  The non-equilibrium dynamics of a system that is located in the vicinity of a
quantum critical point is affected by the critical slowing down of
order-parameter correlations with the potential for novel out-of-equilibrium
universality. After a quantum quench, i.e. a sudden change of a parameter in
the Hamiltonian such a system is expected to almost instantly fall out of
equilibrium and undergo aging dynamics, i.e. dynamics that depends on the time
passed since the quench. Investigating the quantum dynamics of a $N$-component
$\varphi^{4}$-model coupled to an external bath, we determine this universal
aging and demonstrate that the system undergoes a coarsening, governed by a
critical exponent that is unrelated to the equilibrium exponents of the system.
We analyze this behavior in the large-$N$ limit, which is complementary to our
earlier renormalization group analysis, allowing in particular the direct
investigation of the order-parameter dynamics in the symmetry broken phase and
at the upper critical dimension. By connecting the long time limit of
fluctuations and response, we introduce a distribution function that shows that
the system remains non-thermal and exhibits quantum coherence even on long
timescales.


  Phase resetting curves characterize the way a system with a collective
periodic behavior responds to perturbations. We consider globally coupled
ensembles of Sakaguchi-Kuramoto oscillators, and use the Ott-Antonsen theory of
ensemble evolution to derive the analytical phase resetting equations. We show
the final phase reset value to be composed of two parts: an immediate phase
reset directly caused by the perturbation, and the dynamical phase reset
resulting from the relaxation of the perturbed system back to its dynamical
equilibrium. Analytical, semi-analytical and numerical approximations of the
final phase resetting curve are constructed. We support our findings with
extensive numerical evidence involving identical and non-identical oscillators.
The validity of our theory is discussed in the context of large ensembles
approximating the thermodynamic limit.


  We consider the NP-hard problem of minimizing a convex quadratic function
over the integer lattice ${\bf Z}^n$. We present a simple semidefinite
programming (SDP) relaxation for obtaining a nontrivial lower bound on the
optimal value of the problem. By interpreting the solution to the SDP
relaxation probabilistically, we obtain a randomized algorithm for finding good
suboptimal solutions, and thus an upper bound on the optimal value. The
effectiveness of the method is shown for numerical problem instances of various
sizes.


  This paper presents GelSight Svelte Hand, a novel 3-finger 2-DoF tactile
robotic hand that is capable of performing precision grasps, power grasps, and
intermediate grasps. Rich tactile signals are obtained from one camera on each
finger, with an extended sensing area similar to the full length of a human
finger. Each finger of GelSight Svelte Hand is supported by a semi-rigid
endoskeleton and covered with soft silicone materials, which provide both
rigidity and compliance. We describe the design, fabrication, functionalities,
and tactile sensing capability of GelSight Svelte Hand in this paper. More
information is available on our website:
\url{https://gelsight-svelte.alanz.info}.


  We study a non-equilibrium dynamical model: a marked continuous contact model
in $d$-dimensional space, $d \ge 1$. In contrast with the continuous contact
model in a critical regime, see \cite{KKP}, \cite{KPZ}, the model under
consideration is in the subcritical regime and it contains an additional
spontaneous spatially homogeneous birth from an external source. We prove that
this system has an invariant measure. We prove also that the process starting
from any initial distribution converges to this invariant measure.


  The work is devoted to the theoretical and experimental study of quantum
states of light conditionally prepared by subtraction of a random number of
photons from the initial multimode thermal state. A fixed number of photons is
subtracted from a multimode quantum state, but only a subsystem of a lower
number of modes is registered, in which the number of subtracted photons turns
out to be a non-fixed random variable. It is shown that the investigation of
multiphoton subtracted multimode thermal states provides a direct study of the
fundamental quantum-statistical properties of bosons using a simple
experimental implementation. The developed experimental setup plays a role of a
specific boson lototron, which is based on the fundamental link between the
statistics of boson systems and the Polya distribution. It is shown that the
calculation of the photon number distribution based on the Polya urn scheme is
equivalent to a calculation using statistical weights for boson systems. A
mathematical model based on the composition of the Polya distribution and
thermal state is developed and verified. The experimental results are in a good
agreement with the developed theory.


  The science of complex networks is a new interdisciplinary branch of science
which has arisen recently on the interface of physics, biology, social and
computer sciences, and others. Its main goal is to discover general laws
governing the creation and growth as well as processes taking place on
networks, like e.g. the Internet, transportation or neural networks. It turned
out that most real-world networks cannot be simply reduced to a compound of
some individual components. Fortunately, the statistical mechanics, being one
of pillars of modern physics, provides us with a very powerful set of tools and
methods for describing and understanding these systems. In this thesis, we
would like to present a consistent approach to complex networks based on
statistical mechanics, with the central role played by the concept of
statistical ensemble of networks. We show how to construct such a theory and
present some practical problems where it can be applied. Among them, we pay
attention to the problem of finite-size corrections and the dynamics of a
simple model of mass transport on networks.


  In this article, we consider $\mathcal{C}$-semigroups in $\mathbb{N}^d$. We
start with symmetric and almost symmetric $\mathcal{C}$-semigroups and prove
that these notions are independent of term orders. We further investigate the
conductor and the Ap\'ery set of a $\mathcal{C}$-semigroup with respect to a
minimal extremal ray. Building upon this, we extend the notion of reduced type
to $\mathcal{C}$-semigroups and study its extremal behavior. For all $d$ and
fixed $e \geq 2d$, we give a class of $\mathcal{C}$-semigroups of embedding
dimension $e$ such that both the type and the reduced type do not have any
upper bound in terms of the embedding dimension. We further explore irreducible
decompositions of a $\mathcal{C}$-semigroup and give a lower bound on the
irreducible components in an irreducible decomposition. Consequently, we deduce
that for each positive integer $k$, there exists a $\mathcal{C}$-semigroup $S$
such that the number of irreducible components of $S$ is at least $k$. A
$\mathcal{C}$-semigroup is known as a generalized numerical semigroup when the
rational cone spanned by the semigroup is full. We classify all the symmetric
generalized numerical semigroups of embedding dimension $2d+1$. Consequently,
when $d>1$, we deduce that a generalized numerical semigroup of embedding
dimension $2d+1$ is almost symmetric if and only if it is symmetric.


  We revisit Weyl invariance of string theories in generalized supergravity
backgrounds. In the previous work arXiv:1703.09213, a possible counterterm was
constructed, but it seems to be a point of controversy in some literatures
whether it is non-local or not. To settle down this issue, we show that the
counterterm may be local and exactly cancels out the one-loop trace anomaly in
generalized supergravity backgrounds.


  We investigate how the integrability conditions for conformal anomalies
constrain the form of the effective action in even-dimensional quantum
geometry. We show that the effective action of four-dimensional quantum
geometry (4DQG) satisfying integrability has a manifestly diffeomorphism
invariant and regularization scheme-independent form. We then generalize the
arguments to six dimensions and propose a model of 6DQG. A hypothesized form of
the 6DQG effective action is given.


  Let $\mathit{\Pi}$ be a cohomological irreducible cuspidal automorphic
representation of ${\rm GL}_2(\mathbb{A}_{\mathbb F})$ with central character
$\omega_{\mathit{\Pi}}$ over a totally real number field ${\mathbb F}$. In this
paper, we prove the algebraicity of the near central non-critical value of the
symmetric fourth $L$-function of $\mathit{\Pi}$ twisted by
$\omega_{\mathit{\Pi}}^{-2}$. The algebraicity is expressed in terms of the
Petersson norm of the normalized newform of $\mathit{\Pi}$ and the top degree
Whittaker period of the Gelbart-Jacquet lift ${\rm Sym}^2\mathit{\Pi}$ of
$\mathit{\Pi}$.


  The classical energy conditions are known to not be fundamental physics --
they are typically violated by semiclassical quantum effects. Consequently,
some effort has gone into finding possible semiclassical replacements for the
classical energy conditions -- the most well developed being the Ford-Roman
quantum inequalities. In the current article we shall instead develop classical
and quantum versions of a "flux energy condition" (FEC and QFEC) based on the
notion of constraining the possible fluxes measured by timelike observers. The
naive classical FEC will be seen to be satisfied in some situations, and even
for some quantum vacuum states, while its quantum analogue (the QFEC) is
satisfied (for naturally defined quantum vacuum states) under a rather wide
range of conditions. The situation for completely general (nonvacuum) quantum
states is less clear.


  We present the ROSAT All-Sky Survey Bright Source Catalogue (RASS-BSC,
revision 1RXS) derived from the all-sky survey performed during the first half
year (1990/91) of the ROSAT mission. 18,811 sources are catalogued (i) down to
a limiting ROSAT PSPC count-rate of 0.05 cts/s in the 0.1-2.4 keV energy band,
(ii) with a detection likelihood of at least 15 and (iii) at least 15 source
counts. The 18,811 sources underwent both an automatic validation and an
interactive visual verification process in which for 94% of the sources the
results of the standard processing were confirmed. The remaining 6% have been
analyzed using interactive methods and these sources have been flagged. Flags
are given for (i) nearby sources; (ii) sources with positional errors; (iii)
extended sources; (iv) sources showing complex emission structures; and (v)
sources which are missed by the standard analysis software. Broad band (0.1-2.4
keV) images are available for sources flagged by (ii), (iii) and (iv). For each
source the ROSAT name, position in equatorial coordinates, positional error,
source count-rate and error, background count-rate, exposure time, two
hardness-ratios and errors, extent and likelihood of extent, likelihood of
detection, and the source extraction radius are provided. At a brightness limit
of 0.1 cts/s (8,547 sources) the catalogue represents a sky coverage of 92%.
The RASS-BSC, the table of possible identification candidates, and the broad
band images are available in electronic form (Voges et al. 1996a) via
http://wave.xray.mpe.mpg.de/rosat/catalogues/rass-bsc .


  Quantum error mitigation (QEM) is vital for noisy intermediate-scale quantum
(NISQ) devices. While most conventional QEM schemes assume discrete gate-based
circuits with noise appearing either before or after each gate, the assumptions
are inappropriate for describing realistic noise that may have strong
gate-dependence and complicated nonlocal effects, and general computing models
such as analog quantum simulators. To address these challenges, we first extend
the scenario, where each computation process, being either digital or analog,
is described by a continuous time evolution. For noise from imperfections of
the engineered Hamiltonian or additional noise operators, we show it can be
effectively suppressed by a novel stochastic QEM method. Since our method only
assumes accurate single qubit controls, it is applicable to all digital quantum
computers and various analog simulators. Meanwhile, errors in the mitigation
procedure can be suppressed by leveraging the Richardson extrapolation method.
As we numerically test our method with various Hamiltonians under energy
relaxation and dephasing noise and digital quantum circuits with additional
two-qubit crosstalk, we show an improvement of simulation accuracy by two
orders. We assess the resource cost of our scheme and conclude the feasibility
of accurate quantum computing with NISQ devices.


  Recent advances in computer vision (CV) and natural language processing have
been driven by exploiting big data on practical applications. However, these
research fields are still limited by the sheer volume, versatility, and
diversity of the available datasets. CV tasks, such as image captioning, which
has primarily been carried out on natural images, still struggle to produce
accurate and meaningful captions on sketched images often included in
scientific and technical documents. The advancement of other tasks such as 3D
reconstruction from 2D images requires larger datasets with multiple
viewpoints. We introduce DeepPatent2, a large-scale dataset, providing more
than 2.7 million technical drawings with 132,890 object names and 22,394
viewpoints extracted from 14 years of US design patent documents. We
demonstrate the usefulness of DeepPatent2 with conceptual captioning. We
further provide the potential usefulness of our dataset to facilitate other
research areas such as 3D image reconstruction and image retrieval.


  Recent work has illuminated the vulnerability of speaker recognition systems
(SRSs) against adversarial attacks, raising significant security concerns in
deploying SRSs. However, they considered only a few settings (e.g., some
combinations of source and target speakers), leaving many interesting and
important settings in real-world attack scenarios alone. In this work, we
present AS2T, the first attack in this domain which covers all the settings,
thus allows the adversary to craft adversarial voices using arbitrary source
and target speakers for any of three main recognition tasks. Since none of the
existing loss functions can be applied to all the settings, we explore many
candidate loss functions for each setting including the existing and newly
designed ones. We thoroughly evaluate their efficacy and find that some
existing loss functions are suboptimal. Then, to improve the robustness of AS2T
towards practical over-the-air attack, we study the possible distortions
occurred in over-the-air transmission, utilize different transformation
functions with different parameters to model those distortions, and incorporate
them into the generation of adversarial voices. Our simulated over-the-air
evaluation validates the effectiveness of our solution in producing robust
adversarial voices which remain effective under various hardware devices and
various acoustic environments with different reverberation, ambient noises, and
noise levels. Finally, we leverage AS2T to perform thus far the largest-scale
evaluation to understand transferability among 14 diverse SRSs. The
transferability analysis provides many interesting and useful insights which
challenge several findings and conclusion drawn in previous works in the image
domain. Our study also sheds light on future directions of adversarial attacks
in the speaker recognition domain.


  The description of interactions in strongly-correlated topological phases of
matter remains a challenge. Here, we develop a stochastic functional approach
for interacting topological insulators including both charge and spin channels.
We find that the Mott transition of the Kane-Mele-Hubbard model may be
described by the variational principle with one equation. We present different
views of this equation from the electron Green's function, the free-energy and
the Hellmann-Feynman theorem. The band gap remains finite at the transition and
the Mott phase is characterized by antiferromagnetism in the $x-y$ plane. The
interacting topological phase is described through a $\mathbb{Z}_2$ number
related to helical edge modes. Our results then show that improving stochastic
approaches can give further insight on the understanding of interacting phases
of matter.


  High-temperature superconductivity is closely adjacent to a long-range
antiferromagnet, which is called a parent compound. In cuprates, all parent
compounds are alike and carrier doping leads to superconductivity, so a unified
phase diagram can be drawn. However, the properties of parent compounds for
iron-based superconductors show significant diversity and both carrier and
isovalent dopings can cause superconductivity, which casts doubt on the idea
that there exists a unified phase diagram for them. Here we show that the
ordered moments in a variety of iron pnictides are inversely proportional to
the effective Curie constants of their nematic susceptibility. This unexpected
scaling behavior suggests that the magnetic ground states of iron pnictides can
be achieved by tuning the strength of nematic fluctuations. Therefore, a
unified phase diagram can be established where superconductivity emerges from a
hypothetical parent compound with a large ordered moment but weak nematic
fluctuations, which suggests that iron-based superconductors are strongly
correlated electron systems.


  In real-world applications, e.g. law enforcement and video retrieval, one
often needs to search a certain person in long videos with just one portrait.
This is much more challenging than the conventional settings for person
re-identification, as the search may need to be carried out in the environments
different from where the portrait was taken. In this paper, we aim to tackle
this challenge and propose a novel framework, which takes into account the
identity invariance along a tracklet, thus allowing person identities to be
propagated via both the visual and the temporal links. We also develop a novel
scheme called Progressive Propagation via Competitive Consensus, which
significantly improves the reliability of the propagation process. To promote
the study of person search, we construct a large-scale benchmark, which
contains 127K manually annotated tracklets from 192 movies. Experiments show
that our approach remarkably outperforms mainstream person re-id methods,
raising the mAP from 42.16% to 62.27%.


  Let R be a regular local ring, containing an infinite field. Let G be a
reductive group scheme over R. We prove that a principal G-bundle over R is
trivial, if it is trivial over the fraction field of R.


  We present magneto transport experiments of quasi 3D PbTe wide quantum wells.
A plateau-like structure in the Hall resistance is observed, which corresponds
to the Shubnikov de Haas oscillations in the same manner as known from the
quantum Hall effect. The onsets of plateaux in Rxy do not correspond to 2D
filling factors but coincide with the occupation of 3D (bulk-) Landau levels.
At the same time a non-local signal is observed which corresponds to the
structure in Rxx and Rxy and fulfils exactly the Onsager-Casimir relation
(Rij,kl(B) = Rkl,ij(-B)). We explain the behaviour in terms of edge channel
transport which is controlled by a permanent backscattering across a system of
"percolative EC - loops" in the bulk region. Long range potential fluctuations
with an amplitude of the order of the subband splitting are explained to play
an essential role in this electron system.


  A ChatGPT-like system for drug compounds could be a game-changer in
pharmaceutical research, accelerating drug discovery, enhancing our
understanding of structure-activity relationships, guiding lead optimization,
aiding drug repurposing, reducing the failure rate, and streamlining clinical
trials. In this work, we make an initial attempt towards enabling ChatGPT-like
capabilities on drug molecule graphs, by developing a prototype system
DrugChat. DrugChat works in a similar way as ChatGPT. Users upload a compound
molecule graph and ask various questions about this compound. DrugChat will
answer these questions in a multi-turn, interactive manner. The DrugChat system
consists of a graph neural network (GNN), a large language model (LLM), and an
adaptor. The GNN takes a compound molecule graph as input and learns a
representation for this graph. The adaptor transforms the graph representation
produced by the GNN into another representation that is acceptable to the LLM.
The LLM takes the compound representation transformed by the adaptor and users'
questions about this compound as inputs and generates answers. All these
components are trained end-to-end. To train DrugChat, we collected instruction
tuning datasets which contain 10,834 drug compounds and 143,517 question-answer
pairs. The code and data is available at
\url{https://github.com/UCSD-AI4H/drugchat}


  We present one-loop perturbative results of the renormalization functions for
a complete set of nonlocal quark bilinear operators containing an asymmetric
staple-shaped Wilson line, using a family of improved lattice actions. This
study is relevant for the nonperturbative investigations regarding the
renormalization of the unpolarized, helicity and transversity
transverse-momentum dependent parton distribution functions (TMDPDFs) in
lattice QCD. We employ a number of different versions of
regularization-independent (RI$'$) renormalization prescriptions which address
the power and logarithmic divergences of such nonlocal operators, the
pinch-pole singularities at infinite Wilson-line lengths, as well as the mixing
among operators of different Dirac structures, as dictated by discrete
symmetries. All cancelations of divergences and admixtures are confirmed by our
results at one-loop level. We compare all the different prescriptions and we
provide the conversion matrices at one-loop order which relate the matrix
elements of the staple operators in RI$'$ to the reference scheme
$\overline{\rm MS}$.


  In the following article we discuss Delaunay triangulations for a point cloud
on an embedded surface in $\mathbb{R}^3$. We give sufficient conditions on the
point cloud to show that the diagonal switch algorithm finds an embedded
Delaunay triangulation.


  We study the effect of quenched disorder on the semimetal-superconductor
quantum phase transition in a model of two-dimensional Dirac semimetal with $N$
flavors of two-component Dirac fermions, using perturbative renormalization
group methods at one-loop order in a double epsilon expansion. For $N\geq 2$ we
find that the Harris-stable clean critical behavior gives way, past a certain
critical disorder strength, to a finite-disorder critical point characterized
by non-Gaussian critical exponents, a noninteger dynamic critical exponent
$z>1$, and a finite Yukawa coupling between Dirac fermions and bosonic order
parameter fluctuations. For $N\geq 7$ the disordered quantum critical point is
described by a renormalization group fixed point of stable-focus type and
exhibits oscillatory corrections to scaling.


  We present a new method to estimate the absolute ages of stellar systems.
This method is based on the difference in magnitude between the main sequence
turn-off (MSTO) and a well defined knee located along the lower main sequence
(MSK). This feature is caused by the collisionally induced absorption of
molecular hydrogen and it can be easily identified in near-infrared (NIR) and
in optical-NIR color-magnitude diagrams of stellar systems. We took advantage
of deep and accurate NIR images collected with the Multi-Conjugate Adaptive
Optics Demonstrator temporarily available on the Very Large Telescope and of
optical images collected with the Advanced Camera for Surveys Wide Field Camera
on the Hubble Space Telescope and with ground-based telescopes to estimate the
absolute age of the globular NGC3201 using both the MSTO and the
Delta(MSTO-MSK). We have adopted a new set of cluster isochrones and we found
that the absolute ages based on the two methods agree to within one sigma.
However, the errors of the ages based on the Delta(MSTO-MSK) method are
potentially more than a factor of two smaller, since they are not affected by
uncertainties in cluster distance or reddening.Current isochrones appear to
predict slightly bluer (~0.05mag) NIR and optical-NIR colors than observed for
magnitudes fainter than the MSK.


  In this study we consider a coupled system of partial differential equations
(PDE's) which describes a certain structural acoustics interaction. One
component of this PDE system is a wave equation, which serves to model the
interior acoustic wave medium within a given three dimensional chamber $%
\Omega $. This acoustic wave equation is coupled on a boundary interface ($%
\Gamma _{0}$) to a two dimensional system of thermoelasticity: this
thermoelastic PDE comprises a structural beam or plate equation, which governs
the vibrations of flexible wall portion $\Gamma _{0}$ of the chamber $\Omega $;
the elastic dynamics is coupled to a heat equation which also evolves on
$\Gamma _{0}$, and which imparts a thermal damping onto the entire structural
acoustic system. As we said, the interaction between the wave and thermoelastic
PDE components takes place on the boundary interface $% \Gamma _{0}$, and
involves coupling boundary terms which are above the level of finite energy. We
analyze the stability properties of this coupled structural acoustics PDE
model, in the absence of \ any additive feedback dissipation on the hard walls
$\Gamma _{1}$ of the boundary $\partial \Omega $. Under a certain geometric
assumption on $\Gamma _{1}$, an assumption which has appeared in the literature
in conection with structural acoustic flow, and which allows for the invocation
of a recently derived microlocal boundary trace estimate, we show that
classical solutions of this thermally damped structural acoustics PDE decay
uniformly to zero, with a rational rate of decay.


  Marcasite class of compounds provide facile platform to explore novel
phenomena of fundamental and technological importance, such as unconventional
superconductivity or high performance electrocatalyst. We report the synthesis
and experimental investigation of a new marcasite CoSeAs in this letter.
Experimental investigation of the new material using neutron scattering
measurements reveal weak magnetic correlation of cobalt ions below $T$ = 36.2
K. The modest isotropic exchange interaction between cobalt moments, inferred
from random phase approximation analysis, hints of magnetically unstable
environment. It is a desirable characteristic to induce unconventional
superconductivity via chemical pressure application


  Recommender system has become an inseparable part of online shopping and its
usability is increasing with the advancement of these e-commerce sites. An
effective and efficient recommender system benefits both the seller and the
buyer significantly. We considered user activities and product information for
the filtering process in our proposed recommender system. Our model has
achieved inspiring result (approximately 58% true-positive and 13%
false-positive) for the data set provided by RecSys Challenge 2015. This paper
aims to describe a statistical model that will help to predict the buying
behavior of a user in real-time during a session.


  A quantum mechanical description of vortices in two dimensional superfluid
$^4$He flims is presented. Single vortex creation and annihilation operators
are defined and wavefunctions for these states are explicitly constructed. A
hamitonian for these states is then proposed.


  We engineer a class of quiver gauge theories with several interesting
features by studying D-branes at a simple Calabi-Yau singularity. At weak 't
Hooft coupling we argue using field theory techniques that these theories admit
both supersymmetric vacua and meta-stable non-supersymmetric vacua, though the
arguments indicating the existence of the supersymmetry breaking states are not
decisive. At strong 't Hooft coupling we find simple candidate gravity dual
descriptions for both sets of vacua.


  Transformer-based pre-trained language models (PLMs) mostly suffer from
excessive overhead despite their advanced capacity. For resource-constrained
devices, there is an urgent need for a spatially and temporally efficient model
which retains the major capacity of PLMs. However, existing statically
compressed models are unaware of the diverse complexities between input
instances, potentially resulting in redundancy and inadequacy for simple and
complex inputs. Also, miniature models with early exiting encounter challenges
in the trade-off between making predictions and serving the deeper layers.
Motivated by such considerations, we propose a collaborative optimization for
PLMs that integrates static model compression and dynamic inference
acceleration. Specifically, the PLM is slenderized in width while the depth
remains intact, complementing layer-wise early exiting to speed up inference
dynamically. To address the trade-off of early exiting, we propose a joint
training approach that calibrates slenderization and preserves contributive
structures to each exit instead of only the final layer. Experiments are
conducted on GLUE benchmark and the results verify the Pareto optimality of our
approach at high compression and acceleration rate with 1/8 parameters and 1/19
FLOPs of BERT.


  We propose a multicarrier chirp-division multiplexing (MCDM) system in which
orthogonal chirp waveforms are utilized as frequency subcarriers. Orthogonal
characteristics of chirp subcarriers are analyzed in respect to
cross-correlation coefficients among subcarriers. Moreover, orthogonal chirp
transform (OCT) is developed to implement MCDM systems. In addition, we design
a low complexity receiver, including packet synchronization, carrier frequency
offset compensation, channel estimation, and symbol detection. Proposed MCDM
systems have both advantages of chirp waveforms and multicarrier architectures.
Computational complexity of our proposed detector is discussed in detail. The
bit-error-rate (BER) performance of the MCDM system is evaluated in simulations
and indoor radio frequency (RF) experiments. We have demonstrated effectiveness
of MCDM systems both in simulation and experimental results, comparing to
orthogonal frequency division multiplexing (OFDM) systems. Moreover, MCDM can
be further applied to higher order modulations for enabling higher data rates
for RF wireless communications.


  We present a systematic study of sunspot physical parameters using full disk
magnetograms from MDI/SoHO and HMI/SDO. Our aim is to use uniform datasets and
analysis procedures to characterize the sunspots, paying particular attention
to the differences and similarities between "Hale" and "anti-Hale" spots.
Included are measurements of the magnetic tilt angles, areas, fluxes and
polarity pole separations for 4385 sunspot groups in Cycles 23 and 24 each
measured, on average, at $\sim$66 epochs centered on meridian-crossing. The
sunspots are classified as either "Hale" or "anti-Hale", depending on whether
their polarities align or anti-align with Hale's hemispheric polarity rule. We
find that (1) The "anti-Hale" sunspots constitute a fraction ($8.1\pm0.4$)\% of
all sunspots, and this fraction is the same in both hemispheres and cycles, (2)
"Hale" sunspots obey Joy's law in both hemispheres and cycles but "anti-Hale"
sunspots do not. Three equivalent forms of Joy's law are derived,
$\sin\gamma=(0.38\pm0.05)\sin\phi$, $\gamma=(0.39\pm0.06)\phi$, and
$\gamma=(23.80\pm3.51)\sin\phi$, where $\gamma$ is the tilt angle and $\phi$ is
the heliospheric latitude, (3) The average Hale sunspot tilt angle is
$\overline{\gamma} = 5.49^\circ\pm0.09$, (4) The tilt angles, magnetic fluxes
and pole separations of sunspots are interrelated, with larger fluxes
correlated with larger pole separations and smaller tilt angles. We present
empirical relations between these quantities. Cycle 24 is a much weaker cycle
than Cycle 23 in sunspot numbers, cumulative magnetic flux, and average sunspot
magnetic flux. The "anti-Hale" sunspots are also much weaker than "Hale"
sunspots in those parameters, but they share similar magnetic flux
distributions and average latitudes. We characterize the two populations, and
aim to shed light on the origin of "anti-Hale" sunspots.


  We study exciton spin decay in the regime of strong electron-hole exchange
interaction. In this regime the electron spin precession is restricted within a
sector formed by the external magnetic field and the effective exchange fields
triggered by random spin flips of the hole. Using Hanle effect measurements, we
demonstrate that this mechanism dominates our experiments in CdTe/(Cd,Mg)Te
quantum wells. The calculations provide a consistent description of the
experimental results, which is supported by independent measurements of the
parameters entering the model.


  Transformer-based large language models (LLMs) have demonstrated impressive
capabilities in a variety of natural language processing (NLP) tasks.
Nonetheless, it is challenging to deploy and fine-tune LLMs on mobile edge
devices with limited computing, memory, and energy budgets. In this paper, we
propose Confidant, a multi-backend collaborative training framework for
customizing state-of-the-art LLMs on commodity mobile devices like smartphones.
Confidant partitions an LLM into several sub-models so that each fits into a
mobile device's memory. A pipeline parallel training mechanism is further
developed to ensure fast and efficient distributed training. In addition, we
propose a novel backend scheduler to allocate different attention heads to
heterogeneous compute hardware, including mobile CPU and GPUs, to maximize the
compute resource utilization on each edge device. Our preliminary experimental
results show that Confidant achieves at most 45.3% memory reduction and 8.03x
inference speedup in practical settings.


  We show that the Diederich-Fornaess index of a domain in a Stein manifold is
invariant under CR-diffeomorphisms. For this purpose we also improve
CR-extension theorem.


  We show that bounded families of global classical relativistic strings that
can be written as graphs are relatively compact in C0 topology, but their
accumulation points include many non relativistic strings. We also provide an
alternative formulation of these relativistic strings and characterize their
``semi-relativistic'' completion.


  Variational hybrid quantum-classical algorithms are promising candidates for
near-term implementation on quantum computers. In these algorithms, a quantum
computer evaluates the cost of a gate sequence (with speedup over classical
cost evaluation), and a classical computer uses this information to adjust the
parameters of the gate sequence. Here we present such an algorithm for quantum
state diagonalization. State diagonalization has applications in condensed
matter physics (e.g., entanglement spectroscopy) as well as in machine learning
(e.g., principal component analysis). For a quantum state $\rho$ and gate
sequence $U$, our cost function quantifies how far $ U\rho U^{\dagger}$ is from
being diagonal. We introduce novel short-depth quantum circuits to quantify our
cost. Minimizing this cost returns a gate sequence that approximately
diagonalizes $\rho$. One can then read out approximations of the largest
eigenvalues, and the associated eigenvectors, of $\rho$. As a
proof-of-principle, we implement our algorithm on Rigetti's quantum computer to
diagonalize one-qubit states and on a simulator to find the entanglement
spectrum of the Heisenberg model ground state.


  The performance of quantum key distribution (QKD) protocols is evaluated
based on the ease of implementation and key generation rate. Among major
protocols, the differential-phase-shift (DPS) protocol has the advantage of
simple implementation using a train of coherent pulses and a passive detection
unit. Unfortunately, however, its key rate is known to be at least proportional
to $\eta^2$ with respect to channel transmission $\eta\to0$. If one can only
prove the rate proportional to $\eta^2$ and cannot improve the analysis beyond
that, then the DPS protocol will be deemed inferior to other major protocols,
such as the decoy BB84 protocol. In this paper, we consider a type of DPS
protocol in which the phase of each emitted block comprising $n$ pulses is
randomized and significantly improve the analysis of its key rate.
Specifically, we reveal that the key rate is proportional to
$\eta^{1+\frac{1}{n-2}}$ and this rate is tight. This implies that the DPS
protocol can achieve a key rate proportional to $\eta$ for a large number of
$n$, which is the same scaling as the decoy BB84 protocol. Our result suggests
that the DPS protocol can achieve a combination of both advantages of ease of
implementation and a high key generation rate.


  We study the unitary supermultiplets of the N=8, d=5 anti-de Sitter (AdS)
superalgebra SU(2,2|4) which is the symmetry algebra of the IIB string theory
on AdS_5 X S^5. We give a complete classification of the doubleton
supermultiplets of SU(2,2|4) which do not have a Poincare limit and correspond
to d=4 conformal field theories (CFT) living on the boundary of AdS_5. The CPT
self-conjugate irreducible doubleton supermultiplet corresponds to d=4, N = 4
super Yang-Mills theory. The other irreducible doubleton supermultiplets come
in CPT conjugate pairs. The maximum spin range of the general doubleton
supermultiplets is 2. In particular, there exists a CPT conjugate pair of
doubleton supermultiplets corresponding to the fields of N=4 conformal
supergravity in d=4 which can be coupled to N=4 super Yang-Mills theory in d=4.
We also study the "massless" supermultiplets of SU(2,2|4) which can be obtained
by tensoring two doubleton supermultiplets. The CPT self-conjugate "massless"
supermultiplet is the N=8 graviton supermultiplet in AdS_5. The other
"massless" supermultiplets generally come in conjugate pairs and can have
maximum spin range of 4. We discuss the implications of our results for the
conjectured CFT/AdS dualities.


  We present our method for tackling the legal case retrieval task of the
Competition on Legal Information Extraction/Entailment 2019. Our approach is
based on the idea that summarization is important for retrieval. On one hand,
we adopt a summarization based model called encoded summarization which encodes
a given document into continuous vector space which embeds the summary
properties of the document. We utilize the resource of COLIEE 2018 on which we
train the document representation model. On the other hand, we extract lexical
features on different parts of a given query and its candidates. We observe
that by comparing different parts of the query and its candidates, we can
achieve better performance. Furthermore, the combination of the lexical
features with latent features by the summarization-based method achieves even
better performance. We have achieved the state-of-the-art result for the task
on the benchmark of the competition.


  A new adaptive predictive controller for constrained linear systems is
presented. The main feature of the proposed controller is the partition of the
input in two components. The first part is used to persistently excite the
system, in order to guarantee accurate and convergent parameter estimates in a
deterministic framework. An MPC-inspired receding horizon optimization problem
is developed to achieve the required excitation in a manner that is optimal for
the plant. The remaining control action is employed by a conventional tube MPC
controller to regulate the plant in the presence of parametric uncertainty and
the excitation generated for estimation purposes. Constraint satisfaction,
robust exponential stability, and convergence of the estimates are guaranteed
under design conditions mildly more demanding than that of standard MPC
implementations.


  We present a method for solving the transshipment problem - also known as
uncapacitated minimum cost flow - up to a multiplicative error of $1 +
\varepsilon$ in undirected graphs with non-negative edge weights using a
tailored gradient descent algorithm. Using $\tilde{O}(\cdot)$ to hide
polylogarithmic factors in $n$ (the number of nodes in the graph), our gradient
descent algorithm takes $\tilde O(\varepsilon^{-2})$ iterations, and in each
iteration it solves an instance of the transshipment problem up to a
multiplicative error of $\operatorname{polylog} n$. In particular, this allows
us to perform a single iteration by computing a solution on a sparse spanner of
logarithmic stretch. Using a randomized rounding scheme, we can further extend
the method to finding approximate solutions for the single-source shortest
paths (SSSP) problem. As a consequence, we improve upon prior work by obtaining
the following results: (1) Broadcast CONGEST model: $(1 +
\varepsilon)$-approximate SSSP using $\tilde{O}((\sqrt{n} +
D)\varepsilon^{-3})$ rounds, where $ D $ is the (hop) diameter of the network.
(2) Broadcast congested clique model: $(1 + \varepsilon)$-approximate
transshipment and SSSP using $\tilde{O}(\varepsilon^{-2})$ rounds. (3)
Multipass streaming model: $(1 + \varepsilon)$-approximate transshipment and
SSSP using $\tilde{O}(n)$ space and $\tilde{O}(\varepsilon^{-2})$ passes. The
previously fastest SSSP algorithms for these models leverage sparse hop sets.
We bypass the hop set construction; computing a spanner is sufficient with our
method. The above bounds assume non-negative edge weights that are polynomially
bounded in $n$; for general non-negative weights, running times scale with the
logarithm of the maximum ratio between non-zero weights.


  In this paper we study the production of Primordial Black Holes (PBHs) from
inflation in order to explain the Dark Mater (DM) in the Universe. The
evaluation of the fractional PBHs abundance to DM is sensitive to the value of
the threshold $\mathrm{\delta_c}$ and the exact value of $\mathrm{\delta_c}$ is
sensitive to the specific shape of the cosmological fluctuations. Different
mechanisms producing PBHs lead to different thresholds and hence to different
fractional abundances of PBHs. In this study, we examine various classes of
inflationary models proposed in the existing literature to elucidate the
formation of PBHs and we evaluate numerically the associated threshold values.
  Having evaluated the thresholds we compute the abundances of PBHs to DM using
the Press Schecter approach and the Peak Theory. Given the influence of
different power spectra on the thresholds, we investigate whether these
inflationary models can successfully account for a significant fraction of DM.
Moreover, we provide suggested values for the critical threshold. By examining
the interplay between inflationary models, threshold values, and PBH
abundances, our study aims to shed light on the viability of PBHs as a
candidate for DM and contributes to the ongoing discussion regarding the nature
of DM in the Universe


  We analyze cloaking due to anomalous localized resonance in the quasistatic
regime in the case when a general charge density distribution is brought near a
slab superlens. If the charge density distribution is within a critical
distance of the slab, then the power dissipation within the slab blows up as
certain electrical dissipation parameters go to zero. The potential remains
bounded far away from the slab in this limit, which leads to cloaking due to
anomalous localized resonance. On the other hand, if the charge density
distribution is further than this critical distance from the slab, then the
power dissipation within the slab remains bounded and cloaking due to anomalous
localized resonance does not occur. The critical distance is shown to strongly
depend on the the rate at which the dissipation outside of the slab goes to
zero.


  Modeling low energy eigenstates of fermionic systems can provide insight into
chemical reactions and material properties and is one of the most anticipated
applications of quantum computing. We present three techniques for reducing the
cost of preparing fermionic Hamiltonian eigenstates using phase estimation.
First, we report a polylogarithmic-depth quantum algorithm for antisymmetrizing
the initial states required for simulation of fermions in first quantization.
This is an exponential improvement over the previous state-of-the-art. Next, we
show how to reduce the overhead due to repeated state preparation in phase
estimation when the goal is to prepare the ground state to high precision and
one has knowledge of an upper bound on the ground state energy that is less
than the excited state energy (often the case in quantum chemistry). Finally,
we explain how one can perform the time evolution necessary for the phase
estimation based preparation of Hamiltonian eigenstates with exactly zero error
by using the recently introduced qubitization procedure.


  Motivated both by recently introduced forms of list colouring and by earlier
work on independent transversals subject to a local sparsity condition, we use
the semi-random method to prove the following result.
  For any function $\mu$ satisfying $\mu(d)=o(d)$ as $d\to\infty$, there is a
function $\lambda$ satisfying $\lambda(d)=d+o(d)$ as $d\to\infty$ such that the
following holds. For any graph $H$ and any partition of its vertices into parts
of size at least $\lambda$ such that (a) for each part the average over its
vertices of degree to other parts is at most $d$, and (b) the maximum degree
from a vertex to some other part is at most $\mu$, there is guaranteed to be a
transversal of the parts that forms an independent set of $H$.
  This is a common strengthening of two results of Loh and Sudakov (2007) and
Molloy and Thron (2012), each of which in turn implies an earlier result of
Reed and Sudakov (2002).


  We find necessary and sufficient conditions under which the complex
coordinates on a flag manifold of a classical group described in [2] are
Bochner coordinates.


  We are presenting a method for computing the Fourier coefficients of a given
polynomial regression by using the trapezoidal rule for numerical integration.
As function basis we use the orthogonal Legendre polynomials. The results are
accurate and stable compared to Forsythe's method.


  Understanding the emergence of cooperation in systems of computational agents
is crucial for the development of effective cooperative AI. Interaction among
individuals in real-world settings are often sparse and occur within a broad
spectrum of incentives, which often are only partially known. In this work, we
explore how cooperation can arise among reinforcement learning agents in
scenarios characterised by infrequent encounters, and where agents face
uncertainty about the alignment of their incentives with those of others. To do
so, we train the agents under a wide spectrum of environments ranging from
fully competitive, to fully cooperative, to mixed-motives. Under this type of
uncertainty we study the effects of mechanisms, such as reputation and
intrinsic rewards, that have been proposed in the literature to foster
cooperation in mixed-motives environments. Our findings show that uncertainty
substantially lowers the agents' ability to engage in cooperative behaviour,
when that would be the best course of action. In this scenario, the use of
effective reputation mechanisms and intrinsic rewards boosts the agents'
capability to act nearly-optimally in cooperative environments, while greatly
enhancing cooperation in mixed-motive environments as well.


  This paper proposes a pipeline for quantitatively evaluating interactive
Large Language Models (LLMs) using publicly available datasets. We carry out an
extensive technical evaluation of LLMs using Big-Vul covering four different
common software vulnerability tasks. This evaluation assesses the multi-tasking
capabilities of LLMs based on this dataset. We find that the existing
state-of-the-art approaches and pre-trained Language Models (LMs) are generally
superior to LLMs in software vulnerability detection. However, in software
vulnerability assessment and location, certain LLMs (e.g., CodeLlama and
WizardCoder) have demonstrated superior performance compared to pre-trained
LMs, and providing more contextual information can enhance the vulnerability
assessment capabilities of LLMs. Moreover, LLMs exhibit strong vulnerability
description capabilities, but their tendency to produce excessive output
significantly weakens their performance compared to pre-trained LMs. Overall,
though LLMs perform well in some aspects, they still need improvement in
understanding the subtle differences in code vulnerabilities and the ability to
describe vulnerabilities to fully realize their potential. Our evaluation
pipeline provides valuable insights into the capabilities of LLMs in handling
software vulnerabilities.


  Recent cosmological data favour R^2-inflation and some amount of non-standard
dark radiation in the Universe. We show that a framework of high energy scale
invariance can explain these data. The spontaneous breaking of this symmetry
provides gravity with the Planck mass and particle physics with the electroweak
scale. We found that the corresponding massless Nambu--Goldstone bosons --
dilatons -- are produced at reheating by the inflaton decay right at the amount
needed to explain primordial abundances of light chemical elements and
anisotropy of the cosmic microwave background. Then we extended the discussion
on the interplay with Higgs-inflation and on general class of inflationary
models where dilatons are allowed and may form the dark radiation. As a result
we put a lower limit on the reheating temperature in a general scale invariant
model of inflation.


  Different forms of the metric for the Kerr-NUT-(anti-)de Sitter space-time
are being widely used in its extension to higher dimensions. The purpose of
this note is to relate the parameters that are being used to the physical
parameters (mass, rotation, NUT and cosmological constant) in the basic four
dimensional situation.


  In this paper we carry out a preliminary study of the dependence of the
Tully-Fisher Relation (TFR) with the width and intensity level of the absolute
magnitude interval of a limited sample of 2411 galaxies taken from Mathewson \&
Ford (1996). The galaxies in this sample do not differ significantly in
morphological type, and are distributed over an $\sim11$-magnitude interval
($-24.4 < I < -13.0$). We take as directives the papers by Nigoche-Netro et al.
(2008, 2009, 2010) in which they study the dependence of the Kormendy (KR), the
Fundamental Plane (FPR) and the Faber-Jackson Relations (FJR) with the
magnitude interval within which the observed galaxies used to derive these
relations are contained. We were able to characterise the behaviour of the TFR
coefficients $(\alpha, \beta)$ with respect to the width of the magnitude
interval as well as with the brightness of the galaxies within this magnitude
interval. We concluded that the TFR for this specific sample of galaxies
depends on observational biases caused by arbitrary magnitude cuts, which in
turn depend on the width and intensity of the chosen brightness levels.


  After briefly outlining the formalism of the Generalized Parton Distributions
(GPDs) in the first sections, we discuss some general considerations for their
experimental study : in particular, the relation between GPDs and experimental
observables and the need and requirements for a dedicated experimental
facility. Also, we review and comment the first experimental signatures of this
physics recently observed by the HERMES and CLAS (at JLab) collaborations.


  We investigate the age constraint on the agegraphic dark energy model by
using two old galaxies (LBDS 53W091 and LBDS 53W069) and the old high redshift
quasar APM 08279+5255. We find that the agegraphic dark energy model can easily
accommodate LBDS 53W091 and LBDS 53W069. To accommodate APM 08279+5255, one can
take the reduced Hubble parameter as large as h=0.64, when the fraction matter
energy density $\Omega_{m0}\approx 0.22$.


  In this paper, we propose a numerical method for verifying the positiveness
of solutions to semilinear elliptic equations. We provide a sufficient
condition for a solution to an elliptic equation to be positive in the domain
of the equation, which can be checked numerically without requiring a
complicated computation. We present some numerical examples.


  The goal of this paper is to consider some relations between varieties of
representations of groups and varieties of associative algebras. The main
emphasis is put on the varieties of representations of groups induced by the
varieties of associative algebras. We provide the reader with the list of some
open problems.


  Deep machine learning methods have been studied for the software trigger of
the future PANDA experiment at FAIR, using Monte Carlo simulated data from the
GEANT-based detector simulation framework PandaRoot. Ten physics channels that
cover the main physics topics, including electromagnetic, exotic, charmonium,
open charm, and baryonic reaction channels, have been investigated at four
different anti-proton beam momenta. Binary and multi-class classification
together with seven different network architectures have been studied. Finally
a residual convolutional neural network with four residual blocks in a binary
classification scheme has been chosen due to its extendability, performance and
stability. The presented study represents a feasibility study of a completely
software-based trigger system. Compared to a conventional selection method, the
deep machine learning approach achieved a significant efficiency gain of up to
200\%, while keeping the background reduction factor at the required level of
1/1000. Furthermore, it is shown that the use of additional input variables can
improve the data quality for subsequent analysis. This study shows that the
PANDA software trigger can benefit greatly from the deep machine learning
methods.


  The cross section of the process e+e- -> Ze+e is measured with 0.7fb^-1 of
data collected with the L3 detector at LEP. Decays of the Z boson into quarks
and muons are considered at centre-of-mass energies ranging from 183GeV up to
209GeV. The measurements are found to agree with Standard Model predictions,
achieving a precision of about 10% for the hadronic channel.


  We introduce a certain quantum superalgebra in the Drinfeld realization and
show that the quantum affine superalgebra of type $B$ is its homomorphic image
(conjecturally isomorphic). We also define a braid group action on quantum
affine superalgebra for any choice of parity.


  We present the dark matter (DM) extension (by N) of the minimal
supersymmetric standard model to give the recent trend of the high energy
positron spectrum of the PAMELA/HEAT experiments. If the trend survives by
future experiments, the MSSM needs to be extended. Here, we minimally extend
the MSSM with one more DM component N together with a heavy lepton E, and
introduce the coupling e_R E_R^c N_R. This coupling naturally appears in the
flipped SU(5) GUT models. This N_{DM}MSSM contains the discrete symmetry Z_6,
and for some parameter ranges there result two DM components. For the MSSM
fields, the conventional R-parity, which is a subgroup of Z_6, is preserved. We
also present the needed parameter ranges of these additional particles.


  A very famous ``test'' of the General Theory of Relativity (GTR) is the
advance of Mercury's perihelion (and of other planets too). To be more precise,
this is not a prediction of General Relativity, since the anomaly was known in
the XIXth century, but no consistent explanation had been found yet at the time
GTR was elaborated. Einstein came up with a solution to the problem in 1914.
  In the case of Mercury, the closest planet to the Sun, the effect is more
pronounced than for other planets, and observed from Earth; there is an advance
of the perihelion of Mercury of about 5550~arc seconds per century (as/cy).
Among these, about $5000$ are due to the equinox precession (the precise value
is {$5025.645$}~as/cy) and about $500$ ({$531.54$}) to the influence of the
external planets. The remaining, about $50$~as/cy ({$42.56$}), are not
understood within Newtonian mechanics. Here, we revisit the problem in some
detail for a presentation at the undergraduate level.


  Power corrections to the Q**2 behavior of the Nachtmann moments of the proton
polarized structure function g1p are investigated at large Bjorken-x by
developing a phenomenological fit of both the resonance (including the photon
point) and deep inelastic data up to Q**2 ~ 50 (GeV/c)**2. The leading twist is
treated at NLO in the strong coupling constant and the effects of higher orders
of the perturbative series are estimated using soft-gluon resummation
techniques. In case of the first moment higher-twist effects are found to be
quite small for
  Q**2 > 1 (GeV/c)**2, and the singlet axial charge is determined to be a0[10
(GeV/c)**2] = 0.16 +/- 0.09. In case of higher order moments, which are
sensitive to the large-x region, higher-twist effects are significantly reduced
by the introduction of soft gluon contributions, but they are still relevant at
Q**2 ~ few (GeV/c)**2 at variance with the case of the unpolarized transverse
structure function of the proton. This finding suggests that spin-dependent
correlations among partons may have more impact than spin-independent ones. It
is also shown that the parton-hadron local duality is violated in the region of
polarized electroproduction of the Delta(1232) resonance.


  We study reinforcement learning (RL) for text-based games, which are
interactive simulations in the context of natural language. While different
methods have been developed to represent the environment information and
language actions, existing RL agents are not empowered with any reasoning
capabilities to deal with textual games. In this work, we aim to conduct
explicit reasoning with knowledge graphs for decision making, so that the
actions of an agent are generated and supported by an interpretable inference
procedure. We propose a stacked hierarchical attention mechanism to construct
an explicit representation of the reasoning process by exploiting the structure
of the knowledge graph. We extensively evaluate our method on a number of
man-made benchmark games, and the experimental results demonstrate that our
method performs better than existing text-based agents.


  The system considered in this paper consists of two equations $(k=1,2)$ $\dot
x(t)=(-1)^{k-1} (0\le t<\infty),\,k(0)=1,\,x(0)=0,\,x(t)\not\in\{0,1\}(-1\le
t<0),$ that change mutually in every instant $t$ for which
$x(t-\tau)\in\{0,1\}$, where $\tau={\rm const}>0$ is given. In this paper the
behavior of the solutions is characterized for every $\tau\in(4/3, 3/2)$, i. e.
in case not covered in \cite{ADM}; as it was noted there, this behavior turned
out to be more complex then when $\tau\in(3/2,\infty)$. Thus the behavior of
the solutions of this system with critical set $K=\{0,1\}$ is characterized for
every $\tau>0$.


  We study a new example of equation obtained as a result of a recent
generalized symmetry classification of differential-difference equations
defined on five points of one-dimensional lattice. We have established that in
the continuous limit this new equation goes into the well-known
Kaup-Kupershmidt equation. We have also proved its integrability by
constructing an $L-A$ pair and conservation laws. Moreover, we present a
possibly new scheme for deriving conservation laws from $L-A$ pairs.


  The introduction of loopy belief propagation (LBP) revitalized the
application of graphical models in many domains. Many recent works present
improvements on the basic LBP algorithm in an attempt to overcome convergence
and local optima problems. Notable among these are convexified free energy
approximations that lead to inference procedures with provable convergence and
quality properties. However, empirically LBP still outperforms most of its
convex variants in a variety of settings, as we also demonstrate here.
Motivated by this fact we seek convexified free energies that directly
approximate the Bethe free energy. We show that the proposed approximations
compare favorably with state-of-the art convex free energy approximations.


  The nature of the deconfining phase transition in the 2+1-dimensional SU(N)
Georgi-Glashow model is investigated. Within the dimensional-reduction
hypothesis, the properties of the transition are described by a two-dimensional
vectorial Coulomb gas models of electric and magnetic charges. The resulting
critical properties are governed by a generalized SU(N) sine-Gordon model with
self-dual symmetry. We show that this model displays a massless flow to an
infrared fixed point which corresponds to the Z$\_N$ parafermions conformal
field theory. This result, in turn, supports the conjecture of Kogan, Tekin,
and Kovner that the deconfining transition in the 2+1-dimensional SU(N)
Georgi-Glashow model belongs to the Z$\_N$ universality class.


  Brain science is an evolving research area inviting great enthusiasm with its
potential for providing insights and thereby, preventing, and treating multiple
neuronal disorders affecting millions of patients. Discovery of relationships,
such as brain connectivity, is a major goal in basic, translational, and
clinical science. Algorithms for causal discovery are used in diverse fields
for tackling problems similar to the task of reconstruction of neuronal brain
connectivity. Our aim is to understand the strengths and limitations of these
methods, measure performance and its determinants, and provide insights to
enhance their performance and applicability. We performed extensive empirical
testing and benchmarking of reconstruction performance of several
state-of-the-art algorithms along with several ensemble techniques used to
combine them. Our experiments used a clear and broadly relevant gold standard
based on calcium fluorescence time series recordings of thousands of neurons
sampled from a previously validated realistic, neuronal model. Correlation,
entropy-based measures, Cross-Correlation for short time lags, and Generalized
Transfer Entropy had the best performances with area under ROC curve (AUC) in
the range of 0.7-0.8 even for smaller sample sizes of n = 100 to 1,000 and
converged quickly (at less than n = 1,000). Ensembles of best-performing
methods using random forests and neural networks generated AUC of ~0.9 with n =
10,000. Several important insights regarding parameter choice and sample size
were gained for guiding the experimental design of studies. Our data are also
supportive of the feasibility of reliably reconstructing complex neuronal
connectivity using existing techniques.


  This is the second paper in a sequence on Krull dimension for limit groups,
answering a question of Z. Sela. In it we develop the notion of a resolution of
a sequence of limit groups and show how to derive resolutions of low complexity
from resolutions of high complexity.


  We study spectral instability of steady states to the linearized 2D Euler
equations on the torus written in vorticity form via certain Birman-Schwinger
type operators $K_{\lambda}(\mu)$ and their associated 2-modified perturbation
determinants $\mathcal D(\lambda,\mu)$. Our main result characterizes the
existence of an unstable eigenvalue to the linearized vorticity operator
$L_{\rm vor}$ in terms of zeros of the 2-modified Fredholm determinant
$\mathcal D(\lambda,0)=\det_{2}(I-K_{\lambda}(0))$ associated with the Hilbert
Schmidt operator $K_{\lambda}(\mu)$ for $\mu=0$. As a consequence, we are also
able to provide an alternative proof to an instability theorem first proved by
Zhiwu Lin which relates existence of an unstable eigenvalue for $L_{\rm vor}$
to the number of negative eigenvalues of a limiting elliptic dispersion
operator $A_{0}$.


  Large-scale perturbations in the microbiome constitution are strongly
correlated, whether as a driver or a consequence, with the health and
functioning of human physiology. However, understanding the difference in the
microbiome profiles of healthy and ill individuals can be complicated due to
the large number of complex interactions among microbes. We propose to model
these interactions as a time-evolving graph whose nodes are microbes and edges
are interactions among them. Motivated by the need to analyse such complex
interactions, we develop a method that learns a low-dimensional representation
of the time-evolving graph and maintains the dynamics occurring in the
high-dimensional space. Through our experiments, we show that we can extract
graph features such as clusters of nodes or edges that have the highest impact
on the model to learn the low-dimensional representation. This information can
be crucial to identify microbes and interactions among them that are strongly
correlated with clinical diseases. We conduct our experiments on both synthetic
and real-world microbiome datasets.


  We theoretically investigate a scheme for atom interferometry that surpasses
the standard quantum limit. A four-wave mixing scheme similar to the recent
experiment performed by Pertot et al. \cite{pertot} is used to generate
sub-shot noise correlations between two modes. These two modes are then
interfered with the remaining two modes in such a way as to surpass the
standard quantum limit, whilst utilising all of the available atoms. Our scheme
can be viewed as using two correlated interferometers. That is, the signal from
each interferometer when looked at individually is classical, but there are
correlations between the two interferometers that allow for the standard
quantum limit to be surpassed.


  We obtain necessary conditions for the existence of complete vertical graphs
of constant mean curvature in the Hyperbolic and Steady State spaces. In the
two-dimensional case we prove Bernstein-type results in each of these ambient
spaces.


  Haldane fractional exclusion statistics (FES) has a long history of intense
studies, but its realization in physical systems is rare. Here we study
repulsively interacting Bose gases at and near a quantum critical point, and
find evidences that such strongly correlated gases obey simple non-mutual FES
over a wide range of interaction strengths in both one and two dimensions.
Based on exact solutions in one dimension, quantum Monte Carlo simulations and
experiments in both dimensions, we show that the thermodynamic properties of
these interacting gases, including entropy per particle, density and pressure,
are essentially equivalent to those of non-interacting particles with FES.
Accordingly, we establish a simple interaction-to-FES mapping that reveals the
statistical nature of particle-hole symmetry breaking induced by interaction in
such quantum many-body systems. Whereas strongly interacting Bose gases reach
full fermionization in one dimension, they exhibit incomplete fermionization in
two dimensions. Our results open a route to understanding correlated
interacting systems via non-interacting particles with FES in arbitrary
dimensions.


  K(BEDT-TTF)2Cu(NCS)2 has been investigated by Raman scattering in both bulk
and nanoparticle compounds. Phonon modes from 20 to 1600 cm-1 have been
assigned. Focusing on the unexplored low frequency phonons, a plateau in
frequencies is observed in the bulk phonons between 50 and 100 K and assigned
to the signature of the bad metal phase. Nanoparticles of K(BEDT-TTF)2Cu(NCS)2
exhibit anomalies at 50 K associated to the crossover from a bad metal to a
Fermi liquid whose origins are discussed.


  As discussed elsewhere, the measurement of a non-zero value for $\theta_{13}$
would open up a wide range of possibilities to explore CP-violation and the
mass hierarchy. Experimental methods to measure currently the unknown mixing
angle $\theta_{13}$ include accelerator searches for the $\nu_{e}$ appearance
and precise measurements of reactor antineutrino disappearance. The reactor
antineutrino experiments are designed to search for a non-vanishing mixing
angle $\theta_{13}$ with unprecedented sensitivity. This document describes
current reactor antineutrino experiments and synergy between accelerator
searches for the $\nu_{e}$ appearance and precise measurements of reactor
antineutrino disappearance.


  Solutions to a class of conservation laws with discontinuous flux are
constructed relying on the Crandall-Liggett theory of nonlinear contractive
semigroups~\cite{CL}. In particular, the paper studies the existence of
backward Euler approximations, and their convergence to a unique
entropy-admissible solution to the Cauchy problem. The proofs are achieved
through the study of the backward Euler approximations to the viscous
conservation laws.


  Underwater vehicles are employed in the exploration of dynamic environments
where tuning of a specific controller for each task would be time-consuming and
unreliable as the controller depends on calculated mathematical coefficients in
idealised conditions. For such a case, learning task from experience can be a
useful alternative. This paper explores the capability of probabilistic
inference learning to control autonomous underwater vehicles that can be used
for different tasks without re-programming the controller. Probabilistic
inference learning uses a Gaussian process model of the real vehicle to learn
the correct policy with a small number of real field experiments. The use of
probabilistic reinforced learning looks for a simple implementation of
controllers without the burden of coefficients calculation, controller tuning
or system identification. A series of computational simulations were employed
to test the applicability of model-based reinforced learning in underwater
vehicles. Three simulation scenarios were evaluated: waypoint tracking, depth
control and 3D path tracking control. The 3D path tracking is done by coupling
together a line-of-sight law with probabilistic inference for learning control.
As a comparison study LOS-PILCO algorithm can perform better than a robust
LOS-PID. The results shows that probabilistic model based reinforced learning
is a possible solution to motion control of underactuated AUVs as can generate
capable policies with minimum quantity of episodes.


  A recurrence relation between equal mass two-loop sunrise diagrams differing
in dimensionality by 2 is derived and it's solution in terms of Gauss' 2F1 and
Appell's F_2 hypergeometric functions is presented. For arbitrary space-time
dimension d the imaginary part of the diagram on the cut is found to be the 2F1
hypergeometric function with argument proportional to the maximum of the Kibble
cubic form. The analytic expression for the threshold value of the diagram in
terms of the hypergeometric function 3F2 of argument -1/3 is given.


  Computing the stationary distributions of a continuous-time Markov chain
(CTMC) involves solving a set of linear equations. In most cases of interest,
the number of equations is infinite or too large, and the equations cannot be
solved analytically or numerically. Several approximation schemes overcome this
issue by truncating the state space to a manageable size. In this review, we
first give a comprehensive theoretical account of the stationary distributions
and their relation to the long-term behaviour of CTMCs that is readily
accessible to non-experts and free of irreducibility assumptions made in
standard texts. We then review truncation-based approximation schemes for CTMCs
with infinite state spaces paying particular attention to the schemes'
convergence and the errors they introduce, and we illustrate their performance
with an example of a stochastic reaction network of relevance in biology and
chemistry. We conclude by discussing computational trade-offs associated with
error control and several open questions.


  This paper highlights several properties of large urban networks that can
have an impact on machine learning methods applied to traffic signal control.
In particular, we show that the average network flow tends to be independent of
the signal control policy as density increases. This property, which so far has
remained under the radar, implies that deep reinforcement learning (DRL)
methods becomes ineffective when trained under congested conditions, and might
explain DRL's limited success for traffic signal control. Our results apply to
all possible grid networks thanks to a parametrization based on two network
parameters: the ratio of the expected distance between consecutive traffic
lights to the expected green time, and the turning probability at
intersections. Networks with different parameters exhibit very different
responses to traffic signal control. Notably, we found that no control (i.e.
random policy) can be an effective control strategy for a surprisingly large
family of networks. The impact of the turning probability turned out to be very
significant both for baseline and for DRL policies. It also explains the loss
of symmetry observed for these policies, which is not captured by existing
theories that rely on corridor approximations without turns. Our findings also
suggest that supervised learning methods have enormous potential as they
require very little examples to produce excellent policies.


  We prove a generalized isoperimetric inequality for a domain diffeomorphic to
a sphere that replaces filling volume with $k$-dilation. Suppose $U$ is an open
set in $\mathbb{R}^n$ diffeomorphic to a Euclidean $n$-ball. We show that in
dimensions at least 4 there is a map from a standard Euclidean ball of radius
about $vol(\partial U)^{1/(n-1)}$ to $U$, with degree 1 on the boundary, and
$(n-1)$-dilation bounded by some constant only depending on $n$. We also give
an example in dimension 3 of an open set where no such map with small
$(n-1)$-dilation can be found. The generalized isoperimetric inequality is
reduced to a theorem about thick embeddings of graphs which is proved using the
Kolmogorov-Barzdin theorem and the max-flow min-cut theorem. The proof of the
counterexample in dimension 3 relies on the coarea inequality and a short
winding number computation.


  The ability to edit 3D assets from natural language presents a compelling
paradigm to aid in the democratization of 3D content creation. However, while
natural language is often effective at communicating general intent, it is
poorly suited for specifying precise manipulation. To address this gap, we
introduce ParSEL, a system that enables controllable editing of high-quality 3D
assets from natural language. Given a segmented 3D mesh and an editing request,
ParSEL produces a parameterized editing program. Adjusting the program
parameters allows users to explore shape variations with a precise control over
the magnitudes of edits. To infer editing programs which align with an input
edit request, we leverage the abilities of large-language models (LLMs).
However, while we find that LLMs excel at identifying initial edit operations,
they often fail to infer complete editing programs, and produce outputs that
violate shape semantics. To overcome this issue, we introduce Analytical Edit
Propagation (AEP), an algorithm which extends a seed edit with additional
operations until a complete editing program has been formed. Unlike prior
methods, AEP searches for analytical editing operations compatible with a range
of possible user edits through the integration of computer algebra systems for
geometric analysis. Experimentally we demonstrate ParSEL's effectiveness in
enabling controllable editing of 3D objects through natural language requests
over alternative system designs.


  The apparent finding of a 125 GeV light Higgs boson would close the minimal
Standard Model (SM), that is weakly interacting. This is an exceptional feature
not generally true if new physics exists beyond the mass gap found at the LHC
up to 700 GeV.
  Any such new physics would induce departures from the SM in the low-energy
dynamics for the minimal electroweak symmetry-breaking sector (EWSBS), with
three Goldstone bosons (related to longitudinal W and Z bosons) and one light
Higgs-like scalar.
  With no new particle content, for most of the parameter space, the scattering
is actually strongly interacting (with the SM a remarkable exception). We
therefore explore various unitarization methods, that have already be applied
to the tree-level WL WL amplitude; we find and study a natural second
sigma-like scalar pole there. Of note is its appearance due to either elastic
or coupled-channel dynamics, especially since the later is largely
unconstrained by current LHC data and could be large.


  Let $\varepsilon>0$ be a small constant. In the present paper we prove that
whenever $\eta$ is real and constants $\lambda _i$ satisfy some necessary
conditions, then there exist infinitely many prime triples $p_1,\, p_2,\, p_3$
satisfying the inequality \begin{equation*} |\lambda _1p_1 + \lambda _2p_2 +
\lambda _3p_3+\eta|<\varepsilon \end{equation*} and such that $p_3=x^2 + y^2
+1$.


  A model-independent treatment of dark-matter particle elastic scattering has
been developed, yielding the most general interaction for WIMP-nucleon
low-energy scattering, and the resulting amplitude has been embedded in the
nucleus, taking into account the selection rules imposed by parity and
time-reversal. One finds that, in contrast to the usual
spin-independent/spin-dependent (SI/SD) formulation, the resulting cross
section contains six independent nuclear response functions, three of which are
associated with possible velocity-dependent interactions. We find that current
experiments are four orders of magnitude more sensitive to derivative couplings
than is apparent in the standard SI/SD treatment, which necessarily associates
such interactions with cross sections proportional to the square of the WIMP
velocity relative to the nuclear center of mass.


  We show that the little hierarchy problem can be solved in the no-scale
supergravity framework. In this model the supersymmetry breaking scale is
generated when the electroweak symmetry breaking condition is satisfied and
therefore, unlike usual supersymmetric models, the correlation between the
electroweak symmetry breaking scale and the average stop mass scale can be
justified. This correlation solves the little hierarchy puzzle. Using minimal
supergravity boundary conditions, we find that the parameter space predicted by
no-scale supergravity is allowed by all possible experimental constraints. The
predicted values of supersymmetric particle masses are low enough to be very
easily accessible at the LHC. This parameter space will also be probed in the
upcoming results from the dark matter direct detection experiments.


  During its first cycle of observations, the MAGIC (Major Atmospheric
Gamma-ray Imaging Cherenkov) telescope has observed very high energy gamma-rays
from five galactic objects: the Crab Nebula, the SNRs HESS J1813-178 and HESS
J1834-087, the Galactic Center and the gamma-ray binary LS I +61 303. After a
short introduction to the MAGIC telescope and the data analysis procedure, the
results of these five sources are reviewed.


  This paper presents new formulae for the harmonic numbers of order $k$,
$H_{k}(n)$, and for the partial sums of two Fourier series associated with
them, denoted here by $C^m_{k}(n)$ and $S^m_{k}(n)$. I believe this new formula
for $H_{k}(n)$ is an improvement over the digamma function, $\psi$, because
it's simpler and it stems from Faulhaber's formula, which provides a
closed-form for the sum of powers of the first $n$ positive integers. We
demonstrate how to create an exact power series for the harmonic numbers, a new
integral representation for $\zeta(2k+1)$ and a new generating function for
$\zeta(2k+1)$, among many other original results. The approaches and formulae
discussed here are entirely different from solutions available in the
literature.


  The paper gives a definition of exponential arcs in the manifold of
non-degenerate density matrices and uses it as a starting point to develop a
parameter-free version of non-commutative Information Geometry in the
finite-dimensional case. Given the Bogoliubov metric the m- and e-connections
are each other dual. Convex potentials are introduced. They allow to introduce
dual charts. Affine coordinates are introduced at the end to make the
connection with the more usual approach.


  Metzler matrices play a crucial role in positive linear dynamical systems.
Finding the closest stable Metzler matrix to an unstable one (and vice versa)
is an important issue with many applications. The stability considered here is
in the sense of Hurwitz, and the distance between matrices is measured in
$l_\infty,\ l_1$, and in the max norms. We provide either explicit solutions or
efficient algorithms for obtaining the closest (un)stable matrix. The procedure
for finding the closest stable Metzler matrix is based on the recently
introduced selective greedy spectral method for optimizing the Perron
eigenvalue. Originally intended for non-negative matrices, here is generalized
to Metzler matrices. The efficiency of the new algorithms is demonstrated in
examples and by numerical experiments in the dimension of up to 2000.
Applications to dynamical systems, linear switching systems, and sign-matrices
are considered.


  Recovering intrinsic low dimensional subspaces from data distributed on them
is a key preprocessing step to many applications. In recent years, there has
been a lot of work that models subspace recovery as low rank minimization
problems. We find that some representative models, such as Robust Principal
Component Analysis (R-PCA), Robust Low Rank Representation (R-LRR), and Robust
Latent Low Rank Representation (R-LatLRR), are actually deeply connected. More
specifically, we discover that once a solution to one of the models is
obtained, we can obtain the solutions to other models in closed-form
formulations. Since R-PCA is the simplest, our discovery makes it the center of
low rank subspace recovery models. Our work has two important implications.
First, R-PCA has a solid theoretical foundation. Under certain conditions, we
could find better solutions to these low rank models at overwhelming
probabilities, although these models are non-convex. Second, we can obtain
significantly faster algorithms for these models by solving R-PCA first. The
computation cost can be further cut by applying low complexity randomized
algorithms, e.g., our novel $\ell_{2,1}$ filtering algorithm, to R-PCA.
Experiments verify the advantages of our algorithms over other state-of-the-art
ones that are based on the alternating direction method.


  The hardware requirements of useful quantum algorithms remain unmet by the
quantum computers available today. Because it was designed to soften these
requirements, the Variational Quantum Eigensolver (VQE) has gained popularity
as a contender for a chance at quantum advantage with near-term quantum
computers. The ansatz, a parameterized circuit that prepares trial states, can
dictate the success (or lack thereof) of a VQE. Too deep ans\"atze can hinder
near-term viability, or lead to trainability issues that render the algorithm
inefficient. The purpose of this thesis was to analyse different ans\"atze
proposed for quantum chemistry, examining their noise-resilience and viability
in state-of-the-art quantum computers. In particular, dynamic ans\"atze
(ADAPT-VQEs) were explored, and the impact of the choice of pool and selection
criterion on their performance was analysed.


  Submodular maximization has been the backbone of many important
machine-learning problems, and has applications to viral marketing,
diversification, sensor placement, and more. However, the study of maximizing
submodular functions has mainly been restricted in the context of selecting a
set of items. On the other hand, many real-world applications require a
solution that is a ranking over a set of items. The problem of ranking in the
context of submodular function maximization has been considered before, but to
a much lesser extent than item-selection formulations. In this paper, we
explore a novel formulation for ranking items with submodular valuations and
budget constraints. We refer to this problem as max-submodular ranking (MSR).
In more detail, given a set of items and a set of non-decreasing submodular
functions, where each function is associated with a budget, we aim to find a
ranking of the set of items that maximizes the sum of values achieved by all
functions under the budget constraints. For the MSR problem with cardinality-
and knapsack-type budget constraints we propose practical algorithms with
approximation guarantees. In addition, we perform an empirical evaluation,
which demonstrates the superior performance of the proposed algorithms against
strong baselines.


  We develop a corrective mechanism for neural network approximation: the total
available non-linear units are divided into multiple groups and the first group
approximates the function under consideration, the second group approximates
the error in approximation produced by the first group and corrects it, the
third group approximates the error produced by the first and second groups
together and so on. This technique yields several new representation and
learning results for neural networks. First, we show that two-layer neural
networks in the random features regime (RF) can memorize arbitrary labels for
arbitrary points under under Euclidean distance separation condition using
$\tilde{O}(n)$ ReLUs which is optimal in $n$ up to logarithmic factors. Next,
we give a powerful representation result for two-layer neural networks with
ReLUs and smoothed ReLUs which can achieve a squared error of at most
$\epsilon$ with $O(C(a,d)\epsilon^{-1/(a+1)})$ for $a \in \mathbb{N}\cup\{0\}$
when the function is smooth enough (roughly when it has $\Theta(ad)$ bounded
derivatives). In certain cases $d$ can be replaced with effective dimension $q
\ll d$. Previous results of this type implement Taylor series approximation
using deep architectures. We also consider three-layer neural networks and show
that the corrective mechanism yields faster representation rates for smooth
radial functions. Lastly, we obtain the first $O(\mathrm{subpoly}(1/\epsilon))$
upper bound on the number of neurons required for a two layer network to learn
low degree polynomials up to squared error $\epsilon$ via gradient descent.
Even though deep networks can express these polynomials with
$O(\mathrm{polylog}(1/\epsilon))$ neurons, the best learning bounds on this
problem require $\mathrm{poly}(1/\epsilon)$ neurons.


  We report on photometry and imaging of Comet 103P/Hartley 2 obtained at
Lowell Observatory from 1991 through 2011. We acquired photoelectric photometry
on two nights in 1991, four nights in 1997/98, and 13 nights in 2010/11. We
observed a strong secular decrease in water and all other observed species
production in 2010/11 from the 1991 and 1997/98 levels. We see evidence for a
strong asymmetry with respect to perihelion in the production rates of our
usual bandpasses, with peak production occurring ~10 days post-perihelion and
production rates considerably higher post-perihelion. The composition was
"typical", in agreement with the findings of other investigators. We obtained
imaging on 39 nights from 2010 July until 2011 January. We find that, after
accounting for their varying parentage and lifetimes, the C2 and C3 coma
morphology resemble the CN morphology we reported previously. These species
exhibited an hourglass shape in October and November, and the morphology
changed with rotation and evolved over time. The OH and NH coma morphology
showed hints of an hourglass shape near the nucleus, but was also enhanced in
the anti-sunward hemisphere. This tailward brightness enhancement did not vary
significantly with rotation and evolved with the viewing geometry. We conclude
that all five gas species likely originate from the same source regions on the
nucleus, but that OH and NH were derived from small grains of water and ammonia
ice that survived long enough to be affected by radiation pressure and driven
in the anti-sunward direction. We detected the faint, sunward facing dust jet
reported by other authors, and did not detect a corresponding gas feature. This
jet varied little during a night but exhibited some variations from night to
night, suggesting it is located near the total angular momentum vector.


  The magnetization characteristic in a permalloy thin strip is investigated by
electrically measuring the anisotropic magnetoresistance and ferromagnetic
resonance in in-plane and out-of-plane configurations. Our results indicate
that the magnetization vector can rotate in the film plane as well as out of
the film plane by changing the intensity of external magnetic field of certain
direction. The magnetization characteristic can be explained by considering
demagnetization and magnetic anisotropy. Our method can be used to obtain the
demagnetization factor, saturated magnetic moment and the magnetic anisotropy.


  Any learner with the ability to predict the future of a structured
time-varying signal must maintain a memory of the recent past. If the signal
has a characteristic timescale relevant to future prediction, the memory can be
a simple shift register---a moving window extending into the past, requiring
storage resources that linearly grows with the timescale to be represented.
However, an independent general purpose learner cannot a priori know the
characteristic prediction-relevant timescale of the signal. Moreover, many
naturally occurring signals show scale-free long range correlations implying
that the natural prediction-relevant timescale is essentially unbounded. Hence
the learner should maintain information from the longest possible timescale
allowed by resource availability. Here we construct a fuzzy memory system that
optimally sacrifices the temporal accuracy of information in a scale-free
fashion in order to represent prediction-relevant information from
exponentially long timescales. Using several illustrative examples, we
demonstrate the advantage of the fuzzy memory system over a shift register in
time series forecasting of natural signals. When the available storage
resources are limited, we suggest that a general purpose learner would be
better off committing to such a fuzzy memory system.


  The existence of antimatter stars in the Galaxy as possible signature for
inflationary models with non-homogeneous baryo-synthesis may leave the trace by
antimatter cosmic rays as well as by their secondaries (anti-planets and
anti-meteorites) diffused bodies in our galactic halo. The anti-meteorite flux
may leave its explosive gamma signature by colliding on lunar soil as well as
on terrestrial, jovian and solar atmospheres. However the propagation in galaxy
and the consequent evaporation in galactic matter gas suppress the lightest (m
< 10^(-2)g) anti-meteorites. Anisotropic annihilation of larger anti-meteorites
within a narrow mass window, maybe rarely deflected, bounced by the galactic
gas disk, escaping detection in our solar system. Nevertheless heaviest
anti-meteorites (m > 10^(-1)g up to 10^(6)g) are unable to be deflected by the
thin galactic gas surface annihilation; they might hit the Sun (or rarely
Jupiter) leading to an explosive gamma event and a spectacular track with a
bouncing and even a propelling annihilation on cromosphere and photosphere.
Their anti-nuclei annihilation in pions and their final hard gammas showering
may be observabe as a "solar flare" at a rate nearly comparable to the observed
ones. From their absence we may infer bounds on antimatter-matter ratio near or
below 10^(-9) limit: already recorded data in BATSE catalog might be applied.


  Coordination graph is a promising approach to model agent collaboration in
multi-agent reinforcement learning. It conducts a graph-based value
factorization and induces explicit coordination among agents to complete
complicated tasks. However, one critical challenge in this paradigm is the
complexity of greedy action selection with respect to the factorized values. It
refers to the decentralized constraint optimization problem (DCOP), which and
whose constant-ratio approximation are NP-hard problems. To bypass this
systematic hardness, this paper proposes a novel method, named Self-Organized
Polynomial-time Coordination Graphs (SOP-CG), which uses structured graph
classes to guarantee the accuracy and the computational efficiency of
collaborated action selection. SOP-CG employs dynamic graph topology to ensure
sufficient value function expressiveness. The graph selection is unified into
an end-to-end learning paradigm. In experiments, we show that our approach
learns succinct and well-adapted graph topologies, induces effective
coordination, and improves performance across a variety of cooperative
multi-agent tasks.


  The aim of this paper is to introduce and study quadratic Hom-Lie algebras,
which are Hom-Lie algebras with symmetric invariant nondegenerate bilinear
forms. We provide several constructions leading to examples and extend the
double extension theory to Hom-Lie algebras. We reduce the case where the twist
map is invertible to the study of involutive quadratic Lie algebras. We
establish a correspondence between the class of involutive quadratic Hom-Lie
algebras and quadratic simple Lie algebras with symmetric involution.
Centerless involutive quadratic Hom-Lie algebras are characterized. Also
elements of a representation theory for Hom-Lie algebras, including adjoint and
coadjoint representations are supplied with application to quadratic Hom-Lie
algebras.


  Given enough multi-view image corresponding points (also called tie points)
and ground control points (GCP), bundle adjustment for high-resolution
satellite images is used to refine the orientations or most often used
geometric parameters Rational Polynomial Coefficients (RPC) of each satellite
image in a unified geodetic framework, which is very critical in many
photogrammetry and computer vision applications. However, the growing number of
high resolution spaceborne optical sensors has brought two challenges to the
bundle adjustment: 1) images come from different satellite cameras may have
different imaging dates, viewing angles, resolutions, etc., thus resulting in
geometric and radiometric distortions in the bundle adjustment; 2) The
large-scale mapping area always corresponds to vast number of bundle adjustment
corrections (including RPC bias and object space point coordinates). Due to the
limitation of computer memory, it is hard to refine all corrections at the same
time. Hence, how to efficiently realize the bundle adjustment in large-scale
regions is very important. This paper particularly addresses the multi-view
large-scale bundle adjustment problem by two steps: 1) to get robust tie points
among different satellite images, we design a multi-view, multi-source tie
point matching algorithm based on plane rectification and epipolar constraints,
which is able to compensate geometric and local nonlinear radiometric
distortions among satellite datasets, and 2) to solve dozens of thousands or
even millions of variables bundle adjustment corrections in the large scale
bundle adjustment, we use an efficient solution with only a little computer
memory. Experiments on in-track and off-track satellite datasets show that the
proposed method is capable of computing sub-pixel accuracy bundle adjustment
results.


  We present a one-parameter family of exact solutions to Einstein equations
that may be used to study the nature of the Green-Wald backreaction framework.
Our explicit example is a family of Einstein-Rosen waves coupled to a massless
scalar field. This solution may be reinterpreted as a generalized three-torus
polarized Gowdy cosmology with scalar and gravitational waves. We use it to
illustrate essential properties of the Green-Wald approach. Among other things
we show that within our model the Green-Wald framework uniquely determines
backreaction for finite size inhomogeneities on a predefined background. The
results agree with those calculated in the Charach-Malin approach. In the
vacuum limit, the Green-Wald, the Charach-Malin and the Isaacson method imply
identical backreaction as expected.


  We study the electrodynamics of generic charged particles (bosons, fermions,
relativistic or not) constrained to move on an infinite plane. An effective
gauge theory in 2+1 dimensional spacetime which describes the real
electromagnetic interaction of this particles is obtained. The relationship
between this effective theory with the Chern-Simons theory is explored. It is
shown that the QED lagrangian {\it per se} produces the Chern-Simons constraint
relating the current to the effective gauge field in 2+1 D. It is also shown
that the geometry of the system unavoidably induces a contribution from the
topological $\theta$-term that generates an explicit Chern-Simons term for the
effective 2+1 dimensional gauge field as well as a minimal coupling of the
matter to it. The possible relation of the effective three dimensional theory
with the bosonization of the Dirac fermion field in 2+1 D is briefly discussed
as well as the potential applications in Condensed Matter systems.


  In Fourier-domain optical coherence tomography (OCT), the finite bandwidth of
the acquisition electronics constrains the depth range and speed of the system.
Circular-ranging (CR) OCT methods use optical-domain compression to surpass
this limit. However, the CR-OCT system architectures of prior reports were
limited by poor stability and were confined to the 1.55 um wavelength range. In
this work, we describe a novel CR-OCT architecture that is free from these
limitations. To ensure stable operation, temperature sensitive optical modules
within the system were replaced; the kilometer-length fiber spools used in the
stretched-pulse mode-locked (SPML) laser was eliminated in favor of a single 10
meter, continuously chirped fiber Bragg grating, and the interferometer's
passive optical quadrature demodulation circuit was replaced by an active
technique using a lithium niobate phase modulator. For improved imaging
penetration in biological tissues, the system operating wavelength was shifted
to a center wavelength of 1.29 um by leveraging the wavelength flexibility
intrinsic to CFBG-based dispersive fibers. These improvements were achieved
while maintaining a broad (100 nm) optical bandwidth, a long 4 cm imaging
range, and a high 7.6 MHz A-line rate. By enhancing stability, simplifying
overall system design, and operating at 1.3 um, this CR-OCT architecture will
allow a broader exploration of CR-OCT in both medical and non-medical
applications.