  Our goal is to see if there is molecular gas extending throughout the optical
low surface brightness disk of the galaxy Malin 2. We used the heterodyne
receiver array (HERA) mounted on the IRAM 30m telecope to make deep
observations at the frequency of the CO(2--1) line at nine different positions
of Malin~2. With a total observing time of 11 hours at a velocity resolution of
11 km/s we achieve a sensitivity level of ~1 mK. We detect CO(2-1) line
emission from Malin~2. The line is detected in four of the nine HERA beams; a
fifth beam shows a marginal detection. These results not only confirm that
there is molecular gas in the disk of Malin 2, but they also show that it is
spread throughout the inner 34~kpc radius as sampled by the observations of the
galaxy disk. The mean molecular gas surface density in the disk is
$1.1\pm0.2~M_{\odot}~pc^{-2}$ and the molecular gas mass lies between the
limits $4.9\times10^{8}$ to $8.3\times10^{8}~M_{\odot}$. The observed velocity
dispersion of the molecular gas is higher ($\sim 13$\,km\,s$^{-1}$) than in
star forming galactic disks. This could explain the disk stability and its low
star formation activity.


  The effective field theory of cosmological perturbations stems from
considering a cosmological background solution as a state displaying
spontaneous breaking of time translations and (adiabatic) perturbations as the
related Nambu-Goldstone modes. With this insight, one can systematically
develop a theory for the cosmological perturbations during inflation and, with
minor modifications, also describe in full generality the gravitational
interactions of dark energy, which are relevant for late-time cosmology. The
formalism displays a unique set of Lagrangian operators containing an
increasing number of cosmological perturbations and derivatives. We give an
introductory description of the unitary gauge formalism for theories with
broken gauge symmetry---that allows to write down the most general
Lagrangian---and of the Stueckelberg "trick"---that allows to recover gauge
invariance and to make the scalar field explicit. We show how to apply this
formalism to gravity and cosmology and we reproduce the detailed analysis of
the action in the ADM variables. We also review some basic applications to
inflation and dark energy.


  The Very Large Area gamma-ray Space Telescope (VLAST) is a mission concept
proposed to detect gamma-ray photons through both the Compton scattering and
electron-positron pair production mechanisms, enabling the detection of photons
with energies ranging from MeV to TeV. This project aims to conduct a
comprehensive survey of the gamma-ray sky from a low Earth orbit using an
anti-coincidence detector, a tracker detector that also serves as a low energy
calorimeter, and a high energy imaging calorimeter. We developed a Monte Carlo
simulation application of the detector with the GEANT4 toolkit to evaluate the
instrument performance including the effective area, angular resolution and
energy resolution, as well as explored specific optimizations of the detector
configuration. Our simulation-based analysis indicates that the VLAST's current
design is physically feasible, with an acceptance larger than 10~$\rm m^2\ sr$
which is four times larger than Fermi-LAT, an energy resolution better than 2\%
at 10~GeV, and an angular resolution better than 0.2 degrees at 10~GeV. The
VLAST project is expected to make significant contribution to the field of
gamma-ray astronomy and to enhance our understanding of the cosmos.


  The main result of the present paper is that the stable and unstable
C*-algebras associated to a mixing Smale space always contain nonzero
projections. This gives a positive answer to a question of the first listed
author and Karen Strung and has implications for the structure of these
algebras in light of the Elliott program for simple C*-algebras. Using our main
result, we also show that the homoclinic, stable, and unstable algebras each
have real rank zero.


  Learning involves relations, interactions and connections between learners,
teachers and the world at large. Such interactions are essentially temporal and
unfold in time. Yet, researchers have rarely combined the two aspects (the
temporal and relational aspects) in an analytics framework. Temporal networks
allow modeling of the temporal learning processes i.e., the emergence and flow
of activities, communities, and social processes through fine-grained dynamic
analysis. This can provide insights into phenomena like knowledge
co-construction, information flow, and relationship building. This chapter
introduces the basic concepts of temporal networks, their types and techniques.
A detailed guide of temporal network analysis is introduced in this chapter,
that starts with building the network, visualization, mathematical analysis on
the node and graph level. The analysis is performed with a real-world dataset.
The discussion chapter offers some extra resources for interested users who
want to expand their knowledge of the technique.


  Denoising diffusion probabilistic models (DDPMs) are a recent family of
generative models that achieve state-of-the-art results. In order to obtain
class-conditional generation, it was suggested to guide the diffusion process
by gradients from a time-dependent classifier. While the idea is theoretically
sound, deep learning-based classifiers are infamously susceptible to
gradient-based adversarial attacks. Therefore, while traditional classifiers
may achieve good accuracy scores, their gradients are possibly unreliable and
might hinder the improvement of the generation results. Recent work discovered
that adversarially robust classifiers exhibit gradients that are aligned with
human perception, and these could better guide a generative process towards
semantically meaningful images. We utilize this observation by defining and
training a time-dependent adversarially robust classifier and use it as
guidance for a generative diffusion model. In experiments on the highly
challenging and diverse ImageNet dataset, our scheme introduces significantly
more intelligible intermediate gradients, better alignment with theoretical
findings, as well as improved generation results under several evaluation
metrics. Furthermore, we conduct an opinion survey whose findings indicate that
human raters prefer our method's results.


  Galaxy clusters are luminous tracers of the most massive dark matter haloes
in the Universe. To use them as a cosmological probe, a detailed description of
the properties of dark matter haloes is required. We characterize how the
dynamical state of haloes impacts the halo mass function at the high-mass end.
We used the dark matter-only MultiDark suite of simulations and the high-mass
objects M > 2.7e13 M/h therein. We measured mean relations of concentration,
offset, and spin as a function of halo mass and redshift. We investigated the
distributions around the mean relations. We measured the halo mass function as
a function of offset, spin, and redshift. We formulated a generalized mass
function framework that accounts for the dynamical state of the dark matter
haloes. We confirm the discovery of the concentration upturn at high masses and
provide a model that predicts the concentration for different values of mass
and redshift with one single equation. We model the distributions around the
mean concentration, offset, and spin with modified Schechter functions. The
concentration of low-mass haloes shows a faster redshift evolution compared to
high-mass haloes, especially in the high-concentration regime. The offset
parameter is smaller at low redshift, in agreement with the relaxation of
structures at recent times. The peak of its distribution shifts by a factor of
1.5 from z = 1.4 to z = 0. The individual models are combined into a
comprehensive mass function model, as a function of spin and offset. Our model
recovers the fiducial mass function with 3% accuracy at redshift 0 and accounts
for redshift evolution up to z = 1.5. This approach accounts for the dynamical
state of the halo when measuring the halo mass function. It offers a connection
with dynamical selection effects in galaxy cluster observations. This is key
toward precision cosmology using cluster counts as a probe.


  We study the relative succinctness and expressiveness of modal logics, and
prove that these relationships can be as complex as any countable partial
order. For this, we use two uniform formalisms to define modal operators, and
obtain results on succinctness and expressiveness in these two settings. Our
proofs are based on formula size games introduced by Adler and Immerman and
bisimulations.


  For directed polymers, the shape function computes the limiting average
energy accrued by paths with a given average slope. We prove that, for a large
family of directed polymer models in discrete time and continuous space in
dimension $1+1$, for positive and zero temperature, the shape function is
differentiable with respect to the slope on the entire real line.


  Gadolinium-doped strontium titanate is a typical perovskite structure
material which has been studied due their thermomechanical, termoelectrical and
electrochemical properties. In this study, local and electronic structure of
Sr1-xGdxTiO3 samples were analyzed through X-ray absorption spectroscopy
measurements. The results obtained with the adjustment of extended X-ray
absorption fine structure (EXAFS) spectra at Sr K-edge show that
crystallographic model of Pm-3m space group is consistent with local structure
around Sr atoms, as expected. This same analysis also reveals an increasing of
the Debye-Waller as a function of the Gd content in some shells, which is
associated with disorder induced by Sr vacancies due to the heterovalent Gd
incorporation. EXAFS spectra at Gd LIII-edge for Sr1-xGdxTiO3 samples indicates
regular GdO12 dodecahedra without displacement of Gd atoms from centrosymmetric
position. A disorder was also identified in the shells beyond the first 12 O
neighbors in which neither the crystallographic cubic structure of the SrTiO3
nor the orthorhombic structure of the GdTiO3 fits well. X-ray absorption near
edge spectroscopy (XANES) spectrum at Ti LIII,II-edges shows an asymmetric peak
because of the splitting between the eg orbitals of 3d band for SrTiO3 sample.
The addition of Gd atoms to SrTiO3 structure cause an enlargement of this peak
and this split is associated with a small displacement of Ti atoms from their
centrosymmetric position. Several features of the XANES spectra at O k-edge for
Sr1-xGdxTiO3 samples are affected by the increase of Gd concentration.
According to our calculated projected density of states, these transitions are
related to a reduction in the number of unoccupied O 2p - Ti 3d states caused
by the split of Ti 3d band. Moreover, these XANES spectra also show a
dependence of the increasing of the hybridization between O 2p and Gd 5d4f6s
states.


  As an application of the theory of linear parabolic differential equations on
noncompact Riemannian manifolds, developed in earlier papers, we prove a
maximal regularity theorem for nonuniformly parabolic boundary value problems
in Euclidean spaces. The new feature of our result is the fact that, besides of
obtaining an optimal solution theory, we consider the `natural' case where the
degeneration occurs only in the normal direction.


  This paper develops a nonparametric statistical model of wealth distribution
that imposes little structure on the fluctuations of household wealth. In this
setting, we use new techniques to obtain a closed-form household-by-household
characterization of the stable distribution of wealth and show that this
distribution is shaped entirely by two factors - the reversion rates (a measure
of cross-sectional mean reversion) and idiosyncratic volatilities of wealth
across different ranked households. By estimating these factors, our model can
exactly match the U.S. wealth distribution. This provides information about the
current trajectory of inequality as well as estimates of the distributional
effects of progressive capital taxes. We find evidence that the U.S. wealth
distribution might be on a temporarily unstable trajectory, thus suggesting
that further increases in top wealth shares are likely in the near future. For
capital taxes, we find that a small tax levied on just 1% of households
substantially reshapes the distribution of wealth and reduces inequality.


  Weakly Interacting Massive Particles (WIMPs) may constitute most of the
matter in the Universe. The ability to detect the directionality of recoil
nuclei will considerably facilitate detection of WIMPs. In this paper we
propose a novel type of dark matter detector: detectors made of DNA or RNA
could provide nanometer resolution for tracking, an energy threshold of 0.5
keV, and can operate at room temperature. When a WIMP from the Galactic Halo
elastically scatters off of a nucleus in the detector, the recoiling nucleus
then traverses hundreds of strings of single stranded nucleic acids (ssNA) with
known base sequences and severs ssNA strands along its trajectory. The location
of the break can be identified by amplifying and identifying the segments of
cut ssNA using techniques well known to biologists. Thus the path of the
recoiling nucleus can be tracked to nanometer accuracy. In one such detector
concept, the transducers are nanometer-thick Au-foils of 1m x 1m, and the
direction of recoiling nuclei is measured by "NA Tracking Chamber" consisting
of ordered array of ssNA strands. Polymerase Chain Reaction (PCR) and ssNA
sequencing are used to read-out the detector. The proposed detector is smaller
and cheaper than other alternatives: 1 kg of gold and 0.1 to 4 kg of ssNA
(depending on length and strand density), packed into 0.01m$^3$, can be used to
study 10 GeV WIMPs. A variety of other detector target elements could be used
in this detector to optimize for different WIMP masses and to identify WIMP
properties. By leveraging advances in molecular biology, we aim to achieve
about 1,000-fold better spatial resolution than in conventional WIMP detectors
at reasonable cost.


  We consider the scalar Zakharov system in $\R^3$ for initial conditions
$(\psi(0), n(0), n_t(0)) \in H^{\ell+1/2} \times H^\ell \times H^{\ell-1} $,
  $0\leq\ell \leq 1$. Assuming that the solution blows up in a finite time $t^*
< \infty$, we establish a lower bound for the rate of blow-up of the
corresponding Sobolev norms in the form $$ \|\psi(t)\|_{H^{\ell+1/2}}
+\|n(t)\|_{H^{\ell}} + \|n_t(t)\|_{H^{\ell-1}} > C(t^*-t)^{-\theta_\ell} $$
with $\theta_\ell = \frac{1}{4}(1+ 2 \ell)^-$. The analysis is a reappraisal of
the local wellposedness theory of Ginibre, Tsutsumi and Velo (1997) combined
with an argument developed by Cazenave and Weissler (1990) in the context of
nonlinear Schr\"odinger equations.


  In this project, the behavior of Generalized Approximate Message-Passing
Decoder for BSC and Z Channel is studied using i.i.d matrices for constructing
the codewords. The performance of GAMP in AWGN Channel is already evaluated in
the previous scientific work of Jean Barbier, therefore, this project mainly
focuses on the performance of GAMP decoder for BSC and Z Channel. We evaluate
the performance of the GAMP decoder for sparse superposition codes at various
settings and compare the performance of decoder for different channels and
parameters.


  In this paper, we consider the soliton cellular automaton introduced in
[Takahashi 1990] with a random initial configuration. We give multiple
constructions of a Young diagram describing various statistics of the system in
terms of familiar objects like birth-and-death chains and Galton-Watson
forests. Using these ideas, we establish limit theorems showing that if the
first $n$ boxes are occupied independently with probability $p\in(0,1)$, then
the number of solitons is of order $n$ for all $p$, and the length of the
longest soliton is of order $\log n$ for $p<1/2$, order $\sqrt{n}$ for $p=1/2$,
and order $n$ for $p>1/2$. Additionally, we uncover a condensation phenomenon
in the supercritical regime: For each fixed $j\geq 1$, the top $j$ soliton
lengths have the same order as the longest for $p\leq 1/2$, whereas all but the
longest have order at most $\log n$ for $p>1/2$. As an application, we obtain
scaling limits for the lengths of the $k^{\text{th}}$ longest increasing and
decreasing subsequences in a random stack-sortable permutation of length $n$ in
terms of random walks and Brownian excursions.


  Gravitational wave detectors, such as KAGRA, require complex mirror
suspension systems to reach high sensitivity. One particular concern in these
suspensions is the presence of crackling noise, where motion of the steel
crystal structure disturbs material defects, causing impulse force release and
exciting mirror motion. Crackling in the Geometric Anti Spring filters (GAS) in
KAGRA's suspension system could introduce noise in the gravitational wave
detection band. We investigate crackling noise in a miniature GAS with a
low-frequency cyclical stress. We developed a scaling law between miniature and
KAGRA GAS. Applying experimental results to the scaling law allows us to
estimate the upper limit of crackling noise in KAGRA. It is found that
crackling noise should be below the target sensitivity for gravitational waves
above 60 Hz.


  The Coriolis force is a significant source of systematic phase errors and
dephasing in atom interferometry and is often compensated by counter-rotating
the interferometry laser beam against Earth's rotation. We present a novel
method for performing Coriolis force compensation for long-baseline atom
interferometry which mitigates atom-beam misalignment due to beam rotation, an
effect which is magnified by the long lever arm of the baseline length. The
method involves adjustment of the angle of the interferometer beam prior to a
magnifying telescope, enabling the beam to pivot around a tunable position
along the interferometer baseline. By tuning the initial atom kinematics, and
adjusting the angle with which the interferometer beam pivots about this point,
we can ensure that the atoms align with the center of the beam during the atom
optics laser pulses. This approach will be used in the MAGIS-100 atom
interferometer and could also be applied to other long-baseline atom
interferometers. An additional challenge associated with long baseline
interferometry is that since long-baseline atom interferometers are often
located outside of typical laboratory environments, facilities constraints may
require lasers to be housed in a climate-controlled room a significant distance
away from the main experiment. Nonlinear effects in optical fibers restrict the
use of fiber-based transport of the high-power interferometry beam from the
laser room to the experiment. We present the design of and prototype data from
a laser transport system for MAGIS-100 that maintains robustness against
alignment drifts despite the absence of a long fiber.


  We point out how Banach Fixed Point Theorem, and the Picard successive
approximation methods induced by it, allows us to treat some mathematical
methods in Combinatorics. In particular we get, by this way, a proof and an
iterative algorithm for the Lagrange Inversion Formula.


  We present the application of Principal Component Analysis for data acquired
during the design of a natural gesture interface. We investigate the concept of
an eigengesture for motion capture hand gesture data and present the
visualisation of principal components obtained in the course of conducted
experiments. We also show the influence of dimensionality reduction on
reconstructed gesture data quality.


  Full understanding of synchronous behavior in coupled dynamical systems
beyond the identical case requires an explicit construction of the generalized
synchronization manifold, whether we wish to compare the systems, or to
understand their stability. Nonetheless, while synchronization has become an
extremely popular topic, the bulk of the research in this area has been focused
on the identical case, specifically because its invariant manifold is simply
the identity function, and there have yet to be any generally workable methods
to compute the generalized synchronization manifolds for non-identical systems.
Here, we derive time dependent PDEs whose stationary solution mirrors exactly
the generalized synchronization manifold, respecting its stability. We
introduce a novel method for dealing with subtle issues with boundary
conditions in the numerical scheme to solve the PDE, and we develop first order
expansions close to the identical case. We give several examples of increasing
sophistication, including coupled non-identical Van der Pol oscillators. By
using the manifold equation, we also discuss the design of coupling to achieve
desired synchronization.


  A method to calculate the form factor for an external current with
non-derivative coupling for the three-body system in an effective field theory
(EFT) of short-range interactions is shown. Using this method the point charge
radius of ${}^3\mathrm{He}$ is calculated to next-to-next-to-leading order
(NNLO) in pionless EFT ($\mathrm{EFT}(\not{\!\pi})$), and the magnetic moment
and magnetic radius of ${}^3\mathrm{H}$ and ${}^3\mathrm{He}$ are calculated to
next-to-leading order (NLO). For the ${}^3\mathrm{He}$ charge and magnetic form
factors Coulomb interactions are ignored. The ${}^3\mathrm{He}$ point charge
radius is given by 1.74(4) fm at NNLO. This agrees well with the experimental
${}^3\mathrm{He}$ point charge radius of 1.7753(54) fm [Angeli and Marinova,
At. Data Nucl. Data Tables 99, 69 (2013)]. The ${}^3\mathrm{H}$
(${}^3\mathrm{He}$) magnetic moment in units of nuclear magnetons is found to
be 2.92(35) (-2.08(25)) at NLO in agreement with the experimental value of
2.979 (-2.127). For ${}^3\mathrm{H}$ (${}^3\mathrm{He}$) the NLO magnetic
radius is 1.78(11) fm (1.85(11) fm) which agrees with the experimental value of
1.840(182) fm (1.965(154) fm) [I. Sick, Prog. Part. Nucl. Phys. 47, 245
(2001)]. The fitting of the low-energy constant $L_{1}$ of the isovector
two-body magnetic current and the consequences of Wigner-SU(4) symmetry for the
three-nucleon magnetic moments are also discussed.


  Large language models (LLMs) have emerged as powerful machine-learning
systems capable of handling a myriad of tasks. Tuned versions of these systems
have been turned into chatbots that can respond to user queries on a vast
diversity of topics, providing informative and creative replies. However, their
application to physical science research remains limited owing to their
incomplete knowledge in these areas, contrasted with the needs of rigor and
sourcing in science domains. Here, we demonstrate how existing methods and
software tools can be easily combined to yield a domain-specific chatbot. The
system ingests scientific documents in existing formats, and uses text
embedding lookup to provide the LLM with domain-specific contextual information
when composing its reply. We similarly demonstrate that existing image
embedding methods can be used for search and retrieval across publication
figures. These results confirm that LLMs are already suitable for use by
physical scientists in accelerating their research efforts.


  By measuring Drell-Yan massive lepton-pair's angular distributions, we can
identify the polarization of the virtual photon of invariant mass $Q$ which
decays immediately into the lepton-pair. In terms of a modified QCD
factorization formula for Drell-Yan process, which is valid even if $Q_T\gg Q$,
we calculate the massive lepton-pair's angular distributions at large $Q_T$. We
find that the virtual photons produced at high $Q_T$ are more likely to be
transversely polarized. We discuss the implications of this finding to the
J/$\psi$ mesons' polarization measured recently at Fermilab.


  Contact tracing is an important instrument for national health services to
fight epidemics. As part of the COVID-19 situation, many proposals have been
made for scaling up contract tracing capacities with the help of smartphone
applications, an important but highly critical endeavor due to the privacy
risks involved in such solutions. Extending our previously expressed concern,
we clearly articulate in this article, the functional and non-functional
requirements that any solution has to meet, when striving to serve, not mere
collections of individuals, but the whole of a nation, as required in face of
such potentially dangerous epidemics. We present a critical information
infrastructure, PriLock, a fully-open preliminary architecture proposal and
design draft for privacy preserving contact tracing, which we believe can be
constructed in a way to fulfill the former requirements. Our architecture
leverages the existing regulated mobile communication infrastructure and builds
upon the concept of "checks and balances", requiring a majority of independent
players to agree to effect any operation on it, thus preventing abuse of the
highly sensitive information that must be collected and processed for efficient
contact tracing. This is enforced with a largely decentralised layout and
highly resilient state-of-the-art technology, which we explain in the paper,
finishing by giving a security, dependability and resilience analysis, showing
how it meets the defined requirements, even while the infrastructure is under
attack.


  We study the hydrodynamics of the hard rod model proposed by Boldrighini,
Dobrushin and Soukhov by describing the displacement of each quasiparticle with
respect to the corresponding ideal gas particle as a height difference in a
related field. Starting with a family of nonhomogeneous Poisson processes
contained in the position-velocity-length space $\mathbb{R}^3$, we show laws of
large numbers for the quasiparticle positions and the length fields, and the
joint convergence of the quasiparticle fluctuations to a Levy Chentsov field.
We allow variable rod lengths, including negative lengths.


  Bitcoin, as well as many of its successors, require the whole transaction
record to be reliably acquired by all nodes to prevent double-spending.
Recently, many blockchains have been proposed to achieve scale-out throughput
by letting nodes only acquire a fraction of the whole transaction set. However,
these schemes, e.g., sharding and off-chain techniques, suffer from a
degradation in decentralization or the capacity of fault tolerance.
  In this paper, we show that the complete set of transactions is not a
necessity for the prevention of double-spending if the properties of value
transfers is fully explored. In other words, we show that a value-transfer
ledger like Bitcoin has the potential to scale-out by its nature without
sacrificing security or decentralization. Firstly, we give a formal definition
for the value-transfer ledger and its distinct features from a generic
database. Then, we introduce an off-chain based scheme with a shared main chain
for consensus and an individual chain for each node for recording transactions.
A locally executable validation scheme is proposed with uncompromising validity
and consistency. A beneficial consequence of our design is that nodes will
spontaneously try to reduce their transmission cost by only providing the
transactions needed to show that their transactions are double-spending-proof.
As a result, the network is sharded as each node only acquires part of the
transaction record and a scale-out throughput could be achieved, which we call
"spontaneous sharding".


  The linearity defect, introduced by Herzog and Iyengar, is a numerical
measure for the complexity of minimal free resolutions. Employing a
characterization of the linearity defect due to \c{S}ega, we study the behavior
of linearity defect along short exact sequences. We point out two classes of
short exact sequences involving Koszul modules, along which linearity defect
behaves nicely. We also generalize the notion of Koszul filtrations from the
graded case to the local setting. Among the applications, we prove that if
$R\to S$ is a surjection of noetherian local rings such that $S$ is a Koszul
$R$-module, and $N$ is a finitely generated $S$-module, then the linearity
defect of $N$ as an $R$-module is the same as its linearity defect as an
$S$-module. In particular, we confirm that specializations of absolutely Koszul
algebras are again absolutely Koszul, answering positively a question due to
Conca, Iyengar, Nguyen and R\"omer.


  We show that recent experiments based on Josephson junctions, SQUIDS, and
coupled Josephson qubits have a cosmological interpretation in terms of axionic
dark matter physics, in the sense that they allow for analogue simulation of
early-universe axion physics. We propose new experimental setups in which
SQUID-like axionic interactions in a resonant Josephson junction environment
can be tested, similar in nature to recent experiments that test for quantum
entanglement of two coupled Josephson qubits. We point out that the parameter
values relevant for early-universe axion cosmology are accessible with present
day's achievements in nanotechnology.


  Quantitative characterization of randomly roving agents in Agent Based
Intrusion Detection Environment (ABIDE) is studied. Formula simplifications
regarding known results and publications are given. Extended Agent Based
Intrusion Detection Environment (EABIDE) is introduced and quantitative
characterization of roving agents in EABIDE is studies.


  We revisit the formulation of the principle of minimal flavor violation (MFV)
in the minimal supersymmetric extension of the standard model, both at moderate
and large tan(beta), and with or without new CP-violating phases. We introduce
a counting rule which keeps track of the highly hierarchical structure of the
Yukawa matrices. In this manner, we are able to control systematically which
terms can be discarded in the soft SUSY breaking part of the Lagrangian. We
argue that for the implementation of this counting rule, it is convenient to
introduce a new basis of matrices in which both the squark (and slepton) mass
terms as well as the trilinear couplings can be expanded. We derive the RGE for
the MFV parameters and show that the beta functions also respect the counting
rule. For moderate tan(beta), we provide explicit analytic solutions of these
RGE and illustrate their behaviour by analyzing the neighbourhood (also
switching on new phases) of the SPS-1a benchmark point. We then show that even
in the case of large tan(beta), the RGE remain valid and that the analytic
solutions obtained for moderate tan(beta) still allow us to understand the most
important features of the running of the parameters, as illustrated with the
help of the SPS-4 benchmark point.


  Interactions among multiple genes across the genome may contribute to the
risks of many complex human diseases. Whole-genome single nucleotide
polymorphisms (SNPs) data collected for many thousands of SNP markers from
thousands of individuals under the case--control design promise to shed light
on our understanding of such interactions. However, nearby SNPs are highly
correlated due to linkage disequilibrium (LD) and the number of possible
interactions is too large for exhaustive evaluation. We propose a novel
Bayesian method for simultaneously partitioning SNPs into LD-blocks and
selecting SNPs within blocks that are associated with the disease, either
individually or interactively with other SNPs. When applied to homogeneous
population data, the method gives posterior probabilities for LD-block
boundaries, which not only result in accurate block partitions of SNPs, but
also provide measures of partition uncertainty. When applied to case--control
data for association mapping, the method implicitly filters out SNP
associations created merely by LD with disease loci within the same blocks.
Simulation study showed that this approach is more powerful in detecting
multi-locus associations than other methods we tested, including one of ours.
When applied to the WTCCC type 1 diabetes data, the method identified many
previously known T1D associated genes, including PTPN22, CTLA4, MHC, and IL2RA.


  We study an equivalence of (i) deterministic pathwise statements appearing in
the online learning literature (termed \emph{regret bounds}), (ii)
high-probability tail bounds for the supremum of a collection of martingales
(of a specific form arising from uniform laws of large numbers for
martingales), and (iii) in-expectation bounds for the supremum. By virtue of
the equivalence, we prove exponential tail bounds for norms of Banach space
valued martingales via deterministic regret bounds for the online mirror
descent algorithm with an adaptive step size. We extend these results beyond
the linear structure of the Banach space: we define a notion of
\emph{martingale type} for general classes of real-valued functions and show
its equivalence (up to a logarithmic factor) to various sequential complexities
of the class (in particular, the sequential Rademacher complexity and its
offset version). For classes with the general martingale type 2, we exhibit a
finer notion of variation that allows partial adaptation to the function
indexing the martingale. Our proof technique rests on sequential symmetrization
and on certifying the \emph{existence} of regret minimization strategies for
certain online prediction problems.


  We present a maximum probability approach to reconstructing spatial maps of
the peculiar velocity field at redshifts $z\sim0.1$, where the velocities have
been measured from distance indicators (DI) such as $D_n-\sigma$ relations or
Tully-Fisher. With the large statistical uncertainties associated with DIs, our
reconstruction method aims to recover the underlying true peculiar velocity
field by reducing these errors with the use of two physically motivated
filtering prior terms. The first constructs an estimate of the velocity field
derived from the galaxy over-density {\deltag} and the second makes use of the
matter linear density power spectrum {\pk}. Using $N$-body simulations we find,
with an SDSS-like sample ($N_{gal}\simeq33$ per deg$^2$), an average
correlation coefficient value of $r=0.55\pm{0.02}$ between our reconstructed
velocity field and that of the true velocity field from the simulation.
However, with a suitably high number density of galaxies from the next
generation surveys (e.g. $N_{gal}\simeq140$ per deg$^2$) we can achieve an
average $r=0.70\pm{0.02}$ out to moderate redshifts $z\sim0.1$. This will prove
useful for future tests of gravity, as these relatively deep maps are
complementary to weak lensing maps at the same redshift.


  In this paper we use a hybrid Monte Carlo-Optimal quantization method to
approximate the conditional survival probabilities of a firm, given a
structural model for its credit defaul, under partial information. We consider
the case when the firm's value is a non-observable stochastic process $(V_t)_{t
\geq 0}$ and inverstors in the market have access to a process $(S_t)_{t \geq
0}$, whose value at each time t is related to $(V_s, s \leq t)$. We are
interested in the computation of the conditional survival probabilities of the
firm given the "investor information". As a application, we analyse the shape
of the credit spread curve for zero coupon bonds in two examples.


  We present a sample of 383 X-ray selected galaxy groups and clusters with
spectroscopic redshift measurements (up to z ~ 0.79) from the 2XMMi/SDSS Galaxy
Cluster Survey. The X-ray cluster candidates were selected as serendipitously
detected sources from the 2XMMi-DR3 catalogue that were located in the
footprint of the Sloan Digital Sky Survey (SDSS-DR7). The cluster galaxies with
available spectroscopic redshifts were selected from the SDSS-DR10. We
developed an algorithm for identifying the cluster candidates that are
associated with spectroscopically targeted luminous red galaxies and for
constraining the cluster spectroscopic redshift. A cross-correlation of the
constructed cluster sample with published optically selected cluster catalogues
yielded 264 systems with available redshifts. The present redshift measurements
are consistent with the published values. The current cluster sample extends
the optically confirmed cluster sample from our cluster survey by 67 objects.
Moreover, it provides spectroscopic confirmation for 78 clusters among our
published cluster sample, which previously had only photometric redshifts. Of
the new cluster sample that comprises 67 systems, 55 objects are newly X-ray
discovered clusters and 52 systems are sources newly discovered as galaxy
clusters in optical and X-ray wavelengths. Based on the measured redshifts and
the fluxes given in the 2XMMi-DR3 catalogue, we estimated the X-ray
luminosities and masses of the cluster sample.


  We report magnetotransport study on type-II Weyl semimetal WP$_2$ single
crystals. Magnetoresistance (MR) exhibits a nonsaturating $H^{n}$ field
dependence (14,300\% at 2 K and 9 T) whereas systematic violation of Kohler's
rule was observed. Quantum oscillations reveal a complex multiband electronic
structure. The cyclotron effective mass close to the mass of free electron
m$_e$ was observed in quantum oscillations along $b$-axis, while reduced
effective mass of about 0.5$m_e$ was observed in $a$-axis quantum oscillations,
suggesting Fermi surface anisotropy. Temperature dependence of the resistivity
shows a large upturn that cannot be explained by the multi-band
magnetoresistance of conventional metals. Even though crystal structure of
WP$_{2}$ is not layered as in transition metal dichalcogenides, quantum
oscillations suggest partial two-dimensional character.


  The recent precision electroweak data on $\Gamma^l, \bar s^2_W$ and $M_W/M_Z$
are compared with the tree-level and the dominant-fermion-loop as well as the
full one-loop standard-model predictions. While the tree-level predictions are
ruled out, the dominant-fermion-loop predictions, defined by using $\alpha
(M^2_Z)\cong 1/128.9$ in the tree-level formulae, as well as the full one-loop
predictions are consistent with the experimental data. Deviations from the
dominant-fermion-loop predictions are quantified in terms of an effective
Lagrangian containing three additional parameters which have a simple meaning
in terms of $SU(2)$ symmetry violation. The effective Lagrangian yields the
standard one-loop predictions for specific values of these parameters, which
are determined by $m_t$ and $m_H$.


  We present a fully relativistic calculation of the observed galaxy number
counts in the linear regime. We show that besides the density fluctuations and
redshift-space distortions, various relativistic effects contribute to
observations at large scales. These effects all have the same physical origin:
they result from the fact that our coordinate system, namely the galaxy
redshift and the incoming photons' direction, is distorted by inhomogeneities
in our universe. We then discuss the impact of the relativistic effects on the
angular power spectrum and on the two-point correlation function in
configuration space. We show that the latter is very well adapted to isolate
the relativistic effects since it naturally makes use of the symmetries of the
different contributions. In particular, we discuss how the Doppler effect and
the gravitational redshift distortions can be isolated by looking for a dipole
in the cross-correlation function between a bright and a faint population of
galaxies.


  Material failure is ubiquitous, with implications from geology to everyday
life and material science. It often involves sudden, unpredictable events, with
little or no macroscopically detectable precursors. A deeper understanding of
the microscopic mechanisms eventually leading to failure is clearly required,
but experiments remain scarce. Here, we show that the microscopic dynamics of a
colloidal gel, a model network-forming system, exhibit dramatic changes that
precede its macroscopic failure by thousands of seconds. Using an original
setup coupling light scattering and rheology, we simultaneously measure the
macroscopic deformation and the microscopic dynamics of the gel, while applying
a constant shear stress. We show that the network failure is preceded by
qualitative and quantitative changes of the dynamics, from reversible particle
displacements to a burst of irreversible plastic rearrangements.


  In the research of Intelligent Transportation Systems (ITS), traffic
simulation is a key procedure for the evaluation of new methods and
optimization of strategies. However, existing traffic simulation systems face
two challenges. First, how to balance simulation scale with realism is a
dilemma. Second, it is hard to simulate realistic results, which requires
realistic travel demand data and simulator. These problems limit computer-aided
optimization of traffic management strategies for large-scale road networks and
reduce the usability of traffic simulations in areas where real-world travel
demand data are lacking. To address these problems, we design and implement
MObility Simulation System (MOSS). MOSS adopts GPU acceleration to
significantly improve the efficiency and scale of microscopic traffic
simulation, which enables realistic and fast simulations for large-scale road
networks. It provides realistic travel Origin-Destination (OD) matrices
generation through a pre-trained generative neural network model based on
publicly available data on a global scale, such as satellite imagery, to help
researchers build meaningful travel demand data. It also provides a complete
open toolchain to help users with road network construction, demand generation,
simulation, and result analysis. The whole toolchain including the simulator
can be accessed at https://moss.fiblab.net and the codes are open-source for
community collaboration.


  The fundamental assumption of conventional transition state theory is the
existence of a dividing surface having the property that trajectories
originating in reactants must cross the surface only once and then proceed to
products. Recently it has been shown how to construct a dividing surface in
phase space for Hamiltonian systems with an arbitrary (but finite) number of
degrees of freedom having the property that trajectories only cross once
locally. In this letter we provide an argument showing that the flux across
this dividing surface is a minimum with respect to certain types of variations
of the dividing surface. In this sense, conventional transition state theory is
shown to be equivalent to variational transition state theory.


  We are working towards 3D reconstruction of indoor spaces using a pair of HDR
cameras in a stereo vision configuration mounted on an indoor mobile floor
robot that captures various textures and spatial features as 2D images and this
data is simultaneously utilized as a feed to our algorithm which will allow us
to visualize the depth map.


  Presheaf models provide a formulation of labelled transition systems that is
useful for, among other things, modelling concurrent computation. This paper
aims to extend such models further to represent stochastic dynamics such as
shown in quantum systems. After reviewing what presheaf models represent and
what certain operations on them mean in terms of notions such as internal and
external choices, composition of systems, and so on, I will show how to extend
those models and ideas by combining them with ideas from other
category-theoretic approaches to relational models and to stochastic processes.
It turns out that my extension yields a transitional formulation of
sheaf-theoretic structures that Abramsky and Brandenburger proposed to
characterize non-locality and contextuality. An alternative characterization of
contextuality will then be given in terms of a dynamic modal logic of the
models I put forward.


  We show that a capillary surface in a solid cone, that is, a surface that has
constant mean curvature and the boundary of surface meets the boundary of the
cone with a constant angle, is radially graphical if the mean curvature is
non-positive with respect to the Gauss map pointing toward the domain bounded
by the surface and the boundary of the cone. In the particular case that the
cone is circular, we prove that the surface is a spherical cap or a planar
disc. The proofs are based on an extension of the Alexandrov reflection method
by using inversions about spheres.


  We present an approach for state and parameter estimation in retinal laser
treatment by a novel setup where both measurement and heating is performed by a
single laser. In this medical application, the temperature that is induced by
the laser in the patient's eye is critical for a successful and safe treatment.
To this end, we pursue a model-based approach using a model given by a heat
diffusion equation on a cylindrical domain, where the source term is given by
the absorbed laser power. The model is parametric in the sense that it involves
an absorption coefficient, which depends on the treatment spot and plays a
central role in the input-output behavior of the system. After discretization,
we apply a particularly suited parametric model order reduction to ensure
real-time tractability while retaining parameter dependence. We augment known
state estimation techniques, i.e., extended Kalman filtering and moving horizon
estimation, with parameter estimation to estimate the absorption coefficient
and the current state of the system. Eventually, we show first results for
simulated and experimental data from porcine eyes. We find that, regarding
convergence speed, the moving horizon estimation slightly outperforms the
extended Kalman filter on measurement data in terms of parameter and state
estimation, however, on simulated data the results are very similar.


  The effect of noise on a quantum system can be described by a set of
operators obtained from the interaction Hamiltonian. Recently it has been shown
that generalized quantum error correcting codes can be derived by studying the
algebra of this set of operators. This led to the discovery of noiseless
subsystems. They are described by a set of operators obtained from the
commutant of the noise generators. In this paper we derive a general method to
compute the structure of this commutant in the case of unital noise.


  Adopting a statistical approach we study the degradation of entanglement of a
quantum system under the action of an ensemble of randomly distributed
Markovian noise. This enables us to address scenarios where only limited
information is available on the mechanisms that rule the noisy evolution of the
model. As an application, we characterize the statistic of entanglement
deterioration for a quantum memory formed by $n$ qudits that undergo randomly
distributed local, uniform, Markovian noise evolution.


  We propose isomorphism type identities for nonlinear functionals of general
infinitely divisible processes. Such identities can be viewed as an analogy of
the Cameron-Martin formula for Poissonian infinitely divisible processes but
with random translations. The applicability of these tools relies on a precise
understanding of L\'evy measures of infinitely divisible processes and their
representations, which are developed here in full generality. We illustrate
this approach on examples of squared Bessel processes, Feller diffusions,
permanental processes, as well as L\'evy processes.


  This paper studies the \emph{subset sampling} problem. The input is a set
$\mathcal{S}$ of $n$ records together with a function $\textbf{p}$ that assigns
each record $v\in\mathcal{S}$ a probability $\textbf{p}(v)$. A query returns a
random subset $X$ of $\mathcal{S}$, where each record $v\in\mathcal{S}$ is
sampled into $X$ independently with probability $\textbf{p}(v)$. The goal is to
store $\mathcal{S}$ in a data structure to answer queries efficiently. If
$\mathcal{S}$ fits in memory, the problem is interesting when $\mathcal{S}$ is
dynamic. We develop a dynamic data structure with
$\mathcal{O}(1+\mu_{\mathcal{S}})$ expected \emph{query} time, $\mathcal{O}(n)$
space and $\mathcal{O}(1)$ amortized expected \emph{update}, \emph{insert} and
\emph{delete} time, where
$\mu_{\mathcal{S}}=\sum_{v\in\mathcal{S}}\textbf{p}(v)$. The query time and
space are optimal. If $\mathcal{S}$ does not fit in memory, the problem is
difficult even if $\mathcal{S}$ is static. Under this scenario, we present an
I/O-efficient algorithm that answers a \emph{query} in
$\mathcal{O}\left((\log^*_B n)/B+(\mu_\mathcal{S}/B)\log_{M/B} (n/B)\right)$
amortized expected I/Os using $\mathcal{O}(n/B)$ space, where $M$ is the memory
size, $B$ is the block size and $\log^*_B n$ is the number of iterative
$\log_2(.)$ operations we need to perform on $n$ before going below $B$. In
addition, when each record is associated with a real-valued key, we extend the
\emph{subset sampling} problem to the \emph{range subset sampling} problem, in
which we require that the keys of the sampled records fall within a specified
input range $[a,b]$. For this extension, we provide a solution under the
dynamic setting, with $\mathcal{O}(\log n+\mu_{\mathcal{S}\cap[a,b]})$ expected
\emph{query} time, $\mathcal{O}(n)$ space and $\mathcal{O}(\log n)$ amortized
expected \emph{update}, \emph{insert} and \emph{delete} time.


  We have measured the differential cross sections for the production of
$\pi^{+}$, $K^{+}$, $K^{0}$, $K^{*0}$, $\phi$, p, $\Lambda$ and their
corresponding antiparticles in separate samples of flavor-tagged $Z^{0}\to$
light-flavor ($u\bar{u}$, $d\bar{d}$, or $s\bar{s}$), $Z^{0}\to c\bar{c}$ and
$Z^{0}\to b\bar{b}$ events. Clear flavor dependences are observed, and the
results are compared with the predictions of three fragmentation models. We
have also performed a direct measurement of $A_{s}$, the parity-violating
coupling of the $Z^{0}$ to strange quarks, by measuring the
left-right-forward-backward production asymmetry in polar angle of the tagged
$s$ quark. Our preliminary result is $A_{s}$ = $0.82\pm 0.10(stat.)\pm
0.07(syst.)$.


  We propose four different thermodynamically stable structural phases of
arsenic monolayers based on ab-initio density functional theory calculations
all of which undergo a topological phase transition on application of a
perpendicular electric field. All the four arsenic monolayer allotropes have a
wide band gap, varying from 1.21 eV to 3.0 eV (based on GW calculations), and
in general they undergo a metal-insulator quantum phase transition on
application of uniaxial in-layer strain. Additionally an increasing transverse
electric field induces band-inversion at the {\Gamma} point in all four
monolayer allotropes, leading to a nontrivial topological phase (insulating for
three and metallic for one allotrope), characterized by the switching of the Z2
index, from 0 (before band inversion) to 1 (after band inversion). The
topological phase tuned by the transverse electric field, should support
spin-separated gapless edge states which should manifest in quantum spin Hall
effect.


  Conditional diffusion models have demonstrated impressive performance on
various tasks like text-guided semantic image editing. Prior work requires
image regions to be identified manually by human users or use an object
detector that only perform well for object-centric manipulations. For example,
if an input image contains multiple objects with the same semantic meaning
(such as a group of birds), object detectors may struggle to recognize and
localize the target object, let alone accurately manipulate it. To address
these challenges, we propose a two-stage method for achieving complex scene
image editing by Scene Graph Comprehension (SGC-Net). In the first stage, we
train a Region of Interest (RoI) prediction network that uses scene graphs and
predict the locations of the target objects. Unlike object detection methods
based solely on object category, our method can accurately recognize the target
object by comprehending the objects and their semantic relationships within a
complex scene. The second stage uses a conditional diffusion model to edit the
image based on our RoI predictions. We evaluate the effectiveness of our
approach on the CLEVR and Visual Genome datasets. We report an 8 point
improvement in SSIM on CLEVR and our edited images were preferred by human
users by 9-33% over prior work on Visual Genome, validating the effectiveness
of our proposed method. Code is available at
github.com/Zhongping-Zhang/SGC_Net.


  Epidemiology characterizes the influence of causes to disease and health
conditions of defined populations. Cohort studies are population-based studies
involving usually large numbers of randomly selected individuals and comprising
numerous attributes, ranging from self-reported interview data to results from
various medical examinations, e.g., blood and urine samples. Since recently,
medical imaging has been used as an additional instrument to assess risk
factors and potential prognostic information. In this chapter, we discuss such
studies and how the evaluation may benefit from visual analytics. Cluster
analysis to define groups, reliable image analysis of organs in medical imaging
data and shape space exploration to characterize anatomical shapes are among
the visual analytics tools that may enable epidemiologists to fully exploit the
potential of their huge and complex data. To gain acceptance, visual analytics
tools need to complement more classical epidemiologic tools, primarily
hypothesis-driven statistical analysis.


  We derive quantum trajectories (also known as stochastic master equations)
that describe an arbitrary quantum system probed by a propagating wave packet
of light prepared in a continuous-mode Fock state. We consider three detection
schemes of the output light: photon counting, homodyne detection, and
heterodyne detection. We generalize to input field states that are
superpositions and or mixtures of Fock states and illustrate the formalism with
several examples.


  An intense investigation of possible non-Fermi liquid states of matter has
been inspired by two of the most intriguing phenomena discovered in the past
quarter century, namely high temperature superconductivity and the fractional
quantum Hall effect. Despite enormous conceptual strides, these two fields have
developed largely along separate paths. Two widely employed theories are the
resonating valence bond theory for high temperature superconductivity and the
composite fermion theory for the fractional quantum Hall effect. The goal of
this "perspective" article is to note that they subscribe to a common
underlying paradigm: they both connect these exotic quantum liquids to certain
ordinary Fermi liquids residing in unphysical Hilbert spaces. Such a relation
yields numerous nontrivial experimental consequences, exposing these theories
to rigorous and definitive tests.


  We present a new scheme for teleporting a quantum state between two parties
whose local reference frames are misaligned by the action of a finite symmetry
group. Unlike other proposals, our scheme requires the same amount of classical
communication and entangled resources as conventional teleportation, does not
reveal any reference frame information, and is robust against changes in
reference frame alignment while the protocol is underway. The mathematical
foundation of our scheme is a unitary error basis which is permuted up to a
phase by the conjugation action of the group. We completely classify such
unitary error bases for qubits, exhibit constructions in higher dimension, and
provide a method for proving nonexistence in some cases.


  This work addresses the resolvent convergence of generalized MIT bag
operators to Dirac operators with zigzag type boundary conditions. We prove
that the convergence holds in strong but not in norm resolvent sense. Moreover,
we show that the only obstruction for having norm resolvent convergence is the
existence of an eigenvalue of infinite multiplicity for the limiting operator.
More precisely, we prove the convergence of the resolvents in operator norm
once projected into the orthogonal of the corresponding eigenspace.


  We present a sensor capable of detecting solution-based nanoparticles using
an optical fiber tip functionalized with a photonic crystal cavity. When sensor
tips are retracted from a nanoparticle solution after being submerged, we find
that a combination of convective fluid forces and optically-induced trapping
cause an aggregation of nanoparticles to form directly on cavity surfaces. A
simple readout of quantum dot photoluminescence coupled to the optical fiber
shows that nanoparticle presence and concentration can be detected through
modified cavity properties. Our sensor can detect both gold and iron oxide
nanoparticles and can be utilized for molecular sensing applications in
biomedicine.


  The world's largest particle accelerator, located at CERN, produces petabytes
of data that need to be analysed efficiently, to study the fundamental
structures of our universe. ROOT is an open-source C++ data analysis framework,
developed for this purpose. Its high-level data analysis interface, RDataFrame,
currently only supports CPU parallelism. Given the increasing heterogeneity in
computing facilities, it becomes crucial to efficiently support GPGPUs to take
advantage of the available resources. SYCL allows for a single-source
implementation, which enables support for different architectures. In this
paper, we describe a CUDA implementation and the migration process to SYCL,
focusing on a core high energy physics operation in RDataFrame --
histogramming. We detail the challenges that we faced when integrating SYCL
into a large and complex code base. Furthermore, we perform an extensive
comparative performance analysis of two SYCL compilers, AdaptiveCpp and DPC++,
and the reference CUDA implementation. We highlight the performance bottlenecks
that we encountered, and the methodology used to detect these. Based on our
findings, we provide actionable insights for developers of SYCL applications.


  Analytical and semi-analytical models for stream depletion with transient
stream stage drawdown induced by groundwater pumping are developed to address a
deficiency in existing models, namely, the use of a fixed stream stage
condition at the stream-aquifer interface. Field data are presented to
demonstrate that stream stage drawdown does indeed occur in response to
groundwater pumping near aquifer connected streams. A model that predicts
stream depletion with transient stream drawdown is developed, based on stream
channel mass conservation and finite stream channel storage. The resulting
models are shown to reduce to existing fixed-stage models in the limit as
stream channel storage becomes infinitely large, and to the confined aquifer
flow with a no-flow boundary at the streambed in the limit as stream storage
becomes vanishingly small. The model is applied to field measurements of
aquifer and stream drawdown, giving estimates of aquifer hydraulic parameters,
streambed conductance and a measure of stream channel storage. The results of
the modeling and data analysis presented herein have implications for
sustainable groundwater management.


  Using three newly identified galaxy clusters at z~1 (photometric redshift) we
measure the evolution of the galaxies within clusters from high redshift to the
present day by studying the growth of the red cluster sequence. The clusters
are located in the Spitzer Infrared Array Camera (IRAC) Dark Field, an
extremely deep mid-infrared survey near the north ecliptic pole with photometry
in 18 total bands from X-ray through far-IR. Two of the candidate clusters are
additionally detected as extended emission in matching Chandra data in the
survey area allowing us to measure their masses to be M_{500}= 6.2 \pm 1.0
\times 10^{13} and 3.6 \pm 1.1 \times 10^{13} solar masses. For all three
clusters we create a composite color magnitude diagram in rest-frame B-K using
our deep HST and Spitzer imaging. By comparing the fraction of low luminosity
member galaxies on the composite red sequence with the corresponding population
in local clusters at z=0.1 taken from the COSMOS survey, we examine the effect
of a galaxy's mass on its evolution. We find a deficit of faint galaxies on the
red sequence in our z~1 clusters which implies that more massive galaxies have
evolved in clusters faster than less massive galaxies, and that the less
massive galaxies are still forming stars in clusters such that they have not
yet settled onto the red sequence.


  Complex networks represent the natural backbone to study epidemic processes
in populations of interacting individuals. Such a modeling framework, however,
is naturally limited to pairwise interactions, making it less suitable to
properly describe social contagion, where individuals acquire new norms or
ideas after simultaneous exposure to multiple sources of infections. Simplicial
contagion has been proposed as an alternative framework where simplices are
used to encode group interactions of any order. The presence of higher-order
interactions leads to explosive epidemic transitions and bistability which
cannot be obtained when only dyadic ties are considered. In particular,
critical mass effects can emerge even for infectivity values below the standard
pairwise epidemic threshold, where the size of the initial seed of infectious
nodes determines whether the system would eventually fall in the endemic or the
healthy state. Here we extend simplicial contagion to time-varying networks,
where pairwise and higher-order simplices can be created or destroyed over
time. By following a microscopic Markov chain approach, we find that the same
seed of infectious nodes might or might not lead to an endemic stationary
state, depending on the temporal properties of the underlying network
structure, and show that persistent temporal interactions anticipate the onset
of the endemic state in finite-size systems. We characterize this behavior on
higher-order networks with a prescribed temporal correlation between
consecutive interactions and on heterogeneous simplicial complexes, showing
that temporality again limits the effect of higher-order spreading, but in a
less pronounced way than for homogeneous structures. Our work suggests the
importance of incorporating temporality, a realistic feature of many real-world
systems, into the investigation of dynamical processes beyond pairwise
interactions.


  We investigate the implications of one vanishing minor in neutrino mass
matrix using trimaximal mixing matrix. In this context, we analyse all six
patterns of one vanishing minor zero in neutrino mass matrix and present
correlations of the neutrino oscillation parameters. All the six patterns are
found to be phenomenologically viable with the present neutrino oscillation
data. We also predict the values of effective Majorana mass, the effective
electron anti-neutrino mass and the total neutrino mass for all the patterns.
The value obtained for the effective neutrino mass is within the reach future
neutrinoless double $\beta$ decay experiments. We also propose a flavor model
where such patterns can be generated within the seesaw model.


  Open Radio Access Network (Open RAN) has gained tremendous attention from
industry and academia with decentralized baseband functions across multiple
processing units located at different places. However, the ever-expanding scope
of RANs, along with fluctuations in resource utilization across different
locations and timeframes, necessitates the implementation of robust function
management policies to minimize network energy consumption. Most recently
developed strategies neglected the activation time and the required energy for
the server activation process, while this process could offset the potential
energy savings gained from server hibernation. Furthermore, user plane
functions, which can be deployed on edge computing servers to provide
low-latency services, have not been sufficiently considered. In this paper, a
multi-agent deep reinforcement learning (DRL) based function deployment
algorithm, coupled with a heuristic method, has been developed to minimize
energy consumption while fulfilling multiple requests and adhering to latency
and resource constraints. In an 8-MEC network, the DRL-based solution
approaches the performance of the benchmark while offering up to 51% energy
savings compared to existing approaches. In a larger network of 14-MEC, it
maintains a 38% energy-saving advantage and ensures real-time response
capabilities. Furthermore, this paper prototypes an Open RAN testbed to verify
the feasibility of the proposed solution.


  Few-shot image classification is the task of classifying unseen images to one
of N mutually exclusive classes, using only a small number of training examples
for each class. The limited availability of these examples (denoted as K)
presents a significant challenge to classification accuracy in some cases. To
address this, we have developed a method for augmenting the set of K with an
addition set of A retrieved images. We call this system Retrieval-Augmented
Few-shot Image Classification (RAFIC). Through a series of experiments, we
demonstrate that RAFIC markedly improves performance of few-shot image
classification across two challenging datasets. RAFIC consists of two main
components: (a) a retrieval component which uses CLIP, LAION-5B, and faiss, in
order to efficiently retrieve images similar to the supplied images, and (b)
retrieval meta-learning, which learns to judiciously utilize the retrieved
images. Code and data is available at github.com/amirziai/rafic.


  The dependence of the magnetocrystalline anisotropy energy (MAE) of MCo5 (M =
Y, La) on the Coulomb correlations and strength of spin orbit (SO) interaction
within the GGA + U scheme is investigated. A range of parameters suitable for
the satisfactory description of key magnetic properties is determined. The
origin of MAE in these materials is mostly related to the large orbital moment
anisotropy of Co atoms on the 2c crystallographic site. Dependence of
relativistic effects on Coulomb correlations, applicability of the second order
perturbation theory for the description of MAE and effective screening of the
SO interaction in these systems are discussed using a generalized virial
theorem.


  We consider a scalar field theory on AdS in both minimally and non-minimally
coupled cases. We show that there exist constraints which arise in the
quantization of the scalar field theory on AdS which cannot be reproduced
through the usual AdS/CFT prescription. We argue that the usual energy, defined
through the stress-energy tensor, is not the natural one to be considered in
the context of the AdS/CFT correspondence. We analyze a new definition of the
energy which makes use of the Noether current corresponding to time
displacements in global coordinates. We compute the new energy for Dirichlet,
Neumann and mixed boundary conditions on the scalar field and for both the
minimally and non-minimally coupled cases. Then, we perform the quantization of
the scalar field theory on AdS showing that, for `regular' and `irregular'
modes, the new energy is conserved, positive and finite. We show that the
quantization gives rise, in a natural way, to a generalized AdS/CFT
prescription which maps to the boundary all the information contained in the
bulk. In particular, we show that the divergent local terms of the on-shell
action contain information about the Legendre transformed generating
functional, and that the new constraints for which the irregular modes
propagate in the bulk are the same constraints for which such divergent local
terms cancel out. In this situation, the addition of counterterms is not
required. We also show that there exist particular cases for which the
unitarity bound is reached, and the conformal dimension becomes independent of
the effective mass. This phenomenon has no bulk counterpart.


  The vanishing gradient problem was a major obstacle for the success of deep
learning. In recent years it was gradually alleviated through multiple
different techniques. However the problem was not really overcome in a
fundamental way, since it is inherent to neural networks with activation
functions based on dot products. In a series of papers, we are going to analyze
alternative neural network structures which are not based on dot products. In
this first paper, we revisit neural networks built up of layers based on
distance measures and Gaussian activation functions. These kinds of networks
were only sparsely used in the past since they are hard to train when using
plain stochastic gradient descent methods. We show that by using Root Mean
Square Propagation (RMSProp) it is possible to efficiently learn multi-layer
neural networks. Furthermore we show that when appropriately initialized these
kinds of neural networks suffer much less from the vanishing and exploding
gradient problem than traditional neural networks even for deep networks.


  The recent study of holographic superconductors has shown the emergence of a
Kasner universe behind the event horizon. This paper serves to add to the
discussion by introducing two modifications to the holographic superconductor
model: an axion field term and an Einstein-Maxwell-scalar (EMS) coupling term.
We first discuss the effect the modification parameters have on the condensate
then explore the black hole interior dynamics. Features previously identified
in the interior are found in the model presented, including the collapse of the
Einstein-Rosen bridge, Josephson oscillations and Kasner
inversions/transitions. However, we find that by increasing the EMS coupling
parameter, the collapse does not occur near the axion-Reissner-Nordstr\"om
horizon and the oscillations are no longer present; the geometry entering into
a Kasner regime after a large-$r$ collapse instead.


  Utility functions or their equivalents (value functions, objective functions,
loss functions, reward functions, preference orderings) are a central tool in
most current machine learning systems. These mechanisms for defining goals and
guiding optimization run into practical and conceptual difficulty when there
are independent, multi-dimensional objectives that need to be pursued
simultaneously and cannot be reduced to each other. Ethicists have proved
several impossibility theorems that stem from this origin; those results appear
to show that there is no way of formally specifying what it means for an
outcome to be good for a population without violating strong human ethical
intuitions (in such cases, the objective function is a social welfare
function). We argue that this is a practical problem for any machine learning
system (such as medical decision support systems or autonomous weapons) or
rigidly rule-based bureaucracy that will make high stakes decisions about human
lives: such systems should not use objective functions in the strict
mathematical sense.
  We explore the alternative of using uncertain objectives, represented for
instance as partially ordered preferences, or as probability distributions over
total orders. We show that previously known impossibility theorems can be
transformed into uncertainty theorems in both of those settings, and prove
lower bounds on how much uncertainty is implied by the impossibility results.
We close by proposing two conjectures about the relationship between
uncertainty in objectives and severe unintended consequences from AI systems.


  The risk of a financial position is usually summarized by a risk measure. As
this risk measure has to be estimated from historical data, it is important to
be able to verify and compare competing estimation procedures. In statistical
decision theory, risk measures for which such verification and comparison is
possible, are called elicitable. It is known that quantile based risk measures
such as value at risk are elicitable. In this paper we show that law-invariant
spectral risk measures such as expected shortfall are not elicitable unless
they reduce to minus the expected value. Hence, it is unclear how to perform
forecast verification or comparison. However, the class of elicitable
law-invariant coherent risk measures does not reduce to minus the expected
value. We show that it consists of certain expectiles.


  We extend the recently developed converse NMR approach [T. Thonhauser, D.
Ceresoli, A. Mostofi, N. Marzari, R. Resta, and D. Vanderbilt, J. Chem. Phys.
\textbf{131}, 101101 (2009)] such that it can be used in conjunction with
norm-conserving, non-local pseudopotentials. This extension permits the
efficient ab-initio calculation of NMR chemical shifts for elements other than
hydrogen within the convenience of a plane-wave pseudopotential approach. We
have tested our approach on several finite and periodic systems, finding very
good agreement with established methods and experimental results.


  The origin of Uranus and Neptune has long been challenging to explain, due to
the large orbital distances from the Sun. After a planetary embryo has been
formed, the main accretion processes are likely pebble, gas and planetesimal
accretion. Previous studies of Uranus and Neptune formation typically don't
consider all three processes; and furthermore, do not investigate how the
formation of the outer planet impacts the inner planet. In this paper we study
the concurrent formation of Uranus and Neptune via both pebble, gas and
planetesimal accretion. We use a dust-evolution model to predict the size and
mass flux of pebbles, and derive our own fit for gas accretion. We do not
include migration, but consider a wide range of formation locations between 12
and 40au. If the planetary embryos form at the same time and with the same
mass, our formation model with an evolving dust population is unable to produce
Uranus and Neptune analogues. This is because the mass difference between the
planets and the H-He mass fractions become too high. However, if the outer
planetary embryo forms earlier and/or more massive than the inner embryo, the
two planets do form in a few instances when the disk is metal-rich and
dissipates after a few Myr. Furthermore, our study suggests that in-situ
formation is rather unlikely. Nethertheless, giant impacts and/or migration
could potentially aid in the formation, and future studies including these
processes could bring us one step closer to understanding how Uranus and
Neptune formed.


  The HST archive contains a large collection of images of eta Carinae, and
this paper analyzes those most suitable for measuring its expanding Homunculus
Nebula. Multiple intensity tracings through the Homunculus reveal the
fractional increase in the overall size of the nebula; this avoids registration
uncertainty, mitigates brightness fluctuations, and is independent of previous
methods. Combining a 13-yr baseline of Wide Field Planetary Camera 2 (WFPC2)
images in the F631N filter, with a 4-yr baseline of Advanced Camera for
Surveys/High Resolution Channel (ACS/HRC) images in the F550M filter, yields an
ejection date (assuming linear motion) of 1847.1 ($\pm$0.8 yr). This result
improves the precision, but is in excellent agreement with the previous study
by Morse et al.\ (2001) that used a shorter time baseline and a different
analysis method. This more precise date is inconsistent with ejection during a
periastron passage of the eccentric binary. Ejection occured well into the main
plateau of the Great Eruption, and not during the brief peaks in 1843 and 1838.
The age uncertainty is dominated by a real spread in ages of various knots, and
by some irregular brightness fluctuations. Several knots appear to have been
ejected decades before or after the mean date, implying a complicated history
of mass-loss episodes outside the main bright phase of the eruption. The
extended history of mass ejection may have been largely erased by the passage
of a shock through clumpy ejecta, as most material was swept into a thin shell
with nearly uniform apparent age.


  The polarization properties of monochromatic light beams are studied. In
contrast to the idealization of an electromagnetic plane wave, finite beams
which are everywhere linearly polarized in the same direction do not exist.
Neither do beams which are everywhere circularly polarized in a fixed plane. It
is also shown that transversely finite beams cannot be purely transverse in
both their electric and magnetic vectors, and that their electromagnetic energy
travels at less than c. The electric and magnetic fields in an electromagnetic
beam have different polarization properties in general, but there exists a
class of steady beams in which the electric and magnetic polarizations are the
same (and in which energy density and energy flux are independent of time).
Examples are given of exactly and approximately linearly polarized beams, and
of approximately circularly polarized beams.


  This paper presents a novel attack on voice-controlled digital assistants
using nonsensical word sequences. We present the results of experimental work
which demonstrates that it is possible for malicious actors to gain covert
access to a voice-controlled system by hiding commands in apparently
nonsensical sounds of which the meaning is opaque to humans. Several instances
of nonsensical word sequences were identified which triggered a target command
in a voice-controlled digital assistant, but which were incomprehensible to
humans, as shown in tests with human experimental subjects. Our work confirms
the potential for hiding malicious voice commands to voice-controlled digital
assistants or other speech-controlled devices in speech sounds which are
perceived by humans as nonsensical.


  Some years ago, Borcherds described in [Bo1] two methods for constructing
modular forms on modular varieties related to the orthogonal group ${\O}(2,n)$.
They are the so called Borcherds' additive and multiplicative lifting. The
multiplicative lifting has been used by Borcherds himself and other authors to
construct modular forms with known vanishing locus and interesting properties.
The additive lifting has been used to construct explicit maps from some modular
varieties $\O(2,n)$. In this paper we try a more systematic treatment in
certain level 2 cases giving connections with Kondo's works


  In M(atrix) theory, there exist membranes and longitudinal 5-branes
(L5-branes) as extended objects. Transverse components of these brane solutions
are known to be described by fuzzy CP^k (k=1,2), where k=1 and k=2 correspond
to spherical membranes and L5-branes of CP^2 \times S^1 world-volume geometry,
respectively. In addition to these solutions, we here show the existence of
L7-branes of CP^3 \times S^1 geometry, introducing extra potentials to the
M(atrix) theory Lagrangian. As in the cases of k=1,2, the L7-branes
(corresponding to k=3) also break the supersymmetries of M(atrix) theory. The
extra potentials are introduced such that the energy of a static L7-brane
solution becomes finite in the large N limit where N represents the matrix
dimension of fuzzy CP^3. As a consequence, fluctuations from the L7-branes are
suppressed, which effectively describes compactification of M(atrix) theory
down to 7 dimensions. We show that one of the extra potentials can be
considered as a matrix-valued 7-form. The presence of the 7-form in turn
supports a possibility of Freund-Rubin type compactification. This suggests
that our modification of M(atrix) theory can also lead to a physically
interesting matrix model in four dimensions. In hope of such a possibility, we
further consider compactification of M(atrix) theory down to fuzzy S^4 which
can be defined in terms of fuzzy CP^3. Along the way, we also find a new
L5-brane solution to M(atrix) theory which has purely spherical geometry in the
transverse directions.


  Mesoscale objects with unusual structural features may serve as the analogues
of atoms in the design of larger-scale materials with novel optical, electronic
or mechanical behaviour. In this paper we investigate the structural features
and the equilibrium dynamics of micron-scale spherical crystals formed by
polystyrene particles adsorbed on the surface of a spherical water droplet. The
ground state of sufficiently large crystals possesses finite-length grain
boundaries (scars). We determine the elastic response of the crystal by
measuring single-particle diffusion and quantify the fluctuations of individual
dislocations about their equilibrium positions within a scar determining the
dislocation spring constants. We observe rapid dislocation glide with
fluctuations over the barriers separating one local Peierls minimum from the
next and rather weak binding of dislocations to their associated scars. The
long-distance (renormalised) dislocation diffusion glide constant is extracted
directly from the experimental data and is found to be moderately faster than
single particle diffusion. We are also able to determine the parameters of the
Peierls potential induced by the underlying crystalline lattice.


  When studying quantum field theories and lattice models, it is often useful
to analytically continue the number of field or spin components from an integer
to a real number. In spite of this, the precise meaning of such analytic
continuations has never been fully clarified, and in particular the symmetry of
these theories is obscure. We clarify these issues using Deligne categories and
their associated Brauer algebras, and show that these provide logically
satisfactory answers to these questions. Simple objects of the Deligne category
generalize the notion of an irreducible representations, avoiding the need for
such mathematically nonsensical notions as vector spaces of non-integer
dimension. We develop a systematic theory of categorical symmetries, applying
it in both perturbative and non-perturbative contexts. A partial list of our
results is: categorical symmetries are preserved under RG flows; continuous
categorical symmetries come equipped with conserved currents; CFTs with
categorical symmetries are necessarily non-unitary.


  Geant4 Detector Construction Pattern (GDCP) is a C++ package containing a set
of utility classes for developers to utilize during the detector construction
phase of a Geant4 application. The main objective of this study is to provide
an interface that helps users develop a highly flexible, understandable, and
maintainable detector construction code. The package also contains a couple of
helper classes facilitating the implementation of optical components in
scintillation detectors. Finally, an advanced Geant application has been
provided to demonstrate the package's utility. Program summary Program title:
GDCP CPC Library link to program files: Licensing provisions: GNU General
Public License 3 Programming language: C++ External routines/libraries: Geant4
Nature of problem: Geant4 provides an abstract class,
G4VUserDetectorConstruction, that is used for the whole detector construction.
This is sufficient for a simple detector setup but implementing a single class
for building a complex detector leads to complexity in the code. To solve this
issue it is recommended to split the implementation into more methods or
classes; however, there is no standard solution published yet and it is
entirely left to the users' ability. Solution method: To address this issue, I
propose to apply the "Builder design pattern" in the detector construction
phase. For this, the elements of the Builder design pattern have been
introduced and made available for developers. Keywords:
G4VUserDetectorConstruction, Builder design pattern, Detector construction,
Component builder, Optical photon, Scintillator


  We study quantum interference effects due to electron motion on a
three-dimensional cubic lattice in a continuously-tunable magnetic field of
arbitrary orientation and magnitude. These effects arise from the interference
between magnetic phase factors associated with different electron closed paths.
The sums of these phase factors, called lattice path-integrals, are
``many-loop" generalizations of the standard ``one-loop" Aharonov-Bohm-type
argument. Our lattice path integral calculation enables us to obtain various
important physical quantities through several different methods. The spirit of
our approach follows Feynman's programme: to derive physical quantities in
terms of ``sums over paths". From these lattice path-integrals we compute
analytically, for several lengths of the electron path, the half-filled
Fermi-sea ground-state energy of noninteracting spinless electrons in a cubic
lattice. Our results are valid for any strength of the applied magnetic field
in any direction. We also study in detail two experimentally important
quantities: the magnetic moment and orbital susceptibility at half-filling, as
well as the zero-field susceptibility as a function of the Fermi energy.


  When performing the resilience enhancement for distribution networks, there
are two obstacles to reliably model the uncertain contingencies: 1)
decision-dependent uncertainty (DDU) due to various line hardening decisions,
and 2) distributional ambiguity due to limited outage information during
extreme weather events (EWEs). To address these two challenges, this paper
develops scenario-wise decision-dependent ambiguity sets (SWDD-ASs), where the
DDU and distributional ambiguity inherent in EWE-induced contingencies are
simultaneously captured for each possible EWE scenario. Then, a two-stage
trilevel decision-dependent distributionally robust resilient enhancement
(DD-DRRE) model is formulated, whose outputs include the optimal line
hardening, distributed generation (DG) allocation, and proactive network
reconfiguration strategy under the worst-case distributions in SWDD-ASs.
Subsequently, the DD-DRRE model is equivalently recast to a mixed-integer
linear programming (MILP)-based master problem and multiple scenario-wise
subproblems, facilitating the adoption of a customized column-and-constraint
generation (C&CG) algorithm. Finally, case studies demonstrate a remarkable
improvement in the out-of-sample performance of our model, compared to its
prevailing stochastic and robust counterparts. Moreover, the potential values
of incorporating the ambiguity and distributional information are
quantitatively estimated, providing a useful reference for planners with
different budgets and risk-aversion levels.


  We develop a renormalization group approach for analyzing Fr\"ohlich polarons
and apply it to a problem of impurity atoms immersed in a Bose-Einstein
condensate of ultra cold atoms. Polaron energies obtained by our method are in
excellent agreement with recent diagrammatic Monte Carlo calculations for a
wide range of interaction strengths. We calculate the effective mass of
polarons and find a smooth crossover from weak to strong coupling regimes.
Possible experimental tests of our results in current experiments with ultra
cold atoms are discussed.


  Precision measurements of neutrino-electron scattering may provide a viable
way to test the non-minimal form of the charged and neutral current weak
interactions within a hypothetical near-detector setup for the Deep Underground
Neutrino Experiment (DUNE). Although low-statistics, these processes are clean
and provide information complementing the results derived from oscillation
studies. They could shed light on the scale of neutrino mass generation in
low-scale seesaw schemes.


  A discrete Klein-Gordon model with asymmetric potential that supports kinks
free of the Peierls-Nabarro potential (PNp) is constructed. Undamped ratchet of
kinks under harmonic AC driving force is investigated in this model numerically
and contrasted with the kink ratchets in the conventional discrete model where
kinks experience the PNp. We show that the PNp-free kinks exhibit ratchet
dynamics very much different from that reported for the conventional lattice
kinks which experience PNp [see, e.g., Phys. Rev. E {\bf 73}, 066621 (2006)].
Particularly, we could not observe any significant influence of the
discreteness parameter on the acceleration of PNp-free kinks induced by the AC
driving.


  The physics case is summarised for the investigation of high energy spin
phenomena by placing an internal polarised target into HERA's unpolarised
proton beam. The luminosity and experimental sensitivity are discussed.
Estimating the physics reach of single spin asymmetries in different final
states reveals a considerable physics potential in testing the spin sector of
perturbative QCD.


  We present preliminary results on the possible effects that primordial
magnetic fields can have for a warm inflation scenario, based on global
supersymmetry, with a new-inflation-type potential. This work is motivated by
two considerations: first, magnetic fields seem to be present in the universe
on all scales, which rises the possibility that they could also permeate the
early universe; second, the recent emergence of inflationary models where the
inflaton is not assumed to be isolated but instead it is taken as an
interacting field, even during the inflationary expansion. The effects of
magnetic fields are included resorting to Schwinger proper time method.


  The Rayleigh limit and low Signal-to-Noise Ratio (SNR) scenarios pose
significant limitations to optical imaging systems used in remote sensing,
infrared thermal imaging, and space domain awareness. In this study, we
introduce a Stochastic Sub-Rayleigh Imaging (SSRI) algorithm to localize point
objects and estimate their positions, brightnesses, and number in low SNR
conditions, even below the Rayleigh limit. Our algorithm adopts a maximum
likelihood approach and exploits the Poisson distribution of incoming photons
to overcome the Rayleigh limit in low SNR conditions. In our experimental
validation, which closely mirrors practical scenarios, we focus on conditions
with closely spaced sources within the sub-Rayleigh limit (0.49-1.00R) and weak
signals (SNR less than 1.2). We use the Jaccard index and Jaccard efficiency as
a figure of merit to quantify imaging performance in the sub-Rayleigh region.
Our approach consistently outperforms established algorithms such as
Richardson-Lucy and CLEAN by 4X in the low SNR, sub-Rayleigh regime. Our SSRI
algorithm allows existing telescope-based optical/infrared imaging systems to
overcome the extreme limit of sub-Rayleigh, low SNR source distributions,
potentially impacting a wide range of fields, including passive thermal
imaging, remote sensing, and space domain awareness.


  We report measurements of the resistivity in the ferromagnetic state of
epitaxial thin films of La_{1-x}Ca_{x}MnO_{3} and the low temperature specific
heat of a polycrystalline La_{0.8}Ca_{0.2}MnO_{3}. The resistivity below 100 K
can be well fitted by \rho - \rho_{o} = E \omega_{s}/sinh^{2}(\hbar
\omega_{s}/2k_{B}T) with \hbar \omega_{s}/k_{B} \simeq 100 K and E being a
constant. Such behavior is consistent with small-polaron coherent motion which
involves a relaxation due to a soft optical phonon mode. The specific heat data
also suggest the existence of such a phonon mode. The present results thus
provide evidence for small-polaron metallic conduction in the ferromagnetic
state of manganites.


  In his 1982 paper, Ogus defined a class of cycles in the de Rham cohomology
of smooth proper varieties over number fields. This notion is a crystalline
analogue of $\ell$-adic Tate cycles. In the case of abelian varieties, this
class includes all the Hodge cycles by the work of Deligne, Ogus, and Blasius.
Ogus predicted that such cycles coincide with Hodge cycles for abelian
varieties. In this paper, we confirm Ogus' prediction for some families of
abelian varieties. These families include abelian varieties that have both
prime dimension and nontrivial endomorphism ring. The proof is based on a
crystalline analogue of Faltings' isogeny theorem due to Bost and the known
cases of the Mumford--Tate conjecture.


  We study the effect an atmosphere has on pebble orbits and spin build-up on a
planet's surface during pebble accretion in the extreme case of a static
atmosphere. We numerically integrate the equations of motion of pebbles in a
planar, global frame with a planet, a central star and gas from a
protoplanetary disc. An adiabatic atmosphere is then placed around the planet,
and the spin deposited onto the planet's surface is measured. These simulations
are evaluated for different distances to the star, Stokes numbers, and planet
masses. Pebble feedback to the gas is not taken into account. We find that a
static atmosphere dampens the spin the planet's surface receives by absorbing
part of the angular momentum of the pebbles and circularising their orbits.
This could prevent the excessive spin values predicted in some 3D pebble
accretion simulations without an atmosphere. For planets larger than 0.5 Earth
masses, a stationary atmosphere absorbs all angular momentum, leaving no spin
for the surface. Significant quantities of angular momentum are stored in the
inner and intermediate atmosphere ($<0.3$ Bondi radii). Depending on the
atmospheric and disc model, this spin could be transported either to the disc
through atmospheric recycling or to the planet through drag between the surface
and the atmosphere. Further research is required to quantify the spin transfer
within the atmosphere.


  We discuss quantitative estimates of the local spectral dimension of the
two-dimensional Sierpinski gasket. The present arguments were inspired by a
previous study of the distribution of the Kusuoka measure by R. Bell, C.-W. Ho,
and R. S. Strichartz [Energy measures of harmonic functions on the Sierpi\'nski
gasket, Indiana Univ. Math. J. 63 (2014), 831-868].


  The goal of self-supervised learning (SSL) for automatic speech recognition
(ASR) is to learn good speech representations from a large amount of unlabeled
speech for the downstream ASR task. However, most SSL frameworks do not
consider noise robustness which is crucial for real-world applications. In this
paper we propose wav2vec-Switch, a method to encode noise robustness into
contextualized representations of speech via contrastive learning.
Specifically, we feed original-noisy speech pairs simultaneously into the
wav2vec 2.0 network. In addition to the existing contrastive learning task, we
switch the quantized representations of the original and noisy speech as
additional prediction targets of each other. By doing this, it enforces the
network to have consistent predictions for the original and noisy speech, thus
allows to learn contextualized representation with noise robustness. Our
experiments on synthesized and real noisy data show the effectiveness of our
method: it achieves 2.9--4.9% relative word error rate (WER) reduction on the
synthesized noisy LibriSpeech data without deterioration on the original data,
and 5.7% on CHiME-4 real 1-channel noisy data compared to a data augmentation
baseline even with a strong language model for decoding. Our results on CHiME-4
can match or even surpass those with well-designed speech enhancement
components.


  We obtain a new weak Hilton-Milner type result for intersecting families of
$k$-spaces in $\mathbb{F}_q^{2k}$, which improves several known results. In
particular the chromatic number of the $q$-Kneser graph $qK_{n:k}$ was
previously known for $n > 2k$ (except for $n=2k+1$ and $q=2$) or $k < q \log q
- q$. Our result determines the chromatic number of $qK_{2k:k}$ for $q \geq 5$,
so that the only remaining open cases are $(n, k) = (2k, k)$ with $q \in \{ 2,
3, 4 \}$ and $(n, k) = (2k+1, k)$ with $q = 2$.


  The geometric phase is a fundamental quantity characterizing the holonomic
feature of quantum systems. It is well known that the evolution operator of a
quantum system undergoing a cyclic evolution can be simply written as the
product of holonomic and dynamical components for the three special cases
concerning the Berry phase, adiabatic non-Abelian geometric phase, and
nonadiabatic Abelian geometric phase. However, for the most general case
concerning the nonadiabatic non-Abelian geometric phase, how to separate the
evolution operator into holonomic and dynamical components is a long-standing
open problem. In this work, we solve this open problem. We show that the
evolution operator of a quantum system can always be separated into the product
of holonomy and dynamic operators. Based on it, we further derive a matrix
representation of this separation formula for cyclic evolution, and give a
necessary and sufficient condition for a general evolution being purely
holonomic. Our finding is not only of theoretical interest itself, but also of
vital importance for the application of quantum holonomy. It unifies the
representations of all four types of evolution concerning the
adiabatic/nonadiabatic Abelian/non-Abelian geometric phase, and provides a
general approach to realizing purely holonomic evolution.


  We perform frequentist and Bayesian statistical analyses of Higgs- and
Z-portal models of dark matter particles with spin 0, 1/2 and 1. Our analyses
incorporate data from direct detection and indirect detection experiments, as
well as LHC searches for monojet and monophoton events, and we also analyze the
potential impacts of future direct detection experiments. We find acceptable
regions of the parameter spaces for Higgs-portal models with real scalar,
neutral vector, Majorana or Dirac fermion dark matter particles, and Z-portal
models with Majorana or Dirac fermion dark matter particles. In many of these
cases, there are interesting prospects for discovering dark matter particles in
Higgs or Z decays, as well as dark matter particles weighing $\gtrsim 100$ GeV.
Negative results from planned direct detection experiments would still allow
acceptable regions for Higgs- and Z-portal models with Majorana or Dirac
fermion dark matter particles.


  We here numerically investigate the heat transport behavior in a
one-dimensional lattice with a soft-type (ST) anharmonic interparticle
interaction. It is found that with the increase of system's temperature, while
the introduction of ST anharmonicity softens phonons and decreases their
velocities, this type of nonlinearity like its counterpart of hard type (HT),
can still not be able to fully damp the longest wave phonons. Therefore, an
anomalous temperature dependent heat transport with certain scaling properties
similarly to those in the Fermi-Pasta-Ulam like systems with HT interactions
can be seen. Our detailed examination from simulations well verify this
temperature dependent behavior.


  The Fourth Open Gravitational-wave Catalogue (4-OGC) presented parameter
estimation analyses for a number of gravitational wave triggers which had not
previously been presented in catalogues published by the LIGO, Virgo, and KAGRA
Collaborations (LVK). In this paper we present an analysis of these new
triggers using the same analysis workflow which was used to generate the
GWTC-2.1 and GWTC-3 catalogues published by the LVK, using a comparable
analysis configuration. We do not find any significant differences between our
analysis and that previously presented by 4-OGC, providing a reassuring
cross-check between two differing analysis techniques. We provide our parameter
estimation results in a format comparable to those of the GWTC-3 data release.