  Although code generation for Convolution Neural Network (CNN) models has been
extensively studied, performing efficient data slicing and parallelization for
highly-constrai\-ned Multicore Neural Processor Units (NPUs) is still a
challenging problem. Given the size of convolutions' input/output tensors and
the small footprint of NPU on-chip memories, minimizing memory transactions
while maximizing parallelism and MAC utilization are central to any effective
solution. This paper proposes a TensorFlow XLA/LLVM compiler optimization pass
for Multicore NPUs, called Tensor Slicing Optimization (TSO), which: (a)
maximizes convolution parallelism and memory usage across NPU cores; and (b)
reduces data transfers between host and NPU on-chip memories by using DRAM
memory burst time estimates to guide tensor slicing. To evaluate the proposed
approach, a set of experiments was performed using the NeuroMorphic Processor
(NMP), a multicore NPU containing 32 RISC-V cores extended with novel CNN
instructions. Experimental results show that TSO is capable of identifying the
best tensor slicing that minimizes execution time for a set of CNN models.
Speed-ups of up to 21.7\% result when comparing the TSO burst-based technique
to a no-burst data slicing approach. To validate the generality of the TSO
approach, the algorithm was also ported to the Glow Machine Learning framework.
The performance of the models were measured on both Glow and TensorFlow
XLA/LLVM compilers, revealing similar results.


  We employ adaptive activation functions for regression in deep and
physics-informed neural networks (PINNs) to approximate smooth and
discontinuous functions as well as solutions of linear and nonlinear partial
differential equations. In particular, we solve the nonlinear Klein-Gordon
equation, which has smooth solutions, the nonlinear Burgers equation, which can
admit high gradient solutions, and the Helmholtz equation. We introduce a
scalable hyper-parameter in the activation function, which can be optimized to
achieve best performance of the network as it changes dynamically the topology
of the loss function involved in the optimization process. The adaptive
activation function has better learning capabilities than the traditional one
(fixed activation) as it improves greatly the convergence rate, especially at
early training, as well as the solution accuracy. To better understand the
learning process, we plot the neural network solution in the frequency domain
to examine how the network captures successively different frequency bands
present in the solution. We consider both forward problems, where the
approximate solutions are obtained, as well as inverse problems, where
parameters involved in the governing equation are identified. Our simulation
results show that the proposed method is a very simple and effective approach
to increase the efficiency, robustness and accuracy of the neural network
approximation of nonlinear functions as well as solutions of partial
differential equations, especially for forward problems.


  Object detectors have demonstrated vulnerability to adversarial examples
crafted by small perturbations that can deceive the object detector. Existing
adversarial attacks mainly focus on white-box attacks and are merely valid at a
specific viewpoint, while the universal multi-view black-box attack is less
explored, limiting their generalization in practice. In this paper, we propose
a novel universal multi-view black-box attack against object detectors, which
optimizes a universal adversarial UV texture constructed by multiple image
stickers for a 3D object via the designed layout optimization algorithm.
Specifically, we treat the placement of image stickers on the UV texture as a
circle-based layout optimization problem, whose objective is to find the
optimal circle layout filled with image stickers so that it can deceive the
object detector under the multi-view scenario. To ensure reasonable placement
of image stickers, two constraints are elaborately devised. To optimize the
layout, we adopt the random search algorithm enhanced by the devised
important-aware selection strategy to find the most appropriate image sticker
for each circle from the image sticker pools. Extensive experiments conducted
on four common object detectors suggested that the detection performance
decreases by a large magnitude of 74.29% on average in multi-view scenarios.
Additionally, a novel evaluation tool based on the photo-realistic simulator is
designed to assess the texture-based attack fairly.


  Quantum computing has recently emerged as a transformative technology. Yet,
its promised advantages rely on efficiently translating quantum operations into
viable physical realizations. In this work, we use generative machine learning
models, specifically denoising diffusion models (DMs), to facilitate this
transformation. Leveraging text-conditioning, we steer the model to produce
desired quantum operations within gate-based quantum circuits. Notably, DMs
allow to sidestep during training the exponential overhead inherent in the
classical simulation of quantum dynamics -- a consistent bottleneck in
preceding ML techniques. We demonstrate the model's capabilities across two
tasks: entanglement generation and unitary compilation. The model excels at
generating new circuits and supports typical DM extensions such as masking and
editing to, for instance, align the circuit generation to the constraints of
the targeted quantum device. Given their flexibility and generalization
abilities, we envision DMs as pivotal in quantum circuit synthesis, enhancing
both practical applications but also insights into theoretical quantum
computation.


  In the absence of a tractable theory of quantum gravity, quantum matter field
effects have been so far computed by treating gravity at the Background Field
Approximation. The principle aim of this paper is to investigate the validity
of this approximation which is not specific to gravity. To this end, for
reasons of simplicity and clarity, we shall compare the descriptions of thermal
processes induced by constant acceleration (i.e. the Unruh effect) in four
dynamical frameworks. In this problem, the position of the ``heavy''
accelerated system plays the role of gravity. In the first framework, the
trajectory is treated at the BFA: it is given from the outset and unaffected by
radiative processes. In the second one, recoil effects induced by these
emission processes are taken into account by describing the system's position
by WKB wave functions. In the third one, the accelerated system is described by
second quantized fields and in the fourth one, gravity is turned on. It is most
interesting to see when and why transitions amplitudes evaluated in different
frameworks but describing the same process do agree. It is indeed this
comparison that determines the validity of the BFA. It is also interesting to
notice that the abandonment of the BFA delivers new physical insights
concerning the processes. For instance, in the fourth framework, the
``recoils'' of gravity show that the acceleration horizon area acts as an
entropy in delivering heat to accelerated systems.


  Exponential time integrators have been applied successfully in several
physics-related differential equations. However, their application in
hyperbolic systems with absorbing boundaries, like the ones arising in seismic
imaging, still lacks theoretical and experimental investigations. The present
work conducts an in-depth study of exponential integration using Faber
polynomials, consisting of a generalization of a popular exponential method
that uses Chebyshev polynomials. This allows solving non-symmetric operators
that emerge from classic seismic wave propagation problems with absorbing
boundaries. Theoretical as well as numerical results are presented for Faber
approximations. One of the theoretical contributions is the proposal of a sharp
bound for the approximation error of the exponential of a normal matrix. We
also show the practical importance of determining an optimal ellipse
encompassing the full spectrum of the discrete operator, in order to ensure and
enhance convergence of the Faber exponential series. Furthermore, based on
estimates of the spectrum of the discrete operator of the wave equations with a
widely used absorbing boundary method, we numerically investigate stability,
dispersion, convergence and computational efficiency of the Faber exponential
scheme. Overall, we conclude that the method is suitable for seismic wave
problems and can provide accurate results with large time step sizes, with
computational efficiency increasing with the increase of the approximation
degree.


  We report on the mobility and orientation of finite-size, neutrally buoyant
prolate ellipsoids (of aspect ratio $\Lambda=4$) in Taylor-Couette flow, using
interface resolved numerical simulations. The setup consists of a
particle-laden flow in between a rotating inner and a stationary outer
cylinder. We simulate two particle sizes $\ell/d=0.1$ and $\ell/d=0.2$, $\ell$
denoting the particle major axis and $d$ the gap-width between the cylinders.
The volume fractions are $0.01\%$ and $0.07\%$, respectively. The particles,
which are initially randomly positioned, ultimately display characteristic
spatial distributions which can be categorised into four modes. Modes $(i)$ to
$(iii)$ are observed in the Taylor vortex flow regime, while mode ($iv$)
encompasses both the wavy vortex, and turbulent Taylor vortex flow regimes.
Mode $(i)$ corresponds to stable orbits away from the vortex cores. Remarkably,
in a narrow $\textit{Ta}$ range, particles get trapped in the Taylor vortex
cores (mode ($ii$)). Mode $(iii)$ is the transition when both modes $(i)$ and
$(ii)$ are observed. For mode $(iv)$, particles distribute throughout the
domain due to flow instabilities. All four modes show characteristic
orientational statistics. We find the particle clustering for mode ($ii$) to be
size-dependent, with two main observations. Firstly, particle agglomeration at
the core is much higher for $\ell/d=0.2$ compared to $\ell/d=0.1$. Secondly,
the $\textit{Ta}$ range for which clustering is observed depends on the
particle size. For this mode $(ii)$ we observe particles to align strongly with
the local cylinder tangent. The most pronounced particle alignment is observed
for $\ell/d=0.2$ around $\textit{Ta}=4.2\times10^5$. This observation is found
to closely correspond to a minimum of axial vorticity at the Taylor vortex core
($\textit{Ta}=6\times10^5$) and we explain why.


  While object detection methods traditionally make use of pixel-level masks or
bounding boxes, alternative representations such as polygons or active contours
have recently emerged. Among them, methods based on the regression of Fourier
or Chebyshev coefficients have shown high potential on freeform objects. By
defining object shapes as polar functions, they are however limited to
star-shaped domains. We address this issue with SCR: a method that captures
resolution-free object contours as complex periodic functions. The method
offers a good compromise between accuracy and compactness thanks to the design
of efficient geometric shape priors. We benchmark SCR on the popular COCO 2017
instance segmentation dataset, and show its competitiveness against existing
algorithms in the field. In addition, we design a compact version of our
network, which we benchmark on embedded hardware with a wide range of power
targets, achieving up to real-time performance.


  We compute the Itzykson-Zuber (IZ) integral for the superunitary group
U(m|n). As a consequence, we are able to find the non-zero correlations of
superunitary matrices


  In the present paper we consider the problem of the existence of
pre-semigeodesic coordinates on manifolds with affine connection. We proved
that pre-semigeodesic coordinates exist in the case when the components of the
affine connection are twice differentiable functions.


  The much-anticipated proof of cosmic ray (CR) acceleration in supernova
remnants (SNR) must hinge on full consistency of acceleration theory with the
observations; direct proof is impossible because of the orbit scrambling of CR
particles. The PAMELA orbital telescope revealed deviation between helium and
proton CR spectra deemed inconsistent with the theory, since the latter does
not differentiate between elements of ultrarelativistic rigidity. By
considering an initial (injection-) phase of the diffusive shock acceleration
(DSA), where elemental similarity does not apply, we demonstrate that the
spectral difference is, in fact, a unique signature of the DSA. Collisionless
plasma SNR shocks inject more He2+ relative to protons when they are stronger
and so produce harder helium spectra. The injection bias is due to Alfven waves
driven by the more abundant protons, so the He2+ ions are harder to trap by
these waves because of the larger gyroradii. By fitting the p/He ratio to the
PAMELA data, we bolster the DSA-case for resolving the century-old mystery of
CR origin.


  Non-linear source separation is a challenging open problem with many
applications. We extend a recently proposed Adversarial Non-linear ICA (ANICA)
model, and introduce Cramer-Wold ICA (CW-ICA). In contrast to ANICA we use a
simple, closed--form optimization target instead of a discriminator--based
independence measure. Our results show that CW-ICA achieves comparable results
to ANICA, while foregoing the need for adversarial training.


  While deep reinforcement learning has shown important empirical success, it
tends to learn relatively slow due to slow propagation of rewards information
and slow update of parametric neural networks. Non-parametric episodic memory,
on the other hand, provides a faster learning alternative that does not require
representation learning and uses maximum episodic return as state-action values
for action selection. Episodic memory and reinforcement learning both have
their own strengths and weaknesses. Notably, humans can leverage multiple
memory systems concurrently during learning and benefit from all of them. In
this work, we propose a method called Two-Memory reinforcement learning agent
(2M) that combines episodic memory and reinforcement learning to distill both
of their strengths. The 2M agent exploits the speed of the episodic memory part
and the optimality and the generalization capacity of the reinforcement
learning part to complement each other. Our experiments demonstrate that the 2M
agent is more data efficient and outperforms both pure episodic memory and pure
reinforcement learning, as well as a state-of-the-art memory-augmented RL
agent. Moreover, the proposed approach provides a general framework that can be
used to combine any episodic memory agent with other off-policy reinforcement
learning algorithms.


  We present some data on the cohomology of the motivic Steenrod algebra over
an algebraically closed field. We discuss several features of the associated
Adams spectral sequence, including the basic construction and convergence
properties. The paper also deals with motivic versions of the May and
Adams-Novikov spectral sequences.
  It is shown how these tools can be used to give new proofs of some classical
results in algebraic topology. Also, the considerations reveal the existence of
certain "exotic" motivic homotopy classes which have no classical analogues.


  In this paper we present an improved dqds algorithm for computing all the
singular values of a bidiagonal matrix to high relative accuracy. There are two
key contributions: a novel deflation strategy that improves the convergence for
badly scaled matrices, and some modifications to certain shift strategies that
accelerate the convergence for most bidiagonal matrices. These techniques
together ensure linear worst case complexity of the improved algorithm (denoted
by V5). Our extensive numerical experiments indicate that V5 is typically
1.2x--4x faster than DLASQ (the LAPACK-3.4.0 implementation of dqds) without
any degradation in accuracy. On matrices for which DLASQ shows very slow
convergence, V5 can be 3x--10x faster. At the end of this paper, a hybrid
algorithm (HDLASQ) is developed by combining our improvements with the
aggressive early deflation strategy (AggDef2 in [SIAM J. Matrix Anal. Appl.,
33(2012), 22-51]). Numerical results show that HDLASQ is the fastest among
these different versions.


  We continue the study of strong, weak, and $dc$-weak eigenforms introduced by
Chen, Kiming, and Wiese. We completely determine all systems of Hecke
eigenvalues of level $1$ modulo $128$, showing there are finitely many. This
extends results of Hatada and can be considered as evidence for the more
general conjecture formulated by the author together with Kiming and Wiese on
finiteness of systems of Hecke eigenvalues modulo prime powers at any fixed
level. We also discuss the finiteness of systems of Hecke eigenvalues of level
$1$ modulo $9$, reducing the question to the finiteness of a single eigenvalue.
Furthermore, we answer the question of comparing weak and $dc$-weak eigenforms
and provide the first known examples of non-weak $dc$-weak eigenforms.


  We study the integral Chow ring of the stack $\mathcal{H}_{g,n}$
parametrizing $n$-pointed smooth hyperelliptic curves of genus $g$. We compute
the integral Chow ring of $\mathcal{H}_{g,n}$ for $n=1,2$ completely, while for
$3\leq n\leq2g+2$ we compute it up to the additive order of a single class in
degree 2. We obtain partial results also for $n=2g+3$. In particular, taking
$g=2$ and recalling that $\mathcal{H}_{2,n}=\mathcal{M}_{2,n}$, our results
hold for $\mathrm{CH}^*(\mathcal{M}_{2,n})$ for $1\leq n\leq7$.


  The physics of the glass transition and amorphous materials continues to
attract the attention of a wide research community after decades of effort.
Supercooled liquids and glasses have been studied numerically since the advent
of molecular dynamics and Monte Carlo simulations in the last century. Computer
studies have greatly enhanced both experimental discoveries and theoretical
developments and constitute an active and continually expanding research field.
Our goal in this review is to provide a modern perspective on this area. We
describe the need to go beyond canonical methods to attack a problem that is
notoriously difficult in terms of time scales, length scales, and physical
observables. We first summarise recent algorithmic developments to achieve
enhanced sampling and faster equilibration using replica exchange methods,
cluster and swap Monte Carlo algorithms, and other techniques. We then review
some major recent advances afforded by these novel tools regarding the
statistical mechanical description of the liquid-to-glass transition as well as
the mechanical, vibrational and thermal properties of the glassy solid. We
finally describe some important challenges for future research.


  We examine the diffraction properties of lattice dynamical systems of
algebraic origin. It is well-known that diverse dynamical properties occur
within this class. These include different orders of mixing (or higher-order
correlations), the presence or absence of measure rigidity (restrictions on the
set of possible shift-invariant ergodic measures to being those of algebraic
origin), and different entropy ranks (which may be viewed as the maximal
spatial dimension in which the system resembles an i.i.d.\ process). Despite
these differences, it is shown that the resulting diffraction spectra are
essentially indistinguishable, thus raising further difficulties for the
inverse problem of structure determination from diffraction spectra. Some of
them may be resolved on the level of higher-order correlation functions, which
we also briefly compare.


  V909 Cas is a little-studied example of a \b{eta} Cep pulsating variable
located in the OB association Cas OB8 in the Perseus spiral arm of the Milky
Way. Photometric observations in 2016-7 provided 30 new times of pulsation
extrema and enabled its mean pulsation period to be determined as 0.2067798(1)
d. From spectroscopic observations we determined its interstellar extinction
and absolute magnitude and luminosity, and located it with other \b{eta} Cep
stars in the OB instability region of the H-R diagram.


  Visualization tools for supervised learning allow users to interpret,
introspect, and gain an intuition for the successes and failures of their
models. While reinforcement learning practitioners ask many of the same
questions, existing tools are not applicable to the RL setting as these tools
address challenges typically found in the supervised learning regime. In this
work, we design and implement an interactive visualization tool for debugging
and interpreting RL algorithms. Our system addresses many features missing from
previous tools such as (1) tools for supervised learning often are not
interactive; (2) while debugging RL policies researchers use state
representations that are different from those seen by the agent; (3) a
framework designed to make the debugging RL policies more conducive. We provide
an example workflow of how this system could be used, along with ideas for
future extensions.


  We study the quasiparticle spectrum of 2D topological $s$-wave
superconductors with the Zeeman magnetic field and the Rashba spin-orbit
coupling in the presence of spatial inhomogeneity. Solving the real-space
Bogoliubov-de Gennes equations, we focus on the excitations within the
superconducting gap amplitude, i.e., the appearance of mid-gap states. Two
kinds of potential functions, line-type (a chain of impurities) and point-type
(a single impurity) ones are examined to take spatial inhomogeneity into
account. The line setting shows a link of the mid-gap states with the gapless
surface modes indicated by the bulk-boundary correspondence in topological
superfluid. The point one shows that the quasiparticles with mid-gap energy are
much easily excited by an impurity when the Zeeman magnetic field increases
within the topological number to be unchanged. Thus, we obtain insights into
the robustness of a topological superconductor against non-magnetic impurities.
Moreover, we derive an effective theory applicable to high magnetic fields. The
effective gap is the mixture of the chiral $p$-wave and $s$-wave characters.
The former is predominant when the magnetic field increases. Therefore, we
claim that a chiral $p$-wave character of the effective gap function creates
the mid-gap states.


  This study focuses on long-term forecasting (LTF) on continuous-time dynamic
graph networks (CTDGNs), which is important for real-world modeling. Existing
CTDGNs are effective for modeling temporal graph data due to their ability to
capture complex temporal dependencies but perform poorly on LTF due to the
substantial requirement for historical data, which is not practical in most
cases. To relieve this problem, a most intuitive way is data augmentation. In
this study, we propose \textbf{\underline{U}ncertainty \underline{M}asked
\underline{M}ix\underline{U}p (UmmU)}: a plug-and-play module that conducts
uncertainty estimation to introduce uncertainty into the embedding of
intermediate layer of CTDGNs, and perform masked mixup to further enhance the
uncertainty of the embedding to make it generalize to more situations. UmmU can
be easily inserted into arbitrary CTDGNs without increasing the number of
parameters. We conduct comprehensive experiments on three real-world dynamic
graph datasets, the results demonstrate that UmmU can effectively improve the
long-term forecasting performance for CTDGNs.


  We consider quantum decay and photofragmentation processes in open chaotic
systems in the semiclassical limit. We devise a semiclassical approach which
allows us to consistently calculate quantum corrections to the classical decay
to high order in an expansion in the inverse Heisenberg time. We present
results for systems with and without time reversal symmetry and also for the
symplectic case, as well as extending recent results to non-localized initial
states. We further analyze related photodissociation and photoionization
phenomena and semiclassically compute cross-section correlations, including
their Ehrenfest time dependence.


  Using data collected at the psi(3770) resonance with the CLEO-c detector at
the Cornell e^+e^- storage ring, we present searches for 25 charmless decay
modes of the psi(3770), mostly multibody final states. No evidence for
charmless decays is found.


  The generation of controlled and arbitrarily tunable terahertz radiation,
essential for many applications, has proven challenging due to the complexity
of experimental setups and fabrication techniques. We introduce a new strategy
involving control over a terahertz repetition rate integrated frequency comb,
using Kerr-induced synchronization, that results in a
terahertz-voltage-controlled oscillator. By modulating the reference laser, we
can transfer any microwave waveform onto the microcomb repetition rate via a
linear transfer function based on optical frequency division. The resulting
frequency comb with a terahertz carrier can be created using integrated
components, with a bandwidth constrained only by the synchronization bandwidth
and high coherence resulting from the low-noise soliton microcomb in the
Kerr-induced synchronized state.


  There is a growing interest on formal methods-based robotic planning for
temporal logic objectives. In this work, we extend the scope of existing
synthesis methods to hyper-temporal logics. We are motivated by the fact that
important planning objectives, such as optimality, robustness, and privacy,
(maybe implicitly) involve the interrelation between multiple paths. Such
objectives are thus hyperproperties, and cannot be expressed with usual
temporal logics like the linear temporal logic (LTL). We show that such
hyperproperties can be expressed by HyperLTL, an extension of LTL to multiple
paths. To handle the complexity of planning with HyperLTL specifications, we
introduce a symbolic approach for synthesizing planning strategies on discrete
transition systems. Our planning method is evaluated on several case studies.


  For autonomous vehicles to operate without human intervention, information
sharing from local sensors plays a fundamental role. This can be challenging to
handle with bandwidth-constrained communication systems, which calls for the
adoption of new wireless technologies, like in the mmwave bands, to solve
capacity issues. Another approach is to exploit uav, able to provide human
users and their cars with an aerial bird's-eye view of the scene otherwise
unavailable, thus offering broader and more centralized observations. In this
article we combine both aspects and design a novel framework in which uav,
operating at mmwave, broadcast sensory information to the ground as a means to
extend the (local) perception range of vehicles. To do so, we conduct a
full-stack end-to-end simulation campaign with ns-3 considering real UAV data
from the Stanford Drone Dataset, and study four scenarios representing
different uav-to-ground communication strategies. Our results focus on the
trade-off between centralized data processing in the sky vs. distributed local
processing on the ground, with considerations related to the throughput,
latency and reliability of the communication process.


  We analyze an inverse problem associated with the time-harmonic Rayleigh
system on a flat elastic half-space concerning the recovery of Lam\'{e}
parameters in a slab beneath a traction-free surface. We employ the
Markushevich substitution, while the data are captured in a Jost function, and
point out parallels with a corresponding problem for the Schr\"{o}dinger
equation. The Jost function can be identified with spectral data. We derive a
Gel'fand-Levitan type equation and obtain uniqueness with two distinct
frequencies.


  We propose an effective method for the precise investigation of the
fusion-fission mechanism in the superheavy-mass region, using the
fluctuation-dissipation model. The trajectory calculation with friction is
performed in the nuclear deformation space using the Langevin equation. In the
reaction $^{48}$Ca+$^{244}$Pu, the trajectories are classified into the
fusion-fission process, the quasi-fission process and the deep quasi-fission
process. By analyzing the time evolution of each trajectory, the mechanism of
each process is clearly revealed, i.e., it is explained why a trajectory takes
a characteristic path in this model. We discuss, in particular, the condition
under which the fusion path is followed, which is crucial in the discussion of
the possibility of synthesizing superheavy elements.


  We present a complete 12CO J = 1-0 map of the prominent molecular ridge in
the Large Magellanic Cloud (LMC) obtained with the 22-m ATNF Mopra Telescope.
The region stretches southward by ~2 degrees, (or 1.7kpc) from 30 Doradus, the
most vigorous star-forming region in the Local Group. The location of this
molecular ridge is unique insofar as it allows us to study the properties of
molecular gas as a function of the ambient radiation field in a low-metallicity
environment. We find that the physical properties of CO-emitting clumps within
the molecular ridge do not vary with the strength of the far-ultraviolet (FUV)
radiation field. Since the peak CO brightness of the clumps shows no
correlation with the radiation field strength, the observed constant value for
CO-to-H_2 conversion factor along the ridge seems to require an increase in the
kinetic temperature of the molecular gas that is offset by a decrease in the
angular filling factor of the CO emission. We find that the difference between
the CO-to-H_2 conversion factor in the molecular ridge and the outer Milky Way
is smaller than has been reported by previous studies of the CO emission:
applying the same cloud identification and analysis methods to our CO
observations of the LMC molecular ridge and CO data from the outer Galaxy
survey by Dame et al. (2001), we find that the average CO-to-H_2 conversion
factor in the molecular ridge is X_CO = (3.9+/-2.5)10^20 cm^-2 (K km s^-1)^-1,
approximately twice the value that we determine for the outer Galaxy clouds.
The mass spectrum and the scaling relations between the properties of the CO
clumps in the molecular ridge are similar, but not identical, to those that
have been established for Galactic molecular clouds.


  Large-scale task planning is a major challenge. Recent work exploits large
language models (LLMs) directly as a policy and shows surprisingly interesting
results. This paper shows that LLMs provide a commonsense model of the world in
addition to a policy that acts on it. The world model and the policy can be
combined in a search algorithm, such as Monte Carlo Tree Search (MCTS), to
scale up task planning. In our new LLM-MCTS algorithm, the LLM-induced world
model provides a commonsense prior belief for MCTS to achieve effective
reasoning; the LLM-induced policy acts as a heuristic to guide the search,
vastly improving search efficiency. Experiments show that LLM-MCTS outperforms
both MCTS alone and policies induced by LLMs (GPT2 and GPT3.5) by a wide
margin, for complex, novel tasks. Further experiments and analyses on multiple
tasks -- multiplication, multi-hop travel planning, object rearrangement --
suggest minimum description length (MDL) as a general guiding principle: if the
description length of the world model is substantially smaller than that of the
policy, using LLM as a world model for model-based planning is likely better
than using LLM solely as a policy.


  Internet is growing at a fast pace. The link speeds are surging toward 40
Gbps with the emergence of faster link technologies. New applications are
coming up which require intelligent processing at the intermediate routers.
Switches and routers are becoming the bottlenecks in fast communication. On one
hand faster links deliver more packets every second and on the other hand
intelligent processing consumes more CPU cycles at the router. The conflicting
goals of providing faster but computationally expensive processing call for new
approaches in designing routers.
  This survey takes a look at the core functionalities, like packet
classification, buffer memory management, switch scheduling and output link
scheduling performed by a router in its data path processing and discusses the
algorithms that aim to reduce the performance bound for these operations. An
important requirement for the routers is to provide Quality of Service
guarantees. We propose an algorithm to guarantee QoS in Input Queued Routers.
The hardware solution to speed up router operation was Application Specific
Integrated Circuits (ASICs). But the inherent inflexibility of the method is a
demerit as network standards and application requirements are constantly
evolving, which seek a faster turnaround time to keep up with the changes. The
promise of Network Processors (NP) is the flexibility of general-purpose
processors together with the speed of ASICs. We will study the architectural
choices for the design of Network Processors and focus on some of the
commercially available NPs. There is a plethora of NP vendors in the market.
The discussion on the NP benchmarks sets the normalizing platform to evaluate
these NPs.


  We express Wronskian Hermite polynomials in the Hermite basis and obtain an
explicit formula for the coefficients. From this we deduce an upper bound for
the modulus of the roots in the case of partitions of length 2. We also derive
a general upper bound for the modulus of the real and purely imaginary roots.
These bounds are very useful in the study of irreducibility of Wronskian
Hermite polynomials. Additionally, we generalize some of our results to a
larger class of polynomials.


  Automorphic forms on a bounded symmetric domain D=G/K can be viewed as
holomorphic sections of $L^{\otimes k}$, where L is a quantizing line bundle on
a compact quotient of D and k is a positive integer.
  Let $\Gamma$ be a cocompact discrete subgroup of SU(n,1) which acts freely on
SU(n,1)/U(n). We suggest a construction of relative Poincar\'e series
associated to loxodromic elements in $\Gamma$. In complex dimension 2 we
describe Bohr-Sommerfeld tori in $\Gamma\backslash SU(n,1)/U(n)$ associated to
hyperbolic elements of $\Gamma$ and prove that the relative Poincar\'e series
associated to the hyperbolic elements of $\Gamma$ are not identically zero for
large k.


  A simple model of a glass former fluid, consisting of a bidisperse mixture of
penetrable spheres is studied. The model shows a transition from fragile to
strong behavior as temperature is reduced. This transition is driven by the
competition between the two mechanisms that contribute to diffusivity in the
model: collective rearrangement of particles (responsible for the fragile
behavior), and individual particle motion (which gives rise to the strong
behavior at low temperature). We also observe a maximum of diffusivity as a
function of pressure that can be interpreted within the same framework. The
connection between this behavior and polyamorphism is addressed.


  We evaluate the spin-orbit and spin-spin interaction between two fermions in
strongly coupled gauge theories in their Coulomb phase. We use the
quasi-instantaneous character of Coulomb's law at strong coupling to resum a
class of ladder diagrams. For ${\cal N}=4$ SYM we derive both weak and strong
coupling limits of the the spin-orbit and spin-spin interactions, and find that
in the latter case these interactions are subleading corrections and do not
seriously affect the deeply bound Coulomb states with large angular momentum,
pointed out in our previous paper. The results are important for understanding
of the regime of intermediate coupling, which is the case for QCD somewhat
above the chiral transition temperature.


  Optical communication channels have redefined the purview and applications of
classical computing; similarly, photonic transfer of quantum information
promises to open new horizons for quantum computing. The implementation of
light-matter interfaces that preserve quantum information is technologically
challenging, but key building blocks for such devices have recently been
demonstrated in several research groups. Here, we outline the theoretical
framework for information transfer between nodes of a quantum network, review
the current experimental state of the art, and discuss the prospects for hybrid
systems currently in development.


  Particle channeling in a bent crystal lattice has led to an efficient
instrument for beam steering at accelerators, demonstrated from MeV to TeV
energies. In particular, crystal focusing of high energy protons to micron size
has been demonstrated at IHEP with the results well in match with Lindhard
(critical angle) prediction. Channeling in crystal microstructures has been
proposed as a unique source of a microbeam of high-energy particles. Channeling
in nanostructures (single-wall and multi-wall nanotubes) offers the
opportunities to produce ion beams on nanoscale. Particles channeled in a
nanotube (with typical diameter of about 1 nanometer) are trapped in two
dimensions and can be steered (deflected, focused) with the efficiency similar
to that of crystal channeling or better. This technique has been a subject of
computer simulations, with experimental efforts under way in several high
energy labs, including IHEP. We present the theoretical outlook for making
channeling-based nanoscale ion beams and report the experience with
crystal-focused microscale proton beams.


  We compute holographically the dispersion relation for a hydrodynamic mode of
fluctuation (the phonino) of the density of supersymmetry current in N = 4 SYM
at strong coupling. The mode appears as a pole at low frequency and momentum in
the correlator of supercurrents. It has a wave-like propagation, and we find
its speed and coefficient of attenuation.


  The study of colliding galaxies has progressed rapidly in the last few years,
driven by observations with powerful new ground and space-based instruments.
These instruments have used for detailed studies of specific nearby systems,
statistical studies of large samples of relatively nearby systems, and
increasingly large samples of high redshift systems. Following a brief summary
of the historical context, this review attempts to integrate these studies to
address the following key issues. What role do collisions play in galaxy
evolution, and how can recently discovered processes like downsizing resolve
some apparently contradictory results of high redshift studies? What is the
role of environment in galaxy collisions? How is star formation and nuclear
activity orchestrated by the large scale dynamics, before and during merger?
Are novel modes of star formation involved? What are we to make of the
association of ultraluminous X-ray sources with colliding galaxies? To what do
degree do mergers and feedback trigger long-term secular effects? How far can
we push the archaeology of individual systems to determine the nature of
precursor systems and the precise effect of the interaction? Tentative answers
to many of these questions have been suggested, and the prospects for answering
most of them in the next few decades are good.


  We investigate a two-dimensional single-band Hubbard model with a
nearest-neighbor hopping. We treat a commensurate collinear order as well as
incommensurate spiral magnetic phases at a finite temperature using a
Hubbard-Stratonovich transformation with a two-field representation and solve
this problem in a static approximation. We argue that temperature dramatically
influence the collinear and spiral magnetic phases, phase separation in the
vicinity of half-filling. The results imply a possible interpretation of
unusual behavior of magnetic properties of single-layer cuprates.


  In the realm of natural language processing, the understanding of tabular
data has perpetually stood as a focal point of scholarly inquiry. The emergence
of expansive language models, exemplified by the likes of ChatGPT, has ushered
in a wave of endeavors wherein researchers aim to harness these models for
tasks related to table-based question answering. Central to our investigative
pursuits is the elucidation of methodologies that amplify the aptitude of such
large language models in discerning both the structural intricacies and
inherent content of tables, ultimately facilitating their capacity to provide
informed responses to pertinent queries. To this end, we have architected a
distinctive module dedicated to the serialization of tables for seamless
integration with expansive language models. Additionally, we've instituted a
corrective mechanism within the model to rectify potential inaccuracies.
Experimental results indicate that, although our proposed method trails the
SOTA by approximately 11.7% in overall metrics, it surpasses the SOTA by about
1.2% in tests on specific datasets. This research marks the first application
of large language models to table-based question answering tasks, enhancing the
model's comprehension of both table structures and content.


  We study the minimally displaced set of irreducible automorphisms of a free
group. Our main result is the co-compactness of the minimally displaced set of
an irreducible automorphism with exponential growth $\phi$, under the action of
the centraliser $C(\phi)$. As a corollary, we get that the same holds for the
action of $<\phi>$ on $Min(\phi)$. Finally, we prove that the minimally
displaced set of an irreducible automorphism of growth rate one is consisted of
a single point.


  This paper develops an agent-level simulation model, termed ALPS, for
simulating the spread of an infectious disease in a confined community. The
mechanism of transmission is agent-to-agent contact, using parameters reported
for Corona COVID-19 pandemic. The main goal of the ALPS simulation is analyze
effects of preventive measures -- imposition and lifting of lockdown norms --
on the rates of infections, fatalities and recoveries. The model assumptions
and choices represent a balance between competing demands of being realistic
and being efficient for real-time inferences. The model provides quantification
of gains in reducing casualties by imposition and maintenance of restrictive
measures in place.


  The CP violating asymmetries for Cabibbo suppressed charged D meson decays in
the standard model are estimated in the factorized approximation, using the
two-loop effective hamiltonian and a model for final state interactions
previously tested for Cabibbo allowed D decays. No new parameters are added.
The predictions are larger than expected and not too far from the experimental
possibilities.


  Let $k$ be a field and $X$ be a smooth projective surface over $k$ with a
rational point, we discuss the condition of splitting off the top cell for the
motivic stable homotopy type of $X$. We also study some outlying examples, such
as K3 surfaces.


  Zassenhaus has proved that if U is a subnormal subalgebra of a
finite-dimensional Lie algebra L and V is a finite-dimensional irreducible
L-module, then all U-module composition factors of V are isomorphic. Schenkman
has proved that if U is a subnormal subalgebra of a finite-dimensional Lie
algebra L, then the nilpotent residual of U is an ideal of L. These useful
results generalise to Leibniz algebras.


  A tree-based dictionary learning model is developed for joint analysis of
imagery and associated text. The dictionary learning may be applied directly to
the imagery from patches, or to general feature vectors extracted from patches
or superpixels (using any existing method for image feature extraction). Each
image is associated with a path through the tree (from root to a leaf), and
each of the multiple patches in a given image is associated with one node in
that path. Nodes near the tree root are shared between multiple paths,
representing image characteristics that are common among different types of
images. Moving toward the leaves, nodes become specialized, representing
details in image classes. If available, words (text) are also jointly modeled,
with a path-dependent probability over words. The tree structure is inferred
via a nested Dirichlet process, and a retrospective stick-breaking sampler is
used to infer the tree depth and width.


  There are numerous studies which suggest that perhaps music is truly the
language of emotions. Music seems to have an almost willful, evasive quality,
defying simple explanation, and indeed requires deeper neurophysiological
investigations to gain a better understanding. The current study makes an
attempt in that direction to explore the effect of context on music perception.
To investigate the same, we measured Galvanic Skin Responses (GSR) and
self-reported emotion on 18 participants while listening to different Ragas
(musical stimulus) composed of different Rasa's (emotional expression) in the
different context (Neutral, Pleasant, and Unpleasant). The IAPS pictures were
used to induce the emotional context in participants. Our results from this
study suggest that the context can modulate emotional response in music
perception but only for a shorter time scale. Interestingly, here we
demonstrate by combining GSR and self-reports that this effect gradually
vanishes over time and shows emotional adaptation irrespective of context. The
overall findings suggest that specific context effects of music perception are
transitory in nature and gets saturated on a longer time scale.


  We describe three-dimensional Lorentzian homogeneous Ricci solitons, showing
that all types (i.e. shrinking, expanding and steady) exist. Moreover, all
non-trivial examples have non-diagonalizable Ricci operator with one only
eigenvalue.


  Let $G$ be a finite abelian group acting faithfully on a finite set $X$. As a
natural generalization of the perfect nonlinearity of Boolean functions, the
$G$-bentness and $G$-perfect nonlinearity of functions on $X$ are studied by
Poinsot et al. [6,7] via Fourier transforms of functions on $G$. In this paper
we introduce the so-called $G$-dual set $\widehat X$ of $X$, which plays the
role similar to the dual group $\widehat G$ of $G$, and the Fourier transforms
of functions on $X$, a generalization of the Fourier transforms of functions on
finite abelian groups. Then we characterize the bent functions on $X$ in terms
of their own Fourier transforms on $\widehat X$. Bent (perfect nonlinear)
functions on finite abelian groups and $G$-bent ($G$-perfect nonlinear)
functions on $X$ are treated in a uniform way in this paper, and many known
results in [4,2,6,7] are obtained as direct consequences. Furthermore, we will
prove that the bentness of a function on $X$ can be determined by its distance
from the set of $G$-linear functions. In order to explain the main results
clearly, examples are also presented.


  New hot topic in ARPES on HTSC, the observation of the so called
"waterfalls", is addressed. The energy scale at about 0.2-0.3 eV that can be
derived from the coherent component of ARPES spectra measured along the nodal
direction is not new but has been already discussed in terms of a coupling to a
bosonic continuum. However, the waterfalls, namely the long vertical parts of
the experimental dispersion around the center of the Brillouin zone (BZ), seem
to be purely artificial. They are a consequence of simple matrix-element
effect: a complete suppression of the photoemission intensity from both the
coherent and "incoherent" components. When the matrix-elements are taken into
account, the latter reveals a grid-like structure along the bonding directions
in the BZ.


  Canonical analysis leading to formal quantisation of the higher derivative
theories are considered. The first order formalism is adopted where all the
configuration space variables along with their higher time derivatives are
considered to be independent fields. A systematic algorithm of abstracting the
independent gauge symmetries is developed which is an extension of the method
developed by Banerjee et al. for the usual first order theories. For the
massive relativistic particle model with curvature, we solve the mismatch in
the no of independent gauge parameters and no of independent primary fist class
constarints. In addition, we show a direct connection between the gauge
symmetry and the $W_3$-algebra for the rigid relativistic particle. Also, BRST
symmetries for both the massive and massless particle models have been
considered and its connection to $W_3$-algebras is demonstrated. The exact
mapping of this gauge symmetry is shown with the reparametrisation invariance.
Different models from field theory, gravity and membrane theory have been
considered as illustrative examples from a new perspective to clarify many not
so adequately addressed issues.


  We present a numerical study of the process of the kink-antikink collisions
in the coupled one-dimensional two-component $\phi^4$ model. Our results reveal
two different soliton solutions which represent double kink configuration and
kink-non-topological soliton (lump) bound state. Collision of these solitons
leads to very reach resonance structure which is related to reversible energy
exchange between the kinks, non-topological solitons and the internal
vibrational modes. Various channels of the collisions are discussed, it is
shown there is a new type of self-similar fractal structure which appears in
the collisions of the relativistic kinks, there the width of the resonance
windows increases with the increase of the impact velocity. An analytical
approximation scheme is discussed in the limit of the perturbative coupling
between the sectors. Considering the spectrum of linear fluctuations around the
solitons we found that the double kink configuration is unstable if the
coupling constant between the sectors is negative.


  Why do we see certain types of strongly interacting elementary particles and
not others? This question was posed over 50 years ago in the context of the
quark model. M. Gell-Mann and G. Zweig proposed that the known mesons were $q
\bar q$ and baryons $qqq$, with quarks known at the time $u$ ("up"), $d$
("down"), and $s$ ("strange") having charges (2/3,-1/3,-1/3). Mesons and
baryons would then have integral charges. Mesons such as $qq \bar q \bar q$ and
baryons such as $qqqq \bar q$ would also have integral charges. Why weren't
they seen? They have now been seen, but only with additional heavy quarks and
under conditions which tell us a lot about the strong interactions and how they
manifest themselves. The present article describes recent progress in our
understanding of such "exotic" mesons and baryons.


  The lowest temptation level (T = 1) is considered a trivial case for the
Prisoner's Dilemma. Here, we show that this statement is true only for a very
particular case, where the players interact with only one player. Otherwise, if
the players interact with more than one player, the system presents the same
possible behaviors observed for $T > 1$. In the steady state, the system can
reach the cooperative, chaotic or defective phases, when adopting the Darwinian
Evolutionary Strategy and the cooperative or quasi-regular phases, adopting the
Pavlovian Evolutionary Strategy.


  The extended Hubbard Hamiltonian on a bcc lattice is studied at half-filling
and for a finite hopping between next-nearest-neighbours, in mean-field
approximation. An ionic insulating broken-symmetry phase is predicted for any
hydrogenoid bcc solid in the density range 1.0 < r sub s < 2.6. The occurrence
of an ionic phase would explain the failure to achieve hydrogen metallization
at high pressures. Moreover, a metal-insulator transition is expected for
sodium in the 100 GPa region.


  We consider static neutron stars within the framework of $R^2$ gravity. The
neutron fluid is described by three different types of realistic equations of
state (soft, moderately stiff, and stiff). Using the observational data on the
neutron star mass-radius relation, it is demonstrated that the characteristics
of the objects supported by the isotropic fluid agree with the observations
only if one uses the soft equation of state. We show that the inclusion of the
fluid anisotropy enables one also to employ more stiff equations of state to
model configurations that will satisfy the observational constraints
sufficiently. Also, using the standard thin accretion disk model, we
demonstrate potentially observable differences, which allow us to distinguish
the neutron stars constructed within the modified gravity framework from those
described in Einstein's general relativity.


  Theory predicts that two-dimensional (2D) materials may only exist in the
presence of out-ofplane deformations on atomic length scales, frequently
referred to as ripples. While such ripples can be detected via electron
microscopy, their direct observation via surface-based techniques and
characterization in terms of interaction forces and energies remain limited,
preventing an unambiguous study of their effect on mechanical characteristics,
including but not limited to friction anisotropy. Here, we employ
high-resolution atomic force microscopy to demonstrate the presence of
atomic-scale ripples on supported samples of few-layer molybdenum disulfide
(MoS$_{2}$). Three-dimensional force / energy spectroscopy is utilized to study
the effect of ripples on the interaction landscape. Friction force microscopy
reveals multiple symmetries for friction anisotropy, explained by studying
rippled sample areas as a function of scan size. Our experiments contribute to
the continuing development of a rigorous understanding of the nanoscale
mechanics of 2D materials.


  Using both two orbital and five orbital models, we investigate the
quasiparticle interference (QPI) patterns in the superconducting (SC) state of
iron-based superconductors. We compare the results for nonmagnetic and magnetic
impurities in sign-changed s-wave $\cos(k_x)\cdot\cos(k_y)$ and sign-unchanged
$|\cos(k_x)\cdot\cos(k_y)|$ SC states. While the patterns strongly depend on
the chosen band structures, the sensitivity of peaks around $(\pm\pi,0)$ and
$(0,\pm\pi)$ wavevectors on magnetic or non-magnetic impurity, and sign change
or sign unchanged SC orders is common in two models. Our results strongly
suggest that QPI may provide direct information of band structures and evidence
of the pairing symmetry in the SC states.


  We present a model, in which some nodes (called interconnecting nodes) in two
networks merge and play the roles in both the networks. The model analytic and
simulation discussions show a monotonically increasing dependence of
interconnecting node topological position difference and a monotonically
decreasing dependence of the interconnecting node number on function difference
of both networks. The dependence function details do not influence the
qualitative relationship. This online manuscript presents the details of the
model simulation and analytic discussion, as well as the empirical
investigations performed in eight real world bilayer networks. The analytic and
simulation results with different dependence function forms show rather good
agreement with the empirical conclusions.


  Regression factor score predictors have the maximum factor score determinacy,
i.e., the maximum correlation with the corresponding factor, but they do not
have the same inter-correlations as the factors. As it might be useful to
compute factor score predictors that have the same inter-correlations as the
factors, correlation-preserving factor score predictors have been proposed.
However, correlation-preserving factor score predictors have smaller
correlations with the corresponding factors (factor score determinacy) than
regression factor score predictors. Thus, higher factor score determinacy goes
along with bias of the inter-correlations and unbiased inter-correlations go
along with lower factor score determinacy. The aim of the present study was
therefore to investigate the size of the trade-off between factor score
determinacy and bias of inter-correlations by means of a simulation study. It
turns out that under several conditions very small gains of factor score
determinacy of the regression factor score predictor go along with a large bias
of inter-correlations. Instead of using the regression factor score predictor
by default, it is proposed to check whether substantial bias of
inter-correlations can be avoided without substantial loss of factor score
determinacy by using a correlation-preserving factor score predictor. A syntax
that allows to compute correlation-preserving factor score predictors from
regression factor score predictors and to compare factor score determinacy and
inter-correlations of the factor score predictors is given in the Appendix.


  A decentralized online quantum cash system, called qBitcoin, is given. We
design the system which has great benefits of quantization in the following
sense. Firstly, quantum teleportation technology is used for coin transaction,
which prevents from the owner of the coin keeping the original coin data even
after sending the coin to another. This was a main problem in a classical
circuit and a blockchain was introduced to solve this issue. In qBitcoin, the
double-spending problem never happens and its security is guaranteed
theoretically by virtue of quantum information theory. Making a block is time
consuming and the system of qBitcoin is based on a quantum chain, instead of
blocks. Therefore a payment can be completed much faster than Bitcoin. Moreover
we employ quantum digital signature so that it naturally inherits properties of
peer-to-peer (P2P) cash system as originally proposed in Bitcoin.


  With companies, states, and countries targeting net-zero emissions around
midcentury, there are questions about how these targets alter household welfare
and finances, including distributional effects across income groups. This paper
examines the distributional dimensions of technology transitions and net-zero
policies with a focus on welfare impacts across household incomes. The analysis
uses a model intercomparison with a range of energy-economy models using
harmonized policy scenarios reaching economy-wide, net-zero CO2 emissions
across the United States in 2050. We employ a novel linking approach that
connects output from detailed energy system models with survey microdata on
energy expenditures across income classes to provide distributional analysis of
net-zero policies. Although there are differences in model structure and input
assumptions, we find broad agreement in qualitative trends in policy incidence
and energy burdens across income groups. Models generally agree that direct
energy expenditures for many households will likely decline over time with
reference and net-zero policies. However, there is variation in the extent of
changes relative to current levels, energy burdens relative to reference
levels, and electricity expenditures. Policy design, primarily how climate
policy revenues are used, has first-order impacts on distributional outcomes.
Net-zero policy costs, in both absolute and relative terms, are unevenly
distributed across households, and relative increases in energy expenditures
are higher for lowest-income households. However, we also find that recycled
revenues from climate policies have countervailing effects when rebated on a
per-capita basis, offsetting higher energy burdens and potentially even leading
to net progressive outcomes.


  We use a random forest model to predict the critical cooling rate (RC) for
glass formation of various alloys from features of their constituent elements.
The random forest model was trained on a database that integrates multiple
sources of direct and indirect RC data for metallic glasses to expand the
directly measured RC database of less than 100 values to a training set of over
2,000 values. The model error on 5-fold cross validation is 0.66 orders of
magnitude in K/s. The error on leave out one group cross validation on alloy
system groups is 0.59 log units in K/s when the target alloy constituents
appear more than 500 times in training data. Using this model, we make
predictions for the set of compositions with melt-spun glasses in the database,
and for the full set of quaternary alloys that have constituents which appear
more than 500 times in training data. These predictions identify a number of
potential new bulk metallic glass (BMG) systems for future study, but the model
is most useful for identification of alloy systems likely to contain good glass
formers, rather than detailed discovery of bulk glass composition regions
within known glassy systems.


  Complex network theory has shown success in understanding the emergent and
collective behavior of complex systems [1]. Many real-world complex systems
were recently discovered to be more accurately modeled as multiplex networks
[2-6]---in which each interaction type is mapped to its own network layer;
e.g.~multi-layer transportation networks, coupled social networks, metabolic
and regulatory networks, etc. A salient physical phenomena emerging from
multiplexity is super-diffusion: exhibited by an accelerated diffusion admitted
by the multi-layer structure as compared to any single layer. Theoretically
super-diffusion was only known to be predicted using the spectral gap of the
full Laplacian of a multiplex network and its interacting layers. Here we turn
to machine learning which has developed techniques to recognize, classify, and
characterize complex sets of data. We show that modern machine learning
architectures, such as fully connected and convolutional neural networks, can
classify and predict the presence of super-diffusion in multiplex networks with
94.12\% accuracy. Such predictions can be done {\it in situ}, without the need
to determine spectral properties of a network.


  Quantum data locking is a unique quantum phenomenon that allows a relatively
short key to (un)lock an arbitrarily long message encoded in a quantum state,
in such a way that an eavesdropper who measures the state but does not know the
key has essentially no information about the encrypted message. The application
of quantum data locking in cryptography would allow one to overcome the
limitations of the one-time pad encryption, which requires the key to have the
same length as the message. However, it is known that the strength of quantum
data locking is also its Achilles heel, as the leakage of a few bits of the key
or the message may in principle allow the eavesdropper to unlock a
disproportionate amount of information. In this paper we show that there exist
quantum data locking schemes that can be made robust against information
leakage by increasing the length of the shared key by a proportionate amount.
This implies that a constant size key can still encrypt an arbitrarily long
message as long as a fraction of it remains secret to the eavesdropper.
Moreover, we greatly simplify the structure of the protocol by proving that
phase modulation suffices to generate strong locking schemes, paving the way to
optical experimental realizations. Also, we show that successful data locking
protocols can be constructed using random codewords, which very well could be
helpful in discovering random codes for data locking over noisy quantum
channels.


  A seminal result of Kamp is that over the reals Linear Temporal Logic (LTL)
has the same expressive power as first-order logic with binary order relation <
and monadic predicates. A key question is whether there exists an analogue of
Kamp's theorem for Metric Temporal Logic (MTL) -- a generalization of LTL in
which the Until and Since modalities are annotated with intervals that express
metric constraints. Hirshfeld and Rabinovich gave a negative answer, showing
that first-order logic with binary order relation < and unary function +1 is
strictly more expressive than MTL with integer constants. However, a recent
result of Hunter, Ouaknine and Worrell shows that with rational timing
constants, MTL has the same expressive power as first-order logic, giving a
positive answer. In this paper we generalize these results by giving a precise
characterization of those sets of constants for which MTL and first-order logic
have the same expressive power. We also show that full first-order
expressiveness can be recovered with the addition of counting modalities,
strongly supporting the assertion of Hirshfeld and Rabinovich that Q2MLO is one
of the most expressive decidable fragments of FO(<,+1).


  In this article we introduce the ultrametric networks which are p-adic
continuous analogues of the standard Markov state models constructed using
master equations. A p-adic transition network (or an ultrametric network) is a
model of a complex system consisting of a hierarchical energy landscape, a
Markov process on the energy landscape, and a master equation. We focus on
networks where the transition rates between two different basins are constant
functions, and the jumping process inside of each basin is controlled by a
p-adic radial function. We solve explicitly the Cauchy problem for the master
equation attached to this type of networks. The solution of this problem is the
network response to a given initial concentration. If the Markov process
attached to the network is conservative, the long term response of the network
is controlled by a Markov chain. If the process is not conservative the network
has absorbing states. We define an absorbing time, which depends on the initial
concentration, if this time is finite the network reaches an absorbing state in
a finite time. We identify in the response of the network the terms responsible
for bringing the network to an absorbing state, we call them the fast
transition modes. The existence of the fast transition modes is a consequence
of the assumption that the energy landscape is ultrametric (hierarchical), and
to the best of our understanding this result cannot be obtained using standard
methods of Markov state models. Nowadays, it is widely accepted that protein
native states are kinetic hubs that can be reached quickly from any other
state. The existence of fast transition modes implies that certain states on an
ultrametric network work as kinetic hubs.


  We study the classical dynamics of the Abelian Higgs model employing an
asymptotic multiscale expansion method, which uses the ratio of the Higgs to
the gauge field amplitudes as a small parameter. We derive an effective
nonlinear Schr\"{o}dinger equation for the gauge field, and a linear equation
for the scalar field containing the gauge field as a nonlinear source. This
equation is used to predict the existence of oscillons and oscillating kinks
for certain regimes of the ratio of the Higgs to the gauge field masses.
Results of numerical simulations are found to be in very good agreement with
the analytical findings, and show that the oscillons are robust, while kinks
are unstable. It is also demonstrated that oscillons emerge spontaneously as a
result of the onset of the modulational instability of plane wave solutions of
the model. Connections of the obtained solutions with the phenomenology of
superconductors is discussed.


  Widespread deployment of societal-scale machine learning systems necessitates
a thorough understanding of the resulting long-term effects these systems have
on their environment, including loss of trustworthiness, bias amplification,
and violation of AI safety requirements. We introduce a repeated learning
process to jointly describe several phenomena attributed to unintended hidden
feedback loops, such as error amplification, induced concept drift, echo
chambers and others. The process comprises the entire cycle of obtaining the
data, training the predictive model, and delivering predictions to end-users
within a single mathematical model. A distinctive feature of such repeated
learning setting is that the state of the environment becomes causally
dependent on the learner itself over time, thus violating the usual assumptions
about the data distribution. We present a novel dynamical systems model of the
repeated learning process and prove the limiting set of probability
distributions for positive and negative feedback loop modes of the system
operation. We conduct a series of computational experiments using an exemplary
supervised learning problem on two synthetic data sets. The results of the
experiments correspond to the theoretical predictions derived from the
dynamical model. Our results demonstrate the feasibility of the proposed
approach for studying the repeated learning processes in machine learning
systems and open a range of opportunities for further research in the area.


  In adversarial training (AT), the main focus has been the objective and
optimizer while the model has been less studied, so that the models being used
are still those classic ones in standard training (ST). Classic network
architectures (NAs) are generally worse than searched NAs in ST, which should
be the same in AT. In this paper, we argue that NA and AT cannot be handled
independently, since given a dataset, the optimal NA in ST would be no longer
optimal in AT. That being said, AT is time-consuming itself; if we directly
search NAs in AT over large search spaces, the computation will be practically
infeasible. Thus, we propose a diverse-structured network (DS-Net), to
significantly reduce the size of the search space: instead of low-level
operations, we only consider predefined atomic blocks, where an atomic block is
a time-tested building block like the residual block. There are only a few
atomic blocks and thus we can weight all atomic blocks rather than find the
best one in a searched block of DS-Net, which is an essential trade-off between
exploring diverse structures and exploiting the best structures. Empirical
results demonstrate the advantages of DS-Net, i.e., weighting the atomic
blocks.


  Habitability has been generally defined as the capability of an environment
to support life. Ecologists have been using Habitat Suitability Models (HSMs)
for more than four decades to study the habitability of Earth from local to
global scales. Astrobiologists have been proposing different habitability
models for some time, with little integration and consistency between them and
different in function to those used by ecologists. In this white paper, we
suggest a mass-energy habitability model as an example of how to adapt and
expand the models used by ecologists to the astrobiology field. We propose to
implement these models into a NASA Habitability Standard (NHS) to standardize
the habitability objectives of planetary missions. These standards will help to
compare and characterize potentially habitable environments, prioritize target
selections, and study correlations between habitability and biosignatures.
Habitability models are the foundation of planetary habitability science. The
synergy between the methods used by ecologists and astrobiologists will help to
integrate and expand our understanding of the habitability of Earth, the Solar
System, and exoplanets.


  We address the kinetic competition between charge striped order and
superconductivity in La$_{1.675}$Eu$_{0.2}$Sr$_{0.125}$CuO$_{4}$. Ultrafast
optical excitation is tuned to a mid-infrared vibrational resonance that
destroys charge order and promptly establishes transient coherent interlayer
coupling in this material. This effect is evidenced by the appearance of a
longitudinal plasma mode reminiscent of a Josephson plasma resonance. We find
that coherent interlayer coupling can be generated up to the charge order
transition $T_{CO} \approx$ 80 K, far above the equilibrium superconducting
transition temperature of any lanthanide cuprate. Two key observations are
extracted from the relaxation kinetics of the interlayer coupling. Firstly, the
plasma mode relaxes through a collapse of its coherence length and not its
density. Secondly, two distinct kinetic regimes are observed for this
relaxation, above and below spin order transition $T_{SO} =$ 25 K. Especially,
the temperature independent relaxation rate observed below $T_{SO}$ is
anomalous and suggests coexistence of superconductivity and stripes rather than
competition. Both observations support arguments that a low temperature
coherent stripe (or pair density wave) phase suppresses c-axis tunnelling by
disruptive interference rather than by depleting the condensate.


  We review the study, on the lattice, of the Green-Schwarz gauge-fixed string
action describing worldsheet fluctuations about the minimal surface
holographically dual to the null cusp Wilson loop, useful to evaluate the cusp
anomaly of N = 4 super Yang-Mills (sYM). We comment on discretization,
numerical explorations and challenges for the non-perturbative study of this
benchmark model of gauge-fixed worldsheet actions.


  In addition to conformal weldings $\varphi$, simple curves $\gamma$ growing
in the upper half plane generate driving functions $\xi$ and hitting times
$\tau$ through Loewner's differential equation. While the Loewner transform
$\gamma \mapsto \xi$ and its inverse $\xi \mapsto \gamma$ have been carefully
examined, less attention has been paid to the maps $\xi \mapsto \tau \mapsto
\varphi$. We study their continuity properties and show that uniform driver
convergence implies uniform hitting time convergence and uniform welding
convergence, even when the corresponding curves do not converge. Welding
convergence implies neither hitting time nor driver convergence, while hitting
time convergence implies driver convergence in (at least) the case of constant
drivers.
  As an application, we show that a curve $\gamma$ of finite Loewner energy can
be well approximated by an energy minimizer that matches $\gamma$'s welding on
a sufficiently-fine mesh.


  Hawking radiation emanating from two-dimensional charged and uncharged
dilatonic black holes - dimensionally reduced from (2+1) spinning and spinless,
respectively, BTZ black holes - is viewed as a tunnelling process. Two
dimensional dilatonic black holes (AdS(2) included) are treated as dynamical
backgrounds in contrast to the standard methodology where the background
geometry is fixed when evaluating Hawking radiation. This modification to the
geometry gives rise to a nonthermal part in the radiation spectrum. Nonzero
temperature of the extremal two-dimensional charged black hole is found.
  The Bekenstein-Hawking area formula is easily derived for these dynamical
geometries.


  The rotational bands in the neutron-rich nuclei $^{153-157}$Pm are
investigated by a particle-number conserving method. The kinematic moments of
inertia for the 1-quasiparticle bands in odd-$A$ Pm isotopes $^{153, 155,
157}$Pm are reproduced quite well by the present calculation. By comparison
between the experimental and calculated moments of inertia for the three
2-quasiparticle bands in the odd-odd nuclei $^{154, 156}$Pm, their
configurations and bandhead spins have been assigned properly. For the
2-quasiparticle band in $^{154}$Pm, the configuration is assigned as
$\pi5/2^-[532]\otimes \nu3/2^-[521]$ ($K^\pi=4^+$) with the bandhead spin
$I_0=4\hbar$. In $^{156}$Pm, the same configuration and bandhead spin
assignments have been made for the 2-quasiparticle band with lower excitation
energy. The configuration $\pi5/2^+[413]\otimes \nu5/2^+[642]$ ($K^\pi=5^+$)
with the bandhead spin $I_0=5\hbar$ is assigned for that with higher excitation
energy.


  Attosecond observations of coherent electron dynamics in molecules and
nanostructures can be achieved by combining conventional scanning tunneling
microscopy (STM) with ultrashort femtosecond laser pulses. While experimental
studies in the sub-cycle regime are underway, a robust strong-field theory
description has remained elusive. Here we devise a model based on the
strong-field approximation. Valid in all regimes, it provides a surprising
analogy to the standard model of STM. We also show that the intuitive
three-step model of attosecond science directly emerges from our model and
describe the optimal conditions for attosecond STM experiments.


  The relationship between the Near-Earth Objects (3200) Phaethon and (155140)
2005 UD is unclear. While both are parents to Meteor Showers, (the Geminids and
Daytime Sextantids, respectively), have similar visible-wavelength reflectance
spectra and orbits, dynamical investigations have failed to find any likely
method to link the two objects in the recent past. Here we present the first
near-infrared reflectance spectrum of 2005 UD, which shows it to be
consistently linear and red-sloped unlike Phaethon's very blue and concave
spectrum. Searching for a process that could alter some common starting
material to both of these end states, we hypothesized that the two objects had
been heated to different extents, motivated by their near-Sun orbits, the
composition of Geminid meteoroids, and previous models of Phaethon's surface.
We thus set about building a new laboratory apparatus to acquire reflectance
spectra of meteoritic samples after heating to higher temperatures than
available in the literature to test this hypothesis and were loaned a sample of
the CI Chondrite Orgueil from the Vatican Meteorite Collection for testing. We
find that while Phaethon's spectrum shares many similarities with different CI
Chondrites, 2005 UD's does not. We thus conclude that the most likely
relationship between the two objects is that their similar properties are only
by coincidence as opposed to a parent-fragment scenario, though the ultimate
test will be when JAXA's DESTINY+ mission visits one or both objects later this
decade. We also discuss possible paths forward to understanding Phaethon's
properties from dynamical and compositional grounds.


  Neutrino oscillations occur due to non-zero masses and mixings and most
importantly they are believed to maintain quantum coherence even over
astrophysical length scales. In the present study, we explore the quantumness
of three flavour neutrino oscillations by studying the extent of violation of
Leggett-Garg inequalities (LGI) if non-standard interactions are taken into
account. We report an enhancement in violation of LGI with respect to the
standard scenario for appropriate choice of NSI parameters.


  Under low concentrations of antibiotics causing DNA damage,
\textit{Escherichia coli} bacteria can trigger stochastically a stress response
known as the SOS response. While the expression of this stress response can
make individual cells transiently able to overcome antibiotic treatment, it can
also delay cell division, thus impacting the whole population's ability to grow
and survive. In order to study the trade-offs that emerge from this phenomenon,
we propose a bi-type age-structured population model that captures the
phenotypic plasticity observed in the stress response. Individuals can belong
to two types: either a fast-dividing but prone to death ``vulnerable'' type, or
a slow-dividing but ``tolerant'' type. We study the survival probability of the
population issued from a single cell as well as the population growth rate in
constant and periodic environments. We show that the sensitivity of these two
different notions of fitness with respect to the parameters describing the
phenotypic plasticity differs between the stochastic approach (survival
probability) and the deterministic approach (population growth rate). Moreover,
under a more realistic configuration of periodic stress, our results indicate
that optimal population growth can only be achieved through fine-tuning
simultaneously both the induction of the stress response and the repair
efficiency of the damage caused by the antibiotic.


  This paper discusses difference-in-differences (DID) estimation when there
exist many control variables, potentially more than the sample size. In this
case, traditional estimation methods, which require a limited number of
variables, do not work. One may consider using statistical or machine learning
(ML) methods. However, by the well-known theory of inference of ML methods
proposed in Chernozhukov et al. (2018), directly applying ML methods to the
conventional semiparametric DID estimators will cause significant bias and make
these DID estimators fail to be sqrt{N}-consistent. This article proposes three
new DID estimators for three different data structures, which are able to
shrink the bias and achieve sqrt{N}-consistency and asymptotic normality with
mean zero when applying ML methods. This leads to straightforward inferential
procedures. In addition, I show that these new estimators have the small bias
property (SBP), meaning that their bias will converge to zero faster than the
pointwise bias of the nonparametric estimator on which it is based.


  We investigate the production of primordial black holes and their
contribution to the presently observed dark matter in a dilaton two-field
extension of Starobinsky's quadratic $f(R)$ model of inflation. The model
features a multi-field amplification mechanism which leads to the generation of
a sharp peak in the inflationary power spectrum at small wavelengths
responsible for the production of primordial black holes. This mechanism is
significantly different from single-field models and requires a stochastic
treatment during an intermediate phase of the inflationary dynamics. We find
that the model leads to a successful phase of effective single-field
Starobinsky inflation for wavelengths probed by the cosmic microwave background
radiation and explains the observed cold dark matter content in the Universe by
the formation of primordial black holes.


  We present a chemodynamical analysis of the Leo~V dwarf galaxy, based on Keck
II DEIMOS spectra of 8 member stars. We find a systemic velocity for the system
of $\langle v_r\rangle = 170.9^{+ 2.1}_{-1.9}$kms$^{-1}$, and barely resolve a
velocity dispersion for the system, with $\sigma_{vr} =
2.3^{+3.2}_{-1.6}$kms$^{-1}$, consistent with previous studies of Leo~V. The
poorly resolved dispersion means we are unable to adequately constrain the dark
matter content of Leo~V. We find an average metallicity for the dwarf of
[Fe/H]$ = -2.48\pm0.21$, and measure a significant spread in the iron abundance
of its member stars, with $-3.1\le$[Fe/H]$\le-1.9$ dex, which cleanly
identifies Leo~V as a dwarf galaxy that has been able to self-enrich its
stellar population through extended star formation. Owing to the tentative
photometric evidence for tidal substructure around Leo~V, we also investigate
whether there is any evidence for tidal stripping or shocking of the system
within its dynamics. We measure a significant velocity gradient across the
system, of $\frac{{\rm d}v}{{\rm d}\chi} = -4.1^{+2.8}_{-2.6}$kms$^{-1}$ per
arcmin (or $\frac{{\rm d}v}{{\rm d}\chi} =
-71.9^{+50.8}_{-45.6}$kms$^{-1}$~kpc$^{-1}$), which points almost directly
toward the Galactic centre. We argue that Leo~V is likely a dwarf on the brink
of dissolution, having just barely survived a past encounter with the centre of
the Milky Way.


  We investigate interaction-induced valley domain walls in bilayer graphene in
the $\nu=0$ quantum Hall state, subject to a perpendicular electric field that
is antisymmetric across a line in the sample. Such a state can be realized in a
double-gated suspended sample, where the electric field changes sign across a
line in the middle. The non-interacting energy spectrum of the ground state is
characterized by a sharp domain wall between two valley-polarized regions.
Using the Hartree-Fock approximation, we find that the Coulomb interaction
opens a gap between the two lowest-lying states near the Fermi level, yielding
a smooth domain wall with a kink configuration in the valley index. Our results
suggest the possibility to visualize the domain wall via measuring the charge
density difference between the two graphene layers, which we find exhibits a
characteristic pattern. The width of the kink and the resulting pattern can be
tuned by the interplay between the magnetic field and gate electric fields.


  We consider the distribution of the orbits of the number 1 under the
$\beta$-transformations $T_\beta$ as $\beta$ varies. Mainly, the size of the
set of $\beta>1$ for which a given point can be well approximated by the orbit
of 1 is measured by its Hausdorff dimension. That is, the dimension of the
following set $$ E\big({\ell_n}_{n\ge 1}, x_0\big)=\Big{\beta>1:
|T^n_{\beta}1-x_0|<\beta^{-\ell_n}, {for infinitely many} n\in \N\Big} $$ is
determined, where $x_0$ is a given point in $[0,1]$ and ${\ell_n}_{n\ge 1}$ is
a sequence of integers tending to infinity as $n\to \infty$. For the proof of
this result, the notion of the recurrence time of a word in symbolic space is
introduced to characterize the lengths and the distribution of cylinders (the
set of $\beta$ with a common prefix in the expansion of 1) in the parameter
space ${\beta\in \R: \beta>1}$.


  We present a novel derivation of the boundary term for the action in
Lanczos-Lovelock gravity, starting from the boundary contribution in the
variation of the Lanczos-Lovelock action. The derivation presented here is
straightforward, i.e., one starts from the Lanczos-Lovelock action principle
and the action itself dictates the boundary structure and hence the boundary
term one needs to add to the action to make it well-posed. It also gives the
full structure of the contribution at the boundary of the complete action,
enabling us to read off the degrees of freedom to be fixed at the boundary,
their corresponding conjugate momenta and the total derivative contribution on
the boundary. We also provide a separate derivation of the Gauss-Bonnet case.


  Cross-lingual word embeddings (CLEs) enable multilingual modeling of meaning
and facilitate cross-lingual transfer of NLP models. Despite their ubiquitous
usage in downstream tasks, recent increasingly popular projection-based CLE
models are almost exclusively evaluated on a single task only: bilingual
lexicon induction (BLI). Even BLI evaluations vary greatly, hindering our
ability to correctly interpret performance and properties of different CLE
models. In this work, we make the first step towards a comprehensive evaluation
of cross-lingual word embeddings. We thoroughly evaluate both supervised and
unsupervised CLE models on a large number of language pairs in the BLI task and
three downstream tasks, providing new insights concerning the ability of
cutting-edge CLE models to support cross-lingual NLP. We empirically
demonstrate that the performance of CLE models largely depends on the task at
hand and that optimizing CLE models for BLI can result in deteriorated
downstream performance. We indicate the most robust supervised and unsupervised
CLE models and emphasize the need to reassess existing baselines, which still
display competitive performance across the board. We hope that our work will
catalyze further work on CLE evaluation and model analysis.


  Driver inattention is a large problem on the roads around the world. The
objective of this project was to develop an eye tracking algorithm with
sufficient computational efficiency and accuracy, to successfully realize when
the driver was looking away from the road for an extended period. The method of
tracking involved the minimization of a functional, using the gradient descent
and level set methods. The algorithm was then discretized and implemented using
C and MATLAB. Multiple synthetic images, grey-scale and colour images were
tested using the final design, with a desired region coverage of 82%. Further
work is needed to decrease the computation time, increase the robustness of the
algorithm, develop a small device capable of running the algorithm, as well as
physically implement this device into various vehicles.


  We define gauge transformations of Jacobi structures on a manifold. This is
related to gauge transformations of Poisson structures via the Poissonization.
Finally, we discuss how the contact structure of a contact groupoid is effected
by a gauge transformation of the Jacobi structure on its base.


  How smart is your kettle? How smart are things in your kitchen, your house,
your neighborhood, on the internet? With the advent of Internet of Things, and
the move of making devices `smart' by utilizing AI, a natural question arrises,
how can we evaluate the progress. The standard way of evaluating AI is through
the Turing Test. While Turing Test was designed for AI; the device that it was
tailored to was a computer. Applying the test to variety of devices that
constitute Internet of Things poses a number of challenges which could be
addressed through a number of adaptations.


  Community analysis algorithm proposed by Clauset, Newman, and Moore (CNM
algorithm) finds community structure in social networks. Unfortunately, CNM
algorithm does not scale well and its use is practically limited to networks
whose sizes are up to 500,000 nodes. The paper identifies that this
inefficiency is caused from merging communities in unbalanced manner. The paper
introduces three kinds of metrics (consolidation ratio) to control the process
of community analysis trying to balance the sizes of the communities being
merged. Three flavors of CNM algorithms are built incorporating those metrics.
The proposed techniques are tested using data sets obtained from existing
social networking service that hosts 5.5 million users. All the methods exhibit
dramatic improvement of execution efficiency in comparison with the original
CNM algorithm and shows high scalability. The fastest method processes a
network with 1 million nodes in 5 minutes and a network with 4 million nodes in
35 minutes, respectively. Another one processes a network with 500,000 nodes in
50 minutes (7 times faster than the original algorithm), finds community
structures that has improved modularity, and scales to a network with 5.5
million.


  The problem of efficiently generating random samples from high-dimensional
and non-log-concave posterior measures arising from nonlinear regression
problems is considered. Extending investigations from arXiv:2009.05298, local
and global stability properties of the model are identified under which such
posterior distributions can be approximated in Wasserstein distance by suitable
log-concave measures. This allows the use of fast gradient based sampling
algorithms, for which convergence guarantees are established that scale
polynomially in all relevant quantities (assuming `warm' initialisation). The
scope of the general theory is illustrated in a non-linear inverse problem from
integral geometry for which new stability results are derived.


  We study the decentralized distributed computation of discrete approximations
for the regularized Wasserstein barycenter of a finite set of continuous
probability measures distributedly stored over a network. We assume there is a
network of agents/machines/computers, and each agent holds a private continuous
probability measure and seeks to compute the barycenter of all the measures in
the network by getting samples from its local measure and exchanging
information with its neighbors. Motivated by this problem, we develop, and
analyze, a novel accelerated primal-dual stochastic gradient method for general
stochastic convex optimization problems with linear equality constraints. Then,
we apply this method to the decentralized distributed optimization setting to
obtain a new algorithm for the distributed semi-discrete regularized
Wasserstein barycenter problem. Moreover, we show explicit non-asymptotic
complexity for the proposed algorithm.


  In this article we provide new applications for exponential approximation
using the framework of Pek\"oz and R\"ollin (in press), which is based on
Stein's method. We give error bounds for the nearly critical Galton-Watson
process conditioned on non-extinction, and for the occupation times of Markov
chains; for the latter, in particular, we give a new exponential approximation
rate for the number of revisits to the origin for general two dimensional
random walk, also known as the Erd\H{o}s-Taylor theorem.


  A new fast algebraic method for obtaining an $\mathcal{H}^2$-approximation of
a matrix from its entries is presented. The main idea behind the method is
based on the nested representation and the maximum-volume principle to select
submatrices in low-rank matrices. A special iterative approach for the
computation of so-called representing sets is established. The main advantage
of the method is that it uses only the hierarchical partitioning of the matrix
and does not require special "proxy surfaces" to be selected in advance.
  The numerical experiments for the electrostatic problem and for the boundary
integral operator confirm the effectiveness and robustness of the approach. The
complexity is linear in the matrix size and polynomial in the ranks. The
algorithm is implemented as an open-source Python package that is available
online.


  We theoretically study the spin-dependent transport in a ferromagnet/super-
conductor/ferromagnet double tunnel junction. The tunneling current in the
antiferromagnetic alignment of the magnetizations gives rise to a spin
imbalance in the superconductor. The resulting nonequilibrium spin density
strongly suppresses the superconductivity with increase of bias voltage and
destroys it at a critical voltage Vc. The results provide a new method not only
for measuring the spin polarization of ferromagnets but also for controlling
superconductivity and tunnel magnetoresistance (TMR) by applying the bias
voltage.


  The effects of the physical aging on the vibrational density of states (VDOS)
of a polymeric glass is studied. The VDOS of a poly(methyl methacrylate) glass
at low-energy (<15 meV), was determined from inelastic neutron scattering at
low-temperature for two different physical thermodynamical states. One sample
was annealed during a long time at temperature lower than Tg, and another was
quenched from a temperature higher than Tg. It was found that the VDOS around
the boson peak, relatively to the one at higher energy, decreases with the
annealing at lower temperature than Tg, i.e., with the physical aging.


  We investigate the concept of equivariant quantization over the superspace
R^{p+q|2r}, with respect to the orthosymplectic algebra osp(p+1,q+1|2r). Our
methods and results vary upon the superdimension p+q-2r. When the
superdimension is nonzero, we manage to obtain a result which is similar to the
classical theorem of Duval, Lecomte and Ovsienko: we prove the existence and
uniqueness of the equivariant quantization except in some resonant situations.
To do so, we have to adapt their methods to take into account the fact that the
Casimir operator of the orthosymplectic algebra on supersymmetric tensors is
not always diagonalizable, when the superdimension is negative and even. When
the superdimension is zero, the situation is always resonant, but we can show
the existence of a one-parameter family of equivariant quantizations for
symbols of degree at most two.


  Protein contacts provide key information for the understanding of protein
structure and function, and therefore contact prediction from sequences is an
important problem. Recent research shows that some correctly predicted
long-range contacts could help topology-level structure modeling. Thus, contact
prediction and contact-assisted protein folding also proves the importance of
this problem. In this thesis, I will briefly introduce the extant related work,
then show how to establish the contact prediction through unsupervised
graphical models with topology constraints. Further, I will explain how to use
the supervised deep learning methods to further boost the accuracy of contact
prediction. Finally, I will propose a scoring system called diversity score to
measure the novelty of contact predictions, as well as an algorithm that
predicts contacts with respect to the new scoring system.


  Quantum coherence, present whenever a quantum system exists in a
superposition of multiple classically distinct states, marks one of the
fundamental departures from classical physics. Quantum coherence has recently
been investigated rigorously within a resource-theoretic formalism. However,
the finer-grained notion of multilevel coherence, which explicitly takes into
account the number of superposed classical states, has remained relatively
unexplored. A comprehensive analysis of multi-level coherence, which acts as
the single-party analogue to multi-partite entanglement, is essential for
understanding natural quantum processes as well as for gauging the performance
of quantum technologies. Here we develop the theoretical and experimental
groundwork for characterizing and quantifying multilevel coherence. We prove
that non-trivial levels of purity are required for multilevel coherence, as
there is a ball of states around the maximally mixed state that do not exhibit
multilevel coherence in any basis. We provide a simple necessary and sufficient
analytical criterion to verify multilevel coherence, which leads to a complete
classification for three-level systems. We present the robustness of multilevel
coherence, a bona fide quantifier which we show to be numerically computable
via semidefinite programming and experimentally accessible via multilevel
coherence witnesses. We further verify and lower-bound the robustness of
multilevel coherence by performing a semi-device-independent phase
discrimination task, implemented experimentally with four-level probes in a
photonic setup. Our results contribute to understanding the operational
relevance of genuine multilevel coherence, also by demonstrating the key role
it plays in enhanced phase discrimination---a primitive for quantum
communication and metrology---and suggest new ways to reliably test the quantum
behaviour of physical systems.


  We investigate the ground state density distributions of anti-ferromagnetic
spin-1 Bose gases in one dimensional harmonic potential in the full interacting
regimes. The ground state is obtained by diagonalizing the Hamiltonian in the
Hilbert space composed of the lowest eigenstates of noninteracting Bose gas and
spin components. The study reveals that in the situation of weak spin-dependent
interaction the total density profiles evolve from Gaussian-like distribution
to a Fermi-like shell structure of $N$ peaks with the increasing of
spin-independent interaction. While the increasing spin-exchange interaction
always weaken the fermionization of density distribution such that the total
density profiles show shell structure of less peaks and even show single peak
structure in the limit of strong spin-exchange interaction. The weakening of
fermionization results from the formation of composite atoms induced by
spin-exchange interaction. It is also shown that phase separation occurs for
the spinor Bose gas with weak spin-exchange interaction, meanwhile strong
spin-independent interaction.