  The question about the existence and characterization of bounded solutions to
linear functional-differential equations with both advanced and delayed
arguments was posed in early 1970s by T. Kato in connection with the analysis
of the pantograph equation, y'(x)=ay(qx)+by(x). In the present paper, we answer
this question for the balanced generalized pantograph equation of the form -a_2
y''(x)+a_1 y'(x)+y(x)=int_0^infty y(qx) m(dq), where a_1 > or = 0, a_2 > or =
0, a_1^2+a_2^2>0, and m is a probability measure. Namely, setting
K:=int_0^infty ln(q) m(dq), we prove that if K < or = 0 then the equation does
not have nontrivial (i.e., nonconstant) bounded solutions, while if K>0 then
such a solution exists. The result in the critical case, K=0, settles a
long-standing problem. The proof exploits the link with the theory of Markov
processes, in that any solution of the balanced pantograph equation is an
L-harmonic function relative to the generator L of a certain diffusion process
with "multiplication" jumps. The paper also includes three "elementary" proofs
for the simple prototype equation y'(x)+y(x)=(1/2)y(qx)+(1/2)y(x/q), based on
perturbation, analytical, and probabilistic techniques, respectively, which may
appear useful in other situations as efficient exploratory tools.


  There is abundant evidence that heating processes in the central regions of
elliptical galaxies has both prevented large-scale cooling flows and assisted
in the expulsion of metal rich gas. We now know that each such spheroidal
system harbors in its core a massive black hole weighing approximately 0.13% of
the mass in stars and also know that energy was emitted by each of these black
holes with an efficiency exceeding 10% of its rest mass. Since, if only 0.5% of
that radiant energy were intercepted by the ambient gas, its thermal state
would be drastically altered, it is worth examining in detail the interaction
between the out-flowing radiation and the equilibrium or inflowing gas. On the
basis of detailed hydrodynamic computations we find that relaxation
oscillations are to be expected with the radiative feedback quite capable of
regulating both the growth of the central black hole and also the density and
thermal state of the gas in the galaxy. Mechanical input of energy by jets may
assist or dominate over these radiative effects. We propose specific
observational tests to identify systems which have experienced strong bursts of
radiative heating from their central black holes.


  In this paper, we study the problem of identifying the impulse response of a
linear time invariant (LTI) dynamical system from the knowledge of the input
signal and a finite set of noisy output observations. We adopt an approach
based on regularization in a Reproducing Kernel Hilbert Space (RKHS) that takes
into account both continuous and discrete time systems. The focus of the paper
is on designing spaces that are well suited for temporal impulse response
modeling. To this end, we construct and characterize general families of
kernels that incorporate system properties such as stability, relative degree,
absence of oscillatory behavior, smoothness, or delay. In addition, we discuss
the possibility of automatically searching over these classes by means of
kernel learning techniques, so as to capture different modes of the system to
be identified.


  The gravitational effects in the relativistic quantum mechanics are
investigated in a relativistically derived version of Heaviside's speculative
Gravity (in flat space-time) named here as Maxwellian Gravity. The standard
Dirac's approach to the intrinsic spin in the fields of Maxwellian Gravity
yields the gravitomagnetic moment of a Dirac (spin 1/2) particle exactly equals
to its intrinsic spin. Violation of The Equivalence Principle (both at
classical and quantum mechanical level) in the relativistic domain has also
been reported in this work.


  Electron scattering measurements from high-momentum nucleons in nuclei at
SLAC and Jefferson Lab (JLab) have shown that these nucleons are generally
associated with two-nucleon short-range correlations (2N-SRCs). These SRCs are
formed when two nucleons in the nucleus interact at short distance via the
strong tensor attraction or repulsive core of the NN potential. A series of
measurements at JLab have mapped out the A dependence and isospin dependence of
2N-SRCs, and have begun to map out their momentum structure. However, we do not
yet know if 3N-SRCs, similar high-momentum configurations of three nucleons,
play an important role in nuclei. We summarize here previous attempts to
isolate 3N-SRCs, go over the limitations of these previous attempts, and
discuss the present and near-term prospects for searching for 3N-SRCs, mapping
out their A dependence in nuclei, and constraining their isospin and momentum
structure.


  The influence of surface small scale magnetic field on the heating of PSR
J0250+5854 polar cap is considered. It is assumed that polar cap is heated only
by reverse positrons, accelerated in pulsar diode. It is supposed that pulsar
diode is in stationary state with lower plate nearby the star surface (polar
cap model), occupies all pulsar tube crosssection and operates in regime of
steady space charge limited electron flow. The influence of small scale
magnetic field on electric field inside pulsar diode is taken into account. To
calculate the electron-positron pairs production rate we take into account only
the curvature radiation of primary electrons and its absorption in magnetic
field. It is assumed that part of electro-positron pairs may be created in
bound state (positronium). And later such positroniums are photoionized by
thermal photons from star surface.


  Inclusive momentum spectra are measured for all charged particles and for
each of $\pi^{\pm}$, $K^{\pm}$, $K^0/\bar{K^0}$, and $p/\bar{p}$ in hadronic
events produced via $e^+e^-$ annihilation at $\sqrt{s}$=58GeV . The measured
spectra are compared with QCD predictions based on the modified leading log
approximation(MLLA). The MLLA model reproduces the measured spectra well. The
energy dependence of the peak positions of the spectra is studied by comparing
the measurements with those at other energies. The energy dependence is also
well described by the MLLA model.


  Using printed photograph and replaying videos of biometric modalities, such
as iris, fingerprint and face, are common attacks to fool the recognition
systems for granting access as the genuine user. With the growing online
person-to-person shopping (e.g., Ebay and Craigslist), such attacks also
threaten those services, where the online photo illustration might not be
captured from real items but from paper or digital screen. Thus, the study of
anti-spoofing should be extended from modality-specific solutions to
generic-object-based ones. In this work, we define and tackle the problem of
Generic Object Anti-Spoofing (GOAS) for the first time. One significant cue to
detect these attacks is the noise patterns introduced by the capture sensors
and spoof mediums. Different sensor/medium combinations can result in diverse
noise patterns. We propose a GAN-based architecture to synthesize and identify
the noise patterns from seen and unseen medium/sensor combinations. We show
that the procedure of synthesis and identification are mutually beneficial. We
further demonstrate the learned GOAS models can directly contribute to
modality-specific anti-spoofing without domain transfer. The code and GOSet
dataset are available at cvlab.cse.msu.edu/project-goas.html.


  We consider a quantum many-body system - the Bose-Hubbard system on three
sites - which has a classical limit, and which is neither strongly chaotic nor
integrable but rather shows a mixture of the two types of behavior. We compare
quantum measures of chaos (eigenvalue statistics and eigenvector structure) in
the quantum system, with classical measures of chaos (Lyapunov exponents) in
the corresponding classical system. As a function of energy and interaction
strength, we demonstrate a strong overall correspondence between the two cases.
In contrast to both strongly chaotic and integrable systems, the largest
Lyapunov exponent is shown to be a multi-valued function of energy.


  Part I. We prove a one-to-one correspondence between differential symmetry
breaking operators for equivariant vector bundles over two homogeneous spaces
and certain homomorphisms for representations of two Lie algebras, in
connection with branching problems of the restriction of representations. We
develop a new method (F-method) based on the algebraic Fourier transform for
generalized Verma modules, which characterizes differential symmetry breaking
operators by means of certain systems of partial differential equations. In
contrast to the setting of real flag varieties, continuous symmetry breaking
operators of Hermitian symmetric spaces are proved to be differential operators
in the holomorphic setting. In this case symmetry breaking operators are
characterized by differential equations of second order via the F-method.
  Part II. Rankin--Cohen brackets are symmetry breaking operators for the
tensor product of two holomorphic discrete series representations of SL(2,R).
We address a general problem to find explicit formulae for such intertwining
operatorsin the setting of multiplicity-free branching laws for reductive
symmetric pairs. We discover explicit formulae of new differential symmetry
breaking operators for all the six different complex geometries arising from
semisimple symmetric pairs of split rank one, and reveal an intrinsic reason
why the coefficients of orthogonal polynomials appear in these operators
(Rankin--Cohen type) in the three geometries and why normal derivatives are
symmetry breaking operators in the other three cases. Further, we analyze a new
phenomenon that the multiplicities in the branching laws of Verma modules may
jump up at singular parameters.


  We explore new implications of the $M(r,s)$ and $M^*(r,s)$ properties for
Banach spaces. We show that a Banach space $X$ satisfying property $M(1,s)$ for
some $0<s\leq 1$, admitting a point $x_{0}$ in its unit sphere at which the
relative weak and norm topologies agree, satisfies the generalized Gossez-Lami
Dozo property. We establish sufficient conditions, in terms of the $(r,
s)$-Lipschitz weak$^*$ Kadec-Klee property on a Banach space $X$, to guarantee
that its dual space satisfies the UKK$^*$ property. We determine appropriate
conditions to assure that a Banach space $X$ satisfies the $(r, s)$-Lipschitz
weak$^*$ Kadec-Klee property. These results are applied to prove that every
spin factor satisfies the UKK property, and consequently, the KKP and the UKK
properties are equivalent for real and complex JB$^*$-triples.


  We show that for any union-closed family $\mathcal{F} \subseteq 2^{[n]},
\mathcal{F} \neq \{\emptyset\}$, there exists an $i \in [n]$ which is contained
in a $0.01$ fraction of the sets in $\mathcal{F}$. This is the first known
constant lower bound, and improves upon the
$\Omega(\log_2(|\mathcal{F}|)^{-1})$ bounds of Knill and W\'{o}jick. Our result
follows from an information theoretic strengthening of the conjecture.
Specifically, we show that if $A, B$ are independent samples from a
distribution over subsets of $[n]$ such that $Pr[i \in A] < 0.01$ for all $i$
and $H(A) > 0$, then $H(A \cup B) > H(A)$.


  In the model of de Sitter gauge theory of gravity, the empty homogenous and
isotropic spacetimes with constant curvature scalar and nonvanishing homogenous
and isotropic torsion must have de Sitter metrics. The static de Sitter
spacetime with static, O(3)-symmetric, vector torsion is the only spherically
symmetric, vacuum solution with the metric of the form $g_{\mu\nu}={\rm
diag}(A^2(r),-B^2(r),-r^2,-r^2\sin^2\th)$. The expressions of the torsion for
different de Sitter spacetimes are presented. They are different from one to
another. The properties of different de Sitter spacetimes with torsion are also
studied.


  The influence of carrier type on superconductivity has been an important
issue for understanding both conventional and unconventional superconductors
[1-7]. For elements that superconduct, it is known that hole-carriers govern
the superconductivity for transition and main group metals [8-10]. The role of
hole-carriers in elements that are not normally conducting but can be converted
to superconductors, however, remains unclear due to the lack of experimental
data. Here we report the first in-situ high pressure Hall effect measurements
on single crystal black phosphorus, measured up to ~ 50 GPa, and find a
correlation between the Hall coefficient and the superconducting transition
temperature (TC). Our results reveal that hole-carriers play a vital role in
developing superconductivity and enhancing TC. Importantly, we also find a
Lifshitz transition in the high-pressure cubic phase at ~17.2GPa, which
uncovers the origin of a puzzling valley in the superconducting TC-pressure
phase diagram. These results offer insight into the role of hole-carriers in
developing superconductivity in simple semiconducting solids under pressure.


  A model for opinion dynamics (Model I) has been recently introduced in which
the binary opinions of the individuals are determined according to the size of
their neighboring domains (population having the same opinion). The coarsening
dynamics of the equivalent Ising model shows power law behavior and has been
found to belong to a new universality class with the dynamic exponent $z=1.0
\pm 0.01$ and persistence exponent $\theta \simeq 0.235$ in one dimension. The
critical behavior has been found to be robust for a large variety of annealed
disorder that has been studied. Further, by mapping Model I to a system of
random walkers in one dimension with a tendency to walk towards their nearest
neighbour with probability $\epsilon$, we find that for any $\epsilon > 0.5$,
the Model I dynamical behaviour is prevalent at long times.


  Causal discovery in time series is a rapidly evolving field with a wide
variety of applications in other areas such as climate science and
neuroscience. Traditional approaches assume a stationary causal graph, which
can be adapted to nonstationary time series with time-dependent effects or
heterogeneous noise. In this work we address nonstationarity via
regime-dependent causal structures. We first establish identifiability for
high-order Markov Switching Models, which provide the foundations for
identifiable regime-dependent causal discovery. Our empirical studies
demonstrate the scalability of our proposed approach for high-order
regime-dependent structure estimation, and we illustrate its applicability on
brain activity data.


  As the SALT High Resolution Spectrograph completion is nearing we plan to
extend the Pennsylvania-Torun Planets Search (PTPS) with HET to the southern
hemisphere. Due to overlap of the skies available for both HET and SALT in the
declination range (+10, -10) deg some cooperation and immediate follow up is
possible. Here we present, as an example, a $\sim$ 1000 star sample of evolved
stars for the future SALT Planet Search.


  Using the method of shape invariant potentials, a number of exact solutions
of one dimensional effective mass Schrodinger equation are obtained. The
solutions with equi-spaced spectrum are discussed in detail.


  A survey is made of several aspects of the dynamics of networks, with special
emphasis on unsupervised learning processes, non-Gaussian data analysis and
pattern recognition in networks with complex nodes.


  In this article, we study the relation between Sobolev-type embeddings for
Sobolev spaces or Besov spaces or Triebel-Lizorkin spaces defined either on a
doubling or on a geodesic metric measure space and lower bound for measure of
balls either in the whole space or in a domain inside the space.


  Magnetization reversal of individual, isolated high-aspect-ratio Fe
nanoparticles with diameters comparable to the magnetic exchange length is
studied by high-sensitivity submicron Hall magnetometry. For a Fe nanoparticle
with diameter of 5 nm, the magnetization reversal is found to be an incoherent
process with localized nucleation assisted by thermal activation, even though
the particle has a single-domain static state. For a larger elongated Fe
nanoparticle with a diameter greater than 10 nm, the inhomogeneous magnetic
structure of the particle plays important role in the reversal process.


  Previous divide-and-conquer segmentation analyses of DNA sequences do not
provide a satisfactory stopping criterion for the recursion. This paper
proposes that segmentation be considered as a model selection process. Using
the tools in model selection, a limit for the stopping criterion on the relaxed
end can be determined. The Bayesian information criterion, in particular,
provides a much more stringent stopping criterion than what is currently used.
Such a stringent criterion can be used to delineate larger DNA domains. A
relationship between the stopping criterion and the average domain size is
empirically determined, which may aid in the determination of isochore borders.


  The singular density of states and the two Fermi wavevectors resulting from a
ring-shaped or "Mexican hat" valence band give rise to unique trends in the
charged impurity scattering rates and charged impurity limited mobilities. Ring
shaped valence bands are common features of many monolayer and few-layer
two-dimensional materials including the III-VI materials GaS, GaSe, InS, and
InSe. The wavevector dependence of the screening, calculated within the random
phase approximation, is so strong that it is the dominant factor determining
the overall trends of the scattering rates and mobilities with respect to
temperature and hole density. Charged impurities placed on the substrate and in
the 2D channel are considered. The different wavevector dependencies of the
bare Coulomb potentials alter the temperature dependence of the mobilities.
Moving the charged impurities 5 $\AA$ from the center of the channel to the
substrate increases the mobility by an order of magnitude.


  Relationships are essential to our happiness and wellbeing. The dissolution
of a relationship, the final stage of relationship's lifecycle and one of the
most stressful events in an individual's life, can have profound and
long-lasting impacts on people. With the breakup process increasingly
facilitated by computer-mediated communication (CMC), and the likely future
influence of AI-mediated communication (AIMC) tools, we conducted a
semi-structured interview study with 21 participants. We aim to understand: 1)
the current role of technology in the breakup process, 2) the needs and support
individuals have during the process, and 3) how AI might address these needs.
Our research shows that people have distinct needs at various stages of ending
a relationship. Presently, technology is used for information gathering and
community support, acting as a catalyst for breakups, enabling ghosting and
blocking, and facilitating communication. Participants anticipate that AI could
aid in sense-making of their relationship leading up to the breakup, act as a
mediator, assist in crafting appropriate wording, tones, and language during
breakup conversations, and support companionship, reflection, recovery, and
growth after a breakup. Our findings also demonstrate an overlap between the
breakup process and the Transtheoretical Model (TTM) of behavior change.
Through the lens of TTM, we explore the potential support and affordances AI
could offer in breakups, including its benefits and the necessary precautions
regarding AI's role in this sensitive process.


  FastFlow is a structured parallel programming framework targeting shared
memory multicores. Its layered design and the optimized implementation of the
communication mechanisms used to implement the FastFlow streaming networks
provided to the application programmer as algorithmic skeletons support the
development of efficient fine grain parallel applications. FastFlow is
available (open source) at SourceForge
(http://sourceforge.net/projects/mc-fastflow/). This work introduces FastFlow
programming techniques and points out the different ways used to parallelize
existing C/C++ code using FastFlow as a software accelerator. In short: this is
a kind of tutorial on FastFlow.


  In recent years, deep neural network is widely used in machine learning. The
multi-class classification problem is a class of important problem in machine
learning. However, in order to solve those types of multi-class classification
problems effectively, the required network size should have hyper-linear growth
with respect to the number of classes. Therefore, it is infeasible to solve the
multi-class classification problem using deep neural network when the number of
classes are huge. This paper presents a method, so called Label Mapping (LM),
to solve this problem by decomposing the original classification problem to
several smaller sub-problems which are solvable theoretically. Our method is an
ensemble method like error-correcting output codes (ECOC), but it allows base
learners to be multi-class classifiers with different number of class labels.
We propose two design principles for LM, one is to maximize the number of base
classifier which can separate two different classes, and the other is to keep
all base learners to be independent as possible in order to reduce the
redundant information. Based on these principles, two different LM algorithms
are derived using number theory and information theory. Since each base learner
can be trained independently, it is easy to scale our method into a large scale
training system. Experiments show that our proposed method outperforms the
standard one-hot encoding and ECOC significantly in terms of accuracy and model
complexity.


  The full moments expansion of the joint probability distribution of an
isotropic random field, its gradient and invariants of the Hessian is presented
in 2 and 3D. It allows for explicit expression for the Euler characteristic in
ND and computation of extrema counts as functions of the excursion set
threshold and the spectral parameter, as illustrated on model examples.


  In this paper, we report dynamic Monte Carlo simulations of melting and
crystallization in a single-chain system. Their free energy barriers are
calculated by the umbrella sampling method and can be described well by a
simple expression DeltaF = n Deltaf+sigma (N-n)^(2/3), where n is the amount of
molten bonds, Deltaf is the free energy change of each molten bond from a
crystalline state, N is the chain length, and sigma is the surface free energy
of crystallite. We found that, together with the expression Delta F = n Delta
f+ sigma (N-n)^(1/2) for molecular nucleation, the molecular-weight dependent
properties of the free-energy barriers for polymer primary and secondary
nucleation, in particular, the molecular segregation during crystal growth, can
be reproduced. Then for the mechanism of polymer crystallization, we suggested
a quantitative model of intramolecular nucleation, as a direct development from
the previous qualitative description of molecular nucleation model.


  We use limit cycle oscillators to model Bipolar II disorder, which is
characterized by alternating hypomanic and depressive episodes and afflicts
about one percent of the United States adult population. We consider two
nonlinear oscillator models of a single bipolar patient. In both frameworks, we
begin with an untreated individual and examine the mathematical effects and
resulting biological consequences of treatment. We also briefly consider the
dynamics of interacting bipolar II individuals using weakly-coupled,
weakly-damped harmonic oscillators. We discuss how the proposed models can be
used as a framework for refined models that incorporate additional biological
data. We conclude with a discussion of possible generalizations of our work, as
there are several biologically-motivated extensions that can be readily
incorporated into the series of models presented here.


We discuss a few selected topics in finite temperature field theory.


  Experimental data obtained for PbFe$_{1 / 2}$Ta$_{1 / 2}$O$_{3}$ (PFT) and
NaNbO$_{3}$: Gd (NaNbGd) single crystals show a diffused dielectric
permittivity peak that is inherent to relaxor ferroelectrics. However some
deviations from the normal relaxor properties were also observed and are under
discussion. One of the key features of the relaxors is the existence of the
Burns temperature, at which the polar regions appear. We found out that PFT
shows this feature but the NaNbGd dielectric behavior is different. We analyse
these properties within a phenomenological theory and propose a microscopic
model.


  In continuation to earlier works where the problem of joint information
embedding and lossless compression (of the composite signal) was studied in the
absence \cite{MM03} and in the presence \cite{MM04} of attacks, here we
consider the additional ingredient of protecting the secrecy of the watermark
against an unauthorized party, which has no access to a secret key shared by
the legitimate parties. In other words, we study the problem of joint coding
for three objectives: information embedding, compression, and encryption.Our
main result is a coding theorem that provides a single--letter characterization
of the best achievable tradeoffs among the following parameters: the distortion
between the composite signal and the covertext, the distortion in
reconstructing the watermark by the legitimate receiver, the compressibility of
the composite signal (with and without the key), and the equivocation of the
watermark, as well as its reconstructed version, given the composite signal. In
the attack--free case, if the key is independent of the covertext, this coding
theorem gives rise to a {\it threefold} separation principle that tells that
asymptotically, for long block codes, no optimality is lost by first applying a
rate--distortion code to the watermark source, then encrypting the compressed
codeword, and finally, embedding it into the covertext using the embedding
scheme of \cite{MM03}. In the more general case, however, this separation
principle is no longer valid, as the key plays an additional role of side
information used by the embedding unit.


  Analyzing concentration of large random matrices is a common task in a wide
variety of fields. Given independent random variables, many tools are available
to analyze random matrices whose entries are linear in the variables, e.g. the
matrix-Bernstein inequality. However, in many applications, we need to analyze
random matrices whose entries are polynomials in the variables. These arise
naturally in the analysis of spectral algorithms, e.g., Hopkins et al. [STOC
2016], Moitra-Wein [STOC 2019]; and in lower bounds for semidefinite programs
based on the Sum of Squares hierarchy, e.g. Barak et al. [FOCS 2016], Jones et
al. [FOCS 2021]. In this work, we present a general framework to obtain such
bounds, based on the matrix Efron-Stein inequalities developed by
Paulin-Mackey-Tropp [Annals of Probability 2016]. The Efron-Stein inequality
bounds the norm of a random matrix by the norm of another simpler (but still
random) matrix, which we view as arising by "differentiating" the starting
matrix. By recursively differentiating, our framework reduces the main task to
analyzing far simpler matrices. For Rademacher variables, these simpler
matrices are in fact deterministic and hence, analyzing them is far easier. For
general non-Rademacher variables, the task reduces to scalar concentration,
which is much easier. Moreover, in the setting of polynomial matrices, our
results generalize the work of Paulin-Mackey-Tropp. Using our basic framework,
we recover known bounds in the literature for simple "tensor networks" and
"dense graph matrices". Using our general framework, we derive bounds for
"sparse graph matrices", which were obtained only recently by Jones et al.
[FOCS 2021] using a nontrivial application of the trace power method, and was a
core component in their work. We expect our framework to be helpful for other
applications involving concentration phenomena for nonlinear random matrices.


  This work provides a computable, direct, and mathematically rigorous
approximation to the differential geometry of class manifolds for
high-dimensional data, along with nonlinear projections from input space onto
these class manifolds. The tools are applied to the setting of neural network
image classifiers, where we generate novel, on-manifold data samples, and
implement a projected gradient descent algorithm for on-manifold adversarial
training. The susceptibility of neural networks (NNs) to adversarial attack
highlights the brittle nature of NN decision boundaries in input space.
Introducing adversarial examples during training has been shown to reduce the
susceptibility of NNs to adversarial attack; however, it has also been shown to
reduce the accuracy of the classifier if the examples are not valid examples
for that class. Realistic "on-manifold" examples have been previously generated
from class manifolds in the latent of an autoencoder. Our work explores these
phenomena in a geometric and computational setting that is much closer to the
raw, high-dimensional input space than can be provided by VAE or other black
box dimensionality reductions. We employ conformally invariant diffusion maps
(CIDM) to approximate class manifolds in diffusion coordinates, and develop the
Nystr\"{o}m projection to project novel points onto class manifolds in this
setting. On top of the manifold approximation, we leverage the spectral
exterior calculus (SEC) to determine geometric quantities such as tangent
vectors of the manifold. We use these tools to obtain adversarial examples that
reside on a class manifold, yet fool a classifier. These misclassifications
then become explainable in terms of human-understandable manipulations within
the data, by expressing the on-manifold adversary in the semantic basis on the
manifold.


  An appeal for symmetry is made to build established notions of specific
representation and specific nonlinearity of measurement (often called model
error) into a canonical linear regression model. Additive components are
derived from the trivially complete model M = m. Factor analysis and equation
error motivate corresponding notions of representation and nonlinearity in an
errors-in-variables framework, with a novel interpretation of terms. It is
suggested that a modern interpretation of correlation involves both linear and
nonlinear association.


  There is much discussion of scenarios where the space-time coordinates x^\mu
are noncommutative. The discussion has been extended to include nontrivial
anticommutation relations among spinor coordinates in superspace. A number of
authors have studied field theoretical consequences of the deformation of N=1
superspace arising from nonanticommutativity of coordinates \theta, while
leaving \bar{theta}'s anticommuting. This is possible in Euclidean superspace
only. In this note we present a way to extend the discussion by making both
\theta and \bar{theta} coordinates non-anticommuting in Minkowski superspace.
We present a consistent algebra for the supercoordinates, find a star-product,
and give the Wess-Zumino Lagrangian L_{WZ} within our model. It has two extra
terms due to non(anti)commutativity. The Lagrangian in Minkowski superspace is
always manifestly Hermitian and for L_{WZ} it preserves Lorentz invariance.


  Let a random simplex in a d-dimensional convex body be the convex hull of d+1
random points from the body. We study the following question: As a function of
the convex body, is the expected volume of a random simplex monotone
non-decreasing under inclusion? We show that this holds if d is 1 or 2, and
does not hold if d >= 4. We also prove similar results for higher moments of
the volume of a random simplex, in particular for the second moment, which
corresponds to the determinant of the covariance matrix of the convex body.
These questions are motivated by the slicing conjecture.


  In these proceedings we present recent efforts to understand the energetics
of magnetohydrodynamic (MHD) turbulence driven by the magneto-rotational
instability (MRI). These studies are carried out in the local (shearing box)
approximation using the Athena simulation code. Athena is a higher order
Godunov algorithm based on the piecewise parabolic method (PPM), the corner
transport upwind (CTU) integration algorithm, and the constrained transport
(CT) algorithm for evolving the magnetic field. This algorithm is particularly
suited for these studies owing to the conservation properties of a Godunov
scheme and the particular implementation of the shearing box source terms used
here. We present a variety of calculations which may be compared directly to
previously published results and discuss them in some detail. The only
significant discrepancy found between the results presented here and in the
published literature involves the turbulent heating rate. We observe the
presence of recurrent channel solutions in calculations involving a mean
vertical magnetic field and the associated time lag between the energy
injection and thermalization rate. We also present the results of a shearing
box calculation which includes an optically thin radiative term with a cooling
rate selected to match the turbulent heating rate. Some properties which we
find uniformly present in all of the calculations presented here are
compressible fluctuations, spiral waves and weak shocks. It is found that these
compressible modes dominate the temporal fluctuations in the probability
distribution functions for most of the thermodynamic variables; only the
specific entropy is relatively immune to their effects.


  This paper studies the relationship between disjunctive form, a syntactic
normal form for the modal mu calculus, and the alternation hierarchy. First it
shows that all disjunctive formulas which have equivalent tableau have the same
syntactic alternation depth. However, tableau equivalence only preserves
alternation depth for the disjunctive fragment: there are disjunctive formulas
with arbitrarily high alternation depth that are tableau equivalent to
alternation-free non-disjunctive formulas. Conversely, there are
non-disjunctive formulas of arbitrarily high alternation depth that are tableau
equivalent to disjunctive formulas without alternations. This answers
negatively the so far open question of whether disjunctive form preserves
alternation depth. The classes of formulas studied here illustrate a previously
undocumented type of avoidable syntactic complexity which may contribute to our
understanding of why deciding the alternation hierarchy is still an open
problem.


  According to the holographic principle, the description of a volume of space
can be thought of as encoded on its boundary. Holographic principle establishes
equivalence, or duality, between theoretical description of volume physics,
which involves gravity, and the gravity-free field theory, which describes
physics on its surface. While generally accepted as a theoretical framework, so
far there was no known experimental system which would exhibit explicit
holographic duality and be amenable to direct experimental testing. Here we
demonstrate that nonlinear optics of hyperbolic metamaterials admits such a
dual holographic description. Wave equation which describes propagation of
extraordinary light through the volume of metamaterial exhibits 2+1 dimensional
Lorentz symmetry. The role of time in the corresponding effective 3D Minkowski
spacetime is played by the spatial coordinate aligned with the optical axis of
the material. Nonlinear optical Kerr effect bends this spacetime resulting in
effective gravitational interaction between extraordinary photons. On the other
hand, a holographic dual theory may be formulated on the metamaterial surface,
which describes its nonlinear optics via interaction of cylindrical surface
plasmons possessing conserved charges proportional to their angular momenta.
Potential implications of this duality for superconductivity of hyperbolic
metamaterials are discussed.


  In this paper, we focus on the problem of unsupervised image-sentence
matching. Existing research explores to utilize document-level structural
information to sample positive and negative instances for model training.
Although the approach achieves positive results, it introduces a sampling bias
and fails to distinguish instances with high semantic similarity. To alleviate
the bias, we propose a new sampling strategy to select additional
intra-document image-sentence pairs as positive or negative samples.
Furthermore, to recognize the complex pattern in intra-document samples, we
propose a Transformer based model to capture fine-grained features and
implicitly construct a graph for each document, where concepts in a document
are introduced to bridge the representation learning of images and sentences in
the context of a document. Experimental results show the effectiveness of our
approach to alleviate the bias and learn well-aligned multimodal
representations.


  Recently, there has been substantial progress in image synthesis from
semantic labelmaps. However, methods used for this task assume the availability
of complete and unambiguous labelmaps, with instance boundaries of objects, and
class labels for each pixel. This reliance on heavily annotated inputs
restricts the application of image synthesis techniques to real-world
applications, especially under uncertainty due to weather, occlusion, or noise.
On the other hand, algorithms that can synthesize images from sparse labelmaps
or sketches are highly desirable as tools that can guide content creators and
artists to quickly generate scenes by simply specifying locations of a few
objects. In this paper, we address the problem of complex scene completion from
sparse labelmaps. Under this setting, very few details about the scene (30\% of
object instances) are available as input for image synthesis. We propose a
two-stage deep network based method, called `Halluci-Net', that learns
co-occurence relationships between objects in scenes, and then exploits these
relationships to produce a dense and complete labelmap. The generated dense
labelmap can then be used as input by state-of-the-art image synthesis
techniques like pix2pixHD to obtain the final image. The proposed method is
evaluated on the Cityscapes dataset and it outperforms two baselines methods on
performance metrics like Fr\'echet Inception Distance (FID), semantic
segmentation accuracy, and similarity in object co-occurrences. We also show
qualitative results on a subset of ADE20K dataset that contains bedroom images.


  Optical interferometry is the only technique giving access to milli-arcsecond
(mas) resolution at infrared wavelengths. For Cepheids, this is a powerful and
unique tool to detect the orbiting companions and the circumstellar envelopes
(CSE). CSEs are interesting because they might be used to trace the Cepheid
evolution history, and more particularly they could impact the distance scale.
Cepheids belonging to binary systems offer an unique opportunity to make
progress in resolving the Cepheid mass discrepancy. The combination of
spectroscopic and interferometric measurements will allow us to derive the
orbital elements, distances, and dynamical masses. Here we focus on recent
results using 2- to 6-telescopes beam combiners for the Cepheids X Sgr, T Mon
and V1334 Cyg.


  The observed delay in the arrival times between high and low energy photons
in gamma-ray bursts (GRBs) has been shown by Norris et al. to be correlated to
the absolute luminosity of a GRB. Despite the apparent importance of this
spectral lag, there has yet to be a full explanation of its origin. We put
forth that the lag is directly due to the evolution of the GRB spectra. In
particular, as the energy at which the GRB's $\nu F_{\nu}$ spectra is a maximum
($E_{pk}$) decays through the four BATSE channels, the photon flux peak in each
individual channel will inevitably be offset producing what we measure as lag.
We test this hypothesis by measuring the rate of $E_{pk}$ decay ($\Phi_{o}$)
for a sample of clean single peaked bursts with measured lag. We find a direct
correlation between the decay timescale and the spectral lag, demonstrating the
relationship between time delay of the low energy photons and the decay of
$E_{pk}$. This implies that the luminosity of a GRB is directly related to the
burst's rate of spectral evolution, which we believe begins to reveal the
underlying physics behind the lag-luminosity correlation. We discuss several
possible mechanisms that could cause the observed evolution and its connection
to the luminosity of the burst.


  In this paper a new method is presented for the formulation and solution of
two-time, response-excitation moment equations for a nonlinear dynamical system
excited by colored, Gaussian or non-Gaussian processes. Starting from equations
for the two-time moments (e.g. for Cxy(t,s), Cxx(t,s)), the method uses an
exact time-closure condition, in addition to a Gaussian moment closure, in
order to obtain a closed, non-local in time (causal) subsystem for the one-time
(t=s) moments. After solving this causal system, the two-time moments can be
calculated for all (t,s) pairs as well. The present method differs essentially
from the classical It\^o/FPK approach since it does not involve any specific
assumptions regarding the correlation structure of the excitation. In the case
where the input random process can be obtained as the solution of an It\^o
equation (as, e.g., happens with an Ornstein-Uhlenbeck process), the proposed
non-local system is localized, leading to moment equations identical with the
usual ones. The closed, non-local in time, moment system is numerically solved
by means of an appropriate, two-scale, iterative scheme, and numerical results
are presented for two families of colored stochastic excitations. The results
are confirmed by means of extensive Monte Carlo simulations. It is found that
both the correlation time and the details of the shape of the input random
function affect appreciable the response covariance. In the present paper we
focus on a monostable cubic half-oscillator, excited by a smoothly-correlated,
linear-plus-cubic-Gaussian (non-Gaussian) random input. The bistable case, as
well as more general nonlinear systems can be treated by the same method,
provided that a more elaborate moment closure will be used.


  We define the star transform as a generalization of the broken ray transform
introduced by us in previous work. The advantages of using the star transform
include the possibility to reconstruct the absorption and the scattering
coefficients of the medium separately and simultaneously (from the same data)
and the possibility to utilize scattered radiation which, in the case of the
conventional X-ray tomography, is discarded. In this paper, we derive the star
transform from physical principles, discuss its mathematical properties and
analyze numerical stability of inversion. In particular, it is shown that
stable inversion of the star transform can be obtained only for configurations
involving odd number of rays. Several computationally-efficient inversion
algorithms are derived and tested numerically.


  Diffusion Transformers have recently shown remarkable effectiveness in
generating high-quality 3D point clouds. However, training voxel-based
diffusion models for high-resolution 3D voxels remains prohibitively expensive
due to the cubic complexity of attention operators, which arises from the
additional dimension of voxels. Motivated by the inherent redundancy of 3D
compared to 2D, we propose FastDiT-3D, a novel masked diffusion transformer
tailored for efficient 3D point cloud generation, which greatly reduces
training costs. Specifically, we draw inspiration from masked autoencoders to
dynamically operate the denoising process on masked voxelized point clouds. We
also propose a novel voxel-aware masking strategy to adaptively aggregate
background/foreground information from voxelized point clouds. Our method
achieves state-of-the-art performance with an extreme masking ratio of nearly
99%. Moreover, to improve multi-category 3D generation, we introduce
Mixture-of-Expert (MoE) in 3D diffusion model. Each category can learn a
distinct diffusion path with different experts, relieving gradient conflict.
Experimental results on the ShapeNet dataset demonstrate that our method
achieves state-of-the-art high-fidelity and diverse 3D point cloud generation
performance. Our FastDiT-3D improves 1-Nearest Neighbor Accuracy and Coverage
metrics when generating 128-resolution voxel point clouds, using only 6.5% of
the original training cost.


  We present a catalog of 150 variable stars, including 13 stars with exoplanet
candidates. 37 stars were identified as variables for the first time. As a
result of a 2.5-year photometric survey of exoplanets, we have obtained and
analyzed light curves for almost 50 thousand stars in fields around white
dwarfs WD 0009+501 and GRW +708247. Here we describe observations and data
processing, the search for variable stars, their cross-identification with
other catalogs and classification. The catalog is published in open access and
contains the primary classification of variability, light curves and their
parameters.


  Helicity amplitudes for the $\gamma^* N \to \Delta$ transition are calculated
using the cloudy bag model. A correction for center-of-mass motion is carried
out using a modified Peierls-Thouless projection method. This reduces the
magnitude of the transition amplitudes at small momentum transfer and enhances
them at modest momentum transfers. Our calculation shows that the pion cloud
contributes substantially to the transition helicity amplitudes, with the final
result giving reasonable agreement with the corresponding experimental values.


  We consider achieving equivariance in machine learning systems via frame
averaging. Current frame averaging methods involve a costly sum over large
frames or rely on sampling-based approaches that only yield approximate
equivariance. Here, we propose Minimal Frame Averaging (MFA), a mathematical
framework for constructing provably minimal frames that are exactly
equivariant. The general foundations of MFA also allow us to extend frame
averaging to more groups than previously considered, including the Lorentz
group for describing symmetries in space-time, and the unitary group for
complex-valued domains. Results demonstrate the efficiency and effectiveness of
encoding symmetries via MFA across a diverse range of tasks, including $n$-body
simulation, top tagging in collider physics, and relaxed energy prediction. Our
code is available at https://github.com/divelab/MFA.


  We address the detection of a low rank $n\times n$deterministic matrix
$\mathbf{X}_{0}$ from the noisy observation ${\bf X}_{0}+{\bf Z}$ when
$n\to\infty$, where ${\bf Z}$ is a complex Gaussian random matrix with
independent identically distributed $\mathcal{N}_{c}(0,\frac{1}{n})$ entries.
Thanks to large random matrix theory results, it is now well-known that if the
largest singular value $\lambda_{1}$ of ${\bf X}_{0}$ verifies $\lambda_{1}>1$,
then it is possible to exhibit consistent tests. In this contribution, we prove
a contrario that under the condition $\lambda_{1}<1$, there are no consistent
tests. Our proof is rather simple, inspired by previous works devoted to the
case of rank 1 matrices ${\bf X}_{0}$.


  I give an overview of open, closed and heterotic N=2 strings. At the tree
level I derive the effective field theories of all the strings, and discuss the
group theory of the N=2 open string and the interaction between its open and
closed sectors. At one loop N=2 string loop amplitudes and partition functions
have incurable infra-red divergences, and show puzzling disagreements on the
dimension of spacetime when compared to their effective field theories. I show
that the closed-string three-point amplitude can be written directly in terms
of a Schwinger parameter, so explicitly exhibiting the inconsistency. I finally
discuss the possibility that the puzzles posed by the loop amplitudes could be
solved if the N=2 theories were Lorentz invariant and supersymmetric, and I
speculate on possible modifications of the string calculations.


  In recent years, Artificial Intelligence techniques have emerged as useful
tools for solving various engineering problems that were not possible or
convenient to handle by traditional methods. AI has directly influenced many
areas of computer science and becomes an important part of the engineering
curriculum. However, determining the important topics for a single semester AI
course is a nontrivial task, given the lack of a general methodology. AI
concepts commonly overlap with many other disciplines involving a wide range of
subjects, including applied approaches to more formal mathematical issues. This
paper presents the use of a simple robotic platform to assist the learning of
basic AI concepts. The study is guided through some simple experiments using
autonomous mobile robots. The central algorithm is the Learning Automata. Using
LA, each robot action is applied to an environment to be evaluated by means of
a fitness value. The response of the environment is used by the automata to
select its next action. This procedure holds until the goal task is reached.
The proposal addresses the AI study by offering in LA a unifying context to
draw together several of the topics of AI and motivating the students to learn
by building some hands on laboratory exercises. The presented material has been
successfully tested as AI teaching aide in the University of Guadalajara
robotics group as it motivates students and increases enrolment and retention
while educating better computer engineers.


  The emerging quantum technologies rely on our ability to establish and
control quantum systems in nonclassical states, exhibiting entanglement and
quantum coherence. It is thus crucial to understand how entanglement and
coherence can be created in the most efficient way. In this work we study
optimal ways to create a large amount of quantum coherence via quantum
channels. For this, we compare different scenarios, where the channel is acting
on an incoherent state, on states which have coherence, and also on subsystems
of multipartite quantum states. We show that correlations in multipartite
systems do not enhance the ability of a quantum channel to create coherence. We
also study the ability of quantum channels to destroy coherence, proving that a
channel can destroy more coherence when acting on a subsystem of a bipartite
state. Crucially, we also show that the destroyed coherence on multipartite
system can exceed the upper bound of those on the single system when the total
state is entangled. Our results significantly simplify the evaluation of
coherence generating capacity of quantum channels, which we also discuss.


  In 1961 G.Polya published a paper about the eigenvalues of vibrating
membrane. The "free vibrating membrane"' corresponds to the Neumann-Laplace
operator in bounded plane domains. In this paper we obtain estimates for the
first eigenvalue of this operator in a large class of domains that we call as
conformal regular domains, that includes convex domains, John domains etc... On
the base of our estimates we conjecture that the eigenvalues of the
Neumann-Laplace operator depend on the hyperbolic metrics of plane domains. We
propose a new method for the estimates that is based on weighted
Poincar\'e-Sobolev inequalities obtained by the authors recently.


  We study the transverse electrical conductivity and the corresponding
magnetic noise of a two-dimensional U(1) spin liquid state with a spinon Fermi
surface. We show that in the quasi-static regime these responses have the same
wave-vector dependence as that of a metal but are reduced by a dimensionless
pre-factor controlled by the ratio of orbital diamagnetic susceptibilities of
the spinons and chargons, correcting previous work. We estimate that this
quasi-static regime is comfortably accessed by the typical NV center splittings
of a few GHz and estimate that the expected T1 times for an NV center placed
above candidate materials, such as the organic dmit and ET salts, monolayer
1T-TaS2/Se2, would range from several tens to a few hundred milliseconds.


  We consider the generalized Fornberg-Whitham equation. We study sufficient
conditions for blow-up of solutions and show the global existence with small
initial data. Also we give some relations to the Burgers equation.


  Generative models can produce impressively realistic images. This paper
demonstrates that generated images have geometric features different from those
of real images. We build a set of collections of generated images, prequalified
to fool simple, signal-based classifiers into believing they are real. We then
show that prequalified generated images can be identified reliably by
classifiers that only look at geometric properties. We use three such
classifiers. All three classifiers are denied access to image pixels, and look
only at derived geometric features. The first classifier looks at the
perspective field of the image, the second looks at lines detected in the
image, and the third looks at relations between detected objects and shadows.
Our procedure detects generated images more reliably than SOTA local signal
based detectors, for images from a number of distinct generators. Saliency maps
suggest that the classifiers can identify geometric problems reliably. We
conclude that current generators cannot reliably reproduce geometric properties
of real images.


  We analyze renormalization of the pi band of n-doped epitaxial graphene on
Ir(111) induced by electron-phonon coupling. Our procedure of extracting the
bare band relies on recursive self-consistent refining of the functional form
of the bare-band until the convergence. We demonstrate that the components of
the self-energy, as well as the spectral intensity obtained from angle-resolved
photoelectron spectroscopy (ARPES) show that the renormalization is due to the
coupling to two distinct phonon excitations. From the velocity renormalization
and an increase of the imaginary part of the self-energy we find the
electron-phonon coupling constant to be ~0.2, which is in fair agreement with a
previous study of the same system, despite the notable difference in the width
of spectroscopic curves. Our experimental results also suggest that potassium
intercalated between graphene and Ir(111) does not introduce any additional
increase of the quasiparticle scattering rate.


  Nucleon flow in Au+Au collisions at 1 GeV/nucleon region and dilepton spectra
in S+Au collisions at SPS energies are analysed in the relativistic transport
model. They are shown to be sensitive to the nucleon vector and scalar
potentials, respectively, and are thus useful probes of these potentials in
dense matter. A recently developed effective Lagrangian with self-interactions
of vector as well as scalar fields is found to describe both data reasonably
well.


  We show that the exchange interaction of a singlet-triplet spin qubit
confined in double quantum dots, when being controlled by the barrier method,
is insensitive to a charged impurity lying along certain directions away from
the center of the double-dot system. These directions differ from the polar
axis of the double dots by the magic angle, equaling
$\arccos\left(1/\sqrt{3}\right)\approx 54.7^\circ$, a value previously found in
atomic physics and nuclear magnetic resonance. This phenomenon can be
understood from an expansion of the additional Coulomb interaction created by
the impurity, but also relies on the fact that the exchange interaction solely
depends on the tunnel coupling in the barrier-control scheme. Our results
suggest that for a scaled-up qubit array, when all pairs of double dots rotate
their respective polar axes from the same reference line by the magic angle,
cross-talks between qubits can be eliminated, allowing clean single-qubit
operations. While our model is a rather simplified version of actual
experiments, our results suggest that it is possible to minimize unwanted
couplings by judiciously designing the layout of the qubits.


  We study the morphology, luminosity and mass of the superclusters from the
BOSS Great Wall (BGW), a recently discovered very rich supercluster complex at
the redshift $z = 0.47$. We have employed the Minkowski functionals to quantify
supercluster morphology. We calculate supercluster luminosities and masses
using two methods. Firstly, we used data about the luminosities and stellar
masses of high stellar mass galaxies with $\log(M_*/h^{-1}M_\odot) \geq 11.3$.
Secondly, we applied a scaling relation that combines morphological and
physical parameters of superclusters to obtain supercluster luminosities, and
obtained supercluster masses using the mass-to-light ratios found for local
rich superclusters. We find that the BGW superclusters are very elongated
systems, with shape parameter values of less than $0.2$. This value is lower
than that found for the most elongated local superclusters. The values of the
fourth Minkowski functional $V_3$ for the richer BGW superclusters ($V_3 = 7$
and $10$) show that they have a complicated and rich inner structure. We
identify two Planck SZ clusters in the BGW superclusters, one in the richest
BGW supercluster, and another in one of the poor BGW superclusters. The
luminosities of the BGW superclusters are in the range of $1 -
8\times~10^{13}h^{-2}L_\odot$, and masses in the range of $0.4 -
2.1\times~10^{16}h^{-1}M_\odot$. Supercluster luminosities and masses obtained
with two methods agree well. We conclude that the BGW is a complex of massive,
luminous and large superclusters with very elongated shape. The search and
detailed study, including the morphology analysis of the richest superclusters
and their complexes from observations and simulations can help us to understand
formation and evolution of the cosmic web.


  This paper introduces yet another stochastic model replicating chain-ladder
estimates and furthermore considers extensions that add flexibility to the
modeling. In its simplest form, the proposed model replicates the
chain-ladder's development factors using a GLM model with averaged hazard rates
running in reversed development time as response. This is in contrast to the
existing reserving literature within the GLM framework where claim amounts are
modeled as response. Modeling the averaged hazard rate corresponds to modeling
the claim development and is arguably closer to the actual chain-ladder
algorithm. Furthermore, since exposure does not need to be modeled, the model
only has half the number of parameters compared to when modeling the claim
amounts. This lesser complexity can be used to easily introduce model
extensions that may better fit the data. We provide a new R-package,
$\texttt{clmplus}$, where the models are implemented and can be fed with
run-off triangles. We conduct an empirical study on 30 publicly available
run-off triangles making a case for the benefit of having $\texttt{clmplus}$ in
the actuary's toolbox.


  We present a formula for the calculation of K-edge resonant inelastic x-ray
scattering on transition metal compounds, based on a local interaction between
the valence shell electrons and the $1s$ core hole. Extending a previous
result, we include explicit momentum dependence and a basis with multiple
core-hole sites. We apply this formula to a single-layered charge, orbital and
spin ordered manganite, La$_{0.5}$Sr$_{1.5}$MnO$_4$, and obtain good agreement
with experimental data, in particular with regards to the large variation of
the intensity with momentum. We find that the screening in
La$_{0.5}$Sr$_{1.5}$MnO$_4$ is highly localized around the core-hole site and
demonstrate the potential of K-edge resonant inelastic x-ray scattering as a
probe of screening dynamics in materials.


  We present a search for the dark photon $A^{\prime}$ in the $B^0 \to
A^{\prime} A^{\prime}$ decays, where $A^{\prime}$ subsequently decays to $e^+
e^-$, $\mu^+ \mu^-$, and $\pi^+ \pi^-$. The search is performed by analyzing
$772 \times 10^6$ $B\overline{B}$ events collected by the Belle detector at the
KEKB $e^+ e^-$ energy-asymmetric collider at the $\Upsilon (4S)$ resonance. No
signal is found in the dark photon mass range $0.01~\mathrm{GeV}/c^2 \le
m_{A^{\prime}} \le 2.62~\mathrm{GeV}/c^2$, and we set upper limits of the
branching fraction of $B^0 \to A^{\prime} A^{\prime}$ at the 90\% confidence
level. The products of branching fractions, $\mathcal{B}(B^0 \to A^{\prime}
A^{\prime}) \times \mathcal{B}(A^{\prime} \to e^+ e^-)^2$ and $\mathcal{B}(B^0
\to A^{\prime} A^{\prime}) \times \mathcal{B}(A^{\prime} \to \mu^+ \mu^-)^2$,
have limits of the order of $10^{-8}$ depending on the $A^{\prime}$ mass.
Furthermore, considering $A^{\prime}$ decay rate to each pair of charged
particles, the upper limits of $\mathcal{B}(B^0 \to A^{\prime} A^{\prime})$ are
of the order of $10^{-8}$-$10^{-5}$. From the upper limits of $\mathcal{B}(B^0
\to A^{\prime} A^{\prime})$, we obtain the Higgs portal coupling for each
assumed dark photon and dark Higgs mass. The Higgs portal couplings are of the
order of $10^{-2}$-$10^{-1}$ at $m_{h'} \simeq m_{B^0} \pm 40~\mathrm{MeV}/c^2$
and $10^{-1}$-$1$ at $m_{h'} \simeq m_{B^0} \pm 3~\mathrm{GeV}/c^2$.


  We study almost-envy-freeness in house allocation, where $m$ houses are to be
allocated among $n$ agents so that every agent receives exactly one house. An
envy-free allocation need not exist, and therefore we may have to settle for
relaxations of envy-freeness. But typical relaxations such as envy-free up to
one good do not make sense for house allocation, as every agent is required to
receive exactly one house. Hence we turn to different aggregate measures of
envy as markers of fairness. In particular, we define the amount of envy
experienced by an agent $a$ w.r.t. an allocation to be the number of agents
that agent $a$ envies under that allocation. We quantify the envy generated by
an allocation using three different metrics: 1) the number of agents who are
envious; 2) the maximum amount of envy experienced by any agent; and 3) the
total amount of envy experienced by all agents, and look for allocations that
minimize one of the three metrics. We thus study three computational problems
corresponding to each of the three metrics and prove a host of algorithmic and
hardness results. We also suggest practical approaches for these problems via
integer linear program (ILP) formulations and report the findings of our
experimental evaluation of ILPs. Finally, we study the price of fairness (PoF),
which quantifies the loss of welfare we must suffer due to the fairness
requirements, and we prove a number of results on PoF, including tight bounds
as well as algorithms that simultaneously optimize both welfare and fairness.


  Zero energy modes are shown to exist in silicene under suitably chosen
magnetic as well as electric fields. Two Majorana modes are found on the
application of opposite local magnetization on the silicene sub-lattices. We
identify a non-Majorana zero energy mode carrying pure spin current under the
influence of inhomogeneous gate electric field. In both cases, wave functions
reveal subtle interference pattern in phase space, showing structures finer
than the Planck constant $\hbar$. A spin system coupled through spin-spin
($\sigma_{z}\otimes\sigma_{z}$) interaction with the Majorana modes exhibits
periodic revival of coherence with a minimum period $\sim $1/n. The same system
shows decoherence-free evolution in the case of gate electric field. Under a
momentum dependent interaction, one Majorana mode having a bound state in the
continuum character is found to be more robust as compared to the other. The
mode arising on application of electric field shows rapid loss of coherence for
such an interaction.


  A fundamental endeavor in exoplanetary research is to characterize the bulk
compositions of planets via measurements of their masses and radii. With future
sample sizes of hundreds of planets to come from TESS and PLATO, we develop a
statistical method that can flexibly yet robustly characterize these
compositions empirically, via the exoplanet M-R relation. Although the M-R
relation has been explored in many prior works, they mostly use a power-law
model, with assumptions that are not flexible enough to capture important
features in current and future M-R diagrams. To address these shortcomings, a
nonparametric approach is developed using a sequence of Bernstein polynomials.
We demonstrate the benefit of taking the nonparametric approach by benchmarking
our findings with previous work and showing that a power-law can only
reasonably describe the M-R relation of the smallest planets and that the
intrinsic scatter can change non-monotonically with different values of a
radius. We then apply this method to a larger dataset, consisting of all the
Kepler observations in the NASA Exoplanet Archive. Our nonparametric approach
provides a tool to estimate the M-R relation by incorporating heteroskedastic
measurement errors into the model. As more observations will be obtained in the
near future, this approach can be used with the provided R code to analyze a
larger dataset for a better understanding of the M-R relation.


  We examine the moduli space E=T* of complex tori T(t)=C/L(t) where
L(t)=cost.n(t)Lt. We find that the Dedekind eta function furnishes a bridge
between the euclidean and hyperbolic structures on T*=C-L/L as well as between
the doubly periodic Weierstrass function p on T* and the theta function for the
lattice E(8). The former one allows us to rewrite the Lame equation for the
Bers embedding of T(1,1) in a new form. We show that L has natural
decomposition into 8 sublattices (each equivalent to L) together with
appropriate half-points and that this leads to some local functions and to a
relation with E(8)


  The fluctuating diamagnetic magnetization Mfl at constant field H as a
function of temperature and the isothermal magnetization Mfl vs H are measured
in MgB2, above the superconducting transition temperature. The expressions for
Mfl in randomly oriented powders are derived in the Gaussian approximation of
local Ginzburg-Landau theory and used for the analysis of the data. The scaled
magnetization Mfl/H^{1/2}*T is found to be field dependent. In the limit of
evanescent field the behaviour for Gaussian fluctuations is obeyed while for
H>~ 100 Oe the field tends to suppress the fluctuating pairs, with a field
dependence of Mfl close to the one expected when short wavelength fluctuations
and non-local electrodynamic effects are taken into account. Our data, besides
providing the isothermal magnetization curves for T>Tc(0) in a BCS-type
superconductor such as MgB2, evidence an enhancement of the fluctuating
diamagnetism which is related to the occurrence in this new superconductor of
an anisotropic spectrum of the superconducting fluctuations.


  A model for describing structural pointlike defects in nanoscaled
ferromagnetic materials is presented. Its details are explicitly developed
whenever interacting with a vortex-like state comprised in a thin nanodisk.
Among others, our model yields results for the vortex equilibrium position
under the influence of several defects along with an external magnetic field in
good qualitative agreement with experiments. We also discuss how such defects
may affect the vortex motion, like its gyrotropic oscillation and dynamical
polarization reversal.


  Semi-leptonic $B_s \to K \ell \nu$ and $B_s \to D_s \ell \nu$ decays provide
an alternative $b$-decay channel to determine the CKM matrix elements
$|V_{ub}|$ and $|V_{cb}|$ or to obtain $R$-ratios to investigate lepton flavor
universality violations. In addition, these decays may shed further light on
the discrepancies seen in the analysis of inclusive vs. exclusive decays. Using
the nonperturbative methods of lattice QCD, theoretical results are obtained
with good precision and full control over systematic uncertainties. This talk
will highlight ongoing efforts of the $B$-physics program by the RBC-UKQCD
collaboration.


  Raw data sizes are growing and proliferating in scientific research, driven
by the success of data-hungry computational methods, such as machine learning.
The preponderance of proprietary and shoehorned data formats make computations
slower and make it harder to reproduce research and to port methods to new
platforms. Here we present the RawArray format: a simple, fast, and extensible
format for archival storage of multidimensional numeric arrays on disk.
  The RawArray file format is a simple concatenation of a header array and a
data array. The header comprises seven or more 64-bit unsigned integers. The
array data can be anything. Arbitrary user metadata can be appended to an
RawArray file if desired, for example to store measurement details, color
palettes, or geolocation data.
  We present benchmarks showing a factor of 2--3$\times$ speedup over HDF5 for
a range of array sizes and a speedup of up to 20$\times$ in reading the common
deep learning datasets MNIST and CIFAR10.


  It has been shown recently that the values of $J_T$ and $J_L$ which appear in
Eqs.(2) and (5) of the above paper and which are taken from the work of
Aurenche et al are too large by a factor of 4. Correcting for this changes the
Fig.~2. More-over, now the emissions from the quark matter dominate only for
$p_T <$ 1 GeV/$c$. The basic result of the paper, that the upper limit of the
single-photon production in the WA80 experiment is consistent with the rates
for photon production at two-loop level remains valid.


  We report on the near-infrared polarimetric observations of RCW 120 with the
1.4 m IRSF telescope. The starlight polarization of the background stars
reveals for the first time the magnetic field of RCW 120. The global magnetic
field of RCW 120 is along the direction of $20^\circ$, parallel to the Galactic
plane. The field strength on the plane of the sky is $100\pm26\,\mu$G. The
magnetic field around the eastern shell shows evidence of compression by the
HII region. The external pressure (turbulent pressure + magnetic pressure) and
the gas density of the ambient cloud are minimum along the direction where RCW
120 breaks out, which explains the observed elongation of RCW 120. The
dynamical age of RCW 120, depending on the magnetic field strength, is
$\sim\,1.6\,\mathrm{Myr}$ for field strength of $100\,\mu$G, older than the
hydrodynamic estimates. In direction perpendicular to the magnetic field, the
density contrast of the western shell is greatly reduced by the strong magnetic
field. The strong magnetic field in general reduces the efficiency of triggered
star formation, in comparison with the hydrodynamic estimates. Triggered star
formation via the "collect and collapse" mechanism could occur in the direction
along the magnetic field. Core formation efficiency (CFE) is found to be higher
in the southern and eastern shells of RCW 120 than in the infrared dark cloud
receiving little influence from the HII region, suggesting increase in the CFE
related to triggering from ionization feedback.


  Using a spectral decomposition technique (Soto & Martin 2012, hereafter Paper
I), we investigate the physical origin of the high-velocity emission line gas
in a sample of 39 gas-rich, ultraluminous infrared galaxy (ULIRG) mergers.
Regions with shock-like excitation were identified in two kinematically
distinct regimes, characterized by broad ($\sigma >$ 150 \kms) and narrow
linewidths. Here we investigate the physical origin of the high-velocity
(broad) emission with shock-like line ratios. Considering the large amount of
extinction in these galaxies, the blueshift of the broad emission suggests an
origin on the near side of the galaxy and therefore an interpretation as a
galactic outflow. The large spatial extent of the broad, shocked emission
component is generally inconsistent with an origin in the narrow-line region of
a AGN, so we conclude that energy and momentum supplied by the starburst drives
these outflows. The new data are used to examine the fraction of the supernova
energy radiated by shocks and the mass loss rate in the warm-ionized phase of
the wind. We show that the shocks produced by galactic outflows can be
recognized in moderately high-resolution, integrated spectra of these nearby,
ultraluminous starbursts. The spectral fitting technique introduced in Paper I
may therefore be used to improve the accuracy of the physical properties
measured for high-redshift galaxies from their (observed frame) infrared
spectra.


This paper has been withdrawn by the author


  We characterize all fields F for which a group with an F-locally split root
group datum admits an Iwasawa decomposition. This class of groups in particular
includes the split semisimple algebraic groups and the split Kac-Moody groups.


  This is the first of a series of papers to construct the deformation theory
of the form Schr\"odinger equation, which is related to a section-bundle system
$(M,g,f)$, where $(M,g)$ is a noncompact complete K\"ahler manifold with
bounded geometry and $f$ is a holomorphic function defined on $M$.
  This work is also the first step attempting to understand the whole
Landau-Ginzburg B-model including the higher genus invariants. Our work is
mainly based on the pioneer work of Cecotti, Cecotti and Vafa
\cite{Ce1,Ce2,CV}.


  We have studied the connectivity percolation transition in suspensions of
attractive square-well spherocylinders by means of Monte Carlo simulation and
connectednes percolation theory. In the 1980s the percolation threshold of
slender fibres has been predicted to scale as the fibres' inverse aspect ratio
(Phys.~Rev.~B {\bf 30}, 3933 (1984)). The main finding of our study is that the
attractive spherocylinder system reaches this inverse scaling regime at much
lower aspect ratios than found in suspensions of hard spherocylinders. We
explain this difference by showing that third virial corrections of the pair
connectedness functions, which are responsible for the deviation from the
scaling regime, are less important for attractive potentials than for hard
particles.


  We analyze new optical spectra of a sample of 502 galaxies in close pairs and
n-tuples, separated by <= 50/h kpc. We extracted the sample objectively from
the CfA2 redshift survey, without regard to the surroundings of the tight
systems. We probe the relationship between star formation and the dynamics of
the systems of galaxies. The equivalent widths of H\alpha (EW(H\alpha) and
other emission lines anti-correlate strongly with pair spatial separation
(\Delta D) and velocity separation. We use the measured EW(H\alpha) and the
starburst models of Leitherer et al. to estimate the time since the most recent
burst of star for- mation began for each galaxy. In the absence of a large
contribution from an old stellar population to the continuum around H\alpha,
the observed \Delta D -- EW(H\alpha) correlation signifies that starbursts with
larger separations on the sky are, on average, older. By matching the dynamical
timescale to the burst timescale, we show that the data support a simple
picture in which a close pass initiates a starburst; EW(H\alpha) decreases with
time as the pair separation increases, accounting for the anti-correlation.
This picture leads to a method for measuring the duration and the initial mass
function of interaction-induced starbursts: our data are compatible with the
starburst and orbit models in many respects, as long as the starburst lasts
longer than \sim10^8 years and the delay between the close pass and the
initiation of the starburst is less than a few \times 10^7 years. If there is
no large contribution from an old stellar population to the continuum around
H\alpha the Miller-Scalo and cutoff (M <= 30 M_\sun) Salpeter initial mass
functions fit the data much better than a standard Salpeter IMF. (Abridged.)


  We have employed the relativistic coupled-cluster theory to calculate the
electric dipole matrix elements in the singly ionized barium (Ba$^+$) and
radium (Ra$^+$). Matrix elements of Ba$^+$ are used to determine the
light-shift ratios for two different wavelengths on which recent experiments
are carried out. By combining the measured light-shift ratios and our
calculations, we are able to estimate possible errors associate with the used
matrix elements in Ba$^+$. Static polarizabilities of the low-lying states and
lifetimes of the first excited P-states are also determined using these matrix
elements in Ba$^+$. A similar approach has been followed to estimate the
lifetimes and light-shift ratios in Ra$^+$.


  In his 1981 article, Roberts highlights the term 'stellify' defined as "to
transform (a person or thing) into a star or constellation, to place among the
stars." Using the case of the Tabwa people of central Africa, not the
Democratic Republic of Congo, Roberts presents among other things the sky as a
mnemonic for remembering migrations and remembering culture heroes. We do not
know the details of the processes of stellification, however we do know what
has been stellified in many cultures by examining their names for stars and
asterisms and their skylore. Of the many ideas presented in his latest book,
Aveni teases out the ideas of the sky stories having connections to celestial
motions, as well as being a mnemonic for remembering seasonal activities and a
mnemonic for remembering locally embedded moral, ethical, and sociocultural
codes, thus overlapping with Roberts' supposition of the sky serving as a
mnemonic. I draw on case studies to flesh out three themes 1. celestial
motions, 2. moral, ethical, and sociocultural codes, and 3. seasonal activities
within African sky stories. As previously stated, though the human process of
assigning names and stories to the night sky as well as stellifying aspects of
their lives is not fully understood, these three themes hold promise for being
foundational if not part of every culture's practice of stellification.


  Sparse feature selection is necessary when we fit statistical models, we have
access to a large group of features, don't know which are relevant, but assume
that most are not. Alternatively, when the number of features is larger than
the available data the model becomes over parametrized and the sparse feature
selection task involves selecting the most informative variables for the model.
When the model is a simple location model and the number of relevant features
does not grow with the total number of features, sparse feature selection
corresponds to sparse mean estimation. We deal with a simplified mean
estimation problem consisting of an additive model with gaussian noise and mean
that is in a restricted, finite hypothesis space. This restriction simplifies
the mean estimation problem into a selection problem of combinatorial nature.
Although the hypothesis space is finite, its size is exponential in the
dimension of the mean. In limited data settings and when the size of the
hypothesis space depends on the amount of data or on the dimension of the data,
choosing an approximation set of hypotheses is a desirable approach. Choosing a
set of hypotheses instead of a single one implies replacing the bias-variance
trade off with a resolution-stability trade off. Generalization capacity
provides a resolution selection criterion based on allowing the learning
algorithm to communicate the largest amount of information in the data to the
learner without error. In this work the theory of approximation set coding and
generalization capacity is explored in order to understand this approach. We
then apply the generalization capacity criterion to the simplified sparse mean
estimation problem and detail an importance sampling algorithm which at once
solves the difficulty posed by large hypothesis spaces and the slow convergence
of uniform sampling algorithms.


  We test the operation of two methods for selective application of Artificial
Viscosity (AV) in SPH simulations of Keplerian Accretion Disks, using a ring
spreading test to quantify effective viscosity, and a correlation coefficient
technique to measure the formation of unwanted prograde alignments of
particles. Neither the Balsara Switch nor Time Dependent Viscosity work
effectively, as they leave AV active in areas of smooth shearing flow, and do
not eliminate the accumulation of alignments of particles in the prograde
direction. The effect of both switches is periodic, the periodicity dependent
on radius and unaffected by the density of particles. We demonstrate that a
very simple algorithm activates AV only when truly convergent flow is detected
and reduces the unwanted formation of prograde alignments. The new switch works
by testing whether all the neighbours of a particle are in Keplerian orbit
around the same point, rather than calculating the divergence of the velocity
field, which is very strongly affected by Poisson noise in the positions of the
SPH particles.


  Towards the network innovation, the Beyond Five-Generation (B5G) networks
envision the use of machine learning (ML) methods to predict the network
conditions and performance indicators in order to best make decisions and
allocate resources. In this paper, we propose a new ML approach to accomplish
predictions in B5G networks. Instead of handling the time-series in the network
domain of values, we transform them into image thus allowing to apply advanced
ML methods of Computer Vision field to reach better predictions in B5G
networks. Particularly, we analyze different techniques to transform
time-series of network measures into image representation, e.g., Recurrence
Plots, Markov Transition Fields, and Gramian Angular Fields. Then, we apply
deep neural networks with convolutional layers to predict different 5G radio
signal quality indicators. When comparing with other ML-based solutions,
experimental results from 5G transmission datasets showed the feasibility and
small prediction errors of the proposed approach.


  Using direct numerical simulations, we study the statistical properties of
reversals in two-dimensional Rayleigh-B\'enard convection for infinite Prandtl
number. We find that the large-scale circulation reverses irregularly, with the
waiting time between two consecutive genuine reversals exhibiting a Poisson
distribution on long time scales, while the interval between successive
crossings on short time scales shows a power law distribution. We observe that
the vertical velocities near the sidewall and at the center show different
statistical properties. The velocity near the sidewall shows a longer
autocorrelation and $1/f^2$ power spectrum for a wide range of frequencies,
compared to shorter autocorrelation and a narrower scaling range for the
velocity at the center. The probability distribution of the velocity near the
sidewall is bimodal, indicating a reversing velocity field. We also find that
the dominant Fourier modes capture the dynamics at the sidewall and at the
center very well. Moreover, we show a signature of weak intermittency in the
fluctuations of velocity near the sidewall by computing temporal structure
functions.


  Very recently Girardeau and Minguzzi [arXiv:0807.3366v2, Phys. Rev. A 79,
033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core
bosons. In particular they deal with the general case where the mass of the
impurity is different from the mass of the bosons and the impurity-boson
interaction is not necessarily infinitely repulsive. We show that one of their
initial step is erroneous, contradicting both physical intuition and known
exact results. Their results in the general case apply only actually when the
mass of the impurity is infinite.


  The field of experimental particle physics has become more sophisticated over
time, as fewer, larger experimental collaborations search for small signals in
samples with large components of background. The search for and the observation
of electroweak single top quark production by the CDF and DZero collaborations
at Fermilab's Tevatron collider are an example of an elaborate effort to
measure the rate of a very rare process in the presence of large backgrounds
and to learn about the properties of the top quark's weak interaction. We
present here the techniques used to make this groundbreaking measurement and
the interpretation of the results in the context of the Standard Model.


  For a prime $p$ and an integer $x$, the $p$-adic valuation of $x$ is denoted
by $\nu_{p}(x)$. For a polynomial $Q$ with integer coefficients, the sequence
of valuations $\nu_{p}(Q(n))$ is shown to be either periodic or unbounded. The
first case corresponds to the situation where $Q$ has no roots in the ring of
$p$-adic integers. In the periodic situation, the period length is determined.


  Using inelastic neutron scattering and molecular dynamics simulations on a
model Zr-Cu-Al metallic glass, we show that transverse phonons persist well
into the high-frequency regime, and can be detected at large momentum transfer.
Furthermore, the apparent peak width of the transverse phonons was found to
follow the static structure factor. The one-to-one correspondence, which was
demonstrated for both Zr-Cu-Al metallic glass and a 3-dimensional Lennard-Jones
model glass, suggests a universal correlation between the phonon dynamics and
the underlying disordered structure. This remarkable correlation, not found for
longitudinal phonons, underscores the key role that transverse phonons hold for
understanding the structure-dynamics relationship in disordered materials.


  During a search for previously unknown Galactic emission nebulae, we
discovered a faint 36' diameter Halpha emission nebula centered around the
periodic variable YY Hya. Although this star has been classified as RR-Lyr
variable, such a classification is inconsistent Gaia distance of ~450 pc. GALEX
image data also shows YY Hya to have a strong UV excess, suggesting the
existence of a hot, compact binary companion. In addition to our discovery
image data, we obtained image of the region with CHILESCOPE time-series
spectroscopy at MDM observatory. Also, we used data from various space missions
to derive an exact orbital period and a SED. We find that YY Hya is a compact
binary system containing a K dwarf star which is strongly irradiated by a hot
WD companion. The spectral characteristics of the emission lines, visible only
during maximum light of the perfectly sinusoidal optical}light curve shows
signatures much like members of the BE UMa variable family. These are post
common envelope pre-cataclysmic variables. However the companion star here is
more massive than found in other group members and the progenitor of the white
dwarf must have been a 3 to 4 Mo star. The nebula seems to be an ejected common
envelope shell with a mass in the order of one Mo and an age of 500000 years.
This makes it to be the biggest hitherto known such shell. Alignment of
neighboring nebulosities some 45' to the northeast and southwest of YY Hya
suggests that the system had strong bipolar outflows. We briefly speculate it
might be related to the 1065 BP "guest-star" reported in ancient Chinese
records as well.


  The main goal of this paper is to define the so-called Chow weight structure
for the category of Beilinson motives over any 'reasonable' base scheme $S$
(this is the version of Voevodsky's motives over $S$ defined by Cisinski and
Deglise). We also study the functoriality properties of the Chow weight
structure (they are very similar to the well-known functoriality of weights for
mixed complexes of sheaves). As shown in a preceding paper, the Chow weight
structure automatically yields an exact conservative weight complex functor
(with values in $K^b(Chow(S))$). Here $Chow(S)$ is the heart of the Chow weight
structure; it is 'generated' by motives of regular schemes that are projective
over $S$. Besides, Grothendiek's group of $S$-motives is isomorphic to
$K_0(Chow(S))$; we also define a certain 'motivic Euler characteristic' for
$S$-schemes. We obtain (Chow)-weight spectral sequences and filtrations for any
cohomology of motives; we discuss their relation to Beilinson's 'integral part'
of motivic cohomology and to weights of mixed complexes of sheaves. For the
study of the latter we introduce a new formalism of relative weight structures.


  Self-supervised Learning (SSL) has emerged as a powerful technique in
pre-training deep learning models without relying on expensive annotated
labels, instead leveraging embedded signals in unlabeled data. While SSL has
shown remarkable success in computer vision tasks through intuitive data
augmentation, its application to graph-structured data poses challenges due to
the semantic-altering and counter-intuitive nature of graph augmentations.
Addressing this limitation, this paper introduces a novel non-contrastive SSL
approach to Explicitly Generate a compositional Relation Graph (ExGRG) instead
of relying solely on the conventional augmentation-based implicit relation
graph. ExGRG offers a framework for incorporating prior domain knowledge and
online extracted information into the SSL invariance objective, drawing
inspiration from the Laplacian Eigenmap and Expectation-Maximization (EM).
Employing an EM perspective on SSL, our E-step involves relation graph
generation to identify candidates to guide the SSL invariance objective, and
M-step updates the model parameters by integrating the derived relational
information. Extensive experimentation on diverse node classification datasets
demonstrates the superiority of our method over state-of-the-art techniques,
affirming ExGRG as an effective adoption of SSL for graph representation
learning.


  We show that semiconductor nanowires coupled to an s-wave superconductor
provide a playground to study effects of interactions between different
topological superconducting phases supporting Majorana zero-energy modes. We
consider quasi-one dimensional system where the topological phases emerge from
different transverse subbands in the nanowire. In a certain parameter space, we
show that there is a multicritical point in the phase diagram where the
low-energy theory is equivalent to the one describing two coupled Majorana
chains. We study effect of interactions as well as symmetry-breaking
perturbations on the topological phase diagram in the vicinity of this
multicritical point. Our results shed light on the stability of the topological
phase around the multicritical point and have important implications for the
experiments on Majorana nanowires.


  The Fokker-Planck equation has been very useful for studying dynamic behavior
of stochastic differential equations driven by Gaussian noises. However, there
are both theoretical and empirical reasons to consider similar equations driven
by strongly non-Gaussian noises. In particular, they yield strongly
non-Gaussian anomalous diffusion which seems to be relevant in different
domains of Physics. We therefore derive in this paper a Fractional
Fokker-Planck equation for the probability distribution of particles whose
motion is governed by a nonlinear Langevin-type equation, which is driven by a
Levy-stable noise rather than a Gaussian. We obtain in fact a general result
for a Markovian forcing. We also discuss the existence and uniqueness of the
solution of the Fractional Fokker-Planck equation


  This paper investigates the joint power allocation and user association
problem in multi-cell Massive MIMO (multiple-input multiple-output) downlink
(DL) systems. The target is to minimize the total transmit power consumption
when each user is served by an optimized subset of the base stations (BSs),
using non-coherent joint transmission. We first derive a lower bound on the
ergodic spectral efficiency (SE), which is applicable for any channel
distribution and precoding scheme. Closed-form expressions are obtained for
Rayleigh fading channels with either maximum ratio transmission (MRT) or zero
forcing (ZF) precoding. From these bounds, we further formulate the DL power
minimization problems with fixed SE constraints for the users. These problems
are proved to be solvable as linear programs, giving the optimal power
allocation and BS-user association with low complexity. Furthermore, we
formulate a max-min fairness problem which maximizes the worst SE among the
users, and we show that it can be solved as a quasi-linear program. Simulations
manifest that the proposed methods provide good SE for the users using less
transmit power than in small-scale systems and the optimal user association can
effectively balance the load between BSs when needed. Even though our framework
allows the joint transmission from multiple BSs, there is an overwhelming
probability that only one BS is associated with each user at the optimal
solution.


  The internal flow in corrugated tubes of different helical pitch, covering
from the laminar to turbulent regime, was studied in order to characterize the
three-dimensional flow and the influence of corrugation geometry on pressure
drop and convective heat transfer. With water as working fluid and an imposed
wall heat flux, ranging from around 4 to 33 kW/m2, a numerical model was
developed with a CFD commercial software, where k-omega SST was used to model
turbulence. Experimental tests were performed covering Reynolds numbers in the
range from around 300 up to 5000, which allowed to identify the transition
region and validate the numerical model. The results show that due to the swirl
induced by the corrugation, the critical Reynolds number for the start of
transition to turbulent flow is reduced. The thermal performance factor, which
quantifies the heat transfer enhancement at the expense of pressure drop, was
used to compare the corrugated tubes against the reference case of smooth tube.
Based on this, all investigated corrugated geometries performed better than the
smooth tube, except for low Reynolds numbers (Re<500) in the laminar regime.
Overall, the corrugated tube with the lowest pitch showed a clearly better
performance for the intermediate range of Reynolds numbers (1000<Re<2300),
being an optimal choice for a wider range of operating conditions in the
transitional and turbulent flow regimes.


  We study QCD hard processes at scales of order k^2 > Lambda^2 in the limit in
which the beta-function coefficient - b is taken to be small, but alphas(k) is
kept fixed. The (nonperturbative) Pomeron is exponentially suppressed in this
limit, making it possible to define purely perturbative high-energy Green's
functions. The hard Pomeron exponent acquires diffusion and running coupling
corrections which can be expanded in the b parameter and turn out to be
dependent on the effective coupling b alphas^2 Y. We provide a general setup
for this b-expansion and we calculate the first few terms both analytically and
numerically.


  The latest global financial tsunami and its follow-up global economic
recession has uncovered the crucial impact of housing markets on financial and
economic systems. The Chinese stock market experienced a markedly fall during
the global financial tsunami and China's economy has also slowed down by about
2\%-3\% when measured in GDP. Nevertheless, the housing markets in diverse
Chinese cities seemed to continue the almost nonstop mania for more than ten
years. However, the structure and dynamics of the Chinese housing market are
less studied. Here we perform an extensive study of the Chinese housing market
by analyzing ten representative key cities based on both linear and nonlinear
econophysical and econometric methods. We identify a common collective driving
force which accounts for 96.5\% of the house price growth, indicating very high
systemic risk in the Chinese housing market. The ten key cities can be
categorized into clubs and the house prices of the cities in the same club
exhibit an evident convergence. These findings from different methods are
basically consistent with each other. The identified city clubs are also
consistent with the conventional classification of city tiers. The house prices
of the first-tier cities grow the fastest, and those of the third- and
fourth-tier cities rise the slowest, which illustrates the possible presence of
a ripple effect in the diffusion of house prices in different cities.


  We give a combinatorial characterization of isotropic subspaces in the Orlik-
Solomon algebra of a hyperplane arrangement in terms of decorations of its
intersection lattice. We then use this characterization to prove a result that
relates these isotropic subspaces with linear systems supported on the
arrangement, for arrangements with isolated non-normal crossings of a
particular form.


  Generic arguments lead to the idea that quantum gravity has a minimal length
scale. A possible observational signal of such a minimal length scale is that
photons should exhibit dispersion. In 2009 the observation of a short gamma ray
burst seemed to bound the minimal length scale to distances smaller than the
Planck length, implying that spacetime appeared continuous to distances below
the Planck length. This poses a challenge for such minimal distance models.
Here we propose a modification of the position and momentum operators, ${\hat
x}$ and ${\hat p}$, which lead to a minimal length scale, but preserve the
photon energy-momentum relationship $E = p c$. In this way there is no
dispersion of photons with different energies. This can be accomplished without
modifying the commutation relationship $[{\hat x}, {\hat p}] = i \hbar$.


  The dynamical analog of the Kohn Anomaly image of the Fermi Surface is
demonstrated for the response functions to the surface acoustic waves in
Quantum Hall Systems near $\nu = 1/2$. Kinks appear in the velocity shift
$Delta s/s$ and attenuation coefficient $\Gamma$. The effect is considerably
enhanced under periodic modulation and should be observable.


  In this paper we demonstrate, for the first time, selective thermal emitters
based on metamaterials perfect absorbers. We experimentally realize a narrow
band mid-infrared (MIR) thermal emitter. Multiple metamaterial sublattices
further permit construction of a dual-band MIR emitter. By performing both
emissivity and absorptivity measurements, we find that emissivity and
absorptivity agree very well as predicted by Kirchhoff's law of thermal
radiation. Our results directly demonstrate the great flexibility of
metamaterials for tailoring blackbody emission.


  We discuss the critical properies of the three-dimensional Gross-Neveu model
at nonzero temperature and nonzero chemical potential. We also present
numerical and analytical results for the in-medium interaction due to scalar
meson exchange. Further, we discuss in-medium modifications of mesonic
dispersion relations and wavefunctions.