  In this paper we study the derived category of sheaves on the affine
Grassmannian of a complex reductive group G, contructible with respect to the
stratification by G(C[[x]])-orbits. Following ideas of Ginzburg and
Arkhipov-Bezrukavnikov-Ginzburg, we describe this category (and a mixed
version) in terms of coherent sheaves on the nilpotent cone of its Langlands
dual reductive group. We also show, in the mixed case, that restriction to the
nilpotent cone of a Levi subgroup corresponds to hyperbolic localization on
affine Grassmannians.


  The interesting properties of Kagome bands, consisting of Dirac bands and a
flat band, have attracted extensive attention. However, the materials with only
one Kagome band around the Fermi level cannot possess physical properties of
Dirac fermions and strong correlated fermions simultaneously. Here, we propose
a new type of band structure --- double Kagome bands, which can realize
coexistence of the two kinds of fermions. Moreover, the new band structure is
found to exist in a new two-dimensional material, phosphorus carbide P2C3. The
carbide material shows good stability and unusual electronic properties. Strong
magnetism appears in the structure by hole doping of the flat band, which
results in spin splitting of the Dirac bands. The edge states induced by Dirac
and flat bands coexist on the Fermi level, indicating outstanding transport
characteristics. In addition, a possible route to experimentally grow P2C3 on
some suitable substrates such as the Ag (111) surface is also discussed.


  Sausage modes that are axisymmetric fast magnetoacoustic oscillations of
solar coronal loops are characterized by variation of the plasma density and
magnetic field, and hence cause time variations of the electron plasma
frequency and cyclotron frequency. The latter parameters determine the
condition for the double plasma resonance (DPR), which is responsible for the
appearance of zebra-pattern (ZP) structures in time spectra of solar type IV
radio bursts. We perform numerical simulations of standing and propagating
sausage oscillations in a coronal loop modeled as a straight, field-aligned
plasma slab, and determine the time variation of the DPR layer locations.
Instant values of the plasma density and magnetic field at the DPR layers
allowed us to construct skeletons of the time variation of ZP stripes in radio
spectra. In the presence of a sausage oscillation, the ZP structures are shown
to have characteristic wiggles with the time period prescribed by the sausage
oscillation. Standing and propagating sausage oscillations are found to have
different signatures in ZP patterns. We conclude that ZP wiggles can be used
for the detection of short-period sausage oscillations and the exploitation of
their seismological potential.


  The generation of droplets at low Reynolds numbers is driven by non-linear
dynamics that give rise to complex patterns concerning both the
droplet-to-droplet spacing and the individual droplet sizes. Here we
demonstrate an experimental system in which a time-varying energy landscape
provides a periodic magnetic force that generates an array of droplets from an
immiscible mixture of ferrofluid and silicone oil. The resulting droplet
patterns are periodic, owing to the nature of the magnetic force, yet the
droplet spacing and size can vary greatly by tuning a single bias pressure
applied on the ferrofluid phase; for a given cycle period of the magnetic
force, droplets can be generated either at integer multiples (1, 2, etc.), or
at rational fractions (3/2, 5/3, 5/2, etc.) of this period with mono- or
multidisperse droplet sizes. We develop a discrete-time dynamical systems model
not only to reproduce the phenotypes of the observed patterns but also provide
a framework for understanding systems driven by such periodic energy
landscapes.


  In this work we analyze the combined effects of gender, age and academic rank
on the propensity of individual scholars to diversify their scientific
activity. The aspect of research diversification is measured along three main
dimensions, namely its extent and intensity and the cognitive relatedness of
the fields of diversification. We apply two regression models to the dataset of
scientific output of all Italian professors in the sciences over the period
2004-2008. The aim is to understand how personal and organizational traits can
influence individual behaviors in terms of research diversification. Among
other considerations, our findings urge caution in identifying research
diversification as a co-determinant of the gender productivity gap between
males and females.


  DNS over TLS (DoT) and DNS over HTTPS (DoH) promise to improve privacy and
security of DNS by encrypting DNS messages, especially when messages are padded
to a uniform size. Firstly, to demonstrate the limitations of recommended
padding approaches, we present Segram, a novel app fingerprinting attack that
allows adversaries to infer which mobile apps are executed on a device.
Secondly, we record traffic traces of 118 Android apps using 10 different
DoT/DoH resolvers to study the effectiveness of Segram under different
conditions. According to our results, Segram identifies apps with accuracies of
up to 72% with padding in a controlled closed world setting. The effectiveness
of Segram is comparable with state-of-the-art techniques but Segram requires
less computational effort. We release our datasets and code. Thirdly, we study
the prevalence of padding among privacy-focused DoT/DoH resolvers, finding that
up to 81% of our sample fail to enable padding. Our results suggest that
recommended padding approaches are less effective than expected and that
resolver operators are not sufficiently aware about this feature.


  In this work, we seek to exploit the deep structure of multi-modal data to
robustly exploit the group subspace distribution of the information using the
Convolutional Neural Network (CNN) formalism. Upon unfolding the set of
subspaces constituting each data modality, and learning their corresponding
encoders, an optimized integration of the generated inherent information is
carried out to yield a characterization of various classes. Referred to as deep
Multimodal Robust Group Subspace Clustering (DRoGSuRe), this approach is
compared against the independently developed state-of-the-art approach named
Deep Multimodal Subspace Clustering (DMSC). Experiments on different multimodal
datasets show that our approach is competitive and more robust in the presence
of noise.


  This work investigates the impacts of energy-momentum conservation violation
on the configuration of strange stars constraint with gravitational wave (GW)
event GW190814 as well as eight recent observations of compact objects. The GW
echoes from these interesting classes of compact objects are also calculated.
To describe the matter of strange stars, we have used two different equations
of state (EoSs): first an ad-hoc exotic EoS, the stiffer MIT Bag model and next
realistic CFL phase of quark matter EoS. We choose Rastall gravity as a simple
model with energy-momentum conservation violation with a set of model parameter
values. Our results show that this gravity theory permits stable solutions of
strange stars and the resulting structures can foster GW echoes. We illustrate
the implication of the gravity theory and found that the negative values of the
Rastall parameter result in more compact stellar configurations and lower GW
echo frequency. With an increase in the Rastall parameter, both the compactness
of the stellar configurations and echo time decrease. It is worth mentioning
here that with the chosen set of some probable strange star candidates from
observational data and also in light of GW 190814, we have evaluated the radii
of stellar models. Also, the GW echo frequencies associated with strange stars
are found to be in the range of {$\approx 9-27$ kHz} for both cases. {From this
work, it is also inferred that the assumption regarding the equivalence of
Rastall's theory to Einstein's theory is refuted as we have noticed many
deviations in the physical properties of the considered compact stars.


  Learning fine-grained movements is a challenging topic in robotics,
particularly in the context of robotic hands. One specific instance of this
challenge is the acquisition of fingerspelling sign language in robots. In this
paper, we propose an approach for learning dexterous motor imitation from video
examples without additional information. To achieve this, we first build a URDF
model of a robotic hand with a single actuator for each joint. We then leverage
pre-trained deep vision models to extract the 3D pose of the hand from RGB
videos. Next, using state-of-the-art reinforcement learning algorithms for
motion imitation (namely, proximal policy optimization and soft actor-critic),
we train a policy to reproduce the movement extracted from the demonstrations.
We identify the optimal set of hyperparameters for imitation based on a
reference motion. Finally, we demonstrate the generalizability of our approach
by testing it on six different tasks, corresponding to fingerspelled letters.
Our results show that our approach is able to successfully imitate these
fine-grained movements without additional information, highlighting its
potential for real-world applications in robotics.


  We give lower bounds on the complexity of the word problem of certain
non-solvable groups: for a large class of non-solvable infinite groups,
including in particular free groups, Grigorchuk's group and Thompson's groups,
we prove that their word problem is $\mathsf{NC}^1$-hard. For some of these
groups (including Grigorchuk's group and Thompson's groups) we prove that the
compressed word problem (which is equivalent to the circuit evaluation problem)
is $\mathsf{PSPACE}$-complete.


  The abBA collaboration proposes to conduct a comprehensive program of precise
measurements of neutron $\beta$-decay coefficients $a$ (the correlation between
the neutrino momentum and the decay electron momentum), $b$ (the electron
energy spectral distortion term), $A$ (the correlation between the neutron spin
and the decay electron momentum), and $B$ (the correlation between the neutron
spin and the decay neutrino momentum) at a cold neutron beam facility. We have
used a GEANT4-based code to simulate the propagation of decay electrons and
protons in the electromagnetic spectrometer and study the energy and timing
response of a pair of Silicon detectors. We used these results to examine
systematic effects and find the uncertainties with which the physics parameters
$a$, $b$, $A$, and $B$ can be extracted from an over-determined experimental
data set.


  The concordance cosmological model based on cold dark matter makes definitive
predictions for the growth of galaxies in the Universe, which are being
actively studied using numerical simulations. These predictions appear to
contradict the observations of dwarf galaxies. Dwarf dark matter halos are more
numerous and have steeper central density profiles than the observed galaxies.
The first of these small-scale problems, the "missing satellites problem", can
be resolved by accounting for the low efficiency of gas cooling and star
formation in dwarf halos. A newly-discovered class of HyperVelocity Stars will
soon allow us to test another generic prediction of CDM models, the triaxial
shapes of dark matter halos. Measuring the proper motions of HVS will probe the
gravitational potential out to 100 kpc and will constrain the axis ratios and
the orientation of the Galactic halo.


  Jet Flavor Tomography is a powerful tool used to probe the properties of
Quark Gluon Plasma formed in heavy ion collisions at RHIC and LHC. A new Monte
Carlo model of jet quenching developed at Columbia University, CUJET, was
applied to predict the jet flavor and centrality dependence of the nuclear
modification factor $R_{AA}$. The predictions for fragments $f=\pi,D,B,e$,
derived from quenched jet flavors $a=g,u,c,b$ in central and peripheral
collisions at RHIC and LHC, exhibit novel features such as a level crossing
pattern in $R_{AA\rightarrow a\rightarrow f}$ over a broad transverse momentum
range which can test jet-medium dynamics in quark gluon plasmas and help
discriminate between current energy loss models. Furthermore, the inclusion of
running coupling effects seems to change the jet energy dependence of the jet
energy loss to a non trivial constant behavior, with a visible impact on the
predictions for $R_{AA}$.


  Growing robots based on the eversion principle are known for their ability to
extend rapidly, from within, along their longitudinal axis, and, in doing so,
reach deep into hitherto inaccessible, remote spaces. Despite many advantages,
eversion robots also present significant challenges, one of which is
maintaining sensory payload at the tip without restricting the eversion
process. A variety of tip mechanisms has been proposed by the robotics
community, among them rounded caps of relatively complex construction that are
not always compatible with functional hardware, such as sensors or navigation
pouches, integrated with the main eversion structure. Moreover, many tip
designs incorporate rigid materials, reducing the robot's flexibility and
consequent ability to navigate through narrow openings. Here, we address these
shortcomings and propose a design to overcome them: a soft, entirely fabric
based, cylindrical cap that can easily be slipped onto the tip of eversion
robots. Having created a series of caps of different sizes and materials, an
experimental study was conducted to evaluate our new design in terms of four
key aspects: eversion robot made from multiple layers of everting material,
solid objects protruding from the eversion robot, squeezability, and
navigability. In all scenarios, we can show that our soft, flexible cap is
robust in its ability to maintain its position and is capable of transporting
payloads such as a camera across long distances.


  Text-to-video (T2V) synthesis has gained increasing attention in the
community, in which the recently emerged diffusion models (DMs) have
promisingly shown stronger performance than the past approaches. While existing
state-of-the-art DMs are competent to achieve high-resolution video generation,
they may largely suffer from key limitations (e.g., action occurrence
disorders, crude video motions) with respect to the intricate temporal dynamics
modeling, one of the crux of video synthesis. In this work, we investigate
strengthening the awareness of video dynamics for DMs, for high-quality T2V
generation. Inspired by human intuition, we design an innovative dynamic scene
manager (dubbed as Dysen) module, which includes (step-1) extracting from input
text the key actions with proper time-order arrangement, (step-2) transforming
the action schedules into the dynamic scene graph (DSG) representations, and
(step-3) enriching the scenes in the DSG with sufficient and reasonable
details. Taking advantage of the existing powerful LLMs (e.g., ChatGPT) via
in-context learning, Dysen realizes (nearly) human-level temporal dynamics
understanding. Finally, the resulting video DSG with rich action scene details
is encoded as fine-grained spatio-temporal features, integrated into the
backbone T2V DM for video generating. Experiments on popular T2V datasets
suggest that our Dysen-VDM consistently outperforms prior arts with significant
margins, especially in scenarios with complex actions. Codes at
https://haofei.vip/Dysen-VDM


  In this work, we prove several relations between three different energy
minimization techniques. A recently proposed methods for determining a provably
optimal partial assignment of variables by Ivan Kovtun (IK), the linear
programming relaxation approach (LP) and the popular expansion move algorithm
by Yuri Boykov. We propose a novel sufficient condition of optimal partial
assignment, which is based on LP relaxation and called LP-autarky. We show that
methods of Kovtun, which build auxiliary submodular problems, fulfill this
sufficient condition. The following link is thus established: LP relaxation
cannot be tightened by IK. For non-submodular problems this is a non-trivial
result. In the case of two labels, LP relaxation provides optimal partial
assignment, known as persistency, which, as we show, dominates IK. Relating IK
with expansion move, we show that the set of fixed points of expansion move
with any "truncation" rule for the initial problem and the problem restricted
by one-vs-all method of IK would coincide -- i.e. expansion move cannot be
improved by this method. In the case of two labels, expansion move with a
particular truncation rule coincide with one-vs-all method.


  The grokking phenomenon as reported by Power et al. ( arXiv:2201.02177 )
refers to a regime where a long period of overfitting is followed by a
seemingly sudden transition to perfect generalization. In this paper, we
attempt to reveal the underpinnings of Grokking via a series of empirical
studies. Specifically, we uncover an optimization anomaly plaguing adaptive
optimizers at extremely late stages of training, referred to as the Slingshot
Mechanism. A prominent artifact of the Slingshot Mechanism can be measured by
the cyclic phase transitions between stable and unstable training regimes, and
can be easily monitored by the cyclic behavior of the norm of the last layers
weights. We empirically observe that without explicit regularization, Grokking
as reported in ( arXiv:2201.02177 ) almost exclusively happens at the onset of
Slingshots, and is absent without it. While common and easily reproduced in
more general settings, the Slingshot Mechanism does not follow from any known
optimization theories that we are aware of, and can be easily overlooked
without an in depth examination. Our work points to a surprising and useful
inductive bias of adaptive gradient optimizers at late stages of training,
calling for a revised theoretical analysis of their origin.


  We study multi-player general-sum Markov games with one of the players
designated as the leader and the other players regarded as followers. In
particular, we focus on the class of games where the followers are myopic,
i.e., they aim to maximize their instantaneous rewards. For such a game, our
goal is to find a Stackelberg-Nash equilibrium (SNE), which is a policy pair
$(\pi^*, \nu^*)$ such that (i) $\pi^*$ is the optimal policy for the leader
when the followers always play their best response, and (ii) $\nu^*$ is the
best response policy of the followers, which is a Nash equilibrium of the
followers' game induced by $\pi^*$. We develop sample-efficient reinforcement
learning (RL) algorithms for solving for an SNE in both online and offline
settings. Our algorithms are optimistic and pessimistic variants of
least-squares value iteration, and they are readily able to incorporate
function approximation tools in the setting of large state spaces. Furthermore,
for the case with linear function approximation, we prove that our algorithms
achieve sublinear regret and suboptimality under online and offline setups
respectively. To the best of our knowledge, we establish the first provably
efficient RL algorithms for solving for SNEs in general-sum Markov games with
myopic followers.


  Distributed point charge models (DCM) and their minimal variants (MDCM) have
been integrated with tools widely used for condensed-phase simulations,
including a virial-based barostat and a slow-growth algorithm for thermodynamic
integration. Minimal DCM is further developed with a systematic approach to
reduce fitting errors in the electrostatic interaction energy and a new
fragment-based approach offers considerable speedup of the MDCM fitting process
for larger molecules with increased numbers of off-centered charged sites.
Finally, polarizable (M)DCM is also introduced in the present work. The
developments are used in condensed-phase simulations of popular force fields
with commonly applied simulation conditions. (M)DCM equivalents for a range of
widely used water force fields and for fluorobenzene (PhF) are developed and
applied along with the original models to evaluate the impact of reformulating
the electrostatic term. Comparisons of the molecular electrostatic potential
(MEP), electrostatic interaction energies, and bulk properties from molecular
dynamics simulations for a range of models from simple TIP$n$P ($n = 3-5$) to
the polarizable, multipolar iAMOEBA models for water and an existing
quadrupolar model for PhF confirm that DCMs retain the accuracy of the original
models, providing a homogeneous, efficient, and generic point charge
alternative to a multipolar electrostatic model for force field development and
multilevel simulations.


  In the field of face recognition, it is always a hot research topic to
improve the loss solution to make the face features extracted by the network
have greater discriminative power. Research works in recent years has improved
the discriminative power of the face model by normalizing softmax to the cosine
space step by step and then adding a fixed penalty margin to reduce the
intra-class distance to increase the inter-class distance. Although a great
deal of previous work has been done to optimize the boundary penalty to improve
the discriminative power of the model, adding a fixed margin penalty to the
depth feature and the corresponding weight is not consistent with the pattern
of data in the real scenario. To address this issue, in this paper, we propose
a novel loss function, InterFace, releasing the constraint of adding a margin
penalty only between the depth feature and the corresponding weight to push the
separability of classes by adding corresponding margin penalties between the
depth features and all weights. To illustrate the advantages of InterFace over
a fixed penalty margin, we explained geometrically and comparisons on a set of
mainstream benchmarks. From a wider perspective, our InterFace has advanced the
state-of-the-art face recognition performance on five out of thirteen
mainstream benchmarks. All training codes, pre-trained models, and training
logs, are publicly released
\footnote{$https://github.com/iamsangmeng/InterFace$}.


  Distributed optimization is manifesting great potential in multiple fields,
e.g., machine learning, control, and resource allocation. Existing
decentralized optimization algorithms require sharing explicit state
information among the agents, which raises the risk of private information
leakage. To ensure privacy security, combining information security mechanisms,
such as differential privacy and homomorphic encryption, with traditional
decentralized optimization algorithms is a commonly used means. However, this
would either sacrifice optimization accuracy or incur heavy computational
burden. To overcome these shortcomings, we develop a novel privacy-preserving
decentralized optimization algorithm, called PPSD, that combines gradient
tracking with a state decomposition mechanism. Specifically, each agent
decomposes its state associated with the gradient into two substates. One
substate is used for interaction with neighboring agents, and the other
substate containing private information acts only on the first substate and
thus is entirely agnostic to other agents. For the strongly convex and smooth
objective functions, PPSD attains a $R$-linear convergence rate. Moreover, the
algorithm can preserve the agents' private information from being leaked to
honest-but-curious neighbors. Simulations further confirm the results.


  There is a wealth of data on air pollution within several users' reach,
including modelled concentrations and depositions as well as observations from
air quality stations. However, data integration to perceive spatial and
temporal trends at the national level is a complex undertaking. The
difficulties are mainly related to the data sources (many files with a lot of
information and in different formats). In addition, the processing of this data
is time-consuming and impractical when the time period under analysis
increases. Furthermore,the processing of spatial-temporal data requires the use
of multiple specific tools, such as geographic information systems software and
statistical, which are not readily accessible to non-specialised users. The
proposed solution is to develop libraries that are responsible for aggregating
different types of data related with pollution. In addition to allowing the
integration of different data, the libraries are also the basis for developing
web applications. The libraries allow the collection of data made available by
the Portuguese Environment Agency (APA) and official modelling results for
Europe. The applications developed will extend the libraries to allow data
processing and representation through Dashboards. These Dashboards provide
access to non-specialised users, namely regarding the trends of pollutants in
each region. The implemented libraries allow the development of projects that
would need access to the same data sources. These Dashboards allow for
simplified access to data and for studies that have so far been beyond the
reach of researchers.


  We calculate the interference correction to the conductivity of doped
transition metal dichalcogenide (TMDC) monolayers. Because of the interplay
between valley structure and intrinsic spin-orbit coupling (SOC), these
materials exhibit a rich weak localization (WL) behavior that is qualitatively
different from conventional metals or similar two-dimensional materials such as
graphene. Our results can also be used to describe graphene/TMDC
heterostructures, where the SOC is induced in the graphene sheet. We discuss
new parameter regimes that go beyond existing theories, and can be used to
interpret recent experiments in order to assess the strength of SOC and
disorder. Furthermore, we show that an in-plane Zeeman field can be used to
distinguish the contributions of different kinds of SOC to the WL
magnetoconductance.


  We present a large spectroscopic campaign with Keck/MOSFIRE targeting
Lyman-alpha emission (Ly$\alpha$) from intrinsically faint Lyman-break Galaxies
(LBGs) behind 12 efficient galaxy cluster lenses. Gravitational lensing allows
us to probe the more abundant faint galaxy population to sensitive Ly$\alpha$
equivalent width limits. During the campaign we targeted 70 LBG candidates with
MOSFIRE Y-band, selected photometrically to cover Ly$\alpha$ over the range
$7<z<8.2$. We detect $S/N>5$ emission lines in 2 of these galaxies and find
that they are likely Ly$\alpha$ at $z=7.148\pm0.001$ and $z=7.161\pm0.001$. We
present new lens models for 4 of the galaxy clusters, using our previously
published lens models for the remaining clusters to determine the magnification
factors for the source galaxies. Using a Bayesian framework that employs large
scale reionization simulations of the intergalactic medium (IGM) as well as
realistic properties of the interstellar medium and circumgalactic medium, we
infer the volume-averaged neutral hydrogen fraction,
$\overline{x}_{\mathrm{HI}}$, in the IGM during reionization to be
$\overline{x}_{\mathrm{HI}}=0.88^{+0.05}_{-0.10}$ at $z=7.6\pm0.6$. Our result
is consistent with a late and rapid reionization scenario inferred by Planck.


  In this paper, we write down the separable Werner state in a two-qubit system
explicitly as a convex combination of product states, which is different from
the convex combination obtained by Wootters' method. The Werner state in a
two-qubit system has a single real parameter and varies from inseparable state
to separable state according to the value of its parameter. We derive a hidden
variable model that is induced by our decomposed form for the separable Werner
state. From our explicit form of the convex combination of product states, we
understand the following: The critical point of the parameter for separability
of the Werner state comes from positivity of local density operators of the
qubits.


  "This study provides a modified Bass model to deal with trend curves for
basic issues of relevance to individuals from all over the world, for which we
collected 16 data sets from 2004 to 2022 and that are available on Google
servers as "google trends". It was discovered that the Bass model did not
forecast well for curves that have a mono peak with a sharp decrease to some
level then have semi-stable with small decrement sales for a long time, thus a
new parameter based on r1 and r2 (ratios of average sales) was introduced,
which improved the model's prediction ability and provided better results. The
model was also applied to a data set taken from the Kaggle website about a
subscriber digital product offering for financial services that include
newsletters, webinars, and investment recommendations. The data contain 508932
data points about the products sold during 2016-2022. Compared to the
traditional Bass model, the modified model showed better results in dealing
with this condition, as the expected curve shape was closer to real sales, and
the sum of squares error (SSE) value was reduced to a ratio ranging between
(36.35-79.3%). Therefore, the improved model can be relied upon in these
conditions."


  We define the virtual bridge number $vb(K)$ and the virtual unknotting number
$vu(K)$ invariants for virtual knots. For ordinary knots $K$ they are closely
related to the bridge number $b(K)$ and the unknotting number $u(K)$ and we
have $vu(K)\leq u(K), vb(K)\leq b(K).$
  There are no ordinary knots $K$ with $b(K)=1.$ We show there are infinitely
many homotopy classes of virtual knots each of which contains infinitely many
isotopy classes of $K$ with $vb(K)=1.$ In fact for each $i\in \N$ there exists
$K$ virtually homotopic (but not virtually isotopic) to the unknot with
$vb(K)=1$ and $vu(K)=i.$


  We study generic matter coupled to a $D$-dimensional supergravity using a
formulation of Double Field Theory (DFT), where all the fields are encoded in
O$(D,D)$ multiplets. We study both the case when the matter comes from a
variational principle, as well as the case where the matter comes from a
statistical or thermodynamic approach. For the latter, we construct the
distribution function for the perfect fluid and its entropy current, which is a
conserved quantity. We then include general viscous and elastic terms in the
generalized energy-momentum tensor which, in the general case, lead to entropy
production. We consistently deform the conservation law of the generalized
entropy current and identify a particular non-dissipative deformation. Using
the generalized fluid model, we revisit the issue of non-covariance of perfect
fluids under T-dualities and we show how to resolve it in our DFT model with
matter.


  We consider the Schrodinger equation on a compact manifold, in the presence
of a nonlinear damping term, which is homogeneous and sublinear. For initial
data in the energy space, we construct a weak solution, defined for all
positive time, which is shown to be unique. In the one-dimensional case, we
show that it becomes zero in finite time. In the two and three-dimensional
cases, we prove the same result under the assumption of extra regularity on the
initial datum.


  A microscopic theory of the electrical conductivity $\sigma(\omega)$ within
the t-J model is developed. An exact representation for $\sigma(\omega)$ is
obtained using the memory-function technique for the relaxation function in
terms of the Hubbard operators, and the generalized Drude law is derived. The
relaxation rate due to the decay of charge excitations into particle-hole pairs
assisted by antiferromagnetic spin fluctuations is calculated in the
mode-coupling approximation. Using results for the spectral function of spin
excitations calculated previously, the relaxation rate and the optical and dc
conductivities are calculated in a broad region of doping and temperatures. The
reasonable agreement of the theory with experimental data for cuprates proves
the important role of spin-fluctuation scattering in the charge dynamics.


  In the rapidly evolving landscape of developer communities, Q&A platforms
serve as crucial resources for crowdsourcing developers' knowledge. A notable
trend is the increasing use of images to convey complex queries more
effectively. However, the current state-of-the-art method of duplicate question
detection has not kept pace with this shift, which predominantly concentrates
on text-based analysis. Inspired by advancements in image processing and
numerous studies in software engineering illustrating the promising future of
image-based communication on social coding platforms, we delved into
image-based techniques for identifying duplicate questions on Stack Overflow.
When focusing solely on text analysis of Stack Overflow questions and omitting
the use of images, our automated models overlook a significant aspect of the
question. Previous research has demonstrated the complementary nature of images
to text. To address this, we implemented two methods of image analysis: first,
integrating the text from images into the question text, and second, evaluating
the images based on their visual content using image captions. After a rigorous
evaluation of our model, it became evident that the efficiency improvements
achieved were relatively modest, approximately an average of 1%. This marginal
enhancement falls short of what could be deemed a substantial impact. As an
encouraging aspect, our work lays the foundation for easy replication and
hypothesis validation, allowing future research to build upon our approach.


  A two-valued fitness landscape is introduced for the classical Eigen's
quasispecies model. This fitness landscape can be considered as a direct
generalization of the so-called single or sharply peaked landscape. A general,
non permutation invariant quasispecies model is studied, therefore the
dimension of the problem is $2^N\times 2^N$, where $N$ is the sequence length.
It is shown that if the fitness function is equal to $w+s$ on a $G$-orbit $A$
and is equal to $w$ elsewhere, then the mean population fitness can be found as
the largest root of an algebraic equation of degree at most $N+1$. Here $G$ is
an arbitrary isometry group acting on the metric space of sequences of zeroes
and ones of the length $N$ with the Hamming distance. An explicit form of this
exact algebraic equation is given in terms of the spherical growth function of
the $G$-orbit $A$. Sufficient conditions for the so-called error threshold for
sequences of orbits are given. Motivated by the analysis of the two-valued
fitness landscapes an abstract generalization of Eigen's model is introduced
such that the sequences are identified with the points of a finite metric space
$X$ together with a group of isometries acting transitively on $X$. In
particular, a simplicial analogue of the original quasispecies model is
discussed, which can be considered as a mathematical model of the switching of
the antigenic variants for some bacteria.


  Subset selection, which aims to select a subset from a ground set to maximize
some objective function, arises in various applications such as influence
maximization and sensor placement. In real-world scenarios, however, one often
needs to find a subset which is robust against (i.e., is good over) a number of
possible objective functions due to uncertainty, resulting in the problem of
robust subset selection. This paper considers robust subset selection with
monotone objective functions, relaxing the submodular property required by
previous studies. We first show that the greedy algorithm can obtain an
approximation ratio of $1-e^{-\beta\gamma}$, where $\beta$ and $\gamma$ are the
correlation and submodularity ratios of the objective functions, respectively;
and then propose EPORSS, an evolutionary Pareto optimization algorithm that can
utilize more time to find better subsets. We prove that EPORSS can also be
theoretically grounded, achieving a similar approximation guarantee to the
greedy algorithm. In addition, we derive the lower bound of $\beta$ for the
application of robust influence maximization, and further conduct experiments
to validate the performance of the greedy algorithm and EPORSS.


  We study the theory $T_{m,n}$ of existentially closed incidence structures
omitting the complete incidence structure $K_{m,n}$, which can also be viewed
as existentially closed $K_{m,n}$-free bipartite graphs. In the case $m = n =
2$, this is the theory of existentially closed projective planes. We give an
$\forall\exists$-axiomatization of $T_{m,n}$, show that $T_{m,n}$ does not have
a countable saturated model when $m,n\geq 2$, and show that the existence of a
prime model for $T_{2,2}$ is equivalent to a longstanding open question about
finite projective planes. Finally, we analyze model theoretic notions of
complexity for $T_{m,n}$. We show that $T_{m,n}$ is NSOP$_1$, but not simple
when $m,n\geq 2$, and we show that $T_{m,n}$ has weak elimination of
imaginaries but not full elimination of imaginaries. These results rely on
combinatorial characterizations of various notions of independence, including
algebraic independence, Kim independence, and forking independence.


  The quantization of the electromagnetic field in lossy and dispersive
dielectric media has been widely studied during the last few decades. However,
several aspects of energy transfer and its relation to consistently defining
position-dependent ladder operators for the electromagnetic field in
nonequilibrium conditions have partly escaped the attention. In this work we
define the position-dependent ladder operators and an effective local
photon-number operator that are consistent with the canonical commutation
relations and use these concepts to describe the energy transfer and thermal
balance in layered geometries. This approach results in a position-dependent
photon-number concept that is simple and consistent with classical energy
conservation arguments. The operators are formed by first calculating the
vector potential operator using Green's function formalism and Langevin noise
source operators related to the medium and its temperature, and then defining
the corresponding position-dependent annihilation operator that is required to
satisfy the canonical commutation relations in arbitrary geometry. Our results
suggest that the effective photon number associated with the electric field is
generally position dependent and enables a straightforward method to calculate
the energy transfer rate between the field and the local medium. In particular,
our results predict that the effective photon number in a vacuum cavity formed
between two lossy material layers can oscillate as a function of the position
suggesting that also the local field temperature oscillates. These oscillations
are expected to be directly observable using relatively straightforward
experimental setups in which the field-matter interaction is dominated by the
coupling to the electric field.


  The coherent oscillations of mobile charge carriers near the surface of good
conductors-surface plasmons-are been exploited in many applications in
information technologies, clean energy, high-density data storage,
photovoltaics, chemistry, biology, medicine and security. Light can be coupled
to surface plasmons and trapped near the interface between a metal and an
adjacent material. This leads to the nanoscale confinement of light, impossible
by any other means, and a related electromagnetic field enhancement.
Microscopic electron dynamic effects associated with surface plasmons are
capable of significantly influencing physical and chemical processes near a
conductor surface, not only as a result of the high electric fields, but also
via the excitation of energetic charge carriers: holes below Fermi level or
electrons above it. When remaining inside plasmonic media, these so-called hot
carriers result in nonlinear, Kerr-type, optical effects important for
controlling light with light. They can also transfer into the surroundings of
the nanostructures, resulting in photocurrent, or they can interact with
adjacent molecules and materials, inducing photochemical transformations.
Understanding the dynamics of hot carriers and related effects in plasmonic
nanostructures is essential for the development of ultrafast detectors and
nonlinear optical components, broadband photocatalysis, enhanced nanoscale
optoelectronic devices, nanoscale and ultrafast temperature control, and other
technologies of tomorrow. This review will discuss the basics of
plasmonically-engendered hot electrons, theoretical descriptions and
experimental methods to study them, and describe prototypical processes and
examples of the most promising applications of hot-electron processes at the
metal interfaces.


  Copulas. We study the model risk of multivariate risk models in a
comprehensive empirical study on Copula-GARCH models used for forecasting
Value-at-Risk and Expected Shortfall. To determine whether model risk inherent
in the forecasting of portfolio risk is caused by the candidate marginal or
copula models, we analyze different groups of models in which we fix either the
marginals, the copula, or neither. Model risk is economically significant, is
especially high during periods of crisis, and is almost completely due to the
choice of the copula. We then propose the use of the model confidence set
procedure to narrow down the set of available models and reduce model risk for
Copula-GARCH risk models. Our proposed approach leads to a significant
improvement in the mean absolute deviation of one day ahead forecasts by our
various candidate risk models.


  The present work aims to explore the model given by Lanczos-Lovelock gravity
theories indexed by a fixed integer to require a unique anti-de Sitter vacuum,
dressed by a scalar field non-minimal coupling. For this model, we add a
special matter source characterized by a non-linear Maxwell field coupling with
a function depending on the scalar field. Computing its thermodynamics
parameters by using the Euclidean action, we obtain interesting and non zero
thermodynamical quantities, unlike its original version, allowing analyzing
thermodynamical stability. Together with the above, we found that these
solutions satisfy the First Law of Thermodynamics as well as a Smarr relation.


  Sterile neutrinos with keV-MeV masses and non-zero transition magnetic
moments can be probed through low-energy nuclear or electron recoil
measurements. Here we determine the sensitivities of current and future
searches, showing how they can probe a previously unexplored parameter region.
Future coherent elastic neutrino-nucleus scattering (CE$\nu$NS) or elastic
neutrino-electron scattering (E$\nu$ES) experiments using a monochromatic
$^{51}$Cr source can fully probe the region indicated by the recent XENON1T
excess.


  The low-lying eigenstates of a system of two electrons confined within a
two-dimensional quantum dot with a hard polygonal boundary are obtained by
means of exact diagonalization. The transition from a weakly correlated charge
distribution for small dots to a strongly correlated "Wigner molecule" for
large dots is studied, and the behaviour at the crossover is determined. In
sufficiently large dots, a recently proposed mapping to an effective
charge-spin model is investigated, and is found to produce the correct ordering
of the energy levels and to give a good first approximation to the size of the
level spacings. We conclude that this approach is a valuable method to obtain
the low energy spectrum of few-electron quantum dots.


  We propose a simple method for the deterministic generation of an arbitrary
continuous quantum state of the center-of-mass of an atom. The method's spatial
resolution gradually increases with the interaction time with no apparent
fundamental limitations. Such de-Broglie Wave-Front Engineering of the atomic
density can find applications in Atom Lithography, and we discuss possible
implementations of our scheme in atomic beam experiments.


  One of the major discoveries of Hinode's Extreme-ultraviolet Imaging
Spectrometer (EIS) is the presence of upflows at the edges of active regions.
As active regions are magnetically connected to the large-scale field of the
corona, these upflows are a likely contributor to the global mass cycle in the
corona. Here we examine the driving mechanism(s) of the very strong upflows
with velocities in excess of 70 km/s, known as blue-wing asymmetries, observed
during the eruption of a flux rope in AR 10977 (eruptive flare
SOL2007-12-07T04:50). We use Hinode/EIS spectroscopic observations combined
with magnetic-field modeling to investigate the possible link between the
magnetic topology of the active region and the strong upflows. A Potential
Field Source Surface (PFSS) extrapolation of the large-scale field shows a
quadrupolar configuration with a separator lying above the flux rope. Field
lines formed by induced reconnection along the separator before and during the
flux-rope eruption are spatially linked to the strongest blue-wing asymmetries
in the upflow regions. The flows are driven by the pressure gradient created
when the dense and hot arcade loops of the active region reconnect with the
extended and tenuous loops overlying it. In view of the fact that separator
reconnection is a specific form of the more general quasi-separatrix (QSL)
reconnection, we conclude that the mechanism driving the strongest upflows is,
in fact, the same as the one driving the persistent upflows of approx. 10 - 20
km/s observed in all active regions.


  Rowmotion is an invertible operator on the order ideals of a poset which has
been extensively studied and is well understood for the rectangle poset. In
this paper, we show that rowmotion is equivariant with respect to a bijection
of Hamaker, Patrias, Pechenik and Williams between order ideals of rectangle
and trapezoid posets, thereby affirming a conjecture of Hopkins that the
rectangle and trapezoid posets have the same rowmotion orbit structures. Our
main tools in proving this are $K$-jeu-de-taquin and (weak) $K$-Knuth
equivalence of increasing tableaux. We define $almost$ $minimal$ $tableaux$ as
a family of tableaux naturally arising from order ideals and show for any
$\lambda$, the almost minimal tableaux of shape $\lambda$ are in different
(weak) $K$-Knuth equivalence classes. We also discuss and make some progress on
related conjectures of Hopkins on down-degree homomesy.


  Operadic tangent cohomology generalizes the existing theories of Harrison
cohomology, Chevalley--Eilenberg cohomology and Hochschild cohomology. These
are usually non-trivial to compute. We complement the existing computational
techniques by producing a spectral sequence that converges to the operadic
tangent cohomology of a fixed algebra. Our main technical tool is that of
filtrations arising from towers of cofibrations of algebras, which play the
same role cell attaching maps and skeletal filtrations do for topological
spaces.
  As an application, we consider the rational Adams--Hilton construction on
topological spaces, where our spectral sequence gives rise to a seemingly new
and completely algebraic description of the Serre spectral sequence, which we
also show is multiplicative and converges to the Chas--Sullivan loop product.
Finally, we consider relative Sullivan--de Rham models of a fibration $p$,
where our spectral sequence converges to the rational homotopy groups of the
identity component of the space of self-fiber homotopy equivalences of $p$.


  We report on the automation of a technique to prove the correctness of
program transformations in higher-order program calculi which may permit
recursive let-bindings as they occur in functional programming languages. A
program transformation is correct if it preserves the observational semantics
of programs. In our LRSX Tool the so-called diagram method is automated by
combining unification, matching, and reasoning on alpha-renamings on the
higher-order meta-language, and automating induction proofs via an encoding
into termination problems of term rewrite systems. We explain the techniques,
we illustrate the usage of the tool, and we report on experiments.


  We study the problem of high-dimensional Principal Component Analysis (PCA)
with missing observations. In simple, homogeneous missingness settings with a
noise level of constant order, we show that an existing inverse-probability
weighted (IPW) estimator of the leading principal components can (nearly)
attain the minimax optimal rate of convergence. However, deeper investigation
reveals both that, particularly in more realistic settings where the
missingness mechanism is heterogeneous, the empirical performance of the IPW
estimator can be unsatisfactory, and moreover that, in the noiseless case, it
fails to provide exact recovery of the principal components. Our main
contribution, then, is to introduce a new method for high-dimensional PCA,
called `primePCA', that is designed to cope with situations where observations
may be missing in a heterogeneous manner. Starting from the IPW estimator,
primePCA iteratively projects the observed entries of the data matrix onto the
column space of our current estimate to impute the missing entries, and then
updates our estimate by computing the leading right singular space of the
imputed data matrix. It turns out that the interaction between the
heterogeneity of missingness and the low-dimensional structure is crucial in
determining the feasibility of the problem. We therefore introduce an
incoherence condition on the principal components and prove that in the
noiseless case, the error of primePCA converges to zero at a geometric rate
when the signal strength is not too small. An important feature of our
theoretical guarantees is that they depend on average, as opposed to
worst-case, properties of the missingness mechanism. Our numerical studies on
both simulated and real data reveal that primePCA exhibits very encouraging
performance across a wide range of scenarios.


  We review observational evidence for a matter-antimatter asymmetry in the
early universe, which leads to the remnant matter density we observe today. We
also discuss observational bounds on the presence of antimatter in the present
day universe, including the possibility of a large lepton asymmetry in the
cosmic neutrino background. We briefly review the theoretical framework within
which baryogenesis, the dynamical generation of a matter-antimatter asymmetry,
can occur. As an example, we discuss a testable minimal model that
simultaneously explains the baryon asymmetry of the universe, neutrino
oscillations and dark matter.


  The superfluidity and Bose-Einstein condensation of indirect excitons in
two-dimensional quantum dot are studied by path-integral Monte Carlo
simulations. The temperature dependence of superfluid and bose-condensed
fraction are calculated at different strengths of interaction. Using the
Kosterlitz-Thouless recursion relations, we also predict behavior of superfluid
fraction in macroscopic large systems.


  The presence of thermal gradients in alloys often leads to non-uniformity in
concentration profiles, which can induce the thermomigration of microstructural
features such as precipitates. To investigate such microstructural changes, we
present a phase-field model that incorporates coupling between concentration
and thermal gradients. First, we simulated the evolution of non-uniform
concentration profiles in the single-phase regions of Fe-C and Fe-N alloy
systems due to imposed thermal gradients. To validate our model with the
classical experiments performed by Darken and Oriani, we studied the evolution
of spatially varying concentration profiles where thermal gradients encompass
single-phase and two-phase regions. We developed a parameterized thermodynamic
description of the two-phase region of a binary alloy to systematically study
the effect of interactions between chemically-driven and thermal
gradient-driven diffusion of solute on the evolution of precipitates. Our
simulations show how thermal gradient, precipitate size, and interparticle
distance influence the migration and associated morphological changes of
precipitates. The composition profiles and migration rates obtained from
single-particle simulations show an exact match with our analytical model. We
use twoparticle simulations to show conditions under which thermomigration
induces the growth of the smaller particle and shrinkage of the larger one in
contrast to the isothermal Ostwald ripening behavior. Our multiparticle
simulations show similar behavior during coarsening. Moreover, in the presence
of a thermal gradient, there is a shift in the center of mass of the
precipitates towards the high-temperature region. Thus, our study offers new
insights into the phenomena of microstructure evolution in the presence of
thermal gradient.


  We test and present the application of the full rescaling method by Angulo &
White (2010) to change the cosmology of halo catalogues in numerical
simulations for cosmological parameter search using semi-analytic galaxy
properties. We show that a reduced form of the method can be applied in small
simulations with box side of ~50/h Mpc. We perform statistical tests on the
accuracy of the properties of rescaled individual haloes, and also on the
rescaled population as a whole. We find that individual positions and
velocities are recovered with almost no detectable biases. The dispersion in
the recovered halo mass does not seem to depend on the resolution of the
simulation. Regardless of the halo mass, the individual accretion histories,
spin parameter evolution and fraction of mass in substructures are well
recovered. The mass of rescaled haloes can be underestimated (overestimated)
for negative (positive) variations of either sigma_8 or Omega_m, in a way that
does not depend on the halo mass. Statistics of abundances and correlation
functions of haloes show also small biases of <10 percent when moving away from
the base simulation by up to 2 times the uncertainty in the WMAP7 cosmological
parameters. The merger tree properties related to the final galaxy population
in haloes also show small biases; the time since the last major merger, the
assembly time-scale, and a time-scale related to the stellar ages show
correlated biases which indicate that the spectral shapes of galaxies would
only be affected by global age changes of ~150 Myr. We show some of these
biases for different separations in the cosmological parameters with respect to
the desired cosmology so that these can be used to estimate the expected
accuracy of the resulting halo population. We also present a way to construct
grids of simulations to provide stable accuracy across the Omega_m vs sigma_8
parameter space.


  The goal of this work is to train effective representations for keyword
spotting via metric learning. Most existing works address keyword spotting as a
closed-set classification problem, where both target and non-target keywords
are predefined. Therefore, prevailing classifier-based keyword spotting systems
perform poorly on non-target sounds which are unseen during the training stage,
causing high false alarm rates in real-world scenarios. In reality, keyword
spotting is a detection problem where predefined target keywords are detected
from a variety of unknown sounds. This shares many similarities to metric
learning problems in that the unseen and unknown non-target sounds must be
clearly differentiated from the target keywords. However, a key difference is
that the target keywords are known and predefined. To this end, we propose a
new method based on metric learning that maximises the distance between target
and non-target keywords, but also learns per-class weights for target keywords
\`a la classification objectives. Experiments on the Google Speech Commands
dataset show that our method significantly reduces false alarms to unseen
non-target keywords, while maintaining the overall classification accuracy.


  We consider the Dirac equation for the classical spinor field placed in an
external, time-dependent electromagnetic field of the form typical for
scattering settings:
$F=F^\mathrm{ret}+F^\mathrm{in}=F^\mathrm{adv}+F^\mathrm{out}$, where the
current producing $F^{\mathrm{ret}/\mathrm{adv}}$ has past and future
asymptotes homogeneous of degree $-3$, and the free fields
$F^{\mathrm{in}/\mathrm{out}}$ are radiation fields produced by currents with
similar asymptotic behavior. We show the existence of the electromagnetic
gauges in which the particle has 'in' and 'out' asymptotic states approaching
free field states, with no long-time corrections of the free dynamics. Using a
special Cauchy foliation of the spacetime we show in this context the existence
and asymptotic completeness of the wave operators. Moreover, we define a
special 'evolution picture' in which the free evolution operator has
well-defined limits for $t\to\pm\infty$, thus the scattering wave operators do
not need the free evolution counteraction.


  Brain tumor classification is a challenging task in medical image analysis.
In this paper, we propose a novel approach to brain tumor classification using
a vision transformer with a novel cross-attention mechanism. Our approach
leverages the strengths of transformers in modeling long-range dependencies and
multi-scale feature fusion. We introduce two new mechanisms to improve the
performance of the cross-attention fusion module: Feature Calibration Mechanism
(FCM) and Selective Cross-Attention (SCA). FCM calibrates the features from
different branches to make them more compatible, while SCA selectively attends
to the most informative features. Our experiments demonstrate that the proposed
approach outperforms other state-of-the-art methods in brain tumor
classification, achieving improved accuracy and efficiency. The proposed FCM
and SCA mechanisms can be easily integrated into other vision transformer
architectures, making them a promising direction for future research in medical
image analysis. Experimental results confirm that our approach surpasses
existing methods, achieving state-of-the-art performance in brain tumor
classification tasks.


  We analyze the temporal variation of the diurnal anisotropy of sub-TeV cosmic
ray intensity observed with the Matsushiro (Japan) underground muon detector
over two full solar activity cycles in 1985-2008. The average sidereal
amplitude over the entire period is 0.034+-0.003 %, which is roughly one third
of the amplitude reported from AS and deep-underground muon experiments
monitoring multi-TeV GCR intensity suggesting a significant attenuation of the
anisotropy due to the solar modulation. We find, on the other hand, only weak
correlations either with the solar activity- or magnetic-cycles. We examine the
temporal variation of the "single-band valley depth" (SBVD) quoted by the
Milagro experiment and, by contrast with recent Milagro reports, we find no
steady increase in the Matsushiro observations in a 7-year period between 2000
and 2007. We suggest, therefore, that the steady increase of the SBVD reported
by the Milagro experiment is not caused by the decreasing solar modulation in
the declining phase of the 23rd solar activity cycle.


  Atomic-level imperfections play an increasingly critical role in nanophotonic
device performance. However, it remains challenging to accurately characterize
the sidewall roughness with sub-nanometer resolution and directly correlate
this roughness with device performance. We have developed a method that allows
us to measure the sidewall roughness of waveguides made of any material
(including dielectrics) using the high resolution of atomic force microscopy.
We illustrate this method by measuring state-of-the-art photonic devices made
of silicon nitride. We compare the roughness of devices fabricated using both
DUV photo-lithography and electron-beam lithography for two different etch
processes. To correlate roughness with device performance we describe what we
call a new Payne-Lacey Bending model, which adds a correction factor to the
widely used Payne-Lacey model so that losses in resonators and waveguides with
bends can be accurately predicted given the sidewall roughness, waveguide width
and bending radii. Having a better way to measure roughness and use it to
predict device performance can allow researchers and engineers to optimize
fabrication for state-of-the-art photonics using many materials.


  In a recent work PRD 106, L021501 (2022), a new geometric approach is
proposed to obtain the photon sphere (circular photon orbit) and the black hole
shadow radius. In this approach, photon spheres and the black hole shadow
radius are determined using geodesic curvature and Gaussian curvature in the
optical geometry of black hole spacetimes. However, the calculations in PRD
106, L021501 (2022) only restricted to a subclass of static and spherically
symmetric black holes with spacetime metric $g_{tt} \cdot g_{rr}=-1$,
$g_{\theta\theta}=r^{2}$ and $g_{\phi\phi}=r^{2}\sin^{2}\theta$. In this work,
we extend this approach to more general spherically symmetric black holes (with
spacetime metric
$ds^{2}=g_{tt}dt^{2}+g_{rr}dr^{2}+g_{\theta\theta}d\theta^{2}+g_{\phi\phi}d\phi^{2}$).
Furthermore, it can be proved that our results from the geometric approach are
completely equivalent to those from conventional approach based on effective
potentials of test particles.


  In this article we prove the existence and uniqueness of a (weak) solution
$u$ in $L_p\left((0,T) , \Lambda_{\gamma+m}\right)$ to the Cauchy problem
\begin{align}
  \notag &\frac{\partial u}{\partial t}(t,x)=\psi(t,i\nabla)u(t,x)+f(t,x),\quad
(t,x) \in (0,T) \times \mathbf{R}^d
  \label{main eqn} & u(0,x)=0, \end{align} where $d \in \mathbb{N}$, $p \in
(1,\infty]$, $\gamma,m \in (0,\infty)$, $\Lambda_{\gamma+m}$ is the Lipschitz
space on $\mathbf{R}^d$ whose order is $\gamma+m$, $f \in L_p\left((0,T) ,
\Lambda_{\gamma} \right)$, and $\psi(t,i\nabla)$ is a time measurable
pseudo-differential operator whose symbol is $\psi(t,\xi)$, i.e. $$
\psi(t,i\nabla)u(t,x)=\cF^{-1}\left[\psi(t,\xi)\cF\left[u(t,\cdot)\right](\xi)\right](x),
$$ with the assumptions \begin{align*} \Re[\psi(t,\xi)] \leq
-\nu|\xi|^{\gamma}, \end{align*} and \begin{align*}
|D_{\xi}^{\alpha}\psi(t,\xi)|\leq\nu^{-1}|\xi|^{\gamma-|\alpha|}. \end{align*}
Furthermore, we show \begin{align}
  \label{e 1028 1} \int_0^T \|u(t,\cdot)\|^p_{\Lambda_{\gamma+m}} dt \leq N
\int_0^T \|f(t,\cdot)\|^p_{\Lambda_{m}} dt, \end{align} where $N$ is a positive
constant depending only on $d$, $p$, $\gamma$, $\nu$, $m$, and $T$,
  The unique solvability of equation (\ref{main eqn}) in $L_p$-H\"older space
is also considered. More precisely, for any $f \in L_p((0,T);C^{n+\alpha})$,
there exists a unique solution $u \in
L_p((0,T);C^{\gamma+n+\alpha}(\mathbf{R}^d))$ to equation (\ref{main eqn}) and
for this solution $u$, \begin{align}
  \label{e 1029 1} \int_0^T \|u(t,\cdot)\|^p_{C^{\gamma+n+\alpha}}dt \leq N
\int_0^T \|f(t,\cdot)\|^p_{C^{n+\alpha}}dt, \end{align} where $n \in
\mathbb{Z}_+$, $\alpha \in (0,1)$, and $\gamma+\alpha \notin \mathbb{Z}_+$.


  Let $u\ne \pm 1$, and $v\ne \pm 1$ be a pair of fixed relatively prime
squarefree integers, and let $d\geq 1$, and $e \geq1$ be a pair of fixed
integers. It is shown that there are infinitely many primes $p\geq 2$ such that
$u$ and $v$ have simultaneous prescribed multiplicative orders
$\text{ord}_pu=(p-1)/d$ and $\text{ord}_pv=(p-1)/e$ respectively,
unconditionally. In particular, a squarefree odd integer $u>2$ and $v=2$ are
simultaneous primitive roots and quadratic residues (or quadratic nonresidues)
modulo $p$ for infinitely many primes $p$, unconditionally.


  For quadratic curves over $Q$ in $F_p$, the number of solutions, which is
governed by an analogue of the Mordell-Weil group, is expressed with the
Legendre symbol of a coefficient of quadratic curves. Focusing on the number of
solutions, a quadratic curve analogue of the modular form in the
Taniyama-Shimura conjecture is proposed. This modular form yields the Gaussian
sum and also possesses some modular transformation structure.


  Sets in the parameter space corresponding to complex exceptional points have
high codimension and by this reason they are difficult objects for numerical
localization. However, complex EPs play an important role in the problems of
stability of dissipative systems where they are frequently considered as
precursors to instability. We propose to localize the set of complex EPs using
the fact that the minimum of the spectral abscissa of a polynomial is attained
at the EP of the highest possible order. Applying this approach to the problem
of self-stabilization of a bicycle we find explicitly the EP sets that suggest
scaling laws for the design of robust bikes that agree with the design of the
known experimental machines


  New line lists are presented for the two most abundant water isotopologues;
H$_{2}$$^{16}$O and H$_{2}$$^{18}$O. The H$_{2}$$^{16}$O line list extends to
25710 cm$^{-1}$ with intensity stabilities provided via ratios of calculated
intensities obtained from two different semi-empirical potential energy
surfaces. The line list for H$_{2}$$^{18}$O extends to 20000 cm$^{-1}$. The
minimum intensity considered for all is $10^{-30}$ cm molecule$^{-1}$ at 296~K,
assuming 100\% abundance for each isotopologue. Fluctuation of calculated
intensities caused by changes in the underlying potential energy are found to
be significant, particularly for weak transitions. Direct comparisons are made
against eighteen different sources of line intensities, both experimental and
theoretical, many of which are used within the HITRAN2016 database. With some
exceptions, there is excellent agreement between our line lists and the
experimental intensities in HITRAN2016. In the infrared region, many
H$_{2}$$^{16}$O bands which exhibit intensity differences of 5-10\% between to
the most recent 'POKAZATEL' line list (Polyansky \textit{et al.}, [Mon. Not.
Roy. Astron. Soc. \textbf{480}, 2597 (2018)] and observation, are now generally
predicted to within 1\%. For H$_{2}$$^{18}$O, there are systematic differences
in the strongest intensities calculated in this work versus those obtained from
semi-empirical calculations. In the visible, computed cross sections show
smaller residuals between our work and both HITRAN2016 and HITEMP2010 than
POKAZATEL. While our line list accurately reproduces HITEMP2010 cross sections
in the observed region, residuals produced from this comparison do however
highlight the need to update line positions in the visible spectrum of
HITEMP2010. These line lists will be used to update many transition intensities
and line positions in the HITRAN2016 database.


  We perform a thermodynamic analysis of various contributions to the size
dependence of the contact angle cosine for axisymmetric and cylindrical sessile
droplets. This shows that a widely used method to determine the line tension
from the slope of the contact angle cosine dependence on the three-phase
contact line curvature (for axisymmetric droplets) provides a certain
combination of the line tension, adsorptions at the three interfaces, and the
macroscopic contact angle. To extract the leading-order contact-line-related
contribution and determine the line tension, we propose a simple technique
using contact angle size dependences for axisymmetric and cylindrical droplets
at the same conditions.


  Each oscillator in a linear chain (a string) interacts with a local Ising
spin in contact with a thermal bath. These spins evolve according to Glauber
dynamics. Below a critical temperature, a rippled state in the string is
accompanied by a nonzero spin polarization. The system is shown to form ripples
in the string which, for slow spin relaxation, vibrates rapidly about
quasi-stationary states described as snapshots of a coarse-grained stroboscopic
map. For moderate observation times, ripples are observed irrespective of the
final thermodynamically stable state (rippled or not).


  The momentum dependent two-loop contributions of the order
$\mathcal{O}$($\alpha_s \alpha_t$) to the masses in the Higgs-boson sector of
the MSSM are computed. Adopting the Feynman-diagrammatic approach and using a
mixed on-shell/$\overline{DR}$ renormalization scheme, the new corrections can
directly be matched onto the higher-order corrections included in the code
FeynHiggs. Two-loop diagrams involving several mass scales are evaluated with
the program SecDec. The combination of the new momentum dependent two-loop
contribution with the existing one- and two-loop corrections leads to an
improved prediction of the light MSSM Higgs-boson mass with reduced theoretical
uncertainty. The resulting shifts in the lightest Higgs-boson mass $M_h$ can
extend up to the level of the current experimental uncertainty of about 500 MeV
in the scenario considered in these proceedings.


  We exactly calculate the full temperature dependence of Casimir-like forces
appearing between two and three static impurities loaded in the ideal Bose gas
below the Bose-Einstein condensation transition point. Assuming the
short-ranged character of the boson-impurity interaction, the calculation
procedure presented here can be easily extended on a Bose system with an
arbitrary number of impurities immersed.


  A signed graph offers richer information than an unsigned graph, since it
describes both collaborative and competitive relationships in social networks.
In this paper, we study opinion dynamics on a signed graph, based on the
Friedkin-Johnsen model. We first interpret the equilibrium opinion in terms of
a defined random walk on an augmented signed graph, by representing the
equilibrium opinion of every node as a combination of all nodes' internal
opinions, with the coefficient of the internal opinion for each node being the
difference of two absorbing probabilities. We then quantify some relevant
social phenomena and express them in terms of the $\ell_2$ norms of vectors. We
also design a nearly-linear time signed Laplacian solver for assessing these
quantities, by establishing a connection between the absorbing probability of
random walks on a signed graph and that on an associated unsigned graph. We
further study the opinion optimization problem by changing the initial opinions
of a fixed number of nodes, which can be optimally solved in cubic time. We
provide a nearly-linear time algorithm with error guarantee to approximately
solve the problem. Finally, we execute extensive experiments on sixteen
real-life signed networks, which show that both of our algorithms are effective
and efficient, and are scalable to massive graphs with over 20 million nodes.


  With the help of Monte Carlo simulations and a mean-field theory, we
investigate the ordered steady-state structures resulting from the motion of a
single vacancy on a periodic lattice which is filled with two species of
oppositely ``charged'' particles. An external field biases particle-vacancy
exchanges according to the particle's charge, subject to an excluded volume
constraint. The steady state exhibits charge segregation, and the vacancy is
localized at one of the two characteristic interfaces. Charge and hole density
profiles, an appropriate order parameter and the interfacial regions themselves
exhibit characteristic scaling properties with system size and field strength.
The lattice spacing is found to play a significant role within the mean-field
theory.


  The SOSS mode of the NIRISS instrument is poised to be one of the workhorse
modes for exoplanet atmosphere observations with the newly launched James Webb
Space Telescope. One of the challenges of the SOSS mode, however, is the
physical overlap of the first two diffraction orders of the G700XD grism on the
detector. Recently, the ATOCA algorithm was developed and implemented as an
option in the official JWST pipeline, as a method to extract SOSS spectra by
decontaminating the detector -- that is, separating the first and second
orders. Here, we present APPLESOSS (A Producer of ProfiLEs for SOSS), which
generates the spatial profiles for each diffraction order upon which ATOCA
relies. We validate APPLESOSS using simulated SOSS time series observations of
WASP-52\,b, and compare it to ATOCA extractions using two other spatial
profiles (a best and worst case scenario on-sky), as well as a simple box
extraction performed without taking into account the order contamination. We
demonstrate that APPLESOSS profiles retain a high degree of fidelity to the
true underlying spatial profiles, and therefore yield accurate extracted
spectra. We further confirm that the effects of the order contamination for
relative measurements (e.g., exoplanet transmission or emission observations)
is small -- the transmission spectrum obtained from each of our four tests,
including the contaminated box extraction, is consistent at the $\sim$1$\sigma$
level with the atmosphere model input into our noiseless simulations. We
further confirm via a retrieval analysis that the atmosphere parameters
(metallicity and C/O) obtained from each transmission spectrum are consistent
with the true underlying values.


  Nowadays, the usage of smartphones and their applications have become rapidly
increasing popular in people's daily life. Over the last decade, availability
of mobile money services such as mobile-payment systems and app markets have
significantly increased due to the different forms of apps and connectivity
provided by mobile devices such as 3G, 4G, GPRS, and Wi-Fi, etc. In the same
trend, the number of vulnerabilities targeting these services and communication
networks has raised as well. Therefore, smartphones have become ideal target
devices for malicious programmers. With increasing the number of
vulnerabilities and attacks, there has been a corresponding ascent of the
security countermeasures presented by the researchers. Due to these reasons,
security of the payment systems is one of the most important issues in mobile
payment systems. In this survey, we aim to provide a comprehensive and
structured overview of the research on security solutions for smartphone
devices. This survey reviews the state of the art on security solutions,
threats, and vulnerabilities during the period of 2011-2017, by focusing on
software attacks, such those to smartphone applications. We outline some
countermeasures aimed at protecting smartphones against these groups of
attacks, based on the detection rules, data collections and operating systems,
especially focusing on open source applications. With this categorization, we
want to provide an easy understanding for users and researchers to improve
their knowledge about the security and privacy of smartphones.


  LISA Pathfinder is a technology demonstration mission for the Laser
Interferometer Space Antenna (LISA). The main experiment on-board LISA
Pathfinder is the so-called LISA Technology Package (LTP) which has the aim to
measure the differential acceleration between two free-falling test masses with
an accuracy of 3x10^(-14) ms^(-2)/sqrt[Hz] between 1 mHz and 30 mHz. This
measurement is performed interferometrically by the Optical Metrology System
(OMS) on-board LISA Pathfinder. In this paper we present the development of an
experimental end-to-end testbed of the entire OMS. It includes the
interferometer and its sub-units, the interferometer back-end which is a
phasemeter and the processing of the phasemeter output data. Furthermore,
3-axes piezo actuated mirrors are used instead of the free-falling test masses
for the characterisation of the dynamic behaviour of the system and some parts
of the Drag-free and Attitude Control System (DFACS) which controls the test
masses and the satellite. The end-to-end testbed includes all parts of the LTP
that can reasonably be tested on earth without free-falling test masses. At its
present status it consists mainly of breadboard components. Some of those have
already been replaced by Engineering Models of the LTP experiment. In the next
steps, further Engineering Models and Flight Models will also be inserted in
this testbed and tested against well characterised breadboard components. The
presented testbed is an important reference for the unit tests and can also be
used for validation of the on-board experiment during the mission.


  We present a theoretical method for a direct evaluation of the average and
reliability error exponents in low-density parity-check error-correcting codes
using methods of statistical physics. Results for the binary symmetric channel
(BSC) are presented for codes of both finite and infinite connectivity.


  We use the INTEGRAL all-sky hard X-ray survey to perform a statistical study
of a representative sample of nearby AGN. Our entire all-sky sample consists of
127 AGN, of which 91 are confidently detected (>5 sigma) on the time-averaged
map obtained with the IBIS/ISGRI instrument and 36 are detected only during
single observations. Among the former there are 66 non-blazar AGN located at
|b|>5 deg, where the survey's identification completeness is ~93%, which we use
for calculating the AGN luminosity function and X-ray absorption distribution.
In broad agreement with previous studies, we find that the fraction of obscured
(log NH>22) objects is much higher (~70%) among the low-luminosity AGN
(Lx<10^43.6 erg/s) than among the high-luminosity ones (Lx>10^43.6 erg/s),
\~25%, where Lx is the luminosity in the 17-60 keV energy band. We also find
that locally the fraction of Compton-thick AGN is less than 20% unless there is
a significant population of AGN that are so strongly obscured that their
observed hard
  X-ray luminosities fall below 10^40-10^41 erg/s, the effective limit of our
survey. The constructed hard X-ray luminosity function has a canonical,
smoothly broken power-law shape in the range 40<log Lx<45.5 with a
characteristic luminosity of log L*=43.40+/-0.28. The estimated local
luminosity density due to AGN with log Lx>40 is (1.4+/-0.3) 10^39 erg/s/Mpc^3
(17-60 keV). We demonstrate that the spectral shape and amplitude of the CXB
are consistent with the simple scenario in which the NH distribution of AGN
(for a given
  Lx/L*(z) ratio has not changed significantly since z~1.5, while the AGN
luminosity function has experienced pure luminosity evolution.


  We present an agent based model of a single asset financial market that is
capable of replicating several non-trivial statistical properties observed in
real financial markets, generically referred to as stylized facts. While
previous models reported in the literature are also capable of replicating some
of these statistical properties, in general, they tend to oversimplify either
the trading mechanisms or the behavior of the agents. In our model, we strived
to capture the most important characteristics of both aspects to create agents
that employ strategies inspired on those used in real markets, and, at the same
time, a more realistic trade mechanism based on a double auction order book. We
study the role of the distinct types of trader on the return statistics:
specifically, correlation properties (or lack thereof), volatilty clustering,
heavy tails, and the degree to which the distribution can be described by a
log-normal. Further, by introducing the practice of profit taking, our model is
also capable of replicating the stylized fact related to an asymmetry in the
distribution of losses and gains.


  We propose a new process of mu(-) e(-) -> e(-) e(-) in a muonic atom for a
quest of charged lepton flavor violation. The Coulomb attraction from the
nucleus in a heavy muonic atom leads to significant enhancement in its rate,
compared to mu(+) e(-) -> e(+) e(-). The upper limit of the branching ratio is
estimated to be of the orders of O[10^(-17)-10^(-18)] for the photonic and the
four Fermi interactions from the present experimental constraints. The search
for this process could serve complementarily with the other relevant processes
to shed lights upon the nature of charged lepton flavor violation.


  We study some fundamental issues related to the Hilbert space representation
of quantum mechanics in the presence of a minimal length and maximal momentum.
In this framework, the maximally localized states and quasi-position
representation introduced by Kempf et al. are reconsidered and modified. We
show that all studies in recent years, including [15] and [16] need serious
modification in order to be a consistent framework for quantum mechanics in
Planck scale.


  We predict the existence of a new defect-lattice phase near the nematic -
smectic-C (NC) transition. This tilt- analogue of the blue phase is a lattice
of double-tilt cylinders. We discuss the structure and stability of the cone
phase. We suggest that many `nematics' exhibiting short range layering and tilt
order may in fact be in the molten cone phase, which is a line liquid.


  A rich variety of order parameter manifolds of multicomponent Bose-Einstein
condensates (BECs) admit various kinds of topological excitations, such as
fractional vortices, monopoles, skyrmions, and knots. In this paper, we discuss
two topological excitations in spinor BECs: non-Abelian vortices and knots.
Unlike conventional vortices, non-Abelian vortices neither reconnect themselves
nor pass through each other, but create a rung between them in a topologically
stable manner. We discuss the collision dynamics of non-Abelian vortices in the
cyclic phase of a spin-2 BEC. In the latter part, we show that a knot, which is
a unique topological object characterized by a linking number or a Hopf
invariant [$\pi_3 (S^2)=Z$], can be created using a conventional quadrupole
magnetic field in a cold atomic system.


  In Traditional Chinese Medicine (TCM), facial features are important basis
for diagnosis and treatment. A doctor of TCM can prescribe according to a
patient's physical indicators such as face, tongue, voice, symptoms, pulse.
Previous works analyze and generate prescription according to symptoms.
However, research work to mine the association between facial features and
prescriptions has not been found for the time being. In this work, we try to
use deep learning methods to mine the relationship between the patient's face
and herbal prescriptions (TCM prescriptions), and propose to construct
convolutional neural networks that generate TCM prescriptions according to the
patient's face image. It is a novel and challenging job. In order to mine
features from different granularities of faces, we design a multi-scale
convolutional neural network based on three-grained face, which mines the
patient's face information from the organs, local regions, and the entire face.
Our experiments show that convolutional neural networks can learn relevant
information from face to prescribe, and the multi-scale convolutional neural
networks based on three-grained face perform better.


  It has been suggested that the origins of cognitive modernity in the
Middle/Upper Paleolithic following the appearance of anatomically modern humans
was due to the onset of dual processing or contextual focus (CF), the ability
to shift between different modes of thought: an explicit mode conducive to
logical problem solving, and an implicit mode conducive to free-association and
breaking out of a rut. Mathematical and computational models of CF supported
this hypothesis, showing that CF is conducive to making creative connections by
placing concepts in new contexts. This paper proposes that CF was made possible
by mutation of the FOXP2 gene in the Paleolithic. FOXP2, once thought to be the
'language gene', turned out not to be uniquely associated with language. In its
modern form FOXP2 enabled fine-tuning of the neurological mechanisms underlying
the capacity to shift between processing modes by varying the size of the
activated region of memory.


  This short article, which appeared in the MSRI Fall 2004 newletter, is
intended for a general mathematical audience. It describes some mathematical
themes from the Winter 2004 program at MSRI in topological aspects of real
algebraic geometry in the context of an interpolation problem involving real
rational plane curves.


  This paper proposes a method to use deep neural networks as end-to-end
open-set classifiers. It is based on intra-class data splitting. In open-set
recognition, only samples from a limited number of known classes are available
for training. During inference, an open-set classifier must reject samples from
unknown classes while correctly classifying samples from known classes. The
proposed method splits given data into typical and atypical normal subsets by
using a closed-set classifier. This enables to model the abnormal classes by
atypical normal samples. Accordingly, the open-set recognition problem is
reformulated into a traditional classification problem. In addition, a
closed-set regularization is proposed to guarantee a high closed-set
classification performance. Intensive experiments on five well-known image
datasets showed the effectiveness of the proposed method which outperformed the
baselines and achieved a distinct improvement over the state-of-the-art
methods.


  We derive a local, gauge invariant action for the SU(N) non-linear
sigma-model in 2+1 dimensions. In this setting, the model is defined in terms
of a self-interacting pseudo vector-field \theta_\mu, with values in the Lie
algebra of the group SU(N). Thanks to a non-trivially realized gauge
invariance, the model has the correct number of degrees of freedom: only one
polarization of \theta_\mu, like in the case of the familiar Yang-Mills theory
in 2+1 dimensions. Moreover, since \theta_\mu is a pseudo-vector, the physical
content corresponds to one massless pseudo-scalar field in the Lie algebra of
SU(N), as in the standard representation of the model. We show that the
dynamics of the physical polarization corresponds to that of the SU(N)
non-linear sigma model in the standard representation, and also construct the
corresponding BRST invariant gauge-fixed action.


  We extend our analysis of the effects of the interplay of quantum phases and
nonlinearity to address saturation effects in small quantum systems.
  We find that initial phases dramatically control the dependence of
self-trapping on initial asymmetry of quasiparticle population and can compete
or act with nonlinearity as well as saturation effects. We find that there is a
minimum finite saturation value in order to obtain self-trapping that crucially
depends on the initial quasiparticle phases and present a detailed
phase-diagram in terms of the control parameters of the system: nonlinearity
and saturation.


  Introduced by Kiefer and Wolfowitz \cite{KW56}, the nonparametric maximum
likelihood estimator (NPMLE) is a widely used methodology for learning mixture
odels and empirical Bayes estimation. Sidestepping the non-convexity in mixture
likelihood, the NPMLE estimates the mixing distribution by maximizing the total
likelihood over the space of probability measures, which can be viewed as an
extreme form of overparameterization.
  In this paper we discover a surprising property of the NPMLE solution.
Consider, for example, a Gaussian mixture model on the real line with a
subgaussian mixing distribution. Leveraging complex-analytic techniques, we
show that with high probability the NPMLE based on a sample of size $n$ has
$O(\log n)$ atoms (mass points), significantly improving the deterministic
upper bound of $n$ due to Lindsay \cite{lindsay1983geometry1}. Notably, any
such Gaussian mixture is statistically indistinguishable from a finite one with
$O(\log n)$ components (and this is tight for certain mixtures). Thus, absent
any explicit form of model selection, NPMLE automatically chooses the right
model complexity, a property we term \emph{self-regularization}. Extensions to
other exponential families are given. As a statistical application, we show
that this structural property can be harnessed to bootstrap existing Hellinger
risk bound of the (parametric) MLE for finite Gaussian mixtures to the NPMLE
for general Gaussian mixtures, recovering a result of Zhang
\cite{zhang2009generalized}.


  We present the Standard Model Effective Field Theories (SMEFT) from purely
on-shell arguments. Starting from a few basic assumptions such as Poincar\'e
invariance and locality, we classify all the renormalisable and
non-renormalisable interactions at the lowest order in the couplings. From
these building blocks, we review how locality and unitarity enforce Lie algebra
structures to appear in the S-matrix elements together with relations among
couplings (and hypercharges). Furthermore, we give a fully on-shell algorithm
to compute any higher-point tree-level amplitude (or form factor) in generic
EFTs, bypassing BCFW-like recursion relations which are known to be problematic
when non-renormalisable interactions are involved. Finally, using known
amplitudes techniques we compute the mixing matrix of SMEFT irrelevant
interactions up to mass dimension 8, to linear order in the effective
interactions.


  The impact of a heavier droplet into a deep pool of lighter liquid is
investigated using three-dimensional numerical simulations. Unprecedented to
any numerical simulations, we demonstrate that the heavier droplets can hang
from the surface of a lighter liquid using surface tension. The impact
phenomenon and the evolution of the heavier droplet as a function of its size
and release height are explored. A theoretical model is also formulated to
understand the role of different forms of energies associated with the hanging
droplet. We further solve the force balance equations for the hanging droplets
analytically and demonstrate that the results obtained from our simulations
match very well with the analytical solution. This research offers
opportunities in many areas, including drug and gene delivery, encapsulation of
biomolecules, microfluidics, soft robots, and remediation of oil spills.


  Quantum error correction is crucial for any quantum computing platform to
achieve truly scalable quantum computation. The surface code and its variants
have been considered the most promising quantum error correction scheme due to
their high threshold, low overhead, and relatively simple structure that can
naturally be implemented in many existing qubit architectures, such as
superconducting qubits. The recent development of Floquet codes offers another
promising approach. By going beyond the usual paradigm of stabilizer codes,
Floquet codes achieve similar performance while being constructed entirely from
two-qubit measurements. This makes them particularly suitable for platforms
where two-qubit measurements can be implemented directly, such as
measurement-only topological qubits based on Majorana zero modes (MZMs). Here,
we explain how two variants of Floquet codes can be implemented on MZM-based
architectures without any auxiliary qubits for syndrome measurement and with
shallow syndrome extraction sequences. We then numerically demonstrate their
favorable performance. In particular, we show that they improve the threshold
for scalable quantum computation in MZM-based systems by an order of magnitude,
and significantly reduce space and time overheads below threshold.


  We analyse the events with two same-flavour, opposite-sign leptons +
$E_T^{miss}$ + (jets) as expected in pp collisions at LHC within the framework
of the minimal Supergravity Model. The objective is the determination of the
parameters m_0 and m_{1/2} of this model (for a given value of $\tan\beta$).
The signature $l^+ l^- + E_T^{miss}$ + (jets) selects the leptonic decays of
$\tilde{\chi}^0_2$, $\tilde{\chi}^0_2 \to \tilde{\chi}^0_1 l^+ l^- $,
$\tilde{\chi}^0_2 \to \tilde{l}_{L,R}^{\pm} l^{\mp} \to \tilde{\chi}^0_1 l^+
l^-$. We exploit the fact that the invariant dilepton mass distribution has a
pronounced structure with a sharp edge at the kinematical endpoint even in such
an inclusive final state over a significant part of parameter space. We
determine the domain of parameter space where the edge is expected to be
visible. We show that a measurement of this edge already constrains the model
parameters essentially to three lines in the ($m_0, m_{1/2}$) parameter plane.
We work out a strategy to discriminate between the three-body leptonic decays
of $\tilde{\chi}^0_2$ and the decays into sleptons $\tilde{l}_{L,R}$. This
procedure may make it possible to get information on SUSY particle masses
already with low luminosity, L_{int}=10^3 pb^{-1}.


  This article shows an It\^o-Wentzell type formula adapted to rough paths with
$\alpha$-H\"older regularity $\alpha \in (\frac{1}{3},\frac{1}{2}]$. We improve
previous results of R. Castrequini and P. Catuogno for the Young integral and
C. Keller and J. Zhang for rough paths.


  The spatial distribution of stellar populations, the star formation history,
and other properties of the dIrr galaxy DDO 190 have been analyzed using
color--magnitude diagrams (CMDs) of about 3900 resolved stars and the Ha fluxes
of HII regions. From the mean color index of the red giant branch, a mean
metallicity [Fe/H]=-2.0 is obtained. The I magnitude of the TRGB has been used
to estimate the distance. DDO 190 is 2.9+/-0.2 Mpc from the Milky Way, 2.1 Mpc
from the M 94 group (CnV-I), 2.4 Mpc from the M 81 group and 2.9 Mpc from the
barycenter of the Local Group, all indicating that it is an isolated, field
galaxy. The surface-brightness distribution of the galaxy is well fitted by
ellipses of ellipticity e=1-a/b=0.1 and P.A.=82deg. The radial star density
distribution follows an exponential law of scale length a=43."4, corresponding
to 611 pc. The Holmberg semi-major axis to mu_B=26.5 is estimated to be
r^B_(26.5)=3.'0. Stellar populations of different ages in DDO 190 show strong
spatial decoupling, the oldest population appearing much more extended than the
youngest. Stars younger than 0.1 Gyr occupy only the central 40'' (0.55 kpc);
stars younger than a few (~4) Gyr extend out to ~80'' (125 kpc), and for larger
galactocentric distances only older stars seem to be present. This behavior is
found in all the dIrr galaxies for which spatially extended studies have been
performed and could be related with the kinematical history of the galaxy.


  We present a new way to solve the platform deformation problem of co-planar
interferometers. The platform of a co-planar interferometer can be deformed due
to driving forces and gravity. A deformed platform will induce extra components
into the geometric delay of each baseline, and change the phases of observed
visibilities. The reconstructed images will also be diluted due to the errors
of the phases. The platform deformations of The Yuan-Tseh Lee Array for
Microwave Background Anisotropy (AMiBA) were modelled based on photogrammetry
data with about 20 mount pointing positions. We then used the differential
optical pointing error between two optical telescopes to fit the model
parameters in the entire horizontal coordinate space. With the platform
deformation model, we can predict the errors of the geometric phase delays due
to platform deformation with given azimuth and elevation of the targets and
calibrators. After correcting the phases of the radio point sources in the
AMiBA interferometric data, we recover 50% - 70% flux loss due to phase errors.
This allows us to restore more than 90% of a source flux. The method outlined
in this work is not only applicable to the correction of deformation for other
co-planar telescopes but also to single dish telescopes with deformation
problems. This work also forms the basis of the upcoming science results of
AMiBA-13.


  The computation of multi-loop multi-leg scattering amplitudes plays a key
role to improve the precision of theoretical predictions for particle physics
at high-energy colliders. In this work, we focus on the mathematical properties
of the novel integrand-level representation of Feynman integrals, which is
based on the Loop-Tree Duality (LTD). We explore the behaviour of the
multi-loop iterated residues and explicitly show, by developing a general
formal proof for the first time, that contributions associated to displaced
poles are cancelled out. The remaining residues, called nested residues as
originally introduced in Ref. \cite{Verdugo:2020kzh}, encode the relevant
physical information and are naturally mapped onto physical configurations
associated to nondisjoint on-shell states. By going further on the mathematical
structure of the nested residues, we prove that unphysical singularities
vanish, and show how the final expressions can be written by using only causal
denominators. In this way, we provide a mathematical proof for the all-loop
formulae presented in Ref. \cite{Aguilera-Verdugo:2020kzc}.


  We consider the application of KronPCA spatio-temporal modeling techniques
[Greenewald et al 2013, Tsiligkaridis et al 2013] to the extraction of
spatiotemporal features for video dismount classification. KronPCA performs a
low-rank type of dimensionality reduction that is adapted to spatio-temporal
data and is characterized by the T frame multiframe mean and covariance of p
spatial features. For further regularization and improved inverse estimation,
we also use the diagonally corrected KronPCA shrinkage methods we presented in
[Greenewald et al 2013]. We apply this very general method to the modeling of
the multivariate temporal behavior of HOG features extracted from pedestrian
bounding boxes in video, with gender classification in a challenging dataset
chosen as a specific application. The learned covariances for each class are
used to extract spatiotemporal features which are then classified, achieving
competitive classification performance.


  In this study, we develop experimental apparatus for contactless electrical
conductivity measurements under pulsed high magnetic fields over 100 T using a
self-resonant-type high-frequency circuit. The resonant power spectra were
numerically analyzed, and the conducted simulations showed that the apparatus
is optimal for electrical conductivity measurements of materials with high
electrical conductivity. The newly developed instruments were applied to a
high-temperature cuprate superconductor La$_{2-x}$Sr$_x$CuO$_4$ to show
conductivity changes in magnetic fields up to 102 T with a good signal-to-noise
ratio. The upper critical field was determined with high accuracy.