  In this work we introduce a new theoretical framework for
Einstein-Gauss-Bonnet theories of gravity, which results to particularly
elegant, functionally simple and transparent gravitational equations of motion,
slow-roll indices and the corresponding observational indices. The main
requirement is that the Einstein-Gauss-Bonnet theory has to be compatible with
the GW170817 event, so the gravitational wave speed $c_T^2$ is required to be
$c_T^2\simeq 1$ in natural units. This assumption was also made in a previous
work of ours, but in this work we express all the related quantities as
functions of the scalar field. The constraint $c_T^2\simeq 1$ restricts the
functional form of the scalar Gauss-Bonnet coupling function $\xi(\phi)$ and of
the scalar potential $V(\phi)$, which must satisfy a differential equation.
However, by also assuming that the slow-roll conditions hold true, the
resulting equations of motion and the slow-roll indices acquire particularly
simple forms, and also the relation that yields the $e$-foldings number is
$N=\int_{\phi_i}^{\phi_f}\xi''/\xi'd \phi$, a fact that enables us to perform
particularly simple calculations in order to study the inflationary
phenomenological implications of several models. As it proves, the models we
presented are compatible with the observational data, and also satisfy all the
assumptions made during the process of extracting the gravitational equations
of motion. More interestingly, we also investigated the phenomenological
implications of an additional condition $\xi'/\xi''\ll 1$, which is motivated
by the slow-roll conditions that are imposed on the scalar field evolution and
on the Hubble rate, in which case the study is easier. Our approach opens a new
window in viable Einstein-Gauss-Bonnet theories of gravity.


  We have performed first-principles calculations of thick slabs of Ti-doped
sodium alanate (NaAlH_4), which allows to study the system energetics as the
dopant progresses from the surface to the bulk. Our calculations predict that
Ti stays on the surface, substitutes for Na, and attracts a large number of H
atoms to its vicinity. Molecular dynamics simulations suggest that the most
likely product of the Ti-doping is the formation of H-rich TiAl_n (n>1)
compounds on the surface, and hint at the mechanism by which Ti enhances the
reaction kinetics of NaAlH_4.


  This paper constructs a doubly robust estimator for continuous dose-response
estimation. An outcome regression model is augmented with a set of inverse
generalized propensity score covariates to correct for potential
misspecification bias. From the augmented model we can obtain consistent
estimates of mean average potential outcomes for distinct strata of the
treatment. A polynomial regression is then fitted to these point estimates to
derive a Taylor approximation to the continuous dose-response function. The
bootstrap is used for variance estimation. Analytical results and simulations
show that our approach can provide a good approximation to linear or nonlinear
dose-response functions under various sources of misspecification of the
outcome regression or propensity score models. Efficiency in finite samples is
good relative to minimum variance consistent estimators.


  We study a class of semi-linear differential Volterra equations with
polynomial-type potentials that incorporates the effects of memory while being
subjected to random perturbations via an additive Gaussian noise. We show that
for a broad class of non-linear potentials and sufficiently regular noise the
system always admits invariant probability measures, defined on the extended
phase space, that possess higher regularity properties dictated by the
structure of the nonlinearities in the equation. Furthermore, we investigate
the singular limit as the memory kernel collapses to a Dirac function.
Specifically, provided sufficiently many directions in the phase space are
stochastically forced, we show that there is a unique stationary measure to
which the system converges, in a suitable Wasserstein distance, at exponential
rates independent of the decay of the memory kernel. We then prove the
convergence of the statistically steady states to the unique invariant
probability of the classical stochastic reaction-diffusion equation in the
desired singular limit. As a consequence, we establish the validity of the
small memory approximation for solutions on the infinite time horizon
$[0,\infty)$.


  We derive and apply a partial differential equation for the moment generating
function of the Wright-Fisher model of population genetics.


  We present a new framework to conceptualize and operationalize the total user
experience of search, by studying the entirety of a search journey from an
utilitarian point of view.
  Web search engines are widely perceived as "free". But search requires time
and effort: in reality there are many intermingled non-monetary costs (e.g.
time costs, cognitive costs, interactivity costs) and the benefits may be
marred by various impairments, such as misunderstanding and misinformation.
This characterization of costs and benefits appears to be inherent to the human
search for information within the pursuit of some larger task: most of the
costs and impairments can be identified in interactions with any web search
engine, interactions with public libraries, and even in interactions with
ancient oracles. To emphasize this innate connection, we call these costs and
benefits Delphic, in contrast to explicitly financial costs and benefits.
  Our main thesis is that the users' satisfaction with a search engine mostly
depends on their experience of Delphic cost and benefits, in other words on
their utility. The consumer utility is correlated with classic measures of
search engine quality, such as ranking, precision, recall, etc., but is not
completely determined by them. To argue our thesis, we catalog the Delphic
costs and benefits and show how the development of search engines over the last
quarter century, from classic Information Retrieval roots to the integration of
Large Language Models, was driven to a great extent by the quest of decreasing
Delphic costs and increasing Delphic benefits.
  We hope that the Delphic costs framework will engender new ideas and new
research for evaluating and improving the web experience for everyone.


  Motivated by conjectures about near-horizon dynamics in quantum gravity, we
search for lines of perturbatively accessible fixed points emanating from
models of $N$ free fermions. Through two loops we find a new class of models,
apart from the well-known Abelian Thirring models. Further study is needed to
see whether these can lead to true conformal manifolds, or perhaps a new class
of large N fixed points.


  Distributed software engineering is widely recognized as a complex task.
Among the inherent complexities is the process of obtaining a system design
from its global requirement specification. This paper deals with such
transformation process and suggests an approach to derive the behavior of a
given system components, in the form of distributed Finite State Machines, from
the global system requirements, in the form of an augmented UML Activity
Diagrams notation. The process of the suggested approach is summarized in three
steps: the definition of the appropriate source Meta-Model (requirements
Meta-Model), the definition of the target Design Meta-Model and the definition
of the rules to govern the transformation during the derivation process. The
derivation process transforms the global system requirements described as UML
diagram activities (extended with collaborations) to system roles behaviors
represented as UML finite state machines. The approach is implemented using
Atlas Transformation Language (ATL).


  We consider the problem of estimating the maximum posterior probability (MAP)
state sequence for a finite state and finite emission alphabet hidden Markov
model (HMM) in the Bayesian setup, where both emission and transition matrices
have Dirichlet priors. We study a training set consisting of thousands of
protein alignment pairs. The training data is used to set the prior
hyperparameters for Bayesian MAP segmentation. Since the Viterbi algorithm is
not applicable any more, there is no simple procedure to find the MAP path, and
several iterative algorithms are considered and compared. The main goal of the
paper is to test the Bayesian setup against the frequentist one, where the
parameters of HMM are estimated using the training data.


  Scene text images contain not only style information (font, background) but
also content information (character, texture). Different scene text tasks need
different information, but previous representation learning methods use tightly
coupled features for all tasks, resulting in sub-optimal performance. We
propose a Disentangled Representation Learning framework (DARLING) aimed at
disentangling these two types of features for improved adaptability in better
addressing various downstream tasks (choose what you really need).
Specifically, we synthesize a dataset of image pairs with identical style but
different content. Based on the dataset, we decouple the two types of features
by the supervision design. Clearly, we directly split the visual representation
into style and content features, the content features are supervised by a text
recognition loss, while an alignment loss aligns the style features in the
image pairs. Then, style features are employed in reconstructing the
counterpart image via an image decoder with a prompt that indicates the
counterpart's content. Such an operation effectively decouples the features
based on their distinctive properties. To the best of our knowledge, this is
the first time in the field of scene text that disentangles the inherent
properties of the text images. Our method achieves state-of-the-art performance
in Scene Text Recognition, Removal, and Editing.


  Beam dump experiments have been used to search for new particles, $\phi$,
with null results interpreted in terms of limits on masses $m_\phi$ and
coupling constants $\epsilon$. However these limits have been obtained by using
approximations [including the Weizs\"{a}cker-Williams (WW) approximation] or
Monte-Carlo simulations. We display methods to obtain the cross section and the
resulting particle production rates without using approximations on the phase
space integral or Monte-Carlo simulations. In our previous work we examined the
case of the new scalar boson production; in this paper we explore all possible
new spin-0 and spin-1 particles. We show that the approximations cannot be used
to obtain accurate values of cross sections. The corresponding exclusion plots
differ by substantial amounts when seen on a linear scale. Furthermore, a new
region ($m_\phi<2m_e$) of parameter space can be explored without using one of
the common approximations, $m_\phi\gg m_e$. We derive new expressions for the
three photon decays of dark photon and four photon decays of new axial-vector
bosons. As a result, the production cross section and exclusion region of
different low mass ($m_\phi<2m_e$) bosons are very different. Moreover, our
method can be used as a consistency check for Monte-Carlo simulations.


  In this tutorial, we illustrate through examples how we can combine two
classical models, namely those of pushdown automata (PDA) and timed automata,
in order to obtain timed pushdown automata (TPDA). Furthermore, we describe how
the reachability problem for TPDAs can be reduced to the reachability problem
for PDAs.


  We present the results of high velocity and high spatial resolution HI
synthesis observations of the blue compact dwarf galaxy IZw18 to investigate
the link between its unique evolutionary history and the neutral gas
distribution and kinematics. The HI distribution is extensive, with diffuse
neutral gas extending to the northwest and south of the main component. This
diffuse gas may be a remnant of the nascent HI cloud. The kinematics of the
IZw18 system are complex, with 4 components identified: HI-A, HI-C, HI-I, and
HI-SX. The gas associated with the main body, HI-A, has a steep velocity
gradient; although our analysis is hindered by poor spatial resolution relative
to the extent of the system, the main body appears to be undergoing solid body
rotation. The optical condensation to the northwest of IZw18 is embedded in the
common HI envelope, and is found to be kinematically separate from the main
body (HI-C). The interbody gas, HI-I, connects HI-A and HI-C. Finally, a large
diffuse, kinematically distinct, gas component extends at least 1 arcmin to the
south of the main body (HI-SX), with no known optical counterpart. The peak of
the gas column density coincides with the SE HII region in the main body; two
other HI peaks are associated with the NW HII region and an HII region in the
optical condensation to the northwest. In many respects, the HI properties of
the main body of IZw18 (HI-A) are not unusual for dwarf galaxies; the peak
column density, gas dispersion, M_H/L_B, and M_H/M_T are remarkably similar to
other low mass systems. The neutral gas associated with IZw18 is best described
as a fragmenting HI cloud in the early stages of galaxy evolution.


  We investigate the completely positive semidefinite cone $\mathcal{CS}_+^n$,
a new matrix cone consisting of all $n\times n$ matrices that admit a Gram
representation by positive semidefinite matrices (of any size). In particular
we study relationships between this cone and the completely positive and doubly
nonnegative cones, and between its dual cone and trace positive non-commutative
polynomials.
  We use this new cone to model quantum analogues of the classical independence
and chromatic graph parameters $\alpha(G)$ and $\chi(G)$, which are roughly
obtained by allowing variables to be positive semidefinite matrices instead of
$0/1$ scalars in the programs defining the classical parameters. We can
formulate these quantum parameters as conic linear programs over the cone
$\mathcal{CS}_+^n$. Using this conic approach we can recover the bounds in
terms of the theta number and define further approximations by exploiting the
link to trace positive polynomials.


  We give a simplified definition of topological T-duality that applies to
arbitrary torus bundles. The new definition does not involve Chern classes or
spectral sequences, only gerbes and morphisms between them. All the familiar
topological conditions for T-duals are shown to follow. We determine necessary
and sufficient conditions for existence of a T-dual in the case of affine torus
bundles. This is general enough to include all principal torus bundles as well
as torus bundles with arbitrary monodromy representations. We show that
isomorphisms in twisted cohomology, twisted K-theory and of Courant algebroids
persist in this general setting. We also give an example where twisted K-theory
groups can be computed by iterating T-duality.


  Within the key issues of hadronic physics one of the interesting issues in
nuclear physics is whether there is a transition region between meson-nucleon
and quark-gluon degrees of freedom in the NN interaction. This question is
relevant for pairs of free nucleons as well as for nucleon pairs immersed in
nuclear matter. From NN phase shifts we deduce a dibaryonic scale of 1 GeV for
the soft core NN potential strengths at nucleon separation r equal 0.25 to 0.5
fm. A short range intermediate transition, with fusion and fission of the two
scattered nucleons into a dibaryon with prevailing quark-gluon dynamics, is
conjectured from NN optical models for T-lab greater 1.5 GeV. From efforts and
progress of nucleon-nucleus scattering analysis in the GeV region some results
are presented. This is our first step for an in-medium search for transitions
from the meson-nucleon into the quark-gluon sector using NA optical models.


  Safety critical avionics software is a natural application area for formal
verification. This is reflected in the formal method's inclusion into the
certification guideline DO-178C and its formal methods supplement DO-333.
Airbus and Dassault-Aviation, for example, have conducted studies in using
formal verification. A large German national research project, Verisoft XT,
also examined the application of formal methods in the avionics domain.
  However, formal methods are not yet mainstream, and it is questionable if
formal verification, especially formal deduction, can be integrated into the
software development processes of a resource constrained small or medium
enterprise (SME). ESG, a Munich based medium sized company, has conducted a
small experimental study on the application of formal verification on a small
portion of a real avionics project. The low level specification of a software
function was formalized with ACSL, and the corresponding source code was
partially verified using Frama-C and the WP plugin, with Alt-Ergo as automated
prover.
  We established a couple of criteria which a method should meet to be fit for
purpose for industrial use in SME, and evaluated these criteria with the
experience gathered by using ACSL with Frama-C on a real world example. The
paper reports on the results of this study but also highlights some issues
regarding the method in general which, in our view, will typically arise when
using the method in the domain of embedded real-time programming.


  Colorectal polyp segmentation (CPS), an essential problem in medical image
analysis, has garnered growing research attention. Recently, the deep
learning-based model completely overwhelmed traditional methods in the field of
CPS, and more and more deep CPS methods have emerged, bringing the CPS into the
deep learning era. To help the researchers quickly grasp the main techniques,
datasets, evaluation metrics, challenges, and trending of deep CPS, this paper
presents a systematic and comprehensive review of deep-learning-based CPS
methods from 2014 to 2023, a total of 115 technical papers. In particular, we
first provide a comprehensive review of the current deep CPS with a novel
taxonomy, including network architectures, level of supervision, and learning
paradigm. More specifically, network architectures include eight subcategories,
the level of supervision comprises six subcategories, and the learning paradigm
encompasses 12 subcategories, totaling 26 subcategories. Then, we provided a
comprehensive analysis the characteristics of each dataset, including the
number of datasets, annotation types, image resolution, polyp size, contrast
values, and polyp location. Following that, we summarized CPS's commonly used
evaluation metrics and conducted a detailed analysis of 40 deep SOTA models,
including out-of-distribution generalization and attribute-based performance
analysis. Finally, we discussed deep learning-based CPS methods' main
challenges and opportunities.


  Let $M_k$ ($k\in \mathbb Z$ and $|k|>4$) be the $3$-manifold obtained by
doing $k$ Dehn surgery on the figure-eight knot, and $X_t$ be the canonical
Anosov flow on $M_k$ that is constructed by Goodman. The main result of this
article is that if $|k|\gg 0$, then $Mod (M_k) \cong \mathbb {Z}_2 \oplus
\mathbb {Z}_2$ and every element of the mapping class group of $M_k$ can be
represented by a self orbit equivalence of $X_t$.


  Adversarial formulations such as generative adversarial networks (GANs) have
rekindled interest in two-player min-max games. A central obstacle in the
optimization of such games is the rotational dynamics that hinder their
convergence. In this paper, we show that game optimization shares dynamic
properties with particle systems subject to multiple forces, and one can
leverage tools from physics to improve optimization dynamics. Inspired by the
physical framework, we propose LEAD, an optimizer for min-max games. Next,
using Lyapunov stability theory and spectral analysis, we study LEAD's
convergence properties in continuous and discrete time settings for a class of
quadratic min-max games to demonstrate linear convergence to the Nash
equilibrium. Finally, we empirically evaluate our method on synthetic setups
and CIFAR-10 image generation to demonstrate improvements in GAN training.


  Given a Lie algebra $L$ graded by a group $G$, if $L$ is does not contain
orthogonal graded ideals and $G$ is generated by the support of $L$, then $G$
is an abelian group.


  This paper proposes an acoustic beam splitter based on acoustic Luneburg
lens. A two-dimensional acoustic Luneburg lens with gradient refractive index
is achieved to provide a practical realization for the acoustic beam splitter.
The acoustic wave propagation through the beam splitter was explored
theoretically, numerically and experimentally. Results show that three output
channels can be achieved using a point source on the edge of the beam splitter
in a broadband frequency range. Furthermore, the output channel directions can
be tuned via changing the design parameter.


  We establish some algebraic properties of the group
$\mathrm{Diff}(\mathbb{C}^n,0)$ of germs of analytic diffeomorphisms of
$\mathbb{C}^n$, and its formal completion
$\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$. For instance we describe the
commutator of $\mathrm{Diff}(\mathbb{C}^n,0)$, but also prove that any finitely
generated subgroup of $\mathrm{Diff}(\mathbb{C}^n,0)$ is residually finite; we
thus obtain some constraints of groups that embed into
$\mathrm{Diff}(\mathbb{C}^n,0)$. We show that
$\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$ is an Hopfian group, and that
$\mathrm{Diff}(\mathbb{C}^n,0)$ and $\widehat{\mathrm{Diff}}(\mathbb{C}^n,0)$
are not co-Hopfian. We end by the description of the automorphisms groups of
$\widehat{\mathrm{Diff}}(\mathbb{C},0)$, and $\mathrm{Diff}(\mathbb{C},0)$.


  The search for ``biologically plausible'' learning algorithms has converged
on the idea of representing gradients as activity differences. However, most
approaches require a high degree of synchronization (distinct phases during
learning) and introduce substantial computational overhead, which raises doubts
regarding their biological plausibility as well as their potential utility for
neuromorphic computing. Furthermore, they commonly rely on applying
infinitesimal perturbations (nudges) to output units, which is impractical in
noisy environments. Recently it has been shown that by modelling artificial
neurons as dyads with two oppositely nudged compartments, it is possible for a
fully local learning algorithm named ``dual propagation'' to bridge the
performance gap to backpropagation, without requiring separate learning phases
or infinitesimal nudging. However, the algorithm has the drawback that its
numerical stability relies on symmetric nudging, which may be restrictive in
biological and analog implementations. In this work we first provide a solid
foundation for the objective underlying the dual propagation method, which also
reveals a surprising connection with adversarial robustness. Second, we
demonstrate how dual propagation is related to a particular adjoint state
method, which is stable regardless of asymmetric nudging.


  Lie group methods are applied to the time-dependent, monoenergetic neutron
diffusion equation in materials with spatial and time dependence. To accomplish
this objective, the underlying 2nd order partial differential equation (PDE) is
recast as an exterior differential system so as to leverage the isovector
symmetry analysis approach. Some of the advantages of this method as compared
to traditional symmetry analysis approaches are revealed through its use in the
context of a 2nd order PDE. In this context, various material properties
appearing in the mathematical model (e.g., a diffusion coefficient and
macroscopic cross section data) are left as arbitrary functions of space and
time. The symmetry analysis that follows is restricted to a search for
translation and scaling symmetries; consequently the Lie derivative yields
specific material conditions that must be satisfied in order to maintain the
presence of these important similarity transformations. The principal outcome
of this work is thus the determination of analytic material property functions
that enable the presence of various translation and scaling symmetries within
the time- dependent, monoenergetic neutron diffusion equation. The results of
this exercise encapsulate and generalize many existing results already
appearing in the literature. While the results contained in this work are
primarily useful as phenomenological guides pertaining to the symmetry behavior
of the neutron diffusion equation under certain assumptions, they may
eventually be useful in the construction of exact solutions to the underlying
mathematical model. The results of this work are also useful as a starting
point or framework for future symmetry analysis studies pertaining to the
neutron transport equation and its many surrogates.


  Electron-hole hybridization in InAs/GaSb double quantum well structures leads
to the formation of a mini band gap. We experimentally and theoretically
studied the impact of strain on the transport properties of this material
system. Thinned samples were mounted to piezo electric elements to exert strain
along the [011] and [001] crystal directions. When the Fermi energy is tuned
through the mini gap, a dramatic impact on the resistivity at the charge
neutrality point is found which depends on the amount of applied external
strain. In the electron and hole regimes, strain influences the Landau level
structure. By analyzing the intrinsic strain from the epitaxial growth, the
external strain from the piezo elements and combining our experimental results
with numerical simulations of strained and unstrained quantum wells, we
compellingly illustrate why the InAs/GaSb material system is regularly found to
be semimetallic.


  Selected by NASA for an Astrophysics Science SmallSat study, The Virtual
Telescope for X-Ray Observations (VTXO) is a small satellite mission being
developed by NASAs Goddard Space Flight Center (GSFC) and New Mexico State
University (NMSU). VTXO will perform X-ray observations with an angular
resolution around 50 milliarcseconds, an order of magnitude better than is
achievable by current state of the art X-ray telescopes. VTXOs fine angular
resolution enables measuring the environments closer to the central engines in
compact X-ray sources. This resolution will be achieved by the use of Phased
Fresnel Lenses (PFLs) optics which provide near diffraction-limited imaging in
the X-ray band. However, PFLs require long focal lengths in order to realize
their imaging performance, for VTXO this dictates that the telescopes optics
and the camera will have a separation of 1 km. As it is not realistic to build
a structure this large in space, the solution being adapted for VTXO is to
place the camera, and the optics on two separate spacecraft and fly them in
formation with the necessary spacing. This requires centimeter level control,
and sub-millimeter level knowledge of the two spacecrafts relative transverse
position. This paper will present VTXOs current baseline, with particular
emphasis on the missions flight dynamics design.


  We study a stochastic process $X_t$ related to the Bessel and the Rayleigh
processes, with various applications in physics, chemistry, biology, economics,
finance and other fields. The stochastic differential equation is $dX_t =
(nD/X_t) dt + \sqrt{2D} dW_t$, where $W_t$ is the Wiener process. Due to the
singularity of the drift term for $X_t = 0$, different natures of boundary at
the origin arise depending on the real parameter $n$: entrance, exit, and
regular. For each of them we calculate analytically and numerically the
probability density functions of first-passage times or first-exit times.
Nontrivial behaviour is observed in the case of a regular boundary.


  Pansharpening is a widely used image enhancement technique for remote
sensing. Its principle is to fuse the input high-resolution single-channel
panchromatic (PAN) image and low-resolution multi-spectral image and to obtain
a high-resolution multi-spectral (HRMS) image. The existing deep learning
pansharpening method has two shortcomings. First, features of two input images
need to be concatenated along the channel dimension to reconstruct the HRMS
image, which makes the importance of PAN images not prominent, and also leads
to high computational cost. Second, the implicit information of features is
difficult to extract through the manually designed loss function. To this end,
we propose a generative adversarial network via the fast guided filter (FGF)
for pansharpening. In generator, traditional channel concatenation is replaced
by FGF to better retain the spatial information while reducing the number of
parameters. Meanwhile, the fusion objects can be highlighted by the spatial
attention module. In addition, the latent information of features can be
preserved effectively through adversarial training. Numerous experiments
illustrate that our network generates high-quality HRMS images that can surpass
existing methods, and with fewer parameters.


  The soft dipole modes in neutron rich even-even Ni-isotopes are investigated
in the quasiparticle relativistic random phase approximation. We study the
evolution of strengths distribution, centroid energies of dipole excitation in
low-lying and normal GDR regions with the increase of the neutron excess. It is
found in the present study that the centroid energies of the soft dipole
strengths strongly depend on the thickness of neutron skin along with the
neutron rich even-even Ni-isotopes.


  In this work, a framework for deriving theoretical equations for mean squared
displacement (MSD) and fractional Fokker-Planck (FFP) is developed for any
arbitrary rheological model. The obtained general results are then specified
for different fractional rheological models. To test the novel equations
extracted from our framework and bridge the gap between microrheology and
fractional rheological models, microrheology of polystyrene (PS) in
tetrahydrofuran (THF) solutions at several polymer concentrations is measured.
By comparing the experimental and theoretical MSDs, we find the fractional
rheological parameters and demonstrate for the first time that the polymer
concentration regimes can be distinguished using the fractional exponent and
relaxation time data because of the existence of a distinct behavior in each
regime. We suggest novel and simple approximations for the critical overlap
concentration and the shear viscosity of viscoelastic liquid-like solutions.
This work provides a new and more sensitive approach for distinguishing
different polymer concentration regimes and measuring the critical overlap
concentration and shear viscosity of polymeric solutions, which is useful when
conventional rheological characterization methods are unreliable due to the
volatility and low viscosity of the samples.


  Neural networks have been shown to improve performance across a range of
natural-language tasks. However, designing and training them can be
complicated. Frequently, researchers resort to repeated experimentation to pick
optimal settings. In this paper, we address the issue of choosing the correct
number of units in hidden layers. We introduce a method for automatically
adjusting network size by pruning out hidden units through $\ell_{\infty,1}$
and $\ell_{2,1}$ regularization. We apply this method to language modeling and
demonstrate its ability to correctly choose the number of hidden units while
maintaining perplexity. We also include these models in a machine translation
decoder and show that these smaller neural models maintain the significant
improvements of their unpruned versions.


  Reinforcement learning algorithms utilizing policy gradients (PG) to optimize
Conditional Value at Risk (CVaR) face significant challenges with sample
inefficiency, hindering their practical applications. This inefficiency stems
from two main facts: a focus on tail-end performance that overlooks many
sampled trajectories, and the potential of gradient vanishing when the lower
tail of the return distribution is overly flat. To address these challenges, we
propose a simple mixture policy parameterization. This method integrates a
risk-neutral policy with an adjustable policy to form a risk-averse policy. By
employing this strategy, all collected trajectories can be utilized for policy
updating, and the issue of vanishing gradients is counteracted by stimulating
higher returns through the risk-neutral component, thus lifting the tail and
preventing flatness. Our empirical study reveals that this mixture
parameterization is uniquely effective across a variety of benchmark domains.
Specifically, it excels in identifying risk-averse CVaR policies in some Mujoco
environments where the traditional CVaR-PG fails to learn a reasonable policy.


  In this short note we extend an estimate due to J. Simons on the first
stability eigenvalue of minimal hypersurfaces in spheres to the singular
setting. Specifically, we show that any singular minimal hypersurface in
$S^{n+1}$, which is not totally geodesic and satisfies the \alpha-structural
hypothesis, has first stability eigenvalue at most -2n, with equality if and
only if it is a product of two round spheres. The equality case was settled
independently in the classical setting by Wu and Perdomo.


  Under very general conditions the hitting time of a set by a stochastic
process is a stopping time. We give a new simple proof of this fact. The
section theorems for optional and predictable sets are easy corollaries of the
proof.


  We construct an explicit Green's function for the conjugated Laplacian
$e^{-\omega \cdot x/h}\Delta e^{-\omega \cdot x/h}$, which let us control our
solutions on roughly half of the boundary. We apply the Green's function to
solve a partial data inverse problem for the Schr\"odinger equation with
potential $q \in L^{n/2}$. We also use this Green's function to derive $L^p$
Carleman estimates similar to the ones in Kenig-Ruiz-Sogge \cite{krs}, but for
functions with support up to part of the boundary.


  Small footprint embedded devices require keyword spotters (KWS) with small
model size and detection latency for enabling voice assistants. Such a keyword
is often referred to as \textit{wake word} as it is used to wake up voice
assistant enabled devices. Together with wake word detection, accurate
estimation of wake word endpoints (start and end) is an important task of KWS.
In this paper, we propose two new methods for detecting the endpoints of wake
words in neural KWS that use single-stage word-level neural networks. Our
results show that the new techniques give superior accuracy for detecting wake
words' endpoints of up to 50 msec standard error versus human annotations, on
par with the conventional Acoustic Model plus HMM forced alignment. To our
knowledge, this is the first study of wake word endpoints detection methods for
single-stage neural KWS.


  The discrete Gaussian model for the surface of a crystal deposited on a
disordered substrate is studied by Monte Carlo simulations. A continuous
transition is found from a phase with a thermally-induced roughness to a glassy
one in which the roughness is driven by the disorder. The behavior of the
height-height correlations is consistent with the one-step replica symmetry
broken solution of the variational approximation. The results differ from the
renormalization group predictions and from recent simulations of a 2D
vortex-glass model which belongs to the same universality class.


  The transition from supernovae (SNe) to supernova remnants (SNRs) remains
poorly understood, given the age gap between well-studied examples of the two.
In order to bridge this gap, we analysed archival Chandra data for some of the
oldest supernovae detected in X-rays, in order to extend their light curves out
to late times. We fitted the spectra with thermal models. All the SNe with
multiple X-ray data points were found to have similar X-ray luminosity, which
was decreasing with time. The X-ray luminosity will likely continue to decrease
while the SNe are evolving in a wind medium, but is anticipated to increase in
the Sedov phase when the SNe are interacting with a constant density
interstellar medium, bringing it in line with observed SNRs.


  In this paper, I revoke a debate about an origin of Type Ia supernova (SN Ia)
dimming. I argue that except for a commonly accepted accelerating expansion of
the Universe, a conceivable alternative for explaining this observation is
universe opacity caused by light extinction by intergalactic dust, even though
it is commonly assumed that this effect is negligible. Using data of the
Union2.1 SN Ia compilation, I find that the standard $\Lambda$CDM model and the
opaque universe model fit the SN Ia measurements at redshifts $z < 1.4$
comparably well. The optimum solution for the opaque universe model is
characterized by the B-band intergalactic opacity $\lambda_B = 0.10 \pm 0.03 \,
\mathrm{Gpc}^{-1}$ and the Hubble constant $H_0 = 68.0 \pm 2.5 \,
\mathrm{km\,s^{-1}\, Mpc^{-1}}$. The intergalactic opacity is higher than that
obtained from independent observations but still within acceptable limits. This
result emphasizes that the issue of the accelerating expansion of the Universe
as the origin of the SN Ia dimming is not yet definitely resolved. Obviously,
the opaque universe model as an alternative to the $\Lambda$CDM model is
attractive, because it avoids puzzles and controversies associated with dark
energy and the accelerating expansion.


  Let T be a homogeneous tree and L the Laplace operator on T. We consider the
semilinear Schrodinger equation associated to L with a power-like nonlinearity
F of degree d. We first obtain dispersive estimates and Strichartz estimates
with no admissibility conditions. We next deduce global well-posedness for
small L2 data with no gauge invariance assumption on the nonlinearity F. On the
other hand if F is gauge invariant, L2 conservation leads to global
well-posedness for arbitrary L2 data. Notice that, in contrast with the
Euclidean case, these global well-posedness results hold with no restriction on
d > 1. We finally prove scattering for small L2 data, with no gauge invariance
assumption.


  In obstetric ultrasound (US) scanning, the learner's ability to mentally
build a three-dimensional (3D) map of the fetus from a two-dimensional (2D) US
image represents a significant challenge in skill acquisition. We aim to build
a US plane localization system for 3D visualization, training, and guidance
without integrating additional sensors. This work builds on top of our previous
work, which predicts the six-dimensional (6D) pose of arbitrarily oriented US
planes slicing the fetal brain with respect to a normalized reference frame
using a convolutional neural network (CNN) regression network. Here, we analyze
in detail the assumptions of the normalized fetal brain reference frame and
quantify its accuracy with respect to the acquisition of transventricular (TV)
standard plane (SP) for fetal biometry. We investigate the impact of
registration quality in the training and testing data and its subsequent effect
on trained models. Finally, we introduce data augmentations and larger training
sets that improve the results of our previous work, achieving median errors of
2.97 mm and 6.63 degrees for translation and rotation, respectively.


  The QCD phase transition at finite temperature is studied with the dual
Ginzburg-Landau theory, which is the QCD effective theory based on the dual
Higgs mechanism by QCD-monopole condensation. At high temperature, the
confinement force is largely reduced by thermal effects, which leads to the
swelling of hadrons. Simple formulae for the surface tension and the thickness
of the phase boundary are derived from the shape of the effective potential at
the critical temperature. We investigate also the process of the hadron-bubble
formation in the early Universe.


  The following paper is devoted to the study of type I locally compact quantum
groups. We show how various operators related to the modular theory of the Haar
integrals on $\mathbb{G}$ and $\widehat{\mathbb{G}}$ act on the level of direct
integrals. Using these results we derive a web of implications between
properties such as unimodularity or traciality of the Haar integrals. We also
study in detail two examples: discrete quantum group
$\widehat{\mathrm{SU}_q(2)}$ and the quantum $az+b$ group.


  Motivated by certain applications from physics, biochemistry, economics, and
computer science, in which the objects under investigation are not accessible
because of various limitations, we propose a trial-and-error model to examine
algorithmic issues in such situations. Given a search problem with a hidden
input, we are asked to find a valid solution, to find which we can propose
candidate solutions (trials), and use observed violations (errors), to prepare
future proposals. In accordance with our motivating applications, we consider
the fairly broad class of constraint satisfaction problems, and assume that
errors are signaled by a verification oracle in the format of the index of a
violated constraint (with the content of the constraint still hidden).
  Our discoveries are summarized as follows. On one hand, despite the seemingly
very little information provided by the verification oracle, efficient
algorithms do exist for a number of important problems. For the Nash, Core,
Stable Matching, and SAT problems, the unknown-input versions are as hard as
the corresponding known-input versions, up to a factor of polynomial. We
further give almost tight bounds on the latter two problems' trial
complexities. On the other hand, there are problems whose complexities are
substantially increased in the unknown-input model. In particular, no
time-efficient algorithms exist (under standard hardness assumptions) for Graph
Isomorphism and Group Isomorphism problems. The tools used to achieve these
results include order theory, strong ellipsoid method, and some non-standard
reductions.
  Our model investigates the value of information, and our results demonstrate
that the lack of input information can introduce various levels of extra
difficulty. The model exhibits intimate connections with (and we hope can also
serve as a useful supplement to) certain existing learning and complexity
theories.


  Reinforcement learning from human feedback (RLHF) is a popular strategy for
aligning large language models (LLMs) with desired behaviors. Reward modeling
is a crucial step in RLHF. However, collecting paired preference data for
training reward models is often costly and time-consuming, especially for
domain-specific preferences requiring expert annotation. To address this
challenge, we propose the \textbf{Do}main knowled\textbf{ge} merged
\textbf{R}eward \textbf{M}odel (DogeRM), a novel framework that integrates
domain-specific knowledge into a general reward model by model merging. The
experiments demonstrate that DogeRM enhances performance across different
benchmarks and provide a detailed analysis showcasing the effects of model
merging, showing the great potential of facilitating model alignment.


  We propose and demonstrate a simple route to few-optical-cycle pulse
generation from a mid-infrared fiber laser through nonlinear compression of
pulses from a holmium-doped fiber oscillator using a short length of
chalcogenide fiber and a grating pair. Pulses from the oscillator with 265-fs
duration at 2.86 {\mu}m are spectrally broadened through self-phase modulation
in step-index As2S3 fiber to 141-nm bandwidth and then re-compressed to 70 fs
(7.3 optical cycles). These are the shortest pulses from a mid-infrared fiber
system to date, and we note that our system is compact, robust, and uses only
commercially available components. The scalability of this approach is also
discussed, supported by numerical modeling.


  Electron-electron and electron-phonon interactions are two major driving
forces that stabilize various charge-ordered phases of matter. The intricate
interplay between the two give rises to a peculiar charge density wave (CDW)
state, which is also known as a Mott insulator, as the ground state of layered
compound 1T-TaS2. The delicate balance also makes it possible to use external
perturbations to create and manipulate novel phases in this material. Here, we
study a mosaic CDW phase induced by voltage pulses from the tip of a scanning
tunneling microscope (STM), and find that the new phase exhibit electronic
structures that are entirely different from the Mott ground state of 1T-TaS2 at
low temperatures. The mosaic phase consists of nanometer-sized domains
characterized by well-defined phase shifts of the CDW order parameter in the
topmost layer, and by altered stacking relative to the layer underneath. We
discover that the nature of the new phases is dictated by the stacking order,
and our results shed fresh light on the origin of the Mott phase in this
layered compound.


  In our previous paper, we evaluated the transit duration variation (TDV)
effect for a co-aligned planet-moon system at an orbital inclination of i=90
degrees. Here, we will consider the effect for the more general case of i <= 90
degrees and an exomoon inclined from the planet-star plane by Euler rotation
angles $\alpha$, $\beta$ and $\gamma$. We find that the TDV signal has two
major components, one due to the velocity variation effect described in our
first paper and one new component due to transit impact parameter variation. By
evaluating the dominant terms, we find the two effects are additive for
prograde exomoon orbits, and deductive for retrograde orbits. This asymmetry
could allow for future determination of the orbital sense of motion. We
re-evaluate the ratio of TDV and TTV effects, $\eta$, in the more general case
of an inclined planetary orbit with a circular orbiting moon and find that it
is still possible to directly determine the moon's orbital separation from just
the ratio of the two amplitudes, as first proposed in our previous paper.


  Entropy is one of physical bases for fractal dimension definition, and the
generalized fractal dimension was defined by Renyi entropy. Using fractal
dimension, we can describe urban growth and form and characterize spatial
complexity. A number of fractal models and measurements have been proposed for
urban studies. However, the precondition for fractal dimension application is
to find scaling relations in cities. In absence of scaling property, we can
make use of entropy function and measurements. This paper is devoted to
researching how to describe urban growth by using spatial entropy. By analogy
with fractal dimension growth models of cities, a pair of entropy increase
models can be derived and a set of entropy-based measurements can be
constructed to describe urban growing process and patterns. First, logistic
function and Boltzmann equation are utilized to model the entropy increase
curves of urban growth. Second, a series of indexes based on spatial entropy
are used to characterize urban form. Further, multifractal dimension spectrums
are generalized to spatial entropy spectrums. Conclusions are drawn as follows.
Entropy and fractal dimension have both intersection and different spheres of
application to urban research. Thus, for a given spatial measurement scale,
fractal dimension can often be replaced by spatial entropy for simplicity. The
models and measurements presented in this work are significant for integrating
entropy and fractal dimension into the same framework of urban spatial analysis
and understanding spatial complexity of cities.


  We study post-inflationary evolution in $\alpha$-attractor T-models of
inflation. We consider the dynamics of both scalar fields present in these
models: the inflaton and the spectator, as a negative field-space curvature may
lead to geometrical destabilization of the spectator. We perform
state-of-the-art lattice simulations with a dedicated numerical code optimized
for those models. We corroborate earlier findings that the perturbations of the
spectator field are much more unstable than the perturbations of the inflaton
field, so the dynamics of early stages of preheating is dominated by the
evolution of spectator perturbations. We also calculate the spectrum of
gravitational waves originating from scalar fluctuations in order to determine
if the $\alpha$-attractor T-models can be constrained or even ruled out by
present cosmological observations, but not by direct searches of gravitational
waves.


  In biomedical studies, researchers are often interested in assessing the
association between one or more ordinal explanatory variables and an outcome
variable, at the same time adjusting for covariates of any type. The outcome
variable may be continuous, binary, or represent censored survival times. In
the absence of precise knowledge of the response function, using monotonicity
constraints on the ordinal variables improves efficiency in estimating
parameters, especially when sample sizes are small. An active set algorithm
that can efficiently compute such estimators is proposed, and a
characterization of the solution is provided. Having an efficient algorithm at
hand is especially relevant when applying likelihood ratio tests in restricted
generalized linear models, where one needs the value of the likelihood at the
restricted maximizer. The algorithm is illustrated on a real life data set from
oncology.


  This work deals with the problem of simultaneous regulation and model
parameter estimation in adaptive model predictive control. We propose an
adaptive model predictive control and conditions which guarantee a persistently
exciting closed loop sequence by only looking forward in time into the receding
prediction horizon. Earlier works needed to look backwards and preserve prior
regressor data. Instead, we present a procedure for the offline generation of a
persistently exciting reference trajectory perturbing the equilibrium. With the
new approach we demonstrate exponential convergence of nonlinear systems under
the influence of the adaptive model predictive control combined with a
recursive least squares identifier with forgetting factor despite bounded
noise. The results are, at this stage, local in state and parameter-estimate
space.


  Millimeter-wave (mmWave) offers high data rate and bandwidth for
air-to-everything (A2X) communications including air-to-air, air-to-ground, and
air-to-tower. MmWave communication in the A2X network is sensitive to buildings
blockage effects. In this paper, we propose an analytical framework to define
and characterise the connectivity for an aerial access point (AAP) by jointly
using stochastic geometry and random shape theory. The buildings are modelled
as a Boolean line-segment process with fixed height. The blocking area for an
arbitrary building is derived and minimized by optimizing the altitude of AAP.
A lower bound on the connectivity probability is derived as a function of the
altitude of AAP and different parameters of users and buildings including their
densities, sizes, and heights. Our study yields guidelines on practical mmWave
A2X networks deployment.


  The behaviour of the critical point between quantum Hall plateaux, as the
Zeeman energy is varied, is analysed using modular symmetry of the Hall
conductivities following from the law of corresponding states. Flow diagrams
for the conductivities as a function of temperature, with the magnetic field
fixed, are constructed for different Zeeman energies, for samples with
particle-hole symmetry.


  Interstitial topological objects, such as skyrmions, within a natural 1-D
helix are predicted to be free from ambiguous 'skyrmion Hall effect'. The
helical ambience precipitate an additional potential that counteract the Magnus
force arising from the gyrotropic motion of skyrmion. Here, we present the
observation of $\pm$ $\frac{1}{2}$ topological charge objects (anti)merons
within the 1-D helical stripes in D$_{2d}$ symmetric
Mn$_{1.4}$Pt$_{0.9}$Pd$_{0.1}$Sn$_{1-x}$In$_{x}$ system. With the help of
Lorentz transmission electron microscopy study we demonstrate that the
pair-wise meron and antimeron chains can be spontaneously stabilized for a
critical In concentration in the system. The exchange frustration induced
proportionate fragmentation of the magnetic moment in the in-plane and
easy-axis directions acts as a basic ingredient for the formation of
(anti)merons within the helical stripe. A constrained drift motion of
(anti)merons along the stripe makes this system an ideal platform for the
realization of skyrmion Hall free track motion. Moreover, the observation of
(anti)merons in addition to the skyrmion and antiskyrmion in D$_{2d}$ materials
makes them a suitable horizon for zoo of topology.


  We investigate the phase transition of Bose-Einstein particles with the
hard-core repulsion in the grand canonical ensemble within the Van der Waals
approximation. It is shown that the pressure of non-relativistic Bose-Einstein
particles is mathematically equivalent to the pressure of simplified version of
the statistical multifragmentation model of nuclei with the vanishing surface
tension coefficient and the Fisher exponent $\tau_F = \frac{5}{2}$, which for
such parameters has the 1-st order phase transition. The found similarity of
these equations of state allows us to show that within the present approach the
high density phase of Bose-Einstein particles is a classical macro-cluster with
vanishing entropy at any temperature which, similarly to the classical hard
spheres, is a kind of solid state. To show this we establish new relations
which allow us to identically represent the pressure of Fermi-Dirac particles
in terms of pressures of Bose-Einstein particles of two sorts.


  We study self-interacting dark matter (SIDM) scenarios, where the $s$-wave
self-scattering cross section almost saturates the Unitarity bound. Such
self-scattering cross sections are singly parameterized by the dark matter
mass, and are featured by strong velocity dependence in a wide range of
velocities. They may be indicated by observations of dark matter halos in a
wide range of masses, from Milky Way's dwarf spheroidal galaxies to galaxy
clusters. We pin down the model parameters that saturates the Unitarity bound
in well-motivated SIDM models: the gauged $L_{\mu} - L_{\tau}$ model and
composite asymmetric dark matter model. We discuss implications and predictions
of such model parameters for cosmology like the $H_{0}$ tension and dark-matter
direct-detection experiments, and particle phenomenology like the beam-dump
experiments.


  One of the outstanding problems in general relativistic cosmology is that of
the averaging. That is, how the lumpy universe that we observe at small scales
averages out to a smooth Friedmann-Lemaitre-Robertson-Walker (FLRW) model. The
root of the problem is that averaging does not commute with the Einstein
equations that govern the dynamics of the model. This leads to the well-know
question of backreaction in cosmology. In this work, we approach the problem
using the covariant framework of Macroscopic Gravity (MG). We use its
cosmological solution with a flat FLRW macroscopic background where the result
of averaging cosmic inhomogeneities has been encapsulated into a backreaction
density parameter denoted $\Omega_\mathcal{A}$. We constrain this averaged
universe using available cosmological data sets of expansion and growth
including, for the first time, a full CMB analysis from Planck temperature
anisotropy and polarization data, the supernovae data from Union 2.1, the
galaxy power spectrum from WiggleZ, the weak lensing tomography shear-shear
cross correlations from the CFHTLenS survey and the baryonic acoustic
oscillation data from 6Df, SDSS DR7 and BOSS DR9. We find that $-0.0155 \le
\Omega_\mathcal{A} \le 0$ (at the 68\% CL) thus providing a tight upper-bound
on the backreaction term. We also find that the term is strongly correlated
with cosmological parameters such $\Omega_\Lambda$, $\sigma_8$ and $H_0$. While
small, a backreaction density parameter of a few percent should be kept in
consideration along with other systematics for precision cosmology.


  A nonstandard proof of a generalization of Karamata uniform convergence
theorem for slowly varying functions is presented. Properties of a related
operator $\mathcal{L}$ and its connection with slowly varying functions are
discussed.


  We make the case for an electronic origin of the strong mode, recently seen
in ARPES experiments, and, in this regard, further discuss the physics of the
spin resonance peak.


  We present results from extensive broadband follow-up of GRB 210204A over the
period of thirty days. We detect optical flares in the afterglow at 7.6 x 10^5
s and 1.1 x 10^6 s after the burst: the most delayed flaring ever detected in a
GRB afterglow. At the source redshift of 0.876, the rest-frame delay is 5.8 x
10^5 s (6.71 d). We investigate possible causes for this flaring and conclude
that the most likely cause is a refreshed shock in the jet. The prompt emission
of the GRB is within the range of typical long bursts: it shows three disjoint
emission episodes, which all follow the typical GRB correlations. This suggests
that GRB 210204A might not have any special properties that caused late-time
flaring, and the lack of such detections for other afterglows might be
resulting from the paucity of late-time observations. Systematic late-time
follow-up of a larger sample of GRBs can shed more light on such afterglow
behaviour. Further analysis of the GRB 210204A shows that the late time bump in
the light curve is highly unlikely due to underlying SNe at redshift (z) =
0.876 and is more likely due to the late time flaring activity. The cause of
this variability is not clearly quantifiable due to the lack of multi-band data
at late time constraints by the bad weather conditions. The flare of GRB
210204A is the latest flare detected to date.


  We propose a system of coupled quantum dots in proximity to a superconductor
and driven by separate ac potentials to realize and detect Floquet Majorana
fermions. We show that the appearance of Floquet Majorana fermions can be
finely controlled in the expanded parameter space of the drive frequency,
amplitude, and phase difference across the two dots. While these Majorana
fermions are not topologically protected, the highly tunable setup provides a
realistic system for observing the exotic physics associated with Majorana
fermions as well as their dynamical generation and manipulation.


  A droplet can deform a soft substrate due to capillary forces when they are
in contact. We study the static deformation of a soft solid layer coated on a
rigid cylindrical fiber when an axisymmetric barrel-shaped droplet is embracing
it. We find that the elastic deformation increases with decreasing rigid fiber
radius. Significant disparities of deformation between the solid-liquid side
and the solid-gas side are found when their solid surface tensions are
different. When the coated layer is soft enough and the rigid fiber radius is
less than the thickness of the coated layer, pronounced displacement
oscillations are observed. Such slow decay of deformation with distances from
the contact line position suggests a possible long-range interaction between
droplets on a soft-layer-coated fiber.


  A coherent terahertz needle radiation emission mechanism is proposed. This
mechanism can be realized in the experiments on femtosecond laser pulses
interacting with surface of nanostructured ferromagnetic metal film. The
proposed mechanism is based on exciting of coupled coherent phonon-magnon modes
on a nanostructured metal surface by laser femtosecond pulse. The value of the
Poynting vector for the terahertz radiation is estimated.


  We consider the combined measurements of CP-averaged decay rates and direct
CP asymmetries of $B^\pm\to K^\pm \ell^+ \ell^-$ and $B^\pm\to \pi^\pm \ell^+
\ell^-$ to probe (non-local) four-quark operator matrix element contributions
to rare semileptonic B meson decays. We also explore how their effects could be
in principle disentangled from possible local new physics effects using
$U$-spin relations. To this end, we construct a ratio of CP-odd decay rate
differences which are exactly predicted within the standard model in the
$U$-spin limit, while the leading $U$-spin breaking effects can also be
systematically calculated. Our results motivate binned measurements of the
direct CP asymmetry in $B^\pm\to \pi^\pm \ell^+ \ell^-$ as well as dedicated
theoretical estimates of $U$-spin breaking both in local form factors as well
as in four-quark matrix elements.


  In this study, we have carried out a detailed, statistical analysis of
isolated model galaxies, taking advantage of publicly available hierarchical
galaxy formation models. To select isolated galaxies, we employ 2D methods
widely used in the observational literature, as well as a more stringent 3D
isolation criterion that uses the full 3D-real space information. In
qualitative agreement with observational results, isolated model galaxies have
larger fractions of late-type, star forming galaxies with respect to randomly
selected samples of galaxies with the same mass distribution. We also find that
the samples of isolated model galaxies typically contain a fraction of less
than 15 per cent of satellite galaxies, that reside at the outskirts of their
parent haloes where the galaxy number density is low. Projection effects cause
a contamination of 2D samples of about 18 per cent, while we estimate a typical
completeness of 65 per cent. Our model isolated samples also include a very
small (few per cent) fraction of bulge dominated galaxies (B/T > 0.8) whose
bulges have been built mainly by minor mergers. Our study demonstrates that
about 65-70 per cent of 2D isolated galaxies that are classified as isolated at
z = 0 have indeed been completely isolated since z = 1 and only 7 per cent have
had more than 3 neighbours within a comoving radius of 1 Mpc. Irrespectively of
the isolation criteria, roughly 45 per cent of isolated galaxies have
experienced at least one merger event in the past (most of the mergers are
minor, with mass ratios between 1:4 and 1:10). The latter point validates the
approximation that isolated galaxies have been mainly influenced by internal
processes.


  All-dielectric, sub-micrometric particles have been successfully exploited
for light management in a plethora of applications at visible and near-infrared
frequency. However, the investigation of the intricacies of the Mie resonances
at the sub-wavelength scale has been hampered by the limitation of conventional
near-field methods. Here we address spatial and spectral mapping of multi-polar
modes of a Si island by hyper-spectral imaging. The simultaneous detection of
several resonant modes allows to clarify the role of substrate and incidence
angle of the impinging light, highlighting spectral splitting of the
quadrupolar mode and resulting in different spatial features of the field
intensity. We explore theoretically and experimentally such spatial features.
Details as small as 200 nm can be detected and are in agreement with
simulations based on a Finite Difference Time Domain method. Our results are
relevant to near-field imaging of dielectric structures, to the comprehension
of the photophysics of resonant Mie structures, to beam steering and to the
resonant coupling with light emitters. Our analysis paves the way for a novel
approach to control the spatial overlap of a single emitter with localized
electric field maxima.


  Control Barrier Functions (CBFs) are becoming popular tools in guaranteeing
safety for nonlinear systems and constraints, and they can reduce a constrained
optimal control problem into a sequence of Quadratic Programs (QPs) for affine
control systems. The recently proposed High Order Control Barrier Functions
(HOCBFs) work for arbitrary relative degree constraints. One of the challenges
in a HOCBF is to address the relative degree problem when a system has multiple
control inputs, i.e., the relative degree could be defined with respect to
different components of the control vector. This paper proposes two methods for
HOCBFs to deal with systems with multiple control inputs: a general integral
control method and a method which is simpler but limited to specific classes of
physical systems. When control bounds are involved, the feasibility of the
above mentioned QPs can also be significantly improved with the proposed
methods. We illustrate our approaches on a unicyle model with two control
inputs, and compare the two proposed methods to demonstrate their effectiveness
and performance.


  We use non-perturbative linked-cluster expansions to determine the
ground-state energy per site of the spin-one Heisenberg model on the kagome
lattice. To this end, a parameter is introduced allowing to interpolate between
a fully trimerized state and the isotropic model. The ground-state energy per
site of the full graph decomposition up to graphs of six triangles (18 spins)
displays a complex behaviour as a function of this parameter close to the
isotropic model which we attribute to divergencies of partial series in the
graph expansion of quasi-1d unfrustrated chain graphs. More concretely, these
divergencies can be traced back to a quantum critical point of the
one-dimensional unfrustrated chain of coupled triangles. Interestingly, the
reorganization of the non-perturbative linked-cluster expansion in terms of
clusters with enhanced symmetry yields a ground-state energy per site of the
isotropic two-dimensional model being in quantitative agreement with other
numerical approaches in favor of a spontaneous trimerization of the system. Our
findings are of general importance for any non-perturbative linked-cluster
expansion on geometrically frustrated systems.


  Possibility of asymmetric square convection is investigated numerically using
a few mode Lorenz-like model for thermal convection in Boussinesq fluids
confined between two stress free and conducting flat boundaries. For relatively
large value of Rayleigh number, the stationary rolls become unstable and
asymmetric squares appear as standing waves at the onset of secondary
instability. Asymmetric squares, two dimensional rolls and again asymmetric
squares with their corners shifted by half a wavelength form a stable limit
cycle.


  We investigate hadrons and direct photon production in pp collisions at the
LHC energy within the color-dipole approach. We show that greatest sensitivity
to gluon saturation effects is reached at very forward rapidities in pp
collisions at LHC (\sqrt{s}=14 TeV). The discrepancies among various saturation
models (fitted to HERA data) results can be about a factor of 2-3 at forward
rapidities. We found that the ratio of direct-photon to pion production can be
about 20-10 at forward rapidities \eta=7-8. Therefore, direct photon production
at forward rapidities should provide a rather clean probe as the background
from radiative hadronic decays is significantly suppressed.


  Background and objective
  Risk prediction models aim at identifying people at higher risk of developing
a target disease. Feature selection is particularly important to improve the
prediction model performance avoiding overfitting and to identify the leading
cancer risk (and protective) factors. Assessing the stability of feature
selection/ranking algorithms becomes an important issue when the aim is to
analyze the features with more prediction power. Methods
  This work is focused on colorectal cancer, assessing several feature ranking
algorithms in terms of performance for a set of risk prediction models (Neural
Networks, Support Vector Machines (SVM), Logistic Regression, k-Nearest
Neighbors and Boosted Trees). Additionally, their robustness is evaluated
following a conventional approach with scalar stability metrics and a visual
approach proposed in this work to study both similarity among feature ranking
techniques as well as their individual stability. A comparative analysis is
carried out between the most relevant features found out in this study and
features provided by the experts according to the state-of-the-art knowledge.
Results
  The two best performance results in terms of Area Under the ROC Curve (AUC)
are achieved with a SVM classifier using the top-41 features selected by the
SVM wrapper approach (AUC=0.693) and Logistic Regression with the top-40
features selected by the Pearson (AUC=0.689). Experiments showed that
performing feature selection contributes to classification performance with a
3.9% and 1.9% improvement in AUC for the SVM and Logistic Regression
classifier, respectively, with respect to the results using the full feature
set. The visual approach proposed in this work allows to see that the Neural
Network-based wrapper ranking is the most unstable while the Random Forest is
the most stable.


  A previous result about the decategorified bordered (sutured) Heegaard Floer
invariants of surfaces glued together along intervals, generalizing the
decategorified content of Rouquier and the author's higher-tensor-product-based
gluing theorem in cornered Heegaard Floer homology, was proved only over
$\mathbb{F}_2$ and without gradings. In this paper we add signs and prove a
graded version of the interval gluing theorem over $\mathbb{Z}$, enabling a
more detailed comparison of these aspects of decategorified Heegaard Floer
theory with modern work on non-semisimple 3d TQFTs in mathematics and physics.


  In order to uncover users' attitudes towards ChatGPT in mental health, this
study examines public opinions about ChatGPT in mental health discussions on
Reddit. Researchers used the bert-base-multilingual-uncased-sentiment
techniques for sentiment analysis and the BERTopic model for topic modeling. It
was found that overall, negative sentiments prevail, followed by positive ones,
with neutral sentiments being the least common. The prevalence of negative
emotions has increased over time. Negative emotions encompass discussions on
ChatGPT providing bad mental health advice, debates on machine vs. human value,
the fear of AI, and concerns about Universal Basic Income (UBI). In contrast,
positive emotions highlight ChatGPT's effectiveness in counseling, with
mentions of keywords like "time" and "wallet." Neutral discussions center
around private data concerns. These findings shed light on public attitudes
toward ChatGPT in mental health, potentially contributing to the development of
trustworthy AI in mental health from the public perspective.


  In this paper, we address the formation of a magnetic flux rope (MFR) that
erupted on 2012 July 12 and caused a strong geomagnetic storm event on July 15.
Through analyzing the long-term evolution of the associated active region
observed by the Atmospheric Imaging Assembly and the Helioseismic and Magnetic
Imager on board the Solar Dynamics Observatory, it is found that the twisted
field of an MFR, indicated by a continuous S-shaped sigmoid, is built up from
two groups of sheared arcades near the main polarity inversion line half day
before the eruption. The temperature within the twisted field and sheared
arcades is higher than that of the ambient volume, suggesting that magnetic
reconnection most likely works there. The driver behind the reconnection is
attributed to shearing and converging motions at magnetic footpoints with
velocities in the range of 0.1--0.6 km s$^{-1}$. The rotation of the preceding
sunspot also contributes to the MFR buildup. Extrapolated three-dimensional
non-linear force-free field structures further reveal the locations of the
reconnection to be in a bald-patch region and in a hyperbolic flux tube. About
two hours before the eruption, indications for a second MFR in the form of an
S-shaped hot channel are seen. It lies above the original MFR that continuously
exists and includes a filament. The whole structure thus makes up a stable
double-decker MFR system for hours prior to the eruption. Eventually, after
entering the domain of instability, the high-lying MFR impulsively erupts to
generate a fast coronal mass ejection and X-class flare; while the low-lying
MFR remains behind and continuously maintains the sigmoidicity of the active
region.


  We propose a simple generalization of the matrix resolvent to a resolvent for
real symmetric tensors $T\in \otimes^p \mathbb{R}^N$ of order $p\ge 3$. The
tensor resolvent yields an integral representation for a class of tensor
invariants and its singular locus can be understood in terms of the real
eigenvalues of tensors. We then consider a random Gaussian (real symmetric)
tensor. We show that in the large $N$ limit the expected resolvent has a finite
cut in the complex plane and that the associated "spectral density", that is
the discontinuity at the cut, obeys a universal law which generalizes the
Wigner semicircle law to arbitrary order. Finally, we consider a spiked tensor
for $p\ge 3$, that is the sum of a fixed tensor $b\,v^{\otimes p}$ with $v\in
\mathbb{R}^N$ (the signal) and a random Gaussian tensor $T$ (the noise). We
show that in the large $N$ limit the expected resolvent undergoes a sharp
transition at some threshold value of the signal to noise ratio $b$ which we
compute analytically.


  Quantum Machine Learning (QML) has surfaced as a pioneering framework
addressing sequential control tasks and time-series modeling. It has
demonstrated empirical quantum advantages notably within domains such as
Reinforcement Learning (RL) and time-series prediction. A significant
advancement lies in Quantum Recurrent Neural Networks (QRNNs), specifically
tailored for memory-intensive tasks encompassing partially observable
environments and non-linear time-series prediction. Nevertheless, QRNN-based
models encounter challenges, notably prolonged training duration stemming from
the necessity to compute quantum gradients using backpropagation-through-time
(BPTT). This predicament exacerbates when executing the complete model on
quantum devices, primarily due to the substantial demand for circuit evaluation
arising from the parameter-shift rule. This paper introduces the Quantum Fast
Weight Programmers (QFWP) as a solution to the temporal or sequential learning
challenge. The QFWP leverages a classical neural network (referred to as the
'slow programmer') functioning as a quantum programmer to swiftly modify the
parameters of a variational quantum circuit (termed the 'fast programmer').
Instead of completely overwriting the fast programmer at each time-step, the
slow programmer generates parameter changes or updates for the quantum circuit
parameters. This approach enables the fast programmer to incorporate past
observations or information. Notably, the proposed QFWP model achieves learning
of temporal dependencies without necessitating the use of quantum recurrent
neural networks. Numerical simulations conducted in this study showcase the
efficacy of the proposed QFWP model in both time-series prediction and RL
tasks. The model exhibits performance levels either comparable to or surpassing
those achieved by QLSTM-based models.


  More than twenty years after its introduction, Annealed Importance Sampling
(AIS) remains one of the most effective methods for marginal likelihood
estimation. It relies on a sequence of distributions interpolating between a
tractable initial distribution and the target distribution of interest which we
simulate from approximately using a non-homogeneous Markov chain. To obtain an
importance sampling estimate of the marginal likelihood, AIS introduces an
extended target distribution to reweight the Markov chain proposal. While much
effort has been devoted to improving the proposal distribution used by AIS, an
underappreciated issue is that AIS uses a convenient but suboptimal extended
target distribution. We here leverage recent progress in score-based generative
modeling (SGM) to approximate the optimal extended target distribution
minimizing the variance of the marginal likelihood estimate for AIS proposals
corresponding to the discretization of Langevin and Hamiltonian dynamics. We
demonstrate these novel, differentiable, AIS procedures on a number of
synthetic benchmark distributions and variational auto-encoders.


  We describe a previously unexplored effect of the continuous spontaneous
localization model whereby a correlation develops in the distributions of two
nearby non-interacting particles following a period of diffusion. We propose
the use of this effect as an experimental test differentiating between the
continuous spontaneous localization model and standard quantum theory. The test
involves building a joint probability distribution for the locations of the two
particles by repeatedly releasing them from two nearby traps and subsequently
measuring their positions after a brief period of time. We examine the scales
of time, trap size, and particle mass necessary for observation.


  Galaxy cross-correlations with high-fidelity redshift samples hold the
potential to precisely calibrate systematic photometric redshift uncertainties
arising from the unavailability of complete and representative training and
validation samples of galaxies. However, application of this technique in the
Dark Energy Survey (DES) is hampered by the relatively low number density,
small area, and modest redshift overlap between photometric and spectroscopic
samples. We propose instead using photometric catalogs with reliable
photometric redshifts for photo-z calibration via cross-correlations. We verify
the viability of our proposal using redMaPPer clusters from the Sloan Digital
Sky Survey (SDSS) to successfully recover the redshift distribution of SDSS
spectroscopic galaxies. We demonstrate how to combine photo-z with
cross-correlation data to calibrate photometric redshift biases while
marginalizing over possible clustering bias evolution in either the calibration
or unknown photometric samples. We apply our method to DES Science Verification
(DES SV) data in order to constrain the photometric redshift distribution of a
galaxy sample selected for weak lensing studies, constraining the mean of the
tomographic redshift distributions to a statistical uncertainty of $\Delta z
\sim \pm 0.01$. We forecast that our proposal can in principle control
photometric redshift uncertainties in DES weak lensing experiments at a level
near the intrinsic statistical noise of the experiment over the range of
redshifts where redMaPPer clusters are available. Our results provide strong
motivation to launch a program to fully characterize the systematic errors from
bias evolution and photo-z shapes in our calibration procedure.


  In G dwarfs, the surface distribution, coverage and lifetimes of starspots
deviate from solar-like patterns as the rotation rate increases. We set up a
numerical platform which includes the large-scale rotational and surface flow
effects, aiming to simulate evolving surface patterns over an activity cycle
for up to 8 times the solar rotation and flux emergence rates. At the base of
the convection zone, we assume a solar projected butterfly diagram. We then
follow the rotationally distorted trajectories of rising thin flux tubes to
obtain latitudes and tilt angles. Using them as source distributions, we run a
surface flux transport model with solar parameters. Our model predicts surface
distributions of the signed radial fields and the starspots that qualitatively
agree with observations.


  Let $\mathcal{N}$ be the Nevanlinna class and let $B$ be a Blaschke product.
It is shown that the natural invertibility criterion in the quotient algebra
$\mathcal{N} / B \mathcal{N}$, that is, $|f| \ge e^{-H} $ on the set
$B^{-1}\{0\}$ for some positive harmonic function $H$, holds if and only if the
function $- \log |B|$ has a harmonic majorant on the set
$\{z\in\mathbb{D}:\rho(z,\Lambda)\geq e^{-H(z)}\}$; at least for large enough
functions $H$. We also study the corresponding class of positive harmonic
functions $H$ in the unit disc such that the latter condition holds. We also
discuss the analogous invertibility problem in quotients of the Smirnov class.


  Quantum state tomography is the standard tool in current experiments for
verifying that a state prepared in the lab is close to an ideal target state,
but up to now there were no rigorous methods for evaluating the precision of
the state preparation in tomographic experiments. We propose a new estimator
for quantum state tomography, and prove that the (always physical) estimates
will be close to the true prepared state with high probability. We derive an
explicit formula for evaluating how high the probability is for an arbitrary
finite-dimensional system and explicitly give the one- and two-qubit cases as
examples. This formula applies for any informationally complete sets of
measurements, arbitrary finite number of data sets, and general loss functions
including the infidelity, the Hilbert-Schmidt, and the trace distances. Using
the formula, we can evaluate not only the difference between the estimated and
prepared states, but also the difference between the prepared and target
states. This is the first result directly applicable to the problem of
evaluating the precision of estimation and preparation in quantum tomographic
experiments.


  Polynomial system solving is a classical problem in mathematics with a wide
range of applications. This makes its complexity a fundamental problem in
computer science. Depending on the context, solving has different meanings. In
order to stick to the most general case, we consider a representation of the
solutions from which one can easily recover the exact solutions or a certified
approximation of them. Under generic assumption, such a representation is given
by the lexicographical Gr\"obner basis of the system and consists of a set of
univariate polynomials. The best known algorithm for computing the
lexicographical Gr\"obner basis is in $\widetilde{O}(d^{3n})$ arithmetic
operations where $n$ is the number of variables and $d$ is the maximal degree
of the equations in the input system. The notation $\widetilde{O}$ means that
we neglect polynomial factors in $n$. We show that this complexity can be
decreased to $\widetilde{O}(d^{\omega n})$ where $2 \leq \omega < 2.3727$ is
the exponent in the complexity of multiplying two dense matrices. Consequently,
when the input polynomial system is either generic or reaches the B\'ezout
bound, the complexity of solving a polynomial system is decreased from
$\widetilde{O}(D^3)$ to $\widetilde{O}(D^\omega)$ where $D$ is the number of
solutions of the system. To achieve this result we propose new algorithms which
rely on fast linear algebra. When the degree of the equations are bounded
uniformly by a constant we propose a deterministic algorithm. In the unbounded
case we present a Las Vegas algorithm.


  Keyword extraction is one of the core tasks in natural language processing.
Classic extraction models are notorious for having a short attention span which
make it hard for them to conclude relational connections among the words and
sentences that are far from each other. This, in turn, makes their usage
prohibitive for generating keywords that are inferred from the context of the
whole text. In this paper, we explore using Large Language Models (LLMs) in
generating keywords for items that are inferred from the items textual
metadata. Our modeling framework includes several stages to fine grain the
results by avoiding outputting keywords that are non informative or sensitive
and reduce hallucinations common in LLM. We call our LLM-based framework
Theme-Aware Keyword Extraction (LLM TAKE). We propose two variations of
framework for generating extractive and abstractive themes for products in an E
commerce setting. We perform an extensive set of experiments on three real data
sets and show that our modeling framework can enhance accuracy based and
diversity based metrics when compared with benchmark models.


  We propose a focus of attention mechanism to speed up the Perceptron
algorithm. Focus of attention speeds up the Perceptron algorithm by lowering
the number of features evaluated throughout training and prediction. Whereas
the traditional Perceptron evaluates all the features of each example, the
Attentive Perceptron evaluates less features for easy to classify examples,
thereby achieving significant speedups and small losses in prediction accuracy.
Focus of attention allows the Attentive Perceptron to stop the evaluation of
features at any interim point and filter the example. This creates an attentive
filter which concentrates computation at examples that are hard to classify,
and quickly filters examples that are easy to classify.


  The effective free energy of globular protein chain is considered to be a
functional defined on smooth curves in three dimensional Euclidean space. From
the requirement of geometrical invariance, together with basic facts on
conformation of helical proteins and dynamical characteristics of the protein
chains, we are able to determine, in a unique way, the exact form of the free
energy functional. Namely, the free energy density should be a linear function
of the curvature of curves on which the free energy functional is defined. We
briefly discuss the possibility of using the model proposed in Monte Carlo
simulations of exhaustive searching the native stable state of the protein
chain. The relation of this model to the rigid relativistic particles and
strings is also considered.


  Ultrarelativistic collisions of black holes are ideal gedanken experiments to
study the nonlinearities of general relativity. In this paper we use
semianalytical tools to better understand the nature of these collisions and
the emitted gravitational radiation. We explain many features of the energy
spectra extracted from numerical relativity simulations using two complementary
semianalytical calculations. In the first calculation we estimate the radiation
by a "zero-frequency limit" analysis of the collision of two point particles
with finite impact parameter. In the second calculation we replace one of the
black holes by a point particle plunging with arbitrary energy and impact
parameter into a Schwarzschild black hole, and we explore the multipolar
structure of the radiation paying particular attention to the near-critical
regime. We also use a geodesic analogy to provide qualitative estimates of the
dependence of the scattering threshold on the black hole spin and on the
dimensionality of the spacetime.


  The main objective of this paper is to fill a critical gap in the literature
by analyzing the effects of decentralization on the macroeconomic stability. A
survey of the voluminous literature on decentralization suggests that the
question of the links between decentralization and macroeconomic stability has
been relatively scantily analyzed. Even though there is still a lot of room for
analysis as far as the effects of decentralization on other aspects of the
economy are concerned, we believe that it is in this area that a more thorough
analyses are mostly called for. Through this paper, we will try to shed more
light on the issue notably by looking at other dimension of macroeconomic
stability than the ones usually employed in previous studies as well as by
examining other factors that might accentuate or diminish the effects of
decentralization on macroeconomic stability. Our results found that
decentralization appears to lead to a decrease in inflation rate. However, we
do not find any correlation between decentralization with the level of fiscal
deficit. Our results also show that the impact of decentralization on inflation
is conditional on the level of perceived corruption and political institutions.


  The COVID-19 pandemic has demonstrated the increasing need of policymakers
for timely estimates of macroeconomic variables. A prior UNCTAD research paper
examined the suitability of long short-term memory artificial neural networks
(LSTM) for performing economic nowcasting of this nature. Here, the LSTM's
performance during the COVID-19 pandemic is compared and contrasted with that
of the dynamic factor model (DFM), a commonly used methodology in the field.
Three separate variables, global merchandise export values and volumes and
global services exports, were nowcast with actual data vintages and performance
evaluated for the second, third, and fourth quarters of 2020 and the first and
second quarters of 2021. In terms of both mean absolute error and root mean
square error, the LSTM obtained better performance in two-thirds of
variable/quarter combinations, as well as displayed more gradual forecast
evolutions with more consistent narratives and smaller revisions. Additionally,
a methodology to introduce interpretability to LSTMs is introduced and made
available in the accompanying nowcast_lstm Python library, which is now also
available in R, MATLAB, and Julia.


  A straight-line drawing $\Gamma$ of a graph $G=(V,E)$ is a drawing of $G$ in
the Euclidean plane, where every vertex in $G$ is mapped to a distinct point,
and every edge in $G$ is mapped to a straight line segment between their
endpoints. A path $P$ in $\Gamma$ is called increasing-chord if for every four
points (not necessarily vertices) $a,b,c,d$ on $P$ in this order, the Euclidean
distance between $b,c$ is at most the Euclidean distance between $a,d$. A
spanning tree $T$ rooted at some vertex $r$ in $\Gamma$ is called
increasing-chord if $T$ contains an increasing-chord path from $r$ to every
vertex in $T$. In this paper we prove that given a vertex $r$ in a
straight-line drawing $\Gamma$, it is NP-complete to determine whether $\Gamma$
contains an increasing-chord spanning tree rooted at $r$. We conjecture that
finding an increasing-chord path between a pair of vertices in $\Gamma$, which
is an intriguing open problem posed by Alamdari et al., is also NP-complete,
and show a (non-polynomial) reduction from the 3-SAT problem.


  We revisit the global fit to electroweak precision observables in the
Standard Model and present model-independent bounds on several general new
physics scenarios. We present a projection of the fit based on the expected
experimental improvements at future $e^+ e^-$ colliders, and compare the
constraining power of some of the different experiments that have been
proposed. All results have been obtained with the HEPfit code.


  The paper deals with special types of $L$-ordered set, $L$-fuzzy complete
lattices, and fuzzy directed complete posets (fuzzy $dcpo$s). First, a theorem
for constructing monotone maps is proved, a characterization for monotone maps
on an $L$-fuzzy complete lattice is obtained, and it is proved that if $f$ is a
monotone map on an $L$-fuzzy complete lattice $(P;e)$, then $\sqcap S_f$ is the
least fixpoint of $f$. A relation between $L$-fuzzy complete lattices and
fixpoints is found and fuzzy versions of monotonicity, rolling, fusion and
exchange rules on $L$-complete lattices are stated. Finally, we investigate
$Hom(P,P)$, where $(P;e)$ is a fuzzy $dcpo$, and we show that $Hom(P,P)$ is a
fuzzy $dcpo$, the map $\gamma\mapsto \bigwedge_{x\in P}e(x,\gamma(x))$ is a
fuzzy directed subset of $Hom(P,P)$, and we investigate its join.


  The future space-based gravitational wave observatory LISA will consist of a
constellation of three spacecraft in a triangular constellation, connected by
laser interferometers with 2.5 million-kilometer arms. Among other challenges,
the success of the mission strongly depends on the quality of the cancellation
of laser frequency noise, whose power lies eight orders of magnitude above the
gravitational signal. The standard technique to perform noise removal is
time-delay interferometry (TDI). TDI constructs linear combinations of delayed
phasemeter measurements tailored to cancel laser noise terms. Previous work has
demonstrated the relationship between TDI and principal component analysis
(PCA). We build on this idea to develop an extension of TDI based on a model
likelihood that directly depends on the phasemeter measurements. Assuming
stationary Gaussian noise, we decompose the measurement covariance using PCA in
the frequency domain. We obtain a comprehensive and compact framework that we
call PCI for "principal component interferometry," and show that it provides an
optimal description of the LISA data analysis problem.


  Let $H$ be a Hopf algebra and let $A\subset H$ be a right coideal subalgebra.
We show that if $A$ is a direct summand in $H$ as a right $A$-module, then $H$
is faithfully flat as a right $A$-module.


  Applying the main results of math.AG/0408295, we identify the motives
occurring as cones in the co-localization and localization filtrations of the
boundary motive of a Shimura variety.


  We describe the properties of instantons in lattice gauge theory when the
action is a fixed point action of some renormalization group transformation. We
present a theoretically consistent method for measuring topological charge
using an inverse renormalization group transformation. We show that, using a
fixed point action, the action of smooth configurations with non-zero
topological charge is greater than or equal to its continuum value
$8\pi^2/g^2$.


  This note shows that the prime values of the Ramanujan tau function
$\tau(n)=\pm p$ misses every prime $p\leq 8.0\times 10^{25}$.


  We address the problem of the relative importance of the intrinsic chaos and
the external noise in determining the complexity of population dynamics. We use
a recently proposed method for studying the complexity of nonlinear random
dynamical systems. The new measure of complexity is defined in terms of the
average number of bits per time-unit necessary to specify the sequence
generated by the system. This measure coincides with the rate of divergence of
nearby trajectories under two different realizations of the noise. In
particular, we show that the complexity of a nonlinear time-series model
constructed from sheep populations comes completely from the environmental
variations. However, in other situations, intrinsic chaos can be the crucial
factor. This method can be applied to many other systems in biology and
physics.


  The set of ultrametrics on $[n]$ nodes that are $\ell^\infty$-nearest to a
given dissimilarity map forms a $(\max,+)$ tropical polytope. Previous work of
Bernstein has given a superset of the set containing all the phylogenetic trees
that are extreme rays of this polytope. In this paper, we show that Bernstein's
necessary condition of tropical extreme rays is sufficient only for $n=3$ but
not for $n\geq 4$. Our proof relies on the exterior description of this
tropical polytope, together with the tangent hypergraph techniques for
extremality characterization. The sufficiency of the case $n=3$ is proved by
explicitly finding all extreme rays through the exterior description.
Meanwhile, an inductive construction of counterexamples is given to show the
insufficiency for $n\geq 4$.


  In 1998 the Adapted Ordering Method was developed for the representation
theory of the superconformal algebras in two dimensions. It allows: to
determine maximal dimensions for a given type of space of singular vectors, to
identify all singular vectors by only a few coefficients, to spot subsingular
vectors and to set the basis for constructing embedding diagrams. In this
article we present the Adapted Ordering Method for general Lie algebras and
superalgebras, and their generalizations, provided they can be triangulated. We
also review briefly the results obtained for the Virasoro algebra and for the
N=2 and Ramond N=1 superconformal algebras.


  We propose a finite volume scheme for a class of nonlinear parabolic
equations endowed with non-homogeneous Dirichlet boundary conditions and which
admit relative en-tropy functionals. For this kind of models including porous
media equations, Fokker-Planck equations for plasma physics or dumbbell models
for polymer flows, it has been proved that the transient solution converges to
a steady-state when time goes to infinity. The present scheme is built from a
discretization of the steady equation and preserves steady-states and natural
Lyapunov functionals which provide a satisfying long-time behavior. After
proving well-posedness, stability, exponential return to equilibrium and
convergence, we present several numerical results which confirm the accuracy
and underline the efficiency to preserve large-time asymptotic.


  We show that a TeV scale inverse seesaw model for neutrino masses can be
realized within the framework of a supersymmetric SO(10) model consistent with
gauge coupling unification and observed neutrino masses and mixing. We present
our expectations for non-unitarity effects in the leptonic mixing matrix some
of which are observable at future neutrino factories as well as the next
generation searches for lepton flavor violating processes such as \mu --> e +
\gamma. The model has TeV scale W_R and Z' bosons which are accessible at the
Large Hadron Collider.


  A great amount of endeavour has recently been devoted to the joint device
activity detection and channel estimation problem in massive machine-type
communications. This paper targets at two practical issues along this line that
have not been addressed before: asynchronous transmission from uncoordinated
users and efficient algorithms for real-time implementation in systems with a
massive number of devices. Specifically, this paper considers a practical
system where the preamble sent by each active device is delayed by some unknown
number of symbols due to the lack of coordination. We manage to cast the
problem of detecting the active devices and estimating their delay and channels
into a group LASSO problem. Then, a block coordinate descent algorithm is
proposed to solve this problem globally, where the closed-form solution is
available when updating each block of variables with the other blocks of
variables being fixed, thanks to the special structure of our interested
problem. Our analysis shows that the overall complexity of the proposed
algorithm is low, making it suitable for real-time application.


  The notion of innocent strategy was introduced by Hyland and Ong in order to
capture the interactive behaviour of lambda-terms and PCF programs. An innocent
strategy is defined as an alternating strategy with partial memory, in which
the strategy plays according to its view. Extending the definition to
non-alternating strategies is problematic, because the traditional definition
of views is based on the hypothesis that Opponent and Proponent alternate
during the interaction. Here, we take advantage of the diagrammatic
reformulation of alternating innocence in asynchronous games, in order to
provide a tentative definition of innocence in non-alternating games. The task
is interesting, and far from easy. It requires the combination of true
concurrency and game semantics in a clean and organic way, clarifying the
relationship between asynchronous games and concurrent games in the sense of
Abramsky and Melli\`es. It also requires an interactive reformulation of the
usual acyclicity criterion of linear logic, as well as a directed variant, as a
scheduling criterion.