  Proofs of Tychonoff's theorem often seem to require a bit of magic. Machinery
such as ultrafilters, nets or maximal families with the finite intersection
property are employed to give proofs that can be very neat, but not the kind of
thing that one would naturally think of when presented with the problem (given
a background in standard open set topology). Here we present a direct and
pretty simple proof of Tychonoff's theorem, straight from the open cover
definition of compactness.


  In this study, we explore the black bounce solution in Rastall gravity and
its potential source field, which can be described as a black hole or wormhole
solution depending on certain parameters. We focus on the Bardeen-Type black
bounce and Simpson-Visser solution and aim to identify an appropriate source
field for these solutions. Our findings suggest that in Rastall gravity, a
source for the black bounce solution with non-linear electromagnetic can be
found. However, in the presence of a non-linear electromagnetic source, it is
impossible to identify an appropriate source for the black bounce solution
without a scalar field. We also investigate the energy conditions outside the
event horizon for two types of black bounce solutions: Simpson-Visser and
Bardeen. We find that these solutions do not satisfy the null energy condition,
but we also reveal that Rastall gravity has more flexibility for maintaining
some of the energy conditions by selecting an appropriate value for the Rastall
parameter $\gamma$.


  Designing an efficient scheme in physical layer enables cognitive radio (CR)
users to efficiently utilize resources dedicated to primary users (PUs). In
this paper in order to maximize the SU's throughput, the SU's transceivers
beamforming is designed through new model considering the presence of the PU's
transmitter. Since presence of primary transmitter basically degrades CR's
system performance; proposed beamforming design considers intra-system
interference between PUs and SUs. An optimization problem based on maximizing
CR network throughput subject to controlling interference power from SU
transmitter to PU receiver has been formulated. Due to limited cooperation
between PU and SU network, channel state information (CSI) between two networks
are assumed to be partially available, subsequently conventional CSI
uncertainty model known as norm bounded error model has been employed. The
proposed optimization problem, which is basically difficult to solve, has been
converted to a semi definite program which can be efficiently solved by
optimization toolbox software e.g., CVX-Mathlab. Furthermore, alternative time
efficient and close form solutions are derived. The superiority of the proposed
approach in comparison with the previous works has been confirmed through the
simulation results.


  The development of various sensing technologies is improving measurements of
stress and the well-being of individuals. Although progress has been made with
single signal modalities like wearables and facial emotion recognition,
integrating multiple modalities provides a more comprehensive understanding of
stress, given that stress manifests differently across different people.
Multi-modal learning aims to capitalize on the strength of each modality rather
than relying on a single signal. Given the complexity of processing and
integrating high-dimensional data from limited subjects, more research is
needed. Numerous research efforts have been focused on fusing stress and
emotion signals at an early stage, e.g., feature-level fusion using basic
machine learning methods and 1D-CNN Methods. This paper proposes a multi-modal
learning approach for stress detection that integrates facial landmarks and
biometric signals. We test this multi-modal integration with various
early-fusion and late-fusion techniques to integrate the 1D-CNN model from
biometric signals and 2-D CNN using facial landmarks. We evaluate these
architectures using a rigorous test of models' generalizability using the
leave-one-subject-out mechanism, i.e., all samples related to a single subject
are left out to train the model. Our findings show that late-fusion achieved
94.39\% accuracy, and early-fusion surpassed it with a 98.38\% accuracy rate.
This research contributes valuable insights into enhancing stress detection
through a multi-modal approach. The proposed research offers important
knowledge in improving stress detection using a multi-modal approach.


  The Dead Leaves Model (DLM) provides a random tessellation of $d$-space,
representing the visible portions of fallen leaves on the ground when $d=2$.
For $d=1$, we establish formulae for the intensity, two-point correlations, and
asymptotic covariances for the point process of cell boundaries, along with a
functional CLT. For $d=2$ we establish analogous results for the random surface
measure of cell boundaries, and also determine the intensity of cells in a more
general setting than in earlier work of Cowan and Tsang. We introduce a general
notion of Dead Leaves Random Measures and give formulae for means, asymptotic
variances and functional CLTs for these measures; this has applications to
various other quantities associated with the DLM.


  Mechanical resonances are used in a wide variety of devices; from smart phone
accelerometers to computer clocks and from wireless communication filters to
atomic force microscope sensors. Frequency stability, a critical performance
metric, is generally assumed to be tantamount to resonance quality factor (the
inverse of the linewidth and of the damping). Here we show that frequency
stability of resonant nanomechanical sensors can generally be made independent
of quality factor. At high bandwidths, we show that quality factor reduction is
completely mitigated by increases in signal to noise ratio. At low bandwidths,
strikingly, increased damping leads to better stability and sensor resolution,
with improvement proportional to damping. We confirm the findings by
demonstrating temperature resolution of 50 \mu K at 200 Hz bandwidth. These
results open the door for high performance ultrasensitive resonant sensors in
gaseous or liquid environments, single cell nanocalorimetry, nanoscale gas
chromatography, and atmospheric pressure nanoscale mass spectrometry.


  Permanent magnet materials require a high uniaxial magneto-crystalline
anisotropy. Exchange coupling between small crystallites with easy-plane
anisotropy induces an effective uniaxial anisotropy if arranged accordingly.
Nanostructuring of materials with easy-plane anisotropy is an alternative way
to create hard-magnetic materials. The coercivity increases with decreasing
feature size. The resulting coercive field is about 12 percent of the
anisotropy field for a crystal size of 3.4 times the Bloch parameter.


  While automatic summarization evaluation methods developed for English are
routinely applied to other languages, this is the first attempt to
systematically quantify their panlinguistic efficacy. We take a summarization
corpus for eight different languages, and manually annotate generated summaries
for focus (precision) and coverage (recall). Based on this, we evaluate 19
summarization evaluation metrics, and find that using multilingual BERT within
BERTScore performs well across all languages, at a level above that for
English.


  Lung cancer is one of the deadliest cancers, and in part its effective
diagnosis and treatment depend on the accurate delineation of the tumor.
Human-centered segmentation, which is currently the most common approach, is
subject to inter-observer variability, and is also time-consuming, considering
the fact that only experts are capable of providing annotations. Automatic and
semi-automatic tumor segmentation methods have recently shown promising
results. However, as different researchers have validated their algorithms
using various datasets and performance metrics, reliably evaluating these
methods is still an open challenge. The goal of the Lung-Originated Tumor
Segmentation from Computed Tomography Scan (LOTUS) Benchmark created through
2018 IEEE Video and Image Processing (VIP) Cup competition, is to provide a
unique dataset and pre-defined metrics, so that different researchers can
develop and evaluate their methods in a unified fashion. The 2018 VIP Cup
started with a global engagement from 42 countries to access the competition
data. At the registration stage, there were 129 members clustered into 28 teams
from 10 countries, out of which 9 teams made it to the final stage and 6 teams
successfully completed all the required tasks. In a nutshell, all the
algorithms proposed during the competition, are based on deep learning models
combined with a false positive reduction technique. Methods developed by the
three finalists show promising results in tumor segmentation, however, more
effort should be put into reducing the false positive rate. This competition
manuscript presents an overview of the VIP-Cup challenge, along with the
proposed algorithms and results.


  Obtaining initial conditions and parameterizations leading to a model
consistent with available measurements or safety specifications is important
for many applications. Examples include model (in-)validation, prediction,
fault diagnosis, and controller design. We present an approach to determine
inner- and outer-approximations of the set containing all consistent initial
conditions/parameterizations for nonlinear continuous-time systems. These
approximations are found by occupation measures that encode the system dynamics
and measurements, and give rise to an infinite-dimensional linear program. We
exploit the flexibility and linearity of the decision problem to incorporate
uncertain-but-bounded and pointwise-in-time state and output constraints, a
feature which was not addressed in previous works. The infinite-dimensional
linear program is relaxed by a hierarchy of LMI problems that provide
certificates in case no consistent initial condition/parameterization exists.
Furthermore, the applied LMI relaxation guarantees that the approximations
converge (almost uniformly) to the true consistent set. We illustrate the
approach with a biochemical reaction network involving unknown initial
conditions and parameters.


  Warped models with the Higgs confined to the weak brane and the gauge and
matter fields accessing the $AdS_5$ bulk provide viable setting to address the
gauge hierarchy problem. Brane kinetic terms for the bulk fields are known to
ease some of the tensions of these models with precision electroweak
observables and flavor constraints. We study the loop-driven Higgs coupling to
the gluons that are relevant to the Higgs program at LHC, in this scenario. We
demonstrate a partial cancellation in the contribution of the fermionic
Kaluza-Klein (KK) towers within such framework relatively independent of the 5D
parameters. The entire dependence of this coupling on the new physics arises
from the mixing between the Standard Model states and the KK excitations. We
find that the present precision in measurement of these couplings can lead to a
constraint on the KK scale up to 1.2 TeV at $95\%$ confidence level.


  Multi-task learning (MTL) in deep neural networks for NLP has recently
received increasing interest due to some compelling benefits, including its
potential to efficiently regularize models and to reduce the need for labeled
data. While it has brought significant improvements in a number of NLP tasks,
mixed results have been reported, and little is known about the conditions
under which MTL leads to gains in NLP. This paper sheds light on the specific
task relations that can lead to gains from MTL models over single-task setups.


  In the present paper, we apply a global branch approach to study the
existence, non-existence and multiplicity of positive normalized solutions
$(\lambda_c, u_c)\in \mathbb{R}\times H^1(\mathbb{R}^N)$ to the following
Kirchhoff problem $$ -\left(a+b\int_{\mathbb{R}^N}|\nabla u|^2dx\right)\Delta
u+\lambda u=g(u)~\hbox{in}~\mathbb{R}^N,\;N\geq 1 $$ satisfying the
normalization constraint $ \displaystyle\int_{\mathbb{R}^N}u^2=c, $ which
appears in free vibrations of elastic strings. The parameters $a,b>0$ are
prescribed as well as the mass $c>0$. Due to the presence of the non-local term
$b\int_{\mathbb{R}^N}|\nabla u|^2dx \Delta u$, such problems lack the mountain
pass geometry in the higher dimension case $N\geq 5$. Our result seems to be
the first attempt in this aspect.


  We introduce a new class of renormalisable models, consisting of a dark
$SU(2)_D$ gauge sector connected to the Standard Model (SM) through a
Vector-Like (VL) fermion mediator, not requiring a Higgs portal, in which a
massive vector boson is the Dark Matter (DM) candidate. These models are
labelled Fermion Portal Vector Dark Matter (FPVDM). Multiple realisations are
possible, depending on the properties of the VL partner and of the scalar
potential. One example is discussed in detail. FPVDM models have a large number
of applications in collider and non-collider experiments, depending on the
mediator sector.


  We used the large binocular camera (LBC) mounted on the large binocular
telescope (LBT) to observe the Lockman Hole in the U, B, and V bands. Our
observations cover an area of 925 sq.arcmin. We reached depths of 26.7, 26.3,
and 26.3 mag(AB) in the three bands, respectively, in terms of 50% source
detection efficiency, making this survey the deepest U-band survey and one of
the deepest B and V band surveys with respect to its covered area. We extracted
a large number of sources (~89000), detected in all three bands and examined
their surface density, comparing it with models of galaxy evolution. We find
good agreement with previous claims of a steep faint-end slope of the
luminosity functions, caused by late-type and irregular galaxies at z>1.5. A
population of dwarf star-forming galaxies at 1.5<z<2.5 is needed to explain the
U-band number counts. We also find evidence of strong supernova feedback at
high redshift. This survey is complementary to the r, i, and z Lockman Hole
survey conducted with the Subaru telescope and provides the essential
wavelength coverage to derive photometric redshifts and select different types
of sources from the Lockman Hole for further study.


  The nonperturbative regime of electron-positron pair creation by a
relativistic proton beam colliding with a highly intense bichromatic laser
field is studied. The laser wave is composed of a strong low-frequency and a
weak high-frequency mode, with mutually orthogonal polarization vectors. We
show that the presence of the high-frequency field component can strongly
enhance the pair-creation rate. Besides, a characteristic influence of the
high-frequency mode on the angular and energy distributions of the created
particles is demonstrated, both in the nuclear rest frame and the laboratory
frame.


  A phylogenetic network is a directed acyclic graph that visualises an
evolutionary history containing so-called reticulations such as recombinations,
hybridisations or lateral gene transfers. Here we consider the construction of
a simplest possible phylogenetic network consistent with an input set T, where
T contains at least one phylogenetic tree on three leaves (a triplet) for each
combination of three taxa. To quantify the complexity of a network we consider
both the total number of reticulations and the number of reticulations per
biconnected component, called the level of the network. We give polynomial-time
algorithms for constructing a level-1 respectively a level-2 network that
contains a minimum number of reticulations and is consistent with T (if such a
network exists). In addition, we show that if T is precisely equal to the set
of triplets consistent with some network, then we can construct such a network
with smallest possible level in time O(|T|^(k+1)), if k is a fixed upper bound
on the level of the network.


  In this paper, we explore the potential of server waiting before packet
transmission in improving the Age of Information (AoI) in status update
systems. We consider a non-preemptive queue with Poisson arrivals and
independent general service distribution and we incorporate waiting before
serving in two packet management schemes: M/GI/1/1 and M/GI/1/$2^*$. In
M/GI/1/1 scheme, the server waits for a deterministic time immediately after a
packet enters the server. In M/GI/1/$2^*$ scheme, depending on idle or busy
system state, the server waits for a deterministic time before starting service
of the packet. In both cases, if a potential newer arrival is captured existing
packet is discarded. Different from most existing works, we analyze AoI
evolution by indexing the incoming packets, which is enabled by an alternative
method of partitioning the area under the evolution of instantaneous AoI to
calculate its time average. We obtain expressions for average and average peak
AoI for both queueing disciplines with waiting. Our numerical results
demonstrate that waiting before service can bring significant improvement in
average age, particularly, for heavy-tailed service distributions. This
improvement comes at the expense of an increase in average peak AoI. We
highlight the trade-off between average and average peak AoI generated by
waiting before serving.


  In this paper, we present an approach to enhance interpolation and
approximation error estimates. Based on a previously derived first-order
Taylor-like formula, we demonstrate its applicability in improving the
$P_1$-interpolation error estimate. Following the same principles, we also
develop a novel numerical scheme for the heat equation that yields a better
error estimate compared to the classical implicit finite differences scheme.


  Using the braided version of Lawvere's algebraic theories and Mac Lane's
PROPs, we introduce polynomial identities for arbitrary algebraic structures in
a braided monoidal category C as well as their codimensions in the case when C
is linear over some field. The new cases include coalgebras, bialgebras, Hopf
algebras, braided vector spaces, Yetter-Drinfel'd modules, etc. We find bases
for polynomial identities and calculate codimensions in some important
particular cases.


  While compressible flow theory has relied on the perfect gas model as its
workhorse for the past century, compressible dynamics in dense gases, solids
and liquids have relied on many complex equations of state, yielding limited
insight on the hydrodynamic aspect of the problems solved. Recently, Le
M\'etayer and Saurel studied a simple yet promising equation of state owing to
its ability to model both the thermal and compressibility aspects of the
medium. It is a hybrid of the Noble-Abel equation of state and the stiffened
gas model, labeled the Noble-Able Stiffened Gas (NASG) equation of state. In
the present work, we derive the closed form analytical framework for modelling
compressible flow in a medium approximated by the NASG equations of state. We
derive the expressions for the isentrope, sound speed, the isentropic exponent,
Riemann variables in the characteristic description, and jump conditions for
shocks, deflagrations and detonations. We also illustrate the usefulness by
addressing the Riemann problem. The closed form solutions generalize in a
transparent way the well-established models for a perfect gas, highlighting the
role of the medium's compressibility.


  Numerical computations based on the Wiener Chaos Expansion (WCE) are carried
out to approximate the solutions of the stochastic generalized
Kuramoto--Sivashinsky (SgKS) equation driven by Brownian motion forcing. In the
assessment of the accuracy of the WCE based approximate numerical solutions,
the WCE based solutions are contrasted with semi-analytical solutions, and the
absolute and relative errors are evaluated. It is found that the absolute error
is $O(\varsigma t)$, where $\varsigma$ is small constant and $t$ is the time
variabe; and the relative error is order $10^{-2}$ or less. This demonstrates
that numerical methods based on the WCE are powerful tools to solve the SgKS
equation or other related stochastic evolution equations.


  We formulate a simple model for a gas of extended hadrons at zero chemical
potential by taking inspiration from the compressible bag model. We show that a
crossover transition qualitatively similar to lattice QCD can be reproduced by
such a system by including some appropriate additional dynamics. Under certain
conditions, at high temperature, the system consists of a finite number of
infinitely extended bags, which occupy the entire space. In this situation the
system behaves as an ideal gas of quarks and gluons.


  Measuring the polarization fractions of the $W^+W^-$ scattering reveals the
interactions of the Higgs boson as well as new neutral states that are related
to the standard model electroweak symmetry breaking. The dileptonic channel has
a relatively lower background rate, but the kinematics of its final states can
not be fully reconstructed due to the presence of two neutrinos. We propose
neural networks to establish maps between the distributions of measurable
quantities and the distributions of the lepton angles in $W$ boson rest frames.
New physics contributions and collision energy can largely affect the kinematic
properties of the $W^+W^-$ scattering beside the lepton angles. To make the
network in ignorance of that information, the loss function is modified in two
different ways. We show that the networks are promising in reproducing the
lepton angle distributions, and the precision of the fitted polarization
fractions obtained from network predictions is comparable to that obtained with
the truth lepton angle. Although the best-fit values of polarization fractions
do not change much after including the background uncertainty, the precisions
is substantially reduced. Our trained models are available at GitHub.


  We discuss groups corresponding to Kohno Lie algebra of infinitesimal braids
and actions of such groups. We construct homomorphisms of Lie braid groups to
the group of symplectomorphisms of the space of point configurations in $R^3$
and to groups of symplectomorphisms of coadjoint orbits of SU(n).


  We study Harish-Chandra bimodules over the rational Cherednik algebra
$H_{c}(W)$ associated to a complex reflection group $W$ with parameter $c$. Our
results allow us to partially reduce the study of these bimodules to smaller
algebras. We classify those pairs of parameters $(c,c')$ for which there exist
fully supported Harish-Chandra bimodules, and give a description of the
category of all Harish-Chandra bimodules modulo those without full support.
When $W$ is a symmetric group we are able to classify all irreducible
Harish-Chandra bimodules. Our proofs are based on localization techniques, the
action of the Namikawa-Weyl group on the set of parameters, and the study of
partial KZ functors.


  The dust mass absorption coefficient, $\kappa_{d}$, is the conversion
function used to infer physical dust masses from observations of dust emission.
However, it is notoriously poorly constrained, and it is highly uncertain how
it varies, either between or within galaxies. Here we present the results of a
proof-of concept study, using the DustPedia data for two nearby face-on spiral
galaxies M74 (NGC 628) and M83 (NGC 5236), to create the first ever maps of
$\kappa_{d}$ in galaxies. We determine $\kappa_{d}$ using an empirical method
that exploits the fact that the dust-to-metals ratio of the interstellar medium
is constrained by direct measurements of the depletion of gas-phase metals. We
apply this method pixel-by-pixel within M74 and M83, to create maps of
$\kappa_{d}$. We also demonstrate a novel method of producing metallicity maps
for galaxies with irregularly-sampled measurements, using the machine learning
technique of Gaussian process regression. We find strong evidence for
significant variation in $\kappa_{d}$. We find values of $\kappa_{d}$ at 500
$\mu$m spanning the range 0.11-0.25 ${\rm m^{2}\,kg^{-1}}$ in M74, and
0.15-0.80 ${\rm m^{2}\,kg^{-1}}$ in M83. Surprisingly, we find that
$\kappa_{d}$ shows a distinct inverse correlation with the local density of the
interstellar medium. This inverse correlation is the opposite of what is
predicted by standard dust models. However, we find this relationship to be
robust against a large range of changes to our method - only the adoption of
unphysical or highly unusual assumptions would be able to suppress it.


  We calculate the nucleon self-energies in nuclear matter in the QCD sum rules
approach, taking into account the contributions of the four-quark condensates.
We analyze the dependence of the results on the model employed for the
calculation of the condensates and demonstrate that the relativistic character
of the models is important. The condensates are calculated with inclusion of
the most important terms beyond the gas approximation. This corresponds to
inclusion of the two-body nucleon forces and of the most important three-body
forces. The results are consistent with the convergence of the operator product
expansion. The density dependence of the nucleon self-energies is obtained. The
results are consistent with those obtained by the standard nuclear physics
methods, thus inspiring further development of the approach.


  Major breakthrough in quantum computation has recently been achieved using
quantum annealing to develop analog quantum computers instead of gate based
computers. After a short introduction to quantum computation, we retrace very
briefly the history of these developments and discuss the Indian researches in
this connection and provide some interesting documents (in the Figs.) obtained
from a chosen set of high impact papers (and also some recent news etc. blogs
appearing in the Internet). This note is also designed to supplement an earlier
note by Bose (Science and Culture, 79, pp. 337-378, 2013).


  Directional light scattering by spherical silicon nanoparticles in the
visible spectral range is experimentally demonstrated for the first time. These
unique scattering properties arise due to simultaneous excitation and mutual
interference of magnetic and electric dipole resonances inside a single
nanosphere. Directivity of the far-field radiation pattern can be controlled by
changing light wavelength and the nanoparticle size. Forward-to-backward
scattering ratio above 6 can be experimentally obtained at visible wavelengths.
These unique properties of silicon nanoparticles make them promising for design
of novel low-loss visible- and telecom-range nanoantenna devices.


  A novel approach is presented for discovering PDEs that govern the motion of
satellites in space. The method is based on SINDy, a data-driven technique
capable of identifying the underlying dynamics of complex physical systems from
time series data. SINDy is utilized to uncover PDEs that describe the laws of
physics in space, which are non-deterministic and influenced by various factors
such as drag or the reference area (related to the attitude of the satellite).
In contrast to prior works, the physically interpretable coordinate system is
maintained, and no dimensionality reduction technique is applied to the data.
By training the model with multiple representative trajectories of LEO -
encompassing various inclinations, eccentricities, and altitudes - and testing
it with unseen orbital motion patterns, a mean error of around 140 km for the
positions and 0.12 km/s for the velocities is achieved. The method offers the
advantage of delivering interpretable, accurate, and complex models of orbital
motion that can be employed for propagation or as inputs to predictive models
for other variables of interest, such as atmospheric drag or the probability of
collision in an encounter with a spacecraft or space objects. In conclusion,
the work demonstrates the promising potential of using SINDy to discover the
equations governing the behaviour of satellites in space. The technique has
been successfully applied to uncover PDEs describing the motion of satellites
in LEO with high accuracy. The method possesses several advantages over
traditional models, including the ability to provide physically interpretable,
accurate, and complex models of orbital motion derived from high-entropy
datasets. These models can be utilised for propagation or as inputs to
predictive models for other variables of interest.


  We study the gravitational Dirichlet problem in AdS spacetimes with a view to
understanding the boundary CFT interpretation. We define the problem as bulk
Einstein's equations with Dirichlet boundary conditions on fixed timelike
cut-off hypersurface. Using the fluid/gravity correspondence, we argue that one
can determine non-linear solutions to this problem in the long wavelength
regime. On the boundary we find a conformal fluid with Dirichlet constitutive
relations, viz., the fluid propagates on a `dynamical' background metric which
depends on the local fluid velocities and temperature. This boundary fluid can
be re-expressed as an emergent hypersurface fluid which is non-conformal but
has the same value of the shear viscosity as the boundary fluid. The
hypersurface dynamics arises as a collective effect, wherein effects of the
background are transmuted into the fluid degrees of freedom. Furthermore, we
demonstrate that this collective fluid is forced to be non-relativistic below a
critical cut-off radius in AdS to avoid acausal sound propagation with respect
to the hypersurface metric. We further go on to show how one can use this
set-up to embed the recent constructions of flat spacetime duals to
non-relativistic fluid dynamics into the AdS/CFT correspondence, arguing that a
version of the membrane paradigm arises naturally when the boundary fluid lives
on a background Galilean manifold.


  In this paper, we study the nonexistence of positive solutions for the
following two mixed boundary value problems. The first problem is the mixed
nonlinear-Neumann boundary value problem $$ \left\{
  \begin{array}{ll}
  \displaystyle -\Delta u=f(u) &{\rm in}\quad \R, \\ \displaystyle \\
\frac{\partial u}{\partial \nu}=g(u) &{\rm on}\quad \Gamma_1,\\ \displaystyle
\\ \frac{\partial u}{\partial \nu}=0 &{\rm on}\quad \Gamma_0 \end{array}
\right. $$ and the second is the nonlinear-Dirichlet boundary value problem $$
\left\{
  \begin{array}{ll}
  \displaystyle -\Delta u=f(u) &{\rm in}\quad \R, \\ \displaystyle \\
\frac{\partial u}{\partial \nu}=g(u) &{\rm on}\quad \Gamma_1,\\ \displaystyle
\\ u=0 &{\rm on}\quad \Gamma_0, \end{array} \right. $$ where $\R=\{x\in \mathbb
R^N:x_N>0\}$, $\Gamma_1=\{x\in \mathbb R^N:x_N=0,x_1<0\}$ and $\Gamma_0=\{x\in
\mathbb R^N:x_N=0,x_1>0\}$. We will prove that these problems possess no
positive solution under some assumptions on the nonlinear terms. The main
technique we use is the moving plane method in an integral form.


  The computation of the entries of Jacobi operators associated with orthogonal
polynomials has important applications in numerical analysis. From truncating
the operator to form a Jacobi matrix, one can apply the Golub--Welsh algorithm
to compute the Gaussian quadrature weights and nodes. Furthermore, the entries
of the Jacobi operator are the coefficients in the three-term recurrence
relationship for the polynomials. This provides an efficient method for
evaluating the orthogonal polynomials. Here, we present an $\mathcal O(N)$
method to compute the first $N$ rows of Jacobi operators from the associated
weight. The method exploits the Riemann--Hilbert representation of the
polynomials by solving a deformed Riemann--Hilbert problem numerically. We
further adapt this computational approach to certain entire weights that are
beyond the reach of current asymptotic Riemann--Hilbert techniques.


  Numerical simulations of the semilinear Klein--Gordon equation in the de
Sitter spacetime are performed. We use two structure-preserving discrete forms
of the Klein--Gordon equation. The disparity between the two forms is the
discretization of the differential term. We show that one of the forms has
higher numerical stability and second-order numerical accuracy with respect to
the grid, and we explain the reason for the instability of the other form.


  When humans write, they may unintentionally omit some information.
Complementing the omitted information using a computer is helpful in providing
writing support. Recently, in the field of story understanding and generation,
story completion (SC) was proposed to generate the missing parts of an
incomplete story. Although its applicability is limited because it requires
that the user have prior knowledge of the missing part of a story, missing
position prediction (MPP) can be used to compensate for this problem. MPP aims
to predict the position of the missing part, but the prerequisite knowledge
that "one sentence is missing" is still required. In this study, we propose
Variable Number MPP (VN-MPP), a new MPP task that removes this restriction;
that is, the task to predict multiple missing sentences or to judge whether
there are no missing sentences in the first place. We also propose two methods
for this new MPP task. Furthermore, based on the novel task and methods, we
developed a creative writing support system, COMPASS. The results of a user
experiment involving professional creators who write texts in Japanese confirm
the efficacy and utility of the developed system.


  In this paper we present the PUMP (Parallel Uncertainty-aware Multiobjective
Planning) algorithm for addressing the stochastic kinodynamic motion planning
problem, whereby one seeks a low-cost, dynamically-feasible motion plan subject
to a constraint on collision probability (CP). To ensure exhaustive evaluation
of candidate motion plans (as needed to tradeoff the competing objectives of
performance and safety), PUMP incrementally builds the Pareto front of the
problem, accounting for the optimization objective and an approximation of CP.
This is performed by a massively parallel multiobjective search, here
implemented with a focus on GPUs. Upon termination of the exploration phase,
PUMP searches the Pareto set of motion plans to identify the lowest cost
solution that is certified to satisfy the CP constraint (according to an
asymptotically exact estimator). We introduce a novel particle-based CP
approximation scheme, designed for efficient GPU implementation, which accounts
for dependencies over the history of a trajectory execution. We present
numerical experiments for quadrotor planning wherein PUMP identifies solutions
in ~100 ms, evaluating over one hundred thousand partial plans through the
course of its exploration phase. The results show that this multiobjective
search achieves a lower motion plan cost, for the same CP constraint, compared
to a safety buffer-based search heuristic and repeated RRT trials.


  Topological insulators in free fermion systems have been well characterized
and classified. However, it is not clear in strongly interacting boson or
fermion systems what symmetry protected topological orders exist. In this
paper, we present a model in a 2D interacting spin system with nontrivial
on-site $Z_2$ symmetry protected topological order. The order is nontrivial
because we can prove that the 1D system on the boundary must be gapless if the
symmetry is not broken, which generalizes the gaplessness of Wess-Zumino-Witten
model for Lie symmetry groups to any discrete symmetry groups. The construction
of this model is related to a nontrivial 3-cocycle of the $Z_2$ group and can
be generalized to any symmetry group. It potentially leads to a complete
classification of symmetry protected topological orders in interacting boson
and fermion systems of any dimension. Specifically, this exactly solvable model
has a unique gapped ground state on any closed manifold and gapless excitations
on the boundary if $Z_2$ symmetry is not broken. We prove the latter by
developing the tool of matrix product unitary operator to study the nonlocal
symmetry transformation on the boundary and revealing the nontrivial 3-cocycle
structure of this transformation. Similar ideas are used to construct a 2D
fermionic model with on-site $Z_2$ symmetry protected topological order.


  When the cooling rate $v$ is smaller than a certain material-dependent
threshold, the glass transition temperature $T_g$ becomes to a certain degree
the "material parameter" being nearly independent on the cooling rate. The
common method to determine $T_g$ is to extrapolate viscosity $\nu$ of the
liquid state at temperatures not far above the freezing conditions to lower
temperatures where liquid freezes and viscosity is hardly measurable. It is
generally accepted that the glass transition occurs when viscosity drops by
$13\leq n\leq17$ orders of magnitude. The accuracy of $T_g$ depends on the
extrapolation quality. We propose here an algorithm for a unique determining of
$T_g$. The idea is to unambiguously extrapolate $\nu(T)$ to low temperatures
without relying upon a specific model. It can be done using the numerical
analytical continuation of $\nu(T)$-function from above $T_g$ where it is
measurable, to $T\gtrsim T_g$. For numerical analytical continuation, we use
the Pade approximant method.


  We report on the extraction of the target mass contributions to the
unpolarized proton structure functions by applying an unfolding procedure to
the available world data from charged lepton scattering. The method employed is
complementary to recent and future parton distribution function fits including
target mass contributions and the results obtained can be utilized to further
study perturbative QCD at large Bjorken x and small $Q^2$ . Global fits are
performed to both the available $F^2$ and the separated $F_L$ ($F_1$) data
which yield excellent descriptions and provides parameterizations of the
extracted target mass contributions.


  This article presents an overview of results pertaining to electronic
structure, transport properties, and interaction effects in ballistic quantum
wires with Rashba spin splitting. Limits of weak and strong spin--orbit
coupling are distinguished, and spin properties of the electronic states
elucidated. The case of strong Rashba spin splitting where the spin--precession
length is comparable to the wire width turns out to be particularly
interesting. Hybridization of spin--split quantum--wire subbands leads to an
unusual spin structure where the direction of motion for electrons can fix
their spin state. This peculiar property has important ramifications for linear
transport in the quantum wire, giving rise to spin accumulation without
magnetic fields or ferromagnetic contacts. A description for interacting
Rashba--split quantum wires is developed, which is based on a generalization of
the Tomonaga--Luttinger model.


  We propose an input/output conformance testing theory utilizing Modal
Interface Automata with Input Refusals (IR-MIA) as novel behavioral formalism
for both the specification and the implementation under test. A modal
refinement relation on IR-MIA allows distinguishing between obligatory and
allowed output behaviors, as well as between implicitly underspecified and
explicitly forbidden input behaviors. The theory therefore supports positive
and negative conformance testing with optimistic and pessimistic environmental
assumptions. We further show that the resulting conformance relation on IR-MIA,
called modal-irioco, enjoys many desirable properties concerning
component-based behaviors. First, modal-irioco is preserved under modal
refinement and constitutes a preorder under certain restrictions which can be
ensured by a canonical input completion for IR-MIA. Second, under the same
restrictions, modal-irioco is compositional with respect to parallel
composition of IR-MIA with multi-cast and hiding. Finally, the quotient
operator on IR-MIA, as the inverse to parallel composition, facilitates
decompositionality in conformance testing to solve the unknown-component
problem.


  We use lattice sum rules for the static quark potential to determine the
beta-function for symmetric and asymmetric lattices non-perturbatively. We also
study the colour field distributions in excited gluonic states.


  Given an abstract simplicial complex G, the connection graph G' of G has as
vertex set the faces of the complex and connects two if they intersect. If A is
the adjacency matrix of that connection graph, we prove that the Fredholm
characteristic det(1+A) takes values in {-1,1} and is equal to the Fermi
characteristic, which is the product of the w(x), where w(x)=(-1)^dim(x). The
Fredholm characteristic is a special value of the Bowen-Lanford zeta function
and has various combinatorial interpretations. The unimodularity theorem proven
here shows that it is a cousin of the Euler characteristic as the later is the
sum of the w(x). Unimodularity implies that the matrix 1+A has an inverse which
takes integer values. Experiments suggest the conjecture that the range of the
Green function values, the union of the entries of the inverse of 1+A form a
combinatorial invariant of the simplicial complex and do not change under
Barycentric or edge refinements.


  The metrics of the global, Poincar\'e, and Rindler AdS$_{d+1}$ are explicitly
reconstructed with given lightcone cuts. We first compute the metric up to a
conformal factor with the lightcone cuts method introduced by Engelhardt and
Horowitz. While a general prescription to determine the conformal factor is not
known, we recover the factor by identifying the causal information surfaces
from the lightcone cuts and finding that they are minimal. In addition, we
propose a new type of kinematic space as the space of minimal surfaces in
AdS$_{d+1}$, where a metric is introduced as a generalization of the case of
$d=2$. This metric defines the set of bulk points, which is equivalent to that
of lightcone cuts. Some other properties are also studied towards establishing
a reconstruction procedure for general bulk metrics.


  After a short review of one of proposals to avoid complex stochastic
processes in Complex Langevin studies, the recent progress in the former is
reported. In particular, the new developments allow now to construct positive
and normalizable representations for gaussian quantum mechanical, as well as
field theoretical, path integrals directly in the Minkowski time. A relation to
the idea of thimbles is also discussed.


  We explore the possible tie between the naturalness of having a very small
strong CP $\theta$ parameter in the Kobayashi-Maskawa Model and the flavor
symmetry. We provide many examples in which the flavor symmetry group at high
energy can naturally give rise to Kobayashi-Maskawa Model at low energy with a
naturally small theta.


  Data are presented on the reaction pbar-p -> omega-omega-pizero at rest from
the Crystal Barrel detector. These data identify a strong signal due to
f2(1565) -> omega-omega. The relative production from initial pbar-p states
3P2, 3P1 and 1S0 is well determined from omega-omega decay angular
correlations; P-state annihilation dominates strongly. A combined fit is made
with data on pbar-p -> 3pizero at rest, where f2(1565) -> pizero-pizero is
observed.


  Estimation of quantiles is one of the most fundamental real-time analysis
tasks. Most real-time data streams vary dynamically with time and incremental
quantile estimators document state-of-the art performance to track quantiles of
such data streams. However, most are not able to make joint estimates of
multiple quantiles in a consistent manner, and estimates may violate the
monotone property of quantiles. In this paper we propose the general concept of
*conditional quantiles* that can extend incremental estimators to jointly track
multiple quantiles. We apply the concept to propose two new estimators.
Extensive experimental results, on both synthetic and real-life data, show that
the new estimators clearly outperform legacy state-of-the-art joint quantile
tracking algorithm and achieve faster adaptivity in dynamically varying data
streams.


  Recent years have seen a surge in interest in building deep learning-based
fully data-driven models for weather prediction. Such deep learning models if
trained on observations can mitigate certain biases in current state-of-the-art
weather models, some of which stem from inaccurate representation of
subgrid-scale processes. However, these data-driven models, being
over-parameterized, require a lot of training data which may not be available
from reanalysis (observational data) products. Moreover, an accurate,
noise-free, initial condition to start forecasting with a data-driven weather
model is not available in realistic scenarios. Finally, deterministic
data-driven forecasting models suffer from issues with long-term stability and
unphysical climate drift, which makes these data-driven models unsuitable for
computing climate statistics. Given these challenges, previous studies have
tried to pre-train deep learning-based weather forecasting models on a large
amount of imperfect long-term climate model simulations and then re-train them
on available observational data. In this paper, we propose a convolutional
variational autoencoder-based stochastic data-driven model that is pre-trained
on an imperfect climate model simulation from a 2-layer quasi-geostrophic flow
and re-trained, using transfer learning, on a small number of noisy
observations from a perfect simulation. This re-trained model then performs
stochastic forecasting with a noisy initial condition sampled from the perfect
simulation. We show that our ensemble-based stochastic data-driven model
outperforms a baseline deterministic encoder-decoder-based convolutional model
in terms of short-term skills while remaining stable for long-term climate
simulations yielding accurate climatology.


  Dusty debris disks around main-sequence stars are signposts for the existence
of planetesimals and exoplanets. From cross-correlating \hip stars with the
\iras catalogs, we identify 146 stars within 120 pc of Earth that show excess
emission at 60 $\micron$. This search took special precautions to avoid false
positives. Our sample is reasonably well distributed from late B to early
K-type stars, but it contains very few later type stars. Even though \iras flew
more than 20 years ago and many astronomers have cross-correlated its catalogs
with stellar catalogs, we were still able to newly identify debris disks at as
many as 33 main-sequence stars; of these, 32 are within 100 pc of Earth. The
power of an all-sky survey satellite like \iras is evident when comparing our
33 new debris disks with the total of only 22 dusty debris disk stars detected
first with the more sensitive, but pointed, satellite \iso. Our investigation
focuses on the mass, dimensions, and evolution of dusty debris disks.


  We discuss a simple and powerful approach for the ab initio identification of
cis-regulatory motifs involved in transcriptional regulation. The method we
present integrates several elements: human-mouse comparison, statistical
analysis of genomic sequences and the concept of coregulation. We apply it to a
complete scan of the human genome. By using the catalogue of conserved upstream
sequences collected in the CORG database we construct sets of genes sharing the
same overrepresented motif (short DNA sequence) in their upstream regions both
in human and in mouse. We perform this construction for all possible motifs
from 5 to 8 nucleotides in length and then filter the resulting sets looking
for two types of evidence of coregulation: first, we analyze the Gene Ontology
annotation of the genes in the set, searching for statistically significant
common annotations; second, we analyze the expression profiles of the genes in
the set as measured by microarray experiments, searching for evidence of
coexpression. The sets which pass one or both filters are conjectured to
contain a significant fraction of coregulated genes, and the upstream motifs
characterizing the sets are thus good candidates to be the binding sites of the
TF's involved in such regulation. In this way we find various known motifs and
also some new candidate binding sites.


  Therapeutic intervention in neurological disorders still relies heavily on
pharmacological solutions, while the treatment of patients with drug resistance
remains an open challenge. This is particularly true for patients with
epilepsy, 30% of whom are refractory to medications. Implantable devices for
chronic recording and electrical modulation of brain activity have proved a
viable alternative in such cases. To operate, the device should detect the
relevant electrographic biomarkers from Local Field Potentials (LFPs) and
determine the right time for stimulation. To enable timely interventions, the
ideal device should attain biomarker detection with low latency while operating
under low power consumption to prolong the battery life. Neuromorphic networks
have progressively gained reputation as low-latency low-power computing
systems, which makes them a promising candidate as processing core of
next-generation implantable neural interfaces. Here we introduce a fully-analog
neuromorphic device implemented in CMOS technology for analyzing LFP signals in
an in vitro model of acute ictogenesis. We show that the system can detect
ictal and interictal events with ms-latency and with high precision, consuming
on average 3.50 nW during the task. Our work paves the way to a new generation
of brain implantable devices for personalized closed-loop stimulation for
epilepsy treatment.


  One of the major challenges of ECoG-based Brain-Machine Interfaces is the
movement prediction of a human subject. Several methods exist to predict an arm
2-D trajectory. The fourth BCI Competition gives a dataset in which the aim is
to predict individual finger movements (5-D trajectory). The difficulty lies in
the fact that there is no simple relation between ECoG signals and finger
movement. We propose in this paper to decode finger flexions using switching
models. This method permits to simplify the system as it is now described as an
ensemble of linear models depending on an internal state. We show that an
interesting accuracy prediction can be obtained by such a model.


  Axially symmetric static vacuum exact solution (ASSVES) in Weyl coordinates
are studied in $f(R)$ theories of gravity. In particular, we obtain a general
explicit expression for the dependence between $df(R)/dR$ and the $r$ and $z$
coordinates and then the corresponding explicit form of $f(R)$ is obtained.
Next, we present in detail the explicit solution of the modified field
equations corresponding to the Newtonian potential due to a punctual mass
placed at the origin of coordinates and also the Schwarzschild solution to the
modified field equations.


  The latest severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2)
variant Omicron (B.1.1.529) has ushered panic responses around the world due to
its contagious and vaccine escape mutations. The essential infectivity and
antibody resistance of the SARS-CoV-2 variant are determined by its mutations
on the spike (S) protein receptor-binding domain (RBD). However, a complete
experimental evaluation of Omicron might take weeks or even months. Here, we
present a comprehensive quantitative analysis of Omicron's infectivity,
vaccine-breakthrough, and antibody resistance. An artificial intelligence (AI)
model, which has been trained with tens of thousands of experimental data
points and extensively validated by experimental data on SARS-CoV-2, reveals
that Omicron may be over ten times more contagious than the original virus or
about twice as infectious as the Delta variant. Based on 132 three-dimensional
(3D) structures of antibody-RBD complexes, we unveil that Omicron may be twice
more likely to escape current vaccines than the Delta variant. The Food and
Drug Administration (FDA)-approved monoclonal antibodies (mAbs) from Eli Lilly
may be seriously compromised. Omicron may also diminish the efficacy of mAbs
from Celltrion and Rockefeller University. However, its impact on Regeneron mAb
cocktail appears to be mild.


  A combined Short-Term Learning (STL) and Long-Term Learning (LTL) approach to
solving mobile-robot navigation problems is presented and tested in both the
real and virtual domains. The LTL phase consists of rapid simulations that use
a Genetic Algorithm to derive diverse sets of behaviours, encoded as variable
sets of attributes, and the STL phase is an idiotypic Artificial Immune System.
Results from the LTL phase show that sets of behaviours develop very rapidly,
and significantly greater diversity is obtained when multiple autonomous
populations are used, rather than a single one. The architecture is assessed
under various scenarios, including removal of the LTL phase and switching off
the idiotypic mechanism in the STL phase. The comparisons provide substantial
evidence that the best option is the inclusion of both the LTL phase and the
idiotypic system. In addition, this paper shows that structurally different
environments can be used for the two phases without compromising
transferability.


  In the present paper we are interested in properties of forcing notions which
measure in a sense the distance between the ground model reals and the reals in
the extension. We look at the ways the ``new'' reals can be aproximated by
``old'' reals. We consider localizations for infinite subsets of omega. Though
each member of [omega]^omega can be identified with its increasing enumeration,
the (standard) localizations of the enumeration does not provide satisfactory
information on successive points of the set. They give us ``candidates'' for
the n-th point of the set but the same candidates can appear several times for
distinct n. That led to a suggestion that we should consider disjoint subsets
of omega as sets of ``candidates'' for successive points of the localized set.
We have two possibilities. Either we can demand that each set from the
localization contains a limited number of members of the localized set or we
can postulate that each intersection of that kind is large. Localizations of
this kind are studied in section 1. In the second section we investigate
localizations of infinite subsets of omega by sets of integers from the ground
model. These localizations might be thought as localizations by partitions of
omega into successive intervals.


  Agile quadrotor flight relies on rapidly planning and accurately tracking
time-optimal trajectories, a technology critical to their application in the
wild. However, the computational burden of computing time-optimal trajectories
based on the full quadrotor dynamics (typically on the order of minutes or even
hours) can hinder its ability to respond quickly to changing scenarios.
Additionally, modeling errors and external disturbances can lead to deviations
from the desired trajectory during tracking in real time. This letter proposes
a novel approach to computing time-optimal trajectories, by fixing the nodes
with waypoint constraints and adopting separate sampling intervals for
trajectories between waypoints, which significantly accelerates trajectory
planning. Furthermore, the planned paths are tracked via a time-adaptive model
predictive control scheme whose allocated tracking time can be adaptively
adjusted on-the-fly, therefore enhancing the tracking accuracy and robustness.
We evaluate our approach through simulations and experimentally validate its
performance in dynamic waypoint scenarios for time-optimal trajectory
replanning and trajectory tracking.


  By means of high-resolution cosmological hydrodynamical simulations of Milky
Way-like disc galaxies, we conduct an analysis of the associated stellar
metallicity distribution functions (MDFs). After undertaking a kinematic
decomposition of each simulation into spheroid and disc sub-components, we
compare the predicted MDFs to those observed in the solar neighbourhood and the
Galactic bulge. The effects of the star formation density threshold are visible
in the star formation histories, which show a modulation in their behaviour
driven by the threshold. The derived MDFs show median metallicities lower by
0.2-0.3 dex than the MDF observed locally in the disc and in the Galactic
bulge. Possible reasons for this apparent discrepancy include the use of low
stellar yields and/or centrally-concentrated star formation. The dispersions
are larger than the one of the observed MDF; this could be due to simulated
discs being kinematically hotter relative to the Milky Way. The fraction of low
metallicity stars is largely overestimated, visible from the more negatively
skewed MDF with respect to the observational sample. For our fiducial Milky Way
analog, we study the metallicity distribution of the stars born "in situ"
relative to those formed via accretion (from disrupted satellites), and
demonstrate that this low-metallicity tail to the MDF is populated primarily by
accreted stars. Enhanced supernova and stellar radiation energy feedback to the
surrounding interstellar media of these pre-disrupted satellites is suggested
as an important regulator of the MDF skewness.


  Public infrastructure-as-a-service clouds, such as Amazon EC2, Google Compute
Engine (GCE) and Microsoft Azure allow clients to run virtual machines (VMs) on
shared physical infrastructure. This practice of multi-tenancy brings economies
of scale, but also introduces the risk of sharing a physical server with an
arbitrary and potentially malicious VM. Past works have demonstrated how to
place a VM alongside a target victim (co-location) in early-generation clouds
and how to extract secret information via side- channels. Although there have
been numerous works on side-channel attacks, there have been no studies on
placement vulnerabilities in public clouds since the adoption of stronger
isolation technologies such as Virtual Private Clouds (VPCs).
  We investigate this problem of placement vulnerabilities and quantitatively
evaluate three popular public clouds for their susceptibility to co-location
attacks. We find that adoption of new technologies (e.g., VPC) makes many prior
attacks, such as cloud cartography, ineffective. We find new ways to reliably
test for co-location across Amazon EC2, Google GCE, and Microsoft Azure. We
also found ways to detect co-location with victim web servers in a multi-tiered
cloud application located behind a load balancer.
  We use our new co-residence tests and multiple customer accounts to launch VM
instances under different strategies that seek to maximize the likelihood of
co-residency. We find that it is much easier (10x higher success rate) and
cheaper (up to $114 less) to achieve co-location in these three clouds when
compared to a secure reference placement policy.


  We model an extreme mass ratio merger (EMR) as a point particle radially
plunging into a large Schwarzschild black hole. We assume that the mass of the
point particle, $\mu$, is much smaller than the black hole mass M. Under this
assumption we can employ the Zerilli formalism modified to include a source
term which arises from the energy-momentum tensor of the small object. We solve
the Zerilli equation by numerically evolving initial data. Then, we ray trace
the null geodesics of the event horizon from after the merger backward in time
to extract the geometry of the perturbed event horizon. Further, we take
advantage of the axisymmetry of the setup to locate the apparent horizon and
study its geometry.


  Multicolour near IR photometry for a sample of 32 large barred spiral
galaxies is presented. By applying ellipse fitting techniques, we identify
significant isophote twists with respect to the primary bar axis in the nuclear
regions of $\sim$70 \%\ of the sample. These twists are identified in galaxies
as late as SBbc and are clearly distinguishable from spiral arm morphology. At
most seven of the galaxies with isophote twists are inferred to possess
secondary (nuclear) bars, the axis ratios of which appear to correlate with
morphological type. The remainder may result from triaxial bulges, or from
oblate bulges misaligned with the primary bar. The near IR colour distributions
in these data show evidence for (red) circumnuclear star forming rings in 4
galaxies. The majority of the sample (19) also possess striking blue nuclear
regions, bluer than typical old stellar populations by $\sim$0.3 mag. in (J--H)
and $\sim$0.23 mag. in (H--K). Such blue colours do not appear to correlate
with the presence of nuclear rings or pseudo--rings, nor with the activity of
the host galaxy (as determined from emission--line spectroscopic
characteristics). Several mechanisms to explain this blue colour are
considered.


  The signal from many single molecule experiments monitoring molecular
processes, such as enzyme turnover via fluorescence and opening and closing of
ion channel via the flux of ions, consists of a time series of stochastic on
and off (or open and closed) periods, termed a two-state trajectory. This
signal reflects the dynamics in the underlying multi-substate on-off kinetic
scheme (KS) of the process. The determination of the underlying KS is difficult
and sometimes even impossible due to the loss of information in the mapping of
the mutli dimensional KS onto two dimensions. Here we introduce a new procedure
that efficiently and optimally relates the signal to all equivalent underlying
KSs. This procedure partitions the space of KSs into canonical (unique) forms
that can handle any KS, and obtains the topology and other details of the
canonical form from the data without the need for fitting. Also established are
relationships between the data and the topology of the canonical form to the
on-off connectivity of a KS. The suggested canonical forms constitute a
powerful tool in discriminating between KSs. Based on our approach, the upper
bound on the information content in two state trajectories is determined.


  In 1967 Kasteleyn introduced a powerful method for enumerating the 1-factors
of planar graphs. In fact his method can be extended to graphs which permit an
orientation under which every alternating circuit is clockwise odd. Graphs with
this property are called {\it Pfaffian}. Little characterised Pfaffian
bipartite graphs in terms of forbidden subgraphs in 1975. We extend his
characterisation to near bipartite graphs.


  Purpose: To analyze and remove protected feature effects in chest radiograph
embeddings of deep learning models. Methods: An orthogonalization is utilized
to remove the influence of protected features (e.g., age, sex, race) in CXR
embeddings, ensuring feature-independent results. To validate the efficacy of
the approach, we retrospectively study the MIMIC and CheXpert datasets using
three pre-trained models, namely a supervised contrastive, a self-supervised
contrastive, and a baseline classifier model. Our statistical analysis involves
comparing the original versus the orthogonalized embeddings by estimating
protected feature influences and evaluating the ability to predict race, age,
or sex using the two types of embeddings. Results: Our experiments reveal a
significant influence of protected features on predictions of pathologies.
Applying orthogonalization removes these feature effects. Apart from removing
any influence on pathology classification, while maintaining competitive
predictive performance, orthogonalized embeddings further make it infeasible to
directly predict protected attributes and mitigate subgroup disparities.
Conclusion: The presented work demonstrates the successful application and
evaluation of the orthogonalization technique in the domain of chest X-ray
image classification.


  Superconducting qubits have emerged as a potentially foundational platform
technology for addressing complex computational problems deemed intractable
with classical computing. Despite recent advances enabling multiqubit designs
that exhibit coherence lifetimes on the order of hundreds of $\mu$s, material
quality and interfacial structures continue to curb device performance. When
niobium is deployed as the superconducting material, two-level system defects
in the thin film and adjacent dielectric regions introduce stochastic noise and
dissipate electromagnetic energy at the cryogenic operating temperatures. In
this study, we utilize time-of-flight secondary ion mass spectrometry
(TOF-SIMS) to understand the role specific fabrication procedures play in
introducing such dissipation mechanisms in these complex systems. We
interrogated Nb thin films and transmon qubit structures fabricated by Rigetti
Computing and at the National Institute of Standards and Technology through
slight variations in the processing and vacuum conditions. We find that when Nb
film is sputtered onto the Si substrate, oxide and silicide regions are
generated at various interfaces. We also observe that impurity species such as
niobium hydrides and carbides are incorporated within the niobium layer during
the subsequent lithographic patterning steps. The formation of these resistive
compounds likely impact the superconducting properties of the Nb thin film.
Additionally, we observe the presence of halogen species distributed throughout
the patterned thin films. We conclude by hypothesizing the source of such
impurities in these structures in an effort to intelligently fabricate
superconducting qubits and extend coherence times moving forward.


  We derive new results regarding the controllability and the reachability of
multitime controlled linear PDE systems of first order. These systems describe
some important multitime evolution in engineering, economics and biology. Some
of them come from evolution PDEs of superior order. The original results
include a refinement and a supplement of multitime optimal control theory,
developed in some recent papers by the second author. They refer to the
complete integrability conditions, conditions for the existence of solutions,
path independent curvilinear integrals, the multitime fundamental matrix,
multitime adjoint Cauchy problems, control space, controllability and
reachability of phases, controllability gramian, reachability gramian,
controllability matrix, counter-examples and commentaries.


  The most luminous galaxies at high-redshift are generally considered to be
hosted in massive dark-matter halos of comparable number density, hence
residing at the center of overdensities/protoclusters. We assess the validity
of this assumption by investigating the clustering around the brightest
galaxies populating the cosmic web at redshift $z\sim8-9$ through a combination
of semi-analytic modeling and Monte Carlo simulations of mock Hubble Space
Telescope WFC3 observations. The innovative aspect of our approach is the
inclusion of a log-normal scatter parameter $\Sigma$ in the galaxy luminosity
versus halo mass relation, extending to high-$z$ the conditional luminosity
function framework extensively used at low redshift. Our analysis shows that
the larger the value of $\Sigma$, the less likely that the brightest source in
a given volume is hosted in the most massive halo, and hence the weaker the
overdensity of neighbors. We derive a minimum value of $\Sigma$ as a function
of redshift by considering stochasticity in the halo assembly times, which
affects galaxy ages and star formation rates in our modeling. We show that
$\Sigma_{min}(z)\sim0.15-0.3$, with $\Sigma_{min}$ increasing with redshift as
a consequence of shorter halo assembly periods at higher redshifts. Current
observations ($m_{AB}\sim27$) of the environment of spectroscopically confirmed
bright sources at $z>7.5$ do not show strong evidence of clustering and are
consistent with our modeling predictions for $\Sigma\geq\Sigma_{min}$. Deeper
future observations reaching $m_{AB}\sim28.2-29$ would have the opportunity to
clearly quantify the clustering strength, and hence to constrain $\Sigma$,
investigating the physical processes that drive star formation in the early
Universe.


  We present a unified approach to improved $L^p$ Hardy inequalities in $\R^N$.
We consider Hardy potentials that involve either the distance from a point, or
the distance from the boundary, or even the intermediate case where distance is
taken from a surface of codimension $1<k<N$. In our main result we add to the
right hand side of the classical Hardy inequality, a weighted $L^p$ norm with
optimal weight and best constant. We also prove non-homogeneous improved Hardy
inequalities, where the right hand side involves weighted L^q norms, q \neq p.


  We associate to each stable Higgs pair $(A_0,\Phi_0)$ on a compact Riemann
surface $X$ a singular limiting configuration $(A_\infty,\Phi_\infty)$,
assuming that $\det \Phi$ has only simple zeroes. We then prove a
desingularization theorem by constructing a family of solutions $(A_t,t\Phi_t)$
to Hitchin's equations which converge to this limiting configuration as $t \to
\infty$. This provides a new proof, via gluing methods, for elements in the
ends of the Higgs bundle moduli space and identifies a dense open subset of the
boundary of the compactification of this moduli space.


  NSVS 02502726 has been known as a double-lined, detached eclipsing binary
that consists of two low-mass stars. We obtained $BVRI$ photometric follow-up
observations in 2009 and 2011 to measure improved physical properties of the
binary star. Each set of light curves, including the 2008 data given by
\cCakirli et al., was simultaneously analyzed with the previously published
radial-velocity curves using the Wilson-Devinney binary code. The conspicuous
seasonal light variations of the system are satisfactorily modelled by a
two-spot model with one starspot on each component and by changes of the spot
parameters with time. Based on 23 eclipse timings calculated from the synthetic
model and one ephemeris epoch, an orbital period study of NSVS 02502726 reveals
that the period has experienced a continuous decrease of $-5.9\times10^{-7}$ d
yr$^{-1}$ or a sinusoidal variation with a period and semi-amplitude of 2.51
yrs and 0.0011 d, respectively. The timing variations could be interpreted as
either the light-travel-time effect due to the presence of an unseen third
body, or as the combination of this effect and angular momentum loss via
magnetic stellar wind braking. Individual masses and radii of both components
are determined to be $M_1$=0.689$\pm$0.016 M$_\odot$, $M_2$=0.341$\pm$0.009
M$_\odot$, $R_1$=0.707$\pm$0.007 R$_\odot$, and $R_2$=0.657$\pm$0.008
R$_\odot$. The results are very different from those of \cCakirli et al. with
the primary's radius (0.674$\pm$0.006 R$_\odot$) smaller the secondary's
(0.763$\pm$0.007 R$_\odot$). We compared the physical parameters presented in
this paper with current low-mass stellar models and found that the measured
values of the primary star are best fitted to a 79-Myr isochrone. The primary
is in good agreement with the empirical mass-radius relation from low-mass
binaries, but the secondary is oversized by about 85%.


  In this paper we discuss the field enhancement due to surface plasmons
resonances of metallic nanostructures, in particular nano spheres on top of a
metal, and find maximum field enhancement of the order of 10^2, intensities
enhancement of the order of 10^4. Naturally these fields can produce temporal
fields of the order of 0.5V/{\AA} that yield field emission of electrons.
Although the fields enhancements we calculated are factor of 10 smaller than
those reported in recent experiments, our results explain very well the
experimental data. Very large atomic fields destabilize the system completely
emitting ions, at least for static field, and produce electric breakdown. In
any case, we prove that the data are striking and can solve problems in
providing stabilized current of static fields for which future experiments
should be done for obtaining pulsed beams of electrons.


  Even if students can make the blend, interpret physics correctly in
mathematical symbology and graphs, they still need to be able to apply that
knowledge in productive and coherent ways. As instructors, we can show our
solutions to complex problems in class. We can give complex problems to
students as homework. But our students are likely to still have trouble because
they are missing a key element of making sense of how we think about physics:
How to tell the story of what's happening.


  We study the geometry of a Picard modular fourfold which parametrizes abelian
fourfolds of Weil type for the field of cube roots of unity. We find a
projective model of this fourfold as a singular, degree ten, hypersurface X in
projective 5-space. The Weyl group W(E_6) acts on X and we provide an explicit
description of this action. Moreover, we describe various special subvarieties
as well as the boundary of X.


  Based on Fick's 2nd law the development of moving particle semi-implicit
method for predicting diffusion process is proposed in this study


  For a set of ten crystalline materials (oxides and semiconductors), we
compute the electronic band structures using the Tran-Blaha [Phys. Rev. Lett.
102, 226401 (2009)] (TB09) functional. The band widths and gaps are compared
with those from the local-density approximation (LDA) functional, many-body
perturbation theory (MBPT), and experiments. At the density-functional theory
(DFT) level, TB09 leads to band gaps in much better agreement with experiments
than LDA. However, we observe that it globally underestimates, often strongly,
the valence (and conduction) band widths (more than LDA). MBPT corrections are
calculated starting from both LDA and TB09 eigenenergies and wavefunctions.
They lead to a much better agreement with experimental data for band widths.
The band gaps obtained starting from TB09 are close to those from
quasi-particle self-consistent GW calculations, at a much reduced cost.
Finally, we explore the possibility to tune one of the semi-empirical
parameters of the TB09 functional in order to obtain simultaneously better band
gaps and widths. We find that these requirements are conflicting.


  We investigate reduced-order models for acoustic and electromagnetic wave
problems in parametrically defined domains. The parameter-to-solution maps are
approximated following the so-called Galerkin POD-NN method, which combines the
construction of a reduced basis via proper orthogonal decomposition (POD) with
neural networks (NNs). As opposed to the standard reduced basis method, this
approach allows for the swift and efficient evaluation of reduced-order
solutions for any given parametric input.
  As is customary in the analysis of problems in random or parametrically
defined domains, we start by transporting the formulation to a reference
domain. This yields a parameter-dependent variational problem set on
parameter-independent functional spaces. In particular, we consider
affine-parametric domain transformations characterized by a high-dimensional,
possibly countably infinite, parametric input. To keep the number of
evaluations of the high-fidelity solutions manageable, we propose using
low-discrepancy sequences to sample the parameter space efficiently. Then, we
train an NN to learn the coefficients in the reduced representation. This
approach completely decouples the offline and online stages of the reduced
basis paradigm.
  Numerical results for the three-dimensional Helmholtz and Maxwell equations
confirm the method's accuracy up to a certain barrier and show significant
gains in online speed-up compared to the traditional Galerkin POD method.


  Let $G$ be a semisimple Lie group acting on a space $X$, let $\mu$ be a
compactly supported measure on $G$, and let $A$ be a strongly irreducible
linear cocycle over the action of $G$. We then have a random walk on $X$, and
let $T$ be the associated shift map. We show that the cocycle $A$ over the
action of $T$ is conjugate to a block conformal cocycle.
  This statement is used in the recent paper by Eskin-Mirzakhani on the
classifications of invariant measures for the SL(2,R) action on moduli space.
The ingredients of the proof are essentially contained in the papers of
Guivarch and Raugi and also Goldsheid and Margulis.


  In this letter, we study the problem of accelerating reaching average
consensus over connected graphs in a discrete-time communication setting.
Literature has shown that consensus algorithms can be accelerated by increasing
the graph connectivity or optimizing the weights agents place on the
information received from their neighbors. Here, instead of altering the
communication graph, we investigate two methods that use buffered states to
accelerate reaching average consensus over a given graph. In the first method,
we study how convergence rate of the well-known first-order Laplacian average
consensus algorithm changes when agreement feedback is generated from buffered
states. For this study, we obtain a sufficient condition on the ranges of
buffered state that leads to faster convergence. In the second proposed method,
we show how the average consensus problem can be cast as a convex optimization
problem and solved by first-order accelerated optimization algorithms for
strongly-convex cost functions. We construct an accelerated average consensus
algorithm using the so-called Triple Momentum optimization algorithm. The first
approach requires less global knowledge for choosing the step size, whereas the
second one converges faster in our numerical results by using extra information
from the graph topology. We demonstrate our results by implementing the
proposed algorithms in a Gaussian Mixture Model (GMM) estimation problem used
in sensor networks.


  The discovery of transiting planets around bright stars holds the potential
to greatly enhance our understanding of planetary atmospheres. In this work we
present the search for transits of HD 168443b, a massive planet orbiting the
bright star HD 168443 V=6.92 with a period of 58.11 days. The high eccentricity
of the planetary orbit e=0.53 significantly enhances the a-priori transit
probability beyond that expected for a circular orbit, making HD 168443 a
candidate for our ongoing Transit Ephemeris Refinement and Monitoring Survey
(TERMS). Using additional radial velocities from Keck-HIRES, we refined the
orbital parameters of this multi-planet system and derived a new transit
ephemeris for HD 168443b. The reduced uncertainties in the transit window make
a photometric transit search practicable. Photometric observations acquired
during predicted transit windows were obtained on three nights. CTIO 1.0 m
photometry acquired on 2010 September 7 had the required precision to detect a
transit but fell just outside of our final transit window. Nightly photometry
from the T8 0.8 m Automated Photometric Telescope (APT) at Fairborn
Observatory, acquired over a span of 109 nights, demonstrates that HD 168443 is
constant on a time scale of weeks. Higher-cadence photometry on 2011 April 28
and June 25 shows no evidence of a transit. We are able to rule out a
non-grazing transit of HD 168443b.


  By using a generalization of the multiple scales technique we develop a
method to derive amplitude equations for zero--dimensional forced systems. The
method allows to consider either additive or multiplicative forcing terms and
can be straightforwardly applied to the case that the forcing is white noise.
We give examples of the use of this method to the case of the van der
Pol--Duffing oscillator. The writing of the amplitude equations in terms of a
Lyapunov potential allow us to obtain an analytical expression for the
probability distribution function which reproduces reasonably well the
numerical simulation results.


  The paper [arXiv:1506.06999] has studied a derived equivalence between two
Calabi-Yau fivefolds. In this paper, we propose a new understanding from the
viewpoint of the GLSM, by realizing these two Calabi-Yau fivefolds in two
different phases of a $U(1)\times U(2)$ GLSM. We find that this method can be
generalized to construct other examples of derived equivalence. The functor for
the equivalence can be realized by the brane transport along a path across
different phases. To implement the brane transport, we compute the small window
categories for anomalous $U(2)$ theories, extending previous results on window
categories.


  In this paper we discuss computer simulations of de Sitter and anti de Sitter
spacetimes, which are maximally symmetric, relativistic analogs of
non-Euclidean geometries. We present prototype games played in these
spacetimes; such games and visualizations can help the players gain intuition
about these spacetimes. We discuss the technical challenges in creating such
simulations, and discuss the geometric and relativistic effects that can be
witnessed by the players.


  This thesis reports advances in the theory of design, characterization and
simulation of multi-photon multi-channel interferometers. I advance the design
of interferometers through an algorithm to realize an arbitrary discrete
unitary transformation on the combined spatial and internal degrees of freedom
of light. This procedure effects an arbitrary $n_{s}n_{p}\times n_{s}n_{p}$
unitary matrix on the state of light in $n_{s}$ spatial and $n_{p}$ internal
modes.
  I devise an accurate and precise procedure for characterizing any multi-port
linear optical interferometer using one- and two-photon interference. Accuracy
is achieved by estimating and correcting systematic errors that arise due to
spatiotemporal and polarization mode mismatch. Enhanced accuracy and precision
are attained by fitting experimental coincidence data to a curve simulated
using measured source spectra. The efficacy of our characterization procedure
is verified by numerical simulations.
  I develop group-theoretic methods for the analysis and simulation of linear
interferometers. I devise a graph-theoretic algorithm to construct the boson
realizations of the canonical SU$(n)$ basis states, which reduce the canonical
subgroup chain, for arbitrary $n$. The boson realizations are employed to
construct $\mathcal{D}$-functions, which are the matrix elements of arbitrary
irreducible representations, of SU$(n)$ in the canonical basis. I show that
immanants of principal submatrices of a unitary matrix $T$ are a sum of the
diagonal $\mathcal{D}(\Omega)$-functions of group element $\Omega$ over $t$
determined by the choice of submatrix and over the irrep $(\lambda)$ determined
by the immanant under consideration. The algorithm for $\mathrm{SU}(n)$
$\mathcal{D}$-function computation and the results connecting these functions
with immanants open the possibility of group-theoretic analysis and simulation
of linear optics.


  This paper is a mathematical investigation on Epstein semantics. One of the
main tools of the present paper is the model-theoretic S-set construction
introduced in (Krawczyk 2022). We use it to prove several results: 1) that each
Epstein model has uncountably many equivalent Epstein models, 2) that the logic
of generalised Epstein models is the S-set invariant fragment of CPL (analogon
of the celebrated van Benthem characterization theorem for modal logic), 3)
that several sets of Epstein relations are undefinable, 4) that logics of
undefinable sets of relations can be finitely axiomatised. We also use other
techniques to prove: 5) that there is uncountably many Epstein-incomplete
logics and that 6) the logic of generalised Epstein models has the
interpolation property.


  Modeling of planets' climate and habitability requires as fundamental input
the UV emission of the hosting star. \citet{lovric2017} employed SORCE/SOLSTICE
solar observations to introduce a UV color index which is a descriptor of the
UV radiation that modulates the photochemistry of planets atmospheres. After
correcting the SOLSTICE data for residual instrumental effects that produced
asymmetric signals during different phases of the cycles analyzed, the authors
found that the UV color index is linearly correlated with the Mg II index.In
this paper we employ an irradiance reconstruction technique to synthetize the
UV color and Mg II index with the purpose of investigating whether the
correction applied by \citet{lovric2017} to SORCE/SOLSTICE data might have
compensated for solar variations, and to investigate the physical mechanisms
that produce such a strong correlation between the UV color index and the solar
activity. Reconstructed indices reproduce very well the observations and
present the same strong linear dependence. Moreover our reconstruction, which
extends back to 1989, shows that the UV color - Mg II index relation can be
described by the same linear relation for almost three cycles, thus ruling out
an overcompensation of SORCE/SOLTICE data in the analysis of
\citet{lovric2017}. We suggest that the strong correlation between the indices
results from the fact that most of the Far- and Middle- UV radiation originates
in the chromosphere, where atmosphere models of quiet and magnetic features
present similar temperature and density gradients.


  This paper proposes a methodology for generating a stopword list from online
social network (OSN) corpora in Egyptian Dialect(ED). The aim of the paper is
to investigate the effect of removingED stopwords on the Sentiment Analysis
(SA) task. The stopwords lists generated before were on Modern Standard Arabic
(MSA) which is not the common language used in OSN. We have generated a
stopword list of Egyptian dialect to be used with the OSN corpora. We compare
the efficiency of text classification when using the generated list along with
previously generated lists of MSA and combining the Egyptian dialect list with
the MSA list. The text classification was performed using Na\"ive Bayes and
Decision Tree classifiers and two feature selection approaches, unigram and
bigram. The experiments show that removing ED stopwords give better performance
than using lists of MSA stopwords only.


  We analyze the effects of noise correlations in the input to, or among, BCM
neurons using the Wigner semicircular law to construct random,
positive-definite symmetric correlation matrices and compute their eigenvalue
distributions. In the finite dimensional case, we compare our analytic results
with numerical simulations and show the effects of correlations on the
lifetimes of synaptic strengths in various visual environments. These
correlations can be due either to correlations in the noise from the input LGN
neurons, or correlations in the variability of lateral connections in a network
of neurons. In particular, we find that for fixed dimensionality, a large noise
variance can give rise to long lifetimes of synaptic strengths. This may be of
physiological significance.


  It has been shown recently that a nonrelativistic quantum particle
constrained to a hard-wall layer of constant width built over a geodesically
complete simply connected noncompact curved surface can have bound states
provided the surface is not a plane. In this paper we study the weak-coupling
asymptotics of these bound states, i.e. the situation when the surface is a
mildly curved plane. Under suitable assumptions about regularity and decay of
surface curvatures we derive the leading order in the ground-state eigenvalue
expansion. The argument is based on Birman-Schwinger analysis of Schroedinger
operators in a planar hard-wall layer.


  Call graphs depict the static, caller-callee relation between "functions" in
a program. With most source/target languages supporting functions as the
primitive unit of composition, call graphs naturally form the fundamental
control flow representation available to understand/develop software. They are
also the substrate on which various interprocedural analyses are performed and
are integral part of program comprehension/testing. Given their universality
and usefulness, it is imperative to ask if call graphs exhibit any intrinsic
graph theoretic features -- across versions, program domains and source
languages. This work is an attempt to answer these questions: we present and
investigate a set of meaningful graph measures that help us understand call
graphs better; we establish how these measures correlate, if any, across
different languages and program domains; we also assess the overall, language
independent software quality by suitably interpreting these measures.


  In the search for neutrinoless double-beta decay, the high-pressure gaseous
Time Projection Chamber has a distinct advantage, because the ionization charge
tracks produced by particle interactions are extended and the detector captures
the full three-dimensional charge distribution with appropriate charge readout
systems. Such information of tracks provides a crucial extra-handle for
discriminating signal events against backgrounds. In this paper, we constructed
a toy model to demonstrate where the discrimination power comes from and how
much of it the neural network models have already harnessed. Then we adapted
3-dimensional convolutional and residual neural networks on the simulated
double-beta and background charge tracks and tested their capabilities in
classifying these two types of events. We show that both the 3D structure and
the overall depth of the neural networks significantly improve the accuracy of
the classifier and lead to results better than previous works. We also studied
their performance under various spatial granularities as well as different
diffusion and noise conditions. The results indicate that the methods are
stable and generalize well despite varying experimental conditions.


  We present an elementary proof for an approximate expression of the Bergman
kernel on homogeneous spaces, and products of them. The error term is
exponentially small with respect to the inverse semiclassical parameter.


  Vector/Pest control is essential to reduce the risk of vector-borne diseases
or losses in crop fields. Among biological control tools, the sterile insect
technique (SIT), is the most promising one. SIT control generally consists of
massive releases of sterile insects in the targeted area in order to reach
elimination or to lower the pest population under a certain threshold. The
models presented here are minimalistic with respect to the number of parameters
and variables. The first model deals with the dynamics of the vector population
while the second model, the SIT model, tackles the interaction between treated
males and wild female vectors. For the vector population model, the elimination
equilibrium $\mathbb{0}$ is globally asymptotically stable when the basic
offspring number, $\mathcal{R}$, is lower or equal to one, whereas $\mathbb{0}$
becomes unstable and one stable positive equilibrium exists, with
well-determined basins of attraction, when $\mathcal{R}>1$. For the SIT model,
we obtain a threshold number of treated male vectors above which the control of
wild female vectors is effective: the massive release control. When the amount
of treated male vectors is lower than the aforementioned threshold number, the
SIT model experiences a bistable situation involving the elimination
equilibrium and a positive equilibrium. However, practically, massive releases
of sterile males are only possible for a short period of time. That is why,
using the bistability property, we develop a new strategy to maintain the wild
population under a certain threshold, for a permanent and sustainable low level
of SIT control. We illustrate our theoretical results with numerical
simulations, in the case of SIT mosquito control.


  Escape from a potential well can occur in different physical systems, such as
capsize of ships, resonance transitions in celestial mechanics, and dynamic
snap-through of arches and shells, as well as molecular reconfigurations in
chemical reactions. The criteria and routes of escape in one-degree of freedom
systems has been well studied theoretically with reasonable agreement with
experiment. The trajectory can only transit from the hilltop of the
one-dimensional potential energy surface. The situation becomes more
complicated when the system has higher degrees of freedom since it has multiple
routes to escape through an equilibrium of saddle-type, specifically, an
index-1 saddle. This paper summarizes the geometry of escape across a saddle in
some widely known physical systems with two degrees of freedom and establishes
the criteria of escape providing both a methodology and results under the
conceptual framework known as tube dynamics. These problems are classified into
two categories based on whether the saddle projection and focus projection in
the symplectic eigenspace are coupled or not when damping and/or gyroscopic
effects are considered. To simplify the process, only the linearized system
around the saddle points are analyzed. We define a transition region,
$\mathcal{T}_h$, as the region of initial conditions of a given initial energy
$h$ which transit from one side of a saddle to the other. We find that in
conservative systems, the boundary of the transition region, $\partial
\mathcal{T}_h$, is a cylinder, while in dissipative systems, $\partial
\mathcal{T}_h$ is an ellipsoid.


  If light enough primordial black holes (PBH) account for dark matter, then
its density decreases with time as they lose mass via Hawking radiation. We
show that this time-dependence of the matter density can be formulated as an
equivalent $w(z)$ dark energy model and we study its implications on the
expansion history. Using our approach and comparing with the latest
cosmological data, including the supernovae type Ia, Baryon Acoustic
Oscillations, Cosmic Microwave Background and the Hubble expansion H(z) data,
we place observational constraints on the PBH model. We find that it is
statistically consistent with $\Lambda$CDM according to the AIC statistical
tool. Furthermore, we entertain the idea of having a population of ultra-light
PBHs, decaying around neutrino decoupling, on top of the dark matter fluid and
show how this offers a natural dark matter-radiation coupling altering the
expansion history of the Universe and alleviating the $H_0$ tension.


  We consider a system of laser-cooled ions in a linear harmonic trap and study
the phenomenon of squeezing exchange between their internal and motional
degrees of freedom. An interesting relation between the quantum noise reduction
(squeezing) and the dynamical evolution is found when the internal and motional
subsystems are prepared in properly squeezed (intelligent) states.
Specifically, the evolution of the system is fully governed by the relative
strengths of spectroscopic and motional squeezing, including the phenomenon of
total cancellation of the interaction when the initial squeezing parameters are
equal.


  Wi-Fi signals-based person identification attracts increasing attention in
the booming Internet-of-Things era mainly due to its pervasiveness and
passiveness. Most previous work applies gaits extracted from WiFi distortions
caused by the person walking to achieve the identification. However, to extract
useful gait, a person must walk along a pre-defined path for several meters,
which requires user high collaboration and increases identification time
overhead, thus limiting use scenarios. Moreover, gait based work has severe
shortcoming in identification performance, especially when the user volume is
large. In order to eliminate the above limitations, in this paper, we present
an operation-free person identification system, namely WiPIN, that requires
least user collaboration and achieves good performance. WiPIN is based on an
entirely new insight that Wi-Fi signals would carry person body information
when propagating through the body, which is potentially discriminated for
person identification. Then we demonstrate the feasibility on commodity
off-the-shelf Wi-Fi devices by well-designed signal pre-processing, feature
extraction, and identity matching algorithms. Results show that WiPIN achieves
92% identification accuracy over 30 users, high robustness to various
experimental settings, and low identifying time overhead, i.e., less than
300ms.


  In this work, we focus on the problem of image instance retrieval with deep
descriptors extracted from pruned Convolutional Neural Networks (CNN). The
objective is to heavily prune convolutional edges while maintaining retrieval
performance. To this end, we introduce both data-independent and data-dependent
heuristics to prune convolutional edges, and evaluate their performance across
various compression rates with different deep descriptors over several
benchmark datasets. Further, we present an end-to-end framework to fine-tune
the pruned network, with a triplet loss function specially designed for the
retrieval task. We show that the combination of heuristic pruning and
fine-tuning offers 5x compression rate without considerable loss in retrieval
performance.


  Quantum networks are a new paradigm of complex networks, allowing us to
harness networked quantum technologies and to develop a quantum internet. But
how robust is a quantum network when its links and nodes start failing? We show
that quantum networks based on typical noisy quantum-repeater nodes are prone
to discontinuous phase transitions with respect to the random loss of operating
links and nodes, abruptly compromising the connectivity of the network, and
thus significantly limiting the reach of its operation. Furthermore, we
determine the critical quantum-repeater efficiency necessary to avoid this
catastrophic loss of connectivity as a function of the network topology, the
network size, and the distribution of entanglement in the network. In
particular, our results indicate that a scale-free topology is a crucial design
principle to establish a robust large-scale quantum internet.


  We consider polynomials with integer coefficients and discuss their
factorization properties in Z[[x]], the ring of formal power series over Z. We
treat polynomials of arbitrary degree and give sufficient conditions for their
reducibility as power series. Moreover, if a polynomial is reducible over
Z[[x]], we provide an explicit factorization algorithm. For polynomials whose
constant term is a prime power, our study leads to the discussion of p-adic
integers.


  We present the complete solution of the problem of determination of
trace-norm geometric discord for arbitrary two-qubit state. Final answer is
achieved due to effective reduction of the problem to the study of critical
points of certain mapping depending on projectors. Our results are illustrated
on various, also new, families of two-qubit states and compared to already
known special solutions.


  We generalize, to any space-time dimension, the unitarity bounds of highest
weight UIR's of the conformal groups with Lie algebras $so(2,d)$. We classify
gauge theories invariant under $so(2,d)$, both integral and half-integral
spins. A similar analysis is carried out for the algebras $so^*(2n)$. We study
new unitary modules of the conformal algebra in $d>4$, that have no analogue
for $d\leq 4$ as they cannot be obtained by "squaring" singletons. This may
suggest the interpretation of higher dimensional non-trivial conformal field
theories as theories of "tensionless" $p$-branes of which tensionless strings
in $d=6$ are just particular examples.