  Approximating the ground states of strongly interacting electron systems in
quantum chemistry and condensed matter physics is expected to be one of the
earliest applications of quantum computers. In this paper, we prepare highly
accurate ground states of the Fermi-Hubbard model for small grids up to 6 sites
(12 qubits) by using an interpretable, adaptive variational quantum
eigensolver(VQE) called ADAPT-VQE. In contrast with non-adaptive VQE, this
algorithm builds a system-specific ansatz by adding an optimal gate built from
one-body or two-body fermionic operators at each step. We show this adaptive
method outperforms the non-adaptive counterpart in terms of fewer variational
parameters, short gate depth, and scaling with the system size. The fidelity
and energy of the prepared state appear to improve asymptotically with ansatz
depth. We also demonstrate the application of adaptive variational methods by
preparing excited states and Green functions using a proposed ADAPT-SSVQE
algorithm. Lower depth, asymptotic convergence, noise tolerance of a
variational approach, and a highly controllable, system-specific ansatz make
the adaptive variational methods particularly well-suited for NISQ devices.


  We consider a class of doubly nonlinear degenerate hyperbolic-parabolic
equations with homogeneous Dirichlet boundary conditions, for which we first
establish the existence and uniqueness of entropy solutions. We then turn to
the construction and analysis of discrete duality finite volume schemes (in the
spirit of Domelevo and Omn\`es \cite{DomOmnes}) for these problems in two and
three spatial dimensions. We derive a series of discrete duality formulas and
entropy dissipation inequalities for the schemes. We establish the existence of
solutions to the discrete problems, and prove that sequences of approximate
solutions generated by the discrete duality finite volume schemes converge
strongly to the entropy solution of the continuous problem. The proof revolves
around some basic a priori estimates, the discrete duality features,
Minty-Browder type arguments, and "hyperbolic" $L^\infty$ weak-$\star$
compactness arguments (i.e., propagation of compactness along the lines of
Tartar, DiPerna, ...). Our results cover the case of non-Lipschitz
nonlinearities.


  Fields of spin $s \geq 1/2$ satisfying wave equations in a curved space obey
the Huygens principle under certain conditions clarified by a known theorem.
Here this theorem is generalized to spin zero and applied to an inflaton field
in de Sitter-like space, showing that tails of scalar radiation are an
unavoidable physical feature. Requiring the absence of tails, on the contrary,
necessarily implies an unnatural tuning between cosmological constant, scalar
field mass, and coupling constant to the curvature.


  The existence of a "Plastikstufe" for a contact structure implies the
Weinstein conjecture for all supporting contact forms.


  We study the effect of phase separating diffusive dynamics on the mean time
to extinction in several reaction-diffusion models with slow reactions. We
consider a continuum theory similar to model AB, and a simple model where
individual particles on two sites undergo on-site reactions and hopping between
the sites. In the slow-reaction limit, we project the models' dynamics onto
suitable one-dimensional reaction coordinates, which allows derivation of
quasi-equilibrium effective free energies. For weak noise, this enables
characterisation of the mean time to extinction. This time can be enhanced or
suppressed by the addition of phase separation, compared with homogeneous
reference cases. We also discuss how Allee effects can be affected by phase
separation.


  This paper investigates the impact of carrier frequency offset (CFO) and
sampling frequency offset (SFO) on the performance of different MIMO-OFDM
schemes with high spectral efficiency for next generation of terrestrial
digital TV. We analyze particularly orthogonal Alamouti scheme, and
non-orthogonal (NO) schemes like VBLAST, linear dispersion (LD) code and Golden
code. This analysis gives a global view on the best suitable MIMO-OFDM scheme
with respect to CFO and SFO. We show that for high spectral efficiency,
Alamouti is more sensitive to CFO and SFO. Moreover, we show that all studied
MIMO-OFDM schemes are sensitive to CFO when it is greater than 1% of
inter-carrier spacing. Their sensitivity due to SFO is less than that due to
CFO.


  We propose a compartmental model for a disease with temporary immunity and
secondary infections. From our assumptions on the parameters involved in the
model, the system naturally evolves in three time scales. We characterize the
equilibria of the system and analyze their stability. We find conditions for
the existence of two endemic equilibria, for some cases in which $\mathcal{R}_0
< 1$. Then, we unravel the interplay of the three time scales, providing
conditions to foresee whether the system evolves in all three scales, or only
in the fast and the intermediate ones. We conclude with numerical simulations
and bifurcation analysis, to complement our analytical results.


  We find static fluid solutions of Einstein and pure Lovelock equations with
$p_r=0$, $p_t=k\rho$, which could be possible models for the interior of a
Buchdahl-like star. Buchdahl star is a limiting stellar configuration without a
horizon whose formation does not need any exotic matter.


  I discuss the state-of-the-art knowledge of long-distance singularities in
multi-leg gauge-theory scattering amplitudes and report on an on-going
calculation of the three-loop soft anomalous dimension through the
renormalization of correlators of semi-infinite Wilson lines. I also discuss
the non-Abelian exponentiation theorem that has been recently generalised to
multiple Wilson lines and demonstrate its application in computing the soft
anomalous dimension. Finally, I present recent results for
multiple-gluon-exchange webs and discuss their analytic structure.


  We show that spherical accretion onto astrophysical black holes can be
considered as a natural example of analogue system. We provide, for the first
time, an exact analytical scheme for calculating the analogue Hawking
temperature and surface gravity for general relativistic accretion onto
astrophysical black holes. Our calculation may bridge the gap between the
theory of transonic astrophysical accretion and the theory of analogue Hawking
radiation. We show that the domination of the analogue Hawking temperature over
the actual Hawking temperature may be a real astrophysical phenomena. We also
discuss the possibilities of the emergence of analogue white holes around
astrophysical black holes. Our calculation is general enough to accommodate
accreting black holes with any mass.


  We investigate the dynamics of the two-dimensional periodic Kolmogorov flow
of a viscoelastic fluid, described by the Oldroyd-B model, by means of direct
numerical simulations. Above a critical Weissenberg number the flow displays a
transition from stationary to randomly fluctuating states, via periodic ones.
The increasing complexity of the flow in both time and space at progressively
higher values of elasticity accompanies the establishment of mixing features.
The peculiar dynamical behavior observed in the simulations is found to be
related to the appearance of filamental propagating patterns, which develop
even in the limit of very small inertial non-linearities, thanks to the
feedback of elastic forces on the flow.


  In this paper we show that solutions of the cubic nonlinear Schr\"odinger
equation are asymptotic limit of solutions to the Benney system. Due to the
special characteristic of the one-dimensional transport equation same result is
obtained for solutions of the one-dimensional Zakharov and
1d-Zakharov-Rubenchik systems. Convergence is reached in the topology
$L^2(\mathbb{R})\times L^2(\mathbb{R})$ and with an approximation in the energy
space $H^1(\mathbb{R})\times L^2(\mathbb{R})$. In the case of the Zakharov
system this is achieved without the condition $\partial_t n(x,0) \in \dot
H^{-1}(\mathbb{R})$ for the wave component, improving previous results.


  While the accelerated expansion of the Universe is by now well established,
an underlying scalar field potential possibly responsible for this acceleration
remains unconstrained. We present an attempt to reconstruct this potential
using recent SN data, under the assumption that the acceleration is driven by a
single scalar field. Current approaches to such reconstructions are based upon
simple parametric descriptions of either the luminosity distance or the dark
energy equation of state. We find that these various approximations lead to a
range of derived evolutionary histories of the dark energy equation of state
(although there is considerable overlap between the different potential shapes
allowed by the data). Instead of these indirect reconstruction schemes, we
discuss a technique to determine the potential directly from the data by
expressing it in terms of a binned scalar field. We apply this technique to a
recent SN dataset, and compare the results with model-dependent approaches. In
a similar fashion to direct estimates of the dark energy equation of state, we
advocate direct reconstruction of the scalar field potential as a way to
minimize prior assumptions on the shape, and thus minimize the introduction of
bias in the derived potential.


  The objective of this research is to explore a convex feasibility problem,
which consists of a monotone variational inequality problem and a fixed point
problem. We introduce four inertial extragradient algorithms that are motivated
by the inertial method, the subgradient extragradient method, the Tseng's
extragradient method and the Mann-type method endowed with a simple step size.
Strong convergence theorems of the algorithms are established under some
standard and suitable conditions enforced by the cost operators. Finally, we
implement some computational tests to show the efficiency and advantages of the
proposed algorithms and compare them with some existing ones.


  With the surge in the development of large language models, embodied
intelligence has attracted increasing attention. Nevertheless, prior works on
embodied intelligence typically encode scene or historical memory in an
unimodal manner, either visual or linguistic, which complicates the alignment
of the model's action planning with embodied control. To overcome this
limitation, we introduce the Multimodal Embodied Interactive Agent (MEIA),
capable of translating high-level tasks expressed in natural language into a
sequence of executable actions. Specifically, we propose a novel Multimodal
Environment Memory (MEM) module, facilitating the integration of embodied
control with large models through the visual-language memory of scenes. This
capability enables MEIA to generate executable action plans based on diverse
requirements and the robot's capabilities. Furthermore, we construct an
embodied question answering dataset based on a dynamic virtual cafe environment
with the help of the large language model. In this virtual environment, we
conduct several experiments, utilizing multiple large models through zero-shot
learning, and carefully design scenarios for various situations. The
experimental results showcase the promising performance of our MEIA in various
embodied interactive tasks.


  Here we present a sample of 12 massive quiescent galaxy candidates at z~3-4
observed with the James Webb Space Telescope (JWST) Near Infrared Spectrograph
(NIRSpec). These galaxies were pre-selected from the Hubble Space Telescope
imaging and 10 of our sources were unable to be spectroscopically confirmed by
ground based spectroscopy. By combining spectroscopic data from NIRSpec with
multi-wavelength imaging data from the JWST Near Infrared Camera (NIRCam), we
analyse their stellar populations and their formation histories. We find that
all of our galaxies classify as quiescent based on the reconstruction of their
star formation histories but show a variety of quenching timescales and ages.
All our galaxies are massive ($\sim0.1-1.2 \times 10^{11} M\odot$), with masses
comparable to massive galaxies in the local Universe. We find that the oldest
galaxy in our sample formed $\sim1.0\times10^{11} M\odot$ of mass within the
first few hundred million years of the Universe and has been quenched for more
than a billion years by the time of observation at z$\sim$3.2 ($\sim$2 billion
years after the Big Bang). Our results point to very early formation of massive
galaxies requiring a high conversion rate of baryons to stars in the early
Universe.


  Blind image deblurring remains a challenging problem for modern artificial
neural networks. Unlike other image restoration problems, deblurring networks
fail behind the performance of existing deblurring algorithms in case of
uniform and 3D blur models. This follows from the diverse and profound effect
that the unknown blur-kernel has on the deblurring operator.
  We propose a new architecture which breaks the deblurring network into an
analysis network which estimates the blur, and a synthesis network that uses
this kernel to deblur the image. Unlike existing deblurring networks, this
design allows us to explicitly incorporate the blur-kernel in the network's
training. In addition, we introduce new cross-correlation layers that allow
better blur estimations, as well as unique components that allow the estimate
blur to control the action of the synthesis deblurring action.
  Evaluating the new approach over established benchmark datasets shows its
ability to achieve state-of-the-art deblurring accuracy on various tests, as
well as offer a major speedup in runtime.


  Based on the effective field theory philosophy, a universal form of the
scaling laws could be easily derived with the scaling anomalies naturally
clarified as the decoupling effects of underlying physics. In the novel
framework, the conventional renormalization group equations and Callan-Symanzik
equations could be reproduced as special cases and a number of important and
difficult issues around them could be clarified. The underlying theory point of
view could envisage a harmonic scaling law that help to fix the form of the
loop amplitudes through anomalies, and the heavy field decoupling can be
incorporated in this underlying theory approach in a more unified manner.


  We study a relation between two refinements of the rank one abelian
Gross-Stark conjecture: For a suitable abelian extension $H/F$ of number
fields, a Gross-Stark unit is defined as a $p$-unit of $H$ satisfying some
proporties. Let $\tau \in \mathrm{Gal}(H/F)$. Yoshida and the author
constructed the symbol $Y_p(\tau)$ by using $p$-adic $\log$ multiple gamma
functions, and conjectured that the $\log_p$ of a Gross-Stark unit can be
expressed by $Y_p(\tau)$. Dasgupta constructed the symbol $u_T(\tau)$ by using
the $p$-adic multiplicative integration, and conjectured that a Gross-Stark
unit can be expressed by $u_T(\tau)$. In this paper, we give an explicit
relation between $Y_p(\tau)$ and $u_T(\tau)$.


  According to the standard scenario of plasma emission, escaping radiations
are generated by the nonlinear development of the kinetic bump-on-tail
instability driven by a single beam of energetic electrons interacting with
plasmas. Here we conduct fully-kinetic electromagnetic particle-in-cell
simulations to investigate plasma emission induced by the ring-distributed
energetic electrons interacting with overdense plasmas. Efficient excitations
of the fundamental (F) and harmonic (H) emissions are revealed with radiation
mechanism(s) different from the standard scenario: (1) The primary modes
accounting for the radiations are generated through the electron cyclotron
maser instability (for the upper-hybrid (UH) and Z modes) and the thermal
anisotropic instability (for the whistler (W) mode); the F emission is
generated by the nonlinear coupling of the Z and W modes and the H emission by
the nonlinear coupling of the UH modes. This presents an alternative mechanism
of coherent radiation in overdense plasmas.


  The world average values for the probabilities that a charm quark fragments
into D^*+ and Ds^+ have been calculated to be
f(c->D^*+)=0.235+/-0.007(+/-0.007) and f(c->Ds^+)=0.101+/-0.009(+/-0.025),
respectively. The average values for D^0, D^+ and Lambda_c^+ have been also
calculated.


  A discrete model of traffic on a multilane road is considered. The traffic is
presented as particles movement with a deterministic component and a stochastic
one. Formulas for the traffic characteristics have been found. The model can
explain theoretically some phenomena that have been discovered earlier on the
basis of the experimental results.


  In pervasive computing environment, Location Based Services (LBSs) are
getting popularity among users because of their usefulness in day-to-day life.
LBSs are information services that use geospatial data of mobile device and
smart phone users to provide information, entertainment and security in real
time. A key concern in such pervasive computing environment is the need to
reveal the user's exact location which may allow an adversary to infer private
information about the user. To address the privacy concerns of LBS users, a
large number of security approaches have been proposed based on the concept of
k-anonymity. The central idea in location k-anonymity is to find a set of k-1
users confined in a given geographical area of the actual user, such that the
location of these k users are indistinguishable from one another, thus
protecting the identity of the user. Although a number of performance
parameters like success rate, amount of privacy achieved are used to measure
the performance of the k-anonymity approaches, they make the implicit,
unrealistic assumption that the k-1 users are readily available. As such these
approaches ignore the turnaround time to process a user request, which is
crucial for a real-time application like LBS. In this work, we model the
k-anonymity approaches using queuing theory to compute the average sojourn time
of users and queue length of the system. To demonstrate that queuing theory can
be used to model all k-anonymity approaches, we consider graph-based
k-anonymity approaches. The proposed analytical model is further validated with
experimental results.


  We generalize the classical Bass model of innovation diffusion to include a
new class of agents --- Luddites --- that oppose the spread of innovation. Our
model also incorporates ignorants, susceptibles, and adopters. When an ignorant
and a susceptible meet, the former is converted to a susceptible at a given
rate, while a susceptible spontaneously adopts the innovation at a constant
rate. In response to the \emph{rate} of adoption, an ignorant may become a
Luddite and permanently reject the innovation. Instead of reaching complete
adoption, the final state generally consists of a population of Luddites,
ignorants, and adopters. The evolution of this system is investigated
analytically and by stochastic simulations. We determine the stationary
distribution of adopters, the time needed to reach the final state, and the
influence of the network topology on the innovation spread. Our model exhibits
an important dichotomy: when the rate of adoption is low, an innovation spreads
slowly but widely; in contrast, when the adoption rate is high, the innovation
spreads rapidly but the extent of the adoption is severely limited by Luddites.


  A model is proposed to describe a transition from a charged black hole of
mass $M$ and charge $Q$ to one of mass $\bar{M}$ and charge $\bar{Q}$. The
basic equations are derived from the non-vacuum Einstein field equations
sourced by the Coulomb field and by a null scalar field with a nonvanishing
trace anomaly. It is shown that the nonvanishing trace of the energy-momentum
tensor prevents the formation of a naked singularity.


  The Mermin-Wagner theorem states that long-range magnetic order does not
exist in one- or two-dimensional (2D) isotropic magnets with short-ranged
interactions. The theorem has been a milestone in magnetism and has been
driving the research of recently discovered 2D van der Waals (vdW) magnetic
materials from fundamentals up to potential applications. In such systems, the
existence of magnetic ordering is typically attributed to the presence of a
significant magnetic anisotropy, which is known to introduce a spin-wave gap
and circumvent the core assumption of the theorem. Here we show that in
finite-size 2D vdW magnets typically found in lab setups (e.g., within
millimetres), short-range interactions can be large enough to allow the
stabilisation of magnetic order at finite temperatures without any magnetic
anisotropy for practical implementations. We demonstrate that magnetic ordering
can be created in flakes of 2D materials independent of the lattice symmetry
due to the intrinsic nature of the spin exchange interactions and finite-size
effects in two-dimensions. Surprisingly we find that the crossover temperature,
where the intrinsic magnetisation changes from superparamagnetic to a
completely disordered paramagnetic regime, is weakly dependent on the system
length, requiring giant sizes (e.g., of the order of the observable universe
~10$^{26}$ m) in order to observe the vanishing of the magnetic order at
cryogenic temperatures as expected from the Mermin-Wagner theorem. Our findings
indicate exchange interactions as the main driving force behind the
stabilisation of short-range order in 2D magnetism and broaden the horizons of
possibilities for exploration of compounds with low anisotropy at an atomically
thin level.


  In this paper, we prove the Evans-Krylov theorem for nonlocal parabolic fully
nonlinear equations.


  Thin-walled straight circular tubes (SCT) are frequently used as energy
absorbing devices in the crashworthy applications. This paper introduces a
various tubal configuration, namely aluminium foam filled corrugation tube and
tapered tube with graded thickness, to control the collapse mode, and minimize
the peak crushing force and fluctuations in force-displacement curves. Dynamic
crushing simulations were carried out using commercially available finite
element package ABAQUS explicit 6.13 at impact velocity of 60 km/h
(corresponding to 16.7 m/s). A comparative study on the dynamic crushing
behaviour of aluminum foam-filled tapered with graded thickness and corrugated
tubes were performed. The results showed that deformation mode of corrugated
tube is more controllable and predictable in the case of empty tubes. In foam
filled tubes the mode of deformation changing from diamond or mixed mode to
concertina mode which is useful for crashworthy applications. The crushing
force efficiency of foam filled tubes increases when compared with the empty
tubes because of a higher mean force which can be achieved by less fluctuations
in force-displacement curves. The effects of corrugation wavelength and
amplitude of corrugation tubes on the collapse mode, peak crushing force and
energy absorption were studied. Compared to the conventional straight circular
tube, initial peak force and fluctuation in the force-displacement curves of
corrugated tube is considerably less. Desired crashworthy characteristics can
be obtained by changing corrugation wavelength and amplitude of corrugated
tubes.


  In the paradigm of object detection, the decision head is an important part,
which affects detection performance significantly. Yet how to design a
high-performance decision head remains to be an open issue. In this paper, we
propose a novel approach to combine decision trees and deep neural networks in
an end-to-end learning manner for object detection. First, we disentangle the
decision choices and prediction values by plugging soft decision trees into
neural networks. To facilitate effective learning, we propose randomized
decision routing with node selective and associative losses, which can boost
the feature representative learning and network decision simultaneously.
Second, we develop the decision head for object detection with narrow branches
to generate the routing probabilities and masks, for the purpose of obtaining
divergent decisions from different nodes. We name this approach as the
randomized decision routing for object detection, abbreviated as R(Det)$^2$.
Experiments on MS-COCO dataset demonstrate that R(Det)$^2$ is effective to
improve the detection performance. Equipped with existing detectors, it
achieves $1.4\sim 3.6$\% AP improvement.


  In the context of three-flavor neutrino mixing, we present a thorough study
of the phenomenological constraints applicable to three observables sensitive
to absolute neutrino masses: The effective neutrino mass in Tritium beta decay
(m_beta); the effective Majorana neutrino mass in neutrinoless double beta
decay (m_2beta); and the sum of neutrino masses in cosmology (Sigma). We
discuss the correlations among these variables which arise from the combination
of all the available neutrino oscillation data, in both normal and inverse
neutrino mass hierarchy. We set upper limits on m_beta by combining updated
results from the Mainz and Troitsk experiments. We also consider the latest
results on m_2beta from the Heidelberg-Moscow experiment, both with and without
the lower bound claimed by such experiment. We derive upper limits on Sigma
from an updated combination of data from the Wilkinson Microwave Anisotropy
Probe (WMAP) satellite and the 2 degrees Fields (2dF) Galaxy Redshifts Survey,
with and without Lyman-alpha forest data from the Sloan Digital Sky Survey
(SDSS), in models with a non-zero running of the spectral index of primordial
inflationary perturbations. The results are discussed in terms of
two-dimensional projections of the globally allowed region in the
(m_beta,m_2beta,Sigma) parameter space, which neatly show the relative impact
of each data set. In particular, the (in)compatibility between Sigma and
m_2beta constraints is highlighted for various combinations of data. We also
briefly discuss how future neutrino data (both oscillatory and non-oscillatory)
can further probe the currently allowed regions.


  In this paper we present a new approach to solve the satisfiability problem
(SAT), based on boolean networks (BN). We define a mapping between a SAT
instance and a BN, and we solve SAT problem by simulating the BN dynamics. We
prove that BN fixed points correspond to the SAT solutions. The mapping
presented allows to develop a new class of algorithms to solve SAT. Moreover,
this new approach suggests new ways to combine symbolic and connectionist
computation and provides a general framework for local search algorithms.


  The next-to-leading order (NLO) QCD calculation for the isolated photon and
isolated photon plus jet photoproduction at the ep collider DESY HERA is
presented. The predictions for the isolated photon with no restrictions imposed
on the jet are compared with the previous ones obtained in the small cone
approximation, and the differences are found to be below 2%. The theoretical
uncertainties in the cross section of the photoproduction of the photon plus
jet are discussed. A short comparison with the new preliminary H1 data and with
the NLO predictions of Fontannaz et al. is also presented.


  In previous work, two of us constructed the holographic dual of a single
Einstein-Podolsky-Rosen (EPR) pair in maximally supersymmetric Yang-Mills
theory. Here we extend that work in two directions. First, we use a
Randall-Sundrum brane to couple the entangled pair to dynamical gravity.
Second, we consider the entangled pair in the background of a black hole with
the particles on opposite sides of the horizon, turning the EPR pair into a
Hawking pair. We give general arguments that ER=EPR should be understood as a
duality between two equivalent descriptions of the same physical reality.


  At small AdS radius, the superstring on $AdS_5\times S^5$ was conjectured by
Maldacena to be equivalent to ${\cal N}=4$ super-Yang-Mills at small `t Hooft
coupling where thickened Feynman diagrams can be used to compute scattering
amplitudes. It was previously shown that the pure spinor worldsheet action of
the $AdS_5\times S^5$ superstring can be expressed as the sum of a BRST-trivial
term and a `B-term' which is antisymmetric in worldsheet derivatives. Using the
explicit form of the pure spinor vertex operators, it will be argued here that
the free super-Yang-Mills Feynman diagrams are described by the BRST-trivial
term where the thickened propagators are the regions of the string worldsheet
near the AdS boundary and the holes are the regions near the AdS horizon.
Evidence will then be presented that the antisymmetric B-term generates the
super-Yang-Mills vertex so that, at small radius and arbitrary genus, the
superstring amplitudes correctly reproduce the super-Yang-Mills Feynman diagram
expansion.


  We consider the eigenvalues of the biharmonic operator subject to several
homogeneous boundary conditions (Dirichlet, Neumann, Navier, Steklov). We show
that simple eigenvalues and elementary symmetric functions of multiple
eigenvalues are real analytic, and provide Hadamard-type formulas for the
corresponding shape derivatives. After recalling the known results in shape
optimization, we prove that balls are always critical domains under volume
constraint.


  Strengthening the classical concept of Steiner trees, West and Wu [J. Combin.
Theory Ser. B 102 (2012), 186--205] introduced the notion of a $T$-connector in
a graph $G$ with a set $T$ of terminals. They conjectured that if the set $T$
is $3k$-edge-connected in $G$, then $G$ contains $k$ edge-disjoint
$T$-connectors. We disprove this conjecture by constructing infinitely many
counterexamples for $k=1$ and for each even $k$.


  We address the question about the origin of the $\frac12 \frac{e^2}{h}$
conductance plateau observed in a recent experiment on an integer quantum Hall
(IQH) film covered by a superconducting (SC) film. Since 1-dimensional (1D)
chiral Majorana fermions on the edge of the above device can give rise to the
half quantized plateau, such a plateau was regarded as a smoking-gun evidence
for the chiral Majorana fermions. However, in this paper we give another
mechanism for the $\frac12 \frac{e^2}{h}$ conductance plateau. We find the
$\frac12 \frac{e^2}{h}$ conductance plateau to be a general feature of a good
electric contact between the IQH film and SC film, and cannot distinguish the
existence or the non-existence of 1D chiral Majorana fermions. We also find
that the contact conductance between SC and an IQH edge channel has a non-Ohmic
form $\sigma_\text{SC-Hall} \propto V^2$ in $k_BT \ll eV$ limit, if the SC and
IQH bulks are fully gapped.


  The barrier billiard is the simplest example of pseudo-integrable models with
interesting and intricate classical and quantum properties. Using the
Wiener-Hopf method it is demonstrated that quantum mechanics of a rectangular
billiard with a barrier in the centre can be reduced to the investigation of a
certain unitary matrix. Under heuristic assumptions this matrix is substituted
by a special low-complexity random unitary matrix of independent interest. The
main results of the paper are (i) spectral statistics of such billiards is
insensitive to the barrier height and (ii) it is well described by the
semi-Poisson distributions.


  The numbers $f_\lambda$ of standard tableaux of shape $\lambda\vdash n$
satisfy 2 fundamental recursions: $f_\lambda = \sum f_{\lambda^-}$ and $(n +
1)f_\lambda=\sum f_{\lambda^+}$, where $\lambda^-$ and $\lambda^+$ run over all
shapes obtained from $\lambda$ by adding or removing a square respectively. The
first of these recursions is trivial; the second can be proven algebraically
from the first. These recursions together imply algebraically the dimension
formula $n! =\sum f_\lambda^2$ for the irreducible representations of $S_n$. We
show that a combinatorial analysis of this classical algebraic argument
produces an infinite family of algorithms, among which are the classical
Robinson-Schensted row and column insertion algorithms. Each of our algorithms
yields a bijective proof of the dimension formula.


  The present paper is about estimation and prediction in high-dimensional
additive models under a sparsity assumption ($p\gg n$ paradigm). A PAC-Bayesian
strategy is investigated, delivering oracle inequalities in probability. The
implementation is performed through recent outcomes in high-dimensional MCMC
algorithms, and the performance of our method is assessed on simulated data.


  A wide range of mechanisms have been proposed to supply the energy for
gamma-ray bursts (GRB) at cosmological distances. It is a common misconception
that some of these, notably NS-NS mergers, cannot meet the energy requirements
suggested by recent observations. We show here that GRB energies, even at the
most distant redshifts detected, are compatible with current binary merger or
collapse scenarios involving compact objects. This is especially so if, as
expected, there is a moderate amount of beaming, since current observations
constrain the energy per solid angle much more strongly and directly than the
total energy. All plausible progenitors, ranging from NS-NS mergers to various
hypernova-like scenarios, eventually lead to the formation of a black hole with
a debris torus around it, so that the extractable energy is of the same order,
1E+54 ergs, in all cases. MHD conversion of gravitational into kinetic and
radiation energy can significantly increase the probability of observing large
photon fluxes, although significant collimation may achieve the same effect
with neutrino annihilation in short bursts. The lifetime of the debris torus is
dictated by a variety of physical processes, such as viscous accretion and
various instabilities; these mechanisms dominate at different stages in the
evolution of the torus and provide for a range of gamma-ray burst lifetimes.


  Predicting future 3D LiDAR pointclouds is a challenging task that is useful
in many applications in autonomous driving such as trajectory prediction, pose
forecasting and decision making. In this work, we propose a new LiDAR
prediction framework that is based on generative models namely Variational
Recurrent Neural Networks (VRNNs), titled Stochastic LiDAR Prediction and
Completion (SLPC). Our algorithm is able to address the limitations of previous
video prediction frameworks when dealing with sparse data by spatially
inpainting the depth maps in the upcoming frames. Our contributions can thus be
summarized as follows: we introduce the new task of predicting and completing
depth maps from spatially sparse data, we present a sparse version of VRNNs and
an effective self-supervised training method that does not require any labels.
Experimental results illustrate the effectiveness of our framework in
comparison to the state of the art methods in video prediction.


  The increasing use of large language models (LLMs) trained by third parties
raises significant security concerns. In particular, malicious actors can
introduce backdoors through poisoning attacks to generate undesirable outputs.
While such attacks have been extensively studied in image domains and
classification tasks, they remain underexplored for natural language generation
(NLG) tasks. To address this gap, we conduct an investigation of various
poisoning techniques targeting the LLM's fine-tuning phase via prefix-tuning, a
Parameter Efficient Fine-Tuning (PEFT) method. We assess their effectiveness
across two generative tasks: text summarization and text completion; and we
also introduce new metrics to quantify the success and stealthiness of such NLG
poisoning attacks. Through our experiments, we find that the prefix-tuning
hyperparameters and trigger designs are the most crucial factors to influence
attack success and stealthiness. Moreover, we demonstrate that existing popular
defenses are ineffective against our poisoning attacks. Our study presents the
first systematic approach to understanding poisoning attacks targeting NLG
tasks during fine-tuning via PEFT across a wide range of triggers and attack
settings. We hope our findings will aid the AI security community in developing
effective defenses against such threats.


  The spin-1 Ising (BEG) model with the nearest-neighbour bilinear and
biquadratic interactions and single-ion anisotropy is simulated on a cellular
automaton which improved from the Creutz cellular automaton(CCA) for a simple
cubic lattice. The simulations have been made for several sets of parameters
$K/J$ and $D/J$ in the $-3<D/J\leq 0$ and $-1\leq K/J\leq 0$ parameter regions.
The re-entrant and double re-entrant phase transitions of the BEG model are
determined from the temperature variations of the thermodynamic quantities
($M$, $Q$ and $\chi $). The phase diagrams characterizing phase transitions are
compared with those obtained from other methods.


  The present monograph explores the correspondence between quantum and
classical mechanics in the particular context of spin systems, that is,
SU(2)-symmetric mechanical systems. Here, a detailed presentation of quantum
spin-j systems, with emphasis on the SO(3)-invariant decomposition of their
operator algebras, is followed by an introduction to the Poisson algebra of the
classical spin system and a similarly detailed presentation of its
SO(3)-invariant decomposition. Subsequently, this monograph proceeds with a
detailed and systematic study of general quantum-classical symbol
correspondences for spin-j systems and their induced twisted products of
functions on the 2-sphere. This original systematic presentation culminates
with the study of twisted products in the asymptotic limit of high spin
numbers. In the context of spin systems, it shows how classical mechanics may
or may not emerge as an asymptotic limit of quantum mechanics.


  It was demonstrated recently [Dunajski, Ferapontov and Kruglikov (2014)] that
the Manakov-Santini system describes a local form of general Lorentzian
Einstein-Weyl geometry. We introduce integrable matrix extension of the
Manakov-Santini system and show that it describes (2+1)-dimensional integrable
chiral model in Einstein-Weyl space. We develop a dressing scheme for the
extended MS system and define an extended hierarchy. Matrix extension of Toda
type system connected with another local form of Einstein-Weyl geometry is also
considered.


  We numerically study whether there exist nowhere vanishing harmonic $1$-forms
on the real locus of some carefully constructed examples of Calabi-Yau
manifolds, which would then give rise to potentially new examples of
$G_2$-manifolds and an explicit description of their metrics. We do this in two
steps: first, we use a neural network to compute an approximate Calabi-Yau
metric on each manifold. Second, we use another neural network to compute an
approximately harmonic $1$-form with respect to the approximate metric, and
then inspect the found solution. On two manifolds existence of a nowhere
vanishing harmonic $1$-form can be ruled out using differential geometry. The
real locus of a third manifold is diffeomorphic to $S^1 \times S^2$, and our
numerics suggest that when the Calabi-Yau metric is close to a singular limit,
then it admits a nowhere vanishing harmonic $1$-form. We explain how such an
approximate solution could potentially be used in a numerically verified proof
for the fact that our example manifold must admit a nowhere vanishing harmonic
$1$-form.


  This paper studies the estimation of cascaded channels in passive intelligent
reflective surface (IRS)- aided multiple-input multiple-output (MIMO) systems
employing hybrid precoders and combiners. We propose a low-complexity solution
that estimates the channel parameters progressively. The angles of departure
(AoDs) and angles of arrival (AoAs) at the transmitter and receiver,
respectively, are first estimated using inductive matrix completion (IMC)
followed by root-MUSIC based super-resolution spectrum estimation.
Forward-backward spatial smoothing (FBSS) is applied to address the coherence
issue. Using the estimated AoAs and AoDs, the training precoders and combiners
are then optimized and the angle differences between the AoAs and AoDs at the
IRS are estimated using the least squares (LS) method followed by FBSS and the
root-MUSIC algorithm. Finally, the composite path gains of the cascaded channel
are estimated using on-grid sparse recovery with a small-size dictionary. The
simulation results suggest that the proposed estimator can achieve improved
channel parameter estimation performance with lower complexity as compared to
several recently reported alternatives, thanks to the exploitation of the
knowledge of the array responses and low-rankness of the channel using
low-complexity algorithms at all the stages.


  This paper introduces a set of terms that are intended to act as an interface
between cyber ontologies (like a file system ontology or a data fusion
ontology) and top- and mid-level ontologies, specifically Basic Formal Ontology
and the Common Core Ontologies. These terms center on what makes
cyberinformation management unique: numerous acts of copying items of
information, the aggregates of copies that result from those acts, and the
faithful members of those aggregates that represent all other members.


  The state of a finite-dimensional quantum system is described by a density
matrix that can be decomposed into a real diagonal, a real off-diagonal and and
an imaginary off-diagonal part. The latter plays a peculiar role. While it is
intuitively clear that some of the imaginary coordinates cannot have the same
extension as their real counterparts the precise relation is not obvious. We
give a complete characterization of the constraints in terms of tight
inequalities for real and imaginary Bloch-type coordinates. Our description
entails a three-dimensional Bloch ball-type model for the state space. We
uncover a surprising qualitative difference for the state-space boundaries in
even and odd dimensions.


  Dynamical simulation of the cascade failures on the EU and USA high-voltage
power grids has been done via solving the second-order Kuramoto equation. We
show that synchronization transition happens by increasing the global coupling
parameter $K$ with metasatble states depending on the initial conditions so
that hysteresis loops occur. We provide analytic results for the time
dependence of frequency spread in the large $K$ approximation and by comparing
it with numerics of $d=2,3$ lattices, we find agreement in the case of ordered
initial conditions. However, different power-law (PL) tails occur, when the
fluctuations are strong. After thermalizing the systems we allow a single line
cut failure and follow the subsequent overloads with respect to threshold
values $T$. The PDFs $p(N_f)$ of the cascade failures exhibit PL tails near the
synchronization transition point $K_c$. Near $K_c$ the exponents of the PL-s
for the US power grid vary with $T$ as $1.4 \le \tau \le 2.1$, in agreement
with the empirical blackout statistics, while on the EU power grid we find
somewhat steeper PL-s characterized by $1.4 \le \tau \le 2.4$. Below $K_c$ we
find signatures of $T$-dependent PL-s, caused by frustrated synchronization,
reminiscent of Griffiths effects. Here we also observe stability growth
following the blackout cascades, similar to intentional islanding, but for $K >
K_c$ this does not happen. For $T < T_c$, bumps appear in the PDFs with large
mean values, known as "dragon king" blackout events. We also analyze the
delaying/stabilizing effects of instantaneous feedback or increased dissipation
and show how local synchronization behaves on geographic maps.


  Electromagnetic mean squared radii of Lambda(1405) are evaluated in chiral
unitary approach. In this approach we regard Lambda(1405) as dynamically
generated resonances in the octet meson and octet baryon scattering, and also
as KbarN bound state. Especially for the Lambda(1405) as KbarN bound state we
obtain negative electric mean squared radius. With the small binding energy of
Lambda(1405) in the chiral unitary approach, our results imply that
Lambda(1405) has structure that K^- is widely spread around p.


  We propose FindIt, a simple and versatile framework that unifies a variety of
visual grounding and localization tasks including referring expression
comprehension, text-based localization, and object detection. Key to our
architecture is an efficient multi-scale fusion module that unifies the
disparate localization requirements across the tasks. In addition, we discover
that a standard object detector is surprisingly effective in unifying these
tasks without a need for task-specific design, losses, or pre-computed
detections. Our end-to-end trainable framework responds flexibly and accurately
to a wide range of referring expression, localization or detection queries for
zero, one, or multiple objects. Jointly trained on these tasks, FindIt
outperforms the state of the art on both referring expression and text-based
localization, and shows competitive performance on object detection. Finally,
FindIt generalizes better to out-of-distribution data and novel categories
compared to strong single-task baselines. All of these are accomplished by a
single, unified and efficient model. The code will be released.


  We investigate the effect of quantum errors on a monitored Brownian
Sachdev-Ye-Kitaev (SYK) model featuring a measurement-induced phase transition
that can be understood as a symmetry-breaking transition of an effective $Z_4$
magnet in the replica space. The errors describe the loss of information about
the measurement outcomes and are applied during the non-unitary evolution or at
the end of the evolution. In the former case, we find that this error can be
mapped to an emergent magnetic field in the $Z_4$ magnet, and as a consequence,
the symmetry is explicitly broken independent of the measurement rate. R\'enyi
entropies computed by twisting boundary conditions now generate domain walls
even in the would-be symmetric phase at a high measurement rate. The entropy is
therefore volume-law irrespective of the measurement rate. In the latter case,
the error-induced magnetic field only exists near the boundary of the magnet.
Varying the magnetic field leads to a pinning transition of domain walls,
corresponding to error threshold of the quantum code prepared by the
non-unitary SYK dynamics.


  The contribution contains the preface to the Proceedings to the 17th Workshop
"What Comes Beyond the Standard Models", Bled, July 20 - 28, 2014, published in
Bled workshops in physics, Vol.15, No. 2, DMFA-Zaloznistvo, Ljubljana, Dec.
2014, links to (most of) the published contributions and section (by M.Yu.
Khlopov) on VIA at Bled 2014.


  Gaussian processes (GPs) provide a powerful non-parametric framework for
reasoning over functions. Despite appealing theory, its superlinear
computational and memory complexities have presented a long-standing challenge.
State-of-the-art sparse variational inference methods trade modeling accuracy
against complexity. However, the complexities of these methods still scale
superlinearly in the number of basis functions, implying that that sparse GP
methods are able to learn from large datasets only when a small model is used.
Recently, a decoupled approach was proposed that removes the unnecessary
coupling between the complexities of modeling the mean and the covariance
functions of a GP. It achieves a linear complexity in the number of mean
parameters, so an expressive posterior mean function can be modeled. While
promising, this approach suffers from optimization difficulties due to
ill-conditioning and non-convexity. In this work, we propose an alternative
decoupled parametrization. It adopts an orthogonal basis in the mean function
to model the residues that cannot be learned by the standard coupled approach.
Therefore, our method extends, rather than replaces, the coupled approach to
achieve strictly better performance. This construction admits a straightforward
natural gradient update rule, so the structure of the information manifold that
is lost during decoupling can be leveraged to speed up learning. Empirically,
our algorithm demonstrates significantly faster convergence in multiple
experiments.


  Quasi-symmetric functions show up in an approach to solve the
Kadomtsev-Petviashvili (KP) hierarchy. This moreover features a new
nonassociative product of quasi-symmetric functions that satisfies simple
relations with the ordinary product and the outer coproduct. In particular,
supplied with this new product and the outer coproduct, the algebra of
quasi-symmetric functions becomes an infinitesimal bialgebra. Using these
results we derive a sequence of identities in the algebra of quasi-symmetric
functions that are in formal correspondence with the equations of the KP
hierarchy.


  We describe two methods relevant to multi-lingual machine translation
systems, which can be used to port linguistic data (grammars, lexicons and
transfer rules) between systems used for processing related languages. The
methods are fully implemented within the Spoken Language Translator system, and
were used to create versions of the system for two new language pairs using
only a month of expert effort.


  Inspired by a recent sharp Sobolev trace inequality of order four on the
balls $\mathbb B^{n+1}$ found by Ache and Chang [AC15], we propose a slightly
different approach to reprove Ache-Chang's trace inequality. To illustrate this
approach, we reprove the classical Sobolev trace inequality of order two on
$\mathbb B^{n+1}$ and provide sharp Sobolev trace inequalities of orders six
and eight on $\mathbb B^{n+1}$. As the limiting case of the Sobolev trace
inequality, a Lebedev-Milin type inequality of order up to eight is also
considered.


  Among the detectors used for rare event searches, such as neutrinoless Double
Beta Decay (0$\nu$DBD) and Dark Matter experiments, bolometers are very
promising because of their favorable properties (excellent energy resolution,
high detector efficiency, a wide choice of different materials used as
absorber, ...). However, up to now, the actual interesting possibility to
identify the interacting particle, and thus to greatly reduce the background,
can be fulfilled only with a double read-out (i.e. the simultaneous and
independent read out of heat and scintillation light or heat and ionization).
This double read-out could greatly complicate the assembly of a huge,
multi-detector array, such as CUORE and EURECA. The possibility to recognize
the interacting particle through the shape of the thermal pulse is then clearly
a very interesting opportunity.
  While detailed analyses of the signal time development in purely thermal
detectors have not produced so far interesting results, similar analyses on
macro-bolometers ($\sim$10-500 g) built with scintillating crystals showed that
it is possible to distinguish between an electron or $\gamma$-ray and an
$\alpha$ particle interaction (i.e. the main source of background for 0$\nu$DBD
experiments based on the bolometric technique). Results on pulse shape analysis
of a CaMoO$_4$ crystal operated as bolometer is reported as an example. An
explanation of this behavior, based on the energy partition in the heat and
scintillation channels, is also presented.


  The two-dimensional color code is an alternative to the toric code that
encodes more logical qubits while maintaining crucial features of the
$\mathbb{Z}_2\times\mathbb{Z}_2$ toric code in the long wavelength limit.
However its short range physics include single qubit Pauli operations that
violate either three or six stabilisers as opposed to the toric code where
single qubit Pauli operations violate two or four stabilisers. Exploiting this
fact we construct several non-CSS versions of the two-dimensional color code
falling into two families - those where either three, four or five stabilisers
are violated and those which violate exactly four stabilisers for all the three
types of single qubit Pauli operations. These models are not equivalent to the
original color code by a local unitary transformation. Nevertheless the code
spaces of the CSS and non-CSS versions are related by local unitaries which
reflects the fact that their long range physics coincide. This also implies
that the non-CSS versions host transversal Clifford gates and hence support
fault-tolerant computations. As a consequence of the non-CSS structure, the
logical operators are of a mixed type which in some cases include all the three
Pauli operators making them potentially useful for protection against biased
Pauli noise.


  In this paper we consider a classical treatment of a very dense collection of
photons forming a self-sustained globe under its own gravitational influence.
We call this a "photonic globe" We show that such a dense photonic globe will
have a radius closely corresponding to the Schwarzschild radius. Thus lending
substance to the conjuncture that the region within the Schwarzschild radius of
a black hole contains only pure radiation. As an application example, we
consider the case of a very large photonic globe whose radius corresponds to
the radius of the universe and containing radiation of the frequency of the
microwave background (160.2 GHZ). It so turns out that such a photonic globe
has an average density which closely corresponds to the observed average
density of our universe.


  In response to the increasing deployment of battery storage systems for cost
reduction and grid stress mitigation, this study presents the development of a
new real-time Markov decision process model to efficiently schedule battery
systems in buildings under electrical load uncertainty. The proposed model
incorporates quantile Fourier regression for load fitting, leading to a
large-scale optimization problem with approximately a million decision
variables and constraints. To address this complexity, the problem is
formulated as a linear program and solved using a commercial solver, ensuring
effective navigation and identification of optimal solutions. The model's
performance is evaluated by considering different pricing policies and
scenarios, including demand peak shaving. Validation of the Markov model is
conducted using one year of historical demand data from a school. Findings
indicate that MDP performance in adapting to uncertain loads can range from 30
to 99% depending on the pricing policy.


  We study the properties of simulated high-redshift galaxies using
cosmological N-body/gasdynamical runs from the OverWhelmingly Large Simulations
(OWLS) project. The runs contrast several feedback implementations of varying
effectiveness: from no-feedback, to supernova-driven winds to powerful
AGN-driven outflows. These different feedback models result in large variations
in the abundance and structural properties of bright galaxies at z=2. We find
that feedback affects the baryonic mass of a galaxy much more severely than its
spin, which is on average roughly half that of its surrounding dark matter halo
in our runs. Feedback induces strong correlations between angular momentum
content and galaxy mass that leave their imprint on galaxy scaling relations
and morphologies. Encouragingly, we find that galaxy disks are common in
moderate-feedback runs, making up typically ~50% of all galaxies at the centers
of haloes with virial mass exceeding 1e11 M_sun. The size, stellar masses, and
circular speeds of simulated galaxies formed in such runs have properties that
straddle those of large star-forming disks and of compact early-type galaxies
at z=2. Once the detailed abundance and structural properties of these rare
objects are well established it may be possible to use them to gauge the
overall efficacy of feedback in the formation of high redshift galaxies.


  Credit card plays a very important rule in today's economy. It becomes an
unavoidable part of household, business and global activities. Although using
credit cards provides enormous benefits when used carefully and
responsibly,significant credit and financial damages may be caused by
fraudulent activities. Many techniques have been proposed to confront the
growth in credit card fraud. However, all of these techniques have the same
goal of avoiding the credit card fraud; each one has its own drawbacks,
advantages and characteristics. In this paper, after investigating difficulties
of credit card fraud detection, we seek to review the state of the art in
credit card fraud detection techniques, data sets and evaluation criteria.The
advantages and disadvantages of fraud detection methods are enumerated and
compared.Furthermore, a classification of mentioned techniques into two main
fraud detection approaches, namely, misuses (supervised) and anomaly detection
(unsupervised) is presented. Again, a classification of techniques is proposed
based on capability to process the numerical and categorical data sets.
Different data sets used in literature are then described and grouped into real
and synthesized data and the effective and common attributes are extracted for
further usage.Moreover, evaluation employed criterions in literature are
collected and discussed.Consequently, open issues for credit card fraud
detection are explained as guidelines for new researchers.


  This article showcases a personal decision support tool (PDST) called
HOPLITE, for performing insightful and actionable quantitative assessments of
hospital capacity, to support hospital planners and health care managers. The
tool is user-friendly and intuitive, automates tasks, provides instant
reporting, and is extensible. It has been developed as an Excel Visual Basic
for Applications (VBA) due to its perceived ease of deployment, ease of use,
Office's vast installed userbase, and extensive legacy in business. The
methodology developed in this article bridges the gap between mathematical
theory and practice, which our inference suggests, has restricted the uptake
and or development of advanced hospital planning tools and software. To the
best of our knowledge, no personal decision support tool (PDST) has yet been
created and installed within any existing hospital IT systems, to perform the
aforementioned tasks. This article demonstrates that the development of a PDST
for hospitals is viable and that optimization methods can be embedded quite
simply at no cost. The results of extensive development and testing indicate
that HOPLITE can automate many nuanced tasks. Furthermore, there are few
limitations and only minor scalability issues with the application of free to
use optimization software. The functionality that HOPLITE provides may make it
easier to calibrate hospitals strategically and/or tactically to demands. It
may give hospitals more control over their case-mix and their resources,
helping them to operate more proactively and more efficiently.


  This paper explores the capacity of computer vision models to discern
temporal information in visual content, focusing specifically on historical
photographs. We investigate the dating of images using OpenCLIP, an open-source
implementation of CLIP, a multi-modal language and vision model. Our experiment
consists of three steps: zero-shot classification, fine-tuning, and analysis of
visual content. We use the \textit{De Boer Scene Detection} dataset, containing
39,866 gray-scale historical press photographs from 1950 to 1999. The results
show that zero-shot classification is relatively ineffective for image dating,
with a bias towards predicting dates in the past. Fine-tuning OpenCLIP with a
logistic classifier improves performance and eliminates the bias. Additionally,
our analysis reveals that images featuring buses, cars, cats, dogs, and people
are more accurately dated, suggesting the presence of temporal markers. The
study highlights the potential of machine learning models like OpenCLIP in
dating images and emphasizes the importance of fine-tuning for accurate
temporal analysis. Future research should explore the application of these
findings to color photographs and diverse datasets.


  Existing Masked Image Modeling (MIM) depends on a spatial patch-based
masking-reconstruction strategy to perceive objects'features from unlabeled
images, which may face two limitations when applied to chest CT: 1) inefficient
feature learning due to complex anatomical details presented in CT images, and
2) suboptimal knowledge transfer owing to input disparity between upstream and
downstream models. To address these issues, we propose a new MIM method named
Tissue-Contrastive Semi-Masked Autoencoder (TCS-MAE) for modeling chest CT
images. Our method has two novel designs: 1) a tissue-based
masking-reconstruction strategy to capture more fine-grained anatomical
features, and 2) a dual-AE architecture with contrastive learning between the
masked and original image views to bridge the gap of the upstream and
downstream models. To validate our method, we systematically investigate
representative contrastive, generative, and hybrid self-supervised learning
methods on top of tasks involving segmenting pneumonia, mediastinal tumors, and
various organs. The results demonstrate that, compared to existing methods, our
TCS-MAE more effectively learns tissue-aware representations, thereby
significantly enhancing segmentation performance across all tasks.


  Neural networks have become standard tools in the analysis of data, but they
lack comprehensive mathematical theories. For example, there are very few
statistical guarantees for learning neural networks from data, especially for
classes of estimators that are used in practice or at least similar to such. In
this paper, we develop a general statistical guarantee for estimators that
consist of a least-squares term and a regularizer. We then exemplify this
guarantee with $\ell_1$-regularization, showing that the corresponding
prediction error increases at most sub-linearly in the number of layers and at
most logarithmically in the total number of parameters. Our results establish a
mathematical basis for regularized estimation of neural networks, and they
deepen our mathematical understanding of neural networks and deep learning more
generally.


  We examine the weakly interacting atoms in an ultracold Fermi gas leading to
a state of macroscopic coherence, from a theoretical perspective. It has been
shown that this state can be described as a fermionic coherent state. These
coherent states are the eigenstates of fermionic annihilation operators, the
eigenvalues being anti-commuting numbers or Grassmann numbers. By exploiting
the simple rules of Grassmann algebra and a close kinship between relations
evaluated for more familiar bosonic fields and those for fermionic fields, we
derive the thermodynamic limit, the spontaneous symmetry breaking and the
quasi-particle spectrum of the fermionic system.


  The optical conductivity is the basic defining property of materials
characterizing the current response toward time-dependent electric fields. In
this work, following the approach of Kubo's response theory, we study the
general properties of the nonlinear optical conductivities of quantum many-body
systems both in equilibrium and non-equilibrium. We obtain an expression of the
second- and the third-order optical conductivity in terms of correlation
functions and present a perturbative proof of the generalized Kohn formula
proposed recently. We also discuss a generalization of the $f$-sum rule to a
non-equilibrium setting by focusing on the instantaneous response.


  In this paper we propose algebraic universal procedure for deriving "fusion
rules" and Baxter equation for any integrable model with $U_q(\widehat{sl}_2)$
symmetry of Quantum Inverse Scattering Method. Universal Baxter Q- operator is
got from the certain infinite dimensional representation called q-oscillator
one of the Universal R- matrix for $U_q(\widehat{sl}_2)$ affine algebra (first
proposed by V. Bazhanov, S.Lukyanov and A.Zamolodchikov for quantum KdV case).
We also examine the algebraic properties of Q-operator.


  The projected random phase approximation (PRPA) for charge-exchange
excitations is derived from the time-dependent variational principle. Explicit
results for the unperturbed energies (including the self-energy corrections),
the PRPA matrices, and the transition matrix elements are presented. The effect
of the projection procedure on the two-neutrino $\beta\beta$ decay in $^{76}Ge$
is briefly discussed.


  Supersymmetry (SUSY) is one of the most relevant scenarios of new physics
searched by the ATLAS experiment at the CERN Large Hadron Collider. In this
writeup the principal search strategies employed by ATLAS are outlined and the
most recent results for analyses targeting SUSY discovery are discussed. A wide
range of signatures is covered motivated by various theoretical scenarios and
topologies: strong production, third-generation fermions, long-lived particles
and R-parity violation, among others. The results are based on up to ~5 fb-1 of
data recorded during 2010-2011 at sqrt(s) = 7 TeV centre-of-mass energy by the
ATLAS experiment at the LHC.


  In their seminal work, Mustafa and Ray (2009) showed that a wide class of
geometric set cover (SC) problems admit a PTAS via local search -- this is one
of the most general approaches known for such problems. Their result applies if
a naturally defined "exchange graph" for two feasible solutions is planar and
is based on subdividing this graph via a planar separator theorem due to
Frederickson (1987). Obtaining similar results for the related maximum
k-coverage problem (MC) seems non-trivial due to the hard cardinality
constraint. In fact, while Badanidiyuru, Kleinberg, and Lee (2012) have shown
(via a different analysis) that local search yields a PTAS for two-dimensional
real halfspaces, they only conjectured that the same holds true for dimension
three. Interestingly, at this point it was already known that local search
provides a PTAS for the corresponding set cover case and this followed directly
from the approach of Mustafa and Ray.
  In this work we provide a way to address the above-mentioned issue. First, we
propose a color-balanced version of the planar separator theorem. The resulting
subdivision approximates locally in each part the global distribution of the
colors. Second, we show how this roughly balanced subdivision can be employed
in a more careful analysis to strictly obey the hard cardinality constraint.
More specifically, we obtain a PTAS for any "planarizable" instance of MC and
thus essentially for all cases where the corresponding SC instance can be
tackled via the approach of Mustafa and Ray. As a corollary, we confirm the
conjecture of Badanidiyuru, Kleinberg, and Lee regarding real half spaces in
dimension three. We feel that our ideas could also be helpful in other
geometric settings involving a cardinality constraint.


  Two-term asymptotic formulae for the probability distribution functions for
the smallest eigenvalue of the Jacobi $ \beta $-Ensembles are derived for
matrices of large size in the r\'egime where $ \beta > 0 $ is arbitrary and one
of the model parameters $ \alpha_1 $ is an integer. By a straightforward
transformation this leads to corresponding results for the distribution of the
largest eigenvalue. The explicit expressions are given in terms of
multi-variable hypergeometric functions, and it is found that the first-order
corrections are proportional to the derivative of the leading order limiting
distribution function. In some special cases $ \beta = 2 $ and/or small values
of $ \alpha_1 $, explicit formulae involving more familiar functions, such as
the modified Bessel function of the first kind, are presented.


  Next generation of ultra-intense laser facilities will lead to novel physical
conditions ruled by collective and quantum electrodynamics effects, such as
synchrotron-like emission of high-energy photons and electron-positron pair
generation. In view of the future experiments performed in this regime, the
latter processes have been implemented into the particle-in-cell code CALDER.


  In this paper we revisit the anisotropic isoperimetric and the
Brunn-Minkowski inequalities for convex sets. The best known constant
$C(n)=Cn^{7}$ depending on the space dimension $n$ in both inequalities is due
to Segal [\ref{bib:Seg.}]. We improve that constant to $Cn^6$ for convex sets
and to $Cn^5$ for centrally symmetric convex sets. We also conjecture, that the
best constant in both inequalities must be of the form $Cn^2,$ i.e., quadratic
in $n.$ The tools are the Brenier's mapping from the theory of mass
transportation combined with new sharp geometric-arithmetic mean and some
algebraic inequalities plus a trace estimate by Figalli, Maggi and Pratelli.


  The electronic structure of four polytypes (beta, gamma, delta and epsilon)
of hexagonal GaSe and InSe is calculated from first principles, using the
WIEN2k and VASP codes and PBEsol prescription for the exchange-correlation
potential, aiming specifically at elucidating the crystallographic parameters
and comparing the energy placement of corresponding competing structures.
Further on, the compounds with different composition of the same constituents,
namely the ordered-vacancies systems Ga2Se3 and In2Se3, were subject to a
similar study, of which the relaxed crystal structure data for three different
phases is reported. Comparison is done with the nomi- nal wurtzite structure
over which the cation vacancies are introduced, and the relaxation pattern
discussed.


  With the rise of internet technology amidst increasing rates of urbanization,
sharing information has never been easier thanks to globally-adopted platforms
for digital communication. The resulting output of massive amounts of
user-generated data can be used to enhance our understanding of significant
societal issues particularly for urbanizing areas. In order to better analyze
protest behavior, we enhanced the GSR dataset and manually labeled all the
images. We used deep learning techniques to analyze social media data to detect
social unrest through image classification, which performed good in predict
multi-attributes, then also used map visualization to display protest behaviors
across the country.


  We consider a Bose-Einstein condensate (BEC) with attractive two-body
interactions in a cigar-shaped trap, initially prepared in its ground state for
a given negative scattering length, which is quenched to a larger absolute
value of the scattering length. Using the mean-field approximation, we compute
numerically, for an experimentally relevant range of aspect ratios and initial
strengths of the coupling, two critical values of quench: one corresponds to
the weakest attraction strength the quench to which causes the system to
collapse before completing even a single return from the narrow configuration
("perihelion") in its breathing cycle. The other is a similar critical point
for the occurrence of collapse before completing two returns. In the latter
case, we also compute the limiting value, as we keep increasing the strength of
the post-quench attraction towards its critical value, of the time interval
between the first two perihelia. We also use a Gaussian variational model to
estimate the critical quenched attraction strength below which the system is
stable against the collapse for long times. These time intervals and critical
attraction strengths---apart from being fundamental properties of nonlinear
dynamics of self-attractive BECs---may provide clues to the design of upcoming
experiments that are trying to create robust BEC breathers.


  We have studied the effects of optical-frequency light on proximitized
InAs/Al Josephson junctions based on highly n-doped InAs nanowires at varying
incident photon flux and at three different photon wavelengths. The
experimentally obtained IV curves were modeled using a shunted junction model
which takes scattering at the contact interfaces into account. The Josephson
junctions were found to be surprisingly robust, interacting with the incident
radiation only through heating, whereas above the critical current our devices
showed non-thermal effects resulting from photon exposure. Our work provides
important guidelines for the co-integration of Josephson junctions alongside
quantum photonic circuits and lays the foundation for future work on
nanowire-based hybrid photon detectors.


  We study the QCD topology and axion properties at finite temperature and
chemical potential in the framework of the two-flavor Nambu$-$Jona-Lasinio
model. We find that the behaviors of the two lowest cumulants of the QCD
topological charge distribution and axion properties are highly sensitive to
the critical behavior of the chiral phase transition. In particular, the
topological susceptibility and the axion mass follow the response of the chiral
condensate to temperature and chemical potential, showing that both quantities
decrease monotonically with the increment of temperature and/or chemical
potential. However, it is important to note that the normalized fourth cumulant
behaves differently depending on the temperature. At low temperatures, it is a
non-monotonic function of the chemical potential, while at high temperatures,
it monotonically decreases. Additionally, its value invariably approaches the
asymptotic value of $b_2^{\text {inst }}=-1/12$, predicted by the dilute
instanton gas model. We also observe that with the increase in chemical
potential at relatively low temperatures, the axion self-coupling constant
exhibits a sharp peak around the critical point, which can even be more than
twice its vacuum value. After that, the self-coupling drops sharply to a much
lower value than its vacuum value, eventually approaching zero in the high
chemical potential limit. The finding that the axion self-coupling constant is
significantly enhanced in high-density environments near the chiral phase
transition could lead to the creation or enhancement of an axion Bose-Einstein
condensate in compact astrophysical objects.


  Developing domain-specific conversational agents (CAs) has been challenged by
the need for extensive domain-focused data. Recent advancements in Large
Language Models (LLMs) make them a viable option as a knowledge backbone. LLMs
behaviour can be enhanced through prompting, instructing them to perform
downstream tasks in a zero-shot fashion (i.e. without training). To this end,
we incorporated structural knowledge into prompts and used prompted LLMs to
build domain-specific voice-based CAs. We demonstrate this approach for the
specific domain of textile circularity in form of the design, development, and
evaluation of TextileBot. We present the design and development of the voice
agent TextileBot and also the insights from an in-person user study (N=30)
evaluating three variations of TextileBots. We analyse the human-agent
interactions, combining quantitative and qualitative methods. Our results
suggest that participants engaged in multi-turn conversations, and their
perceptions of the three variation agents and respective interactions varied
demonstrating the effectiveness of our prompt-based LLM approach. We discuss
the dynamics of these interactions and their implications for designing future
voice-based CAs. The results show that our method's potential for building
domain-specific CAs. Furthermore, most participants engaged in multi-turn
conversations, and their perceptions of the three voice agents and respective
interactions varied demonstrating the effectiveness of our prompt-based LLM
approach. We discuss the dynamics of these interactions and their implications
for designing future voice-based CAs.


  We give here new upper bounds on the size of a smallest feedback vertex set
in planar graphs with high girth. In particular, we prove that a planar graph
with girth $g$ and size $m$ has a feedback vertex set of size at most
$\frac{4m}{3g}$, improving the trivial bound of $\frac{2m}{g}$. We also prove
that every $2$-connected graph with maximum degree $3$ and order $n$ has a
feedback vertex set of size at most $\frac{n+2}{3}$.


  To a vector space V equipped with a non-quasiclassical involutary solution of
the quantum Yang-Baxter equation and a partition $\lambda$, we associate a
vector space $\Vl$ and compute its dimension. The functor $V\mapsto \Vl$ is an
analogue of the well-known Schur functor. The category generated by the objects
$\Vl$ is called the Schur-Weyl category. We suggest a way to construct some
related twisted varieties looking like orbits of semisimple elements in
sl(n)^*. We consider in detail a particular case of such "twisted orbits",
namely the twisted non-quasiclassical hyperboloid and we define the twisted
Casimir operator on it. In this case, we obtain a formula looking like the Weyl
formula, and describing the asymptotic behavior of the function
$N(\la)=\{\sharp \la_i\leq\la\}$, where $\la_i$ are the eigenvalues of this
operator.


  We study the density of rational points on a higher-dimensional orbifold
$(\mathbb{P}^{n-1},D)$ when $D$ is a $\mathbb{Q}$-divisor involving
hyperplanes. This allows us to address a question of Tanimoto about whether the
set of rational points on such an orbifold constitutes a thin set. Our approach
relies on the Hardy-Littlewood circle method to first study an asymptotic
version of Waring's problem for mixed powers. In doing so we make crucial use
of the recent resolution of the main conjecture in Vinogradov's mean value
theorem, due to Bourgain-Demeter-Guth and Wooley.


  The galaxy M49 (NGC 4472) is the brightest early-type galaxy in the Virgo
Cluster. It is located in Subcluster B and has an unusually blue, metal-poor
outer halo. Planetary nebulae (PNe) are excellent tracers of diffuse galaxy and
intragroup light. We present a photometric survey of PNe in the galaxy's
extended halo to characterise its PN population, as well as the surrounding
intragroup light (IGL) of the Subcluster B. PNe were identified based on their
bright [OIII]5007 \AA\ emission and absence of a broad-band continuum. We
identify 738 PNe out to a radius of 155 kpc from M49's centre from which we
define a complete sample of 624 PNe within a limiting magnitude of m_5007=28.8.
Comparing the PN number density to the broad-band stellar surface brightness
profile, we find a variation of the PN-specific frequency (alpha-parameter)
with radius. The outer halo beyond 60 kpc has a 3.2 times higher
alpha-parameter compared to the main galaxy halo, which is likely due to
contribution from the surrounding blue IGL. We use the Planetary Nebulae
Luminosity Function (PNLF) as an indicator of distance and stellar population.
Its slope, which correlates empirically with galaxy type, varies within the
inner halo. In the eastern quadrant of M49, the PNLF slope is shallower,
indicating an additional localised, bright PN population following an accretion
event, likely that of the dwarf irregular galaxy VCC1249. We also determined a
distance modulus of mu = 31.29+/-0.08 for M49, corresponding to a physical
distance of 18.1+/-0.6 Mpc, which agrees with a recent surface-brightness
fluctuations distance. The PN populations in the outer halo of M49 are
consistent with the presence of a main Sersic galaxy halo with a slight (B-V)
colour gradient of 10${}^{-4}$ mag/arcsec surrounded by intragroup light with a
very blue colour of (B-V)=0.25 and a constant surface brightness mu_V=28.0
mag/arcsec${}^2$.


  We propose a nonlinear sigma model for the description of quantum transport
in a mesoscopic metallic conductor with magnetic impurities frozen in a spin
glass phase. It accounts for the presence of both the corresponding scalar and
magnetic random potentials. In a spin glass, this magnetic random potential is
correlated between different realizations. As the strength of the magnetic
potential is varied, this model describes the crossover between orthogonal and
unitary universality classes of the nonlinear sigma model. We apply this
technique to the calculations of the correlation of conductance between two
frozen spin configurations in terms of dephasing rates for the usual low energy
modes of weak localization theory.


  We present a general theory for the onset of coherence in collections of
heterogeneous maps interacting via a complex connection network. Our method
allows the dynamics of the individual uncoupled systems to be either chaotic or
periodic, and applies generally to networks for which the number of connections
per node is large. We find that the critical coupling strength at which a
transition to synchrony takes place depends separately on the dynamics of the
individual uncoupled systems and on the largest eigenvalue of the adjacency
matrix of the coupling network. Our theory directly generalizes the Kuramoto
model of equal strength, all-to-all coupled phase oscillators to the case of
oscillators with more realistic dynamics coupled via a large heterogeneous
network.


  Satisfiability Modulo Theories (SMT) solvers check the satisfiability of
quantifier-free first-order logic formulas. We consider the theory of
non-linear real arithmetic where the formulae are logical combinations of
polynomial constraints. Here a commonly used tool is the Cylindrical Algebraic
Decomposition (CAD) to decompose real space into cells where the constraints
are truth-invariant through the use of projection polynomials.
  An improved approach is to repackage the CAD theory into a search-based
algorithm: one that guesses sample points to satisfy the formula, and
generalizes guesses that conflict constraints to cylindrical cells around
samples which are avoided in the continuing search. Such an approach can lead
to a satisfying assignment more quickly, or conclude unsatisfiability with
fewer cells. A notable example of this approach is Jovanovi\'c and de Moura's
NLSAT algorithm. Since these cells are produced locally to a sample we might
need fewer projection polynomials than the traditional CAD projection. The
original NLSAT algorithm reduced the set a little; while Brown's single cell
construction reduced it much further still. However, the shape and size of the
cell produced depends on the order in which the polynomials are considered.
  This paper proposes a method to construct such cells levelwise, i.e. built
level-by-level according to a variable ordering. We still use a reduced number
of projection polynomials, but can now consider a variety of different
reductions and use heuristics to select the projection polynomials in order to
optimise the shape of the cell under construction. We formulate all the
necessary theory as a proof system: while not a common presentation for work in
this field, it allows an elegant decoupling of heuristics from the algorithm
and its proof of correctness.


  We study a model of a quantum spin register interacting with an environment
of spin particles in quantum-measurement limit. In the limit of collective
decoherence we obtain the form of state vectors that constitute
high-dimensional decoherence-free subspaces (DFS). In a more general setting we
present sufficient and necessary conditions for existence of low-dimensional
DFSs that can be used to construct subspaces of higher dimension.


  We derive a Cartesian componentwise description of the covariant derivative
of tangential tensor fields of any degree on general manifolds. This allows to
reformulate any vector- and tensor-valued surface PDE in a form suitable to be
solved by established tools for scalar-valued surface PDEs. We consider
piecewise linear Lagrange surface finite elements on triangulated surfaces and
validate the approach by a vector- and a tensor-valued surface Helmholtz
problem on an ellipsoid. We experimentally show optimal (linear) order of
convergence for these problems. The full functionality is demonstrated by
solving a surface Landau-de Gennes problem on the Stanford bunny. All tools
required to apply this approach to other vector- and tensor-valued surface PDEs
are provided.


  This is the second of three papers I will present as an application of the
Basic Unit System concept, a complex mathematical unit presented in The Basic
Unit System concept and The Principle of Synergy. In this case this Bus concept
is used as a powerful tool to obtain again the Lorentz Transformation Groups of
equations, and then to present the emergent proposal that the fundamental is
the magnetic field, and not the charge concept. The need to obtain "waves
solution" is solved concomitant with the Bus concept as we have seen in the
physics/9908040 .


  Deep learning and convolutional neural networks (ConvNets) have been
successfully applied to most relevant tasks in the computer vision community.
However, these networks are computationally demanding and not suitable for
embedded devices where memory and time consumption are relevant.
  In this paper, we propose DecomposeMe, a simple but effective technique to
learn features using 1D convolutions. The proposed architecture enables both
simplicity and filter sharing leading to increased learning capacity. A
comprehensive set of large-scale experiments on ImageNet and Places2
demonstrates the ability of our method to improve performance while
significantly reducing the number of parameters required. Notably, on Places2,
we obtain an improvement in relative top-1 classification accuracy of 7.7\%
with an architecture that requires 92% fewer parameters compared to VGG-B. The
proposed network is also demonstrated to generalize to other tasks by
converting existing networks.


  We derive an explicit expression for the quantum conductivity of a molecular
wire containing a redox center, which is embedded in an electrochemical
environment. The redox center interacts with the solvent, and the average over
the solvent configurations is performed numerically. Explicit calculations have
been performed for a chain of three atoms. When the redox center interacts
strongly with neighboring electronic levels, the current-potential curves show
interesting features like rectification, current plateaus and negative
differential resistance. Electronic spectroscopy of intermediate states can be
performed at constant small bias by varying the electrochemical potential of
the wire.


  We study the exceptionally short (32-41 ms) precursors of two
intermediate-duration thermonuclear X-ray bursts observed with RXTE from the
neutron stars in 4U 0614+09 and 2S 0918-549. They exhibit photon fluxes that
surpass those at the Eddington limit later in the burst by factors of 2.6 to
3.1. We are able to explain both the short duration and the super-Eddington
flux by mildly relativistic outflow velocities of 0.1$c$ to 0.3$c$ subsequent
to the thermonuclear shell flashes on the neutron stars. These are the highest
velocities ever measured from any thermonuclear flash. The precursor rise times
are also exceptionally short: about 1 ms. This is inconsistent with predictions
for nuclear flames spreading laterally as deflagrations and suggests
detonations instead. This is the first time that a detonation is suggested for
such a shallow ignition column depth ($y_{\rm ign}$ = 10$^{10}$ g cm$^{-2}$).
The detonation would possibly require a faster nuclear reaction chain, such as
bypassing the alpha-capture on $^{12}$C with the much faster
$^{12}$C(p,$\gamma$)$^{13}$N($\alpha$,p)$^{16}$O process previously proposed.
We confirm the possibility of a detonation, albeit only in the radial
direction, through the simulation of the nuclear burning with a large nuclear
network and at the appropriate ignition depth, although it remains to be seen
whether the Zel'dovich criterion is met. A detonation would also provide the
fast flame spreading over the surface of the neutron star to allow for the
short rise times. (...) As an alternative to the detonation scenario, we
speculate on the possibility that the whole neutron star surface burns almost
instantly in the auto-ignition regime. This is motivated by the presence of 150
ms precursors with 30 ms rise times in some superexpansion bursts from 4U
1820-30 at low ignition column depths of ~10$^8$ g cm$^{-2}$.


  A totally green chemistry alternative that would lead both to energy
production from renewable feedstocks and to solutions of parts of ecological
problems related to waste disposals would be very attractive. Pyrolysis of used
frying oils seems to be one option for this attractive alternative as we
propose to demonstrate in this study. Since 2002, the whole production of waste
edible oils (around 100 000 tons per year in France) must be collected and
transformed into secondary raw material by specific companies. The general aim
of the present work is to produce one of the following target sources of
energy: (i) H2 for fuel cells, (ii) H2/CO in satisfactory ratios to produce
biodiesel by Fischer-Tropsch (FT) reaction, or (iii) hydrocarbon mixtures with
high added value. Therefore, in this work, the conversion of a crude used
frying oil, named VEGETAMIXOIL^(r); from Ecogras Company (France), was
investigated (weight composition: C 73.6%; O 9.7%; H 12.2%). In support of our
knowledge related to fatty acids and methyl esters, a laboratory pilot plant
was built to study the pyrolysis of used frying oils. Effects of temperature
(700-800 degrees C), residence time, addition of reaction initiator (H2O2) or
inhibitor (thiophene), and diluent (water or nitrogen) were analysed with
regard to the nature and amounts of pyrolysis products. Results led to the
conclusion that the best operating conditions of pyrolysis are 800 degrees C
with water as diluent, leading to the production of dihydrogen (40%) and
hydrocarbons from methane to propylene, essentially. CO and CO2 are also
produced but with low molar fractions. Furthermore, a ratio H2/CO favourable
for low temperature FT is obtained.


  Vision Transformers (ViTs) have attracted a lot of popularity in recent
years, due to their exceptional capabilities in modeling long-range spatial
dependencies and scalability for large scale training. Although the training
parallelism of self-attention mechanism plays an important role in retaining
great performance, its quadratic complexity baffles the application of ViTs in
many scenarios which demand fast inference. This effect is even more pronounced
in applications in which autoregressive modeling of input features is required.
In Natural Language Processing (NLP), a new stream of efforts has proposed
parallelizable models with recurrent formulation that allows for efficient
inference in generative applications. Inspired by this trend, we propose a new
class of computer vision models, dubbed Vision Retention Networks (ViR), with
dual parallel and recurrent formulations, which strike an optimal balance
between fast inference and parallel training with competitive performance. In
particular, ViR scales favorably for image throughput and memory consumption in
tasks that require higher-resolution images due to its flexible formulation in
processing large sequence lengths. The ViR is the first attempt to realize dual
parallel and recurrent equivalency in a general vision backbone for recognition
tasks. We have validated the effectiveness of ViR through extensive experiments
with different dataset sizes and various image resolutions and achieved
competitive performance. Code: https://github.com/NVlabs/ViR


  We describe here the construction and characterization of a high-resolution
optical magnetometer to measure the full vector magnetic field on an ultrathin
layer near the surface of the device. This solid-state device is based on
quantum sensors created by a layer of nitrogen-vacancy (NV) centers less than
20 nm below the surface of an ultrapure diamond. This ensemble of nanosensors
provides a versatile device capable of mapping magnetic fields and surface
current densities with a sub-micrometer resolution and high sensitivity, making
it suitable for many applications. Here, we show a custom-built prototype to
demonstrate an operating proof-of-concept device.


  We study numerically the wavefunction evolution of a Bose-Einstein condensate
in a Bunimovich stadium billiard being governed by the Gross-Pitaevskii
equation. We show that for a moderate nonlinearity, above a certain threshold,
there is emergence of dynamical thermalization which leads to the Bose-Einstein
probability distribution over the linear eigenmodes of the stadium. This
distribution is drastically different from the energy equipartition over
oscillator degrees of freedom which would lead to the ultra-violet catastrophe.
We argue that this interesting phenomenon can be studied in cold atom
experiments.


  Interacting Fock space connects the study of quantum probability theory,
classical random variables, and orthogonal polynomials. It is a pre-Hilbert
space associated with creation, preservation, and annihilation processes. We
prove that if three processes are asymptotically commutative, the arcsine law
arises as the "large quantum number limits." As a corollary, it is shown that
for many probability measures, asymptotic behavior of orthogonal polynomials is
described by the arcsine function. A weaker form of asymptotic commutativity
provides us a discretized arcsine law.


  We develop a novel approach to the dark matter halos in the context of 4
dimensional Einstein--scalar-Gauss-Bonnet gravity to reproduce the flat
rotation curves of galaxies. Moreover, the Gauss-Bonnet coupling describes the
interior structure of the galaxies, while there is a presence of a scalar field
$\phi $ in the galaxy edges. This can provide an interesting interpretation for
the functional coupling $f(\phi )$. We discuss how this comparison can
naturally drive the observed percentages of matter and dark matter in the
Universe. The effective mass range\ in our model is $% 10^{-2}kg-10^{3}kg$,
which is in good agreement with the constraints on primordial black holes.


  We present results from a set of high (512^3 effective resolution), and
ultra-high (1024^3) SPH adiabatic cosmological simulations of cluster formation
aimed at studying the internal structure of the intracluster medium (ICM). We
derive a self-consistent analytical model of the structure of the intracluster
medium (ICM). We discuss the radial structure and scaling relations expected
from purely gravitational collapse, and show that the choice of a particular
halo model can have important consequences on the interpretation of
observational data. The validity of the approximations of hydrostatic
equilibrium and a polytropic equation of state are checked against results of
our simulations. The properties of the ICM are fully specified when a
'universal' profile is assumed for either the dark or the baryonic component.
We also show the first results from an unprecedented large-scale simulation of
500 Mpc/h and 2 times 512^3 gas and dark matter particles. This experiment will
make possible a detailed study of the large-scale distribution of clusters as a
function of their X-ray properties.


  We propose a model for high-T$_{c}$ superconductors, valid for
$0\leq\delta\leq\delta_{SC}$, that includes both the spin fluctuations of the
Cu$^{++}$ magnetic ions and of the O$^{--}$ doped holes. Spin-charge separation
is taken into account with the charge of the doped holes being associated to
quantum skyrmion excitations (holons) of the Cu$^{++}$ spin background. The
holon effective interaction potential is evaluated as a function of doping,
indicating that Cooper pair formation is determined by the competition between
the spin fluctuations of the Cu$^{++}$ background and of spins of the O$^{--}$
doped holes (spinons). The superconducting transition occurs when the spinon
fluctuations dominate, thereby reversing the sign of the interaction. At this
point ($\delta = \delta_{SC}$), the theory is supersymmetric at short distances
and, as a consequence, the leading order results are not modified by radiative
corrections. The critical doping parameter for the onset of superconductivity
at T=0 is obtained and found to be a universal constant determined by the shape
of the Fermi surface. Our theoretical values for $\delta_{SC}$ are in good
agreement with the experiment for both LSCO and YBCO.


  Accurately assessing the impact of electron-phonon interaction (EPI) on the
lattice thermal conductivity of semiconductors is crucial for the thermal
management of electronic devices and a unified physical understanding of this
issue is highly desired. In this work, we predict the lattice thermal
conductivities of typical direct and indirect bandgap semiconductors accounting
for EPI based on mode-level first-principles calculations. It is found that EPI
has a larger effect on the lattice thermal conductivity of $p$-type doping
compared to $n$-type doping in the same semiconductor at high charge carrier
concentrations. The stronger EPI in $p$-type doping is attributed to the
relatively higher electron density of states caused by the relatively larger
$p$-orbital component. Furthermore, EPI has a stronger influence on the lattice
thermal conductivity of $n$-type indirect bandgap semiconductors than $n$-type
direct bandgap semiconductors. This is attributed to the relatively lower
electron density of states in direct bandgap semiconductors stemming from the
$s$-orbital component. This work reveals that there exist diverse responses in
lattice thermal conductivity of $n$-type/$p$-type semiconductors, which can be
attributed to asymmetric EPIs.


  Non-linearity of the current-phase relationship of a Josephson junction is
the key resource for a Josephson parametric amplifier (JPA), the only device in
which the quantum limit has so far been achieved at microwave frequencies. A
standard approach to describe JPA takes into account only the lowest order
(cubic) non-linearity resulting in a Duffing-like oscillator equation of motion
or in a Kerr-type non-linearity term in the Hamiltonian. In this paper we
derive the quantum expression for the gain of JPA including all orders of the
Josephson junction non-linearity in the linear response regime. We then analyse
gain saturation effect for stronger signals within semi-classical approach. Our
results reveal non-linear effects of higher orders and their implications for
operation of a JPA.