  Musical acoustics is an interesting sub-field of physics which is usually
able to engage students in a dual perspective, by combining science and art
together. The physics principles involved in most musical instruments can be
easily demonstrated with standard laboratory equipment and can become part of
lecture or lab activities. In particular, we will show in this paper how to
simulate a guitar using a conventional sonometer, in relation to the problem of
the instrument intonation, i.e., how to obtain correctly tuned notes on a
guitar or similar string instruments.


  Several dihedral angles prediction methods were developed for protein
structure prediction and their other applications. However, distribution of
predicted angles would not be similar to that of real angles. To address this
we employed generative adversarial networks (GAN). Generative adversarial
networks are composed of two adversarially trained networks: a discriminator
and a generator. A discriminator distinguishes samples from a dataset and
generated samples while a generator generates realistic samples. Although the
discriminator of GANs is trained to estimate density, GAN model is intractable.
On the other hand, noise-contrastive estimation (NCE) was introduced to
estimate a normalization constant of an unnormalized statistical model and thus
the density function. In this thesis, we introduce noise-contrastive estimation
generative adversarial networks (NCE-GAN) which enables explicit density
estimation of a GAN model. And a new loss for the generator is proposed. We
also propose residue-wise variants of auxiliary classifier GAN (AC-GAN) and
Semi-supervised GAN to handle sequence information in a window. In our
experiment, the conditional generative adversarial network (C-GAN), AC-GAN and
Semi-supervised GAN were compared. And experiments done with improved
conditions were invested. We identified a phenomenon of AC-GAN that
distribution of its predicted angles is composed of unusual clusters. The
distribution of the predicted angles of Semi-supervised GAN was most similar to
the Ramachandran plot. We found that adding the output of the NCE as an
additional input of the discriminator is helpful to stabilize the training of
the GANs and to capture the detailed structures. Adding regression loss and
using predicted angles by regression loss only model could improve the
conditional generation performance of the C-GAN and AC-GAN.


  Gravitational waves from a merger of two neutron stars (NSs) were discovered
for the first time in GW170817, together with diverse electromagnetic (EM)
counterparts. To make constraints on a relativistic jet from the NS merger, we
calculate the EM signals in (1) the short gamma-ray burst sGRB 170817A from an
off-axis jet, (2) the optical-infrared macronova (or kilonova), especially the
blue macronova, from a jet-powered cocoon, and (3) the X-ray and radio
afterglows from the interaction between the jet and interstellar medium. We
find that a typical sGRB jet is consistent with these observations, and there
is a parameter space to explain all the observations in a unified fashion with
an isotropic energy $\sim 10^{51}$-$10^{52}$ erg, opening angle $\sim
20^{\circ}$, and viewing angle $\sim 30^{\circ}$. The off-axis emission is less
de-beamed than the point-source case because the viewing angle is comparable to
the opening angle. We also analytically show that the jet energy accelerates a
fair fraction of the merger ejecta to a sub-relativistic velocity $\sim
0.3$-$0.4$c as a cocoon in a wide parameter range. The ambient density might be
low $\sim 10^{-3}$-$10^{-6}$ cm$^{-3}$, which can be tested by future
observations of radio flares and X-ray remnants.


  The accurate approximation of high-dimensional functions is an essential task
in uncertainty quantification and many other fields. We propose a new function
approximation scheme based on a spectral extension of the tensor-train (TT)
decomposition. We first define a functional version of the TT decomposition and
analyze its properties. We obtain results on the convergence of the
decomposition, revealing links between the regularity of the function, the
dimension of the input space, and the TT ranks. We also show that the
regularity of the target function is preserved by the univariate functions
(i.e., the "cores") comprising the functional TT decomposition. This result
motivates an approximation scheme employing polynomial approximations of the
cores. For functions with appropriate regularity, the resulting
\textit{spectral tensor-train decomposition} combines the favorable
dimension-scaling of the TT decomposition with the spectral convergence rate of
polynomial approximations, yielding efficient and accurate surrogates for
high-dimensional functions. To construct these decompositions, we use the
sampling algorithm \texttt{TT-DMRG-cross} to obtain the TT decomposition of
tensors resulting from suitable discretizations of the target function. We
assess the performance of the method on a range of numerical examples: a
modifed set of Genz functions with dimension up to $100$, and functions with
mixed Fourier modes or with local features. We observe significant improvements
in performance over an anisotropic adaptive Smolyak approach. The method is
also used to approximate the solution of an elliptic PDE with random input
data. The open source software and examples presented in this work are
available online.


  The search for refining 3D LiDAR data has attracted growing interest
motivated by recent techniques such as supervised learning or generative
model-based methods. Existing approaches have shown the possibilities for using
diffusion models to generate refined LiDAR data with high fidelity, although
the performance and speed of such methods have been limited. These limitations
make it difficult to execute in real-time, causing the approaches to struggle
in real-world tasks such as autonomous navigation and human-robot interaction.
In this work, we introduce a novel approach based on conditional diffusion
models for fast and high-quality sparse-to-dense upsampling of 3D scene point
clouds through an image representation. Our method employs denoising diffusion
probabilistic models trained with conditional inpainting masks, which have been
shown to give high performance on image completion tasks. We introduce a series
of experiments, including multiple datasets, sampling steps, and conditional
masks. This paper illustrates that our method outperforms the baselines in
sampling speed and quality on upsampling tasks using the KITTI-360 dataset.
Furthermore, we illustrate the generalization ability of our approach by
simultaneously training on real-world and synthetic datasets, introducing
variance in quality and environments.


  The almost universal availability of electronic connectivity, portable
devices, and the web is bringing about a major revolution: information of all
kinds is rapidly becoming accessible to everyone, transforming social, economic
and cultural life practically everywhere in the world. Internet technologies
represent an unprecedented and extraordinary two-way channel of communication
between producers and users of data. Open Universe is an initiative proposed to
the United Nations Committee on the Peaceful Uses of Outer Space (COPUOS) and
currently in implementation under the leadership of the United Nations Office
for Outer Space Affairs (UN-OOSA). Its primary objective is to stimulate a
dramatic increase in the availability and usability of space science data,
extending the potential of scientific discovery to new participants in all
parts of the world. This paper describes the initiative in general, some of the
activities carried out to demonstrate its feasibility, and its use in the
context of the BRICS Astronomy Programme.


  For each $r\ge 4$, we show that any graph $G$ with minimum degree at least
$(1-1/100r)|G|$ has a fractional $K_r$-decomposition. This improves the best
previous bounds on the minimum degree required to guarantee a fractional
$K_r$-decomposition given by Dukes (for small $r$) and Barber, K\"uhn, Lo,
Montgomery and Osthus (for large $r$), giving the first bound that is tight up
to the constant multiple of $r$ (seen, for example, by considering Tur\'an
graphs).
  In combination with work by Glock, K\"uhn, Lo, Montgomery and Osthus, this
shows that, for any graph $F$ with chromatic number $\chi(F)\ge 4$, and any
$\varepsilon>0$, any sufficiently large graph $G$ with minimum degree at least
$(1-1/100\chi(F)+\varepsilon)|G|$ has, subject to some further simple necessary
divisibility conditions, an (exact) $F$-decomposition.


  The first goal of this article is to give a complete classification (up to
Real biholomorphisms) of Real primary Hopf surfaces $(H,s)$, and, for any such
pair, to describe in detail the following naturally associated objects : the
group $\mathrm{Aut}_h(H,s)$ of Real automorphisms, the Real Picard group
$(\mathrm{Pic}(H),\hat s^*)$, and the Picard group of Real holomorphic line
bundles $\mathrm{Pic}_{\mathbb{R}}(H)$. Our second goal: the classification of
Real primary Hopf surfaces up to equivariant diffeomorphisms, which will allow
us to describe explicitly in each case the real locus $H(\mathbb{R})=H^s$ and
the quotient $H/\langle s\rangle$.


  Halo bias is the main link between the matter distribution and dark matter
halos. In its simplest form, halo bias is determined by halo mass, but there
are known additional dependencies on other halo properties which are of
consequence for accurate modeling of galaxy clustering. Here we present the
most precise measurement of these secondary-bias dependencies on halo age,
concentration, and spin, for a wide range of halo masses spanning from
10$^{10.7}$ to 10$^{14.7}$ $h^{-1}$ M$_{\odot}$. At the high-mass end, we find
no strong evidence of assembly bias for masses above M$_{vir}$ $\sim10^{14}$
$h^{-1}$ M$_{\odot}$. Secondary bias exists, however, for halo concentration
and spin, up to cluster-size halos, in agreement with previous findings. For
halo spin, we report, for the first time, two different regimes: above
M$_{vir}\sim$10$^{11.5}$ $h^{-1}$ M$_{\odot}$, halos with larger values of spin
have larger bias, at fixed mass, with the effect reaching almost a factor 2.
This trend reverses below this characteristic mass. In addition to these
results, we test, for the first time, the performance of a multi-tracer method
for the determination of the relative bias between different subsets of halos.
We show that this method increases significantly the signal-to-noise of the
secondary-bias measurement as compared to a traditional approach. This analysis
serves as the basis for follow-up applications of our multi-tracer method to
real data.


  We calculate the s- and d-wave superconductor order parameter in the vicinity
of a tilt grain boundary. We do this self-consistently within the Bogoliubov de
Gennes equations, using a realistic microscopic model of the grain boundary. We
present the first self-consistent calculations of supercurrent flows in such
boundaries, obtaining the current-phase characteristics of grain boundaries in
both s-wave and d-wave superconductors.


  Text-based speech editing allows users to edit speech by intuitively cutting,
copying, and pasting text to speed up the process of editing speech. In the
previous work, CampNet (context-aware mask prediction network) is proposed to
realize text-based speech editing, significantly improving the quality of
edited speech. This paper aims at a new task: adding emotional effect to the
editing speech during the text-based speech editing to make the generated
speech more expressive. To achieve this task, we propose Emo-CampNet (emotion
CampNet), which can provide the option of emotional attributes for the
generated speech in text-based speech editing and has the one-shot ability to
edit unseen speakers' speech. Firstly, we propose an end-to-end
emotion-selectable text-based speech editing model. The key idea of the model
is to control the emotion of generated speech by introducing additional emotion
attributes based on the context-aware mask prediction network. Secondly, to
prevent the emotion of the generated speech from being interfered by the
emotional components in the original speech, a neutral content generator is
proposed to remove the emotion from the original speech, which is optimized by
the generative adversarial framework. Thirdly, two data augmentation methods
are proposed to enrich the emotional and pronunciation information in the
training set, which can enable the model to edit the unseen speaker's speech.
The experimental results that 1) Emo-CampNet can effectively control the
emotion of the generated speech in the process of text-based speech editing;
And can edit unseen speakers' speech. 2) Detailed ablation experiments further
prove the effectiveness of emotional selectivity and data augmentation methods.
The demo page is available at https://hairuo55.github.io/Emo-CampNet/


  Unexplained periodic fluctuations in the decay rates of Si-32 and Ra-226 have
been reported by groups at Brookhaven National Laboratory (Si-32), and at the
Physikalisch-Technische-Bundesandstalt in Germany (Ra-226). We show from an
analysis of the raw data in these experiments that the observed fluctuations
are strongly correlated in time, not only with each other, but also with the
distance between the Earth and the Sun. Some implications of these results are
also discussed, including the suggestion that discrepancies in published
half-life determinations for these and other nuclides may be attributable in
part to differences in solar activity during the course of the various
experiments, or to seasonal variations in fundamental constants.


  We carry out three-dimensional magnetohydrodynamical simulations of the
magnetorotational (Balbus-Hawley) instability in weakly-ionized plasmas. We
adopt a formulation in which the ions and neutrals each are treated as separate
fluids coupled only through a collisional drag term. Ionization and
recombination processes are not considered. The linear stability of the
ion-neutral system has been previously considered by Blaes and Balbus (1994).
Here we extend their results into the nonlinear regime by computing the
evolution of Keplerian angular momentum distribution in the local shearing box
approximation. We find significant turbulence and angular momentum transport
when the collisional frequency is on order 100 times the orbital frequency. At
higher collision rates, the two-fluid system studied here behaves much like the
fully ionized systems studied previously. At lower collision rates the
evolution of the instability is determined primarily by the properties of the
ions, with the neutrals acting as a sink for the turbulence. Since in this
regime saturation occurs when the magnetic field is superthermal with respect
to the ion pressure, we find the amplitude of the magnetic energy and the
corresponding angular momentum transport rate is proportional to the ion
density. Our calculations show the ions and neutrals are essentially decoupled
when the collision frequency is less than 0.01 times the orbital frequency; in
this case the ion fluid behaves as in the single fluid simulations and the
neutrals remain quiescent. We find that purely toroidal initial magnetic field
configurations are unstable to the magnetorotational instability across the
range of coupling frequencies.


  We present IAS15, a 15th-order integrator to simulate gravitational dynamics.
The integrator is based on a Gau\ss-Radau quadrature and can handle
conservative as well as non-conservative forces. We develop a step-size control
that can automatically choose an optimal timestep. The algorithm can handle
close encounters and high-eccentricity orbits. The systematic errors are kept
well below machine precision and long-term orbit integrations over $10^9$
orbits show that IAS15 is optimal in the sense that it follows Brouwer's law,
i.e. the energy error behaves like a random walk. Our tests show that IAS15 is
superior to a mixed-variable symplectic integrator (MVS) and other popular
integrators, including high-order ones, in both speed and accuracy. In fact,
IAS15 preserves the symplecticity of Hamiltonian systems better than the
commonly-used nominally symplectic integrators to which we compared it.
  We provide an open-source implementation of IAS15. The package comes with
several easy-to-extend examples involving resonant planetary systems,
Kozai-Lidov cycles, close encounters, radiation pressure, quadrupole moment,
and generic damping functions that can, among other things, be used to simulate
planet-disc interactions. Other non-conservative forces can be added easily.


  Text mining is a broad field having sentiment mining as its important
constituent in which we try to deduce the behavior of people towards a specific
item, merchandise, politics, sports, social media comments, review sites etc.
Out of many issues in sentiment mining, analysis and classification, one major
issue is that the reviews and comments can be in different languages like
English, Arabic, Urdu etc. Handling each language according to its rules is a
difficult task. A lot of research work has been done in English Language for
sentiment analysis and classification but limited sentiment analysis work is
being carried out on other regional languages like Arabic, Urdu and Hindi. In
this paper, Waikato Environment for Knowledge Analysis (WEKA) is used as a
platform to execute different classification models for text classification of
Roman Urdu text. Reviews dataset has been scrapped from different automobiles
sites. These extracted Roman Urdu reviews, containing 1000 positive and 1000
negative reviews, are then saved in WEKA attribute-relation file format (arff)
as labeled examples. Training is done on 80% of this data and rest of it is
used for testing purpose which is done using different models and results are
analyzed in each case. The results show that Multinomial Naive Bayes
outperformed Bagging, Deep Neural Network, Decision Tree, Random Forest,
AdaBoost, k-NN and SVM Classifiers in terms of more accuracy, precision, recall
and F-measure.


  The solid-solid coexistence of a polydisperse hard sphere system is studied
by using the Monte Carlo simulation. The results show that for large enough
polydispersity the solid-solid coexistence state is more stable than the
single-phase solid. The two coexisting solids have different composition
distributions but the same crystal structure. Moreover, there is evidence that
the solid-solid transition terminates in a critical point as in the case of the
fluid-fluid transition.


  Speech recognition from raw waveform involves learning the spectral
decomposition of the signal in the first layer of the neural acoustic model
using a convolution layer. In this work, we propose a raw waveform
convolutional filter learning approach using soft self-attention. The acoustic
filter bank in the proposed model is implemented using a parametric
cosine-modulated Gaussian filter bank whose parameters are learned. A
network-in-network architecture provides self-attention to generate attention
weights over the sub-band filters. The attention weighted log filter bank
energies are fed to the acoustic model for the task of speech recognition.
Experiments are conducted on Aurora-4 (additive noise with channel artifact),
and CHiME-3 (additive noise with reverberation) databases. In these
experiments, the attention based filter learning approach provides considerable
improvements in ASR performance over the baseline mel filter-bank features and
other robust front-ends (average relative improvement of 7% in word error rate
over baseline features on Aurora-4 dataset, and 5% on CHiME-3 database). Using
the self-attention weights, we also present an analysis on the interpretability
of the filters for the ASR task.


  Ultrasound is a vital imaging modality utilized for a variety of diagnostic
and interventional procedures. However, an expert sonographer is required to
make accurate maneuvers of the probe over the human body while making sense of
the ultrasound images for diagnostic purposes. This procedure requires a
substantial amount of training and up to a few years of experience. In this
paper, we propose an autonomous robotic ultrasound system that uses Bayesian
Optimization (BO) in combination with the domain expertise to predict and
effectively scan the regions where diagnostic quality ultrasound images can be
acquired. The quality map, which is a distribution of image quality in a
scanning region, is estimated using Gaussian process in BO. This relies on a
prior quality map modeled using expert's demonstration of the high-quality
probing maneuvers. The ultrasound image quality feedback is provided to BO,
which is estimated using a deep convolution neural network model. This model
was previously trained on database of images labelled for diagnostic quality by
expert radiologists. Experiments on three different urinary bladder phantoms
validated that the proposed autonomous ultrasound system can acquire ultrasound
images for diagnostic purposes with a probing position and force accuracy of
98.7% and 97.8%, respectively.


  The 6d $\mathcal{N}=(2,0)$ theory has natural surface operator observables,
which are akin in many ways to Wilson loops in gauge theories. We propose a
definition of a "locally BPS" surface operator and study its conformal
anomalies, the analog of the conformal dimension of local operators. We study
the abelian theory and the holographic dual of the large $N$ theory refining
previously used techniques. Introducing non-constant couplings to the scalar
fields allows for an extra anomaly coefficient, which we find in both cases to
be related to one of the geometrical anomaly coefficients, suggesting a general
relation due to supersymmetry. We also comment on surfaces with conical
singularities.


  We deal with the study of the evolution of the allelic frequencies, at a
single locus, for a population distributed continuously over a bounded habitat.
We consider evolution which occurs under the joint action of selection and
arbitrary migration, that is independent of genotype, in absence of mutation
and random drift. The focus is on a conjecture, that was raised up in
literature of population genetics, about the possible uniqueness of polymorphic
equilibria, which are known as clines, under particular circumstances. We study
the number of these equilibria, making use of topological tools, and we give a
negative answer to that question by means of two examples. Indeed, we provide
numerical evidence of multiplicity of positive solutions for two different
Neumann problems satisfying the requests of the conjecture.


  Molecular beam epitaxy has been employed to obtain Ga1-xMnxN films with x up
to 10% and Curie temperatures T_C up to 13 K. The magnitudes of T_C and their
dependence on x, T_C(x) ~ x^m, where m = 2.2 +/- 0.2 are quantitatively
described by a tight binding model of superexchange interactions and Monte
Carlo simulations of T_C. The critical behavior of this dilute magnetic
insulator shows strong deviations from the magnetically clean case (x = 1), in
particular, (i) an apparent breakdown of the Harris criterion; (ii) a
non-monotonic crossover in the values of the susceptibility critical exponent
gamma_eff between the high temperature and critical regimes, and (iii) a
smearing of the critical region, which can be explained either by the Griffiths
effects or by macroscopic inhomogeneities in the spin distribution with a
variance Delta x = (0.2 +/- 0.1)%.


  Rotors of reaction and diffusion, that revolve around a circular singularity,
and the corresponding spiral wave activity around it, influence the nature of
several excitable media. Their dynamics are known to be affected by target
waves and external gradients. When the core of two spirals come very close to
each other, they could either repel or attract, depending on their relative
chirality and the distance separating them. Multiple pairs of spiral waves, in
close vicinity, could alter the paths of the individual rotors. A single spiral
core, will be influenced most by the rotor closest to it, or linked to it by a
common wave. If within a limiting distance, they would attract each other, and
annihilate. Else, they will push each other away, until they reach a critical
distance, beyond which, all interactions seem to cease. We have carried out
numerical simulations based on a reaction-diffusion model to show the possible
interactions of multiple spiral rotors. We are able to find a quantitative
measurement of the distances determining the kind of interaction. Some unique
dynamics is also unraveled. Experiments with the Belousov-Zhabotinsky reaction
have successfully demonstrated the validity of our numerical results.


  Using target space null reduction of the Polyakov action we find a novel
covariant action for strings moving in a torsional Newton-Cartan geometry.
Sending the string tension to zero while rescaling the Newton-Cartan clock
1-form, so as to keep the string action finite, we obtain a non-relativistic
string moving in a new type of non-Lorentzian geometry that we call
$U(1)$-Galilean geometry. We apply this to strings on $AdS_5 \times S^5$ for
which we show that the zero tension limit is realized by the Spin Matrix theory
limits of the AdS/CFT correspondence. This is closely related to limits of spin
chains studied in connection to integrability in AdS/CFT. The simplest example
gives a covariant version of the Landau-Lifshitz sigma-model.


  Long gamma-ray bursts (GRB), explosions of very massive stars, provide
crucial information on stellar and galaxy evolution, even at redshifts z ~ 8 -
9.5, when the Universe was only 500-600 million years old. Recently, during
observations of a galaxy at a redshift of z ~ 11 (400 million years after the
Big Bang), a bright signal, named GN-z11-flash, shorter than 245 s was detected
and interpreted as an ultraviolet flash associated with a GRB in this galaxy,
or a shock-breakout in a Population III supernova. Its resulting luminosity
would be consistent with that of other GRBs, but a discussion based on
probability arguments started on whether this is instead a signal from a
man-made satellite or a Solar System object. Here we show a conclusive
association of GN-z11-flash with Breeze-M upper stage of a Russian Proton
rocket on a highly elliptical orbit. This rules out GN-z11-flash as the most
distant GRB ever detected. It also implies that monitoring of a larger sample
of very high redshift galaxies is needed to detect such distant GRBs. This also
highlights the importance of a complete database of Earth satellites and
debris, which can allow proper interpretation of astronomical observations.


  We report the direct observation of the current-driven domain wall (DW)
motion by magnetic force microscopy in a structured Co/Ni wire with
perpendicular magnetic anisotropy. The wire has notches to define the DW
position. It is demonstrated that single current pulses can precisely control
the DW position from notch to notch with high DW velocity of 40 m/s.


  We study a non-Hermitian generalization of strongly correlated quantum
systems in which the transfer energy of electrons is asymmetric. It is known
that a non-Hermitian critical point is equal to the inverse localization length
of a Hermitian non-interacting random electron system. We here conjecture that
we can obtain in the same way the correlation length of a Hermitian interacting
non-random system. We confirm the conjecture using exact solutions and
numerical finite-size data of the Hubbard model and the antiferromagnetic XXZ
model in one dimension.


  In this paper, we characterize a novel separation property for IFS-attractors
on complete metric spaces. Such a separation property is weaker than the strong
open set condition (SOSC) and becomes necessary to reach the equality between
the similarity and the Hausdorff dimensions of strict self-similar sets. We
also investigate the size of the overlaps from the viewpoint of that separation
property. In addition, we contribute some equivalent conditions to reach the
equality between the similarity dimension and a new Hausdorff type dimension
for IFS-attractors introduced by the authors in terms of finite coverings.


  In this work we present denoiSplit, a method to tackle a new analysis task,
i.e. the challenge of joint semantic image splitting and unsupervised
denoising. This dual approach has important applications in fluorescence
microscopy, where semantic image splitting has important applications but noise
does generally hinder the downstream analysis of image content. Image splitting
involves dissecting an image into its distinguishable semantic structures. We
show that the current state-of-the-art method for this task struggles in the
presence of image noise, inadvertently also distributing the noise across the
predicted outputs. The method we present here can deal with image noise by
integrating an unsupervised denoising sub-task. This integration results in
improved semantic image unmixing, even in the presence of notable and realistic
levels of imaging noise. A key innovation in denoiSplit is the use of
specifically formulated noise models and the suitable adjustment of
KL-divergence loss for the high-dimensional hierarchical latent space we are
training. We showcase the performance of denoiSplit across 4 tasks on
real-world microscopy images. Additionally, we perform qualitative and
quantitative evaluations and compare results to existing benchmarks,
demonstrating the effectiveness of using denoiSplit: a single Variational
Splitting Encoder-Decoder (VSE) Network using two suitable noise models to
jointly perform semantic splitting and denoising.


  We demonstrate that a scalar field is unable to reverse its direction of
motion while continuously exchanging energy with another fluid. If the rate of
transfer is modulated by the scalar's acceleration, the field can undergo a
rapid process of freezing, despite being displaced from the local minimum of
its potential. This enables dark energy to form from any potential, regardless
of its shape. The field's equation of state mimicks that of a cosmological
constant. We present a physically motivated realisation in the form of a
derivative neutrino-majoron coupling. Coherent motions, which form only once
the neutrinos become non-relativistic, could be responsible for instigating the
freezing process. This would provide a natural resolution to the dark energy
coincidence problem, while avoiding the dynamical instabilities associated with
mass-varying neutrino models. Finally we discuss possible means by which this
model could be experimentally verified.


  We present a quantitative experimental and theoretical study of shot-to-shot
intensity fluctuations in the emitted light of a random laser. A model that
clarifies these intrinsic fluctuations is developed. We describe the output
versus input power graphs of the random laser with an effective spontaneous
emission factor (beta factor).


  We modify the Relative State Interpretation (RSI) of Quantum Mechanics so
that it does not imply many worlds and parallel realities. We drop the
assumption that probability amplitudes correspond one-to-one with reality: Not
all information is contained in amplitudes, and not all amplitudes need be
realized. Amplitudes do not "collapse" after a measurement, but evolve
continuously, including unrealized ones. After each "event" only one possible
outcome is realized. Therefore, if a value is measured, that value is real, all
others are not; there is only one reality and one world. Reality content is
"quantized" : unity for realized outcomes, zero for all others. It is
"conserved": can move along any possible sequence of events, but only one at a
time. The modified RSI is is strictly deterministic in the sense that the
"global" probability amplitudes of the universe are determined for all times by
the laws of physics and the initial conditions. They guide all events. But it
is not deterministic in the sense that from the amplitudes one can not predict
which outcome actually happens; that represents new information that
accumulates as history unfolds. To the extent that information is part of the
physical world, the coming into being of the universe is ongoing, even after
the Big Bang. All predictions of the two versions agree, except possibly in
esoteric, untested cases.


  Let $S$ be a point set in the plane such that each of its elements is colored
either red or blue. A matching of $S$ with rectangles is any set of
pairwise-disjoint axis-aligned rectangles such that each rectangle contains
exactly two points of $S$. Such a matching is monochromatic if every rectangle
contains points of the same color, and is bichromatic if every rectangle
contains points of different colors. In this paper we study the following two
problems:
  1. Find a maximum monochromatic matching of $S$ with rectangles.
  2. Find a maximum bichromatic matching of $S$ with rectangles.
  For each problem we provide a polynomial-time approximation algorithm that
constructs a matching with at least $1/4$ of the number of rectangles of an
optimal matching. We show that the first problem is $\mathsf{NP}$-hard even if
either the matching rectangles are restricted to axis-aligned segments or $S$
is in general position, that is, no two points of $S$ share the same $x$ or $y$
coordinate. We further show that the second problem is also $\mathsf{NP}$-hard,
even if $S$ is in general position. These $\mathsf{NP}$-hardness results follow
by showing that deciding the existence of a perfect matching is
$\mathsf{NP}$-complete in each case. The approximation results are based on a
relation of our problem with the problem of finding a maximum independent set
in a family of axis-aligned rectangles. With this paper we extend previous ones
on matching one-colored points with rectangles and squares, and matching
two-colored points with segments. Furthermore, using our techniques, we prove
that it is $\mathsf{NP}$-complete to decide a perfect matching with rectangles
in the case where all points have the same color, solving an open problem of
Bereg, Mutsanas, and Wolff [CGTA (2009)].


  The $c$-axis penetration depth $\Delta\lambda_c$ in
Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ (BSCCO) single crystals as a function of
temperature has been determined using two techniques, namely, measurements of
the ac-susceptibility at a frequency of 100 kHz and the surface impedance at
9.4 GHz. Both techniques yield an almost linear function
$\Delta\lambda_c(T)\propto T$ in the temperature range T<0.5 T_c.
Electrodynamic analysis of the impedance anisotropy has allowed us to estimate
$\lambda_c(0)\approx 50 \mu$m in BSCCO crystals overdoped with oxygen
($T_c\approx 84$ K) and $\lambda_c(0)\approx 150 \mu$m at the optimal doping
level ($T_c\approx 90$ K).


  We formulate the equations for point vortex dynamics on a closed two
dimensional Riemann manifold in the language of affine and other kinds of
connections. The speed of a vortex is then expressed in terms of the difference
between an affine connection derived from the coordinate Robin function and the
Levi-Civita connection associated to the Riemannian metric.
  A Hamiltonian formulation of the same dynamics is also given. The relevant
Hamiltonian function consists of two main terms. One of the terms is the
well-known quadratic form based on a matrix whose entries are Green and Robin
functions, while the other term describes the energy contribution from those
circulating flows which are not implicit in the Green functions. One main issue
of the paper is the clarification of the somewhat intricate exchanges of energy
between these two terms of the Hamiltonian.


  An optimization of caching strategies is proposed as a formal approach
allowing us a more efficient use of two-level computer memory. This approach is
based on a set of mathematical models and a set of theorems, permitting
analytical determination of optimal caching strategy operating characteristics,
thus minimising time loss caused by optimal strategy search.


  We report on the observation of quantum criticality forming at the transition
point between topological Anderson insulator phases in a one-dimensional
photonic quantum walk with spin. The walker's probability distribution reveals
a time-staggered profile of the dynamical spin-susceptibility, recently
suggested as a smoking gun signature for topological Anderson criticality in
the chiral symmetry class AIII. Controlled breaking of phase coherence removes
the signal, revealing its origin in quantum coherence.


  The research aims to analyze the impact that severe plastic deformation
arising during Rotary Swaging has on mechanical properties and corrosion
resistance of a near-a-titanium alloy Ti-2.5Al-2.6Zr (Russian industrial name
PT7M). The nature of corrosion decay in fine-grained alloys caused by hot salt
corrosion is known to vary from pit corrosion to intercrystalline corrosion at
the onset of recrystallization processes. Resistance to hot salt corrosion in a
fine-grained titanium alloy Ti-2.5Al-2.6Zr is shown to depend on the
structural-phase state of grain boundaries that varies during their migration
as a result of covering corrosive doping elements (aluminum, zirconium)
distributed in the crystal lattice of a titanium alloy.


  We theoretically study spin-wave modes and their intense excitations
activated by microwave magnetic fields in the skyrmion-crystal phase of
insulating magnets by numerically analyzing a two-dimensional spin model using
the Landau-Lifshitz-Gilbert equation. Two peaks of spin-wave resonances with
frequencies of ~1 GHz are found for in-plane a.c. magnetic field where
distribution of the out-of-plane spin components circulates around each
skyrmion core. Directions of the circulations are opposite between these two
modes, and hence the spectra exhibit salient dependence on the circular
polarization of irradiating microwave. A breathing-type mode is also found for
out-of-plane a.c. magnetic field. By intensively exciting these collective
modes, melting of the skyrmion crystal accompanied by a red shift of the
resonant frequency is achieved within nano seconds.


  We present an approach called Dialogue Action Tokens (DAT) that adapts
language model agents to plan goal-directed dialogues. The core idea is to
treat each utterance as an action, thereby converting dialogues into games
where existing approaches such as reinforcement learning can be applied.
Specifically, we freeze a pretrained language model and train a small planner
model that predicts a continuous action vector, used for controlled generation
in each round. This design avoids the problem of language degradation under
reward optimization. When evaluated on the Sotopia platform for social
simulations, the DAT-steered LLaMA model surpasses GPT-4's performance. We also
apply DAT to steer an attacker language model in a novel multi-turn red-teaming
setting, revealing a potential new attack surface.


  Recent progress in table-top experiments offers the opportunity to show for
the first time that gravity is not compatible with a classical description. In
all current experimental proposals, such as the generation of gravitationally
induced entanglement between two quantum sources of gravity, gravitational
effects can be explained with the Newton potential, namely in a regime that is
consistent with the weak-field limit of general relativity and does not probe
the field nature of gravity. Hence, the Newtonian origin of the effects is a
limitation to the conclusions on the nature of gravity that can be drawn from
these experiments.
  Here, we identify two effects that overcome this limitation: they cannot be
reproduced using the Newton potential and are independent of graviton emission.
First, we show that the interaction between two generic quantum sources of
gravity, e.g. in wide Gaussian states, cannot be reproduced with the Newton
potential nor with a known classical theory or gravity. Hence, observing the
form of this interaction would require either a modification to classical
gravity or its quantum description. Second, we show that the quantum commutator
between the gravitational field and its canonically conjugate momentum appears
as an additional term in the relative phase of a generic quantum source
interacting with a test particle. Observing this term in the phase would be a
test of the gravitational field as a quantum mediator.
  Identifying stronger quantum aspects of gravity than those reproducible with
the Newton potential is crucial to prove the nonclassicality of the
gravitational field and to plan a new generation of experiments testing quantum
aspects of gravity in a broader sense than what proposed so far.


  Strong electric fields are known to create biased adatom migration on
metallic surfaces. We present a Kinetic Monte Carlo model that can simulate
adatom migration on a tungsten (W) surface in electric fields. We validate our
model by using it to calculate the drift velocity of the adatom at different
fields and temperature and comparing the results with experimental data from
the literature. We obtain excellent agreement.


  Despite the success achieved by existing image generation and editing
methods, current models still struggle with complex problems including
intricate text prompts, and the absence of verification and self-correction
mechanisms makes the generated images unreliable. Meanwhile, a single model
tends to specialize in particular tasks and possess the corresponding
capabilities, making it inadequate for fulfilling all user requirements. We
propose GenArtist, a unified image generation and editing system, coordinated
by a multimodal large language model (MLLM) agent. We integrate a comprehensive
range of existing models into the tool library and utilize the agent for tool
selection and execution. For a complex problem, the MLLM agent decomposes it
into simpler sub-problems and constructs a tree structure to systematically
plan the procedure of generation, editing, and self-correction with
step-by-step verification. By automatically generating missing position-related
inputs and incorporating position information, the appropriate tool can be
effectively employed to address each sub-problem. Experiments demonstrate that
GenArtist can perform various generation and editing tasks, achieving
state-of-the-art performance and surpassing existing models such as SDXL and
DALL-E 3, as can be seen in Fig. 1. Project page is
https://zhenyuw16.github.io/GenArtist_page.


  In this paper, our focus is on enhancing steering angle prediction for
autonomous driving tasks. We initiate our exploration by investigating two
veins of widely adopted deep neural architectures, namely ResNets and
InceptionNets. Within both families, we systematically evaluate various model
sizes to understand their impact on performance. Notably, our key contribution
lies in the incorporation of an attention mechanism to augment steering angle
prediction accuracy and robustness. By introducing attention, our models gain
the ability to selectively focus on crucial regions within the input data,
leading to improved predictive outcomes. Our findings showcase that our
attention-enhanced models not only achieve state-of-the-art results in terms of
steering angle Mean Squared Error (MSE) but also exhibit enhanced adversarial
robustness, addressing critical concerns in real-world deployment. For example,
in our experiments on the Kaggle SAP and our created publicly available
datasets, attention can lead to over 6% error reduction in steering angle
prediction and boost model robustness by up to 56.09%.


  Groups of enterprises can serve as guarantees for one another and form
complex networks when obtaining loans from commercial banks. During economic
slowdowns, corporate default may spread like a virus and lead to large-scale
defaults or even systemic financial crises. To help financial regulatory
authorities and banks manage the risk associated with networked loans, we
identified the default contagion risk, a pivotal issue in developing preventive
measures, and established iConVis, an interactive visual analysis tool that
facilitates the closed-loop analysis process. A novel financial metric, the
contagion effect, was formulated to quantify the infectious consequences of
guarantee chains in this type of network. Based on this metric, we designed and
implement a series of novel and coordinated views that address the analysis of
financial problems. Experts evaluated the system using real-world financial
data. The proposed approach grants practitioners the ability to avoid previous
ad hoc analysis methodologies and extend coverage of the conventional Capital
Accord to the banking industry.


  We show different expressions of distribution functions (DFs) which depend
only on the two classical integrals of the energy and the magnitude of the
angular momentum with respect to the axis of symmetry for stellar systems with
known axisymmetric densities. The density of the system is required to be a
product of functions separable in the potential and the radial coordinate,
where the functions of the radial coordinate are powers of a sum of a square of
the radial coordinate and its unit scale. The even part of the two-integral DF
corresponding to this type of density is in turn a sum or an infinite series of
products of functions of the energy and of the magnitude of the angular
momentum about the axis of symmetry. A similar expression of its odd part can
be also obtained under the assumption of the rotation laws. It can be further
shown that these expressions are in fact equivalent to those obtained by using
Hunter and Qian's contour integral formulae for the system. This method is
generally computationally preferable to the contour integral method. Two
examples are given to obtain the even and odd parts of their two-integral DFs.
One is for the prolate Jaffe model and the other for the prolate Plummer model.
  It can be also found that the Hunter-Qian contour integral formulae of the
two-integral even DF for axisymmetric systems can be recovered by use of the
Laplace-Mellin integral transformation originally developed by Dejonghe.


  Controllability and observability have long been recognized as fundamental
structural properties of dynamical systems, but have recently seen renewed
interest in the context of large, complex networks of dynamical systems. A
basic problem is sensor and actuator placement: choose a subset from a finite
set of possible placements to optimize some real-valued controllability and
observability metrics of the network. Surprisingly little is known about the
structure of such combinatorial optimization problems. In this paper, we show
that an important class of metrics based on the controllability and
observability Gramians has a strong structural property that allows efficient
global optimization: the mapping from possible placements to the trace of the
associated Gramian is a modular set function. We illustrate the results via
placement of power electronic actuators in a model of the European power grid.


  We report the implementation of a general-order relativistic coupled-cluster
method for performing high-precision calculations of atomic and molecular
properties. As a first application, the static dipole polarizabilities of the
ground and first excited states of Al+ have been determined to precisely
estimate the uncertainty associated with the BBR shift of its clock frequency
measurement. The obtained relative BBR shift is -3.66+-0.44 for the 3s^2
^1S_0^0 --> 3s3p ^3P_0^0 transition in Al+ in contrast to the value obtained in
the latest clock frequency measurement, -9+-3 [Phys. Rev. Lett. 104, 070802
(2010)]. The method developed in the present work can be employed to study a
variety of subtle effects such as fundamental symmetry violations in atoms.


  The state-of-the-art smart city has been calling for an economic but
efficient energy management over large-scale network, especially for the
electric power system. It is a critical issue to monitor, analyze and control
electric loads of all users in system. In this paper, we employ the popular
computer vision techniques of AI to design a non-invasive load monitoring
method for smart electric energy management. First of all, we utilize both
signal transforms (including wavelet transform and discrete Fourier transform)
and Gramian Angular Field (GAF) methods to map one-dimensional current signals
onto two-dimensional color feature images. Second, we propose to recognize all
electric loads from color feature images using a U-shape deep neural network
with multi-scale feature extraction and attention mechanism. Third, we design
our method as a cloud-based, non-invasive monitoring of all users, thereby
saving energy cost during electric power system control. Experimental results
on both public and our private datasets have demonstrated our method achieves
superior performances than its peers, and thus supports efficient energy
management over large-scale Internet of Things (IoT).


  With their high beam energy and intensity, existing and near-future proton
beam dumps provide an excellent opportunity to search for new very weakly
coupled particles in the MeV to GeV mass range. One particularly interesting
example is a so-called axion-like particle (ALP), i.e. a pseudoscalar coupled
to two photons. The challenge in proton beam dumps is to reliably calculate the
production of the new particles from the interactions of two composite objects,
the proton and the target atoms. In this work we argue that Primakoff
production of ALPs proceeds in a momentum range where production rates and
angular distributions can be determined to sufficient precision using simple
electromagnetic form factors. Reanalysing past proton beam dump experiments for
this production channel, we derive novel constraints on the parameter space for
ALPs. We show that the NA62 experiment at CERN could probe unexplored parameter
space by running in 'dump mode' for a few days and discuss opportunities for
future experiments such as SHiP.


  We show that microscopic entropy formula based on Virasoro algebra follows
from properties of stationary Killing horizons for Lagrangians with arbitrary
dependence on Riemann tensor. The properties used are consequence of regularity
of invariants of Riemann tensor on the horizon. Eventual generalisation of
these results to Lagrangians with derivatives of Riemann tensor, as suggested
by an example treated in the paper, relies on assuming regularity of invariants
involving derivatives of Riemann tensor. This assumption however leads also to
new interesting restrictions on metric functions near horizon.


  We have studied strength in the BCS pairing force, used as a residual
interaction to the relativistic mean-field to reproduce the height of the inner
fission barriers for actinide nuclei. It was found that increasing the pairing
strength by about 13% makes reproduce the inner fission barriers better over a
wide range of actinide nuclei. This result was verified by using the
moment-of-inertia of pairing rotational energy, which was introduced to avoid
mean-field and odd-mass effects in the pairing interaction to deduce purely the
pairing strength. The pairing interaction thus determined could simultaneously
improve the description of the binding energy of heavy nuclei as well. As a
result, a consistent picture among inner fission barrier, binding energy, and
pairing moment of inertia could be obtained in terms of the relativistic
mean-field + BCS theory for a broad region of the actinide nuclei.


  Artificial Intelligence techniques such as Machine Learning (ML) have not
been exploited to their maximum potential in the legal domain. This has been
partially due to the insufficient explanations they provided about their
decisions. Automatic expert systems with explanatory capabilities can be
specially useful when legal practitioners search jurisprudence to gather
contextual knowledge for their cases. Therefore, we propose a hybrid system
that applies ML for multi-label classification of judgements (sentences) and
visual and natural language descriptions for explanation purposes, boosted by
Natural Language Processing techniques and deep legal reasoning to identify the
entities, such as the parties, involved. We are not aware of any prior work on
automatic multi-label classification of legal judgements also providing natural
language explanations to the end-users with comparable overall quality. Our
solution achieves over 85 % micro precision on a labelled data set annotated by
legal experts. This endorses its interest to relieve human experts from
monotonous labour-intensive legal classification tasks.


  This work considers a discrete-time Poisson noise channel with an input
amplitude constraint $\mathsf{A}$ and a dark current parameter $\lambda$. It is
known that the capacity-achieving distribution for this channel is discrete
with finitely many points. Recently, for $\lambda=0$, a lower bound of order
$\sqrt{\mathsf{A}}$ and an upper bound of order $\mathsf{A} \log^2(\mathsf{A})$
have been demonstrated on the cardinality of the support of the optimal input
distribution.
  In this work, we improve these results in several ways. First, we provide
upper and lower bounds that hold for non-zero dark current. Second, we produce
a sharper upper bound with a far simpler technique. In particular, for
$\lambda=0$, we sharpen the upper bound from the order of $\mathsf{A}
\log^2(\mathsf{A})$ to the order of $\mathsf{A}$. Finally, some other
additional information about the location of the support is provided.


  We construct an equivariant algebraic cobordism theory for schemes with an
action by a linear algebraic group over a field of characteristic zero.


  Efficiently capturing the long-range patterns in sequential data sources
salient to a given task -- such as classification and generative modeling --
poses a fundamental challenge. Popular approaches in the space tradeoff between
the memory burden of brute-force enumeration and comparison, as in
transformers, the computational burden of complicated sequential dependencies,
as in recurrent neural networks, or the parameter burden of convolutional
networks with many or large filters. We instead take inspiration from
wavelet-based multiresolution analysis to define a new building block for
sequence modeling, which we call a MultiresLayer. The key component of our
model is the multiresolution convolution, capturing multiscale trends in the
input sequence. Our MultiresConv can be implemented with shared filters across
a dilated causal convolution tree. Thus it garners the computational advantages
of convolutional networks and the principled theoretical motivation of wavelet
decompositions. Our MultiresLayer is straightforward to implement, requires
significantly fewer parameters, and maintains at most a $\mathcal{O}(N\log N)$
memory footprint for a length $N$ sequence. Yet, by stacking such layers, our
model yields state-of-the-art performance on a number of sequence
classification and autoregressive density estimation tasks using CIFAR-10,
ListOps, and PTB-XL datasets.


  We consider general field theories in six dimensions, with two of the
dimensions compactified on a T_{2}/Z_{4} orbifold. Six-dimensional Weyl
fermions propagating on this background give rise to a chiral zero-mode, which
makes them interesting for phenomenological applications. The compact
two-dimensional space is flat and has three conical singularities. We consider
the one-loop structure of these theories, and show that the presence of
logarithmic divergences requires the introduction of counterterms precisely at
these three singular points. We also show that the corresponding localized
operators are rotationally symmetric in the plane of the two extra dimensions,
as expected from the geometry about the singularities. We derive the
propagators for spin-0, spin-1/2 and spin-1 fields in momentum space, in such a
way that the appropriate boundary conditions are satisfied. This allows us to
efficiently calculate loop diagrams in any given model. We give general
expressions for the mass splittings among Kaluza-Klein modes within a given
level. Our results can also be used to obtain interesting KK-parity preserving
interactions among Kaluza-Klein modes. We pay special attention to the
components of six-dimensional gauge fields that transform as scalars under the
four-dimensional Lorentz group. These states provide a characteristic signature
for these scenarios. In particular, we find that they can easily be the
lightest particles in the Kaluza-Klein spectrum.


  We apply a recently developed adaptive algorithm that systematically improves
the efficiency of parallel tempering or replica exchange methods in the
numerical simulation of small proteins. Feedback iterations allow us to
identify an optimal set of temperatures/replicas which are found to concentrate
at the bottlenecks of the simulations. A measure of convergence for the
equilibration of the parallel tempering algorithm is discussed. We test our
algorithm by simulating the 36-residue villin headpiece sub-domain HP-36
wherewe find a lowest-energy configuration with a root-mean-square-deviation of
less than 4 Angstroem to the experimentally determined structure.


  The relaxation of an elastic network, constructed by a contact map of a
fractal (crumpled) polymer globule is investigated. We found that: i) the
slowest mode of the network is separated from the rest of the spectrum by a
wide gap, and ii) the network quickly relaxes to a low--dimensional
(one-dimensional, in our demonstration) manifold spanned by slowest degrees of
freedom with a large basin of attraction, and then slowly approaches the
equilibrium not escaping this manifold. By these dynamic properties, the
fractal globule elastic network is similar to real biological molecular
machines, like myosin. We have demonstrated that unfolding of a fractal globule
can be described as a cascade of equilibrium phase transitions in a
hierarchical system. Unfolding manifests itself in a sequential loss of
stability of hierarchical levels with the temperature change.


  Let S be a complete star-omega semiring and Sigma be an alphabet. For a
weighted omega-pushdown automaton P with stateset 1...n, n greater or equal to
1, we show that there exists a mixed algebraic system over a complete
semiring-semimodule pair ((S<<Sigma*>>)^nxn, (S<<Sigma^omega>>)^n) such that
the behavior ||P|| of P is a component of a solution of this system. In case
the basic semiring is the Boolean semiring or the semiring of natural numbers
(augmented with infinity), we show that there exists a mixed context-free
grammar that generates ||P||. The construction of the mixed context-free
grammar from P is a generalization of the well known triple construction and is
called now triple-pair construction for omega-pushdown automata.


  We introduce an infinite set of jet substructure observables, derived as
projections of $N$-point energy correlators, that are both convenient for
experimental studies and maintain remarkable analytic properties derived from
their representations in terms of a finite number of light ray operators. We
show that these observables can be computed using tracking or charge
information with a simple reweighting by integer moments of non-perturbative
track or fragmentation functions. Our results for the projected $N$-point
correlators are analytic functions of $N$, allowing us to derive resummed
results to next-to-leading logarithmic accuracy for all $N$. We analytically
continue our results to non-integer values of $N$ and define a corresponding
analytic continuation of the observable, which we term a $\nu$-correlator, that
can be measured on jets of hadrons at the LHC. This enables observables that
probe the leading twist collinear dynamics of jets to be placed into a single
analytic family, which we hope will lead to new insights into jet substructure.


  Zero Trust is a new security vision for 6G networks that emphasises the
philosophy of never trust and always verify. However, there is a fundamental
trade-off between the wireless transmission efficiency and the trust level,
which is reflected by the verification interval and its adaptation strategy.
More importantly, the mathematical framework to characterise the trust level of
the adaptive verification strategy is still missing. Inspired by this vision,
we propose a concept called age of trust (AoT) to capture the characteristics
of the trust level degrading over time, with the definition of the time elapsed
since the last verification of the target user's trust plus the initial age,
which depends on the trust level evaluated at that verification. The higher the
trust level, the lower the initial age. To evaluate the trust level in the long
term, the average AoT is used. We then investigate how to find a compromise
between average AoT and wireless transmission efficiency with limited
resources. In particular, we address the bi-objective optimization (BOO)
problem between average AoT and throughput over a single link with arbitrary
service process, where the identity of the receiver is constantly verified, and
we devise a periodic verification scheme and a Q-learning-based scheme for
constant process and random process, respectively. We also tackle the BOO
problem in a multiple random access scenario, where a trust-enhanced
frame-slotted ALOHA is designed. Finally, the numerical results show that our
proposals can achieve a fair compromise between trust level and wireless
transmission efficiency, and thus have a wide application prospect in various
zero-trust architectures.


  Let $\alpha_1,\ldots,\alpha_r$ be algebraic numbers in a number field $K$
generating a subgroup of rank $r$ in $K^\times$. We investigate under GRH the
number of primes $\mathfrak p$ of $K$ such that each of the orders of
$(\alpha_i\bmod\mathfrak p)$ lies in a given arithmetic progression associated
to $\alpha_i$. We also study the primes $\mathfrak p$ for which the index of
$(\alpha_i\bmod\mathfrak p)$ is a fixed integer or lies in a given set of
integers for each $i$. An additional condition on the Frobenius conjugacy class
of $\mathfrak p$ may be considered. Such results are generalizations of a
theorem of Ziegler from 2006, which concerns the case $r=1$ of this problem.


  The velocity function is a fundamental observable statistic of the galaxy
population, similarly impor- tant as the luminosity function, but much more
difficult to measure. In this work we present the first directly measured
circular velocity function that is representative between 60 < v_circ < 320
km/s for galaxies of all morphological types at a given rotation velocity. For
the low mass galaxy population (60 < v_circ < 170 km/s), we use the HIPASS
velocity function. For the massive galaxy population (170 < v_circ < 320 km/s),
we use stellar circular velocities from the Calar Alto Legacy Integral Field
Area Survey (CALIFA). In earlier work we obtained the measurements of circular
velocity at the 80% light radius for 226 galaxies and demonstrated that the
CALIFA sample can produce volume- corrected galaxy distribution functions. The
CALIFA velocity function includes homogeneous velocity measurements of both
late and early-type rotation-supported galaxies and has the crucial advantage
of not missing gas-poor massive ellipticals that HI surveys are blind to. We
show that both velocity functions can be combined in a seamless manner, as
their ranges of validity overlap. The resulting observed velocity function is
compared to velocity functions derived from cosmological simulations of the z =
0 galaxy population. We find that dark matter-only simulations show a strong
mismatch with the observed VF. Hydrodynamic simulations fare better, but still
do not fully reproduce observations.


  Recently, a class of machine learning methods called physics-informed neural
networks (PINNs) has been proposed and gained prevalence in solving various
scientific computing problems. This approach enables the solution of partial
differential equations (PDEs) via embedding physical laws into the loss
function. Many inverse problems can be tackled by simply combining the data
from real life scenarios with existing PINN algorithms. In this paper, we
present a multi-task learning method using uncertainty weighting to improve the
training efficiency and accuracy of PINNs for inverse problems in linear
elasticity and hyperelasticity. Furthermore, we demonstrate an application of
PINNs to a practical inverse problem in structural analysis: prediction of
external loads of diverse engineering structures based on limited displacement
monitoring points. To this end, we first determine a simplified loading
scenario at the offline stage. By setting unknown boundary conditions as
learnable parameters, PINNs can predict the external loads with the support of
measured data. When it comes to the online stage in real engineering projects,
transfer learning is employed to fine-tune the pre-trained model from offline
stage. Our results show that, even with noisy gappy data, satisfactory results
can still be obtained from the PINN model due to the dual regularization of
physics laws and prior knowledge, which exhibits better robustness compared to
traditional analysis methods. Our approach is capable of bridging the gap
between various structures with geometric scaling and under different loading
scenarios, and the convergence of training is also greatly accelerated through
not only the layer freezing but also the multi-task weight inheritance from
pre-trained models, thus making it possible to be applied as surrogate models
in actual engineering projects.


  We give an overview of track fitting using the Kalman filter method in the
NOMAD detector at CERN, and emphasize how the wealth of by-product information
can be used to analyze track breakpoints (discontinuities in track parameters
caused by scattering, decay, etc.). After reviewing how this information has
been previously exploited by others, we describe extensions which add power to
breakpoint detection and characterization. We show how complete fits to the
entire track, with breakpoint parameters added, can be easily obtained from the
information from unbroken fits. Tests inspired by the Fisher F-test can then be
used to judge breakpoints. Signed quantities (such as change in momentum at the
breakpoint) can supplement unsigned quantities such as the various chisquares.
We illustrate the method with electrons from real data, and with Monte Carlo
simulations of pion decays.


  We propose an axisymmetric angle-dependent gap (ADG) state with the broken
rotational symmetry in isospin-asymmetric nuclear matter. In this state, the
deformed Fermi spheres of neutrons and protons increase the pairing
probabilities along the axis of symmetry breaking near the average Fermi
surface. We find that the state possesses lower free energy and larger gap
value than the angle-averaged gap state at large isospin asymmetries. These
properties are mainly caused by the coupling of different m_{j} components of
the pairing gap. Furthermore, we find the transition from the ADG state to the
normal state is of second order and the ADG state vanishes at the critical
isospin asymmetry m_{j} where the angle-averaged gap vanishes.


  The aim of this paper is to discuss potential advances in PET kinetic models
and direct reconstruction of kinetic parameters. As a prominent example we
focus on a typical task in perfusion imaging and derive a system of
transport-reaction-diffusion equations, which is able to include macroscopic
flow properties in addition to the usual exchange between arteries, veins, and
tissues.
  For this system we propose an inverse problem of estimating all relevant
parameters from PET data. We interpret the parameter identification as a
nonlinear inverse problem, for which we formulate and analyze variational
regularization approaches. For the numerical solution we employ gradient-based
methods and appropriate splitting methods, which are used to investigate some
test cases.


  The recent detection of a young pulsar powering ``the Mouse'', G359.23--0.82,
as well as detailed imaging of surrounding nebular X-ray emission, have
motivated us to investigate the structural details and polarization
characteristics of the radio emission from this axisymmetric source with a
supersonic bow shock. Using polarization data at 3.6 and 6cm, we find that the
magnetic field wraps around the bow shock structure near the apex of the
system, but downnstream runs parallel to the inferred direction of the pulsar's
motion. The rotation measure (RM) distribution of the Mouse also suggests that
the low degree of polarization combined with a high RM ahead of the pulsar
result from internal plasma within the bowshock region. In addition, using
sub-arcsecond radio image of the Mouse, we identify modulations in the
brightness distribution of the Mouse that may be associated with the unshocked
pulsar wind behind the pulsar. Lastly, we discuss the relationship between the
Mouse and its neighboring shell-type supernova remnant G359.1--0.5 and argue
that these two sources could potentially have the same origin.


  We present results of long-term photometric monitoring of SS433 which proves
a secular evolutionary increase of the orbital period of SS433 at a rate of
$(1.14\pm 0.25)\times 10^{-7}$ s~s$^{-1}$. Using a physical model of
non-conservative mass transfer in SS433 through a supercritical accretion disc
around the compact companion, we reliably confirm that the binary mass ratio in
SS433, $q=M_x/M_v$ is $\gtrsim 0.8$. For an optical star mass $M_v\sim 10
M_\odot$ the compact object in SS433 is a black hole with mass $M_{BH}\gtrsim 8
M_\odot$. We discuss evolutionary implications of the found orbital period
increase in SS433 -- a secular change in the orbital separation and a size of
the Roche lobe of the optical star. We show that for the mass-loss rate
$dM_v/dt\sim 10^{-4}-3\times 10^{-5} M_\odot$ per year and an optical star mass
$M_v \sim 10-15 M_\odot$ the found orbital period increase implies the
corresponding orbital separation increase while the Roche lobe size can shrink
or expand around a mean constant value depending on the optical star mass-loss
rate which may be modulated with the precessional period.


  Locally repairable codes have become a key instrument in large-scale
distributed storage systems. This paper focuses on the construction of locally
repairable codes with $(r,\delta)$-locality that achieve the equality in the
Singleton-type bound. We use matrix-product codes to propose two infinite
families of $q$-ary optimal $(r,\delta)$ locally repairable codes of lengths up
to $q^2+q$. The ingredients in the matrix-product codes are either linear
maximum distance separable codes or optimal locally repairable codes of small
lengths. Further analysis and refinement yield a construction of another
infinite family of optimal $(r,\delta)$ locally repairable codes. The codes in
this third family have unbounded lengths not divisible by $(r+\delta-1)$.
  The three families of optimal $(r,\delta)$ locally repairable codes
constructed here are new. Previously constructed codes in the literature have
not covered the same sets of parameters. Our construction proposals are
flexible since one can easily vary $r$ and $\delta$ to come up with particular
parameters that can suit numerous scenarios.


  Due to the emergence of powerful computing resources and large-scale
annotated datasets, deep learning has seen wide applications in our daily life.
However, most current methods require extensive data collection and retraining
when dealing with novel classes never seen before. On the other hand, we humans
can quickly recognize new classes by looking at a few samples, which motivates
the recent popularity of few-shot learning (FSL) in machine learning
communities. Most current FSL approaches work on 2D image domain, however, its
implication in 3D perception is relatively under-explored. Not only needs to
recognize the unseen examples as in 2D domain, 3D few-shot learning is more
challenging with unordered structures, high intra-class variances, and subtle
inter-class differences. Moreover, different architectures and learning
algorithms make it difficult to study the effectiveness of existing 2D methods
when migrating to the 3D domain. In this work, for the first time, we perform
systematic and extensive studies of recent 2D FSL and 3D backbone networks for
benchmarking few-shot point cloud classification, and we suggest a strong
baseline and learning architectures for 3D FSL. Then, we propose a novel
plug-and-play component called Cross-Instance Adaptation (CIA) module, to
address the high intra-class variances and subtle inter-class differences
issues, which can be easily inserted into current baselines with significant
performance improvement. Extensive experiments on two newly introduced
benchmark datasets, ModelNet40-FS and ShapeNet70-FS, demonstrate the
superiority of our proposed network for 3D FSL.


  Deep learning models for image classification are often trained at a
resolution of 224 x 224 pixels for historical and efficiency reasons. However,
chest X-rays are acquired at a much higher resolution to display subtle
pathologies. This study investigates the effect of training resolution on chest
X-ray classification performance, using the chest X-ray 14 dataset. The results
show that training with a higher image resolution, specifically 1024 x 1024
pixels, results in the best overall classification performance with a mean AUC
of 84.2 % compared to 82.7 % when trained with 256 x 256 pixel images.
Additionally, comparison of bounding boxes and GradCAM saliency maps suggest
that low resolutions, such as 256 x 256 pixels, are insufficient for
identifying small pathologies and force the model to use spurious
discriminating features. Our code is publicly available at
https://gitlab.lrz.de/IP/cxr-resolution


  We present some generalizations of the well-known correspondence, found by R.
Exel, between partial actions of a group $G$ on a set $X$ and semigroup
homomorphism of $S(G)$ on the semigroup $I(X)$ of partial bijections of $X,$
being $S(G)$ an inverse monoid introduced by Exel. We show that any unital
premorphism $\theta:G\to S$, where $S$ is an inverse monoid, can be extended to
a semigroup homomorphism $\theta^*:T\to S$ for any inverse semigroup $T$ with
$S(G)\subseteq T\subseteq P^*(G)\times G,$ being $P^*(G)$ the semigroup of
non-empty subset of $G$, and such that $E(S)$ satisfies some lattice
theoretical condition. We also consider a topological version of this result.
We present a minimal Hausdorff inverse semigroup topology on $\Gamma(X)$, the
inverse semigroup of partial homeomorphism between open subsets of a locally
compact Hausdorff space $X$.


  In a recent paper, the authors proved that no spin foliation on a compact
enlargeable manifold with Hausdorff homotopy graph admits a metric of positive
scalar curvature on its leaves. This result extends groundbreaking results of
Lichnerowicz, Gromov and Lawson, and Connes on the non-existence of metrics of
positive scalar curvature. In this paper we review in more detail the material
needed for the proof of our theorem and we extend our non-existence results to
non-compact manifolds of bounded geometry. We also give a first obstruction
result for the existence of metric with (not necessarily uniform) leafwise PSC
in terms of the A-hat class in Haefliger cohomology.


  We find a group-theoretical condition under which a twist of a group algebra,
in Movshev's way, admits an integral Hopf order. Let $K$ be a (large enough)
number field with ring of integers $R$. Let $G$ be a finite group and $M$ an
abelian subgroup of $G$ of central type. Consider the twist $J$ for
$K\hspace{-0.8pt}G$ afforded by a non-degenerate $2$-cocycle on the character
group $\widehat{M}$. We show that if there is a Lagrangian decomposition
$\widehat{M} \simeq L \times \widehat{L}$ such that $L$ is contained in a
normal abelian subgroup $N$ of $G$, then the twisted group algebra
$(K\hspace{-0.8pt}G)_J$ admits a Hopf order $X$ over $R$. The Hopf order $X$ is
constructed as the $R$-submodule generated by the primitive idempotents of
$K\hspace{-1.1pt}N$ and the elements of $G$. It is indeed a Hopf order of
$K\hspace{-0.8pt}G$ such that $J^{\pm 1} \in X \otimes_R X$. Furthermore, we
give some criteria for this Hopf order to be unique. We illustrate this
construction with several families of examples. As an application, we provide a
further example of simple and semisimple complex Hopf algebra that does not
admit integral Hopf orders.


  The complex field $\Phi$ containing the QCD axion has a natural portal
coupling to the Higgs doublet of the form $\lambda_{h \phi}|\Phi|^2 |H|^2$.
Here we consider the possibility that $\lambda_{h \phi}$ has a natural
magnitude for a dimensionless coupling, $\lambda_{h \phi} \sim 0.1-1$. This is
possible if the total mass squared parameter of the Higgs in the vacuum,
including quadratic divergent and the $\Phi$ vacuum expectation value
contributions, is renormalized to reproduce the observed Higgs boson mass. It
is then possible for the axion sector to stabilize the electroweak vacuum. We
show the requirement of electroweak vacuum stability implies that the axion
decay constant satisfies $f_{a} < 1.3 \times 10^{10}$ GeV.


  Improving road safety and setting targets for reducing traffic-related
crashes and deaths are highlighted as part of the United Nation's sustainable
development goals and vision zero efforts around the globe. The advent of
transportation network companies, such as ridesourcing, expands mobility
options in cities and may impact road safety outcomes. In this study, we
analyze the effects of ridesourcing use on road crashes, injuries, fatalities,
and driving while intoxicated (DWI) offenses in Travis County Texas. Our
approach leverages real-time ridesourcing volume to explain variation in road
safety outcomes. Spatial panel data models with fixed effects are deployed to
examine whether the use of ridesourcing is significantly associated with road
crashes and other safety metrics. Our results suggest that for a 10% increase
in ridesourcing trips, we expect a 0.12% decrease in road crashes (p<0.05), a
0.25% decrease in road injuries (p<0.001), and a 0.36% decrease in DWI offenses
(p<0.0001) in Travis County. Ridesourcing use is not associated with road
fatalities at a 0.05 significance level. This study augments existing work
because it moves beyond binary indicators of ridesourcing presence or absence
and analyzes patterns within an urbanized area rather than metropolitan-level
variation. Contributions include developing a data-rich approach for assessing
the impacts of ridesourcing use on our transportation system's safety, which
may serve as a template for future analyses of other US cities. Our findings
provide feedback to policymakers by clarifying associations between
ridesourcing use and traffic safety, while helping identify sets of actions to
achieve safer and more efficient shared mobility systems.


  Let r mod m be the least positive residue of r modulo m, and set the height
of a pair (r,s) of integers, both relatively prime to m, to be the minimum over
k, with 0<k<m, of (k r mod m) + (k s mod m). Denote this quantity by h(m,r,s).
We give a formula for the height in terms of the continued fraction of r*s'/m,
where s' is the inverse of s modulo m. Now define SPECTRUM to be the set of
real numbers x with the property that there is a sequence (m_i,r_i,s_i) with
m_i --> infinity, gcd(r_i,m_i)=gcd(s_i,m_i)=1, and m_i^{-1} h(m_i,r_i,s_i) -->
x. The main result here is that SPECTRUM is the union of {0} and {1/k : k
=1,2,...}.


  Recent advances in convex optimization have led to new strides in the phase
retrieval problem over finite-dimensional vector spaces. However, certain
fundamental questions remain: What sorts of measurement vectors uniquely
determine every signal up to a global phase factor, and how many are needed to
do so? Furthermore, which measurement ensembles lend stability? This paper
presents several results that address each of these questions. We begin by
characterizing injectivity, and we identify that the complement property is
indeed a necessary condition in the complex case. We then pose a conjecture
that 4M-4 generic measurement vectors are both necessary and sufficient for
injectivity in M dimensions, and we prove this conjecture in the special cases
where M=2,3. Next, we shift our attention to stability, both in the worst and
average cases. Here, we characterize worst-case stability in the real case by
introducing a numerical version of the complement property. This new property
bears some resemblance to the restricted isometry property of compressed
sensing and can be used to derive a sharp lower Lipschitz bound on the
intensity measurement mapping. Localized frames are shown to lack this property
(suggesting instability), whereas Gaussian random measurements are shown to
satisfy this property with high probability. We conclude by presenting results
that use a stochastic noise model in both the real and complex cases, and we
leverage Cramer-Rao lower bounds to identify stability with stronger versions
of the injectivity characterizations.


  In a strongly frustrated square-lattice antiferromagnet with diagonal
coupling J', for J/(2J') < 1, an incommensurate spiral state with propagation
vector Q = (\pi +/- \delta, \pi +/- \delta) near (\pi,\pi) competes closely
with the Neel collinear antiferromagnetic ground state. For classical
Heisenberg spins the energy of the spiral state can be lowered as it adapts to
the distortion of the crystal lattice. As a result, a weak superstructural
modulation such as exist in doped cuprates might stabilize an incommensurate
spiral phase for some range of the parameter J/(2J') close to 1.


  We relate the strategy sets that a player ends up with after refining his own
strategies according to two very different models of rationality: namely,
utility maximization and regret minimization.


  The Fibonacci polynomials $\big\{F_n(x)\big\}_{n\ge 0}$ have been studied in
multiple ways. In this paper we study them by means of the theory of Heaps of
Viennot. In this setting our polynomials form a basis $\big\{P_n(x)\big\}_{n\ge
0}$ with $P_n(x)$ monic of degree $n$. This given, we are forced to set
$P_n(x)=F_{n+1}(x)$. The Heaps setting extends the Flajolet view of the
classical theory of orthogonal polynomials given by a three term recursion.
Thus with Heaps most of the identities for our $P_n(x)'s$ can be derived by
combinatorial arguments. Using the present setting we derive a variety of new
identities. We must mention that the theory of Heaps is presented here without
restrictions. This is much more than needed to deal with the Fibonacci
polynomials. We do this to convey a flavor of the power of Heaps. In the
lecture notes there is a chapter dedicated to Heaps where most of its contents
are dedicated to applications of the theory.


  Ground-based high-resolution spectra provide a powerful tool for
characterising exoplanet atmospheres. However, they are greatly hampered by the
dominating telluric and stellar lines, which need to be removed prior to any
analysis. Such removal techniques ("preparing pipelines") deform the spectrum,
hence a key point is to account for this process in the forward models used in
retrievals. We develop a formal derivation on how to prepare froward models for
retrievals, in the case where the telluric and instrumental deformations can be
represented as a matrix multiplied element-wise with the data. We also
introduce the notion of "Bias Pipeline Metric" (BPM), that can be used to
compare the bias potential of preparing pipelines. We use the resulting
framework to retrieve simulated observations of 1-D and 3-D exoplanet
atmospheres and to re-analyse high-resolution ($\mathcal{R} \approx 80\,400$)
near infrared (0.96--1.71 $\mu$m) CARMENES transit data of HD~189733~b. We
compare these results with those obtained from a CCF analysis. With our
fiducial retrieval, we find a blueshift of the absorption features of
$-5.51^{+0.66}_{-0.53}$ km$\cdot$s$^{-1}$. In addition, we retrieve a H$_2$O
$\log_{10}$(VMR) of $-2.39^{+0.12}_{-0.16}$ and a temperature of
$660^{+6}_{-11}$ K. We are also able to put upper limits for the abundances of
CH$_4$, CO, H$_2$S, HCN and NH$_3$, consistent with a sub-solar metallicity
atmosphere enriched in H$_2$O. We retrieve a broadened line shape, consistent
with rotation- and wind-induced line broadening. Finally, we find a lower limit
for the pressure of an opaque cloud consistent with a clear atmosphere, and
find no evidence for hazes.


  We consider a group-theoretic analogue of the classic subset sum problem. It
is known that every virtually nilpotent group has polynomial time decidable
subset sum problem. In this paper we use subgroup distortion to show that every
polycyclic non-virtually-nilpotent group has NP-complete subset sum problem.


  At a future Linear Collider one will be able to determine the masses of
charginos and neutralinos and their pair production cross sections to high
accuracies. We show how systematically including the cross sections into the
analysis improves the measurement of the underlying mass parameters, including
potential CP violating phases. In addition, we investigate how experimental
errors will affect the determination of these parameters. We present a first
estimate on the lower limit of observable small phases and on the accuracy in
determining large phases.


  We present the linearized metrizability problem in the context of parabolic
geometries and subriemannian geometry, generalizing the metrizability problem
in projective geometry studied by R. Liouville in 1889. We give a general
method for linearizability and a classification of all cases with irreducible
defining distribution where this method applies. These tools lead to natural
subriemannian metrics on generic distributions of interest in geometric control
theory.


  The Large Vision-Language Models (LVLMs) have demonstrated great abilities in
image perception and language understanding. However, existing multimodal
benchmarks focus on primary perception abilities and commonsense knowledge
which are insufficient to reflect the comprehensive capabilities of LVLMs. We
propose GAOKAO-MM, a multimodal benchmark based on the Chinese College Entrance
Examination (GAOKAO), comprising of 8 subjects and 12 types of images, such as
diagrams, function graphs, maps and photos. GAOKAO-MM derives from native
Chinese context and sets human-level requirements for the model's abilities,
including perception, understanding, knowledge and reasoning. We evaluate 10
LVLMs and find that the accuracies of all of them are lower than 50%, with
GPT-4-Vison (48.1%), Qwen-VL-Plus (41.2%) and Gemini-Pro-Vision (35.1%) ranking
in the top three positions. The results of our multi-dimension analysis
indicate that LVLMs have moderate distance towards Artificial General
Intelligence (AGI) and provide insights facilitating the development of
multilingual LVLMs.


  The large spin-orbit coupling in the valence band of group IV semiconductors
provides an electric field knob for spin-qubit manipulation. This fact can be
exploited with acceptor based qubits. Spin manipulation of holes bound to
acceptors in engineered SiGe quantum wells depends very strongly on the
electric field applied and on the heterostructure parameters. The g-factor is
enhanced by the Ge content and can be tuned by shifting the hole wave-function
between the heterostructure constituent layers. The lack of inversion symmetry
induced both by the quantum well and the electric fields together with the
g-factor tunability allows the possibility of different qubit manipulation
methods such as electron spin resonance, electric dipole spin resonance and
g-tensor modulation resonance. Rabi frequencies up to hundreds of MHz can be
achieved with heavy-hole qubits, and of the order of GHz with light-hole
qubits.


  The finite-size spectrum in the Kondo problem is obtained from the
Bethe-ansatz solution of the exactly solved models. We investigate the Anderson
model, the highly correlated SU($\nu$) Anderson model and the {\it s-d}
exchange model. For all these models we find that the spectra exhibit the
properties characteristic of the Fermi liquid fixed point, and hence our
microscopic calculations are in accordance with the results obtained by
boundary conformal field theory with current algebra symmetry.


  Using the bijection between partitions and vacillating tableaux, we establish
a correspondence between pairs of noncrossing free Dyck paths of length $2n$
and noncrossing partitions of $[2n+1]$ with $n+1$ blocks. In terms of the
number of up steps at odd positions, we find a characterization of Dyck paths
constructed from pairs of noncrossing free Dyck paths by using the Labelle
merging algorithm.


  We define the notion of subspace of an arithmetic universe by using its
internal dependent type theory.


  This paper consists of two parts. The first part is devoted to empirical
analysis of consolidated order book (COB) for the index RTS futures. In the
second part we consider Poissonian multi--agent model of the COB. By varying
parameters of different groups of agents submitting orders to the book we are
able to model various real life phenomenons. In particular we model the spread,
the profile of the book and large price changes. Two different mechanisms of
large price changes are considered in detail. One is the disbalance of
liquidity in the COB and another is the disbalance of sell and buy orders in
the order flow.


  We investigate the dependence of cluster abundance $n(>M,r_{cl})$, i.e., the
number density of clusters with mass larger than $M$ within radius $r_{cl}$, on
scale parameter $r_{cl}$. Using numerical simulations of clusters in the CDM
cosmogonic theories, we notice that the abundance of rich clusters shows a
simple scale invariance such that $n[>(r_{cl}/r_0)^{\alpha}M, r_{cl}]=
n(>M,r_0)$, in which the scaling index $\alpha$ remains constant in a scale
range where halo clustering is fully developed. The abundances of scale
$r_{cl}$ clusters identified from IRAS are found basically to follow this
scaling, and yield $\alpha \sim 0.5$ in the range $1.5 < r_{cl} < 4 h^{-1}$Mpc.
The scaling gains further supports from independent measurements of the index
$\alpha$ using samples of X-ray and gravitational lensing mass estimates. We
find that all the results agree within error limit as: $\alpha \sim 0.5 - 0.7$
in the range of $1.5 < r_{cl} < 4 h^{-1}$Mpc. These numbers are in good
consistency with the predictions of OCDM ($\Omega_M=0.3$) and LCDM
($\Omega_M+\Omega_{\Lambda} =1$), while the standard CDM model has different
behavior. The current result seems to favor models with a low mass density.


  We explore a possibility that the daily sea-level pressure (SLP) over South
Korea responds to the high-speed solar wind event. This is of interest in two
aspects: First, if there is a statistical association this can be another piece
of evidence showing that various meteorological observables indeed respond to
variations in the interplanetary environment. Second, this can be a very
crucial observational constraint since most models proposed so far are expected
to preferentially work in higher latitude regions than the low latitude region
studied here. We have examined daily solar wind speed ${\rm V}$, daily SLP
difference ${\rm \Delta SLP}$, and daily ${\rm \log(BV^{2})}$ using the
superposed epoch analysis in which the key date is set such that the daily
solar wind speed exceeds 800 ${\rm kms^{-1}}$. We find that the daily ${\rm
\Delta SLP}$ averaged out of 12 events reaches its peak at day +1 and gradually
decreases back to its normal level. The amount of positive deviation of ${\rm
\Delta SLP}$ is +2.5 hPa. The duration of deviation is a few days. We also find
that ${\rm \Delta SLP}$ is well correlated with both the speed of solar wind
and ${\rm \log(BV^{2})}$. The obtained linear correlation coefficients and
chance probabilities with one-day lag for two cases are $r \simeq 0.81$ with
$P> 99.9%$, and $r \simeq 0.84$ with $P> 99.9%$, respectively. We conclude by
briefly discussing future direction to pursue.


  Spectroscopic studies of few-body systems at ultracold temperatures provide
valuable information that often cannot be extracted in a hot environment.
Considering a pair of atoms, we propose a cooling mechanism that makes use of a
scattering Feshbach resonance. Application of a series of time-dependent
magnetic field ramps results in the situation in which either zero, one, or two
atoms remain trapped. If two atoms remain in the trap after the field ramps are
completed, then they have been cooled. Application of the proposed cooling
mechanism to optical traps or lattices is considered.


  The purpose is to study the CR-manifold with a contact structure conformal to
the Heisenberg group. In our previous work \cite{WY}, we have proved that if
the $Q'$-curvature is nonnegative, and the integral of $Q'$-curvature is below
the dimensional bound $c_1'$, then we have the isoperimetric inequality. In
this paper, we manage to drop the condition on the nonnegativity of the
$Q'$-curvature. We prove that the volume form $e^{4u}$ is a strong $A_\infty$
weight. As a corollary, we prove the Sobolev-Poincar\'e inequality on a class
of CR-manifolds with integrable $Q'$-curvature.


  By implementing the exact density matrix for the rotating anisotropic
harmonic trap, we derive a class of very fast and accurate fourth order
algorithms for evolving the Gross-Pitaevskii equation in imaginary time. Such
fourth order algorithms are possible only with the use of {\it forward},
positive time step factorization schemes. These fourth order algorithms
converge at time-step sizes an order-of-magnitude larger than conventional
second order algorithms. Our use of time-dependent factorization schemes
provides a systematic way of devising algorithms for solving this type of
nonlinear equations.


  High-quality data is essential for conversational recommendation systems and
serves as the cornerstone of the network architecture development and training
strategy design. Existing works contribute heavy human efforts to manually
labeling or designing and extending recommender dialogue templates. However,
they suffer from (i) the limited number of human annotators results in that
datasets can hardly capture rich and large-scale cases in the real world, (ii)
the limited experience and knowledge of annotators account for the
uninformative corpus and inappropriate recommendations. In this paper, we
propose a novel automatic dataset synthesis approach that can generate both
large-scale and high-quality recommendation dialogues through a data2text
generation process, where unstructured recommendation conversations are
generated from structured graphs based on user-item information from the real
world. In doing so, we comprehensively exploit: (i) rich personalized user
profiles from traditional recommendation datasets, (ii) rich external knowledge
from knowledge graphs, and (iii) the conversation ability contained in
human-to-human conversational recommendation datasets. Extensive experiments
validate the benefit brought by the automatically synthesized data under
low-resource scenarios and demonstrate the promising potential to facilitate
the development of a more effective conversational recommendation system.


  Let $k$ be a perfect field of odd characteristic and $X$ a smooth algebraic
variety over $k$ which is $W_2$-liftable. We show that the exponent twisiting
of the classical Cartier descent gives an equivalence of categories between the
category of nilpotent Higgs sheaves of exponent $\leq p-1$ over $X/k$ and the
category of nilpotent flat sheaves of exponent $\leq p-1$ over $X/k$, and it is
equivalent up to sign to the inverse Cartier and Cartier transforms for these
nilpotent objects constructed in the nonabelian Hodge theory in positive
characteristic by Ogus-Vologodsky. In view of the crucial role that
Deligne-Illusie's lemma has ever played in their algebraic proof of $E_1$
degeneration and Kodaira vanishing theorem in abelian Hodge theory, it may not
be overly surprising that again this lemma plays a significant role via the
concept of Higgs-de Rham flow in establishing $p$-adic Simpson correspondence
in nonabelian Hodge theory and Langer's algebraic proof of Bogomolov inequality
for semistable Higgs bundles and Miyaoka-Yau inequality.


  This work focuses on the study of quantum stochastic walks, which are a
generalization of coherent, i. e. unitary quantum walks. Our main goal is to
present a measure of a coherence of the walk. To this end, we utilize the
asymptotic scaling exponent of the second moment of the walk i. e. of the mean
squared distance covered by a walk. As the quantum stochastic walk model
encompasses both classical random walks and quantum walks, we are interested
how the continuous change from one regime to the other influences the
asymptotic scaling exponent. Moreover this model allows for behavior which is
not found in any of the previously mentioned model -- the model with global
dissipation. We derive the probability distribution for the walker, and
determine the asymptotic scaling exponent analytically, showing that ballistic
regime of the walk is maintained even at large dissipation strength.


  This paper is devoted to the description of the lack of compactness of
$H^1_{rad}(\R^2)$ in the Orlicz space. Our result is expressed in terms of the
concentration-type examples derived by P. -L. Lions. The approach that we adopt
to establish this characterization is completely different from the methods
used in the study of the lack of compactness of Sobolev embedding in Lebesgue
spaces and take into account the variational aspect of Orlicz spaces. We also
investigate the feature of the solutions of non linear wave equation with
exponential growth, where the Orlicz norm plays a decisive role.


  As part of his study of representations of the polycylic monoids, M.V. Lawson
described all the closed inverse submonoids of a polycyclic monoid $P_n$ and
classified them up to conjugacy. We show that Lawson's description can be
extended to closed inverse subsemigroups of graph inverse semigroups. We then
apply B. Schein's theory of cosets in inverse semigroups to the closed inverse
subsemigroups of graph inverse semigroups: we give necessary and sufficient
conditions for a closed inverse subsemigroup of a graph inverse semigroup to
have finite index, and determine the value of the index when it is finite.