  We use singular value decomposition to derive a tight lower bound for
geometric discord of arbitrary bipartite states. In a single shot this also
leads to an upper bound of measurement-induced non locality which in turn
yields that for Werner and isotropic states the two measures coincide. We also
emphasize that our lower bound is saturated for all $2\otimes n$ states. Using
this we show that both the generalized Greenberger-Horne-Zeilinger and $W$
states of $N$ qubits satisfy monogamy of geometric discord. Indeed, the same
holds for all $N$-qubit pure states which are equivalent to $W$ states under
stochastic local operations and classical communication. We show by giving an
example that not all pure states of four or higher qubits satisfy monogamy.


  We analyze competition on nonlinear prices in homogeneous goods markets with
consumer search. In equilibrium firms offer two-part tariffs consisting of a
linear price and lump-sum fee. The equilibrium production is socially efficient
as the linear price of equilibrium two-part tariffs equals to the production
marginal cost. Firms thus compete in lump-sum fees, which are dispersed in
equilibrium. We show that sellers enjoy higher profit, whereas consumers are
worse-off with two-part tariffs than with linear prices. The competition
softens because with two-part tariffs firms can make effective per-consumer
demand less elastic than the actual demand.


  We construct mixing processes over an infinite alphabet and ergodic processes
over a finite alphabet for which Shannon mutual information between adjacent
blocks of length $n$ grows as $n^\beta$, where $\beta\in(0,1)$. The processes
are a modification of nonergodic Santa Fe processes, which were introduced in
the context of natural language modeling. The rates of mutual information for
the latter processes are alike and also established in this paper. As an
auxiliary result, it is shown that infinite direct products of mixing processes
are also mixing.


  Standard quantum physics prevents the existence of a joint statistics for
complementary observables. Nevertheless, a joint distribution for complementary
observables can be derived from their imperfect simultaneous measurement
followed by a suitable data inversion. Quantumness is reflected then in the
pathologies of the inferred distribution. We apply this program to the
paradigmatic example of complementarity: the wave-particle duality in a Young
interferometer.


  The Straightness is a measure designed to characterize a pair of vertices in
a spatial graph. It is defined as the ratio of the Euclidean distance to the
graph distance between these vertices. It is often used as an average, for
instance to describe the accessibility of a single vertex relatively to all the
other vertices in the graph, or even to summarize the graph as a whole. In some
cases, one needs to process the Straightness between not only vertices, but
also any other points constituting the graph of interest. Suppose for instance
that our graph represents a road network and we do not want to limit ourselves
to crossroad-to-crossroad itineraries, but allow any street number to be a
starting point or destination. In this situation, the standard approach
consists in: 1) discretizing the graph edges, 2) processing the
vertex-to-vertex Straightness considering the additional vertices resulting
from this discretization, and 3) performing the appropriate average on the
obtained values. However, this discrete approximation can be computationally
expensive on large graphs, and its precision has not been clearly assessed. In
this article, we adopt a continuous approach to average the Straightness over
the edges of spatial graphs. This allows us to derive 5 distinct measures able
to characterize precisely the accessibility of the whole graph, as well as
individual vertices and edges. Our method is generic and could be applied to
other measures designed for spatial graphs. We perform an experimental
evaluation of our continuous average Straightness measures, and show how they
behave differently from the traditional vertex-to-vertex ones. Moreover, we
also study their discrete approximations, and show that our approach is
globally less demanding in terms of both processing time and memory usage. Our
R source code is publicly available under an open source license.


  We show that the following semirings satisfy the same identities: the
semiring $\mathcal{R}_n$ of all reflexive binary relations on a set with $n$
elements, the semiring $\mathcal{U}_n$ of all $n\times n$ upper triangular
matrices over the boolean semiring, the semiring $\mathcal{C}_n$ of all order
preserving and extensive transformations of a chain with $n$ elements. In view
of the result of Kl\'ima and Pol\'ak, which states that $\mathcal{C}_n$ has a
finite basis of identities for all $n$, this implies that the identities of
$\mathcal{R}_n$ and $\mathcal{U}_n$ admit a finite basis as well.


  We have studied thermal gradients in thin Cu and AlMn wires, both
experimentally and theoretically. In the experiments, the wires were Joule
heated non-uniformly at sub-Kelvin temperatures, and the resulting temperature
gradients were measured using normal metal-insulator-superconducting tunnel
junctions. The data clearly shows that even in reasonably well conducting thin
wires with a short ($\sim 10 \mu$m) non-heated portion, significant temperature
differences can form. In most cases, the measurements agree well with a model
which includes electron-phonon interaction and electronic thermal conductivity
by the Wiedemann-Franz law.


  In this paper we study the scalar(tensor) and vector unparticle corrections
for cosmic and black strings. Initially we have considered an static cosmic
string ansatz from which we obtain the solution in terms of first and second
kind Bessel functions. We have also obtained the solution for black string in
the unparticle scenario. We could identify two regimes, namely, a gravity
dominated regime and an ungravity dominated regime. In the gravity dominated
regime the black string solution recovers the usual solution for black strings.
The Hawking temperature was also studied in both regimes and in the ungravity
dominated regime. As in the static and rotating black hole, we found a
fractalization of the event horizon. This points to the fact that
fractalization is a natural consequence of unparticles. Finally, we study the
thermodynamic of the black string in the ungravity scenario by computing the
entropy, heat capacity and free energy. For both cases we find that, depending
on the region of the parameter $d_U$, we can have phase transitions.


  The paper represents original development of thermodynamic criteria of
occurrence conditions of steam-gas explosions in the process of severe
accidents. The received results can be used for modelling of processes of
severe accidents in pressure vessel reactors.


  Context. The first studies with Parker Solar Probe (PSP) data have made
significant progress toward the understanding of the fundamental properties of
ion cyclotron waves in the inner heliosphere. The survey mode particle
measurements of PSP, however, did not make it possible to measure the coupling
between electromagnetic fields and particles on the time scale of the wave
periods.
  Aims. We present a novel approach to study wave-particle energy exchange with
PSP.
  Methods. We use the Flux Angle operation mode of the Solar Probe Cup in
conjunction with the electric field measurements and present a case study when
the Flux Angle mode measured the direct interaction of the proton velocity
distribution with an ion cyclotron wave.
  Results. Our results suggest that the energy transfer from fields to
particles on the timescale of a cyclotron period is equal to approximately 3-6%
of the electromagnetic energy flux. This rate is consistent with the hypothesis
that the ion cyclotron wave was locally generated in the solar wind.


  A complete analysis is given of the implications of the empirical indications
for a positive strangeness magnetic moment $\mu_s$ of the proton on the
possible configurations of the $uuds\bar s$ component of the proton. A positive
value for $\mu_s$ is obtained in the $s\bar s$ configuration where the $uuds$
subsystem is in an orbitally excited state with $[4]_{[FS]}[22]_F[22]_S$
flavor-spin symmetry, which is likely to have the lowest energy. The
configurations in which the $\bar s$ is orbitally excited, which include the
conventional $K^+\Lambda^0$ configuration, with exception of that in which the
$uuds$ component has spin 2, yield negative values for $\mu_s$. The hidden
strangeness analogues of recently proposed quark cluster models for the
$\theta^+$ pentaquark give differing signs for $\mu_s$.


  Optical flow, which expresses pixel displacement, is widely used in many
computer vision tasks to provide pixel-level motion information. However, with
the remarkable progress of the convolutional neural network, recent
state-of-the-art approaches are proposed to solve problems directly on
feature-level. Since the displacement of feature vector is not consistent to
the pixel displacement, a common approach is to:forward optical flow to a
neural network and fine-tune this network on the task dataset. With this
method,they expect the fine-tuned network to produce tensors encoding
feature-level motion information. In this paper, we rethink this de facto
paradigm and analyze its drawbacks in the video object detection task. To
mitigate these issues, we propose a novel network (IFF-Net) with an
\textbf{I}n-network \textbf{F}eature \textbf{F}low estimation module (IFF
module) for video object detection. Without resorting pre-training on any
additional dataset, our IFF module is able to directly produce \textbf{feature
flow} which indicates the feature displacement. Our IFF module consists of a
shallow module, which shares the features with the detection branches. This
compact design enables our IFF-Net to accurately detect objects, while
maintaining a fast inference speed. Furthermore, we propose a transformation
residual loss (TRL) based on \textit{self-supervision}, which further improves
the performance of our IFF-Net. Our IFF-Net outperforms existing methods and
sets a state-of-the-art performance on ImageNet VID.


  Swarm robotics systems have the potential to transform warfighting in urban
environments, but until now have not seen large-scale field testing. We present
the Rapid Integration Swarming Ecosystem (RISE), a platform for future
multi-agent research and deployment. RISE enables rapid integration of
third-party swarm tactics and behaviors, which was demonstrated using both
physical and simulated swarms. Our physical testbed is composed of more than
250 networked heterogeneous agents and has been extensively tested in mock
warfare scenarios at five urban combat training ranges. RISE implements live,
virtual, constructive simulation capabilities to allow the use of both virtual
and physical agents simultaneously, while our "fluid fidelity" simulation
enables adaptive scaling between low and high fidelity simulation levels based
on dynamic runtime requirements. Both virtual and physical agents are
controlled with a unified gesture-based interface that enables a greater than
150:1 agent-to-operator ratio. Through this interface, we enable efficient
swarm-based mission execution. RISE translates mission needs to robot actuation
with rapid tactic integration, a reliable testbed, and efficient operation.


  Multi-core vector processor architectures excel in handling computationally
intensive vectorizable tasks but struggle to achieve optimal resource
utilization when facing sequential and control tasks that cannot be vectorized.
This work presents Spatzformer, the first reconfigurable RISC-V V (RVV)
architecture developed from a baseline open-source dual-core cluster based on
Snitch scalar cores augmented with compact Spatz vector units. Spatzformer
operates in two distinct modes: split mode, working as a dual-core vector
architecture to handle vectorizable tasks concurrently, and merge mode, where
two vector units are driven by a single scalar core, allowing the remaining
scalar core to handle non-vectorizable control tasks. We implement Spatzformer
in a 12-nm technology node and characterize the cost of the added architectural
reconfigurability. We show that merge mode accelerates mixed scalar-vector
kernels by up to 1.8x compared to split mode. Moreover, it accelerates the
vector kernels that require fine-grained synchronization (such as FFT) by up to
20% with respect to the baseline. The reconfigurability features do not degrade
the architecture's maximum frequency (1.2GHz, TT, 0.8V, 25C) and have a
negligible area impact (+1.4%), with a worst-case energy efficiency drop of
only 7% with respect to the non-reconfigurable baseline.


  For smooth projective G-varieties, we equate the gauged Gromov-Witten
invariants for sufficiently small area and genus zero with the invariant part
of equivariant Gromov-Witten invariants. As an application we deduce a gauged
version of abelianization for Gromov-Witten invariants. In the symplectic
setting, we prove that any sequence of genus zero symplectic vortices with
vanishing area has a subsequence that converges after gauge transformation to a
holomorphic map with zero average moment map.


  How long until this paper is forgotten? Collective forgetting is the process
by which the attention received by cultural pieces decays as time passes.
Recent work modeled this decay as the result of two different processes, one
linked to communicative memory --memories sustained by human communication--
and cultural memory --memories sustained by the physical recording of content.
Yet, little is known on how the collective forgetting dynamic changes over
time. Are older cultural pieces forgotten at a lower rate than newer ones?
Here, we study the temporal changes of collective memory and attention by
focusing on two knowledge communities: inventors and physicists. We use data on
patents from the United States Patent and Trademark Office (USPTO) and physics
papers published in the American Physical Society (APS) to quantify how
collective forgetting has changed over time. The model enables us to
distinguish between two branches of forgetting. One branch is short-lived,
going directly from communicative memory to oblivion. The other one is
long-lived going from communicative to cultural memory and then to oblivion.
The data analysis shows an increasing forgetting rate for both communities as
the information grows. Furthermore, these knowledge communities seem to be
increasing their selectivity at storing valuable cultural pieces in their
cultural memory. These findings provide empirical confirmation on the
forgetting as an annulment hypothesis and show that knowledge communities can
effectively slow down the rising of collective forgetting at improving their
cultural selectivity.


  We present the Simple Intensity Map Producer for Line Emission (SIMPLE), a
public code for quickly simulating mock line-intensity maps, and an analytical
framework for modeling intensity maps including observational effects. SIMPLE
can be applied to any spectral line sourced by galaxies. The SIMPLE code is
based on lognormal mock catalogs of galaxies including positions and velocities
and assigns luminosities following the luminosity function. After applying a
selection function to distinguish between detected and undetected galaxies, the
code generates an intensity map, which can be modified with anisotropic
smoothing, noise, a mask, and sky subtraction, and calculates the power
spectrum multipoles. We show that the intensity autopower spectrum and the
galaxy-intensity cross-power spectrum agree well with the analytical estimates
in real space. We derive and show that the sky subtraction suppresses the
intensity autopower spectrum and the cross-power spectrum on scales larger than
the size of an individual observation. As an example application, we make
forecasts for the sensitivity of an intensity mapping experiment similar to the
Hobby-Eberly Telescope Dark Energy Experiment (HETDEX) to the cross-power
spectrum of Ly$\alpha$-emitting galaxies and the Ly$\alpha$ intensity. We
predict that HETDEX will measure the galaxy-intensity cross-power spectrum with
a high signal-to-noise ratio on scales of $0.04\, h\,\mathrm{Mpc}^{-1} < k <
1\, h\,\mathrm{Mpc}^{-1}$.


  We present the construction of additive multilevel preconditioners, also
known as BPX preconditioners, for the solution of the linear system arising in
isogeometric adaptive schemes with (truncated) hierarchical B-splines. We show
that the locality of hierarchical spline functions, naturally defined on a
multilevel structure, can be suitably exploited to design and analyze efficient
multilevel decompositions. By obtaining smaller subspaces with respect to
standard tensor-product B-splines, the computational effort on each level is
reduced. We prove that, for suitably graded hierarchical meshes, the condition
number of the preconditioned system is bounded independently of the number of
levels. A selection of numerical examples validates the theoretical results and
the performance of the preconditioner.


  Consider an algebraic number field, $K$, and its ring of integers,
$\mathcal{O}_K$. There exists a smallest $B_K>1$ such that for any $x>1$ we can
find a prime ideal, $\mathfrak{p}$, in $\mathcal{O}_K$ with norm
$N(\mathfrak{p})$ in the interval $[x,B_Kx]$. This is a generalization of
Bertrand's postulate to number fields, and in this paper we produce bounds on
$B_K$ in terms of the invariants of $K$ from an effective prime ideal theorem
due to Lagarias and Odlyzko. We also show that a bound on $B_K$ can be obtained
from an asymptotic estimate for the number of ideals in $\mathcal{O}_K$ less
than $x$.


  The main result is the identification of the orthogonal complement of the
subalgebra of conformal vector field inside the algebra of all vector fields of
a compact flat 2-manifold. As a fundamental tool, the complete Hodge
decomposition for manifold with boundary is used. The identification allows the
derivation of governing differential equations for variational problems on the
space of conformal vector fields. Several examples are given. In addition, the
paper also gives a review, in full detail, of already known vector field
decompositions involving subalgebras of volume preserving and symplectic vector
fields.


  Unsupervised Domain Adaptation (UDA) aims to solve the problem of label
scarcity of the target domain by transferring the knowledge from the label rich
source domain. Usually, the source domain consists of synthetic images for
which the annotation is easily obtained using the well known computer graphics
techniques. However, obtaining annotation for real world images (target domain)
require lot of manual annotation effort and is very time consuming because it
requires per pixel annotation. To address this problem we propose SegDA module
to enhance transfer performance of UDA methods by learning the maximum
separable segment representation. This resolves the problem of identifying
visually similar classes like pedestrian/rider, sidewalk/road etc. We leveraged
Equiangular Tight Frame (ETF) classifier inspired from Neural Collapse for
maximal separation between segment classes. This causes the source domain pixel
representation to collapse to a single vector forming a simplex vertices which
are aligned to the maximal separable ETF classifier. We use this phenomenon to
propose the novel architecture for domain adaptation of segment representation
for target domain. Additionally, we proposed to estimate the noise in labelling
the target domain images and update the decoder for noise correction which
encourages the discovery of pixels for classes not identified in pseudo labels.
We have used four UDA benchmarks simulating synthetic-to-real,
daytime-to-nighttime, clear-to-adverse weather scenarios. Our proposed approach
outperforms +2.2 mIoU on GTA -> Cityscapes, +2.0 mIoU on Synthia -> Cityscapes,
+5.9 mIoU on Cityscapes -> DarkZurich, +2.6 mIoU on Cityscapes -> ACDC.


  The recently-discovered giant exoplanet HR5183b exists on a wide,
highly-eccentric orbit ($a=18$\,au, $e=0.84$). Its host star possesses a common
proper-motion companion which is likely on a bound orbit. In this paper, we
explore scenarios for the excitation of the eccentricity of the planet in
binary systems such as this, considering planet-planet scattering, Lidov-Kozai
cycles from the binary acting on a single-planet system, or Lidov-Kozai cycles
acting on a two-planet system that also undergoes scattering. Planet-planet
scattering, in the absence of a binary companion, has a $2.8-7.2\%$ probability
of pumping eccentricities to the observed values in our simulations, depending
on the relative masses of the two planets. Lidov-Kozai cycles from the binary
acting on an initially circular orbit can excite eccentricities to the observed
value, but require very specific orbital configurations for the binary and
overall there is a low probability of catching the orbit at the high observed
high eccentricity ($0.6\%$). The best case is provided by planet-planet
scattering in the presence of a binary companion: here, the scattering provides
the surviving planet with an initial eccentricity boost that is subsequently
further increased by Kozai cycles from the binary. We find a success rate of
$14.5\%$ for currently observing $e\ge0.84$ in this set-up. The single-planet
plus binary and two-planet plus binary cases are potentially distinguishable if
the mutual inclination of the binary and the planet can be measured, as the
latter permits a broader range of mutual inclinations. The combination of
scattering and Lidov-Kozai forcing may also be at work in other wide-orbit
eccentric giant planets, which have a high rate of stellar binary companions.


  We investigate the relationship between the halo mass, M_200, and
concentration, c, for a sample of 26 group- and cluster-scale strong
gravitational lenses. In contrast with previous results, we find that these
systems are only ~ 0.1 dex more over-concentrated than similar-mass halos from
dark matter simulations; the concentration of a halo with M_200 = 10^14 M_sun
is log c = 0.78\pm0.05, while simulations of halos with this mass at similar
redshifts (z ~ 0.4) predict log c ~ 0.56 - 0.71. We also find that we are
unable to make informative inference on the slope of the M_200-c relation in
spite of our large sample size; we note that the steep slopes found in previous
studies tend to follow the slope in the covariance between M_200 and c,
indicating that these results may be measuring the scatter in the data rather
than the intrinsic signal. Furthermore, we conclude that our inability to
constrain the M_200-c slope is due to a limited range of halo masses, as
determined by explicitly modelling our halo mass distribution, and we suggest
that other studies may be producing biased results by using an incorrect
distribution for their halo masses.


  The concept of quantum coherence, including various ways to quantify the
degree of coherence with respect to the prescribed basis, is currently the
subject of active research. The complementarity of quantum coherence in
different bases was studied by deriving upper bounds on the sum of the
corresponding measures. To obtain a two-sided estimate, lower bounds on the
coherence quantifiers are also of interest. Such bounds are naturally referred
to as uncertainty relations for quantum coherence. We obtain new uncertainty
relations for coherence quantifiers averaged with respect to a set of mutually
unbiased bases (MUBs). To quantify the degree of coherence, the relative
entropy of coherence and the geometric coherence are used. Further, we also
derive novel state-independent uncertainty relations for a set of MUBs in terms
of the min-entropy.


  This work describes the operation of a High Frequency Gravitational Wave
detector based on a cryogenic Bulk Acoustic Wave (BAW) cavity and reports
observation of rare events during 153 days of operation over two seperate
experimental runs (Run 1 and Run 2). In both Run 1 and Run 2 two modes were
simultaneously monitored. Across both runs, the 3rd overtone of the fast shear
mode (3B) operating at 5.506 MHz was monitored, while in Run 1 the second mode
was chosen to be the 5th OT of the slow shear mode (5C) operating at 8.392 MHz.
However, in Run 2 the second mode was selected to be closer in frequency to the
first mode, and chosen to be the 3rd overtone of the slow shear mode (3C)
operating at 4.993 MHz. Two strong events were observed as transients
responding to energy deposition within acoustic modes of the cavity. The first
event occurred during Run 1 on the 12/05/2019 (UTC), and was observed in the
5.506 MHz mode, while the second mode at 8.392 MHz observed no event. During
Run 2, a second event occurred on the 27/11/2019(UTC) and was observed by both
modes. Timing of the events were checked against available environmental
observations as well as data from other detectors. Various possibilities
explaining the origins of the events are discussed.


  Interaction-free measurement (IFM), just as its name implies, can enable one
to detect an object without interacting with it, i.e., substantially reducing
the damage to the object. With the help of quantum channel theory, we
investigate the general model of "quantum-Zeno-like" IFM, whose optics setup is
a Mach-Zehnder like interferometer utilizing the quantum Zeno effect, where the
object to be detected is semitransparent and the interrogation cycle number $N$
is finite. And we define two important probabilities $P_{\rm loss}$ and $P_{\rm
error}$ to evaluate the IFM process, which describe the photon loss rate and
the error of discriminating the presenece/absence of the object respectively.
The minimum values of these two probabilities and the corresponding initial
input states to reach them are attained via this model. And we find that when
the interrogation cycle $N$ approaches infinity, the object can be perfectly
detected, where the minimum values of these two probabilities are both zero and
the initial input state to reach them becomes the same state $|1\rangle$ in our
system. In addition, we also study whether quantum correlation can benefit IFM
or not, but the answer is no, in the sense that the entangled photon input
state cannot minimize $P_{\rm loss}$, $P_{\rm error}$ more than single photon
input state. Our work provides principal theoretic support for the practical
realization of IFM and the employed analysis technique can be applied to other
quantum facilitating scenarios.


  Super Hydrophobic (SH) coatings are widely used to mitigate drag in various
applications. Numerous studies have demonstrated that the beneficial wall-slip
effect produced by these materials disappears in laminar flow regimes. The main
mechanisms considered to be behind the decrease in performance are
Marangoni-induced stresses and air/liquid interface deformation. In the present
study, a new mechanism is proposed to explain the loss of performances of
SH-surfaces in laminar flow regimes. Here we consider the flow of air inside
the plastron and the associated momentum loses induced by roughness elements
with different geometric characteristics. The effects of air motion within the
plastron is coupled to the outer fluid with a homogenised boundary condition
approach. To this end, numerical simulations at the scale of the roughness
element were conducted as a function of the porosity and the tortuosity of the
domain to determine the slip velocity at the air-liquid interface.
  The homogenised boundary condition is then implemented in a theoretical model
for the outer flow to compute drag on SH-spheres at low $Re$ numbers.
Experiments of laminar SH falling spheres indicate that high values of the
tortuosity and low values of porosity lead to a loss of performances when
considering drag reduction. As anticipated, a 3D printed sphere with low
tortuosity and similar porosity demonstrated near-optimal drag reductions. A
comparative study between the predicted values and experiments shows that the
homogenised model is able to accurately predict the drag on SH surfaces for
values of the porosity and tortuosity estimated from microscopy images of the
SH textured surface.


  As part of a quality control process in manufacturing it is often necessary
to test whether all parts of a product satisfy a required property, with as few
inspections as possible. When multiple inspection apparatuses with different
costs and precision exist, it is desirable that testing can be carried out
cost-effectively by properly controlling the trade-off between the costs and
the precision. In this paper, we formulate this as a level set estimation (LSE)
problem under cost-dependent input uncertainty - LSE being a type of active
learning for estimating the level set, i.e., the subset of the input space in
which an unknown function value is greater or smaller than a pre-determined
threshold. Then, we propose a new algorithm for LSE under cost-dependent input
uncertainty with theoretical convergence guarantee. We demonstrate the
effectiveness of the proposed algorithm by applying it to synthetic and real
datasets.


  The degree of insulation of a prime $p$ is defined as the largest interval
around it in which no other prime exists. Based on this, the $n$-th prime
$p_{n}$ is said to be insulated if and only if its degree of insulation is
higher than its neighboring primes. Consequently, a new special sequence
emerges given as 7, 13, 23, 37, 53, 67, 89, 103, 113, 131, 139, 157, 173, 181,
193, 211, 233, 277, 293, and so on. This paper presents several properties and
intriguing relations concerning degree of insulation and insulated primes.
Finally, the reader is left with a captivating open problem.


  We use the Random Phase Approximation (RPA) to compute the structure factor,
S(q), of a solution of chains interacting through a soft and short range
repulsive potential V. Above a threshold polymer concentration, whose magnitude
is essentially controlled by the range of the potential, S(q) exhibits a peak
whose position depends on the concentration. We take advantage of the close
analogy between polymers and wormlike micelles and apply our model, using a
Gaussian function for V, to quantitatively analyze experimental small angle
neutron scattering profiles of semi-dilute solutions of hairy wormlike
micelles. These samples, which consist in surfactant self-assembled flexible
cylinders decorated by amphiphilic copolymer, provide indeed an appropriate
experimental model system to study the structure of sterically interacting
polymer solutions.


  This paper studies a low-communication algorithm for solving elliptic partial
differential equations (PDE's) on high-performance machines, the nested
iteration with range decomposition algorithm (NIRD). Previous work has shown
that NIRD converges to a high level of accuracy within a small, fixed number of
iterations (usually one or two) when applied to simple elliptic problems. This
paper makes some improvements to the NIRD algorithm (including the addition of
adaptivity during preprocessing, wider choice of partitioning functions, and
modified error measurement) that enhance the method's accuracy and scalability,
especially on more difficult problems. In addition, an updated convergence
proof is presented based on heuristic assumptions that are supported by
numerical evidence. Furthermore, a new performance model is developed that
shows increased performance benefits for NIRD when problems are more expensive
to solve using traditional methods. Finally, extensive testing on a variety of
elliptic problems provides additional insight into the behavior of NIRD and
additional evidence that NIRD achieves excellent convergence on a wide class of
elliptic PDE's and, as such, should be a very competitive method for solving
PDE's on large parallel computers.


  We present results from the analysis of a BeppoSAX observation of the
Centaurus Cluster. The radial metal abundance profile shows evidence of a large
enhancement in the core, where Ab $>$ 1 (sol. units). The temperature map
indicates that the cluster is characterized by a gradient oriented in the NW/SE
direction, with cooler gas in the NW and hotter gas in the SE (\Delta kT \sim 1
keV). In hard X-rays, where the PDS detects emission with a flux of $2.2 \times
10^{-11}$ erg/cm^2/s in the 20-200 keV band, the spectrum lies above the
extrapolation of the cluster thermal emission. We discuss several possible
interpretations for the hard excess finding that none is completely
satisfactory.


  We investigate a total thermodynamic entropy production rate of an isolated
quantum system. In particular, we consider a quantum model of coupled harmonic
oscillators in a star configuration, where a central harmonic oscillator
(system) is coupled to a finite number of surrounding harmonic oscillators
(bath). In this model, when the initial state of the total system is given by
the tensor product of the Gibbs states of the system and the bath, every
harmonic oscillator is always in a Gibbs state with a time-dependent
temperature. This enables us to define time-dependent thermodynamic entropy for
each harmonic oscillator and total nonequilibrium thermodynamic entropy as the
summation of them. We analytically confirm that the total thermodynamic entropy
satisfies the third law of thermodynamics. Our numerical solutions show that,
even when the dynamics of the system is well approximated by the
Gorini-Kossakowski-Sudarshan-Lindblad (GKSL)-type Markovian master equation,
the total thermodynamic entropy production rate can be negative, while the
total thermodynamic entropy satisfies the second law of thermodynamics. This
result is a counterexample to the common belief that the total entropy
production rate is non-negative when the system is under the GKSL-type
Markovian dynamics.


  The aim of this paper is to study differential properties of orthogonal
polynomials with respect to a discrete Laguerre-Sobolev bilinear form with mass
point at zero. In particular we construct the orthogonal polynomials using
certain Casorati determinants. Using this construction, we prove that they are
eigenfunctions of a differential operator (which will be explicitly
constructed). Moreover, the order of this differential operator is explicitly
computed in terms of the matrix which defines the discrete Laguerre-Sobolev
bilinear form.


  We investigate the effect of inhomogeneous Dzyaloshinskii-Moriya interaction
(DMI) on antiferromagnetic spin-wave propagation theoretically and numerically.
We find that antiferromagnetic spin waves can be amplified at a boundary where
the DMI varies. The inhomogeneous DMI also provides a way to construct a
magnonic crystal with forbidden and allowed antiferromagnetic spin-wave bands
in terahertz frequency ranges. In contrast to ferromagnetic spin waves,
antiferromagnetic spin waves experience a polarization-dependent phase shift
when passing through the inhomogeneous DMI, offering a magnonic crystal that
also serves as a spin-wave polarizer.


  As mobile technologies have become ubiquitous in recent years, computer-based
cognitive tests have become more popular and efficient. In this work, we focus
on assessing motor function in children by analyzing their gait movements.
Although there has been a lot of research on designing automated assessment
systems for gait analysis, most of these efforts use obtrusive wearable sensors
for measuring body movements. We have devised a computer vision-based
assessment system that only requires a camera which makes it easier to employ
in school or home environments. A dataset has been created with 27 children
performing the test. Furthermore in order to improve the accuracy of the
system, a deep learning based model was pre-trained on NTU-RGB+D 120 dataset
and then it was fine-tuned on our gait dataset. The results highlight the
efficacy of proposed work for automating the assessment of children's
performances by achieving 76.61% classification accuracy.


  There is a number of indications that scattering amplitudes in the
Aharony-Bergman-Jafferis-Maldacena theory might have a dual description in
terms of a holonomy of a supergauge connection on a null polygonal contour in a
way analogous to the four-dimensional maximally supersymmetric Yang-Mills
theory. However, so far its explicit implementations evaded a successful
completion. The difficulty is intimately tied to the lack of the T-self-duality
of the sigma model on the string side of the gauge/string correspondence.
Unscathed by the last misfortune, we initiate with this study an application of
the pentagon paradigm to scattering amplitudes of the theory. With the language
being democratic and nondiscriminatory to whether one considers a Wilson loop
expectation value or an amplitude, the success in the application of the
program points towards a possible unified observable on the field theory side.
Our present consideration is focused on two-loop perturbation theory in the
planar limit, begging for higher loop data in order to bootstrap current
analysis to all orders in the 't Hooft coupling.


  Big data analytics on geographically distributed datasets (across data
centers or clusters) has been attracting increasing interests from both
academia and industry, but also significantly complicates the system and
algorithm designs. In this article, we systematically investigate the
geo-distributed big-data analytics framework by analyzing the fine-grained
paradigm and the key design principles. We present a dynamic global manager
selection algorithm (GMSA) to minimize energy consumption cost by fully
exploiting the system diversities in geography and variation over time. The
algorithm makes real-time decisions based on the measurable system parameters
through stochastic optimization methods, while achieving the performance
balances between energy cost and latency. Extensive trace-driven simulations
verify the effectiveness and efficiency of the proposed algorithm. We also
highlight several potential research directions that remain open and require
future elaborations in analyzing geo-distributed big data.


  \v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la [J. Math. Phys. \textbf{44}, 962
- 968 (2003)] introduced in connection with the summation of the divergent
perturbation expansion of the hydrogen atom in an external magnetic field a new
sequence transformation which uses as input data not only the elements of a
sequence $\{s_n \}_{n=0}^{\infty}$ of partial sums, but also explicit estimates
$\{\omega_n \}_{n=0}^{\infty}$ for the truncation errors. The explicit
incorporation of the information contained in the truncation error estimates
makes this and related transformations potentially much more powerful than for
instance Pad\'{e} approximants. Special cases of the new transformation are
sequence transformations introduced by Levin [Int. J. Comput. Math. B
\textbf{3}, 371 - 388 (1973)] and Weniger [Comput. Phys. Rep. \textbf{10}, 189
- 371 (1989), Sections 7 -9; Numer. Algor. \textbf{3}, 477 - 486 (1992)] and
also a variant of Richardson extrapolation [Phil. Trans. Roy. Soc. London A
\textbf{226}, 299 - 349 (1927)]. The algebraic theory of these transformations
- explicit expressions, recurrence formulas, explicit expressions in the case
of special remainder estimates, and asymptotic order estimates satisfied by
rational approximants to power series - is formulated in terms of hitherto
unknown mathematical properties of the new transformation introduced by
\v{C}\'{\i}\v{z}ek, Zamastil, and Sk\'{a}la. This leads to a considerable
formal simplification and unification.


  Weyl and Dirac relativistic fermions are ubiquitous in topological matter.
Their relativistic character enables high energy physics phenomena like the
chiral anomaly to occur in solid state, which allows to experimentally probe
and explore fundamental relativistic theories. Here we show that on smooth
interfaces between a trivial and a topological material, massless Weyl and
massive Dirac fermions intrinsically coexist. The emergence of the latter,
known as Volkov-Pankratov states, is directly revealed by magneto-optical
spectroscopy, evidencing that their energy spectrum is perfectly controlled by
the smoothness of topological interface. Simultaneously, we reveal the optical
absorption of the zero-energy chiral Weyl state, whose wavefunction is
drastically transformed when the topological interface is smooth. Artificial
engineering of the topology profile thus provides a novel textbook system to
explore the rich relativistic energy spectra in condensed matter
heterostructures.


  We compute the suppression of the bottomonia states Upsilon(1S), Upsilon(2S),
Upsilon(3S), chi_b(1P), chi_b(2P), and chi_b(3P) states in Large Hadron
Collider (LHC) sqrt(s_NN)) = 5.023 TeV Pb-Pb collisions. For the background
evolution we use 3+1d anisotropic hydrodynamics with conditions extrapolated
from sqrt(s_NN) = 2.76 TeV and we self-consistently compute bottomonia decay
rates including non-equilibrium corrections to the interaction potential. For
our final results, we make predictions for R_AA as function of centrality,
rapidity, and p_T for the Upsilon(1S) and Upsilon(2S) states, including feed
down effects. In order to assess the dependence on some of the model
assumptions, we vary the shear viscosity-to-entropy density ratio, 4 pi eta/s =
(1, 2, 3), and the initial momentum-space anisotropy parameter, xi_0 = (0, 10,
50), while holding the total light hadron multiplicity fixed.


  In a recent paper Garber, Gavrilyuk and Magazinov proposed a sufficient
combinatorial condition for a parallelohedron to be affinely Voronoi. We show
that this condition holds for all five-dimensional Voronoi parallelohedra.
Consequently, the Voronoi conjecture in $\mathbb R^5$ holds if and only if
every five-dimensional parallelohedron is combinatorially Voronoi. Here, by
saying that a parallelohedron $P$ is combinatorially Voronoi, we mean that the
tiling $\mathcal T(P)$ by translates of $P$ is combinatorially isomorphic to
some tiling $\mathcal T(P')$, where $P'$ is a Voronoi parallelohedron, and that
the isomorphism naturally induces a linear isomorphism of lattices $\Lambda(P)$
and $\Lambda(P')$.
  We also propose a new sufficient condition implying that a parallelohedron is
affinely Voronoi. The condition is based on the new notion of the Venkov
complex associated with a parallelohedron.


  This paper assesses the accuracy and convergence of the linear-elastic,
bond-based Peridynamic model with brittle failure, known as the prototype
micro-brittle (PMB) model. We investigate the discrete equations of this model,
suitable for numerical implementation. It is shown that the widely used
discretization approach incurs rather large errors. Motivated by this
observation, a correction is proposed, which significantly increases the
accuracy by cancelling errors associated with the discretization. As an
additional result, we derive equations to treat the interactions between
differently sized particles, i.e., a non-homogeneous discretization spacing.
This presents an important step forward for the applicability of the PMB model
to complex geometries, where it is desired to model interesting parts with a
fine resolution (small particle spacings) and other parts with a coarse
resolution in order to gain numerical efficiency. Validation of the corrected
Peridynamic model is performed by comparing longitudinal sound wave propagation
velocities with exact theoretical results. We find that the corrected approach
correctly reproduces the sound wave velocity, while the original approach
severely overestimates this quantity. Additionally, we present simulations for
a crack growth problem which can be analytically solved within the framework of
Linear Elastic Fracture Mechanics Theory. We find that the corrected
Peridynamics model is capable of quantitatively reproducing crack initiation
and propagation.


  A Weierstrass fibration is an elliptic fibration $Y\to B$ whose total space
$Y$ may be given by a global Weierstrass equation in a $\mathbb{P}^2$-bundle
over $B$. In this note, we compute stringy Hirzebruch classes of singular
Weierstrass fibrations associated with constructing non-Abelian gauge theories
in $F$-theory. For each Weierstrass fibration $Y\to B$ we then derive a
generating function $\chi^{\text{str}}_y(Y;t)$, whose degree-$d$ coefficient
encodes the stringy $\chi_y$-genus of $Y\to B$ over an unspecified base of
dimension $d$, solely in terms of invariants of the base. To facilitate our
computations, we prove a formula for general characteristic classes of blowups
along (possibly singular) complete intersections.


  How physical networks of neurons, bound by spatio-temporal locality
constraints, can perform efficient credit assignment, remains, to a large
extent, an open question. In machine learning, the answer is almost universally
given by the error backpropagation algorithm, through both space and time.
However, this algorithm is well-known to rely on biologically implausible
assumptions, in particular with respect to spatio-temporal (non-)locality.
Alternative forward-propagation models such as real-time recurrent learning
only partially solve the locality problem, but only at the cost of scaling, due
to prohibitive storage requirements.
  We introduce Generalized Latent Equilibrium (GLE), a computational framework
for fully local spatio-temporal credit assignment in physical, dynamical
networks of neurons. We start by defining an energy based on neuron-local
mismatches, from which we derive both neuronal dynamics via stationarity and
parameter dynamics via gradient descent. The resulting dynamics can be
interpreted as a real-time, biologically plausible approximation of
backpropagation through space and time in deep cortical networks with
continuous-time neuronal dynamics and continuously active, local synaptic
plasticity. In particular, GLE exploits the morphology of dendritic trees to
enable more complex information storage and processing in single neurons, as
well as the ability of biological neurons to phase-shift their output rate with
respect to their membrane potential, which is essential in both directions of
information propagation. For the forward computation, it enables the mapping of
time-continuous inputs to neuronal space, effectively performing a
spatio-temporal convolution. For the backward computation, it permits the
temporal inversion of feedback signals, which consequently approximate the
adjoint variables necessary for useful parameter updates.


  Even as the understanding of the mechanism behind correlated insulating
states in magic-angle twisted bilayer graphene converges towards various kinds
of spontaneous symmetry breaking, the metallic "normal state" above the
insulating transition temperature remains mysterious, with its excessively high
entropy and linear-in-temperature resistivity. In this work, we focus on the
effects of fluctuations of the order-parameters describing correlated
insulating states at integer fillings of the low-energy flat bands on charge
transport. Motivated by the observation of heterogeneity in the order-parameter
landscape at zero magnetic field in certain samples, we conjecture the
existence of frustrating extended range interactions in an effective Ising
model of the order-parameters on a triangular lattice. The competition between
short-distance ferromagnetic interactions and frustrating extended range
antiferromagnetic interactions leads to an emergent length scale that forms
stripe-like mesoscale domains above the ordering transition. The gapless
fluctuations of these heterogeneous configurations are found to be responsible
for the linear-in-temperature resistivity as well as the enhanced low
temperature entropy. Our insights link experimentally observed
linear-in-temperature resistivity and enhanced entropy to the strength of
frustration, or equivalently, to the emergence of mesoscopic length scales
characterizing order-parameter domains.


  We present non-perturbative renormalization constants of fermionic bilinears
on the lattice in the quenched approximation at beta=6.1 using an overlap
fermion action with hypercubic(HYP)-blocked links. We consider the effects of
the exact zero modes of the Dirac operator and find they are important in
calculating the renormalization constants of the scalar and pseudoscalar
density. The results are given in the RI' and MS bar schemes and compared to
the perturbative calculations.


  We provide a dynamical proof of the van der Corput inequality for sequences
in Hilbert spaces that is based on the Furstenberg correspondence principle.
This is done by reducing the inequality to the mean ergodic theorem for
contractions on Hilbert spaces. The key difficulty therein is that the
Furstenberg correspondence principle is, a priori, limited to scalar-valued
sequences. We therefore discuss how interpreting the Furstenberg correspondence
principle via the Gelfand--Naimark--Segal construction for C*-algebras allows
to study not just scalar but general Hilbert space-valued sequences in terms of
unitary operators. This yields a proof of the van der Corput inequality in the
spirit of the Furstenberg correspondence principle and the flexibility of this
method is discussed via new proofs for different variants of the inequality.


  Business process deviance refers to the phenomenon whereby a subset of the
executions of a business process deviate, in a negative or positive way, with
respect to {their} expected or desirable outcomes. Deviant executions of a
business process include those that violate compliance rules, or executions
that undershoot or exceed performance targets. Deviance mining is concerned
with uncovering the reasons for deviant executions by analyzing event logs
stored by the systems supporting the execution of a business process. In this
paper, the problem of explaining deviations in business processes is first
investigated by using features based on sequential and declarative patterns,
and a combination of them. Then, the explanations are further improved by
leveraging the data attributes of events and traces in event logs through
features based on pure data attribute values and data-aware declarative rules.
The explanations characterizing the deviances are then extracted by direct and
indirect methods for rule induction. Using real-life logs from multiple
domains, a range of feature types and different forms of decision rules are
evaluated in terms of their ability to accurately discriminate between
non-deviant and deviant executions of a process as well as in terms of
understandability of the final outcome returned to the users.


  Exposure mappings are widely used to model potential outcomes in the presence
of interference, where each unit's outcome may depend not only on its own
treatment, but also on the treatment of other units as well. However, in
practice these models may be only a crude proxy for social dynamics. In this
work, we give estimands and estimators that are robust to the misspecification
of an exposure model. In the first part, we require the treatment effect to be
nonnegative (or "monotone") in both direct effects and spillovers. In the
second part, we consider a weaker estimand ("contrasts attributable to
treatment") which makes no restrictions on the interference at all.


  We study the effect of system reservoir coupling on currents flowing through
quantum junctions. We consider two simple double-quantum dot configurations
coupled to two external fermionic reservoirs and study the net current flowing
between the two reservoirs. The net current is partitioned into currents
carried by the eigenstates of the system and by the coherences between the
eigenstates induced due to coupling with the reservoirs. We find that current
carried by populations is always positive whereas current carried by coherences
are negative for large couplings. This results in a non-monotonic dependence of
the net current on the coupling strength. We find that in certain cases, the
net current can vanish at large couplings due to cancellation between currents
carried by the eigenstates and by the coherences. These results provide new
insights into the non-trivial role of system-reservoir couplings on electron
transport through quantum dot junctions. In the presence of weak coulomb
interactions, net current as a function of system reservoir coupling strength
shows similar trends as for the non-interacting case.


  Post-processing of static embedding has beenshown to improve their
performance on both lexical and sequence-level tasks. However, post-processing
for contextualized embeddings is an under-studied problem. In this work, we
question the usefulness of post-processing for contextualized embeddings
obtained from different layers of pre-trained language models. More
specifically, we standardize individual neuron activations using z-score,
min-max normalization, and by removing top principle components using the
all-but-the-top method. Additionally, we apply unit length normalization to
word representations. On a diverse set of pre-trained models, we show that
post-processing unwraps vital information present in the representations for
both lexical tasks (such as word similarity and analogy)and sequence
classification tasks. Our findings raise interesting points in relation to
theresearch studies that use contextualized representations, and suggest
z-score normalization as an essential step to consider when using them in an
application.


  It is shown that the general solution of classical equations of motion in two
dimensional dilaton gravity proposed by Callan, Giddings, Harvey and Strominger
(CGHS) includes a Lorentzian wormhole solution in addition to a black hole
solution. We also show that matter perturbation of the wormhole by a shock wave
leads to the formation of a black hole where the curvature singularity is
cloaked by the global event horizon. It is also argued that the classical
wormhole would be stable against quantum corrections.


  When looking for analytical approaches to treat frustrated quantum magnets,
it is often very useful to start from a limit where the ground state is highly
degenerate. This chapter discusses several ways of deriving {effective
Hamiltonians} around such limits, starting from standard {degenerate
perturbation theory} and proceeding to modern approaches more appropriate for
the derivation of high-order effective Hamiltonians, such as the perturbative
continuous unitary transformations or contractor renormalization. In the course
of this exposition, a number of examples taken from the recent literature are
discussed, including frustrated ladders and other dimer-based Heisenberg models
in a field, as well as the mapping between frustrated Ising models in a
transverse field and quantum dimer models.


  A precise theoretical investigation has been made on dust-acoustic (DA) waves
(DAWs) in a four components dusty plasma medium having inertial warm adiabatic
dust grains and inertialess $q$-distributed electrons as well as isothermal
ions and positrons. The nonlinear and dispersive parameters of the nonlinear
Schr\"{o}dinger equation (NLSE), which develops by using reductive
perturbations technique, have been used to recognize the stable and unstable
parametric regions of the DAWs as well as associated DA rogue waves (DARWs) in
the unstable parametric regime of the DAWs. The effects of the light positrons
and massive dust grains in determining the amplitude and width of the DARWs
associated with DAWs are examined. The findings of our present investigation
may be useful for understanding different nonlinear electrostatic phenomena in
both space and laboratory plasmas.


  The concept of deep dictionary learning has been recently proposed. Unlike
shallow dictionary learning which learns single level of dictionary to
represent the data, it uses multiple layers of dictionaries. So far, the
problem could only be solved in a greedy fashion; this was achieved by learning
a single layer of dictionary in each stage where the coefficients from the
previous layer acted as inputs to the subsequent layer (only the first layer
used the training samples as inputs). This was not optimal; there was feedback
from shallower to deeper layers but not the other way. This work proposes an
optimal solution to deep dictionary learning whereby all the layers of
dictionaries are solved simultaneously. We employ the Majorization Minimization
approach. Experiments have been carried out on benchmark datasets; it shows
that optimal learning indeed improves over greedy piecemeal learning.
Comparison with other unsupervised deep learning tools (stacked denoising
autoencoder, deep belief network, contractive autoencoder and K-sparse
autoencoder) show that our method supersedes their performance both in accuracy
and speed.


  Gauge theories are the most successful theories for describing nature at its
fundamental level, but obtaining analytical or numerical solutions often
remains a challenge. We propose an experimental quantum simulation scheme to
study ground state properties in two-dimensional quantum electrodynamics (2D
QED) using existing quantum technology. The proposal builds on a formulation of
lattice gauge theories as effective spin models in arXiv:2006.14160, which
reduces the number of qubits needed by eliminating redundant degrees of freedom
and by using an efficient truncation scheme for the gauge fields. The latter
endows our proposal with the perspective to take a well-controlled continuum
limit. Our protocols allow in principle scaling up to large lattices and offer
the perspective to connect the lattice simulation to low energy observable
quantities, e.g. the hadron spectrum, in the continuum theory. By including
both dynamical matter and a non-minimal gauge field truncation, we provide the
novel opportunity to observe 2D effects on present-day quantum hardware. More
specifically, we present two Variational Quantum Eigensolver (VQE) based
protocols for the study of magnetic field effects, and for taking an important
first step towards computing the running coupling of QED. For both instances,
we include variational quantum circuits for qubit-based hardware, which we
explicitly apply to trapped ion quantum computers. We simulate the proposed VQE
experiments classically to calculate the required measurement budget under
realistic conditions. While this feasibility analysis is done for trapped ions,
our approach can be easily adapted to other platforms. The techniques presented
here, combined with advancements in quantum hardware pave the way for reaching
beyond the capabilities of classical simulations by extending our framework to
include fermionic potentials or topological terms.


  The Kerr black holes possess a photon region with prograde and retrograde
orbits radii, respectively, $M\leq r_p^-\leq 3M$ and $3M\leq r_p^+\leq 4M$, and
thereby always cast a closed photon ring or a shadow silhouette for $a\leq M$.
For $a>M$, it is a no-horizon spacetime (naked singularity) wherein prograde
orbits spiral into the central singularity, and retrograde orbits produce an
arc-like shadow with a dark spot at the center. We compare Kerr black holes'
photon ring structure with those produced by three rotating regular spacetimes,
viz. Bardeen, Hayward, and nonsingular. These are non-Kerr black hole metrics
with an additional deviation parameter of $g$ related to the nonlinear
electrodynamics charge. It turns out that for a given $ a $, there exists a
critical value of $ g $, $g_E$ such that $\Delta=0$ has no zeros for $ g >
g_E$, one double zero at $ r = r_E $ for $ g = g_E $, respectively,
corresponding to a no-horizon regular spacetime and extremal black hole with
degenerate horizon. We demonstrate that, unlike the Kerr naked singularity,
no-horizon regular spacetimes can possess closed photon ring when $g_E< g \leq
g_c$, e.g., for $a=0.10M$, Bardeen ($g_E=0.763332M<g\leq g_c= 0.816792M$),
Hayward ($g_E=1.05297M < g\leq g_c = 1.164846M$) and nonsingular ($g_E=1.2020M
< g \leq g_c= 1.222461M$) no-horizon spacetimes have closed photon ring. These
results confirm that the mere existence of a closed photon ring does not prove
that the compact object is necessarily a black hole. The ring circularity
deviation observable $\Delta C$ for the three no-horizon rotating spacetimes
satisfy $\Delta C\leq 0.10$ as per the M87* black hole shadow observations. We
have also appended the case of Kerr-Newman no-horizon spacetimes (naked
singularities) with similar features.


  While globally optimal solutions to many convex programs can be computed
efficiently in polynomial time, this is, in general, not possible for nonconvex
optimization problems. Therefore, locally optimal approaches or other efficient
suboptimal heuristics are usually applied for practical implementations.
However, there is also a strong interest in computing globally optimal
solutions of nonconvex problems in offline simulations in order to benchmark
the faster suboptimal algorithms. Global solutions often rely on monotonicity
properties. A common approach is to reformulate problems into a canonical
monotonic optimization problem where the monotonicity becomes evident, but this
often comes at the cost of nested optimizations, increased numbers of
variables, and/or slow convergence. The framework of mixed monotonic
programming (MMP) proposed in this paper avoids such performance-deteriorating
reformulations by revealing hidden monotonicity properties directly in the
original problem formulation. By means of a wide range of application examples
from the area of signal processing for communications (including energy
efficiency for green communications, resource allocation in interference
networks, scheduling for fairness and quality of service, as well as beamformer
design in multiantenna systems), we demonstrate that the novel MMP approach
leads to tremendous complexity reductions compared to state-of-the-art methods
for global optimization. However, the framework is not limited to optimizing
communication systems, and we expect that similar speed-ups can be obtained for
optimization problems from other areas of research as well.


  Tests based on the $2$- and $\infty$-norm have received considerable
attention in high-dimensional testing problems, as they are powerful against
dense and sparse alternatives, respectively. The power enhancement principle of
Fan et al. (2015) combines these two norms to construct tests that are powerful
against both types of alternatives. Nevertheless, the $2$- and $\infty$-norm
are just two out of the whole spectrum of $p$-norms that one can base a test
on. In the context of testing whether a candidate parameter satisfies a large
number of moment equalities, we construct a test that harnesses the strength of
all $p$-norms with $p\in[2, \infty]$. As a result, this test consistent against
strictly more alternatives than any test based on a single $p$-norm. In
particular, our test is consistent against more alternatives than tests based
on the $2$- and $\infty$-norm, which is what most implementations of the power
enhancement principle target.
  We illustrate the scope of our general results by using them to construct a
test that simultaneously dominates the Anderson-Rubin test (based on $p=2$) and
tests based on the $\infty$-norm in terms of consistency in the linear
instrumental variable model with many (weak) instruments.


  We present the results of mechanical characterizations of many different
high-quality optical coatings made of ion-beam-sputtered titania-doped tantala
and silica, developed originally for interferometric gravitational-wave
detectors. Our data show that in multi-layer stacks (like high-reflection Bragg
mirrors, for example) the measured coating dissipation is systematically higher
than the expectation and is correlated with the stress condition in the sample.
This has a particular relevance for the noise budget of current advanced
gravitational-wave interferometers, and, more generally, for any experiment
involving thermal-noise limited optical cavities.


  Attention mechanism in sequence-to-sequence models is designed to model the
alignments between acoustic features and output tokens in speech recognition.
However, attention weights produced by models trained end to end do not always
correspond well with actual alignments, and several studies have further argued
that attention weights might not even correspond well with the relevance
attribution of frames. Regardless, visual similarity between attention weights
and alignments is widely used during training as an indicator of the models
quality. In this paper, we treat the correspondence between attention weights
and alignments as a learning problem by imposing a supervised attention loss.
Experiments have shown significant improved performance, suggesting that
learning the alignments well during training critically determines the
performance of sequence-to-sequence models.


  Using the Large Binocular Telescope (LBT)/Multi-Object Dual Spectrograph
(MODS), we have obtained optical spectroscopy of one of the most metal-poor
dwarf star-forming galaxies (SFG) in the local Universe, J2229+2725. This
galaxy with a redshift z=0.0762 was selected from the Data Release 16 (DR16) of
the Sloan Digital Sky Survey (SDSS). Its properties derived from the LBT
observations are most extreme among SFGs in several ways. Its oxygen abundance
12+logO/H=7.085+/-0.031 is among the lowest ever observed for a SFG. With its
very low metallicity, an absolute magnitude Mg=-16.39 mag, a low stellar mass
Mstar=9.1x10^6 Msun and a very low mass-to-light ratio Mstar/Lg~0.0166 (in
solar units), J2229+2725 deviates strongly from the luminosity-metallicity
relation defined by the bulk of the SFGs in the SDSS. J2229$+$2725 has a very
high specific star-formation rate sSFR~75 Gyr^-1, indicating very active
ongoing star formation. Three other features of J2229+2725 are most striking,
being the most extreme among lowest-metallicity SFGs: 1) a ratio
O32=I([OIII]5007)/I([OII]3727)~53, 2) an equivalent width of the Hbeta emission
line EW(Hbeta) of 577A, and 3) an electron number density of ~1000 cm^-3. These
properties imply that the starburst in J2229+2725 is very young. Using the
extremely high O32 in J2229+2725, we have improved the strong-line calibration
for the determination of oxygen abundances in the most metal-deficient
galaxies, in the range 12 + logO/H<7.3.


  Optical waveguides in the form of glass fibers are the backbone of global
telecommunication networks. In such optical fibers, the light is guided over
long distances by continuous total internal reflection which occurs at the
interface between the fiber core with a higher refractive index and the lower
index cladding. Although this mechanism ensures that no light escapes from the
waveguide, it gives rise to an evanescent field in the cladding. While this
field is protected from interacting with the environment in standard optical
fibers, it is routinely employed in air- or vacuum-clad fibers in order to
efficiently couple light fields to optical components or emitters using, e.g.,
tapered optical fiber couplers. Remarkably, the strong confinement imposed by
the latter can lead to significant coupling of the light's spin and orbital
angular momentum. Taking advantage of this effect, we demonstrate the
controlled directional spontaneous emission of light by quantum emitters into a
sub-wavelength-diameter waveguide. The effect is investigated in a paradigmatic
setting, comprising cesium atoms which are located in the vicinity of a
vacuum-clad silica nanofiber. We experimentally observe an asymmetry higher
than 10:1 in the emission rates into the counterpropagating fundamental guided
modes of the nanofiber. Moreover, we demonstrate that this asymmetry can be
tailored by state preparation and suitable excitation of the quantum emitters.
We expect our results to have important implications for research in
nanophotonics and quantum optics and for implementations of integrated optical
signal processing in the classical as well as in the quantum regime.


  Continued self-supervised (SSL) pre-training for adapting existing SSL models
to the target domain has shown to be extremely effective for low-resource
Automatic Speech Recognition (ASR). This paper proposes Stable Distillation, a
simple and novel approach for SSL-based continued pre-training that boosts ASR
performance in the target domain where both labeled and unlabeled data are
limited. Stable Distillation employs self-distillation as regularization for
continued pre-training, alleviating the over-fitting issue, a common problem
continued pre-training faces when the source and target domains differ.
Specifically, first, we perform vanilla continued pre-training on an initial
SSL pre-trained model on the target domain ASR dataset and call it the teacher.
Next, we take the same initial pre-trained model as a student to perform
continued pre-training while enforcing its hidden representations to be close
to that of the teacher (via MSE loss). This student is then used for downstream
ASR fine-tuning on the target dataset. In practice, Stable Distillation
outperforms all our baselines by 0.8 - 7 WER when evaluated in various
experimental settings.


  The interactions of tiny objects with their environment are dominated by
thermal fluctuations. Guided by theory and assisted by micromanipulation tools,
scientists have begun to study such interactions in detail.


  It has been proposed that quantum complexity is dual to the volume of the
extremal surface, the action of the Wheeler-DeWitt patch, and the spacetime
volume of the patch. Recently, a generalized volume-complexity observable was
formulated as an equivalently good candidate for the dual holographic
complexity. This proposal is abbreviated as ``complexity=anything." This
proposal offers greater flexibility in selecting extremal surfaces and
evaluating physical quantities, e.g., volume or action, on these surfaces. In
this study, we explore the 'complexity=anything' proposal for Gauss-Bonnet
black holes in asymptotic anti-de Sitter space in various dimensions. We
demonstrate that this proposal guarantees the linear growth of the generalized
volume at late times, regardless of the coupling parameters for
four-dimensional Gauss-Bonnet gravity. However, this universality does not hold
for higher dimensions. Moreover, discontinuous deformations of the extremal
surfaces emerge when multiple peaks exist in the effective potential, which is
reminiscent of a phase transition. Additionally, we present constraints on the
coupling parameters of five-dimensional models in order for the generalized
volume to be a viable candidate for holographic complexity.


  We investigate adaptive sublinear algorithms for detecting monotone patterns
in an array. Given fixed $2 \leq k \in \mathbb{N}$ and $\varepsilon > 0$,
consider the problem of finding a length-$k$ increasing subsequence in an array
$f \colon [n] \to \mathbb{R}$, provided that $f$ is $\varepsilon$-far from free
of such subsequences. Recently, it was shown that the non-adaptive query
complexity of the above task is $\Theta((\log n)^{\lfloor \log_2 k \rfloor})$.
In this work, we break the non-adaptive lower bound, presenting an adaptive
algorithm for this problem which makes $O(\log n)$ queries. This is optimal,
matching the classical $\Omega(\log n)$ adaptive lower bound by Fischer [2004]
for monotonicity testing (which corresponds to the case $k=2$), and implying in
particular that the query complexity of testing whether the longest increasing
subsequence (LIS) has constant length is $\Theta(\log n)$.


  Data augmentation is an effective technique to improve the generalization of
deep neural networks. However, previous data augmentation methods usually treat
the augmented samples equally without considering their individual impacts on
the model. To address this, for the augmented samples from the same training
example, we propose to assign different weights to them. We construct the
maximal expected loss which is the supremum over any reweighted loss on
augmented samples. Inspired by adversarial training, we minimize this maximal
expected loss (MMEL) and obtain a simple and interpretable closed-form
solution: more attention should be paid to augmented samples with large loss
values (i.e., harder examples). Minimizing this maximal expected loss enables
the model to perform well under any reweighting strategy. The proposed method
can generally be applied on top of any data augmentation methods. Experiments
are conducted on both natural language understanding tasks with token-level
data augmentation, and image classification tasks with commonly-used image
augmentation techniques like random crop and horizontal flip. Empirical results
show that the proposed method improves the generalization performance of the
model.


  In this paper we present weak lensing observations of the fields around 8 z~1
luminous radio sources. These data are searched for the lensing signatures of
clusters that are either physically associated with the radio objects, or are
foreground systems projected along the line of sight. The radio sources were
all imaged with WFPC-2/HST providing high quality shape information on large
numbers of faint galaxies around them. Statistical analysis of the coherent
shear field visible in the shapes of the faint galaxies indicates that we have
detected a weak lensing signal close to one of the targets, 3C336 at z=0.927,
with a high level of confidence. A second, independent WFPC-2 observation of
this target reinforces this detection. Our results support the earlier
suggestion of weak lensing in this field by Fort et al (1996) using
ground-based data. We also combined the shear distributions in the remaining 7
field to improve our sensitivity to weak shear signals from any structure
typically associated with these sources. We find no detectable signal and
estimate an upper limit on the maximum shear allowed by our observations. Using
an N(z) estimated from lensing analyses we convert our observed lensing signal
and limits into estimates of the masses of the various structures. We suggest
that further lensing observations of distant radio sources and their host
environments may allow the cluster L_X-mass relationship to be mapped at
high-z. This is crucial for interpreting the results of the next generation of
deep X-ray surveys, and thus constraining the redshift evolution of the cluster
mass function out to z=1.


  For a prime number $p$, a finite $p$-group of order $p^n$ has maximal class
if it has nilpotency class $n-1$. Here we examine saturated fusion systems on
maximal class $p$-groups and, in particular, we describe all the reduFor a
prime number $p$, a finite $p$-group of order $p^n$ has maximal class if and
only if it has nilpotency class $n-1$. Here we examine saturated fusion systems
$\mathcal F$ on maximal class $p$-groups $S$ of order at least $p^4$. The
Alperin-Goldschmidt Theorem for saturated fusion systems yields that $\mathcal
F$ is entirely determined by the $\mathcal F$-automorphisms of its $\mathcal
F$-essential subgroups and of $S$ itself. If an $\mathcal F$-essential subgroup
either has order $p^2$ or is non-abelian of order $p^3$, then it is called an
$\mathcal F$-pearl. The facilitating and technical theorem in this work shows
that an $\mathcal F$-essential subgroup is either an $\mathcal F$-pearl, or one
of two explicitly determined maximal subgroups of $S$. This result is easy to
prove if $S$ is a $2$-group and can be read from the work of D'\iaz, Ruiz, and
Viruel together with that of Parker and Semeraro when $p=3$. The main
contribution is for $p \ge 5$ as in this case there is no classification of the
maximal class $p$-groups.
  The main Theorem describes all the reduced saturated fusion systems on a
maximal class $p$-group of order at least $p^4$ and follows from two more
extensive theorems. These two theorems describe all saturated fusion systems,
not restricting to the reduced ones for example, on exceptional and
non-exceptional maximal class $p$-groups respectively. As a corollary, we have
the easy to remember result that states that, if $O_p(\mathcal F)=1$, then
either $\mathcal F$ has $\mathcal F$-pearls or $S$ is isomorphic to a Sylow
$p$-subgroup of $\mathrm G_2(p)$ with $p\ge 5$ and the fusion systems are
explicitly described.


  We give a survey of various rigidity results involving scalar curvature. Many
of these results are inspired by the positive mass theorem in general
relativity. In particular, we discuss the recent solution of Min-Oo's
Conjecture for the hemisphere (cf. [13]). We also analyze the case of equality
in Bray's volume comparison theorem.


  This paper gives a short survey of recent trends in the emerging field of big
data. It explains the definitions and useful methods. In addition, application
fields of smart buildings and smart grids are discussed.


  We study the presence of lumplike solutions in models described by a single
real scalar field with standard kinematics in two-dimensional spacetime. The
results show several distinct models that support the presence of bell-shaped,
lumplike structures which may live in a compact space.


  Automatic metrics for evaluating translation quality are typically validated
by measuring how well they correlate with human assessments. However,
correlation methods tend to capture only the ability of metrics to
differentiate between good and bad source-translation pairs, overlooking their
reliability in distinguishing alternative translations for the same source. In
this paper, we confirm that this is indeed the case by showing that current
metrics are insensitive to nuanced differences in translation quality. This
effect is most pronounced when the quality is high and the variance among
alternatives is low. Given this finding, we shift towards detecting
high-quality correct translations, an important problem in practical
decision-making scenarios where a binary check of correctness is prioritized
over a nuanced evaluation of quality. Using the MQM framework as the gold
standard, we systematically stress-test the ability of current metrics to
identify translations with no errors as marked by humans. Our findings reveal
that current metrics often over or underestimate translation quality,
indicating significant room for improvement in automatic evaluation methods.


  The main aim of this paper is to propose a color texture classification
approach which uses color sensor information and texture features jointly. High
accuracy, low noise sensitivity and low computational complexity are specified
aims for our proposed approach. One of the efficient texture analysis
operations is local binary patterns. The proposed approach includes two steps.
First, a noise resistant version of color local binary patterns is proposed to
decrease sensitivity to noise of LBP. This step is evaluated based on
combination of color sensor information using AND operation. In second step, a
significant points selection algorithm is proposed to select significant LBP.
This phase decreases final computational complexity along with increasing
accuracy rate. The Proposed approach is evaluated using Vistex, Outex, and KTH
TIPS2a data sets. Our approach has been compared with some state of the art
methods. It is experimentally demonstrated that the proposed approach achieves
highest accuracy. In two other experiments, result show low noise sensitivity
and low computational complexity of the proposed approach in comparison with
previous versions of LBP. Rotation invariant, multi resolution, general
usability are other advantages of our proposed approach. In the present paper,
a new version of LBP is proposed originally, which is called Hybrid color local
binary patterns. It can be used in many image processing applications to
extract color and texture features jointly. Also, a significant point selection
algorithm is proposed for the first time to select key points of images.


  New solutions to the abelian U(1) Higgs model, corresponding to vortices of
integer and half-integer winding number bound onto the edges of domain walls
and possibly surrounded by annular current flows, are described, based on a
fine-grained analysis of the topology of such configurations in spacetime. The
existence of these states, which saturate BPS bounds in specific limits and are
quite reminiscent of D-branes and membranes in general, could have interesting
and some important consequences in a wide range of physical contexts. For
instance, they raise the possibility that for some regimes of couplings the
usual vortex of unit winding number would split into two vortices each of
one-half winding number bound by a domain wall. A similar approach may also be
relevant to other known topological states of field theory.


  The aim of the present paper is to study conditions under which all the
non-wandering points are periodic points, for a discrete dynamical system of
two variables defined on a compact manifold. We include a survey of known
results in all dimensions, and study the remaining open question in dimension
two. We present two results, one positive and one negative. The negative
result: we construct a Kupka--Smale diffeomorphism in $\mathbb{R}^2$ (which can
be extended to a diffeomorphism of the sphere) with a closed set of periodic
points that differs from the set of nonwandering points. The positive result:
we present a condition on the widely studied H\'{e}non family which guarantees
that all nonwandering points are periodic. Finally, we close by describing what
future work may be needed to resolve our broad goals.


  We show how a Heisenberg spin chain emerges from the two-dimensional
${\mathcal N}$=(2,2) gauge theory at an intermediate scale, which relies on the
renormalization group flow guided by the global symmetries and the dynamics of
domain walls. The discussion of higher-dimensional gauge theories with four
supercharges is similar by compactifying them into two dimensions. Instead of
utilizing the bosonic fields solely in the literature, adopting the fermionic
degrees of freedom of gauge theory is a crucial step in our construction. From
the perspective of the spin chain, we observe that the Seiberg(-like) duality
between two gauge theories is manifest since it is a finite symmetry in the
closed spin chain. Based on this, we further conjecture gauge theories with the
same global symmetries could be unified into a single system: the Heisenberg
spin chain. At least, we prove this conjecture at the intermediate scale.
Finally, we also comment on other formulations of an integrable system centered
on the Heisenberg spin chain.


  The problem of singularities associated with Dirac strings and closed
timelike curves in classical solutions of pure gravity is analyzed here. A
method to eliminate these is introduced and established first for the Taub-NUT
geometry. This is superceded by a smooth solution of first order field
equations, which is defined to be a unique extension of the Taub Universe to a
degenerate metric phase. As an additional feature, this framework naturally
provides a geometric interpretation of the magnetic charge in the context of
gravity theory without matter. Finally, exploiting the two phases of the metric
determinant, we find a (smooth and unique) continuation of the Misner geometry
as well, ridding it of closed timelike worldlines which exist in its otherwise
Einsteinian manifestation.


  The hippocampal system contains neural populations that encode an animal's
position and velocity as it navigates through space. Here, we show that such
populations can embed two codes within their spike trains: a firing rate code
(R) conveyed by within-cell spike intervals, and a co-firing rate code (R')
conveyed by between-cell spike intervals. These two codes behave as conjugates
of one another, obeying an analog of the uncertainty principle from physics:
information conveyed in R comes at the expense of information in R', and vice
versa. An exception to this trade-off occurs when spike trains encode a pair of
conjugate variables, such as position and velocity, which do not compete for
capacity across R and R'. To illustrate this, we describe two biologically
inspired methods for decoding R and R', referred to as sigma and sigma-chi
decoding, respectively. Simulations of head direction (HD) and grid cells show
that if firing rates are tuned for position (but not velocity), then position
is recovered by sigma decoding, whereas velocity is recovered by sigma-chi
decoding. Conversely, simulations of oscillatory interference among
theta-modulated "speed cells" show that if co-firing rates are tuned for
position (but not velocity), then position is recovered by sigma-chi decoding,
whereas velocity is recovered by sigma decoding. Between these two extremes,
information about both variables can be distributed across both channels, and
partially recovered by both decoders. These results suggest that neurons with
different spatial and temporal tuning properties-such as speed versus grid
cells-might not encode different information, but rather, distribute similar
information about position and velocity in different ways across R and R'.


  While homology theory of associative structures, such as groups and rings,
has been extensively studied in the past beginning with the work of Hopf,
Eilenberg, and Hochschild, homology of non-associative distributive structures,
such as quandles, were neglected until recently. Distributive structures have
been studied for a long time. In 1880, C.S. Peirce emphasized the importance of
(right) self-distributivity in algebraic structures. However, homology for
these universal algebras was introduced only sixteen years ago by Fenn, Rourke,
and Sanderson. We develop this theory in the historical context and propose a
general framework to study homology of distributive structures. We illustrate
the theory by computing some examples of 1-term, 2-term, and 3-term homology,
and then discussing 4-term homology for Boolean algebras and distributive
lattices. We outline potential relations to Khovanov homology, via the
Yang-Baxter operator.


  We study generic effects of new physics on the rare decay modes $K_L \to
\pi^0 \nu \bar\nu$ and $K^+ \to \pi^+ \nu \bar\nu$. We discuss several cases:
left-handed neutrino couplings; right handed neutrino couplings; neutrino
lepton flavour violating (LFV) interactions; and $\Delta I =3/2$ interactions.
The first of these cases has been studied before as it covers many new physics
extensions of the standard model; the second one requires the existence of a
new light (sterile) right-handed neutrino and its contribution to both
branching ratios is always additive to the SM. The case of neutrino LFV
couplings introduces a CP conserving contribution to $K_L \to \pi^0 \nu
\bar\nu$ which affects the rates in a similar manner as a right handed neutrino
as neither one of these interferes with the standard model amplitudes. Finally,
we consider new physics with $\Delta I =3/2$ interactions to go beyond the
Grossman-Nir bound. We find that the rare kaon rates are only sensitive to new
physics scales up to a few GeV for this scenario.


  Standard Model may allow an extended gauge sector with anomaly-free flavored
gauge symmetries, such as $L_{i} - L_{j}$, $B_{i} - L_{j}$, and $B - 3L_{i}$,
where $i,j=1,2,3$ are flavor indices. We investigate phenomenological
implications of the new flavored gauge boson $Z^{\prime}$ in the above three
classes of gauge symmetries. Focusing on the gauge boson mass above 5 GeV, we
use the lepton universality test in the $Z$ and $\tau/\mu$ decays, LEP
searches, LHC searches, neutrino trident production bound, and LHC
$Z\rightarrow 4\mu$ searches to put constraints on the
$g^{\prime}-M_{Z^{\prime}}$ plane. When $L_1$ is involved, the LEP bounds on
the $e^{-}e^{+} \rightarrow \ell^{-}\ell^{+}$ processes give the most stringent
bounds, while the LHC bound becomes the strongest constraints in the large
$M_{Z^{\prime}}$ region when $B_{i}$ is involved. The bound from $Z\rightarrow
4\mu$ productions, which is applicable for $L_2$-involved scenarios, provides
stringent bounds in the small $M_{Z^{\prime}}$ region. One exception is the
$B-3L_2$ scenario, in which case only a small region is favored due to the
lepton universality.


  In future normal-conducting linear colliders, the beams will be delivered in
short bursts with a length of the order of 100 ns. The pulses will be separated
by several ms. In order to maintain high luminosity, feedback is necessary on a
pulse-to-pulse basis. In addition, intra-pulse feedback that can correct beam
positions and angles within one pulse seem technically feasible. The likely
performances of different feedback options are simulated for the NLC (Next
Linear Collider) and CLIC (Compact Linear Collider).


  We study the necking of a filament of complex fluid or soft solid subject to
uniaxial tensile stretching, under conditions of constant imposed stress and
force, by means of linear stability analysis and nonlinear simulations. We
demonstrate necking to be a flow instability that is an unavoidable consequence
of the constitutive behaviour of essentially any viscoelastic material. We
derive criteria for the onset of necking that can be reported in terms of
characteristic signatures in the shapes of the experimentally measured material
functions, and that should therefore apply universally to all materials. To
confirm their generality, we show them to hold numerically in six constitutive
models. Under conditions of constant stress, we find two distinct dynamical
regimes as a function of time. In the first regime the strain rate quickly
attains a value prescribed by the fluid's underlying homogeneous constitutive
curve, at the given stress. In this first regime, no appreciable necking
arises. A second regime then ensues in which the homogeneous flow destabilises
to form a neck. This necking instability can occur via two distinct modes. The
first mode is relatively gentle and arises in any regime where the slope of the
constitutive curve is positive. It has a rate of necking per accumulated strain
unit set by the inverse of the slope of the constitutive curve. The second mode
sets in when a carefully defined `elastic derivative' of the tensile force
first slopes down as a function of the time. We discuss the way in which these
modes of instability manifest themselves in entangled polymeric fluids,
demonstrating four distinct regimes of necking behaviour as a function of
stress. Under conditions of constant imposed force, typically the flow sweeps
up the underlying constitutive curve of the fluid in question, with instability
to necking in any regime where that curve is positively sloping.


  In a two-dimensional arrangement of closely spaced elliptical nanomagnets
with in-plane magnetic anisotropy, whose major axes are aligned along columns
and minor axes along rows, dipole coupling will make the magnetic ordering
"ferromagnetic" along the columns and "anti-ferromagnetic" along the rows.
Noise and other perturbations can drive the system out of this ground state
configuration and pin it in a metastable state where the magnetization
orientations will not follow this pattern. Internal energy barriers,
sufficiently larger than the thermal energy kT, will prevent the system from
leaving the metastable state and decaying spontaneously to the ground state.
These barriers can be temporarily eroded by globally straining the nanomagnets
with time-varying strain if the nanomagnets are magnetostrictive, which will
allow the system to return to ground state after strain is removed. This is a
hardware emulation of simulated annealing in an interacting many body system.
Here, we demonstrate this function experimentally.


  This paper introduces Wasserstein Adversarially Regularized Graph Autoencoder
(WARGA), an implicit generative algorithm that directly regularizes the latent
distribution of node embedding to a target distribution via the Wasserstein
metric. The proposed method has been validated in tasks of link prediction and
node clustering on real-world graphs, in which WARGA generally outperforms
state-of-the-art models based on Kullback-Leibler (KL) divergence and typical
adversarial framework.


  This paper considers signal detection in coexisting wireless sensor networks
(WSNs). We characterize the aggregate signal and interference from a Poisson
random field of nodes and define a binary hypothesis testing problem to detect
a signal in the presence of interference. For the testing problem, we introduce
the maximum likelihood (ML) detector and simpler alternatives. The proposed
mixed-fractional lower order moment (FLOM) detector is computationally simple
and close to the ML performance, and robust to estimation errors in system
parameters. We also derived asymptotic theoretical performances for the
proposed simple detectors. Monte-Carlo simulations are used to supplement our
analytical results and compare the performance of the receivers.


  Secure data deletion enables data owners to fully control the erasure of
their data stored on local or cloud data centers and is essential for
preventing data leakage, especially for cloud storage. However, traditional
data deletion based on unlinking, overwriting, and cryptographic key management
either ineffectiveness in cloud storage or rely on unpractical assumption. In
this paper, we present SevDel, a secure and verifiable data deletion scheme,
which leverages the zero-knowledge proof to achieve the verification of the
encryption of the outsourced data without retrieving the ciphertexts, while the
deletion of the encryption keys are guaranteed based on Intel SGX. SevDel
implements secure interfaces to perform data encryption and decryption for
secure cloud storage. It also utilizes smart contract to enforce the operations
of the cloud service provider to follow service level agreements with data
owners and the penalty over the service provider, who discloses the cloud data
on its servers. Evaluation on real-world workload demonstrates that SevDel
achieves efficient data deletion verification and maintain high bandwidth
savings.


  The weak $r$-coloring numbers $wcol_r(G)$ of a graph $G$ were introduced by
the first two authors as a generalization of the usual coloring number
$col(G)$, and have since found interesting theoretical and algorithmic
applications. This has motivated researchers to establish strong bounds on
these parameters for various classes of graphs.
  Let $G^p$ denote the $p$-th power of $G$. We show that, all integers $p >0$
and $\Delta \ge 3$ and graphs $G$ with $\Delta(G) \leq \Delta$ satisfy
$col(G^p) \in O(p \cdot wcol_{\lceil p/2\rceil}(G)(\Delta-1)^{\lfloor
p/2\rfloor})$; for fixed tree width or fixed genus the ratio between this upper
bound and worst case lower bounds is polynomial in $p$. For the square of
graphs $G$, we also show that, if the maximum average degree $2k-2 < mad(G)
\leq 2k$, then $ col(G^2) \leq (2k-1)\Delta(G)+2k+1$.


  Massive particles are radiated from black holes through the Hawking mechanism
together with the more familiar radiation of massless particles. For $E >= m$,
the emission rate is identical to the massless case. But $E < m$ particles can
also tunnel across the horizon. A study of the dispersion relation and wave
packet simulations show that their classical trajectory is similar to that of a
boomerang. The tunneling formalism is used to calculate the probability for
detecting such $E < m$ particles, for a Schwarzschild black hole of
astrophysical size or in an analogue gravity experiment, as a function of the
distance from the horizon and the energy of the particle.


  In this paper, we introduce a set representation called polynomial logical
zonotopes for performing exact and computationally efficient reachability
analysis on logical systems. Polynomial logical zonotopes are a generalization
of logical zonotopes, which are able to represent up to 2^n binary vectors
using only n generators. Due to their construction, logical zonotopes are only
able to support exact computations of some logical operations (XOR, NOT, XNOR),
while other operations (AND, NAND, OR, NOR) result in over-approximations in
the reduced space, i.e., generator space. In order to perform all fundamental
logical operations exactly, we formulate a generalization of logical zonotopes
that is constructed by dependent generators and exponent matrices. We prove
that through this polynomial-like construction, we are able to perform all of
the fundamental logical operations (XOR, NOT, XNOR, AND, NAND, OR, NOR) exactly
in the generator space. While we are able to perform all of the logical
operations exactly, this comes with a slight increase in computational
complexity compared to logical zonotopes. We show that we can use polynomial
logical zonotopes to perform exact reachability analysis while retaining a low
computational complexity. To illustrate and showcase the computational benefits
of polynomial logical zonotopes, we present the results of performing
reachability analysis on two use cases: (1) safety verification of an
intersection crossing protocol and (2) reachability analysis on a
high-dimensional Boolean function. Moreover, to highlight the extensibility of
logical zonotopes, we include an additional use case where we perform a
computationally tractable exhaustive search for the key of a linear feedback
shift register.


  We analyze future direct data matter detection experiments using Effective
Field Theory (EFT) operators with light, $\lesssim 100$ MeV mass mediators. We
compare the nuclear recoil energy spectra from these operators to the predicted
high energy solar neutrino spectrum. A set of operators that generate spectra
similar to the neutrino background is identified, however this set is distinct
from those that mimic the neutrino background for heavy, $\gtrsim 100$ MeV mass
mediators. We outline a general classification scheme based on momentum
dependence of the dark matter-nucleus interaction to determine how strong the
discovery limit for a given operator saturates in the presence of the neutrino
background. Our results highlight the benefit of considering a general
theoretical framework regarding dark matter, and motivate continued
experimental progress towards lower nuclear recoil energy thresholds.