  We study the magnetic phases of two coupled two-dimensional electron gases in
order to determine under what circumstances these phases may occur in real
semiconductor quantum wells and what the experimental properties of the
broken-symmetry ground states may be. Within the local-density-approximation to
time-dependent density functional theory (DFT), we find a phase transition
signaled by the vanishing of the intersubband spin-density excitations at low
but accessible (\sim 10^10-10^11 cm^{-2}) electron densities. Through a
self-consistent Hartree-Fock calculation, we associate this transition with an
antiferromagnetic phase and study the phase diagram, thermodynamics, and
collective modes in it. The collective modes are in principle observable in
inelastic light scattering experiments, and we discuss the implications of our
calculations for these measurements. We also examine the ferromagnetic
transition in both single and double quantum wells within the
local-spin-density approximation to DFT and obtain a critical density which
depends on the well width and which is far below that of the antiferromagnetic
transition.


  Adversarial training (AT) defends deep neural networks against adversarial
attacks. One challenge that limits its practical application is the performance
degradation on clean samples. A major bottleneck identified by previous works
is the widely used batch normalization (BN), which struggles to model the
different statistics of clean and adversarial training samples in AT. Although
the dominant approach is to extend BN to capture this mixture of distribution,
we propose to completely eliminate this bottleneck by removing all BN layers in
AT. Our normalizer-free robust training (NoFrost) method extends recent
advances in normalizer-free networks to AT for its unexplored advantage on
handling the mixture distribution challenge. We show that NoFrost achieves
adversarial robustness with only a minor sacrifice on clean sample accuracy. On
ImageNet with ResNet50, NoFrost achieves $74.06\%$ clean accuracy, which drops
merely $2.00\%$ from standard training. In contrast, BN-based AT obtains
$59.28\%$ clean accuracy, suffering a significant $16.78\%$ drop from standard
training. In addition, NoFrost achieves a $23.56\%$ adversarial robustness
against PGD attack, which improves the $13.57\%$ robustness in BN-based AT. We
observe better model smoothness and larger decision margins from NoFrost, which
make the models less sensitive to input perturbations and thus more robust.
Moreover, when incorporating more data augmentations into NoFrost, it achieves
comprehensive robustness against multiple distribution shifts. Code and
pre-trained models are public at
https://github.com/amazon-research/normalizer-free-robust-training.


  One of the motivations for property testing of boolean functions is the idea
that testing can serve as a preprocessing step before learning. However, in
most machine learning applications, it is not possible to request for labels of
fictitious examples constructed by the algorithm. Instead, the dominant query
paradigm in applied machine learning, called active learning, is one where the
algorithm may query for labels, but only on points in a given polynomial-sized
(unlabeled) sample, drawn from some underlying distribution D. In this work, we
bring this well-studied model in learning to the domain of testing.
  We show that for a number of important properties, testing can still yield
substantial benefits in this setting. This includes testing unions of
intervals, testing linear separators, and testing various assumptions used in
semi-supervised learning. In addition to these specific results, we also
develop a general notion of the testing dimension of a given property with
respect to a given distribution. We show this dimension characterizes (up to
constant factors) the intrinsic number of label requests needed to test that
property. We develop such notions for both the active and passive testing
models. We then use these dimensions to prove a number of lower bounds,
including for linear separators and the class of dictator functions.
  Our results show that testing can be a powerful tool in realistic models for
learning, and further that active testing exhibits an interesting and rich
structure. Our work in addition brings together tools from a range of areas
including U-statistics, noise-sensitivity, self-correction, and spectral
analysis of random matrices, and develops new tools that may be of independent
interest.


  In this paper, a kinematically modular approach to robot control is
presented. The method involves structures called Elementary Dynamic Actions and
a network model combining these elements. With this control framework, a rich
repertoire of movements can be generated by combination of basic modules. The
problems of solving inverse kinematics, managing kinematic singularity and
kinematic redundancy are avoided. The modular approach is robust against
contact and physical interaction, which makes it particularly effective for
contact-rich manipulation. Each kinematic module can be learned by Imitation
Learning, thereby resulting in a modular learning strategy for robot control.
The theoretical foundations and their real robot implementation are presented.
Using a KUKA LBR iiwa14 robot, three tasks were considered: (1) generating a
sequence of discrete movements, (2) generating a combination of discrete and
rhythmic movements, and (3) a drawing and erasing task. The results obtained
indicate that this modular approach has the potential to simplify the
generation of a diverse range of robot actions.


  New findings in natural language processing (NLP) demonstrate that the strong
memorization capability contributes a lot to the success of Large Language
Models (LLM). This inspires us to explicitly bring an independent memory
mechanism into CTR ranking model to learn and memorize cross features'
representations. In this paper, we propose multi-Hash Codebook NETwork (HCNet)
as the memory mechanism for efficiently learning and memorizing representations
of cross features in CTR tasks. HCNet uses a multi-hash codebook as the main
memory place and the whole memory procedure consists of three phases:
multi-hash addressing, memory restoring, and feature shrinking. We also propose
a new CTR model named MemoNet which combines HCNet with a DNN backbone.
Extensive experimental results on three public datasets and online test show
that MemoNet reaches superior performance over state-of-the-art approaches.
Besides, MemoNet shows scaling law of large language model in NLP, which means
we can enlarge the size of the codebook in HCNet to sustainably obtain
performance gains. Our work demonstrates the importance and feasibility of
learning and memorizing representations of cross features, which sheds light on
a new promising research direction.


  Understanding surface reactivity is crucial in many fields, going from
heterogeneous catalysis to materials oxidation and corrosion. In order to
decipher the surface reactions of ZrB2 exposed to the harsh environment of
aerospace components, the chemical activity of both Zr- and B-surfaces is
predicted and compared by using density functional theory and nudged elastic
band methods. In particular the adsorption, dissociation and diffusion of O2,
CO and H2O are extensively examined through the calculation of surface
adsorption energies and reaction pathways. We find the dissociative adsorption
of O2 dominating the reactivity of ZrB2 surfaces, while the dissociation of H2O
and CO is weakly active on Zr-surfaces, and even less activated on B-terminated
ones. Importantly, we discover that the reaction of O2 and H2O can trigger
strong surface reconstruction at B-surfaces. Our work thus provides significant
insights into the diverse adsorption and reaction mechanisms of ZrB2 surfaces.


  We study the topology of analytic families of $n$-dimensional complex
hypersurfaces having an isolated singularity at the origin. We prove that such
a family is $\mu$-constant if and only if it admits an uniform Milnor radius,
which happens if and only if it has constant embedded topological type. In
particular, this solves the $\mu$-constant problem, formulated by D.T. L\^e and
C.P. Ramanujam in 1976.


  Multi-agent path finding (MAPF) is a well-studied problem in artificial
intelligence, where one needs to find collision-free paths for agents with
given start and goal locations. In video games, agents of different types often
form teams. In this paper, we demonstrate the usefulness of MAPF algorithms
from artificial intelligence for moving such non-homogeneous teams in congested
video game environments.


  In the quest for materials hosting Kitaev spin liquids, much of the efforts
have been focused on the fourth- and fifth-row transition metal compounds,
which are spin-orbit coupling assisted Mott insulators. Here, we study the
structural and magnetic properties of 3$d$ transition metal oxides,
Na$_2$Co$_2$TeO$_6$ and Na$_3$Co$_2$SbO$_6$. The partial occupancy of sodium in
former compound is addressed using a cluster expansion, and a honeycomb lattice
of sodiums is found to be energetically favored. Starting from the \textit{ab
initio} band structures, a many-body second order perturbation theory leads to
a pseudospin-$\frac{1}{2}$ Hamiltonian with estimated magnetic interactions. We
show that the experimentally observed zigzag magnetic state is stabilized only
when the first neighbor Kitaev coupling dominates over the Heisenberg term,
both of which are highly suppressed due to presence of $e_g$ orbitals. A third
neighbor Heisenberg interaction is found dominant in both these compounds. We
also present a phase diagram for Na$_2$Co$_2$TeO$_6$ by varying the
electron-electron and spin-orbit interactions. The computed spin excitation
spectra are found to capture essential features of recent experimental magnon
spectrum, lending support to our results.


  In this article, we are interested in the physical model of general quantum
protocols implementing secure two-party computations in the light of Mayers'
and Lo's & Chau's no-go theorems of bit commitment and oblivious transfer. In
contrast to the commonly adobted quantum pure two-party model in the literature
where classical communication is normally ignored, we propose an alternative
interpretation for the purification of classical communication in two-party
protocols by introducing a quantum third party for the classical channel. This
interpretation leads to a global three-party model, involving Alice's and Bob's
machines and the environment coupled to the macroscopic channel, using the
decoherence scheme in quantum measurements. This model could give a more
general view on the concealing/binding trade-off of quantum bit commitment
protocols.
  Inspired from this three-party interpretation, we extend the no-go theorems
for denying some classes of two-party protocols having access to some
particular quantum trusted third-parties, known as quantum two-party oracles.
The extension implies that a quantum protocol for implementing secure two-party
computations musts have access to a trusted third-party which erases
information and thus makes dissipation of heat to the environment.


  Signaling pathways serve to communicate information about extracellular
conditions into the cell, to both the nucleus and cytoplasmic processes to
control cell responses. Genetic mutations in signaling network components are
frequently associated with cancer and can result in cells acquiring an ability
to divide and grow uncontrollably. Because signaling pathways play such a
significant role in cancer initiation and advancement, their constituent
proteins are attractive therapeutic targets. In this review, we discuss how
signaling pathway modeling can assist with identifying effective drugs for
treating diseases, such as cancer. An achievement that would facilitate the use
of such models is their ability to identify controlling biochemical parameters
in signaling pathways, such as molecular abundances and chemical reaction
rates, because this would help determine effective points of attack by
therapeutics.


  This paper studies the quasi-maximum-likelihood estimator (QMLE) in a general
conditionally heteroscedastic time series model of multiplicative form
$X_t=\sigma_tZ_t$, where the unobservable volatility $\sigma_t$ is a parametric
function of $(X_{t-1},...,X_{t-p},\sigma_{t-1},... ,\sigma_{t-q})$ for some
$p,q\ge0$, and $(Z_t)$ is standardized i.i.d. noise. We assume that these
models are solutions to stochastic recurrence equations which satisfy a
contraction (random Lipschitz coefficient) property. These assumptions are
satisfied for the popular GARCH, asymmetric GARCH and exponential GARCH
processes. Exploiting the contraction property, we give conditions for the
existence and uniqueness of a strictly stationary solution $(X_t)$ to the
stochastic recurrence equation and establish consistency and asymptotic
normality of the QMLE. We also discuss the problem of invertibility of such
time series models.


  We investigate higher order symplectic integration strategies within Bayesian
cosmic density field reconstruction methods. In particular, we study the
fourth-order discretisation of Hamiltonian equations of motion (EoM). This is
achieved by recursively applying the basic second-order leap-frog scheme
(considering the single evaluation of the EoM) in a combination of even numbers
of forward time integration steps with a single intermediate backward step.
This largely reduces the number of evaluations and random gradient
computations, as required in the usual second-order case for high-dimensional
cases. We restrict this study to the lognormal-Poisson model, applied to a full
volume halo catalogue in real space on a cubical mesh of 1250 $h^{-1}$ Mpc side
and 256$^3$ cells. Hence, we neglect selection effects, redshift space
distortions, and displacements. We note that those observational and cosmic
evolution effects can be accounted for in subsequent Gibbs-sampling steps
within the COSMIC BIRTH algorithm. We find that going from the usual second to
fourth-order in the leap-frog scheme shortens the burn-in phase by a factor of
at least $\sim30$. This implies that 75-90 independent samples are obtained
while the fastest second-order method converges. After convergence, the
correlation lengths indicate an improvement factor of about 3.0 fewer gradient
computations for meshes of 256$^3$ cells. In the considered cosmological
scenario, the traditional leap-frog scheme turns out to outperform higher order
integration schemes only at lower dimensional problems, e.g. meshes with 64$^3$
cells. This gain in computational efficiency can help to go towards a full
Bayesian analysis of the cosmological large-scale structure for upcoming galaxy
surveys.


  We introduce the algebra $\mathcal{G}^{\operatorname{f}}$, which is equipped
with natural maps into the algebra of (combinatorial) multiple Eisenstein
series and that of multiple q-zeta values. Similar to Racinet's approach to
formal multiple zeta values, we consider an affine scheme BM corresponding to
the algebra $\mathcal{G}^{\operatorname{f}}$. We show that Racinet's affine
scheme DM represented by the algebra of formal multiple zeta values embeds into
this affine scheme BM. This leads to a projection from the algebra
$\mathcal{G}^{\operatorname{f}}$ onto the algebra of formal multiple zeta
values. Via the above natural maps, this projection corresponds to taking the
constant terms of multiple Eisenstein series or the limit $q\to1$ of multiple
q-zeta values.


  In this paper, we consider a three-state solid-on-solid (SOS) model with two
competing interactions (nearest-neighbour, one-level next-nearest-neighbour) on
the Cayley tree of order two. We show that at some values of parameters the
model exhibits a phase transition. We prove that for the model under some
conditions there is no antiferromagnetic phases.


  The open radio access network (O-RAN) architecture's native virtualization
and embedded intelligence facilitate RAN slicing and enable comprehensive
end-to-end services in post-5G networks. However, any vulnerabilities could
harm security. Therefore, artificial intelligence (AI) and machine learning
(ML) security threats can even threaten O-RAN benefits. This paper proposes a
novel approach to estimating the optimal number of predefined VNFs for each
slice while addressing secure AI/ML methods for dynamic service admission
control and power minimization in the O-RAN architecture. We solve this problem
on two-time scales using mathematical methods for determining the predefined
number of VNFs on a large time scale and the proximal policy optimization
(PPO), a Deep Reinforcement Learning algorithm, for solving dynamic service
admission control and power minimization for different slices on a small-time
scale. To secure the ML system for O-RAN, we implement a moving target defense
(MTD) strategy to prevent poisoning attacks by adding uncertainty to the
system. Our experimental results show that the proposed PPO-based service
admission control approach achieves an admission rate above 80\% and that the
MTD strategy effectively strengthens the robustness of the PPO method against
adversarial attacks.


  We construct a supersymmetric grand unified model in the framework of a
latticized extra dimension. The SU(5) symmetries on the lattice are broken by
the vacuum expectation values of the link fields connecting adjacent SU(5)
sites, leaving just the MSSM at low energies. Below the SU(5) breaking scale,
the theory gives rise to a similar spectrum as in orbifold breaking of SU(5)
symmetry in 5 dimensions, and shares many features with the latter scenario. We
discuss gauge coupling unification and proton decay emphasizing the differences
with respect to the usual grand unified theories. Our model may be viewed as an
effective four dimensional description of the orbifold symmetry breaking in
higher dimensions.


  This paper studies the case of possibly high-dimensional covariates in the
regression discontinuity design (RDD) analysis. In particular, we propose
estimation and inference methods for the RDD models with covariate selection
which perform stably regardless of the number of covariates. The proposed
methods combine the local approach using kernel weights with
$\ell_{1}$-penalization to handle high-dimensional covariates. We provide
theoretical and numerical results which illustrate the usefulness of the
proposed methods. Theoretically, we present risk and coverage properties for
our point estimation and inference methods, respectively. Under certain special
case, the proposed estimator becomes more efficient than the conventional
covariate adjusted estimator at the cost of an additional sparsity condition.
Numerically, our simulation experiments and empirical example show the robust
behaviors of the proposed methods to the number of covariates in terms of bias
and variance for point estimation and coverage probability and interval length
for inference.


  Blind motion deblurring is one of the most basic and challenging problems in
image processing and computer vision. It aims to recover a sharp image from its
blurred version knowing nothing about the blur process. Many existing methods
use Maximum A Posteriori (MAP) or Expectation Maximization (EM) frameworks to
deal with this kind of problems, but they cannot handle well the figh frequency
features of natural images. Most recently, deep neural networks have been
emerging as a powerful tool for image deblurring. In this paper, we prove that
encoder-decoder architecture gives better results for image deblurring tasks.
In addition, we propose a novel end-to-end learning model which refines
generative adversarial network by many novel training strategies so as to
tackle the problem of deblurring. Experimental results show that our model can
capture high frequency features well, and the results on benchmark dataset show
that proposed model achieves the competitive performance.


  In forensic genetics, short tandem repeats (STRs) are used for human
identification (HID). Degraded biological trace samples with low amounts of
short DNA fragments (low-quality DNA samples) pose a challenge for STR typing.
Predefined single nucleotide polymorphisms (SNPs) can be amplified on short PCR
fragments and used to generate SNP profiles from low-quality DNA samples.
However, the stochastic results from low-quality DNA samples may result in
frequent locus drop-outs and insufficient numbers of SNP genotypes for
convincing identification of individuals. Shotgun DNA sequencing potentially
analyses all DNA fragments in a sample in contrast to the targeted PCR-based
sequencing methods and may be applied to DNA samples of very low quality, like
heavily compromised crime-scene samples and ancient DNA samples. Here, we
developed a statistical model for shotgun sequencing, sequence alignment, and
genotype calling. Results from replicated shotgun sequencing of buccal swab
(high-quality samples) and hair samples (low-quality samples) were arranged in
a genotype-call confusion matrix to estimate the calling error probability by
maximum likelihood and Bayesian inference. We developed formulas for
calculating the evidential weight as a likelihood ratio (LR) based on data from
dynamically selected SNPs from shotgun DNA sequencing. The method accounts for
potential genotyping errors. Different genotype quality filters may be applied
to account for genotyping errors. An error probability of zero resulted in the
forensically commonly used LR formula. When considering a single SNP marker's
contribution to the LR, error probabilities larger than zero reduced the LR
contribution of matching genotypes and increased the LR in the case of a
mismatch. We developed an open-source R package, wgsLR, which implements the
method, including estimating the calling error probability and calculating LR
values.


  The energy spectra of TeV gamma-rays from blazars, after being corrected for
intergalatic absorption in the Extragalactic Background Light (EBL), appear
unusually hard, a fact that poses challenges to the conventional models of
particle acceleration in TeV blazars and/or to the EBL models. In this paper we
show that the internal absorption of gamma-rays caused by interactions with
dense narrow-band radiation fields in the vicinity of compact gamma-ray
production regions can lead to the formation of gamma-ray spectra of an almost
arbitrary hardness. This allows significant relaxation of the current tight
constraints on particle acceleration and radiation models, although at the
expense of enhanced requirements to the available nonthermal energy budget. The
latter, however, is not a critical issue, as long as it can be largely
compensated by the Doppler boosting, assuming very large ($\geq 30$) Doppler
factors of the relativistically moving gamma-ray production regions. The
suggested scenario of formation of hard gamma-ray spectra predicts detectable
synchrotron radiation of secondary electron-positron pairs which might require
a revision of the current ``standard paradigm'' of spectral energy
distributions of gamma-ray blazars. If the primary gamma-rays are of hadronic
origin related to $pp$ or $p \gamma$ interactions, the ``internal gamma-ray
absorption'' model predicts neutrino fluxes close to the detection threshold of
the next generation high energy neutrino detectors.


  We consider the problem of the computation of $\inf_p \theta p$ over the set
of exponent pairs $P \ni p$ under linear constraints for a certain class of
objective functions $\theta$. An effective algorithm is presented. The output
of the algorithm leads to the improvement and establishing new estimates in the
various divisor problems in the analytic number theory.


  In this talk a review on the exclusive determination of Vcb is presented.
Updated values of this quantity obtained from B->Dlnu and B->D*lnu decays are
given. New measurements from B-factories are expected to come soon and the main
challenges to improve the accuracy on Vcb extracted from these decays are
discussed.


  We study correlations in fermionic lattice systems with long-range
interactions in thermal equilibrium. We prove a bound on the correlation decay
between anti-commuting operators and generalize a long-range Lieb-Robinson type
bound. Our results show that in these systems of spatial dimension $D$ with,
not necessarily translation invariant, two-site interactions decaying
algebraically with the distance with an exponent $\alpha \geq 2\,D$,
correlations between such operators decay at least algebraically with an
exponent arbitrarily close to $\alpha$ at any non-zero temperature. Our bound
is asymptotically tight, which we demonstrate by a high temperature expansion
and by numerically analyzing density-density correlations in the 1D quadratic
(free, exactly solvable) Kitaev chain with long-range pairing.


  Properties of X(3872) are studied by regarding it as a $DD^{\ast}$ hadronic
molecule with $J^{PC} = 2^{-+}$ in the phenomenological Lagrangian approach. We
find that our model with about 97.6% isospin zero component explains the
existing data nicely, for example, the ratio $\mathcal{B}(X(3872) \to
J/\psi\pi^+\pi^-\pi^0)/\mathcal{B}(X(3872) \to J/\psi\pi^+\pi^-)$. We predict
the partial widths of the radiative decays of $X(3872) \to \gamma J/\psi$,
$\gamma \psi(2S) $ and the strong decays of $X(3872) \to J/\psi \pi^+ \pi^-$,
$J/\psi \pi^+\pi^-\pi^0$ as well as $X(3872) \to \chi_{cJ}\pi^0$. Our analysis
shows that the measurement of the ratio $\mathcal{B}(X(3872) \to
\chi_{c0}\pi^0)/\mathcal{B}(X(3872) \to \chi_{c1}\pi^0)$ may signal the nature
of X(3872).


  Let (M,g) a compact Riemannian $n$-dimensional manifold with umbilic
boundary. It is well know that, under certain hypothesis, in the conformal
class of g there are scalar-flat metrics that have the boundary of M as a
constant mean curvature hypersurface. In this paper we prove that these metrics
are a compact set in the case of low dimensional manifolds, that is n=6,7,8,
provided that the Weyl tensor is always not vanishing on the boundary.


  Rare-earth-doped fiber lasers are emerging as promising high-power
mid-infrared sources for the 2.6-3.0 {\mu}m and 3.3-3.8 {\mu}m regions based on
erbium and holmium ions. The intermediate wavelength range, however, remains
vastly underserved, despite prospects for important manufacturing and defense
applications. Here, we demonstrate the potential of dysprosium-doped fiber to
solve this problem, with a simple in-band pumped grating-stabilized linear
cavity generating up to 1.06 W at 3.15 {\mu}m. A slope efficiency of 73% with
respect to launched power (77% relative to absorbed power) is achieved: the
highest value for any mid-infrared fiber laser to date, to the best of our
knowledge. Opportunities for further power and efficiency scaling are also
discussed.


  Given a differential operator defined in terms of left-invariant vector
fields on a Lie group, we prove that the local condition defining maximal
hypoellipticity is equivalent to a global estimate if the operator is left
invariant. As a consequence, we characterize the domain of the closure in $L^p$
of certain maximal hypoelliptic differential operators on test functions on Lie
groups.


  With the rising popularity of the internet and the widespread use of networks
and information systems via the cloud and data centers, the privacy and
security of individuals and organizations have become extremely crucial. In
this perspective, encryption consolidates effective technologies that can
effectively fulfill these requirements by protecting public information
exchanges. To achieve these aims, the researchers used a wide assortment of
encryption algorithms to accommodate the varied requirements of this field, as
well as focusing on complex mathematical issues during their work to
substantially complicate the encrypted communication mechanism. as much as
possible to preserve personal information while significantly reducing the
possibility of attacks. Depending on how complex and distinct the requirements
established by these various applications are, the potential of trying to break
them continues to occur, and systems for evaluating and verifying the
cryptographic algorithms implemented continue to be necessary. The best
approach to analyzing an encryption algorithm is to identify a practical and
efficient technique to break it or to learn ways to detect and repair weak
aspects in algorithms, which is known as cryptanalysis. Experts in
cryptanalysis have discovered several methods for breaking the cipher, such as
discovering a critical vulnerability in mathematical equations to derive the
secret key or determining the plaintext from the ciphertext. There are various
attacks against secure cryptographic algorithms in the literature, and the
strategies and mathematical solutions widely employed empower cryptanalysts to
demonstrate their findings, identify weaknesses, and diagnose maintenance
failures in algorithms.


  The aim of this paper is to describe the long time behavior of solutions of
linearized Navier Stokes equations near a concave shear layer profile in the
long waves regime, namely for small horizontal Fourier variable $\alpha$, when
the viscosity $\nu$ vanishes. We show that the solutions converge exponentially
to $0$, except in some range of $\alpha$, namely for $\nu^{1/4} \lesssim
|\alpha| \lesssim \nu^{1/6}$, where there exists one unique unstable mode, with
an associated eigenvalue $\lambda$, such that $\Re \lambda$ is of order
$\nu^{1/4}$. In this regime we give a complete description of the solutions of
linearized Navier Stokes equations as the sum of the projection over the unique
exponentially growing mode and of an exponentially decaying term. The study of
this linear instability is a key point in the study of the nonlinear
instability of Prandtl bounday layers and of shear layer profiles.


  For a complex tensor A, Minimal Gersgorin tensor eigenvalue inclusion set of
A is presented, and its sufficient and necessary condition is given.
Furthermore, we study its boundary by the spectrums of the equimodular set and
the extended equimodular set for A. Lastly, for an irreducible tensor, a
numerical approximation to Minimal Gersgorin tensor eigenvalue inclusion set is
given.


  We investigate the possibility that the anomalous acceleration of the Pioneer
10 and 11 spacecraft is due to the recoil force associated with an anisotropic
emission of thermal radiation off the vehicles. To this end, relying on the
project and spacecraft design documentation, we constructed a comprehensive
finite-element thermal model of the two spacecraft. Then, we numerically solve
thermal conduction and radiation equations using the actual flight telemetry as
boundary conditions. We use the results of this model to evaluate the effect of
the thermal recoil force on the Pioneer 10 spacecraft at various heliocentric
distances. We found that the magnitude, temporal behavior, and direction of the
resulting thermal acceleration are all similar to the properties of the
observed anomaly. As a novel element of our investigation, we develop a
parameterized model for the thermal recoil force and estimate the coefficients
of this model independently from navigational Doppler data. We find no
statistically significant difference between the two estimates and conclude
that once the thermal recoil force is properly accounted for, no anomalous
acceleration remains.


  In stationary subspace analysis (SSA) one assumes that the observable
p-variate time series is a linear mixture of a k-variate nonstationary time
series and a (p-k)-variate stationary time series. The aim is then to estimate
the unmixing matrix which transforms the observed multivariate time series onto
stationary and nonstationary components. In the classical approach multivariate
data are projected onto stationary and nonstationary subspaces by minimizing a
Kullback-Leibler divergence between Gaussian distributions, and the method only
detects nonstationarities in the first two moments. In this paper we consider
SSA in a more general multivariate time series setting and propose SSA methods
which are able to detect nonstationarities in mean, variance and
autocorrelation, or in all of them. Simulation studies illustrate the
performances of proposed methods, and it is shown that especially the method
that detects all three types of nonstationarities performs well in various time
series settings. The paper is concluded with an illustrative example.


  When processing dense emulsions, complex flows stretch and deform droplets to
the point of breakup, changing the droplet size distribution and the mechanical
properties of the final product. For steady homogeneous flows, a droplet's
shape and proclivity to breakup can be inferred from a Capillary number,
comparing the strain rate with the typical shape relaxation time. More
generally, a droplet's shape depends on its whole history of deformation, and
this distinction can be salient under conditions relevant to industrial
processing. Here, we develop a coupled population balance and droplet shape
evolution model (STEPB) with a breaking rate determined by the droplet's shape.
In a first application of the STEPB model, we consider droplet breakup during
relaxation of step shear, where we predict non-trivial strain-dependent final
daughter droplet distributions. We also compare predictions from STEPB against
experimental observations in steady flow conditions, illuminating key
weaknesses in the model due to neglected terms.


  We analyze the Lyapunov spectrum of the relative Ruelle operator associated
with a skew product whose base is an ergodic automorphism and whose fibers are
full shifts. We prove that these operators can be approximated in the
$C^0$-topology by positive matrices with an associated dominated splitting.


  We introduce a framework that predicts the goals behind observable human
action in video. Motivated by evidence in developmental psychology, we leverage
video of unintentional action to learn video representations of goals without
direct supervision. Our approach models videos as contextual trajectories that
represent both low-level motion and high-level action features. Experiments and
visualizations show our trained model is able to predict the underlying goals
in video of unintentional action. We also propose a method to "automatically
correct" unintentional action by leveraging gradient signals of our model to
adjust latent trajectories. Although the model is trained with minimal
supervision, it is competitive with or outperforms baselines trained on large
(supervised) datasets of successfully executed goals, showing that observing
unintentional action is crucial to learning about goals in video. Project page:
https://aha.cs.columbia.edu/


  I present interferometric images (approx. 7" resolution) of CO emission in
five elliptical galaxies and nondetections in two others. These data double the
number of elliptical galaxies whose CO emission has been fully mapped. The
sample galaxies have 10^8 to 5x10^9 solar masses of molecular gas distributed
in mostly symmetric rotating disks with diameters of 2 to 12 kpc. Four out of
the five molecular disks show remarkable alignment with the optical major axes
of their host galaxies. The molecular masses are a few percent of the total
dynamical masses which are implied if the gas is on circular orbits. If the
molecular gas forms stars, it will make rotationally supported stellar disks
which will be very similar in character to the stellar disks now known to be
present in many ellipticals. Comparison of stellar kinematics to gas kinematics
in NGC 4476 implies that the molecular gas did not come from internal stellar
mass loss because the specific angular momentum of the gas is about three times
larger than that of the stars.


  The extended minimal geometric deformation (EMGD) is employed on the fluid
membrane paradigm, to describe compact stellar objects as Bose--Einstein
condensates (BEC) consisting of gravitons. The black hole quantum portrait,
besides deriving a preciser phenomenological bound for the fluid brane tension,
is then scrutinized from the point of view of the configurational entropy. It
yields a range for the critical density of the EMGD BEC, whose configurational
entropy has global minima suggesting the configurational stability of the EMGD
BEC.


  Mapping with uncertainty representation is required in many research domains,
especially for localization. Although there are many investigations regarding
the uncertainty of the pose estimation of an ego-robot with map information,
the quality of the reference maps is often neglected. To avoid potential
problems caused by the errors of maps and a lack of uncertainty quantification,
an adequate uncertainty measure for the maps is required. In this letter,
uncertain building models with abstract map surfaces using Gaussian Processes
(GPs) are proposed to describe the map uncertainty in a probabilistic way. To
reduce the redundant computation for simple planar objects, extracted facets
from a Gaussian Mixture Model (GMM) are combined with an implicit GP map, also
employing local GP-block techniques. The proposed method is evaluated on LiDAR
point clouds of city buildings collected by a mobile mapping system. Compared
to the performance of other methods such as OctoMap, GP Occupancy Map (GPOM),
Bayesian Generalized Kernel OctoMap (BGKOctoMap), Local automatic relevance
determination Hilbert map (LARD-HM) and Gaussian Implicit Surface map (GPIS),
our method achieves a higher Precision-Recall AUC for the evaluated buildings.


  The present work introduces a new form of explicitly correlated factor in the
context of the transcorrelated methods. The new correlation factor is obtained
from the r 12 $\approx$ 0 mathematical analysis of the transcorrelated
Hamiltonian, and its analytical form is obtained such that the leading order in
1/r 12 of the scalar part of the effective two-electron potential reproduces
the long-range interaction of the range-separated density functional theory.
The resulting correlation factor exactly imposes the cusp and is tuned by a
unique parameter $\mu$ which controls both the depth of the coulomb hole and
its typical range in r 12. The transcorrelated Hamiltonian obtained with such a
new correlation factor has a straightforward analytical expression depending on
the same parameter $\mu$, and its physical contents continuously change by
varying $\mu$ : one can change from a non divergent repulsive Hamiltonian at
large $\mu$ to a purely attractive one at small $\mu$. We investigate the
convergence of the ground state eigenvalues and right-eigenvectors of such new
transcorrelated Hamiltonian as a function of the basis set and as a function of
$\mu$ on a series of two-electron systems. We found that the convergence
towards the complete basis set is much faster for a quite wide range values of
$\mu$. We also propose a specific value of $\mu$ which essentially reproduce
the results obtained with the frozen Gaussian geminal introduced by Ten-No
[CPL-330,169 (2000)].


  The local Rademacher complexity framework is one of the most successful
general-purpose toolboxes for establishing sharp excess risk bounds for
statistical estimators based on the framework of empirical risk minimization.
Applying this toolbox typically requires using the Bernstein condition, which
often restricts applicability to convex and proper settings. Recent years have
witnessed several examples of problems where optimal statistical performance is
only achievable via non-convex and improper estimators originating from
aggregation theory, including the fundamental problem of model selection. These
examples are currently outside of the reach of the classical localization
theory.
  In this work, we build upon the recent approach to localization via offset
Rademacher complexities, for which a general high-probability theory has yet to
be established. Our main result is an exponential-tail excess risk bound
expressed in terms of the offset Rademacher complexity that yields results at
least as sharp as those obtainable via the classical theory. However, our bound
applies under an estimator-dependent geometric condition (the "offset
condition") instead of the estimator-independent (but, in general,
distribution-dependent) Bernstein condition on which the classical theory
relies. Our results apply to improper prediction regimes not directly covered
by the classical theory.


  Objective: Muscle contractions are commonly detected by performing EMG
measurements. The major disadvantage of this technique is that mechanical
disturbances to the electrodes are in the same frequency and magnitude range as
the desired signal. In this work we propose an approach and a realized
measurement system to combine EMG and bioimpedance measurements for higher
reliabilities of muscle contraction detections. Methods: We propose the
development of a modular four-channel measurement system, whereat each channel
is capable of acquiring EMG, the bioimpedance magnitude and phase,
simultaneously. The modules are synchronized by an additional interface board,
which communicates with a PC. A graphical user interface enables to control the
bioimpedance excitation current in a range from 100 {\mu}A to 1 mA in a
frequency range from 50 kHz to 333 kHz. Results: A system characterization
demonstrated that bioimpedance magnitude changes of less than 250 ppm and phase
changes below 0.05{\deg} can be detected reliably. Measurements from a subject
have shown the timing relationship between EMG and bioimpedance signals as well
as their robustness against mechanical disturbances. A measurement of five
exemplary hand gestures has demonstrated the increase of usable information for
detecting muscle contractions. Conclusion: Bioimpedance measurements of muscles
provide useful information about contractions. Furthermore, the usage of a
known high-frequency excitation current enables a reliable differentiation
between the actual information and disturbances. Significance: By combining EMG
and bioimpedance measurements, muscle contractions can be detected much more
reliably. This setup can be adopted to prostheses and many other human-computer
interfaces.


  Despite intensive studies of kink oscillations of coronal loops in the last
decade, a large scale statistically significant investigation of the
oscillation parameters has not been made using data from the Solar Dynamics
Observatory (SDO).
  We carry out a statistical study of kink oscillations using Extreme
Ultra-Violet (EUV) imaging data from a previously compiled catalogue.
  We analysed 58 kink oscillation events observed by the Atmospheric Imaging
Assembly (AIA) onboard SDO during its first four years of operation
(2010-2014). Parameters of the oscillations, including the initial apparent
amplitude, period, length of the oscillating loop, and damping are studied for
120 individual loop oscillations.
  Analysis of the initial loop displacement and oscillation amplitude leads to
the conclusion that the initial loop displacement prescribes the initial
amplitude of oscillation in general. The period is found to scale with the loop
length, and a linear fit of the data cloud gives a kink speed of Ck
=(1330+/-50) km s-1 . The main body of the data corresponds to kink speeds in
the range Ck =(800-3300) km s-1. Measurements of 52 exponential damping times
were made, and it was noted that at least 22 of the damping profiles may be
better approximated by a combination of non-exponential and exponential
profiles, rather than a purely exponential damping envelope. There are an
additional 10 cases where the profile appears to be purely non-exponential, and
no damping time was measured. A scaling of the exponential damping time with
the period is found, following the previously established linear scaling
between these two parameters.


  In this paper, we study Jarzynski's equality and fluctuation theorems for
diffusion processes. While some of the results considered in the current work
are known in the (mainly physics) literature, we review and generalize these
nonequilibrium theorems using mathematical arguments, therefore enabling
further investigations in the mathematical community. On the numerical side,
variance reduction approaches such as importance sampling method are studied in
order to compute free energy differences based on Jarzynski's equality.


  All planets and satellites of our solar system are subject to a continuous
rain of material, ranging in size from specks of dust to objects the size of
boulders. Upon impact, these objects deposit their kinetic energy into the
incident surface or atmosphere and affect the environment of the target body in
ways not yet well understood. Recent high-profile events - impact flashes on
Jupiter and the encounter of comet C/Siding Spring with Mars - brought the
study of "extraterrestrial meteors" and their effects into the fore. Here we
review the history, status and future prospects of meteor studies on planets
other than the Earth. Would bright meteors appear in the atmosphere of Mars and
what are the long-term effects on the planet's atmosphere? How do high-speed
impacts of particulate matter on the airless surfaces of Mercury and the Moon
affect their environment and those of the countless other bodies like them?
These are some of the questions we attempt to answer in this Chapter.


  The long-term goal of NA62 is to measure the ultra rare K+/- -> pi+/- nu
anti-nu decay with a sensitivity of 10^-12 per event. This is done by using the
decay - in - flight technique which allows a signal acceptance of ~10% . The
aim is to collect about 100 signal events in two years of data taking with a
background to signal ratio smaller than 10%. The principle of the experimental
measurement and the layout of the detector are presented. During 2007/2008 a
dedicated run devoted to NA62 prototype tests and study of K_e2 decays was
taken. The first phase of the NA62 experiment is aiming at a high precision
test of the lepton universality by measuring the helicity suppressed ratio R_K.
The preliminary result based on 40% of the 2007 NA62 data sample, R_K =
K_e2/K_mu2 = (2.500 +/- 0.016) x 10^-5, which is the first result with a
precision better than 1%, is consistent with the Standard Model.
  Aiming at charge asymmetry measurements, the NA48/2 experiment collected an
unprecedented amount of charged K_(3 pi) events. The large samples allowed a
precision measurement of rare charged kaon decays. New measurements of the
K+/-_(pi l l) decays based on the full NA48/2 data sample collected during
2003/2004 are reported in this paper. Samples of about 7200 reconstructed K+/-
-> pi+/- e+ e- events, and more than 3000 K+/- -> pi+/- mu+ mu- events, with a
few percent background contamination, have been collected. A precise
measurement of the branching fractions and the form factors of the rare decays
K+/-_(pi l l)$ were performed. Measurements of the CP-violating and the
forward-backward asymmetries are reported.


  Pre-trained language models have been known to perpetuate biases from the
underlying datasets to downstream tasks. However, these findings are
predominantly based on monolingual language models for English, whereas there
are few investigative studies of biases encoded in language models for
languages beyond English. In this paper, we fill this gap by analysing gender
bias in West Slavic language models. We introduce the first template-based
dataset in Czech, Polish, and Slovak for measuring gender bias towards male,
female and non-binary subjects. We complete the sentences using both mono- and
multilingual language models and assess their suitability for the masked
language modelling objective. Next, we measure gender bias encoded in West
Slavic language models by quantifying the toxicity and genderness of the
generated words. We find that these language models produce hurtful completions
that depend on the subject's gender. Perhaps surprisingly, Czech, Slovak, and
Polish language models produce more hurtful completions with men as subjects,
which, upon inspection, we find is due to completions being related to
violence, death, and sickness.


  We investigate the orientation dependence of molecular high-order harmonic
generation (HHG) both numerically and analytically. We show that the molecular
recollision electronic wave packets (REWPs) in the HHG are closely related to
the ionization potential as well as the particular orbital from which it
ionized. As a result, the spectral amplitude of the molecular REWP can be
significantly different from its reference atom (i.e., with the same ionization
potential as the molecule under study) in some energy regions due to the
interference between the atomic cores of the molecules. This finding is
important for molecular orbital tomography using HHG[Nature \textbf{432},
867(2004)].


  A canonical pseudo-Nambu Goldstone Boson (pNGB) can play the role of a dark
energy field responsible for present cosmic acceleration. Confronting with the
recent cosmological data, we find that the pNGB field requires spontaneous
symmetry breaking scale $f$ close to $M_P$ and the initial field value
fine-tuned. It is difficult to achieve a large $f$ in a theoretically
consistent set-up. A possible resolution can be achieved by increasing the
Hubble friction in well motivated particle physics models in the general set-up
of modified gravity theories. We show two phenomenological examples of this
set-up where the standard pNGB action have been modified by introducing terms
motivated from galileon cosmology. We confront those examples with the recent
supernovae, PLANCK and BAO data. We find that moderate values of the
dimensionless constants that increase the friction, make $f << M_{P}$ and the
generic initial conditions also favourable by the data. We also comment how the
fifth force constraints arising in these modified theories can be evaded.


  In this erratum we report changes on the $D^0$ $p_T$ spectra and nuclear
modification factor ($R_{AA}$) in Au+Au collisions at
$\sqrt{s_{_{\mathrm{NN}}}}$ = 200 GeV by fixing the errors in the efficiency
and selection criteria that affected the Au+Au results. The p+p reference
spectrum has changed as well and is updated with new fragmentation parameters.


  In this article, we give a new proof of the It\^o formula for some integral
processes related to the space-time L\'evy white noise introduced in Balan
(2015) as an alternative for the Gaussian white noise perturbing an SPDE. We
discuss two applications of this result, which are useful in the study of SPDEs
driven by a space-time L\'evy noise with finite variance: a maximal inequality
for the $p$-th moment of the stochastic integral, and the It\^o representation
theorem leading to a chaos expansion similar to the Gaussian case.


  We study the relation between the X-ray luminosity of compact sources and the
SFR of the host galaxy. Our sample includes 38 galaxies for which a uniform set
of X-ray, infra-red and ultraviolet data from Chandra, Spitzer and GALEX has
been collected. Our primary goals are (i) to obtain a more accurate calibration
of the Lx-SFR relation and (ii) to understand the origin of the dispersion in
the Lx-SFR relation observed in previous studies. Preliminary results of this
project are reported below.


  Recent analyses have shown that a sequential fourth generation can be
consistent with precision electroweak data. We consider the possibility that
the new generation could be a mirror generation with $V+A$ rather than $V-A$
interactions. Specifically we consider an extension of the minimal
supersymmetric standard model with a light mirror generation (mirMSSM) .
Implications of this extension are explored. One consequence is an enhancement
of the tau neutrino magnetic moment by several orders of magnitude consistent
with the current limits on the magnetic moment of the tau. The masses of the
mirror generation arise due to electroweak symmetry breaking, and if a mirror
generation exists its mass spectrum must lye below a TeV, and thus should be
discovered at the LHC. Mirror particles and mirror sparticles produce many
characteristic signatures which should be detectable at the LHC. Heavy higgs
boson decays into mirror particles and an analysis of the forward-backward
asymmetries can distinguish a mirror generation from a sequential fourth
generation. The validity of the model can thus be tested at the LHC. A model of
the type discussed here could arise from a more unified structure such as grand
unification or strings where a mirror generation escapes the survival
hypothesis, i.e., a generation and a mirror generation do not tie up to acquire
a mass of size $M_{GUT}$ or $M_{string}$ due to a symmetry, and thus remain
massless down to the electroweak scale.


  Using new ultraviolet (UV) spectra of five background quasars from the Cosmic
Origins Spectrograph on the Hubble Space Telescope, we analyze the low-latitude
(|b|=20-30 degree) regions of the Fermi Bubbles, the giant gamma-ray emitting
lobes at the Galactic Center. We combine these data with previous UV and atomic
hydrogen (HI) datasets to build a comprehensive picture of the kinematics and
metal column densities of the cool outflowing clouds entrained in the Fermi
Bubbles. We find that the number of UV absorption components per sightline
decreases as a function of increasing latitude, suggesting that the outflowing
clouds become less common with increasing latitude. The Fermi Bubble HI clouds
are accelerated up to b~7 degree, whereas when we model the UV Fermi Bubbles
clouds deprojected flow velocities, we find that they are flat or even
accelerating with distance from the Galactic center. This trend, which holds in
both the northern and southern hemispheres, indicates that the nuclear outflow
accelerates clouds throughout the Fermi Bubbles or has an acceleration phase
followed by a coasting phase. Finally, we note the existence of several
blueshifted high-velocity clouds at latitudes exceeding ~30 degree, whose
velocities cannot be explained by gas clouds confined to the inside of the
gamma-ray defined Fermi Bubbles. These anomalous velocity clouds are likely in
front of the Fermi Bubbles and could be remnants from past nuclear outflows.
Overall, these observations form a valuable set of empirical data on the
properties of cool gas in nuclear winds from star-forming galaxies.


  We consider renormalization group flow applied to the cosmological dynamical
equations. A consistency condition arising from energy-momentum conservation
links the flow parameters to the cosmological evolution, restricting possible
behaviors. Three classes of cosmological fixed points for dark energy plus a
barotropic fluid are found: a dark energy dominated universe, which can be
either accelerating or decelerating depending on the RG flow parameters, a
barotropic dominated universe where dark energy fades away, and solutions where
the gravitational and potential couplings cease to flow. If the IR fixed point
coincides with the asymptotically safe UV fixed point then the dark energy
pressure vanishes in the first class, while (only) in the de Sitter limit of
the third class the RG cutoff scale becomes the Hubble scale.


  Signers compose sign language phonemes that enable communication by combining
phonological parameters such as handshape, orientation, location, movement, and
non-manual features. Linguistic research often breaks down signs into their
constituent parts to study sign languages and often a lot of effort is invested
into the annotation of the videos. In this work we show how a single model can
be used to recognise the individual phonological parameters within sign
languages with the aim of either to assist linguistic annotations or to
describe the signs for the sign recognition models. We use Danish Sign Language
data set `Ordbog over Dansk Tegnsprog' to generate multiple data sets using
pose estimation model, which are then used for training the multi-label Fast
R-CNN model to support multi-label modelling. Moreover, we show that there is a
significant co-dependence between the orientation and location phonological
parameters in the generated data and we incorporate this co-dependence in the
model to achieve better performance.


  What are the fundamental limits and advantages of using a catalyst to aid
thermodynamic transformations between quantum systems? In this work, we answer
this question by focusing on transformations between energy-incoherent states
under the most general energy-conserving interactions among the system, the
catalyst, and a thermal environment. The sole constraint is that the catalyst
must return unperturbed and uncorrelated with the other subsystems. More
precisely, we first characterise the set of states to which a given initial
state can thermodynamically evolve (the catalysable future) or from which it
can evolve (the catalysable past) with the help of a strict catalyst. Secondly,
we derive lower bounds on the dimensionality required for the existence of
catalysts under thermal process, along with bounds on the catalyst's state
preparation. Finally, we quantify the catalytic advantage in terms of the
volume of the catalysable future and demonstrate its utility in an exemplary
task of generating entanglement using thermal resources.


  We discuss unusual aspects of symmetry that can happen due to entropic
effects in the context of multi-scalar field theories at finite temperature. We
present their consequences, in special, for the case of nonrelativistic models
of hard core spheres. We show that for nonrelativistic models phenomena like
inverse symmetry breaking and symmetry non-restoration cannot take place, but a
reentrant phase at high temperatures is shown to be possible for some region of
parameters. We then develop a model of interest in studies of Bose-Einstein
condensation in dilute atomic gases and discuss about its phase transition
patterns. In this application to a Bose-Einstein condensation model, however,
no reentrant phases are found.


  Phase transition and current of planar clusters with loops of Josephson $\pi$
junction is of great importance for application in the adiabatic quantum
computation devices (AQC). Each $\pi$-ring possesses an orbital moment with a
current. The orientation of these orbital moments is altered by
self-interactions and controlled with a bias current. In the current research,
we construct the phase diagram of semi-hydrogenated SiB (H-SiB) semiconductor
using a two-dimensional (2D) Ising model with considering nearest-neighbor and
diagonal interactions of spin planes on the on the hexagonal lattice. Our
findings reveal that by decreasing temperature, two phase transitions of order
and disorder occur and at low temperatures a glassy state appears, where this
model maps to spin qubit. We theoretically study the magnetostriction effect by
considering of laser electromagnetic field coupled to the spin planes of
electric polarization of magnetic insulator for both unstrained and strained
H-SiB monolayers. The dynamic of laser-spin coupling and spin current shows
nonlinear optical effects and high-harmonic generation (HHG) under both
terahertz (THz) and gigahertz (GHz) electromagnetic waves. The findings of this
research open an avenue for experimentalists how to detect HHG in the
topological insulators, Dirac systems, Mott insulators, and superconducting
memories.


  In this paper, we extend the additive average Schwarz method to solve second
order elliptic boundary value problems with heterogeneous coefficients inside
the subdomains and across their interfaces by the mortar technique, where the
mortar finite element discretization is on nonmatching meshes. In this
two-level method, we enrich the coarse space in two different ways, i.e., by
adding eigenfunctions of two variants of the generalized eigenvalue problems.
We prove that the condition numbers of the systems of algebraic equations
resulting from the extended additive average Schwarz method, corresponding to
both coarse spaces, are of the order O(H/h) and independent of jumps in the
coefficients, where H and h are the mesh parameters.


  We prove that the finitistic test ideal $\tau_{\rm fg}(R, \Delta,
\mathfrak{a}^t)$ coincides with the big test ideal $\tau_{\rm b}(R, \Delta,
\mathfrak{a}^t)$ if the pair $(R,\Delta)$ is numerically log
$\mathbb{Q}$-Gorenstein.


  In the present paper we have discussed in detail electromagnetically induced
transparency and signal storing in the case of one signal pulses propagating in
a classical electric medium resembling this of four-level atoms in the tripod
configuration. Our theoretical results confirm recently observed dependence of
transparency windows position on coupling parameters. In the process of storing
the pulse energy is confined inside the metamaterial as electric charge
oscillations and after required time it is possible to switch the control
fields on again and to release the trapped signal. By manipulating the driving
fields one can thus control the parameters of the released signal and even to
divide it on demand into arbitrary parts.


  We discuss experimental effects in the implementation of a recent scheme for
performing bus mediated entangling operations between qubits. Here a bus mode,
a strong coherent state, successively undergoes weak Kerr-type non-linear
interactions with qubits. A quadrature measurement on the bus then projects the
qubits into an entangled state. This approach has the benefit that entangling
gates are non-destructive, may be performed non-locally, and there is no need
for efficient single photon detection. In this paper we examine practical
issues affecting its experimental implementation. In particular, we analyze the
effects of post-selection errors, qubit loss, bus loss, mismatched coupling
rates and mode-mismatch. We derive error models for these effects and relate
them to realistic fault-tolerant thresholds, providing insight into realistic
experimental requirements.


  The Grothendieck construction is a fundamental link between indexed
categories and opfibrations. This work is a detailed study of the Grothendieck
construction over a small tight bipermutative category in the context of
Cat-enriched multicategories, with applications to inverse K-theory and pseudo
symmetric E-infinity-algebras.
  The ordinary Grothendieck construction over a small category C is a
2-equivalence that sends a C-indexed category to an opfibration over C. We show
that the Grothendieck construction over a small tight bipermutative category D
is a pseudo symmetric Cat-multifunctor that is generally not a Cat-multifunctor
in the symmetric sense. When the projection to D is taken into account, we
prove that the Grothendieck construction over D lifts to a non-symmetric
Cat-multiequivalence whose codomain is a non-symmetric Cat-multicategory with
small permutative opfibrations over D as objects.
  As applications we show that inverse K-theory, from Gamma-categories to small
permutative categories, is a pseudo symmetric Cat-multifunctor but not a
Cat-multifunctor in the symmetric sense. It follows that inverse K-theory
preserves algebraic structures parametrized by non-symmetric and pseudo
symmetric Cat-multifunctors but not Cat-multifunctors in general. As a special
case, we observe that inverse K-theory sends pseudo symmetric
E-infinity-algebras in Gamma-categories to pseudo symmetric E-infinity-algebras
in small permutative categories.


  The electron localization tensor, Born effective charges, dielectric
constants and phonon dispersion relations of the skutterudite CoSb$_3$ and the
filled skutterudite TlFeCo$_3$Sb$_{12}$ have been studied using density
functional perturbation theory. The origin of the low energy peak in the phonon
density of states of TlFeCo$_3$Sb$_{12}$ observed recently by Neutron inelastic
scattering [R. P. Hermann {\it et al.}, Phys. Rev. Lett. {\bf 90}, 135505
(2003)] is attributed to the vibrations of Tl that show only weak coupling with
the normal modes of the host crystal. Moreover, the dielectric properties of
these materials show unsual features such as giant Born effective charges and a
strong increase of the optical and static dielectric tensor in the filled
compound.


  The transversity distribution, which describes transversely polarized quarks
in transversely polarized nucleons, is a fundamental component of the spin
structure of the nucleon, and is only loosely constrained by global fits to
existing semi-inclusive deep inelastic scattering (SIDIS) data. In transversely
polarized $p^\uparrow+p$ collisions it can be accessed using transverse
polarization dependent fragmentation functions which give rise to azimuthal
correlations between the polarization of the struck parton and the final state
scalar mesons.
  This letter reports on spin dependent di-hadron correlations measured by the
STAR experiment. The new dataset corresponds to 25 pb$^{-1}$ integrated
luminosity of $p^\uparrow+p$ collisions at $\sqrt{s}=500$ GeV, an increase of
more than a factor of ten compared to our previous measurement at
$\sqrt{s}=200$ GeV. Non-zero asymmetries sensitive to transversity are observed
at a $Q^2$ of several hundred GeV and are found to be consistent with the
former measurement and a model calculation. %we observe consistent with the
former measurement are observed.} We expect that these data will enable an
extraction of transversity with comparable precision to current SIDIS datasets
but at much higher momentum transfers where subleading effects are suppressed.


  We consider massive spin 1 fields, in Riemann-Cartan space-times, described
by Duffin-Kemmer-Petiau theory. We show that this approach induces a coupling
between the spin 1 field and the space-time torsion which breaks the usual
equivalence with the Proca theory, but that such equivalence is preserved in
the context of the Teleparallel Equivalent of General Relativity.


  Local representation learning has been a key challenge to promote the
performance of the histopathological whole slide images analysis. The previous
representation learning methods followed the supervised learning paradigm.
However, manual annotation for large-scale WSIs is time-consuming and
labor-intensive. Hence, the self-supervised contrastive learning has recently
attracted intensive attention. The present contrastive learning methods treat
each sample as a single class, which suffers from class collision problems,
especially in the domain of histopathology image analysis. In this paper, we
proposed a novel contrastive representation learning framework named
Lesion-Aware Contrastive Learning (LACL) for histopathology whole slide image
analysis. We built a lesion queue based on the memory bank structure to store
the representations of different classes of WSIs, which allowed the contrastive
model to selectively define the negative pairs during the training. Moreover,
We designed a queue refinement strategy to purify the representations stored in
the lesion queue. The experimental results demonstrate that LACL achieves the
best performance in histopathology image representation learning on different
datasets, and outperforms state-of-the-art methods under different WSI
classification benchmarks. The code is available at
https://github.com/junl21/lacl.


  We consider undirected graphs that arise as deterministic functions of
stationary point processes such that each point has degree bounded by two. For
a large class of point processes and edge-drawing rules, we show that the
arising graph has no infinite connected component, almost surely. In
particular, this extends our previous result for SINR graphs based on
stabilizing Cox point processes and verifies the conjecture of Balister and
Bollob\'as that the bidirectional $k$-nearest neighbor graph of a
two-dimensional homogeneous Poisson point process does not percolate for $k=2$.


  Aequitas Flow is an open-source framework for end-to-end Fair Machine
Learning (ML) experimentation in Python. This package fills the existing
integration gaps in other Fair ML packages of complete and accessible
experimentation. It provides a pipeline for fairness-aware model training,
hyperparameter optimization, and evaluation, enabling rapid and simple
experiments and result analysis. Aimed at ML practitioners and researchers, the
framework offers implementations of methods, datasets, metrics, and standard
interfaces for these components to improve extensibility. By facilitating the
development of fair ML practices, Aequitas Flow seeks to enhance the adoption
of these concepts in AI technologies.


  We propose a novel integral model describing the motion of curved slender
fibers in viscous flow, and develop a numerical method for simulating dynamics
of rigid fibers. The model is derived from nonlocal slender body theory (SBT),
which approximates flow near the fiber using singular solutions of the Stokes
equations integrated along the fiber centerline. In contrast to other models
based on (singular) SBT, our model yields a smooth integral kernel which
incorporates the (possibly varying) fiber radius naturally. The integral
operator is provably negative definite in a non-physical idealized geometry, as
expected from PDE theory. This is numerically verified in physically relevant
geometries. We propose a convergent numerical method for solving the integral
equation and discuss its convergence and stability. The accuracy of the model
and method is verified against known models for ellipsoids. Finally, a fast
algorithm for computing dynamics of rigid fibers with complex geometries is
developed.


  The anodic release of carbon dioxide gas in the molten salt Hall-Heroult
process can be used to power a turbine for electricity generation. The
application of this new concept in molten salt reprocessing in the nuclear
industry is considered because it could facilitate the suitability of carbon
dioxide cycles to certain types of nuclear reactor. The theoretical power of
27.8 MW generated by a molten salt Hall-Heroult reactor is comparable with a
next-generation biomass plant that sources low-grade wood fuel to generate
renewable heat and power using CHP steam turbine technology.


  We have developed a new type of magnetometer consisting of a Hybrid Quantum
Interference Device (HyQUID) that is set in a bi-stable state. We demonstrate
its operation in a latching mode that can be employed to measure small changes
in the applied flux. The device can be used to probe the flux state of a
superconducting circuit using straightforward electrical resistance
measurements, making it suitable as a simple qubit readout with low
back-action.


  The single phase polycrystalline Ba1/4Sr3/4MnO3 layered perovskite manganite
has been synthesized by combustion method having various crystallite sizes. The
room temperature X-ray diffraction patterns reveal that Ba1/4Sr3/4MnO3
crystallizes into hexagonal crystal structure with space group P63/mmc as
confirmed by Rietveld refinement. The scanning electron micrographs of
Ba1/4Sr3/4MnO3 reveal uniform crystallite size of the samples. Effect of
crystallite size on lattice strain and crystal structure has been studied using
Rietveld refinement and Williamson-Hall plot, respectively. The structural
lattice parameters decrease with increasing crystallite size. However, lattice
strain increases with increasing crystallite-size.


  Monolayer C$_3$N is an emerging two-dimensional indirect band gap
semiconductor with interesting mechanical, thermal, and electronic properties.
In this work we present a description of C$_3$N electronic and dielectric
properties, focusing on the so-called momentum-resolved exciton band structure.
Excitation energies and oscillator strengths are computed in order to
characterize bright and dark states, and discussed also with respect to the
crystal symmetry. Activation of excitonic states is observed for finite
transferred momenta: Indeed, we find an active indirect exciton at $\sim$ 0.9
eV, significantly lower than the direct optical gap of 1.96 eV, with excitonic
binding energies in the range 0.6-0.9 eV for the lowest states. As for other 2D
materials, we find a quasi-linear excitonic dispersion close to $\Gamma$, which
however shows a downward convexity related to the indirect band gap of C$_3$N
as well as to the dark nature of the involved excitons.


  The relation between Einstein gravity and the Chern-Simons gauge theory of
the Poincare' group is discussed at the classical level.


  In this article we prove a general result which in particular suggests that,
on a simply connected domain in C, all the derivatives and anti-derivatives of
the generic holomorphic function are unbounded. A similar result holds for the
operator of partial sums of the Taylor expansion with center z at 0, seen as
functions of the center z. We also discuss a universality result of these
operators.


  We consider the limit behavior of an excited random walk (ERW), i.e., a
random walk whose transition probabilities depend on the number of times the
walk has visited to the current state. We prove that an ERW being naturally
scaled converges in distribution to an excited Brownian motion that satisfies
an SDE, where the drift of the unknown process depends on its local time.
Similar result was obtained by Raimond and Schapira, their proof was based on
the Ray-Knight type theorems. We propose a new method of investigations based
on a study of the Radon-Nikodym density of the ERW distribution with respect to
the distribution of a symmetric random walk.


  Marine plankton are usually modeled as settling elongated micro-swimmers. For
the first time, we consider the torque induced by fluid inertia on such
swimmers, and we discover that they spontaneously swim in the direction
opposite to gravity. We analyze the equilibrium orientation of swimmers in
quiescent fluid and the mean orientation in turbulent flows using direct
numerical simulations. Similar to well-known gyrotaxis mechanisms, the effect
of fluid inertial torque can be quantified by an effective reorientation time
scale. We show that the orientation of swimmers strongly depends on the
reorientation time scale, and swimmers exhibit strong preferential alignment in
upward direction when the time scale is of the same order of Kolmogorov time
scale. Our findings suggest that the fluid inertial torque is a new mechanism
of gyrotaxis that stabilizes the upward orientation of micro-swimmers such as
plankton.


  Purpose: Biophysical tissue models are increasingly used in the
interpretation of diffusion MRI (dMRI) data, with the potential to provide
specific biomarkers of brain microstructural changes. However, the general
Standard Model has recently shown that model parameter estimation from dMRI
data is ill-posed unless very strong magnetic gradients are used. We analyse
this issue for the Neurite Orientation Dispersion and Density Imaging with
Diffusivity Assessment (NODDIDA) model and demonstrate that its extension from
Single Diffusion Encoding (SDE) to Double Diffusion Encoding (DDE) solves the
ill-posedness and increases the accuracy of the parameter estimation. Methods:
We analyse theoretically the cumulant expansion up to fourth order in b of SDE
and DDE signals. Additionally, we perform in silico experiments to compare SDE
and DDE capabilities under similar noise conditions. Results: We prove
analytically that DDE provides invariant information non-accessible from SDE,
which makes the NODDIDA parameter estimation injective. The in silico
experiments show that DDE reduces the bias and mean square error of the
estimation along the whole feasible region of 5D model parameter space.
Conclusions: DDE adds additional information for estimating the model
parameters, unexplored by SDE, which is enough to solve the degeneracy in the
NODDIDA model parameter estimation.


  Systems of coupled cavity modes have the potential to provide bright quantum
optical states of light in a highly versatile manner. Microring resonators for
instance are highly scalable candidates for photon sources thanks to CMOS
fabrication techniques, their small footprint and the relative ease of coupling
many such microrings together, however, surface roughness of the wave-guides,
and defects in the coupler geometry routinely induce splitting of the cavity
modes due to backscattering and backcoupling. The parasitic back-propagating
mode in the microring leads to hybridisation of the modes, altering the linear
and nonlinear properties of this system of coupled cavity modes, and ultimately
constraining the fidelity of quantum light sources that can be produced. In
this paper, we derive a comprehensive general model for Gaussian nonlinear
processes in systems of coupled cavity modes, based on an effective field
Hamiltonian and a dispersive input-output model. The resulting dynamics of the
equations of motion are evaluated in a Gaussian process formalism via the
symplectic transformations on the optical modes. We then use this framework to
numerically model and explore the problem of backscattering in microring
resonators in physically relevant parameter regimes, involving the splitting of
various resonances, we calculate the consequent impurity and heralding
efficiency of various heralded photon schemes, we explore a perturbative
explanation of the observations and assess the correspondence between
spontaneous and stimulated processes in these systems.


  When compiling databases, for example to meet the needs of healthcare
establishments, there is quite a common problem with the introduction and
further processing of names and last names of doctors and patients that are
highly specialized both in terms of pronunciation and writing. This is because
names and last names of people cannot be unique, their notation is not subject
to any rules of phonetics, while their length in different languages may not
match. With the advent of the Internet, this situation has become generally
critical and can lead to that multiple copies of e-mails are sent to one
address. It is possible to solve the specified problem by using phonetic
algorithms for comparing words Daitch-Mokotoff, Soundex, NYSIIS, Polyphone, and
Metaphone, as well as the Levenshtein and Jaro algorithms, Q-gram-based
algorithms, which make it possible to find distances between words. The most
widespread among them are the Soundex and Metaphone algorithms, which are
designed to index the words based on their sound, taking into consideration the
rules of pronunciation. By applying the Metaphone algorithm, an attempt has
been made to optimize the phonetic search processes for tasks of fuzzy
coincidence, for example, at data deduplication in various databases and
registries, in order to reduce the number of errors of incorrect input of last
names. An analysis of the most common last names reveals that some of them are
of the Ukrainian or Russian origin. At the same time, the rules following which
the names are pronounced and written, for example in Ukrainian, differ
radically from basic algorithms for English and differ quite significantly for
the Russian language. That is why a phonetic algorithm should take into
consideration first of all the peculiarities in the formation of Ukrainian last
names, which is of special relevance now.


  Symmetries occur naturally in CSP or SAT problems and are not very difficult
to discover, but using them to prune the search space tends to be very
challenging. Indeed, this usually requires finding specific elements in a group
of symmetries that can be huge, and the problem of their very existence is
NP-hard. We formulate such an existence problem as a constraint problem on one
variable (the symmetry to be used) ranging over a group, and try to find
restrictions that may be solved in polynomial time. By considering a simple
form of constraints (restricted by a cardinality k) and the class of groups
that have the structure of Fp-vector spaces, we propose a partial algorithm
based on linear algebra. This polynomial algorithm always applies when k=p=2,
but may fail otherwise as we prove the problem to be NP-hard for all other
values of k and p. Experiments show that this approach though restricted should
allow for an efficient use of at least some groups of symmetries. We conclude
with a few directions to be explored to efficiently solve this problem on the
general case.


  Radar sensors employed for environment perception, e.g. in autonomous
vehicles, output a lot of unwanted clutter. These points, for which no
corresponding real objects exist, are a major source of errors in following
processing steps like object detection or tracking. We therefore present two
novel neural network setups for identifying clutter. The input data, network
architectures and training configuration are adjusted specifically for this
task. Special attention is paid to the downsampling of point clouds composed of
multiple sensor scans. In an extensive evaluation, the new setups display
substantially better performance than existing approaches. Because there is no
suitable public data set in which clutter is annotated, we design a method to
automatically generate the respective labels. By applying it to existing data
with object annotations and releasing its code, we effectively create the first
freely available radar clutter data set representing real-world driving
scenarios. Code and instructions are accessible at
www.github.com/kopp-j/clutter-ds.


  We fill up a gap in Henn's proof concerning large automorphism groups of
function fields of degree 1 over an algebraically closed field of positive
characteristic.


  We present the first Monte Carlo based global QCD analysis of spin-averaged
and spin-dependent parton distribution functions (PDFs) that includes nucleon
isovector matrix elements in coordinate space from lattice QCD. We investigate
the degree of universality of the extracted PDFs when the lattice and
experimental data are treated under the same conditions within the Bayesian
likelihood analysis. For the unpolarized sector, we find rather weak
constraints from the current lattice data on the phenomenological PDFs, and
difficulties in describing the lattice matrix elements at large spatial
distances. In contrast, for the polarized PDFs we find good agreement between
experiment and lattice data, with the latter providing significant constraints
on the spin-dependent isovector quark and antiquark distributions.


  We present a model for the thermally activated propagation of cracks in
elastic matrices. The propagation is considered as a subcritical phenomenon,
the kinetics of which being described by an Arrhenius law. In this law, we take
the thermal evolution of the crack front into account, assuming that a portion
of the released mechanical energy is transformed into heat in a plastic process
zone. We show that such a model leads to a two-phase crack propagation: a first
phase at low velocity in which the temperature elevation is of little effect
and the propagation is mainly governed by the mechanical load and by the
toughness of the medium, and a second phase in which the crack is thermally
weakened and propagates at greater velocity. Such a dual behavior can
potentially explain the usual stick-slip in brittle fracturing, and we
illustrate how with numerical simulations of mode I cracks propagating in thin
disordered media. In addition, we predict the existence of a limiting ambient
temperature above which the weakened phase ceases to exist and we propose this
critical phenomenon as a novel explanation for the brittle-ductile transition
of solids.


  We propose a platform to realize nodal topological superconductors in a
superconducting monolayer of MoX$_2$ (X$=$S, Se, Te) using an in-plane magnetic
field. The bulk nodal points appear where the spin splitting due to spin-orbit
coupling vanishes near the $\pm \boldsymbol{K}$ valleys of the Brillouin zone,
and are six or twelve per valley in total. In the nodal topological
superconducting phase, the nodal points are connected by flat bands of
zero-energy Andreev edge states. These flat bands, which are protected by
chiral symmetry, are present for all lattice-termination boundaries except
zigzag.


  Data deduplication is the task of detecting records in a database that
correspond to the same real-world entity. Our goal is to develop a procedure
that samples uniformly from the set of entities present in the database in the
presence of duplicates. We accomplish this by a two-stage process. In the first
step, we estimate the frequencies of all the entities in the database. In the
second step, we use rejection sampling to obtain a (approximately) uniform
sample from the set of entities. However, efficiently estimating the frequency
of all the entities is a non-trivial task and not attainable in the general
case. Hence, we consider various natural properties of the data under which
such frequency estimation (and consequently uniform sampling) is possible.
Under each of those assumptions, we provide sampling algorithms and give proofs
of the complexity (both statistical and computational) of our approach. We
complement our study by conducting extensive experiments on both real and
synthetic datasets.


  Gowdy waves, one of the standard 'apples with apples' tests, is proposed as a
test-bed for constraint-preserving boundary conditions in the non-linear
regime. As an illustration, energy-constraint preservation is separately tested
in the Z4 framework. Both algebraic conditions, derived from energy estimates,
and derivative conditions, deduced from the constraint-propagation system, are
considered. The numerical errors at the boundary are of the same order than
those at the interior points.


  A coherent state of many spins contains quantum entanglement which increases
with a decrease in the collective spin value. We present a scheme to engineer
this class of pure state based on incoherent spin pumping with a few collective
raising/lowering operators. In a pumping scenario aimed for maximum
entanglement, the steady-state of N pumped spin qubits realizes the ideal
resource for the 1 to N/2 quantum telecloning. We show how the scheme can be
implemented in a realistic system of atomic spin qubits in optical lattice.
Error analysis show that high fidelity state engineering is possible for N ~
O(100) spins in the presence of decoherence. The scheme can also prepare a
resource state for the secret sharing protocol and for the construction of
large scale Affleck-Kennedy-Lieb-Tasaki (AKLT) state.


  We present, solve and numerically simulate a simple model that describes the
consequences of increased longevity on fertility rates, population growth and
the distribution of wealth in developed societies. We look at the consequences
of the repeated use of life extension techniques and show that they represent a
novel commodity whose introduction will profoundly influence key aspects of
economy and society in general. In particular, we uncover two phases within our
simplified model, labeled as 'mortal' and 'immortal'. Within the life extension
scenario it is possible to have sustainable economic growth in a population of
stable size, as a result of dynamical equilibrium between the two phases.


  One of the most important problems in hybrid systems is the {\em reachability
problem}. The reachability problem has been shown to be undecidable even for a
subclass of {\em linear} hybrid systems. In view of this, the main focus in the
area of hybrid systems has been to find {\em effective} semi-decision
procedures for this problem. Such an algorithmic approach involves finding
methods of computation and representation of reach sets of the continuous
variables within a discrete state of a hybrid system. In this paper, after
presenting a brief introduction to hybrid systems and reachability problem, we
propose a computational method for obtaining the reach sets of continuous
variables in a hybrid system. In addition to this, we also describe a new
algorithm to over-approximate with polyhedra the reach sets of the continuous
variables with linear dynamics and polyhedral initial set. We illustrate these
algorithms with typical interesting examples.


  We investigate magic-angle twisted bilayer graphene (MATBG) with
proximity-induced Ising and Rashba spin-orbit couplings (SOC) in the top layer,
as recently achieved experimentally. Utilizing the Bistritzer-MacDonald model
with SOCs, we reveal a rich single-particle topological phase diagram featuring
topological flat bands across different twist angles and interlayer hopping
energies. The evolution of Dirac cones and Chern numbers is examined to
understand the topological phase transitions. We find that all phases can be
achieved with an experimentally accessible SOC strength ($\sim$1 meV) in
systems with angles very close to the magic angle. Furthermore, the van Hove
singularity for each topological flat band splits in the presence of SOC,
significantly altering the electronic properties. Additionally, we investigate
the spin textures of each band in momentum space, discovering a skyrmion-like
spin texture in the center of the moir\'e Brillouin zone, which is correlated
with the topological phase transitions and can be tuned via the SOCs and an
out-of-plane electric field. Our findings provide a comprehensive understanding
of the topological flat bands, establishing a foundation for grasping the
intrinsic and rich roles of SOCs in MATBG.


  This article extends a recently proposed heterogeneous data assimilation
technique for site characterization to estimate compression and shear wave
velocity (Vp and Vs, respectively) and damping at Treasure Island and Delaney
Park downhole arrays. The adopted method is based on the joint inversion of
earthquake acceleration time series and experimental surface wave dispersion
data, and including physical constraints to improve the inverse problem's
well-posedness. We first use synthetic data at these two sites to refine the
proposed approach and then apply the refined algorithm to real data sets
available at the Treasure Island and Delaney Park downhole arrays. The joint
inversion results show that the estimated Vs and Vp profiles are in very good
agreement with measured profiles at these two sites. Our synthetic and real
data experiment results suggest that Vp estimation from inversion at downhole
arrays can be improved by integrating the water table depth information or the
higher modes of the Rayleigh wave dispersion data. Depending on the site
complexity, water table information can also help reduce uncertainties
associated with damping estimation. In the last part of this article, we
compare the performance of the inverted profiles to other methods used to
incorporate spatial variability and wave scattering effects in 1D ground
response analysis (GRA). The comparisons show that the joint inversion-based Vs
and Vp profiles and damping ratios estimated in this article can effectively
integrate the effects of spatial variability and wave scattering into 1D GRAs,
especially at the Delaney Park downhole array, which is classified as a poorly
modeled site using traditional 1D GRA.


  In a 1999 paper, Bercovici and Pata showed that a natural bijection between
the classically, free and Boolean infinitely divisible measures held at the
level of limit theorems of triangular arrays. This result was extended to
include monotone convolution by the authors. In recent years, operator-valued
versions of free, Boolean and monotone probability have also been developed.
Belinschi, Popa and Vinnikov showed that the Bercovici-Pata bijection holds for
the operator-valued versions of free and Boolean probability. In this article,
we extend the bijection to include monotone probability theory even in the
operator-valued case. To prove this result, we develop the general theory of
composition semigroups of non-commutative functions and largely recapture
Berkson and Porta's classical results on composition semigroups of complex
functions in operator-valued setting. As a biproduct, we deduce that
operator-valued monotonically infinitely divisible distributions belong to
monotone convolution semigroups. Finally, in the appendix, we extend the result
of the second author on the classification of Cauchy transforms for
non-commutative distributions to the Cauchy transforms associated to more
general completely positive maps.


  In many binary classification applications such as disease diagnosis and spam
detection, practitioners often face great needs to control type I errors (i.e.,
the conditional probability of misclassifying a class 0 observation as class 1)
so that it remains below a desired threshold. To address this need, the
Neyman-Pearson (NP) classification paradigm is a natural choice; it minimizes
type II error (i.e., the conditional probability of misclassifying a class 1
observation as class 0) while enforcing an upper bound, $\alpha$, on the type I
error. Although the NP paradigm has a century-long history in hypothesis
testing, it has not been well recognized and implemented in classification
schemes. Common practices that directly limit the empirical type I error to no
more than $\alpha$ do not satisfy the type I error control objective because
the resulting classifiers are still likely to have type I errors much larger
than $\alpha$. As a result, the NP paradigm has not been properly implemented
for many classification scenarios in practice. In this work, we develop the
first umbrella algorithm that implements the NP paradigm for all scoring-type
classification methods, including popular methods such as logistic regression,
support vector machines and random forests. Powered by this umbrella algorithm,
we propose a novel graphical tool for NP classification methods: NP receiver
operating characteristic (NP-ROC) bands, motivated by the popular receiver
operating characteristic (ROC) curves. NP-ROC bands will help choose $\alpha$
in a data adaptive way and compare different NP classifiers. We demonstrate the
use and properties of the NP umbrella algorithm and NP-ROC bands, available in
the R package nproc, through simulation and real data case studies.


  RENO (Reactor Experiment for Neutrino Oscillation) is the reactor neutrino
experiment which has been taking data from August 2011 with two identical near
and far detectors at Hanbit Nuclear Power Plant, Yonggwang, Korea. Using 1,500
live days of data, $\sin^2 2\theta_{13}$ and $|\Delta m^2_{ee}|$ are updated
using spectral measurements: $\sin^2 2\theta_{13} = 0.086 \pm 0.006 ({\rm
stat.}) \pm 0.005 ({\rm syst.})$ and $|\Delta m^2_{ee}| = 2.61+0.15-0.16 ({\rm
stat.}) \pm 0.09 ({\rm syst.}) (\times 10^{-3} {\rm eV^2})$. The 5 MeV excess
dependency on the reactor thermal power rate is again clearly observed with the
increased data set.


  Bit commitment is a fundamental cryptographic primitive in which Bob wishes
to commit a secret bit to Alice. Perfectly secure bit commitment has been
proven impossible through asynchronous exchange of classical and quantum
information. Perfect security is however possible by restraining the exchange
of classical and quantum information to suitably chosen relativistic
constraints. This requires Alice (and Bob) to split into two remote agents
performing space-like separated classical communication, and in one agent
exchanging quantum bits with the other party. The duration of the commitment is
given by the distance between the two remote agents. The original protocol
requires the quantum communication to happen at a precise location and time
with respect to the classical communication. We show how the protocol can be
modified to relax this constraint such that the quantum part of the protocol
can be performed at any time before the actual commitment, making it much more
practical. Finally, we present an experimental demonstration of this protocol
realized with a commercial quantum key distribution system and with
synchronized classical agents located in Geneva and Singapore, yielding a
commitment time of 15 ms. Our work includes a complete security analysis,
accounting for experimental imperfections (multi-photon emission, transmission
loss, detector inefficiency and dark counts) and finite statistics.


  We explore the impact of the Sandage-Loeb (SL) test on the precision of
cosmological constraints for $f(T)$ gravity theories. The SL test is an
important supplement to current cosmological observations because it measures
the redshift drift in the Lyman-$\alpha$ forest in the spectra of distant
quasars, covering the "redshift desert" of $2 \lesssim z \lesssim5$. To avoid
data inconsistency, we use the best-fit models based on current combined
observational data as fiducial models to simulate 30 mock SL test data. We
quantify the impact of these SL test data on parameter estimation for $f(T)$
gravity theories. Two typical $f(T)$ models are considered, the power-law model
$f(T)_{PL}$ and the exponential-form model $f(T)_{EXP}$. The results show that
the SL test can effectively break the existing strong degeneracy between the
present-day matter density $\Omega_m$ and the Hubble constant $H_0$ in other
cosmological observations. For the considered $f(T)$ models, a 30-year
observation of the SL test can improve the constraint precision of $\Omega_m$
and $H_0$ enormously but cannot effectively improve the constraint precision of
the model parameters.


  The large growth of flash ADC techniques for processing signals, especially
in applications of streaming data, raises issues such as data flow through an
acquisition system, long-term storage, and greater complexity in data analysis.
In addition, experiments that push the limits of sensitivity need to
distinguish legitimate signals from noise. The use of correlation coefficients
is examined to address these issues. They are found to be quite successful well
into the noise region. The methods can also be extended to Field Programmable
Gate Array modules for compressing the data flow and greatly enhancing the
event rate capabilities.


  Many biological systems can sense periodical variations in a stimulus input
and produce well-timed, anticipatory responses after the input is removed. Such
systems show memory effects for retaining timing information in the stimulus
and cannot be understood from traditional synchronization consideration of
passive oscillatory systems. To understand this anticipatory phenomena, we
consider oscillators built from excitable systems with the addition of an
adaptive dynamics. With such systems, well-timed post-stimulus responses
similar to those from experiments can be obtained. Furthermore, a well-known
model of working memory is shown to possess similar anticipatory dynamics when
the adaptive mechanism is identified with synaptic facilitation. The last
finding suggests that this type of oscillators can be common in neuronal
systems with plasticity.