  We investigate the mechanisms of control and suppression of
pre-thermalization in $N$-component alkaline earth gases. To this end, we
compute the short-time dynamics of the instantaneous momentum distribution and
the relative population for different initial conditions after an interaction
quench, accounting for the 11 peffect of initial interactions. We find that
switching on an interaction that breaks the SU$(N)$ symmetry of the initial
Hamiltonian, thus allowing for the occurrence of spin-changing collisions, does
not necessarily lead to a suppression of pre-thermalization. However, the
suppression will be most effective in the presence of SU$(N)$-breaking
interactions provided the number of components $N \ge 4$ and the initial state
contains a population imbalance that breaks the SU$(N)$ symmetry. We also find
the conditions on the imbalance initial state that allow for a pre-thermal
state to be stabilized for a certain time. Our study highlights the important
role played by the initial state in the pre-thermalization dynamics of
multicomponent Fermi gases. It also demonstrates that alkaline-earth Fermi
gases provide an interesting playground for the study and control of
pre-thermalization.


  Bi$_{1-x}$Sb$_x$ is a topological insulator (TI) for $x \approx 0.03
$--$0.20$. Close to the Topological phase transition at $x = 0.03$, a magnetic
field induced Weyl semi-metal (WSM) state is stabilized due to the splitting of
the Dirac cone into two Weyl cones of opposite chirality. A signature of the
Weyl state is the observation of a Chiral anomaly [negative longitudnal
magnetoresistance (LMR)] and a violation of the Ohm's law (non-linear $I-V$).
We report the unexpected discovery of a Chiral anomaly in the whole range ($x =
0.032, 0.072, 0.16$) of the TI state. This points to a field induced WSM state
in an extended $x$ range and not just near the topological transition at $x =
0.03$. Surprisingly, the strongest Weyl phase is found at $x = 0.16$ with a
non-saturating negative LMR much larger than observed for $x = 0.03$. The
negative LMR vanishes rapidly with increasing angle between $B$ and $I$.
Additionally, non-linear $I$--$V$ is found for $x = 0.16$ indicating a
violation of Ohm's law. This unexpected observation of a strong Weyl state in
the whole TI regime in Bi$_{1-x}$Sb$_x$ points to a gap in our understanding of
the detailed electronic structure evolution in this alloy system.


  The maximum energy loss (Bragg peak) located near the end of range is a
characteristic feature of ion stopping in matter, which generates an acoustic
pulse, if ions are deposited into a medium in adequately short bunches. This
so-called ionoacoustic effect has been studied for decades, mainly for
astrophysical applications, and it has recently found renewed interest in
proton therapy for precise range measurements in tissue. After detailed
preparatory studies with 20 MeV protons at the MLL tandem accelerator,
ionoacoustic range measurements were performed in water at the upgraded SIS18
synchrotron of GSI with 238U and 124Xe ion beams of energy about 300 MeV/u, and
12C ions of energy about 200 MeV/u using fast beam extraction to get 1
microsecond pulse lengths. Acoustic signals were recorded in axial geometry by
standard piezo-based transducers at a 500 kHz mean frequency and evaluated in
both the time and frequency domains. The resulting ranges for the different
ions and energies were found to agree with Geant4 simulations as well as
previous measurements to better than 1%. Given the high accuracy provided by
ionoacoustic range measurements in water and their relative simplicity, we
propose this new method for stopping power measurements for heavy ions at GeV
energies and above. Our experimental results clearly demonstrate the potential
of an ionoacoustic particle monitor especially for very intense heavy ion beams
foreseen at future accelerator facilities.


  Classification tasks require a balanced distribution of data to ensure the
learner to be trained to generalize over all classes. In real-world datasets,
however, the number of instances vary substantially among classes. This
typically leads to a learner that promotes bias towards the majority group due
to its dominating property. Therefore, methods to handle imbalanced datasets
are crucial for alleviating distributional skews and fully utilizing the
under-represented data, especially in text classification. While addressing the
imbalance in text data, most methods utilize sampling methods on the numerical
representation of the data, which limits its efficiency on how effective the
representation is. We propose a novel training method, Sequential
Targeting(ST), independent of the effectiveness of the representation method,
which enforces an incremental learning setting by splitting the data into
mutually exclusive subsets and training the learner adaptively. To address
problems that arise within incremental learning, we apply elastic weight
consolidation. We demonstrate the effectiveness of our method through
experiments on simulated benchmark datasets (IMDB) and data collected from
NAVER.


  We give a classification of four-circulant singly even self-dual $[60,30,d]$
codes for $d=10$ and $12$. These codes are used to construct extremal singly
even self-dual $[60,30,12]$ codes with weight enumerator for which no extremal
singly even self-dual code was previously known to exist. From extremal singly
even self-dual $[60,30,12]$ codes, we also construct extremal singly even
self-dual $[58,29,10]$ codes with weight enumerator for which no extremal
singly even self-dual code was previously known to exist. Finally, we give some
restriction on the possible weight enumerators of certain singly even self-dual
codes with shadow of minimum weight $1$.


  We study the long-term quasi-steady evolution of the force-free magnetosphere
of a magnetar coupled to its internal magnetic field. We find that
magnetospheric currents can be maintained on long timescales of the order of
thousands of years. Meanwhile, the energy, helicity and twist stored in the
magnetosphere all gradually increase over the course of this evolution, until a
critical point is reached, beyond which a force-free magnetosphere cannot be
constructed. At this point, some large-scale magnetospheric rearrangement,
possibly resulting in an outburst or a flare, must occur, releasing a large
fraction of the stored energy, helicity and twist. After that, the quasi-steady
evolution should continue in a similar manner from the new initial conditions.
The timescale for reaching this critical point depends on the overall magnetic
field strength and on the relative fraction of the toroidal field. The energy
stored in the force-free magnetosphere is found to be up to $\sim 30\%$ larger
than the corresponding vacuum energy. This implies that for a $10^{14}$ G field
at the pole, the energy budget available for fast magnetospheric events is of
the order of a few $10^{44}$ erg. The spindown rate is estimated to increase by
up to $\sim 60\%$, since the dipole content in the magnetosphere is enhanced by
the currents present there. A rough estimate of the braking index $n$ reveals
that it is systematically $n < 3$ for the most part of the evolution,
consistent with actual measurements for pulsars and early estimates for several
magnetars.


  Graphene-based materials are thought to revolutionize entire industries.
Therefore, many research are being carried on graphene theoretically and
experimentally. On the other hand, recent studies show that the use of Dunkl
derivative, instead of ordinary derivative, allows the concept of parity to be
interpreted together with other physical quantities. In this manuscript, we
investigate the thermal quantities of graphene under the constant magnetic
field with the Dunkl-formalism. We observe that only at low temperatures
Dunkl-parameters, thus parity, modify the conventional results.


  In a pair of recent papers, Andrews, Fraenkel and Sellers provide a complete
characterization for the number of $m$-ary partitions modulo $m$, with and
without gaps. In this paper we extend these results to the case of coloured
$m$-ary partitions, with and without gaps. Our method of proof is different,
giving explicit expansions for the generating functions modulo $m$


  The existence of magnetic fields associated with the intracluster medium in
clusters of galaxies is now well established through different methods of
analysis. Magnetic fields are investigated in the radio band from studies of
the rotation measure of polarized radio galaxies and the synchrotron emission
of cluster-wide diffuse sources. Other techniques include X-ray studies of the
inverse Compton emission and of cold fronts and magneto hydrodynamic
simulations. We review the main issues that have led to our knowledge on
magnetic fields in clusters of galaxies. Observations show that cluster fields
are at the $\mu$G level, with values up to tens of $\mu$G at the center of
cooling core clusters. Estimates obtained from different observational
approaches may differ by about an order of magnitude. However, the discrepancy
may be alleviated by considering that the magnetic field is not constant
through the cluster, and shows a complex structure. In particular, the magnetic
field intensity declines with the cluster radius with a rough dependence on the
thermal gas density. Moreover, cluster magnetic fields are likely to fluctuate
over a wide range of spatial scales with values from a few kpc up to hundreds
kpc. Important information on the cluster field are obtained by comparing the
observational results with the prediction from numerical simulations. The
origin of cluster magnetic fields is still debated. They might originate in the
early Universe, either before or after the recombination, or they could have
been deposited in the intracluster medium by normal galaxies, starburst
galaxies, or AGN. In either case, magnetic fields undergo significant
amplification during the cluster merger processes.


  Researchers often delve into the connections between different factors
derived from the historical data of software projects. For example, scholars
have devoted their endeavors to the exploration of associations among these
factors. However, a significant portion of these studies has failed to consider
the limitations posed by the temporal interdependencies among these variables
and the potential risks associated with the use of statistical methods
ill-suited for analyzing data with temporal connections. Our goal is to
highlight the consequences of neglecting time dependence during data analysis
in current research. We pinpointed out certain potential problems that arise
when disregarding the temporal aspect in the data, and support our argument
with both theoretical and real examples.


  We study the scenario of dark matter in the minimal left-right symmetric
theory at the TeV scale. The only viable candidate is found to be the lightest
right-handed neutrino with a mass of keV. To satisfy the dark matter relic
abundance, the relic yield is diluted by late decays of the two heavier
neutrinos. We point out that the QCD phase transition temperature coincidences
with the typical freeze-out temperature governed by right-handed interactions,
which helps to alleviate the problem of overproduction. A careful numerical
study reveals a narrow window for the mass of the right-handed gauge boson,
within the reach of the LHC.


  We used an optical reflection method to measure the temperature-dependence of
the piezoelectricity, electrostriction and time constant of a morphotropic
phase boundary (MPB) thin film. We obtained the piezoelectric constant and the
electrostrictive constant as a function of temperature by curve fitting the
experimental data. We also obtained the time constant as a function of
temperature and applied voltage. An abnormal behavior of the strain that was
larger at 275 K than at 285 K was observed. This observation was also
consistent with the minimal hysteresis behavior of the time constant at 275 K.
We provided a possible explanation for this observation.


  Decreasing magnetic resonance (MR) image acquisition times can potentially
reduce procedural cost and make MR examinations more accessible. Compressed
sensing (CS)-based image reconstruction methods, for example, decrease MR
acquisition time by reconstructing high-quality images from data that were
originally sampled at rates inferior to the Nyquist-Shannon sampling theorem.
In this work we propose a hybrid architecture that works both in the k-space
(or frequency-domain) and the image (or spatial) domains. Our network is
composed of a complex-valued residual U-net in the k-space domain, an inverse
Fast Fourier Transform (iFFT) operation, and a real-valued U-net in the image
domain. Our experiments demonstrated, using MR raw k-space data, that the
proposed hybrid approach can potentially improve CS reconstruction compared to
deep-learning networks that operate only in the image domain. In this study we
compare our method with four previously published deep neural networks and
examine their ability to reconstruct images that are subsequently used to
generate regional volume estimates. We evaluated undersampling ratios of 75%
and 80%. Our technique was ranked second in the quantitative analysis, but
qualitative analysis indicated that our reconstruction performed the best in
hard to reconstruct regions, such as the cerebellum. All images reconstructed
with our method were successfully post-processed, and showed good volumetry
agreement compared with the fully sampled reconstruction measures.


  In this paper we investigate algebraic, differential and asymptotic
properties of polynomials $p_n(x)$ that are orthogonal with respect to the
complex oscillatory weight $w(x)=e^{i\omega x}$ on the interval $[-1,1]$, where
$\omega>0$. We also investigate related quantities such as Hankel determinants
and recurrence coefficients. We prove existence of the polynomials $p_{2n}(x)$
for all values of $\omega>0$, as well as degeneracy of $p_{2n+1}(x)$ at certain
values of $\omega$ (called kissing points). We obtain detailed asymptotic
information as $\omega\to\infty$, using recent theory of multivariate highly
oscillatory integrals, and we complete the analysis with the study of complex
zeros of Hankel determinants, using the large $\omega$ asymptotics obtained
before.


  We prove the equivalence of the invariants EH(L) and LOSS-(L) for oriented
Legendrian knots L in the 3-sphere equipped with the standard contact
structure, partially extending a previous result by Stipsicz and Vertesi. In
the course of the proof we relate the sutured Floer homology groups associated
with a knot complement and knot Floer homology, and define intermediate
Legendrian invariants.


  We studied the structural, dynamical properties and melting of a
quasi-one-dimensional system of charged particles, interacting through a
screened Coulomb potential. The ground state energy was calculated and,
depending on the density and the screening length, the system crystallizes in a
number of chains. As a function of the density (or the confining potential),
the ground state configurations and the structural transitions between them
were analyzed both by analytical and Monte Carlo calculations. The system
exhibits a rich phase diagram at zero temperature with continuous and
discontinuous structural transitions. We calculated the normal modes of the
Wigner crystal and the magneto-phonons when an external constant magnetic field
$B$ is applied. At finite temperature the melting of the system was studied via
Monte Carlo simulations using the $modified$ $Lindemann$ $criterion$ (MLC). The
melting temperature as a function of the density was obtained for different
screening parameters. Reentrant melting as a function of the density was found
as well as evidence of directional dependent melting. The single chain regime
exhibits anomalous melting temperatures according to the MLC and as a check we
study the pair correlation function at different densities and different
temperatures, formulating a different criterion. Possible connection with
recent theoretical and experimental results are discussed and experiments are
proposed.


  We are developing the frequency domain multiplexing (FDM) read-out of
transition-edge sensor (TES) microcalorimeters for the X-ray Integral Field
Unit (X-IFU) instrument on board of the future European X-Ray observatory
Athena. The X-IFU instrument consists of an array of $\sim$3840 TESs with a
high quantum efficiency ($>$90 \%) and spectral resolution $\Delta E$=2.5 eV
$@$ 7 keV ($E/\Delta E\sim$2800). FDM is currently the baseline readout system
for the X-IFU instrument. Using high quality factor LC filters and room
temperature electronics developed at SRON and low-noise two stage SQUID
amplifiers provided by VTT, we have recently demonstrated good performance with
the FDM readout of Mo/Au TES calorimeters with Au/Bi absorbers. An integrated
noise equivalent power resolution of about 2.0 eV at 1.7 MHz has been
demonstrated with a pixel from a new TES array from NASA/Goddard (GSFC-A2). We
have achieved X-ray energy resolutions $\sim$2.5 eV at AC bias frequency at 1.7
MHz in the single pixel read-out. We have also demonstrated for the first time
an X-ray energy resolution around 3.0 eV in a 6 pixel FDM read-out with TES
array (GSFC-A1). In this paper we report on the single pixel performance of
these microcalorimeters under MHz AC bias, and further results of the
performance of these pixels under FDM.


  In this paper, a quadratic optimal control problem is considered for
second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in
which the "point" control function (depending only on time) constitutes a
source term. These problems involve choosing a control function (with or
without "peak-value" constraints) to approximately steer the solution of the
PDE in question to a desired function at the end of a prescribed (finite)
time-interval. To compute approximations to the desired optimal control
functions, semi-discrete, Galerkin approximations to the equation involved are
introduced and the corresponding (approximating) control problems are tackled.
It is shown that the sequences of solutions to both the constrained and
unconstrained approximating (finite-dimensional) control problems converge,
respectively, to the optimal solutions of the control problems involving the
original initial/boundary value problem. The solution to the unconstrained
approximating problem can be quite explicitly characterized, with the main
numerical step for its computation requiring only the solution of a Lyapunov
equation. Whereas approximate solutions to the constrained control problems can
be obtained on the basis of Lagrangian duality and piecewise linear
multipliers. These points are worked out in detail and illustrated by numerical
examples involving the heat equation (HEq).


  We report the generation of multimode solitons in step-index fiber. The
solitons are superpositions of 5-10 temporally-aligned transverse modes, they
exhibit speckled beam profiles, and the spatio-spectral variation across the
soliton can be complex. Greater understanding of multimode solitons should
create a foundation for further research into complex multimode nonlinear
phenomena in step-index fibers. With energies of tens of nanojoules and
durations around 100 fs, the multimode solitons are speckled fields with peak
powers that can exceeed 300 kW, parameters which may be valuable in
applications.


  Optical wireless communication is a promising technology for underwater
broadband access networks, which are particularly important for high-resolution
environmental monitoring applications. This paper focuses on a deep sea
monitoring system, where an underwater optical wireless network is deployed on
the seafloor. We model such an optical wireless network as a general queueing
network and formulate an optimal relay placement problem, whose objective is to
maximize the stability region of the whole system, i.e., the supremum of the
traffic volume that the network is capable of accommodating. The formulated
optimization problem is further shown to be non-convex, so that its global
optimization is non-trivial. In this paper, we develop a global optimization
method for this problem and we provide an efficient algorithm to compute an
optimal solution. Through numerical evaluations, we show that a significant
performance gain can be obtained by using the derived optimal solution.


  In this paper we classify compact minimal surfaces in $S^5$ with non-negative
Gaussian curvature using the notion of a contact angle.


  We present a scheme to achieve maximally entangled states, controlled
phase-shift gate, and SWAP gate for two
superconducting-quantum-interference-device (SQUID) qubits, by placing SQUIDs
in a microwave cavity. We also show how to transfer quantum information from
one SQUID qubit to another. In this scheme, no transfer of quantum information
between the SQUIDs and the cavity is required, the cavity field is only
virtually excited and thus the requirement on the quality factor of the cavity
is greatly relaxed.


  We generalize the theoretical modeling of collective atomic super- and
subradiance to the multilevel case including spontaneous emission from several
excited states towards a common ground state. We show that in a closely packed
ensemble of $N$ atoms with $N-1$ distinct excited states each, one can find a
new class of non-radiating dark states,, which allows for long-term storage of
$N-1$ photonic excitations. Via dipole-dipole coupling only a single atom in
the ground state is sufficient in order to suppress the decay of all $N-1$
other atoms. By means of some generic geometric configurations, like a triangle
of V-type atoms or a chain of atoms with a $J=0 \to J=1$ transition, we study
such subradiance including dipole-dipole interactions and show that even at
finite distances long lifetimes can be observed. While generally hard to
prepare deterministically, we identify various possibilities for a
probabilistic preparation via a phase controlled laser pump and decay.


  We present the Gallery of Planetary Nebula Spectra now available at
http://oit.williams.edu/nebulae The website offers high-quality, moderate
resolution (~7-10 A FWHM) spectra of 128 Galactic planetary nebulae from
3600-9600 A, obtained by Kwitter, Henry, and colleagues with the Goldcam
spectrograph at the KPNO 2.1-m or with the RC spectrograph at the CTIO 1.5-m.
The master PN table contains atlas data and an image link. A selected object's
spectrum is displayed in a zoomable window; line identification templates are
provided. In addition to the spectra themselves, the website also contains a
brief discussion of PNe as astronomical objects and as contributors to our
understanding of stellar evolution. We envision that this website, which
concentrates a large amount of data in one place, will be of interest to a
variety of users: researchers might need to check the spectrum of a particular
object of interest; the non-specialist astronomer might simply be interested in
perusing such a collection of spectra; and finally, teachers of introductory
astronomy can use this database to illustrate basic principles of atomic
physics and radiation. To particularly encourage this last use, we have
developed two paper-and-pencil exercises to introduce beginning astronomy
students to the wealth of information that PN spectra contain.


  Previously, it has been shown that rapid cooling of yttrium-iron-garnet
(YIG)/platinum (Pt) nano structures, preheated by an electric current sent
through the Pt layer, leads to overpopulation of a magnon gas and to subsequent
formation of a Bose-Einstein condensate (BEC) of magnons. The spin Hall effect
(SHE), which creates a spin-polarized current in the Pt layer, can inject or
annihilate magnons depending on the electric current and applied field
orientations. Here we demonstrate that the injection or annihilation of magnons
via the SHE can prevent or promote the formation of a rapid cooling induced
magnon BEC. Depending on the current polarity, a change in the BEC threshold of
-8% and +6% was detected. These findings demonstrate a new method to control
macroscopic quantum states, paving the way for their application in spintronic
devices.


  Accurate automated analysis of electroencephalography (EEG) would largely
help clinicians effectively monitor and diagnose patients with various brain
diseases. Compared to supervised learning with labelled disease EEG data which
can train a model to analyze specific diseases but would fail to monitor
previously unseen statuses, anomaly detection based on only normal EEGs can
detect any potential anomaly in new EEGs. Different from existing anomaly
detection strategies which do not consider any property of unavailable abnormal
data during model development, a task-oriented self-supervised learning
approach is proposed here which makes use of available normal EEGs and expert
knowledge about abnormal EEGs to train a more effective feature extractor for
the subsequent development of anomaly detector. In addition, a specific two
branch convolutional neural network with larger kernels is designed as the
feature extractor such that it can more easily extract both larger scale and
small-scale features which often appear in unavailable abnormal EEGs. The
effectively designed and trained feature extractor has shown to be able to
extract better feature representations from EEGs for development of anomaly
detector based on normal data and future anomaly detection for new EEGs, as
demonstrated on three EEG datasets. The code is available at
https://github.com/ironing/EEG-AD.


  We performed first-principles calculations aimed to investigate the role of
an heteroatom like N in the chemical and the long-range van der Waals (vdW)
interactions for a flat adsorption of several pi-conjugated molecules on the
Cu(110) surface. Our study reveals that the alignment of the molecular orbitals
at adsorbate-substrate interface depends on the number of heteroatoms. As a
direct consequence, the molecule-surface vdW interactions involve not only
pi-like orbitals which are perpendicular to the molecular plane but also
sigma-like orbitals delocalized in the molecular plane.


  Simulators often provide the best description of real-world phenomena.
However, they also lead to challenging inverse problems because the density
they implicitly define is often intractable. We present a new suite of
simulation-based inference techniques that go beyond the traditional
Approximate Bayesian Computation approach, which struggles in a
high-dimensional setting, and extend methods that use surrogate models based on
neural networks. We show that additional information, such as the joint
likelihood ratio and the joint score, can often be extracted from simulators
and used to augment the training data for these surrogate models. Finally, we
demonstrate that these new techniques are more sample efficient and provide
higher-fidelity inference than traditional methods.


  We present a theoretical study of correlated atomic wires deposited on
substrates in two parts. In this first part, we propose lattice models for a
one-dimensional quantum wire on a three-dimensional substrate and map them onto
effective two-dimensional lattices using the Lanczos algorithm. We then discuss
the approximation of these two-dimensional lattices by narrow ladder models
that can be investigated with well-established methods for one-dimensional
correlated quantum systems, such as the density-matrix renormalization group or
bosonization. The validity of this approach is studied first for noninteracting
electrons and then for a correlated wire with a Hubbard electron-electron
repulsion using quantum Monte Carlo simulations. While narrow ladders cannot be
used to represent wires on metallic substrates, they capture the physics of
wires on insulating substrates if at least three legs are used. In the second
part [arXiv:1704.07359], we use this approach for a detailed numerical
investigation of a wire with a Hubbard-type interaction on an insulating
substrate.


Deep neural networks are vulnerable to adversarial attacks.


  This work deals with the ill-posed inverse problem of reconstructing a
function $f$ given implicitly as the solution of $g = Af$, where $A$ is a
compact linear operator with unknown singular values and known eigenfunctions.
We observe the function $g$ and the singular values of the operator subject to
Gaussian white noise with respective noise levels $\varepsilon$ and $\sigma$.
  We develop a minimax theory in terms of both noise levels and propose an
orthogonal series estimator attaining the minimax rates. This estimator
requires the optimal choice of a dimension parameter depending on certain
characteristics of $f$ and $A$. This work addresses the fully data-driven
choice of the dimension parameter combining model selection with Lepski's
method. We show that the fully data-driven estimator preserves minimax
optimality over a wide range of classes for $f$ and $A$ and noise levels
$\varepsilon$ and $\sigma$. The results are illustrated considering Sobolev
spaces and mildly and severely ill-posed inverse problems.


  In this paper, we investigate the Leray problem for steady Navier-Stokes
system under full slip boundary conditions in a two dimensional channel with
straight outlets. The existence of solutions with arbitrary flux in a general
channel with slip boundary conditions is established, which tend to the shear
flows at far fields. Furthermore, if the flux is suitably small, the solutions
are proved to be unique. One of the crucial ingredients is to construct an
appropriate flux carrier and to show a Hardy type inequality for flows with
full slip boundary conditions.


  We compute the cross section of inclusive dijet photoproduction in
ultraperipheral Pb-Pb collisions at the LHC using next-to-leading order
perturbative QCD. We demonstrate that our theoretical calculations provide a
good description of various kinematic distributions measured by the ATLAS
collaboration. We find that the calculated dijet photoproduction cross section
is sensitive to nuclear modifications of parton distribution functions (PDFs)
at the level of 10 to 20%. Hence, this process can be used to reduce
uncertainties in the determination of these nuclear PDFs, whose current
magnitude is comparable to the size of the calculated nuclear modifications of
the dijet photoproduction cross section.


  We study the planar Coulomb gas in the regime where the inverse temperature
$\beta_n$ grows at least logarithmically with respect to the number of
particles $n$ (freezing regime, $\beta_n\gtrsim \log n$). We show that, almost
surely for large $n$, the discrepancy between the number of particles in any
microscopic region and their expected value (given with adequate precision by
the equilibrium measure) is, up to log factors, of the order of the perimeter
of the observation window. The estimates are valid throughout the whole droplet
(the region where the particles accumulate), and are particularly interesting
near the boundary, while in the bulk they offer technical improvements over
known results.
  Our work builds on recent results on equidistribution at low temperatures and
improves on them by providing refined spectral asymptotics for certain Toeplitz
operators on the range of the erfc-kernel (sometimes called Faddeeva or plasma
dispersion kernel).


  Could a conformal Galileon be describing a gauge mode of a broader
diffeomorphism invariant theory? We answer this question affirmatively in 3D by
using a coset construction for a nonlinearly realized conformal symmetry. In
particular, we show that the conformal Galileon emerges as a St\"uckelberg
field of a local Weyl symmetry. The coset construction gives us a
diffeomorphism and Weyl invariant 3D theory containing first, second, and third
powers of the curvatures, their couplings to certain tensors made of the
Galileon and its derivatives, and the conformal Galileon terms. In a theory
with a boundary additional surface terms are required for the boundary Weyl
anomaly cancellation. When gravity is switched off, the theory reduces to the
conformal Galileon plus a boundary term. On the other hand, it reduces to a
generalization of "New Massive Gravity" by A. Sinha, if the Weyl symmetry is
gauge-fixed in a particular way. Last but not least, there exists a parameter
space for which the theory has no propagating ghosts. Thus we show by an
explicit construction that "New Massive Gravity" (and its generalization) is a
unique scalar ghost free low energy effective field theory non-linearly
realizing conformal symmetry in 3D.


  Several topics in QCD are reviewed, including: the light-cone Fock state
representation, which encodes the flavor, spin and other quark and gluon
correlations of hadrons in the form of universal process-independent
amplitudes; the light-cone factorization scheme for inclusive and exclusive
processes; the application of the light-cone formalism to semi-leptonic B decay
amplitudes; self-resolving diffractive interactions as a tool for measuring
light-cone wavefunctions; and the use of conformal symmetry as a template for
QCD predictions, such as commensurate scale relations, which relate observable
to observable at fixed relative scale without renormalization scale or scheme
ambiguities.


  We study the scenario where a sneutrino is the next lightest supersymmetric
particle (NLSP) and decays into a gravitino and standard model particles. The
daughter particles such as neutrinos and quarks cause electro- and hadronic
showers and affect big-bang nucleosynthesis. It is found that despite a small
branching ratio, four-body processes including quarks in the final state give
the most stringent constraint on the sneutrino abundance for gravitino mass of
1 $-$ 100 GeV. Pion production by high energy neutrinos is important when the
sneutrinos decay at $\sim$ 1 sec. We also discuss the thermal leptogenesis in
the sneutrino NLSP scenario.


  Exchanging a $Z^\prime$ gauge boson is a favored mechanism to solve the muon
$(g-2)_\mu$ anomaly. Among such models the $Z^\prime$ from $U(1)_{L_\mu -
L_\tau}$ gauge group has been extensively studied. In this model the same
interaction addressing $(g-2)_\mu$, leads to an enhanced muon neutrino trident
(MNT) process $\nu_\mu N \to \nu_\mu \mu \bar \mu N$ constraining the
$Z^\prime$ mass to be less than a few hundred MeV. Many other $Z^\prime$ models
face the same problem. It has long been realized that the coupling of
$Z^\prime$ in the model can admit $(\bar \mu \gamma^\mu \tau + \bar \nu_\mu
\gamma^\mu L \nu_\tau)Z^\prime_\mu$ interaction which does not contribute to
the MNT process. It can solve $(g-2)_\mu$ anomaly for a much wider $Z^\prime$
mass range. However this new interaction induces $\tau \to \mu \bar\nu_\mu
\nu_\tau$ which rules out it as a solution to $(g-2)_\mu$ anomaly. Here we
propose a mechanism by introducing type-II seesaw $SU(2)_L$ triplet scalars to
evade constraints from all known data to allow a wide $Z^\prime$ mass range to
solve the $(g-2)_\mu$ anomaly. This mechanism opens a new window for $Z^\prime$
physics.


  There is a big difference between "quasi-galois" in the eprint
(arXiv:0907.0842) and "pseudo-galois" in the sense of Suslin-Voevodsky.


  Recently, there is much interest in droplet condensation on soft or
liquid/liquid-like substrates. Droplets can deform soft and liquid interfaces
resulting in a wealth of phenomena not observed on hard, solid surfaces (e.g.,
increased nucleation, inter-droplet attraction). Here, we describe a unique
complex collective motion of condensate water droplets that emerges
spontaneously when a solid substrate is covered with a thin oil film. Droplets
move first in a serpentine, self-avoiding fashion before transitioning to
circular motions. We show that this self-propulsion (with speeds in the 0.1-1
mm/s range) is fuelled by the interfacial energy release upon merging with
newly condensed but much smaller droplets. The resultant collective motion
spans multiple length scales from submillimetre to several centimetres, with
potentially important heat-transfer and water-harvesting applications.


  Following the recent discovery of a large population of young stars in front
of the Orion Nebula, we carried out an observational campaign with the DECam
wide-field camera covering ~10~deg^2 centered on NGC 1980 to confirm, probe the
extent of, and characterize this foreground population of pre-main-sequence
stars. We confirm the presence of a large foreground population towards the
Orion A cloud. This population contains several distinct subgroups, including
NGC1980 and NGC1981, and stretches across several degrees in front of the Orion
A cloud. By comparing the location of their sequence in various color-magnitude
diagrams with other clusters, we found a distance and an age of 380pc and
5~10Myr, in good agreement with previous estimates. Our final sample includes
2123 candidate members and is complete from below the hydrogen-burning limit to
about 0.3Msun, where the data start to be limited by saturation. Extrapolating
the mass function to the high masses, we estimate a total number of ~2600
members in the surveyed region. We confirm the presence of a rich, contiguous,
and essentially coeval population of about 2600 foreground stars in front of
the Orion A cloud, loosely clustered around NGC1980, NGC1981, and a new group
in the foreground of the OMC-2/3. For the area of the cloud surveyed, this
result implies that there are more young stars in the foreground population
than young stars inside the cloud. Assuming a normal initial mass function, we
estimate that between one to a few supernovae must have exploded in the
foreground population in the past few million years, close to the surface of
Orion A, which might be responsible, together with stellar winds, for the
structure and star formation activity in these clouds. This long-overlooked
foreground stellar population is of great significance, calling for a revision
of the star formation history in this region of the Galaxy.


  We consider the class of semi-stable positive solutions to semilinear
equations $-\Delta u=f(u)$ in a bounded domain $\Omega\subset\mathbb R^n$ of
double revolution, that is, a domain invariant under rotations of the first $m$
variables and of the last $n-m$ variables. We assume $2\leq m\leq n-2$. When
the domain is convex, we establish a priori $L^p$ and $H^1_0$ bounds for each
dimension $n$, with $p=\infty$ when $n\leq7$. These estimates lead to the
boundedness of the extremal solution of $-\Delta u=\lambda f(u)$ in every
convex domain of double revolution when $n\leq7$. The boundedness of extremal
solutions is known when $n\leq3$ for any domain $\Omega$, in dimension $n=4$
when the domain is convex, and in dimensions $5\leq n\leq9$ in the radial case.
Except for the radial case, our result is the first partial answer valid for
all nonlinearities $f$ in dimensions $5\leq n\leq 9$.


  Motivated by the moduli theory of taut contact circles on spherical
3-manifolds, we relate taut contact circles to transversely holomorphic flows.
We give an elementary survey of such 1-dimensional foliations from a
topological viewpoint. We describe a complex analogue of the classical
Godbillon-Vey invariant, the so-called Bott invariant, and a logarithmic
monodromy of closed leaves. The Bott invariant allows us to formulate a
generalised Gau{\ss}-Bonnet theorem. We compute these invariants for the
Poincar\'e foliations on the 3-sphere and derive rigidity statements, including
a uniformisation theorem for orbifolds. These results are then applied to the
classification of taut contact circles.


  In this paper, we study the representations of the periplectic Lie
superalgebra using the Duflo-Serganova functor. Given a simple
$\mathfrak{p}(n)$-module $L$ and a certain element $x\in \mathfrak{p}(n)$ of
rank $1$, we give an explicit description of the composition factors of the
$\mathfrak{p}(n-1)$-module $DS_x(L)$, which is defined as the homology of the
complex $$\Pi M \xrightarrow{x} M \xrightarrow{x} \Pi M.$$ In particular, we
show that this $\mathfrak{p}(n-1)$-module is multiplicity-free. We then use
this result to give a simple explicit combinatorial formula for the
superdimension of a simple integrable finite-dimensional
$\mathfrak{p}(n)$-module, based on its highest weight. In particular, this
reproves the Kac-Wakimoto conjecture for $\mathfrak{p}(n)$, which was proved
earlier by the authors.


  We show elasto-capillary folding of silicon nitride objects with accurate
folding angles between flaps of 70.6$\pm$0.1{\deg} and demonstrate the
feasibility of such accurate micro-assembly with a final folding angle of
90{\deg}. The folding angle is defined by stop-programmable hinges that are
fabricated starting from silicon molds employing accurate three-dimensional
corner lithography. This nano-patterning method exploits the conformal
deposition and the subsequent timed isotropic etching of a thin film in a 3D
shaped silicon template. The technique leaves a residue of the thin film in
sharp concave corners which can be used as an inversion mask in subsequent
steps. Hinges designed to stop the folding at 70.6{\deg} were fabricated
batchwise by machining the V-grooves obtained by KOH etching in (110) silicon
wafers; 90{\deg} stop-programmable hinges were obtained starting from silicon
molds obtained by dry etching on (100) wafers. The presented technique is
applicable to any folding angle and opens a new route towards creating
structures with increased complexity, which will ultimately lead to a novel
method for device fabrication.


  With COVID-19 having emerged as the most widespread human pandemic disease in
a century, the need to control its spread to avoid massive loss of life became
more than necessary, and extremely fast. Several vaccines were developed and
the task of policy makers was suddenly to convince the reluctant population to
be vaccinated by various means. While some countries have chosen a policy of
mandatory vaccination or punitive incentives, many states in the United States
have adopted various incentives to try to increase vaccination coverage. A
study we conducted in recent months quantified the effect of these measures on
the proportion of the population vaccinated, using the synthetic control
method, by simulating what would have happened without these measures. The aim
now is to generalize this study to smaller scales, to improve the results of
our previous study, to quantify their robustness and to provide a tool that can
be used by policy makers to adapt their behavior in light of the results
obtained.


  Spatial-temporal forecasting has attracted tremendous attention in a wide
range of applications, and traffic flow prediction is a canonical and typical
example. The complex and long-range spatial-temporal correlations of traffic
flow bring it to a most intractable challenge. Existing works typically utilize
shallow graph convolution networks (GNNs) and temporal extracting modules to
model spatial and temporal dependencies respectively. However, the
representation ability of such models is limited due to: (1) shallow GNNs are
incapable to capture long-range spatial correlations, (2) only spatial
connections are considered and a mass of semantic connections are ignored,
which are of great importance for a comprehensive understanding of traffic
networks. To this end, we propose Spatial-Temporal Graph Ordinary Differential
Equation Networks (STGODE). Specifically, we capture spatial-temporal dynamics
through a tensor-based ordinary differential equation (ODE), as a result,
deeper networks can be constructed and spatial-temporal features are utilized
synchronously. To understand the network more comprehensively, semantical
adjacency matrix is considered in our model, and a well-design temporal
dialated convolution structure is used to capture long term temporal
dependencies. We evaluate our model on multiple real-world traffic datasets and
superior performance is achieved over state-of-the-art baselines.


  The subject of this thesis is the coupling of quantum fields to a classical
gravitational background in a semiclassical fashion. It contains a thorough
introduction into quantum field theory on curved spacetime with a focus on the
stress-energy tensor and the semiclassical Einstein equation. Basic notions of
differential geometry, topology, functional and microlocal analysis, causality
and general relativity will be summarised, and the algebraic approach to QFT on
curved spacetime will be reviewed. Apart from these foundations, the original
research of the author and his collaborators will be presented: Together with
Fewster, the author studied the up and down structure of permutations using
their decomposition into so-called atomic permutations. The relevance of these
results to this thesis is their application in the calculation of the moments
of quadratic quantum fields. In a work with Pinamonti, the author showed the
local and global existence of solutions to the semiclassical Einstein equation
in flat cosmological spacetimes coupled to a scalar field by solving
simultaneously for the quantum state and the Hubble function in an
integral-functional equation. The theorem is proved with a fixed-point theorem
using the continuous functional differentiability and boundedness of the
integral kernel of the integral-functional equation. In another work with
Pinamonti the author proposed an extension of the semiclassical Einstein
equations which couples the moments of a stochastic Einstein tensor to the
moments of the quantum stress-energy tensor. In a toy model of a Newtonianly
perturbed exponentially expanding spacetime it is shown that the quantum
fluctuations of the stress-energy tensor induce an almost scale-invariant power
spectrum for the perturbation potential and that non-Gaussianties arise
naturally.


  In this paper, we first address the dynamics of the elegant multi-valued
quaternionic Hopfield neural network (MV-QHNN) proposed by Minemoto and
collaborators. Contrary to what was expected, we show that the MV-QHNN, as well
as one of its variation, does not always come to rest at an equilibrium state
under the usual conditions. In fact, we provide simple examples in which the
network yields a periodic sequence of quaternionic state vectors. Afterward, we
turn our attention to the continuous-valued quaternionic Hopfield neural
network (CV-QHNN), which can be derived from the MV-QHNN by means of a limit
process. The CV-QHNN can be implemented more easily than the MV-QHNN model.
Furthermore, the asynchronous CV-QHNN always settles down into an equilibrium
state under the usual conditions. Theoretical issues are all illustrated by
examples in this paper.


  The purpose of this paper is to introduce a new Markov chain Monte Carlo
method and exhibit its efficiency by simulation and high-dimensional asymptotic
theory. Key fact is that our algorithm has a reversible proposal transition
kernel, which is designed to have a heavy-tailed invariant probability
distribution. The high-dimensional asymptotic theory is studied for a class of
heavy-tailed target probability distribution. As the number of dimension of the
state space goes to infinity, we will show that our algorithm has a much better
convergence rate than that of the preconditioned Crank Nicolson (pCN) algorithm
and the random-walk Metropolis (RWM) algorithm. We also show that our algorithm
is at least as good as the pCN algorithm and better than the RWM algorithm for
light-tailed target probability distribution.


  Multiple access mobile edge computing is an emerging technique to bring
computation resources close to end mobile users. By deploying edge servers at
WiFi access points or cellular base stations, the computation capabilities of
mobile users can be extended. Existing works mostly assume the remote cloud
server can be viewed as a special edge server or the edge servers are willing
to cooperate, which is not practical. In this work, we propose an edge-cloud
cooperative architecture where edge servers can rent for the remote cloud
servers to expedite the computation of tasks from mobile users. With this
architecture, the computation offloading problem is modeled as a mixed integer
programming with delay constraints, which is NP-hard. The objective is to
minimize the total energy consumption of mobile devices. We propose a greedy
algorithm as well as a simulated annealing algorithm to effectively solve the
problem. Extensive simulation results demonstrate that, the proposed greedy
algorithm and simulated annealing algorithm can achieve the near optimal
performance. On average, the proposed greedy algorithm can achieve the same
application completing time budget performance of the Brute Force optional
algorithm with only 31\% extra energy cost. The simulated annealing algorithm
can achieve similar performance with the greedy algorithm.


  We show that the coarse-grained quantum baker's map exhibits a linear entropy
increase at an asymptotic rate given by the Kolmogorov-Sinai entropy of the
classical chaotic baker's map. The starting point of our analysis is a symbolic
representation of the map on a string of $N$ qubits, i.e., an $N$-bit register
of a quantum computer. To coarse-grain the quantum evolution, we make use of
the decoherent histories formalism. As a byproduct, we show that the condition
of medium decoherence holds asymptotically for the coarse-grained quantum
baker's map.


  We investigate some aspects of the soliton dynamics in an alpha-helical
protein macromolecule within the steric Davydov-Scott model. Our main objective
is to elucidate the important role of the helical symmetry in the formation,
stability and dynamical properties of Davydov's solitons in an alpha-helix. We
show, analytically and numerically, that the corresponding system of nonlinear
equations admits several types of stationary soliton solutions and that
solitons which preserve helical symmetry are dynamically unstable: once formed,
they decay rapidly when they propagate. On the other hand, the soliton which
spontaneously breaks the local translational and helical symmetries possess the
lowest energy and is a robust localized entity. We also demonstrate that this
soliton is the result of an hybridization of the quasiparticle states from the
two lowest degenerate bands and has an inner structure which can be described
as a modulated multi-hump amplitude distribution of excitations on individual
spines. The complex and composite structure of the soliton manifests itself
distinctly when the soliton is moving and some interspine oscillations take
place. Such a soliton structure and the interspine oscillations have previosly
been observed numerically in [A.C. Scott, Phys.Rev. A 26 578 (1982)]. Here we
argue that the solitons studied by A. Scott, are hybrid solitons and that the
oscillations arise due to the helical symmetry of the system and result from
the motion of the soliton along the $\alpha$-helix. The frequency of the
interspine oscillations is shown to be proportional to the soliton velocity.


  We present a quenched lattice QCD calculation of the first few moments of the
polarized and un-polarized structure functions of the nucleon. Our calculations
are done using domain wall fermions and the DBW2 gauge action with inverse
lattice spacing ~1.3GeV, physical volume approximatelly (2.4 fm)^3, and light
quark masses down to about 1/4 the strange quark mass. Values of the individual
moments are found to be significantly larger than experiment, as in past
lattice calculations, but interestingly the chiral symmetry of domain wall
fermions allows for a precise determination of the ratio of the flavor
non-singlet momentum fraction to the helicity distribution, which is in very
good agreement with experiment. We discuss the implications of this result.
Next, we show that the chiral symmetry of domain wall fermions is useful in
eliminating mixing of power divergent lower dimensional operators with twist-3
operators. Finally, we find the isovector tensor charge at renormalization
scale 2 GeV in the MS bar scheme to be 1.192(30), where the error is the
statistical error only.


  We report measurements of the neutron diffuse scattering in a single crystal
of the relaxor ferroelectric material
95.5%Pb(Zn$_{1/3}$Nb$_{2/3}$)O$_3$-4.5%PbTiO$_3$ (PZN-4.5%PT). Our results
suggest that the nanometer scale structure in this compound exhibits both
$<100>$ and $<110>$ polarizations, which contribute to different portions of
the total diffuse scattering intensity. These contributions can be
distinguished by the differing responses to an electric field applied along
[001]. While diffuse scattering intensities associated with $<110>$ (T2-type)
polarizations show little to no change in a [001] field, those associated with
$<100>$ (T1-type) polarizations are partially suppressed by the field at
temperatures below the Curie temperature \emph{T$_C$} $\sim 475$ K. Neutron
spin-echo measurements show that the diffuse scattering at (0.05,0,1) is
largely dynamic at high temperature and gradually freezes on cooling, becoming
mostly static at 200 K.


  In this paper, we propose a unified approach for solving structure-preserving
eigenvalue embedding problem (SEEP) for quadratic regular matrix polynomials
with symmetry structures. First, we determine perturbations of a quadratic
matrix polynomial, unstructured or structured, such that the perturbed
polynomials reproduce a desired invariant pair while maintaining the invariance
of another invariant pair of the unperturbed polynomial. If the latter is
unknown, it is referred to as no spillover perturbation. Then we use these
results for solving the SEEP for structured quadratic matrix polynomials that
include: symmetric, Hermitian, $\star$-even and $\star$-odd quadratic matrix
polynomials. Finally, we show that the obtained analytical expressions of
perturbations can realize existing results for structured polynomials that
arise in real-world applications, as special cases. The obtained results are
supported with numerical examples.


  Training graph classifiers able to distinguish between healthy brains and
dysfunctional ones, can help identifying substructures associated to specific
cognitive phenotypes. However, the mere predictive power of the graph
classifier is of limited interest to the neuroscientists, which have plenty of
tools for the diagnosis of specific mental disorders. What matters is the
interpretation of the model, as it can provide novel insights and new
hypotheses.
  In this paper we propose \emph{counterfactual graphs} as a way to produce
local post-hoc explanations of any black-box graph classifier. Given a graph
and a black-box, a counterfactual is a graph which, while having high
structural similarity with the original graph, is classified by the black-box
in a different class. We propose and empirically compare several strategies for
counterfactual graph search. Our experiments against a white-box classifier
with known optimal counterfactual, show that our methods, although heuristic,
can produce counterfactuals very close to the optimal one. Finally, we show how
to use counterfactual graphs to build global explanations correctly capturing
the behaviour of different black-box classifiers and providing interesting
insights for the neuroscientists.


  In this paper we consider weakly holomorphic modular forms (i.e. those
meromorphic modular forms for which poles only possibly occur at the cusps) of
weight $2-k\in 2\Z$ for the full modular group $\SL_2(\Z)$. The space has a
distinguished set of generators $f_{m,2-k}$. Such weakly holomorphic modular
forms have been classified in terms of finitely many Eisenstein series, the
unique weight 12 newform $\Delta$, and certain Faber polynomials in the modular
invariant $j(z)$, the Hauptmodul for $\SL_2(\Z)$. We employ the theory of
harmonic weak Maass forms and (non-holomorphic) Maass-Poincar\'e series in
order to obtain the asymptotic growth of the coefficients of these Faber
polynomials. Along the way, we obtain an asymptotic formula for the partial
derivatives of the Maass-Poincar\'e series with respect to $y$ as well as
extending an asymptotic for the growth of the $\ell$-th repeated integral of
the Gauss error function at $x$ to include $\ell\in \R$ and a wider range of
$x$.


  Existing Visual Question Answering (VQA) methods tend to exploit dataset
biases and spurious statistical correlations, instead of producing right
answers for the right reasons. To address this issue, recent bias mitigation
methods for VQA propose to incorporate visual cues (e.g., human attention maps)
to better ground the VQA models, showcasing impressive gains. However, we show
that the performance improvements are not a result of improved visual
grounding, but a regularization effect which prevents over-fitting to
linguistic priors. For instance, we find that it is not actually necessary to
provide proper, human-based cues; random, insensible cues also result in
similar improvements. Based on this observation, we propose a simpler
regularization scheme that does not require any external annotations and yet
achieves near state-of-the-art performance on VQA-CPv2.


  In the representation theory of finite groups, there is a well-known and
important conjecture due to M. Brou\'e. He conjectures that, for any prime p,
if a p-block A of a finite group G has an abelian defect group P, then A and
its Brauer corresponding block A_N of the normaliser N_G(P) of P in G are
derived equivalent (Rickard equivalent). This conjecture is called Strong
Version of Brou\'e's Abelian Defect Group Conjecture. In this paper, we prove
that the strong version of Brou\'e's abelian defect group conjecture is true
for the non-principal 2-block A with an elementary abelian defect group P of
order 8 of the sporadic simple Conway group Co_3. This result completes the
verification of the strong version of Brou\'e's abelian defect group conjecture
for all primes p and for all p-blocks of Co_3.


  The new class of Janus two-dimensional (2D) transition-metal dichalcogenides
with two different interfaces are currently gaining increasing attention due to
their distinct properties different from the typical 2D materials. Here, we
show that in-plane anisotropy of a 2D atomic crystal, like ReS$_{2}$ or
ReSe$_{2}$, allows formation of a large number of inequivalent Janus
monolayers. We use first-principles calculations to investigate the structural
stability of 29 distinct ReX$_{2-x}$Y$_{x}$ ($\mathrm{X,Y \in \{S,Se\}}$)
structures, which can be obtained by selective exchange of exposed chalcogens
in a ReX$_{2}$ monolayer. We also examine the electronic properties and work
function of the most stable Janus monolayers and show that the large number of
inequivalent structures provides a way to engineer spin-orbit splitting of the
electronic bands. We find that the breaking of inversion symmetry leads to
sizable spin splittings and spontaneous diople moments than are larger than
those in other Janus dichalcogenides. Moreover, our caluclations suggest that
the work function of the Janus monolayers can be tuned by varying the content
of the substituting chalcogen. Our work demonstrates that in-plane anisotropy
provides additional flexibility in sub-layer engineering of 2D atomic crystals.


  We examine long-wavelength correlation functions of massive scalar fields in
de Sitter spacetime. For the theory with a quartic self-interaction, the
two-point function is calculated up to two loops. Comparing our results with
the Hartree-Fock approximation and with the stochastic approach shows that the
former resums only the cactus type diagrams, whereas the latter contains the
sunset diagram as well and produces the correct result. We also demonstrate
that the long-wavelength expectation value of the commutator of two fields is
equal to zero both for spacelike and timelike separated points.


  Stacking and twisting atom-thin sheets create superlattice structures with
unique emergent properties, while tailored light fields can manipulate coherent
electron transport on ultrafast timescales. The unification of these two
approaches may lead to ultrafast creation and manipulation of band structure
properties, which is a crucial objective for the advancement of quantum
technology. Here, we address this by demonstrating a tailored lightwave-driven
analogue to twisted layer stacking. This results in sub-femtosecond control of
time-reversal symmetry breaking and thereby band structure engineering in a
hexagonal boron nitride monolayer. The results practically demonstrate the
realization of the topological Haldane model in an insulator. Twisting the
lightwave relative to the lattice orientation enables switching between band
configurations, providing unprecedented control over the magnitude and location
of the band gap, and curvature. A resultant asymmetric population at
complementary quantum valleys lead to a measurable valley Hall current,
detected via optical harmonic polarimetry. The universality and robustness of
the demonstrated sub-femtosecond control opens a new way to band structure
engineering on the fly paving a way towards large-scale ultrafast quantum
devices for real-world applications.


  Network connectivity is one of the major design issues in the context of
mobile sensor networks. Due to diverse communication patterns, some nodes lying
in high-traffic zones may consume more energy and eventually die out resulting
in network partitioning. This phenomenon may deprive a large number of alive
nodes of sending their important time critical data to the sink. The
application of data caching in mobile sensor networks is exponentially
increasing as a high-speed data storage layer. This paper presents a deep
learning-based beamforming approach to find the optimal transmission strategies
for cache-enabled backhaul networks. In the proposed scheme, the sensor nodes
in isolated partitions work together to form a directional beam which
significantly increases their overall communication range to reach out a
distant relay node connected to the main part of the network. The proposed
methodology of cooperative beamforming-based partition connectivity works
efficiently if an isolated cluster gets partitioned with a favorably large
number of nodes. We also present a new cross-layer method for link cost that
makes a balance between the energy used by the relay. By directly adding the
accessible auxiliary nodes to the set of routing links, the algorithm chooses
paths which provide maximum dynamic beamforming usage for the intermediate
nodes. The proposed approach is then evaluated through simulation results. The
simulation results show that the proposed mechanism achieves up to 30% energy
consumption reduction through beamforming as partition healing in addition to
guarantee user throughput.


  This paper proposes to use a deep neural network (DNN)-based symbol detector
for mmWave systems such that CSI acquisition can be bypassed. In particular, we
consider a sliding bidirectional recurrent neural network (BRNN) architecture
that is suitable for the long memory length of typical mmWave channels. The
performance of the DNN detector is evaluated in comparison to that of the
Viterbi detector. The results show that the performance of the DNN detector is
close to that of the optimal Viterbi detector with perfect CSI, and that it
outperforms the Viterbi algorithm with CSI estimation error. Further
experiments show that the DNN detector is robust to a wide range of noise
levels and varying channel conditions, and that a pretrained detector can be
reliably applied to different mmWave channel realizations with minimal
overhead.


  One of the preeminent obstacles to scaling multi-agent reinforcement learning
to large numbers of agents is assigning credit to individual agents' actions.
In this paper, we address this credit assignment problem with an approach that
we call \textit{partial reward decoupling} (PRD), which attempts to decompose
large cooperative multi-agent RL problems into decoupled subproblems involving
subsets of agents, thereby simplifying credit assignment. We empirically
demonstrate that decomposing the RL problem using PRD in an actor-critic
algorithm results in lower variance policy gradient estimates, which improves
data efficiency, learning stability, and asymptotic performance across a wide
array of multi-agent RL tasks, compared to various other actor-critic
approaches. Additionally, we relate our approach to counterfactual multi-agent
policy gradient (COMA), a state-of-the-art MARL algorithm, and empirically show
that our approach outperforms COMA by making better use of information in
agents' reward streams, and by enabling recent advances in advantage estimation
to be used.


  Starting from a degenerate Bose gas in a hybrid trap combining a magnetic
quadrupole trap and an attractive optical trap resulting from a focused laser
beam, we demonstrate the efficient loading of this quantum gas into a
shell-shaped trap. The shell trap is purely magnetic and relies on adiabatic
potentials for atoms in an inhomogeneous magnetic field dressed by a
radiofrequency (rf) field. We show that direct rf evaporation in the hybrid
trap enables an efficient and simple preparation of the cold sample, well
adapted to the subsequent loading procedure. The transfer into the shell trap
is adiabatic and limits the final excitation of the center-of-mass motion to
below 2 micrometres.


  The spatial Fourier spectrum of the electron density distribution in a finite
1D system and the distribution function of electrons over single-particle
states are studied in detail to show that there are two universal features in
their behavior, which characterize the electron ordering and the deformation of
Wigner crystal by boundaries. The distribution function has a $\delta$-like
singularity at the Fermi momentum $k_F$. The Fourier spectrum of the density
has a step-like form at the wavevector $2k_F$, with the harmonics being absent
or vanishing above this threshold. These features are found by calculations
using exact diagonalization method. They are shown to be caused by Wigner
ordering of electrons, affected by the boundaries. However the common Luttinger
liquid model with open boundaries fails to capture these features, because it
overestimates the deformation of the Wigner crystal. An improvement of the
Luttinger liquid model is proposed which allows one to describe the above
features correctly. It is based on the corrected form of the density operator
conserving the particle number.


  The predicted formation of moire superlattices leading to confined excitonic
states in heterostructures formed by stacking two lattice mismatched transition
metal dichalcogenide (TMD) monolayers was recently experimentally confirmed.
Such periodic potential in TMD heterostructure functions as a diffusion barrier
that affects the energy transport and dynamics of interlayer excitons (electron
and hole spatially concentrated in different monolayers). Understanding the
transport of excitons under such condition is essential to establish the
material system as a next generation device platform. In this work, we
experimentally quantify the diffusion barrier experienced by the interlayer
excitons in a hexagonal boron nitride (hBN) encapsulated, molybdenum diselenide
tungsten/diselenide (MoSe2/WSe2) heterostructure by studying the exciton
transport at various temperatures.


  We consider a multiphoton Bell-type inequality to study nonlocality in
four-mode continuous variable systems, which goes beyond two-photon states and
can be applied to mixed as well as states with fluctuating photon number. We
apply the inequality to a wide variety of states such as pure and mixed
Gaussian states (including squeezed thermal states) and non-Gaussian states. We
consider beam splitters as a model for leakage and show that the inequality is
able to detect nonclassicality of noisy Gaussian states as well. Finally, we
investigate nonlocality in pair-coherent states and entangled coherent states,
which are prominent examples of nonclassical, non-Gaussian states.


  Hadwiger and Debrunner showed that for families of convex sets in
$\mathbb{R}^d$ with the property that among any $p$ of them some $q$ have a
common point, the whole family can be stabbed with $p-q+1$ points if $p \geq q
\geq d+1$ and $(d-1)p < d(q-1)$. This generalizes a classical result by Helly.
We show how such a stabbing set can be computed for a family of convex polygons
in the plane with a total of $n$ vertices in $O((p-q+1)n^{4/3}\log^{8}
n(\log\log n)^{1/3} + np^2)$ expected time. For polyhedra in $\mathbb{R}^3$, we
get an algorithm running in $O((p-q+1)n^{5/2}\log^{10} n(\log\log n)^{1/6} +
np^3)$ expected time. We also investigate other conditions on convex polygons
for which our algorithm can find a fixed number of points stabbing them.
Finally, we show that analogous results of the Hadwiger and Debrunner
$(p,q)$-theorem hold in other settings, such as convex sets in
$\mathbb{R}^d\times\mathbb{Z}^k$ or abstract convex geometries.


  The most of the people have their account on social networks (e.g. Facebook,
Vkontakte) where they express their attitude to different situations and
events. Facebook provides only the positive mark as a like button and share.
However, it is important to know the position of a certain user on posts even
though the opinion is negative. Positive, negative and neutral attitude can be
extracted from the comments of users. Overall information about positive,
negative and neutral opinion can bring the understanding of how people react in
a position. Moreover, it is important to know how attitude is changing during
the time period. The contribution of the paper is a new method based on
sentiment text analysis for detection and prediction negative and positive
patterns for Facebook comments which combines (i) real-time sentiment text
analysis for pattern discovery and (ii) batch data processing for creating
opinion forecasting algorithm. To perform forecast we propose two-steps
algorithm where: (i) patterns are clustered using unsupervised clustering
techniques and (ii) trend prediction is performed based on finding the nearest
pattern from the certain cluster. Case studies show the efficiency and accuracy
(Avg. MAE = 0.008) of the proposed method and its practical applicability.
Also, we discovered three types of users attitude patterns and described them.


  This paper discusses local features in the source function that generate in
the far zone simultaneously (a) a quadratic decay of the source spectrum and
(b) the loss of radiation directivity at high frequencies. A. Gusev drew
attention to this problem and suggested that a positive solution can be
obtained for earthquake rupture front with a rather complex ("lace") structure.
Below we give a theoretical solution of the problem and show that the front
structure can be simple enough, but not smooth.


  Sex trafficking is a global epidemic. Escort websites are a primary vehicle
for selling the services of such trafficking victims and thus a major driver of
trafficker revenue. Many law enforcement agencies do not have the resources to
manually identify leads from the millions of escort ads posted across dozens of
public websites. We propose an ordinal regression neural network to identify
escort ads that are likely linked to sex trafficking. Our model uses a modified
cost function to mitigate inconsistencies in predictions often associated with
nonparametric ordinal regression and leverages recent advancements in deep
learning to improve prediction accuracy. The proposed method significantly
improves on the previous state-of-the-art on Trafficking-10K, an
expert-annotated dataset of escort ads. Additionally, because traffickers use
acronyms, deliberate typographical errors, and emojis to replace explicit
keywords, we demonstrate how to expand the lexicon of trafficking flags through
word embeddings and t-SNE.


  Given an array of $n$ elements from a total order, we propose encodings that
support various range queries (range minimum, range maximum and their
variants), and previous and next smaller/larger value queries. When query time
is not of concern, we obtain a $4.088n + o(n)$-bit encoding that supports all
these queries. For the case when we need to support all these queries in
constant time, we give an encoding that takes $4.585n + o(n)$ bits, where $n$
is the length of input array. This improves the $5.08n+o(n)$-bit encoding
obtained by encoding the colored $2d$-Min and Max heaps proposed by
Fischer~[TCS, 2011]. We first extend the original DFUDS [Algorithmica, 2005]
encoding of the colored 2d-Min (Max) heap that supports the queries in constant
time. Then, we combine the extended DFUDS of $2d$-Min heap and $2d$-Max heap
using the Min-Max encoding of Gawrychowski and Nicholson [ICALP, 2015] with
some modifications. We also obtain encodings that take lesser space and support
a subset of these queries.


  We present a compact source of cold sodium atoms suitable for the production
of quantum degenerate gases and versatile for a multi-species experiment. The
magnetic field produced by permanent magnets allows to simultaneously realize a
Zeeman slower and a two-dimensional MOT within an order of magnitude smaller
length than standard sodium sources. We achieve an atomic flux exceeding 4x10^9
atoms/s loaded in a MOT, with a most probable longitudinal velocity of 20 m/s,
and a brightness larger than 2.5x10^(12) atoms/s/sr. This atomic source allowed
us to produce a pure BEC with more than 10^7 atoms and a background pressure
limited lifetime of 5 minutes.


  We theoretically study the spin Hall effect in a simple tight-binding model
of stacked-kagome Weyl semimetal Co3Sn2S2 with ferromagnetic ordering. We focus
on the two types of the spin Hall current: one flowing in the in-plane
direction with respect to the kagome lattice (in-plane spin Hall current), and
one flowing in the stacking direction (out-of-plane spin Hall current). We show
the spin Hall conductivities for those spin currents drastically change
depending on the direction of the magnetic moment. Especially, the out-of-plane
spin Hall current may induce surface spin accumulation, which are useful for
the perpendicular magnetization switching via spin-orbit torque.


  In this paper, we want to clarify the Gibbs phenomenon when continuous and
discontinuous finite elements are used to approximate discontinuous or nearly
discontinuous PDE solutions from the approximation point of view.
  For a simple step function, we explicitly compute its continuous and
discontinuous piecewise constant or linear projections on discontinuity matched
or non-matched meshes. For the simple discontinuity-aligned mesh case,
piecewise discontinuous approximations are always good. For the general
non-matched case, we explain that the piecewise discontinuous constant
approximation combined with adaptive mesh refinements is a good choice to
achieve accuracy without overshoots. For discontinuous piecewise linear
approximations, non-trivial overshoots will be observed unless the mesh is
matched with discontinuity. For continuous piecewise linear approximations, the
computation is based on a "far-away assumption", and non-trivial overshoots
will always be observed under regular meshes. We calculate the explicit
overshoot values for several typical cases. Numerical tests are conducted for a
singularly-perturbed reaction-diffusion equation and linear hyperbolic
equations to verify our findings in the paper. Also, we discuss the
$L^1$-minimization-based methods and do not recommend such methods due to their
similar behavior to $L^2$-based methods and more complicated implementations.


  Online action detection (OAD) is challenging since 1) robust yet
computationally expensive features cannot be straightforwardly used due to the
real-time processing requirements and 2) the localization and classification of
actions have to be performed even before they are fully observed. We propose a
new random forest (RF)-based online action detection framework that addresses
these challenges. Our algorithm uses computationally efficient skeletal joint
features. High accuracy is achieved by using robust convolutional neural
network (CNN)-based features which are extracted from the raw RGBD images, plus
the temporal relationships between the current frame of interest, and the past
and future frames. While these high-quality features are not available in
real-time testing scenario, we demonstrate that they can be effectively
exploited in training RF classifiers: We use these spatio-temporal contexts to
craft RF's new split functions improving RFs' leaf node statistics. Experiments
with challenging MSRAction3D, G3D, and OAD datasets demonstrate that our
algorithm significantly improves the accuracy over the state-of-the-art online
action detection algorithms while achieving the real-time efficiency of
existing skeleton-based RF classifiers.


  In this paper, we describe our system for Task 4 of SemEval 2020, which
involves differentiating between natural language statements that confirm to
common sense and those that do not. The organizers propose three subtasks -
first, selecting between two sentences, the one which is against common sense.
Second, identifying the most crucial reason why a statement does not make
sense. Third, generating novel reasons for explaining the against common sense
statement. Out of the three subtasks, this paper reports the system description
of subtask A and subtask B. This paper proposes a model based on transformer
neural network architecture for addressing the subtasks. The novelty in work
lies in the architecture design, which handles the logical implication of
contradicting statements and simultaneous information extraction from both
sentences. We use a parallel instance of transformers, which is responsible for
a boost in the performance. We achieved an accuracy of 94.8% in subtask A and
89% in subtask B on the test set.


  These lecture notes are designed to accompany an imaginary, virtual,
undergraduate, one or two semester course on fundamentals of Parallel Computing
as well as to serve as background and reference for graduate courses on
High-Performance Computing, parallel algorithms and shared-memory
multiprocessor programming. They introduce theoretical concepts and tools for
expressing, analyzing and judging parallel algorithms and, in detail, cover the
two most widely used concrete frameworks OpenMP and MPI as well as the
threading interface pthreads for writing parallel programs for either shared or
distributed memory parallel computers with emphasis on general concepts and
principles. Code examples are given in a C-like style and many are actual,
correct C code. The lecture notes deliberately do not cover GPU architectures
and GPU programming, but the general concerns, guidelines and principles (time,
work, cost, efficiency, scalability, memory structure and bandwidth) will be
just as relevant for efficiently utilizing various GPU architectures. Likewise,
the lecture notes focus on deterministic algorithms only and do not use
randomization. The student of this material will find it instructive to take
the time to understand concepts and algorithms visually. The exercises can be
used for self-study and as inspiration for small implementation projects in
OpenMP and MPI that can and should accompany any serious course on Parallel
Computing. The student will benefit from actually implementing and carefully
benchmarking the suggested algorithms on the parallel computing system that may
or should be made available as part of such a Parallel Computing course. In
class, the exercises can be used as basis for hand-ins and small programming
projects for which sufficient, additional detail and precision should be
provided by the instructor.


  We undertake a systematic study of Lipschitz Normally Embedded normal complex
surface germs. We prove in particular that the topological type of such a germ
determines the combinatorics of its minimal resolution which factors through
the blowup of its maximal ideal and through its Nash transform, as well as the
polar curve and the discriminant curve of a generic plane projection, thus
generalizing results of Spivakovsky and Bondil that were known for minimal
surface singularities. In an appendix, we give a new example of a Lipschitz
Normally Embedded surface singularity.


  Dynamic tensor data are becoming prevalent in numerous applications. Existing
tensor clustering methods either fail to account for the dynamic nature of the
data, or are inapplicable to a general-order tensor. Also there is often a gap
between statistical guarantee and computational efficiency for existing tensor
clustering solutions. In this article, we aim to bridge this gap by proposing a
new dynamic tensor clustering method, which takes into account both sparsity
and fusion structures, and enjoys strong statistical guarantees as well as high
computational efficiency. Our proposal is based upon a new structured tensor
factorization that encourages both sparsity and smoothness in parameters along
the specified tensor modes. Computationally, we develop a highly efficient
optimization algorithm that benefits from substantial dimension reduction. In
theory, we first establish a non-asymptotic error bound for the estimator from
the structured tensor factorization. Built upon this error bound, we then
derive the rate of convergence of the estimated cluster centers, and show that
the estimated clusters recover the true cluster structures with a high
probability. Moreover, our proposed method can be naturally extended to
co-clustering of multiple modes of the tensor data. The efficacy of our
approach is illustrated via simulations and a brain dynamic functional
connectivity analysis from an Autism spectrum disorder study.


  The Solar Gravitational Lens (SGL) is a gift of nature that Humanity is now
ready to exploit. SGL physics started with Einstein's 1936 paper on the
gravitational lensing; it was not until 1979 that the idea of a space mission
reaching the Sun's nearest focal sphere at 550 Astronomical Units (AU) was put
forward by Von Eshleman. By the year 2000, the senior author of this paper (CM)
had submitted a relevant formal proposal to ESA about the relevant space
mission to 550 AU. He presented his ideas at NASA-JPL for the first time on
August 18. In 2020 NASA awarded a $2million grant to JPL to prepare for the
first FOCAL space mission. But radio bridges between the Sun and any nearby
star may also be conceived. The idea is that, if Humanity will be able to send
unmanned space probes to the nearest stars in the future, each of these probes
could be placed behind the star of arrival and along the star-Sun line, thus
allowing for TWO gravitational lenses to work together. That will result in a
permanent communication system with much REDUCED POWERS to keep the radio link
between the two stellar systems: a veritable Galactic Internet. In this paper,
we study for the first time the 50 radio bridges between the Sun and each of
the nearest 100 stars in the Galaxy. Of course, this work is for the centuries
to come. But knowing which natural radio bridge between the Sun and each of the
nearest 50 stars is MORE CONVENIENT, will open the ROAD MAP for the HUMAN
EXPANSION into the Galaxy.


  Floquet theory has spawned many exciting possibilities for electronic
structure control with light with enormous potential for future applications.
The experimental realization in solids, however, largely remains pending. In
particular, the influence of scattering on the formation of Floquet-Bloch
states remains poorly understood. Here we combine time- and angle-resolved
photoemission spectroscopy with time-dependent density functional theory and a
two-level model with relaxation to investigate the survival of Floquet-Bloch
states in the presence of scattering. We find that Floquet-Bloch states will be
destroyed if scattering -- activated by electronic excitations -- prevents the
Bloch electrons from following the driving field coherently. The two-level
model also shows that Floquet-Bloch states reappear at high field intensities
where energy exchange with the driving field dominates over energy dissipation
to the bath. Our results clearly indicate the importance of long scattering
times combined with strong driving fields for the successful realization of
various Floquet phenomena.


  We consider evolutionary models for the population of short-period (<10 hr)
low-mass black-hole binaries (LMBHBs) and compare them with observations of
soft X-ray transients (SXTs). We show that assuming strongly reduced magnetic
braking (as suggested by us before for low-mass semidetached binaries) the
calculated masses and effective temperatures of secondaries are encouragingly
close to the observed masses and effective temperatures (as inferred from their
spectra) of donor stars in short-period LMBHBs. Theoretical mass-transfer rates
in SXTs are consistent with the observed ones if one assumes that accretion
discs in these systems are truncated (``leaky''). We find that the population
of short-period SXTs is formed mainly by systems which had unevolved or
slightly evolved main-sequence donors ($M_2 \lesssim 1.2M_\odot$) with a
hydrogen abundance in the center $X_c > 0.35$ at the Roche-lobe overflow
(RLOF). Longer period (0.5 - 1) day) SXTs might descend from systems with
initial donor masses of about 1 $M_\odot$ and $X_c < 0.35$. Thus, one can
explain the origin of short period LMBHB without invoking donors with cores
almost totally depleted of hydrogen. Our models suggest that, unless the
currently accepted empirical estimates of mass-loss rates by winds for massive
O-stars and Wolf-Rayet stars are significantly over-evaluated, a very high
efficiency of common-envelope ejection is necessary to form short-period
LMBHBs.


  We show how to convert an arbitrary stabilizer code into a bipartite quantum
code. A bipartite quantum code is one that involves two senders and one
receiver. The two senders exploit both nonlocal and local quantum resources to
encode quantum information with local encoding circuits. They transmit their
encoded quantum data to a single receiver who then decodes the transmitted
quantum information. The nonlocal resources in a bipartite code are ebits and
nonlocal information qubits and the local resources are ancillas and local
information qubits. The technique of bipartite quantum error correction is
useful in both the quantum communication scenario described above and in
fault-tolerant quantum computation. It has application in fault-tolerant
quantum computation because we can prepare nonlocal resources offline and
exploit local encoding circuits. In particular, we derive an encoding circuit
for a bipartite version of the Steane code that is local and additionally
requires only nearest-neighbor interactions. We have simulated this encoding in
the CNOT extended rectangle with a publicly available fault-tolerant simulation
software. The result is that there is an improvement in the "pseudothreshold"
with respect to the baseline Steane code, under the assumption that quantum
memory errors occur less frequently than quantum gate errors.


  This paper investigates adaptive streaming codes over a three-node relayed
network. In this setting, a source node transmits a sequence of message packets
to a destination through a relay. The source-to-relay and relay-to-destination
links are unreliable and introduce at most $N_1$ and $N_2$ packet erasures,
respectively. The destination node must recover each message packet within a
strict delay constraint $T$. The paper presents achievable streaming codes for
all feasible parameters $\{N_1, N_2, T\}$ that exploit the fact that the relay
naturally observes the erasure pattern occurring in the link from source to
relay, thus it can adapt its relaying strategy based on these observations. In
a recent work, Fong et al. provide streaming codes featuring
channel-state-independent relaying strategies. The codes proposed in this paper
achieve rates higher than the ones proposed by Fong et al. whenever $N_2 >
N_1$, and achieve the same rate when $N_2 = N_1$. The paper also presents an
upper bound on the achievable rate that takes into account erasures in both
links in order to bound the rate in the second link. The upper bound is shown
to be tighter than a trivial bound that considers only the erasures in the
second link.


  Recent results from the Planck satellite combined with earlier observations
from WMAP, ACT, SPT and other experiments eliminate a wide spectrum of more
complex inflationary models and favor models with a single scalar field, as
reported by the Planck Collaboration. More important, though, is that all the
simplest inflaton models are disfavored statistically relative to those with
plateau-like potentials. We discuss how a restriction to plateau-like models
has three independent serious drawbacks: it exacerbates both the initial
conditions problem and the multiverse-unpredictability problem and it creates a
new difficulty that we call the inflationary "unlikeliness problem." Finally,
we comment on problems reconciling inflation with a standard model Higgs, as
suggested by recent LHC results. In sum, we find that recent experimental data
disfavors all the best-motivated inflationary scenarios and introduces new,
serious difficulties that cut to the core of the inflationary paradigm.
Forthcoming searches for B-modes, non-Gaussianity and new particles should be
decisive.


  A construction of Calabi-Yaus as quotients of products of lower-dimensional
spaces in the context of weighted hypersurfaces is discussed, including
desingularisation. The construction leads to Calabi-Yaus which have a fiber
structure, in particular one case has K3 surfaces as fibers. These Calabi-Yaus
are of some interest in connection with Type II -heterotic string dualities in
dimension 4. A section at the end of the paper summarises this for the
non-expert mathematician.


  For several important classes of manifolds acted on by the torus, the
information about the action can be encoded combinatorially by a regular
n-valent graph with vector labels on its edges, which we refer to as the torus
graph. By analogy with the GKM-graphs, we introduce the notion of equivariant
cohomology of a torus graph, and show that it is isomorphic to the face ring of
the associated simplicial poset. This extends a series of previous results on
the equivariant cohomology of torus manifolds. As a primary combinatorial
application, we show that a simplicial poset is Cohen-Macaulay if its face ring
is Cohen-Macaulay. This completes the algebraic characterisation of
Cohen-Macaulay posets initiated by Stanley. We also study blow-ups of torus
graphs and manifolds from both the algebraic and the topological points of
view.


  We report on the observation of terahertz radiation induced photoconductivity
and of terahertz analog of the microwave-induced resistance oscillations (MIRO)
in HgTe-based quantum well (QW) structures of different width. The MIRO-like
effect has been detected in QWs of 20 nm thickness with inverted band structure
and a rather low mobility of about 3 $\times$ 10$^5$ cm$^2$/V s. In a number of
other structures with QW widths ranging from 5 to 20 nm and lower mobility we
observed an unconventional non-oscillatory photoconductivity signal which
changes its sign upon magnetic field increase. This effect was observed in
structures characterized by both normal and inverted band ordering, as well as
in QWs with critical thickness and linear dispersion. In samples having Hall
bar and Corbino geometries an increase of the magnetic field resulted in a
single and double change of the sign of the photoresponse, respectively. We
show that within the bolometric mechanism of the photoresponse these unusual
features imply a non-monotonic behavior of the transport scattering rate, which
should decrease (increase) with temperature for magnetic fields below (above)
the certain value. This behavior is found to be consistent with the results of
dark transport measurements of magnetoresistivity at different sample
temperatures. Our experiments demonstrate that photoconductivity is a very
sensitive probe of the temperature variations of the transport characteristics,
even those that are hardly detectable using standard transport measurements.


  Autonomous navigation in unstructured vegetated environments remains an open
challenge. To successfully operate in these settings, ground vehicles must
assess the traversability of the environment and determine which vegetation is
pliable enough to push through. In this work, we propose a novel method that
combines a high-fidelity and feature-rich 3D voxel representation while
leveraging the structural context and sparseness of SCNN's to assess
Traversability Estimation (TE) in densely vegetated environments. The proposed
method is thoroughly evaluated on an accurately-labeled real-world data set
that we provide to the community. It is shown to outperform state-of-the-art
methods by a significant margin (0.59 vs. 0.39 MCC score at 0.1m voxel
resolution) in challenging scenes and to generalize to unseen environments. In
addition, the method is economical in the amount of training data and training
time required: a model is trained in minutes on a desktop computer. We show
that by exploiting the context of the environment, our method can use different
feature combinations with only limited performance variations. For example, our
approach can be used with lidar-only features, whilst still assessing complex
vegetated environments accurately, which was not demonstrated previously in the
literature in such environments. In addition, we propose an approach to assess
a traversability estimator's sensitivity to information quality and show our
method's sensitivity is low.


  We discuss a new type of Higgs-portal dark matter (DM)-production mechanism,
called bosonic-seesaw portal (BSP) scenario. The BS provides the dynamical
origin of the electroweak symmetry breaking, triggered by mixing between the
elementary Higgs and a composite Higgs generated by a new-color strong
dynamics, hypercolor (HC). At the HC strong coupling scale, the classical-scale
invariance assumed in the model is dynamically broken as well as the "chiral"
symmetry present in the HC sector. In addition to the composite Higgs, HC
baryons emerge to potentially be stable because of the unbroken HC baryon
number symmetry. Hence the lightest HC baryon can be a DM candidate. Of
interest in the present scenario is that HC pions can be as heavy as the HC
baryon due to the possibly enhanced-explicit "chiral"-breaking effect triggered
after the BS mechanism, so the HC baryon pair cannot annihilate into HC pions.
As in the standard setup of freeze-in scenario, it is assumed that the DM was
never in the thermal equilibrium, which ends up with no thermal abundance. It
is then the non-thermal BSP process that crucially comes into the game below
the HC scale: the HC baryon significantly couples to the standard-model Higgs
via the BS mechanism, and can non-thermally be produced from the thermal plasma
below the HC scale, which turns out to allow the TeV mass scale for the
composite baryonic DM, much smaller than the generic bound placed in the
conventional thermal freeze-out scenario, to account for the observed relic
abundance. Thus the DM can closely be related to the mechanism of the
electroweak symmetry breaking.


  We introduce a universal scheme to divide the power output of a periodically
driven quantum heat engine into a classical contribution and one stemming
solely from quantum coherence. Specializing to Lindblad-dynamics and small
driving amplitudes, we derive general upper bounds on both, the coherent and
the total power. These constraints imply that, in the linear-response regime,
coherence inevitably leads to power losses. To illustrate our general analysis,
we explicitly work out the experimentally relevant example of a single-qubit
engine.


  In this paper the relations between the existence of Lagrangian fibration of
Hyper-K\"{a}hler manifolds and the existence of the Large Radius Limit is
established. It is proved that if the the rank of the second homology group of
a Hyper-K\"{a}hler manifold N of complex dimension $2n\geq4$ is at least 5,
then there exists an unipotent element T in the mapping class group $\Gamma
$(N) such that its action on the second cohomology group satisfies
$(T-id)^{2}\neq0$ and $(T-id)^{3}=0.$ A Theorem of Verbitsky implies that the
symmetric power $S^{n}(T)$ acts on $H^{2n}$ and it satisfies $(S^{n}%
(T)-id)^{2n}\neq0$ and $(S^{n}(T)-id)^{2n+1}=0.$ This fact established the
existence of Large Radius Limit for Hyper-K\"{a}hler manifolds for polarized
algebraic Hyper-K\"{a}hler manifolds. Using the theory of vanishing cycles it
is proved that if a Hyper-K\"{a}hler manifold admits a Lagrangian fibration
then the rank of the second homology group is greater than or equal to five. It
is also proved that the fibre of any Lagrangian fibration of a Hyper-K\"{a}hler
manifold is homological to a vanishing invariant $2n$ cycle of a maximal
unipotent element acting on the middle homology. According to Clemens this
vanishing invariant cycle can be realized as a torus. I conjecture that the SYZ
conjecture implies finiteness of the topological types of Hyper-K\"{a}hler
manifolds of fix dimension.


  The Nambu - Jona-Lasinio model in 2+1 dimensions is simulated for non-zero
baryon chemical potential with a diquark source term. No evidence for a BCS
condensate or gap is seen at high density; rather, critical behaviour with
novel exponents is observed, suggesting that 2d superfluidity as first
described by Kosterlitz and Thouless is realised, but with the universality
class determined by the presence of relativistic fermions.