  We have developed a method to accurately and efficiently determine the
vibrational free energy as a function of temperature and volume for
substitutional alloys from first principles. Taking Ti$_{1-x}$Al$_x$N alloy as
a model system, we calculate the isostructural phase diagram by finding the
global minimum of the free energy, corresponding to the true equilibrium state
of the system. We demonstrate that the anharmonic contribution and temperature
dependence of the mixing enthalpy have a decisive impact on the calculated
phase diagram of a Ti$_{1-x}$Al$_x$N alloy, lowering the maximum temperature
for the miscibility gap from 6560 K to 2860 K. Our local chemical composition
measurements on thermally aged Ti$_{0.5}$Al$_{0.5}$N alloys agree with the
calculated phase diagram.


  Although ordinary differential equations (ODEs) provide insights for
designing network architectures, its relationship with the non-residual
convolutional neural networks (CNNs) is still unclear. In this paper, we
present a novel ODE model by adding a damping term. It can be shown that the
proposed model can recover both a ResNet and a CNN by adjusting an
interpolation coefficient. Therefore, the damped ODE model provides a unified
framework for the interpretation of residual and non-residual networks. The
Lyapunov analysis reveals better stability of the proposed model, and thus
yields robustness improvement of the learned networks. Experiments on a number
of image classification benchmarks show that the proposed model substantially
improves the accuracy of ResNet and ResNeXt over the perturbed inputs from both
stochastic noise and adversarial attack methods. Moreover, the loss landscape
analysis demonstrates the improved robustness of our method along the attack
direction.


  For a long time the consensus has been that star formation rates are higher
in the interior of spiral arms in galaxies, compared to inter-arm regions.
However, recent studies have found that the star formation inside the arms is
not more efficient than elsewhere in the galaxy. Previous studies have based
their conclusion mainly on integrated light. We use resolved stellar
populations to investigate the star formation rates throughout the nearby
spiral galaxy NGC 5236. We aim to investigate how the star formation rate
varies in the spiral arms compared to the inter-arm regions, using optical
space-based observations of NGC 5236. Using ground-based H\alpha images we
traced regions of recent star formation, and reconstructed the arms of the
galaxy. Using HST/ACS images we estimate star formation histories by means of
the synthetic CMD method. Arms based on H\alpha images showed to follow the
regions where stellar crowding is higher. Star formation rates for individual
arms over the fields covered were estimated between 10 to 100 Myr, where the
stellar photometry is less affected by incompleteness. Comparison between arms
and inter-arm surface star formation rate densities (\Sigma$_{SFR}$) suggested
higher values in the arms (\sim0.6 dex). Over a small fraction of one arm we
checked how the \Sigma$_{SFR}$ changes for the trailing and leading part. The
leading part of the arm showed to have a higher \Sigma$_{SFR}$ in the age range
10-100 Myr. Predictions from the density wave theory of a rapid increase in the
star formation at the edge where the stars and the gas enter the density wave
are confirmed. The \Sigma$_{SFR}$ presents a steep decrease with distance from
the center of the arms through the inter-arm regions.


  We present ProvG-Searcher, a novel approach for detecting known APT behaviors
within system security logs. Our approach leverages provenance graphs, a
comprehensive graph representation of event logs, to capture and depict data
provenance relations by mapping system entities as nodes and their interactions
as edges. We formulate the task of searching provenance graphs as a subgraph
matching problem and employ a graph representation learning method. The central
component of our search methodology involves embedding of subgraphs in a vector
space where subgraph relationships can be directly evaluated. We achieve this
through the use of order embeddings that simplify subgraph matching to
straightforward comparisons between a query and precomputed subgraph
representations. To address challenges posed by the size and complexity of
provenance graphs, we propose a graph partitioning scheme and a
behavior-preserving graph reduction method. Overall, our technique offers
significant computational efficiency, allowing most of the search computation
to be performed offline while incorporating a lightweight comparison step
during query execution. Experimental results on standard datasets demonstrate
that ProvG-Searcher achieves superior performance, with an accuracy exceeding
99% in detecting query behaviors and a false positive rate of approximately
0.02%, outperforming other approaches.


  We study large Wigner random matrices in the case when the marginal
distributions of matrix entries have heavy tails. We prove that the largest
eigenvalues of such matrices have Poisson statistics.


  The event-by-event analysis of heavy ions collisions is becoming possible
with advent of large acceptance detectors: it can provide dynamical information
which cannot be obtained from inclusive spectra. We identify some observables
which can be related to standard thermodynamical fluctuations and therefore may
provide information about properties of hadronic matter at the freeze-out
stage. Among those are fluctuations of ``apparent temperature'' (the $p_t$
slope), as well as the population of different bins of the pion momentum
distribution.


  We present photoelectric and spectral observations of a hot candidate
proto-planetary nebula - early B-type supergiant with emission lines in
spectrum - IRAS 19336-0400. The light and color curves display fast irregular
brightness variations with maximum amplitudes dV=0.30 mag, dB=0.35 mag, dU=0.40
mag and color-brightness correlations. By the variability characteristics IRAS
19336-0400 appears similar to other hot proto-planetary nebulae. Based on
low-resolution spectra in the range lambda 4000-7500 A we have derived absolute
intensities of the emission lines H_alpha, H_beta, H_gamma, [SII], [NII],
physical conditions in gaseous nebula: n_e=10^4 cm^{-3}, T_e=7000 \pm 1000 K.
The emission line H_alpha, H_beta equivalent widths are found to be
considerably variable and related to light changes. By UBV-photometry and
spectroscopy the color excess has been estimated: E(B-V)=0.50-0.54. Joint
photometric and spectral data analysis allows us to assume that the star
variability is caused by stellar wind variations.


  If the positron fraction and combined electron-positron flux excesses
recently observed by PAMELA, Fermi and HESS have a dark matter origin, final
state radiation (FSR) photons from dark matter annihilation into lepton-rich
final states may be detected with observations of satellite dwarf galaxies of
the Milky Way by ground-based atmospheric Cherenkov telescopes (ACTs). We find
that current and near-future ACTs have excellent potential for such detection,
although a discovery cannot be guaranteed due to large uncertainties in the
distribution of dark matter within the dwarfs. We find that models predicting
dark matter annihilation into two-lepton final states and those favoring
four-lepton final states (as in, for example, "axion portal" models) can be
reliably distinguished using the FSR photon spectrum once measured, and the
dark matter particle mass can also be accurately determined.


  In this work, we propose device independent true random numbers generation
protocols based on non-inequality paradoxes such as Hardy's and Cabello's
non-locality argument. The efficiency of generating randomness in our protocols
are far better than any other proposed protocols certified by CHSH inequality
or other non-locality test involving inequalities. Thus, highlighting
non-inequality paradox as an important resource for device independent quantum
information processing in particular generating true randomness. As a
byproduct, we find that the non-local bound of the Cabello's argument with
arbitrary dimension is the same as the one achieved in the qubits system. More
interestingly, we propose a new dimension witness paradox based on the
Cabello's argument, which can be used for constructing semi-device-independent
true random numbers generation protocol.


  We provide a general condition under which e-variables in the form of a
simple-vs.-simple likelihood ratio exist when the null hypothesis is a
composite, multivariate exponential family. Such `simple' e-variables are easy
to compute and expected-log-optimal with respect to any stopping time. Simple
e-variables were previously only known to exist in quite specific settings, but
we offer a unifying theorem on their existence for testing exponential
families. We start with a simple alternative $Q$ and a regular exponential
family null. Together these induce a second exponential family ${\cal Q}$
containing $Q$, with the same sufficient statistic as the null. Our theorem
shows that simple e-variables exist whenever the covariance matrices of ${\cal
Q}$ and the null are in a certain relation. Examples in which this relation
holds include some $k$-sample tests, Gaussian location- and scale tests, and
tests for more general classes of natural exponential families.


  We study the first order phase transition of Euler-Heisenberg-AdS black hole
based on free energy landscape. By solving the Fokker-Planck equation, we
research the probability distribution of the system states. The small (large)
black hole can have the chance to switch to the large (small) black hole due to
the change of the temperature $T$ or Euler-Heisenberg parameter $a$. A higher
(lower) $T$ corresponds to a larger probability for a large (small) black hole.
The coexistent small and large black hole states can be acquired for some
conditions. For $0< a\leq \frac{32}{7} Q^2 $, the small-large black hole phase
transition can be acquired with a small $a$. The probability of small (large)
black holes will decrease to zero for a large $a$. For a small $a$, a higher
peak of the first passage time can be acquired for higher (lower) $T$ or
smaller (larger) $a$ with the initial small (large) black hole state. For
$a<0$, a smaller (larger) $a$ corresponds to a larger probability for a large
(small) black hole. A higher peak of the first passage time can also be
obtained for higher (lower) $T$ or smaller (larger) $a$ with initial small
(large) black hole state.


  We report the discovery of a planetary system in which a super-earth orbits a
late M-dwarf host. The planetary system was found from the analysis of the
microlensing event OGLE-2017-BLG-0482, wherein the planet signal appears as a
short-term anomaly to the smooth lensing light curve produced by the host.
Despite its weak signal and short duration, the planetary signal was firmly
detected from the dense and continuous coverage by three microlensing surveys.
We find a planet/host mass ratio of $q\sim 1.4\times 10^{-4}$. We measure the
microlens parallax $\pi_{\rm E}$ from the long-term deviation in the observed
lensing light curve, but the angular Einstein radius $\theta_{\rm E}$ cannot be
measured because the source trajectory did not cross the planet-induced
caustic. Using the measured event timescale and the microlens parallax, we find
that the masses of the planet and the host are $M_{\rm p}=9.0_{-4.5}^{+9.0}\
M_\oplus$ and $M_{\rm host}=0.20_{-0.10}^{+0.20}\ M_\odot$, respectively, and
the projected separation between them is $a_\perp=1.8_{-0.7}^{+0.6}$ au. The
estimated distance to the lens is $D_{\rm L}=5.8_{-2.1}^{+1.8}$ kpc. The
discovery of the planetary system demonstrates that microlensing provides an
important method to detect low-mass planets orbiting low-mass stars.


  There has become of increasing interest in transcranial alternating current
stimulation (tACS) since its inception nearly a decade ago. tACS in modulating
brain state is an active area of research and has been demonstrated effective
in various neuropsychological and clinical domains. In the visual domain, much
effort has been dedicated to brain rhythms and rhythmic stimulation, i.e.,
tACS. However, little is known about the interplay between the rhythmic
stimulation and visual stimulation. Here, we used steady-state visual evoked
potential (SSVEP), induced by flickering driving as a widely used technique for
frequency-tagging, to investigate the aftereffect of tACS in healthy human
subjects. Seven blocks of 64-channel electroencephalogram were recorded before
and after the administration of 20-min 10-Hz tACS, while subjects performed
several blocks of SSVEP tasks. We characterized the physiological properties of
tACS aftereffect by comparing and validating the temporal, spatial,
spatiotemporal and signal-to-noise ratio (SNR) patterns between and within
blocks in real tACS and sham tACS. Our result revealed that tACS boosted the
10-Hz SSVEP significantly. Besides, the aftereffect on SSVEP was mitigated with
time and lasted up to 5 min. Our results demonstrate the feasibility of
facilitating the flickering driving by external rhythmic stimulation and open a
new possibility to alter the brain state in a direction by noninvasive
transcranial brain stimulation.


  Let $n_1,\ldots,n_k $ be integers larger than or equal to 2. We characterize
linear maps $\phi: M_{n_1\cdots n_k}\rightarrow M_{n_1\cdots n_k}$ such that
$${\mathrm rank}\,(\phi(A_1\otimes \cdots \otimes
A_k))=1\quad\hbox{whenever}\quad{\mathrm rank}\, (A_1\otimes \cdots \otimes
A_k)=1 \quad \hbox{for all}\quad A_i \in M_{n_i},\, i = 1,\dots,k.$$ Applying
this result, we extend two recent results on linear maps that preserving the
rank of special classes of matrices.


  This paper deals with two-sided matching market with two disjoint sets, i.e.
the set of buyers and the set of sellers. Each seller can trade with at most
with one buyer and vice versa. Money is transferred from sellers to buyers for
an indivisible goods that buyers own. Valuation functions, for participants of
both sides, are represented by strictly increasing functions with money
considered as discrete variable. An algorithm is devised to prove the existence
of stability for this model.


  For a discrete group G with Fourier algebra A(G), we study the topological
centre $Z_t$ of the bidual. If G is amenable, then $Z_t$ = A(G). But if G
contains a non-abelian free group $F_r$, we show that $Z_t$ is strictly larger
than A(G). Furthermore, it is shown that the subalgebra of radial functions in
A(G) is Arens regular.


  Concurrent programming is used in all large and complex computer systems.
However, concurrency errors and system failures (ex: crashes and deadlocks) are
common. We find that Petri nets can be used to model concurrent systems and
find and remove errors ahead of time. We introduce a novel generalization of
Petri nets with nondeterministic transition nodes to match real systems. These
allow for a compact way to construct, optimize, and prove computer programs at
the concurrency level. Petri net programs can also be optimized by
automatically solving for maximal concurrency, where the maximum number of
valid threads is determined by the structure of the Petri net prior to
execution. We discuss an algorithm to compute the state graph of a given Petri
net start state pair. We introduce our open source software framework which
implements this theory as a general purpose concurrency focused middle-ware.


  Consider the primitive equations on $\R^2\times (z_0,z_1)$ with initial data
$a$ of the form $a=a_1+a_2$, where $a_1 \in BUC_\sigma(\R^2;L^1(z_0,z_1))$ and
$a_2 \in L^\infty_\sigma(\R^2;L^1(z_0,z_1))$ and where $BUC_\sigma(L^1)$ and
$L^\infty_\sigma(L^1)$ denote the space of all solenoidal, bounded uniformly
continuous and all solenoidal, bounded functions on $\R^2$, respectively, which
take values in $L^1(z_0,z_1)$. These spaces are scaling invariant and represent
the anisotropic character of these equations. It is shown that, if
$\|a_2\|_{L^\infty_\sigma(L^1)}$ is sufficiently small, then this set of
equations has a unique, local, mild solution. If in addition $a$ is periodic in
the horizontal variables, then this solution is a strong one and extends to a
unique, global, strong solution. The primitive equations are thus strongly and
globally well-posed for these data. The approach depends crucially on mapping
properties of the hydrostatic Stokes semigroup in the $L^\infty(L^1)$-setting
and can thus be seen as the counterpart of the classical iteration schemes for
the Navier-Stokes equations for the situation of the primitive equations.


  This article is a draft of a book chapter of the book entitled "Quantum
Percolation and Breakdown", to appear 2008.


  A controllable $\pi$-SQUID is a DC SQUID with two controllable
$\pi$-junctions as weak links. A controllable $\pi$-junction consists of a
superconducting - normal metal - superconducting Josephson junction with two
additional contacts to the normal region of the junction. By applying a voltage
$V_c$ over these contacts it is possible to control the sate of the junction,
i.e. a conventional (0) state or a $\pi$-state, depending on the magnitude of
$V_c$. We demonstrate experimentally that, by putting one junction into a
$\pi$-state, a screening current is generated around the SQUID loop at integer
external flux. To be able to do this, we have fabricated controllable
$\pi$-junctions, based on Cu-Nb or Ag-Nb, in a new geometry. We show that at
1.4 K only the Nb-Ag device shows the transition to a $\pi$-state as a function
of $V_c$ consistent with theoretical predictions. In a controllable $\pi$ SQUID
based on Nb-Ag we observe, a part from a screening current at integer external
flux, a phase shift of $\pi$ of the $V_{SQUID}-B$ oscillations under suitable
current bias, depending on the magnitude of $V_c$.


  We suggest a structure for the vacuum comprised of a network of tightly
knotted/linked flux tubes formed in a QCD-like cosmological phase transition
and show that such a network can drive cosmological inflation. As the network
can be topologically stable only in three space dimensions, this scenario
provides a dynamical explanation for the existence of exactly three large
spatial dimensions in our Universe.


  Bayesian Optimization is methodology used in statistical modelling that
utilizes a Gaussian process prior distribution to iteratively update a
posterior distribution towards the true distribution of the data. Finding
unbiased informative priors to sample from is challenging and can greatly
influence the outcome on the posterior distribution if only few data are
available. In this paper we propose a novel approach to utilize meta-learning
to automate the estimation of informative conjugate prior distributions given a
distribution class. From this process we generate priors that require only few
data to estimate the shape parameters of the original distribution of the data.


  We present a Mathematica package for performing algebraic and numerical
computations in cosmological models based on supersymmetric theories. The
programs allow for (I) evaluation and study of the properties of a scalar
potential in a large class of supergravity models with any number of moduli and
arbitrary superpotential, Kahler potential, and D-term; (II) numerical solution
of a system of scalar and Friedmann equations for the flat FRW universe, with
any number of scalar moduli and arbitrary moduli space metric. We are using
here a simple set of first order differential equations which we derived in a
Hamiltonian framework. Using our programs we present some new results: (I) a
shift-symmetric potential of the inflationary model with a mobile D3 brane in
an internal space with stabilized volume; (II) a KKLT-based dark energy model
with the acceleration of the universe due to the evolution of the axion partner
of the volume modulus. The gzipped package can be downloaded from
http://www.stanford.edu/~prok/SuperCosmology/ or from
http://www.stanford.edu/~rkallosh/SuperCosmology/


  We study second order finite temperature phase transitions of the 2D quantum
Ising and interacting honeycomb fermions models using infinite projected
entangled pair states (iPEPS). We obtain an iPEPS thermal state representation
by Variational Tensor Network Renormalization (VTNR). We find that at the
critical temperature $T_c$ the iPEPS correlation length is finite for the
computationally accessible values of the iPEPS bond dimension $D$. Motivated by
this observation we investigate the application of Finite Correlation Length
Scaling (FCLS), which has been previously used for iPEPS simulations of quantum
critical points at $T=0$, to obtain precise values of $T_c$ and the universal
critical exponents. We find that in the vicinity of $T_c$ the behavior of
observables follows well the one predicted by FCLS. Using FCLS we obtain $T_c$
and the critical exponents in agreement with Quantum Monte Carlo (QMC) results
except for couplings close to the quantum critical points where larger bond
dimensions are required.


  Gluons dominate the proton behavior at high energy collisions, they can be
condensed at ultra high energy. The collisions of the accelerated high energy
protons with interplanetary matter in cosmic rays will produce a huge number of
secondary particles at the gluon condensate energy region, which break the
primary power-law of cosmic rays. The above predictions seem to be consistent
with the recent DAMPE data concerning the electron plus positron spectra. We
find that the smoothly broken power-law at $\sim 0.9 TeV$ and $3\sim 4 TeV$ in
the DAMPE data can be understood as the gluon condensation effects in proton.


  We propose new simultaneous inference methods for diagnostic trials with
elaborate factorial designs. Instead of the commonly used total area under the
receiver operating characteristic (ROC) curve, our parameters of interest are
partial areas under ROC curve segments that represent clinically relevant
biomarker cut-off values. We construct a nonparametric multiple contrast test
for these parameters and show that it asymptotically controls the family-wise
type one error rate. Finite sample properties of this test are investigated in
a series of computer experiments. We provide empirical and theoretical evidence
supporting the conjecture that statistical inference about partial areas under
ROC curves is more efficient than inference about the total areas.


  An infinite matroid is graphic if all of its finite minors are graphic and
the intersection of any circuit with any cocircuit is finite. We show that a
matroid is graphic if and only if it can be represented by a graph-like
topological space: that is, a graph-like space in the sense of Thomassen and
Vella. This extends Tutte's characterization of finite graphic matroids.
  The representation we construct has many pleasant topological properties.
Working in the representing space, we prove that any circuit in a 3-connected
graphic matroid is countable.


  Integrated sensing and communication (ISAC), which simultaneously performs
sensing and communication functions within a shared frequency band and hardware
platform, has emerged as a promising technology for future wireless systems.
Nevertheless, the weak echo signal received by the low-sensitivity ISAC
receiver significantly constrains sensing performance in scenarios involving
obstructed targets. Active reconfigurable intelligent surface (RIS) has become
a prospective solution by situationally manipulating the wireless propagations
and amplifying the signals. In this paper, we investigate active RIS-empowered
ISAC systems to enhance radar echo signal quality as well as communication
performance. In particular, we focus on the joint design of the base station
(BS) transmit precoding and the active RIS reflection beamforming to optimize
the parameter estimation performance in terms of Cramer-Rao bound (CRB) subject
to the communication users' signal-to-interference-plus-noise ratio (SINR)
requirements. An efficient algorithm based on alternating optimization,
semidefinite relaxation (SDR), and majorization-minimization (MM) is proposed
to solve the formulated challenging non-convex problem. Finally, simulation
results validate the effectiveness of the developed algorithm and the potential
of employing active RIS in ISAC systems to enhance direct-of-arrival (DoA)
estimation performance.


  Recently, L.Rozansky and E.Witten (hep-th/9612216) associated to any
hyperKaehler manifold X a system of "weights" (numbers, one for each trivalent
graph) and used them to construct invariants of topological 3-manifolds. We
give a very simple cohomological definition of these weights in terms of the
Atiyah class of X (the obstruction to existence of a holomorphic connection).
We show that the analogy between the tensor of curvature of a hyperKaehler
metric and the tensor of structure constants of a Lie algebra observed by
Rozansky and Witten, holds in fact for any complex manifold, if we work on the
level of cohomology and for any Kaehler manifold, if we work on the level of
Dolbeault forms. In particular, for any sheaf A of commutative algebras on any
complex manifold the shifted cohomology of the tangent sheaf tensored with A is
a graded Lie algebra. We also show that a certain system of Gilkey-type
complexes of "natural tensors" on Kaehler manifolds is, up to suspension
(accounting for various changes of signs), identified with the PROP (in the
sense of Adams and MacLane) describing Lie algebras "up to higher homotopies".
As an outcome of our considerations, we give a formula for the Rozansky-Witten
classes using any Kaehler metric on a holomorphic symplectic manifold.


  This work addresses the question of the interplay of DNA demixing and
supercoiling in bacterial cells. Demixing of DNA from other globular
macromolecules results from the overall repulsion between all components of the
system and leads to the formation of the nucleoid, which is the region of the
cell that contains the genomic DNA in a rather compact form. Supercoiling
describes the coiling of the axis of the DNA double helix to accommodate the
torsional stress injected in the molecule by topoisomerases. Supercoiling is
able to induce some compaction of the bacterial DNA, although to a lesser
extent than demixing. In this paper, we investigate the interplay of these two
mechanisms, with the goal of determining whether the total compaction ratio of
the DNA is the mere sum or some more complex function of the compaction ratios
due to each mechanism. To this end, we developed a coarse-grained
bead-and-spring model and investigated its properties through Brownian dynamics
simulations. This work reveals that there actually exist different regimes,
depending on the crowder volume ratio and the DNA superhelical density. In
particular, a regime where the effects of DNA demixing and supercoiling on the
compaction of the DNA coil simply add up is shown to exist up to moderate
values of the superhelical density. In contrast, the mean radius of the DNA
coil no longer decreases above this threshold and may even increase again for
sufficiently large crowder concentrations. Finally, the model predicts that the
DNA coil may depart from the spherical geometry very close to the jamming
threshold, as a trade-off between the need to minimize both the bending energy
of the stiff plectonemes and the volume of the DNA coil to accommodate
demixing.


  Picking unseen objects from clutter is a difficult problem because of the
variability in objects (shape, size, and material) and occlusion due to
clutter. As a result, it becomes difficult for grasping methods to segment the
objects properly and they fail to singulate the object to be picked. This may
result in grasp failure or picking of multiple objects together in a single
attempt. A push-to-move action by the robot will be beneficial to disperse the
objects in the workspace and thus assist the grasping and vision algorithm. We
propose a disperse and pick method for domain-independent robotic grasping in a
highly cluttered heap of objects. The novel contribution of our framework is
the introduction of a heuristic clutter removal method that does not require
deep learning and can work on unseen objects. At each iteration of the
algorithm, the robot either performs a push-to-move action or a grasp action
based on the estimated clutter profile. For grasp planning, we present an
improved and adaptive version of a recent domain-independent grasping method.
The efficacy of the integrated system is demonstrated in simulation as well as
in the real-world.


  Recent experiments on the role of electron-electron interactions in fractal
Dirac systems have revealed a host of interesting effects, in particular, the
unique nature of the magnetic field dependence of butterfly gaps in graphene.
The novel gap structure observed in the integer quantum Hall effect is quite
intriguing [Nat. Phys. 10, 525 (2014)], where one observes a suppression of the
ferromagnetic state at one value of the commensurable flux but a reentrant
ferromagnetic state at another. Our present work that includes the interplay
between the electron-electron interaction and the periodic potential, explains
the underlying physical processes that can lead to such a unique behavior of
the butterfly gaps in that system where spin flip transitions are involved in
the ground state.


  We study the evolution of the energy and magnetic moment of a quantum charged
particle placed in a homogeneous magnetic field, when this field changes
adiabatically its sign. We show that after a single magnetic field passage
through zero value, the famous adiabatic invariant ratio of energy to frequency
is reestablished again, but with the proportionality coefficient higher than in
the initial state. The concrete value of this proportionality coefficient
depends on the power index of the frequency dependence on time near zero point.
In particular, the adiabatic ratio of the initial ground state (with zero
radial and angular quantum numbers) triplicates if the frequency tends to zero
linearly as function of time. If the Larmor frequency attains zero more than
once, the adiabatic proportionality coefficient strongly depends on the lengths
of the time intervals between zero points, so that the mean energy behavior can
be quasi-stochastic after many passages through zero value. The original
Born-Fock adiabatic theorem does not work after the frequency passes through
zero. However, its generalization is found: the initial Fock state becomes a
wide superposition of many instantaneous Fock states, whose weights do not
depend on time in the new adiabatic regime.


  We study non-linear differential equations on the punctured formal disc by
considering the natural derived enhancements of their spaces of solutions. In
particular, by appealing to results of the inverse theory in the calculus of
variations, we show that a variational formulation of a differential equation
is \emph{equivalent} to the residue pairing inducing a (-1)-symplectic form on
the derived space of solutions equipped with a certain decoration of its
tangent complex.


  Quantum gravitational tunneling effects are expected to give rise to a number
of interesting observable phenomena, including, in particular, the evolution of
black holes at the end of their existence or the emergence of the early
universe from a quantum phase. Covariant Loop Quantum Gravity provides a
framework to study these phenomena, yet a precise identification of tunneling
processes is still not known. Motivated by this question, we consider a
related, simpler case, that of Ponzano-Regge amplitudes: we find a surprising
and detailed analogy of a class of simple transition amplitudes with tunneling
processes in non-relativistic quantum mechanics.


  We report the initial results from a systematic study of the hyperfine (HF)
structure of antiprotonic helium (n,l) = (37,~35) carried out at the Antiproton
Decelerator (AD) at CERN. We performed a laser-microwave-laser resonance
spectroscopy using a continuous wave (cw) pulse-amplified laser system and
microwave cavity to measure the HF transition frequencies. Improvements in the
spectral linewidth and stability of our laser system have increased the
precision of these measurements by a factor of five and reduced the line width
by a factor of three compared to our previous results. A comparison of the
experimentally measured transition frequencies with three body QED calculations
can be used to determine the antiproton spin magnetic moment, leading towards a
test of CPT invariance.


  Large Multimodal Models (LMMs) have achieved impressive success in visual
understanding and reasoning, remarkably improving the performance of
mathematical reasoning in a visual context. Yet, a challenging type of visual
math lies in the multimodal graph theory problem, which demands that LMMs
understand the graphical structures accurately and perform multi-step reasoning
on the visual graph. Additionally, exploring multimodal graph theory problems
will lead to more effective strategies in fields like biology, transportation,
and robotics planning. To step forward in this direction, we are the first to
design a benchmark named VisionGraph, used to explore the capabilities of
advanced LMMs in solving multimodal graph theory problems. It encompasses eight
complex graph problem tasks, from connectivity to shortest path problems.
Subsequently, we present a Description-Program-Reasoning (DPR) chain to enhance
the logical accuracy of reasoning processes through graphical structure
description generation and algorithm-aware multi-step reasoning. Our extensive
study shows that 1) GPT-4V outperforms Gemini Pro in multi-step graph
reasoning; 2) All LMMs exhibit inferior perception accuracy for graphical
structures, whether in zero/few-shot settings or with supervised fine-tuning
(SFT), which further affects problem-solving performance; 3) DPR significantly
improves the multi-step graph reasoning capabilities of LMMs and the GPT-4V
(DPR) agent achieves SOTA performance.


  The multi-vector generalization of a rigid, partially-broken $\mathcal{N}=2$
supersymmetric theory is presented as a rigid limit of a suitable gauged
$\mathcal{N}=2$ supergravity with electric, magnetic charges and antisymmetric
tensor fields. This on the one hand generalizes a known result by Ferrara,
Girardello and Porrati while on the other hand allows to recover the
multi-vector BI models from $\mathcal{N}=2$ supergravity as the end-point of a
hierarchical limit in which the Planck mass first and then the supersymmetry
breaking scale are sent to infinity.
  We define, in the parent supergravity model, a new symplectic frame in which,
in the rigid limit, manifest symplectic invariance is preserved and the
electric and magnetic Fayet-Iliopoulos terms are fully originated from the
dyonic components of the embedding tensor. The supergravity origin of several
features of the resulting rigid supersymmetric theory will be elucidated, such
as the presence of a traceless ${\rm SU}(2)$- Lie algebra term in the Ward
identity and the existence of a central charge in the supersymmetry algebra
which manifests itself as a harmless gauge transformation on the gauge vectors
of the rigid theory; we show that this effect can be interpreted as a kind of
"superspace non-locality" which does not affect the rigid theory on space-time.
  To set the stage of our analysis we take the opportunity in this paper to
provide and prove the relevant identities of the most general dyonic gauging of
Special-Kaehler and Quaternionic-Kaehler isometries in a generic
$\mathcal{N}=2$ model, which include the supersymmetry Ward identity, in a
fully symplectic-covariant formalism.


  Inelastic neutron scattering (INS) and specific heat measurements have been
performed on the intermediate valence compound CeRuSi$_3$, which is
isostructural to the noncentrosymmetric pressure-induced superconductors
CeRhSi$_3$, CeIrSi$_3$ and CeCoGe$_3$. INS measurements at 7~K reveal a broad
peak at (58.5~$\pm$~1.4)~meV, while at 300~K, broad quasielastic scattering is
observed. This indicates a large Kondo temperature of $T_{\rm K}~\sim~680$~K.
The magnetic contribution to the specific heat ($C_{\rm mag}$) has a value of
$\gamma~=~62.5(1)$~mJ/mol~K$^2$ at low temperatures and above about 100~K can
be well accounted for by the Coqlbin-Schrieffer model with a characteristic
temperature of $T_0$~=~680~K, which is further evidence that CeRuSi$_3$ is in
the intermediate valence regime.


  In the present paper some consequences of the assumption that in the center
of the Galaxy there is a supermassive compact object without the events horizon
are considered. The possibility of existence of such object has been argued
earlier. It is shown, that accretion of a surrounding gas onto the object can
cause nuclear burning in a superficial layer which owing to comptonization in a
hotter layer, laying above, can manifest itself in observable IR and X spectra.
The contribution of an intrinsic magnetic moment of the object in the
observable synchrotron radiation is considered, using transfer equations,
taking into account influence of gravitation on the energy and movement of
photons.


  The Pierre Auger Observatory has been taking data on the highest energy
cosmic rays for the equivalent of over a year of full detector aperture.
Comments are presented on results published so far.


  High energy resolution neutron spin-echo spectroscopy has been used to
measure intrinsic width of diffuse scattering discovered earlier in relaxor
ferroelectric crystals. The anisotropic and transverse components of the
scattering have been observed in different Brillouin zones. Both components are
found to be elastic within experimental accuracy of 1 eV. Possible
physical origin of the static-like behavior is discussed for each diffuse
scattering contribution.


  CDF2PDF is a method of PDF estimation by approximating CDF. The original idea
of it was previously proposed in [1] called SIC. However, SIC requires
additional hyper-parameter tunning, and no algorithms for computing higher
order derivative from a trained NN are provided in [1]. CDF2PDF improves SIC by
avoiding the time-consuming hyper-parameter tuning part and enabling higher
order derivative computation to be done in polynomial time. Experiments of this
method for one-dimensional data shows promising results.


  This paper presents an improved active disturbance rejection control scheme
(IFO-ADRC) with an improved fractional-order extended state observer (IFO-ESO).
The structural information of the system is utilized in IFO-ESO rather than
buried as in the typical fractional-order extended state observer (FO-ESO) and
help significantly improve the performance of IFO-ESO and closed-loop system.
Compared with the integer-order active disturbance rejection controller
(IO-ADRC), the auxiliary tracking controller of IFO-ADRC has a simpler form and
fewer parameters need to be tuned. Frequency-domain analysis shows that IFO-ESO
has better performance over the larger frequency band than FO-ESO, and
time-domain simulation shows that IFO-ADRC has better transient performance and
is more robust against the parameter variations than traditional
fractional-order active disturbance rejection controller (FO-ADRC) and IO-ADRC.
The IFO-ADRC is applied to permanent magnet synchronous motor (PMSM) servo
control system and demonstrates its capability in the real-world application.


  We present the first results of our spectroscopic follow-up of 6.5 < z < 10
candidate galaxies behind clusters of galaxies. We report the spectroscopic
confirmation of an intrinsically faint Lyman break galaxy (LBG) identified as a
z 850LP-band dropout behind the Bullet Cluster. We detect an emission line at
{\lambda} = 9412 {\AA} at >5{\sigma} significance using a 16 hr long exposure
with FORS2 VLT. Based on the absence of flux in bluer broadband filters, the
blue color of the source, and the absence of additional lines, we identify the
line as Ly{\alpha} at z = 6.740 \pm 0.003. The integrated line flux is f = (0.7
\pm 0.1 \pm 0.3) \times 10^{-17} erg^{-1} s^{-1} cm^{-2} (the uncertainties are
due to random and flux calibration errors, respectively) making it the faintest
Ly{\alpha} flux detected at these redshifts. Given the magnification of {\mu} =
3.0 \pm 0.2 the intrinsic (corrected for lensing) flux is f^int = (0.23 \pm
0.03 \pm 0.10 \pm 0.02) \times 10^{-17} erg^{-1} s^{-1} cm^{-2} (additional
uncertainty due to magnification), which is ~2-3 times fainter than other such
measurements in z ~ 7 galaxies. The intrinsic H 160W-band magnitude of the
object is m^int(H_160W)=27.57 \pm 0.17, corresponding to 0.5 L* for LBGs at
these redshifts. The galaxy is one of the two sub-L* LBG galaxies
spectroscopically confirmed at these high redshifts (the other is also a lensed
z = 7.045 galaxy), making it a valuable probe for the neutral hydrogen fraction
in the early universe.


  We investigate the role of quantum coherence in tunneling conductance, where
quantum criticality turns out to suppress Fano resonance. Based on the
nonequilibrium noncrossing approximation, we show that the linear tunneling
conductance exhibits weak Fano line-shape with sharp cusp at zero energy in the
multichannel Kondo effect, resulting from incoherence associated with quantum
criticality of impurity dynamics. In particular, shift of the peak position in
the Fano resonance is predicted not to occur for the multichannel Kondo effect,
distinguished from the Fermi liquid theory in the single channel Kondo effect.


  The ZX-calculus is an algebraic formalism that allows quantum computations to
be simplified via a small number of simple graphical rewrite rules. Recently,
it was shown that, when combined with a family of "sum-over-Cliffords"
techniques, the ZX-calculus provides a powerful tool for classical simulation
of quantum circuits. However, for several important classical simulation tasks,
such as computing the probabilities associated with many measurement outcomes
of a single quantum circuit, this technique results in reductions over many
very similar diagrams, where much of the same computational work is repeated.
In this paper, we show that the majority of this work can be shared across
branches, by developing reduction strategies that can be run parametrically on
diagrams with boolean free parameters. As parameters only need to be fixed
after the bulk of the simplification work is already done, we show that it is
possible to perform the final stage of classical simulation quickly utilising a
high degree of GPU parallelism. Using these methods, we demonstrate speedups
upwards of 100x for certain classical simulation tasks vs. the non-parametric
approach.


  We construct a geodesic net in the plane with four unbalanced (boundary)
vertices that has 16 balanced vertices and does not contain proper geodesic
subnets. This is the first example of an irreducible geodesic net in the
Euclidean plane with 4 boundary vertices that is not a tree.


  Recent advances in modelling VDJ recombination and subsequent selection of T
and B cell receptors provide useful tools to analyze and compare immune
repertoires across time, individuals, and tissues. A suite of tools--IGoR [1],
OLGA [2] and SONIA [3]--have been publicly released to the community that allow
for the inference of generative and selection models from high-throughput
sequencing data. However using these tools requires some scripting or
command-line skills and familiarity with complex datasets. As a result the
application of the above models has not been available to a broad audience. In
this application note we fill this gap by presenting Simple OLGA & SONIA (SOS),
a web-based interface where users with no coding skills can compute the
generation and post-selection probabilities of their sequences, as well as
generate batches of synthetic sequences. The application also functions on
mobile phones.


  We give a simple and explicit presentation of the Z/2-equivariant complex
cobordism ring.


  Consider in $L^2(R^d)$, $d\geq 1$, the operator family $H(g):=H_0+igW$. $\ds
H_0= a^\ast_1a_1+... +a^\ast_da_d+d/2$ is the quantum harmonic oscillator with
rational frequencies, $W$ a $P$ symmetric bounded potential, and $g$ a real
coupling constant. We show that if $|g|<\rho$, $\rho$ being an explicitly
determined constant, the spectrum of $H(g)$ is real and discrete. Moreover we
show that the operator $\ds H(g)=a^\ast_1 a_1+a^\ast_2a_2+ig a^\ast_2a_1$ has
real discrete spectrum but is not diagonalizable.


  We re-examine the zero temperature phase diagram of the two-leg Hubbard
ladder in the small $U$ limit, both analytically and using density-matrix
renormalization group (DMRG). We find a ubiquitous Luther-Emery phase, but with
a crossover in behavior at a characteristic interaction strength, $U^\star$;
for $U \gtrsim U^\star$, there is a single emergent correlation length
$\log[\xi] \sim 1/U$, characterizing the gapped modes of the system, but for
$U\lesssim U^\star$ there is a hierarchy of length scales, differing
parametrically in powers of $U$, reflecting a two-step renormalization group
flow to the ultimate fixed point. Finally, to illustrate the versatility of the
approach developed here, we sketch its implications for a half-filled
triangular lattice Hubbard model on a cylinder, and find results in conflict
with inferences concerning the small $U$ phase from recent DMRG studies of the
same problem.


  We study the quantum computational power of a generic class of anisotropic
solid state Hamiltonians. A universal set of encoded logic operations are found
which do away with difficult-to-implement single-qubit gates in a number of
quantum computer proposals, e.g., quantum dots and donor atom spins with
anisotropic exchange coupling, quantum Hall systems, and electrons floating on
helium.We show how to make the corresponding Hamiltonians universal by encoding
one qubit into two physical qubits, and by controlling nearest neighbor
interactions.


  In-memory computing is an emerging non-von Neumann computing paradigm where
certain computational tasks are performed in memory by exploiting the physical
attributes of the memory devices. Memristive devices such as phase-change
memory (PCM), where information is stored in terms of their conductance levels,
are especially well suited for in-memory computing. In particular, memristive
devices, when organized in a crossbar configuration can be used to perform
matrix-vector multiply operations by exploiting Kirchhoff's circuit laws. To
explore the feasibility of such in-memory computing cores in applications such
as deep learning as well as for system-level architectural exploration, it is
highly desirable to develop an accurate hardware emulator that captures the key
physical attributes of the memristive devices. Here, we present one such
emulator for PCM and experimentally validate it using measurements from a PCM
prototype chip. Moreover, we present an application of the emulator for neural
network inference where our emulator can capture the conductance evolution of
approximately 400,000 PCM devices remarkably well.


  We study the quantum correlations induced by spontaneous parametric
down-conversion (SPDC) of a frequency comb. We derive a theoretical method to
find the output state corresponding to a pump with an arbitrary spectral
profile. After applying it to the relevant example of a spectrally chirped
pump, we run an optimization algorithm to numerically find the pump profiles
maximizing some target functions. These include the number of independently
squeezed modes and the variances of nullifiers defining cluster states used in
many continuous-variable quantum information protocols. To assess the
advantages of pump-shaping in real experiments we take into account the
physical limitations of the pulse shaper.


  Capillary phenomena are involved in many industrial processes, especially
those dealing with composite manufacturing. However, their modelling is still
challenging. Therefore, a finite element setting is proposed to better
investigate this complex issue. The variational formulation of a liquid-air
Stokes system is established, while the solid substrate is described through
boundary conditions. Expressing the weak form of Laplace's law over liquid-air,
liquid-solid and air-solid interfaces, leads to a natural enforcement of the
mechanical equilibrium over the wetting line, without imposing explicitly the
contact angle itself. The mechanical problem is discretized by using finite
elements, linear both in velocity and pressure, stabilized with a variational
multiscale method, including the possibility of enrichment of the pressure
space. The moving interface is captured by a Level-Set methodology, combined
with a mesh adaptation technique with respect to both pressure and level-set
fields. Our methodology can simulate capillary-driven flows in 2D and 3D with
the desired precision: droplet spreading, droplet coalescence, capillary rise.
In each case, the equilibrium state expected in terms of velocity, pressure and
contact angle is reached.


  The notion of quantized characters is introduced in our previous paper as a
natural quantization of characters in the context of asymptotic representation
theory for compact quantum groups. As in the case of ordinary groups, the
representation associated with any extremal quantized character generates von
Neumann factor. In the viewpoint of operator algebras (and measurable dynamical
systems), it is natural to ask what is the Murray-von Neumann-Connes type of
the resulting factor. In this paper, we give a complete solution to this
question when the inductive system is of quantum unitary groups $U_q(N)$.


  We investigate finite size scaling in percolating widthless stick systems
with variable aspect ratios in an extensive Monte Carlo simulation study. A
generalized scaling function is introduced to describe the scaling behavior of
the percolation distribution moments and probability at the percolation
threshold. We show that the prefactors in the generalized scaling function
depend on the system aspect ratio and exhibit features that are generic to
whole class of the percolating systems. In particular, we demonstrate existence
of characteristic aspect ratio for which percolation probability at the
threshold is scale invariant and definite parity of the prefactors in
generalized scaling function for the first two percolation probability moments.


  The Fermilab Short-Baseline Neutrino (SBN) experiments, MicroBooNE, ICARUS,
and SBND, are expected to have significant sensitivity to light weakly coupled
hidden sector particles. Here we study the capability of the SBN experiments to
probe dark scalars interacting through the Higgs portal. We investigate
production of dark scalars using both the Fermilab Booster 8 GeV and NuMI 120
GeV proton beams, simulating kaons decaying to dark scalars and taking into
account the beamline geometry. We also investigate strategies to mitigate
backgrounds from beam-related neutrino scattering events. We find that SBND,
with its comparatively short ${\cal O}(100\ {\rm m})$ baseline, will have the
best sensitivity to scalars produced with Booster, while ICARUS, with its large
detector volume, will provide the best limits on off-axis dark scalar
production from NuMI. The SBN experiments can provide leading tests of dark
scalars with masses in the 50 - 350 MeV range in the near term. Our results
motivate dedicated experimental searches for dark scalars and other long-lived
hidden sector states at these experiments.


  The least mean-square (LMS) filter is one of the most common adaptive linear
estimation algorithms. In many practical scenarios, and particularly in digital
communications systems, the signal of interest (SOI) and the input signal are
jointly wide-sense cyclostationary. Previous works analyzing the performance of
LMS filters for this important case assume specific probability distributions
of the considered signals or specific models that relate the input signal and
the SOI. In this work, we provide a general transient and steady-state
performance analysis that is free of specific distributional or model
assumptions. We obtain conditions for convergence and derive analytical
expressions for the non-asymptotic and steady-state mean-squared error. The
accuracy of our analysis is demonstrated in simulation studies that correspond
to practical communications scenarios.


  Although there is a broad consensus on the fact that critical behavior in
stacked triangular Heisenberg antiferromagnets --an example of frustrated
magnets with competing interactions-- is described by a Landau-Ginzburg-Wilson
Hamiltonian with O(3)$\times$O(2) symmetry, the nature of the phase transition
in three dimensions is still debated. We show that spin-one Bose gases provide
us with a simulator of the O(3)$\times$O(2) model. Using a
renormalization-group approach, we argue that the transition is weakly first
order and shows pseudoscaling behavior, and give estimates of the
pseudocritical exponent $\nu$ in $^{87}$Rb, $^{41}$K and $^7$Li atom gases
which can be tested experimentally.


  The discriminators of quark-gluon jets developed for $pp$ collisions at the
LHC can be used to measure the gluon jet fraction in a jet sample. It allows to
measure various characteristics of the quark and gluon jets. The methodology of
such measurements for modern hadron colliders is discussed.


  Image super-resolution reconstruction is an important task in the field of
image processing technology, which can restore low resolution image to high
quality image with high resolution. In recent years, deep learning has been
applied in the field of image super-resolution reconstruction. With the
continuous development of deep neural network, the quality of the reconstructed
images has been greatly improved, but the model complexity has also been
increased. In this paper, we propose two lightweight models named as MSwinSR
and UGSwinSR based on Swin Transformer. The most important structure in MSwinSR
is called Multi-size Swin Transformer Block (MSTB), which mainly contains four
parallel multi-head self-attention (MSA) blocks. UGSwinSR combines U-Net and
GAN with Swin Transformer. Both of them can reduce the model complexity, but
MSwinSR can reach a higher objective quality, while UGSwinSR can reach a higher
perceptual quality. The experimental results demonstrate that MSwinSR increases
PSNR by $\mathbf{0.07dB}$ compared with the state-of-the-art model SwinIR,
while the number of parameters can reduced by $\mathbf{30.68\%}$, and the
calculation cost can reduced by $\mathbf{9.936\%}$. UGSwinSR can effectively
reduce the amount of calculation of the network, which can reduced by
$\mathbf{90.92\%}$ compared with SwinIR.


  LISA (Laser Interferometer Space Antenna) is a space mission that has
recently entered the implementation phase. The main goal of LISA is to survey,
for the first time, the observable universe by detecting low-frequency
gravitational waves (GWs). One of the main GW sources that LISA will detect is
the coalescence and merger of Massive Black Hole Binaries (MBHBs). In this
work, we explore the application of Sequential Neural Likelihood, a
simulation-based inference algorithm, to the detection and parameter estimation
of MBHBs signals in the LISA data. Instead of sampling from the conventional
likelihood function, which typically relies on the assumptions of Gaussianity
and stationarity of the noise and requires a forward simulation for each
evaluation, this method constructs a surrogate likelihood that is ultimately
described by a neural network trained from a dataset of simulations (noise +
MBHB). Since the likelihood is independent of the priors, we can iteratively
train models that target specific observations in a fraction of the time and
computational cost that other traditional and machine learning-based strategies
would require. One key aspect of the method is the compression of the data.
Because of the iterative nature of the method, we are able to train models to
obtain qualitatively similar posteriors with less than 2% of the simulator
calls that Markov Chain Monte Carlo methods would require. We compare these
posteriors with those obtained from standard techniques and discuss the
differences that appear, some of which can be identified as caused by the loss
of information from the data compression we use. We also discuss future
improvements to this method.


  Owing to its two dimensional electronic structure, graphene exhibits many
unique properties. One of them is a wave vector and temperature dependent
plasmon in the infrared range. Theory predicts that due to these plasmons,
graphene can be used as a universal material to enhance nanoscale radiative
heat exchange for any dielectric substrate. Here we report on radiative heat
transfer experiments between SiC and a SiO2 sphere which have non matching
phonon polariton frequencies, and thus only weakly exchange heat in near field.
We observed that the heat flux contribution of graphene epitaxially grown on
SiC dominates at short distances. The influence of plasmons on radiative heat
transfer is further supported with measurements for doped silicon. These
results highlight graphenes strong potential in photonic nearfield and energy
conversion devices.


  We prove a lower bound expansion on the probability that a random $\pm 1$
matrix is singular, and conjecture that such expansions govern the actual
probability of singularity. These expansions are based on naming the most
likely, second most likely, and so on, ways that a Bernoulli matrix can be
singular; the most likely way is to have a null vector of the form $e_i \pm
e_j$, which corresponds to the integer partition 11, with two parts of size 1.
The second most likely way is to have a null vector of the form $e_i \pm e_j
\pm e_k \pm e_\ell$, which corresponds to the partition 1111. The fifth most
likely way corresponds to the partition 21111.
  We define and characterize the "novel partitions" which show up in this
series. As a family, novel partitions suffice to detect singularity, i.e., any
singular Bernoulli matrix has a left null vector whose underlying integer
partition is novel. And, with respect to this property, the family of novel
partitions is minimal.
  We prove that the only novel partitions with six or fewer parts are 11, 1111,
21111, 111111, 221111, 311111, and 322111. We prove that there are fourteen
novel partitions having seven parts.
  We formulate a conjecture about which partitions are "first place and runners
up," in relation to the Erd\H{o}s-Littlewood-Offord bound.
  We prove some bounds on the interaction between left and right null vectors.


  This paper introduces a novel framework for the solution of (large-scale)
Lyapunov and Sylvester equations derived from numerical integration methods.
Suitable systems of ordinary differential equations are introduced. Low-rank
approximations of their solutions are produced by Runge-Kutta methods.
Appropriate Runge-Kutta methods are identified following the idea of geometric
numerical integration to preserve a geometric property, namely a low rank
residual. For both types of equations we prove the equivalence of one
particular instance of the resulting algorithm to the well known ADI iteration.
As the general approach suggested here leads to complex valued computation even
for real problems, we present a general realification approach based on
similarity transformation.


  The longitudinal and transverse resistivities of differently strained
(Ga,Mn)As layers are theoretically and experimentally studied as a function of
the magnetization orientation. The strain in the series of (Ga,Mn)As layers is
gradually varied from compressive to tensile using (In,Ga)As templates with
different In concentrations. Analytical expressions for the resistivities are
derived from a series expansion of the resistivity tensor with respect to the
direction cosines of the magnetization. In order to quantitatively model the
experimental data, terms up to the fourth order have to be included. The
expressions derived are generally valid for any single-crystalline cubic and
tetragonal ferromagnet and apply to arbitrary surface orientations and current
directions. The model phenomenologically incorporates the longitudinal and
transverse anisotropic magnetoresistance as well as the anomalous Hall effect.
The resistivity parameters obtained from a comparison between experiment and
theory are found to systematically vary with the strain in the layer.


  Quasiparticles in the cuprates appear to be subject to anomalously strong
inelastic damping mechanisms. To explain the phenomenon, Sachdev and
collaborators recently proposed to couple the system to a critically
fluctuating order parameter mode of either id_{xy}- or is-symmetry. Motivated
by the observation that the energies relevant for the dynamics of this mode are
comparable to the scattering rate induced by even moderate impurity
concentrations, we here generalize the approach to the presence of static
disorder. In the id-case, we find that the coupling to disorder renders the
order parameter dynamics diffusive but otherwise leaves much of the
phenomenology observed in the clean case intact. In contrast, the interplay of
impurity scattering and order parameter fluctuations of is-symmetry entails the
formation of a secondary superconductor transition, with a critical temperature
exponentially sensitive to the disorder concentration.


  We study the Feynman integral for the three-banana graph defined as the
scalar two-point self-energy at three-loop order. The Feynman integral is
evaluated for all identical internal masses in two space-time dimensions. Two
calculations are given for the Feynman integral; one based on an interpretation
of the integral as an inhomogeneous solution of a classical Picard-Fuchs
differential equation, and the other using arithmetic algebraic geometry,
motivic cohomology, and Eisenstein series. Both methods use the rather special
fact that the Feynman integral is a family of regulator periods associated to a
family of K3 surfaces. We show that the integral is given by a sum of elliptic
trilogarithms evaluated at sixth roots of unity. This elliptic trilogarithm
value is related to the regulator of a class in the motivic cohomology of the
K3 family. We prove a conjecture by David Broadhurst that at a special
kinematical point the Feynman integral is given by a critical value of the
Hasse-Weil L-function of the K3 surface. This result is shown to be a
particular case of Deligne's conjectures relating values of L-functions inside
the critical strip to periods.


  We propose a systematic method to extract conformal loop models for rational
conformal field theories (CFT). Method is based on defining an ADE model for
boundary primary operators by using the fusion matrices of these operators as
adjacency matrices. These loop models respect the conformal boundary
conditions. We discuss the loop models that can be extracted by this method for
minimal CFTs and then we will give dilute O(n) loop models on the square
lattice as examples for these loop models. We give also some proposals for WZW
SU(2) models.


  We prove several differential Harnack inequalities for positive solutions to
nonlinear backward heat equations with different potentials coupled with the
Ricci flow. We also derive an interpolated Harnack inequality for the nonlinear
heat equation under the $\varepsilon$-Ricci flow on a closed surface. These new
Harnack inequalities extend the previous differential Harnack inequalities for
linear heat equations with potentials under the Ricci flow.


  The paper is withdrawn and will be replaced at a later time by a
significantly revised and extended version.


  In these proceedings we discuss recent progress in nucleon structure using
lattice QCD simulations at or near the physical value of the pion mass. Main
focus will be given in observables such as the nucleon axial charge and the
first moments of parton distributions, for both the valence and sea quark
contributions, and discuss their implications on the spin content of the
nucleon. We will will also report developments on the evaluation of the gluon
momentum fraction, which contributes significantly to the nucleon spin.


  The exponential growth of mobile devices has raised concerns about sensitive
data leakage. In this paper, we make the first attempt to identify suspicious
location-related HTTP transmission flows from the user's perspective, by
answering the question: Is the transmission user-intended? In contrast to
previous network-level detection schemes that mainly rely on a given set of
suspicious hostnames, our approach can better adapt to the fast growth of app
market and the constantly evolving leakage patterns. On the other hand,
compared to existing system-level detection schemes built upon program taint
analysis, where all sensitive transmissions as treated as illegal, our approach
better meets the user needs and is easier to deploy. In particular, our
proof-of-concept implementation (FlowIntent) captures sensitive transmissions
missed by TaintDroid, the state-of-the-art dynamic taint analysis system on
Android platforms. Evaluation using 1002 location sharing instances collected
from more than 20,000 apps shows that our approach achieves about 91% accuracy
in detecting illegitimate location transmissions.


  SiD is a robust, silicon-based detector proposed for the International Linear
Collider (ILC). SiD employs a sampling silicon-tungsten electromagnetic
calorimeter (ECal) to accurately measure the energies of electrons, positrons,
and photons produced in collisions, and to contribute to jet energy
measurements through the particle flow technique. Due to the nature of the
detector and its design constraints, a portion of the electron, positron, and
photon energy exits the ECal undetected. Here, we establish a methodology for
estimating the exiting energy and correctly determining the energies of
electrons (and photons) in the ECal by analyzing patterns in the total energy
deposition in each layer using neural networks. We studied a reduced
calorimeter design with fewer layers (16 thin layers, 8 thick layers) than the
proposed SiD design (20 thin layers, 10 thick layers) to evaluate if the
resulting energy leakage could be determined and corrected. We evaluated the
effectiveness of the correction on various electron energies and incidence
angles in a Geant4 simple stack as well as in a modified version of the full
DD4hep SiD model. The correction methodology showed significant improvement in
measurement accuracy and resolution over uncorrected events, especially at high
energies and shallow angles. These results provide a basis for effective energy
correction in the SiD ECal and suggest that precise energy measurements with a
smaller, less expensive ECal are viable.


  Expecting the shipment of 1 billion Android devices in 2017, cyber criminals
have naturally extended their vicious activities towards Google's mobile
operating system. With an estimated number of 700 new Android applications
released every day, keeping control over malware is an increasingly challenging
task. In recent years, a vast number of static and dynamic code analysis
platforms for analyzing Android applications and making decision regarding
their maliciousness have been introduced in academia and in the commercial
world. These platforms differ heavily in terms of feature support and
application properties being analyzed. In this paper, we give an overview of
the state-of-the-art dynamic code analysis platforms for Android and evaluate
their effectiveness with samples from known malware corpora as well as known
Android bugs like Master Key. Our results indicate a low level of diversity in
analysis platforms resulting from code reuse that leaves the evaluated systems
vulnerable to evasion. Furthermore the Master Key bugs could be exploited by
malware to hide malicious behavior from the sandboxes.


  We consider the problem of density estimation on Riemannian manifolds.
Density estimation on manifolds has many applications in fluid-mechanics,
optics and plasma physics and it appears often when dealing with angular
variables (such as used in protein folding, robot limbs, gene-expression) and
in general directional statistics. In spite of the multitude of algorithms
available for density estimation in the Euclidean spaces $\mathbf{R}^n$ that
scale to large n (e.g. normalizing flows, kernel methods and variational
approximations), most of these methods are not immediately suitable for density
estimation in more general Riemannian manifolds. We revisit techniques related
to homeomorphisms from differential geometry for projecting densities to
sub-manifolds and use it to generalize the idea of normalizing flows to more
general Riemannian manifolds. The resulting algorithm is scalable, simple to
implement and suitable for use with automatic differentiation. We demonstrate
concrete examples of this method on the n-sphere $\mathbf{S}^n$.


  In this work a new strategy is proposed in order to build analytic and
microscopic models of fluctuating polymer rings subjected to topological
constraints. The topological invariants used to fix these constraints belong to
a wide class of the so-called numerical topological invariants. For each
invariant it is possible to derive a field theory that describes the
statistical behavior of knotted and linked polymer rings following a
straightforward algorithm. The treatment is not limited to the partition
function of the system, but it allows also to express the expectation values of
general observables as field theory amplitudes.
  Our strategy is illustrated taking as examples the Gauss linking number and a
topological invariant belonging to a class of invariants due to Massey. The
consistency of the new method developed here is checked by reproducing a
previous field theoretical model of two linked polymer rings. After the passage
to field theory, the original topological constraints imposed on the
fluctuating paths of the polymers become constraints over the configurations of
the topological fields that mediate the interactions of topological origin
between the monomers. These constraints involve quantities like the
cross-helicity which are of interest in other disciplines, like for instance in
modeling the solar magnetic field.
  While the calculation of the vacuum expectation values of generic observables
remains still challenging due to the complexity of the problem of topological
entanglement in polymer systems, we succeed here to reduce the evaluation of
the moments of the Gauss linking number for two linked polymer rings to the
computation of the amplitudes of a free field theory.


  Many fields of science rely on relational database management systems to
analyze, publish and share data. Since RDBMS are originally designed for, and
their development directions are primarily driven by, business use cases they
often lack features very important for scientific applications. Horizontal
scalability is probably the most important missing feature which makes it
challenging to adapt traditional relational database systems to the ever
growing data sizes. Due to the limited support of array data types and metadata
management, successful application of RDBMS in science usually requires the
development of custom extensions. While some of these extensions are specific
to the field of science, the majority of them could easily be generalized and
reused in other disciplines. With the Graywulf project we intend to target
several goals. We are building a generic platform that offers reusable
components for efficient storage, transformation, statistical analysis and
presentation of scientific data stored in Microsoft SQL Server. Graywulf also
addresses the distributed computational issues arising from current RDBMS
technologies. The current version supports load balancing of simple queries and
parallel execution of partitioned queries over a set of mirrored databases.
Uniform user access to the data is provided through a web based query interface
and a data surface for software clients. Queries are formulated in a slightly
modified syntax of SQL that offers a transparent view of the distributed data.
The software library consists of several components that can be reused to
develop complex scientific data warehouses: a system registry, administration
tools to manage entire database server clusters, a sophisticated workflow
execution framework, and a SQL parser library.


  The restricted maximum likelihood (REML) estimator of the dispersion matrix
for random coefficient models is rewritten in terms of the sufficient
statistics of the individual regressions.


  An accretion outburst in an X-ray transient deposits material onto the
neutron star primary; this accumulation of matter induces reactions in the
neutron star's crust. During the accretion outburst these reactions heat the
crust out of thermal equilibrium with the core. When accretion halts, the crust
cools to its long-term equilibrium temperature on observable timescales. Here
we examine the accreting neutron star transient MAXI J0556-332, which is the
hottest transient, at the start of quiescence, observed to date. Models of the
quiescent light curve require a large deposition of heat in the shallow outer
crust from an unknown source. The additional heat injected is $\approx
4\textrm{-}10\,\mathrm{MeV}$ per accreted nucleon; when the observed decline in
accretion rate at the end of the outburst is accounted for, the required
heating increases to $\approx 6\textrm{-}16\,\mathrm{MeV}$. This shallow
heating is still required to fit the lightcurve even after taking into account
a second accretion episode, uncertainties in distance, and different surface
gravities. The amount of shallow heating is larger than that inferred for other
neutron star transients and is larger than can be supplied by nuclear reactions
or compositionally driven convection; but it is consistent with stored
mechanical energy in the accretion disk. The high crust temperature ($T_b
\gtrsim 10^{9} \, {\rm K}$) makes its cooling behavior in quiescence largely
independent of the crust composition and envelope properties, so that future
observations will probe the gravity of the source. Fits to the lightcurve
disfavor the presence of Urca cooling pairs in the crust.


  In theories with $N=2$ supersymmetry on $R^{3,1}$, BPS bound states can decay
across walls of marginal stability in the space of Coulomb branch parameters,
leading to discontinuities in the BPS indices $\Omega(\gamma,u)$. We consider a
supersymmetric index $I$ which receives contributions from 1/2-BPS states,
generalizing the familiar Witten index $Tr (-1)^F e^{-\beta H}$. We expect $I$
to be smooth away from loci where massless particles appear, thanks to
contributions from the continuum of multi-particle states. Taking inspiration
from a similar phenomenon in the hypermultiplet moduli space of $N=2$ string
vacua, we conjecture a formula expressing $I$ in terms of the BPS indices
$\Omega(\gamma,u)$, which is continuous across the walls and exhibits the
expected contributions from single particle states at large $\beta$. This gives
a universal prediction for the contributions of multi-particle states to the
index $I$. This index is naturally a function on the moduli space after
reduction on a circle, closely related to the canonical hyperk\"ahler metric
and hyperholomorphic connection on this space.


  We propose a semantic segmentation model that exploits rotation and
reflection symmetries. We demonstrate significant gains in sample efficiency
due to increased weight sharing, as well as improvements in robustness to
symmetry transformations. The group equivariant CNN framework is extended for
segmentation by introducing a new equivariant (G->Z2)-convolution that
transforms feature maps on a group to planar feature maps. Also, equivariant
transposed convolution is formulated for up-sampling in an encoder-decoder
network. To demonstrate improvements in sample efficiency we evaluate on
multiple data regimes of a rotation-equivariant segmentation task: cancer
metastases detection in histopathology images. We further show the
effectiveness of exploiting more symmetries by varying the size of the group.


  The rapid expansion of computational capabilities and the ever-growing scale
of modern HPC systems present formidable challenges in managing exascale
scientific data. Faced with such vast datasets, traditional lossless
compression techniques prove insufficient in reducing data size to a manageable
level while preserving all information intact. In response, researchers have
turned to error-bounded lossy compression methods, which offer a balance
between data size reduction and information retention. However, despite their
utility, these compressors employing conventional techniques struggle with
limited reconstruction quality. To address this issue, we draw inspiration from
recent advancements in deep learning and propose GWLZ, a novel group-wise
learning-based lossy compression framework with multiple lightweight learnable
enhancer models. Leveraging a group of neural networks, GWLZ significantly
enhances the decompressed data reconstruction quality with negligible impact on
the compression efficiency. Experimental results on different fields from the
Nyx dataset demonstrate remarkable improvements by GWLZ, achieving up to 20%
quality enhancements with negligible overhead as low as 0.0003x.


  A numerical bifurcation analysis of the electrically driven plane sheet pinch
is presented. The electrical conductivity varies across the sheet such as to
allow instability of the quiescent basic state at some critical Hartmann
number. The most unstable perturbation is the two-dimensional tearing mode.
Restricting the whole problem to two spatial dimensions, this mode is followed
up to a time-asymptotic steady state, which proves to be sensitive to
three-dimensional perturbations even close to the point where the primary
instability sets in. A comprehensive three-dimensional stability analysis of
the two-dimensional steady tearing-mode state is performed by varying
parameters of the sheet pinch. The instability with respect to
three-dimensional perturbations is suppressed by a sufficiently strong magnetic
field in the invariant direction of the equilibrium. For a special choice of
the system parameters, the unstably perturbed state is followed up in its
nonlinear evolution and is found to approach a three-dimensional steady state.


  The Quantum Fourier transform (QFT) is a key ingredient in most quantum
algorithms. We have compared various spin-based quantum computing schemes to
implement the QFT from the point of view of their actual time-costs and the
accuracy of the implementation. We focus here on an interesting decomposition
of the QFT as a product of the non-selective Hadamard transformation followed
by multiqubit gates corresponding to square- and higher-roots of controlled-NOT
gates. This decomposition requires only O(n) operations and is thus linear in
the number of qubits $n$. The schemes were implemented on a two-qubit NMR
quantum information processor and the resultant density matrices reconstructed
using standard quantum state tomography techniques. Their experimental
fidelities have been measured and compared.


  Generative AI (GenAI) and large language models in particular, are disrupting
Computer Science Education. They are proving increasingly capable at more and
more challenges. Some educators argue that they pose a serious threat to
computing education, and that we should ban their use in the classroom. While
there are serious GenAI issues that remain unsolved, it may be useful in the
present moment to step back and examine the overall trajectory of Computer
Science writ large. Since the very beginning, our discipline has sought to
increase the level of abstraction in each new representation. We have
progressed from hardware dip switches, through special purpose languages and
visual representations like flow charts, all the way now to ``natural
language.'' With the advent of GenAI, students can finally change the
abstraction level of a problem to the ``language'' they've been ``problem
solving'' with all their lives. In this paper, we argue that our programming
abstractions were always headed here -- to natural language. Now is the time to
adopt a ``Prompts First'' approach to Computer Science Education.


  Let $H_1, H_2$ be complex Hilbert spaces and $T$ be a densely defined closed
linear operator from its domain $D(T)$, a dense subspace of $H_1$, into $H_2$.
Let $N(T)$ denote the null space of $T$ and $R(T)$ denote the range of $T$.
  Recall that $C(T) := D(T) \cap N(T)^{\perp}$ is called the {\it carrier space
of} $T$ and the {\it reduced minimum modulus } $\gamma(T)$ of $T$ is defined
as: $$ \gamma(T) := \inf \{\|T(x)\| : x \in C(T), \|x\| = 1 \} .$$
  Further, we say that $T$
  {\it attains its reduced minimum modulus} if there exists $x_0 \in C(T) $
such that $\|x_0\| = 1$ and $\|T(x_0)\| = \gamma(T)$.
  We discuss some properties of operators that attain reduced minimum modulus.
In particular, the following results are proved.


  We propose a new uniform framework for text classification and ranking that
can automate the process of identifying check-worthy sentences in political
debates and speech transcripts. Our framework combines the semantic analysis of
the sentences, with additional entity embeddings obtained through the
identified entities within the sentences. In particular, we analyse the
semantic meaning of each sentence using state-of-the-art neural language models
such as BERT, ALBERT, and RoBERTa, while embeddings for entities are obtained
from knowledge graph (KG) embedding models. Specifically, we instantiate our
framework using five different language models, entity embeddings obtained from
six different KG embedding models, as well as two combination methods leading
to several Entity-Assisted neural language models. We extensively evaluate the
effectiveness of our framework using two publicly available datasets from the
CLEF' 2019 & 2020 CheckThat! Labs. Our results show that the neural language
models significantly outperform traditional TF.IDF and LSTM methods. In
addition, we show that the ALBERT model is consistently the most effective
model among all the tested neural language models. Our entity embeddings
significantly outperform other existing approaches from the literature that are
based on similarity and relatedness scores between the entities in a sentence,
when used alongside a KG embedding.


  This thesis consists of two parts, connected by one central theme: the
dynamics of the "shape of space". The first part of the thesis concerns the
construction of a theory of gravity dynamically equivalent to general
relativity (GR) in 3+1 form (ADM). What is special about this theory is that it
does not possess foliation invariance, as does ADM. It replaces that "symmetry"
by another: local conformal invariance. In so doing it more accurately reflects
a theory of the "shape of space", giving us reason to call it \emph{shape
dynamics} (SD). In the first part we will try to present some of the highlights
of results so far, and indicate what we can and cannot do with shape dynamics.
Because this is a young, rapidly moving field, we have necessarily left out
some interesting new results which are not yet in print and were developed
alongside the writing of the thesis. The second part of the thesis will develop
a gauge theory for "shape of space"--theories. To be more precise, if one
admits that the physically relevant observables are given by shape, our
descriptions of Nature carry a lot of redundancy, namely absolute local size
and absolute spatial position. This redundancy is related to the action of the
infinite-dimensional conformal and diffeomorphism groups on the geometry of
space. We will show that the action of these groups can be put into a language
of infinite-dimensional gauge theory, taking place in the configuration space
of 3+1 gravity. In this context gauge connections acquire new and interesting
meanings, and can be used as "relational tools".


  We show that the supermembrane theory compactified on a torus is invariant
under T-duality. There are two different topological sectors of the
compactified supermembrane (M2) classified according to a vanishing or
nonvanishing second cohomology class. We find the explicit T-duality
transformation that acts locally on the supermembrane theory and we show that
it is an exact symmetry of the theory. We give a global interpretation of the
T-duality in terms of bundles. It has a natural description in terms of the
cohomology of the base manifold and the homology of the target torus. We show
that in the limit when the torus degenerate into a circle and the M2 mass
operator restricts to the string-like configurations, the usual closed string
T-duality transformation between the type IIA and type IIB mass operators is
recovered. Moreover if we just restrict M2 mass operator to string-like
configurations but we perform a generalized T-duality we find the SL(2,Z)
non-perturbative multiplet of IIA.


  We address an optimal transmit power allocation problem that minimizes the
outage probability of a secondary user (SU) who is allowed to coexist with a
primary user (PU) in a narrowband spectrum sharing cognitive radio network,
under a long term average transmit power constraint at the secondary
transmitter (SU-TX) and an average interference power constraint at the primary
receiver (PU-RX), with quantized channel state information (CSI) (including
both the channels from SU-TX to SU-RX, denoted as $g_1$ and the channel from
SU-TX to PU-RX, denoted as $g_0$) at the SU-TX. The optimal quantization
regions in the vector channel space is shown to have a 'stepwise' structure.
With this structure, the above outage minimization problem can be explicitly
formulated and solved by employing the Karush-Kuhn-Tucker (KKT) necessary
optimality conditions to obtain a locally optimal quantized power codebook. A
low-complexity near-optimal quantized power allocation algorithm is derived for
the case of large number of feedback bits. An explicit expression for the
asymptotic SU outage probability at high rate quantization (as the number of
feedback bits goes to infinity) is also provided, and is shown to approximate
the optimal outage behavior extremely well for large number of bits of feedback
via numerical simulations. Numerical results also illustrate that with 6 bits
of feedback, the derived algorithms provide SU outage performance very close to
that with full CSI at the SU-TX.


  Integer-forcing (IF) precoding, also known as downlink IF, is a promising new
approach for communication over multiple-input multiple-output (MIMO) broadcast
channels. Inspired by the integer-forcing linear receiver for multiple-access
channels, it generalizes linear precoding by inducing an effective channel
matrix that is approximately integer, rather than approximately identity.
Combined with lattice encoding and a pre-inversion of the channel matrix at the
transmitter, the scheme has the potential to outperform any linear precoding
scheme, despite enjoying similar low complexity.
  In this paper, a specific IF precoding scheme, called diagonally-scaled exact
IF (DIF), is proposed and shown to achieve maximum spatial multiplexing gain.
For the special case of two receivers, in the high SNR regime, an optimal
choice of parameters is derived analytically, leading to an almost closed-form
expression for the achievable sum rate. In particular, it is shown that the gap
to the sum capacity is upper bounded by 0.27 bits for any channel realization.
For general SNR, a regularized version of DIF (RDIF) is proposed. Numerical
results for two receivers under Rayleigh fading show that RDIF can achieve
performance superior to optimal linear precoding and very close to the sum
capacity.


  We develop a 3D dynamical model of dust outflows from galactic discs. The
outflows are initiated by multiple SN explosions in a magnetized interstellar
medium (ISM) with a gravitationally stratified density distribution. Dust
grains are treated as particles in cells interacting collisionally with gas,
and forced by stellar radiation of the disc and Lorenz force. We show that
magnetic field plays a crucial role in accelerating the charged dust grains and
expelling them out of the disc: in 10--20~Myr they can be elevated at distances
up to 10~kpc above the galactic plane. The dust-to-gas ratio in the outflowing
medium varies in the range $5 \cdot 10^{-4} - 5 \cdot 10^{-2}$ along the
vertical stream. Overall the dust mass loss rate depends on the parameters of
ISM and may reach up to $3\times 10^{-2}$~\Msun~yr$^{-1}$


  We introduce a first theory of price impact in presence of an interest-rates
term structure. We explain how one can formulate instantaneous and transient
price impact on bonds with different maturities, including a cross price impact
that is endogenous to the term structure. We connect the introduced impact to
classic no-arbitrage theory for interest rate markets, showing that impact can
be embedded in the pricing measure and that no-arbitrage can be preserved. We
present pricing examples in presence of price impact and numerical examples of
how impact changes the shape of the term structure. Finally, to show that our
approach is applicable we solve an optimal execution problem in interest rate
markets with the type of price impact we developed in the paper.


  We present self-consistent three-dimensional core-collapse supernova
simulations of a rotating $20M_\odot$ progenitor model with various initial
angular velocities from $0.0$ to $4.0$ rad s$^{-1}$ using a smoothed particle
hydrodynamics code, SPHYNX, and a grid-based hydrodynamics code, FLASH. We
identify two strong gravitational-wave features, with peak frequencies of
$\sim300$ Hz and $\sim1.3$ kHz in the first $100$ ms postbounce. We demonstrate
that these two features are associated with the $m=1$ deformation from the
proto-neutron star (PNS) modulation induced by the low-$T/|W|$ instability,
regardless of the simulation code. The $300$ Hz feature is present in models
with an initial angular velocity between $1.0$ and $4.0$ rad s$^{-1}$, while
the $1.3$ kHz feature is present only in a narrower range, from $1.5$ to $3.5$
rad s$^{-1}$. We show that the $1.3$ kHz signal originates from the
high-density inner core of the PNS, and the $m=1$ deformation triggers a strong
asymmetric distribution of electron anti-neutrinos. In addition to the $300$ Hz
and $1.3$ kHz features, we also observe one weaker but noticeable
gravitational-wave feature from higher-order modes in the range between $1.5$
and $3.5$ rad s$^{-1}$. Its peak frequency is around $800$ Hz initially and
gradually increases to $900-1000$ Hz. Therefore, in addition to the
gravitational bounce signal, the detection of the $300$ Hz, $1.3$ kHz, the
higher-order mode, and even the related asymmetric emission of neutrinos, could
provide additional diagnostics to estimate the initial angular velocity of a
collapsing core.


  In this paper, we propose two arbitrary order eXtended hybridizable
Discontinuous Galerkin (X-HDG) methods for second order elliptic interface
problems in two and three dimensions. The first X-HDG method applies to any
piecewise $C^2$ smooth interface. It uses piecewise polynomials of degrees $k$
$(k>= 1)$ and $k-1$ respectively for the potential and flux approximations in
the interior of elements inside the subdomains, and piecewise polynomials of
degree $ k$ for the numerical traces of potential on the inter-element
boundaries inside the subdomains. Double value numerical traces on the parts of
interface inside elements are adopted to deal with the jump condition. The
second X-HDG method is a modified version of the first one and applies to any
fold line/plane interface, which uses piecewise polynomials of degree $ k-1$
for the numerical traces of potential. The X-HDG methods are of the local
elimination property, then lead to reduced systems which only involve the
unknowns of numerical traces of potential on the inter-element boundaries and
the interface. Optimal error estimates are derived for the flux approximation
in $L^2$ norm and for the potential approximation in piecewise $H^1$ seminorm
without requiring "sufficiently large" stabilization parameters in the schemes.
In addition, error estimation for the potential approximation in $L^2$ norm is
performed using dual arguments. Finally, we provide several numerical examples
to verify the theoretical results.


  We work out the method for evaluating the QCD coupling constant at finite
temperature ($T$) by making use of the finite $T$ renormalization group
equation up to the one-loop order on the basis of the background field method
with the imaginary time formalism. The background field method, which maintains
the explicit gauge invariance, provides notorious simplifications since one has
to calculate only the renormalization constant of the background field gluon
propagator. The results for the evolution of the QCD coupling constant at
finite $T$ reproduce partially the ones obtained in the literature. We discuss,
in particular, the origin of the discrepancies between different calculations,
such as the choice of gauge, the break-down of Lorentz invariance, imaginary
versus real time formalism and the applicability of the Ward identities at
finite $T$.


  Monocular visual-inertial odometry (VIO) is a critical problem in robotics
and autonomous driving. Traditional methods solve this problem based on
filtering or optimization. While being fully interpretable, they rely on manual
interference and empirical parameter tuning. On the other hand, learning-based
approaches allow for end-to-end training but require a large number of training
data to learn millions of parameters. However, the non-interpretable and heavy
models hinder the generalization ability. In this paper, we propose a fully
differentiable, and interpretable, bird-eye-view (BEV) based VIO model for
robots with local planar motion that can be trained without deep neural
networks. Specifically, we first adopt Unscented Kalman Filter as a
differentiable layer to predict the pitch and roll, where the covariance
matrices of noise are learned to filter out the noise of the IMU raw data.
Second, the refined pitch and roll are adopted to retrieve a gravity-aligned
BEV image of each frame using differentiable camera projection. Finally, a
differentiable pose estimator is utilized to estimate the remaining 3 DoF poses
between the BEV frames: leading to a 5 DoF pose estimation. Our method allows
for learning the covariance matrices end-to-end supervised by the pose
estimation loss, demonstrating superior performance to empirical baselines.
Experimental results on synthetic and real-world datasets demonstrate that our
simple approach is competitive with state-of-the-art methods and generalizes
well on unseen scenes.


  In content-based mobile ad hoc networks (CB-MANETs), random linear network
coding (NC) can be used to reliably disseminate large files under intermittent
connectivity. Conventional NC involves random unrestricted coding at
intermediate nodes. This however is vulnerable to pollution attacks. To avoid
attacks, a brute force approach is to restrict the mixing at the source.
However, source restricted NC generally reduces the robustness of the code in
the face of errors, losses and mobility induced intermittence. CB-MANETs
introduce a new option. Caching is common in CB MANETs and a fully reassembled
cached file can be viewed as a new source. Thus, NC packets can be mixed at all
sources (including the originator and the intermediate caches) yet still
providing protection from pollution. The hypothesis we wish to test in this
paper is whether in CB-MANETs with sufficient caches of a file, the performance
(in terms of robustness) of the restricted coding equals that of unrestricted
coding.
  In this paper, we examine and compare unrestricted coding to full cache
coding, source only coding, and no coding. As expected, we find that full cache
coding remains competitive with unrestricted coding while maintaining full
protection against pollution attacks.


  Modal analysis of fluid flows is essential to understand flow physics and
fluid-solid interaction mechanisms, and to implement flow control. Unlike
unstable flow, the intrinsic attenuation of subcritical flow has led to
failures to experimentally extract the subcritical flow modes clearly. To this
end, this paper proposes a modal testing method for subcritical flows. Using
Dynamic Mode Decomposition (DMD), dominate modes of flow around a cylinder at
subcritical Reynolds numbers are extracted experimentally for the first time.
The extracted structures and parameters of the modes are in good agreement with
the numerical results in the literature. It is found that the first-order von
K\'arm\'an mode can be observed at a Reynolds number as low as 19.3, which is
very close to the lower boundary of subcritical vortex induced vibrations
(VIV). This experimental observation elucidates the correlation between von
K\'arm\'an mode and fluid-solid interaction instability in subcritical flows.


  We study hyperelliptic curves C with an action of an affine group of
automorphisms G. We establish a closed form expression for the quotient curve
C/G and for the first etale cohomology group of C as a representation of G. The
motivation comes from the arithmetic of hyperelliptic curves over local fields,
specifically their local Galois representations and the associated invariants.


  State-of-the-art methods on conversational recommender systems (CRS) leverage
external knowledge to enhance both items' and contextual words' representations
to achieve high quality recommendations and responses generation. However, the
representations of the items and words are usually modeled in two separated
semantic spaces, which leads to misalignment issue between them. Consequently,
this will cause the CRS to only achieve a sub-optimal ranking performance,
especially when there is a lack of sufficient information from the user's
input. To address limitations of previous works, we propose a new CRS framework
KLEVER, which jointly models items and their associated contextual words in the
same semantic space. Particularly, we construct an item descriptive graph from
the rich items' textual features, such as item description and categories.
Based on the constructed descriptive graph, KLEVER jointly learns the
embeddings of the words and items, towards enhancing both recommender and
dialog generation modules. Extensive experiments on benchmarking CRS dataset
demonstrate that KLEVER achieves superior performance, especially when the
information from the users' responses is lacking.