  Experiments at the LHC may yet discover a dijet resonance indicative of
Beyond the Standard Model (BSM) physics. In this case, the question becomes:
what BSM theories are consistent with the unexpected resonance? One possibility
would be a spin-2 object called the colorphilic graviton--a spin-2
color-singlet particle which couples exclusively to the quark and gluon
stress-energy tensors. We assess the possibility of this state's discovery in
the dijet channel as an s-channel resonance, and report the regions of
parameter space where colorphilic gravitons have not yet been excluded by
LHC-13 data but still may be discovered in the dijet channel at LHC-14 for
integrated luminosities of 0.3, 1, and 3 ab$^{-1}$. We then delineate which of
those regions remain accessible to future collider searches, once one accounts
for applicability of the narrow-width approximation, detector mass resolution,
and self-consistency according to tree-level partial-wave unitarity. We
discover that--despite the strong constraints unitarity imposes on collider
searches--the colorphilic graviton remains potentially discoverable in the LHC
dijet channel. A means of investigation would be to apply the color
discriminant variable (CDV), a dimensionless combination of quantities
(cross-section, decay width, and invariant mass) that can be quickly measured
after the discovery of a dijet resonance. Previous publications have
demonstrated the CDV's utility when applied to theories containing Z',
colorons, excited quarks, and diquarks. We extend this analysis to the
colorphilic graviton by applying the CDV to the appropriate region of parameter
space. We conclude that resolvable, discoverable dijet resonances consistent
with colorphilic gravitons span a narrower range of masses than those
consistent with leptophobic Z' models, and can be distinguished from those
originating from coloron, excited quark, and diquark models.


  In recent years, bankruptcy forecasting has gained lot of attention from
researchers as well as practitioners in the field of financial risk management.
For bankruptcy prediction, various approaches proposed in the past and
currently in practice relies on accounting ratios and using statistical
modeling or machine learning methods. These models have had varying degrees of
successes. Models such as Linear Discriminant Analysis or Artificial Neural
Network employ discriminative classification techniques. They lack explicit
provision to include prior expert knowledge. In this paper, we propose another
route of generative modeling using Expert Bayesian framework. The biggest
advantage of the proposed framework is an explicit inclusion of expert judgment
in the modeling process. Also the proposed methodology provides a way to
quantify uncertainty in prediction. As a result the model built using Bayesian
framework is highly flexible, interpretable and intuitive in nature. The
proposed approach is well suited for highly regulated or safety critical
applications such as in finance or in medical diagnosis. In such cases accuracy
in the prediction is not the only concern for decision makers. Decision makers
and other stakeholders are also interested in uncertainty in the prediction as
well as interpretability of the model. We empirically demonstrate these
benefits of proposed framework on real world dataset using Stan, a
probabilistic programming language. We found that the proposed model is either
comparable or superior to the other existing methods. Also resulting model has
much less False Positive Rate compared to many existing state of the art
methods. The corresponding R code for the experiments is available at Github
repository.


  We consider first-passage percolation on the edges of $\mathbb{Z}^2 \times
\{1, \cdots, k\},$ namely the slab $\mathbb{S}_k$ of width $k$. Each edge is
assigned independently a passage time of either 0 (with probability
$p_c(\mathbb{S}_k)$) or 1 ( with probability $1-p_c(\mathbb{S}_k)$) where $p_c$
is the critical probability for Bernouilli percolation. We prove central limit
theorems for point-to-point and point-to-line passage times. These generalize
the results of Kesten and Zhang \cite{kestenzhang} to non-planar graphs.


  In this paper, we investigate tropical secant varieties of ordinary linear
spaces. These correspond to the log-limit sets of ordinary toric varieties; we
show that their interesting parts are combinatorially isomorphic to a certain
natural subcomplex of the complex of regular subdivisions of a corresponding
point set, and we display the range of behavior of this object. We also use
this characterization to reformulate the question of determining Barvinok rank
into a question regarding regular subdivisions of products of simplices.


  In this paper, a dynamic model of reconstruction of the shear force $g(t)$ in
the Atomic Force Microscopy (AFM) cantilever tip-sample interaction is
proposed. The interaction of the cone-shaped cantilever tip with the surface of
the specimen (sample) is modeled by the damped Euler-Bernoulli beam equation
$\rho_A(x)u_{tt}$ $+\mu(x)u_{t}+(r(x)u_{xx}+\kappa(x)u_{xxt})_{xx}=0$,
$(x,t)\in (0,\ell)\times (0,T)$, subject to the following initial, $u(x,0)=0$,
$u_t(x,0)=0$ and boundary, $u(0,t)=0$, $u_{x}(0,t)=0$, $\left
(r(x)u_{xx}(x,t)+\kappa(x)u_{xxt} \right )_{x=\ell}=M(t)$, $\left
(-(r(x)u_{xx}+\kappa(x)u_{xxt})_x\right )_{x=\ell}=g(t)$ conditions, where
$M(t):=2h\cos \theta\,g(t)/\pi$ is the momentum generated by the transverse
shear force $g(t)$. For the reconstruction of $g(t)$ the measured displacement
$\nu(t):=u(\ell,t)$ is used as an additional data. The least square functional
$J(F)=\frac{1}{2}\Vert u(\ell,\cdot)-\nu \Vert_{L^2(0,T)}^2$ is introduced and
an explicit gradient formula for the Fr\'echet derivative through the solution
of the adjoint problem is derived. This allows to construct a gradient based
numerical algorithm for the reconstructions of the shear force from noise free
as well as from random noisy measured output $\nu (t)$. Computational
experiments show that the proposed algorithm is very fast and robust. This
allows to develop a numerical "gadget" for computational experiments of generic
AFMs.


  Current pre-training methods in computer vision focus on natural images in
the daily-life context. However, abstract diagrams such as icons and symbols
are common and important in the real world. This work is inspired by Tangram, a
game that requires replicating an abstract pattern from seven dissected shapes.
By recording human experience in solving tangram puzzles, we present the
Tangram dataset and show that a pre-trained neural model on the Tangram helps
solve some mini visual tasks based on low-resolution vision. Extensive
experiments demonstrate that our proposed method generates intelligent
solutions for aesthetic tasks such as folding clothes and evaluating room
layouts. The pre-trained feature extractor can facilitate the convergence of
few-shot learning tasks on human handwriting and improve the accuracy in
identifying icons by their contours. The Tangram dataset is available at
https://github.com/yizhouzhao/Tangram.


  Drawing insights from the triumph of relativistic over classical mechanics
when velocities approach the speed of light, we explore a similar improvement
to the seminal Black-Scholes (Black and Scholes (1973)) option pricing formula
by considering a relativist version of it, and then finding a respective
solution. We show that our solution offers a significant improvement over
competing solutions (e.g., Romero and Zubieta-Martinez (2016)), and obtain a
new closed-form option pricing formula, containing the speed limit of
information transfer c as a new parameter. The new formula is rigorously shown
to converge to the Black-Scholes formula as c goes to infinity. When c is
finite, the new formula can flatten the standard volatility smile which is more
consistent with empirical observations. In addition, an alternative family of
distributions for stock prices arises from our new formula, which offer a
better fit, are shown to converge to lognormal, and help to better explain the
volatility skew.


  Recent approaches to goal recognition have leveraged planning landmarks to
achieve high-accuracy with low runtime cost. These approaches, however, lack a
probabilistic interpretation. Furthermore, while most probabilistic models to
goal recognition assume that the recognizer has access to a prior probability
representing, for example, an agent's preferences, virtually no goal
recognition approach actually uses the prior in practice, simply assuming a
uniform prior. In this paper, we provide a model to both extend landmark-based
goal recognition with a probabilistic interpretation and allow the estimation
of such prior probability and its usage to compute posterior probabilities
after repeated interactions of observed agents. We empirically show that our
model can not only recognize goals effectively but also successfully infer the
correct prior probability distribution representing an agent's preferences.


  Quantum machine learning has the potential to computationally outperform
classical machine learning, but it is not yet clear whether it will actually be
valuable for practical problems. While some artificial scenarios have shown
that certain quantum machine learning techniques may be advantageous compared
to their classical counterpart, it is unlikely that quantum machine learning
will outclass traditional methods on popular classical datasets such as MNIST.
In contrast, dealing with quantum data, such as quantum states or circuits, may
be the task where we can benefit from quantum methods. Therefore, it is
important to develop practically meaningful quantum datasets for which we
expect quantum methods to be superior. In this paper, we propose a machine
learning task that is likely to soon arise in the real world: clustering and
classification of quantum circuits. We provide a dataset of quantum circuits
optimized by the variational quantum eigensolver. We utilized six common types
of Hamiltonians in condensed matter physics, with a range of 4 to 16 qubits,
and applied ten different ans\"{a}tze with varying depths (ranging from 3 to
32) to generate a quantum circuit dataset of six distinct classes, each
containing 300 samples. We show that this dataset can be easily learned using
quantum methods. In particular, we demonstrate a successful classification of
our dataset using real 4-qubit devices available through IBMQ. By providing a
setting and an elementary dataset where quantum machine learning is expected to
be beneficial, we hope to encourage and ease the advancement of the field.


  The impact of weak disorder and its spatial correlation on the topology of a
Floquet system is not well understood so far. In this study, we investigate a
model closely related to a two-dimensional Floquet system that has been
realized in experiments. In the absence of disorder, we determine the phase
diagram and identify a new phase characterized by edge states with alternating
chirality in adjacent gaps. When weak disorder is introduced, we examine the
disorder-averaged Bott index and analyze why the anomalous Floquet topological
insulator is favored by both uncorrelated and correlated disorder, with the
latter having a stronger effect. For a system with a ring-shaped gap, the Born
approximation fails to explain the topological phase transition, unlike for a
system with a point-like gap.


  This thesis focuses on a variety of active research topics, such as nuclear
matter, neutron stars, and phase transition within the framework of the RMF
model. We use the previously successful effective field theory-driven
Relativistic Mean Field (RMF) and density-dependent RMF (DD-RMF)formalisms for
analyzing hadron matter to examine the infinite nuclear matter and neutron
stars. The presence of exotic phases such as quarks has been investigated using
the MIT Bag model and its variants, such as the vBag model, at various bag
constants. The other exotic phases, such as hyperons, have also been studied
under the influence of a strong magnetic field.


  With a view toward the problem of computing the linearized cosmological
perturbations in Randall-Sundrum cosmological models where a Z2 symmetry has
been imposed about a boundary brane, we derive the form of the linearized
Israel matching conditions and the auxiliary gauge conditions on the boundary
when Lorentz gauge has been imposed in the bulk. This gauge is completely
covariant and local, manifestly respecting all the AdS5 symmetries in the bulk
and not relying on a decomposition into pure scalar, vector, and tensor
sectors, which is necessarily nonlocal. We demonstrate that the auxiliary gauge
conditions on the boundary ensure that bulk gravitons upon reflection off the
brane do not emit polarizations that violate the bulk Lorentz gauge condition.
We also characterize the residual gauge freedom, embodied by five longitudinal
(pure gauge) graviton polarizations in the bulk, four of which correspond to
reparameterizations of the induced brane metric and one of which corresponds to
normal displacements of the brane.


  In this article we develop a method of finding the static axisymmetric
space-time corresponding to any given set of multipole moments. In addition to
an implicit algebraic form for the general solution, we also give a power
series expression for all finite sets of multipole moments. As conjectured by
Geroch we prove in the special case of axisymmetry, that there is a static
space-time for any given set of multipole moments subject to a (specified)
convergence criterion. We also use this method to confirm a conjecture of
Hernandez-Pastora and Martin concerning the monopole-quadropole solution.


  In this paper, we review some of our ARPES results on the superconducting and
pseudo gaps in Bi2Sr2CaCu2O8+x. We find that optimally and overdoped samples
exhibit a d-wave gap, which closes at the same temperature, Tc, for all k
points. In underdoped samples, a leading edge gap is found up to a temperature
T* > Tc. We find that T* scales with the maximum low temperature gap,
increasing as the doping is reduced. The momentum dependence of the pseudogap
is similar to that of the superconducting gap; however, the pseudogap closes at
different temperatures for different k points.


  This paper mainly investigates why small-world networks are navigable and how
to navigate small-world networks. We find that the navigability can naturally
emerge from self-organization in the absence of prior knowledge about
underlying reference frames of networks. Through a process of information
exchange and accumulation on networks, a hidden metric space for navigation on
networks is constructed. Navigation based on distances between vertices in the
hidden metric space can efficiently deliver messages on small-world networks,
in which long range connections play an important role. Numerical simulations
further suggest that high cluster coefficient and low diameter are both
necessary for navigability. These interesting results provide profound insights
into scalable routing on the Internet due to its distributed and localized
requirements.


  We investigate the effects of phase-breaking events on electronic transport
through ballistic chaotic cavities. We simulate phase-breaking by a fictitious
lead connecting the cavity to a phase-randomizing reservoir and introduce a
statistical description for the total scattering matrix, including the
additional lead. For strong phase-breaking, the average and variance of the
conductance are calculated analytically. Combining these results with those in
the absence of phase-breaking, we propose an interpolation formula, show that
it is an excellent description of random-matrix numerical calculations, and
obtain good agreement with several recent experiments.


  The recently introduced Thermodynamic Binding Networks (TBN) model was
developed with the purpose of studying self-assembling systems by focusing on
their thermodynamically favorable final states, and ignoring the kinetic
pathways through which they evolve. The model was intentionally developed to
abstract away not only the notion of time, but also the constraints of
geometry. Collections of monomers with binding domains which allow them to form
polymers via complementary bonds are analyzed to determine their final, stable
configurations, which are those which maximize the number of bonds formed (i.e.
enthalpy) and the number of independent components (i.e. entropy). In this
paper, we first develop a definition of what it means for a TBN to perform a
computation, and then present a set of constructions which are capable of
performing computations by simulating the behaviors of space-bounded Turing
machines and boolean circuits. In contrast to previous TBN results, these
constructions are robust to great variability in the counts of monomers
existing in the systems and the numbers of polymers that form in parallel.
Although the Turing machine simulating TBNs are inefficient in terms of the
numbers of unique monomer types required, as compared to algorithmic
self-assembling systems in the abstract Tile Assembly Model (aTAM), we then
show that a general strategy of porting those aTAM system designs to TBNs
produces TBNs which incorrectly simulate computations. Finally, we present a
refinement of the TBN model which we call the Geometric Thermodynamic Binding
Networks (GTBN) model in which monomers are defined with rigid geometries and
form rigid bonds. Utilizing the constraints imposed by geometry, we then
provide a GTBN construction capable of simulating Turing machines as
efficiently as in the aTAM.


  The purely numerical evaluation of multi-loop integrals and amplitudes can be
a viable alternative to analytic approaches, in particular in the presence of
several mass scales, provided sufficient accuracy can be achieved in an
acceptable amount of time. For many multi-loop integrals, the fraction of time
required to perform the numerical integration is significant and it is
therefore beneficial to have efficient and well-implemented numerical
integration methods. With this goal in mind, we present a new stand-alone
integrator based on the use of (quasi-Monte Carlo) rank-1 shifted lattice
rules. For integrals with high variance we also implement a variance reduction
algorithm based on fitting a smooth function to the inverse cumulative
distribution function of the integrand dimension-by-dimension. Additionally,
the new integrator is interfaced to pySecDec to allow the straightforward
evaluation of multi-loop integrals and dimensionally regulated parameter
integrals. In order to make use of recent advances in parallel computing
hardware, our integrator can be used both on CPUs and CUDA compatible GPUs
where available.


  The key polynomials, the Demazure atoms, the Schubert polynomials, and even
the Schur functions can be defined using divided difference operator. In 2000,
Hivert introduced a quasisymmetric analog of the divided difference operator.
In particular, replacing it in a natural way in the definition of the Schur
functions gives Gessel's fundamental basis. This paper is our attempt to apply
the same methods to define the remaining bases and study the results. In
particular, we show both the key polynomials and Demazure atoms have natural
analogs using Hivert's operator and that the resulting bases occur
independently and defined by other means in the work of Assaf and Searles, as
the fundemental slide polynomials and the fundamental particle basis
respectively. We further explore properties of these two bases, including
giving the structure constants for the fundamental particle basis.


  We derive Gamow vectors from S-matrix poles of higher multiplicity in analogy
to the Gamow vectors describing resonances from first-order poles. With these
vectors we construct a density operator that describes resonances associated
with higher order poles that obey an exponential decay law. It turns out that
this operator formed by these higher order Gamow vectors has a unique
structure.


  Critical systems must be designed resilient to all kinds of malfunctions. We
are especially interested by the loss of control authority over actuators. This
malfunction considers actuators producing uncontrolled and possibly undesirable
inputs. We investigate the design of resilient linear systems capable of
reaching their target even after such a malfunction. In contrast with the
settings of robust control and fault-tolerant control, we consider undesirable
but observable inputs of the same magnitude as controls since they are produced
by a faulty actuator of the system. The control inputs can then depend on these
undesirable inputs. Building on our previous work, we focus on designing
resilient systems able to withstand the loss of one or multiple actuators.
Since resilience refers to the existence of a control law driving the state to
the target, we naturally continue with the synthesis of such a control law. We
conclude with a numerical application of our theory on the ADMIRE fighter jet
model.


  Reliable indirect diagnostics of LyC photon escape from galaxies are required
to understand which sources were the dominant contributors to reionization.
While multiple LyC escape fraction ($f_{\rm esc}$) indicators have been
proposed to trace favourable conditions for LyC leakage from the interstellar
medium of low-redshift ''analog'' galaxies, it remains unclear whether these
are applicable at high redshifts where LyC emission cannot be directly
observed. Using a library of 14,120 mock spectra of star-forming galaxies with
redshifts $4.64 \leq z \leq 10$ from the SPHINX$^{20}$ cosmological radiation
hydrodynamics simulation, we develop a framework for the physics that leads to
high $f_{\rm esc}$. We investigate LyC leakage from our galaxies based on the
criteria that successful LyC escape diagnostics must i) track a high specific
star formation rate, ii) be sensitive to stellar population age in the range
$3.5-10~$Myr representing the times when supernova first explode to when LyC
production significantly drops, and iii) include a proxy for neutral gas
content and gas density in the interstellar medium. ${\rm O}_{32}$,
$\Sigma_{\rm SFR}$, M$_{\rm UV}$, and H$\beta$ equivalent width select for one
or fewer of our criteria, rendering them either necessary but insufficient or
generally poor diagnostics. In contrast, UV slope ($\beta$), and ${\rm E(B-V)}$
match two or more of our criteria, rendering them good $f_{\rm esc}$
diagnostics (albeit with significant scatter). Using our library, we build a
quantitative model for predicting $f_{\rm esc}$ based on direct observables.
When applied to bright $z > 6$ Ly$\alpha$ emitters observed with JWST, we find
that the majority of them have $f_{\rm esc} \lesssim 10\%$.


  Cooling the qubit into a pure initial state is crucial for realizing
fault-tolerant quantum information processing. Here we envisage a star-topology
arrangement of reset and computation qubits for this purpose. The reset qubits
cool or purify the computation qubit by transferring its entropy to a heat-bath
with the help of a heat-bath algorithmic cooling procedure. By combining
standard NMR methods with powerful quantum control techniques, we cool central
qubits of two large star topology systems, with 13 and 37 spins respectively.
We obtain polarization enhancements by a factor of over 24, and an associated
reduction in the spin temperature from 298 K down to 12 K. Exploiting the
enhanced polarization of computation qubit, we prepare combination-coherences
of orders up to 15. By benchmarking the decay of these coherences we
investigate the underlying noise process. Further, we also cool a pair of
computation qubits and subsequently prepare them in an effective pure-state.


  Light field technology has increasingly attracted the attention of the
research community with its many possible applications. The lenslet array in
commercial plenoptic cameras helps capture both the spatial and angular
information of light rays in a single exposure. While the resulting high
dimensionality of light field data enables its superior capabilities, it also
impedes its extensive adoption. Hence, there is a compelling need for efficient
compression of light field images. Existing solutions are commonly composed of
several separate modules, some of which may not have been designed for the
specific structure and quality of light field data. This increases the
complexity of the codec and results in impractical decoding runtimes. We
propose a new learning-based, disparity-aided model for compression of 4D light
field images capable of parallel decoding. The model is end-to-end trainable,
eliminating the need for hand-tuning separate modules and allowing joint
learning of rate and distortion. The disparity-aided approach ensures the
structural integrity of the reconstructed light fields. Comparisons with the
state of the art show encouraging performance in terms of PSNR and MS-SSIM
metrics. Also, there is a notable gain in the encoding and decoding runtimes.
Source code is available at https://moha23.github.io/LF-DAAE.


  Recently the memristive electrical transport properties in NbO$_2$ have
attracted much attention for their promising application to the neuromorphic
computation. At the center of debates is whether the metal-to-insulator
transition (MIT) originates from the structural distortion (Peierls) or the
electron correlation (Mott). With inputs from experiments and first principles
calculations, we develop a thermodynamical model rooted in the scenario of the
MIT driven by a $2^{nd}$ order Peierls instability. We find that the
temperature dependence of the electrical conductivity can be accurately fit by
the band gap varying with temperature due to the gradual weakening of the Nb-Nb
dimers. The resistivity switching can consequently be understood by dimer-free
metallic domains induced by local Joule heating. In solving the heat equation,
we find that the steady state can not be reached if the applied voltage exceeds
a threshold, resulting in the chaotic behavior observed in the high voltage and
current states. With the Ginzburg-Landau theory and the Joule heating equation,
the evolution of the metallic domains under bias voltage can be simulated and
directly verified by experiments.


  This work presents the results of our analysis of the accuracy of the pion
form factor derived from the local-duality version of QCD sum rules.


  We study initial sequences of various configurations of planar points. We
answer several questions asked in our previous paper (Symbolic powers of planar
point configurations), and we extend our considerations to the asymptotic
setting of Waldschmidt constants. We introduce the concept of Bezout
Decomposition which might be of independent interest.


  We propose a precise definition of multidimensional fluids generated by
self-gravitating extended objects such as strings and membranes: a
p-dimensional perfect fluid is a smooth involutive p-dimensional distribution
on a spacetime, each integral manifold of which is a timelike, connected,
immersed submanifold of dimension, p -- representing the history of a
(p-1)-dimensional extended object. This geometric formulation of perfect fluids
of higher dimensions naturally leads to the associated stress-energy tensor.
Furthermore, the laws of temporal evolution and symmetries of such systems are
derived, in general, from the Einstein field equations and the integrability
conditions. We also present a matter model based on a 2-dimensional involutive
distribution, and it is shown that the stress-energy tensor for
self-gravitating strings gives rise to a non-trivial spherically symmetric
spacetime with a naked singularity.


  In strongly correlated multi-orbital systems, various ordered phases appear.
In particular, the orbital order in iron-based superconductors attracts much
attention since it is considered to be the origin of the nematic state. In
order to clarify the essential condition for realizing orbital orders, we study
simple two-orbital ($d_{xz}$, $d_{yz}$) Hubbard model. We find that the orbital
order, which corresponds to the nematic order, appears due to the vertex
corrections even in the two-orbital model. Thus, $d_{xy}$ orbital is not
essential to realize the nematic orbital order. The obtained orbital order
depends on the orbital dependence and the topology of fermi surfaces. We also
find that another type of orbital order, which is rotated $45^\circ$, appears
in the heavily hole-doped case.


  We calculate the decay of $\tau^-\to\pi^-\gamma\nu_\tau$ in the framework of
Resonance Chiral Theory ($R\chi T$). By demanding the high energy constraints
from QCD on the related form factors, we could predict the various physical
observables of $\tau^-\to\pi^-\gamma\nu_\tau$ without any free parameter. Our
results show that for a realistic cut on the photon energy (around $100$ MeV)
this mode gives a branching ratio of roughly $0.1%$ that should have already
been detected at the heavy-flavour factories. Another interesting subject we
have studied based on our calculation of the decay
$\tau^-\to\pi^-\gamma\nu_\tau$ is the experimental background estimation of the
lepton flavour violation process $\tau^- \to \mu^- \gamma$. We point out that
although the description of radiation that PHOTOS provides -which has been used
by BaBar and Belle collaborations to estimate this source of background- is in
excellent agreement with the theoretical expectations in the low energy region
in $\tau^-\to\pi^-\gamma\nu_\tau$ decay, this is not the case in the high
energy region, precisely where it is easier that this decay mimics the process
$\tau^-\to\mu^-\gamma$.


  Calculating and categorizing the similarity of curves is a fundamental
problem which has generated much recent interest. However, to date there are no
implementations of these algorithms for curves on surfaces with provable
guarantees on the quality of the measure. In this paper, we present a
similarity measure for any two cycles that are homologous, where we calculate
the minimum area of any homology (or connected bounding chain) between the two
cycles. The minimum area homology exists for broader classes of cycles than
previous measures which are based on homotopy. It is also much easier to
compute than previously defined measures, yielding an efficient implementation
that is based on linear algebra tools. We demonstrate our algorithm on a range
of inputs, showing examples which highlight the feasibility of this similarity
measure.


  The HH 111 protostellar system consists of two Class I sources (VLA 1 and 2)
with putative disks deeply embedded in a flattened envelope at a distance of
400 pc. Here is a follow-up study of this system in C18O (J=2-1), SO (N_J =
5_6-4_5), and 1.33 mm continuum at ~ 1" (400 AU) resolution, and it may show
for the first time how a rotationally supported disk can be formed inside an
infalling envelope. The 1.33 mm continuum emission is seen arisen from both
sources, likely tracing the dusty putative disks around them. In particular,
the emission around the VLA 1 source is elongated in the equatorial plane with
a radius of ~ 300 AU. The envelope is well seen in C18O, extending to ~ 7000 AU
out from the VLA 1 source, with the innermost part overlapping with the dusty
disk. It has a differential rotation, with the outer part (~ 2000-7000 AU)
better described by a rotation that has constant specific angular momentum and
the inner part (~ 60-2000 AU) by a Keplerian rotation. The envelope seems to
also have some infall motion that is smaller than the rotation motion. Thus,
the material in the outer part of the envelope seems to be slowly spiraling
inward with its angular momentum and the rotation can indeed become Keplerian
in the inner part. A compact SO emission is seen around the VLA 1 source with a
radius of ~ 400 AU and it may trace a shock such as an (inner) accretion shock
around the disk.


  The Diffusion Monte Carlo method is devoted to the computation of electronic
ground-state energies of molecules. In this paper, we focus on implementations
of this method which consist in exploring the configuration space with a {\bf
fixed} number of random walkers evolving according to a Stochastic Differential
Equation discretized in time. We allow stochastic reconfigurations of the
walkers to reduce the discrepancy between the weights that they carry. On a
simple one-dimensional example, we prove the convergence of the method for a
fixed number of reconfigurations when the number of walkers tends to $+\infty$
while the timestep tends to 0. We confirm our theoretical rates of convergence
by numerical experiments. Various resampling algorithms are investigated, both
theoretically and numerically


  A new iron-based superconductor, Lix(C6H16N2)yFe2-zSe2, with Tc = 38 K has
successfully been synthesized via the intercalation of lithium and
hexamethylenediamine into FeSe. The superconducting transition has been
confirmed not only by magnetic susceptibility measurements but also by
electrical resistivity ones. The interlayer spacing, namely, the dicstance
between neighboring Fe layers, d, is 16.225(5) $\mathring{\text{A}}$, which is
the largest among those of FeSe-based intercalation compounds. It has been
found that the dependence of Tc on d in FeSe-based intercalation
superconductors appears domic.


  In this paper we present some new results regarding the solvability of
nonlinear Hammerstein integral equations in a special cone of continuous
functions. The proofs are based on a certain fixed point theorem of Leggett and
Williams type. We give an application of the abstract result to prove the
existence of nontrivial solutions of a periodic boundary value problem. We also
investigate, via a version of Krasnosel{\cprime}slki{\u\i}'s theorem for the
sum of two operators, the solvability of perturbed Hammerstein integral
equations in the space of continuous functions of bounded variation in the
sense of Jordan. As an application of these results, we study the solvability
of a boundary value problem subject to integral boundary conditions of
Riemann--Stieltjes type. Some examples are presented in order to illustrate the
obtained results.


  Why microscopic objects exhibit wave properties (are delocalized), but
macroscopic do not (are localized)? Traditional quantum mechanics attributes
wave properties to all objects. When complemented with a deterministic collapse
model (Quantum Stud.: Math. Found. 3, 279 (2016)) quantum mechanics can
dissolve the discrepancy. Collapse in this model means contraction and occurs
when the object gets in touch with other objects and satisfies a certain
criterion. One single collapse usually does not suffice for localization. But
the object rapidly gets in touch with other objects in a short time, leading to
rapid localization. Decoherence is not involved.


  To date, the analysis of high-dimensional, computationally expensive
engineering models remains a difficult challenge in risk and reliability
engineering. We use a combination of dimensionality reduction and surrogate
modelling termed partial least squares-driven polynomial chaos expansion
(PLS-PCE) to render such problems feasible. Standalone surrogate models
typically perform poorly for reliability analysis. Therefore, in a previous
work, we have used PLS-PCEs to reconstruct the intermediate densities of a
sequential importance sampling approach to reliability analysis. Here, we
extend this approach with an active learning procedure that allows for improved
error control at each importance sampling level. To this end, we formulate an
estimate of the combined estimation error for both the subspace identified in
the dimension reduction step and surrogate model constructed therein. With
this, it is possible to adapt the design of experiments so as to optimally
learn the subspace representation and the surrogate model constructed therein.
The approach is gradient-free and thus can be directly applied to black
box-type models. We demonstrate the performance of this approach with a series
of low- (2 dimensions) to high- (869 dimensions) dimensional example problems
featuring a number of well-known caveats for reliability methods besides high
dimensions and expensive computational models: strongly nonlinear limit-state
functions, multiple relevant failure regions and small probabilities of
failure.


  The rise of the World Airline Network over the past century has lead to sharp
changes in our notions of `distance' and `closeness' - both in terms of trade
and travel, but also (less desirably) with respect to the spread of disease.
When novel pathogens are discovered, countries, cities and hospitals are caught
trying to predict how much time they have to prepare. In this paper, by
considering the early stages of epidemic spread as a simple branching process,
we derive the full probability distribution of arrival times. We are able to
re-derive a number of past arrival time results (in suitable limits), and
demonstrate the robustness of our approach, both to parameter values far
outside the traditionally considered regime, and to errors in the parameter
values used. The branching process approach provides some theoretical
justification to the `effective distance' introduced by Brockmann & Helbing
(2013), however we also observe that when compared to real world data, the
predictive power of all methods in this class is significantly lower than has
been previously reported.


  This paper examines five key questions surrounding computer generated art.
Driven by the recent public auction of a work of `AI Art' we selectively
summarise many decades of research and commentary around topics of autonomy,
authenticity, authorship and intention in computer generated art, and use this
research to answer contemporary questions often asked about art made by
computers that concern these topics. We additionally reflect on whether current
techniques in deep learning and Generative Adversarial Networks significantly
change the answers provided by many decades of prior research.


  We continue our study of semi-strict tricategories in which the only weakness
is in vertical composition. We assemble the doubly-degenerate such
tricategories into a 2-category, defining weak functors and transformations. We
exhibit a biadjoint biequivalence between this 2-category and the 2-category of
braided (weakly) monoidal categories, braided (weakly) monoidal functors, and
monoidal transformations.


  Metasurfaces have been rapidly advancing our command over the many degrees of
freedom of light within compact, lightweight devices. However, so far, they
have mostly been limited to manipulating light in free space. Grating couplers
provide the opportunity of bridging far-field optical radiation and in-plane
guided waves, and thus have become fundamental building blocks in photonic
integrated circuits. However, their operation and degree of light control is
much more limited than metasurfaces. Metasurfaces integrated on top of guided
wave photonic systems have been explored to control the scattering of light
off-chip with enhanced functionalities - namely, point-by-point manipulation of
amplitude, phase or polarization. However, these efforts have so far been
limited to controlling one or two optical degrees of freedom at best, and to
device configurations much more complex compared to conventional grating
couplers. Here, we introduce leaky-wave metasurfaces, which are based on
symmetry-broken photonic crystal slabs that support quasi-bound states in the
continuum. This platform has a compact form factor equivalent to the one of
conventional grating couplers, but it provides full command over amplitude,
phase and polarization (four optical degrees of freedom) across large
apertures. We present experimental demonstrations of various functionalities
for operation at wavelengths near 1.55 microns based on leaky-wave
metasurfaces, including devices for phase and amplitude control at a fixed
polarization state, and devices controlling all four optical degrees of
freedom. Our results merge the fields of guided and free-space optics under the
umbrella of metasurfaces, exploiting the hybrid nature of quasi-bound states in
the continuum, for opportunities to advance in disruptive ways imaging,
communications, augmented reality, quantum optics, LIDAR and integrated
photonic systems.


  In this paper, we further investigate the global dynamics of a stochastic
differential equation SIS (Susceptible-Infected-Susceptible) epidemic model
recently proposed in [A. Gray et al., SIAM. J. Appl. Math., 71 (2011),
876-902]. We present a stochastic threshold theorem in term of a
\textit{stochastic basic reproduction number} $R_0^S:$ the disease dies out
with probability one if $R_0^S<1,$ and the disease is recurrent if
$R_0^S\geqslant1.$ We prove the existence and global asymptotic stability of a
unique invariant density for the Fokker-Planck equation associated with the SDE
SIS model when $R_0^S>1.$ In term of the profile of the invariant density, we
define a \textit{persistence basic reproduction number} $R_0^P$ and give a
persistence threshold theorem: the disease dies out with large probability if
$R_0^P\leqslant1,$ while persists with large probability if $R_0^P>1.$
Comparing the \textit{stochastic disease prevalence} with the
\textit{deterministic disease prevalence}, we discover that the stochastic
prevalence is bigger than the deterministic prevalence if the deterministic
basic reproduction number $R_0^D>2.$ This shows that noise may increase
severity of disease. Finally, we study the asymptotic dynamics of the
stochastic SIS model as the noise vanishes and establish a sharp connection
with the threshold dynamics of the deterministic SIS model in term of a
\textit{Limit Stochastic Threshold Theorem}.


  We discuss the bounds on polarized parton distributions which follow from
their definition in terms of cross section asymmetries. We spell out how the
bounds obtained in the naive parton model can be derived within perturbative
QCD at leading order when all quark and gluon distributions are defined in
terms of suitable physical processes. We specify a convenient physical
definition for the polarized and unpolarized gluon distributions in terms of
Higgs production from gluon fusion. We show that these bounds are modified by
subleading corrections, and we determine them up to NLO. We examine the ensuing
phenomenological implications, in particular in view of the determination of
the polarized gluon distribution.


  In this paper, by considering the degenerate two bright soliton solutions of
the nonlocal Manakov system, we bring out three different types of energy
sharing collisions for two different parametric conditions. Among the three,
two of them are new which do not exist in the local Manakov equation. By
performing an asymptotic analysis to the degenerate two-soliton solution, we
explain the changes which occur in the quasi-intensity/quasi-power, phase shift
and relative separation distance during the collision process. Remarkably, the
intensity redistribution reveals that in the new types of shape changing
collisions, the energy difference of soliton in the two modes is not preserved
during collision. In contrast to this, in the other shape changing collision,
the total energy of soliton in the two modes is conserved during collision. In
addition to this, by tuning the imaginary parts of the wave numbers, we observe
localized resonant patterns in both the scenarios. We also demonstrate the
existence of bound states in the CNNLS equation during the collision process
for certain parametric values.


  Goal oriented error estimation and adaptive procedures are essential for the
accurate and efficient evaluation of numerical simulations that involve complex
domains. By locally improving the approximation quality we can solve expensive
problems which could result intractable otherwise. Here, we present an error
estimation technique for enriched finite element approximations that is based
on an equilibrated recovery technique, which considers the stress intensity
factor as the quantity of interest. The locally equilibrated superconvergent
patch recovery is used to obtain enhanced stress fields for the primal and dual
problems defined to evaluate the error estimate.


  By performing numerical simulations of superfluid vortex ring collisions we
make direct quantitative measurements of the sound energy released due to
vortex reconnections. We show that the energy radiated expressed in terms of
the loss of vortex line length is a simple function of the reconnection angle.
In addition, we study the temporal and spatial distribution of the radiation
and show that energy is emitted in the form of a rarefaction pulse. The pulse
evolves into a sound wave with a wavelength of 6-8 healing lengths.


  In this paper, we study irreducible weight modules with infinite dimensional
weight spaces over the mirror-twisted Heisenberg-Virasoro algebra
$\mathcal{D}$. More precisely, the necessary and sufficient conditions for the
tensor products of irreducible highest weight modules and irreducible modules
of intermediates series over $\mathcal{D}$ to be irreducible are determined by
using "shifting technique". This leads to a family of new irreducible weight
modules over $\mathcal{D}$. Then we obtain that any two such tensor products
are isomorphic if and only if the corresponding highest weight modules and
modules of intermediate series are isomorphic respectively. Also we discuss
submodules of the tensor product module when it is not irreducible.


  A recent paper [J. A. Evans, D. Kamensky, Y. Bazilevs, "Variational
multiscale modeling with discretely divergence-free subscales", Computers &
Mathematics with Applications, 80 (2020) 2517-2537] introduced a novel
stabilized finite element method for the incompressible Navier-Stokes
equations, which combined residual-based stabilization of advection, energetic
stability, and satisfaction of a discrete incompressibility condition. However,
the convergence analysis and numerical tests of the cited work were subject to
the restrictive assumption of a divergence-conforming choice of velocity and
pressure spaces, where the pressure space must contain the divergence of every
velocity function. The present work extends the convergence analysis to
arbitrary inf-sup-stable velocity-pressure pairs (while maintaining robustness
in the advection-dominated regime) and demonstrates the convergence of the
method numerically, using both the traditional and isogeometric Taylor-Hood
elements.


  Strong electronic interactions and spin orbit coupling can be conducive for
realizing novel broken symmetry phases supporting quasiparticles with
nontrivial band topology. 227 pyrochlore iridates provide a suitable material
platform for studying such emergent phenomena where both topology and competing
orders play important roles. In contrast to the most members of this material
class, which are thought to display "all-in all-out" (AIAO) type magnetically
ordered low-temperature insulating ground states, Pr$_2$Ir$_2$O$_7$ remains
metallic while exhibiting "spin ice" (SI) correlations at low temperatures.
Additionally, this is the only 227 iridate compound, which exhibits a large
anomalous Hall effect (AHE) along [1,1,1] direction below 1.5 K, without
possessing any measurable magnetic moment. By focusing on the normal state of
227 iridates, described by a parabolic semimetal with quadratic band touching,
we use renormalization group analysis, mean-field theory, and phenomenological
Landau theory as three complementary methods to construct a global phase
diagram in the presence of generic local interactions among itinerant electrons
of Ir ions. While the global phase diagram supports several competing
multipolar orders, motivated by the phenomenology of 227 iridates we
particularly emphasize the competition between AIAO and SI orders and how it
can cause a mixed phase with "three-in one-out" (3I1O) spin configurations. In
terms of topological properties of Weyl quasiparticles of the 3I1O state, we
provide an explanation for the magnitude and the direction of the observed AHE
in Pr$_2$Ir$_2$O$_7$. We propose a strain induced enhancement of the onset
temperature for AHE in thin films of Pr$_2$Ir$_2$O$_7$ and additional
experiments for studying competing orders in the vicinity of the
metal-insulator transition.


  The dynamical growth rate of bubbles nucleating in relativistic plasma in
thermal first-order phase transitions is analyzed. The framework is a
hydrodynamical model which consists of relativistic fluid and an order
parameter field. The results of analytical approximations and numerical
simulations coincide well.


  Many quantum algorithms for machine learning require access to classical data
in superposition. However, for many natural data sets and algorithms, the
overhead required to load the data set in superposition can erase any potential
quantum speedup over classical algorithms. Recent work by Harrow introduces a
new paradigm in hybrid quantum-classical computing to address this issue,
relying on coresets to minimize the data loading overhead of quantum
algorithms. We investigate using this paradigm to perform $k$-means clustering
on near-term quantum computers, by casting it as a QAOA optimization instance
over a small coreset. We compare the performance of this approach to classical
$k$-means clustering both numerically and experimentally on IBM Q hardware. We
are able to find data sets where coresets work well relative to random sampling
and where QAOA could potentially outperform standard $k$-means on a coreset.
However, finding data sets where both coresets and QAOA work well--which is
necessary for a quantum advantage over $k$-means on the entire data
set--appears to be challenging.


  The rapid advancements in artificial intelligence (AI) have led to a growing
trend of human-AI teaming (HAT) in various fields. As machines continue to
evolve from mere automation to a state of autonomy, they are increasingly
exhibiting unexpected behaviors and human-like cognitive/intelligent
capabilities, including situation awareness (SA). This shift has the potential
to enhance the performance of mixed human-AI teams over all-human teams,
underscoring the need for a better understanding of the dynamic SA interactions
between humans and machines. To this end, we provide a review of leading SA
theoretical models and a new framework for SA in the HAT context based on the
key features and processes of HAT. The Agent Teaming Situation Awareness (ATSA)
framework unifies human and AI behavior, and involves bidirectional, and
dynamic interaction. The framework is based on the individual and team SA
models and elaborates on the cognitive mechanisms for modeling HAT. Similar
perceptual cycles are adopted for the individual (including both human and AI)
and the whole team, which is tailored to the unique requirements of the HAT
context. ATSA emphasizes cohesive and effective HAT through structures and
components, including teaming understanding, teaming control, and the world, as
well as adhesive transactive part. We further propose several future research
directions to expand on the distinctive contributions of ATSA and address the
specific and pressing next steps.


  We present 3D hydrodynamic models of the interaction between the outflows of
evolved, pulsating, Asymptotic Giant Branch (AGB) stars and nearby ($< 3$
stellar radii) sub-stellar companions ($M_{\mathrm{comp}} \lesssim 40$ M$_J$).
Our models show that due to resonances between the orbital period of the
companion and the pulsation period of the AGB star, multiple spiral structures
can form; the shocks driven by the pulsations are enhanced periodically in
different regions as they encounter the denser material created by the
sub-stellar companion's wake. We discuss the properties of these spiral
structures and the effect of the companion parameters on them. We also
demonstrate that the gravitational potential of the nearby companion enhances
the mass loss from the AGB star. For more massive ($M_{\mathrm{comp}} > 40$
M$_J$) and more distant companions ($> 4$ stellar radii), a single spiral arm
forms. We discuss the possibility of observing these structures with the new
generations of high-resolution, high-sensitivity instruments, and using them to
`find' sub-stellar companions around bright, evolved stars. Our results also
highlight possible structures that could form in our solar system when the Sun
turns into an AGB star.


  Based on maximally entangled states in the full- and sub-spaces of two
qutrits, we present an alternative decomposition of two-qutrit pure states in a
form $|\Psi>=\frac{p_{1}}{\sqrt{3}}(|00>+|11>+|22>)
+\frac{p_{2}}{\sqrt{2}}(|01>+|12>)+ p_{3}e^{i\theta}|02>$. Similar to the
Schmidt decomposition, all two-qutrit pure states can be transformed into the
alternative decomposition under local unitary transformations, and the
parameter $p_1$ is shown to be an entanglement invariant.


  We explore the phase diagram of the 4D compact U(1) gauge theory at finite
temperature as a function of the gauge coupling and of the compactified
Euclidean time dimension L_t. We show that the strong-to-weak coupling
transition, which is first order at T=0 (L_t=\infty), becomes second order for
high temperatures, i.e. for small values of L_t, with a tricritical temporal
size \bar{L_t} located between 5 and 6. The critical behavior around the
tricritical point explains and reconciles previous contradictory evidences
found in the literature.


  While many quality metrics exist to evaluate the quality of a grasp by
itself, no clear quantification of the quality of a grasp relatively to the
task the grasp is used for has been defined yet. In this paper we propose a
framework to extend the concept of grasp quality metric to task-oriented
grasping by defining affordance functions via basic grasp metrics for an open
set of task affordances. We evaluate both the effectivity of the proposed task
oriented metrics and their practical applicability by learning to infer them
from vision. Indeed, we assess the validity of our novel framework both in the
context of perfect information, i.e., known object model, and in the partial
information context, i.e., inferring task oriented metrics from vision,
underlining advantages and limitations of both situations. In the former,
physical metrics of grasp hypotheses on an object are defined and computed in
known object model simulation, in the latter deep models are trained to infer
such properties from partial information in the form of synthesized range
images.


  Recently Zhang et al. (2019) reported the discovery of FRB 010312 in a
dataset previously searched for FRBs. Here we explain how and why this FRB was
initially missed, and highlight several caveats relevant to FRB search
completeness. It is possible that up to $\sim40$% of discoverable FRBs remain
undiscovered in some existing public domain archival data sets. The situation
could be even more pronounced given that FRB search pipelines generally look
for temporally-symmetric broadband flat-spectrum pulses; most FRBs do not look
like that.


  We derive a general resummation formula for transverse-momentum distributions
of hard processes at the leading logarithmic level in the high-energy limit, to
all orders in the strong coupling. Our result is based on a suitable
generalization of high-energy factorization theorems, whereby all-order
resummation is reduced to the determination of the Born-level process but with
incoming off-shell gluons. We validate our formula by applying it to Higgs
production in gluon fusion in the infinite top mass limit. We check our result
up to next-to-leading order by comparison to the high energy limit of the exact
expression and to next-to-next-to leading by comparison to NNLL order trasverse
momentum (Sudakov) resummation, and we predict the high-energy behaviour at
next$^3$-to-leading order. We also show that the structure of the result in the
small transverse momentum limit agrees to all orders with general constraints
from Sudakov resummation.


  Small, low-cost IoT devices are typically equipped with only a single,
low-quality antenna, significantly limiting communication range and link
quality. In particular, these antennas are typically linearly polarized and
therefore susceptible to polarization mismatch, which can easily cause 10-15
dBm of link loss on communication to and from such devices. In this work, we
highlight this under-appreciated issue and propose the augmentation of IoT
deployment environments with programmable, RF-sensitive surfaces made of
metamaterials. Our smart meta-surface mitigates polarization mismatch by
rotating the polarization of signals that pass through or reflect off the
surface. We integrate our metasurface into an IoT network as LAMA, a Low-power
Lattice of Actuated Metasurface Antennas, designed for the pervasively used 2.4
GHz ISM band. We optimize LAMA's metasurface design for both low transmission
loss and low cost, to facilitate deployment at scale. We then build an
end-to-end system that actuates the metasurface structure to optimize for link
performance in real time. Our experimental prototype-based evaluation
demonstrates gains in link power of up to 15 dBm, and wireless capacity
improvements of 100 and 180 Kbit/s/Hz in through-surface and surface-reflective
scenarios, respectively, attributable to the polarization rotation properties
of LAMA'S metasurface.


  Many current laser wakefield acceleration (LWFA) experiments are carried out
in a regime where the laser pulse length is on the order of or longer than the
wake wavelength and where ionization injection is employed to inject electrons
into the wake. In these experiments, the trapped electrons will co-propagate
with the longitudinal wakefield and the transverse laser field. In this
scenario, the electrons can gain a significant amount of energy from both the
direct laser acceleration (DLA) mechanism as well as the usual LWFA mechanism.
Particle-in-cell (PIC) codes are frequently used to discern the relative
contribution of these two mechanisms. However, if the longitudinal resolution
used in the PIC simulations is inadequate, it can produce numerical heating
that can overestimate the transverse motion, which is important in determining
the energy gain due to DLA. We have therefore carried out a systematic study of
this LWFA regime by varying the longitudinal resolution of PIC simulations from
the standard, best-practice resolution of 30 points per laser wavelength to
four times that value and then examining the energy gain characteristics of
both the highest-energy electrons and the bulk electrons. By calculating the
contribution of DLA to the final energies of the electrons produced from the
LWFA, we find that although the transverse momentum and oscillation radii are
over-estimated in the lower-resolution simulations, this over-estimation does
not lead to artificial energy gain by DLA. Rather, the DLA contribution to the
highest-energy electrons is larger in the higher-resolution cases because the
DLA resonance is better maintained. Thus, even at the highest longitudinal
resolutions, DLA contributes a significant portion of the energy gained by the
highest-energy electrons and also contributes to accelerating the bulk of the
charge in the electron beam produced by the LWFA.


  We obtain an algorithmic meta-theorem for the following optimization problem.
Let \phi\ be a Counting Monadic Second Order Logic (CMSO) formula and t be an
integer. For a given graph G, the task is to maximize |X| subject to the
following: there is a set of vertices F of G, containing X, such that the
subgraph G[F] induced by F is of treewidth at most t, and structure (G[F],X)
models \phi.
  Some special cases of this optimization problem are the following generic
examples. Each of these cases contains various problems as a special subcase:
  1) "Maximum induced subgraph with at most l copies of cycles of length 0
modulo m", where for fixed nonnegative integers m and l, the task is to find a
maximum induced subgraph of a given graph with at most l vertex-disjoint cycles
of length 0 modulo m.
  2) "Minimum \Gamma-deletion", where for a fixed finite set of graphs \Gamma\
containing a planar graph, the task is to find a maximum induced subgraph of a
given graph containing no graph from \Gamma\ as a minor.
  3) "Independent \Pi-packing", where for a fixed finite set of connected
graphs \Pi, the task is to find an induced subgraph G[F] of a given graph G
with the maximum number of connected components, such that each connected
component of G[F] is isomorphic to some graph from \Pi.
  We give an algorithm solving the optimization problem on an n-vertex graph G
in time O(#pmc n^{t+4} f(t,\phi)), where #pmc is the number of all potential
maximal cliques in G and f is a function depending of t and \phi\ only. We also
show how a similar running time can be obtained for the weighted version of the
problem. Pipelined with known bounds on the number of potential maximal
cliques, we deduce that our optimization problem can be solved in time
O(1.7347^n) for arbitrary graphs, and in polynomial time for graph classes with
polynomial number of minimal separators.


  We study in detail the recently-found family of asymptotically AdS$_5\times
S^5$ type IIB supergravity solutions dual to the $\mathcal{N}=1^*$ SYM theory
with equal masses. The backgrounds exhibit a naked singularity and are labelled
by a dimensionless parameter, $\lambda$, which is interpreted as the ratio of
the gaugino condensate and the mass in the dual field theory. When
$|\lambda|<1$ we show that the naked singularity is due to a smeared
distribution of polarized $(p,q)$ five-branes. For this range of parameters we
study the nature of the singularity using probe strings and show that the dual
line operators exhibit screening behavior. These features are in line with the
physics anticipated in the work of Polchinski-Strassler. For $|\lambda|=1$ the
naked singularity has qualitatively different behavior which has no clear brane
interpretation. We show that when $\lambda=1$ the singularity can be excised
and replaced by a smooth Euclidean supergravity solution with an $S^4$
boundary.


  Recent works have empirically analyzed in-context learning and shown that
transformers trained on synthetic linear regression tasks can learn to
implement ridge regression, which is the Bayes-optimal predictor, given
sufficient capacity [Aky\"urek et al., 2023], while one-layer transformers with
linear self-attention and no MLP layer will learn to implement one step of
gradient descent (GD) on a least-squares linear regression objective [von
Oswald et al., 2022]. However, the theory behind these observations remains
poorly understood. We theoretically study transformers with a single layer of
linear self-attention, trained on synthetic noisy linear regression data.
First, we mathematically show that when the covariates are drawn from a
standard Gaussian distribution, the one-layer transformer which minimizes the
pre-training loss will implement a single step of GD on the least-squares
linear regression objective. Then, we find that changing the distribution of
the covariates and weight vector to a non-isotropic Gaussian distribution has a
strong impact on the learned algorithm: the global minimizer of the
pre-training loss now implements a single step of $\textit{pre-conditioned}$
GD. However, if only the distribution of the responses is changed, then this
does not have a large effect on the learned algorithm: even when the response
comes from a more general family of $\textit{nonlinear}$ functions, the global
minimizer of the pre-training loss still implements a single step of GD on a
least-squares linear regression objective.


  Exact solutions are obtained for the mean-field spherical model, with or
without an external magnetic field, for any finite or infinite number N of
degrees of freedom, both in the microcanonical and in the canonical ensemble.
The canonical result allows for an exact discussion of the loci of the Fisher
zeros of the canonical partition function. The microcanonical entropy is found
to be nonanalytic for arbitrary finite N. The mean-field spherical model of
finite size N is shown to be equivalent to a mixed isovector/isotensor
sigma-model on a lattice of two sites. Partial equivalence of statistical
ensembles is observed for the mean-field spherical model in the thermodynamic
limit. A discussion of the topology of certain state space submanifolds yields
insights into the relation of these topological quantities to the thermodynamic
behavior of the system in the presence of ensemble nonequivalence.


  A p-local compact group is an algebraic object modelled on the p-local
homotopy theory of classifying spaces of compact Lie groups and p-compact
groups. In the study of these objects unstable Adams operations, are of
fundamental importance. In this paper we define unstable Adams operations
within the theory of p-local compact groups, and show that such operations
exist under rather mild conditions. More precisely, we prove that for a given
p-local compact group G and a sufficiently large positive integer $m$, there
exists an injective group homomorphism from the group of p-adic units which are
congruent to 1 modulo p^m to the group of unstable Adams operations on G


  Here, we focus on Anderson type operators over infinite graphs where the
randomness acts through higher rank perturbations. We show that for special
family of graphs, the operator has non-trivial multiplicity for its pure point
spectrum. We, also, show that for some family of graphs, any unitary which
fixes the random operator, arising from an automorphism of the graph is
identity; but that, for these graphs the spectrum of the random operator has
non-trivial multiplicity.


  In recent years, Evolutionary Strategies were actively explored in robotic
tasks for policy search as they provide a simpler alternative to reinforcement
learning algorithms. However, this class of algorithms is often claimed to be
extremely sample-inefficient. On the other hand, there is a growing interest in
Differentiable Robot Simulators (DRS) as they potentially can find successful
policies with only a handful of trajectories. But the resulting gradient is not
always useful for the first-order optimization. In this work, we demonstrate
how DRS gradient can be used in conjunction with Evolutionary Strategies.
Preliminary results suggest that this combination can reduce sample complexity
of Evolutionary Strategies by 3x-5x times in both simulation and the real
world.


  It will be shown that a pronounced interfacial pair breaking can be
identified in Josephson tunnel junctions provided the first j_{1c} and the
second j_{2c} harmonics of the supercurrent, as well as the depairing current
in the bulk j_{dp}, are known. Namely, within the Ginzburg-Landau theory a
strong interfacial pair breaking results in the relation
j_{2c}j_{dp}>>j_{1c}^2, while in standard junctions, with negligibly small pair
breaking, the relation of opposite character takes place.


  We focus on the robustness of neural networks for classification. To permit a
fair comparison between methods to achieve robustness, we first introduce a
standard based on the mensuration of a classifier's degradation. Then, we
propose natural perturbed training to robustify the network. Natural
perturbations will be encountered in practice: the difference of two images of
the same object may be approximated by an elastic deformation (when they have
slightly different viewing angles), by occlusions (when they hide differently
behind objects), or by saturation, Gaussian noise etc. Training some fraction
of the epochs on random versions of such variations will help the classifier to
learn better. We conduct extensive experiments on six datasets of varying sizes
and granularity. Natural perturbed learning show better and much faster
performance than adversarial training on clean, adversarial as well as natural
perturbed images. It even improves general robustness on perturbations not seen
during the training. For Cifar-10 and STL-10 natural perturbed training even
improves the accuracy for clean data and reaches the state of the art
performance. Ablation studies verify the effectiveness of natural perturbed
training.


  It is well-known that the first energy shell, \[\mathcal{S}_1^{c_0}:=\{\alpha
\cos(x+\mu)+\beta\cos(y+\lambda): \alpha^2+\beta^2=c_0\,\, \&\,\,
(\mu,\lambda)\in\mathbb{R}^2\}\] of solutions to the 2d Euler equation is
Lyapunov stable on $\mathbb{T}^2$. This is simply a consequence of the
conservation of energy and enstrophy. Using the idea of Wirosoetisno and
Shepherd \cite{WS}, which is to take advantage of conservation of a properly
chosen Casimir, we give a simple and quantitative proof of the $L^2$ stability
of single modes up to translation. In other words, each
\[\mathcal{S}_1^{\alpha,\beta}:=\{\alpha \cos(x+\mu)+\beta\cos(y+\lambda):
(\mu,\lambda)\in\mathbb{R}^2\}\] is Lyapunov stable. Interestingly, our
estimates indicate that the extremal cases $\alpha=0,$ $\beta=0$, and
$\alpha=\pm\beta$ may be markedly less stable than the others.


  Suppose that an automorphism group $G$ acts flag-transitively on a finite
generalized hexagon or octagon $\cS$, and suppose that the action on both the
point and line set is primitive. We show that $G$ is an almost simple group of
Lie type, that is, the socle of $G$ is a simple Chevalley group.


  Dirac matrices, also known as gamma matrices, are defined only up to a
similarity transformation. Usually, some explicit representation of these
matrices is assumed in order to deal with them. In this article, we show how it
is possible to proceed without any such assumption. Various important
identities involving Dirac matrices and spinors have been derived without
assuming any representation at any stage.


  We interpret the function of individual neurons in CLIP by automatically
describing them using text. Analyzing the direct effects (i.e. the flow from a
neuron through the residual stream to the output) or the indirect effects
(overall contribution) fails to capture the neurons' function in CLIP.
Therefore, we present the "second-order lens", analyzing the effect flowing
from a neuron through the later attention heads, directly to the output. We
find that these effects are highly selective: for each neuron, the effect is
significant for <2% of the images. Moreover, each effect can be approximated by
a single direction in the text-image space of CLIP. We describe neurons by
decomposing these directions into sparse sets of text representations. The sets
reveal polysemantic behavior - each neuron corresponds to multiple, often
unrelated, concepts (e.g. ships and cars). Exploiting this neuron polysemy, we
mass-produce "semantic" adversarial examples by generating images with concepts
spuriously correlated to the incorrect class. Additionally, we use the
second-order effects for zero-shot segmentation and attribute discovery in
images. Our results indicate that a scalable understanding of neurons can be
used for model deception and for introducing new model capabilities.


  We give necessary and sufficient conditions for a subfamily of regularly
spaced translates of a function to form a frame (resp. a Riesz basis) for its
span. One consequence is that ifthetranslates are taken only from a subset of
the natural numbers, then this family is a frame if and only if it is a Riesz
basis. We also consider arbitrary sequences of translates and show that for
sparse sets, having an upper frame bound is equivalent to the family being a
frame sequence. Finally, we use the fractional Hausdorff dimension to identify
classes of exact frame sequences.


  This work concerns receiver design for light emitting diode (LED)
communications where the LED nonlinearity can severely degrade the performance
of communications. We propose extreme learning machine (ELM) based
non-iterative receivers and iterative receivers to effectively handle the LED
nonlinearity and memory effects. For the iterative receiver design, we also
develop a data-aided receiver, where data is used as virtual training sequence
in ELM training. It is shown that the ELM based receivers significantly
outperform conventional polynomial based receivers; iterative receivers can
achieve huge performance gain compared to non-iterative receivers; and the
data-aided receiver can reduce training overhead considerably. This work can
also be extended to radio frequency communications, e.g., to deal with the
nonlinearity of power amplifiers.


  We study two variants of the mirror descent-ascent algorithm for solving
min-max problems on the space of measures: simultaneous and sequential. We work
under assumptions of convexity-concavity and relative smoothness of the payoff
function with respect to a suitable Bregman divergence, defined on the space of
measures via flat derivatives. We show that the convergence rates to mixed Nash
equilibria, measured in the Nikaid\`o-Isoda error, are of order
$\mathcal{O}\left(N^{-1/2}\right)$ and $\mathcal{O}\left(N^{-2/3}\right)$ for
the simultaneous and sequential schemes, respectively, which is in line with
the state-of-the-art results for related finite-dimensional algorithms.


  We collect some open problems about minimal presentations of numerical
semigroups and, more generally, about defining ideals and free resolutions of
their semigroup rings and associated graded rings. We emphasize both
long-standing problems and more recent questions and developments.


  We present a new and improved model independent amplitude analysis of
reactions $\pi^+ n_\uparrow \to \pi^+ \pi^- p$ at 5.98 and 11.85 GeV/c and
$\pi^- p_\uparrow \to \pi^- \pi^+ n$ at 17.2 GeV/c measured with transversely
polarized targets at the CERN Proton Synchrotron. A clear signal for
$\sigma(750)$ resonance emerges in all four solutions for $S$-wave intensity
$I_S$ at 5.98 and 11.85 GeV/c and in both solutions for $S$-wave amplitude
$|\overline S|^2\Sigma$ at 17.2 GeV/c. Its $\pi^+\pi^-$ decay width is
estimated to be in the range 200--300 MeV. We find significant suppression of
$\rho^0$ production in the amplitudes $|U|^2\Sigma$, $|\overline N |^2\Sigma$
and, at 17.2 GeV/c, in $|L|^2\Sigma$. The mass dependence of amplitudes
$|\overline L |^2\Sigma$ and $|L|^2\Sigma$ shows unexpected structures within
the $\rho^0$ mass region which correlate the mass spectra corresponding to
opposite nucleon spins. These features of $P$-wave moduli reveal the essential
role of nucleon spin in pion production process and contradict the
factorization hypothesis. Our results emphasize the need for a systematic study
of pion production on the level of amplitudes in a new generation of dedicated
experiments with spin at the recently proposed high-intensity hadron
facilities.


  We study associative graded algebras which have a ``complete flag'' of cyclic
modules with linear free resolutions, i.e., algebras over which there is a
cyclic Koszul module with every admissible number of relations (from zero up to
the number of generators of the algebra). Commutative algebras with the same
property has been studied in several papers by A. Conca and others. Here we
present a non-commutative version.
  We introduce the concept of Koszul filtration in non-commutative algebras and
study its connections with Koszul algebras and algebras with quadratic Groebner
bases. Also, here are considered several examples, such as ``Groebner flags'',
generic algebras, and algebras with one relation. A generalization of the
concept Koszul filtration (generalized Koszul, or rate, filtration) leads to
algebras with finite Backelin's rate and to coherent algebras. One of our main
results is that every algebra with Koszul filtration (or with finite rate
filtration) has rational Hilbert series.


  Video super-resolution aims at generating a high-resolution video from its
low-resolution counterpart. With the rapid rise of deep learning, many recently
proposed video super-resolution methods use convolutional neural networks in
conjunction with explicit motion compensation to capitalize on statistical
dependencies within and across low-resolution frames. Two common issues of such
methods are noteworthy. Firstly, the quality of the final reconstructed HR
video is often very sensitive to the accuracy of motion estimation. Secondly,
the warp grid needed for motion compensation, which is specified by the two
flow maps delineating pixel displacements in horizontal and vertical
directions, tends to introduce additional errors and jeopardize the temporal
consistency across video frames. To address these issues, we propose a novel
dynamic local filter network to perform implicit motion estimation and
compensation by employing, via locally connected layers, sample-specific and
position-specific dynamic local filters that are tailored to the target pixels.
We also propose a global refinement network based on ResBlock and autoencoder
structures to exploit non-local correlations and enhance the spatial
consistency of super-resolved frames. The experimental results demonstrate that
the proposed method outperforms the state-of-the-art, and validate its strength
in terms of local transformation handling, temporal consistency as well as edge
sharpness.


  We prove that the unique SRB measure for a singular hyperbolic attractor
depends continuously on the dynamics in the weak$^\ast$ topology.


  In this paper, we cast Legal Judgment Prediction on European Court of Human
Rights cases into an article-aware classification task, where the case outcome
is classified from a combined input of case facts and convention articles. This
configuration facilitates the model learning some legal reasoning ability in
mapping article text to specific case fact text. It also provides an
opportunity to evaluate the model's ability to generalize to zero-shot settings
when asked to classify the case outcome with respect to articles not seen
during training. We devise zero-shot experiments and apply domain adaptation
methods based on domain discrimination and Wasserstein distance. Our results
demonstrate that the article-aware architecture outperforms straightforward
fact classification. We also find that domain adaptation methods improve
zero-shot transfer performance, with article relatedness and encoder
pre-training influencing the effect.


  Recent works have explored non-perturbative effects due to the existence of
(infinitesimal) Gribov copies in Yang-Mills-Chern-Simons theories in three
Euclidean dimensions. In particular, the removal of such copies modify the
gauge field propagator by a self-consistent dynamically generated mass
parameter, the Gribov parameter. Due to the interplay with the topological mass
introduced by the Chern-Simons term, the propagator features a non-trivial set
of phases with poles of different nature, leading to the possible
interpretation of a confinfing to deconfining phase transition. Inhere, we
restore the BRST symmetry which is softly broken by the elimination of gauge
copies and provide a BRST-invariant discussion of such a transition. In order
to make clear all physical statements, we deal with linear covariant gauges
which contain a gauge parameter and therefore allow for an explicit check of
gauge parameter independence of physical results. We also discuss the
generation of condensates due to the infrared relevance of infinitesimal Gribov
copies.


  In our previous published research we have studied the applications of the
ferrolens for the observation and qualitative analysis of non-homogeneous
magnetic fields. Latest developments over the last few years of the ferrolens
increased multifold the sensitivity of this device allowing it to display
magnetic fields as low as 10mT in strength and therefore it is possible now to
observe also the homogeneous (i.e. straight parallel magnetic flux lines of
uniform density in space) magnetic field existing inside air solenoids and
between N-S poles of two attracting separated permanent magnets. We present and
analyze herein these novel observations of homogeneous magnetic fields with the
ferrolens and as a potential new application of this device. The ferrolens can
now display the projected magnetic field on air from a distance without needing
to be in physical contact with the field source. Experiments were carried out
to demonstrate these new capabilities of the ferrolens as a nanomagnetic flux
viewer, real-time physical device and scientific qualitative tool. We compare
the geometry of magnetic fields of condensed matter ferromagnets with that of
magnetic fields inside electrical air solenoids. Specifically, the homogeneous
field between two N-S attracting magnets at a distance as well as inside air
solenoids and Helmholtz coils and also the non-homogeneous total field of
single dipole permanent magnets were observed using a latest generation very
sensitive ferrolens. The unique feature of this magneto optic fluid thin film
physical device is that it can display discrete magnetic flux lines of the
macroscopic field. Also we show how the ferrolens can be used to detect
qualitatively the symmetry center of a non ideal homogeneous magnetic field.


  Private Information Retrieval (PIR), despite being well studied, is
computationally costly and arduous to scale. We explore lower-cost relaxations
of information-theoretic PIR, based on dummy queries, sparse vectors, and
compositions with an anonymity system. We prove the security of each scheme
using a flexible differentially private definition for private queries that can
capture notions of imperfect privacy. We show that basic schemes are weak, but
some of them can be made arbitrarily safe by composing them with large
anonymity systems.


  We give a general setting for Cram\'er's large deviations theorem for the
empirical means of a sequence of i.i.d. random vectors, which contains
Cram\'er's theorem in a Banach space and Sanov's theorem.
  -----
  Nous \'etablissons un cadre g\'en\'eral pour le th\'eor\`eme de Cram\'er sur
les grandes d\'eviations des moyennes empiriques d'une suite de vecteurs
al\'eatoires i.i.d., cadre qui contient le th\'eor\`eme de Cram\'er dans les
espaces de Banach s\'eparables et le th\'eor\`eme de Sanov.


  With some telescopes standing still, now more than ever simple access to
archival data is vital for astronomers and they need to know how to go about
it. Within European Virtual Observatory (VO) projects, such as AIDA
(2008-2010), ICE (2010-2012), CoSADIE (2013-2015), ASTERICS (2015-2018) and
ESCAPE (since 2019), we have been offering Virtual Observatory schools for many
years. The aim of these schools are twofold: teaching (early career)
researchers about the functionalities and possibilities within the Virtual
Observatory and collecting feedback from the astronomical community. In
addition to the VO schools on the European level, different national teams have
also put effort into VO dissemination. The team at the Centre de Donn\'ees
astronomiques de Strasbourg (CDS) started to explore more and new ways to
interact with the community: a series of blog posts on AstroBetter.com or a
lunch time session at the virtual EAS meeting 2020. The Spanish VO has
conducted virtual VO schools. GAVO has supported online archive workshops and
maintains their Virtual Observatory Text Treasures. In this paper, we present
the different formats in more detail, and report on the resulting interaction
with the community as well as the estimated reach.


  In this paper, we extend the class of kernel methods, the so-called diffusion
maps (DM), and its local kernel variants, to approximate second-order
differential operators defined on smooth manifolds with boundaries that
naturally arise in elliptic PDE models. To achieve this goal, we introduce the
Ghost Point Diffusion Maps (GPDM) estimator on an extended manifold, identified
by the set of point clouds on the unknown original manifold together with a set
of ghost points, specified along the estimated tangential direction at the
sampled points at the boundary. The resulting GPDM estimator restricts the
standard DM matrix to a set of extrapolation equations that estimates the
function values at the ghost points. This adjustment is analogous to the
classical ghost point method in finite-difference scheme for solving PDEs on
flat domain. As opposed to the classical DM which diverges near the boundary,
the proposed GPDM estimator converges pointwise even near the boundary.
Applying the consistent GPDM estimator to solve the well-posed elliptic PDEs
with classical boundary conditions (Dirichlet, Neumann, and Robin), we
establish the convergence of the approximate solution under appropriate
smoothness assumptions. We numerically validate the proposed mesh-free PDE
solver on various problems defined on simple sub-manifolds embedded in
Euclidean spaces as well as on an unknown manifold. Numerically, we also found
that the GPDM is more accurate compared to DM in solving elliptic eigenvalue
problems on bounded smooth manifolds.


  Context: Continuous experimentation and A/B testing is an established
industry practice that has been researched for more than 10 years. Our aim is
to synthesize the conducted research.
  Objective: We wanted to find the core constituents of a framework for
continuous experimentation and the solutions that are applied within the field.
Finally, we were interested in the challenges and benefits reported of
continuous experimentation.
  Method: We applied forward snowballing on a known set of papers and
identified a total of 128 relevant papers. Based on this set of papers we
performed two qualitative narrative syntheses and a thematic synthesis to
answer the research questions.
  Results: The framework constituents for continuous experimentation include
experimentation processes as well as supportive technical and organizational
infrastructure. The solutions found in the literature were synthesized to nine
themes, e.g. experiment design, automated experiments, or metric specification.
Concerning the challenges of continuous experimentation, the analysis
identified cultural, organizational, business, technical, statistical, ethical,
and domain-specific challenges. Further, the study concludes that the benefits
of experimentation are mostly implicit in the studies.
  Conclusions: The research on continuous experimentation has yielded a large
body of knowledge on experimentation. The synthesis of published research
presented within include recommended infrastructure and experimentation process
models, guidelines to mitigate the identified challenges, and what problems the
various published solutions solve.


  Discrete and continuous standard windowing are revisited and a a new taper is
introduced, which is derived from the normal circular distribution by von
Mises. Both the continuous-time and the discrete-time windows are considered,
and their spectra obtained. A brief comparison with further classical window
families is performed in terms of their properties in the spectral domain.
These windows can be used in spectral analysis, and in particular, in the
design of FIR (finite impulse response) filters as an alternative to the Kaiser
window


  In this paper, we formulate a more realistic and difficult problem setup for
the intent detection task in natural language understanding, namely Generalized
Few-Shot Intent Detection (GFSID). GFSID aims to discriminate a joint label
space consisting of both existing intents which have enough labeled data and
novel intents which only have a few examples for each class. To approach this
problem, we propose a novel model, Conditional Text Generation with BERT
(CG-BERT). CG-BERT effectively leverages a large pre-trained language model to
generate text conditioned on the intent label. By modeling the utterance
distribution with variational inference, CG-BERT can generate diverse
utterances for the novel intents even with only a few utterances available.
Experimental results show that CG-BERT achieves state-of-the-art performance on
the GFSID task with 1-shot and 5-shot settings on two real-world datasets.


  We study the integrability of a family of birational maps obtained as
reductions of the discrete Hirota equation, which are related to travelling
wave solutions of the lattice KdV equation. In particular, for reductions
corresponding to waves moving with rational speed N/M on the lattice, where N,M
are coprime integers, we prove the Liouville integrability of the maps when N +
M is odd, and prove various properties of the general case. There are two main
ingredients to our construction: the cluster algebra associated with each of
the Hirota bilinear equations, which provides invariant (pre)symplectic and
Poisson structures; and the connection of the monodromy matrices of the
dressing chain with those of the KdV travelling wave reductions.


  In the framework of heavy-baryon chiral perturbation theory, we investigate
the fixed point structure of renormalization group equations (RGE) for the
ratios of the renormalized low energy constants (LECs) that feature in the
pion-nucleon chiral Lagrangian. The ratios of the LECs deduced from our RGE
analysis are found to be in semi-quantitative agreement with those obtained
from direct fit to the experimental data. The naturalness of this agreement is
discussed using a simple dimensional analysis combined with Wilsonian RGEs.


  The isotropic majority-vote (MV) model which, apart from the one-dimensional
case, is thought to be non-equilibrium and violating the detailed balance
condition. We show that this is not true, when the model is defined on a
complete graph. In the stationary regime, the MV model on a fully connected
graph fulfills the detailed balance. We derive the exact expression for the
probability distribution of finding the system in a given spin configuration.
We show that it only depends on the absolute value of magnetization. Our
theoretical predictions are validated by numerical simulations.


  We present a framework and analysis of consistent binary classification for
complex and non-decomposable performance metrics such as the F-measure and the
Jaccard measure. The proposed framework is general, as it applies to both batch
and online learning, and to both linear and non-linear models. Our work follows
recent results showing that the Bayes optimal classifier for many complex
metrics is given by a thresholding of the conditional probability of the
positive class. This manuscript extends this thresholding characterization --
showing that the utility is strictly locally quasi-concave with respect to the
threshold for a wide range of models and performance metrics. This, in turn,
motivates simple normalized gradient ascent updates for threshold estimation.
We present a finite-sample regret analysis for the resulting procedure. In
particular, the risk for the batch case converges to the Bayes risk at the same
rate as that of the underlying conditional probability estimation, and the risk
of proposed online algorithm converges at a rate that depends on the
conditional probability estimation risk. For instance, in the special case
where the conditional probability model is logistic regression, our procedure
achieves $O(\frac{1}{\sqrt{n}})$ sample complexity, both for batch and online
training. Empirical evaluation shows that the proposed algorithms out-perform
alternatives in practice, with comparable or better prediction performance and
reduced run time for various metrics and datasets.


  Heavy crystal scintillators are used widely in HEP experiments for precision
measurements of photons and electrons. Future HEP experiments, however, require
crystal scintillators of more bright, more fast, more radiation hard and less
cost. This paper discusses several R&D directions for the next generation of
crystal detectors for future HEP experiments.


  Optical bound states in the continuum (BICs) provide a unique mechanism of
light confinement that holds great potential for fundamental and applied
research in optics and photonics. Of particular interest are merging BICs,
realized in planar periodic structures by coalescence of accidental and
symmetry-protected BICs. Topological nature of merging BICs renders their $Q$
factors exceptionally high and robust. However, this cannot be achieved if the
structure lacks the up-down mirror symmetry, which is the case for all
substrate-supported structures. Here, we show that the detrimental effect of
the symmetry breaking can be perfectly compensated for by an additional thin
layer of a dielectric material on one side of the structure. Our approach can
enable flexible design, feasible realization, and extended applications of
various topologically robust systems.


  A toy model of Einstein gravity with a Gauss-Bonnet classically "entropic"
term mimicking a quantum correction is considered. The static black hole
solution due to Tomozawa is found and generalized with the inclusion of non
trivial horizon topology, and its entropy evaluated deriving the first law by
equations of motion. As a result the Bekenstein-Hawking area law turns to be
corrected by a logarithmic area term. A Misner-Sharp expression for the mass of
black hole is found. Within a Friedmann-Lema\^itre-Robertson-Walker (FLRW)
cosmological setting, the model is used in order to derive modified Friedmann
equations. Such new equations are shown to reproduce the first law with the
same formal entropy and quasi local energy of the static case, but here within
a FLRW space-time interpreted as a dynamical cosmological black hole. A
detailed analysis of cosmological solutions is presented, and it is shown that
the presence of the correction term provides regular solutions and interesting
phases of acceleration and decelerations, as well as, with negligible matter,
exact de Sitter solutions.


  In arXiv:2112.09122, we analyzed the reflected entropy ($S_R$) in random
tensor networks motivated by its proposed duality to the entanglement wedge
cross section (EW) in holographic theories, $S_R=2 \frac{EW}{4G}$. In this
paper, we discover further details of this duality by analyzing a simple
network consisting of a chain of two random tensors. This setup models a
multiboundary wormhole. We show that the reflected entanglement spectrum is
controlled by representation theory of the Temperley-Lieb (TL) algebra. In the
semiclassical limit motivated by holography, the spectrum takes the form of a
sum over superselection sectors associated to different irreducible
representations of the TL algebra and labelled by a topological index $k\in
\mathbb{Z}_{\geq 0}$. Each sector contributes to the reflected entropy an
amount $2k \frac{EW}{4G}$ weighted by its probability. We provide a
gravitational interpretation in terms of fixed-area, higher-genus multiboundary
wormholes with genus $2k-1$ initial value slices. These wormholes appear in the
gravitational description of the canonical purification. We confirm the
reflected entropy holographic duality away from phase transitions. We also find
important non-perturbative contributions from the novel geometries with $k\geq
2$ near phase transitions, resolving the discontinuous transition in $S_R$.
Along with analytic arguments, we provide numerical evidence for our results.
We comment on the connection between TL algebras, Type II$_1$ von Neumann
algebras and gravity.


  (1,d)-polarized abelian surfaces in P^(d-1) with two plane cubic curve
fibrations lie in two elliptic P^2-scrolls. The union of these scrolls form a
reducible Calabi-Yau 3-fold. In this paper we show that this occurs when d<10
and analyse the family of such surfaces and 3-folds in detail when d=6. In
particular, the reducible Calabi-Yau 3-folds deform in that case to irreducible
ones with non-normal singularities.


  The problem of the final state interaction in quasi-elastic $(e,e')$
scattering at large $Q^2$, is investigated by exploiting the idea that the
ejected nucleon needs a finite amount of time to assume its asymptotic form. It
is shown that when the dependence of the scattering amplitude of the ejected
nucleon on its virtuality is taken into account, the final state interaction is
decreased. The developed approach is simpler to implement than the one based on
the color transparency description of the damping of the final state
interaction, and is essentially equivalent to the latter in the case of the
single rescattering term. The $(e,e')$ process on the deuteron is numerically
investigated and it is shown that, at $x=1$, appreciable finite formation time
effects at $Q^2$ of the order of 10 (GeV/c)$^2$ are expected.


  Providing initial conditions is an essential procedure for numerical
simulations of galaxies. The initial conditions for idealised individual
galaxies in $N$-body simulations should resemble observed galaxies and be
dynamically stable for time scales much longer than their characteristic
dynamical times. However, generating a galaxy model ab initio as a system in
dynamical equilibrium is a difficult task, since a galaxy contains several
components, including a bulge, disc, and halo. Moreover, it is desirable that
the initial-condition generator be fast and easy to use. We have now developed
an initial-condition generator for galactic $N$-body simulations that satisfies
these requirements. The developed generator adopts a
distribution-function-based method, and it supports various kinds of density
models, including custom-tabulated inputs and the presence of more than one
disc. We tested the dynamical stability of systems generated by our code,
representing early- and late-type galaxies, with $N=$~2,097,152 and 8,388,608
particles, respectively, and we found that the model galaxies maintain their
initial distributions for at least 1~Gyr. The execution times required to
generate the two models were $8.5$ and $221.7$ seconds, respectively, which is
negligible compared to typical execution times for $N$-body simulations. The
code is provided as open-source software and is publicly and freely available
at \url{https://bitbucket.org/ymiki/magi}.


  The notion of chiral symmetry for the conventional Dirac cone is generalized
to include the tilted Dirac cones, where the generalized chiral operator turns
out to be non-hermitian. It is shown that the generalized chiral symmetry
generically protects the zero modes (n=0 Landau level) of the Dirac cone even
when tilted. The present generalized symmetry is equivalent to the condition
that the Dirac Hamiltonian is elliptic as a differential operator, which
provides an explicit relevance to the index theorem.