  Let $n \geq 1$ be an integer, let $V=(\mathbb{Z}/2\mathbb{Z})^{n}$ and let
$X$ be a $V$-CW-complex. If $X$ is a finite $CW$-complexe, the equivariant
modulo $2$ cohomology of the $V$-CW-complexe $X$, denoted by $H_{V}^{*}(X,
\mathbb{F}_{2})$, is a finite type module over the modulo $2$ cohomology of the
group $V$, denoted by $H^{*}(V, \mathbb{F}_{2})$. Let $dth_{H^{*}V}H_{V}^{*}(X,
\mathbb{F}_{2})$ be the depth of the finite type $H^{*}(V,
\mathbb{F}_{2})$-module $H_{V}^{*}(X, \mathbb{F}_{2})$ relatively to the
augmentation ideal, $\widetilde{H^{*}}(V, \mathbb{F}_{2})$, of $H^*(V,
\mathbb{F}_{2})$. \medskip\\ The aim of this paper is to prove the following
result: \medskip\\ {\bf Theorem}: For every subgroup $W$ of $V$, we have:
$dth_{H^{*}W}H_{W}^{*}(X, \mathbb{F}_{2}) \leq dth_{H^{*}V} H_{V}^{*}(X,
\mathbb{F}_{2}) $.


  Certain phase space path integrals can be evaluated exactly using equivariant
cohomology and localization in the canonical loop space. Here we extend this to
a general class of models. We consider hamiltonians which are {\it a priori}
arbitrary functions of the Cartan subalgebra generators of a Lie group which is
defined on the phase space. We evaluate the corresponding path integral and
find that it is closely related to the infinitesimal Lefschetz number of a
Dirac operator on the phase space. Our results indicate that equivariant
characteristic classes could provide a natural geometric framework for
understanding quantum integrability.


  Finding a simple path of even length between two designated vertices in a
directed graph is a fundamental NP-complete problem known as the EvenPath
problem. Nedev proved in 1999, that for directed planar graphs, the problem can
be solved in polynomial time. More than two decades since then, we make the
first progress in extending the tractable classes of graphs for this problem.
We give a polynomial time algorithm to solve the EvenPath problem for classes
of H-minor-free directed graphs,1 where H is a single-crossing graph. We make
two new technical contributions along the way, that might be of independent
interest. The first, and perhaps our main, contribution is the construction of
small, planar, parity-mimicking networks. These are graphs that mimic parities
of all possible paths between a designated set of terminals of the original
graph. Finding vertex disjoint paths between given source-destination pairs of
vertices is another fundamental problem, known to be NP-complete in directed
graphs, though known to be tractable in planar directed graphs. We encounter a
natural variant of this problem, that of finding disjoint paths between given
pairs of vertices, but with constraints on parity of the total length of paths.
The other significant contribution of our paper is to give a polynomial time
algorithm for the 3-disjoint paths with total parity problem, in directed
planar graphs with some restrictions (and also in directed graphs of bounded
treewidth).


  We consider a random sequential adsorption process on the one-dimensional
lattice with nearest-neighbor exclusion. In this model, each site $s \in
\mathbb{Z}$ starts empty and we will try to occupy it in time $t_s$, where
$(t_s)_{s\in\mathbb{Z}}$ is a sequence of independent random variables
uniformly distributed on the interval $[0,1]$. The site will be occupied if
both of its neighbors are vacant. We provide a method to calculate the density
of occupied sites up to the time $t$, as well as the pair correlation function.


  5G is finally here. Initial deployments are already operational in several
major cities and first 5G-capable devices are being released. Though it is not
limited only to millimeter wave deployments, the main promise of 5G lies in the
utilization of the high bandwidth available at high frequencies. However,
high-frequency deployments are coverage-limited and require denser placement of
base stations, which can increase the cost significantly. One of the main
contributing factors to the cost is fiber deployment. Integrated access
backhauling (IAB), where part of the wireless spectrum is used for the backhaul
connection of base stations instead of fiber, is an attractive solution that
could make dense deployments economically viable. With this main objective,
3GPP is in the process of standardizing multi-hop IAB networks. This paper
provides an overview of the main features of the multi-hop IAB 3GPP rel-16
standard and the rationale behind the design choices.


  In this paper a definition is given for an unbounded Toeplitz-like operator
with rational symbol which has poles on the unit circle. It is shown that the
operator is Fredholm if and only if the symbol has no zeroes on the unit
circle, and a formula for the index is given as well. Finally, a matrix
representation of the operator is discussed.


  We discuss in this paper the conformal geometry of bi-invariant metrics on
compact semisimple Lie groups. For this purpose we develop a conformal Cartan
calculus adapted to this problem. In particular, we derive an explicit formula
for the holonomy algebra of the normal conformal Cartan connection of a
bi-invariant metric. As an example, we apply this calculus to the group
$\SO(4)$. Its conformal holonomy group is calculated to be $\SO(7)$.


  We present a study of carbon in N159/N160, an HII region complex in the low
metallicity Large Magellanic Cloud. We have mapped this region, which comprises
four distinct molecular clouds spanning a wide range of star-formation
activity, in four transitions: 13CO (1-0) CO (2-1) and (4-3), and [CI] (1-0).
Combining these data with existing [CII] observations provides a complete
picture of the predominant forms of carbon in the gas phase of the ISM. The new
CO (2-1) data show that the complex is immersed in an envelope of extended, low
level emission, undetected by previous (1-0) mapping efforts. The CO
(2-1)/(1-0) ratio in this envelope is >~3, a value consistent with optically
thin CO emission. The envelope is also relatively bright in [CI] and [CII], and
calculations show that it is mostly photodissociated: it appears to be
translucent (Av<1). Neutral carbon emission in the complex unexpectedly peaks
at the quiescent southern cloud (N159S). In the northern portion of the map
(the N160 nebula), the HII regions prominent in [CII] correspond to holes in
the [CI] distribution. Overall we find that, while the [CII]/CO ratio is
enhanced with respect to similar complexes in the Milky Way, the [CI]/CO ratio
appears to be similar or reduced.


  We derive Berry-Esseen approximation bounds for general functionals of
independent random variables, based on chaos expansions methods. Our results
apply to $U$-statistics satisfying the weak assumption of decomposability in
the Hoeffding sense, and yield Kolmogorov distance bounds instead of the
Wasserstein bounds previously derived in the special case of degenerate
$U$-statistics. Linear and quadratic functionals of arbitrary sequences of
independent random variables are included as particular cases, with new fourth
moment bounds, and applications are given to Hoeffding decompositions, weighted
$U$-statistics, quadratic forms, and random subgraph weighing. In the case of
quadratic forms, our results recover and improve the bounds available in the
literature, and apply to matrices with non-empty diagonals.


  In the present paper, we revisit gravitational theories which are invariant
under TDiffs -- transverse (volume preserving) diffeomorphisms and global scale
transformations. It is known that these theories can be rewritten in an
equivalent diffeomorphism-invariant form with an action including an
integration constant (cosmological constant for the particular case of
non-scale-invariant unimodular gravity). The presence of this integration
constant, in general, breaks explicitly scale invariance and induces a runaway
potential for the (otherwise massless) dilaton, associated with the determinant
of the metric tensor. We show, however, that if the metric carries mass
dimension $\left[\text{GeV}\right]^{-2}$, the scale invariance of the system is
preserved, unlike the situation in theories in which the metric has mass
dimension different from $-2$. The dilaton remains massless and couples to
other fields only through derivatives, without any conflict with observations.
We observe that one can define a specific limit for fields and their
derivatives (in particular, the dilaton goes to zero, potentially related to
the small distance domain of the theory) in which the only singular terms in
the action correspond to the Higgs mass and the cosmological constant. We
speculate that the self-consistency of the theory may require the regularity of
the action, leading to the absence of the bare Higgs mass and cosmological
constant, whereas their small finite values may be generated by nonperturbative
effects.


  Spatial reasoning plays a vital role in both human cognition and machine
intelligence, prompting new research into language models' (LMs) capabilities
in this regard. However, existing benchmarks reveal shortcomings in evaluating
qualitative spatial reasoning (QSR). These benchmarks typically present
oversimplified scenarios or unclear natural language descriptions, hindering
effective evaluation. We present a novel benchmark for assessing QSR in LMs,
which is grounded in realistic 3D simulation data, offering a series of diverse
room layouts with various objects and their spatial relationships. This
approach provides a more detailed and context-rich narrative for spatial
reasoning evaluation, diverging from traditional, toy-task-oriented scenarios.
Our benchmark encompasses a broad spectrum of qualitative spatial
relationships, including topological, directional, and distance relations.
These are presented with different viewing points, varied granularities, and
density of relation constraints to mimic real-world complexities. A key
contribution is our logic-based consistency-checking tool, which enables the
assessment of multiple plausible solutions, aligning with real-world scenarios
where spatial relationships are often open to interpretation. Our benchmark
evaluation of advanced LMs reveals their strengths and limitations in spatial
reasoning. They face difficulties with multi-hop spatial reasoning and
interpreting a mix of different view descriptions, pointing to areas for future
improvement.


  The remaining min-entropy of a secret generated by fuzzy extraction from a
Physical Unclonable Function is typically estimated under the assumption of
independent and identically distributed PUF responses, but this assumption does
not hold in practice. This work analyzes the more realistic case that the
responses are independent but not necessarily identically distributed. For this
case, we extend the (n-k) bound and a tighter bound by Delvaux et al. In
particular, we suggest a grouping bound which provides a trade off for accuracy
vs computational effort. Comparison to previous bounds shows the accuracy and
efficiency of our bound. We also adapt the key rank (a tool from side-channel
analysis) to cross-validate the state-of-the-art and our proposed min-entropy
bounds based on publicly available PUF data from real hardware.


  This paper provides an enhanced modeling of the contingency response that
collectively reflects high-fidelity physical and operational characteristics of
power grids. Integrating active and reactive power contingency responses into
the security-constrained optimal power flow (SCOPF) problem is challenging, due
to the nonsmoothness and nonconvexity of feasible sets in consequence of
piece-wise curves representing generator characteristics. We introduce a
continuously-differentiable model using functions that closely resemble PV/PQ
switching and the generator contingency response. These models enforce physical
and operational limits by optimally allocating active power imbalances among
available generators and deciding the bus type to switch from the PV type to
the PQ type. The efficacy of this method is numerically validated on the IEEE
30-bus, 300-bus, and 118-bus systems with 12, 10, and 100 contingencies,
respectively.


  We have redetermined kinematic parameters of the Gould Belt using currently
available data on the motion of nearby young (log t < 7.91) open clusters, OB
associations, and moving stellar groups. Our modeling shows that the residual
velocities reach their maximum values of -4 km/s for rotation (in the direction
of Galactic rotation) and +4 km/s for expansion at a distance from the
kinematic center of about 300 pc. We have taken the following parameters of the
Gould Belt center: Ro=150 pc and lo=128 degrees. The whole structure is shown
to move relative to the local standard of rest at a velocity of 10.7+-0.7 km/s
in the direction l=274+-4degrees and b=-1+-3 degrees. Using the derived
rotation velocity, we have estimated the virial mass of the Gould Belt to be
1.5E6 Solar mass.


  This paper proposes an easy-to-compute upper bound for the overlap index
between two probability distributions without requiring any knowledge of the
distribution models. The computation of our bound is time-efficient and
memory-efficient and only requires finite samples. The proposed bound shows its
value in one-class classification and domain shift analysis. Specifically, in
one-class classification, we build a novel one-class classifier by converting
the bound into a confidence score function. Unlike most one-class classifiers,
the training process is not needed for our classifier. Additionally, the
experimental results show that our classifier can be accurate with only a small
number of in-class samples and outperform many state-of-the-art methods on
various datasets in different one-class classification scenarios. In domain
shift analysis, we propose a theorem based on our bound. The theorem is useful
in detecting the existence of domain shift and inferring data information. The
detection and inference processes are both computation-efficient and
memory-efficient. Our work shows significant promise toward broadening the
applications of overlap-based metrics.


  The present paper deals with the interior solid-fluid interaction problem in
harmonic regime with randomly perturbed boundaries. Analysis of the shape
derivative and shape Hessian of vector- and tensor-valued functions is
provided. Moments of the random solutions are approximated by those of the
shape derivative and shape Hessian, and the approximations are of third order
accuracy in terms of the size of the boundary perturbation. Our theoretical
results are supported by an analytical example on a square domain.


  For a Calabi-Yau threefold admitting both a $K3$ fibration and an elliptic
fibration (with some extra conditions) we discuss candidate asymptotic
expressions of the genus 0 and 1 Gromov-Witten potentials in the limit
(possibly corresponding to the perturbative regime of a heterotic string) where
the area of the base of the $K3$ fibration is very large. The expressions are
constructed by lifting procedures using nearly holomorphic Weyl-invariant
Jacobi forms. The method we use is similar to the one introduced by Borcherds
for the constructions of automorphic forms on type IV domains as infinite
products and employs in an essential way the elliptic polylogarithms of
Beilinson and Levin. In particular, if we take a further limit where the base
of the elliptic fibration decompactifies, the Gromov-Witten potentials are
expressed simply by these elliptic polylogarithms. The theta correspondence
considered by Harvey and Moore which they used to extract the expression for
the perturbative prepotential is closely related to the Eisenstein-Kronecker
double series and hence the real versions of elliptic polylogarithms introduced
by Zagier.


  In this work, we investigated the effect of knots in the thermal transport of
graphene nanoribbons through non-equilibrium molecular dynamics simulations. We
considered the cases of one, two, and three knots are present. Temperature
jumps appear in the temperature profile where the knots are located, which
indicates that they introduce thermal resistances in the system, similar to
interfacial Kapitza resistance present between two different materials and/or
single materials with defects and/or lattice distortions. We found that the
thermal resistance introduced by each individual knot is essentially the same
as the overall resistance increase linearly with the number of knots, as they
behave as thermal resistances associated in series. Also, the relative position
between each knot in the arrangement does not strongly affect the thermal
current produced by the temperature gradient, showing a weak thermal
rectification effect.


  With the internet, a massive amount of information on species abundance can
be collected under citizen science programs. However, these data are often
difficult to use directly in statistical inference, as their collection is
generally opportunistic, and the distribution of the sampling effort is often
not known. In this paper, we develop a general statistical framework to combine
such "opportunistic data" with data collected using schemes characterized by a
known sampling effort. Under some structural assumptions regarding the sampling
effort and detectability, our approach allows to estimate the relative
abundance of several species in different sites. It can be implemented through
a simple generalized linear model. We illustrate the framework with typical
bird datasets from the Aquitaine region, south-western France. We show that,
under some assumptions, our approach provides estimates that are more precise
than the ones obtained from the dataset with a known sampling effort alone.
When the opportunistic data are abundant, the gain in precision may be
considerable, especially for the rare species. We also show that estimates can
be obtained even for species recorded only in the opportunistic scheme.
Opportunistic data combined with a relatively small amount of data collected
with a known effort may thus provide access to accurate and precise estimates
of quantitative changes in relative abundance over space and/or time.


  In this paper, we consider those multiplication operators M_p on the Bergman
space L_a^2(D^2) over the bidisk, defined by a class of polynomials p. Also,
this paper consider the reducing subspaces of M_p, the von Neumann algebra
W^*(p) generated by M_p, and its commutant V^*(p)=W^*(p)'. The structure of
V^*(p) is completely determined, along with those reducing subspaces of M_p.


  Peer Instruction (PI) is a student-centered instructional approach developed
at Harvard by Eric Mazur (1997). The method has been welcomed by the science
community and adopted by a large number of colleges and universities, due among
other reasons to its common sense approach and its documented effectiveness. In
PI, the progression of any given class depends on the outcome of real-time
student feedback to ConcepTests: multiple-choice conceptual questions. In the
early 1990s, students responded to ConcepTests using flashcards showing their
answer. Instructors would then estimate the proportion of students holding each
alternative conception. A few years later Mazur began using wireless handheld
devices - colloquially called clickers- to replace the flashcards. Previous
users of clickers in university classrooms had reported benefits such as
increased rates of attendance and decreased rates of attrition (Owens et al.,
2004; Lopez-Herrejon & Schulman, 2004). This paper empirically measures the
specific contribution of clickers to conceptual learning and traditional
problem solving skills as compared to low-budget flashcards. Results show that
clickers do not provide any learning advantage when compared to flashcards.
Nevertheless, clickers offer many advantages from a teaching perspective which
should be considered.


  We introduce a new control strategy on a two-way deterministic cryptographic
scheme, which relies on a suitable unitary transformation rather than quantum
measurement. The study is developed for d-ary alphabets and the particular
choice of the transformation works when d is an odd prime power. It leads to an
improvement of the protocol security, which we prove to increase with the
alphabet order d.


  Conditional Generative Models are now acknowledged an essential tool in
Machine Learning. This paper focuses on their control. While many approaches
aim at disentangling the data through the coordinate-wise control of their
latent representations, another direction is explored in this paper. The
proposed CompVAE handles data with a natural multi-ensemblist structure (i.e.
that can naturally be decomposed into elements). Derived from Bayesian
variational principles, CompVAE learns a latent representation leveraging both
observational and symbolic information. A first contribution of the approach is
that this latent representation supports a compositional generative model,
amenable to multi-ensemblist operations (addition or subtraction of elements in
the composition). This compositional ability is enabled by the invariance and
generality of the whole framework w.r.t. respectively, the order and number of
the elements. The second contribution of the paper is a proof of concept on
synthetic 1D and 2D problems, demonstrating the efficiency of the proposed
approach.


  The possibility of generating a large trilinear $A_t$ soft supersymmetry
breaking coupling at low energies through renormalisation group evolution in
the 5D MSSM is investigated. Using the power law running in five dimensions and
a compactification scale in the 10-$10^3$ TeV range, to show that gluino mass
may drive a large enough $A_t$ to reproduce the measured Higgs mass and have a
light stop superpartner below $\sim 1$ TeV as preferred by the fine tuning
argument for the Higgs mass.


  For high-mobility two-dimensional electrons at a GaAs/AlGaAs heterojunction,
we have studied, both experimentally and theoretically, the recently discovered
giant magnetoresistance oscillations with nearly zero resistance in the
oscillation minima which appear under microwave radiation. We have proposed a
model based on nonequilibrium occupation of Landau levels caused by radiation
which describes the oscillation picture.


  The philosophy of science is a discipline concerning the metaphysical aspect
of science. Recently, I proposed measurement theory, which is characterized as
the metaphysical and linguistic interpretation of quantum mechanics. I assert
that this theory is one of the most fundamental languages in science, and thus,
it is located at the central position in science. This assertion will be
examined throughout this preprint, which is written as the draft of my future
book (concerning the philosophy of science). Hence, I hope to hear various
opinions about this draft.


  We consider a finite-horizon market-making problem faced by a dark pool that
executes incoming buy and sell orders. The arrival flow of such orders is
assumed to be random and, for each transaction, the dark pool earns a per-share
commission no greater than the half bid-ask spread. Throughout the entire
period, the main concern is inventory risk, which increases as the number of
held positions becomes critically small or large. The dark pool can control its
inventory by choosing the size of the commission for each transaction, so to
encourage, e.g., buy orders instead of sell orders. Furthermore, it can submit
lit-pool limit orders, of which execution is uncertain, and market orders,
which are expensive. In either case, the dark pool risks an information
leakage, which we model via a fixed penalty for trading in the lit pool. We
solve a double-obstacle impulse-control problem associated with the optimal
management of the inventory, and we show that the value function is the unique
viscosity solution of the associated system of quasi variational inequalities.
We explore various numerical examples of the proposed model, including one that
admits a semi-explicit solution.


  Interest in how democracies form consensus has increased recently, with
statistical physics and economics approaches both suggesting that there is
convergence to a fixed point in belief networks, but with fluctuations in
opinions when there are ``stubborn'' voters. We modify a model of opinion
dynamics in which agents are fully Bayesian to account for two cognitive
biases: confirmation bias and in-group bias. Confirmation bias occurs when the
received information is considered to be more likely when it aligns with the
receiver's beliefs. In-group bias occurs when the receiver further considers
the information to be more likely when the receiver's beliefs and the sender's
beliefs are aligned. We find that when there are no cognitive biases, a network
of agents always converges to complete consensus. With confirmation bias alone,
polarization can occur. With both biases present, consensus and polarization
are possible, but when agents attempt to counteract confirmation bias, there
can be signatures of transient chaos and ongoing opinion fluctuations. Based on
this simple model, we conjecture that complex opinion fluctuations might be a
generic feature of opinion dynamics when agents are Bayesian with biases.


  We suggest a new method of studying coherence in finite level systems coupled
to the environment and use it for the Hamiltonian that has been used to
describe the light-harvesting pigment-protein complex. The method works with
the adiabatic states and transforms the Hamiltonian to a form in which the
terms responsible for decoherence and population relaxation are separated out.
Decoherence is then accounted for non-perturbatively, and population relaxation
using a Markovian master equation. Analytical results can be obtained for the
seven level system and the calculations are very simple for systems with more
levels. We apply the treatment to the seven level system and the results are in
excellent agreement with the exact numerical results of Nalbach et al. (P.
Nalbach, D. Braun, and M. Thorwart, Physical Review E, 84, 041926 (2011)). Our
approach is able to account for decoherence and population relaxation
separately. It is found that decoherence only causes damping of oscillations,
and does not lead to transfer to the reaction centre. Population relaxation is
necessary for efficient transfer to the reaction centre, in agreement with
earlier findings. Our results show that the transformation to the adiabatic
basis followed by a Redfield type of approach leads to results in good
agreement with exact simulation.


This paper was withdrawn as Lemma 2 is incorrect.


  Strong quantum nonlinearity gives rise to many interesting quantum effects
and has wide applications in quantum physics. Herewe investigate the quantum
nonlinear effect of an optomechanical system (OMS) consisting of both linear
and quadratic coupling. Interestingly, a controllable optomechanical
nonlinearity is obtained by applying a driving laser into the cavity. This
controllable optomechanical nonlinearity can be enhanced into a strong coupling
regime, even if the system is initially in the weak-coupling regime. Moreover,
the system dissipation can be suppressed effectively, which allows the
appearance of phonon sideband and photon blockade effects in the weak-coupling
regime. This work may inspire the exploration of a dual-coupling optomechanical
system as well as its applications in modern quantum science.


  Crowd counting is a challenging task due to the heavy occlusions, scales, and
density variations. Existing methods handle these challenges effectively while
ignoring low-resolution (LR) circumstances. The LR circumstances weaken the
counting performance deeply for two crucial reasons: 1) limited detail
information; 2) overlapping head regions accumulate in density maps and result
in extreme ground-truth values. An intuitive solution is to employ
super-resolution (SR) pre-processes for the input LR images. However, it
complicates the inference steps and thus limits application potentials when
requiring real-time. We propose a more elegant method termed Multi-Scale
Super-Resolution Module (MSSRM). It guides the network to estimate the lost de
tails and enhances the detailed information in the feature space. Noteworthy
that the MSSRM is plug-in plug-out and deals with the LR problems with no
inference cost. As the proposed method requires SR labels, we further propose a
Super-Resolution Crowd Counting dataset (SR-Crowd). Extensive experiments on
three datasets demonstrate the superiority of our method. The code will be
available at https://github.com/PRIS-CV/MSSRM.git.


  Electric vehicles represent a promising technology for reducing emissions and
dependence on fossil fuels and have started entering different automotive
markets. In order to bolster their adoption by consumers and hence enhance
their penetration rate, a charging station infrastructure needs to be deployed.
This paper studies decentralized policies that assign electric vehicles to a
network of charging stations with the goal to achieve little to no queueing.
This objective is especially important for electric vehicles, whose charging
times are fairly long. The social optimality of the proposed policies is
established in the many-server regime, where each station is equipped with
multiple charging slots. Further, convergence issues of the algorithm that
achieves the optimal policy are examined. Finally, the results provide insight
on how to address questions related to the optimal location deployment of the
infrastructure.


  Radio interferometry is a powerful technique for astronomical imaging. The
theory of Compressed Sensing (CS) has been applied recently to the ill-posed
inverse problem of recovering images from the measurements taken by radio
interferometric telescopes. We review novel CS radio interferometric imaging
techniques, both at the level of acquisition and reconstruction, and discuss
their superior performance relative to traditional approaches. In order to
remain as close to the theory of CS as possible, these techniques necessarily
consider idealised interferometric configurations. To realise the enhancement
in quality provided by these novel techniques on real radio interferometric
observations, their extension to realistic interferometric configurations is
now of considerable importance. We also chart the future direction of research
required to achieve this goal.


  In an unnormalized Krylov subspace framework for solving symmetric systems of
linear equations, the orthogonal vectors that are generated by a Lanczos
process are not necessarily on the form of gradients. Associating each
orthogonal vector with a triple, and using only the three-term recurrences of
the triples, we give conditions on whether a symmetric system of linear
equations is compatible or incompatible. In the compatible case, a solution is
given and in the incompatible case, a certificate of incompatibility is
obtained. In particular, the case when the matrix is singular is handled.
  We also derive a minimum-residual method based on this framework and show how
the iterates may be updated explicitly based on the triples, and in the
incompatible case a minimum-residual solution of minimum Euclidean norm is
obtained.


  We show that the supersymmetric Wilson loops in IIB matrix model give a
transition operator from reduced supersymmetric Yang-Mills theory to
supersymmetric space-time theory. In comparison with Green-Schwarz superstring
we identify the supersymmetric Wilson loops with the asymptotic states of IIB
superstring. It is pointed out that the supersymmetry transformation law of the
Wilson loops is the inverse of that for the vertex operators of massless modes
in the U(N) open superstring with Dirichlet boundary condition.


  Predicting a reader's rating of text quality is a challenging task that
involves estimating different subjective aspects of the text, like structure,
clarity, etc. Such subjective aspects are better handled using cognitive
information. One such source of cognitive information is gaze behaviour. In
this paper, we show that gaze behaviour does indeed help in effectively
predicting the rating of text quality. To do this, we first model text quality
as a function of three properties - organization, coherence and cohesion. Then,
we demonstrate how capturing gaze behaviour helps in predicting each of these
properties, and hence the overall quality, by reporting improvements obtained
by adding gaze features to traditional textual features for score prediction.
We also hypothesize that if a reader has fully understood the text, the
corresponding gaze behaviour would give a better indication of the assigned
rating, as opposed to partial understanding. Our experiments validate this
hypothesis by showing greater agreement between the given rating and the
predicted rating when the reader has a full understanding of the text.


  We discuss Tsallis holographic dark energy (THDE) model in higher dimension.
An interacting dark energy model is proposed with Generalized Chaplygin Gas
(GCG) in the framework of Compact Kaluza-Klein gravity. It is shown that a
stable configuration can be found in the present epoch which is also compatible
with the observed value of the density parameter. It is noted that dark energy
(DE) might have evolved from a phantom phase in the past. Nature of dark energy
is found to depend on the coupling parameter of the interaction. Classical
stability consideration is also found to put an upper bound on the model
parameter.


  Recently, with the emergence of numerous Large Language Models (LLMs), the
implementation of AI has entered a new era. Irrespective of these models' own
capacity and structure, there is a growing demand for LLMs to possess enhanced
comprehension of longer and more complex contexts with relatively smaller
sizes. Models often encounter an upper limit when processing sequences of
sentences that extend beyond their comprehension capacity and result in
off-topic or even chaotic responses. While several recent works attempt to
address this issue in various ways, they rarely focus on "why models are unable
to compensate or strengthen their capabilities on their own". In this paper, we
thoroughly investigate the nature of information transfer within LLMs and
propose a novel technique called Attention Transition. This technique empowers
models to achieve longer and better context comprehension with minimal
additional training or impact on generation fluency. Our experiments are
conducted on the challenging XSum dataset using LLaMa-7b model with context
token length ranging from 800 to 1900. Results demonstrate that we achieve
substantial improvements compared with the original generation results
evaluated by GPT4.


  Convolutional neural networks (CNNs) have achieved superhuman performance in
multiple vision tasks, especially image classification. However, unlike humans,
CNNs leverage spurious features, such as background information to make
decisions. This tendency creates different problems in terms of robustness or
weak generalization performance. Through our work, we introduce a contrastive
learning-based approach (CLAD) to mitigate the background bias in CNNs. CLAD
encourages semantic focus on object foregrounds and penalizes learning features
from irrelavant backgrounds. Our method also introduces an efficient way of
sampling negative samples. We achieve state-of-the-art results on the
Background Challenge dataset, outperforming the previous benchmark with a
margin of 4.1\%. Our paper shows how CLAD serves as a proof of concept for
debiasing of spurious features, such as background and texture (in
supplementary material).


  A theoretical model for fractal growth of DLA-clusters in two- and
three-dimensional Euclidean space is proposed. This model allows to study some
statistical properties of growing clusters in two different situations: in the
static case (the cluster is fixed), and in the case when the growing structure
has a nonzero rotation around its germ. By the direct computer simulation the
growth of rotating clusters is investigated. The fractal dimension of such
clusters as a function of the rotation velocity is found. It is shown that for
small enough velocities the fractal dimension is growing, but then, with
increasing rotation velocity, it tends to the unity.


  We investigate the problem of discovering and modeling regime shifts in an
ecosystem comprising multiple time series known as co-evolving time series.
Regime shifts refer to the changing behaviors exhibited by series at different
time intervals. Learning these changing behaviors is a key step toward time
series forecasting. While advances have been made, existing methods suffer from
one or more of the following shortcomings: (1) failure to take relationships
between time series into consideration for discovering regimes in multiple time
series; (2) lack of an effective approach that models time-dependent behaviors
exhibited by series; (3) difficulties in handling data discontinuities which
may be informative. Most of the existing methods are unable to handle all of
these three issues in a unified framework. This, therefore, motivates our
effort to devise a principled approach for modeling interactions and
time-dependency in co-evolving time series. Specifically, we model an ecosystem
of multiple time series by summarizing the heavy ensemble of time series into a
lighter and more meaningful structure called a \textit{mapping grid}. By using
the mapping grid, our model first learns time series behavioral dependencies
through a dynamic network representation, then learns the regime transition
mechanism via a full time-dependent Cox regression model. The originality of
our approach lies in modeling interactions between time series in regime
identification and in modeling time-dependent regime transition probabilities,
usually assumed to be static in existing work.


  Symmetry algebras of quantum many-body systems with locality can be
understood using commutant algebras, which are defined as algebras of operators
that commute with a given set of local operators. In this work, we show that
these symmetry algebras can be expressed as frustration-free ground states of a
local superoperator, which we refer to as a "super-Hamiltonian". We demonstrate
this for conventional symmetries such as $Z_2$, $U(1)$, and $SU(2)$, where the
symmetry algebras map to various kinds of ferromagnetic ground states, as well
as for unconventional ones that lead to weak ergodicity breaking phenomena of
Hilbert space fragmentation and quantum many-body scars. In addition, we show
that this super-Hamiltonian is exactly the superoperator that governs the
operator relaxation in noisy symmetric Brownian circuits. This physical
interpretation provides a novel interpretation for Mazur bounds for
autocorrelation functions, and relates the low-energy excitations of the
super-Hamiltonian to approximate symmetries that determine slowly relaxing
modes in symmetric systems. We find examples of gapped/gapless
super-Hamiltonians indicating the absence/presence of slow-modes, which happens
in the presence of discrete/continuous symmetries. In the gapless cases, we
recover slow-modes such as diffusion, tracer diffusion, and asymptotic scars in
the presence of $U(1)$ symmetry, Hilbert space fragmentation, and a tower of
quantum scars respectively. In all, this demonstrates the power of the
commutant algebra framework in obtaining a comprehensive understanding of
symmetries and their dynamical consequences in systems with locality.


  The fluctuation-dissipation theorem, in the Kubo original formulation, is
based on the decomposition of the thermal agitation forces into a dissipative
contribution and a stochastically fluctuating term. This decomposition can be
avoided by introducing a stochastic velocity field, with correlation properties
deriving from linear response theory. Here, we adopt this field as the
comprehensive hydrodynamic/fluctuational driver of the kinematic equations of
motion. With this description, we show that the Langevin equations for a
Brownian particle interacting with a solvent fluid become particularly simple
and can be applied even in those cases in which the classical approach, based
on the concept of a stochastic thermal force, displays intrinsic difficulties
e.g., in the presence of the Basset force. We show that a convenient way for
describing hydrodynamic/thermal fluctuations is by expressing them in the form
of Extended Poisson-Kac Processes possessing prescribed correlation properties
and a continuous velocity density function. We further highlight the importance
of higher-order correlation functions in the description of the stochastic
hydrodynamic velocity field with special reference to short-time properties of
Brownian motion. We conclude by outlining some practical implications in
connection with the statistical description of particle motion in confined
geometries.


  In the paper we begin to explore relation between the question of
unitarizability of classical p-adic groups, and Arthur packets.


  A new Chandra observation of SNR 0506-68.0 (also called N23) reveals a
complex, highly structured morphology in the low energy X-ray band and an
isolated compact central object in the high energy band. Spectral analysis
indicates that the X-ray emission overall is dominated by thermal gas whose
composition is consistent with swept-up ambient material. There is a strong
gradient in ambient density across the diameter of the remnant. Toward the
southeast, near a prominent star cluster, the emitting density is 10 - 23
cm^{-3} while toward the northwest it has dropped to a value of only 1 cm^{-3}.
The total extent of the X-ray remnant is 100" by 120" (24 pc x 29 pc for a
distance of 50 kpc), somewhat larger than previously known. The remnant's age
is estimated to be ~4600 yr. One part of the remnant shows evidence for
enhanced O, Ne, and perhaps Mg abundances, which is interpreted as evidence for
ejecta from a massive star core collapse supernova. The compact central object
has a luminosity of a few times 10^{33} ergs/s and no obvious radio or optical
counterpart. It does not show an extended nebula or pulsed emission as expected
from a young energetic pulsar, but resembles the compact central objects seen
in other core collapse SNe, such as Cas A.


  An $m$-cover of the Hermitian surface $H(3,q^2)$ of $PG(3,q^2)$ is a set
$\mathcal{S}$ of lines of $H(3,q^2)$ such that every point of $H(3,q^2)$ lies
on exactly $m$ lines of $\mathcal{S}$, and $0<m<q+1$. Segre (1965) proved that
if $q$ is odd, then $m=(q+1)/2$, and called such a set $\mathcal{S}$ of lines a
hemisystem. Penttila and Williford (2011) introduced the notion of a relative
hemisystem: a set of lines $\mathcal{R}$ of $H(3,q^2)$, $q$ even, disjoint from
a symplectic subgeometry $W(3,q)$ such that every point of $H(3,q^2)\setminus
W(3,q)$ lies on exactly $q/2$ elements of $\mathcal{R}$. In this paper, we
provide an analogue of Segre's result by introducing relative $m$-covers of
$H(3,q^2)$ with respect to a symplectic subgeometry and proving that $m$ must
necessarily be $q/2$.


  The realistic description of correlated electron systems has taken an
important step forward a few years ago as the combination of density functional
methods and the dynamical mean-field theory was conceived. This framework
allows access to both high and low energy physics and is capable of the
description of the specific physics of strongly correlated materials, like the
Mott metal-insulator transition. A very important step in the procedure is the
interface between the band structure method and the dynamical mean-field theory
and its impurity solver. We present a general interface between a projector
augmented wave based density functional code and many-body methods based on
Wannier functions obtained from a projection on local orbitals. The
implementation is very flexible and allows for various applications. Quantities
like the momentum resolved spectral function are accessible. We present
applications to SrVO$_3$ and the metal-insulator transition in
Ca$_{2-x}$Sr$_{x}$RuO$_4$.


  We derive the equations governing the linear stability of Kerr-Newman
spacetime to coupled electromagnetic-gravitational perturbations. The equations
generalize the celebrated Teukolsky equation for curvature perturbations of
Kerr, and the Regge-Wheeler equation for metric perturbations of
Reissner-Nordstr\"om. Because of the "apparent indissolubility of the coupling
between the spin-1 and spin-2 fields", as put by Chandrasekhar, the stability
of Kerr-Newman spacetime can not be obtained through standard decomposition in
modes. Due to the impossibility to decouple the modes of the gravitational and
electromagnetic fields, the equations governing the linear stability of
Kerr-Newman have not been previously derived. Using a tensorial approach that
was applied to Kerr, we produce a set of generalized Regge-Wheeler equations
for perturbations of Kerr-Newman, which are suitable for the study of
linearized stability by physical space methods. The physical space analysis
overcomes the issue of coupling of spin-1 and spin-2 fields and represents the
first step towards an analytical proof of the stability of the Kerr-Newman
black hole.


  We introduce a new construction of matrix wreath products of algebras that is
similar to wreath products of groups. We then use it to prove embedding
theorems for Jacobson radical, nil, and primitive algebras. In
\S\ref{Section6}, we construct finitely generated nil algebras of arbitrary
Gelfand-Kirillov dimension $\geq 8$ over a countable field which answers a
question from \cite{8}.


  We discuss different formulations and approaches to string theory and $ 2d$
quantum gravity. The generic idea to get a unique description of {\it many}
different string vacua altogether is demonstrated on the examples in $ 2d$
conformal, topological and matrix formulations. The last one naturally brings
us to the appearance of classical integrable systems in string theory. Physical
meaning of the appearing structures is discussed and some attempts to find
directions of possible generalizations to ``higher-dimensional" models are
made. We also speculate on the possible appearence of quantum integrable
structures in string theory.


  We calculate the resonant electronic Raman scattering for the Falicov-Kimball
model near the Mott transition on a hypercubic lattice. The solution is exact,
and employs dynamical mean field theory.


  We study the resolvent of the massive Dirac operator in the
Schwarzschild-Anti-de Sitter space-time. After separation of variables, we use
standard one dimensional techniques to obtain an explicit formula. We then make
use of this formula to extend the resolvent meromorphically accross the real
axis.


  Milnor's triple linking numbers of a link in the 3-sphere are interpreted
geometrically in terms of the pattern of intersections of the Seifert surfaces
of the components of the link. This generalizes the well known formula as an
algebraic count of triple points when the pairwise linking numbers vanish.


  The interaction-driven Mott transition in the half-filled Hubbard model is a
first-order phase transition that terminates at a critical point
$(T_\mathrm{c},U_\mathrm{c})$ in the temperature-interaction plane $T-U$. A
number of crossovers occur along lines that extend for some range above
$(T_\mathrm{c},U_\mathrm{c})$. Asymptotically close to
$(T_\mathrm{c},U_\mathrm{c})$, these lines coalesce into the so-called Widom
line. The existence of $(T_\mathrm{c},U_\mathrm{c})$ and of the associated
crossovers becomes unclear when long-wavelength fluctuations or long-range
order occur above $(T_\mathrm{c},U_\mathrm{c})$. We study this problem using
continuous-time quantum Monte Carlo methods as impurity solvers for both
Dynamical Mean-Field Theory (DMFT) and Cellular Dynamical Mean-Field Theory
(CDMFT). We contrast the cases of the square lattice, where antiferromagnetic
fluctuations dominate in the vicinity of the Mott transition, and the
triangular lattice where they do not. The inflexion points and maxima found
near the Widom line for the square lattice can serve as proxy for the
triangular lattice case. But the only crossover observable in all cases at
sufficiently high temperature is that associated with the opening of the Mott
gap. The same physics also controls an analog crossover in the resistivity
called the "Quantum Widom line".


  We give a method for modeling solid objects undergoing large spatially
varying and/or anisotropic strains, and use it to reconstruct human anatomy
from medical images. Our novel shape deformation method uses plastic strains
and the Finite Element Method to successfully model shapes undergoing large
and/or anisotropic strains, specified by sparse point constraints on the
boundary of the object. We extensively compare our method to standard
second-order shape deformation methods, variational methods and surface-based
methods and demonstrate that our method avoids the spikiness, wiggliness and
other artefacts of previous methods. We demonstrate how to perform such shape
deformation both for attached and un-attached ("free flying") objects, using a
novel method to solve linear systems with singular matrices with a known
nullspace. While our method is applicable to general large-strain shape
deformation modeling, we use it to create personalized 3D triangle and
volumetric meshes of human organs, based on MRI or CT scans. Given a medically
accurate anatomy template of a generic individual, we optimize the geometry of
the organ to match the MRI or CT scan of a specific individual. Our examples
include human hand muscles, a liver, a hip bone, and a gluteus medius muscle
("hip abductor").


  Starting from the quantum theory of identical particles, we show how to
define a classical mechanics that retains information about the quantum
statistics. We consider two examples of relevance for the quantum Hall effect:
identical particles in the lowest Landau level, and vortices in the
Chern-Simons Ginzburg-Landau model. In both cases the resulting {\em classical}
statistical mechanics is shown to be a nontrivial classical limit of Haldane's
exclusion statistics.


  Combined measurements of the production and decay rates of the Higgs boson,
as well as its couplings to vector bosons and fermions, are presented. The
analysis uses the LHC proton-proton collision data set recorded with the CMS
detector in 2016 at $\sqrt{s} =$ 13 TeV, corresponding to an integrated
luminosity of 35.9 fb$^{-1}$. The combination is based on analyses targeting
the five main Higgs boson production mechanisms (gluon fusion, vector boson
fusion, and associated production with a W or Z boson, or a top quark-antiquark
pair) and the following decay modes: H $\to$ $\gamma\gamma$, ZZ, WW,
$\tau\tau$, bb, and $\mu\mu$. Searches for invisible Higgs boson decays are
also considered. The best-fit ratio of the signal yield to the standard model
expectation is measured to be $\mu$ $=$ 1.17 $\pm$ 0.10, assuming a Higgs boson
mass of 125.09 GeV. Additional results are given for parametrizations with
varying assumptions on the scaling behavior of the different production and
decay modes, including generic ones based on ratios of cross sections and
branching fractions or coupling modifiers. The results are compatible with the
standard model predictions in all parametrizations considered. In addition,
constraints are placed on various two Higgs doublet models.


  We give a theoretical description of a coherently driven opto-mechanical
system with a single added photon. The photon source is modeled as a cavity
which initially contains one photon and which is irreversibly coupled to the
opto-mechanical system. We show that the probability for the additional photon
to be emitted by the opto-mechanical cavity will exhibit oscillations under a
Lorentzian envelope, when the driven interaction with the mechanical resonator
is strong enough. Our scheme provides a feasible route towards quantum state
transfer between optical photons and micromechanical resonators.


  Anaphora resolution is an important task for information extraction across a
range of languages, text genres, and domains, motivating the need for methods
that do not require large annotated datasets. In-context learning has emerged
as a promising approach, yet there are a number of challenges in applying
in-context learning to resolve anaphora. For example, encoding a single
in-context demonstration that consists of: an anaphor, a paragraph-length
context, and a list of corresponding antecedents, requires conditioning a
language model on a long sequence of tokens, limiting the number of
demonstrations per prompt. In this paper, we present MICE (Mixtures of
In-Context Experts), which we demonstrate is effective for few-shot anaphora
resolution in scientific protocols (Tamari et al., 2021). Given only a handful
of training examples, MICE combines the predictions of hundreds of in-context
experts, yielding a 30% increase in F1 score over a competitive prompt
retrieval baseline. Furthermore, we show MICE can be used to train compact
student models without sacrificing performance. As far as we are aware, this is
the first work to present experimental results demonstrating the effectiveness
of in-context learning on the task of few-shot anaphora resolution in
scientific protocols.


  The magnetic susceptibilities chi versus temperature T of powders and single
crystals of the ambient-pressure (AP) and high-pressure (HP) phases of
(VO)_{2}P_{2}O_{7} are analyzed using an accurate theoretical prediction of
chi(T, J1, J2) for the spin-1/2 antiferromagnetic alternating-exchange (J1, J2)
Heisenberg chain. The results are consistent with recent models with two
distinct types of alternating-exchange chains in the AP phase and a single type
in the HP phase. The spin gap for each type of chain is derived from the
respective set of two fitted alternating exchange constants and the one-magnon
dispersion relation for each of the two types of chains in the AP phase is
predicted. The influences of interchain coupling on the derived intrachain
exchange constants, spin gaps, and dispersion relations are estimated using a
mean-field approximation for the interchain coupling. The accuracies of the
spin gaps obtained using fits to the low-T chi(T) data by theoretical low-T
approximations are determined. The results of these studies are compared with
previously reported estimates of the exchange couplings and spin gaps in the AP
and HP phases and with the magnon dispersion relations in the AP phase measured
previously using inelastic neutron scattering.


  An complete exposition of Matthias Gunther's elementary proof of Nash's
isometric embedding theorem.


  Emission of anisotropic gravitational radiation from compact binary system
leads to a flux of linear momentum. This results in the recoil of the system.
We investigate the rate of loss of Linear momentum flux in the far zone of the
source using various mass type and current type multipole moments for
inspiralling compact binary mergers in quasi-elliptical orbits at 2.5 Post
Newtonian order. We compute the linear momentum flux accurate up to
$\mathcal{O}(e_t)$ in harmonic coordinate. A 2.5 Post Newtonian Quasi-Keplarian
representation of the parametric solution to the Post Newtonian equation of
motion for the compact binary system has been adopted here. We also provide a
closed-form expression for the accumulated linear momentum from the remote past
through the binary evolution.


  Let G be a connected reductive linear algebraic group over a field k of
characteristic p>0. Let p be large enough with respect to the root system. We
show that if a finitely generated commutative k-algebra A with G-action has
good filtration, then any noetherian A-module with compatible G-action has
finite good filtration dimension.


  We argue that a spontaneous breakdown of local Weyl invariance offers a
mechanism in which gravitational interactions contribute to the generation of
particle masses and their electric charge. The theory is formulated in terms of
a spacetime geometry whose natural connection has both dynamic torsion and
non-metricity. Its structure illuminates the role of dynamic scales used to
determine measurable aspects of particle interactions and it predicts an
additional neutral vector boson with electroweak properties.


  Since OpenAI's release of ChatGPT, generative AI has received significant
attention across various domains. These AI-based chat systems have the
potential to enhance the productivity of knowledge workers in diverse tasks.
However, the use of free public services poses a risk of data leakage, as
service providers may exploit user input for additional training and
optimization without clear boundaries. Even subscription-based alternatives
sometimes lack transparency in handling user data. To address these concerns
and enable Fraunhofer staff to leverage this technology while ensuring
confidentiality, we have designed and developed a customized chat AI called
FhGenie (genie being a reference to a helpful spirit). Within few days of its
release, thousands of Fraunhofer employees started using this service. As
pioneers in implementing such a system, many other organizations have followed
suit. Our solution builds upon commercial large language models (LLMs), which
we have carefully integrated into our system to meet our specific requirements
and compliance constraints, including confidentiality and GDPR. In this paper,
we share detailed insights into the architectural considerations, design,
implementation, and subsequent updates of FhGenie. Additionally, we discuss
challenges, observations, and the core lessons learned from its productive
usage.


  A first-order Lagrangian $L^\nabla $ variationally equivalent to the
second-order Einstein-Hilbert Lagrangian is introduced. Such a Lagrangian
depends on a symmetric linear connection, but the dependence is covariant under
diffeomorphisms. The variational problem defined by $L^\nabla $ is proved to be
regular and its Hamiltonian formulation is studied, including its covariant
Hamiltonian attached to $\nabla $.


  Cloth simulation has wide applications in computer animation, garment design,
and robot-assisted dressing. This work presents a differentiable cloth
simulator whose additional gradient information facilitates cloth-related
applications. Our differentiable simulator extends a state-of-the-art cloth
simulator based on Projective Dynamics (PD) and with dry frictional contact. We
draw inspiration from previous work to propose a fast and novel method for
deriving gradients in PD-based cloth simulation with dry frictional contact.
Furthermore, we conduct a comprehensive analysis and evaluation of the
usefulness of gradients in contact-rich cloth simulation. Finally, we
demonstrate the efficacy of our simulator in a number of downstream
applications, including system identification, trajectory optimization for
assisted dressing, closed-loop control, inverse design, and real-to-sim
transfer. We observe a substantial speedup obtained from using our gradient
information in solving most of these applications.


  We propose a general recipe for chiral topological superconductor (TSC) in
two dimensions with multiple $N$ chiral Majorana fermion modes from a quantied
anomalous Hall insulator in proximity to an s-wave superconductor with
nontrivial band topology. A concrete example is that a $N=3$ chiral TSC may be
realized by coupling a magnetic topological insulator and the ion-based
superconductor such as FeTe$_{1-x}$Se$_{x}$ ($x=0.45$). We further propose the
electrical and thermal transport experiments to detect the Majorana nature of
three chiral edge fermions. A unique signature is that the two-terminal
electrical conductance of a quantized anomalous Hall-TSC junction obeys a
distribution averaged to $(2/3)e^2/h$, which is due to the random edge mode
mixing of chiral Majorana fermions and is distinguished from possible trivial
explanations.


  In a recent paper Birke and Bissantz (2008) considered the problem of
nonparametric estimation in inverse regression models with convolution-type
operators. For multivariate predictors nonparametric methods suffer from the
curse of dimensionality and we consider inverse regression models with the
additional qualitative assumption of additivity. In these models several
additive estimators are studied. In particular, we investigate estimators under
the random design assumption which are applicable when observations are not
available on a grid. Finally, we compare this estimator with the marginal
integration and the non-additive estimator by means of a simulation study. It
is demonstrated that the new method yields a substantial improvement of the
currently available procedures.


  Notions of self-dual and anti self-dual almost quaternionic structures are
introduced. The complete classification of self-dual and anti self-dual
generalized Kaehler manifolds is obtained.


  We study gamma-ray line signatures from electroweakly interacting non-abelian
spin-1 dark matter (DM). In this model, $Z_2$-odd spin-1 particles including a
DM candidate have the SU(2)$_L$ triplet-like features, and the Sommerfeld
enhancement is relevant in the annihilation processes. We derive the
annihilation cross sections contributing to the photon emission and compare
with the SU(2)$_L$ triplet fermions, such as Wino DM in the supersymmetric
Standard Model. The Sommerfeld enhancement factor is approximately the same in
both systems, while our spin-1 DM predicts the larger annihilation cross
sections into $\gamma \gamma/ Z \gamma$ modes than those of the Wino by
$\frac{38}{9}$. This is because a spin-1 DM pair forms not only $J=0$ but also
$J=2$ partial wave states where $J$ denotes the total spin angular momentum.
Our spin-1 DM also has a new annihilation mode into $Z_2$-even extra heavy
vector and photon, $Z' \gamma$. For this mode, the photon energy depends on the
masses of DM and the heavy vector, and thus we have a chance to probe the mass
spectrum. The latest gamma-ray line search in the Galactic Center region gives
a strong constraint on our spin-$1$ DM. We can probe the DM mass for $\lesssim
25.3~$TeV by the Cherenkov Telescope Array experiment even if we assume a
conservative DM density profile.


  The STAR Collaboration reports measurements of the longitudinal double-spin
asymmetry, $A_{LL}$, for neutral pions produced at forward directions in
polarized proton-proton collisions, at a center-of-mass energy of $510$ GeV.
Results are given for transverse momenta in the range $2<p_{T}<10$ GeV/$c$
within two regions of pseudorapidity that span $2.65<\eta<3.9$. These results
are sensitive to the polarized gluon parton distribution function, $\Delta
g(x)$, down to the region of Bjorken $x \sim 10^{-3}$. The asymmetries observed
are less than $\pm 5 \cdot 10^{-3}$ in magnitude, and will help constrain the
contribution to the spin of the proton from polarized gluons at low $x$, when
combined with other measurements as part of a global analysis.


  The truncated Fourier transform (TFT) was introduced by van der Hoeven in
2004 as a means of smoothing the "jumps" in running time of the ordinary FFT
algorithm that occur at power-of-two input sizes. However, the TFT still
introduces these jumps in memory usage. We describe in-place variants of the
forward and inverse TFT algorithms, achieving time complexity O(n log n) with
only O(1) auxiliary space. As an application, we extend the second author's
results on space-restricted FFT-based polynomial multiplication to polynomials
of arbitrary degree.


  Technical means for identifying when tampering occurs is a critical part of
many containment and surveillance technologies. Conventional fiber optic seals
provide methods for monitoring enclosed inventories, but they are vulnerable to
spoofing attacks based on classical physics. We address these vulnerabilities
with the development of a quantum seal that offers the ability to detect the
intercept-resend attack using quantum integrity verification. Our approach
represents an application of entanglement to provide guarantees in the
authenticity of the seal state by verifying it was transmitted coherently. We
implement these ideas using polarization-entangled photon pairs that are
verified after passing through a fiber-optic channel testbed. Using binary
detection theory, we find the probability of detecting inauthentic signals is
greater than 0.9999 with a false alarm chance of $10^{-9}$ for a 10 second
sampling interval. In addition, we show how the Hong-Ou-Mandel effect
concurrently provides a tight bound on redirection attack, in which tampering
modifies the shape of the seal. Our measurements limit the tolerable path
length change to sub-millimeter disturbances. These tamper-indicating features
of the quantum seal offer unprecedented security for unattended monitoring
systems.


  In this study Arduino card based mobile robot design was realized. This robot
can serve as a security robot, an auxiliary robot or a control robot. The
designed robot has two operation modes. The first operating mode is autonomous
mode. In this mode, the robot detects the surroundings with the help of
ultrasonic sensors placed around it, and keeps track of the places it passes by
using the encoder. It is able to navigate without hitting any place and passing
from where it passes, and it transmits the patient's pulse and temperature
condition to the user by other systems installed on it. Also the IP camera
sends the scene on the screen. The emergency button to be placed next to the
patient sends information to the user in emergency situations. If the
abnormality is detected in the temperature and pulse again, the user gives a
message. When the pre-recorded drug use times come, the system can alert the
patient. The second mode is manual mode. In this mode, the user can move the
desired direction of the robot with the Android operating system. In addition,
all data received in autonomous mode can be sent to the user. Thus, the user
can control the mobile robot with the camera image even if it is not in the
vicinity of the robot.


  Split computing has emerged as a recent paradigm for implementation of
DNN-based AI workloads, wherein a DNN model is split into two parts, one of
which is executed on a mobile/client device and the other on an edge-server (or
cloud). Data compression is applied to the intermediate tensor from the DNN
that needs to be transmitted, addressing the challenge of optimizing the
rate-accuracy-complexity trade-off. Existing split-computing approaches adopt
ML-based data compression, but require that the parameters of either the entire
DNN model, or a significant portion of it, be retrained for different
compression levels. This incurs a high computational and storage burden:
training a full DNN model from scratch is computationally demanding,
maintaining multiple copies of the DNN parameters increases storage
requirements, and switching the full set of weights during inference increases
memory bandwidth. In this paper, we present an approach that addresses all
these challenges. It involves the systematic design and training of bottleneck
units - simple, low-cost neural networks - that can be inserted at the point of
split. Our approach is remarkably lightweight, both during training and
inference, highly effective and achieves excellent rate-distortion performance
at a small fraction of the compute and storage overhead compared to existing
methods.


  It has been shown that injecting noise into the neural network weights during
the training process leads to a better generalization of the resulting model.
Noise injection in the distributed setup is a straightforward technique and it
represents a promising approach to improve the locally trained models. We
investigate the effects of noise injection into the neural networks during a
decentralized training process. We show both theoretically and empirically that
noise injection has no positive effect in expectation on linear models, though.
However for non-linear neural networks we empirically show that noise injection
substantially improves model quality helping to reach a generalization ability
of a local model close to the serial baseline.


  We study the trion and biexciton in transition metal dichalcogenides
monolayers within the framework of a nonrelativistic potential model using the
method of hyperspherical harmonics (HH). We solve the three- and four-body
Schr\"odinger equations with the Keldysh potential by expanding the wave
functions of a trion and biexciton in terms of the antisymmetrized HH. Results
of the calculations for the ground state energies are in good agreement with
similar calculations for the Keldysh potential and in reasonable agreement with
experimental measurements of trion and biexciton binding energies.


  We investigate how the proton distribution function evolves when the protons
undergo stochastic heating by strong, low-frequency, Alfv\'en-wave turbulence
under the assumption that $\beta$ is small. We apply our analysis to protons
undergoing stochastic heating in the supersonic fast solar wind and obtain
proton distributions at heliocentric distances ranging from 4 to 30 solar
radii. We find that the proton distribution develops non-Gaussian structure
with a flat core and steep tail. For $r >5 \ R_{\rm S}$, the proton
distribution is well approximated by a modified Moyal distribution. Comparisons
with future measurements from \emph{Solar Probe Plus} could be used to test
whether stochastic heating is occurring in the solar-wind acceleration region.


  We study the nonequilibrium dynamics of the linear to zigzag structural phase
transition exhibited by an ion chain confined in a trap with periodic boundary
conditions. The transition is driven by reducing the transverse confinement at
a finite quench rate, which can be accurately controlled. This results in the
formation of zigzag domains oriented along different transverse planes. The
twists between different domains can be stabilized by the topology of the trap
and under laser cooling the system has a chance to relax to a helical chain
with nonzero winding number. Molecular dynamics simulations are used to obtain
a large sample of possible trajectories for different quench rates. The scaling
of the average winding number with different quench rates is compared to the
prediction of the Kibble-Zurek theory, and a good quantitative agreement is
found.


  We have performed ^{31}P-NMR measurements on Ce(Ru_{1-x}Fe_{x})PO in order to
investigate ferromagnetic (FM) quantum criticality, since heavy-fermion (HF)
ferromagnet CeRuPO with a two-dimensional structure turns to a HF paramagnet by
an isovalent Fe-substitution for Ru. We found that Ce(Ru_{0.15}Fe_{0.85})PO
shows critical fluctuations down to \sim 0.3 K, as well as the continuous
suppression of Curie temperature and the ordered moments by the
Fe-substitution. These experimental results suggest the presence of a FM
quantum critical point (QCP) at x \sim 0.86, which is a rare example among
itinerant ferromagnets. In addition, we point out that the critical behaviors
in Ce(Ru_{0.15}Fe_{0.85})PO share the similarity with those in YbRh_{2}Si_{2},
where the local criticality of $f$ electrons has been discussed. We reveal that
Ce(Ru_{1-x}Fe_{x})PO is a new system to study FM quantum criticality in HF
compounds.


  This paper presents a hierarchical framework to solve the multi-robot
temporal task planning problem. We assume that each robot has its individual
task specification and the robots have to jointly satisfy a global
collaborative task specification, both described in linear temporal logic.
Specifically, a central server firstly extracts and decomposes a collaborative
task sequence from the automaton corresponding to the collaborative task
specification, and allocates the subtasks in the sequence to robots. The robots
can then synthesize their initial execution strategies based on locally
constructed product automatons, combining the assigned collaborative tasks and
their individual task specifications. Furthermore, we propose a distributed
execution strategy adjusting mechanism to iteratively improve the time
efficiency, by reducing wait time in collaborations caused by potential
synchronization constraints. We prove the completeness of the proposed
framework under assumptions, and analyze its time complexity and optimality.
Extensive simulation results verify the scalability and optimization efficiency
of the proposed method.


  In this article we calculate the 1-loop supersymmetric QCD (SQCD) corrections
to the decay $\tilde u_1\to c \tilde\chi^0_1$ in the MSSM with generic flavour
structure. This decay mode is phenomenologically important if the mass
difference between the lightest squark $\tilde u_1$ (which is assumed to be
mainly stop-like) and the neutralino LSP $\tilde \chi^0_1$ is smaller than the
top mass. In such a scenario $\tilde u_1\to t \tilde\chi^0_1$ is kinematically
not allowed and searches for $\tilde u_1\to W b \tilde\chi^0_1$ and $\tilde
u_1\to c \tilde\chi^0_1$ are performed. A large decay rate for $\tilde u_1\to c
\tilde\chi^0_1$ can weaken the LHC bounds from $\tilde u_1\to W b \chi^0_1$
which are usually obtained under the assumption ${\rm Br}[\tilde u_1\to W b
\chi^0_1]=100\%$. We find the SQCD corrections enhance $\Gamma[\tilde u_1\to c
\tilde\chi^0_1]$ by approximately 10\% if the flavour-violation originates from
bilinear terms. If flavour-violation originates from trilinear terms, the
effect can be $\pm 50\%$ or more, depending on the sign of $A^t$. We note that
connecting a theory of SUSY breaking to LHC observables, the shift from the
$\overline{\rm DR}$ to the on-shell mass is numerically very important for
light stop decays.


  Unsupervised text style transfer task aims to rewrite a text into target
style while preserving its main content. Traditional methods rely on the use of
a fixed-sized vector to regulate text style, which is difficult to accurately
convey the style strength for each individual token. In fact, each token of a
text contains different style intensity and makes different contribution to the
overall style. Our proposed method addresses this issue by assigning individual
style vector to each token in a text, allowing for fine-grained control and
manipulation of the style strength. Additionally, an adversarial training
framework integrated with teacher-student learning is introduced to enhance
training stability and reduce the complexity of high-dimensional optimization.
The results of our experiments demonstrate the efficacy of our method in terms
of clearly improved style transfer accuracy and content preservation in both
two-style transfer and multi-style transfer settings.


  Adversarial attacks hamper the decision-making ability of neural networks by
perturbing the input signal. The addition of calculated small distortion to
images, for instance, can deceive a well-trained image classification network.
In this work, we propose a novel attack technique called Sparse Adversarial and
Interpretable Attack Framework (SAIF). Specifically, we design imperceptible
attacks that contain low-magnitude perturbations at a small number of pixels
and leverage these sparse attacks to reveal the vulnerability of classifiers.
We use the Frank-Wolfe (conditional gradient) algorithm to simultaneously
optimize the attack perturbations for bounded magnitude and sparsity with
$O(1/\sqrt{T})$ convergence. Empirical results show that SAIF computes highly
imperceptible and interpretable adversarial examples, and outperforms
state-of-the-art sparse attack methods on the ImageNet dataset.


  Eilenberg-type correspondences, relating varieties of languages (e.g. of
finite words, infinite words, or trees) to pseudovarieties of finite algebras,
form the backbone of algebraic language theory. Numerous such correspondences
are known in the literature. We demonstrate that they all arise from the same
recipe: one models languages and the algebras recognizing them by monads on an
algebraic category, and applies a Stone-type duality. Our main contribution is
a variety theorem that covers e.g. Wilke's and Pin's work on
$\infty$-languages, the variety theorem for cost functions of Daviaud,
Kuperberg, and Pin, and unifies the two previous categorical approaches of
Boja\'nczyk and of Ad\'amek et al. In addition we derive a number of new
results, including an extension of the local variety theorem of Gehrke,
Grigorieff, and Pin from finite to infinite words.


  In this paper, the deductive system for double propositional logic DL and
gamma DL existential graphs are presented. It rigorously proves the consistency
of the DL and that the DL theorems correspond exactly to the valid existential
graphs of gamma DL. When the language of DL is restricted to the language of
classical propositional logic, the restriction associated with gamma DL
coincides with the valid existential graphs of Charles Sanders Peirce's alpha
system. It turns out that intuitionistic propositional logic theorems are DL
theorems; furthermore, when the language of DL is restricted to the language of
IL, the restriction associated with gamma DL coincides with the valid
existential graphs of Arnold Oostra's intuitionistic alpha system. As a
consequence, it is inferred that gamma LD has as particular cases, the alpha
existential graphs of LC and LI. Finally, in DL, the Aristotelian definitions
of truth and falsity are derived, with which the ability of DL to solve a
version of the liar paradox, where LC and LI fail, is illustrated.


  W. A. Moens proved that a Lie algebra is nilpotent if and only if it admits
an invertible Leibniz-derivation. In this paper we show that with the
definition of Leibniz-derivation from W. A. Moens the similar result for non
Lie Leibniz algebras is not true. Namely, we give an example of non nilpotent
Leibniz algebra which admits an invertible Leibniz-derivation. In order to
extend the results of paper W. A. Moens for Leibniz algebras we introduce a
definition of Leibniz-derivation of Leibniz algebras which agrees with
Leibniz-derivation of Lie algebras case. Further we prove that a Leibniz
algebra is nilpotent if and only if it admits an invertible Leibniz-derivation.
Moreover, the result that solvable radical of a Lie algebra is invariant with
respect to a Leibniz-derivation was extended to the case of Leibniz algebras.


  Chaotic cryptography is based on the properties of chaos as source of
entropy. Many different schemes have been proposed to take advantage of those
properties and to design new strategies to encrypt information. However, the
right and efficient use of chaos in the context of cryptography requires a
thorough knowledge about the dynamics of the selected chaotic system. Indeed,
if the final encryption system reveals enough information about the underlying
chaotic system it could be possible for a cryptanalyst to get the key, part of
the key or some information somehow equivalent to the key just analyzing those
dynamical properties leaked by the cryptosystem. This paper shows what those
dynamical properties are and how a cryptanalyst can use them to prove the
inadequacy of an encryption system for the secure exchange of information. This
study is performed through the introduction of a series of mathematical tools
which should be the basic framework of cryptanalysis in the context of digital
chaos-based cryptography.


  We study the list chromatic number of Cartesian products of graphs through
the Alon-Tarsi number as defined by Jensen and Toft (1995) in their seminal
book on graph coloring problems. The Alon-Tarsi number of $G$, $AT(G)$, is the
smallest $k$ for which there is an orientation, $D$, of $G$ with max indegree
$k\!-\!1$ such that the number of even and odd circulations contained in $D$
are different. It is known that $\chi(G) \leq \chi_\ell(G) \leq \chi_p(G) \leq
AT(G)$, where $\chi(G)$ is the chromatic number, $\chi_\ell(G)$ is the list
chromatic number, and $\chi_p(G)$ is the paint number of $G$. In this paper we
find families of graphs $G$ and $H$ such that $\chi(G \square H) = AT(G \square
H)$, reducing this sequence of inequalities to equality. We show that the
Alon-Tarsi number of the Cartesian product of an odd cycle and a path is always
equal to 3. This result is then extended to show that if $G$ is an odd cycle or
a complete graph and $H$ is a graph on at least two vertices containing the
Hamilton path $w_1, w_2, \ldots, w_n$ such that for each $i$, $w_i$ has a most
$k$ neighbors among $w_1, w_2, \ldots, w_{i-1}$, then $AT(G \square H) \leq
\Delta(G)+k$ where $\Delta(G)$ is the maximum degree of $G$. We discuss other
extensions for $G \square H$, where $G$ is such that $V(G)$ can be partitioned
into odd cycles and complete graphs, and $H$ is a graph containing a
Hamiltonian path. We apply these bounds to get chromatic-choosable Cartesian
products, in fact we show that these families of graphs have $\chi(G) = AT(G)$,
improving previously known bounds.


  Recent measurements of cosmic-ray electron and positron fluxes by PAMELA and
ATIC experiments may indicate the existence of annihilating dark matter with
large annihilation cross section. We discuss its possible relation to other
astrophysical/cosmological observations : gamma-rays, neutrinos, and big-bang
nucleosynthesis. It is shown that they give stringent constraints on some
annihilating dark matter models.


  We report the photometric observations of an SU UMa-type dwarf nova VW CrB
during two superoutbursts in 2001 and 2003 and a normal outburst in 2003.
Superhumps with a period of 0.07287(1) d were observed during the 2003
superoutburst. The change rate of the superhump period was positive. During the
normal outburst, there are some hint of modulation up to a 0.2-mag amplitude.
However, any periodicity was not found. The recurrence cycles of the normal
outburst and the superoutburst, and the distance were estimated to be > ~50 d,
270-500 d, and 690(+230, -170) pc, respectively. These recurrence cycles are
usual values for an SU UMa-type dwarf nova having this superhump period. The
superhump period of VW CrB was the longest among those of the SU UMa stars with
positive derivatives of the superhump period. The coverage of our observations
was, however, not enough, and the variation of the Psh change rate of VW CrB is
still unknown. A superhump regrowth and a brightening were seen near the end of
the plateau phase. Measuring the deviation of the start timings of the
brightening and the superhump regrowth (>2 days in VW CrB) will be a key to
reveal the mechanism of these phenomena.


  We investigate the effects of the nearly fulfilled Efimov conditions on the
properties of three-body resonances. Using the hyper-spheric adiabatic
expansion method we compute energy distributions of fragments in a three-body
decay of a nuclear resonance. As a realistic example we investigate the 1-
state in the halo nucleus 11Li within a three-body 9Li+n+n model.
Characteristic features appear as sharp peaks in the energy distributions.
Their origin, as in the Efimov effect, is in the large two-body s-wave
scattering lengths between the pairs of fragments.


  There has recently been ample interest in the question of which sets can be
represented by linear matrix inequalities (LMIs). A necessary condition is that
the set is rigidly convex, and it has been conjectured that rigid convexity is
also sufficient. To this end Helton and Vinnikov conjectured that any real zero
polynomial admits a determinantal representation with symmetric matrices. We
disprove this conjecture. By relating the question of finding LMI
representations to the problem of determining whether a polymatroid is
representable over the complex numbers, we find a real zero polynomial such
that no power of it admits a determinantal representation. The proof uses
recent results of Wagner and Wei on matroids with the half-plane property, and
the polymatroids associated to hyperbolic polynomials introduced by Gurvits.


  Instantons, which are non-perturbative solutions to Yang-Mills equations,
provide a signal for the occurrence of quantum tunneling between distinct
classes of vacua. They can give rise to decays of particles otherwise
forbidden. Using data collected at the Pierre Auger Observatory, we search for
signatures of such instanton-induced processes that would be suggestive of
super-heavy particles decaying in the Galactic halo. These particles could have
been produced during the post-inflationary epoch and match the relic abundance
of dark matter inferred today. The non-observation of the signatures searched
for allows us to derive a bound on the reduced coupling constant of gauge
interactions in the dark sector: $\alpha_X \lesssim 0.09$, for $10^{9} \lesssim
M_X/{\rm GeV} < 10^{19}$. Conversely, we obtain that, for instance, a reduced
coupling constant $\alpha_X = 0.09$ excludes masses $M_X \gtrsim 3\times
10^{13}~$GeV. In the context of dark matter production from gravitational
interactions alone, we illustrate how these bounds are complementary to those
obtained on the Hubble rate at the end of inflation from the non-observation of
tensor modes in the cosmological microwave background.


  We present a complete classification of the electron-electron interaction in
chaotic quantum dots based on expansion in inverse powers of $1/M$, the number
of the electron states in the Thouless window, $M \simeq k_F R$. This
classification is quite universal and extends and enlarges the universal non
interacting RMT statistical ensembles. We show that existing Coulomb blockade
peak spacing data for $B=0$ and $B\ne 0$ is described quite accurately by the
interacting GSE and by its extension to $B\ne 0$. The bimodal structure
existing in the interacting GUE case is completely washed out by the combined
effect of the spin orbit, pairing and higher order residual interactions.


  Due to the highly inhomogeneous distributions of refractive indexes, light
propagation in complex media such as biological tissue experiences multiple
light scattering events. The suppression and control of multiple light
scattering events are investigated because they offer the possibility of
optical focusing and imaging through biological tissues, and they may open new
avenues for diagnosis and treatment of several human diseases. In order to
provide insight into how new optical techniques can address the issues of
multiple light scattering in biomedical applications, the recent progress in
optical wavefront-shaping techniques is summarized.


  In this paper we consider a simple algebraic structure --- sets with a single
endofunction. We shall see that from the point of view of limits, even this
simplest case is both interesting and difficult. Nevertheless we obtain the
shape of limit objects in the full generality, and we prove the inverse theorem
in the easiest case of quantifier-free limits.


  In the recent decades of particle accelerator R&D area, fixed field
alternating gradient (FFAG) accelerator has become a highlight for some
advantages of its higher beam intensity and lower cost, although there are
still some technical challenges. In this paper, FFAG accelerator is adopted to
accelerate helium ion beam on the one hand for the study of helium
embrittlement on fusion reactor envelope material and on the other hand for
promoting the conception research and design of FFAG accelerator and exploring
the possibility of developing high power FFAG accelerators. The conventional
period focusing unit of helium ion FFAG accelerator and three-dimensional model
of the large aperture combinatorial magnet by OPERA-TOSCA are given. For low
energy and low revolution frequency, induction acceleration is proposed to
replace conventional radio frequency(RF) acceleration for helium ion FFAG
accelerator, which avoids the potential breakdown of acceleration field caused
by wake field and improves the acceleration repetition frequency to gain higher
beam intensity. The main parameters and three-dimensional model of induction
cavity are given. Two special constraint waveforms are proposed to refrain from
particle accelerating time slip({\Delta}T) caused by accelerating voltage drop
of flat top and energy deviation. The particle longitudinal motion in two
waveforms is simulated.


  Developing an automatic signature verification system is challenging and
demands a large number of training samples. This is why synthetic handwriting
generation is an emerging topic in document image analysis. Some handwriting
synthesizers use the motor equivalence model, the well-established hypothesis
from neuroscience, which analyses how a human being accomplishes movement.
Specifically, a motor equivalence model divides human actions into two steps:
1) the effector independent step at cognitive level and 2) the effector
dependent step at motor level. In fact, recent work reports the successful
application to Western scripts of a handwriting synthesizer, based on this
theory. This paper aims to adapt this scheme for the generation of synthetic
signatures in two Indic scripts, Bengali (Bangla), and Devanagari (Hindi). For
this purpose, we use two different online and offline databases for both
Bengali and Devanagari signatures. This paper reports an effective synthesizer
for static and dynamic signatures written in Devanagari or Bengali scripts. We
obtain promising results with artificially generated signatures in terms of
appearance and performance when we compare the results with those for real
signatures.


  The weighted entropy $H^{\rm w}_\phi (X)=H^{\rm w}_\phi (f)$ of a random
variable $X$ with values $x$ and a probability-mass/density function $f$ is
defined as the mean value ${\mathbb E} I^{\rm w}_\phi(X)$ of the weighted
information $I^{\rm w}_\phi (x)=-\phi (x)\log\,f(x)$. Here $x\mapsto\phi
(x)\in{\mathbb R}$ is a given weight function (WF) indicating a 'value' of
outcome $x$. For an $n$-component random vector
${\mathbf{X}}_0^{n-1}=(X_0,\ldots ,X_{n-1})$ produced by a random process
${\mathbf{X}}=(X_i,i\in{\mathbb Z})$, the weighted information $I^{\rm
w}_{\phi_n}({\mathbf x}_0^{n-1})$ and weighted entropy $H^{\rm
w}_{\phi_n}({\mathbf{X}}_0^{n-1})$ are defined similarly, with an WF
$\phi_n({\mathbf x}_0^{n-1})$. Two types of WFs $\phi_n$ are considered, based
on additive and a multiplicative forms ($\phi_n({\mathbf
x}_0^{n-1})=\sum\limits_{i=0}^{n-1}{\varphi} (x_i)$ and $\phi_n({\mathbf
x}_0^{n-1})=\prod\limits_{i=0}^{n-1}{\varphi} (x_i)$, respectively). The focus
is upon ${\it rates}$ of the weighted entropy and information, regarded as
parameters related to ${\mathbf{X}}$. We show that, in the context of
ergodicity, a natural scale for an asymptotically additive/multiplicative WF is
$\frac{1}{n^2}H^{\rm w}_{\phi_n}({\mathbf{X}}_0^{n-1})$ and
$\frac{1}{n}\log\;H^{\rm w}_{\phi_n}({\mathbf{X}}_0^{n-1})$, respectively. This
gives rise to ${\it primary}$ ${\it rates}$. The next-order terms can also be
identified, leading to ${\it secondary}$ ${\it rates}$. We also consider
emerging generalisations of the Shannon-McMillan-Breiman theorem.


  We consider the flow of an upper convected Maxwell fluid in the limit of high
Weissenberg and Reynolds number. In this limit, the no-slip condition cannot be
imposed on the solutions. We derive equations for the resulting boundary layer
and prove the well-posedness of these equations. A transformation to Lagrangian
coordinates is crucial in the argument.


  We present results from magnetic monopoles in $SU(2)$ lattice gauge theory at
finite temperature. The lattices are $16^{3}\times N_{t}$, for
$N_{t}=4,6,8,12$, at $\beta=2.5115$. Quantities discussed are: the spacial
string tension, Polyakov loops, and the screening of timelike and spacelike
magnetic currents.


  We generalize to vector bundles the techniques introduced for line bundles in
prior work of the author with Liu, Osserman and Zhang. We then use this method
to prove the injectivity of the Petri map for vector bundles and the
surjectivity of a map related to deformation theory of Poincar\'e sheaves.


  Strongly correlated Fermi systems are among the most intriguing and
fundamental systems in physics. We show that the herbertsmithite ZnCu3(OH)6Cl2
can be viewed as a new type of strongly correlated electrical insulator that
possesses properties of heavy-fermion metals with one exception: it resists the
flow of electric charge. We demonstrate that herbertsmithite's low temperature
properties are defined by a strongly correlated quantum spin liquid made with
such hypothetic particles as fermionic spinons which carry spin 1/2 and no
charge. Our calculations of its thermodynamic and relaxation properties are in
good agreement with recent experimental facts and allow us to reveal their
scaling behavior which strongly resembles that observed in heavy-fermion
metals. Analysis of the dynamic magnetic susceptibility of strongly correlated
Fermi systems suggests that there exist at least two types of its scaling.


  We consider a model Hamiltonian with two SU(4) fermions per site on a square
lattice, showing a competition between bilinear and biquadratic interactions.
This model has generated interest due to possible realizations in ultracold
atom experiments and existence of spin liquid ground states. Using a basis
transformation, we show that part of the phase diagram is amenable to quantum
Monte Carlo simulations without a sign problem. We find evidence for spin
nematic and valence bond crystalline phases, which are separated by a weak
first order phase transition. A U(1) symmetry is found to emerge in the valence
bond crystal histograms, suggesting proximity to a deconfined quantum critical
point. Our results are obtained with the help of a loop algorithm which allows
large-scale simulations of bilinear-biquadratic SO(N ) models on arbitrary
lattices in a certain parameter regime.


  When gauge field theory coherent states for loop quantum gravity (LQG) were
introduced, an optimized semiclassical proper length emerged, corresponding to
the edge length $\epsilon$ of a graph embedded in a given classical geometry.
Here $\epsilon$ is explored in more detail. $\epsilon$ at the Earth's surface
is found to lie between 100 $\mu $m and 0.7 m. The implied quantum fluctuating
space-time strain amplitude and noise spectrum are estimated to be $4\; 1/2$
orders smaller than the current experimental detectability. However, such a
macroscopic $\epsilon $ makes regularization of the semiclassical
electromagnetic Hamiltonian problematic for photon wavelengths shorter than
$\epsilon$. The origin of a large $\epsilon$ is traced to an edge-wise tensor
product of independent edge-based coherent states for the whole graph state.
This provides physical grounds for recently proposed collective coherent
states, where $\epsilon$ acquires the interpretation of a sliding scale. A new
proper distance $\xi$ emerges as the characteristic length of semiclassical
LQG. $\xi$ will affect the LQG photon vacuum dispersion relations, and is also
accessible to current measurements of space-time strain. Matter interactions
may also affect $\xi$.


  We show that for an alternating pretzel knot K the canonical genera of its
Whitehead doubles W(K) are equal to the crossing number c(K) of K, verifying a
conjecture of Tripp in the case of these knots.


  Short period sdB binaries with cool companions are crucial to understand
pre-CV evolution, because they will evolve into cataclysmic variables, when the
sdB will have left the extended horizontal branch. Recently we discovered the
sixth such system, HS 2333+3927, consisting of an sdB star and an M dwarf
(period: 0.172 d) with a very strong reflection effect, but no eclipses. The
reflection is stronger than in any of the other similar systems which renders a
quantitative spectral analysis very difficult because the Balmer line profiles
may be disturbed by the reflected light. A spectroscopic analysis results in
Teff = 36500 K, log g = 5.70, and log (n_He/n_H) = -2.15. Mass-radius relations
were derived from the results of the analysis of light and radial-velocity
curves. Comparison with the mass-radius relation derived from the surface
gravity of the sdB star favours a rather low mass of 0.38 Msun for the primary.
The mass of the companion is 0.29 M_sun. HS 2333+3927 is the only known sdB+dM
system with a period above the CV period gap.


  Non-Hermitian, tight-binding $\mathcal{PT}$-symmetric models are extensively
studied in the literature. Here, we investigate two forms of non-Hermitian
Hamiltonians to study the $\mathcal{PT}$-symmetry breaking thresholds and
features of corresponding surfaces of exceptional points (EPs). They include
one-dimensional chains with uniform or 2-periodic tunnelling amplitudes, one
pair of balanced gain and loss potentials $\Delta\pm\i\gamma$ at
parity-symmetric sites, and periodic or open boundary conditions. By
introducing a Hermitian detuning potential, we obtain the dependence of the
$\mathcal{PT}$-threshold, and therefore the exceptional-point curves, in the
parameter space of detuning and gain-loss strength. By considering several such
examples, we show that EP curves of a given order generically have cusp-points
where the order of the EP increases by one. In several cases, we obtain
explicit analytical expressions for positive-definite intertwining operators
that can be used to construct a complex extension of quantum theory by
re-defining the inner product. Taken together, our results provide a detailed
understanding of detuned tight-binding models with a pair of gain-loss
potentials.


  Numerical simulation has been conducted for the chaotic flow in a 3D
closed-loop pulsating heat pipe (PHP). Heat flux and constant temperature
boundary conditions were applied for evaporator and condenser sections,
respectively. Water and ethanol were used as working fluids. Volume of Fluid
(VOF) method has been employed for two-phase flow simulation. Spectral analysis
of temperature time series was carried out using Power Spectrum Density (PSD)
method. Existence of dominant peak in PSD diagram indicated periodic or
quasi-periodic behavior in temperature oscillations at particular frequencies.
Correlation dimension values for ethanol as working fluid was found to be
higher than that for water under the same operating conditions. Similar range
of Lyapunov exponent values for the PHP with water and ethanol as working
fluids indicated strong dependency of Lyapunov exponent to the structure and
dimensions of the PHP. An O-ring structure pattern was obtained for
reconstructed 3D attractor at periodic or quasi-periodic behavior of
temperature oscillations. Minimum thermal resistance of 0.85 degree/W and 0.88
degree/W were obtained for PHP with water and ethanol, respectively. Simulation
results showed good agreement with experimental results from other work under
the same operating conditions.