matrix
whereas the latter fails to in small genus cases. There are some theoretical
subtleties that arise in the even degree case where the two differential bases
actually lead to different redundant eigenvalues that must be discarded.


  Normality and $\ga$-hermiticity are what gives rise to chiral properties and
rules. The Ginsparg-Wilson (GW) relation is only one of the possible spectral
constraints. The sum rule for chiral differences of real modes has important
consequences. The alternative transformation of L\"uscher gives the same Ward
identity as the usual chiral one (if zero modes are properly treated). Imposing
normality on a general function of the hermitean Wilson-Dirac operator $H$
leads at the same time to the GW relation and to the Neuberger operator.


  Measurements of the diffuse extragalactic gamma-ray background (EGRB) are
complicated by a strong Galactic foreground. Estimates of the EGRB flux and
spectrum, obtained by modeling the Galactic emission, have produced a variety
of (sometimes conflicting) results. The latest analysis of the EGRET data found
an isotropic flux I_x=1.45+-0.05 above 100 MeV, in units of 10^-5 s^-1 cm^-2
sr^-1. We analyze the EGRET data in search for robust constraints on the EGRB
flux, finding the gamma-ray sky strongly dominated by Galactic foreground even
at high latitudes, with no conclusive evidence for an additional isotropic
component. The gamma-ray intensity measured towards the Galactic poles is
similar to or lower than previous estimates of I_x. The high latitude profile
of the gamma-ray data is disk-like for 40<|b[deg]|<70, and even steeper for
|b|>70; overall it exhibits strong Galactic features and is well fit by a
simple Galactic model. Based on the |b|>40 data we find that I_x<0.5 at a 99%
confidence level, with evidence for a much lower flux. We show that
correlations with Galactic tracers, previously used to identify the Galactic
foreground and estimate I_x, are not satisfactory; the results depend on the
tracers used and on the part of the sky examined, because the Galactic emission
is not linear in the Galactic tracers and exhibits spectral variations across
the sky. The low EGRB flux favored by our analysis places stringent limits on
extragalactic scenarios involving gamma-ray emission, such as radiation from
blazars, intergalactic shocks and production of ultra-high energy cosmic rays
and neutrinos. We suggest methods by which future gamma-ray missions such as
GLAST and AGILE could indirectly identify the EGRB.


  Ensuring a permanent increase of magnetic storage densities is one of the
main challenges in magnetic recording. Conventional approaches based on single
phase grains are not suitable to achieve this goal, because their grain volume
is limited due to the superparamagnetic limit. Grains with graded anisotropy
are the most promising candidates to overcome this limit, providing magnetic
memory bits with small volumes, low coercivity and high thermal stability at
the same time. Combining micromagnetic simulations with forward flux sampling
(FFS), a computational method for rare events that has been recently applied to
the magnetic nanostructures, we have determined thermal escape rates and
attempt frequencies of a graded media grain and two single phase grains of the
same geometry. We find that graded anisotropy can increase the thermal
stability of a grain by 12 orders of magnitudes from tens of milliseconds to
centuries without changing the coercive field.


  Deep Neural Networks have proven to be highly accurate at a variety of tasks
in recent years. The benefits of Deep Neural Networks have also been embraced
in power grids to detect False Data Injection Attacks (FDIA) while conducting
critical tasks like state estimation. However, the vulnerabilities of DNNs
along with the distinct infrastructure of cyber-physical-system (CPS) can favor
the attackers to bypass the detection mechanism. Moreover, the divergent nature
of CPS engenders limitations to the conventional defense mechanisms for False
Data Injection Attacks. In this paper, we propose a DNN framework with
additional layer which utilizes randomization to mitigate the adversarial
effect by padding the inputs. The primary advantage of our method is when
deployed to a DNN model it has trivial impact on the models performance even
with larger padding sizes. We demonstrate the favorable outcome of the
framework through simulation using the IEEE 14-bus, 30-bus, 118-bus and 300-bus
systems. Furthermore to justify the framework we select attack techniques that
generate subtle adversarial examples that can bypass the detection mechanism
effortlessly.


  A new sampling methodology based on incomplete cosine expansion series is
presented as an alternative to the traditional sinc function approach.
Numerical integration shows that this methodology is efficient and practical.
Applying the incomplete cosine expansion we obtain a rational approximation of
the complex error function that with the same number of the summation terms
provides an accuracy exceeding the Weideman\text{'}s approximation accuracy by
several orders of the magnitude. Application of the expansion results in an
integration consisting of elementary function terms only. Consequently, this
approach can be advantageous for accurate and rapid computation.


  We construct a pathwise integration theory, associated with a change of
variable formula, for smooth functionals of continuous paths with arbitrary
regularity defined in terms of the notion of $p$-th variation along a sequence
of time partitions. For paths with finite $p$-th variation along a sequence of
time partitions, we derive a change of variable formula for $p$ times
continuously differentiable functions and show pointwise convergence of
appropriately defined compensated Riemann sums. Results for functions are
extended to regular path-dependent functionals using the concept of vertical
derivative of a functional. We show that the pathwise integral satisfies an
`isometry' formula in terms of $p$-th order variation and obtain a `signal plus
noise' decomposition for regular functionals of paths with strictly increasing
$p$-th variation. For less regular ($C^{p-1}$) functions we obtain a
Tanaka-type change of variable formula using an appropriately defined notion of
local time. These results extend to multidimensional paths and yield a natural
higher-order extension of the concept of `reduced rough path'. We show that,
while our integral coincides with a rough-path integral for a certain rough
path, its construction is canonical and does not involve the specification of
any rough-path superstructure.


  We introduce a rigorous framework for defining quasinormal modes on
stationary, asymptotically flat spacetimes as isolated eigenvalues of the
infinitesimal generator of time translations. We consider time functions
corresponding to a foliation of asymptotically hyperboloidal hypersurfaces and
restrict to suitable Hilbert spaces of functions. These functions have finite
Sobolev regularity in bounded regions, but need to be Gevrey-regular at null
infinity. This framework is developed in the context of sub-extremal Kerr
spacetimes, but also gives uniform-in-$\Lambda$ resolvent estimates on Kerr--de
Sitter spacetimes with a small cosmological constant $\Lambda$. As a corollary,
we also construct the meromorphic continuation (in a sector of the complex
plane) of the cut-off resolvent in Kerr that is associated to the standard
Boyer--Lindquist time function. The framework introduced in this paper bridges
different notions of quasinormal modes found in the literature. As further
applications of our methods, we prove stability of quasinormal frequencies in a
sector of the complex plane, with respect to suitably small perturbations and
establish convergence properties for Kerr--de Sitter quasinormal frequencies
when the cosmological constant approaches zero.


  We present a new one parameter family of second derivative discontinuous
solutions to the simplest scale invariant linear ordinary differential
equation. We also point out how the construction could be extended to generate
families of higher derivative discontinuous solutions as well. The
discontinuity can occur only for a subset of even order derivatives, viz.,2nd,
4th, 8th, 16th, ....The solutions are shown to break the discrete parity
(reflection) symmetry of the underlying equation. These results are expected to
gain significance in the contemporary search of a new {\em dynamical principle}
for understanding complex phenomena in Nature.


  For a large class of self-similar sets F in R^d analogues of the higher order
mean curvatures of differentiable submanifolds are introduced, in particular,
the fractal Gauss-type curvature. They are shown to be the densities of
associated fractal curvature measures, which are all multiples of the
corresponding Hausdorff measures on F, due to its self-similarity. This local
approach based on ergodic theory for an associated dynamical system enables us
to extend former global curvature results.


  Consider a network in which $n$ distributed nodes are connected to a single
server. Each node continuously observes a data stream consisting of one value
per discrete time step. The server has to continuously monitor a given
parameter defined over all information available at the distributed nodes. That
is, in any time step $t$, it has to compute an output based on all values
currently observed across all streams. To do so, nodes can send messages to the
server and the server can broadcast messages to the nodes. The objective is the
minimisation of communication while allowing the server to compute the desired
output.
  We consider monitoring problems related to the domain $D_t$ defined to be the
set of values observed by at least one node at time $t$. We provide randomised
algorithms for monitoring $D_t$, (approximations of) the size $|D_t|$ and the
frequencies of all members of $D_t$. Besides worst-case bounds, we also obtain
improved results when inputs are parameterised according to the similarity of
observations between consecutive time steps. This parameterisation allows to
exclude inputs with rapid and heavy changes, which usually lead to the
worst-case bounds but might be rather artificial in certain scenarios.


  A search for the $b\bar b$ decay of the Standard Model Higgs boson produced
through vector-boson fusion is presented. Three mutually exclusive channels are
considered: two all-hadronic channels and a photon-associated channel. Results
are reported from the analysis of up to 30.6 fb$^{-1}$ of $pp$ data at
$\sqrt{s} = 13$ $\mathrm{TeV}$ collected with the ATLAS detector at the LHC.
The measured signal strength relative to the Standard Model prediction from the
combined analysis is $2.5^{+1.4}_{-1.3}$ for inclusive Higgs boson production
and $3.0^{+1.7}_{-1.6}$ for vector-boson fusion production only.


  Despite the recent success of deep learning for many speech processing tasks,
single-microphone, speaker-independent speech separation remains challenging
for two main reasons. The first reason is the arbitrary order of the target and
masker speakers in the mixture permutation problem, and the second is the
unknown number of speakers in the mixture output dimension problem. We propose
a novel deep learning framework for speech separation that addresses both of
these issues. We use a neural network to project the time-frequency
representation of the mixture signal into a high-dimensional embedding space. A
reference point attractor is created in the embedding space to represent each
speaker which is defined as the centroid of the speaker in the embedding space.
The time-frequency embeddings of each speaker are then forced to cluster around
the corresponding attractor point which is used to determine the time-frequency
assignment of the speaker. We propose three methods for finding the attractors
for each source in the embedding space and compare their advantages and
limitations. The objective function for the network is standard signal
reconstruction error which enables end-to-end operation during both training
and test phases. We evaluated our system using the Wall Street Journal dataset
WSJ0 on two and three speaker mixtures and report comparable or better
performance than other state-of-the-art deep learning methods for speech
separation.


  Thompson Sampling has been demonstrated in many complex bandit models,
however the theoretical guarantees available for the parametric multi-armed
bandit are still limited to the Bernoulli case. Here we extend them by proving
asymptotic optimality of the algorithm using the Jeffreys prior for
1-dimensional exponential family bandits. Our proof builds on previous work,
but also makes extensive use of closed forms for Kullback-Leibler divergence
and Fisher information (and thus Jeffreys prior) available in an exponential
family. This allow us to give a finite time exponential concentration
inequality for posterior distributions on exponential families that may be of
interest in its own right. Moreover our analysis covers some distributions for
which no optimistic algorithm has yet been proposed, including heavy-tailed
exponential families.


  We study the representations of the commutator subgroup of the braid group
with n strands in the symmetric group of degree r. Motivated by some
experimental results, we conjecture that for n>r, every such representation is
trivial.


  Often in applications such as rare events estimation or optimal control it is
required that one calculates the principal eigen-function and eigen-value of a
non-negative integral kernel. Except in the finite-dimensional case, usually
neither the principal eigen-function nor the eigen-value can be computed
exactly. In this paper, we develop numerical approximations for these
quantities. We show how a generic interacting particle algorithm can be used to
deliver numerical approximations of the eigen-quantities and the associated
so-called "twisted" Markov kernel as well as how these approximations are
relevant to the aforementioned applications. In addition, we study a collection
of random integral operators underlying the algorithm, address some of their
mean and path-wise properties, and obtain $L_{r}$ error estimates. Finally,
numerical examples are provided in the context of importance sampling for
computing tail probabilities of Markov chains and computing value functions for
a class of stochastic optimal control problems.


  Graph algorithms have wide applicablity to a variety of domains and are often
used on massive datasets. Recent standardization efforts such as the GraphBLAS
specify a set of key computational kernels that hardware and software
developers can adhere to. Graphulo is a processing framework that enables
GraphBLAS kernels in the Apache Accumulo database. In our previous work, we
have demonstrated a core Graphulo operation called \textit{TableMult} that
performs large-scale multiplication operations of database tables. In this
article, we present the results of scaling the Graphulo engine to larger
problems and scalablity when a greater number of resources is used.
Specifically, we present two experiments that demonstrate Graphulo scaling
performance is linear with the number of available resources. The first
experiment demonstrates cluster processing rates through Graphulo's TableMult
operator on two large graphs, scaled between $2^{17}$ and $2^{19}$ vertices.
The second experiment uses TableMult to extract a random set of rows from a
large graph ($2^{19}$ nodes) to simulate a cued graph analytic. These
benchmarking results are of relevance to Graphulo users who wish to apply
Graphulo to their graph problems.


  As a convention, p-value is often computed in frequentist hypothesis testing
and compared with the nominal significance level of 0.05 to determine whether
or not to reject the null hypothesis. The smaller the p-value, the more
significant the statistical test. We consider both one-sided and two-sided
hypotheses in the composite hypothesis setting. For one-sided hypothesis tests,
we establish the equivalence of p-value and the Bayesian posterior probability
of the null hypothesis, which renders p-value an explicit interpretation of how
strong the data support the null. For two-sided hypothesis tests of a point
null, we recast the problem as a combination of two one-sided hypotheses alone
the opposite directions and put forward the notion of a two-sided posterior
probability, which also has an equivalent relationship with the (two-sided)
p-value. Extensive simulation studies are conducted to demonstrate the Bayesian
posterior probability interpretation for the p-value. Contrary to common
criticisms of the use of p-value in evidence-based studies, we justify its
utility and reclaim its importance from the Bayesian perspective, and recommend
the continual use of p-value in hypothesis testing. After all, p-value is not
all that bad.


  T*-categories are introduced as a ternary generalization of C*-categories.
Their linking C*-categories are constructed and the Gelfand-Naimark
representation theorems of Zettl for C*-ternary rings and for W*-ternary rings,
are generalized to T*-categories. Biduals of C*-categories and of T*-categories
are considered.


  Actuators at the nanoscale are assuming great important in todays shrinking
electronics industry where a system-on-chip approach is used to integrate
multi-functional systems and devices. Integration of sensors, actuators,
information processing, and storage have become extremely important, more so at
the sub-micrometer scale. Here we utilized vertically aligned carbon nanotube
forests bonded onto a piezoelectric substrate to provide sensing of nanoscale
forces and actuation on the same platform. This is a demonstration of
integration of two important functions using the functionality of
nanomaterials. This has immediate utility in many areas including outer space
exploration, portable consumer electronics, embedded systems, etc.


  We prove sharp bounds on the probability that the simple random walk on a
vertex-transitive graph escapes the ball of radius $r$ before returning to its
starting point. In particular, this shows that if the ball of radius $r$ has
size slightly greater than quadratic in $r$ then this probability is bounded
from below. On the other hand, we show that if the ball of radius $r$ has
volume slightly less than cubic in $r$ then this probability decays
logarithmically for all larger balls. These results represent a finitary
refinement of Varopoulos's theorem that a random walk on a vertex-transitive
graph is recurrent if and only if the graph has at most quadratic volume
growth. They also imply the existence of a gap at $0$ for escape probabilities:
there exists a universal constant $c>0$ such that the random walk on an
arbitrary vertex-transitive graph is either recurrent or has a probability of
at least $c$ of escaping to infinity. We also prove versions of these results
for finite graphs, in particular confirming and strengthening a conjecture of
Benjamini and Kozma from 2002. Amongst other things, we also generalise our
results to give a sharp finitary version of the characterisation of
$p$-parabolic vertex-transitive graphs, prove a number of sharp isoperimetric
inequalities for vertex-transitive graphs, and prove a locality result for the
escape probability of the random walk on a vertex-transitive graph that can be
seen as an analogue of Schramm's locality conjecture for the critical
percolation probability.


  In this work we study the treatment of asymmetric open quantum systems with
neural networks based on the restricted Boltzmann machine. In particular, we
are interested in the non-equilibrium steady state current in the
boundary-driven (anisotropic) Heisenberg spin chain. We address previously
published difficulties in treating asymmetric dissipative systems with
neural-network quantum states and Monte-Carlo sampling and present an
optimization method and a sampling technique that can be used to obtain
high-fidelity steady state approximations of such systems. We point out some
inherent symmetries of the Lindblad operator under consideration and exploit
them during sampling. We show that local observables are not always a good
indicator of the quality of the approximation and finally present results for
the spin current that are in agreement with known results of simple open
Heisenberg chains.


  In this paper we study the relationship between the optimal value of a
homogeneous quadratic optimization problem and that of its Semidefinite
Programming (SDP) relaxation. We consider two quadratic optimization models:
(1) $\min \{x^* C x \mid x^* A_k x \ge 1, x\in\mathbb{F}^n, k=0,1,...,m\}$; and
(2) $\max \{x^* C x \mid x^* A_k x \le 1, x\in\mathbb{F}^n, k=0,1,...,m\}$. If
\emph{one} of $A_k$'s is indefinite while others and $C$ are positive
semidefinite, we prove that the ratio between the optimal value of (1) and its
SDP relaxation is upper bounded by $O(m^2)$ when $\mathbb{F}$ is the real line
$\mathbb{R}$, and by $O(m)$ when $\mathbb{F}$ is the complex plane
$\mathbb{C}$. This result is an extension of the recent work of Luo {\em et
al.} \cite{LSTZ}. For (2), we show that the same ratio is bounded from below by
$O(1/\log m)$ for both the real and complex case, whenever all but one of
$A_k$'s are positive semidefinite while $C$ can be indefinite. This result
improves the so-called approximate S-Lemma of Ben-Tal {\em et al.}
\cite{BNR02}. We also consider (2) with multiple indefinite quadratic
constraints and derive a general bound in terms of the problem data and the SDP
solution. Throughout the paper, we present examples showing that all of our
results are essentially tight.


  Countries and cities around the world have resorted to unprecedented mobility
restrictions to combat Covid-19 transmission. Here we exploit a natural
experiment whereby Colombian cities implemented varied lockdown policies based
on ID number and gender to analyse the impact of these policies on urban
mobility. Using mobile phone data, we find that the restrictiveness of cities'
mobility quotas (the share of residents allowed out daily according to policy
advice) does not correlate with mobility reduction Instead, we find that
larger, wealthier cities with more formalized and complex industrial structure
experienced greater reductions in mobility. Within cities, wealthier residents
are more likely to reduce mobility, and commuters are especially more likely to
stay home when their work is located in wealthy or commercially/industrially
formalized neighbourhoods..Hence, our results indicate that cities' employment
characteristics and work-from-home capabilities are the primary determinants of
mobility reduction. This finding underscores the need for mitigations aimed at
lower income/informal workers, and sheds light on critical dependencies between
socioeconomic classes in Latin American cities.


  Given $n$ vectors $\mathbf{x}_i\in \mathbb{R}^d$, we want to fit a linear
regression model for noisy labels $y_i\in\mathbb{R}$. The ridge estimator is a
classical solution to this problem. However, when labels are expensive, we are
forced to select only a small subset of vectors $\mathbf{x}_i$ for which we
obtain the labels $y_i$. We propose a new procedure for selecting the subset of
vectors, such that the ridge estimator obtained from that subset offers strong
statistical guarantees in terms of the mean squared prediction error over the
entire dataset of $n$ labeled vectors. The number of labels needed is
proportional to the statistical dimension of the problem which is often much
smaller than $d$. Our method is an extension of a joint subsampling procedure
called volume sampling. A second major contribution is that we speed up volume
sampling so that it is essentially as efficient as leverage scores, which is
the main i.i.d. subsampling procedure for this task. Finally, we show
theoretically and experimentally that volume sampling has a clear advantage
over any i.i.d. sampling when labels are expensive.