  In a molecule formed by two atoms, energy difference between bonding and
antibonding orbitals should depend on distance of the two atoms. However,
exploring molecular orbitals of two natural atoms with tunable distance has
remained an outstanding experimental challenge. Graphene quantum dots (GQDs)
can be viewed as relativistic artificial atoms, therefore, offering a unique
platform to study molecular physics. Here, through scanning tunneling
microscope (STM), we create and directly visualize the formation process of
relativistic artificial molecules based on two coupled GQDs with tunable
distance. Our study indicates that energy difference between the bonding and
antibonding orbitals of the lowest quasibound state increases linearly with
inverse distance of the two GQDs due to the relativistic nature of the
artificial molecule. For quasibound states with higher orbital momenta, the
coupling between these states leads to half-energy spacing of the confined
states because the length of the molecular-like orbit is about twice that of
the atomic-like orbit. Evolution from ring-like whispering-gallery modes in the
artificial atoms to figure-eight orbitals in the artificial molecules is
directly imaged. The ability to resolve the coupling and orbitals of the
relativistic artificial molecule at the nanoscale level yields insights into
the behavior of quantum-relativistic matter.


  We have considered new type of singular beams with fractional topological
charges that were called the optical quarks possessed rather unique properties,
their topological charges being half of the integer order. There are four types
of optical quarks: even and odd with opposite signs of the topological charges.
The sums or difference of the even and odd quarks form the standard vortex (or
non-vortex) beams with the integer order topological charges. All quarks in the
same beam annihilate, the beam vanishes. The analysis of the quark angular
spectra showed that the optical quarks are structurally unstable field forms
under the free-space propagation. We have analyzed their propagation properties
for different types of the beam envelope including the symmetric beam array
with discrete optical quarks. We have discussed the properties of the possible
structurally stable quark forms and medium capable to maintain optical quarks


  It was observed by Tod and later by Dunajski and Tod that the Boyer-Finley
(BF) and the dispersionless Kadomtsev-Petviashvili (dKP) equations possess
solutions whose level surfaces are central quadrics in the space of independent
variables (the so-called central quadric ansatz). It was demonstrated that
generic solutions of this type are described by Painleve equations PIII and
PII, respectively. The aim of our paper is threefold:
  -- Based on the method of hydrodynamic reductions, we classify integrable
models possessing the central quadric ansatz. This leads to the five canonical
forms (including BF and dKP).
  -- Applying the central quadric ansatz to each of the five canonical forms,
we obtain all Painleve equations PI - PVI, with PVI corresponding to the
generic case of our classification.
  -- We argue that solutions coming from the central quadric ansatz constitute
a subclass of two-phase solutions provided by the method of hydrodynamic
reductions.


  There is enormous growth in various fields of research. This development is
accompanied by new problems. To solve these problems efficiently and in an
optimized manner, algorithms are created and described by researchers in the
scientific literature. Scientific algorithms are vital for understanding and
reusing existing work in numerous domains. However, algorithms are generally
challenging to find. Also, the comparison among similar algorithms is difficult
because of the disconnected documentation. Information about algorithms is
mostly present in websites, code comments, and so on. There is an absence of
structured metadata to portray algorithms. As a result, sometimes redundant or
similar algorithms are published, and the researchers build them from scratch
instead of reusing or expanding upon the already existing algorithm. In this
paper, we introduce an approach for automatically developing a knowledge graph
(KG) for algorithmic problems from unstructured data. Because it captures
information more clearly and extensively, an algorithm KG will give additional
context and explainability to the algorithm metadata.


  Let $p$ be a prime number and $E_{p}$ denote the elliptic curve $y^2=x^3+px$.
It is known that for $p$ which is congruent to $1, 9$ modulo $16$, the rank of
$E_{p}$ over $\mathbb{Q}$ is equal to $0, 2$. Under the condition that the
Birch and Swinnerton-Dyer conjecture is true, we give a necessary and
sufficient condition that the rank is $2$ in terms of the constant term of some
polynomial that is defined by a recurrence formula.


  We investigate the effects of stochastic interactions on hydrodynamic
correlation functions using the Schwinger-Keldysh effective field theory. We
identify new "stochastic transport coefficients" that are invisible in the
classical constitutive relations, but nonetheless affect the late-time
behaviour of hydrodynamic correlation functions through loop corrections. These
results indicate that classical transport coefficients do not provide a
universal characterisation of long-distance, late-time correlations even within
the framework of fluctuating hydrodynamics.


  We present recent results from lattice simulations of 2+1 flavors of improved
staggered fermions at zero baryon number density near the high temperature
crossover. Included are new results from simulations of asqtad fermions at Nt =
12 and a nearly physical Goldstone pion mass and from simulations of HISQ
fermions at Nt = 6 and 8. We focus on observables sensitive to chiral symmetry
and confinement. A companion HotQCD talk discusses the effects of
staggered-fermion taste-symmetry breaking on thermodynamic quantities.


  We consider the problem of learning a neural network classifier. Under the
information bottleneck (IB) principle, we associate with this classification
problem a representation learning problem, which we call "IB learning". We show
that IB learning is, in fact, equivalent to a special class of the quantization
problem. The classical results in rate-distortion theory then suggest that IB
learning can benefit from a "vector quantization" approach, namely,
simultaneously learning the representations of multiple input objects. Such an
approach assisted with some variational techniques, result in a novel learning
framework, "Aggregated Learning", for classification with neural network
models. In this framework, several objects are jointly classified by a single
neural network. The effectiveness of this framework is verified through
extensive experiments on standard image recognition and text classification
tasks.


  With the current trend of transforming a centralized power system into a
decentralized one for efficiency, reliability, and environment reasons, the
concept of microgrid that integrates a variety of distributed energy resources
(DERs) on the distribution network is gaining popularity. In this paper, we
investigate the smart charging and parking of plug-in hybrid electric vehicles
(PHEVs) in microgrids with renewable energy sources (RES), such as solar
panels, in grid-connected mode. To address the uncertainties associated with
RES power output and PHEVs charging condition in the microgrid, we propose a
two-stage scenario-based stochastic optimization approach with the objective of
providing a proper scheduling for parking and charging of PHEVs that minimizes
the average total operating cost while maintaining the reliability of the
microgrid. A case study is conducted to show the effectiveness of the proposed
approach. Extensive simulation results show that the microgrid can minimize the
operating cost and ensure its reliability.


  We introduce a new numerical algorithm for solving the stochastic neural
field equation (NFE) with delays. Using this algorithm we have obtained some
numerical results which illustrate the effect of noise in the dynamical
behaviour of stationary solutions of the NFE, in the presence of spatially
heterogeneous external inputs.


  The electroweak production and subsequent decay of single top quarks in the
$t$-channel is determined by the properties of the $Wtb$ vertex, which can be
described by the complex parameters of an effective Lagrangian. An analysis of
a triple-differential decay rate in $t$-channel production is used to
simultaneously determine five generalised helicity fractions and phases, as
well as the polarisation of the produced top quark. The complex parameters are
then constrained. This analysis is based on 20.2 fb$^{-1}$ of proton-proton
collision data at a centre-of-mass energy of 8 TeV collected with the ATLAS
detector at the LHC. The fraction of decays containing transversely polarised
$W$ bosons is measured to be $f_1=0.30 \pm 0.05$. The phase between amplitudes
for transversely and longitudinally polarised $W$ bosons recoiling against
left-handed $b$-quarks, is measured to be $\delta_- =
0.002\pi^{+0.016\pi}_{-0.017\pi}$, giving no indication of CP violation. The
fraction of longitudinal or transverse $W$ bosons accompanied by right-handed
$b$-quarks are also constrained. Based on these measurements, limits are placed
at 95% C.L. on the ratio of the complex coupling parameters
Re$[g_\mathrm{R}/V_\mathrm{L}] \in [-0.12,0.17]$ and
Im$[g_\mathrm{R}/V_\mathrm{L}] \in [-0.07,0.06]$. Constraints are also placed
on the ratios $|V_\mathrm{R}/V_\mathrm{L}|$ and $|g_\mathrm{L}/V_\mathrm{L}|$.
In addition, the polarisation of single top quarks in the $t$-channel is
constrained to be $P > 0.72$ (95% C.L.). None of the above measurements make
assumptions on the value of any of the other parameters or couplings and all of
them are in agreement with the Standard Model.


  Certain topologies on Milnor K-groups of higher local fields K are studied.
These are related to the topology on the multiplicative group and important for
explicit higher local class field theory. The structure of the quotient of
Milnor K-groups modulo the intersection of all neighbourhoods of zero is
described.


  Plankton are effective indicators of environmental change and ecosystem
health in freshwater habitats, but collection of plankton data using manual
microscopic methods is extremely labor-intensive and expensive. Automated
plankton imaging offers a promising way forward to monitor plankton communities
with high frequency and accuracy in real-time. Yet, manual annotation of
millions of images proposes a serious challenge to taxonomists. Deep learning
classifiers have been successfully applied in various fields and provided
encouraging results when used to categorize marine plankton images. Here, we
present a set of deep learning models developed for the identification of lake
plankton, and study several strategies to obtain optimal performances,which
lead to operational prescriptions for users. To this aim, we annotated into 35
classes over 17900 images of zooplankton and large phytoplankton colonies,
detected in Lake Greifensee (Switzerland) with the Dual Scripps Plankton
Camera. Our best models were based on transfer learning and ensembling, which
classified plankton images with 98% accuracy and 93% F1 score. When tested on
freely available plankton datasets produced by other automated imaging tools
(ZooScan, FlowCytobot and ISIIS), our models performed better than previously
used models. Our annotated data, code and classification models are freely
available online.


  We study the inverse problem of recovering the order and the diffusion
coefficient of an elliptic fractional partial differential equation from a
finite number of noisy observations of the solution. We work in a Bayesian
framework and show conditions under which the posterior distribution is given
by a change of measure from the prior. Moreover, we show well-posedness of the
inverse problem, in the sense that small perturbations of the observed solution
lead to small Hellinger perturbations of the associated posterior measures. We
thus provide a mathematical foundation to the Bayesian learning of the order
---and other inputs--- of fractional models.


  Our knowledge on the possible existence in nature of stable exotic particles
depends solely upon experimental observation. Guided by this general principle
and motivated by theoretical hypotheses on the existence of stable particles of
strange quark matter, a variety of experimental searches have been performed.
We provide an introduction to the theoretical hypotheses, an overview of the
past searches, and a more detailed description of a recent search for
helium-like strangelets in the Earth's atmosphere using a sensitive laser
spectroscopy method.


  We introduce the multivariate decomposition finite element method for
elliptic PDEs with lognormal diffusion coefficient $a=\exp(Z)$ where $Z$ is a
Gaussian random field defined by an infinite series expansion
$Z(\boldsymbol{y}) = \sum_{j\ge1} y_j\,\phi_j$ with $y_j\sim\mathcal{N}(0,1)$
and a given sequence of functions $\{\phi_j\}_{j\ge1}$. We use the MDFEM to
approximate the expected value of a linear functional of the solution of the
PDE which is an infinite-dimensional integral over the parameter space. The
proposed algorithm uses the multivariate decomposition method (MDM) to compute
the infinite-dimensional integral by a decomposition into finite-dimensional
integrals, which we resolve using quasi-Monte Carlo (QMC) methods, and for
which we use the finite element method (FEM) to solve different instances of
the PDE.
  We develop higher-order quasi-Monte Carlo rules for integration over the
finite-dimensional Euclidean space with respect to the Gaussian distribution by
use of a truncation strategy. By linear transformations of interlaced
polynomial lattice rules from the unit cube to a multivariate box of the
Euclidean space we achieve higher-order convergence rates for functions
belonging to a class of anchored Gaussian Sobolev spaces, taking into account
the truncation error.
  Under appropriate conditions, the MDFEM achieves higher-order convergence
rates in term of error versus cost, i.e., to achieve an accuracy of
$O(\epsilon)$ the computational cost is $O(\epsilon^{-1/\lambda-d'/\lambda}) =
O(\epsilon^{-(p^*+d'/\tau)/(1-p^*)})$ where $\epsilon^{-1/\lambda}$ and
$\epsilon^{-d'/\lambda}$ are respectively the cost of the quasi-Monte Carlo
cubature and the finite element approximations, with $d' = d \, (1+\delta')$
for some $\delta' \ge 0$ and $d$ the physical dimension, and $0 < p^* \le
(2+d'/\tau)^{-1}$ is a parameter representing the sparsity of
$\{\phi_j\}_{j\ge1}$.


  Aharonov-Bohm effect is a quantum mechanical phenomenon that attracted the
attention of many physicists and mathematicians since the publication of the
seminal paper of Aharonov and Bohm [1] in 1959.
  We consider different types of Aharonov-Bohm effect such as magnetic AB
effect, electric AB effect, combined electromagnetic AB effect, AB effect for
the Schr\"odinger equations with Yang-Mills potentials, and the gravitational
analog of AB effect.
  We shall describe different approaches to prove the AB effect based on the
inverse scattering problems, the inverse boundary value problems in the
presence of obstacles, spectral asymptotics, and the direct proofs of the AB
effect.


  We consider scalar-Gauss-Bonnet and modified Gauss-Bonnet gravities and
reconstruct these theories from the universe expansion history. In particular,
we are able to construct versions of those theories (with and without ordinary
matter), in which the matter dominated era makes a transition to the cosmic
acceleration epoch. It is remarkable that, in several of the cases under
consideration, matter dominance and the deceleration-acceleration transition
occur in the presence of matter only. The late-time acceleration epoch is
described asymptotically by de Sitter space but may also correspond to an exact
$\Lambda$CDM cosmology, having in both cases an effective equation of state
parameter $w$ close to -1. The one-loop effective action of modified
Gauss-Bonnet gravity on the de Sitter background is evaluated and it is used to
derive stability criteria for the ensuing de Sitter universe.


  Self-supervised representation learning methods aim to provide powerful deep
feature learning without the requirement of large annotated datasets, thus
alleviating the annotation bottleneck that is one of the main barriers to
practical deployment of deep learning today. These methods have advanced
rapidly in recent years, with their efficacy approaching and sometimes
surpassing fully supervised pre-training alternatives across a variety of data
modalities including image, video, sound, text and graphs. This article
introduces this vibrant area including key concepts, the four main families of
approach and associated state of the art, and how self-supervised methods are
applied to diverse modalities of data. We further discuss practical
considerations including workflows, representation transferability, and compute
cost. Finally, we survey the major open challenges in the field that provide
fertile ground for future work.


  Let G be a reductive algebraic group over the complex field and O_h be a
closed adjoint orbit through a semisimple element h. By a result of Borho and
Kraft (1979), it is known that the asymptotic cone of the orbit O_h is the
closure of a Richardson nilpotent orbit corresponding to a parabolic subgroup
whose Levi component is the centralizer Z_G(h) in G.
  In this paper, we prove an analogue on a semisimple orbit for a symmetric
pair (G, K).


  In connection with recent and proposed experiments, and new theoretical
results, my previous calculations of the Lamb shift in muonic hydrogen will be
reviewed and compared with other work. In addition, numerical results for
muonic deuterium and helium will be presented. Some previously neglected (but
very small) effects are included.


  This paper presents the analysis and a method to design supplementary damping
controllers (SDCs) for synchronous generators considering the effects of
saturation limits. Usually such saturations of control signals are imposed in
order to enforce practical limitations such as component ratings. However, to
guarantee the stability in the presence of saturation limits, the state
trajectories must remain inside the domain of attraction (DA). In this paper,
the domain of attraction of a single-machine infinite-bus (SMIB) power system
with saturation nonlinearity is estimated and compared with the exact
description of the null controllable region. Then, state-feedback controllers
are designed to enlarge the DA. Our analysis shows that nonlinear effects of
saturation should be considered to guarantee stability and satisfactory
performance. Simulation results on a detailed nonlinear model of a synchronous
generator indicate that the DA enlarges with the proposed controller. The
results also indicate that Critical Clearing Time (CCT) and damping of the
system with saturation can be improved by the proposed method.


  Context: Solar-like protostars are known to be chemically rich, but it is not
yet clear how much their chemical composition can vary and why. So far, two
chemically distinct types of Solar-like protostars have been identified: hot
corinos, which are enriched in interstellar Complex Organic Molecules (iCOMs),
such as methanol (CH$_3$OH) or dimethyl ether (CH$_3$OCH$_3$), and Warm Carbon
Chain Chemistry (WCCC) objects, which are enriched in carbon chain molecules,
such as butadiynyl (C$_4$H) or ethynyl radical (CCH). However, none of these
have been studied so far in environments similar to that in which our Sun was
born, that is, one that is close to massive stars. Aims: In this work, we
search for hot corinos and WCCC objects in the closest analogue to the Sun's
birth environment, the Orion Molecular Cloud 2/3 (OMC-2/3) filament located in
the Orion A molecular cloud. Methods: We obtained single-dish observations of
CCH and CH$_3$OH line emission towards nine Solar-like protostars in this
region. As in other, similar studies of late, we used the [CCH]/[CH$_3$OH]
abundance ratio in order to determine the chemical nature of our protostar
sample. Results: Unexpectedly, we found that the observed methanol and ethynyl
radical emission (over a few thousands au scale) does not seem to originate
from the protostars but rather from the parental cloud and its
photo-dissociation region, illuminated by the OB stars of the region.
Conclusions: Our results strongly suggest that caution should be taken before
using [CCH]/[CH$_3$OH] from single-dish observations as an indicator of the
protostellar chemical nature and that there is a need for other tracers or high
angular resolution observations for probing the inner protostellar layers.


  This paper presents intuitive interpretations of tightly focused beams of
light by drawing analogies to two-dimensional electrostatics, magnetostatics
and fluid dynamics. We use a Helmholtz decomposition of the transverse
polarization components in the transverse plane to introduce generalized radial
and azimuthal polarization states. This reveals the interplay between
transverse and longitudinal polarization components in a transparent fashion.
Our approach yields a comprehensive understanding of tightly focused laser
beams, which we illustrate through several insightful examples.


  A novel algebraic method for finding invariant algebraic curves for a
polynomial vector field in $\mathbb{C}^2$ is introduced. The structure of
irreducible invariant algebraic curves for Li\'{e}nard dynamical systems
$x_t=y$, $y_t=-g(x)y-f(x)$ with $\text{deg} f=\text{deg} g+1$ is obtained. It
is shown that there exist Li\'{e}nard systems that possess more complicated
invariant algebraic curves than it was supposed before.
  As an example, all irreducible invariant algebraic curves for the Li\'{e}nard
differential system with $\text{deg} f=3$, $\text{deg} g=2$ are obtained. All
these results seem to be new.


  The unique global strong solution in the Chemin-Lerner type space to the
Cauchy problem on the Boltzmann equation for hard potentials is constructed in
perturbation framework. Such solution space is of critical regularity with
respect to spatial variable, and it can capture the intrinsic property of the
Botlzmann equation. For the proof of global well-posedness, we develop some new
estimates on the nonlinear collision term through the Littlewood-Paley theory.


  The state-of-the-art pre-trained language representation models, such as
Bidirectional Encoder Representations from Transformers (BERT), rarely
incorporate commonsense knowledge or other knowledge explicitly. We propose a
pre-training approach for incorporating commonsense knowledge into language
representation models. We construct a commonsense-related multi-choice question
answering dataset for pre-training a neural language representation model. The
dataset is created automatically by our proposed "align, mask, and select"
(AMS) method. We also investigate different pre-training tasks. Experimental
results demonstrate that pre-training models using the proposed approach
followed by fine-tuning achieve significant improvements over previous
state-of-the-art models on two commonsense-related benchmarks, including
CommonsenseQA and Winograd Schema Challenge. We also observe that fine-tuned
models after the proposed pre-training approach maintain comparable performance
on other NLP tasks, such as sentence classification and natural language
inference tasks, compared to the original BERT models. These results verify
that the proposed approach, while significantly improving commonsense-related
NLP tasks, does not degrade the general language representation capabilities.


  This paper presents an experimental and theoretical study of the distribution
of carbon atoms in the octahedral interstitial sites of the face-centered cubic
(fcc) phase of the iron-carbon system. The experimental part of the work
consists of Mossbauer measurements in Fe-C alloys with up to about 12 atomic
percent C, which are interpreted in terms of two alternative models for the
distribution of C atoms in the interstitial sites. The theoretical part
combines an analysis of the chemical potential of C based on the quasichemical
approximation to the statistical mechanics of interstitial solutions, with
three-dimensional Monte Carlo simulations. The latter were performed by
assuming a gas like mixture of C atoms and vacancies (Va) in the octahedral
interstitial sites. The number of C-C, C-Va and Va-Va pairs calculated using
Monte Carlo simulations are compared with those given by the quasichemical
model. Furthermore, the relative fraction of the various Fe environments were
calculated and compared with those extracted from the Mossbauer spectra. The
simulations reproduce remarkably well the relative fractions obtained assuming
the Fe(8)C(1-y) model for Mossbauer spectra, which includes some blocking of
the nearest neighbour interstitial sites by a C atom. With the new experimental
and theoretical information obtained in the present study, a critical
discussion is reported of the extent to which such blocking effect is accounted
for in current thermodynamic models of the Fe-C fcc phase.
  Abstract PACS Codes: 2.70.Uu, 76.


  In this paper we obtain parametric as well as numerical solutions of the
sextic diophantine chain $
\phi(x_1,\,y_1,\,z_1)=\phi(x_2,\,y_2,\,z_2)=\phi(x_3,\,y_3,\,z_3)=k$ where
$\phi(x,\,y,\,z)$ is a sextic form defined by $\phi(x,\,y,\,z)$
$=x^6+y^6+z^6-2x^3y^3-2x^3z^3-2y^3z^3$ and $k$ is an integer. Each numerical
solution of such a sextic chain yields, in general, nine rational points on the
Mordell curve $y^2=x^3+k/4$. While all of these nine points are not independent
in the group of rational points of the Mordell curve, we have constructed a
parameterized family of Mordell curves of generic rank $\geq 6$ using the
aforementioned parametric solution of the sextic diophantine chain. Similarly,
the numerical solutions of the sextic chain yield additional examples of
Mordell curves whose rank is $\geq 6$.


  This is a compact review of recent results on supersymmetric Wilson loops in
ABJ(M) and related theories. It aims to be a quick introduction to the state of
the art in the field and a discussion of open problems. It is divided into
short chapters devoted to different questions and techniques. Some new results,
perspectives and speculations are also presented. We hope this might serve as a
baseline for further studies of this topic.


  It is quite common for security testing to be delayed until after the
software has been developed, but vulnerabilities may get noticed throughout the
implementation phase and the earlier they are discovered, the easier and
cheaper it will be to fix them. Software development processes such as the
secure software development lifecycle incorporates security at every stage of
the design and development process. Static code scanning tools find
vulnerabilities in code by highlighting potential security flaws and offer
examples on how to resolve them, and some may even modify the code to remove
the susceptibility. This paper compares static analysis tools for Java and
C/C++ source code, and explores their pros and cons.


  In this paper we show that if a path structure has non-vanishing curvature at
apoint then it has a canonical reduction to a Z/2Z-structure at a neighbourhood
of thatpoint (in many cases it has a canonical parallelism). A simple
implication of this resultis that the automorphism group of a non-flat path
structure is of maximal dimensionthree (a result by Tresse of 1896). We also
classify the invariant path structures onthree-dimensional Lie groups.


  Measurements of ep scattering with squared 4-momentum transfer Q^2 up to
35000 GeV^2 are compared with the expectation of the standard deep-inelastic
model of lepton-nucleon scattering (DIS). For Q^2 > 15000 GeV^2, N_{obs} =12
neutral current candidate events are observed where the expectation is N_DIS =
4.71 \pm 0.76 events. In the same Q^2 range, N_{obs} =4 charged current
candidates are observed where the expectation is N_{DIS} = 1.77 \pm 0.87
events. The probability P(N \geq N_{obs}) that the DIS model signal N
fluctuates to N \geq N_{obs} in a random set of experiments is 6 10^{-3} for
neutral current and 0.14 for charged current. The difference in the observed
and expected number of Neutral Current events is mostly due to events at large
masses M = sqrt{xs} in which the positron is backscattered at large y =
Q^2/M^2.


  We have performed a search among low mass red giants for finding evidence for
merger scenario for triggering He-flash and subsequent Li enhancement. We chose
a sample of red giants from GALAH survey with well-measured Li abundances, and
near and mid-IR fluxes from 2MASS and WISE surveys, respectively. The sample
contains 418 cool red clump giants and 359 upper red giant branch giants. Most
of the giants and majority of super Li-rich giants show no IR excess. Only five
red clump giants and one RGB giant show IR excess. Notably, of the five red
clump giants with IR excess, three are super Li-rich (A(Li) > = 3.2 dex), and
two are Li-rich (A(Li) > = 1.0 dex). Results suggest Li enhancement among red
clump giants may be due to two channels: one resulting from in-situ He-flash in
single star evolution and the other due to He-flash triggered by events like
merger of He-white dwarfs with giants He-inert core on RGB. In the latter case,
IR excess, as a result of mass loss, is expected from merger events. We have
modelled IR excess in all six giants using DUSTY code and derived dust
parameters. The estimated kinematic ages and time scales of dust envelopes of
the super Li-rich phase suggest Li enhancement took place very recently.
Further, the analysis shows a significantly higher proportion (four out of five
red clump giants) of rapid rotators (vsini > = 8 km/s) among Li-rich giants
with IR excess compared to Li-normal and Li-rich giants with no IR excess.


  Using state-of-the-art first-principles calculations we study the properties
of the ferromagnetic Heusler compounds NiYSi where Y stands for V, Cr or Mn.
NiCrSi and NiMnSi contrary to NiVSi are half-metallic at their equilibrium
lattice constant exhibiting integer values of the total spin magnetic moment
and thus we concentrate on these two alloys. The minority-spin gap has the same
characteristics as for the well-known NiMnSb alloy being around $\sim$1 eV.
Upon tetragonalization the gap is present in the density of states even for
expansion or contraction of the out-of-plane lattice parameter by 5%. The Cr-Cr
and Mn-Mn interactions make ferromagnetism extremely stable and the Curie
temperature exceeds 1000 K for NiMnSi. Surface and interfaces with GaP, ZnS and
Si semiconductors are not half-metallic but in the case of NiCrSi the Ni-based
contacts present spin-polarization at the Fermi level over 90%. Finally, we
show that there are two cases of defects and atomic-swaps. The first-ones which
involve the Cr(Mn) and Si atoms induce states at the edges of the gap which
persists for a moderate-concentration of defects. Defects involving Ni atoms
induce states localized within the gap completely destroying the
half-metallicity. Based on single-impurity calculations we associate these
states to the symmetry of the crystal.


  We introduce the notion of p*-values (p*-variables), which generalizes
p-values (p-variables) in several senses. The new notion has four natural
interpretations: operational, probabilistic, Bayesian, and frequentist. A main
example of a p*-value is a mid p-value, which arises in the presence of
discrete test statistics. A unified stochastic representation for p-values, mid
p-values, and p*-values is obtained to illustrate the relationship between the
three objects. We study several ways of merging arbitrarily dependent or
independent p*-values into one p-value or p*-value. Admissible calibrators of
p*-values to and from p-values and e-values are obtained with nice mathematical
forms, revealing the role of p*-values as a bridge between p-values and
e-values. The notion of p*-values becomes useful in many situations even if one
is only interested in p-values, mid p-values, or e-values. In particular,
deterministic tests based on p*-values can be applied to improve some classic
methods for p-values and e-values.


  A theoretical analysis of the internal structure of interphase boundaries
separating domains of coexisting phases are presented for the perovskite
ferroelectric BaTiO3. The temperature dependence of interphase boundary widths
and surface energies are calculated and compared with the corresponding
parameters for different types of domain walls existing within the
ferroelectric phases of BaTiO3.


  Positron emission tomography (PET) is a medical imaging method based on the
measurement of concentrations of positron-emitting radionuclides in a living
body. In the PET imaging system, glucose is labeled with a positron-emitting
radionuclide and injected intravenously. Then, the positrons move through the
tissue and collide with the electrons of the cells in which they interact. As a
result of this interaction, two gamma rays are emitted in the opposite
direction. Gama rays emitted from cancerous tissue that has retained
radioactive glucose are detected through ring-shaped detectors. And the
detected signals are converted into an electrical response. Subsequently, these
responses are sampled with electronic circuits and recorded as histogram matrix
to generate the image set. The gamma rays may not reach the detectors located
in the opposite position in equal time. In PETs having TOF characteristics, it
is aimed to obtain better positioning information by a method based on the
principle of measuring the difference between the reach time of the two photons
to detectors. The measurement of the flight time is carried out with TDC
structures. The measurement of this time difference at the ps level is directly
related to the spatial resolution of the PET system. In this study, 45 nm CMOS
VLSI simulations of TDC structures that have various architectural approaches
were performed for use in PET systems. With the designed TDC architectures, two
gamma photons time reach to detectors have been simulated and the time
difference has been successfully digitized. In addition, various performance
metrics such as input and output voltages, time resolutions, measurement
ranges, and power analysis of TDC architectures have been determined. Proposed
Vernier oscillator-based TDC architecture has been reached 25 ps time
resolution with a low power consumption of 1.62681 mW at 1V supply voltage.


  We investigate the desiccation crack patterns on the surface of a drying
paste made of calcium carbonate (CaCO$_3$) powder and distilled water. Forced
vibration of the CaCO$_3$ paste prior to drying results in an anisotropic crack
pattern, in which many long cracks develop along a specific preferred
direction. We reveal that the preferred direction changes from perpendicular to
parallel to the vibration direction at the threshold velocity of vibration. The
transition is attributed to the reorientation of constituent particles
subjected to the forced oscillatory flow of fluid in the paste.


  The giant collective modes in asymmetric nuclear matter are investigated
within a dynamic relaxation time approximation. We derive a coupled dispersion
relation and show that two sources of coupling appear: (i) a coupling of
isoscalar and isovector modes due to different mean-fields acting and (ii) an
explicit new coupling in asymmetric matter due to collisional interaction. We
show that the latter one is responsible for a new mode arising besides
isovector and isoscalar modes.


  In this paper it is shown that in non-minimally coupled Brans-Dicke theory
containing a self-interacting potential, a suitable conformal transformation
can automatically give rise to an interaction between the normal matter and the
Brans-Dicke scalar field. Considering the scalar field in the Einstein frame as
the quintessence matter, it has been shown that such a non-minimal coupling
between the matter and the scalar field can give rise to a late time
accelerated expansion for the universe preceded by a decelerated expansion for
very high values of the Brans-Dicke parameter $\omega$. We have also studied
the observational constraints on the model parameters considering the Hubble
and Supernova data.


  Shortly after it was first introduced in 2006, differential privacy became
the flagship data privacy definition. Since then, numerous variants and
extensions were proposed to adapt it to different scenarios and attacker
models. In this work, we propose a systematic taxonomy of these variants and
extensions. We list all data privacy definitions based on differential privacy,
and partition them into seven categories, depending on which aspect of the
original definition is modified.
  These categories act like dimensions: variants from the same category cannot
be combined, but variants from different categories can be combined to form new
definitions. We also establish a partial ordering of relative strength between
these notions by summarizing existing results. Furthermore, we list which of
these definitions satisfy some desirable properties, like composition,
post-processing, and convexity by either providing a novel proof or collecting
existing ones.


  We have studied quantum coherent oscillations of two qubits under continuous
measurement by a symmetrically coupled mesoscopic detector. The analysis is
based on a Bayesian formalism that is applicable to individual quantum systems.
Measurement continuously collapses the two-qubit system to one of the
sub-spaces of the Bell basis. For a detector with linear response this
corresponds to measurement of the total spin of the qubits. In the other
extreme of purely quadratic response the operator \sigma_y^1 \sigma_y^2 +
\sigma_z^1 \sigma_z^2 is measured. In both cases, collapse naturally leads to
spontaneous entanglement which can be identified by measurement of the power
spectrum and/or the average current of the detector. Asymmetry between the two
qubits results in evolution between the different measurement subspaces.
However, when the qubits are even weakly coupled to the detector, a kind of
quantum Zeno effect cancels the gradual evolution and replaces it with rare,
abrupt switching events. We obtain the asymptotic switching rates for these
events and confirm them with numerical simulations. We show how such switching
affects the observable power spectrum on different time scales.


  In egocentric action recognition a single population model is typically
trained and subsequently embodied on a head-mounted device, such as an
augmented reality headset. While this model remains static for new users and
environments, we introduce an adaptive paradigm of two phases, where after
pretraining a population model, the model adapts on-device and online to the
user's experience. This setting is highly challenging due to the change from
population to user domain and the distribution shifts in the user's data
stream. Coping with the latter in-stream distribution shifts is the focus of
continual learning, where progress has been rooted in controlled benchmarks but
challenges faced in real-world applications often remain unaddressed. We
introduce EgoAdapt, a benchmark for real-world egocentric action recognition
that facilitates our two-phased adaptive paradigm, and real-world challenges
naturally occur in the egocentric video streams from Ego4d, such as long-tailed
action distributions and large-scale classification over 2740 actions. We
introduce an evaluation framework that directly exploits the user's data stream
with new metrics to measure the adaptation gain over the population model,
online generalization, and hindsight performance. In contrast to single-stream
evaluation in existing works, our framework proposes a meta-evaluation that
aggregates the results from 50 independent user streams. We provide an
extensive empirical study for finetuning and experience replay.


  Gradient clipping is a popular modification to standard (stochastic) gradient
descent, at every iteration limiting the gradient norm to a certain value $c
>0$. It is widely used for example for stabilizing the training of deep
learning models (Goodfellow et al., 2016), or for enforcing differential
privacy (Abadi et al., 2016). Despite popularity and simplicity of the clipping
mechanism, its convergence guarantees often require specific values of $c$ and
strong noise assumptions.
  In this paper, we give convergence guarantees that show precise dependence on
arbitrary clipping thresholds $c$ and show that our guarantees are tight with
both deterministic and stochastic gradients. In particular, we show that (i)
for deterministic gradient descent, the clipping threshold only affects the
higher-order terms of convergence, (ii) in the stochastic setting convergence
to the true optimum cannot be guaranteed under the standard noise assumption,
even under arbitrary small step-sizes. We give matching upper and lower bounds
for convergence of the gradient norm when running clipped SGD, and illustrate
these results with experiments.


  The virtualization of wireless networks enables new services to access
network resources made available by the Network Operator (NO) through a Network
Slicing market. The different service providers (SPs) have the opportunity to
lease the network resources from the NO to constitute slices that address the
demand of their specific network service. The goal of any SP is to maximize its
service utility and minimize costs from leasing resources while facing
uncertainties of the prices of the resources and the users' demand. In this
paper, we propose a solution that allows the SP to decide its online
reservation policy, which aims to maximize its service utility and minimize its
cost of reservation simultaneously. We design the Optimistic Online Learning
for Reservation (OOLR) solution, a decision algorithm built upon the
Follow-the-Regularized Leader (FTRL), that incorporates key predictions to
assist the decision-making process. Our solution achieves a
$\mathcal{O}(\sqrt{T})$ regret bound where $T$ represents the horizon. We
integrate a prediction model into the OOLR solution and we demonstrate through
numerical results the efficacy of the combined models' solution against the
FTRL baseline.


  The time-dependent transverse response of stiff polymers, represented as
weakly-bending wormlike chains (WLCs), is well-understood on the linear level,
where transverse degrees of freedom evolve independently from the longitudinal
ones. We show that, beyond a characteristic time scale, the nonlinear coupling
of transverse and longitudinal motion in an inextensible WLC significantly
weakens the polymer response compared to the widely used linear response
predictions. The corresponding feedback mechanism is rationalized by scaling
arguments and quantified by a multiple scale approach that exploits an inherent
separation of transverse and longitudinal correlation length scales. Crossover
scaling laws and exact analytical and numerical solutions for characteristic
response quantities are derived for different experimentally relevant setups.
Our findings are applicable to cytoskeletal filaments as well as DNA under
tension.


  I investigate non-Gaussian signatures in the context of tachyacoustic
cosmology, that is, a noninflationary model with superluminal speed of sound. I
calculate the full non-Gaussian amplitude $\mathcal{A}$, its size $f_{\rm NL}$,
and corresponding shapes for a red-tilted spectrum of primordial scalar
perturbations. Specifically, for cuscuton-like models I show that $f_{\rm
NL}\sim {\cal O}(1)$, and the shape of its non-Gaussian amplitude peaks for
both equilateral and local configurations, the latter being dominant. These
results, albeit similar, are quantitatively distinct from the corresponding
ones obtained by Magueijo {\it{et. al}} in the context of superluminal bimetric
models.


  Chernov-Nemirovski observed that the existence of a globally hyperbolic
Lorentzian metric on a (3 + 1)-spacetime pins down a smooth structure on the
underlying 4-manifold. In this paper, we point out that the diffeomorphism type
of a globally hyperbolic (n + 1)-spacetime is determined by the h-cobordism
class of its Cauchy surface, hence extending Chernov-Nemirovski's observation
to arbitrary dimensions.


  With the introduction of various hardware/software technologies such as Cloud
Technologies or Virtualization technologies, there has been a great potential
to reuse ICT artifacts thanks to Abstraction and also Exchangeability features
achieved via these technologies. These technologies also provide various
advantages with respect to sustainability including resource consumption
reduction (in the use phase only or in the whole life cycle). However, there is
an additional but untapped potential associated with the anonymization of
resources introduced by both abstraction and exchangeability features. By
realizing on this potential, we can improve cloud solutions and reduce their
by-product opacity, which usually prevents leveraging on the specialized but
tweakable (i.e., nonessential modifications without changing the main function)
features of components that are captured in the component models. This is
especially a challenge in the case heterogeneous/disaggregated infrastructure
where developing models to cover everything is practically impossible. In this
work, by leveraging on the concept of pathways, we develop a few mechanisms
that enable transparency and therefore tweakability of features even in the
presence of abstraction and heterogeneity. In particular, the layered-stack
approach to system decomposition is considered because of its role in both
software defined networking (SDN) and Network Function Virtualization (NFV)
system decompositions. For a concrete example, the case of dynamic frequency
scaling of processors is considered and it is shown that the associated
consumption could be considerably reduced without requiring additional changes
to the middle components.


  Exactly solvable rationally-extended radial oscillator potentials, whose
wavefunctions can be expressed in terms of Laguerre-type exceptional orthogonal
polynomials, are constructed in the framework of $k$th-order supersymmetric
quantum mechanics, with special emphasis on $k=2$. It is shown that for
$\mu=1$, 2, and 3, there exist exactly $\mu$ distinct potentials of $\mu$th
type and associated families of exceptional orthogonal polynomials, where $\mu$
denotes the degree of the polynomial $g_{\mu}$ arising in the denominator of
the potentials.


  We demonstrate a novel method to measure the temporal evolution of electric
fields with optical frequencies. Our technique is based on the detection of
transient currents in air plasma. These directional currents result from
sub-cycle ionization of air with a short pump pulse, and the steering of the
released electrons with the pulse to be sampled. We assess the validity of our
approach by comparing it with different state-of-the-art laser-pulse
characterization techniques. Notably, our method works in ambient air and
facilitates a direct measurement of the field waveform, which can be viewed in
real time on an oscilloscope in the exact same way as a radio frequency signal.


  We study the frictional force exerted on the trapped, interacting 1D Bose gas
under the influence of a moving random potential. Specifically we consider weak
potentials generated by optical speckle patterns with finite correlation
length. We show that repulsive interactions between bosons lead to a superfluid
response and suppression of frictional force, which can inhibit the onset of
Anderson localisation. We perform a quantitative analysis of the Landau
instability based on the dynamic structure factor of the integrable
Lieb-Liniger model and demonstrate the existence of effective mobility edges.


  We extend the definition of boundary expansion to CW complexes and prove a
Cheeger-Buser-type relation between the spectral gap of the Laplacian and the
boundary expansion of an orientable CW complex.


  Electro-disintegration of the deuteron at large $Q^2$ currently represents on
of the most promising reactions which allows to probe the bound nuclear state
at internal momenta comparable to the rest mass of the nucleon. Large internal
momentum in this case makes non-nuncleonic states energetically more feasible
and the question that we address is what are the signatures that will indicate
the existence of such states in the ground state of the nuclear wave function.
  To probe such states we developed a light-front formalism for relativistic
description of a composite pseudo-vector system in which emerging proton and
neutron are observed in electro-disintegration reaction. In leading high energy
approximation our calculations show the possibility of the existence of a new
``incomplete" P-state-like structure in the deuteron at extremely large
internal momenta. The incompleteness of the observed P-state violates the
angular condition for the momentum distribution, which can happen only if the
deuteron contains non-nucleonic structures, such as $\Delta\Delta$, $N^*N$ or
hidden color components. Because such states have distinctive angular momentum
($l=1$) they significantly modify the polarization properties of the deuteron
wave function. As a result in addition to angular anisotropy of the LF momentum
distribution of the nucleon in the deuteron one predicts strong modification of
the tensor polarization asymmetry of the deuteron beyond the S- and D- wave
predictions at large internal momenta in the deuteron.


  Semiconducting carbon nanotubes under high electric field stress (~10 V/um)
display a striking, exponential current increase due to avalanche generation of
free electrons and holes. Unlike in other materials, the avalanche process in
such 1D quantum wires involves access to the third sub-band, is insensitive to
temperature, but strongly dependent on diameter ~exp(-1/d^2). Comparison with a
theoretical model yields a novel approach to obtain the inelastic optical
phonon emission length, L_OP,ems ~ 15d nm. The combined results underscore the
importance of multi-band transport in 1D molecular wires.


  We discuss the different forms of the functional RG equation and their
relation to each other. In particular we suggest a generalized background field
version that is close in spirit to the Polchinski equation as an alternative to
the Wetterich equation to study Weinberg's asymptotic safety program for
defining quantum gravity, and argue that the former is better suited for this
purpose. Using the heat kernel expansion and proper time regularization we find
evidence in support of this program in agreement with previous work.


  In nonsmooth, nonconvex stochastic optimization, understanding the uniform
convergence of subdifferential mappings is crucial for analyzing stationary
points of sample average approximations of risk as they approach the population
risk. Yet, characterizing this convergence remains a fundamental challenge.
  This work introduces a novel perspective by connecting the uniform
convergence of subdifferential mappings to that of subgradient mappings as
empirical risk converges to the population risk. We prove that, for stochastic
weakly-convex objectives, and within any open set, a uniform bound on the
convergence of subgradients -- chosen arbitrarily from the corresponding
subdifferential sets -- translates to a uniform bound on the convergence of the
subdifferential sets itself, measured by the Hausdorff metric.
  Using this technique, we derive uniform convergence rates for subdifferential
sets of stochastic convex-composite objectives. Our results do not rely on key
distributional assumptions in the literature, which require the population and
finite sample subdifferentials to be continuous in the Hausdorff metric, yet
still provide tight convergence rates. These guarantees lead to new insights
into the nonsmooth landscapes of such objectives within finite samples.


  This paper presents a new approach for precisely estimating the renal
vascular dominant region using a Voronoi diagram. To provide computer-assisted
diagnostics for the pre-surgical simulation of partial nephrectomy surgery, we
must obtain information on the renal arteries and the renal vascular dominant
regions. We propose a fully automatic segmentation method that combines a
neural network and tensor-based graph-cut methods to precisely extract the
kidney and renal arteries. First, we use a convolutional neural network to
localize the kidney regions and extract tiny renal arteries with a tensor-based
graph-cut method. Then we generate a Voronoi diagram to estimate the renal
vascular dominant regions based on the segmented kidney and renal arteries. The
accuracy of kidney segmentation in 27 cases with 8-fold cross validation
reached a Dice score of 95%. The accuracy of renal artery segmentation in 8
cases obtained a centerline overlap ratio of 80%. Each partition region
corresponds to a renal vascular dominant region. The final dominant-region
estimation accuracy achieved a Dice coefficient of 80%. A clinical application
showed the potential of our proposed estimation approach in a real clinical
surgical environment. Further validation using large-scale database is our
future work.


  In previous work by this author, the screening paradox - the loss of
predictive power of screening tests over time $t$ - was mathematically
formalized using Bayesian theory. Where $J$ is Youden's statistic, $b$ is the
specificity of the screening test and $\phi$ is the prevalence of disease, the
ratio of positive predictive values at subsequent time $k$, $\rho(\phi_{k})$,
over the original $\rho(\phi_{0})$ at $t_0$ is given by:
  $\zeta(\phi_{0},k) = \frac{\rho(\phi_{k})}{\rho(\phi_{0})}
=\frac{\phi_k(1-b)+J\phi_0\phi_k}{\phi_0(1-b)+J\phi_0\phi_k}$
  Herein, we modify the traditional Kermack-McKendrick SIR Model to include the
fluctuation of the positive predictive value $\rho(\phi)$ (PPV) of a screening
test over time as a function of the prevalence threshold $\phi_e$. We term this
modified model the SIR-P model. Where a = sensitivity, b = specificity, $S$ =
number susceptible, $I$ = number infected, $R$ = number recovered/dead, $\beta$
= infectious rate, $\gamma$ = recovery rate, and $N$ is the total number in the
population, the predictive value $\rho(\phi,t)$ over time $t$ is given by:
  $\rho(\phi,t) = \frac{a[\frac{\beta IS}{N}-\gamma I]}{ a[\frac{\beta
IS}{N}-\gamma I]+(1-b)(1-[\frac{\beta IS}{N}-\gamma I])}$
  Otherwise stated:
  $\rho(\phi,t) = \frac{a\frac{dI}{dt}}{
a\frac{dI}{dt}+(1-b)(1-\frac{dI}{dt})}$ where $\frac{dI}{dt}$ is the
fluctuation of infected individuals over time $t$.


  We study the shear dynamics of higher dimensional
Friedmann-Lema\^{i}tre-Robertson-Walker (FLRW) cosmology by considering a
non-perfect fluid which exerts different pressure in the normal and extra
dimensions. We generalise the definition of shear tensor for higher dimensional
space-time and prove it to be consistent with the evolution equation for shear
tensor obtained from the Ricci identities. The evolution of shear tensor is
investigated numerically. The role of extra dimensions and other parameters
involved in shear dynamics is discussed in detail. We find that with increase
in anisotropy parameter, time of decay of shear increases while with increase
in number of extra dimensions, shear tends to decay early.


  Machine learning has recently become a promising technique in fluid
mechanics, especially for active flow control (AFC) applications. A recent work
[J. Fluid Mech. (2019), vol. 865, pp. 281-302] has demonstrated the feasibility
and effectiveness of deep reinforcement learning (DRL) in performing AFC over a
circular cylinder at $Re = 100$, i.e., in the laminar flow regime. As a
follow-up study, we investigate the same AFC problem at an intermediate
Reynolds number, i.e., $Re = 1000$, where the turbulence in the flow poses
great challenges to the control. The results show that the DRL agent can still
find effective control strategies, but requires much more episodes in the
learning. A remarkable drag reduction of around $30\%$ is achieved, which is
accompanied by elongation of the recirculation bubble and reduction of
turbulent fluctuations in the cylinder wake. To our best knowledge, this study
is the first successful application of DRL to AFC in weak turbulent conditions.
It therefore sets a new milestone in progressing towards AFC in strong
turbulent flows.


  In the present paper we study quasi-Monte Carlo rules for approximating
integrals over the $d$-dimensional unit cube for functions from weighted
Sobolev spaces of regularity one. While the properties of these rules are well
understood for anchored Sobolev spaces, this is not the case for the ANOVA
spaces, which are another very important type of reference spaces for
quasi-Monte Carlo rules.
  Using a direct approach we provide a formula for the worst case error of
quasi-Monte Carlo rules for functions from weighted ANOVA spaces. As a
consequence we bound the worst case error from above in terms of weighted
discrepancy of the employed integration nodes. On the other hand we also obtain
a general lower bound in terms of the number $n$ of used integration nodes.
  For the one-dimensional case our results lead to the optimal integration rule
and also in the two-dimensional case we provide rules yielding optimal
convergence rates.


  Recently, we proposed a unified mass matrix model for quarks and leptons, in
which, mass ratios and mixings of the quarks and neutrinos are described by
using only the observed charged lepton mass values as family-number-dependent
parameters and only six family-number-independent free parameters. In spite of
quite few parameters, the model gives remarkable agreement with observed data
(i.e. CKM mixing, PMNS mixing and mass ratios). Taking this phenomenological
success seriously, we give a formulation of the so-called Yukawaon model in
details from a theoretical aspect, especially for the construction of
superpotentials and $R$ charge assignments of fields. The model is considerably
modified from the previous one, while the phenomenological success is kept
unchanged.


  The spatial structure of fluctuations in spatially inhomogeneous processes
can be modeled in terms of Gibbs random fields. A local low energy estimator
(LLEE) is proposed for the interpolation (prediction) of such processes at
points where observations are not available. The LLEE approximates the spatial
dependence of the data and the unknown values at the estimation points by
low-lying excitations of a suitable energy functional. It is shown that the
LLEE is a linear, unbiased, non-exact estimator. In addition, an expression for
the uncertainty (standard deviation) of the estimate is derived.


  Observations made during the New Horizons flyby provide a detailed snapshot
of the current state of Pluto's atmosphere. While the lower atmosphere (at
altitudes <200 km) is consistent with ground-based stellar occultations, the
upper atmosphere is much colder and more compact than indicated by
pre-encounter models. Molecular nitrogen (N$_2$) dominates the atmosphere (at
altitudes <1800 km or so), while methane (CH$_4$), acetylene (C$_2$H$_2$),
ethylene (C$_2$H$_4$), and ethane (C$_2$H$_6$) are abundant minor species, and
likely feed the production of an extensive haze which encompasses Pluto. The
cold upper atmosphere shuts off the anticipated enhanced-Jeans,
hydrodynamic-like escape of Pluto's atmosphere to space. It is unclear whether
the current state of Pluto's atmosphere is representative of its average
state--over seasonal or geologic time scales.


  In contrast to conventional structures, efficient non-radiative carrier
recombination counteracts the appearance of optical gain in graphene. Based on
a microscopic and fully quantum-mechanical study of the coupled carrier,
phonon, and photon dynamics in graphene, we present a strategy to obtain a
long-lived gain: Integrating graphene into a photonic crystal nanocavity and
applying a high-dielectric substrate gives rise to pronounced coherent light
emission suggesting the design of graphene-based laser devices covering a broad
spectral range.


  The primary goal of this paper is to identify syntomic complexes with the
$p$-adic \'etale Tate twists of Geisser--Schneider--Sato on regular
$p$-torsionfree schemes. Our methods apply naturally to a broader class of
schemes that we call "$F$-smooth". The $F$-smoothness of regular schemes leads
to new results on the absolute prismatic cohomology of regular schemes.


  Change of measures has been an effective method in stochastic control and
analysis; in continuous-time control this follows Girsanov's theorem applied to
both fully observed and partially observed models, in decentralized stochastic
control (or stochastic dynamic team theory) this is known as Witsenhausen's
static reduction, and in discrete-time classical stochastic control Borkar has
considered this method for partially observed Markov Decision processes
(POMDPs) generalizing Fleming and Pardoux's approach in continuous-time. This
method allows for equivalent optimal stochastic control or filtering in a new
probability space where the measurements form an independent exogenous process
in both discrete-time and continuous-time and the Radon-Nikodym derivative
(between the true measure and the reference measure formed via the independent
measurement process) is pushed to the cost or dynamics. However, for this to be
applicable, an absolute continuity condition is necessary. This raises the
following question: can we perturb any discrete-time sequential stochastic
control problem by adding some arbitrarily small additive (e.g. Gaussian or
otherwise) noise to the measurements to make the system measurements absolutely
continuous, so that a change-of-measure (or static reduction) can be applicable
with arbitrarily small error in the optimal cost? That is, are all sequential
stochastic (single-agent or decentralized multi-agent) problems $\epsilon$-away
from being static reducible as far as optimal cost is concerned, for any
$\epsilon > 0$? We show that this is possible when the cost function is bounded
and continuous in controllers' actions and the action spaces are convex. We
also note that the solution and the cost obtained for the perturbed system is
realizable (under a randomized policy) for the original model.


  We consider a transport equation of the Boltzmann-Langevin type for
non-Abelian plasmas close to equilibrium to derive the spectral functions of
the underlying microscopic fluctuations from the entropy. The correlator of the
stochastic source is obtained from the dissipative processes in the plasma.
This approach, based on classical transport theory, exploits the well-known
link between a linearized collision integral, the entropy and the spectral
functions. Applied to the ultra-soft modes of a hot non-Abelian (classical or
quantum) plasma, the resulting spectral functions agree with earlier findings
obtained from the microscopic theory. As a by-product, it follows that
B\"odeker's effective theory is consistent with the fluctuation-dissipation
theorem.


  Solving optimization problems with high performance is the target of existing
works of Quantum Approximate Optimization Algorithm (QAOA). With this
intention, we propose an advanced QAOA based on incremental learning, where the
training trajectory is proactively segmented into incremental phases. Taking
the MaxCut problem as our example, we randomly select a small subgraph from the
whole graph and train the quantum circuit to get optimized parameters for the
MaxCut of the subgraph in the first phase. Then in each subsequent incremental
phase, a portion of the remaining nodes and edges are added to the current
subgraph, and the circuit is retrained to get new optimized parameters. The
above operation is repeated until the MaxCut problem on the whole graph is
solved. The key point is that the optimized parameters of the previous phase
will be reused in the initial parameters of the current phase. Numerous
simulation experiments show our method has superior performance on
Approximation Ratio (AR) and training time compared to prevalent works of QAOA.
Specifically, the AR is higher than standard QAOA by 13.17% on weighted random
graphs.


  We introduce a monoidal category whose morphisms are finite partial orders,
with chosen minimal and maximal elements as source and target respectively.
After recalling the notion of presentation of a monoidal category by the means
of generators and relations, we construct a presentation of our category, which
corresponds to a variant of the notion of bialgebra.


  We show that a generic real projective n-dimensional hypersurface of degree
2n-1 contains "many" real lines, namely, not less than (2n-1)!!, which is
approximately the square root of the number of complex lines. This estimate is
based on the interpretation of a suitable signed count of the lines as the
Euler number of an appropriate bundle.


  In this study, we consider the realm of covariance matrices in machine
learning, particularly focusing on computing Fr\'echet means on the manifold of
symmetric positive definite matrices, commonly referred to as Karcher or
geometric means. Such means are leveraged in numerous machine-learning tasks.
Relying on advanced statistical tools, we introduce a random matrix
theory-based method that estimates Fr\'echet means, which is particularly
beneficial when dealing with low sample support and a high number of matrices
to average. Our experimental evaluation, involving both synthetic and
real-world EEG and hyperspectral datasets, shows that we largely outperform
state-of-the-art methods.


  We show how the discovery of robust scalable numerical solvers for arbitrary
bounded linear operators can be automated as a Game Theory problem by
reformulating the process of computing with partial information and limited
resources as that of playing underlying hierarchies of adversarial information
games. When the solution space is a Banach space $B$ endowed with a quadratic
norm $\|\cdot\|$, the optimal measure (mixed strategy) for such games (e.g. the
adversarial recovery of $u\in B$, given partial measurements $[\phi_i, u]$ with
$\phi_i\in B^*$, using relative error in $\|\cdot\|$-norm as a loss) is a
centered Gaussian field $\xi$ solely determined by the norm $\|\cdot\|$, whose
conditioning (on measurements) produces optimal bets. When measurements are
hierarchical, the process of conditioning this Gaussian field produces a
hierarchy of elementary bets (gamblets). These gamblets generalize the notion
of Wavelets and Wannier functions in the sense that they are adapted to the
norm $\|\cdot\|$ and induce a multi-resolution decomposition of $B$ that is
adapted to the eigensubspaces of the operator defining the norm $\|\cdot\|$.
When the operator is localized, we show that the resulting gamblets are
localized both in space and frequency and introduce the Fast Gamblet Transform
(FGT) with rigorous accuracy and (near-linear) complexity estimates. As the FFT
can be used to solve and diagonalize arbitrary PDEs with constant coefficients,
the FGT can be used to decompose a wide range of continuous linear operators
(including arbitrary continuous linear bijections from $H^s_0$ to $H^{-s}$ or
to $L^2$) into a sequence of independent linear systems with uniformly bounded
condition numbers and leads to $\mathcal{O}(N \operatorname{polylog} N)$
solvers and eigenspace adapted Multiresolution Analysis (resulting in near
linear complexity approximation of all eigensubspaces).


  The question to what extent climate change is responsible for extreme weather
events has been at the forefront of public and scholarly discussion for years.
Proponents of the "risk-based" approach to attribution attempt to give an
unconditional answer based on the probability of some class of events in a
world with and without human influences. As an alternative, so-called
"storyline" studies investigate the impact of a warmer world on a single,
specific weather event. This can be seen as a conditional attribution
statement. In this study, we connect conditional to unconditional attribution
using Bayes theorem: in essence, the conditional statement is composed of two
unconditional statements, one based on all available data (event and
conditions) and one based on the conditions alone. We explore the effects of
the conditioning in a simple statistical toy model and a real-world attribution
of European summer temperatures conditional on blocking. The resulting
attribution statement is generally strengthened if the conditions are not
affected by climate change. Conversely, if part of the trend is contained in
the conditions, a weaker attribution statement may result.


  An ultradiscrete system corresponding to the $q$-Painlev\'e equation of type
$A_6^{(1)}$, which is a $q$-difference analogue of the second Painlev\'e
equation, is proposed. Exact solutions with two parameters are constructed for
the ultradiscrete system.


  We consider spectral clustering algorithms for community detection under a
general bipartite stochastic block model (SBM). A modern spectral clustering
algorithm consists of three steps: (1) regularization of an appropriate
adjacency or Laplacian matrix (2) a form of spectral truncation and (3) a
k-means type algorithm in the reduced spectral domain. We focus on the
adjacency-based spectral clustering and for the first step, propose a new
data-driven regularization that can restore the concentration of the adjacency
matrix even for the sparse networks. This result is based on recent work on
regularization of random binary matrices, but avoids using unknown population
level parameters, and instead estimates the necessary quantities from the data.
We also propose and study a novel variation of the spectral truncation step and
show how this variation changes the nature of the misclassification rate in a
general SBM. We then show how the consistency results can be extended to models
beyond SBMs, such as inhomogeneous random graph models with approximate
clusters, including a graphon clustering problem, as well as general
sub-Gaussian biclustering. A theme of the paper is providing a better
understanding of the analysis of spectral methods for community detection and
establishing consistency results, under fairly general clustering models and
for a wide regime of degree growths, including sparse cases where the average
expected degree grows arbitrarily slowly.


  The cosmic evolution of the chemical elements from the Big Bang to the
present time is driven by nuclear fusion reactions inside stars and stellar
explosions. A cycle of matter recurrently re-processes metal-enriched stellar
ejecta into the next generation of stars. The study of cosmic nucleosynthesis
and of this matter cycle requires the understanding of the physics of nuclear
reactions, of the conditions at which the nuclear reactions are activated
inside the stars and stellar explosions, of the stellar ejection mechanisms
through winds and explosions, and of the transport of the ejecta towards the
next cycle, from hot plasma to cold, star-forming gas. Due to the long
timescales of stellar evolution, and because of the infrequent occurrence of
stellar explosions, observational studies are challenging. Due to their
radioactive lifetime of million years, the 26Al and 60Fe isotopes are suitable
to characterise simultaneously the processes of nuclear fusion reactions and of
interstellar transport. We describe and discuss the nuclear reactions involved
in the production and destruction of 26Al and 60Fe, the key characteristics of
the stellar sites of their nucleosynthesis and their interstellar journey after
ejection from the nucleosynthesis sites. We connect the theoretical
astrophysical aspects to the variety of astronomical messengers, from stardust
and cosmic-ray composition measurements, through observation of gamma rays
produced by radioactivity, to material deposited in deep-sea ocean crusts and
to the inferred composition of the first solids that have formed in the Solar
System. We show that considering measurements of the isotopic ratio of 26Al to
60Fe eliminate some of the unknowns when interpreting astronomical results, and
discuss the lessons learned from these two isotopes on cosmic chemical
evolution.


  Scheduling on dataflow graphs (also known as computation graphs) is an
NP-hard problem. The traditional exact methods are limited by runtime
complexity, while reinforcement learning (RL) and heuristic-based approaches
struggle with determinism and solution quality. This research aims to develop
an innovative approach that employs machine learning (ML) for addressing
combinatorial optimization problems, using scheduling as a case study. The goal
is to provide guarantees in optimality and determinism while maintaining the
runtime cost of heuristic methods. Specifically, we introduce a novel two-phase
RL-to-ILP scheduling framework, which includes three steps: 1) RL solver acts
as coarse-grain scheduler, 2) solution relaxation and 3) exact solving via ILP.
Our framework demonstrates the same scheduling performance compared with using
exact scheduling methods while achieving up to 128 $\times$ speed improvements.
This was conducted on actual EdgeTPU platforms, utilizing ImageNet DNN
computation graphs as input. Additionally, the framework offers improved
on-chip inference runtime and acceleration compared to the commercially
available EdgeTPU compiler.


  Increasing aggregate diversity (or catalog coverage) is an important
system-level objective in many recommendation domains where it may be desirable
to mitigate the popularity bias and to improve the coverage of long-tail items
in recommendations given to users. This is especially important in
multistakeholder recommendation scenarios where it may be important to optimize
utilities not just for the end user, but also for other stakeholders such as
item sellers or producers who desire a fair representation of their items
across recommendation lists produced by the system. Unfortunately, attempts to
increase aggregate diversity often result in lower recommendation accuracy for
end users. Thus, addressing this problem requires an approach that can
effectively manage the trade-offs between accuracy and aggregate diversity. In
this work, we propose a two-sided post-processing approach in which both user
and item utilities are considered. Our goal is to maximize aggregate diversity
while minimizing loss in recommendation accuracy. Our solution is a
generalization of the Deferred Acceptance algorithm which was proposed as an
efficient algorithm to solve the well-known stable matching problem. We prove
that our algorithm results in a unique user-optimal stable match between items
and users. Using three recommendation datasets, we empirically demonstrate the
effectiveness of our approach in comparison to several baselines. In
particular, our results show that the proposed solution is quite effective in
increasing aggregate diversity and item-side utility while optimizing
recommendation accuracy for end users.


  The standard collective quantization treatment of the strangeness content of
the nucleon in chiral soliton models such as the Skyrmion is shown to be
inconsistent with the semi-classical expansion on which the treatment is based.
The strangeness content vanishes at leading order in the semi-classical
expansion. Collective quantization correctly describes some contributions to
the strangeness content at the first nonvanishing order in the expansion, but
neglects others at the same order--namely, those associated with continuum
modes. Moreover, there are fundamental difficulties in computing at a constant
order in the expansion due to the non-renormalizable nature of chiral soliton
models. Moreover, there are fundamental difficulties in computing at a constant
order in the expansion due to the non-renormalizable nature of chiral soliton
models and the absence of any viable power counting scheme. We show that the
continuum mode contribution to the strangeness diverges, and as a result the
computation of the strangeness content at leading non-vanishing order is not a
well-posed mathematical problem in these models.


  Consider an arbitrary network of communicating modules on a chip, each
requiring a local signal telling it when to execute a computational step. There
are three common solutions to generating such a local clock signal: (i) by
deriving it from a single, central clock source, (ii) by local, free-running
oscillators, or (iii) by handshaking between neighboring modules. Conceptually,
each of these solutions is the result of a perceived dichotomy in which
(sub)systems are either clocked or asynchronous. We present a solution and its
implementation that lies between these extremes. Based on a distributed
gradient clock synchronization algorithm, we show a novel design providing
modules with local clocks, the frequency bounds of which are almost as good as
those of free-running oscillators, yet neighboring modules are guaranteed to
have a phase offset substantially smaller than one clock cycle. Concretely,
parameters obtained from a 15nm ASIC simulation running at 2GHz yield
mathematical worst-case bounds of 20ps on the phase offset for a $32 \times 32$
node grid network.


  We prove local quantitative estimates of unique continuation for solutions to
parabolic equations: doubling properties and two-sphere one-cylinder
inequalities.


  By performing resummation of small fermion-antifermion pairs within the
pentagon form factor program to scattering amplitudes in planar N = 4
superYang-Mills theory, we construct multichannel conformal blocks within the
flux-tube picture for N-sided NMHV polygons. This procedure is equivalent to
summation of descendants of conformal primaries in the OPE framework. The
resulting conformal partial waves are determined by multivariable
hypergeometric series of Lauricella-Saran type.


  One of the major terminological forces driving ICT integration in research
today is that of "big data." While the phrase sounds inclusive and integrative,
"big data" approaches are highly selective, excluding input that cannot be
effectively structured, represented, or digitised. Data of this complex sort is
precisely the kind that human activity produces, but the technological
imperative to enhance signal through the reduction of noise does not
accommodate this richness. Data and the computational approaches that
facilitate "big data" have acquired a perceived objectivity that belies their
curated, malleable, reactive, and performative nature. In an input environment
where anything can "be data" once it is entered into the system as "data," data
cleaning and processing, together with the metadata and information
architectures that structure and facilitate our cultural archives acquire a
capacity to delimit what data are. This engenders a process of simplification
that has major implications for the potential for future innovation within
research environments that depend on rich material yet are increasingly
mediated by digital technologies. This paper presents the preliminary findings
of the European-funded KPLEX (Knowledge Complexity) project which investigates
the delimiting effect digital mediation and datafication has on rich, complex
cultural data. The paper presents a systematic review of existing implicit
definitions of data, elaborating on the implications of these definitions and
highlighting the ways in which metadata and computational technologies can
restrict the interpretative potential of data. It sheds light on the gap
between analogue or augmented digital practices and fully computational ones,
and the strategies researchers have developed to deal with this gap. The paper
proposes a reconceptualisation of data as it is functionally employed within
digitally-mediated research so as to incorporate and acknowledge the richness
and complexity of our source materials.


  We present AVOD, an Aggregate View Object Detection network for autonomous
driving scenarios. The proposed neural network architecture uses LIDAR point
clouds and RGB images to generate features that are shared by two subnetworks:
a region proposal network (RPN) and a second stage detector network. The
proposed RPN uses a novel architecture capable of performing multimodal feature
fusion on high resolution feature maps to generate reliable 3D object proposals
for multiple object classes in road scenes. Using these proposals, the second
stage detection network performs accurate oriented 3D bounding box regression
and category classification to predict the extents, orientation, and
classification of objects in 3D space. Our proposed architecture is shown to
produce state of the art results on the KITTI 3D object detection benchmark
while running in real time with a low memory footprint, making it a suitable
candidate for deployment on autonomous vehicles. Code is at:
https://github.com/kujason/avod


  Although kilometer-scale neutrino detectors such as IceCube are discovery
instruments, their conceptual design is very much anchored to the observational
fact that Nature produces protons and photons with energies in excess of 10^20
eV and 10^13 eV, respectively. The puzzle of where and how Nature accelerates
the highest energy cosmic particles is unresolved almost a century after their
discovery. From energetics considerations we anticipate order 10~100 neutrino
events per kilometer squared per year pointing back at the source(s) of both
galactic and extragalactic cosmic rays. In this context, we discuss the results
of the AMANDA and IceCube neutrino telescopes which will deliver a
kilometer-square-year of data over the next 3 years.


  We define the cluster characters for 2-Calabi-Yau Frobenius extriangulated
categories with cluster tilting objects. This provides a unified framework of
cluster characters in 2-Calabi-Yau triangulated categories and 2-Calabi-Yau
Frobenius exact categories given by Palu and Fu-Keller, respectively


  We compute the degree of Stiefel manifolds, that is, the variety of
orthonormal frames in a finite dimensional vector space. Our approach employs
techniques from classical algebraic geometry, algebraic combinatorics, and
classical invariant theory.


  We give a complete solution to the existence problem for gravitating vortices
with non-negative topological constant $c \geqslant 0$. Our first main result
builds on previous results by Yang and establishes the existence of solutions
to the Einstein-Bogomol'nyi equations, corresponding to $c=0$, in all
admissible K\"ahler classes. Our second main result completely solves the
existence problem for $c>0$. Both results are proved by the continuity method
and require that a GIT stability condition for an effective divisor on the
Riemann sphere is satisfied. For the former, the continuity path starts from a
given solution with $c = 0$ and deforms the K\"ahler class. For the latter
result we start from the established solution in any fixed admissible K\"ahler
class and deform the coupling constant $\alpha$ towards $0$. A salient feature
of our argument is a new bound $S_g \geqslant c$ for the curvature of
gravitating vortices, which we apply to construct a limiting solution along the
path via Cheeger-Gromov theory.


  We re-examine the interactions of ultra-high energy cosmic rays (UHECRs) with
photons from the cosmic microwave background (CMB) under a changed, locally
non-linear temperature redshift relation $T(z)$. This changed temperature
redshift relation has recently been suggested by the postulate of subjecting
thermalised and isotropic photon gases such as the CMB to an SU(2) rather than
a U(1) gauge group. This modification of $\Lambda$CDM is called SU(2)$_{\rm
CMB}$, and some cosmological parameters obtained by SU(2)$_{\rm CMB}$ seem to
be in better agreement with local measurements of the same quantities, in
particular $H_0$ and S$_8$. In this work, we apply the reduced CMB photon
density under SU(2)$_{\rm CMB}$ to the propagation of UHECRs. This leads to a
higher UHECR flux just below the ankle in the cosmic ray spectrum and slightly
more cosmogenic neutrinos under otherwise equal conditions for emission and
propagation. Most prominently, the proton flux is significantly increased below
the ankle ($5\times10^{18}$ eV) for hard injection spectra and without
considering the effects of magnetic fields. The reduction in CMB photon density
also favours a decreased cosmic ray source evolution than the best fit using
$\Lambda$CDM. In consequence, it seems that SU(2)$_{\rm CMB}$ favours sources
that evolve as the star formation rate (SFR), like starburst galaxies (SBG) and
gamma-ray bursts (GRB), over active galactic nuclei (AGNs) as origins of
UHECRs. We conclude that the question about the nature of primary sources of
UHECRs is directly affected by the assumed temperature redshift relation of the
CMB.


  SmO thin film is a new Kondo system showing a resistivity upturn around 10 K
and was theoretically proposed to have a topologically nontrivial band
structure. We have performed hard x-ray and soft x-ray photoemission
spectroscopy to elucidate the electronic structure of SmO. From the Sm 3$d$
core-level spectra, we have estimated the valence of Sm to be $\sim$2.96,
proving that the Sm has a mixed valence. The valence-band photoemission spectra
exhibit a clear Fermi edge originating from the Sm 5$d$-derived band. The
present finding is consistent with the theory suggesting a possible topological
state in SmO and show that rare-earth monoxides or their heterostructures can
be a new playground for the interplay of strong electron correlation and
spin-orbit coupling.


  The existence of a positive solution to the following fractional semilinear
equation is proven, in a situation where a ground state solution may not exist.
More precisely, we consider for $0<s<1$ the equation $$ (-\Delta)^s u +
V(x)u=Q(x)|u|^{p-2}u \quad\text{in }\mathbb{R}^N,\ N\geq 1,$$ where the
exponent $p$ is superlinear but subcritical, and $V>0$, $Q\geq 0$ are bounded
functions converging to $1$ as $|x|\to\infty$. Using a min-max procedure
introduced by Bahri and Li we prove the existence of a positive solution under
one-sided asymptotic bounds for $V$ and $Q$.


  Continual learning (CL) remains one of the long-standing challenges for deep
neural networks due to catastrophic forgetting of previously acquired
knowledge. Although rehearsal-based approaches have been fairly successful in
mitigating catastrophic forgetting, they suffer from overfitting on buffered
samples and prior information loss, hindering generalization under low-buffer
regimes. Inspired by how humans learn using strong inductive biases, we propose
IMEX-Reg to improve the generalization performance of experience rehearsal in
CL under low buffer regimes. Specifically, we employ a two-pronged
implicit-explicit regularization approach using contrastive representation
learning (CRL) and consistency regularization. To further leverage the global
relationship between representations learned using CRL, we propose a
regularization strategy to guide the classifier toward the activation
correlations in the unit hypersphere of the CRL. Our results show that IMEX-Reg
significantly improves generalization performance and outperforms
rehearsal-based approaches in several CL scenarios. It is also robust to
natural and adversarial corruptions with less task-recency bias. Additionally,
we provide theoretical insights to support our design decisions further.


  This paper studies cooperative spectrum sensing in cognitive radio networks
where secondary users collect local energy statistics and report their findings
to a secondary base station, i.e., a fusion center. First, the average error
probability is quantitively analyzed to capture the dynamic nature of both
observation and fusion channels, assuming fixed amplifier gains for relaying
local statistics to the fusion center. Second, the system level overhead of
cooperative spectrum sensing is addressed by considering both the local
processing cost and the transmission cost. Local processing cost incorporates
the overhead of sample collection and energy calculation that must be conducted
by each secondary user; the transmission cost accounts for the overhead of
forwarding the energy statistic computed at each secondary user to the fusion
center. Results show that when jointly designing the number of collected energy
samples and transmission amplifier gains, only one secondary user needs to be
actively engaged in spectrum sensing. Furthermore, when number of energy
samples or amplifier gains are fixed, closed form expressions for optimal
solutions are derived and a generalized water-filling algorithm is provided.


  We propose an automatic system for organizing the content of a collection of
unstructured videos of an articulated object class (e.g. tiger, horse). By
exploiting the recurring motion patterns of the class across videos, our
system: 1) identifies its characteristic behaviors; and 2) recovers
pixel-to-pixel alignments across different instances. Our system can be useful
for organizing video collections for indexing and retrieval. Moreover, it can
be a platform for learning the appearance or behaviors of object classes from
Internet video. Traditional supervised techniques cannot exploit this wealth of
data directly, as they require a large amount of time-consuming manual
annotations.
  The behavior discovery stage generates temporal video intervals, each
automatically trimmed to one instance of the discovered behavior, clustered by
type. It relies on our novel motion representation for articulated motion based
on the displacement of ordered pairs of trajectories (PoTs). The alignment
stage aligns hundreds of instances of the class to a great accuracy despite
considerable appearance variations (e.g. an adult tiger and a cub). It uses a
flexible Thin Plate Spline deformation model that can vary through time. We
carefully evaluate each step of our system on a new, fully annotated dataset.
On behavior discovery, we outperform the state-of-the-art Improved DTF
descriptor. On spatial alignment, we outperform the popular SIFT Flow
algorithm.


  Computer vision is a field of artificial intelligence that trains computers
to interpret the visual world in a way similar to that of humans. Due to the
rapid advancements in technology and the increasing availability of
sufficiently large training datasets, the topics within computer vision have
experienced a steep growth in the last decade. Among them, one of the most
promising fields is face detection. Being used daily in a wide variety of
fields; from mobile apps and augmented reality for entertainment purposes, to
social studies and security cameras; designing high-performance models for face
detection is crucial. On top of that, with the aforementioned growth in face
detection technologies, precision and accuracy are no longer the only relevant
factors: for real-time face detection, speed of detection is essential.
SwiftFace is a novel deep learning model created solely to be a fast face
detection model. By focusing only on detecting faces, SwiftFace performs 30%
faster than current state-of-the-art face detection models. Code available at
https://github.com/leo7r/swiftface


  The problem of construction of the Wannier functions (WFs) in a restricted
Hilbert space of eigenstates of the one-electron Hamiltonian $\hat{H}$ (forming
the so-called low-energy part of the spectrum) can be formulated in several
different ways. One possibility is to use the projector-operator techniques,
which pick up a set of trial atomic orbitals and project them onto the given
Hilbert space. Another possibility is to employ the downfolding method, which
eliminates the high-energy part of the spectrum and incorporates all related to
it properties into the energy-dependence of an effective Hamiltonian. We show
that by modifying the high-energy part of the spectrum of the original
Hamiltonian $\hat{H}$, which is rather irrelevant to the construction of WFs in
the low-energy part of the spectrum, these two methods can be formulated in an
absolutely exact and identical form, so that the main difference between them
is reduced to the choice of the trial orbitals. Concerning the latter part of
the problem, we argue that an optimal choice for trial orbitals can be based on
the maximization of the site-diagonal part of the density matrix. The main idea
is illustrated for a simple toy model, consisting of only two bands, as well as
for a more realistic example of $t_{2g}$ bands in V$_2$O$_3$. An analogy with
the search of the ground state of a many-electron system is also discussed.


  Given a physics scenario, different problem types presenting that scenario in
various ways can emphasize different instructional goals. In this
investigation, we examined the views of physics graduate teaching assistants
(TAs) about the instructional benefits of different types of introductory
problems based upon the same problem scenario. Here we report on TAs' views
about two of these problem types that were regarded by TAs as the least
instructionally beneficial of all problem types--the context rich and
multiple-choice formats. Many TAs listed no pros at all for these problem
types, despite being explicitly asked for at least one pro. They viewed
multiple-choice questions nearly exclusively as tools for high-stakes summative
assessment rather than their possible use as formative assessment tools, e.g.,
as clicker questions even in large classes. Similarly, TAs viewed context-rich
problems as overly challenging, unnecessarily wordy, and too time-consuming to
be instructionally beneficial to their students. While TAs' concerns have
obvious validity and value, the benefits of well-designed multiple-choice
questions as a formative assessment tool was not readily identified by them,
nor did the TAs recognize the learning benefits associated with solving
context-rich problems. Given the powerful ways multiple-choice and context-rich
problems can be used for active engagement and formative assessment in
different instructional contexts to meet diverse instructional goals, the lack
of enthusiasm for these types of problems has implications for future TA
professional development programs.


  We systematically study VEVs of a gauge scalar field $\Sigma$ in a bulk U(1)
vector multiplet and scalar fields in brane/bulk hypermultiplets charged under
U(1) in the 5D $S^1/Z_2$ orbifold model with generic FI terms. A non-trivial
VEV of $\Sigma$ generates bulk mass terms for U(1) charged fields, and their
zero modes have non-trivial profiles. In particular, in the SUSY-breaking case,
bosonic and fermionic zero modes have Gaussian profiles. Such non-trivial
profiles are useful to explain hierarchical couplings. A toy model for SUSY
breaking is studied, and it yields sizable $D$-term contributions to scalar
masses. Because the overall magnitude of $D$-term contributions is the same
everywhere in the bulk and also on both branes, we have to take into account
these contributions and other SUSY-breaking terms to obtain a realistic
description. We also give profiles and mass eigenvalues of higher modes.


  The Local Supercluster is an ideal laboratory to study distribution of
luminous and dark matter in the nearby Universe. The 1100 small groups have
been selected using algorithm based on assumption that a total energy of
physical pair of galaxies must be negative. The properties of the groups have
been considered.


  We report the first detections of associated H{\sc i} 21\,cm absorption in
Gigahertz-peaked-spectrum (GPS) sources at high redshifts, $z > 1$, using the
Giant Metrewave Radio Telescope (GMRT). Our GMRT search for associated H{\sc i}
21\,cm absorption in a sample of 12 GPS sources yielded two new detections of
absorption, towards TXS~1200+045 at $z = 1.226$ and TXS~1245$-$197 at $z =
1.275$, and five non-detections. These are only the sixth and seventh
detections of associated H{\sc i} 21\,cm absorption in active galactic nuclei
(AGNs) at $z > 1$. Both H{\sc i} 21\,cm absorption profiles are wide, with
velocity spans between nulls of $\approx 600$~km~s$^{-1}$ (TXS~1200+045) and
$\approx 1100$~km~s$^{-1}$ (TXS~1245$-$197). In both absorbers, the large
velocity spread of the absorption and its blueshift from the AGN, suggests that
it arises in outflowing neutral gas, perhaps driven by the radio jets to high
velocities. We derive mass outflow rates of ${\dot M} \approx 32 \; {\rm
M}_\odot$~yr$^{-1}$ (TXS~1200+045) and ${\dot M} \approx 18 \; {\rm
M}_\odot$~yr$^{-1}$ (TXS~1245$-$197), comparable to the mass outflow rates seen
earlier in low-redshift active galactic nuclei.


  A theoretical framework and numerical simulations quantifying the impact of
atmospheric group velocity dispersion on wireless terahertz communication link
error rate were developed based upon experimental work. We present, for the
first time, predictions of symbol error rate as a function of link distance,
signal bandwidth, signal-to-noise ratio, and atmospheric conditions, revealing
that long-distance, broadband terahertz communication systems may be limited by
inter-symbol interference stemming from group velocity dispersion, rather than
attenuation. In such dispersion limited links, increasing signal strength does
not improve the symbol error rate and, consequently, theoretical predictions of
symbol error rate based only on signal-to-noise ratio are invalid for the
broadband case. This work establishes a new and necessary foundation for link
budget analysis in future long-distance terahertz communication systems that
accounts for the non-negligible effects of both attenuation and dispersion.


  The heat capacity $\mathcal{C}$ of a given probe is a fundamental quantity
that determines, among other properties, the maximum precision in temperature
estimation. In turn, $\mathcal{C}$ is limited by a quadratic scaling with the
number of constituents of the probe, which provides a fundamental limit in
quantum thermometry. Achieving this fundamental bound with realistic probes,
i.e. experimentally amenable, remains an open problem. In this work, we tackle
the problem of engineering optimal thermometers by using networks of spins.
Restricting ourselves to two-body interactions, we derive general properties of
the optimal configurations and exploit machine-learning techniques to find the
optimal couplings. This leads to simple architectures, which we show
analytically to approximate the theoretical maximal value of $\mathcal{C}$ and
maintain the optimal scaling for short- and long-range interactions. Our models
can be encoded in currently available quantum annealers, and find application
in other tasks requiring Hamiltonian engineering, ranging from quantum heat
engines to adiabatic Grover's search.