  Fixed-wind unmanned aerial vehicles (UAVs) are essential for low cost aerial
surveillance and mapping applications in remote regions. One of the main
limitations of UAVs is limited fuel capacity and hence requires periodic
refueling to accomplish a mission. The usual mechanism of commanding the UAV to
return to a stationary base station for refueling can result in fuel wastage
and inefficient mission operation time. Alternatively, unmanned gound vehicle
(UGV) can be used as a mobile refueling unit where the UAV will rendezvous with
the UGV for refueling. In order to accurately perform this task in the presence
of wind disturbances, we need to determine an optimal trajectory in 3D taking
UAV and UGV dynamics and kinematics into account. In this paper, we propose an
optimal control formulation to generate a tunable UAV trajectory for rendezvous
on a moving UGV taking wind disturbances into account. By a suitable choice of
the value of an aggressiveness index in our problem setting, we are able to
control the UAV rendezvous behavior. Several numerical results are presented to
show the reliability and effectiveness of our approach.


  We prove sign-alternation of the structure constants in the basis of
structure sheaves of opposite Schubert varieties in the torus-equivariant
Grothendieck group of coherent sheaves on the flag varieties $G/P$ associated
to an arbitrary symmetrizable Kac-Moody group $G$, where $P$ is any parabolic
subgroup. This generalizes the work of Anderson-Griffeth-Miller from the finite
case to the general Kac-Moody case, and affirmatively answers a conjecture of
Lam-Schilling-Shimozono regarding the signs of the structure constants in the
case of the affine Grassmannian.


  There are two approaches for pairwise sentence scoring: Cross-encoders, which
perform full-attention over the input pair, and Bi-encoders, which map each
input independently to a dense vector space. While cross-encoders often achieve
higher performance, they are too slow for many practical use cases.
Bi-encoders, on the other hand, require substantial training data and
fine-tuning over the target task to achieve competitive performance. We present
a simple yet efficient data augmentation strategy called Augmented SBERT, where
we use the cross-encoder to label a larger set of input pairs to augment the
training data for the bi-encoder. We show that, in this process, selecting the
sentence pairs is non-trivial and crucial for the success of the method. We
evaluate our approach on multiple tasks (in-domain) as well as on a domain
adaptation task. Augmented SBERT achieves an improvement of up to 6 points for
in-domain and of up to 37 points for domain adaptation tasks compared to the
original bi-encoder performance.


  n this article we study the Friedel phase of the electron transport in two
different systems of quantum dots which exhibit bound states in the continuum
(BIC). The Friedel phase jumps abruptly in the energies of the BICs, which is
associated to the vanishing width of these states, as shown by Friedrich and
Wintgen in Phys. Rev. A \textbf{31}, 3964 (1985). This odd behavior of the
Friedel phase has consequences in the charge through the Friedel sum rule.
Namely, if the energy of the BIC drops under the Fermi energy the charge
changes abruptly in a unity. We show that this behavior closely relates with
discontinuities in the conductance predicted for interacting quantum dot
systems.


  We report on the galaxy density environment around a high-z radio galaxy
(HzRG) at z=4.72, HSC J083913.17+011308.1 (HSC J0839+0113), probed using an
r-dropout Lyman break galaxy (LBG) sample from the Hyper Suprime-Cam Subaru
Strategic Program data. We find that HSC J0839+0113 resides in the outskirt of
an overdense region identified by the r-dropout galaxies at a 4.7 sigma
significance level. The projected distance between HSC J0839+0113 and the peak
position of the overdense region is 0.4 physical Mpc which is shorter than the
typical protocluster radius in this epoch. According to the extended Press
Schechter and the light cone models, the HSC J0839+0113-hosted overdense region
is expected to evolve into a halo > 10^14 Msun at z=0 with a high probability
of >80 %. These findings suggest that HSC J0839+0113 is associated with a
protocluster. The HSC J0839+0113 rich-system is the most overdense region of
LBGs among the known protoclusters with LBGs in the same cosmic epoch.


  Ferromagnetic insulator thin films can convey information by spin waves,
avoiding charge displacement and Eddy current losses. The sparsity of
high-temperature insulating ferromagnetic materials hinders the development of
spin wave based devices. Stoichiometric magnesium titanate, MgTiO$_3$, has an
electronic-energy-band structure in which all bands are either full or empty,
being a paramagnetic insulator. The MgTiO$_3$ ilmenite consists of ordered
octahedra and cation network in which one third of the octahedra are vacant,
one third host magnesium and one third titanium. By giving up these
characteristics, a rich variety of different magnetic structures can be formed.
Our experiments and electronic-energy-band-structure computations show that the
magnetic and electric properties of Mg-Ti-O films can drastically be changed
and controlled by Mg- and Ti-cation arrangement and abundancy in the octahedra.
Insulating titanium- and semiconducting magnesium-rich films were ferromagnetic
up to elevated temperatures. The presence and origin of ferromagnetic
insulating phase in the films is not apparent - the expectation, based on the
well-established rules set by Goodenough and Kanamori, is paramagnetic or
antiferromagnetic ordering. We show that ferro- and paramagnetic phases,
possessing the same stoichiometry, can be obtained by merely rearranging the
cations, thus allowing defect-free interfaces in multilayer structures.


  We consider a motion of a weakly relativistic charged particle with an
arbitrary spin in central potential $e/r$ in terms of classical mechanics. We
show that the spin-orbital interaction causes the precession of the plane of
orbit around the vector of total angular momentum. The angular velocity of
precession depends on the distance of the particle from the center. The
effective potential for in-plane motion is central, with the corrections to
Coulomb terms coming from spin-orbital interaction. The possible orbits of a
quantum particle are determined by the Bohr-Sommerfeld quantization rule. We
give examples of orbits corresponding to small quantum numbers, which were
obtained by numerical integration of equations of motion. The energies of
stationary states are determined by spin-orbital interaction.


  Knowing the influence of the substrate type on the diffusion coefficient and
the momentum relaxation in graphene is of great importance for the development
of new device models specifically adapted to the peculiarities of this
material. In this work, the influence of surface polar phonons at low and high
electric fields is evaluated by means of ensemble Monte Carlo simulations for
several types of substrates. The results show that at low fields surface polar
phonons have a major role on reducing the scattering time, breaking the
correlation of velocity fluctuations and degrading the diffusion coefficient.
At high fields the differences with regard to suspended samples in terms of
diffusivity and momentum relaxation tend to reduce, providing at the same time
larger saturation velocities, particularly for h-BN.


  These lectures were a part of the geometry course held during the Fall 2011
Mathematics Advanced Study Semesters (MASS) Program at Penn State
(\url{http://www.math.psu.edu/mass/}).
  The lectures are meant to be accessible to advanced undergraduate and early
graduate students in mathematics. We have placed a great emphasis on clarity
and exposition, and we have included many exercises. Hints and solutions for
most of the exercises are provided in the end.
  The lectures discuss piecewise distance preserving maps from a 2-dimensional
polyhedral space into the plane. Roughly speaking, a polyhedral space is a
space that is glued together out of triangles, for example the surface of a
polyhedron. If one imagines such a polyhedral space as a paper model, then a
piecewise distance preserving map into the plane is essentially a way to fold
the model so that it lays flat on a table.
  We only consider the 2-dimensional case to keep things easy to visualize.
However, most of the results admit generalizations to higher dimensions. These
results are discussed in the Final Remarks, where proper credit and references
are given.


  In this paper we present a physics model for the interactions of stable heavy
hadrons containing a heavy parton with matter. The model presented is a natural
continuation of the work started in hep-ex/0404001. However, changes and
generalisations have been made allowing for the description of a broader scope
of physics scenarios. As a special case the model is tested on the cases of
stable gluino and stop hadrons, thus covering both stable colour triplet and
octet states. Conclusions are drawn regarding the phenomenology of these cases
including how to distinguish between them.


  Local perturbations around contours strongly disturb the final result of
computer vision tasks. It is common to introduce a priori information in the
estimation process. Improvement can be achieved via a deformable model such as
the snake model. In recent works, the deformable contour is modeled by means of
B-spline snakes which allows local control, concise representation, and the use
of fewer parameters. The estimation of the sub-pixel edges using a global
B-spline model relies on the contour global determination according to a
maximum likelihood framework and using the observed data likelihood. This
procedure guarantees that the noisiest data will be filtered out. The data
likelihood is computed as a consequence of the observation model which includes
both orientation and position information. Comparative experiments of this
algorithm and the classical spline interpolation have shown that the proposed
algorithm outperforms the classical approach for Gaussian and Salt & Pepper
noise.


  The canonical perfect lens--comprising three slabs, each made of a linear,
homogeneous, bianisotropic material with orthorhombic symmetry--is Lorentz
covariant.


  Gradients of the perimeter and area of a polygon have straightforward
geometric interpretations. The use of optimality conditions for constrained
problems and basic ideas in triangle geometry show that polygons with
prescribed area minimizing the perimeter must be regular.


  We study the two membranes problem for two different fully nonlinear
operators. We give a viscosity formulation for the problem and prove existence
of solutions. Then we prove a general regularity result and the optimal
$C^{1,1}$ regularity when the operators are the Pucci extremal operators. We
also give an example that shows that no regularity for the free boundary is to
be expected to hold in general.


  In most studies of the channel capacity of quantum channels, it is assumed
that the errors in each use of the channel are independent. However, recent
work has begun to investigate the effects of memory or correlations in the
error. This work has led to speculation that interesting non-analytic behaviour
may occur in the capacity. Motivated by these observations, we connect the
study of channel capacities under correlated error to the study of critical
behaviour in many-body physics. This connection enables us the techniques of
many-body physics to either completely solve or understand qualitatively a
number of interesting models of correlated error. The models can display
analogous behaviour to associated many-body systems, including `phase
transitions'.


  In a recent paper [Phys. Rev. D{\bf 85}, 023528 (2012)] the authors proposed
a generalized Born-Infeld electrodynamics coupled to general relativity which
produces a nonsingular bouncing universe. For a magnetic universe the resulting
cosmic evolution inevitably interpolates between asymptotic de Sitter states.
Here we shall show that (i) the above theory does not have the standard weak
field Maxwell limit, (ii) a sudden curvature singularity -- not better than the
big bang -- arises, (iii) the speed of sound squared is a negative quantity
signaling instability against small perturbations of the background energy
density, and that (iv) the conclusion about the inevitability of the asymptotic
vacuum regime in a magnetic universe is wrong.


  If $\H$ is a Hilbert space, $A$ is a positive bounded linear operator on
$\cH$ and $\cS$ is a closed subspace of $\cH$, the relative position between
$\cS$ and $A^{-1}(\cS \orto)$ establishes a notion of compatibility. We show
that the compatibility of $(A,\cS)$ is equivalent to the existence of a
convenient orthogonal projection in the operator range $R(A^{1/2})$ with its
canonical Hilbertian structure.


  In Cyber-Physical Systems (CPSs), inference based on communicated data is of
critical significance as it can be used to manipulate or damage the control
operations by adversaries. This calls for efficient mechanisms for secure
transmission of data since control systems are becoming increasingly
distributed over larger geographical areas. Distortion based security, recently
proposed as one candidate for CPSs security, is not only more appropriate for
these applications but also quite frugal in terms of prior requirements on
shared keys. In this paper, we propose distortion-based metrics to protect CPSs
communication and show that it is possible to confuse adversaries with just a
few bits of pre-shared keys.


  This paper studies secure layered video transmission in a multiuser
multiple-input single-output (MISO) beamforming downlink communication system.
The power allocation algorithm design is formulated as a non-convex
optimization problem for minimizing the total transmit power while guaranteeing
a minimum received signal-to-interference-plus-noise ratio (SINR) at the
desired receiver. In particular, the proposed problem formulation takes into
account the self-protecting architecture of layered transmission and artificial
noise generation to prevent potential information eavesdropping. A
semi-definite programming (SDP) relaxation based power allocation algorithm is
proposed to obtain an upper bound solution. A sufficient condition for the
global optimal solution is examined to reveal the tightness of the upper bound
solution. Subsequently, two suboptimal power allocation schemes with low
computational complexity are proposed for enabling secure layered video
transmission. Simulation results demonstrate significant transmit power savings
achieved by the proposed algorithms and layered transmission compared to the
baseline schemes.


  \noindent This manuscript proposes a new imaging medium via isotropic
refractive index of heterogeneous medium. We exploit conformal-map to transfers
the full Maxwell fisheye into a mapped profile within a unit circle. The
imaging resolution of this new profile can be maintained as good as the
mirrored Maxwell fisheye profile or its conformally-mapped counterpart in
previous literature.


  Photoelectric heating (PEH) influences the temperature and density of the
interstellar medium (ISM), and potentially also affecting star formation. PEH
is expected to have a stronger effect on massive galaxies, as they host larger
dust reservoirs compared to dwarf systems. Accordingly, in this paper, we study
PEH effects in Milky Way-like galaxies using smoothed particle hydrodynamics
(SPH) code which self-consistently implements the evolution of the gas, dust,
and interstellar radiation field (ISRF). Dust evolution includes dust formation
by stars, destruction by SNe, and growth in dense media. We find that PEH
suppresses star formation due to the excess heating that reduces the ISM
density. This suppression is seen across the entire range of gas fractions,
star formation recipes, dust models, and PEH efficiencies investigated by our
code. The suppression ranges from negligible values to approximately a factor
of five depending on the specific implementation. Galaxy models having higher
gas fraction experience higher star formation suppression. The adopted dust
model also alters the extent of star formation suppression. Moreover, when PEH
is switched on, galaxy models show higher gas outflow rates and have higher
loading factors indicative of enhanced SNe feedback. In gas-rich models (i.e. a
gas fraction of 0.5), we also find that PEH suppresses the formation of disk
clumps via violent disk instabilities, and thus suppresses bulge formation via
clumps migration to the central regions.


  Erd\H os and R\'{e}nyi claimed and Vu proved that for all $h \ge 2$ and for
all $\epsilon > 0$, there exists $g = g_h(\epsilon)$ and a sequence of integers
$A$ such that the number of ordered representations of any number as a sum of
$h$ elements of $A$ is bounded by $g$, and such that $|A \cap [1,x]| \gg x^{1/h
- \epsilon}$.
  We give two new proofs of this result. The first one consists of an explicit
construction of such a sequence. The second one is probabilistic and shows the
existence of such a $g$ that satisfies $g_h(\epsilon) \ll \epsilon^{-1}$,
improving the bound $g_h(\epsilon) \ll \epsilon^{-h+1}$ obtained by Vu.
  Finally we use the "alteration method" to get a better bound for
$g_3(\epsilon)$, obtaining a more precise estimate for the growth of $B_3[g]$
sequences.


  We study the problem of multi-task non-smooth optimization that arises
ubiquitously in statistical learning, decision-making and risk management. We
develop a data fusion approach that adaptively leverages commonalities among a
large number of objectives to improve sample efficiency while tackling their
unknown heterogeneities. We provide sharp statistical guarantees for our
approach. Numerical experiments on both synthetic and real data demonstrate
significant advantages of our approach over benchmarks.


  A detailed mechanism for the four-component RD387 gasoline surrogate
developed by Lawrence Livermore National Laboratory has shown good agreement
with experiments in engine-relevant conditions. However, with 1388 species and
5933 reversible reactions, this detailed mechanism is far too large to use in
practical engine simulations. Therefore, reduction of the detailed mechanism
was performed using a multi-stage approach consisting of the DRGEPSA method,
unimportant reaction elimination, isomer lumping, and analytic QSS reduction
based on CSP analysis. A new greedy sensitivity analysis algorithm was
developed and demonstrated to be capable of removing more species for the same
error limit compared to the conventional sensitivity analysis used in DRG-based
skeletal reduction methods. Using this new greedy algorithm, several skeletal
and reduced mechanisms were developed at varying levels of complexity and for
different target condition ranges. The final skeletal and reduced mechanisms
consisted of 213 and 148 species, respectively, for a lean-to-stoichiometric,
low-temperature HCCI-like range of conditions. For a lean-to-rich,
high-temperature, SI/CI-like range of conditions, skeletal and reduced
mechanisms were developed with 97 and 79 species, respectively. The skeletal
and reduced mechanisms in this study were produced using an error limit of 10%
and validated using homogeneous autoignition simulations over engine-relevant
conditions - all showed good agreement in predicting ignition delay.
Furthermore, extended validation was performed, including comparison of
autoignition temperature profiles, PSR temperature response curves and
extinction turning points, and laminar flame speed calculations. All the
extended validation showed results within the 10% error limit, demonstrating
the adequacy of the resulting reduced chemistry.


  In Fe pnictide (Pn) superconducting materials, neither Mn- nor Cr- doping to
the Fe site induces superconductivity, even though hole carriers are generated.
This is in strong contrast with the superconductivity appearing when holes are
introduced by alkali metal substitution on the insulating blocking layers. We
investigate in detail the effects of Mn doping on magneto-transport properties
in Ba(Fe$_{1-x}$Mn$_x$As)$_2$ for elucidating the intrinsic reason. The
negative Hall coefficient for $x$ = 0 estimated in the low magnetic field ($B$)
regime gradually increases as $x$ increases, and its sign changes to a positive
one at $x$ = 0.020. Hall resistivities as well as simultaneous interpretation
using the magnetoconductivity tensor including both longitudinal and transverse
transport components clarify that minority holes with high mobility are
generated by the Mn doping via spin density wave (SDW) transition at low
temperatures, while original majority electrons and holes residing in the
parabolic-like Fermi surfaces (FSs) of the semimetallic Ba(FeAs)$_2$ are
negligibly affected. Present results indicate that the mechanism of hole doping
in Ba(Fe$_{1-x}$Mn$_x$As)$_2$ is greatly different from that of the other
superconducting FePns family.


  Quantum algorithms are at the heart of the ongoing efforts to use quantum
mechanics to solve computational problems unsolvable on ordinary classical
computers. Their common feature is the use of genuine quantum properties such
as entanglement and superposition of states. Among the known quantum
algorithms, a special role is played by the Shor algorithm, i.e. a
polynomial-time quantum algorithm for integer factorization, with far reaching
potential applications in several fields, such as cryptography. Here we present
a different algorithm for integer factorization based on another genuine
quantum property: quantum measurement. In this new scheme, the factorization of
the integer $N$ is achieved in a number of steps equal to the number $k$ of its
prime factors, -- e.g., if $N$ is the product of two primes, two quantum
measurements are enough, regardless of the number of digits $n$ of the number
$N$. Since $k$ is the lower bound to the number of operations one can do to
factorize a general integer, one sees that a quantum mechanical setup can
saturate such a bound.


  The background due to the direct diffractive dissociation of the photon into
the $\pi^+\pi^-$-pair to the "elastic" diffractive $\rho^0$-meson production in
electron-proton collisions is calculated. At large $Q^2$ the interference
between resonant and non-resonant $\pi^+ \pi^-$ production changes the
$\sigma^L/\sigma^T$ ratio with the mass of the $2\pi$ (i.e. $\rho^0$-meson)
state.


  A ferromagnetic insulator (FI) in contact with a superconductor (S) is known
to induce a spin splitting of the BCS density of states at the FI/S interface.
This spin splitting causes the Cooper pairs to reduce their singlet-state
correlations and acquire odd-in-frequency triplet correlations. We consider a
diffusive FI/S bilayer with a sharp magnetic domain wall in the FI and study
the local quasiparticle density of states and triplet superconducting
correlations. In the case of collinear alignment of the domains, we obtain
analytical results by solving the Usadel equation. For a small enough exchange
field or weak superconductivity, we also find an analytical expression for
arbitrary magnetic textures, which reveals how the triplet component vector
depends on the local magnetization of the FI. For an arbitrary angle between
the magnetizations and the strength of the exchange field, we numerically solve
the problem of a sharp domain wall. We finally propose two different setups
based on FI/S/F stacks, where F is a ferromagnetic layer, to filter out singlet
pairs and detect the presence of triplet correlations via tunneling
differential conductance measurements.


  Single electrons can be conceived as the simplest quantum nodes in a quantum
network. Between electrons, single photons can act as quantum channels to
exchange quantum information. Despite this appealing picture, in conventional
materials, it is extremely difficult to make individual electrons and photons
coherently interact with each other at the visible-infrared wavelengths
suitable for long-distance communication. Here we theoretically demonstrate
that the self-confined single-electron structure in condensed helium-4 can be a
fascinating candidate for single-electron quantum nodes. Each electron in
helium forms a bubble of 1 to 2 nm radius and coherently interacts with
mid-infrared photons. A parametrically amplified femtosecond laser can drive
the electrons into any superposition between the ground and excited states. An
electron inside a slot-waveguide cavity can strongly couple with cavity photons
and exhibits vacuum Rabi oscillations. Two electrons in the cavity naturally
generate entanglement through their respective coupling to the lossy cavity.
The electron-in-helium system offers unique insight in understanding
nonequilibrium quantum dynamics.


  Advanced self-supervised visual representation learning methods rely on the
instance discrimination (ID) pretext task. We point out that the ID task has an
implicit semantic consistency (SC) assumption, which may not hold in
unconstrained datasets. In this paper, we propose a novel contrastive mask
prediction (CMP) task for visual representation learning and design a mask
contrast (MaskCo) framework to implement the idea. MaskCo contrasts
region-level features instead of view-level features, which makes it possible
to identify the positive sample without any assumptions. To solve the domain
gap between masked and unmasked features, we design a dedicated mask prediction
head in MaskCo. This module is shown to be the key to the success of the CMP.
We evaluated MaskCo on training datasets beyond ImageNet and compare its
performance with MoCo V2. Results show that MaskCo achieves comparable
performance with MoCo V2 using ImageNet training dataset, but demonstrates a
stronger performance across a range of downstream tasks when COCO or Conceptual
Captions are used for training. MaskCo provides a promising alternative to the
ID-based methods for self-supervised learning in the wild.


  We study the control band policy arising in the context of cash balance
management. A policy is specified by four parameters (d,D,U,u). The controller
pushes the process up to D as soon as it goes below d and pushes down to U as
soon as it goes above u, while he does not intervene whenever it is within the
set (d, u). We focus on the case when the underlying process is a spectrally
one-sided Levy process and obtain the expected fixed and proportional
controlling costs as well as the holding costs under the band policy.


  We examine the qualitative features of parton production through
materialization in heavy-ion collisions within perturbative QCD, and estimate
the magnitude of the resulting parton density created during the early stage of
the collisions. The implications for ``anomalous'' $J/\psi$ suppression
observed in Pb+Pb collisions at the CERN SPS are discussed. We argue that the
A-dependence of absorption of $J/\psi$ by (partonic) comovers is steeper than
assumed in most phenomenological models, because the absorption process is
dominated by quasi-perturbative QCD interactions. Our argument is supported by
results recently obtained in the framework of the parton cascade model. We
predict significant ``anomalous'' suppression for Pb+Pb collisions at the
CERN-SPS, but not for S+U collisions.


  We introduce a Fourier-based fast algorithm for Gaussian process regression
in low dimensions. It approximates a translationally-invariant covariance
kernel by complex exponentials on an equispaced Cartesian frequency grid of $M$
nodes. This results in a weight-space $M\times M$ system matrix with Toeplitz
structure, which can thus be applied to a vector in ${\mathcal O}(M \log{M})$
operations via the fast Fourier transform (FFT), independent of the number of
data points $N$. The linear system can be set up in ${\mathcal O}(N + M
\log{M})$ operations using nonuniform FFTs. This enables efficient
massive-scale regression via an iterative solver, even for kernels with
fat-tailed spectral densities (large $M$). We provide bounds on both kernel
approximation and posterior mean errors. Numerical experiments for
squared-exponential and Mat\'ern kernels in one, two and three dimensions often
show 1-2 orders of magnitude acceleration over state-of-the-art rank-structured
solvers at comparable accuracy. Our method allows 2D
Mat\'ern-$\mbox{$\frac{3}{2}$}$ regression from $N=10^9$ data points to be
performed in 2 minutes on a standard desktop, with posterior mean accuracy
$10^{-3}$. This opens up spatial statistics applications 100 times larger than
previously possible.


  With the latest technology of vectoring, DSL data rates in the order of
100Mbps have become a reality that is under field deployment. The key is to
cancel crosstalk from other lines, which is also known as multiuser MIMO
cancellation for wireless communications. During the DSL system upgrade phase
of field deployment, mix of legacy and vectoring-enabled VDSL lines is
inevitable and a channel estimation solution for the entire mix is needed
before vectoring can be enforced. This paper describes a practical method for
crosstalk channel estimation for downstream vectoring, assuming that a
vectoring-enabled DSLAM forces DMT symbol-level timing to be aligned for all of
the lines, but also assuming that the location of synch symbols are aligned
only among vectoring-enabled lines. Each vectoring-enabled receiver is capable
of reporting error samples to vectoring-DSLAM. The estimation method is not
only practical, but also matches the performance of Maximum-Likelihood
estimator for the selected training sequences.


  The results of a linear elasticity analysis yields that nano-rod inclusions
aligned along the c axis of a thin film of YBa2Cu3O{7-delta}, such as BaZrO3
and BaSnO3, squeeze that matrix by pure shear. The sensitivity of the
superconducting critical temperature in that material to the latter implies
that the phase boundary separating the nano-rod inclusion from the
superconductor acts as a collective pinning center for the vortex lattice that
appears in external magnetic field. A dominant contribution to the in-field
critical current can result. The elasticity analysis also finds that the growth
of nano-rod inclusions can be weakly metastable when the inclusion is softer
than the matrix.


  Social inequalities are ubiquitous and evolve towards a universal limit.
Herein, we extensively review the values of inequality measures, namely the
Gini ($g$) index and the Kolkata ($k$) index, two standard measures of
inequality used in the analysis of various social sectors through data
analysis. The Kolkata index, denoted as $k$, indicates the proportion of the
`wealth' owned by $(1-k)$ fraction of the `people'. Our findings suggest that
both the Gini index and the Kolkata index tend to converge to similar values
(around $g=k \approx 0.87$, starting from the point of perfect equality, where
$g=0$ and $k=0.5$) as competition increases in different social institutions,
such as markets, movies, elections, universities, prize winning, battle fields,
sports (Olympics), etc., under conditions of unrestricted competition (no
social welfare or support mechanism). In this review, we present the concept of
a generalized form of Pareto's 80/20 law ($k=0.80$), where the coincidence of
inequality indices is observed. The observation of this coincidence is
consistent with the precursor values of the $g$ and $k$ indices for the
self-organized critical (SOC) state in self-tuned physical systems such as sand
piles. These results provide quantitative support for the view that interacting
socioeconomic systems can be understood within the framework of SOC, which has
been hypothesized for many years. These findings suggest that the SOC model can
be extended to capture the dynamics of complex socioeconomic systems and help
us better understand their behavior.


  Black-hole quasinormal modes (QNM) have been the subject of much recent
attention, with the hope that these oscillation frequencies may shed some light
on the elusive theory of quantum gravity. We compare numerical results for the
QNM spectrum of the (rotating) Kerr black hole with an {\it exact} formula
Re$\omega \to T_{BH}\ln 3+\Omega m$, which is based on Bohr's correspondence
principle. We find a close agreement between the two. Possible implications of
this result to the area spectrum of quantum black holes are discussed.


  We extend short-time existence and stability of the Dirichlet energy flow as
proven in a previous paper by the authors to a broader class of energy
functionals. Furthermore, we derive some monotonely decreasing quantities for
the Dirichlet energy flow and investigate an equation of soliton type. In
particular, we show that nearly parallel G_2-structures satisfy this soliton
equation and study their infinitesimal soliton deformations.


  During the last decade coarse-grained nucleotide models have emerged that
allow us to DNA and RNA on unprecedented time and length scales. Among them is
oxDNA, a coarse-grained, sequence-specific model that captures the
hybridisation transition of DNA and many structural properties of single- and
double-stranded DNA. oxDNA was previously only available as standalone
software, but has now been implemented into the popular LAMMPS molecular
dynamics code. This article describes the new implementation and analyses its
parallel performance. Practical applications are presented that focus on
single-stranded DNA, an area of research which has been so far
under-investigated. The LAMMPS implementation of oxDNA lowers the entry barrier
for using the oxDNA model significantly, facilitates future code development
and interfacing with existing LAMMPS functionality as well as other
coarse-grained and atomistic DNA models.


  We prove quantum dynamical lower bounds for one-dimensional continuum
Schr\"odinger operators that possess critical energies for which there is slow
growth of transfer matrix norms and a large class of compactly supported
initial states. This general result is applied to a number of models, including
the Bernoulli-Anderson model with a constant single-site potential.


  For any right-angled Artin group $A_{\Gamma}$ we construct a
finite-dimensional space $\mathcal{O}_{\Gamma}$ on which the group
$\text{Out}(A_{\Gamma})$ of outer automorphisms of $A_{\Gamma}$ acts with
finite point stabilizers. We prove that $\mathcal{O}_{\Gamma}$ is contractible,
so that the quotient is a rational classifying space for
$\text{Out}(A_{\Gamma})$. The space $\mathcal{O}_{\Gamma}$ blends features of
the symmetric space of lattices in $\mathbb{R}^n$ with those of Outer space for
the free group $F_n$. Points in $\mathcal{O}_{\Gamma}$ are locally CAT(0)
metric spaces that are homeomorphic (but not isometric) to certain locally
CAT(0) cube complexes, marked by an isomorphism of their fundamental group with
$A_{\Gamma}$.


  We exploit the excursion set approach in integral formulation to derive
novel, accurate analytic approximations of the unconditional and conditional
first crossing distributions, for random walks with uncorrelated steps and
general shapes of the moving barrier; we find the corresponding approximations
of the unconditional and conditional halo mass functions for Cold Dark Matter
power spectra to represent very well the outcomes of state-of-the-art
cosmological N-body simulations. In addition, we apply these results to derive,
and confront with simulations, other quantities of interest in halo statistics,
including the rates of halo formation and creation, the average halo growth
history, and the halo bias. Finally, we discuss how our approach and main
results change when considering random walks with correlated instead of
uncorrelated steps, and Warm instead of Cold Dark Matter power spectra.


  Human-driven vehicles (HVs) exhibit complex and diverse behaviors. Accurately
modeling such behavior is crucial for validating Robot Vehicles (RVs) in
simulation and realizing the potential of mixed traffic control. However,
existing approaches like parameterized models and data-driven techniques
struggle to capture the full complexity and diversity. To address this, in this
work, we introduce CARL, a hybrid approach that combines imitation learning for
close proximity car-following and probabilistic sampling for larger headways.
We also propose two classes of RL-based RVs: a safety RV focused on maximizing
safety and an efficiency RV focused on maximizing efficiency. Our experiments
show that the safety RV increases Time-to-Collision above the critical 4-second
threshold and reduces Deceleration Rate to Avoid a Crash by up to 80%, while
the efficiency RV achieves improvements in throughput of up to 49%. These
results demonstrate the effectiveness of CARL in enhancing both safety and
efficiency in mixed traffic.


  The continuous and discrete symmetries of a dimensionally reduced type IIB
superstring action are employed to generate four-dimensional cosmological
solutions with non-trivial Neveu-Schwarz/Neveu-Schwarz and Ramond-Ramond
form-fields from the dilaton-moduli-vacuum solutions.


  In this paper we will consider the minisuperspace approach to S-branes
dynamics in the Schr\"odinger picture description. Time-evolution of vacuum
wave functional for quantum field theory on S-brane is studied. Open string
pair production is calculated. The analysis of density matrix for mixed states
is also performed.


  Recently, Baumslag and Wiegold proved that a finite group $G$ is nilpotent if
and only if $o(xy)=o(x)o(y)$ for every $x,y\in G$ of coprime order. Motivated
by this result, we study the groups with the property that $(xy)^G=x^Gy^G$ and
those with the property that $\chi(xy)=\chi(x)\chi(y)$ for every complex
irreducible character $\chi$ of $G$ and every nontrivial $x, y \in G$ of
pairwise coprime order. We also consider several ways of weakening the
hypothesis on $x$ and $y$. While the result of Baumslag and Wiegold is
completely elementary, some of our arguments here depend on (parts of) the
classification of finite simple groups.


  We propose a model predictive control (MPC) based approach to a flock control
problem with obstacle avoidance capability in a leader-follower framework,
utilizing the future trajectory prediction computed by each agent. We employ
the traditional Reynolds' flocking rules (cohesion, separation, and alignment)
as a basis, and tailor the model to fit a navigation (as opposed to formation)
purpose. In particular, we introduce several concepts such as the credibility
and the importance of the gathered information from neighbors, and dynamic
trade-offs between references. They are based on the observations that
near-future predictions are more reliable, agents closer to leaders are
implicit carriers of more educated information, and the predominance of either
cohesion or alignment is dictated by the distance between the agent and its
neighbors. These features are incorporated in the MPC formulation, and their
advantages are discussed through numerical simulations.


  We propose the zero-point of the cluster-cluster correlation function as a
sensitive test for the shape of the power spectrum of initial fluctuations. It
is now possible to go beyond the power law description to measure the point at
which the correlation function becomes zero. Four independent measurements
indicate that the zero point, $r_0$, should be in the range (40-60)$h^{-1}$Mpc.
The large value of $r_0$ at which the zero-point occurs rules out conventional
CDM models independently of the assumed amplitude. Models with $\Omega < 0.25$
should be rejected because they predict too large $r_0$. If the age of the
Universe is assumed to be larger than 15 Gyr, models with either $\Omega<0.5$
or $h> 0.55$ are rejected. We present the results of numerical simulations of
clusters in an $\Omega=1$ cosmological model with a mixture of cold plus hot
dark matter (CHDM). The correlation function we determined for the simulated
clusters has a zero-point, $r_0=55h^{-1}$Mpc that accurately matches the zero
point of the observed function.


  We calculate the reaction and the fusion cross-sections of neutron-rich heavy
nuclei taking light exotic isotopes as projectiles. Results of neutron-rich Pb
and U isotopes are demonstrated as the representative targets and He, B as the
projectiles. The Gluaber Model and the Coupled Channel Formalism are used to
evaluate the reaction and the fusion cross-sections for the cases
considered.Based on the analysis of these cross-sections, we predict the
formation of heavy, superheavy and super-superheavy elements through rapid
neutron/light nuclei capture r-process of the nucleosynthesis in astrophysical
objects.


  We survey results in algebraic complexity theory, focusing on matrix
multiplication. Our goals are
  (i.) to show how open questions in algebraic complexity theory are naturally
posed as questions in geometry and representation theory, (ii.) to motivate
researchers to work on these questions, and (iii.) to point out relations with
more general problems in geometry. The key geometric objects for our study are
the secant varieties of Segre varieties. We explain how these varieties are
also useful for algebraic statistics, the study of phylogenetic invariants, and
quantum computing.


  Let $\mathbb F$ be a finite field and let $\mathcal A$ and $\mathcal B$ be
vector spaces of $\mathbb F$-valued continuous functions defined on locally
compact spaces $X$ and $Y$, respectively. We look at the representation of
linear bijections $H:\mathcal A\longrightarrow \mathcal B$ by continuous
functions $h:Y\longrightarrow X$ as weighted composition operators. In order to
do it, we extend the notion of Hamming metric to infinite spaces. Our main
result establishes that under some mild conditions, every Hamming isometry can
be represented as a weighted composition operator. Connections to coding theory
are also highlighted.


  Suppose $X$ is a smooth quasiprojective variety over $\cc$ and $\rho : \pi
_1(X,x) \to SL(2,\cc)$ is a Zariski-dense representation with quasiunipotent
monodromy at infinity. Then $\rho$ factors through a map $X\to Y$ with $Y$
either a DM-curve or a Shimura modular stack.


  Deep Q-learning based algorithms have been applied successfully in many
decision making problems, while their theoretical foundations are not as well
understood. In this paper, we study a Fitted Q-Iteration with two-layer ReLU
neural network parameterization, and find the sample complexity guarantees for
the algorithm. Our approach estimates the Q-function in each iteration using a
convex optimization problem. We show that this approach achieves a sample
complexity of $\tilde{\mathcal{O}}(1/\epsilon^{2})$, which is order-optimal.
This result holds for a countable state-spaces and does not require any
assumptions such as a linear or low rank structure on the MDP.


  We investigate the moduli space of sheaves supported on space curves of
degree 4 and having Euler characteristic 1. We give an elementary proof of the
fact that this moduli space consists of three irreducible components.


  A recent theory by Bertini, De Sole, Gabrielli, Jona-Lasinio and Landim
predicts a temporal asymmetry in the fluctuation-relaxation paths of certain
observables of nonequilibrium systems in local thermodynamic equilibrium. We
find temporal asymmetries in the fluctuation-relaxation paths of a form of
local heat flow, in the nonequilibrium FPU-$\zb$ model of Lepri, Livi and
Politi.


  In an XMM-Newton raster observation of the bright local group spiral galaxy
M33 we study the population of X-ray sources (X-ray binaries, supernova
remnants, super-shells) down to a 0.5-10 keV luminosity of 10^35 erg s^-1 --
more than a factor of 10 deeper than earlier ROSAT observations. EPIC spectra
and hardness ratios are used to distinguish between different source classes.
We confirmed the 3.45 d orbital light curve of the X-ray binary M33 X7,
detected a transient super-soft source in M33, and searched for short term
variability of the brighter sources. We characterize the diffuse X-ray
component that is correlated with the inner disk and spiral arms. We will
compare the results with other nearby galaxies.


  Generic SO(10) GUT models suffer from the problem that Planck scale induced
non-renormalizable proton decay operators require extreme suppression of their
couplings to be compatible with present experimental upper limits. One way to
resolve this problem is to supplement SO(10) by simple gauged discrete
symmetries which can also simultaneously suppress the renormalizable R-parity
violating ones when they occur and make the theory "more natural". Here we
discuss the phenomenological viability of such models. We first show that for
both classes of models, e.g the ones that use ${\bf 16}_H$ or ${\bf 126}_H$ to
break B-L symmetry, the minimal Higgs content which is sufficient for proton
decay suppression is inadequate for explaining fermion masses despite the
presence of all apparently needed couplings. We then present an extended ${\bf
16}_H$ model, with three {\bf 10} and three {\bf 45}-Higgs, where is free of
this problem. We propose this as a realistic and "natural" model for fermion
unification and discuss the phenomenology of this model e.g. its predictions
for neutrino mixings and lepton flavor violation.


  In this paper, we apply conformal prediction to time series data. Conformal
prediction isa method that produces predictive regions given a confidence
level. The regions outputs arealways valid under the exchangeability
assumption. However, this assumption does not holdfor the time series data
because there is a link among past, current, and future
observations.Consequently, the challenge of applying conformal predictors to
the problem of time seriesdata lies in the fact that observations of a time
series are dependent and therefore do notmeet the exchangeability assumption.
This paper aims to present a way of constructingreliable prediction intervals
by using conformal predictors in the context of time series. Weuse the nearest
neighbors method based on the fast parameters tuning technique in theweighted
nearest neighbors (FPTO-WNN) approach as the underlying algorithm. Dataanalysis
demonstrates the effectiveness of the proposed approach.


  We write down an explicit projection that maps any given 4-spinor to a point
in 3+1 spacetime while commuting with the Lorentz action. This suggests that a
Lorentz invariant theory - including spacetime itself - has a more natural
expression in terms of these primitive spinor variables, while an ordinary
spacetime interpretation may be obtained by projecting solutions. Using this
projection, we show how the real components of a given 4-spinor reference a
point in a five dimensional spacetime.


  Modeling of gamma-ray burst (GRB) prompt emission spectra sometimes requires
a (quasi-) thermal spectral component in addition to the Band function. In
photospheric emission models, a prominent thermal component broadened by
sub-photospheric dissipation is expected to be released at the photospheric
radius, $r_{\rm ph}\sim10^{12}\,$cm. We consider an ultra-relativistic strongly
magnetized outflow with a striped-wind magnetic-field structure undergoing
gradual and continuous magnetic energy dissipation at $r<r_s$ that heats and
accelerates the flow, leading to a bulk Lorentz factor
$\Gamma(r)=\Gamma_\infty\min[1,(r/r_s)^{1/3}]$, where typically $r_{\rm
ph}<r_s$. Similar dynamics and energy dissipation rates are also expected in
highly-variable magnetized outflows without stripes/field-reversals. Two modes
of particle energy injection are considered: (a) power-law electrons, e.g.
accelerated by magnetic reconnection, and (b) continuous distributed heating of
all electrons (and $e^\pm$-pairs), e.g. due to MHD instabilities. Time-resolved
energy spectra are obtained using a numerical code that evolves coupled kinetic
equations for a photon-electron-positron plasma. We find that (i) the thermal
component peaks at $(1+z)E_{\rm pk}\sim0.2-1\,$MeV, for a source at redshift
$z$, and becomes subdominant if the total injected energy density exceeds the
thermal one, (ii) power-law electrons cool mainly by synchrotron emission
whereas mildly relativistic and almost monoenergetic electrons in the
distributed heating scenario cool by Comptonization on thermal peak photons,
(iii) both scenarios can yield a low-energy break at $E_{\rm br}\approx E_{\rm
th}$, and (iv) the $0.5(1+z)^{-1}\,$keV X-ray emission is suppressed in the
power-law injection case, but it is expected for the distributed heating
scenario. Energy-dependent linear polarization can differentiate between the
two energy injection cases.


  We have investigated the optical and transport properties of MBE grown
short-period superlattices of InAs/GaAs with different numbers of periods (3 <=
N <= 24) and a total thickness 14 nm. Bandstructure calculations show that
these superlattices represent a quantum well with average composition
In_0.16Ga_0.84As. The electron wave functions are only slightly modulated by
the superlattice potential as compared to a single quantum well with the same
composition, which was grown as a reference sample. The photoluminescence, the
resistance, the Shubnikov-de Haas effect and the Hall effect have been measured
as a function of the InAs layer thickness Q in the range 0.33 <= Q <= 2.7
monolayers (ML). The electron densities range from 6.8 to 11.5x10^11 cm^-2 for
Q <= 2.0 ML. The photoluminescence and magnetotransport data show that only one
subband is occupied. When Q >= 2.7 ML quantum dots are formed and the metallic
type of conductivity changes to variable range hopping conductivity.


  Fast Radios Bursts (FRBs) show large dispersion measures (DMs), suggesting an
extragalactic location. We analyze the DMs of the 11 known FRBs in detail and
identify steps as integer multiples of half the lowest DM found, 187.5cm$^{-3}$
pc, so that DMs occur in groups centered at 375, 562, 750, 937, 1125cm$^{-3}$
pc, with errors observed <5%. We estimate the likelhood of a coincidence as
5:10,000. We speculate that this could originate from a Galaxy population of
FRBs, with Milky Way DM contribution as model deviations, and an underlying
generator process that produces FRBs with DMs in discrete steps. However, we
find that FRBs tend to arrive at close to the full integer second, like
man-made perytons. If this holds, FRBs would also be man-made. This can be
verified, or refuted, with new FRBs to be detected.


  The reason for the difference in the composite X-ray spectrum between
radio-loud quasars (RLQs) and radio-quiet quasars (RQQs) is still unclear. To
study this difference, we built a new composite X-ray spectrum of RLQs by using
Chandra X-ray data and Sloan Digital Sky Survey (SDSS) optical data for the
sample of 3CRR quasars. We find the X-ray spectra of all 3CRR quasars except
for 3C 351 have no soft X-ray excess and can be fitted with an absorbed
power-law model well. Our composite X-ray spectrum is similar to that of
\cite{ShangEtal2011apjs} for RLQs, showing higher hard X-ray and lower soft
X-ray flux than the composite X-ray spectrum of RQQs. Most blazar-like 3CRR
quasars have higher X-ray flux than the median composite X-ray spectrum, which
could be related to the contribution of beamed jet emission at X-ray band. From
the literature, we find that nineteen 3CRR quasars have extended X-ray emission
related to radio jets, indicating inevitable contribution of jets at X-ray
band. In contrast to RQQs, the X-ray photon index of 3CRR quasars does not
correlate with the Eddington ratio. Our results suggest that the jet emission
at X-ray band in RLQs could be related with the difference of composite X-ray
spectrum between RLQs and RQQs.


  The polaron, an electron dressed with HCB excitations, remains light even in
the strong coupling limit as its effective mass remains of the order of the
free electron mass. This result is in a sharp contrast to the Holstein model
where the electron effective mass increases exponentially with the
electron-phonon coupling. HCB degrees of freedom mediate the attractive
potential between two electrons that form a bound singlet bipolaron state at
any non-zero coupling strength. In the low-frequency regime of the electron
spectral function we observe a quasi-particle (QP) band that is separated from
the continuum of states only in the central part of the Brillouin zone. The
quasiparticle weight approaches zero as the QP band enters the continuum where
it obtains a finite lifetime. At finite temperature an electron can annihilate
thermally excited HCB's. Such thermally activated processes lead to a buildup
of the spectral weight below the QP band. While the investigated model bears a
resemblance with the Holstein model, we point out many important differences
that originate from the binary HCB excitation spectrum, which in turn mimics
spin-$1\over 2$ degrees of freedom


  The $H$-theorem, originally derived at the level of Boltzmann non-linear
kinetic equation for a dilute gas undergoing elastic collisions, strongly
constrains the velocity distribution of the gas to evolve irreversibly towards
equilibrium. As such, the theorem could not be generalized to account for
dissipative systems: the conservative nature of collisions is an essential
ingredient in the standard derivation. For a dissipative gas of grains, we
construct here a simple functional $\mathcal H$ related to the original $H$,
that can be qualified as a Lyapunov functional. It is positive, and results
backed by three independent simulation approaches (a deterministic spectral
method, the stochastic Direct Simulation Monte Carlo technique, and Molecular
Dynamics) indicate that it is also non-increasing. Both driven and unforced
cases are investigated.


  We consider the branching ratio for the process $t \to c \gamma$ in the
context of the General Two Higgs Doublet Model type III. We find that taking
into account reasonable values for the parameter $\tan \beta$ is possible to
get values of this branching ratio up to orders of magnitude lying in the range
of sensitivity of near future top quark experiments. For values of $B(t \to c
\gamma) \sim 1-9 \times 10^{-5}$, values between 8-15 for $\tan \beta$ are
allowed.


  We present an extended discussion of a recently proposed theoretical approach
for off-resonance tunneling transport. The proofs and the arguments are
explained at length and simple analogies and illustrations are used where
possible. The result is an analytic formula for the asymptotic tunneling
conductance which involves the overlap of three well defined physical
quantities. We argue that the formula can be used to gain fresh insight into
the tunneling transport characteristics of various systems. The formalism is
applied here to molecular devices consisting of planar phenyl chains connected
to gold electrodes via amine linkers.


  We analyze stationary current of bosonic carriers in the Bose-Hubbard chain
of length $L$ where the first and the last sites of the chain are attached to
reservoirs of Bose particles acting as the particle source and sink,
respectively. The analysis is curried out by using the pseudoclassical approach
which reduces the original quantum problem to the classical problem for $L$
coupled nonlinear oscillators. It is shown that an increase of oscillator
nonlinearity (which is determined by the strength of inter-particle
interactions) results in a transition from the ballistic transport regime,
where the stationary current is independent of the chain length, to the
diffusive regime, where the current is inverse proportional to $L$.


  This paper presents a generalization of our earlier work in [19]. In this
paper, the two concepts, generic regular decomposition (GRD) and
regular-decomposition-unstable (RDU) variety introduced in [19] for generic
zero-dimensional systems, are extended to the case where the parametric systems
are not necessarily zero-dimensional. An algorithm is provided to compute GRDs
and the associated RDU varieties of parametric systems simultaneously on the
basis of the algorithm for generic zero-dimensional systems proposed in [19].
Then the solutions of any parametric system can be represented by the solutions
of finitely many regular systems and the decomposition is stable at any
parameter value in the complement of the associated RDU variety of the
parameter space. The related definitions and the results presented in [19] are
also generalized and a further discussion on RDU varieties is given from an
experimental point of view. The new algorithm has been implemented on the basis
of DISCOVERER with Maple 16 and experimented with a number of benchmarks from
the literature.


  In the practical work of websites popularization, analysis of their
efficiency and downloading it is of key importance to take into account
web-ratings data. The main indicators of website traffic include the number of
unique hosts from which the analyzed website was addressed and the number of
granted web pages (hits) per unit time (for example, day, month or year). Of
certain interest is the ratio between the number of hits (S) and hosts (H). In
practice there is even used such a concept as "average number of viewed pages"
(S/H), which on default supposes a linear dependence of S on H. What actually
happens is that linear dependence is observed only as a partial case of power
dependence, and not always. Another new power law has been discovered on the
Internet, in particular, on the WWW.


  Multimodal target/aspect sentiment classification combines multimodal
sentiment analysis and aspect/target sentiment classification. The goal of the
task is to combine vision and language to understand the sentiment towards a
target entity in a sentence. Twitter is an ideal setting for the task because
it is inherently multimodal, highly emotional, and affects real world events.
However, multimodal tweets are short and accompanied by complex, possibly
irrelevant images. We introduce a two-stream model that translates images in
input space using an object-aware transformer followed by a single-pass
non-autoregressive text generation approach. We then leverage the translation
to construct an auxiliary sentence that provides multimodal information to a
language model. Our approach increases the amount of text available to the
language model and distills the object-level information in complex images. We
achieve state-of-the-art performance on two multimodal Twitter datasets without
modifying the internals of the language model to accept multimodal data,
demonstrating the effectiveness of our translation. In addition, we explain a
failure mode of a popular approach for aspect sentiment analysis when applied
to tweets. Our code is available at
\textcolor{blue}{\url{https://github.com/codezakh/exploiting-BERT-thru-translation}}.


  Nearly three decades ago, Bar-Noy, Motwani and Naor showed that no online
edge-coloring algorithm can edge color a graph optimally. Indeed, their work,
titled "the greedy algorithm is optimal for on-line edge coloring", shows that
the competitive ratio of $2$ of the na\"ive greedy algorithm is best possible
online. However, their lower bound required bounded-degree graphs, of maximum
degree $\Delta = O(\log n)$, which prompted them to conjecture that better
bounds are possible for higher-degree graphs. While progress has been made
towards resolving this conjecture for restricted inputs and arrivals or for
random arrival orders, an answer for fully general \emph{adversarial} arrivals
remained elusive.
  We resolve this thirty-year-old conjecture in the affirmative, presenting a
$(1.9+o(1))$-competitive online edge coloring algorithm for general graphs of
degree $\Delta = \omega(\log n)$ under vertex arrivals. At the core of our
results, and of possible independent interest, is a new online algorithm which
rounds a fractional bipartite matching $x$ online under vertex arrivals,
guaranteeing that each edge $e$ is matched with probability $(1/2+c)\cdot x_e$,
for a constant $c>0.027$.


  Theoretically and experimentally, we study electroviscous phenomena resulting
from charge-flow coupling in a nanoscale capillary. Our theoretical approach
relies on Poisson-Boltzmann mean-field theory and on coupled linear relations
for charge and hydrodynamic flows, including electro-osmosis and charge
advection. With respect to the unperturbed Poiseuille flow, we define an
electroviscous coupling parameter $\xi$, which turns out to be maximum where
the film thickness $h_0$ is comparable to the screening length $\lambda$. We
also present dynamic AFM data for the visco-elastic response of a confined
water film in sphere-plane geometry; our theory provides a quantitative
description for the electroviscous drag coefficient and the electrostatic
repulsion as a function of the film thickness, with the surface charge density
as the only free parameter. Charge regulation sets in at even smaller
distances.


  We present a method for including steady-state gas flows in the plasma
physics code Cloudy, which was previously restricted to modeling static
configurations. The numerical algorithms are described in detail, together with
an example application to plane-parallel ionization-bounded HII regions. As
well as providing the foundation for future applications to more complex flows,
we find the following specific results regarding the effect of advection upon
ionization fronts in HII regions:
  1. Significant direct effects of advection on the global emission properties
occur only when the ionization parameter is lower than is typical for HII
regions.
  2. The overheating of partially ionized gas in the front is not large, even
for supersonic (R-type) fronts.
  3. The most significant morphological signature of advective fronts is an
electron density spike that occurs at the ionization front. Observational
evidence for such a spike is found in images of the Orion bar.
  4. Plane-parallel, weak-D fronts are found to show at best a shallow
correlation between mean velocity and ionization potential for optical emission
lines even when the flow velocity closely approaches the ionized sound speed.


  We study multidimensional mechanism design in a common scenario where players
have private information about their willingness to pay and their ability to
pay. We provide a complete characterization of dominant-strategy
incentive-compatible direct mechanisms where over-reporting the budget is not
possible. In several settings, reporting larger budgets can be made suboptimal
with a small randomized modification to the payments. We then derive a closely
related partial characterization for the general case where players can
arbitrarily misreport their private budgets. Immediate applications of these
results include simple characterizations for mechanisms with publicly-known
budgets and for mechanisms without monetary transfers.
  The celebrated revenue equivalence theorem states that the seller"s revenue
for a broad class of standard auction formats and settings will be the same in
equilibrium. Our main application is a revenue equivalence theorem for
financially constrained bidders.


  The aim of this thesis is to systematically and consistently study strongly
coupled bosonic and fermionic conformal field theories using the large quantum
number expansion. The idea behind it is to study sectors of conformal field
theories that are characterised by large quantum numbers under global
symmetries. In this limit, the conformal field theories, even if they initially
were strongly coupled and interacting, can now be written in terms of an
effective field theory that is weakly coupled. Some common effective field
theories that appear in the literature are the bosonic conformal superfluid and
the Fermi sphere, condensed matter systems characterised by a high particle
density, making the study of such systems a cross-disciplinary matter.


  We provide a quick proof of the following known result: the Sobolev space
associated with the Euclidean space, endowed with the Euclidean distance and an
arbitrary Radon measure, is Hilbert. Our new approach relies upon the
properties of the Alberti-Marchese decomposability bundle. As a consequence of
our arguments, we also prove that if the Sobolev norm is closable on
compactly-supported smooth functions, then the reference measure is absolutely
continuous with respect to the Lebesgue measure.


  We consider the problem of estimating causal DAG models from a mix of
observational and interventional data, when the intervention targets are
partially or completely unknown. This problem is highly relevant for example in
genomics, since gene knockout technologies are known to have off-target
effects. We characterize the interventional Markov equivalence class of DAGs
that can be identified from interventional data with unknown intervention
targets. In addition, we propose a provably consistent algorithm for learning
the interventional Markov equivalence class from such data. The proposed
algorithm greedily searches over the space of permutations to minimize a novel
score function. The algorithm is nonparametric, which is particularly important
for applications to genomics, where the relationships between variables are
often non-linear and the distribution non-Gaussian. We demonstrate the
performance of our algorithm on synthetic and biological datasets. Links to an
implementation of our algorithm and to a reproducible code base for our
experiments can be found at https://uhlerlab.github.io/causaldag/utigsp.


  Benefiting from massive corpora and advanced hardware, large language models
(LLMs) exhibit remarkable capabilities in language understanding and
generation. However, their performance degrades in scenarios where multiple
tasks are encountered sequentially, also known as catastrophic forgetting. In
this paper, we propose orthogonal low-rank adaptation (O-LoRA), a simple and
efficient approach for continual learning in language models, effectively
mitigating catastrophic forgetting while learning new tasks. Specifically,
O-LoRA learns tasks in different (low-rank) vector subspaces that are kept
orthogonal to each other in order to minimize interference. Our method induces
only marginal additional parameter costs and requires no user data storage for
replay. Experimental results on continual learning benchmarks show that our
method outperforms state-of-the-art methods. Furthermore, compared to previous
approaches, our method excels in preserving the generalization ability of LLMs
on unseen tasks.


  Phenomenological studies of a CP-violating two-Higgs-doublet Model with
type-II Yukawa couplings are presented. In the light of recent LHC data, an
update on the viable parameter space that survives both the experimental and
theoretical constraints is provided. In addition, the scope of the LHC in
exploring this model through the discovery of a charged Higgs boson that decays
in the tauonic mode is analysed. For this, various production channels were
investigated, with emphasis on the boson-associated channel $gg\to H_i\to H^\pm
W^\mp$ and the fermion-associated channels $gb\to H^\pm t$ and $gg\to H^\pm
bt$. For the latter, a signal-over-background analysis is performed.


  In this work, we study the value of an Asian option in the case of
exponential Levy markets. More specifically, we are interested in the NIG
(normal inverse Gaussian) the VG (variance gamma) models. The exponential Levy
models produce incomplete markets. There are therefore an infinite number of
equivalent martingale measures. We are interested in two methods of
constructing of the risk-neutral measures. The first is based on the Esscher
transform, and the other consists of bringing a risk-neutral correction on the
dynamics of the trajectories. It turns out, according to the numerical results
obtained, that the two methods generally produce the same prices.


  We study the dephasing of two-electron states in a single quantum dot in both
GaAs and Si. We investigate dephasing induced by electron-phonon coupling and
by charge noise analytically for pure orbital excitations in GaAs and Si, as
well as for pure valley excitations in Si. In GaAs, polar optical phonons give
rise to the most important contribution, leading to a typical dephasing rate of
~5.9 GHz. For Si, intervalley optical phonons lead to a typical dephasing rate
of ~140 kHz for orbital excitations and ~1.1 MHz for valley excitations. For
harmonic, disorder-free quantum dots, charge noise is highly suppressed for
both orbital and valley excitations, since neither has an appreciable dipole
moment to couple to electric field variations from charge fluctuators. However,
both anharmonicity and disorder break the symmetry of the system, which can
lead to increased dipole moments and therefore faster dephasing rates.


  Many tasks are subject to failure before completion. Two of the most common
failure recovery strategies are restart and checkpointing. Under restart, once
a failure occurs, it is restarted from the beginning. Under checkpointing, the
task is resumed from the preceding checkpoint after the failure. We study
asymptotic efficiency of restart for an infinite sequence of tasks, whose sizes
form a stationary sequence. We define asymptotic efficiency as the limit of the
ratio of the total time to completion in the absence of failures over the total
time to completion when failures take place. Whether the asymptotic efficiency
is positive or not depends on the comparison of the tail of the distributions
of the task size and the random variables governing failures. Our framework
allows for variations in the failure rates and dependencies between task sizes.
We also study a similar notion of asymptotic efficiency for checkpointing when
the task is infinite a.s. and the inter-checkpoint times are i.i.d.. Moreover,
in checkpointing, when the failures are exponentially distributed, we prove the
existence of an infinite sequence of universal checkpoints, which are always
used whenever the system starts from any checkpoint that precedes them.


  We discuss thermal and active fluctuations of a compressible bilayer vesicle
by using the results of hydrodynamic theory for vesicles. Coupled Langevin
equations for the membrane deformation and the density fields are employed to
calculate the power spectral density matrix of membrane fluctuations. Thermal
contribution is obtained by means of the fluctuation dissipation theorem,
whereas active contribution is calculated from exponentially decaying time
correlation functions of active random forces. We obtain the total power
spectral density as a sum of thermal and active contributions. An apparent
response function is further calculated in order to compare with the recent
microrheology experiment on red blood cells. An enhanced response is predicted
in the low-frequency regime for non-thermal active fluctuations.


  An old calculation of the s-wave pi-pi scattering lengths is updated and
supplemented with experimental data on the pi-pi s-wave phase shift. The
results ma0 = .215 and ma2 = -.039 are in excellent agreement with those
obtained from a recent analysis of the results published by the Brookhaven E865
collaboration.


  Large language models (LLMs) have demonstrated significant capability to
generalize across a large number of NLP tasks. For industry applications, it is
imperative to assess the performance of the LLM on unlabeled production data
from time to time to validate for a real-world setting. Human labeling to
assess model error requires considerable expense and time delay. Here we
demonstrate that ensemble disagreement scores work well as a proxy for human
labeling for language models in zero-shot, few-shot, and fine-tuned settings,
per our evaluation on keyphrase extraction (KPE) task. We measure fidelity of
the results by comparing to true error measured from human labeled ground
truth. We contrast with the alternative of using another LLM as a source of
machine labels, or silver labels. Results across various languages and domains
show disagreement scores provide a better estimation of model performance with
mean average error (MAE) as low as 0.4% and on average 13.8% better than using
silver labels.


  Chaotic systems are notoriously challenging to predict because of their
sensitivity to perturbations and errors due to time stepping. Despite this
unpredictable behavior, for many dissipative systems the statistics of the long
term trajectories are governed by an invariant measure supported on a set,
known as the global attractor; for many problems this set is finite
dimensional, even if the state space is infinite dimensional. For Markovian
systems, the statistical properties of long-term trajectories are uniquely
determined by the solution operator that maps the evolution of the system over
arbitrary positive time increments. In this work, we propose a machine learning
framework to learn the underlying solution operator for dissipative chaotic
systems, showing that the resulting learned operator accurately captures
short-time trajectories and long-time statistical behavior. Using this
framework, we are able to predict various statistics of the invariant measure
for the turbulent Kolmogorov Flow dynamics with Reynolds numbers up to 5000.


  There are several models for the effective thermal conductivity of two-phase
composite materials in terms of the conductivity of the solid and the disperse
material. In this paper, we generalise three models of Maxwell type (namely,
the classical Maxwell model and two generalisations of it obtained from
effective medium theory and differential effective medium theory) so that the
resulting effective thermal conductivity accounts for radiative heat transfer
within gas voids. In the high-temperature regime, radiative transfer within
voids strongly influences the thermal conductivity of the bulk material.
Indeed, the utility of these models over classical Maxwell-type models is seen
in the high-temperature regime, where they predict that the effective thermal
conductivity of the composite material levels off to a constant value (as a
function of temperature) at very high temperatures, provided that the material
is not too porous, in agreement with experiments. This behaviour is in contrast
to models which neglect radiative transfer within the pores, or lumped
parameter models, as such models do not resolve the radiative transfer
independently from other physical phenomena. Our results may be of particular
use for industrial and scientific applications involving heat transfer within
porous composite materials taking place in the high-temperature regime.


  The intersections of topology, geometry and strong correlations offer many
opportunities for exotic quantum phases to emerge in condensed matter systems.
Weyl fermions, in particular, provide an ideal platform for exploring the
dynamical instabilities of single-particle physics under interactions. Despite
its fundamental role in relativistic field theory, the concept of causality and
the associated spacetime light cone and event horizon has not been considered
in connection with interacting Weyl fermionic excitations in quantum matter.
Here, by using charge-density wave (CDW) as an example, we unveil the behavior
of interacting Weyl fermions and show that a Weyl fermion in a system can open
a band gap by interacting only with other Weyl fermions that lie within its
energy-momentum dispersion cone. In this sense, causal connections or
interactions are only possible within overlapping dispersion cones and each
dispersion cone thus constitutes a solid-state analogue of the more
conventional `event horizon' of high-energy physics. Our study provides a
universal framework for considering interacting relativistic quasiparticles in
condensed matter by separating them into energy-like and momentum-like
relationships in analogy with the time-like and space-like events in
high-energy physics. Finally, we consider two different candidate materials for
hosting the Weyl CDW phase: (TaSe$_4$)$_2$I and Mo$_3$Al$_2$C. Our study
greatly enriches the phenomenology and unveils new connections between
condensed matter and high-energy physics.


  These notes are concerned with Abel sums and connections with analytic
extensions of Fourier integrals.


  The DUNE neutrino experiment far detector has a fiducial mass of 40 kt. The
O(1M) readout channels are distributed over the four 10 kt modules and need to
be synchronized with respect to each other to a precision of O(10 ns). The
entire system needs to be synchronized with respect to GPS time to O(100 ns).
The system needs to be reliable, simple and affordable. Clock and
synchronization information encoded on the same fibre using a protocol based on
duty cycle shift keying (DCSK) with 8b10b encoding to ensure DC-balance. The
use of DCSK allows the clock to be recovered directly by PLL based clock
generators without needing to use a separate clock and data recovery (CDR)
device. Small scale tests show a timing jitter at the endpoint of approximately
10 ps with respect to the timing master.


  We demonstrate atomic magnetometry using a metasurface polarizing
beamsplitter fabricated on a silicon-on-sapphire (SOS) platform. The
metasurface splits a beam that is near-resonant with the rubidium atoms (795
nm) into orthogonal linear polarizations, enabling measurement of magnetically
sensitive circular birefringence in a rubidium vapor through balanced
polarimetry. We incorporated the metasurface into an atomic magnetometer based
on nonlinear magneto-optical rotation and measured sub-nanotesla sensitivity,
which is limited by low-frequency technical noise and transmission loss through
the metasurface. To our knowledge, this work represents the first demonstration
of SOS nanophotonics for atom-based sensing and paves the way for highly
integrated, miniaturized atomic sensors with enhanced sensitivity and
portability.


  The apparent difficulty in recovering classical nonlinear dynamics and chaos
from standard quantum mechanics has been the subject of a great deal of
interest over the last twenty years. For open quantum systems - those coupled
to a dissipative environment and/or a measurement device - it has been
demonstrated that chaotic-like behaviour can be recovered in the appropriate
classical limit. In this paper, we investigate the entanglement generated
between two nonlinear oscillators, coupled to each other and to their
environment. Entanglement - the inability to factorise coupled quantum systems
into their constituent parts - is one of the defining features of quantum
mechanics. Indeed, it underpins many of the recent developments in quantum
technologies. Here we show that the entanglement characteristics of two
`classical' states (chaotic and periodic solutions) differ significantly in the
classical limit. In particular, we show that significant levels of entanglement
are preserved only in the chaotic-like solutions.


  Researchers often run resource-intensive randomized controlled trials (RCTs)
to estimate the causal effects of interventions on outcomes of interest. Yet
these outcomes are often noisy, and estimated overall effects can be small or
imprecise. Nevertheless, we may still be able to produce reliable evidence of
the efficacy of an intervention by finding subgroups with significant effects.
In this paper, we propose a machine-learning method that is specifically
optimized for finding such subgroups in noisy data. Unlike available methods
for personalized treatment assignment, our tool is fundamentally designed to
take significance testing into account: it produces a subgroup that is chosen
to maximize the probability of obtaining a statistically significant positive
treatment effect. We provide a computationally efficient implementation using
decision trees and demonstrate its gain over selecting subgroups based on
positive (estimated) treatment effects. Compared to standard tree-based
regression and classification tools, this approach tends to yield higher power
in detecting subgroups affected by the treatment.


  A method to improve l1 performance of the CS (Compressive Sampling) for
A-scan SFCW-GPR (Stepped Frequency Continuous Wave-Ground Penetrating Radar)
signals with known spectral energy density is proposed. Instead of random
sampling, the proposed method selects the location of samples to follow the
distribution of the spectral energy. Samples collected from three different
measurement methods; the uniform sampling, random sampling, and energy
equipartition sampling, are used to reconstruct a given monocycle signal whose
spectral energy density is known. Objective performance evaluation in term of
PSNR (Peak Signal to Noise Ratio) indicates empirically that the CS
reconstruction of random sampling outperform the uniform sampling, while the
energy equipartition sampling outperforms both of them. These results suggest
that similar performance improvement can be achieved for the compressive SFCW
(Stepped Frequency Continuous Wave) radar, allowing even higher acquisition
speed.


  In recent work, we have developed a session types discipline for a calculus
that features the usual constructs for session establishment and communication,
but also two novel constructs that enable communicating processes to be
stopped, duplicated, or discarded at runtime. The aim is to understand whether
known techniques for the static analysis of structured communications scale up
to the challenging context of context-aware, adaptable distributed systems, in
which disciplined interaction and runtime adaptation are intertwined concerns.
In this short note, we summarize the main features of our session-typed
framework with runtime adaptation, and recall its basic correctness properties.
We illustrate our framework by means of examples. In particular, we present a
session representation of supervision trees, a mechanism for enforcing
fault-tolerant applications in the Erlang language.


  In relation to the Erd\H os similarity problem (show that for any infinite
set $A$ of real numbers there exists a set of positive Lebesgue measure which
contains no affine copy of $A$) we give some new examples of infinite sets
which are not universal in measure, i.e. they satisfy the above conjecture.
These are symmetric Cantor sets $C$ which can be quite thin: the length of the
$n$-th generation intervals defining the Cantor set is decreasing almost doubly
exponentially. Further, we achieve to construct a set, not just of positive
measure, but of \textit{full measure} not containing any affine copy of $C$.
Our method is probabilistic.


  To determine if the SuperNova Empirical Model (SNEMO) can improve Type Ia
supernova (SN Ia) standardization of several currently available photometric
data sets, we perform an initial test, comparing results with the much-used
SALT2 approach. We fit the SNEMO light-curve parameters and pass them to the
Bayesian hierarchical model UNITY1.2 to estimate the Tripp-like standardization
coefficients, including a host mass term as a proxy for redshift dependent
astrophysical systematics. We find that, among the existing large data sets,
only the Carnegie Supernova Project data set consistently provides the
signal-to-noise and time sampling necessary to constrain the additional five
parameters that SNEMO7 incorporates beyond SALT2. This is an important
consideration for future SN Ia surveys like LSST and WFIRST. Although the
SNEMO7 parameters are poorly constrained by most of the other available data
sets of light curves, we find that the SNEMO2 parameters are just as
well-constrained as the SALT2 parameters. In addition, SNEMO2 and SALT2 have
comparable unexplained intrinsic scatter when fitting the same data. When
looking at the total scatter, SNEMO7 reduces the Hubble-Lemaitre diagram RMS
from 0.148~mag to 0.141~mag. It is not then, the SNEMO methodology, but the
interplay of data quality and the increased number of degrees of freedom that
is behind these reduced constraints. With this in mind, we recommend further
investigation into the data required to use SNEMO7 and the possibility of
fitting the poorer photometry data with intermediate SNEMO-like models with
three to six components.


  In recent years, multi-view learning technologies for various applications
have attracted a surge of interest. Due to more compatible and complementary
information from multiple views, existing multi-view methods could achieve more
promising performance than conventional single-view methods in most situations.
However, there are still no sufficient researches on the unified framework in
existing multi-view works. Meanwhile, how to efficiently integrate multi-view
information is still full of challenges. In this paper, we propose a novel
multi-view learning framework, which aims to leverage most existing graph
embedding works into a unified formula via introducing the graph consensus
term. In particular, our method explores the graph structure in each view
independently to preserve the diversity property of graph embedding methods.
Meanwhile, we choose heterogeneous graphs to construct the graph consensus term
to explore the correlations among multiple views jointly. To this end, the
diversity and complementary information among different views could be
simultaneously considered. Furthermore, the proposed framework is utilized to
implement the multi-view extension of Locality Linear Embedding, named
Multi-view Locality Linear Embedding (MvLLE), which could be efficiently solved
by applying the alternating optimization strategy. Empirical validations
conducted on six benchmark datasets can show the effectiveness of our proposed
method.


  The cardinal invariants $ \mathfrak h, \mathfrak b, \mathfrak s$ of $\mathcal
P (\omega)$ are known to satisfy that $\omega_1 \leq \mathfrak h
\leq\min\{\mathfrak b, \mathfrak s\}$. We prove that all inequalities can be
strict. We also introduce a new upper bound for $\mathfrak h$ and show that it
can be less than $\mathfrak s$. The key method is to utilize finite support
matrix iterations of ccc posets following \cite{BlassShelah}.


  In this short survey article, we present an elementary, yet quite powerful,
method of enumerating independent sets in graphs. This method was first
employed more than three decades ago by Kleitman and Winston and has
subsequently been used numerous times by many researchers in various contexts.
Our presentation of the method is illustrated with several applications of it
to `real-life' combinatorial problems. In particular, we derive bounds on the
number of independent sets in regular graphs, sum-free subsets of $\{1, \ldots,
n\}$, and $C_4$-free graphs and give a short proof of an analogue of Roth's
theorem on $3$-term arithmetic progressions in sparse random sets of integers
which was originally formulated and proved by Kohayakawa, \L uczak, and R\"odl.


  We discuss the renormalization and factorization scale dependence of charm
and bottom production both at fixed-target energies and at present and future
colliders. We investigate whether distributions calculable at leading order can
be extrapolated to next-to-leading order by a constant multiplicative factor.


  We propose a robust data-driven output feedback control algorithm that
explicitly incorporates inherent finite-sample model estimate uncertainties
into the control design. The algorithm has three components: (1) a subspace
identification nominal model estimator; (2) a bootstrap resampling method that
quantifies non-asymptotic variance of the nominal model estimate; and (3) a
non-conventional robust control design method comprising a coupled optimal
dynamic output feedback filter and controller with multiplicative noise. A key
advantage of the proposed approach is that the system identification and robust
control design procedures both use stochastic uncertainty representations, so
that the actual inherent statistical estimation uncertainty directly aligns
with the uncertainty the robust controller is being designed against. Moreover,
the control design method accommodates a highly structured uncertainty
representation that can capture uncertainty shape more effectively than
existing approaches. We show through numerical experiments that the proposed
robust data-driven output feedback controller can significantly outperform a
certainty equivalent controller on various measures of sample complexity and
stability robustness.


  In this work we study the transverse spatial correlation of the pair of
photons generated via the process of spontaneous parametric frequency
down-conversion, in periodically poled non-linear crystals illuminated by a
pulsed laser beam. It is well known that the two-photon state generated in
quasi-phase matching (QPM) configurations depends explicitly on the
characteristics of the pump beam, on the crystal modulated non-linearity, and
on the detection geometry. This has allowed the development of several
techniques for controlling the biphoton spectral and spatial properties. Here
we discuss another technique for implementing the spatial entanglement
modification in QPM gratings. We show, theoretically and experimentally, that
in nearly collinear geometries, the spatial shape modulation of the pump beam
allows for the control of the biphoton transverse spatial correlation.


  We investigated the electronic structures of the bandwidth-controlled
ruthenates, Y$_{2}$Ru$_{2}$O$_{7}$, CaRuO$_{3}$, SrRuO$_{3}$, and Bi$_{2}$Ru$%
_{2}$O$_{7}$, by optical conductivity analysis in a wide energy region of 5 meV
$\sim $ 12 eV. We could assign optical transitions from the systematic changes
of the spectra and by comparison with the O 1$s$ x-ray absorption data. We
estimated some physical parameters, such as the on-site Coulomb repulsion
energy and the crystal-field splitting energy. These parameters show that the
4$d$ orbitals should be more extended than 3$d$ ones. These results are also
discussed in terms of the Mott-Hubbard model.


  Let $f$ be a normalized holomorphic cusp form for $SL_2(\mathbb{Z})$ of
weight $k$ with $k\equiv0\bmod 4$. By the Kuznetsov trace formula for
$GL_3(\mathbb R)$, we obtain the first moment of central values of
$L(s,f\otimes \phi)$, where $\phi$ varies over Hecke-Maass cusp forms for
$SL_3(\mathbb Z)$. As an application, we obtain a non-vanishing result for
$L(1/2,f\otimes\phi)$ and show that such $f$ is determined by
$\{L(1/2,f\otimes\phi)\}$ as $\phi$ varies.


  We study stability and structure of quark matters as a function of density in
a framework of molecular dynamics (MD). Using appropriate effective
interactions and the frictional cooling method, we search for the minimum
energy of the system. Transition from confined to deconfined phase is observed
at densities of 2 -- 3$\rho_0$, where $\rho_0$ is the nuclear matter saturation
density. The $uds$ matter becomes more stable than the charge-neutral $ud$
matter at 3$\rho_0$, but the $udd$ matter is the most stable even at high
density.


  For every even number $n$, and every $n$-dimensional smooth hypersurface of
$\mathbb{P}^{n+1}$ of degree $d$, we compute the periods of all its
$\frac{n}{2}$-dimensional complete intersection algebraic cycles. Furthermore,
we determine the image of the given algebraic cycle under the cycle class map
inside the De Rham cohomology group of the corresponding hypersurface in terms
of its Griffiths basis and the polarization. As an application, we use this
information to address variational Hodge conjecture for a non complete
intersection algebraic cycle. We prove that the locus of general hypersurfaces
containing two linear cycles whose intersection is of dimension less than
$\frac{n}{2}-\frac{d}{d-2}$, corresponds to the Hodge locus of any integral
combination of such linear cycles.


  The processes with single top quark production provide a prototype search for
the types of final state that are expected in many new physics scenarios. Some
distinctive features are considered for particle production in the top sector
in ultra-high energy domain which can be covered partly in the collisions of
cosmic ray particles with atmosphere. The single top quark production through
electroweak interaction is studied within the Standard Model and the Effective
Field Theory approach used for calculations of total partonic cross sections in
$s$-channel. These quantitative results can be important for both the future
collider experiments at center-of-mass energy frontier and the improvement of
the phenomenological models for development of the cosmic ray cascades in
ultra-high energy domain. Thus the study allows the better understanding of
heavy particle production and emphasizes the exciting interrelation between the
high-energy physics on accelerators and ultra-high energy cosmic ray
measurements.


  In this article, the order of some classes of fractional linear differential
equations is determined, based on asymptotic behavior of the solution as time
tends to infinity. The order of fractional derivative has been proved to be of
great importance in an accurately appropriate simulation of the system under
study. Specifically, by representing the asymptotic expansion of the solution,
it could be obviously demonstrated that the decay rate of the solution is in
influenced by the order of fractional differentiation. The numerical
investigation is conducted into the proven formulas.


  We use the edge of the quantum Hall sample to study the possibility for
counter-propagating neutral collective excitations. A novel sample design
allows us to independently investigate charge and energy transport along the
edge. We experimentally observe an upstream energy transfer with respect to the
electron drift for the filling factors 1 and 1/3. Our analysis indicates that a
neutral collective mode at the interaction-reconstructed edge is a proper
candidate for the experimentally observed effect.


  We discuss the elliptic flow dependence on pseudorapidity and number of
participating nucleons in the framework of string percolation, and argue that
the geometry of the initial overlap region of interaction, projected in the
impact parameter plane, determines the experimentally measured azimuthal
asymmetries. We found good agreement with data.


  This paper is being extensively rewritten and will be resubmitted in a
different form.


  Deep neural networks usually require accurate and a large number of
annotations to achieve outstanding performance in medical image segmentation.
One-shot segmentation and weakly-supervised learning are promising research
directions that lower labeling effort by learning a new class from only one
annotated image and utilizing coarse labels instead, respectively. Previous
works usually fail to leverage the anatomical structure and suffer from class
imbalance and low contrast problems. Hence, we present an innovative framework
for 3D medical image segmentation with one-shot and weakly-supervised settings.
Firstly a propagation-reconstruction network is proposed to project scribbles
from annotated volume to unlabeled 3D images based on the assumption that
anatomical patterns in different human bodies are similar. Then a dual-level
feature denoising module is designed to refine the scribbles based on
anatomical- and pixel-level features. After expanding the scribbles to pseudo
masks, we could train a segmentation model for the new class with the noisy
label training strategy. Experiments on one abdomen and one head-and-neck CT
dataset show the proposed method obtains significant improvement over the
state-of-the-art methods and performs robustly even under severe class
imbalance and low contrast.


  This article presents a semantic tracker which simultaneously tracks a single
target and recognises its category. In general, it is hard to design a tracking
model suitable for all object categories, e.g., a rigid tracker for a car is
not suitable for a deformable gymnast. Category-based trackers usually achieve
superior tracking performance for the objects of that specific category, but
have difficulties being generalised. Therefore, we propose a novel unified
robust tracking framework which explicitly encodes both generic features and
category-based features. The tracker consists of a shared convolutional network
(NetS), which feeds into two parallel networks, NetC for classification and
NetT for tracking. NetS is pre-trained on ImageNet to serve as a generic
feature extractor across the different object categories for NetC and NetT.
NetC utilises those features within fully connected layers to classify the
object category. NetT has multiple branches, corresponding to multiple
categories, to distinguish the tracked object from the background. Since each
branch in NetT is trained by the videos of a specific category or groups of
similar categories, NetT encodes category-based features for tracking. During
online tracking, NetC and NetT jointly determine the target regions with the
right category and foreground labels for target estimation. To improve the
robustness and precision, NetC and NetT inter-supervise each other and trigger
network adaptation when their outputs are ambiguous for the same image regions
(i.e., when the category label contradicts the foreground/background
classification). We have compared the performance of our tracker to other
state-of-the-art trackers on a large-scale tracking benchmark (100
sequences)---the obtained results demonstrate the effectiveness of our proposed
tracker as it outperformed other 38 state-of-the-art tracking algorithms.


  A planar node set $\mathcal X,$ with $\#\mathcal X=\binom{n+2}{2},$ is called
$GC_n$ set if each node possesses fundamental polynomial in form of a product
of $n$ linear factors. We say that a node uses a line if the line is a factor
of the fundamental polynomial of the node. A line is called $k$-node line if it
passes through exactly $k$-nodes of $\mathcal X.$ At most $n+1$ nodes can be
collinear in any $GC_n$ set and an $(n+1)$-node line is called a maximal line.
The Gasca-Maeztu conjecture (1982) states that every $GC_n$ set has a maximal
line. Until now the conjecture has been proved only for the cases $n \le 5.$
  Here, for a line $\ell$ we introduce and study the concept of $\ell$-lowering
of the set $\mathcal X$ and define so called proper lines. We also provide
refinements of several basic properties of $GC_n$ sets regarding the maximal
lines, $n$-node lines, the used lines, as well as the subset of nodes that use
a given line.


  We theoretically analyze inverse radiofrequency (rf) spectroscopy experiments
in two-component Fermi gases. We consider a small number of impurity atoms
interacting strongly with a bath of majority atoms. In two-dimensional
geometries we find that the main features of the rf spectrum correspond to an
attractive polaron and a metastable repulsive polaron. Our results suggest that
the attractive polaron has been observed in a recent experiment [Phys. Rev.
Lett. 106, 105301 (2011)].