  The optimized effective potential (OEP) method allows for calculation of the
local, effective single particle potential of density functional theory for
explicitly orbital-dependent approximations to the exchange-correlation energy
functional. In the present work the OEP method is used together with the
approximation due to Krieger, Li and Iafrate (KLI). We present the first
application of this method to polymers. KLI calculations have been performed
for the insulating polyethylene and the results have been compared to those
from other orbital-dependent potentials. Various properties of the band
structure are also calculated. The single-particle band gap strongly depends on
the basis set with larger basis sets yielding narrow gaps. For the highest
occupied orbital energy the difference is more pronounced. In order to get the
right band gap in OEP the exchange contribution to the derivative discontinuity
is calculated and added to the Kohn-Sham gap.


  There has been tremendous research on the design of image regularizers over
the years, from simple Tikhonov and Laplacian to sophisticated sparsity and
CNN-based regularizers. Coupled with a model-based loss function, these are
typically used for image reconstruction within an optimization framework. The
technical challenge is to develop a regularizer that can accurately model
realistic images and be optimized efficiently along with the loss function.
Motivated by the recent plug-and-play paradigm for image regularization, we
construct a quadratic regularizer whose reconstruction capability is
competitive with state-of-the-art regularizers. The novelty of the regularizer
is that, unlike classical regularizers, the quadratic objective function is
derived from the observed data. Since the regularizer is quadratic, we can
reduce the optimization to solving a linear system for applications such as
superresolution, deblurring, inpainting, etc. In particular, we show that using
iterative Krylov solvers, we can converge to the solution in a few iterations,
where each iteration requires an application of the forward operator and a
linear denoiser. The surprising finding is that we can get close to deep
learning methods in terms of reconstruction quality. To the best of our
knowledge, the possibility of achieving near state-of-the-art performance using
a linear solver is novel.


  We summarize recent observations of Cyg X-1 during its 1996 state transition.
The results favor an emission geometry with a central optically thin corona
surrounded by an optically thick, geometrically thin accretion disk. As the
soft state is approached, the inner edge of the disk moves closer to the black
hole, and the corona shrinks, perhaps due to more efficient cooling. Soft
X-rays are from the innermost disk, and inverse-Comptionization by the corona
appears to be responsible for the hard X-ray emission. Both Compton reflection
and an iron emission line have been observed in both states. They are likely to
originate in the inner region of the disk. Also briefly discussed is the
theoretical effort to simultaneously model the observed spectral and temporal
X-ray properties of Cyg X-1.


  Motivated by a recent experiment which synthesizes Landau levels for photons
on cones [Schine {\em et al.}, Nature 534, 671 (2016)], and more generally the
interest in understanding gravitational responses of quantum Hall states, we
study fractional quantum Hall states of bosons on cones. A variety of trial
wave functions for conical systems are constructed and compared with exact
diagonalization results. The tip of a cone is a localized geometrical defect
with singular curvature which can modify the density profiles of quantum Hall
states. The density profiles on cones can be used to extract some universal
information about quantum Hall states. The values of certain quantities are
computed numerically using the density profiles of some quantum Hall states and
they agree with analytical predictions.


  IT professionals have no simple tool to create phishing websites and raise
the awareness of users. We developed a prototype that can dynamically mimic
websites by using enriched screenshots, which requires no additional
programming experience and is simple to set up. The generated websites are
functional and remain up-to-date. We found that 98% of the hyperlinks in
mimicked websites are functional with our tool, compared to 43% with the best
competitor, and only two participants suspected phishing attempts at the time
they were performing tasks with our prototype. This work intends to raise
awareness for phishing attempts especially with local websites by providing an
easy to use prototype to set up such phishing sites.


  Three factors drive the advance of AI: algorithmic innovation, data, and the
amount of compute available for training. Algorithmic progress has
traditionally been more difficult to quantify than compute and data. In this
work, we argue that algorithmic progress has an aspect that is both
straightforward to measure and interesting: reductions over time in the compute
needed to reach past capabilities. We show that the number of floating-point
operations required to train a classifier to AlexNet-level performance on
ImageNet has decreased by a factor of 44x between 2012 and 2019. This
corresponds to algorithmic efficiency doubling every 16 months over a period of
7 years. By contrast, Moore's Law would only have yielded an 11x cost
improvement. We observe that hardware and algorithmic efficiency gains multiply
and can be on a similar scale over meaningful horizons, which suggests that a
good model of AI progress should integrate measures from both.


  We numerically investigate dynamic critical behaviors of two-dimensional (2D)
Josephson-junction arrays with positional disorder in the scheme of the
resistively shunted junction dynamics. Large-scale computation of the current
voltage characteristics reveals an evidence supporting that a phase transition
occurs at a nonzero critical temperature in the strong disorder regime, as well
as in the weak disorder regime. The phase transition at weak disorder appears
to belong to the Berezinskii-Kosterlitz-Thouless (BKT) type. In contrast,
evidence for a non-BKT transition is found in the strong disorder regime. These
results are consistent with the recent experiment %by Yun {\it et al.} in
cond-mat/0509151 on positionally disordered Josephson-junction arrays; in
particular, the critical temperature of the non-BKT transition (ranging from
0.265 down to the minimum 0.22 in units of $E_J/k_B$ with the Josephson
coupling strength $E_J$), the correlation length critical exponent $\nu=1.2$,
and the dynamic critical exponent $z=2.0$ in the strong disorder regime agree
with the existing studies of the 2D gauge-glass model.


  Substantial research has been done in saliency modeling to develop
intelligent machines that can perceive and interpret their surroundings. But
existing models treat videos as merely image sequences excluding any audio
information, unable to cope with inherently varying content. Based on the
hypothesis that an audiovisual saliency model will be an improvement over
traditional saliency models for natural uncategorized videos, this work aims to
provide a generic audio/video saliency model augmenting a visual saliency map
with an audio saliency map computed by synchronizing low-level audio and visual
features. The proposed model was evaluated using different criteria against eye
fixations data for a publicly available DIEM video dataset. The results show
that the model outperformed two state-of-the-art visual saliency models.


  For the singular saddle-point problems with nonsymmetric positive definite
$(1,1)$ block, we present a general constraint preconditioning (GCP) iteration
method based on a singular constraint preconditioner. Using the properties of
the Moore-Penrose inverse, the convergence properties of the GCP iteration
method are studied. In particular, for each of the two different choices of the
$(1,1)$ block of the singular constraint preconditioner, a detailed convergence
condition is derived by analyzing the spectrum of the iteration matrix.
Numerical experiments are used to illustrate the theoretical results and
examine the effectiveness of the GCP iteration method. Moreover, the
preconditioning effects of the singular constraint preconditioner for restarted
generalized minimum residual (GMRES) and quasi-minimal residual (QMR) methods
are also tested.


  We report on magnetoconductance measurements of metallic networks of various
sizes ranging from 10 to $10^{6}$ plaquettes, with anisotropic aspect ratio.
Both Altshuler-Aronov-Spivak (AAS) $h/2e$ periodic oscillations and
Aharonov-Bohm (AB) $h/e$ periodic oscillations are observed for all networks.
For large samples, the amplitude of both oscillations results from the
incoherent superposition of contributions of phase coherent regions. When the
transverse size becomes smaller than the phase coherent length $L_\phi$, one
enters a new regime which is phase coherent (mesoscopic) along one direction
and macroscopic along the other, leading to a new size dependence of the
quantum oscillations.


  While the rheology of non-Brownian suspensions in the dilute regime is
well-understood, their behavior in the dense limit remains mystifying. As the
packing fraction of particles increases, particle motion becomes more
collective, leading to a growing length scale and scaling properties in the
rheology as the material approaches the jamming transition. There is no
accepted microscopic description of this phenomenon. However, in recent years
it has been understood that the elasticity of simple amorphous solids is
governed by a critical point, the unjamming transition where the pressure
vanishes, and where elastic properties display scaling and a diverging length
scale. The correspondence between these two transitions is at present unclear.
Here we show that for a simple model of dense flow, which we argue captures the
essential physics near the jamming threshold, a formal analogy can be made
between the rheology of the flow and the elasticity of simple networks. This
analogy leads to a new conceptual framework to relate microscopic structure to
rheology. It enables us to define and compute numerically normal modes and a
density of states. We find striking similarities between the density of states
in flow, and that of amorphous solids near unjamming: both display a plateau
above some frequency scale \omega* ~ |z_c-z|, where z is the coordination of
the network of particles in contact, z_c = 2D where D is the spatial dimension.
However, a spectacular difference appears: the density of states in flow
displays a single mode at another frequency scale \omega_{min} << \omega*
governing the divergence of the viscosity.


  Ultrafast electron microscopy provides a movie-like access to structural
dynamics of materials in space and time, but fundamental atomic motions or
electron dynamics are, so far, too quick to be resolved. Here we report the
all-optical control, compression and characterization of electron pulses in a
transmission electron microscope by the single optical cycles of
laser-generated terahertz light. This concept provides isolated electron pulses
and merges the spatial resolution of a transmission electron microscope with
the temporal resolution that is offered by a single cycle of laser light.
Central to these achievements is a perforated parallel-plate metallic waveguide
in which transverse velocity mismatch and magnetic forces are mitigated by
electrically constructive and magnetically destructive interferences of
incoming and reflected terahertz half-cycles from a displaced waveguide
termination. Measurements of spatial chirp via energy-filtered imaging reveal
flat pulses with no transversal deflection or temporal aberrations at the
specimen. We also report the all-optical control of multi-electron states and
discover a substantial two-electron and three-electron anti-correlation in the
time domain. These results open up the possibility to visualize atomic and
electronic motions together with their quantum correlations on fundamental
dimensions in space and time.


  In this paper we investigate the feasibility of bremsstrahlung radiation from
`nonthermal' electrons as a source of hard X-rays from the intracluster medium
of clusters of galaxies. With an exact treatment of the Coulomb collisions in a
Fokker-Planck analysis of the electron distribution we find that the severe
difficulties with lifetimes of `nonthermal' particles found earlier by
Petrosian (2001) using a cold target model remain problematic. We then address
possible acceleration of background electrons into a nonthermal tail. We assume
a simplified but generic acceleration rate and determine the expected evolution
of an initially Maxwellian distribution of electrons. We find that strong
nonthermal components arise only for rapid rate of acceleration which also
heats up the entire plasma. These results confirm the conclusion that if the
observed `nonthermal' excesses are due to some process accelerating the
background thermal electrons this process must be short lived.


  In this world of terrorism, it is very important to know the network of
individual suspects. It is also important to analyze the attributes of members
of a network and the relationships that exist between them either directly or
indirectly. This will make it easy for concepts to be built in aiding criminal
investigations. However traditional approaches cannot be used to visualize and
analyze data collected on individuals. With this current day where information
systems play critical role in everyday life of every individual, it is easier
to depend on digital information in fighting crime.Effective computer tools and
intelligent systems that are automated to analyze and interpret criminal data
in real time effectively and efficiently are needed in fighting crime. These
current computer systems should have the capability of providing intelligence
from raw data and creating a visual graph which will make it easy for new
concepts to be built and generated from crime data in order to solve understand
and analyze crime patterns easily. This paper proposes a new method of computer
aided investigation by visualizing and analyzing data of mobile communication
devices using Formal Concept Analysis, or Galois Lattices, a data analysis
technique grounded on Lattice Theory and Propositional Calculus. This method
considered the set of common and distinct attributes of data in such a way that
categorizations are done based on related data with respect to time and events.
This will help in building a more defined and conceptual systems for analysis
of crime data that can easily be visualized and intelligently analyzed by
computer systems.


  A new idea to approximate the second eigenfunction and the second eigenvalue
of $p$-Laplace operator is given. In the case of the Dirichlet boundary
condition, the scheme has the restriction that the positive and the negative
part of the second eigenfunction have equal $L^p$-norm, however, in the case of
Neumann boundary condition, our algorithm has not such restriction. Our
algorithm generates a descending sequence of positive numbers that converges to
the second eigenvalue. We give various examples and computational tests.


  The orbital character, orientation, and magnetic polarization of the O 2$p$
unoccupied states near the Fermi level ($E_F$) in CrO$_2$ was determined using
polarization-dependent X-ray absorption spectroscopy (XAS) and X-ray magnetic
circular dichroism (XMCD) from high-quality, single-crystal films. A sharp peak
observed just above $E_F$ is excited only by the electric field vector ($\bf
E$) normal to the tetragonal $c$-axis, characteristic of a narrow band
($\approx$ 0.7 eV bandwidth) constituted from O 2$p$ orbitals perpendicular to
$c$ (O 2$p_y$) hybridized with Cr 3$d_{xz-yz}$ $t_{2g}$ states. By comparison
with band-structure and configuration-interaction (CI) cluster calculations our
results support a model of CrO$_2$ as a half-metallic ferromagnet with large
exchange-splitting energy ($\Delta_{exch-split}$ $\approx$ 3.0 eV) and
substantial correlation effects.


  We demonstrate a new approach for dynamically manipulating the optical
response of an atomically thin semiconductor, a monolayer of MoSe2, by
suspending it over a metallic mirror. First, we show that suspended van der
Waals heterostructures incorporating a MoSe2 monolayer host spatially
homogeneous, lifetime-broadened excitons. Then, we interface this nearly ideal
excitonic system with a metallic mirror and demonstrate control over the
exciton-photon coupling. Specifically, by electromechanically changing the
distance between the heterostructure and the mirror, thereby changing the local
photonic density of states in a controllable and reversible fashion, we show
that both the absorption and emission properties of the excitons can be
dynamically modulated. This electromechanical control over exciton dynamics in
a mechanically flexible, atomically thin semiconductor opens up new avenues in
cavity quantum optomechanics, nonlinear quantum optics, and topological
photonics.


  The region of the Columbia plot with two light quark flavors is not yet
conclusively understood. Non-perturbative effects, e.g. the magnitude of the
anomalous U(1) axial symmetry breaking, decides on the nature of the phase
transition in this region. We report on our study of this region of the
Columbia plot using lattice techniques. We use gauge field ensembles generated
within the Highly Improved Staggered Quark discretization scheme, with the
strange quark mass fixed at its physical value and the light quark mass varied
such that $m_l=m_s/27$ and $m_s/40$, where $m_l=m_s/27$ corresponds to the
physical light quark mass. We study the eigenvalue spectrum of QCD using the
overlap Dirac operator on these gauge field ensembles at finite temperature
around the chiral transition temperature $T_c$, as the light quark masses
approach the chiral limit, and infer about the fate of the anomalous $U_A(1)$
symmetry breaking.


  Previous studies showed that hydro-climate processes are stochastic and
complex systems, and it is difficult to discover the hidden patterns in the all
non-stationary data and thoroughly understand the hydro-climate relationships.
For the purpose to show multi-time scale responses of a hydrological variable
to climate change, we developed an integrated approach by combining wavelet
analysis and regression method, which is called wavelet regression (WR). The
customization and the advantage of this approach over the existing methods are
presented below: (1) The patterns in the data series of a hydrological variable
and its related climatic factors are revealed by the wavelet analysis at
different time scales. (2) The hydro-climate relationship of each pattern is
revealed by the regression method based on the results of wavelet analysis. (3)
The advantage of this approach over the existing methods is that the approach
provides a routing to discover the hidden patterns in the stochastic and
non-stationary data and quantitatively describe the hydro-climate relationships
at different time scales.


  A Ferrers rook graph is a graph whose vertices correspond to the dots in a
Ferrers diagram, and where two vertices are adjacent if they are in the same
row or the same column. We propose a conjectural formula for the gonality of
Ferrers rook graphs, and prove this conjecture for a few infinite families of
Ferrers diagrams. We also prove the conjecture for all Ferrers diagrams $F$
with $|F| \leq 8$.


  Data on pion polarizabilities obtained in different experiments are reviewed.
The values of the dipole and quadrupole polarizabilities of the pi^0 and
pi^{+-} mesons found are compared with predictions of dispersion sum rules
(DSRs) and two-loop calculations in the framework of chiral perturbation theory
(ChPT). Possible reasons of a difference between the predictions of DSRs and
ChPT are discussed.


  We study the distribution of values of the Riemann zeta function $\zeta(s)$
on vertical lines $\Re s + i \mathbb{R}$, by using the theory of Hilbert space.
We show among other things, that, $\zeta(s)$ has a Fourier expansion in the
half-plane $\Re s \geq 1/2$ and its Fourier coefficients are the binomial
transform involving the Stieltjes constants. As an application, we show
explicit computation of the Poisson integral associated with the logarithm of
$\zeta(s) - s/(s-1)$. Moreover, we discuss our results with respect to the
Riemann and Lindel\"{o}f hypotheses on the growth of the Fourier coefficients.


  The property that the polynomial cohomology with coefficients of a finitely
generated discrete group is canonically isomorphic to the group cohomology is
called the (weak) isocohomological property for the group. In the case when a
group is of type $HF^\infty$, i.e. that has a classifying space with the
homotopy type of a cellular complex with finitely many cells in each dimension,
we show that the isocohomological property is equivalent to the universal cover
of the classifying space satisfying polynomially bounded higher Dehn functions.
If a group is hyperbolic relative to a collection of subgroups, each of which
is polynomially combable (respectively $HF^\infty$ and isocohomological), then
we show that the group itself has these respective properties too. Combining
with the results of Connes-Moscovici and Dru{\c{t}}u-Sapir we conclude that a
group satisfies the Novikov conjecture if it is relatively hyperbolic to
subgroups that are of property RD, of type $HF^\infty$ and isocohomological.


  From the steady Stokes and Navier-Stokes models, a penalization method has
been considered by several authors for approximating those fluid equations
around obstacles. In this work, we present a justification for using fictitious
domains to study obstacles immersed in incompressible viscous fluids through a
simplified version of Brinkman's law for porous media. If the scalar function
$\psi$ is considered as the inverse of permeability, it is possible to study
the singularities of $\psi$ as approximations of obstacles (when $\psi$ tends
to $\infty$) or of the domain corresponding to the fluid (when $\psi = 0$ or is
very close to $0$). The strong convergence of the solution of the perturbed
problem to the solution of the strong problem is studied, also considering
error estimates that depend on the penalty parameter, both for fluids modeled
with the Stokes and Navier-Stokes equations with inhomogeneous boundary
conditions. A numerical experiment is presented that validates this result and
allows to study the application of this perturbed problem simulation of flows
and the identification of obstacles.


  We make an extensive rigorous study on convergent behaviour of Morse-Feshbach
nonlinear perturbation series (MFNPS) to find out energy levels of the
anharmonic oscillator (AHO) in both weak and strong coupling limit. We develop
a new method of multi step optimal splitting in order to get convergency in
MFNPS for ground state of AHO and found that two step optimal splitting is
sufficient to provide convergency in MFNPS. Unlike the ground state the optimal
splitting parameters for excited states is modified according to their
dependency on state in order to achieve convergency in MFNPS.


  The ~15.1 years period found in the long-term UBV photoelectric and
photographic photometry of the symbiotic nova V1016 Cyg is detected also in the
(J-K) colour index and in the UV continuum and emission line fluxes from IUE
and HUT spectra. It could be interpreted either as the effect of recurrent
enhanced mass loss episodes from the Mira type variable companion to a hot
component along its ultra-wide orbit (proposed from recent HST observations) or
the true orbital period of the inner, unresolved binary of a triple system. A
410-day delay of the maximum of UV emission lines fluxes with respect to the
maximum of continuum was found. The pulsation period of the Mira type variable
was improved to 474+/-6 days.


  We show how the unitarized description of pion nucleon scattering within
Heavy Baryon Chiral Perturbation Theory can be considerably improved, by a
suitable reordering of the expansion over the nucleon mass. Within this
framework, the $\Delta$ resonance and its associated pole can be recovered from
the chiral parameters obtained from low-energy determinations. In addition, we
can obtain a good description of the six $S$ and $P$ wave phase shifts in terms
of chiral parameters with a natural size and compatible with the Resonance
Saturation Hypothesis.


  Electricity theft detection issue has drawn lots of attention during last
decades. Timely identification of the electricity theft in the power system is
crucial for the safety and availability of the system. Although sustainable
efforts have been made, the detection task remains challenging and falls short
of accuracy and efficiency, especially with the increase of the data size.
Recently, convolutional neural network-based methods have achieved better
performance in comparison with traditional methods, which employ handcrafted
features and shallow-architecture classifiers. In this paper, we present a
novel approach for automatic detection by using a multi-scale dense connected
convolution neural network (multi-scale DenseNet) in order to capture the
long-term and short-term periodic features within the sequential data. We
compare the proposed approaches with the classical algorithms, and the
experimental results demonstrate that the multiscale DenseNet approach can
significantly improve the accuracy of the detection. Moreover, our method is
scalable, enabling larger data processing while no handcrafted feature
engineering is needed.


  Theories of rough sets and soft sets are powerful mathematical tools for
modelling various types of vagueness. Hybrid model combining a rough set with a
soft set which is called soft rough set proposed by Feng et al. [3] in 2010. In
this paper, we study soft covering based rough sets from the topological view.
We present under which conditions soft covering lower approximation operation
become interior operator and the soft covering upper approximation become
closure operator. Also some new methods for generating topologies are obtained.
Finally, we study the relationship between concepts of topology and soft
covering lower and soft covering upper approximations.


  A real-time path integral for ultrasoft QCD is formulated. It exhibits a
Feynman's influence functional. The statistical properties of the theory and
the gauge symmetry are explicit. The correspondence is established with the
alternative version, where a noise term enters a transport equation.


  We say that an edge-coloring of a graph $G$ is proper if every pair of
incident edges receive distinct colors, and is rainbow if no two edges of $G$
receive the same color. Furthermore, given a fixed graph $F$, we say that $G$
is rainbow $F$-saturated if $G$ admits a proper edge-coloring which does not
contain any rainbow subgraph isomorphic to $F$, but the addition of any edge to
$G$ makes such an edge-coloring impossible. The maximum number of edges in a
rainbow $F$-saturated graph is the rainbow Tur\'an number, whose study was
initiated in 2007 by Keevash, Mubayi, Sudakov, and Verstra\"ete. Recently,
Bushaw, Johnston, and Rombach introduced study of a corresponding saturation
problem, asking for the minimum number of edges in a rainbow $F$-saturated
graph. We term this minimum the proper rainbow saturation number of $F$,
denoted $\mathrm{sat}^*(n,F)$. We asymptotically determine
$\mathrm{sat}^*(n,C_4)$, answering a question of Bushaw, Johnston, and Rombach.
We also exhibit constructions which establish upper bounds for
$\mathrm{sat}^*(n,C_5)$ and $\mathrm{sat}^*(n,C_6)$.


  The edge of the network has the potential to host services for supporting a
variety of user applications, ranging in complexity from data preprocessing,
image and video rendering, and interactive gaming, to embedded systems in
autonomous cars and built environments. However, the computational and data
resources over which such services are hosted, and the actors that interact
with these services, have an intermittent availability and access profile,
introducing significant risk for user applications that must rely on them. This
article investigates the development of an edge marketplace, which is able to
support multiple providers for offering services at the network edge, and to
enable demand supply for influencing the operation of such a marketplace.
Resilience, cost, and quality of service and experience will subsequently
enable such a marketplace to adapt its services over time. This article also
describes how distributed-ledger technologies (such as blockchains) provide a
promising approach to support the operation of such a marketplace and regulate
its behavior (such as the GDPR in Europe) and operation. Two application
scenarios provide context for the discussion of how such a marketplace would
function and be utilized in practice.


  An intriguing question in martingale optimal transport is to characterize the
martingale with prescribed initial and terminal marginals whose transition
kernel is as Gaussian as possible. In this work we address an extension of this
question, in which the role of the Gaussian distribution is replaced by an
arbitrary reference measure $q$. Our first main result is a dual formulation of
the corresponding martingale optimization problem in terms of convex functions.
  In the well-studied case when $q$ is Gaussian, the careful analysis of the
solution to the above-mentioned optimization problem is a crucial building
block in the construction of Bass martingales, i.e., Brownian martingales
induced by gradients of convex functions with possibly non-degenerate starting
laws. In our second main result we extend this concept beyond the Gaussian case
by introducing the notion of $q$-Bass martingales in discrete time, and give
sufficient conditions for their existence.


  The one-loop level mediated $t-> c \gamma$ decay is analyzed in the framework
of 331 models, which induce three-level flavor-changing neutral currents
mediated by an extra neutral gauge boson, Z', and a neutral scalar boson, \phi.
These models also predict new charged gauge and scalar bosons, together with
three new quarks, which can be exotic (with electric charges of -4/3e and 5/3e)
or standard model like. Apart from the contribution of the W boson, the $t\to
c\gamma$ decay receives contributions induced by the extra gauge boson and the
neutral scalar boson, which are generic for 331 models. In the so-called
minimal 331 model, there are additional contributions from the new charged
gauge and scalar bosons accompanied by the exotic quarks. We present analytical
results for the most general $t-> c\gamma$ amplitude in terms of transcendental
functions. For the numerical analysis we focus on the minimal 331 model: the
current bounds on the model parameters are examined and a particular scenario
is discussed in which the corresponding branching ratio could be of the order
of 10^{-6}, with the dominant contributions arising from the charged gauge
bosons and a relatively light neutral scalar boson with flavor-changing
couplings, whereas the Z' contribution would be of the order of 10^{-9} for
m_{Z'}>2 TeV. However, a further suppression could be expected due to a
potential suppression of the values of the flavor-changing coupling constants.
Under the same assumptions, in 331 models without exotic quarks, the $t->
c\gamma$ branching ratio would receive the dominant contribution from the
neutral scalar boson, which could be of the order of 10^{-7} for a Higgs mass
of a few hundreds of GeVs.


  In this article we develop a new methodology to prove weak approximation
results for general stochastic differential equations. Instead of using a
partial differential equation approach as is usually done for diffusions, the
approach considered here uses the properties of the linear equation satisfied
by the error process. This methodology seems to apply to a large class of
processes and we present as an example the weak approximation of stochastic
delay equations.


  In extremely large-scale multiple input multiple output (XL-MIMO) systems for
future sixth-generation (6G) communications, codebook-based beam training
stands out as a promising technology to acquire channel state information
(CSI). Despite their effectiveness, when the pilot overhead is limited,
existing beam training methods suffer from significant achievable rate
degradation for remote users with low signal-to-noise ratio (SNR). To tackle
this challenge, leveraging the error-correcting capability of channel codes, we
introduce channel coding theory into hierarchical beam training to extend the
coverage area. Specifically, we establish the duality between hierarchical beam
training and channel coding, and the proposed coded beam training scheme serves
as a general framework. Then, we present two specific implementations
exemplified by coded beam training methods based on Hamming codes and
convolutional codes, during which the beam encoding and decoding processes are
refined respectively to better accommodate the beam training problem.
Simulation results have demonstrated that the proposed coded beam training
method can enable reliable beam training performance for remote users with low
SNR while keeping training overhead low.


  This paper proposes a model for specifying data flow based parallel data
processing programs agnostic of target Big Data processing frameworks. The
paper focuses on the formal abstract specification of non-iterative and
iterative programs, generalizing the strategies adopted by data flow Big Data
processing frameworks. The proposed model relies on monoid AlgebraandPetri
Netstoabstract Big Data processing programs in two levels: a high level
representing the program data flow and a lower level representing data
transformation operations (e.g., filtering, aggregation, join). We extend the
model for data processing programs proposed in [1], to enable the use of
iterative programs. The general specification of iterative data processing
programs implemented by data flow-based parallel programming models is
essential given the democratization of iterative and greedy Big Data analytics
algorithms. Indeed, these algorithms call for revisiting parallel programming
models to express iterations. The paper gives a comparative analysis of the
iteration strategies proposed byApache Spark, DryadLINQ, Apache Beam and Apache
Flink. It discusses how the model achieves to generalize these strategies.


  The sets of closed and closed-normal subgroups of a profinite group carry a
natural profinite topology. Through a combination of algebraic and topological
methods the size of these subgroup spaces is calculated, and the spaces
partially classified up to homeomorphism.


  We report the pressure-dependent optical conductivity spectra of a heavy
fermion (HF) compound CeIn3 below the Neel temperature of 10 K to investigate
the existence of the HF state in the antiferromagnetic (AFM) phase. The peak
due to the interband transition in the hybridization gap between the conduction
band and nearly localized 4f states (c-f hybridization) appears at the photon
energy of about 20 meV not only in the HF regime but also in the AFM regime.
Both the energy and intensity of the c-f hybridization peak continuously
increase with the application of pressure from the AFM to the HF regime. This
result suggests that the c-f hybridization, as well as the heavy fermions,
exists even in the AFM phase of CeIn3.


  I present some new results related to our understanding of the masses of
galaxies both in the local and high-redshift Universe. At high-redshift new
Spitzer data on galaxies in the Gemini Deep Deep Survey allow us a more
accurate measure of stellar mass to light ratios (using rest frame near-IR
light) showing a refinement of the measurements but not great discrepancies. In
the local universe a new method is explored to estimate the baryonic mass
function of galaxies including contributions from unseen HI. This points to an
interesting result: that the baryonic mass function of galaxies may in fact be
quite steep, of comparable slope to the mass function of dark matter haloes.


  We show that in any $n$-player $m$-action normal-form game, we can obtain an
approximate equilibrium by sampling any mixed-action equilibrium a small number
of times. We study three types of equilibria: Nash, correlated and coarse
correlated. For each one of them we obtain upper and lower bounds on the number
of samples required for the empirical distribution over the sampled action
profiles to form an approximate equilibrium with probability close to one.
  These bounds imply that using a small number of samples we can test whether
or not players are playing according to an approximate equilibrium, even in
games where $n$ and $m$ are large. In addition, our results substantially
improve previously known upper bounds on the support size of approximate
equilibria in games with many players. In particular, for all the three types
of equilibria we show the existence of approximate equilibrium with support
size polylogarithmic in $n$ and $m$, whereas the previously best-known upper
bounds were polynomial in $n$.


  Shortly after the Gor'kov microscopic derivation of the Ginzburg-Landau (GL)
model via a small order parameter expansion in Bardeen-Cooper-Schrieffer theory
of superconductivity, the derivation was carried to next-to-leading order in
that parameter and its spatial derivatives. The aim was to obtain a generalized
GL free energy that approximates the microscopic model better. Since 1960s,
multiple works have claimed or implicitly assumed that this extended GL model
corresponds to the free energy and has solutions in the form of local minima
describing superconductivity, such as vortex solutions. In contrast to this, we
prove that this extended GL functional does not represent free energy since it
does not have any solutions in the form of minima. Accordingly, it cannot be
used to describe superconducting states.


  We prove existence and uniqueness of distributional solutions to the KPZ
equation globally in space and time, with techniques from paracontrolled
analysis. Our main tool for extending the analysis on the torus to the full
space is a comparison result that gives quantitative upper and lower bounds for
the solution. We then extend our analysis to provide a path-by-path
construction of the random directed polymer measure on the real line and we
derive a variational characterisation of the solution to the KPZ equation.


  To each complex semisimple Lie algebra $\mathfrak{g}$ and regular element
$a\in\mathfrak{g}_{\text{reg}}$, one associates a Mishchenko-Fomenko subalgebra
$\mathcal{F}_a\subseteq\mathbb{C}[\mathfrak{g}]$. This subalgebra amounts to a
completely integrable system on the Poisson variety $\mathfrak{g}$, and as such
has a bifurcation diagram $\Sigma_a\subseteq\mathrm{Spec}(\mathcal{F}_a)$. We
prove that $\Sigma_a$ has codimension one in $\mathrm{Spec}(\mathcal{F}_a)$ if
$a\in\mathfrak{g}_{\text{reg}}$ is not nilpotent, and that it has codimension
one or two if $a\in\mathfrak{g}_{\text{reg}}$ is nilpotent. In the nilpotent
case, we show each of the possible codimensions to be achievable. Our results
significantly sharpen existing estimates of the codimension of $\Sigma_a$.


  ML-estimation based on mixtures of Normal distributions is a widely used tool
for cluster analysis. However, a single outlier can make the parameter
estimation of at least one of the mixture components break down. Among others,
the estimation of mixtures of t-distributions by McLachlan and
  Peel [Finite Mixture Models (2000) Wiley, New York] and the addition of a
further mixture component accounting for ``noise'' by Fraley and Raftery
  [The Computer J. 41 (1998) 578-588] were suggested as more robust
alternatives.
  In this paper, the definition of an adequate robustness measure for cluster
analysis is discussed and bounds for the breakdown points of the mentioned
methods are given. It turns out that the two alternatives, while adding
stability in the presence of outliers of moderate size, do not possess a
substantially better breakdown behavior than estimation based on Normal
mixtures. If the number of clusters s is treated as fixed, r additional points
suffice for all three methods to let the parameters of r clusters explode. Only
in the case of r=s is this not possible for t-mixtures. The ability to estimate
the number of mixture components, for example, by use of the Bayesian
information criterion of Schwarz [Ann. Statist. 6 (1978)
  461-464], and to isolate gross outliers as clusters of one point, is crucial
for an improved breakdown behavior of all three techniques. Furthermore, a
mixture of Normals with an improper uniform distribution is proposed to achieve
more robustness in the case of a fixed number of components.


  In this article, I propose a concept of the $p$-on which is modelled on the
multi-photon absorptions in quantum optics. It provides a commutative ring
structure in quantum mechanics. Using it, I will give an operator
representation of the Riemann $\zeta$ function.


  Consider two random strings having the same length and generated by an iid
sequence taking its values uniformly in a fixed finite alphabet. Artificially
place a long constant block into one of the strings, where a constant block is
a contiguous substring consisting only of one type of symbol. The long block
replaces a segment of equal size and its length is smaller than the length of
the strings, but larger than its square-root. We show that for sufficiently
long strings the optimal alignment corresponding to a Longest Common
Subsequence (LCS) treats the inserted block very differently depending on the
size of the alphabet. For two-letter alphabets, the long constant block gets
mainly aligned with the same symbol from the other string, while for three or
more letters the opposite is true and the block gets mainly aligned with gaps.
  We further provide simulation results on the proportion of gaps in blocks of
various lengths. In our simulations, the blocks are "regular blocks" in an iid
sequence, and are not artificially inserted. Nonetheless, we observe for these
natural blocks a phenomenon similar to the one shown in case of
artificially-inserted blocks: with two letters, the long blocks get aligned
with a smaller proportion of gaps; for three or more letters, the opposite is
true.
  It thus appears that the microscopic nature of two-letter optimal alignments
and three-letter optimal alignments are entirely different from each other.


  This paper investigates properties of the class of graphs based on
exchangeable point processes. We provide asymptotic expressions for the number
of edges, number of nodes and degree distributions, identifying four regimes:
(i) a dense regime, (ii) a sparse almost dense regime, (iii) a sparse regime
with power-law behaviour, and (iv) an almost extremely sparse regime. We show
that under mild assumptions, both the global and local clustering coefficients
converge to constants which may or may not be the same. We also derive a
central limit theorem for the number of nodes. Finally, we propose a class of
models within this framework where one can separately control the latent
structure and the global sparsity/power-law properties of the graph.


  In the course of our search for double degenerate (DD) binaries as potential
progenitors of type Ia supernovae with the UVES spectrograph at the ESO VLT
(ESO SN Ia Progenitor surveY - SPY) we discovered that the white dwarf HE
1414-0848 is a double-lined DA+DA binary with an orbital period of P = 12h 25m
39s. Semi-amplitudes of 128km/s and 100km/s are derived for the individual
components. The amplitude ratio and the measured difference in gravitational
redshift is used to estimate the masses of the individual components: 0.55Msol
and 0.71Msol. Hence the total mass of the HE 1414-0848 system is 1.26Msol, only
10% below the Chandrasekhar limit. The results of a model atmosphere analysis
are consistent with our mass estimated from the orbit. Temperatures of the
individual components are also determined. Possible scenarios for the formation
of this system are discussed. The system will merge due to loss of angular
momentum via gravitational wave radiation after two Hubble times. HE 1414-0848
does not qualify as a SN Ia progenitor, but it is the most massive close DD
known today.


  We present a IIB supergravity solution dual to a spatially anisotropic
finite-temperature N=4 super Yang-Mills plasma. The solution is static,
possesses an anisotropic horizon, and is completely regular. The full geometry
can be viewed as a renormalization group flow from an AdS geometry in the
ultraviolet to a Lifshitz-like geometry in the infrared. The anisotropy can be
equivalently understood as resulting from a position-dependent theta-term or
from a non-zero number density of dissolved D7-branes. The holographic stress
tensor is conserved and anisotropic. The presence of a conformal anomaly plays
an important role in the thermodynamics of the system. We construct the phase
diagram, which exhibits homogeneous and inhomogeneous (i.e. mixed) phases, and
comment on similarities with QCD at finite baryon density. At low densities the
homogeneous phase displays several instabilities reminiscent of instabilities
of weakly coupled plasmas.


  We report the fabrication of high Tc superconducting wires by photodoping a
GdBa2Cu3O{6.5} thin film. An optical near-field probe was used to locally
excite carriers in the system at room temperature. Trapping of the
photogenerated electrons define a confining potential for the conducting holes
in the CuO planes. Spatially resolved reflectance measurements show the
photogenerated nanowires to be ~ 250 nm wide. Electron diffusion, before
electron capture, is believed to be responsible for the observed width of the
wires.


  We suggest that tunable orientational nonlinearity of nematic liquid crystals
can be employed for all-optical switching in periodic photonic structures with
liquid-crystal defects. We consider a one-dimensional periodic structure of Si
layers with a local defect created by infiltrating a liquid crystal into a
pore, and demonstrate, by solving numerically a system of coupled nonlinear
equations for the nematic director and the propagating electric field, that the
light-induced Freedericksz transition can lead to a sharp switching and diode
operation in the photonic devices.


  This paper continues the project, begun in \cite{IMF}, of harmonizing
Cartan's classical equivalence method and the modern equivariant moving frame
in a framework dubbed \emph{involutive moving frames}. As an attestation of the
fruitfulness of our framework, we obtain a new, constructive and intuitive
proof of the Lie-Tresse theorem (Fundamental basis theorem) and a first general
upper bound on the minimal number of generating differential invariants for Lie
pseudo-groups. Further, we demonstrate the computational advantages of this
framework by studying the equivalence problem for first order PDE in two
independent variables and one dependent variable under point transformations.


  We derive the radial acceleration of stars in galaxies by using basic
features of thermodynamics, statistical mechanics and general relativity. We
assume that the "dark" component of the radial acceleration is originated from
the reaction of dark energy to the presence of baryonic matter. It can be also
explained as the macroscopic manifestation of a huge number of extremely soft
bosonic excitations of the dark energy medium with wavelength larger than the
size of the cosmological horizon, in thermal equilibrium with de Sitter
spacetime. Our formula agrees with the phenomenological relation proposed by
McGaugh et al. which, in turns, fits a large amount of observational data and
with the MOND theory. We also show that our formula appears as the weak field
limit of Einstein's general relativity sourced by an anisotropic fluid.


  We investigate the coupled dynamics of the local hydrodynamics and global
electric response of an electrodialysis system, which consists of an
electrolyte solution adjacent to a charge selective membrane under electric
forcing. Under a DC electric current, counterions transport through the charged
membrane while the passage of co-ions is restricted, thereby developing ion
concentration polarization (ICP) or gradients. At sufficiently large currents,
simultaneous measurements of voltage drop and flow field reveal several
distinct dynamic regimes. Initially, the electrodialysis system displays a
steady Ohmic voltage difference ($\Delta V_{ohm}$), followed by a constant
voltage jump ($\Delta V_c$). Immediately after this voltage increase,
micro-vortices set in and grow both in size and speed with time. After this
growth, the resultant voltage levels off around a fixed value. The average
vortex size and speed stabilize as well, while the individual vortices become
unsteady and dynamic. These quantitative results reveal that micro-vortices set
in with an excess voltage drop (above $\Delta V_{ohm} + \Delta V_c$) and
sustain an approximately constant electrical conductivity, destroying the
initial ICP with significantly low viscous dissipation.


  Regarding a special class of pure F(R) gravity in three dimensions, we
obtain, analytically, Lifshitz-like black hole solutions. We check the
geometrical properties of the solutions which behave such as charged BTZ black
holes in special limit. We also investigate the thermodynamic properties of the
solutions and examine the first law of thermodynamics and Smarr formula. In
addition, we study thermal stability via the heat capacity and discuss the
possibility of criticality in the extended phase space.


  As a result of multiple mini-jet production, initial conditions of the QCD
plasma formed in ultrarelativistic nuclear collisions may be inhomogeneous,
with large fluctuations of the local energy density (hot spots), and turbulent,
with a chaotic initial transverse velocity field. Assuming rapid local
thermalization, the evolution of such plasmas is computed using longitudinal
boost-invariant 3+1-dimensional hydrodynamics. We compare the evolution in case
that the speed of sound in the plasma is constant to one resulting from an
equation of state involving a strong first order transition, with a minimum of
the velocity of sound as a function of energy density. We find that azimuthally
asymmetric fluctuations and correlations of the transverse energy flow can
develop in both cases due to the initial inhomogeneities. Hot spots also
enhance significantly high-transverse momenta direct photon yields. In the case
with a phase transition, the hadronization surface evolves into an unusual
foam-like structure. Also in that case, we find that hadronization is
considerably delayed relative to the ideal gas case, just as previous studies
have found for homogeneous initial conditions. The time-delay signature of a
rapid cross-over transition region in the QCD equation of state (as observable
via meson interferometry) is thus found to be remarkably robust to
uncertainties in the initial conditions in heavy-ion reactions.


  In 2019, we introduced games in Minkowski spacetime as a generalization of
game theory to special relativity that subsumes games in normal form (spacelike
separation) and games in extensive form (timelike separation). Many concepts
including Nash equilibria naturally extend to spacetime games. We also
emphasized the importance of these games to model quantum experiments such as
Bell experiments and more generally any adaptive measurements. Subsequent work
suggested to formalize a special case of such games in terms of strategy
presheaves. In the case that measurements have a unique causal bridge and if a
natural cover is taken, we show that the two frameworks are isomorphic to each
other and provide complementary perspectives. Spacetime games provide a visual
and intuitive framework that also captures the distinction between joint
experiments and either-or experiments, so that they are rich enough in their
causal structure to imply a natural cover for the corresponding causal
contextuality scenario. Based on this observation, we suggest to define the
strategy presheaf directly based on the pure strategies (and restrictions
thereof) of the spacetime game, and we show that the sheaf property obtains for
the games at hand. The argument is rather simple and similar to event sheaves
for the flat case. Finally, we explain how, in the other direction, the failure
of the sheaf property on strategy distribution presheaves is consistent with
our previous argument that Nash game theory is not compatible with quantum
physics. This shows that the insights of the two frameworks, taken together,
can contribute positively to the advancement of the field of quantum
foundations.


  The 500-meter Aperture Spherical Radio Telescope(FAST) has an active
reflector. During the observation, the reflector will be deformed into a
paraboloid of 300-meters. To improve its surface accuracy, we propose a scheme
for photogrammetry to measure the positions of 2226 nodes on the reflector. And
the way to detect the nodes in the photos is the key problem in photogrammetry.
This paper applies Convolutional Neural Network(CNN) with candidate regions to
detect the nodes in the photos. The experiment results show a high recognition
rate of 91.5%, which is much higher than the recognition rate of traditional
edge detection.


  We present black hole masses and accretion rates for 182 Type 1 AGN in
COSMOS. We estimate masses using the scaling relations for the broad Hb, MgII,
and CIV emission lines in the redshift ranges 0.16<z<0.88, 1<z<2.4, and
2.7<z<4.9. We estimate the accretion rate using an Eddington ratio L_I/L_Edd
estimated from optical and X-ray data. We find that very few Type 1 AGN accrete
below L_I/L_Edd ~ 0.01, despite simulations of synthetic spectra which show
that the survey is sensitive to such Type 1 AGN. At lower accretion rates the
BLR may become obscured, diluted or nonexistent. We find evidence that Type 1
AGN at higher accretion rates have higher optical luminosities, as more of
their emission comes from the cool (optical) accretion disk with respect to
shorter wavelengths. We measure a larger range in accretion rate than previous
works, suggesting that COSMOS is more efficient at finding low accretion rate
Type 1 AGN. However the measured range in accretion rate is still comparable to
the intrinsic scatter from the scaling relations, suggesting that Type 1 AGN
accrete at a narrow range of Eddington ratio, with L_I/L_Edd ~ 0.1.


  In this paper, we apply a novel approach based on physics-informed neural
networks to the computation of quasinormal modes of black hole solutions in
modified gravity. In particular, we focus on the case of
Einstein-scalar-Gauss-Bonnet theory, with several choices of the coupling
function between the scalar field and the Gauss-Bonnet invariant. This type of
calculation introduces a number of challenges with respect to the case of
General Relativity, mainly due to the extra complexity of the perturbation
equations and to the fact that the background solution is known only
numerically. The solution of these perturbation equations typically requires
sophisticated numerical techniques that are not easy to develop in
computational codes. We show that physics-informed neural networks have an
accuracy which is comparable to traditional numerical methods in the case of
numerical backgrounds, while being very simple to implement. Additionally, the
use of GPU parallelization is straightforward thanks to the use of standard
machine learning environments.


  It follows from the work of Artin and Hooley that, under assumption of the
generalized Riemann hypothesis, the density of the set of primes $q$ for which
a given non-zero rational number $r$ is a primitive root modulo $q$ can be
written as an infinite product $\prod_p \delta_p$ of local factors $\delta_p$
reflecting the degree of the splitting field of $X^p-r$ at the primes $p$,
multiplied by a somewhat complicated factor that corrects for the
`entanglement' of these splitting fields. We show how the correction factors
arising in Artin's original primitive root problem and some of its
generalizations can be interpreted as character sums describing the nature of
the entanglement. The resulting description in terms of local contributions is
so transparent that it greatly facilitates explicit computations, and naturally
leads to non-vanishing criteria for the correction factors. The method not only
applies in the setting of Galois representations of the multiplicative group
underlying Artin's conjecture, but also in the GL$_2$-setting arising for
elliptic curves. As an application, we compute the density of the set of primes
of cyclic reduction for Serre curves.


  We show preliminary results of an ongoing investigation aimed at determining
the configuration of the magnetic field vector in the threads of a quiescent
hedgerow solar prominence using high-spatial resolution spectropolarimetric
observations taken in the He I 1083.0 nm multiplet. The data consist of a
two-dimensional map of a quiescent hedgerow prominence showing vertical
threads. The observations were obtained with the Tenerife Infrared Polarimeter
attached to the German Vacuum Tower Telescope at the Observatorio del Teide
(Spain). The He I 1083.0 nm Stokes signals are interpreted with an inversion
code, which takes into account the key physical processes that generate and/or
modify circular and linear polarization signals in the He I 1083.0 nm triplet:
the Zeeman effect, anisotropic radiation pumping, and the Hanle effect. We
present initial results of the inversions, i.e, the strength and orientation of
the magnetic field vector along the prominence and in prominence threads.


  Spin torque oscillators are spintronic devices that generate a periodic
output signal from a non-periodic input, making them promising candidates for
applications like microwave communications and neuromorphic computing. However,
traditional spin torque oscillators suffer from a limited precessional cone
angle and thermal stability, as well as a need for an applied bias magnetic
field. We use micromagnetic simulations to demonstrate a novel spin torque
oscillator that relies on spin-orbit effects in ferromagnets to overcome these
limitations. The key mechanism behind this oscillator is the generation of an
out-of-plane spin current, in which both the spin flow and the spin orientation
are out-of-plane. The torque from this spin current enables easy-plane coherent
magnetic precession with a large cone angle and high thermal stability over a
micron-scale lateral area. Moreover, the precession occurs about an internal
field in the free layer, thereby eliminating the need for an external bias
field. We demonstrate the feasibility of an easy-plane spin-orbit torque
oscillator at room temperature over a wide parameter space, including the ratio
of the out-of-plane spin current to the conventional spin-Hall spin current,
presenting exciting possibilities for this novel spintronic device.


  In general, the summation of a set of sub-Hamiltonians cannot share a common
eigenstate of each one, only if it is an unentangled product state, such as a
phantom helix state in quantum spin system. Here we present a method, referred
to as the building block method (BBM), for constructing possible spin-1/2 XXZ
Heisenberg lattice systems possessing phantom helix states. We focus on two
types of XXZ dimers as basic elements, with a non-Hermitian parity-time (PT )
field and Hermitian Dzyaloshinskii-Moriya interaction (DMI), which share the
same degenerate eigenstates. Based on these two building blocks, one can
construct a variety of Heisenberg quantum spin systems, which support helix
states with zero energy. The underlying mechanism is the existence of a set of
degenerate eigenstates. Furthermore, we show that such systems act as quantum
spin graphs since they obey the analogs of Kirchhoff's laws for sets of spin
helix states when the non-Hermitian PT fields cancel each other out. In
addition, the dynamic response of the helix states for three types of
perturbations is also investigated analytically and numerically. Our findings
provide a way to study quantum spin systems with irregular geometries beyond
the Bethe ansatz approach.


  Let $|\Psi>$ be an arbitrary stabilizer state distributed between three
remote parties, such that each party holds several qubits. Let $S$ be a
stabilizer group of $|\Psi>$. We show that $|\Psi>$ can be converted by local
unitaries into a collection of singlets, GHZ states, and local one-qubit
states. The numbers of singlets and GHZs are determined by dimensions of
certain subgroups of $S$. For an arbitrary number of parties $m$ we find a
formula for the maximal number of $m$-partite GHZ states that can be extracted
from $|\Psi>$ by local unitaries. A connection with earlier introduced measures
of multipartite correlations is made. An example of an undecomposable
four-party stabilizer state with more than one qubit per party is given. These
results are derived from a general theoretical framework that allows one to
study interconversion of multipartite stabilizer states by local Clifford group
operators. As a simple application, we study three-party entanglement in
two-dimensional lattice models that can be exactly solved by the stabilizer
formalism.


  We introduce deep learning based communication methods for successive
refinement of images over wireless channels. We present three different
strategies for progressive image transmission with deep JSCC, with different
complexity-performance trade-offs, all based on convolutional autoencoders.
Numerical results show that deep JSCC not only provides graceful degradation
with channel signal-to-noise ratio (SNR) and improved performance in low SNR
and low bandwidth regimes compared to state-of-the-art digital communication
techniques, but can also successfully learn a layered representation, achieving
performance close to a single-layer scheme. These results suggest that natural
images encoded with deep JSCC over Gaussian channels are almost successively
refinable.


  Large-scale meteorological disasters are increasing around the world, and
power outage damage by natural disaster such as typhoons and earthquakes is
increasing in Japan as well. Corresponding to the need of reduction of economic
losses due to power outages, we are promoting research of resilient grids that
minimizes power outage duration. In this report, we propose PACEM (Poles-Aware
moving Cost Estimation Method) for determining travel costs between failure
points based on the tilt angle and direction of electric poles obtained from
pole-mounted sensors and road condition data. Evaluation result shows that the
total recovery time can be reduced by 28% in the target area.


  Quantum vertex algebra theory, developed by H.-S. Li, allows us to apply
zeroth products of Frenkel-Jing operators, corresponding to Drinfeld
realization of $U_q (\widehat{\mathfrak{sl}}_{n+1})$, on the extension of
Koyama vertex operators. As a result, we obtain an infinite-dimensional space
and describe its structure as a module for the associative algebra $U_q
(\mathfrak{sl}_{n+1})_z$, a certain quantum analogue of
$U(\mathfrak{sl}_{n+1})$ which we introduce in this paper.


  We propose sandwiched video compression -- a video compression system that
wraps neural networks around a standard video codec. The sandwich framework
consists of a neural pre- and post-processor with a standard video codec
between them. The networks are trained jointly to optimize a rate-distortion
loss function with the goal of significantly improving over the standard codec
in various compression scenarios. End-to-end training in this setting requires
a differentiable proxy for the standard video codec, which incorporates
temporal processing with motion compensation, inter/intra mode decisions, and
in-loop filtering. We propose differentiable approximations to key video codec
components and demonstrate that, in addition to providing meaningful
compression improvements over the standard codec, the neural codes of the
sandwich lead to significantly better rate-distortion performance in two
important scenarios.When transporting high-resolution video via low-resolution
HEVC, the sandwich system obtains 6.5 dB improvements over standard HEVC. More
importantly, using the well-known perceptual similarity metric, LPIPS, we
observe 30% improvements in rate at the same quality over HEVC. Last but not
least, we show that pre- and post-processors formed by very
modestly-parameterized, light-weight networks can closely approximate these
results.


  We report results of searches for charmless hadronic B meson decays to
pseudoscalar(pi^+-,K^+-,Pi^0 or Ks^0)-vector(Rho, K* or Omega) final states.
Using 9.7 million BBbar pairs collected with the CLEO detector, we report first
observation of B^- --> Pi^-Rho^0, B^0 --> Pi^+-Rho^-+ and B^- --> Pi^-Omega,
which are expected to be dominated by hadronic b --> u transitions. The
measured branching fractions are (10.4+3.3-3.4+-2.1)x10^-6,
(27.6+8.4-7.4+-4.2)x10^-6 and (11.3+3.3-2.9+-1.4)x10^-6, respectively.
Branching fraction upper limits are set for all the other decay modes
investigated.


  A connection between a unitary quantization scheme and para-Fermi statistics
of order 2 is considered. An appropriate extension of Green's ansatz is
suggested. This extension allows one to transform bilinear and trilinear
commutation relations for the annihilation and creation operators of two
different para-Fermi fields $\phi_{a}$ and $\phi_{b}$ into identity. The way of
incorporating para-Grassmann numbers $\xi_{k}$ into a general scheme of
uniquantization is also offered. For parastatistics of order 2 a new fact is
revealed, namely, the trilinear relations containing both the para-Grassmann
variables $\xi_{k}$ and the field operators $a_{k}$, $b_{m}$ under a certain
invertible mapping go over into the unitary equivalent relations, where
commutators are replaced by anticommutators and vice versa. It is shown that
the consequence of this circumstance is the existence of two alternative
definitions of the coherent state for para-Fermi oscillators. The Klein
transformation for Green's components of the operators $a_{k}$, $b_{m}$ is
constructed in an explicit form that enables us to reduce the initial
commutation rules for the components to the normal commutation relations of
ordinary Fermi fields. A nontrivial connection between trilinear commutation
relations of the unitary quantization scheme and so-called Lie-supertriple
system is analysed. A brief discussion of the possibility of embedding the
Duffin-Kemmer-Petiau theory into the unitary quantization scheme is provided.


  Techniques such as clusterization, neural networks and decision making
usually rely on algorithms that are not well suited to deal with missing
values. However, real world data frequently contains such cases. The simplest
solution is to either substitute them by a best guess value or completely
disregard the missing values. Unfortunately, both approaches can lead to biased
results. In this paper, we propose a technique for dealing with missing values
in heterogeneous data using imputation based on the k-nearest neighbors
algorithm. It can handle real (which we refer to as crisp henceforward),
interval and fuzzy data. The effectiveness of the algorithm is tested on
several datasets and the numerical results are promising.


  In the fast evacuation problem, we study the path planning problem for two
robots who want to minimize the worst-case evacuation time on the unit disk.
The robots are initially placed at the center of the disk. In order to
evacuate, they need to reach an unknown point, the exit, on the boundary of the
disk. Once one of the robots finds the exit, it will instantaneously notify the
other agent, who will make a beeline to it.
  The problem has been studied for robots with the same speed~\cite{s1}. We
study a more general case where one robot has speed $1$ and the other has speed
$s \geq 1$. We provide optimal evacuation strategies in the case that $s \geq
c_{2.75} \approx 2.75$ by showing matching upper and lower bounds on the
worst-case evacuation time. For $1\leq s < c_{2.75}$, we show (non-matching)
upper and lower bounds on the evacuation time with a ratio less than $1.22$.
Moreover, we demonstrate that a generalization of the two-robot search strategy
from~\cite{s1} is outperformed by our proposed strategies for any $s \geq
c_{1.71} \approx 1.71$.


  In a recent series of ground-breaking experiments, Nakajima et al. [Science
308, 414-415 (2005)] showed that the three cyanobacterial clock proteins KaiA,
KaiB, and KaiC are sufficient in vitro to generate circadian phosphorylation of
KaiC. Here, we present a mathematical model of the Kai system. At its heart is
the assumption that KaiC can exist in two conformational states, one favoring
phosphorylation and the other dephosphorylation. Each individual KaiC hexamer
then has a propensity to be phosphorylated in a cyclic manner. To generate
macroscopic oscillations, however, the phosphorylation cycles of the different
hexamers must be synchronized. We propose a novel synchronisation mechanism
based on differential affinity: KaiA stimulates KaiC phosphorylation, but the
limited supply of KaiA dimers binds preferentially to those KaiC hexamers that
are falling behind in the oscillation. KaiB sequesters KaiA and stabilizes the
dephosphorylating KaiC state. We show that our model can reproduce a wide range
of published data, including the observed insensitivity of the oscillation
period to variations in temperature, and that it makes nontrivial predictions
about the effects of varying the concentrations of the Kai proteins.


  Size-structured population models provide a popular means to mathematically
describe phenomena such as bacterial aggregation, schooling fish, and
planetesimal evolution. For parameter estimation, generalized sensitivity
functions (GSFs) provide a tool that quantifies the impact of data from
specific regions of the experimental domain. These functions help identify the
most relevant data subdomains, which enhances the optimization of experimental
design. To our knowledge, GSFs have not been used in the partial differential
equation (PDE) realm, so we provide a novel PDE extension of the discrete and
continuous ordinary differential equation (ODE) concepts of Thomaseth and
Cobelli and Banks et al. respectively. We analyze the GSFs in the context of
size-structured population models, and specifically analyze the Smoluchowski
coagulation equation to determine the most relevant time and volume domains for
three, distinct aggregation kernels. Finally, we provide evidence that
parameter estimation for the Smoluchowski coagulation equation does not require
post-gelation data.


  We study a distinct supersymmetric signal of multi-photons in association
with jets and missing transverse energy. At least one of these photons has the
origin in displaced vertex, thus delayed and non-pointing. We consider a
supersymmetric scenario in which the gravitino is the lightest supersymmetric
particle (LSP) (with a mass $\sim 1~{keV}$) and the lightest neutralino is the
next-to-lightest supersymmetric particle (NLSP). The NLSP decays dominantly
into a photon and a gravitino within the detector with a decay length ranging
from $c\tau_{\tilde{\chi}}\sim$ 50-100 cm. In addition, we assume that the
second lightest neutralino and the lightest neutralino are nearly degenerate
and this leads to a prompt radiative decay of the next-to-lightest neutralino
into a photon and a lightest neutralino with a large branching ratio. Such
degenerate neutralinos can be realised in various representations of the
$SU(5)$, $SO(10)$, and $E(6)$ Grand Unified Theories (GUTs). The non-pointing
photons can be reconstructed at the electromagnetic calorimeter of the ATLAS
inner-detector, which have been designed with good timing and directional
resolution. We find that with a centre-of-mass energy $E_{cm}=14 ~{TeV}$ at an
integrated luminosity of 100 $fb^{-1}$ one may see evidence of hundreds of
tri-photon events and a few four-photons events at the LHC, in addition to
several thousands di-photon events. We also predict the event rates even at the
early phase of LHC run.


  We classify, according to their computational complexity, integer
optimization problems whose constraints and objective functions are polynomials
with integer coefficients and the number of variables is fixed. For the
optimization of an integer polynomial over the lattice points of a convex
polytope, we show an algorithm to compute lower and upper bounds for the
optimal value. For polynomials that are non-negative over the polytope, these
sequences of bounds lead to a fully polynomial-time approximation scheme for
the optimization problem.


  Urban Air Mobility (UAM) represents a promising solution for future
transportation. In this study, we introduce VertiSim, an advanced event-driven
simulator developed to evaluate e-VTOL transportation networks. Uniquely,
VertiSim simultaneously models passenger, aircraft, and energy flows,
reflecting the interrelated complexities of UAM systems. We utilized VertiSim
to assess 19 operational scenarios serving a daily demand for 2,834 passengers
with varying fleet sizes and vertiport distances. The study aims to support
stakeholders in making informed decisions about fleet size, network design, and
infrastructure development by understanding tradeoffs in passenger delay time,
operational costs, and fleet utilization. Our simulations, guided by a
heuristic dispatch and charge policy, indicate that fleet size significantly
influences passenger delay and energy consumption within UAM networks. We find
that increasing the fleet size can reduce average passenger delays, but this
comes at the cost of higher operational expenses due to an increase in the
number of repositioning flights. Additionally, our analysis highlights how
vertiport distances impact fleet utilization: longer distances result in
reduced total idle time and increased cruise and charge times, leading to more
efficient fleet utilization but also longer passenger delays. These findings
are important for UAM network planning, especially in balancing fleet size with
vertiport capacity and operational costs. Simulator demo is available at:
https://tinyurl.com/vertisim-vis


  It is by now clear that the naive rule for the entropy of a black hole,
{entropy} = 1/4 {area of event horizon}, is violated in many interesting cases.
Indeed, several authors have recently conjectured that in general the entropy
of a dirty black hole might be given purely in terms of some surface integral
over the event horizon of that black hole. A formal proof of this conjecture,
using Lorentzian signature techniques, has recently been provided by Wald. This
note performs two functions. Firstly, a rather different proof of this result
is presented --- a proof based on Euclidean signature techniques. The total
entropy is S = 1/4 {k A_H / l_P^2} + \int_H {S} \sqrt{g} d^2x. The integration
runs over a spacelike cross-section of the event horizon H. The surface entropy
density, {S}, is related to the behaviour of the matter Lagrangian under time
dilations. Secondly, I shall consider the specific case of Einstein-Hilbert
gravity coupled to an effective Lagrangian that is an arbitrary function of the
Riemann tensor (though not of its derivatives). In this case a more explicit
result is obtained S = 1/4 {k A_H / l_P^2} + 4 pi {k/hbar} \int_H {partial L /
partial R_{\mu\nu\lambda\rho}} g^\perp_{\mu\lambda} g^\perp_{\nu\rho} \sqrt{g}
d^2x . The symbol $g^\perp_{\mu\nu}$ denotes the projection onto the
two-dimensional subspace orthogonal to the event horizon.


  Naively storing a counter up to value $n$ would require $\Omega(\log n)$ bits
of memory. Nelson and Yu [NY22], following work of [Morris78], showed that if
the query answers need only be $(1+\epsilon)$-approximate with probability at
least $1 - \delta$, then $O(\log\log n + \log\log(1/\delta) +
\log(1/\epsilon))$ bits suffice, and in fact this bound is tight. Morris'
original motivation for studying this problem though, as well as modern
applications, require not only maintaining one counter, but rather $k$ counters
for $k$ large. This motivates the following question: for $k$ large, can $k$
counters be simultaneously maintained using asymptotically less memory than $k$
times the cost of an individual counter? That is to say, does this problem
benefit from an improved {\it amortized} space complexity bound?
  We answer this question in the negative. Specifically, we prove a lower bound
for nearly the full range of parameters showing that, in terms of memory usage,
there is no asymptotic benefit possible via amortization when storing multiple
counters. Our main proof utilizes a certain notion of "information cost"
recently introduced by Braverman, Garg and Woodruff in FOCS 2020 to prove lower
bounds for streaming algorithms.


  Let $(X,T)$ and $(Y,S)$ be two topological dynamical systems, where $(X,T)$
has the weak specification property. Let $\xi$ be an invariant measure on the
product system $(X\times Y, T\times S)$ with marginals $\mu$ on $X$ and $\nu$
on $Y$, with $\mu$ ergodic. Let $y\in Y$ be quasi-generic for $\nu$. Then there
exists a point $x\in X$ generic for $\mu$ such that the pair $(x,y)$ is
quasi-generic for $\xi$. This is a generalization of a similar theorem by T.\
Kamae, in which $(X,T)$ and $(Y,S)$ are full shifts on finite alphabets.


  The isospin distribution of particles and fragments in collisions 96Ru+96Ru,
96Ru+96Zr, 96Zr+96Ru, and 96Zr+96Zr at beam energy 400 AMeV is studied with
isospin dependent QMD model. We find that the rapidity distribution of
differential neutron-proton counting in neutron rich nucleus-nucleus collisions
at intermediate energies is sensitive to the isospin dependent part of nuclear
potential. The study of the N/Z ratio of nucleons, light charged particles
(LCP) and intermediate mass fragments (IMF) shows that the isospin dependent
part of nuclear potential drives IMF to be more isospin symmetric and emitted
nucleons to be more neutron rich. From the study of the time evolution of the
isospin distribution in emitted nucleons, LCP and IMF we find that neutrons
diffuse much faster than protons at beginning and the final isospin
distribution is a result of dynamical balance of symmetry potential and Coulomb
force under the charge conservation.


  Animating virtual avatars with free-view control is crucial for various
applications like virtual reality and digital entertainment. Previous studies
have attempted to utilize the representation power of the neural radiance field
(NeRF) to reconstruct the human body from monocular videos. Recent works
propose to graft a deformation network into the NeRF to further model the
dynamics of the human neural field for animating vivid human motions. However,
such pipelines either rely on pose-dependent representations or fall short of
motion coherency due to frame-independent optimization, making it difficult to
generalize to unseen pose sequences realistically. In this paper, we propose a
novel framework MonoHuman, which robustly renders view-consistent and
high-fidelity avatars under arbitrary novel poses. Our key insight is to model
the deformation field with bi-directional constraints and explicitly leverage
the off-the-peg keyframe information to reason the feature correlations for
coherent results. Specifically, we first propose a Shared Bidirectional
Deformation module, which creates a pose-independent generalizable deformation
field by disentangling backward and forward deformation correspondences into
shared skeletal motion weight and separate non-rigid motions. Then, we devise a
Forward Correspondence Search module, which queries the correspondence feature
of keyframes to guide the rendering network. The rendered results are thus
multi-view consistent with high fidelity, even under challenging novel pose
settings. Extensive experiments demonstrate the superiority of our proposed
MonoHuman over state-of-the-art methods.


  The elemental abundances of planet host stars can shed light on the
conditions of planet forming environments. We test if individual abundances of
130 known/candidate planet hosts in APOGEE are statistically different from
those of a reference doppelganger sample. The reference set comprises objects
selected with the same Teff, logg, [Fe/H], and [Mg/H] as each Kepler Object of
Interest (KOI). We predict twelve individual abundances (X = C, N, O, Na, Al,
Si, Ca, Ti, V, Cr, Mn, Ni) for the KOIs and their doppelgangers using a local
linear model of these four parameters, training on ASPCAP abundance
measurements for a sample of field stars with high fidelity (SNR > 200) APOGEE
observations. We compare element prediction residuals (model-measurement) for
the two samples and find them to be indistinguishable, given a high quality
sample selection. We report median intrinsic dispersions of ~0.038 dex and
~0.041 dex, for the KOI and doppelganger samples, respectively, for these
elements. We conclude that the individual abundances at fixed Teff, logg,
[Fe/H], and [Mg/H] are unremarkable for known planet hosts. Our results
establish an upper limit on the abundance precision required to uncover any
chemical signatures of planet formation in planet host stars.


  The Swift satellite early x-ray data shows a very steep decay in most of the
Gamma-Ray Bursts light curves. This decay is either produced by the rapidly
declining continuation of the central engine activity or by some left-over
radiation starting right after the central engine shuts off. The latter
scenario consists of the emission from an "ember" that cools via adiabatic
expansion and, if the jet angle is larger than the inverse of the source
Lorentz factor, the large angle emission. In this work, we calculate the
temporal and spectral properties of the emission from such a cooling ember,
providing a new treatment for the micro-physics of the adiabatic expansion. We
use the adiabatic invariance of p_{\perp}^2/B (p_{\perp} is the component of
the electrons' momentum normal to the magnetic field, B) to calculate the
electrons' Lorentz factor during the adiabatic expansion; the electron momentum
becomes more and more aligned with the local magnetic field as the expansion
develops. We compare the theoretical expectations of the adiabatic expansion
(and the large angle emission) with the current observations of the early x-ray
data and find that only about 20% of our sample of 107 bursts is potentially
consistent with this model. This leads us to believe that, for most bursts, the
central engine does not turn off completely during the steep decay of the x-ray
light curve; therefore, this phase is produced by the continued rapidly
declining activity of the central engine.


  We prove a result on linear forms related to Peres-Schlag's theorem on badly
approximable numbers with respect to lacunary sequences.


  We consider a stochastic differential game in the context of forward-backward
stochastic differential equations, where one player implements an impulse
control while the opponent controls the system continuously. Utilizing the
notion of "backward semigroups" we first prove the dynamic programming
principle (DPP) for a truncated version of the problem in a straightforward
manner. Relying on a uniform convergence argument then enables us to show the
DPP for the general setting. In particular, this avoids technical constraints
imposed in previous works dealing with the same problem. Moreover, our approach
allows us to consider impulse costs that depend on the present value of the
state process in addition to unbounded coefficients.
  Using the dynamic programming principle we deduce that the upper and lower
value functions are both solutions (in viscosity sense) to the same
Hamilton-Jacobi-Bellman-Isaacs obstacle problem. By showing uniqueness of
solutions to this partial differential inequality we conclude that the game has
a value.


  The variety of all smooth hypersurfaces of given degree and dimension has the
Fermat hypersurface as a natural base point. In order to study the period map
for such varieties, we first determine the integral polarized Hodge structure
of the primitive cohomology of a Fermat hypersurface (as a module over the
automorphism group of the hypersurface). We then focus on the degree 3 case and
show that the period map for cubic fourfolds as analyzed by R. Laza and the
author gives complete information about the period map for cubic hypersurfaces
of lower dimension dimension. In particular, we thus recover the results of
Allcock-Carlson-Toledo on the cubic surface case.


  In structural proof theory, designing and working on large calculi make it
difficult to get intuitions about each rule individually and as part of a whole
system. We introduce two novel tools to help working on calculi using the
approach of graph theory and automata theory. The first tool is a Proof Tree
Automaton (PTA): a tree automaton which language is the derivation language of
a calculus. The second tool is a graphical representation of a calculus called
Proof Tree Graph (PTG). In this directed hypergraph, vertices are sets of terms
(e.g. sequents) and hyperarcs are rules. We explore properties of PTA and PTGs
and how they relate to each other. We show that we can decompose a PTA as a
partial map from a calculus to a traditional tree automaton. We formulate that
statement in the theory of refinement systems. Finally, we compare our
framework to proof nets and string diagrams.


  Sparse matrix vector multiplication (SpMV) is an important kernel in
scientific and engineering applications. The previous optimizations are sparse
matrix format specific and expose the choice of the best format to application
programmers. In this work we develop an auto-tuning framework to bridge gap
between the specific optimized kernels and their general-purpose use. We
propose an SpMV auto-tuner (SMAT) that provides an unified interface based on
compressed sparse row (CSR) to programmers by implicitly choosing the best
format and the fastest implementation of any input sparse matrix in runtime.
SMAT leverage a data mining model, which is formulated based on a set of
performance parameters extracted from 2373 matrices in UF sparse matrix
collection, to fast search the best combination. The experiments show that SMAT
achieves the maximum performance of 75 GFLOP/s in single-precision and 33
GFLOP/s in double-precision on Intel, and 41 GFLOP/s in single-precision and 34
GFLOP/s in double-precision on AMD. Compared with the sparse functions in MKL
library, SMAT runs faster by more than 3 times.


  Human interactions are characterized by explicit as well as implicit channels
of communication. While the explicit channel transmits overt messages, the
implicit ones transmit hidden messages about the communicator (e.g., his/her
intentions and attitudes). There is a growing consensus that providing a
computer with the ability to manipulate implicit affective cues should allow
for a more meaningful and natural way of studying particular non-verbal signals
of human-human communications by human-computer interactions. In this pilot
study, we created a non-dynamic human-computer interaction while manipulating
three specific non-verbal channels of communication: gaze pattern, facial
expression, and gesture. Participants rated the virtual agent on affective
dimensional scales (pleasure, arousal, and dominance) while their physiological
signal (electrodermal activity, EDA) was captured during the interaction.
Assessment of the behavioral data revealed a significant and complex three-way
interaction between gaze, gesture, and facial configuration on the dimension of
pleasure, as well as a main effect of gesture on the dimension of dominance.
These results suggest a complex relationship between different non-verbal cues
and the social context in which they are interpreted. Qualifying considerations
as well as possible next steps are further discussed in light of these
exploratory findings.


  Using the method of paracontrolled distributions, we show the local
well-posedness of an additive noise approximation to the fluctuating
hydrodynamics of the Keller-Segel model on the two-dimensional torus. Our
approximation is a non-linear, non-local, parabolic-elliptic stochastic PDE
with an irregular, heterogeneous space-time noise. As a consequence of the
irregularity and heterogeneity, solutions to this equation must be renormalised
by a sequence of diverging fields. Using the symmetry of the elliptic Green's
function, which appears in our non-local term, we establish that the
renormalisation diverges at most logarithmically, an improvement over the
linear divergence one would expect by power counting. Similar cancellations
also serve to reduce the number of diverging counterterms.


  Photon exchange due to nuclear bremsstrahlung during nuclear collisions can
cause Coulomb excitation in the projectile and the target nuclei. The
corresponding process originated in nuclear timescales can also be observed in
atomic phenomenon experimentally if it delayed by at least with an attosecond
or longer timescales. We have found that this happens due to a mechanism
involving the Eisenbud-Wigner-Smith time delay process. We have estimated
photoionization time delays in atomic collisions utilizing the nonrelativistic
version of random phase approximation with exchange and Hartree-Fock methods.
We present three representative processes in which we can observe the phenomena
in attosecond timescales even though they originate from excitations in the
zeptosecond timescales. Thus the work represents an investigation of parallels
between two neighboring areas of physics. Furthermore the present work suggests
new possibilities for atomic physics research near the Coulomb barrier energy,
where the laser is replaced by nuclear bremsstrahlung.


  Higher-order scalar-tensor theories having an instantaneous mode do not
develop the Ostrogradsky instability even if a seemingly dangerous mode is
present. Such theories satisfy only partially the degeneracy conditions that
are usually imposed to remove the dangerous mode completely, and are dubbed as
U-DHOST theories. We study weak gravitational fields sourced by nonrelativistic
matter distributions in U-DHOST theories. In contrast to the case of totally
degenerate theories where nonlinear derivative interactions are crucial for
exhibiting the Vainshtein mechanism and its partial breaking, we show that in
generic U-DHOST theories the linear analysis is sufficient for weak
gravitational fields. We identify the subset of U-DHOST theories in which solar
system tests are evaded and gravitational waves propagate at the speed of
light. Such theories can however be tested with cosmological observations. We
also point out that there is a particular case of U-DHOST theories where
nonlinear derivative interactions play an important role as in totally
degenerate theories. In that case, it is found, however, that the Vainshtein
mechanism does not operate and gravitational forces are modified.


  Resolution over linear equations is a natural extension of the popular
resolution refutation system, augmented with the ability to carry out basic
counting. Denoted Res(lin_R), this refutation system operates with disjunctions
of linear equations with boolean variables over a ring R, to refute
unsatisfiable sets of such disjunctions. Beginning in the work of [RT08],
through the work of [IS14] which focused on tree-like lower bounds, this
refutation system was shown to be fairly strong. Subsequent work (cf.[Kra17,
IS14, KO18, GK18]) made it evident that establishing lower bounds against
general Res(lin_R) refutations is a challenging and interesting task since the
system captures a 'minimal' extension of resolution with counting gates for
which no super-polynomial lower bounds are known to date.
  We provide the first super-polynomial size lower bounds on general (dag-like)
resolution over linear equations refutations in the large characteristic
regime. In particular we prove that the subset-sum principle 1+x1+...+2^n xn=0
requires refutations of exponential size over Q. Our proof technique is
nontrivial and novel: roughly speaking, we show that under certain conditions
every refutation of a subset-sum instance f=0 must pass through a fat clause
containing an equation f=alpha for each alpha in the image of f under boolean
assignments. We develop a somewhat different approach to prove exponential
lower bounds against tree-like refutations of any subset-sum instance that
depends on n variables, hence also separating tree-like from dag-like
refutations over the rationals. (Abstract continued in the full paper.)


  We investigate the nitrogen substitutional impurity in semiconducting zigzag
and metallic armchair single-wall carbon nanotubes using ab initio density
functional theory. At low concentrations (less than 1 atomic %), the defect
state in a semiconducting tube becomes spatially localized and develops a flat
energy level in the band gap. Such a localized state makes the impurity site
chemically and electronically active. We find that if two neighboring tubes
have their impurities facing one another, an intertube covalent bond forms.
This finding opens an intriguing possibility for tunnel junctions, as well as
the functionalization of suitably doped carbon nanotubes by selectively forming
chemical bonds with ligands at the impurity site. If the intertube bond density
is high enough, a highly packed bundle of interlinked single-wall nanotubes can
form.


  We present the first public version (v0.2) of the open-source and
community-developed Python package, Astropy. This package provides core
astronomy-related functionality to the community, including support for
domain-specific file formats such as Flexible Image Transport System (FITS)
files, Virtual Observatory (VO) tables, and common ASCII table formats, unit
and physical quantity conversions, physical constants specific to astronomy,
celestial coordinate and time transformations, world coordinate system (WCS)
support, generalized containers for representing gridded as well as tabular
data, and a framework for cosmological transformations and conversions.
Significant functionality is under active development, such as a model fitting
framework, VO client and server tools, and aperture and point spread function
(PSF) photometry tools. The core development team is actively making additions
and enhancements to the current code base, and we encourage anyone interested
to participate in the development of future Astropy versions.


  The calculation of finite temperature contributions to the scalar potential
in a quantum field theory is similar to the calculation of loop corrections at
zero temperature. In natural extensions of the Standard Model where loop
corrections to the Higgs potential cancel between Standard Model degrees of
freedom and their symmetry partners, it is interesting to contemplate whether
finite temperature corrections also cancel, raising the question of whether a
broken phase of electroweak symmetry may persist at high temperature. It is
well known that this does not happen in supersymmetric theories because the
thermal contributions of bosons and fermions do not cancel each other. However,
for theories with same spin partners, the answer is less obvious. Using the
Twin Higgs model as a benchmark, we show that although thermal corrections do
cancel at the level of quadratic divergences, subleading corrections still
drive the system to a restored phase. We further argue that our conclusions
generalize to other well-known extensions of the Standard Model where the Higgs
is rendered natural by being the pseudo-Nambu-Goldstone mode of an approximate
global symmetry.


  An observation from the Interface Region Imaging Spectrograph reveals
coherent oscillations in the loops of an M1.6 flare on 2015 March 12. Both the
intensity and Doppler shift of Fe~{\sc{xxi}}~1354.08\AA{}~show clear
oscillations with a period of $\sim$25 seconds. Remarkably similar oscillations
were also detected in the soft X-ray flux recorded by the Geostationary
Operational Environmental Satellites (GOES). With an estimated phase speed of
$\sim$2420~km~s$^{-1}$ and a derived electron density of at least
5.4$\times$10$^{10}$ cm$^{-3}$, the observed short-period oscillation is most
likely the global fast sausage mode of a hot flare loop. We find a phase shift
of $\sim$$\pi$/2 (1/4 period) between the Doppler shift oscillation and the
intensity/GOES oscillations, which is consistent with a recent forward modeling
study of the sausage mode. The observed oscillation requires a density contrast
between the flare loop and coronal background of a factor $\geqslant$42. The
estimated phase speed of the global mode provides an lower limit of the
Alfv\'en speed outside the flare loop. We also find an increase of the
oscillation period, which might be caused by the separation of the loop
footpoints with time.


  We resume the investigation, started in arXiv:1408.6571, of the statistics of
backward clusters in a gas of $N$ hard spheres of small diameter $\varepsilon$.
A backward cluster is defined as the group of particles involved directly or
indirectly in the backwards-in-time dynamics of a given tagged sphere. We
obtain an estimate of the average cardinality of clusters with respect to the
equilibrium measure, global in time, uniform in $\varepsilon, N$ for
$\varepsilon^2 N=1$ (Boltzmann-Grad regime).


  The realization of the Einstein-Podolsky-Rosen effect by the correlation of
spin projections of two particles created in the decay of a single scalar
particle is considered for particles propagating in gravitational field. The
absence of a global definition of spatial directions makes it unclear whether
the correlation may exist in this case and, if yes, what directions in distant
regions must be correlated. It is shown that in a gravitational field an
approximate correlation may exist and the correlated directions are connected
with each other by the parallel transport along the world lines of the
particles. The reason for this is that the actual origin of the quantum
non-locality is founded in local processes.