  A Symmetry Principle has been shown to augment unambiguously the Einstein
Field Equations, promoting the whole closed-string massless NS-NS sector to
stringy graviton fields. Here we consider its weak field approximation, take a
non-relativistic limit, and derive the stringy augmentation of Newton Gravity:
\[ \begin{array}{lll} {\bf{\nabla}^{2}\Phi}=4\pi G
\rho+\bf{H}{\bf{\cdot}}\bf{H}\,, \quad&\qquad\bf{\nabla}\bf{\cdot}\bf{H}=0\,,
\quad&\qquad {\bf{\nabla}\bf{\times}\bf{H}}=4\pi G\, \bf{K}\,. \end{array} \]
Not only the mass density $\rho$ but also the current density $\mathbf{K}$ is
intrinsic to matter. Sourcing $\mathbf{H}$ which is of NS-NS $H$-flux origin,
$\mathbf{K}$ is nontrivial if the matter is `stringy'. $\mathbf{H}$ contributes
quadratically to the Newton potential, but otherwise is decoupled from the
point particle dynamics, i.e. $\bf{\ddot{x}}=-\bf{\nabla}\Phi$. We define
`stringization' analogous to magnetization and discuss regular as well as
monopole-like singular solutions.


  If dark matter is composed of axions, then axion stars form in the cores of
dark matter halos. These stars are unstable above a critical mass, decaying to
radio photons that heat the intergalactic medium, offering a new channel for
axion indirect detection. We recently provided the first accurate calculation
of the axion decay rate due to axion star mergers. In this work we show how
existing data concerning the CMB optical depth leads to strong constraints on
the axion photon coupling in the mass range $10^{-14}\,{\rm eV}\lesssim
m_a\lesssim 10^{-8}\,{\rm eV}$. Axion star decays lead to efficient
reionization of the intergalactic medium during the dark ages. By comparing
this non-standard reionization with Planck legacy measurements of the Thompson
optical width, we show that couplings in the range $10^{-14}\,{\rm GeV}^{-1}
\lesssim g_{a\gamma\gamma} \lesssim 10^{-10}\,{\rm GeV}^{-1}$ are excluded for
our benchmark model of axion star abundance. Future measurements of the 21cm
emission of neutral hydrogen at high redshift could improve this limit by an
order of magnitude or more, providing complementary indirect constraints on
axion dark matter in parameter space also targeted by direct detection
haloscopes.


  We present the results of our recent analysis of the meson-photon transition
form factors $F_{P\gamma}(Q^2)$ for the pseudoscalar mesons $P =
\pi^0,\eta,\eta',\eta_c$, using the local-duality version of QCD sum rules.


  Channel pruning is one of the major compression approaches for deep neural
networks. While previous pruning methods have mostly focused on identifying
unimportant channels, channel pruning is considered as a special case of neural
architecture search in recent years. However, existing methods are either
complicated or prone to sub-optimal pruning. In this paper, we propose a
pruning framework that adaptively determines the number of each layer's
channels as well as the wights inheritance criteria for sub-network. Firstly,
evaluate the importance of each block in the network based on the mean of the
scaling parameters of the BN layers. Secondly, use the bisection method to
quickly find the compact sub-network satisfying the budget. Finally, adaptively
and efficiently choose the weight inheritance criterion that fits the current
architecture and fine-tune the pruned network to recover performance. AdaPruner
allows to obtain pruned network quickly, accurately and efficiently, taking
into account both the structure and initialization weights. We prune the
currently popular CNN models (VGG, ResNet, MobileNetV2) on different image
classification datasets, and the experimental results demonstrate the
effectiveness of our proposed method. On ImageNet, we reduce 32.8% FLOPs of
MobileNetV2 with only 0.62% decrease for top-1 accuracy, which exceeds all
previous state-of-the-art channel pruning methods. The code will be released.


  The search for new materials, based on computational screening, relies on
methods that accurately predict, in an automatic manner, total energy,
atomic-scale geometries, and other fundamental characteristics of materials.
Many technologically important material properties directly stem from the
electronic structure of a material, but the usual workhorse for total energies,
namely density-functional theory, is plagued by fundamental shortcomings and
errors from approximate exchange-correlation functionals in its prediction of
the electronic structure. At variance, the $GW$ method is currently the
state-of-the-art {\em ab initio} approach for accurate electronic structure. It
is mostly used to perturbatively correct density-functional theory results, but
is however computationally demanding and also requires expert knowledge to give
accurate results. Accordingly, it is not presently used in high-throughput
screening: fully automatized algorithms for setting up the calculations and
determining convergence are lacking. In this work we develop such a method and,
as a first application, use it to validate the accuracy of $G_0W_0$ using the
PBE starting point, and the Godby-Needs plasmon pole model
($G_0W_0^\textrm{GN}$@PBE), on a set of about 80 solids. The results of the
automatic convergence study utilized provides valuable insights. Indeed, we
find correlations between computational parameters that can be used to further
improve the automatization of $GW$ calculations. Moreover, we find that
$G_0W_0^\textrm{GN}$@PBE shows a correlation between the PBE and the
$G_0W_0^\textrm{GN}$@PBE gaps that is much stronger than that between $GW$ and
experimental gaps. However, the $G_0W_0^\textrm{GN}$@PBE gaps still describe
the experimental gaps more accurately than a linear model based on the PBE
gaps.


  We examine the effects of turbulent intermittency on the deflagration to
detonation transition (DDT) in Type Ia supernovae. The Zel'dovich mechanism for
DDT requires the formation of a nearly isothermal region of mixed ash and fuel
that is larger than a critical size. We primarily consider the hypothesis by
Khokhlov et al. and Niemeyer and Woosley that the nearly isothermal, mixed
region is produced when the flame makes the transition to the distributed
regime. We use two models for the distribution of the turbulent velocity
fluctuations to estimate the probability as a function of the density in the
exploding white dwarf that a given region of critical size is in the
distributed regime due to strong local turbulent stretching of the flame
structure. We also estimate lower limits on the number of such regions as a
function of density. We find that the distributed regime, and hence perhaps
DDT, occurs in a local region of critical size at a density at least a factor
of 2-3 larger than predicted for mean conditions that neglect intermittency.
This factor brings the transition density to be much larger than the empirical
value from observations in most situations. We also consider the intermittency
effect on the more stringent conditions for DDT by Lisewski et al. and Woosley.
We find that a turbulent velocity of $10^8$ cm/s in a region of size $10^6$ cm,
required by Lisewski et al., is rare. We expect that intermittency gives a
weaker effect on the Woosley model with stronger criterion. The predicted
transition density from this criterion remains below $10^7$ g/cm$^3$ after
accounting for intermittency using our intermittency models.


  The hydrostatic primitive equations (HPE) form the basis of most numerical
weather, climate and global ocean circulation models. Analytical (not
statistical) methods are used to find a scaling proportional to
$(Nu\,Ra\,Re)^{1/4}$ for the range of horizontal spatial sizes in HPE
solutions, which is much broader than currently achievable computationally. The
range of scales for the HPE is determined from an analytical bound on the
time-averaged enstrophy of the horizontal circulation. This bound allows the
formation of very small spatial scales, whose existence would excite
unphysically large linear oscillation frequencies and gravity wave speeds.


  We demonstrate that Kerr-CFT duality can be extended to super-entropic black
holes, which have non-compact horizons with finite area. We demonstrate that
this duality is robust insofar as the ultra-spinning limit of a Kerr-AdS black
hole (which yields the super-entropic class)commutes with the near-horizon
limit (which yields the Kerr-CFT duality). Consequently the Bekeinstein-Hawking
and the CFT entropies are equivalent. We show that the duality holds for both
singly-spinning super-entropic black holes in 4 dimensions and for
doubly-spinning super-entropic black holes of gauged supergravity in 5
dimensions. In both cases we obtain not only the expected left/right
temperatures, but also temperatures associated with electric charge and with a
new thermodynamic parameter specific to super-entropic black holes.


  We introduce a non-commutative deformation of the algebra of bipolar
spherical harmonics supporting the action of the full Lorentz algebra. Our
construction is close in spirit to the one of the non-commutative spherical
harmonics associated to the fuzzy sphere and, as such, it leads to a maximal
value of the angular momentum. We derive the action of Lorentz boost generators
on such non-commutative spherical harmonics and show that it is compatible with
the existence of a maximal angular momentum.


  We explore a class of $\phi^{4n}$ models with kink and antikink solutions
that have long-range tails on both sides, specializing to the cases with $n=2$
and $n=3$. A recently developed method of an accelerating kink ansatz is used
to estimate the force between the kink and the antikink. We use
state-of-the-art numerical methods to initialize the system in a kink-antikink
configuration with a finite initial velocity and to evolve the system according
to the equations of motion. Among these methods, we propose a computationally
efficient way to initialize the velocity field of the system. Interestingly, we
discover that, for this class of models, $\phi^{4n}$ with $n>1$, the
kink-antikink annihilation behaves differently from the archetypal $\phi^4$
model or even the kinks with one long-range tail because there is neither
long-lived bion formation nor resonance windows and the critical velocity is
ultrarelativistic.


  I review recent works showing that information geometry is a useful framework
to characterize quantum coherence and entanglement. Quantum systems exhibit
peculiar properties which cannot be justified by classical physics, e.g.
quantum coherence and quantum correlations. Once confined to thought
experiments, they are nowadays created and manipulated by exerting an exquisite
experimental control of atoms, molecules and photons. It is important to
identify and quantify such quantum features, as they are deemed to be key
resources to achieve supraclassical performances in computation and
communication protocols. The information geometry viewpoint elucidates the
advantage provided by quantum superpositions in phase estimation. Also, it
enables to link measures of coherence and entanglement to observables, which
can be evaluated in a laboratory by a limited number of measurements.


  Financial analyses of stock markets rely heavily on quantitative approaches
in an attempt to predict subsequent or market movements based on historical
prices and other measurable metrics. These quantitative analyses might have
missed out on un-quantifiable aspects like sentiment and speculation that also
impact the market. Analyzing vast amounts of qualitative text data to
understand public opinion on social media platform is one approach to address
this gap. This work carried out topic analysis on 28264 financial tweets [1]
via clustering to discover emerging events in the stock market. Three main
topics were discovered to be discussed frequently within the period. First, the
financial ratio EPS is a measure that has been discussed frequently by
investors. Secondly, short selling of shares were discussed heavily, it was
often mentioned together with Morgan Stanley. Thirdly, oil and energy sectors
were often discussed together with policy. These tweets were semantically
clustered by a method consisting of word2vec algorithm to obtain word
embeddings that map words to vectors. Semantic word clusters were then formed.
Each tweet was then vectorized using the Term Frequency-Inverse Document
Frequency (TF-IDF) values of the words it consisted of and based on which
clusters its words were in. Tweet vectors were then converted to compressed
representations by training a deep-autoencoder. K-means clusters were then
formed. This method reduces dimensionality and produces dense vectors, in
contrast to the usual Vector Space Model. Topic modelling with Latent Dirichlet
Allocation (LDA) and top frequent words were used to analyze clusters and
reveal emerging events.


  Metasurfaces, the two-dimensional (2D) counterpart of metamaterials, have
recently attracted a great attention due to their amazing properties such as
negative refraction, hyperbolic dispersion, manipulation of the evanescent
spectrum. In this work, we propose a theory model for the near field radiative
heat transfer (NFRHT) between two nanoparticles in the presence of an
anisotropic metasurface. Specifically, we set the metasurface as an array of
graphene strips (GS) since it is an ideal platform to implement any metasurface
topology, ranging from isotropic to hyperbolic propagation. We show that the
NFRHT between two nanoparticles can not only be significantly amplified when
they are placed in proximity of the GS, but also be regulated over several
orders of magnitude. In this configuration, the anisotropic surface plasmon
polaritons (SPPs) supported by the GS are excited and provide a new channel for
the near-field energy transport. We analyze how the conductance between two
nanoparticles depends on the orientation, the structure parameters and the
chemical potential of the GS, on the particle-surface or the particle-surface
distances by clearly identifying the characteristics of the anisotropic SPPs
such as dispersion relations, propagation length and decay length. Our findings
provide a powerful way to regulate the energy transport in the particle
systems, meanwhile in turn, open up a way to explore the anisotropic optical
properties of the metasurface based on the measured heat transfer properties.


  We present a theoretical and experimental study of a quasi-one-dimensional
zigzag antiferromagnet (N_2H_5)CuCl_3, which can be viewed as weakly coupled
Heisenberg chains with a frustrated interaction. We first discuss generic
features of the magnetic properties of the zigzag spin chain between the nearly
single chain case and the nearly double chain case, on the basis of the finite
temperature density-matrix renormalization group (DMRG) calculations. We next
show the experimental results for the magnetic susceptibility and the
high-field magnetization of a single crystal of (N_2H_5)CuCl_3 above the Neel
temperature T_N=1.55K. By comparing the experimental data with the DMRG results
carefully, we finally obtain the ratio of the nearest and next-nearest exchange
couplings as J_1/J_2=0.25 with J_2/k_B=16.3K. We also investigate the
three-dimensional (3D) coupling J' effect by using the mean-field theory
combined with the DMRG calculations. The estimated value J' \sim 0.04J_2
supports good one-dimensionality of (N_2H_5)CuCl_3 above T_N.


  Reconstruction and intrinsic decomposition of scenes from captured imagery
would enable many applications such as relighting and virtual object insertion.
Recent NeRF based methods achieve impressive fidelity of 3D reconstruction, but
bake the lighting and shadows into the radiance field, while mesh-based methods
that facilitate intrinsic decomposition through differentiable rendering have
not yet scaled to the complexity and scale of outdoor scenes. We present a
novel inverse rendering framework for large urban scenes capable of jointly
reconstructing the scene geometry, spatially-varying materials, and HDR
lighting from a set of posed RGB images with optional depth. Specifically, we
use a neural field to account for the primary rays, and use an explicit mesh
(reconstructed from the underlying neural field) for modeling secondary rays
that produce higher-order lighting effects such as cast shadows. By faithfully
disentangling complex geometry and materials from lighting effects, our method
enables photorealistic relighting with specular and shadow effects on several
outdoor datasets. Moreover, it supports physics-based scene manipulations such
as virtual object insertion with ray-traced shadow casting.


  We have calculated the next-to-leading order cross sections for the inclusive
production of D* mesons in gamma-p collisions at HERA in two approaches using
massive or massless charm quarks. The usual massive theory for the direct cross
section with charm quarks only in the final state was transformed into a
massive theory with MS-bar subtraction by subtracting the mass divergent and
additional finite terms calculated earlier in connection with the process
gamma+gamma -> D*+X. This theory approaches the massless theory with increasing
transverse momentum. The difference between the massive and the massless
approach with MS-bar subtraction is studied in detail in those kinematic
regions relevant for comparison with experimental data. With these results and
including the resolved cross section which is dominated by the part originating
from the charm in the photon, we compute the fully inclusive D* cross section
and compare it with preliminary data from the ZEUS collaboration at HERA. We
find on average good agreement.


  Let $\mathcal{A}$ be an algorithm with expected running time $e^X$,
conditioned on the value of some random variable $X$. We construct an algorithm
$\mathcal{A'}$ with expected running time $O(e^{E[X]})$, that fully executes
$\mathcal{A}$. In particular, an algorithm whose running time is a random
variable $T$ can be converted to one with expected running time $O(e^{E[\ln
T]})$, which is never worse than $O(E[T])$. No information about the
distribution of $X$ is required for the construction of $\mathcal{A}'$.


  Ferrofluids belong to an important class of highly functional soft matter,
benefiting from their magnetically controllable physical properties. Therefore,
it is of central importance to quantitatively predict the dynamic magnetic
response of ferrofluids. Traditional dynamic theories, however, are often
restricted to the near-equilibrium regime and/or only apply to nearly ideal
ferrofluids that are monodisperse, dilute enough, and weakly interacting. In
this paper I develop a self-consistent and nonperturbative dynamical mean field
theory for typical ferrofluids which are often polydisperse, concentrated, and
strongly interacting, possibly driven far from equilibrium. I obtain a general
nonperturbative expression for the dynamic magnetic susceptibility,
quantitatively agreeing with the spectra obtained from Brownian Dynamics
simulations on both mono- and bidisperse samples. Furthermore, I derive a
generic magnetization relaxation equation (MRE) for both mono- and polydisperse
ferrofluids by employing the projection operator technique in nonequlibrium
statistical mechanics. This MRE is in simple closed form and independent of
which model is employed to approximate the equilibrium magnetization curve.
Existing models can be recovered as low-order approximations of my generic and
nonperturbative MRE. My theory can play a key role in studying the dynamics of
ferrofluids and other polar fluids. It may also have substantial and immediate
consequences to various ferrofluid applications.


  The apparent discrepancy between the bending of light predicted by the
equivalence principle and its corresponding value in general relativity is
resolved by evaluating the deflection of light with respect to a direction that
is parallel transported along the ray trajectory in 3-space. In this way the
bending predicted by the equivalence principle is fulfilled in general
relativity and other alternative metric theories of gravity.


  We study localization of bulk fermions on a string-like defect with the
exponentially decreasing warp factor in six dimensions with inclusion of U(1)
gauge background from the viewpoint of field theory, and give the conditions
under which localized spin 1/2 and 3/2 fermions can be obtained.


  We study the variation of relative cohomology for a pair consisting of a
smooth projective hypersurface and an algebraic subvariety in it. We construct
an inhomogeneous Picard-Fuchs equation by applying a Picard-Fuchs operator to
the holomorphic top form on a toric Calabi-Yau hypersurface, and deriving a
general formula for the $d$-exact form on one side of the equation. We also
derive a double residue formula, giving a purely algebraic way to compute the
inhomogeneous Picard-Fuchs equations for Abel-Jacobi map, which has played an
important role in recent study of D-branes [25]. Using the variation formalism,
we prove that the relative periods of toric B-branes on a toric Calabi-Yau
hypersurface satisfy the enhanced GKZ-hypergeometric system proposed in physics
literature [6], and discuss the relations between the works [25] [21] [6] in
recent study of open string mirror symmetry. We also give the general solutions
to the enhanced hypergeometric system.


  Acute neuroprotection in numerous human clinical trials has been an abject
failure. Major systemic-and procedural-based issues have subsequently been
identified in both clinical trials and preclinical animal model
experimentation. As well, issues related to the neuroprotective moiety itself
have contributed to clinical trial failures, including late delivery,
mono-targeting, low potency and poor tolerability. Conditioning (pre-or post-)
strategies can potentially address these issues and are therefore gaining
increasing attention as approaches to protect the brain from cerebral ischemia.
In principle, conditioning can address concerns of timing (preconditioning
could be pre-emptively applied in high-risk patients, and post-conditioning
after patients experience an unannounced brain infarction) and signaling
(multi-modal). However, acute neuroprotection and conditioning strategies face
a common translational issue: a myriad of possibilities exist, but with no
strategy to select optimal candidates. In this review, we argue that what is
required is a neuroprotective framework to identify the "best" agent(s), at the
earliest investigational stage possible. This may require switching mindsets
from identifying how neuroprotection can be achieved to determining how
neuroprotection can fail, for the vast majority of candidates. Understanding
the basis for failure can in turn guide supplementary treatment, thereby
forming an evidence-based rationale for selecting combinations of therapies. An
appropriately designed in vitro (neuron culture, brain slices) approach, based
on increasing the harshness of the ischemic-like insult, can be useful in
identifying the "best" conditioner or acute neuroprotective therapy, as well as
how the two modalities can be combined to overcome individual limitations. This
would serve as a base from which to launch further investigation into therapies
required to protect the neurovascular unit in in vivo animal models of cerebral
ischemia. Based on these respective approaches, our laboratories suggest that
there is merit in examining synaptic activity-and nutraceutical-based
preconditioning / acute neuroprotection.


  The ability to induce regions of high and low ionic concentration adjacent to
a permeselective membrane or nanochannel subject to an externally applied
electric field (a phenomenon termed concentration-polarization) has been used
for a broad spectrum of applications ranging from on-chip desalination,
bacteria filtration to biomolecule preconcentration. But these applications
have been limited by the ability to control the length of the diffusion layer
that is commonly indirectly prescribed by the fixed geometric and surface
properties of the nanofluidic system. Here, we demonstrate that the depletion
layer can be dynamically varied by inducing controlled electrothermal flow
driven by the interaction of temperature gradients with the applied electric
field. To this end, a series of microscale heaters, which can be individually
activated on demand are embedded at the bottom of the microchannel and the
relationship between their activation and ionic concentration is characterized.
Such spatio-temporal control of the diffusion layer can be used to enhance
on-chip electro-dialysis by producing shorter depletion layers, to dynamically
reduce the microchannel resistance relative to that of the nanochannel for
nanochannel based (bio)sensing, to generate current rectification reminiscent
of a diode like behavior and control the location of the preconcentrated plug
of analytes or the interface of brine and desalted streams.


  The defining conditions for the irreducible tensor operators associated with
the unitary irreducible corepresentions of compact quantum group algebras are
deduced first in both the right and left regular coaction formalisms. In each
case it is shown that there are {\em{two}} types of irreducible tensor
operator, which may be called `ordinary' and `twisted'. The consistency of the
definitions is demonstrated, and various consequences are deduced, including
generalizations of the Wigner-Eckart theorem for both the ordinary and twisted
operators. Also included are discussions (within the regular coaction
formalisms for compact quantum group algebras) of inner-products, basis
functions, projection operators, Clebsch-Gordan coefficients, and two types of
tensor product of corepresentations. The formulation of quantum homogeneous
spaces for compact quantum group algebras is discussed, and the defining
conditions for the irreducible tensor operators associated with such quan!
  tum homogeneous spaces and with the unitary irreducible corepresentions of
the compact quantum group algebras are then deduced. There are two versions,
which correspond to restrictions of the right and left regular coactions. In
each case it is again shown that there are ordinary and twisted irreducible
tensor operators. Various consequences are deduced, including the corresponding
generalizations of the Wigner-Eckart theorem.


  Neural Architecture Search (NAS) methods, which automatically learn entire
neural model or individual neural cell architectures, have recently achieved
competitive or state-of-the-art (SOTA) performance on variety of natural
language processing and computer vision tasks, including language modeling,
natural language inference, and image classification. In this work, we explore
the applicability of a SOTA NAS algorithm, Efficient Neural Architecture Search
(ENAS) (Pham et al., 2018) to two sentence pair tasks, paraphrase detection and
semantic textual similarity. We use ENAS to perform a micro-level search and
learn a task-optimized RNN cell architecture as a drop-in replacement for an
LSTM. We explore the effectiveness of ENAS through experiments on three
datasets (MRPC, SICK, STS-B), with two different models (ESIM, BiLSTM-Max), and
two sets of embeddings (Glove, BERT). In contrast to prior work applying ENAS
to NLP tasks, our results are mixed -- we find that ENAS architectures
sometimes, but not always, outperform LSTMs and perform similarly to random
architecture search.


  It has recently been suggested that the parity doublet structure seen in the
spectrum of highly excited baryons may be due to effective chiral restoration
for these states. We argue how the idea of chiral symmetry restoration high in
the spectrum is consistent with the concept of quark-hadron duality. If chiral
symmetry is effectively restored for highly-lying states, then the baryons
should fall into representations of $SU(2)_L\times SU(2)_R$ that are compatible
with the given parity of the states - the parity-chiral multiplets. We classify
all possible parity-chiral multiplets: (i) $(1/2,0)\oplus(0, 1/2)$ that contain
parity doublet for nucleon spectrum;(ii) $(3/2,0) \oplus (0, 3/2)$ consists of
the parity doublet for delta spectrum; (iii) $(1/2,1) \oplus (1, 1/2)$ contains
one parity doublet in the nucleon spectrum and one parity doublet in the delta
spectrum of the same spin that are degenerate in mass. Here we show that the
available spectroscopic data for nonstrange baryons in the $\sim$ 2 GeV range
is consistent with all possibilities, but the approximate degeneracy of parity
doublets in nucleon and delta spectra support the latter possibility with
excited baryons approximately falling into $(1/2,1) \oplus (1, 1/2)$
representation of $SU(2)_L\timesSU(2)_R$ with approximate degeneracy between
positive and negative parity $N$ and $\Delta$ resonances of the same spin.


  We present the first complete model of the Littlest Modular Seesaw, based on
two right-handed neutrinos, within the framework of multiple modular
symmetries, justifying the use of multiple moduli fields which take their
values at 3 specific stabilizers of $\Gamma_4 \simeq S_4$, including a new
phenomenological possibility. Using a semi-analytical approach, we perform a
$\chi^2$ analysis of each case and show that good agreement with neutrino
oscillation data is obtained, including predictive relations between the
leptonic mixing angles and the ratio of light neutrino masses, which
non-trivially agree with the experimental values. It is noteworthy that in this
very predictive setup, the models fit the global fits of the experimental data
remarkably well, both with and without the Super-Kamiokande atmospheric data,
for both choices of stabilizers. By extending the model to include a weighton
and the double cover group $\Gamma'_4 \simeq S'_4$, we are able to also account
for the hierarchy of the charged leptons using modular symmetries, without
altering the neutrino predictions.


  We report the measurement of the entangled two photon absorption cross
section, $\sigma_E$, at 808 nm on organic chromophores in solution in a low
photon flux regime. We performed measurements on Zinc tetraphenylporphyrin
(ZnTPP) in Toluene and Rhodamine B (RhB) in Methanol. This is, to the best of
our knowledge, the first time that $\sigma_E$ is measured for RhB.
Additionally, we report a systematic study of the dependence of $\sigma_E$ on
the molecular concentration for both molecular systems. In contrast to previous
experiments, our measurements are based on detecting the pairs of photons that
are transmitted by the molecular system. By using a coincidence count circuit
it was possible to improve the signal to noise ratio. This type of work is
important for the development of spectroscopic and microscopic techniques using
entangled photons.


  We show that a new probabilistic technique, recently introduced by the first
author, yields the sharpest bounds obtained to date on mixing times of Markov
chains in terms of isoperimetric properties of the state space (also known as
conductance bounds or Cheeger inequalities). We prove that the bounds for
mixing time in total variation obtained by Lovasz and Kannan, can be refined to
apply to the maximum relative deviation $|p^n(x,y)/\pi(y)-1|$ of the
distribution at time $n$ from the stationary distribution $\pi$. We then extend
our results to Markov chains on infinite state spaces and to continuous-time
chains. Our approach yields a direct link between isoperimetric inequalities
and heat kernel bounds; previously, this link rested on analytic estimates
known as Nash inequalities.


  Galaxies evolve continuously under the influence of self-gravity, rotation,
accretion, mergers and feedback. The currently favored cold dark matter
cosmological framework, suggests a hierarchical process of galaxy formation,
wherein the present properties of galaxies are decided by their individual
histories of being assembled from smaller pieces. However, recent studies have
uncovered surprising correlations among the properties of galaxies, to the
extent of forming a one-parameter set lying on a single fundamental line. It
has been argued in the literature that such simplicity is hard to explain
within the paradigm of hierarchical galaxy mergers. One of the puzzling
results, is the simple linear correlation between the neutral hydrogen mass and
the surface area, implying that widely different galaxies share very similar
neutral hydrogen surface densities. In this work we show that self-regulated
star formation, driven by the competition between gravitational instabilities
and mechanical feedback from supernovae, can explain the nearly constant
neutral hydrogen surface density across galaxies. We therefore recover the
simple scaling relation observed between the neutral hydrogen mass and surface
area. This result furthers our understanding of the surprising simplicity in
the observed properties of diverse galaxies.


  Using three years of game data of the online collectible card game
Hearthstone, we analyse the evolution of the game's system over the period
2016--2019. By considering the frequencies that archetypes are played, and
their corresponding win-rates, we are able to provide narratives of the
system-wide changes that have occurred over time, and player reactions to them.
Applying the archetype frequencies to analyse the system's Shannon entropy, we
characterise the salient features of the time series of player choice. Paying
particular attention to how entropy is affected during periods of both small
and large-scale change, we are able to demonstrate the effects of increased
player experimentation before popular decks and tactics emerge. Furthermore,
constructing conditional probabilities that simulate understandable player
behaviour, we analyse the system's information storage and test the
explain-ability of current player choice based on previous decision-making.


  In this work we set the stage for a new probabilistic pathwise approach to
effectively calibrate a general class of stochastic nonlinear fluid dynamics
models. We focus on a 2D Euler SALT equation, showing that the driving
stochastic parameter can be calibrated in an optimal way to match a set of
given data. Moreover, we show that this model is robust with respect to the
stochastic parameters.


  A strong candidate for the Standard Model Scalar boson, H(126), has been
discovered by the Large Hadron Collider (LHC) experiments. In order to study
this fundamental particle with unprecedented precision, and to perform
precision tests of the closure of the Standard Model, we investigate the
possibilities offered by An e+e- storage ring collider. We use a design
inspired by the B-factories, taking into account the performance achieved at
LEP2, and imposing a synchrotron radiation power limit of 100 MW. At the most
relevant centre-of-mass energy of 240 GeV, near-constant luminosities of 10^34
cm^{-2}s^{-1} are possible in up to four collision points for a ring of 27km
circumference. The achievable luminosity increases with the bending radius, and
for 80km circumference, a luminosity of 5 10^34 cm^{-2}s^{-1} in four collision
points appears feasible. Beamstrahlung becomes relevant at these high
luminosities, leading to a design requirement of large momentum acceptance both
in the accelerating system and in the optics. The larger machine could reach
the top quark threshold, would yield luminosities per interaction point of
10^36 cm^{-2}s^{-1} at the Z pole (91 GeV) and 2 10^35 cm^{-2}s^{-1} at the W
pair production threshold (80 GeV per beam). The energy spread is reduced in
the larger ring with respect to what is was at LEP, giving confidence that beam
polarization for energy calibration purposes should be available up to the W
pair threshold. The capabilities in term of physics performance are outlined.


  Estimating the 6-DoF pose of a rigid object from a single RGB image is a
crucial yet challenging task. Recent studies have shown the great potential of
dense correspondence-based solutions, yet improvements are still needed to
reach practical deployment. In this paper, we propose a novel pose estimation
algorithm named CheckerPose, which improves on three main aspects. Firstly,
CheckerPose densely samples 3D keypoints from the surface of the 3D object and
finds their 2D correspondences progressively in the 2D image. Compared to
previous solutions that conduct dense sampling in the image space, our strategy
enables the correspondence searching in a 2D grid (i.e., pixel coordinate).
Secondly, for our 3D-to-2D correspondence, we design a compact binary code
representation for 2D image locations. This representation not only allows for
progressive correspondence refinement but also converts the correspondence
regression to a more efficient classification problem. Thirdly, we adopt a
graph neural network to explicitly model the interactions among the sampled 3D
keypoints, further boosting the reliability and accuracy of the
correspondences. Together, these novel components make CheckerPose a strong
pose estimation algorithm. When evaluated on the popular Linemod, Linemod-O,
and YCB-V object pose estimation benchmarks, CheckerPose clearly boosts the
accuracy of correspondence-based methods and achieves state-of-the-art
performances. Code is available at https://github.com/RuyiLian/CheckerPose.


  Collecting data about the sequences of function calls executed by an
application while running in the field can be useful to a number of
applications, including failure reproduction, profiling, and debugging.
Unfortunately, collecting data from the field may introduce annoying slowdowns
that negatively affect the quality of the user experience. So far, the impact
of monitoring has been mainly studied in terms of the overhead that it may
introduce in the monitored applications, rather than considering if the
introduced overhead can be really recognized by users. In this paper we take a
different perspective studying to what extent collecting data about sequences
of function calls may impact the quality of the user experience, producing
recognizable effects. Interestingly we found that, depending on the nature of
the executed operation and its execution context, users may tolerate a
non-trivial overhead. This information can be potentially exploited to collect
significant amount of data without annoying users.


  In this paper, we study an approximate controllability for the impulsive
linear evolution equations in Hilbert spaces. The necessary and sufficient
conditions for approximate controllability in terms of resolvent operators are
given. An example is provided to illustrate the application of the obtained
results.


  X-rays and gamma-rays from astronomical sources such as solar flares are
mostly absorbed by the Earth's atmosphere. Resulting electron-ion production
rate as a function of height depends on the intensity and wavelength of the
injected spectrum and therefore the effects vary from one source to another. In
other words, the ion density vs. altitude profile has the imprint of the
incident photon spectrum. In this paper, we investigate whether we can invert
the problem uniquely by deconvolution of the VLF amplitude signal to obtain the
details of the injected spectrum. We find that it is possible to do this up to
a certain accuracy. Our method is useful to carry out a similar exercise to
infer the spectra of more energetic events such as the Gamma Ray Bursts (GRBs),
Soft Gamma Ray Repeaters (SGRs) etc. by probing even the lower part of the
atmosphere. We thus show that to certain extent, the Earth's atmosphere could
be used as a gigantic detector of relatively strong events.


  The task of searching for and tracking of multiple targets is a challenging
one. However, most works in this area do not consider evasive targets that move
faster than the agents comprising the multi-robot system. This is due to the
assumption that the movement patterns of such targets, combined with their
excessive speed, would make the task nearly impossible to accomplish. In this
work, we show that this is not the case and we propose a decentralized search
and tracking strategy in which the level of exploration and exploitation
carried out by the swarm is adjustable. By tuning a swarm's exploration and
exploitation dynamics, we demonstrate that there exists an optimal balance
between the level of exploration and exploitation performed. This optimum
maximizes its tracking performance and changes depending on the number of
targets and the targets' movement profiles. We also show that the use of
agent-based memory is critical in enabling the tracking of an evasive target.
The obtained simulation results are validated through experimental tests with a
decentralized swarm of six robots tracking a virtual fast-moving target.


  With the increase in data availability, it has been widely demonstrated that
neural networks (NN) can capture complex system dynamics precisely in a
data-driven manner. However, the architectural complexity and nonlinearity of
the NNs make it challenging to synthesize a provably safe controller. In this
work, we propose a novel safety filter that relies on convex optimization to
ensure safety for a NN system, subject to additive disturbances that are
capable of capturing modeling errors. Our approach leverages tools from NN
verification to over-approximate NN dynamics with a set of linear bounds,
followed by an application of robust linear MPC to search for controllers that
can guarantee robust constraint satisfaction. We demonstrate the efficacy of
the proposed framework numerically on a nonlinear pendulum system.


  Adversarial examples are malicious inputs crafted to cause a model to
misclassify them. Their most common instantiation, "perturbation-based"
adversarial examples introduce changes to the input that leave its true label
unchanged, yet result in a different model prediction. Conversely,
"invariance-based" adversarial examples insert changes to the input that leave
the model's prediction unaffected despite the underlying input's label having
changed.
  In this paper, we demonstrate that robustness to perturbation-based
adversarial examples is not only insufficient for general robustness, but
worse, it can also increase vulnerability of the model to invariance-based
adversarial examples. In addition to analytical constructions, we empirically
study vision classifiers with state-of-the-art robustness to perturbation-based
adversaries constrained by an $\ell_p$ norm. We mount attacks that exploit
excessive model invariance in directions relevant to the task, which are able
to find adversarial examples within the $\ell_p$ ball. In fact, we find that
classifiers trained to be $\ell_p$-norm robust are more vulnerable to
invariance-based adversarial examples than their undefended counterparts.
  Excessive invariance is not limited to models trained to be robust to
perturbation-based $\ell_p$-norm adversaries. In fact, we argue that the term
adversarial example is used to capture a series of model limitations, some of
which may not have been discovered yet. Accordingly, we call for a set of
precise definitions that taxonomize and address each of these shortcomings in
learning.


  The set of factorizations of permutations in to $m$ transpositions of some
symmetric group $\mathcal{S}_n$ is naturally in bijection with the set of
graphs of order $n$ and size $m$ with both edges and vertices labeled. We
define a notion of duality (the \emph{mind-body duality}) for factorizations
and such labeled graphs and interpret it in terms of Properly Embedded Graphs,
a class of graphs embedded in a bounded compact oriented surface with all the
vertices lying in the boundary, and show a close connection of this duality
with the Hurwitz action of the Braid Group. Connections with the theory of
Cellularly Embedded Graphs are highlighted and hints of possible applications
are given. In this paper we focus on developing the necessary theory, leaving
specific applications and further developments for future projects.


  Numerical simulations of stratified shear flow instabilities are performed in
two dimensions in the Boussinesq limit. The density variation length scale is
chosen to be four times smaller than the velocity variation length scale so
that Holmboe or Kelvin-Helmholtz unstable modes are present depending on the
choice of the global Richardson number Ri. Three different values of Ri were
examined Ri =0.2, 2, 20. The flows for the three examined values are all
unstable due to different modes namely: the Kelvin-Helmholtz mode for Ri=0.2,
the first Holmboe mode for Ri=2, and the second Holmboe mode for Ri=20 that has
been discovered recently and it is the first time that it is examined in the
non-linear stage. It is found that the amplitude of the velocity perturbation
of the second Holmboe mode at the non-linear stage is smaller but comparable to
first Holmboe mode. The increase of the potential energy however due to the
second Holmboe modes is greater than that of the first mode. The
Kelvin-Helmholtz mode is larger by two orders of magnitude in kinetic energy
than the Holmboe modes and about ten times larger in potential energy than the
Holmboe modes. The results in this paper suggest that although mixing is
suppressed at large Richardson numbers it is not negligible, and turbulent
mixing processes in strongly stratified environments can not be excluded.


  We design a neural network based on a single spin-torque vortex
nano-oscillator (STVO) multiplexed in time. The behavior of the STVO is
simulated with an improved ultra-fast and quantitative model based on the
Thiele equation approach. Different mathematical and numerical adaptations are
brought to the model in order to increase the accuracy and the speed of the
simulations. We demonstrate the high added value and adaptability of such a
neural network through the resolution of three standard machine learning tasks
in the framework of reservoir computing. The first one is a task of waveform
(sines and squares) classification. We show the ability of the system to
effectively classify waveforms with high accuracy and low root-mean-square
error thanks to the intrinsic short-term memory of the device. Given the high
throughput of the simulations, two innovative parametric studies on the
intensity of the input signal and the level of noise in the system are
performed to demonstrate the value of our new models. The efficiency of our
system is then tested during a speech recognition task on the TI-46 dataset and
shows the agreement between the new models and the corresponding experimental
measurements. Finally, we use our STVO-based neural network to perform image
recognition on the MNIST dataset. State-of-the-art performances are
demonstrated, and the interest of using the STVO dynamics as an activation
function is highlighted. These results support and facilitate the future
development of neuromorphic STVO-based hardware for energy-efficient machine
learning.


  The COSINE-100 experiment is designed to test the DAMA experiment which
claimed an observation of a dark matter signal from an annual modulation in
their residual event rate. To measure the 1 %-level signal amplitude, it is
crucial to control and monitor nearly all environmental quantities that might
systematically mimic the signal. The environmental monitoring also helps ensure
a stable operation of the experiment. Here, we describe the design and
performance of the centralized environmental monitoring system for the
COSINE-100 experiment.


  The impressive performance of deep neural networks (DNNs) has immensely
strengthened the line of research that aims at theoretically analyzing their
effectiveness. This has incited research on the reaction of DNNs to noisy
input, namely developing adversarial input attacks and strategies that lead to
robust DNNs to these attacks. To that end, in this paper, we derive exact
analytic expressions for the first and second moments (mean and variance) of a
small piecewise linear (PL) network (Affine, ReLU, Affine) subject to Gaussian
input. In particular, we generalize the second-moment expression of Bibi et al.
to arbitrary input Gaussian distributions, dropping the zero-mean assumption.
We show that the new variance expression can be efficiently approximated
leading to much tighter variance estimates as compared to the preliminary
results of Bibi et al. Moreover, we experimentally show that these expressions
are tight under simple linearizations of deeper PL-DNNs, where we investigate
the effect of the linearization sensitivity on the accuracy of the moment
estimates. Lastly, we show that the derived expressions can be used to
construct sparse and smooth Gaussian adversarial attacks (targeted and
non-targeted) that tend to lead to perceptually feasible input attacks.


  Building upon the recent works of Bertola; Fasondini, Olver and Xu, we define
a class of orthogonal polynomials on elliptic curves and establish a
corresponding Riemann-Hilbert framework. We then focus on the special case,
defined by a constant weight function, and use the Riemann-Hilbert problem to
derive recurrence relations and differential equations for the orthogonal
polynomials. We further show that the sub-class of even polynomials is
associated to the elliptic form of Painlev\'e VI, with the tau function given
by the Hankel determinant of even moments, up to a scaling factor. The first
iteration of these even polynomials relates to the special case of Painlev\'e
VI studied by Hitchin in relation to self-dual Einstein metrics.


  This paper discusses the problem of maximizing the total data transmission
utility of the computer network. The total utility is defined as the sum of the
individual (corresponding to each node in the network) utilities that are
concave functions of the data transmission rate. For the case of non-strongly
concave utilities, we propose an approach based on the use of a fast gradient
method to optimize a dually smoothed objective function. As an alternative
approach, we introduce stochastic oracles for the problem under consideration
and interpret them as the messages on the state of some individual node to use
randomized switching mirror descent to solve the problem above. We propose
interpretations of both described approaches allowing the effective
implementation of the protocols of their operation in the real-life computer
networks environment, taking into account the distributed information storage
and the restricted communication capabilities. The numerical experiments were
carried out to compare the proposed approaches on sythetic examples of network
architectures.


  A code design problem for memory devises with restricted state transitions is
formulated as a combinatorial optimization problem that is called a subgraph
domatic partition (subDP) problem. If any neighbor set of a given state
transition graph contains all the colors, then the coloring is said to be
valid. The goal of a subDP problem is to find a valid coloring with the largest
number of colors for a subgraph of a given directed graph. The number of colors
in an optimal valid coloring gives the writing capacity of a given state
transition graph. The subDP problems are computationally hard; it is proved to
be NP-complete in this paper. One of our main contributions in this paper is to
show the asymptotic behavior of the writing capacity $C(G)$ for sequences of
dense bidirectional graphs, that is given by C(G)=Omega(n/ln n) where n is the
number of nodes. A probabilistic method called Lovasz local lemma (LLL) plays
an essential role to derive the asymptotic expression.


  A multipath mechanism similar to that used in Australia sixty years ago by
the Sea-cliff Interferometer is shown to generate correlations between the
periods of oscillations observed by two distant radio telescopes pointed to the
Sun. The oscillations are the result of interferences between the direct wave
detected in the main antenna lobe and its reflection on ground detected in a
side lobe. A model is made of such oscillations in the case of two
observatories located at equal longitudes and opposite tropical latitudes,
respectively in Ha Noi (Viet Nam) and Learmonth (Australia), where similar
radio telescopes are operated at 1.4 GHz. Simple specular reflection from
ground is found to give a good description of the observed oscillations and to
explain correlations that had been previously observed and for which no
satisfactory interpretation, instrumental or other, had been found.


  Results of a large scale numerical simulation show that the high temperature
Chern-Simons number diffusion rate in the electroweak theory has a classical
limit $\Gamma = \kappa (\alpha_w T)^4$, where $\kappa = 1.09\pm 0.04$ and
$\alpha_w$ is the weak fine structure constant.


  Can we better anticipate an actor's future actions (e.g. mix eggs) by knowing
what commonly happens after his/her current action (e.g. crack eggs)? What if
we also know the longer-term goal of the actor (e.g. making egg fried rice)?
The long-term action anticipation (LTA) task aims to predict an actor's future
behavior from video observations in the form of verb and noun sequences, and it
is crucial for human-machine interaction. We propose to formulate the LTA task
from two perspectives: a bottom-up approach that predicts the next actions
autoregressively by modeling temporal dynamics; and a top-down approach that
infers the goal of the actor and plans the needed procedure to accomplish the
goal. We hypothesize that large language models (LLMs), which have been
pretrained on procedure text data (e.g. recipes, how-tos), have the potential
to help LTA from both perspectives. It can help provide the prior knowledge on
the possible next actions, and infer the goal given the observed part of a
procedure, respectively. To leverage the LLMs, we propose a two-stage
framework, AntGPT. It first recognizes the actions already performed in the
observed videos and then asks an LLM to predict the future actions via
conditioned generation, or to infer the goal and plan the whole procedure by
chain-of-thought prompting. Empirical results on the Ego4D LTA v1 and v2
benchmarks, EPIC-Kitchens-55, as well as EGTEA GAZE+ demonstrate the
effectiveness of our proposed approach. AntGPT achieves state-of-the-art
performance on all above benchmarks, and can successfully infer the goal and
thus perform goal-conditioned "counterfactual" prediction via qualitative
analysis. Code and model will be released at
https://brown-palm.github.io/AntGPT


  An explicit construction of a pre-quantum line bundle for the moduli space of
flat G-bundles over a Riemann surface is given, where G is any non-simply
connected compact simple Lie group. This work helps to explain a curious
coincidence previously observed between Toledano-Laredo's work classifying
central extensions of loop groups LG and the author's previous work on the
obstruction to pre-quantization of the moduli space of flat G-bundles.


  The fast multipole method (FMM) performs fast approximate kernel summation to
a specified tolerance $\epsilon$ by using a hierarchical division of the
domain, which groups source and receiver points into regions that satisfy local
separation and the well-separated pair decomposition properties. While square
tilings and quadtrees are commonly used in 2D, we investigate alternative
tilings and associated spatial data structures: regular hexagons (septree) and
triangles (triangle-quadtree). We show that both structures satisfy separation
properties for the FMM and prove their theoretical error bounds and
computational costs. Empirical runtime and error analysis of our
implementations are provided.


  We propose a scheme for conditional quantum logic between two 3-state atoms
that share a quantum data-bus such as a single mode optical field in cavity QED
systems, or a collective vibrational state of trapped ions. Making use of
quantum interference, our scheme achieves successful conditional phase
evolution without any real transitions of atomic internal states or populating
the quantum data-bus. In addition, it only requires common addressing of the
two atoms by external laser fields.


  Micromanipulation of magnetotactic bacteria with a microelectromagnet matrix
was demonstrated. Magnetotactic bacteria synthesize a chain of magnetic
nanoparticles inside their body to guide their motion in the geomagnetic field.
A microelectromagnet matrix consists of two arrays of lithographically
patterned wires, one array perpendicular to the other, that are separated and
covered by insulating layers. By adjusting the current in each wire, a matrix
can create versatile magnetic field patterns on microscopic length scale. Using
a matrix, magnetotactic bacteria were trapped, continuously moved, rotated, and
assembled in water at room temperature.


  The Kennard-Stepanov relation describes a thermodynamic, Boltzmann-type
scaling between the absorption and emission spectral profiles of an absorber,
which applies in many liquid state dye solutions as well as in semiconductor
systems. Here we examine absorption and emission spectra of rubidium atoms in
dense argon buffer gas environment. We demonstrate that the Kennard-Stepanov
relation between absorption and emission spectra is well fulfilled in the
collisionally broadened atomic gas system. Our experimental findings are
supported by a simple theoretical model.


  We are exploring a scintillator-based detector with potential of high
sensitivity, DOI capability and timing resolution in a single-side readout
configuration. Our concept combines: 1) A design with 2+ crystal arrays stacked
with relative offset, with inherent DOI information but good timing performance
has not been shown with conventional light sharing readout. 2) Single crystal
array with one-to-one coupling to the photodetector (PD) array, with good
timing performance, but no DOI. We believe the combination, where the first
layer of a staggered design is coupled one-to-one to a PD array may provide
both DOI and timing. The concept is here evaluated through light transport
simulations. Results show that: 1) In terms of DOI one-to-one readout of the
first layer allows for accurate DOI extraction using a single threshold
relative to the PD sum signal, for up to 4 layers. The number of PD pixels
exceeding the threshold corresponds to the layer of interaction. The
corresponding approach is not possible for the same geometries with a light
sharing readout scheme. 2) When employing a low threshold of 2 optical photons
the layered approach with one-to-one readout of the first layer improves timing
close to the PD compared to single layer, due to reduced crystal thickness.
Single detector timing resolution values of 91, 127, 151 and 164 ps were seen
in the 4-layer design with unpolished pixels, compared to 148 ps for single
array with one-to-one coupling. 3) For the layered design with light sharing
readout, timing improves with increased PD pixel size, with an apparent
tradeoff between spatial resolution and timing not observed for the one-to-one
coupled counterpart. The combination of straightforward and accurate DOI
determination, good timing performance and relatively simple design makes the
proposed detector a promising candidate for brain dedicated DOI TOF-PET.


  In this paper, we consider the classical variational problem in the Galilean
space. we develop the Euler-Lagrange equations for a elastic line on an
oriented surface in the Galilean 3-dimensional space $G_3$. Using the varia-
tion method, we will try to give some characterization for the solution curve
(the elastic line) of energy equation described by the total squared curvature
function of a curve on an oriented surface in $G_3$. Finally, we will
investigate whether or not the relaxed elastic curves are on a geodesic.


  In this work we put forward an effective Gaussian free field description of
critical wavefunctions at the transition between plateaus of the integer
quantum Hall effect. To this end, we expound our earlier proposal that powers
of critical wave intensities prepared via point contacts behave as pure scaling
fields obeying an Abelian operator product expansion. Our arguments employ the
framework of conformal field theory and, in particular, lead to a
multifractality spectrum which is parabolic. We also derive a number of old and
new identities that hold exactly at the lattice level and hinge on the
correspondence between the Chalker-Coddington network model and a
supersymmetric vertex model.


  We derive the universal relations for an ultracold two-component Fermi gas
with spin-orbit coupling (SOC)
$\sum_{\alpha,\beta=x,y,z}\lambda_{\alpha\beta}\sigma_{\alpha}p_{\beta}$, where
$p_{x,y,z}$ and $\sigma_{x,y,z}$ are the single-atom momentum and Pauli
operators for pseudo spin, respectively, and the SOC intensity
$\lambda_{\alpha\beta}$ could take arbitrary value. We consider the system with
an s-wave short-range interspecies interaction, and ignore the SOC-induced
modification for the value of the scattering length. Using the first-quantized
approach developed by S. Tan (Phys. Rev. Lett. \textbf{107}, 145302 (2011)), we
obtain the short-range and high-momentum expansions for the one-body real-space
correlation function and momentum distribution function, respectively. For our
system these functions are $2\times2$ matrix in the pseudo-spin basis. We find
that the leading-order ($1/k^{4}$) behavior of the diagonal elements of the
momentum distribution function (i.e., $n_{\uparrow\uparrow}({\bf k})$ and
$n_{\downarrow\downarrow}({\bf k})$) are not modified by the SOC. However, the
SOC can significantly modify the behavior of the \textit{non-diagonal elements}
of the momentum distribution function, i.e., $n_{\uparrow\downarrow}({\bf k})$
and $n_{\downarrow\uparrow}({\bf k})$, in the large-$k$ limit. In the absence
of the SOC, the leading order of these elements is ${\cal O}(1/k^{6})$. When
SOC appears, it can induce a term on the order of $1/k^{5}$. We further derive
the adiabatic relation and the energy functional. Our results show the SOC can
induce a new term in the energy functional, which simply describe the
contribution from the SOC to the total energy. The form of the adiabatic
relation for our system is not modified by the SOC.


  For $\Lambda$ the category of free opetopic algebras, we construct a model
structure \emph{\`a la Cisinski} on the category of presheaves over $\Lambda$,
and show that is is equivalent to opetopic complete Segal spaces. This
generalizes the results of Joyal and Tierney in the simplicial case, and of
Cisinski and Moerdijk in the planar dendroidal case.


  We revisit the so-called "Three Squares Lemma" by Crochemore and Rytter
[Algorithmica 1995] and, using arguments based on Lyndon words, derive a more
general variant which considers three overlapping squares which do not
necessarily share a common prefix. We also give an improved upper bound of
$n\log_2 n$ on the maximum number of (occurrences of) primitively rooted
squares in a string of length $n$, also using arguments based on Lyndon words.
To the best of our knowledge, the only known upper bound was $n \log_\phi n
\approx 1.441n\log_2 n$, where $\phi$ is the golden ratio, reported by Fraenkel
and Simpson [TCS 1999] obtained via the Three Squares Lemma.


  We give a definition of the Clifford algebra of an antiautomorphism of a
central simple algebra, and compute it for the algebras of degree 2.


  We prove a reflection theorem, conjectured by Nakagawa and Ohno, for the
number of quartic rings, or pairs of ternary quadratic forms, with a given
cubic resolvent. Over $\mathbb{Z}$, our results are unconditional; we also
allow the base to be the ring of integers of a general number field,
conditional on some algebraic identities that are Monte Carlo verified. We also
establish a reflection theorem for quartic $11111$-forms and $48441$-forms that
relates them to the number of $3\times 3$ symmetric matrices with given
characteristic polynomial. Along the way, we find elegant new results on Igusa
zeta functions of conics and the average value of a quadratic character over a
box in a local field.
  We conjecture that a reflection theorem holds for pairs of $n$-ary quadratic
forms for any odd $n$, and we prove this for odd cubefree discriminant. This
furnishes a more satisfactory answer for a question raised by Cohen, Diaz y
Diaz, and Olivier, namely whether there exist an infinite family of reflection
theorems of Ohno-Nakagawa type.


  In this paper we study the asymptotic behavior of the maximum magnitude of a
complex random polynomial with i.i.d. uniformly distributed random roots on the
unit circle. More specifically, let $\{n_k\}_{k=1}^{\infty}$ be an infinite
sequence of positive integers and let $\{z_{k}\}_{k=1}^{\infty}$ be a sequence
of i.i.d. uniform distributed random variables on the unit circle. The above
pair of sequences determine a sequence of random polynomials $P_{N}(z) =
\prod_{k=1}^{N}{(z-z_k)^{n_k}}$ with random roots on the unit circle and their
corresponding multiplicities. In this work, we show that subject to a certain
regularity condition on the sequence $\{n_k\}_{k=1}^{\infty}$, the log maximum
magnitude of these polynomials scales as $s_{N}I^{*}$ where
$s_{N}^{2}=\sum_{k=1}^{N}{n_{k}^{2}}$ and $I^{*}$ is a strictly positive random
variable.


  We suggest a small set of fission observables to be used as test cases for
validation of theoretical calculations. The purpose is to provide common data
to facilitate the comparison of different fission theories and models. The
proposed observables are chosen from fission barriers, spontaneous fission
lifetimes, fission yield characteristics, and fission isomer excitation
energies.


  A high-efficiency fast neutron detector prototype based on a triple Gas
Electron Multiplier (GEM) detector, which coupled with a novel multi-layered
High-Density PolyEthylene (HDPE) as a neutron-to-proton converter for improving
the neutron detection efficiency, is introduced and tested with the Am-Be
neutron source in Institute of Modern Physics (IMP) at Lanzhou in present work.
Firstly, the developed triple GEM detector is tested by measuring its effective
gain and energy resolution with $^{55}$Fe X-ray source to ensure that it has a
good performance. The effective gain and obtained energy resolution is
5.0$\times$10$^{4}$ and around of 19.2\%, respectively. And secondly, the novel
multi-layered HDPE converter is coupled with the cathode of the triple GEM
detector make it a high-effective fast neutron detector. And its effective
neutron response is four times higher than that of the traditional
single-layered conversion technique when the converter layer number is 38.


  In the present contribution, we introduce a wireless optical
communication-based system architecture which is shown to significantly improve
the reliability and the spectral and power efficiency of the transcutaneous
link in cochlear implants (CIs). We refer to the proposed system as optical
wireless cochlear implant (OWCI).In order to provide a quantified understanding
of its design parameters, we establish a theoretical framework that takes into
account the channel particularities, the integration area of the internal unit,
the transceivers misalignment, and the characteristics of the optical units. To
this end, we derive explicit expressions for the corresponding average
signal-to-noise-ratio, outage probability, ergodic spectral efficiency and
capacity of the transcutaneous optical link (TOL). These expressions are
subsequently used to assess the dependence of the TOL's communication quality
on the transceivers design parameters and the corresponding channels
characteristics. The offered analytic results are corroborated with respective
results from Monte Carlo simulations. Our findings reveal that OWCI is a
particularly promising architecture that drastically increases the reliability
and effectiveness of the CI TOL, whilst it requires considerably lower transmit
power compared to the corresponding widely-used radio frequency (RF) solution.


  This work constructs the first-ever sixth-order exponential Runge--Kutta
(ExpRK) methods for the time integration of stiff parabolic PDEs. First, we
leverage the exponential B-series theory to restate the stiff order conditions
for ExpRK methods of arbitrary order based on an essential set of trees only.
Then, we explicitly provide the 36 order conditions required for sixth-order
methods and present convergence results. In addition, we are able to solve the
36 stiff order conditions in both their weak and strong forms, resulting in two
families of sixth-order parallel stages ExpRK schemes. Interestingly, while
these new schemes require a high number of stages, they can be implemented
efficiently similar to the cost of a 6-stage method. Numerical experiments are
given to confirm the accuracy and efficiency of the new schemes.


  This paper focuses on designing motion plans for a heterogeneous team of
robots that has to cooperate in fulfilling a global mission. The robots move in
an environment containing some regions of interest, and the specification for
the whole team can include avoidances, visits, or sequencing when entering
these regions of interest. The specification is expressed in terms of a Petri
net corresponding to an automaton, while each robot is also modeled by a state
machine Petri net. With respect to existing solutions for related problems, the
current work brings the following contributions. First, we propose a novel
model, denoted {High-Level robot team Petri Net (HLPN) system, for
incorporating the specification and the robot models into the Nets-within-Nets
paradigm. A guard function, named Global Enabling Function (gef), is designed
to synchronize the firing of transitions such that the robot motions do not
violate the specification. Then, the solution is found by simulating the HPLN
system in a specific software tool that accommodates Nets-within-Nets. An
illustrative example based on a Linear Temporal Logic (LTL) mission is
described throughout the paper, complementing the proposed rationale of the
framework.


  The superconductor-insulator transition (SIT) is an excellent example for a
quantum phase transition at zero temperature, dominated by quantum
fluctuations. These are expected to be very prominent close to the quantum
critical point. So far most of the experimental study of the SIT has
concentrated on transport properties and tunneling experiments which provide
indirect information on criticality close to the transition. Here we present an
experiment uniquely designed to study the evolution of quantum fluctuations
through the quantum critical point. We utilize the Nernst effect, which has
been shown to be effective in probing superconducting fluctuation. We measure
the Nernst coefficient in amorphous indium oxide films tuned through the SIT
and find a large signal on both the superconducting and the insulating sides
which peaks close to the critical point. The transverse Peltier coefficient,
$\alpha_{xy}$ which is the thermodynamic quantity extracted from these
measurements, follows quantum critical scaling with critical exponents $\nu
\sim 0.7$ and $z \sim 1$ which is consistent with a clean XY model in 2+1
dimensions.


  The growth of graphene during Cu-catalyzed chemical vapor deposition was
studied using 12CH4 and 13CH4 precursor gasses. We suggest that the growth
begins by the formation of a multilayer cluster. This seed increases its size
but the growth speed of a particular layer depends on its proximity to the
copper surface. The layer closest to the substrate grows fastest and thus
further limits the growth rate of the upper layers. Nevertheless, the growth of
the upper layers continues until the copper surface is completely blocked. It
is shown that the upper layers can be removed by modification of the conditions
of the growth by hydrogen etching.


  In the realm of signal and image denoising and reconstruction, $\ell_1$
regularization techniques have generated a great deal of attention with a
multitude of variants. A key component for their success is that under certain
assumptions, the solution of minimum $\ell_1$ norm is a good approximation to
the solution of minimum $\ell_0$ norm. In this work, we demonstrate that this
approximation can result in artifacts that are inconsistent with desired
sparsity promoting $\ell_0$ properties, resulting in subpar results in {some}
instances. With this as our motivation, we develop a multiscale higher order
total variation (MHOTV) approach, which we show is related to the use of
multiscale Daubechies wavelets. We also develop the tools necessary for MHOTV
computations to be performed efficiently, via operator decomposition and
alternatively converting the problem into Fourier space. The relationship of
higher order regularization methods with wavelets, which we believe has
generally gone unrecognized, is shown to hold in several numerical results,
although notable improvements are seen with our approach over both wavelets and
classical HOTV.


  Even if path planning can be solved using standard techniques from dynamic
programming and control, the problem can also be approached using probabilistic
inference. The algorithms that emerge using the latter framework bear some
appealing characteristics that qualify the probabilistic approach as a powerful
alternative to the more traditional control formulations. The idea of using
estimation on stochastic models to solve control problems is not new and the
inference approach considered here falls under the rubric of Active Inference
(AI) and Control as Inference (CAI). In this work, we look at the specific
recursions that arise from various cost functions that, although they may
appear similar in scope, bear noticeable differences, at least when applied to
typical path planning problems. We start by posing the path planning problem on
a probabilistic factor graph, and show how the various algorithms translate
into specific message composition rules. We then show how this unified
approach, presented both in probability space and in log space, provides a very
general framework that includes the Sum-product, the Max-product, Dynamic
programming and mixed Reward/Entropy criteria-based algorithms. The framework
also expands algorithmic design options for smoother or sharper policy
distributions, including generalized Sum/Max-product algorithm, a Smooth
Dynamic programming algorithm and modified versions of the Reward/Entropy
recursions. We provide a comprehensive table of recursions and a comparison
through simulations, first on a synthetic small grid with a single goal with
obstacles, and then on a grid extrapolated from a real-world scene with
multiple goals and a semantic map.


  Bloom Filter is a probabilistic membership data structure and it is
excessively used data structure for membership query. Bloom Filter becomes the
predominant data structure in approximate membership filtering. Bloom Filter
extremely enhances the query response time, and the response time is very fast.
Bloom filter (BF) is used to detect whether an element belongs to a given set
or not. The Bloom Filter returns True Positive (TP), False Positive (FP), or
True Negative (TN). The Bloom Filter is widely adapted in numerous areas to
enhance the performance of a system. In this paper, we present a) in-depth
insight on the Bloom Filter,and b) the prominent variants of the Bloom Filters.


  The set of visited sites and the number of visited sites are two basic
properties of the random walk trajectory. We consider two independent random
walks on a hyper-cubic lattice and study ordering probabilities associated with
these characteristics. The first is the probability that during the time
interval (0,t), the number of sites visited by a walker never exceeds that of
another walker. The second is the probability that the sites visited by a
walker remain a subset of the sites visited by another walker. Using numerical
simulations, we investigate the leading asymptotic behaviors of the ordering
probabilities in spatial dimensions d=1,2,3,4. We also study the evolution of
the number of ties between the number of visited sites. We show analytically
that the average number of ties increases as $a_1\ln t$ with $a_1=0.970508$ in
one dimension and as $(\ln t)^2$ in two dimensions.


  A review on the main results concerning the algebraic and differential
properties of the averaging and coordination operators and the properties of
the space-time averages of macroscopic gravity is given. The algebraic and
differential properties of the covariant space-time averaging procedure by
means of using the parallel transportation averaging bivector operator are
analyzed. The structure of the pseudo-Riemannian space-time manifolds of
general relativity averaged by means of this procedure is discussed. A
comparison of both procedures is given and the directions of further
development of space-time averaging procedures of the physical classical fields
are outlined.


  We experimentally and theoretically investigate electromagnetic cavity modes
in ultra-narrow Al-AlO$_x$-Al and Nb-AlO$_x$-Nb long Josephson junctions.
Experiments show that the voltage spacing between the Fiske steps on the
current-voltage characteristics of sub-$\mu$m wide and several hundred $\mu$m
long Al-AlO$_x$-Al and Nb-AlO$_x$-Nb Josephson junctions increases when
decreasing the width of a junction. This effect is explained by stray magnetic
fields, which become important for narrow junctions. Theoretical estimates of
the Fiske step voltage based on a nonlocal wave propagation equation are in
good agreement with our experimental data. Using the nonlocal model, we
determine the size and mass of a Josephson vortex by means of a variational
approach, and relate vortex size to the experimentally measured critical
magnetic field of the junction.


  We propose an algorithm for optimizing the parameters of single hidden layer
neural networks. Specifically, we derive a blockwise difference-of-convex (DC)
functions representation of the objective function. Based on the latter, we
propose a block coordinate descent (BCD) approach that we combine with a
tailored difference-of-convex functions algorithm (DCA). We prove global
convergence of the proposed algorithm. Furthermore, we mathematically analyze
the convergence rate of parameters and the convergence rate in value (i.e., the
training loss). We give conditions under which our algorithm converges linearly
or even faster depending on the local shape of the loss function. We confirm
our theoretical derivations numerically and compare our algorithm against
state-of-the-art gradient-based solvers in terms of both training loss and test
loss.


  We comment on the relation between string theory and empirical science,
grounding our discussion in cosmology, a subject with increasingly precise data
in which this connection operates at several levels. It is important to take
into account the phenomenon of dangerous irrelevance: over long times or large
field ranges, physics can become sensitive to higher scales than the input
energies. This pertains in inflationary cosmology (and possibly other aspects
of horizon physics). String theory also contributes to our understanding of
observational constraints and search strategies at the level of low energy
field theory. We illustrate this with a current example concerning a new form
of non-Gaussianity generated by very massive degrees of freedom coupling to the
inflaton. New constraints on such fields and couplings can be obtained from
existing data, increasing our empirical knowledge of the universe. This builds
in part from the development of the string landscape, which is neither random
nor an abdication of science as has sometimes been suggested. {\it Invited
contribution to the proceedings of the conference `Why trust a theory'.}


  In the framework of Clifford analysis, a chain of harmonic and monogenic
potentials in the upper half of Euclidean space $\mR^{m+1}$ was recently
constructed, including a higher dimensional analogue of the logarithmic
function in the complex plane. In this construction the distributional limits
of these potentials at the boundary $\mR^{m}$ are crucial. The remarkable
relationship between these distributional boundary values and four basic
pseudodifferential operators linked with the Dirac and Laplace operators is
studied.


  In the paper [G.Pantsulaia, On Uniformly Distributed Sequences on [-1/2,1/2],
Georg. Inter. J. Sci. Tech.,4(3) (2013), 21--27], it was shown that
$\mu$-almost every element of $\mathbf{R}^{\infty}$ is uniformly distributed in
$[-\frac{1}{2}, \frac{1}{2}]$, where $\mu$ denotes Yamasaki-Kharazishvili
measure in $\mathbf{R}^{\infty}$ for which
$\mu([-\frac{1}{2},\frac{1}{2}]^{\infty})=1$. In the present paper the same set
is studying from the point of view of shyness and it is demonstrated that it is
shy in $\mathbf{R}^{\infty}$. In Solovay model, the set of all real valued
sequences uniformly distributed module 1 in $[-\frac{1}{2}, \frac{1}{2}]$ is
studied from the point of view of shyness and it is shown that it is the
prevalent set in $\mathbf{R}^{\infty}$.


  The near-horizon metric for a black brane in Anti-de Sitter (AdS) space and
the metric near the AdS boundary both exhibit hydrodynamic behavior. We
demonstrate the equivalence of this pair of hydrodynamic systems for the sound
mode of a conformal theory. This is first established for Einstein's gravity,
but we then show how the sound damping constant will be modified, from its
Einstein form, for a generalized theory. The modified damping constant is
expressible as the ratio of a pair of gravitational couplings that are
indicative of the sound-channel class of gravitons. This ratio of couplings
differs from both that of the shear diffusion coefficient and the shear
viscosity to entropy ratio. Our analysis is mostly limited to conformal
theories but suggestions are made as to how this restriction might eventually
be lifted.


  The temperature dependence of the magnetic susceptibility, \chi (T), is
investigated for one-dimensional interacting electron systems at
quarter-filling within the Kadanoff-Wilson renormalization-group method.
  The forward scattering on the same branch (the g_4-process) is examined
together with the backward (g_1) and forward (g_2) scattering amplitudes on
opposite branches.
  In connection with lattice models, we show that \chi (T) is strongly enhanced
by the nearest-neighbor interaction, an enhancement that surpasses one of the
next-nearest-neighbor interaction.
  A connection between our predictions for \chi (T) and experimental results
for \chi (T) in quasi-one-dimensional organic conductors is presented.


  We investigate two complementary problems related to maintaining the relative
positions of N random walks on the line: (i) the leader problem, that is, the
probability {\cal L}_N(t) that the leftmost particle remains the leftmost as a
function of time and (ii) the laggard problem, the probability {\cal R}_N(t)
that the rightmost particle never becomes the leftmost. We map these ordering
problems onto an equivalent (N-1)-dimensional electrostatic problem. From this
construction we obtain a very accurate estimate for {\cal L}_N(t) for N=4, the
first case that is not exactly soluble: {\cal L}_4(t) ~ t^{-\beta_4}, with
\beta_4=0.91342(8). The probability of being the laggard also decays
algebraically, {\cal R}_N(t) ~ t^{-\gamma_N}; we derive \gamma_2=1/2,
\gamma_3=3/8, and argue that \gamma_N--> ln N/N$ as N-->oo.


  In the present article, we attempt to devise a typology of forms of part-time
employment by applying a widely used neuronal methodology called Kohonen maps.
Starting out with data that we describe using category-specific variables, we
show how it is possible to represent observations and the modalities of the
variables that define them simultaneously, on a single map. This allows us to
ascertain, and to try to describe, the main categories of part-time employment.


  Let $\gamma(G)$ and $\beta(G)$ denote the domination number and the covering
number of a graph $G$, respectively. A connected non-trivial graph $G$ is said
to be $\gamma\beta$-{perfect} if $\gamma(H)=\beta(H)$ for every non-trivial
induced connected subgraph $H$ of $G$. In this note we present an elementary
proof of a characterization of the $\gamma\beta$-perfect graphs.


  We examine the influence of crystal growth on the spin-pumping induced
inverse spin Hall effect in Fe/Pt bilayers. The morphology of the Fe/Pt
interface influences the effective spin mixing conductance. The increase of
growth temperature leads to smoother and larger grains at the interface that
enhance the effective spin mixing conductance. The spin current injection
efficiency into Pt, measured by the inverse spin Hall effect, is maximized by
optimizing the epitaxy of Pt on Fe. In magnetic field dependent measurements,
the presence of a strong magnetic anisotropy gives rise to two distinct inverse
spin Hall effect voltage peaks.


  In this note we develop and clarify some of the basic combinatorial
properties of the new notion of $n$-dependence (for $1\leq n < \omega$)
recently introduced by Shelah. In the same way as dependence of a theory means
its inability to encode a bipartite random graph with a definable edge
relation, $n$-dependence corresponds to the inability to encode a random
$(n+1)$-partite $(n+1)$-hypergraph with a definable edge relation. Most
importantly, we characterize $n$-dependence by counting $\varphi$-types over
finite sets (generalizing Sauer-Shelah lemma and answering a question of
Shelah) and in terms of the collapse of random ordered $(n+1)$-hypergraph
indiscernibles down to order-indiscernibles (which implies that the failure of
$n$-dependence is always witnessed by a formula in a single free variable).


  We present a concise introduction to a new spinwave expansion scheme for
magnetically ordered Kondo lattice models. This is motivated by consideration
of the ferromagnetically ordered phase of the "double exchange" system
La(1-x)Ca(x)MnO3. A brief overview is given of the consequences of quantum and
thermal fluctuation effects for the magnetic properties of the double exchange
ferromagnet.


  The settling efficiency, and stability with respect to settling, of a dilute
suspension of infinite circular cylinders in a quiescent viscoplastic fluid is
examined by means of direct numerical simulations with varying solid volume
fraction, $\phi$, and yield number, $Y$ . For $Y$ sufficiently large we find
higher settling efficiency for increasing $\phi$, similar to what is found in
shear-thinning fluids and opposite to what is found in Newtonian fluids. The
critical yield number at which the suspension is held stationary in the carrier
fluid is found to increase monotonically with $\phi$, while the transition to
settling is found to be diffuse: in the same suspension, particle clusters may
settle while more isolated particles remain arrested. In this regime, complex
flow features are observed in the sedimenting suspension, including the
mobilization of lone particles by nearby sedimentation clusters. Understanding
this regime, and the transition to a fully arrested state, is relevant to many
industrial and natural problems involving the sedimentation of viscoplastic
suspensions under quiescent flow conditions.


  A thermal gradient-induced circular motion of particles placed on
ferroelectric nematic liquid crystal sessile drops is demonstrated and
explained. Unlike hurricanes and tornadoes that are the prime examples for
thermal motors and where turbulent flows are apparent, here the texture without
tracer particles appears completely steady indicating laminar flow. We provide
a simple model showing that the tangential arrangement of the ferroelectric
polarization combined with the vertical thermal gradient and the
pyroelectricity of the fluid drives the rotation of the tracer particles that
become electrically charged in the fluid. These observations provide a
fascinating example of the unique nature of fluid ferroelectric liquid
crystals.


  We prove, by a direct dimensional reduction and an explicit construction of
the group manifold, that the nonlinear sigma model of the dimensionally reduced
three-dimensional A = R magical supergravity is F4(+4)/(USp(6)xSU(2)). This
serves as a basis for the solution generating technique in this supergravity as
well as allows to give the Lie algebraic characterizations to some of the
parameters and functions in the original D = 5 Lagrangian. Generalizations to
other magical supergravities are also discussed.


  We have investigated photoionization of Ne$^+$ in the combined field of a
short infra-red laser pulse and a delayed ultra-short pulse of the infra-red
laser's 23$^r$$^d$ harmonic. We observe an ionization yield compatible with a
picture in which one electron gets excited into Rydberg states by the harmonic
laser field and is subsequently removed by the infra-red laser field.
Modulations are seen in the ionization yield as a function of time delay. These
modulations originate from the trapping of population in low members of the
Rydberg series with different states being populated at different ranges of
delay times. The calculations further demonstrate that single-threshold
calculations cannot reproduce the Ne$^+$ photoionization yields obtained in
multi-threshold calculations.


  In the context of high-frequency quasi-periodic oscillation (HF QPOs) we
further explore the appearance of an observable signal generated by hot spots
moving along quasi-elliptic trajectories close to the innermost stable circular
orbit in the Schwarzschild spacetime. The aim of our investigation is to reveal
whether observable characteristics of the Fourier power-spectral density can
help us to distinguish between the two competing models, namely, the idea of
bright spots orbiting on the surface of an accretion torus versus the scenario
of intrinsic oscillations of the torus itself. We take the capabilities of the
present observatories (represented by the Rossi X-ray Timing Explorer, RXTE)
into account, and we also consider the proposed future instruments (represented
here by the Large Observatory for X-ray Timing, LOFT).


  Generative Adversarial Networks (GANs) became very popular for generation of
realistically looking images. In this paper, we propose to use GANs to
synthesize artificial financial data for research and benchmarking purposes. We
test this approach on three American Express datasets, and show that properly
trained GANs can replicate these datasets with high fidelity. For our
experiments, we define a novel type of GAN, and suggest methods for data
preprocessing that allow good training and testing performance of GANs. We also
discuss methods for evaluating the quality of generated data, and their
comparison with the original real data.


  The effective potential at finite temperature is constructed within the
minimal standard model when a real Higgs singlet is added on. We find that a
region of parameter space exists for which one can find a first order
transition strong enough to prevent the erasure due to sphalerons of baryon
asymmetry, while keeping the mass of the smallest Higgs boson above the
experimental lower bound of about 60 GeV.


  We describe the procedure, nuances, issues, and choices involved in creating
times-of-arrival (TOAs), residuals and error bars from a set of radio pulsar
timing data. We discuss the issue of mis-matched templates, the problem that
wide- bandwidth backends introduce, possible solutions to that problem, and
correcting for offsets introduced by various observing systems.


  Characterizing the shared memberships of individuals in a classification
scheme poses severe interpretability issues, even when using a moderate number
of classes (say 4). Mixed membership models quantify this phenomenon, but they
typically focus on goodness-of-fit more than on interpretable inference. To
achieve a good numerical fit, these models may in fact require many extreme
profiles, making the results difficult to interpret. We introduce a new class
of multivariate mixed membership models that, when variables can be partitioned
into subject-matter based domains, can provide a good fit to the data using
fewer profiles than standard formulations. The proposed model explicitly
accounts for the blocks of variables corresponding to the distinct domains
along with a cross-domain correlation structure, which provides new information
about shared membership of individuals in a complex classification scheme. We
specify a multivariate logistic normal distribution for the membership vectors,
which allows easy introduction of auxiliary information leveraging a latent
multivariate logistic regression. A Bayesian approach to inference, relying on
P\'olya gamma data augmentation, facilitates efficient posterior computation
via Markov Chain Monte Carlo. We apply this methodology to a spatially explicit
study of malaria risk over time on the Brazilian Amazon frontier.


  We study (approximate) null-controllability of parabolic equations in
$L_p(\mathbb{R}^d)$ and provide explicit bounds on the control cost. In
particular we consider systems of the form $\dot{x}(t) = -A_p x(t) +
\mathbf{1}_E u(t)$, $x(0) = x_0\in L_p (\mathbb{R}^d)$, with interior control
on a so-called thick set $E \subset \mathbb{R}^d$, where $p\in [1,\infty)$, and
where $A$ is an elliptic operator of order $m \in \mathbb{N}$ in
$L_p(\mathbb{R}^d)$. We prove null-controllability of this system via duality
and a sufficient condition for observability. This condition is given by an
uncertainty principle and a dissipation estimate. Our result unifies and
generalizes earlier results obtained in the context of Hilbert and Banach
spaces. In particular, our result applies to the case $p=1$.


  In modern autonomy stacks, prediction modules are paramount to planning
motions in the presence of other mobile agents. However, failures in prediction
modules can mislead the downstream planner into making unsafe decisions.
Indeed, the high uncertainty inherent to the task of trajectory forecasting
ensures that such mispredictions occur frequently. Motivated by the need to
improve safety of autonomous vehicles without compromising on their
performance, we develop a probabilistic run-time monitor that detects when a
"harmful" prediction failure occurs, i.e., a task-relevant failure detector. We
achieve this by propagating trajectory prediction errors to the planning cost
to reason about their impact on the AV. Furthermore, our detector comes
equipped with performance measures on the false-positive and the false-negative
rate and allows for data-free calibration. In our experiments we compared our
detector with various others and found that our detector has the highest area
under the receiver operator characteristic curve.


  We study the impact of LHC forward-backward asymmetry (AFB) measurements at
high invariant-mass in the Drell-Yan process on probes of semileptonic
four-fermion operators in the Standard Model effective field theory (SMEFT). In
particular, we study whether AFB measurements can resolve degeneracies in the
Wilson coefficient parameter space that appear when considering invariant-mass
and rapidity measurements alone. We perform detailed fits of the available
high-energy and high-luminosity ATLAS and CMS data for both invariant-mass
distributions and AFB. While each type of measurement separately exhibits
degeneracies, combining them removes these blind spots in some cases. In other
situations it does not, highlighting the importance of incorporating future
datasets from other experiments to fully explore this sector of the SMEFT. We
investigate the impact of contributions quadratic in the Wilson coefficients on
the description of Drell-Yan data and discuss when such terms are important in
joint fits of the AFB and invariant-mass data.


  We discuss formulation of Wilson polygon - MHV amplitude duality at the
perturbative level in various regularizations. For four gluons it is shown that
at one loop one can formulate diagrammatic correspondence interpolating between
the dimensional regularization and the off-shell one. We suggest new
interpretation of all types of box diagrams in terms of the dual simplex in
dimensional regularization and describe its degeneration to the Wilson polygon.
The interesting nullification phenomena for the low-energy amplitudes in the
Higgsed phase has been found.


  In this paper, we have solved a simple specific model of the five-body
problem in the framework of the Yakubovsky equations, restricted to the
configurations of the alpha-nucleon types only, to investigate the effective
interaction between an inert alpha-particle and a neutron. In general case, the
Yakubovsky scheme for the solution of the five-body system leads to a set of
four coupled equations related to four independent configurations, which can be
restricted to two coupled ones, to describe the effective alpha-nucleon
structure model, namely an inert four-body alpha-core and a nucleon. Hence, in
such a model, the other configurations will not be taken into account. To
calculate the binding energies of the five-body system in the model of alpha-
nucleon structure, the two coupled equations are represented in the momentum
space on the basis of the Jacobi momenta. After an explicit evaluation of the
two coupled integral equations in a partial-wave analysis, the obtained
equations are the starting point for a numerical calculation as an eigenvalue
equation form, using typical iteration method. In the first step to the
calculations, i.e. applying some spin-independent potential models, some
obtained binding energy differences between the four-body as an alpha-particle
and the five-body as an alpha-nucleon systems suggest that a simple effective
interaction between an inert alpha-particle and a nucleon is attractive and of
about 13 MeV. In addition, the represented binding energy results with respect
to the regarded spin-independent potentials are in fair agreement with the
obtained results from other methods.


  In the present work, a machine learning based constitutive model for
electro-mechanically coupled material behavior at finite deformations is
proposed. Using different sets of invariants as inputs, an internal energy
density is formulated as a convex neural network. In this way, the model
fulfills the polyconvexity condition which ensures material stability, as well
as thermodynamic consistency, objectivity, material symmetry, and growth
conditions. Depending on the considered invariants, this physics-augmented
machine learning model can either be applied for compressible or nearly
incompressible material behavior, as well as for arbitrary material symmetry
classes. The applicability and versatility of the approach is demonstrated by
calibrating it on transversely isotropic data generated with an analytical
potential, as well as for the effective constitutive modeling of an
analytically homogenized, transversely isotropic rank-one laminate composite
and a numerically homogenized cubic metamaterial. These examinations show the
excellent generalization properties that physics-augmented neural networks
offer also for multi-physical material modeling such as nonlinear
electro-elasticity.