  We calculate the equation of state of Bose-Bose gases in one and three
dimensions in the framework of an effective quantum field theory. The
beyond-mean-field approximation at zero-temperature and the one-loop
finite-temperature results are obtained performing functional integration on a
local effective action. The ultraviolet divergent zero-point quantum
fluctuations are removed by means of dimensional regularization. We derive the
nonlinear Schr\"odinger equation to describe one- and three-dimensional
Bose-Bose mixtures and solve it analytically in the one-dimensional scenario.
This equation supports self-trapped brightlike solitonic-droplets and
self-trapped darklike solitons. At low temperature, we also find that the
pressure and the number of particles of symmetric quantum droplets have a
nontrivial dependence on the chemical potential and the difference between the
intra- and the inter-species coupling constants.


  This note tries to give an answer to the following question: Is there a
sufficiently rich class of metric vector spaces such that sufficiently large
spaces of continuous linear maps between them are metrizable?


  Thirty-eight indium isotopes (A = 98-135) have so far been observed; the
discovery of these isotopes is discussed. For each isotope a brief summary of
the first refereed publication, including the production and identification
method, is presented.


  The quantum anomalous Hall effect (QAHE) is a robust topological phenomenon
featuring quantized Hall resistance at zero magnetic field. We report the QAHE
in a rhombohedral pentalayer graphene/monolayer WS2 heterostructure. Distinct
from other experimentally confirmed QAHE systems, this system has neither
magnetic element nor moir\'e superlattice effect. The QAH states emerge at
charge neutrality and feature Chern numbers C = +-5 at temperatures up to about
1.5 K. This large QAHE arises from the synergy of the electron correlation in
intrinsic flat bands of pentalayer graphene, the gate-tuning effect, and the
proximity-induced Ising spin-orbit-coupling. Our experiment demonstrates the
potential of crystalline two-dimensional materials for intertwined electron
correlation and band topology physics, and may enable a route for engineering
chiral Majorana edge states.


  The cosmological model of the modified Chaplygin gas interacting with cold
dark matter is studied. Our attention is focused on the final state of universe
in the model. It turns out that there exists a stable scaling solution, which
provides the possibility to alleviate the coincidence problem. In addition, we
investigate the effect of the coupling constants $c_{1}$ and $c_{2}$ on the
dynamical evolution of this model from the statefinder viewpoint. It is found
that the coupling constants play a significant role during the dynamical
evolution of the interacting MCG model. Furthermore, we can distinguish this
interacting model from other dark energy models in the $s-r$ plane.


  Let A be a simple unital AT algebra of real rank zero and Inn(A) the group of
inner automorphisms of A. In the previous paper we have shown that the natural
map of the group of approximately inner automorphisms into Ext(K_1(A),K_0(A))
oplus Ext(K_0(A),K_1(A)) is surjective; the kernel of this map includes the
subgroup of automorphisms which are homotopic to Inn(A). In this paper we
consider the quotient of the group of approximately inner automorphisms by the
smaller normal subgroup AInn(A) which consists of asymptotically inner
automorphisms and describe it as OrderExt(K_1(A),K_0(A)) oplus
Ext(K_0(A),K_1(A)), where OrderExt(K_1(A),K_0(A)) is a kind of extension group
which takes into account the fact that K_0(A) is an ordered group and has the
usual Ext as a quotient.


  The explosion of a carbon-oxygen white dwarf as a Type Ia supernova is known
to be sensitive to the manner in which the burning is ignited. Studies of the
pre-supernova evolution suggest asymmetric, off-center ignition, and here we
explore its consequences in two- and three-dimensional simulations. Compared
with centrally ignited models, one-sided ignitions initially burn less and
release less energy. For the distributions of ignition points studied, ignition
within two hemispheres typically leads to the unbinding of the white dwarf,
while ignition within a small fraction of one hemisphere does not. We also
examine the spreading of the blast over the surface of the white dwarf that
occurs as the first plumes of burning erupt from the star. In particular, our
studies test whether the collision of strong compressional waves can trigger a
detonation on the far side of the star as has been suggested by Plewa et al.
(2004). The maximum temperature reached in these collisions is sensitive to how
much burning and expansion has already gone on, and to the dimensionality of
the calculation. Though detonations are sometimes observed in 2D models, none
ever happens in the corresponding 3D calculations. Collisions between the
expansion fronts of multiple bubbles also seem, in the usual case, unable to
ignite a detonation. "Gravitationally confined detonation" is therefore not a
robust mechanism for the explosion. Detonation may still be possible in these
models however, either following a pulsation or by spontaneous detonation if
the turbulent energy is high enough.


  To study the compactness of bilinear commutators of certain bilinear
Calder\'on--Zygmund operators which include (inhomogeneous) Coifman--Meyer
bilinear Fourier multipliers and bilinear pseudodifferential operators as
special examples, Torres and Xue [Rev. Mat. Iberoam. 36 (2020), 939--956]
introduced a new subspace of BMO$\,(\mathbb{R}^n)$, denoted by
XMO$\,(\mathbb{R}^n)$, and conjectured that it is just the space
VMO$\,(\mathbb{R}^n)$ introduced by D. Sarason. In this article, the authors
give a negative answer to this conjecture by establishing an equivalent
characterization of XMO$\,(\mathbb{R}^n)$, which further clarifies that
XMO$\,(\mathbb{R}^n)$ is a proper subspace of VMO$\,(\mathbb{R}^n)$. This
equivalent characterization of XMO$\,(\mathbb{R}^n)$ is formally similar to the
corresponding one of CMO$\,(\mathbb{R}^n)$ obtained by A. Uchiyama, but its
proof needs some essential new techniques on dyadic cubes as well as some
exquisite geometrical observations. As an application, the authors also obtain
a weighted compactness result on such bilinear commutators, which optimizes the
corresponding result in the unweighted setting.


  We test the capability of state-of-the-art lattice techniques for a precise
determination of relativistic corrections to the static interquark potential,
by use of SU(2) gauge theory. Emphasis is put on the short range structure of
the spin dependent potentials, with lattice resolution a ranging from a approx
0.04 fm (at beta=2.74) down to a approx 0.02 fm (at beta=2.96) on volumes of
32^4 and 48^4 lattice sites. We find a new short range Coulomb-like
contribution to the spin-orbit potential V_1'.


  We present a study of the prospects for the measurement of TeV-scale
light-flavored right-squark masses and the corresponding production cross
section at a 3 TeV e+e- collider based on CLIC technology. The analysis,
performed in the framework of the CLIC Conceptual Design Report, is based on
full Geant4 simulations of the CLIC_ILD detector concept, including standard
model physics background and machine related hadronic background from
two-photon processes. The events are reconstructed using particle flow event
reconstruction, and the mass is obtained from a template fit built from
generator-level simulations with smearing to parametrize the detector response.
For an integrated luminosity of 2/ab, a statistical precision of 5.9 GeV,
corresponding to 0.52%, is obtained for unseparated first and second generation
right squarks. For the combined cross section, a precision of 0.07 fb,
corresponding to 5%, is obtained.


  In this note, we revisit EZBFT[2] and present safety, liveness and execution
consistency violations in the protocol. To demonstrate these violations, we
present simple scenarios, involving only four replicas, two clients, and one or
two owner changes. We also note shortcomings of the presented TLA+
specification used to model check the proposed protocol.


  Stars which are rapidly rotating are expected to show high levels of activity
according to the activity-rotation relation. However, previous TESS studies
have found Ultra Fast Rotating (UFR) M dwarfs with periods less than one day
displaying low levels of flaring activity. As a result, in this study, we
utilise VLT/FORS2 spectropolarimetric data of ten M dwarf UFR stars between
spectral types $\sim$M2 - M6 all with $P_{\rm rot} <$ 1, to detect the presence
of a magnetic field. We divide our sample into rotation period bins of equal
size, with one star having many more flares in the TESS lightcurve than the
other. We also provide an analysis of the long-term variability within our
sample using TESS lightcurves taken during Cycles 1 and 3 (up to three years
apart). We identify 605 flares from our sample which have energies between
2.0$\times$10$^{31}$ and 5.4$\times$10$^{34}$ erg. Although we find no
significance difference in the flare rate between the Cycles, two of our
targets display changes in their lightcurve morphology, potentially caused by a
difference in the spot distribution. Overall, we find five stars (50%) in our
sample have a detectable magnetic field with strengths $\sim$1 - 2 kG. Of these
five, four were the more flare active stars within the period bins with one
being the less flare active star. It would appear the magnetic field strength
may not be the answer to the lack of flaring activity and supersaturation or
magnetic field configuration may play a role. However, it is clear the
relationship between rotation and activity is more complex than a steady
decrease over time.


  We present some problems and results about variants of sunflowers in families
of sets. In particular, we improve an upper bound of the first author, K\"orner
and Monti on the maximum number of binary vectors of length $n$ so that every
four of them are split into two pairs by some coordinate. We also propose a
weaker version of the Erd\H{o}s-Rado sunflower conjecture.


  The next POI (point of interest) recommendation aims to predict users'
immediate future movements based on their prior records and present
circumstances, which will be very beneficial to service providers as well as
users. The popularity of the POI over time is one of the primary deciding
factors for choosing the next POI to visit. The majority of research in recent
times has paid more attention to the number of check-ins to define the
popularity of a point of interest, disregarding the temporal impact or number
of people checking in for a particular POI. In this paper, we propose a
recency-oriented definition of popularity that takes into account the temporal
effect on POI's popularity, the number of check-ins, as well as the number of
people who registered those check-ins. Thus, recent check-ins get prioritized
with more weight compared to the older ones. Experimental results demonstrate
that performance is better with recency-aware popularity definitions for POIs
than with solely check-in count-based popularity definitions.


  This paper proposes a novel and rapid calibration-free wavelength modulation
spectroscopy algorithm based on even-order harmonics. The proposed algorithm,
analytically deduced from Voigt line-shape function, only involves simple
algebraic operations to describe the actual gas absorption spectra, thus
eliminating the time-consuming simulations and line-shape fitting procedures
adopted in traditional algorithms. Instead of acquiring the entirely scanned
absorption line-shape, the proposed technique only requires extraction of the
peak values of the harmonics. This characteristic significantly benefits gas
diagnosis at elevated pressure and/or temperature, in which the entirely
scanned absorption is very difficult to be obtained due to the broadened
line-shapes. The proposed algorithm is validated by both numerical simulation
and condition-controlled experiment, indicating millisecond-level calculation
of gas parameters with the relative error less than 4% in the experiments.


  This technical report describes the CP-JKU team's submission for Task 4 Sound
Event Detection with Heterogeneous Training Datasets and Potentially Missing
Labels of the DCASE 24 Challenge. We fine-tune three large Audio Spectrogram
Transformers, PaSST, BEATs, and ATST, on the joint DESED and MAESTRO datasets
in a two-stage training procedure. The first stage closely matches the baseline
system setup and trains a CRNN model while keeping the large pre-trained
transformer model frozen. In the second stage, both CRNN and transformer are
fine-tuned using heavily weighted self-supervised losses. After the second
stage, we compute strong pseudo-labels for all audio clips in the training set
using an ensemble of all three fine-tuned transformers. Then, in a second
iteration, we repeat the two-stage training process and include a distillation
loss based on the pseudo-labels, boosting single-model performance
substantially. Additionally, we pre-train PaSST and ATST on the subset of
AudioSet that comes with strong temporal labels, before fine-tuning them on the
Task 4 datasets.


  We use dual-site radio observations of interplanetary scintillation (IPS)
with extremely long baselines (ELB) to examine meridional flow characteristics
of the ambient fast solar wind at plane-of-sky heliocentric distances of 24-85
solar radii (R\odot). Our results demonstrate an equatorwards deviation of
3-4{\deg} in the bulk fast solar wind flow direction over both northern and
southern solar hemispheres during different times in the declining phase of
Solar Cycle 23.


  We introduce and study the framework of compact metric structures and their
associated notions of isomorphisms such as homeomorphic and bi-Lipschitz
isomorphism. This is subsequently applied to model various classification
problems in analysis such as isomorphism of C*-algebras and affine
homeomorphism of Choquet simplices, where among other things we provide a
simple proof of the completeness of the isomorphism relation of separable,
simple, nuclear C*-algebras recently established by M. Sabok.


  We apply the Grassmann tensor renormalization group (GTRG) to the one-flavor
lattice Gross-Neveu model in the presence of chemical potential. We compute the
fermion number density and its susceptibility and confirm the validity of GTRG
for the finite density system. We introduce a method analogous to the
reweighting method for Monte Carlo method and test it for some parameters.


  Many image segmentation techniques have been developed over the past two
decades for segmenting the images, which help for object recognition, occlusion
boundary estimation within motion or stereo systems, image compression, image
editing.
  In this, there is a combined approach for segmenting the image. By using
histogram equalization to the input image, from which it gives contrast
enhancement output image .After that by applying median filtering,which will
remove noise from contrast output image . At last I applied fuzzy c-mean
clustering algorithm to denoising output image, which give segmented output
image. In this way it produce better segmented image with less computation
time.


  We study the prophet inequality when the gambler has an access only to a
single sample from each distribution. Rubinstein, Wang and Weinberg showed that
an optimal guarantee of 1/2 can be achieved when the underlying matroid has
rank 1, i.e. in the case of a single choice. We show that this guarantee can be
achieved also in the case of a uniform matroid of rank 2 by a deterministic
mechanism, and we show that this is best possible among deterministic
mechanisms. We also conjecture that a straightforward generalization of our
policy achieves the guarantee of 1/2 for all uniform matroids.


  The tenfold way provides a strong organizing principle for invertible
topological phases of matter. Mathematically, it is intimately connected with
$K$-theory via the fact that there exist exactly ten Morita classes of simple
real superalgebras. This connection is physically unsurprising, since weakly
interacting topological phases are classified by $K$-theory. We argue that when
strong interactions are present, care has to be taken when formulating the
exact ten symmetry groups present in the tenfold way table. We study this
phenomenon in the example of class D by providing two possible mathematical
interpretations of a class D symmetry. These two interpretations of class D
result in Morita-equivalent but different symmetry groups. As $K$-theory cannot
distinguish Morita-equivalent protecting symmetry groups, the two approaches
lead to the same classification of topological phases on the weakly interacting
side. However, we show that these two different symmetry groups yield different
interacting classifications in spacetime dimension 2+1. We use the approach to
interacting topological phases using bordism groups, reducing the relevant
classification problem to a spectral sequence computation.


  Large vision language models (LVLMs) integrate large language models (LLMs)
with pre-trained vision encoders, thereby activating the perception capability
of the model to understand image inputs for different queries and conduct
subsequent reasoning. Improving this capability requires high-quality
vision-language data, which is costly and labor-intensive to acquire.
Self-training approaches have been effective in single-modal settings to
alleviate the need for labeled data by leveraging model's own generation.
However, effective self-training remains a challenge regarding the unique
visual perception and reasoning capability of LVLMs. To address this, we
introduce Self-Training on Image Comprehension (STIC), which emphasizes a
self-training approach specifically for image comprehension. First, the model
self-constructs a preference dataset for image descriptions using unlabeled
images. Preferred responses are generated through a step-by-step prompt, while
dis-preferred responses are generated from either corrupted images or
misleading prompts. To further self-improve reasoning on the extracted visual
information, we let the model reuse a small portion of existing
instruction-tuning data and append its self-generated image descriptions to the
prompts. We validate the effectiveness of STIC across seven different
benchmarks, demonstrating substantial performance gains of 4.0% on average
while using 70% less supervised fine-tuning data than the current method.
Further studies investigate various components of STIC and highlight its
potential to leverage vast quantities of unlabeled images for self-training.
Code and data are made publicly available.


  The main purpose of this paper is to study non-commutative ternary
Nambu-Poisson algebras and their Hom-type version. We provide construction
results dealing with tensor product and direct sums of two (non-commutative)
ternary (Hom-)Nambu-Poisson algebras. Moreover, we explore twisting principle
of (non-commutative) ternary Nambu-Poisson algebras along with an algebra
morphism that lead to construct (non-commutative) ternary Hom-Nambu-Poisson
algebras. Furthermore, we provide examples and a 3-dimensional classification
of non-commutative ternary Nambu-Poisson algebras.


  We present a highly complete and reliable mid-infrared (MIR) colour selection
of luminous AGN candidates using the 3.4, 4.6, and 12 um bands of the WISE
survey. The MIR colour wedge was defined using the wide-angle Bright Ultra-Hard
XMM-Newton Survey (BUXS), one of the largest complete flux-limited samples of
bright (f(4.5-10 keV)>6x10^{-14} erg cm^-2 s^-1) "ultra-hard" (4.5-10 keV)
X-ray selected AGN to date. BUXS includes 258 objects detected over a total sky
area of 44.43 deg^2 of which 251 are spectroscopically identified and
classified, with 145 being type-1 AGN and 106 type-2 AGN. Our technique is
designed to select objects with red MIR power-law spectral energy distributions
(SED) in the three shortest bands of WISE and properly accounts for the errors
in the photometry and deviations of the MIR SEDs from a pure power-law. The
completeness of the MIR selection is a strong function of luminosity. At L(2-10
keV)>10^{44} erg s^-1, where the AGN is expected to dominate the MIR emission,
97.1_{-4.8}^{+2.2}% and 76.5_{-18.4}^{+13.3}% of the BUXS type-1 and type-2 AGN
meet the selection. Our technique shows one of the highest reliability and
efficiency of detection of the X-ray selected luminous AGN population with WISE
amongst those in the literature. In the area covered by the BUXS survey our
selection identifies 2755 AGN candidates detected with SNR>5 in the three
shorter wavelength bands of WISE with 38.5% having a detection at 2-10 keV
X-ray energies. We also analyzed the possibility of including the 22um WISE
band to select AGN candidates, but neither the completeness nor the reliability
of the selection improves. This is likely due to both the significantly
shallower depth at 22um compared with the first three bands of WISE and
star-formation contributing to the 22um emission at the WISE 22um sensitivity.


  An inaccessible cardinal kappa is supercompact when (kappa, lambda)-ITP holds
for all lambda greater than or equal to kappa. We prove that if there is a
model of ZFC with infinitely many supercompact cardinals, then there is a model
of ZFC where for every natural number n greater than 1 and for every ordinal mu
greater than or equal to aleph_n, we have (aleph_n, mu)-ITP.


  The hardware/software boundary in modern heterogeneous multicore computers is
increasingly complex, and diverse across different platforms. A single memory
access by a core or DMA engine traverses multiple hardware translation and
caching steps, and the destination memory cell or register often appears at
different physical addresses for different cores. Interrupts pass through a
complex topology of interrupt controllers and remappers before delivery to one
or more cores, each with specific constraints on their configurations. System
software must not only correctly understand the specific hardware at hand, but
also configure it appropriately at runtime. We propose a formal model of
address spaces and resources in a system that allows us to express and verify
invariants of the system's runtime configuration, and illustrate (and motivate)
it with several real platforms we have encountered in the process of OS
implementation.


  We describe the development of a noise-temperature testing capability for
phased-array antennas operating in receive mode from 0.7 GHz to 1.8 GHz.
Sampled voltages from each array port were recorded digitally as the
zenith-pointing array under test was presented with three scenes: (1) a large
microwave absorber at ambient temperature, (2) the unobstructed radio sky, and
(3) broadband noise transmitted from a reference antenna centred over and
pointed at the array under test. The recorded voltages were processed in
software to calculate the beam equivalent noise temperature for a maximum
signal-to-noise ratio beam steered at the zenith. We introduced the
reference-antenna measurement to make noise measurements with reproducible,
well-defined beams directed at the zenith and thereby at the centre of the
absorber target. We applied a detailed model of cosmic and atmospheric
contributions to the radio sky emission that we used as a noise-temperature
reference. We also present a comprehensive analysis of measurement uncertainty
including random and systematic effects. The key systematic effect was due to
uncertainty in the beamformed antenna pattern and how efficiently it
illuminates the absorber load. We achieved a combined uncertainty as low as 4 K
for a 40 K measurement of beam equivalent noise temperature. The measurement
and analysis techniques described in this paper were pursued to support
noise-performance verification of prototype phased-array feeds for the
Australian Square Kilometre Array Pathfinder telescope.


  A study is presented of the localisation of excitonic states on extended
molecular aggregates composed of identical monomers arising, not from disorder
due to statistical energy shifts of the monomers, induced by environmental
interactions (Anderson localisation), but rather simply due to changes in the
orientation and geometrical arrangement of the transition dipoles. It is shown
further that such small changes nevertheless can have a drastic effect on the
shape of the vibronic spectrum of the aggregate. The vibronic spectra are
calculated using the "coherent exciton scattering" (CES) approximation whose
derivation we generalise to be applicable to aggregates of arbitrary size and
geometry.


  When analyzing the spread of viruses, epidemiologists often need to identify
the location of infected hosts. This information can be found in public
databases, such as GenBank, however, information provided in these databases
are usually limited to the country or state level. More fine-grained
localization information requires phylogeographers to manually read relevant
scientific articles. In this work we propose an approach to automate the
process of place name identification from medical (epidemiology) articles. The
focus of this paper is to propose a deep learning based model for toponym
detection and experiment with the use of external linguistic features and
domain specific information. The model was evaluated using a collection of 105
epidemiology articles from PubMed Central provided by the recent SemEval task
12. Our best detection model achieves an F1 score of $80.13\%$, a significant
improvement compared to the state of the art of $69.84\%$. These results
underline the importance of domain specific embedding as well as specific
linguistic features in toponym detection in medical journals.


  There are indications that the magnetic field evolution in galaxies might be
massively shaped by tidal interactions and mergers between galaxies. The
details of the connection between the evolution of magnetic fields and that of
their host galaxies is still a field of research. We use a combined approach of
magnetohydrodynamics for the baryons and an N-body scheme for the dark matter
to investigate magnetic field amplification and evolution in interacting
galaxies. We find that, for two colliding equal-mass galaxies and for varying
initial relative spatial orientations, magnetic fields are amplified during
interactions, yet cannot be sustained. Furthermore, we find clues for an active
mean-field dynamo.


  The purpose of this paper is to investigate the finite Frobenius groups with
"perfect order classes"; that is, those for which the number of elements of
each order is a divisor of the order of the group. If a finite Frobenius group
has perfect order classes then so too does its Frobenius complement, the
Frobenius kernel is a homocyclic group of odd prime power order, and the
Frobenius complement acts regularly on the elements of prime order in the
Frobenius kernel. The converse is also true.
  Combined with elementary number-theoretic arguments, we use this to provide
characterisations of several important classes of Frobenius groups. The
insoluble Frobenius groups with perfect order classes are fully characterised.
These turn out to be the perfect Frobenius groups whose Frobenius kernel is a
homocyclic $11$-group of rank $2$.
  We also determine precisely which nilpotent Frobenius complements have
perfect order classes, from which it follows that a Frobenius group with
nilpotent complement has perfect order classes only if the Frobenius complement
is a cyclic $\{2,3\}$-group of even order.
  Those Frobenius groups for which the Frobenius complement is a biprimary
group are also described fully, and we show that no soluble Frobenius group
whose Frobenius complement is a $\{2,3,5\}$-group with order divisible by $30$
has perfect order classes.


  This paper considers numerical semigroups $S$ that have a non-principal
relative ideal $I$ such that $\mu_S(I)\mu_S(S-I)=\mu_S(I+(S-I)) $. We show the
existence of an infinite family of such which $I+(S-I)=S\backslash\{0\}$. We
also show examples of such pairs that are not members of this family. We
discuss the computational process used to find these examples and present some
open questions pertaining to them.


  An analysis of wavefront motion in weakly coupled doped semiconductor
superlattices is presented. If a dimensionless doping is sufficiently large,
the superlattice behaves as a discrete system presenting front propagation
failure and the wavefronts can be described near the threshold currents $J_i$
($i=1,2$) at which they depin and move. The wavefront velocity scales with
current as $|J-J_i|^{{1\over 2}}$. If the dimensionless doping is low enough,
the superlattice behaves as a continuum system and wavefronts are essentially
shock waves whose velocity obeys an equal area rule.


  We introduce edge labeled Young tableaux. Our main results provide a
corresponding analogue of [Sch\"{u}tzenberger '77]'s theory of jeu de taquin.
These are applied to the equivariant Schubert calculus of Grassmannians.
Reinterpreting, we present new (semi)standard tableaux to study factorial Schur
polynomials, after [Biedenharn-Louck '89], [Macdonald '92] and [Goulden-Greene
'94] and others.
  Consequently, we obtain new combinatorial rules for the Schubert structure
coefficients, complementing work of [Molev-Sagan '99], [Knutson-Tao '03],
[Molev '08] and [Kreiman '09]. We also describe a conjectural generalization of
one of our rules to the equivariant K-theory of Grassmannians, extending work
of [Thomas-Yong '07]. This conjecture concretely realizes the "positivity"
known to exist by [Anderson-Griffeth-Miller '08]. It provides an alternative to
the conjectural rule of Knutson-Vakil reported in [Coskun-Vakil '06].


  In long-term potentiation (LTP), one of the most studied types of neural
plasticity, synaptic strength is persistently increased in response to
stimulation. Although a number of different proteins have been implicated in
the sub-cellular molecular processes underlying induction and maintenance of
LTP, the precise mechanisms remain unknown. A particular challenge is to
demonstrate that a proposed molecular mechanism can provide the level of
stability needed to maintain memories for months or longer, in spite of the
fact that many of the participating molecules have much shorter life spans.
Here we present a computational model that combines simulations of several
biochemical reactions that have been suggested in the LTP literature and show
that the resulting system does exhibit the required stability. At the core of
the model are two interlinked feedback loops of molecular reactions, one
involving the atypical protein kinase PKM{\zeta} and its messenger RNA, the
other involving PKM{\zeta} and GluA2-containing AMPA receptors. We demonstrate
that robust bistability - stable equilibria both in the synapse's potentiated
and unpotentiated states - can arise from a set of simple molecular reactions.
The model is able to account for a wide range of empirical results, including
induction and maintenance of late-phase LTP, cellular memory reconsolidation
and the effects of different pharmaceutical interventions.


  We consider divergence form elliptic operators L = - div A(x)\nabla, defined
in the half space R^{n+1}_+, n \geq 2, where the coefficient matrix A(x) is
bounded, measurable, uniformly elliptic, t-independent, and not necessarily
symmetric. We establish square function/non-tangential maximal function
estimates for solutions of the homogeneous equation Lu = 0, and we then combine
these estimates with the method of "\epsilon-approximability" to show that
L-harmonic measure is absolutely continuous with respect to surface measure
(i.e., n-dimensional Lebesgue measure) on the boundary, in a scale-invariant
sense: more precisely, that it belongs to the class A_\infty with respect to
surface measure (equivalently, that the Dirichlet problem is solvable with data
in L^p, for some p < \infty). Previously, these results had been known only in
the case n = 1.


  People are concerned about privacy, particularly on the Internet. While many
studies have provided evidence of this concern, few have explored the nature of
the concern in detail, especially for the online environment. With this study,
we have tried to better understand the nature of online privacy concerns; we
look beyond the fact that people are concerned and attempt to understand how
they are concerned. We hope our results will help inform both policy decisions
as well as the development of technology tools that can assist Internet users
in protecting their privacy.
  We present results here from the analysis of 381 questionnaires completed
between November 6 and November 13, 1998 by American Internet users. The sample
was drawn from the FamilyPC magazine/Digital Research, Inc. Family Panel. While
this is not a statistically representative sample of US Internet users, our
respondents are heavy Internet users, and quite possibly lead innovators. As
such, we believe that this sample is important for understanding the future
Internet user population.


  In this paper we study the class of mixed-index time fractional differential
equations in which different components of the problem have different time
fractional derivatives on the left hand side. We prove a theorem on the
solution of the linear system of equations, which collapses to the well-known
Mittag-Leffler solution in the case the indices are the same, and also
generalises the solution of the so-called linear sequential class of time
fractional problems. We also investigate the asymptotic stability properties of
this class of problems using Laplace transforms and show how Laplace transforms
can be used to write solutions as linear combinations of generalised
Mittag-Leffler functions in some cases. Finally we illustrate our results with
some numerical simulations.


  We show that a CP-violating phase can be model-independently determined from
the time-independent measurement of coherent B^0_s\bar{B}^0_s decays into
(D^{(*)\pm}_s K^{(*)\mp})(D^{(*)\pm}_s K^{(*)\mp}) states at the \Upsilon (5S)
resonance. This phase amounts to (-\gamma) within the standard model, where
\gamma is the well-known angle of the quark mixing unitarity triangle. It is
also possible to determine or constrain the B^0_s-\bar{B}^0_s mixing parameter
y_s from the same measurement.


  When a star is described as a spectral class G2V, we know that the star is
similar to our Sun. We know its approximate mass, temperature, age, and size.
When working with an extra-solar planet database, it is very useful to have a
taxonomy scale (classification) such as, for example, the Harvard
classification for stars. The taxonomy has to be easily interpreted and present
the most relevant information about extra-solar planets. I propose the
following the extra-solar planet taxonomy scale with four parameters. The first
parameter concerns the mass of an extra-solar planet in the form of the units
of the mass of other known planets, where M represents the mass of Mercury, E
that of Earth, N Neptune, and J Jupiter. The second parameter is the planet's
distance from its parent star (semi-major axis) described in logarithm with
base 10. The third parameter is the mean Dyson temperature of the extra-solar
planet, for which I established four main temperature classes; F represents the
Freezing class, W the Water Class, G the Gaseous Class, and R the Roasters
Class. I devised one additional class, however: P, the Pulsar Class, which
concerns extra-solar planets orbiting pulsar stars. The fourth parameter is
eccentricity. If the attributes of the surface of the extra-solar planet are
known, we are able to establish this additional parameter where t represents a
terrestrial planet, g a gaseous planet, and i an ice planet. According to this
taxonomy scale, for example, Earth is 1E0W0t, Neptune is 1N1.5F0i, and
extra-solar planet 55 Cnc e is 9E-1.8R1. Key words: Catalogues - Extra-solar
planet - Habitable zone - Planets


  In late 2019, the gravest pandemic in a century began spreading across the
world. A state of uncertainty related to what has become known as SARS-CoV-2
has since fueled conspiracy narratives on social media about the origin,
transmission and medical treatment of and vaccination against the resulting
disease, COVID-19. Using social media intelligence to monitor and understand
the proliferation of conspiracy narratives is one way to analyze the
distribution of misinformation on the pandemic. We analyzed more than 9.5M
German language tweets about COVID-19. The results show that only about 0.6% of
all those tweets deal with conspiracy theory narratives. We also found that the
political orientation of users correlates with the volume of content users
contribute to the dissemination of conspiracy narratives, implying that
partisan communicators have a higher motivation to take part in conspiratorial
discussions on Twitter. Finally, we showed that contrary to other studies,
automated accounts do not significantly influence the spread of misinformation
in the German speaking Twitter sphere. They only represent about 1.31% of all
conspiracy-related activities in our database.


  We investigate Laughlin's fractional quantum Hall effect wave function on a
cylinder. We show that it displays translational symmetry breaking in the axial
direction for sufficiently thin cylinders. At filling factor 1/p, the period is
p times the period of the filled lowest Landau level. The proof uses a
connection with one-dimensional polymer systems and discrete renewal equations.


  For a particular lattice gauge theory with ${\mathbb Z}_2$ gauge invariance
there is confinement for all couplings. The gauge fields, on lattice links, lie
in the closed interval $[-1,1]$. It is proved that the expectation value of a
gauge-invariant loop operator decays as the exponential of minus the area.


  Hand pose estimation from the monocular 2D image is challenging due to the
variation in lighting, appearance, and background. While some success has been
achieved using deep neural networks, they typically require collecting a large
dataset that adequately samples all the axes of variation of hand images. It
would, therefore, be useful to find a representation of hand pose which is
independent of the image appearance~(like hand texture, lighting, background),
so that we can synthesize unseen images by mixing pose-appearance combinations.
In this paper, we present a novel technique that disentangles the
representation of pose from a complementary appearance factor in 2D monochrome
images. We supervise this disentanglement process using a network that learns
to generate images of hand using specified pose+appearance features. Unlike
previous work, we do not require image pairs with a matching pose; instead, we
use the pose annotations already available and introduce a novel use of cycle
consistency to ensure orthogonality between the factors. Experimental results
show that our self-disentanglement scheme successfully decomposes the hand
image into the pose and its complementary appearance features of comparable
quality as the method using paired data. Additionally, training the model with
extra synthesized images with unseen hand-appearance combinations by re-mixing
pose and appearance factors from different images can improve the 2D pose
estimation performance.


  In this paper, we give the mathematical construction of novel core-shell
plasmonic structures that can induce anomalous localized resonance and
invisibility cloaking at certain finite frequencies beyond the quasistatic
limit. The crucial ingredient in our study is that the plasmon constant and the
loss parameter are constructed in a delicate way that are correlated and depend
on the source and the size of the plasmonic structure. As a significant
byproduct of this study, we also derive the complete spectrum of the
Neumann-Poinc\'are operator associated to the Helmholtz equation with finite
frequencies in the radial geometry. The spectral result is the first one in its
type and is of significant mathematical interest for its own sake.


  In this work, we will show through three-dimensional particle-in-cell
simulations that direct laser acceleration in laser a wakefield accelerator can
generate sub-femtosecond electron bunches. Two simulations were done with two
laser pulse durations, such that the shortest laser pulse occupies only a
fraction of the first bubble, whereas the longer pulse fills the entire first
bubble. In the latter case, as the trapped electrons moved forward and
interacted with the high intensity region of the laser pulse, micro-bunching
occurred naturally, producing 0.5 fs electron bunches. This is not observed in
the short pulse simulation.


  We have studied the $\gamma d \to K^+ K^- n p$ reaction in which the LEPS
collaboration found a signal in the $K^+ n$ invariant mass for the claimed
$\Theta(1540)$ pentaquark peak. Our study reveal that the procedure used at
LEPS to reconstruct the $K^+n$ invariant mass generates an artificial strength
in the $\Theta(1540)$ region and that the LEPS collaboration underestimated the
background in that region, such that the signal observed for the $\Theta(1540)$
is compatible with a fluctuation of $2\sigma$ over the calculated background.


  This paper aims to develop a Newton-type method to solve a class of nonconvex
composite programs. In particular, the nonsmooth part is possibly nonconvex. To
tackle the nonconvexity, we develop a notion of strong prox-regularity which is
related to the singleton property, Lipschitz continuity, and monotonicity of
the associated proximal operator, and we verify it in various classes of
functions, including weakly convex functions, indicator functions of proximally
smooth sets, and two specific sphere-related nonconvex nonsmooth functions. In
this case, the problem class we are concerned with covers smooth optimization
problems on manifold and certain composite optimization problems on manifold.
For the latter, the proposed algorithm is the first second-order type method.
Combining with the semismoothness of the proximal operator, we design a
projected semismooth Newton method to find a root of the natural residual
induced by the proximal gradient method. Since the corresponding natural
residual may not be globally monotone, an extra projection is added on the
usual semismooth Newton step and new criteria are proposed for the switching
between the projected semismooth Newton step and the proximal step. The global
convergence is then established under the strong prox-regularity. Based on the
BD regularity condition, we establish local superlinear convergence. Numerical
experiments demonstrate the effectiveness of our proposed method compared with
state-of-the-art ones.


  We have analytically calculated the quantum discord for a system composed of
spin-$j$ and spin-1/2 subsystems possessing SU(2) symmetry. We have compared
our results with the quantum discord of states having similar symmetries and
seen that in our case amount of quantum discord is much higher. Moreover, using
the well known entanglement properties of these states, we have also compared
their quantum discord with entanglement. Although the system under
consideration is separable nearly all throughout of its parameter space as $j$
increases, we have seen that discord content remains significantly large.
Investigation of quantum discord in SU(2) invariant states may find application
in quantum computation protocols that utilize quantum discord as a resource
since they arise in many real physical systems.


  The Large Synoptic Survey Telescope (LSST) surveys have initially been
optimized to omit the inner part of the Milky Way disk/bar from deep and
cadence observations. However it is now clear that the LSST will be powerful
for Galactic astronomy and may play a crucial role in continuing to extend the
Gaia astrometric catalog until a future satellite, either optical or IR,
carries on. LSST will provide metallicities and kinematics for the bulge, and
will map halo structures to as distant as 450 kpc, nearly half the distance to
the Andromeda galaxy. Thanks to the unprecedented calibration effort for its
photometric system, and surprisingly good astrometry (transverse velocity
measurements of 0.2 mas/yr at r=21; 1 mas/yr at r=24). LSST will provide
photometric abundances and distance constraints for a billion or more Milky Way
stars to distances of 450 kpc, and kinematics from proper motions to $\sim100$
kpc. Single observation depths reach $\sim 24$ in the $ugrizy$ bands, while
depths at end of mission reach $\sim 27$. Although halo structures such as
streams and dwarf galaxies are initially identified by the RR Lyrae and giants,
their structure will be fleshed out by the 100$\times$ more abundant dwarfs
that will be detected to 100 kpc (single observation) and $\sim 300$ kpc by end
of mission. More complete mapping of stream structures may constrain the mass
distribution of dark matter and perhaps confirm the interaction of dark matter
halos and streams. I also describe the Blanco DECam Bulge Survey, a 200 deg$^2$
LSST pathfinder survey of the bulge in $ugrizy$ using the Dark Energy Camera on
the Blanco 4m telescope. The purpose of this article is to encourage active
workers on the Milky Way and Local Volume to participate in the LSST project,
in particular to urge that the Galactic Plane receive the same cadence and
depth coverage as the rest of the extragalactic sky.


  This proceeding overviews our current understanding of the orbital history
and mass of the Large and Small Magellanic Clouds. Specifically I will argue
that the Clouds are on their first infall about our Milky Way and that their
total masses are necessarily ~10 times larger than traditionally estimated.
This conclusion is based on the recently revised HST proper motions of the
Clouds and arguments concerning the binary status of the LMC-SMC pair and their
baryon fractions


  This paper presents a new loss function for the prediction of oriented
bounding boxes, named head-tail-loss. The loss function consists in minimizing
the distance between the prediction and the annotation of two key points that
are representing the annotation of the object. The first point is the center
point and the second is the head of the object. However, for the second point,
the minimum distance between the prediction and either the head or tail of the
groundtruth is used. On this way, either prediction is valid (with the head
pointing to the tail or the tail pointing to the head). At the end the
importance is to detect the direction of the object but not its heading. The
new loss function has been evaluated on the DOTA and HRSC2016 datasets and has
shown potential for elongated objects such as ships and also for other types of
objects with different shapes.


  We prove the following new characterization of $C^p$ (Lipschitz) smoothness
in Banach spaces. An infinite-dimensional Banach space $X$ has a $C^p$ smooth
(Lipschitz) bump function if and only if it has another $C^p$ smooth
(Lipschitz) bump function $f$ such that $f'(x)\neq 0$ for every point $x$ in
the interior of the support of $f$ (that is, $f$ does not satisfy Rolle's
theorem). Moreover, the support of this bump can be assumed to be a smooth
starlike body. As a by-product of the proof of this result we also obtain other
useful characterizations of $C^p$ smoothness related to the existence of a
certain kind of deleting diffeomorphisms, as well as to the failure of
Brouwer's fixed point theorem even for smooth self-mappings of starlike bodies
in all infinite-dimensional spaces. Finally, we study the structure of the set
of gradients of bump functions in the Hilbert space $\ell_2$, and as a
consequence of the failure of Rolle's theorem in infinite dimensions we get the
following result. The usual norm of the Hilbert space $\ell_2$ can be uniformly
approximated by $C^1$ smooth Lipschiz functions $\psi$ so that the cones
generated by the sets of derivatives $\psi'(\ell_{2})$ have empty interior.
This implies that there are $C^1$ smooth Lipschitz bumps in $\ell_{2}$ so that
the cones generated by their sets of gradients have empty interior.


  The exact parameter values of mathematical models are often uncertain or even
unknown. Nevertheless, we may have access to crude information about the
parameters, e.g., that some of them are nonzero. Such information can be
captured by so-called pattern matrices, whose symbolic entries are used to
represent the available information about the corresponding parameters. In this
paper, we focus on pattern matrices with three types of symbolic entries: those
that represent zero, nonzero, and arbitrary parameters. We formally define and
study addition and multiplication of such pattern matrices. The results are
then used in the study of three strong structural properties, namely,
controllability of linear descriptor systems, and input-state observability and
output controllability of linear systems.


  We present a method to measure the spectrally-resolved transmission matrix of
a multiply scattering medium, thus allowing for the deterministic
spatiospectral control of a broadband light source by means of wavefront
shaping. As a demonstration, we show how the medium can be used to selectively
focus one or many spectral components of a femtosecond pulse, and how it can be
turned into a controllable dispersive optical element to spatially separate
different spectral components to arbitrary positions.


  Matrix models are proposed as nonperturbative formulations of superstring
theory. We study a concrete correspondence of the analytical result between the
matrix model and the field theory. In this paper, we focus on a fuzzy sphere
and a complex projective space. We show a wave functions/states correspondence
of the zero modes of the Dirac operators under the 't Hooft-Polyakov monopole
background on the continuous/fuzzy sphere. In addition, we propose a Laplacian
for a scalar sector of the matrix model and obtain a concrete construction of
it.


  A convenient bicategory of topological stacks is constructed which is both
complete and Cartesian closed. This bicategory, called the bicategory of
compactly generated stacks, is the analogue of classical topological stacks,
but for a different Grothendieck topology. In fact, there is an equivalence of
bicategories between compactly generated stacks and those classical topological
stacks which admit locally compact Hausdorff atlases. Compactly generated
stacks are also equivalent to a bicategory of topological groupoids and
principal bundles, just as in the classical case. If a classical topological
stack and a compactly generated stack have a presentation by the same
topological groupoid, then they restrict to the same stack over locally compact
Hausdorff spaces and are homotopy equivalent.


  We consider a degenerate parabolic equation associated with the fractional $%
p $-Laplace operator $\left( -\Delta \right) _{p}^{s}$\ ($p\geq 2$, $s\in
\left( 0,1\right) $) and a monotone perturbation growing like $\left\vert
s\right\vert ^{q-2}s,$ $q>p$ and with bad sign at infinity as $\left\vert
s\right\vert \rightarrow \infty $. We show the existence of locally-defined
strong solutions to the problem with any initial condition $u_{0}\in
L^{r}(\Omega )$ where $r\geq 2$ satisfies $r>N(q-p)/sp$. Then, we prove that
finite time blow-up is possible for these problems in the range of parameters
provided for $r,p,q$ and the initial datum $u_0$.


  We present a new semi-analytic model for dynamical friction based on
Chandrasekhar's formalism. The key novelty is the introduction of physically
motivated, radially varying, maximum and minimum impact parameters. With these,
our model gives an excellent match to full N-body simulations for isotropic
background density distributions, both cuspy and shallow, without any
fine-tuning of the model parameters. In particular, we are able to reproduce
the dramatic core-stalling effect that occurs in shallow/constant density
cores, for the first time. This gives us new physical insight into the
core-stalling phenomenon. We show that core stalling occurs in the limit in
which the product of the Coulomb logarithm and the local fraction of stars with
velocity lower than the infalling body tends to zero. For cuspy backgrounds,
this occurs when the infalling mass approaches the enclosed background mass.
For cored backgrounds, it occurs at larger distances from the centre, due to a
combination of a rapidly increasing minimum impact parameter and a lack of slow
moving stars in the core. This demonstrates that the physics of core-stalling
is likely the same for both massive infalling objects and low-mass objects
moving in shallow density backgrounds. We implement our prescription for
dynamical friction in the direct summation code NBODY6 as an analytic
correction for stars that remain within the Roche volume of the infalling
object. This approach is computationally efficient, since only stars in the
inspiralling system need to be evolved with direct summation. Our method can be
applied to study a variety of astrophysical systems, including young star
clusters orbiting near the Galactic Centre; globular clusters moving within the
Galaxy; and dwarf galaxies orbiting within dark matter halos.


  We study quantitative stability results for different classes of Sobolev
inequalities on general compact Riemannian manifolds. We prove that, up to
constants depending on the manifold, a function that nearly saturates a
critical Sobolev inequality is quantitatively $W^{1,2}$-close to a non-empty
set of extremal functions, provided that the corresponding optimal Sobolev
constant satisfies a suitable strict bound. The case of sub-critical Sobolev
inequalities is also covered. Finally, we discuss degenerate phenomena in our
quantitative controls.


  In this paper, we present a method to forecast the spread of SARS-CoV-2
across regions with a focus on the role of mobility. Mobility has previously
been shown to play a significant role in the spread of the virus, particularly
between regions. Here, we investigate under which epidemiological circumstances
incorporating mobility into transmission models yields improvements in the
accuracy of forecasting, where we take the situation in the Netherlands during
and after the first wave of transmission in 2020 as a case study. We assess the
quality of forecasting on the detailed level of municipalities, instead of on a
nation-wide level. To model transmissions, we use a simple mobility-enhanced
SEIR compartmental model with subpopulations corresponding to the Dutch
municipalities. We use commuter information to quantify mobility, and develop a
method based on maximum likelihood estimation to determine the other relevant
parameters. We show that taking inter-regional mobility into account generally
leads to an improvement in forecast quality. However, at times when policies
are in place that aim to reduce contacts or travel, this improvement is very
small.


  Large language models (LLMs) can suffer from hallucinations when generating
text. These hallucinations impede various applications in society and industry
by making LLMs untrustworthy. Current LLMs generate text in an autoregressive
fashion by predicting and appending text tokens. When an LLM is uncertain about
the semantic meaning of the next tokens to generate, it is likely to start
hallucinating. Thus, it has been suggested that hallucinations stem from
predictive uncertainty. We introduce Semantically Diverse Language Generation
(SDLG) to quantify predictive uncertainty in LLMs. SDLG steers the LLM to
generate semantically diverse yet likely alternatives for an initially
generated text. This approach provides a precise measure of aleatoric semantic
uncertainty, detecting whether the initial text is likely to be hallucinated.
Experiments on question-answering tasks demonstrate that SDLG consistently
outperforms existing methods while being the most computationally efficient,
setting a new standard for uncertainty estimation in LLMs.


  The various algorithms used to extrapolate particle trajectories from
measurements are often very time-consuming with computational complexities
which are typically quadratic. In this article, we propose a new algorithm
called GEM with a lower complexity and reasonable performance on linear tracks.
It is an extension of the EM algorithm used to fit Gaussian mixtures. It works
in arbitrary dimension and with an arbitrary number of simultaneous particles.
In a second part, we extend it to circular tracks (for charged particles) and
even a mix of linear and circular tracks. This algorithm is implemented in an
open-source library called libgem and two applications are proposed, based on
data-sets from two kind of particle trackers.


  Subretinal injection methods and other procedures for treating retinal
conditions and diseases (many considered incurable) have been limited in scope
due to limited human motor control. This study demonstrates the next
generation, cooperatively controlled Steady-Hand Eye Robot (SHER 3.0), a
precise and intuitive-to-use robotic platform achieving clinical standards for
targeting accuracy and resolution for subretinal injections. The system design
and basic kinematics are reported and a deflection model for the incorporated
delta stage and validation experiments are presented. This model optimizes the
delta stage parameters, maximizing the global conditioning index and minimizing
torsional compliance. Five tests measuring accuracy, repeatability, and
deflection show the optimized stage design achieves a tip accuracy of <30
$\mu$m, tip repeatability of 9.3 $\mu$m and 0.02{\deg}, and deflections between
20-350 $\mu$m/N. Future work will use updated control models to refine tip
positioning outcomes and will be tested on in vivo animal models.


  Teaching neural models to generate narrative coherent texts is a critical
problem. Recent pre-trained language models have achieved promising results,
but there is still a gap between human written texts and machine-generated
outputs. In this work, we propose a novel multi-task training strategy for
coherent text generation grounded on the cognitive theory of writing, which
empowers the model to learn essential subskills needed for writing including
planning and reviewing besides end-to-end generation. We extensively evaluate
our model on three open-ended generation tasks including story generation, news
article writing and argument generation. Experiments show that our model
achieves better results on both few-shot and fully-supervised settings than
strong baselines, and human evaluations confirm that our model can generate
more coherent outputs.


  This paper presents an effective few-shot point cloud semantic segmentation
approach for real-world applications. Existing few-shot segmentation methods on
point cloud heavily rely on the fully-supervised pretrain with large annotated
datasets, which causes the learned feature extraction bias to those pretrained
classes. However, as the purpose of few-shot learning is to handle
unknown/unseen classes, such class-specific feature extraction in pretrain is
not ideal to generalize into new classes for few-shot learning. Moreover, point
cloud datasets hardly have a large number of classes due to the annotation
difficulty. To address these issues, we propose a contrastive self-supervision
framework for few-shot learning pretrain, which aims to eliminate the feature
extraction bias through class-agnostic contrastive supervision. Specifically,
we implement a novel contrastive learning approach with a learnable augmentor
for a 3D point cloud to achieve point-wise differentiation, so that to enhance
the pretrain with managed overfitting through the self-supervision.
Furthermore, we develop a multi-resolution attention module using both the
nearest and farthest points to extract the local and global point information
more effectively, and a center-concentrated multi-prototype is adopted to
mitigate the intra-class sparsity. Comprehensive experiments are conducted to
evaluate the proposed approach, which shows our approach achieves
state-of-the-art performance. Moreover, a case study on practical CAM/CAD
segmentation is presented to demonstrate the effectiveness of our approach for
real-world applications.


  We present the first measurements of the angular correlation function of
galaxies selected in the far (1530 A) and near (2310 A) Ultraviolet from the
GALEX survey fields overlapping SDSS DR5 in low galactic extinction regions.
The area used covers 120 sqdeg (GALEX - MIS) down to magnitude AB = 22,
yielding a total of 100,000 galaxies. The mean correlation length is ~ 3.7 \pm
0.6 Mpc and no significant trend is seen for this value as a function of the
limiting apparent magnitude or between the GALEX bands. This estimate is close
to that found from samples of blue galaxies in the local universe selected in
the visible, and similar to that derived at z ~ 3 for LBGs with similar rest
frame selection criteria. This result supports models that predict anti-biasing
of star forming galaxies at low redshift, and brings an additional clue to the
downsizing of star formation at z<1.


  In this paper, we investigate the spectrum of light scattered from a
Bose-Einstein condensate in the framework of f-deformed boson. We use an
f-deformed quantum model in which the Gardiners phonon operators for BEC are
deformed by an operator-valued function, f(n), of the particle-number operator
n. We consider the collisions between the atoms as a special kind of
f-deformation. The collision rate k is regarded as the deformation parameter
and the spectrum of light scattered from the deformed BEC is analyzed. In
particular, we find that with increasing the values of deformation parameters k
and eta=1/N (N, total number of condensate atoms) the scattering spectrum shows
deviation from the spectrum associated with nondeformed Bose-Einstein
condensate.


  A non-perturbative quantization of the Yang-Mills energy-mass functional with
a compact semi-simple gauge group entails an infinite discrete energy-mass
spectrum of gauge bosons. The bosonic spectrum is bounded from below, and has a
positive mass gap due to the quartic self-interaction term of pure Yang-Mills
Lagrangian (with no Higgs term involved). This quantization is based on
infinite-dimensional analysis in Kree nuclear triple of sesqui-holomorphic
functionals of initial data for the the non-linear classical Yang-Mills
equations in the temporal gauge.


  In order to nullify the property of randomness perceived in the dispersion of
gamma-ray bursts (GRB's) we introduce two new procedures. 1. Create a segmented
group of sequentially linked GRB's and quantify the resultant angles. 2. Create
segmented groups of sequentially linked GRB's in order to identify the location
of GRB's that are positioned at equidistance, by using the selected GRB as the
origin for a paired point circle, where the circumference of said circle
intercepts the location of other GRB's in the same group.


  In this article, we study small perturbations of the family of
Friedmann-Lema\^itre-Robertson-Walker cosmological background solutions to the
Euler-Einstein system with a positive cosmological constant in 1 + 3
dimensions. The background solutions describe an initially uniform quiet fluid
of positive energy density evolving in a spacetime undergoing accelerated
expansion. We show that under the equation of state p = c_s^2*(energy density),
0 < c_s^2 < 1/3, the background solutions are globally future asymptotically
stable under small irrotational perturbations. In particular, we prove that the
perturbed spacetimes, which have the topological structure [0,infinity) x T^3,
are future causally geodesically complete.


  We present three distinct examples where phaseless auxiliary-field Quantum
Monte Carlo (ph-AFQMC) can be reliably performed with a single-determinant
trial wavefunction with essential symmetry breaking. We first utilized
essential time-reversal symmetry breaking with ph-AFQMC to compute the
triplet-singlet energy gap in the TS12 set. We found statistically better
performance of ph-AFQMC with complex-restricted orbitals than with
spin-unrestricted orbitals. We then showed the utilization of essential spin
symmetry breaking when computing the single-triplet gap of a known
biradicaloid, C$_{36}$. ph-AFQMC with spin-unrestricted Hartree-Fock
(ph-AFQMC+UHF) fails catastrophically even with spin-projection and predicts no
biradicaloid character. With approximate Brueckner orbitals obtained from
regularized orbital-optimized second-order M{\o}ller-Plesset perturbation
theory ($\kappa$-OOMP2), ph-AFQMC quantitatively captures strong biradicaloid
character of C$_{36}$. Lastly, we applied ph-AFQMC to the computation of the
quintet-triplet gap in a model iron porphyrin complex where brute-force methods
with a small active space fail to capture the triplet ground state. We show
unambiguously that neither triplet nor quintet is strongly correlated using
UHF, $\kappa$-OOMP2, and coupled-cluster with singles and doubles (CCSD)
performed on UHF and $\kappa$-OOMP2 orbitals. There is no essential symmetry
breaking in this problem. By virtue of this, we were able to perform
UHF+ph-AFQMC reliably with a cc-pVTZ basis set and predicted a triplet ground
state for this model geometry. The largest ph-AFQMC in this work correlated 186
electrons in 956 orbitals. Our work highlights the utility, scalability, and
accuracy of ph-AFQMC with a single determinant trial wavefunction with
essential symmetry breaking for systems mainly dominated by dynamical
correlation with little static correlation.


  This is a list of some problems and conjectures related to various types of
algebras, that is to algebraic operads. Some comments and hints are included.


  A motion of point vortices with periodic boundary conditions is studied by
using Weierstrass zeta functions. Scattering and recoupling of a vortex pair by
a third vortex becomes remarkable when the vortex density is large. Clustering
of vortices with various initial conditions is quantitated by the $L$ function
used in point process theory in spatial ecology. It is shown that clustering
persists if it is initially clustered like an infinite row or a checkered
pattern.


  Let ${\cal L}$ be a variation of Hodge structures on the complement $X^{*}$
of a normal crossing divisor (NCD) $ Y$ in a smooth analytic variety $X$ and
let $ j: X^{*} = X - Y \to X $ denotes the open embedding. The purpose of this
paper is to describe the weight filtration $W$ on a combinatorial logarithmic
complex computing the (higher) direct image ${\bf j}_{*}{\cal L} $, underlying
a mixed Hodge complex when $X$ is proper, proving in this way the results in
the note [14] generalizing the constant coefficients case. When a morphism $f:
X \to D$ to a complex disc is given with $Y = f^{-1}(0)$, the weight filtration
on the complex of nearby cocycles $\Psi_f ({\cal L})$ on $Y$ can be described
by these logarithmic techniques and a comparison theorem shows that the
filtration coincides with the weight defined by the logarithm of the monodromy
which provides the link with various results on the subject.


  In this talk I give a brief update on the recent progress in the SO(5) theory
of high T_c superconductivity (Science, 275: 1089,1997). Reviewed topics
include SO(5) ladders, the unification of BCS and SDW quasi-particles in the
SO(5) theory and the microscopic origin of the condensation energy.


  Several emerging PoW blockchain protocols rely on a "parallel-chain"
architecture for scaling, where instead of a single chain, multiple chains are
run in parallel and aggregated. A key requirement of practical PoW blockchains
is to adapt to mining power variations over time. In this paper, we consider
the design of provably secure parallel-chain protocols which can adapt to such
mining power variations.
  The Bitcoin difficulty adjustment rule adjusts the difficulty target of block
mining periodically to get a constant mean inter-block time. While
superficially simple, the rule has proved itself to be sophisticated and
successfully secure, both in practice and in theory. We show that natural
adaptations of the Bitcoin adjustment rule to the parallel-chain case open the
door to subtle, but catastrophic safety and liveness breaches. We uncover a
meta-design principle that allow us to design variable mining difficulty
protocols for three popular PoW blockchain proposals (Prism, OHIE, and
Fruitchains) inside a common rubric.
  The principle has three components:(M1) a pivot chain, based on which blocks
in all chains choose difficulty, (M2) a monotonicity condition for referencing
pivot chain blocks and (M3) translating additional protocol aspects from using
levels (depth) to using "difficulty levels". We show that protocols employing a
subset of these principles may have catastrophic failures. The security of the
designs is also proved using a common rubric - the key technical challenge
involves analyzing the interaction between the pivot chain and the other
chains, as well as bounding the sudden changes in difficulty target experienced
in non-pivot chains. We empirically investigate the responsivity of the new
mining difficulty rule via simulations based on historical Bitcoin data, and
find that the protocol very effectively controls the forking rate across all
the chains.


  We develop the Wigner phase space representation of a kicked particle for an
arbitrary but periodic kicking potential. We use this formalism to illustrate
quantum resonances and anti--resonances.


  Analyzing classification model performance is a crucial task for machine
learning practitioners. While practitioners often use count-based metrics
derived from confusion matrices, like accuracy, many applications, such as
weather prediction, sports betting, or patient risk prediction, rely on a
classifier's predicted probabilities rather than predicted labels. In these
instances, practitioners are concerned with producing a calibrated model, that
is, one which outputs probabilities that reflect those of the true
distribution. Model calibration is often analyzed visually, through static
reliability diagrams, however, the traditional calibration visualization may
suffer from a variety of drawbacks due to the strong aggregations it
necessitates. Furthermore, count-based approaches are unable to sufficiently
analyze model calibration. We present Calibrate, an interactive reliability
diagram that addresses the aforementioned issues. Calibrate constructs a
reliability diagram that is resistant to drawbacks in traditional approaches,
and allows for interactive subgroup analysis and instance-level inspection. We
demonstrate the utility of Calibrate through use cases on both real-world and
synthetic data. We further validate Calibrate by presenting the results of a
think-aloud experiment with data scientists who routinely analyze model
calibration.


  In this paper, we present a novel methodology we call MDS-ViTNet (Multi
Decoder Saliency by Vision Transformer Network) for enhancing visual saliency
prediction or eye-tracking. This approach holds significant potential for
diverse fields, including marketing, medicine, robotics, and retail. We propose
a network architecture that leverages the Vision Transformer, moving beyond the
conventional ImageNet backbone. The framework adopts an encoder-decoder
structure, with the encoder utilizing a Swin transformer to efficiently embed
most important features. This process involves a Transfer Learning method,
wherein layers from the Vision Transformer are converted by the Encoder
Transformer and seamlessly integrated into a CNN Decoder. This methodology
ensures minimal information loss from the original input image. The decoder
employs a multi-decoding technique, utilizing dual decoders to generate two
distinct attention maps. These maps are subsequently combined into a singular
output via an additional CNN model. Our trained model MDS-ViTNet achieves
state-of-the-art results across several benchmarks. Committed to fostering
further collaboration, we intend to make our code, models, and datasets
accessible to the public.


  The magneto-optical Kerr effect (MOKE) is often assumed to be proportional to
the magnetisation of a magnetically ordered metallic sample; in metallic
ferrimagnets with chemically distinct sublattices, such as rare-earth
transition-metal alloys, it depends on the difference between the sublattice
contributions. Here we show that in a highly spin polarized, fully compensated
ferrimagnet, where the sublattices are chemically similar, MOKE is observed
even when the net moment is strictly zero. We analyse the spectral ellipsometry
and MOKE of Mn 2 Ru x Ga, and show that this behaviour is due to a highly
spin-polarized conduction band dominated by one of the two manganese
sublattices which creates helicity-dependent reflectivity determined by a broad
Drude tail. Our findings open new prospects for studying spin dynamics in the
infra-red.


  This paper formulates the Nash problem for a pair consisting of a toric
variety and an invariant ideal and gives an affirmative answer to the problem.
We also prove that the minimal log-discrepacy is computed by a divisor
corresponding to a Nash component, if the minimal log-discrepancy is finite. On
the other hand there exists a Nash component such that the corresponding
divisor has negative log-discrepancy, if the minimal log-discrepancy is
$-/infty$.


  Asymptotic behaviors of zero modes of the massless Dirac operator
$H=\alpha\cdot D + Q(x)$ are discussed, where
  $\alpha= (\alpha_1, \alpha_2, \alpha_3)$ is the triple of $4 \times 4$ Dirac
matrices, $ D=\frac{1}{i} \nabla_x$, and $Q(x)=\big(q_{jk} (x) \big)$ is a
$4\times 4$ Hermitian matrix-valued function with
  $| q_{jk}(x) | \le C < x >^{-\rho} $, $\rho >1$.
  We shall show that for every zero mode $f$, the asymptotic limit of
$|x|^2f(x)$ as $|x| \to +\infty$ exists. The limit is expressed in terms of an
integral of $Q(x)f(x)$.


  Broadband microwave waveforms with programmable chirp shapes are captivating
in numerous practical applications. Compared with electronic technology,
photonic-assisted solutions exhibit excellent performance in bandwidth and
flexibility, but still suffer from complex architecture and requirement of
high-speed electronics. Besides, rapid manipulation of chirp shape is still a
challenge in the scientific community. In this paper, we propose and
demonstrate a novel concept for generating broadband microwave waveforms with
programmable chirp shapes. This concept is realized on a simple fiber-optic
platform involving a continuous-wave laser source, a recirculating
phase-modulated optical fiber loop, and low-speed electronics with a sampling
rate at the level of MS/s. Based on this method, chirped microwave waveforms
with a bandwidth up to tens of GHz can be generated, where the chirp shape is
identical to the low-frequency driving waveform of the recirculating
phase-modulated optical fiber loop. In addition, all the parameters of the
generated chirped microwave waveforms can be easily reconfigured in real time,
including the bandwidth, the central frequency, and the temporal duration. In
the experiment, broadband microwave waveforms with customized chirp shapes are
generated, where the center frequency and bandwidth tuning ranges exceed 21
GHz, the temporal duration is tuned in the range of 9 ns to 180 ns, and the
coherent time of the generated microwave waveform is larger than 100 {\mu}s.
This simple fiber-optic platform paves a way to generate broadband microwave
waveforms with user-definable chirp shapes, which can find applications in
broadband radar systems, electronic warfare and wireless communications.


  Mathematical models are important tools to study the excluded volume effects
on reaction-diffusion systems, which are known to play an important role inside
living cells. Detailed microscopic simulations with off-lattice Brownian
dynamics become computationally expensive in crowded environments. In this
paper we therefore investigate to which extent on-lattice approximations, so
called Cellular Automata models, can be used to simulate reactions and
diffusion in the presence of crowding molecules. We show that the diffusion is
most severely slowed down in the off-lattice model, since randomly distributed
obstacles effectively exclude more volume than those ordered on an artificial
grid. Crowded reaction rates can be both increased and decreased by the grid
structure and it proves important to model the molecules with realistic sizes
when excluded volume is taken into account. The grid artifacts increase with
increasing crowder density and we conclude that the computationally more
efficient on-lattice simulations are accurate approximations only for low
crowder densities.


  In this article, the operator $\Diamond_{B}^{k}$ is introduced and named as
the Bessel diamond operator iterated $k$ times and is defined by $
\Diamond_{B}^{k} = [ (B_{x_{1}} + B_{x_{2}} + ... + B_{x_{p}})^{2} - (B_{x_{p +
1}} + ... + B_{x_{p + q}})^{2} ]^{k}$, where $ p + q = n, B_{x_{i}} =
\frac{\partial^{2}}{\partial x_{i}^{2}} + \frac{2v_{i}}{x_{i}}
\frac{\partial}{\partial x_{i}}, $ where $2v_{i} = 2\alpha_{i} + 1$, $
\alpha_{i} > - {1/2} $ [8], $x_{i} > 0$, $i = 1, 2, ..., n, k$ is a
non-negative integer and $n$ is the dimension of $\mathbb{R}_{n}^{+}$. In this
work we study the elementary solution of the Bessel diamond operator and the
elementary solution of the operator $\Diamond_{B}^{k}$ is called the Bessel
diamond kernel of Riesz. Then, we study the Fourier--Bessel transform of the
elementary solution and also the Fourier--Bessel transform of their
convolution.


  We study the problem of the self-assembly of nanoparticles (NPs) into finite
mesoscopic structures with a programmed local morphology and complex overall
shape. Our proposed building blocks are NPs directionally-functionalized with
DNA. The combination of directionality and selectivity of interactions allows
one to avoid unwanted metastable configurations which have been shown to lead
to slow self-assembly kinetics even in much simpler systems. With numerical
simulations, we show that a variety of target mesoscopic objects can be
designed and self-assembled in near perfect yield. They include cubes,
pyramids, boxes and even an Empire State Building model. We summarize our
findings with a set of design strategies that lead to the successful
self-assembly of a wide range of mesostructures.


  Through simultaneous but unequal electromechanical amplification and cooling
processes, we create a method for nearly noiseless pulsed measurement of
mechanical motion. We use transient electromechanical amplification (TEA) to
monitor a single motional quadrature with a total added noise $-8.5\pm2.0$ dB
relative to the zero-point motion of the oscillator, or equivalently the
quantum limit for simultaneous measurement of both mechanical quadratures. We
demonstrate that TEA can be used to resolve fine structure in the phase-space
of a mechanical oscillator by tomographically reconstructing the density matrix
of a squeezed state of motion. Without any inference or subtraction of noise,
we directly observe a squeezed variance $2.8\pm 0.3$ dB below the oscillator's
zero-point motion.


  We obtain the combined mean-field and semiclassical limit from the $N$-body
Schr\"{o}dinger equation for fermions interacting via singular potentials. To
obtain the result, we first prove the uniformity in Planck's constant $h$
propagation of regularity for solutions to the Hartree$\unicode{x2013}$Fock
equation with singular pair interaction potentials of the form $\pm
|x-y|^{-a}$, including the Coulomb and gravitational interactions.
  In the context of mixed states, we use these regularity properties to obtain
quantitative estimates on the distance between solutions to the Schr\"{o}dinger
equation and solutions to the Hartree$\unicode{x2013}$Fock and Vlasov equations
in Schatten norms. For $a\in(0,1/2)$, we obtain local-in-time results when
$N^{-1/2} \ll h \leq N^{-1/3}$. In particular, it leads to the derivation of
the Vlasov equation with singular potentials. For $a\in[1/2,1]$, our results
hold only on a small time scale, or with an $N$-dependent cutoff.


  The theory of discrete-time online learning has been successfully applied in
many problems that involve sequential decision-making under uncertainty.
However, in many applications including contractual hiring in online
freelancing platforms and server allocation in cloud computing systems, the
outcome of each action is observed only after a random and action-dependent
time. Furthermore, as a consequence of certain ethical and economic concerns,
the controller may impose deadlines on the completion of each task, and require
fairness across different groups in the allocation of total time budget $B$. In
order to address these applications, we consider continuous-time online
learning problem with fairness considerations, and present a novel framework
based on continuous-time utility maximization. We show that this formulation
recovers reward-maximizing, max-min fair and proportionally fair allocation
rules across different groups as special cases. We characterize the optimal
offline policy, which allocates the total time between different actions in an
optimally fair way (as defined by the utility function), and impose deadlines
to maximize time-efficiency. In the absence of any statistical knowledge, we
propose a novel online learning algorithm based on dual ascent optimization for
time averages, and prove that it achieves $\tilde{O}(B^{-1/2})$ regret bound.


  As a typical 2D magnetic material with self-intercalated structure, Cr5Te8
exhibits many fascinating magnetic properties. Although the ferromagnetism of
2D Cr5Te8 has been reported, the study of its magnetic domain is still blank.
Herein, we successfully fabricated 2D Cr5Te8 nanosheets with controlled
thickness and lateral size by chemical vapor deposition (CVD). Then magnetic
property measurement system suggested Cr5Te8 nanosheets possessing intense
out-of-plane ferromagnetism with the Curie temperature of 179 K. Most
importantly, we found magnetic bubbles and thickness-dependent maze-like
magnetic domains by cryogenic magnetic force microscopy (MFM) for the first
time. The domain width of the maze-like magnetic domains increases rapidly with
decreasing sample thickness, while domain contrast decreases. This indicates
dipolar interaction is the dominant role over exchange interaction and magnetic
anisotropy. Our work not only paves a way for the controllable growth of 2D
magnetic materials, but also suggests new directions for controlling magnetic
phases and systematically adjusting domain properties.


  Reinforcement learning (RL) agents have long sought to approach the
efficiency of human learning. Humans are great observers who can learn by
aggregating external knowledge from various sources, including observations
from others' policies of attempting a task. Prior studies in RL have
incorporated external knowledge policies to help agents improve sample
efficiency. However, it remains non-trivial to perform arbitrary combinations
and replacements of those policies, an essential feature for generalization and
transferability. In this work, we present Knowledge-Grounded RL (KGRL), an RL
paradigm fusing multiple knowledge policies and aiming for human-like
efficiency and flexibility. We propose a new actor architecture for KGRL,
Knowledge-Inclusive Attention Network (KIAN), which allows free knowledge
rearrangement due to embedding-based attentive action prediction. KIAN also
addresses entropy imbalance, a problem arising in maximum entropy KGRL that
hinders an agent from efficiently exploring the environment, through a new
design of policy distributions. The experimental results demonstrate that KIAN
outperforms alternative methods incorporating external knowledge policies and
achieves efficient and flexible learning. Our implementation is available at
https://github.com/Pascalson/KGRL.git


  We present a generally applicable formalism for modeling the emission,
absorption, reflection, and reprocessing of radiation by moving plasma streams
close to a Kerr Black hole. The formalism can be used to investigate the
observational signatures of a wide range of phenomena, including: (i) the
reflection of coronal X-ray radiation off plasma plunging from the inner edge
of a black hole accretion disk towards the black hole; (ii) the reflection of
coronal X-ray emission off the upper layers of a geometrically thick accretion
flow; (iii) the illumination of the accretion disk by a corona moving with
relativistic velocities towards or away from the accretion disk; (iv) the
emission from a jet forming close to the black hole. After introducing the
general relativistic treatment, we show the results for a fast wind forming
close to a Kerr black hole. The approach presented here can be used to model
X-ray spectral, timing, reverberation, and polarization data.


  A systematic theory for the diffusion--limited reaction processes $A + A \to
0$ and $A \to (m+1) A$ is developed. Fluctuations are taken into account via
the field--theoretic dynamical renormalization group. For $m$ even the mean
field rate equation, which predicts only an active phase, remains qualitatively
correct near $d_c = 2$ dimensions; but below $d_c' \approx 4/3$ a nontrivial
transition to an inactive phase governed by power law behavior appears. For $m$
odd there is a dynamic phase transition for any $d \leq 2$ which is described
by the directed percolation universality class.


  We study Galileon scalar field model by considering the lowest order Galileon
term in the lagrangian, $(\partial_{\mu} \phi)^2 \Box\phi$ by invoking a field
potential. We use Statefinder hierarchy to distinguish the light mass galileon
models with different potentials amongst themselves and from the $\Lambda$CDM
behaviour. The $Om$ diagnostic is applied to cosmological dynamics and
observational constraints on the model parameters are studied using
SN+Hubble+BAO data.


  The long wavelength emission of protostellar objects is commonly attributed
to a disk of gas and dust around the central protostar. In the first stages of
disk accretion or in the case of high mass protostars, the disk mass is likely
to be sufficiently large, so that the disk self-gravity may have an impact on
the dynamics and the emission properties of the disk. In this paper we describe
the spectral energy distribution (SED) produced by a simple, non-flaring,
self-gravitating accretion disk model. Self-gravity is included in the
calculation of the rotation curve of the disk and in the energy balance
equation, as a term of effective heating related to Jeans instability. In order
to quantify in detail the requirements on the mass of the disk and on the
accretion rate posed on the models by realistic situations, we compare the SEDs
produced by these models with the observed SEDs of a small sample of
well-studied protostellar objects. We find that relatively modest disks - even
lighter than the central star - can lead to an interesting fit to the infrared
SED of the FU Orionis objects considered, while in the case of T Tauri stars
the required parameters fall outside the range suggested as acceptable by the
general theoretical and observational scenario. On the basis of the present
results, we may conclude that the contribution of a self-gravitating disk is
plausible in several cases (in particular, for FU Orionis objects) and that, in
the standard irradiation dominated disk scenario, it would help softening the
requirements encountered by Keplerian accretion models.


  We study the behaviour of infinitesimal deformation functors of local group
actions with regard to passing to subgroups and quotient groups. Inspired by
the cohomological information, we conjecture the existence of a decomposition
of a deformation functor of a local $G$-action as a smooth extension of a
fibered product of functors related to a subgroup and a quotient group of $G$.


  Feature attribution methods, or saliency maps, are one of the most popular
approaches for explaining the decisions of complex machine learning models such
as deep neural networks. In this study, we propose a stochastic optimization
approach for the perturbation-based feature attribution method. While the
original optimization problem of the perturbation-based feature attribution is
difficult to solve because of the complex constraints, we propose to
reformulate the problem as the maximization of a differentiable function, which
can be solved using gradient-based algorithms. In particular, stochastic
optimization is well-suited for the proposed reformulation, and we can solve
the problem using popular algorithms such as SGD, RMSProp, and Adam. The
experiment on the image classification with VGG16 shows that the proposed
method could identify relevant parts of the images effectively.


  This paper has been withdrawn by the authors; it is superceeded by the paper:
The real loci of Calogero--Moser spaces, representations of rational Cherednik
algebras and the Shapiro conjecture, by Iain Gordon, Emil Horozov, and Milen
Yakimov, arXiv:0711.4336.


  Next-generation galaxy surveys will increasingly rely on the galaxy
bispectrum to improve cosmological constraints, especially on primordial
non-Gaussianity. A key theoretical requirement that remains to be developed is
the analysis of general relativistic effects on the bispectrum, which arise
from observing galaxies on the past lightcone, {as well as from relativistic
corrections to the dynamics}. {As an initial step towards a fully relativistic
analysis of the galaxy bispectrum, we compute for the first time the local
relativistic lightcone effects on the bispectrum,} which come from Doppler and
gravitational potential contributions. For the galaxy bispectrum, the problem
is much more complex than for the power spectrum, since we need the lightcone
corrections at second order. Mode-coupling contributions at second order mean
that relativistic corrections can be non-negligible at smaller scales than in
the case of the power spectrum. In a primordial Gaussian universe, we show that
the local lightcone corrections for squeezed shapes at $z\sim1$ mean that the
bispectrum can differ from the Newtonian prediction by $\gtrsim 10\%$ when the
short modes are $k\lesssim (50\,{\rm Mpc})^{-1}$. These relativistic projection
effects, if ignored in the analysis of observations, could be mistaken for
primordial non-Gaussianity. For upcoming surveys which probe equality scales
and beyond, {all relativistic lightcone effects and relativistic dynamical
corrections should be included} for an accurate measurement of primordial
non-Gaussianity.


  The presence of silicon at the surface of the two Hyades DA white dwarfs WD
0421+162 and WD 0431+126 requires mechanisms that counteract the effects of the
downward diffusion. Radiative levitation calculations indicate that the silicon
abundance observed in WD 0431+126 corresponds to the abundance supported by
radiative levitation. Detailed time-dependent diffusion calculations that take
into account radiative levitation and accretion indicate that accretion with
rates of dM/dt(Si) < 1.00E4 g/s could also be present without disrupting the
abundance supported by radiative levitation. In the case of WD 0421+162,
accretion with a rate of dM/dt(Si) = 1.25E5 g/s must be invoked, because its
observed silicon abundance is larger than the abundance supported by radiative
levitation. This accretion rate is lower than the accretion rate given by the
accretion-diffusion model, because the radiative levitation slows down the
downward diffusion of silicon. The silicon abundances observed in the two
Hyades white dwarfs cannot be interpreted solely in terms of accretion. The
interpretation of the silicon abundances must take into account the interplay
between radiative levitation and accretion.


  We develop a discrete Morse theory for open simplicial complexes
$K=X\setminus T$ where $X$ is a simplicial complex and $T$ a subcomplex of $X$.
A discrete Morse function $f$ on $K$ gives rise to a discrete Morse function on
the order complex $S_K$ of $K$, and the topology change determined by $f$ on
$K$ can be understood by analyzing the the topology change determined by the
discrete Morse function on $S_K$. This topology change is given by a structure
theorem on the level subcomplexes of $S_K$. Finally, we show that the
Borel-Moore homology of $K$, a homology theory for locally compact spaces, is
isomorphic to the homology induced by a gradient vector field on $K$ and deduce
corresponding weak Morse inequalities.


  One of us (L.S.) and H. Verlinde independently conjectured a holographic
duality between the double-scaled SYK model at infinite temperature and
dimensionally reduced $(2+1)$-dimensional de Sitter space [1]-[8]. Beyond the
statement that such a duality exists there was deep disagreement between the
two proposals [9]. In this note, we trace the origin of the disagreement to a
superficial similarity between two q-deformed algebraic structures: the algebra
of "chords" in DSSYK, and the algebra of line operators in the Chern-Simons
formulation of 3D de Sitter gravity. Assuming that these two structures are the
same requires an identification of parameters [7][10] which leads to a collapse
of the separation of scales [9] -- the separation being required by the
semiclassical limit [3][9]. Dropping that assumption restores the separation of
scales but leaves unexplained the relation between chords and Chern-Simons line
operators. In this note we point out the existence of a third q-deformed
algebra that appears in DSSYK: the algebra of ``wee-chords." Identifying the
Chern-Simons line operators with wee-chords removes the discrepancy and leads
to a satisfying relation between the two sides of the duality.


  Based on easy-to-follow considerations it is not difficult to be vehemently
opposed not only the solutions found in that paper but also the conclusions
manifested there.


  We study the statistical properties of the dynamic trajectory of stochastic
gradient descent (SGD). We approximate the mini-batch SGD and the momentum SGD
as stochastic differential equations (SDEs). We exploit the continuous
formulation of SDE and the theory of Fokker-Planck equations to develop new
results on the escaping phenomenon and the relationship with large batch and
sharp minima. In particular, we find that the stochastic process solution tends
to converge to flatter minima regardless of the batch size in the asymptotic
regime. However, the convergence rate is rigorously proven to depend on the
batch size. These results are validated empirically with various datasets and
models.


  We use scale invariant scattering theory to exactly determine the lines of
renormalization group fixed points for $O(N)$-symmetric models with quenched
disorder in two dimensions. Random fixed points are characterized by two
disorder parameters: a modulus that vanishes when approaching the pure case,
and a phase angle. The critical lines fall into three classes depending on the
values of the disorder modulus. Besides the class corresponding to the pure
case, a second class has maximal value of the disorder modulus and includes
Nishimori-like multicritical points as well as zero temperature fixed points.
The third class contains critical lines that interpolate, as $N$ varies,
between the first two classes. For positive $N$, it contains a single line of
infrared fixed points spanning the values of $N$ from $\sqrt{2}-1$ to $1$. The
symmetry sector of the energy density operator is superuniversal (i.e.
$N$-independent) along this line. For $N=2$ a line of fixed points exists only
in the pure case, but accounts also for the Berezinskii-Kosterlitz-Thouless
phase observed in presence of disorder.


  Psammophilous plants are special plants that flourish in sand moving
environments. There are two main mechanisms by which the wind affects these
plants: (i) sand drift exposes roots and covers branches--the exposed roots
turn into new plants and the covered branches turn into new roots; both
mechanisms result in an enhanced growth rate of the psammophilous plant cover
of the dunes; (ii) strong winds, often associated with sand movement, tear
branches and seed them in nearby locations, resulting in new plants and an
enhanced growth rate of the psammophilous plant cover of the dunes. Despite
their important role in dune dynamics, to our knowledge, psammophilous plants
have never been incorporated into mathematical models of sand dunes. Here, we
attempt to model the effects of these plants on sand dune dynamics. We
construct a set of three ordinary differential equations for the fractions of
surface cover of regular vegetation, biogenic soil crust and psammophilous
plants. The latter reach their optimal growth under (i) specific sand drift or
(ii) specific wind power. We show that psammophilous plants enrich the sand
dune dynamics. Depending on the climatological conditions, it is possible to
obtain one, two, or three steady dune states. The activity of the dunes can be
associated with the surface cover--bare dunes are active, and dunes with
significant cover of vegetation, biogenic soil crust, or psammophilous plants
are fixed. Our model shows that under suitable precipitation rates and wind
power, the dynamics of the different cover types is in accordance with the
common view that dunes are initially stabilized by psammophilous plants that
reduce sand activity, thus enhancing the growth of regular vegetation that
eventually dominates the cover of the dunes and determines their activity.


  We study the real roots of the Yablonskii-Vorob'ev polynomials, which are
special polynomials used to represent rational solutions of the second
Painlev\'e equation. It has been conjectured that the number of real roots of
the nth Yablonskii-Vorob'ev polynomial equals [(n+1)/2]. We prove this
conjecture using an interlacing property between the roots of the
Yablonskii-Vorob'ev polynomials. Furthermore we determine precisely the number
of negative and the number of positive real roots of the nth
Yablonskii-Vorob'ev polynomial.