  We discuss how the simultaneous crossovers of deconfinement and chiral
restoration can be realized. We propose a dynamical mechanism assuming that the
effective potential gives a finite value of the chiral condensate if the
Polyakov loop vanishes. Using a simple model, we demonstrate that our idea
works well for small quark mass, though there should be further constraints to
reach the perfect locking of two phenomena.


  Transport measurements along the node and anti-node directions in the a-b
plane of optimally doped and epitaxial thin films of YBCO are reported. Low
bias magnetoresistance measurements near and below T_c show that the flux flow
resistivity along the node and anti-node directions versus magnetic field are
indistinguishable. This result suggests that within the experimental error of
our measurements, no correspondence is found between the flux pinning
properties in YBCO and the d-wave nature of the order parameter.


  This is primarily an overview article on some results and problems involving
the classical Hardy function $$ Z(t) :=
\zeta(1/2+it){\bigl(\chi(1/2+it)\bigr)}^{-1/2}, \quad \zeta(s) =
\chi(s)\zeta(1-s). $$ In particular, we discuss the first and third moment of
$Z(t)$ (with and without shifts) and the distribution of its positive and
negative values. A new result involving the distribution of its values is
presented.


  The gap equation is a cornerstone in understanding dynamical chiral symmetry
breaking and may also provide clues to confinement. A symmetry-preserving
truncation of its kernel enables proofs of important results and the
development of an efficacious phenomenology. We describe a model of the kernel
that yields: a momentum-dependent dressed-quark propagator in fair agreement
with quenched lattice-QCD results; and chiral limit values: f_pi= 68 MeV and
<q-bar q> = -(190 MeV)^3. It is compared with models inferred from studies of
the gauge sector.


  End-to-end (E2E) automatic speech recognition (ASR) methods exhibit
remarkable performance. However, since the performance of such methods is
intrinsically linked to the context present in the training data, E2E-ASR
methods do not perform as desired for unseen user contexts (e.g., technical
terms, personal names, and playlists). Thus, E2E-ASR methods must be easily
contextualized by the user or developer. This paper proposes an attention-based
contextual biasing method that can be customized using an editable phrase list
(referred to as a bias list). The proposed method can be trained effectively by
combining a bias phrase index loss and special tokens to detect the bias
phrases in the input speech data. In addition, to improve the contextualization
performance during inference further, we propose a bias phrase boosted (BPB)
beam search algorithm based on the bias phrase index probability. Experimental
results demonstrate that the proposed method consistently improves the word
error rate and the character error rate of the target phrases in the bias list
on both the Librispeech-960 (English) and our in-house (Japanese) dataset,
respectively.


  We introduce collages of string diagrams as a diagrammatic syntax for glueing
multiple monoidal categories. Collages of string diagrams are interpreted as
pointed bimodular profunctors. As the main examples of this technique, we
introduce string diagrams for bimodular categories, string diagrams for functor
boxes, and string diagrams for internal diagrams.


  Energy decay plays a central role in a wide range of phenomena, such as
optical emission, nuclear fission, and dissipation in quantum systems. Energy
decay is usually described as a system leaking energy irreversibly into an
environmental bath. Here, we report on energy decay measurements in
nanomechanical systems based on multi-layer graphene that cannot be explained
by the paradigm of a system directly coupled to a bath. As the energy of a
vibrational mode freely decays, the rate of energy decay switches abruptly to a
lower value. This finding can be explained by a model where the measured mode
hybridizes with other modes of the resonator at high energy. Below a threshold
energy, modes are decoupled, resulting in comparatively low decay rates and
giant quality factors exceeding 1 million. Our work opens up new possibilities
to manipulate vibrational states, engineer hybrid states with mechanical modes
at completely different frequencies, and to study the collective motion of this
highly tunable system.


  Quantum annealing is a promising approach for obtaining good approximate
solutions to difficult optimization problems. Folding a protein sequence into
its minimum-energy structure represents such a problem. For testing new
algorithms and technologies for this task, the minimal lattice-based HP model
is well suited, as it represents a considerable challenge despite its
simplicity. The HP model has favorable interactions between adjacent, not
directly bound hydrophobic residues. Here, we develop a novel spin
representation for lattice protein folding tailored for quantum annealing. With
a distributed encoding onto the lattice, it differs from earlier attempts to
fold lattice proteins on quantum annealers, which were based upon chain growth
techniques. With our encoding, the Hamiltonian by design has the quadratic
structure required for calculations on an Ising-type annealer, without having
to introduce any auxiliary spin variables. This property greatly facilitates
the study of long chains. The approach is robust to changes in the parameters
required to constrain the spin system to chain-like configurations, and
performs very well in terms of solution quality. The results are evaluated
against existing exact results for HP chains with up to $N=30$ beads with 100%
hit rate, thereby also outperforming classical simulated annealing. In
addition, the method allows us to recover the lowest known energies for $N=48$
and $N=64$ HP chains, with similar hit rates. These results are obtained by the
commonly used hybrid quantum-classical approach. For pure quantum annealing,
our method successfully folds an $N=14$ HP chain. The calculations were
performed on a D-Wave Advantage quantum annealer.


  Magnetic properties of La2-xSrxCoO4 have been modelled using McPhase for
different doping levels x. Footprints of different interactions, such as local
single ion anisotropy and variations in the exchange interactions have been
identified in the profile of the diffuse elastic neutron scattering cross
section. The role of quantum fluctuations in the formation of the hourglass
spectrum is discussed.


  In this paper, we present a distributional word embedding model trained on
one of the largest available Russian corpora: Araneum Russicum Maximum (over 10
billion words crawled from the web). We compare this model to the model trained
on the Russian National Corpus (RNC). The two corpora are much different in
their size and compilation procedures. We test these differences by evaluating
the trained models against the Russian part of the Multilingual SimLex999
semantic similarity dataset. We detect and describe numerous issues in this
dataset and publish a new corrected version. Aside from the already known fact
that the RNC is generally a better training corpus than web corpora, we
enumerate and explain fine differences in how the models process semantic
similarity task, what parts of the evaluation set are difficult for particular
models and why. Additionally, the learning curves for both models are
described, showing that the RNC is generally more robust as training material
for this task.


  We study the possibility of designing $N^{o(1)}$-round protocols for problems
of substantially super-linear polynomial-time complexity on the congested
clique with about $N^{1/2}$ nodes, where $N$ is the input size. We show that
the exponent of the polynomial (if any) bounding the average time complexity of
local computations performed at a node in such protocols has to be larger than
that of the polynomial bounding the time complexity of the given problem.


  Multiscaling properties of the Anderson localization of the cosmic
electromagnetic fields before the recombination time are studied and results of
a numerical simulation for a random banded matrix ensemble are found to be in
good agreement with the large-scale cosmic data.


  We describe the implementation of 1d1v and 1d2v Vlasov and Fokker-Planck
kinetic solvers with adaptive mesh refinement in phase space (AMPS) and
coupling these kinetic solvers to Poisson equation solver for electric field.
We demonstrate that coupling AMPS kinetic and electrostatic solvers can be done
efficiently without splitting phase-space transport. We show that Eulerian
fluid and kinetic solvers with dynamically adaptive Cartesian mesh can be used
for simulations of collisionless plasma expansion into vacuum. The
Vlasov-Fokker-Planck solver is demonstrated for the analysis of electron
acceleration and scattering as well as the generation of runaway electrons in
spatially inhomogeneous electric fields.


  We present an exposition of the proof of the induced bipartite Ramsey
Theorem.


  We theoretically analyze phase sensitivity using parity detection based Mach
Zehnder interferometer (MZI) with the input states generated by performing
non-Gaussian operations, viz., photon subtraction, photon addition, and photon
catalysis on a two-mode squeezed vacuum (TMSV) state. Since these non-Gaussian
operations are probabilistic, it is of utmost importance to take the success
probability into account. To this end, we consider the realistic model of
photon subtraction, addition, and catalysis and derive a single expression of
the Wigner function for photon subtracted, added, and catalyzed TMSV state. The
Wigner function is used to evaluate the lower bound on the phase sensitivity
via quantum Cramer-Rao bound and parity detection based phase sensitivity in
MZI. We identify the ranges of squeezing and transmissivity parameters where
the non-Gaussian states provide better phase sensitivity than the TMSV state.
On qualitatively taking the success probability into account, it turns out that
the photon addition is the most advantageous non-Gaussian operation. We hope
that the generalized Wigner function derived in this work will be useful in
various quantum information protocols and state characterization.


  A system of N interacting bosons or fermions in a two-dimensional harmonic
potential (or, equivalently, magnetic field) whose states are projected onto
the lowest Landau level is considered. Generic expressions are derived for
matrix elements of any interaction, in the basis of angular momentum
eigenstates. For the fermion "ground state" (N=1 Laughlin state), this makes it
possible to exactly calculate its energy all the way up to the mesoscopic
regime N ~ 1000. It is also shown that for N = 3 and Coulomb interaction,
several rational low-lying values of energy exist, for bosons and fermions
alike.


  We prove that a non-empty set L of at most q^5+q^4+q^3+q^2+q+1 lines of PG(n,
q) with the properties that (1) every point of PG(n,q) is incident with either
0 or q+1 elements of L, (2) every plane plane of PG(n, q) is incident with
either 0, 1 or q+1 elements of L, (3) every solid of PG(n, q) is incident with
either 0, 1, q+1 or 2q+1 elements of L, and (4) every 4-dimensional subspace of
PG(n, q) is incident with at most q^3-q^2+4q elements of L, is necessarily the
set of lines of a split Cayley hexagon H(q) naturally embedded in PG(6, q).


  We report the detection of OH+ and H2O+ in the z=0.89 absorber toward the
lensed quasar PKS1830-211. The abundance ratio of OH+ and H2O+ is used to
quantify the molecular hydrogen fraction (fH2) and the cosmic-ray ionization
rate of atomic hydrogen (zH) along two lines of sight, located at ~2 kpc and ~4
kpc to either side of the absorber's center. The molecular fraction decreases
outwards, from ~0.04 to ~0.02, comparable to values measured in the Milky Way
at similar galactocentric radii. For zH, we find values of ~2x10^-14 s^-1 and
~3x10^-15 s^-1, respectively, which are slightly higher than in the Milky Way
at comparable galactocentric radii, possibly due to a higher average star
formation activity in the z=0.89 absorber. The ALMA observations of OH+, H2O+,
and other hydrides toward PKS1830-211 reveal the multi-phase composition of the
absorbing gas. Taking the column density ratios along the southwest and
northeast lines of sight as a proxy of molecular fraction, we classify the
species ArH+, OH+, H2Cl+, H2O+, CH, and HF as tracing gases increasingly more
molecular. Incidentally, our data allow us to improve the accuracy of H2O+ rest
frequencies and thus refine the spectroscopic parameters.


  Modern field programmable gate array(FPGA) can be partially dynamically
reconfigurable with heterogeneous resources distributed on the chip. And
FPGA-based partially dynamically reconfigurable system(FPGA-PDRS) can be used
to accelerate computing and improve computing flexibility.
  However, the traditional design of FPGA-PDRS is based on manual design.
  Implementing the automation of FPGA-PDRS needs to solve the problems of task
modules partitioning, scheduling, and floorplanning on heterogeneous resources.
  Existing works only partly solve problems for the automation process of
FPGA-PDRS or model homogeneous resource for FPGA-PDRS.
  To better solve the problems in the automation process of FPGA-PDRS and
narrow the gap between algorithm and application, in this paper, we propose a
complete workflow including three parts, pre-processing to generate the list of
task modules candidate shapes according to the resources requirements,
exploration process to search the solution of task modules partitioning,
scheduling, and floorplanning, and post-optimization to improve the success
rate of floorplan.
  Experimental results show that, compared with state-of-the-art work, the
proposed complete workflow can improve performance by 18.7\%, reduce
communication cost by 8.6\%, on average, with improving the resources reuse
rate of the heterogeneous resources on the chip. And based on the solution
generated by the exploration process, the post-optimization can improve the
success rate of the floorplan by 14\%.


  This paper characterizes the impact of covariate serial dependence on the
non-asymptotic estimation error bound of penalized regressions (PRs). Focusing
on the direct relationship between the degree of cross-correlation between
covariates and the estimation error bound of PRs, we show that orthogonal or
weakly cross-correlated stationary AR processes can exhibit high spurious
correlations caused by serial dependence. We provide analytical results on the
distribution of the sample cross-correlation in the case of two orthogonal
Gaussian AR(1) processes, and extend and validate them through an extensive
simulation study. Furthermore, we introduce a new procedure to mitigate
spurious correlations in a time series setting, applying PRs to pre-whitened
(ARMA filtered) time series. We show that under mild assumptions our procedure
allows both to reduce the estimation error and to develop an effective
forecasting strategy. The estimation accuracy of our proposal is validated
through additional simulations, as well as an empirical application to a large
set of monthly macroeconomic time series relative to the Euro Area.


  We extend Langton's valuative criterion for families of coherent algebraic
sheaves to a complex analytic set-up. As a consequence we derive a set of
sufficient conditions for the compactness of a moduli space of semistable
sheaves over a compact complex manifold. This applies also to some cases
appearing in complex projective geometry not covered by previous results.


  Mid-infrared (MIR) quasar spectra exhibit a suite of emission features
including high ionization coronal lines from the narrow line region illuminated
by the ionizing continuum, broad dust bumps from silicates and graphites, and
polycyclic aromatic hydrocarbon (PAH) features from star formation in the host
galaxy. However, in Spitzer Infared Spectrograph (IRS) data, few features are
detected in most individual spectra because of typically low signal-to-noise
ratios (S/N). By generating spectral composites from over 180 IRS observations
of Sloan Digital Sky Survey broad-line quasars, we boost the S/N and reveal
features in the complex spectra that are otherwise lost in the noise. In
addition to an overall composite, we generate composites in three different
luminosity bins that span the range of 5.6 micron luminosities of
10$^{40}$--10$^{46}$ (erg~s$^{-1}$). We detect the high-ionization, forbidden
emission lines of [SIV], [OIV], and [NeV] 14 micron in all templates and PAH
features in all but the most luminous template. Ratios of lines with a range of
ionization potentials show no evidence for a strong difference in the shape of
the 41--97 eV ionizing continuum over this range of luminosities. The scaling
of the emission-line luminosities as a function of continuum luminosity is
consistent with what is expected, and shows no indication of a ``disappearing
narrow-line region.'' The broad 10 and 18 micron silicate features in emission
increase in strength with increasing luminosity, and a broad 3--5 micron black
body consistent with graphite emission at 750 K is evident in the highest
luminosity template. We find that the intrinsic quasar continua for all
luminosity templates are consistent; apparent differences arise primarily from
host galaxy contamination most evident at low luminosity.


  In this note, we prove that the solutions obtained to the spherically
symmetric Euler equations in the recent works [2, 3] are weak solutions of the
multi-dimensional compressible Euler equations. This follows from new uniform
estimates made on the artificial viscosity approximations up to the origin,
removing previous restrictions on the admissible test functions and ruling out
formation of an artificial boundary layer at the origin. The uniform estimates
may be of independent interest as concerns the possible rate of blow-up of the
density and velocity at the origin for spherically symmetric flows.


  Single crystals of the optimally doped, moderately and strongly overdoped
high temperature superconductor Tl2Ba2CuO6+x (Tl-2201) with Tc=80, 56 and 30K,
respectively, have been investigated by polarized Raman scattering. By taking
the peak position of the B_1g component of electronic Raman scattering as
2Delta_0 we found that the reduced gap value (2Delta_0/k_BT_c) strongly
decreases with increasing doping. The behavior of the low frequency scattering
for the B_1g and B_2g scattering components is similar for optimally doped and
overdoped crystals and can be described by a w^3 - and w -law, respectively,
which is consistent with a d-wave symmetry of the order parameter. In contrast
to the optimally doped Tl-2201 in both, moderately and strongly overdoped
Tl-2201, the relative (compared to the B_1g) intensity of the A_1g scattering
component is suppressed. We suggest that the van Hove singularity is
responsible for the observed changes of Raman intensity and reduced gap value
with doping. Electronic Raman scattering in the normal state is discussed in
the context of the scattering from impurities and compared to the existing
infrared data. The scattering rate evaluated from the Raman measurements is
smaller for the overdoped samples, compared to the moderately overdoped
samples.


  For the moonshine module $V^{\natural},$ whose automorphism is the Monster
${\Bbb M},$ We show how to give a uniform existence proof for irreducible
$g$-twisted modules for elements of type $2A,$ $2B$ and $4A$ in ${\Bbb M}.$ The
most interesting of these is the twisted sector $V^{\natural}(2A),$ whose
automorphism group is essentially the centralizer of $2A$ in ${\Bbb M}.$ This
is a 2-fold central extension of the Baby Monster, the second largest sporadic
simple group. We also establish uniqueness of the twisted sectors and the
hauptmodul property for the graded traces of automorphisms of odd order, as
predicted by conformal field theory.


  Motivated by the current strong constraints on the spin-independent dark
matter (DM)-nucleus scattering, we investigate the spin-dependent (SD)
interactions of the light Majorana DM with the nucleus mediated by an
axial-vector boson. Due to the small nucleus recoil energy, the ionization
signals have now been used to probe the light dark matter particles in direct
detection experiments. With the existing ionization data, we derive the
exclusion limits on the SD DM-nucleus scattering through Migdal effect in the
MeV-GeV DM mass range. It is found that the lower limit of the DM mass can
reach about several MeVs. Due to the momentum transfer correction induced by
the light mediator, the bounds on the SD DM-nucleus scattering cross sections
can be weakened in comparison with the heavy mediator.


  Lung cancer is the leading cause of cancer-related death worldwide, and early
diagnosis is critical to improving patient outcomes. To diagnose cancer, a
highly trained pulmonologist must navigate a flexible bronchoscope deep into
the branched structure of the lung for biopsy. The biopsy fails to sample the
target tissue in 26-33% of cases largely because of poor registration with the
preoperative CT map. We developed two deep learning approaches to localize the
bronchoscope in the preoperative CT map in real time and tested the algorithms
across 13 trajectories in a lung phantom and 68 trajectories in 11 human
cadaver lungs. In the lung phantom, we observe performance reaching 95%
precision and recall of visible airways and 3 mm average position error. On a
successful cadaver lung sequence, the algorithms trained on simulation alone
achieved 77%-94% precision and recall of visible airways and 4-6 mm average
position error. We also compare the effect of GAN-stylizing images and we look
at aggregate statistics over the entire set of trajectories.


  It is shown that the criticism of Voitkiv [Phys. Rev. A 74, 027403 (2006)] is
based on one assumption, which is false for an ionized electron, initially
bound by the Coulomb potential, in a strong circularly polarized laser field. A
certain new Coulomb correction to the Volkov wavefunction is proposed.


  Half-Heusler phases have gained recently much interest as thermoelectric
materials. Screening of possible systems was performed by ab-initio simulation
using VASP-software. The energy-versus-Volume (E(V)) curves were calculated and
calibrated. For TiCoSb, NbNiSn, FeMoSb the stability of Half-Heusler phase
against concurrent crystal structures like TiNiSi, ZrCoAl, ZrBeSi, FeSiV, ZrNiP
and Full Heusler was confirmed. However, the thermo-dynamical driving force as
calculated from the difference in lattice energies is less than 0.1eV/atom.
Hence, the fabrication of Half Heusler phases is a challenge and requires three
steps, surface activation of the raw material by ball milling, arc-melting of
pressed pellets and finally long-term annealing treatment in a vacuum furnace.
On doped TiCoSb specimens, Seebeck coefficients up to 0.1 mV/K, on NiNbSn 0.16
mV/K were measured, although the microstructure was not yet optimized.


  A string in four dimensions is constructed by supplementing it with forty
four Majorana fermions. The central charge is 26. The fermions are grouped in
such a way that the resulting action is supersymmetric. The energy momentum and
current generators satisfy the super-Virasoro algebra. The tachyonic ground
state decouples from the physical states. GSO projections are necessary for
proving modular invariance. Space-time supersymmetry provides reasons to
discard the tachyons and is substantiated for modes of zero mass. The symmetry
group of the model descends to the low energy standard model group $SU (3)
\times SU_L (2) \times U_Y (1)$ through the Pati-Salam group. Left right
symmetry is broken spontaneously and the mass of the tau neutrino is calculated
to be about 1/25 electron volt.


  EPR steering is an asymmetric form of correlations which is intermediate
between quantum entanglement and Bell nonlocality, and can be exploited for
quantum communication with one untrusted party. In particular, steering of
continuous variable Gaussian states has been extensively studied as a
manifestation of the EPR paradox. While most of these studies focused on
quadrature measurements for steering detection, two recent works revealed that
there exist Gaussian states which are only steerable by non-Gaussian
measurements. In this paper we perform a systematic investigation of EPR
steering of bipartite Gaussian states by pseudospin measurements, complementing
and extending previous findings. We first derive the density matrix elements of
two-mode squeezed thermal states in the Fock basis, which may be of independent
interest. We then use such a representation to investigate steering of these
states as detected by a nonlinear criterion, based on second moments of the
pseudospin correlation matrix. This analysis reveals previously unexplored
regimes where non-Gaussian measurements are more effective than Gaussian ones
to witness steering of Gaussian states in the presence of local noise. We
further consider an alternative set of pseudospin observables, whose
expectation value can be expressed compactly in terms of Wigner functions for
all two-mode Gaussian states. However, according to the adopted criterion,
these observables are found to be always less sensitive than Gaussian
observables for steering detection. Finally, we investigate continuous variable
Werner states, which are non-Gaussian mixtures of Gaussian states, and find
that pseudospin measurements are always more effective than Gaussian ones to
reveal their steerability. Our results provide useful insights on the role of
non-Gaussian measurements in characterizing quantum correlations of Gaussian
and non-Gaussian states.


  The mechanism for gamma ray bursters and the detection of gravitational waves
(GWs) are two outstanding problems facing modern physics. Many models of gamma
ray bursters predict copious GW emission, so the assumption of an association
between GWs and GRBs may be testable with existing bar GW detector data. We
consider Weber bar data streams in the vicinity of known GRB times and present
calculations of the expected signal after co-addition of 1000 GW/GRBs that have
been shifted to a common zero time. Our calculations are based on assumptions
concerning the GW spectrum and the redshift distribution of GW/GRB sources
which are consistent with current GW/GRB models. We discuss further
possibilities of GW detection associated with GRBs in light of future bar
detector improvements and suggest that co-addition of data from several
improved bar detectors may result in detection of GWs (if the GW/GRB assumption
is correct) on a time scale comparable with the LIGO projects.


  Reachability analysis provides formal guarantees for performance and safety
properties of nonlinear control systems. Here, one aims to compute the backward
reachable set (BRS) or tube (BRT) -- the set of states from which the system
can be driven into a target set at a particular time or within a time interval,
respectively. The computational complexity of current approaches scales
exponentially, making application to high-dimensional systems intractable. We
propose a technique that decomposes the dynamics of a general class of
nonlinear systems into subsystems which may be coupled through common states,
controls, and disturbances. Despite this coupling, BRSs and BRTs can be
computed efficiently using our technique without incurring additional
approximation errors and without the need for linearizing dynamics or
approximating sets as polytopes. Computations of BRSs and BRTs now become
orders of magnitude faster, and for the first time BRSs and BRTs for many
high-dimensional nonlinear control systems can be computed using the
Hamilton-Jacobi (HJ) formulation. In situations involving bounded adversarial
disturbances, our proposed method can obtain slightly conservative results. We
demonstrate our theory by numerically computing BRSs and BRTs using the HJ
formulation for several systems, including the 6D Acrobatic Quadrotor and the
10D Near-Hover Quadrotor.


  Starting from an axiomatic perspective, \emph{fluctuation geometry} is
developed as a counterpart approach of inference geometry. This approach is
inspired on the existence of a notable analogy between the general theorems of
\emph{inference theory} and the the \emph{general fluctuation theorems}
associated with a parametric family of distribution functions
$dp(I|\theta)=\rho(I|\theta)dI$, which describes the behavior of a set of
\emph{continuous stochastic variables} driven by a set of control parameters
$\theta$. In this approach, statistical properties are rephrased as purely
geometric notions derived from the \emph{Riemannian structure} on the manifold
$\mathcal{M}_{\theta}$ of stochastic variables $I$. Consequently, this theory
arises as an alternative framework for applying the powerful methods of
differential geometry for the statistical analysis. Fluctuation geometry has
direct implications on statistics and physics. This geometric approach inspires
a Riemannian reformulation of Einstein fluctuation theory as well as a
geometric redefinition of the information entropy for a continuous
distribution.


  Polyelectrolyte (PE) hydrogels can dynamically respond to external stimuli,
such as changes in pH and temperature, which benefits their use for smart
materials and nanodevices with tunable properties. We investigate equilibrium
conformations and phase transition dynamics of pH-responsive nanogels using
hybrid molecular dynamics/Monte Carlo simulations with full consideration of
electrostatic and hydrodynamic interactions. We demonstrate that PE nanogels
exhibit a closed-loop phase behavior with a discontinuous swelling--collapse
transition that occurs only at intermediate pH values. A 50~nm nanogel particle
close to a critical point functions as a pH-driven actuator with a microsecond
conformational response and work density $\approx 10^5~\mathrm{J/m}^3$, an
order of magnitude larger than skeletal muscles. The collapse/expansion time
scales as $L^{2}$ and the power density scales as $L^{-2}$ where $L$ is the
linear size of the gel. Our work provides fundamental insight into phase
behavior and non-equilibrium dynamics of the swelling--collapse transition, and
our method enables the investigation of charge--structure--hydrodynamic
coupling in soft materials.


  Online feedback optimization (OFO) is an emerging control methodology for
real-time optimal steady-state control of complex dynamical systems. This
tutorial focuses on the application of OFO for the autonomous operation of
large-scale transmission grids, with a specific goal of minimizing renewable
generation curtailment and losses while satisfying voltage and current limits.
When this control methodology is applied to multi-area transmission grids,
where each area independently manages its congestion while being dynamically
interconnected with the rest of the grid, a non-cooperative game arises. In
this context, OFO must be interpreted as an online feedback equilibrium seeking
(FES) scheme. Our analysis incorporates technical tools from game theory and
monotone operator theory to evaluate the stability and performance of
multi-area grid operation. Through numerical simulations, we illustrate the key
challenge of this non-cooperative setting: on the one hand, independent
multi-area decisions are suboptimal compared to a centralized control scheme;
on the other hand, some areas are heavily penalized by the centralized
decision, which may discourage participation in the coordination mechanism.


  We find new relations for the non-universal part of the Yang-Mills amplitudes
by combining the KLT-relation and the soft behavior of gauge and gravity
amplitudes. We also extend the relations to include contributions from
effective operators.


  We introduce algebras which are inductive limits of Banach spaces and carry
inequalities which are counterparts of the inequality for the norm in a Banach
algebra. We then define an associated Wiener algebra, and prove the
corresponding version of the well-known Wiener theorem. Finally, we consider
factorization theory in these algebra, and in particular, in the associated
Wiener algebra.


  We employ the tight-binding propagation method to study Klein tunneling and
quantum interference in large graphene systems. With this efficient numerical
scheme, we model the propagation of a wave packet through a potential barrier
and determine the tunneling probability for different incidence angles. We
consider both sharp and smooth potential barriers in n-p-n and n-n' junctions
and find good agreement with analytical and semiclassical predictions. When we
go outside the Dirac regime, we observe that sharp n-p junctions no longer show
Klein tunneling because of intervalley scattering. However, this effect can be
suppressed by considering a smooth potential. Klein tunneling holds for
potentials changing on the scale much larger than the interatomic distance.
When the energies of both the electrons and holes are above the Van Hove
singularity, we observe total reflection for both sharp and smooth potential
barriers. Furthermore, we consider caustic formation by a two-dimensional
Gaussian potential. For sufficiently broad potentials we find a good agreement
between the simulated wave density and the classical electron trajectories.


  Finite Frobenius rings have been characterized as precisely those finite
rings satisfying the MacWilliams extension property, by work of Wood. In the
present note we offer a generalization of this remarkable result to the realm
of Artinian rings. Namely, we prove that a left Artinian ring has the left
MacWilliams property if and only if it is left pseudo-injective and its
finitary left socle embeds into the semisimple quotient. Providing a
topological perspective on the MacWilliams property, we also show that the
finitary left socle of a left Artinian ring embeds into the semisimple quotient
if and only if it admits a finitarily left torsion-free character, if and only
if the Pontryagin dual of the regular left module is almost monothetic. In
conclusion, an Artinian ring has the MacWilliams property if and only if it is
finitarily Frobenius, i.e., it is quasi-Frobenius and its finitary socle embeds
into the semisimple quotient.


  Deep reinforcement learning (RL) has achieved great empirical successes in
various domains. However, the large search space of neural networks requires a
large amount of data, which makes the current RL algorithms not sample
efficient. Motivated by the fact that many environments with continuous state
space have smooth transitions, we propose to learn a smooth policy that behaves
smoothly with respect to states. We develop a new framework -- \textbf{S}mooth
\textbf{R}egularized \textbf{R}einforcement \textbf{L}earning
($\textbf{SR}^2\textbf{L}$), where the policy is trained with
smoothness-inducing regularization. Such regularization effectively constrains
the search space, and enforces smoothness in the learned policy. Moreover, our
proposed framework can also improve the robustness of policy against
measurement error in the state space, and can be naturally extended to
distribubutionally robust setting. We apply the proposed framework to both
on-policy (TRPO) and off-policy algorithm (DDPG). Through extensive
experiments, we demonstrate that our method achieves improved sample efficiency
and robustness.


  The results of a number of constituent quark models in matter may be
understood in the mean-field approximation by using a simple four-fermi model
in 0+1 dimensions.


  Recent determinations of the mean free path of ionising photons (mfp) in the
intergalactic medium (IGM) at $\rm z=6$ are lower than many theoretical
predictions. To gain insight into this issue, we investigate the evolution of
the mfp in our new massive fully coupled radiation hydrodynamics cosmological
simulation of reionization: Cosmic Dawn III (CoDaIII). CoDaIII's scale ($\rm
94^3 \, cMpc^3$) and resolution ($\rm 8192^3$ grid) make it particularly
suitable to study the evolution of the IGM during Reionization. The simulation
was performed with RAMSES-CUDATON on Summit, and used 131072 processors coupled
to 24576 GPUs, making it the largest Reionization simulation, and largest
RAMSES simulation ever performed. A superior agreement with global constraints
on Reionization is obtained in CoDaIII over CoDaII especially for the evolution
of the neutral hydrogen fraction and the cosmic photo-ionization rate, thanks
to an improved calibration, later end of reionization ($\rm z=5.6$), and higher
spatial resolution. Analyzing the mfp, we find that CoDaIII reproduces the most
recent observations very well, from $\rm z=6$ to $\rm z=4.6$. We show that the
distribution of the mfp in CoDaIII is bimodal, with short (neutral) and long
(ionized) mfp modes, respectively, due to the patchiness of reionization and
the co-existence of neutral versus ionized regions during Reionization. The
neutral mode peaks at sub-kpc to kpc scales of mfp, while the ionized mode peak
evolves from $\rm 0.1 Mpc/h$ at $\rm z=7$ to $\sim 10$ Mpc/h at $\rm z=5.2$.
Computing the mfp as the average of the ionized mode provides the best match to
the recent observational determinations. The distribution reduces to a single
neutral (ionized) mode at $\rm z>13$ ($\rm z<5$).


  In the first part of the paper we generalize a descent technique due to
Harish-Chandra to the case of a reductive group acting on a smooth affine
variety both defined over an arbitrary local field F of characteristic zero.
Our main tool is the Luna Slice Theorem.
  In the second part of the paper we apply this technique to symmetric pairs.
In particular we prove that the pairs (GL(n+k,F), GL(n,F) x GL(k,F)) and
(GL(n,E), GL(n,F)) are Gelfand pairs for any local field F and its quadratic
extension E. In the non-Archimedean case, the first result was proven earlier
by Jacquet and Rallis and the second by Flicker.
  We also prove that any conjugation invariant distribution on GL(n,F) is
invariant with respect to transposition. For non-Archimedean F the latter is a
classical theorem of Gelfand and Kazhdan.


  At zero magnetic field we have observed an electromagnetic radiation from
superconductors subjected by a transverse elastic wave. This radiation has an
inertial origin, and is a manifestation of the acoustic Stewart-Tolman effect.
The effect is used for implementing a method of measurement of an effective
Magnus force in type II superconductors. The method does not require the flux
flow regime and allows to investigate this force for almost the whole range of
the existence of the mixed state. We have studied behavior of the gyroscopic
force in nonmagnetic borocarbides and Nb. It is found that in borocarbides the
sign of the gyroscopic force in the mixed state is the same as in the normal
state, and its value (counted for one vortex of unit length) has only a weak
dependence on the magnetic field. In Nb the change of sign of the gyroscopic
force under the transition from the normal to the mixed state is observed.


  System of two quantum dots attached to external electrodes is considered
theoretically in orbital Kondo regime. In general, the double dot system is
coupled via both Coulomb interaction and direct hoping. Moreover, the indirect
hopping processes between the dots (through the leads) are also taken into
account. To investigate system's electronic properties we apply slave-boson
mean field (SBMF) technique. With help of the SBMF approach the local density
of states for both dots and the transmission (as well as linear and
differencial conductance) is calculated. We show that Dicke- and Fano-like line
shape may emerge in transport characteristics of the double dot system.
Moreover, we observed that these modified Kondo resonances are very susceptible
to the change of the indirect coupling's strength. We have also shown that the
Kondo temperature become suppressed with increasing asymmetry in the dot-lead
couplings when there is no indirect coupling. Moreover, when the indirect
coupling is turned on the Kondo temperature becomes suppressed. By allowing a
relative sign of the nondiagonal elements of the coupling matrix with left and
right electrode, we extend our investigations become more generic. Finally, we
have also included the level renormalization effects due to indirect tunneling,
which in most papers is not taken into account.


  It is shown that every concretizable category can be fully embedded into the
category of accessible set functors and natural transformations.


  Non-rigid structure-from-motion (NRSfM) has so far been mostly studied for
recovering 3D structure of a single non-rigid/deforming object. To handle the
real world challenging multiple deforming objects scenarios, existing methods
either pre-segment different objects in the scene or treat multiple non-rigid
objects as a whole to obtain the 3D non-rigid reconstruction. However, these
methods fail to exploit the inherent structure in the problem as the solution
of segmentation and the solution of reconstruction could not benefit each
other. In this paper, we propose a unified framework to jointly segment and
reconstruct multiple non-rigid objects. To compactly represent complex
multi-body non-rigid scenes, we propose to exploit the structure of the scenes
along both temporal direction and spatial direction, thus achieving a
spatio-temporal representation. Specifically, we represent the 3D non-rigid
deformations as lying in a union of subspaces along the temporal direction and
represent the 3D trajectories as lying in the union of subspaces along the
spatial direction. This spatio-temporal representation not only provides
competitive 3D reconstruction but also outputs robust segmentation of multiple
non-rigid objects. The resultant optimization problem is solved efficiently
using the Alternating Direction Method of Multipliers (ADMM). Extensive
experimental results on both synthetic and real multi-body NRSfM datasets
demonstrate the superior performance of our proposed framework compared with
the state-of-the-art methods.


  Automatic generation of a high-quality video from a single image remains a
challenging task despite the recent advances in deep generative models. This
paper proposes a method that can create a high-resolution, long-term animation
using convolutional neural networks (CNNs) from a single landscape image where
we mainly focus on skies and waters. Our key observation is that the motion
(e.g., moving clouds) and appearance (e.g., time-varying colors in the sky) in
natural scenes have different time scales. We thus learn them separately and
predict them with decoupled control while handling future uncertainty in both
predictions by introducing latent codes. Unlike previous methods that infer
output frames directly, our CNNs predict spatially-smooth intermediate data,
i.e., for motion, flow fields for warping, and for appearance, color transfer
maps, via self-supervised learning, i.e., without explicitly-provided ground
truth. These intermediate data are applied not to each previous output frame,
but to the input image only once for each output frame. This design is crucial
to alleviate error accumulation in long-term predictions, which is the
essential problem in previous recurrent approaches. The output frames can be
looped like cinemagraph, and also be controlled directly by specifying latent
codes or indirectly via visual annotations. We demonstrate the effectiveness of
our method through comparisons with the state-of-the-arts on video prediction
as well as appearance manipulation.


  The group $\Sigma(36\times3)$ with the generalized CP transformation is
introduced to predict the mixing pattern of leptons. Various combinations of
abelian residual flavor symmetries with CP transformations are surveyed. Six
mixing patterns could accommodate the fit data of neutrinos oscillation at
$3\sigma$ level. Among them, two patterns predict the nontrivial Dirac CP
phase, around $\pm 57^{\circ}$ or $\pm 123^{\circ}$, which is in accordance
with the result of the literature and the recent fit data. Furthermore, one
pattern could satisfy the experimental constraints at $1\sigma$ level.


  We study the structure of wave functions in complex Chern-Simons theory on
the complement of a hyperbolic knot, emphasizing the similarities with the
topological string/spectral theory correspondence. We first conjecture a hidden
integrality structure in the holomorphic blocks and show that this structure
guarantees the cancellation of potential singularities in the full
non-perturbative wave function at rational values of the coupling constant. We
then develop various techniques to determine the wave function at such rational
points. Finally, we illustrate our conjectures and obtain explicit results in
the examples of the figure-eight and the three-twist knots. In the case of the
figure-eight knot, we also perform a direct evaluation of the state integral in
the rational case and observe that the resulting wave function has the features
of the ground state for a quantum mirror curve.


  The main purpose of this paper is to introduce the concept of
$e^*$-topological ring. This class appears as a generalized form of the class
of $\beta$-topological rings. In addition, we have discussed the relation
between the concept of $e^*$-topological ring and some other types of
topological rings existing in the literature. Also, some fundamental results
about $e^*$-topological rings are revealed. Furthermore, we give some
counterexamples related to our results.


  In this paper, we are interested in generating an cartoon face of a person by
using unpaired training data between real faces and cartoon ones. A major
challenge of this task is that the structures of real and cartoon faces are in
two different domains, whose appearance differs greatly from each other.
Without explicit correspondence, it is difficult to generate a high quality
cartoon face that captures the essential facial features of a person. In order
to solve this problem, we propose landmark assisted CycleGAN, which utilizes
face landmarks to define landmark consistency loss and to guide the training of
local discriminator in CycleGAN. To enforce structural consistency in
landmarks, we utilize the conditional generator and discriminator. Our approach
is capable to generate high-quality cartoon faces even indistinguishable from
those drawn by artists and largely improves state-of-the-art.


  Recent advancements in diffusion models have shown remarkable proficiency in
editing 2D images based on text prompts. However, extending these techniques to
edit scenes in Neural Radiance Fields (NeRF) is complex, as editing individual
2D frames can result in inconsistencies across multiple views. Our crucial
insight is that a NeRF scene's geometry can serve as a bridge to integrate
these 2D edits. Utilizing this geometry, we employ a depth-conditioned
ControlNet to enhance the coherence of each 2D image modification. Moreover, we
introduce an inpainting approach that leverages the depth information of NeRF
scenes to distribute 2D edits across different images, ensuring robustness
against errors and resampling challenges. Our results reveal that this
methodology achieves more consistent, lifelike, and detailed edits than
existing leading methods for text-driven NeRF scene editing.


  A new model for graphene, epitaxially grown on silicon carbide is proposed.
Density functional theory modelling of epitaxial graphene functionalization by
hydrogen, fluorine and phenyl groups has been performed with hydrogen and
fluorine showing a high probability of cluster formation in high adatom
concentration. It has also been shown that the clusterization of fluorine
adatoms provides midgap states in formation due to significant flat distortion
of graphene. The functionalization of epitaxial graphene using larger species
(methyl and phenyl groups) renders cluster formation impossible, due to the
steric effect and results in uniform coverage with the energy gap opening.


  This is the third paper in a series aims at finding reionzation-era quasars
with the combination of DESI Legacy imaging Surveys (DELS) and near-infrared
imaging surveys, such as the UKIRT Hemisphere Survey (UHS), as well as the
Wide-field Infrared Survey Explore ($WISE$) mid-infrared survey. In this paper,
we describe the updated quasar candidate selection procedure, report the
discovery of 16 quasars at $6.4\lesssim z \lesssim6.9$ from area of
$\sim$13,020 deg$^2$, and present the quasar luminosity function (QLF) at
$z\sim6.7$. The measured QLF follows $\Phi(L_{1450})\propto L_{1450}^{-2.35}$
in the magnitude range $27.6<M_{1450}<-25.5$. We determine the quasar comoving
spatial density at $\langle z \rangle$=6.7 and $M_{1450}<-26.0$ to be $\rm
0.39\pm0.11 Gpc^{-3}$ and find that the exponential density evolution parameter
to be $k=-0.78\pm0.18$ from $z\sim6$ to $z\sim6.7$, corresponding to a rapid
decline by a factor of $\sim 6$ per unit redshift towards earlier epoch, a rate
significantly faster than that at $z\sim 3- 5$. The cosmic time between
$z\sim6$ and $z\sim6.7$ is only 121 Myrs. The quasar density declined by a
factor of more than three within such short time requires that SMBHs must grow
rapidly or they are less radiatively efficient at higher redshifts. We measured
quasar comoving emissivity at $z\sim6.7$ which indicate that high redshift
quasars are highly unlikely to make a significant contribution to hydrogen
reionization. The broad absorption line (BAL) quasar fraction at $z\gtrsim6.5$
is measured to be $\gtrsim$22%. In addition, we also report the discovery of
additional five quasars at $z\sim6$ in the appendix.


  This research paper presents the procedure for shape optimization of flywheel
used in an agricultural thresher machine using a cubic B-spline curve and the
Jaya algorithm. The flywheel is an essential element for storing kinetic energy
in modern machines. Shape optimization of the flywheel was carried out using a
cubic B-spline curve to maximize the kinetic energy of the flywheel subjected
to constraints of mass of flywheel and permissible value of Von-Mises stress in
a flywheel. The B-spline curve was used as it gives local control and is not
restricted by control points. The control points of the B-spline are considered
design variables. The Von-Mises stresses at all points in the flywheel are
determined by solving two-point boundary value differential equations using the
finite difference method. Finally, the optimization problem was solved using
the Jaya algorithm. These results are then compared with results obtained using
other nature-inspired algorithms like a genetic algorithm (GA), and particle
swarm optimization (PSO), and it is found that the Jaya algorithm gives better
results. This project is based on the research paper optimal design of the
flywheel using nature-inspired optimization algorithms (Prem Singh, Himanshu
Choudhary) which applied GA, PSO, and Jaya algorithms.


  Networks are commonly used to model complex systems. The different entities
in the system are represented by nodes of the network and their interactions by
edges. In most real life systems, the different entities may interact in
different ways necessitating the use of multiplex networks where multiple links
are used to model the interactions. One of the major tools for inferring
network topology is community detection. Although there are numerous works on
community detection in single-layer networks, existing community detection
methods for multiplex networks mostly learn a common community structure across
layers and do not take the heterogeneity across layers into account. In this
paper, we introduce a new multiplex community detection method that identifies
communities that are common across layers as well as those that are unique to
each layer. The proposed method, Multiplex Orthogonal Nonnegative Matrix
Tri-Factorization, represents the adjacency matrix of each layer as the sum of
two low-rank matrix factorizations corresponding to the common and private
communities, respectively. Unlike most of the existing methods, which require
the number of communities to be pre-determined, the proposed method also
introduces a two stage method to determine the number of common and private
communities. The proposed algorithm is evaluated on synthetic and real
multiplex networks, as well as for multiview clustering applications, and
compared to state-of-the-art techniques.


  The understanding of the interaction of nucleons in nuclear and neutron-rich
matter at non-zero temperature is important for a variety of applications
ranging from heavy-ion collisions to nuclear astrophysics. In this papre we
apply the Dirac-Brueckner-Hartree-Fock method along with the Bonn B potential
to predict single-particle properties in symmetric nuclear matter and
neutron-rich matter at finite temperature. It is found that temperature effects
are generally small but can be significant at low density and momentum.


  This chapter presents an introduction to graph colouring algorithms. The
focus is on vertex-colouring algorithms that work for general classes of graphs
with worst-case performance guarantees in a sequential model of computation.
The presentation aims to demonstrate the breadth of available techniques and is
organized by algorithmic paradigm.


  In this paper, we derive some identities and recurrence relations for the
degenerate Stirling numbers of the first kind and of the second kind which are
degenerate versions of the ordinary Stirling numbers of the first kind and of
the second kind. They are deduced from the normal oderings of degenerate
integral powers of the number operator and their inversions, certain relations
of boson operators and from the recurrence relations of the Stirling numbers
themselves. Here we note that, while the normal ordering of an integral power
of the number operator is expressed with the help of the Stirling numbers of
the second kind, that of a degenerate integral power of the number operator is
represented by means of the degenerate Stirling numbers of the second kind.


  We propose a model to describe the low energy physics of partially composite
Standard Model, in which the electroweak sector in the Standard Model is weakly
coupled to some strong dynamics. The vector resonances in the strong sector are
introduced as the effective degrees of freedom, W' and Z', which mixes with the
W and Z bosons through the electroweak symmetry breaking. Through the coupling
to the strong sector, the Standard Model Higgs boson becomes partially
composite, and its properties are modified. We study the constraints from the
electroweak precision data and direct searches of W' and Z' at the LHC
expriments, and discuss the effects on the production/decay properties of the
Higgs boson.


  The behavior of solutions to the biharmonic equation is well-understood in
smooth domains. In the past two decades substantial progress has also been made
for the polyhedral domains and domains with Lipschitz boundaries. However, very
little is known about higher order elliptic equations in the general setting.
  In this paper we introduce new integral identities that allow to investigate
the solutions to the biharmonic equation in an arbitrary domain. We establish:
(1) boundedness of the gradient of a solution in any three-dimensional domain;
(2) pointwise estimates on the derivatives of the biharmonic Green function;
(3) Wiener-type necessary and sufficient conditions for continuity of the
gradient of a solution.


  Accelerators magnets must have minimal magnetic field imperfections for
reducing particle-beam instabilities. In the case of coils made of
high-temperature superconducting (HTS) tapes, the field imperfections from
persistent currents need to be carefully evaluated. In this paper we study the
use of superconducting screens based on HTS tapes for reducing the magnetic
field imperfections in accelerator magnets. The screens exploit the
magnetization by persistent currents to cancel out the magnetic field error.
The screens are aligned with the main field components, such that only the
undesired field components are compensated. The screens are passive,
self-regulating, and do not require any external source of energy. Measurements
in liquid nitrogen at 77 Kelvin show for dipole-field configurations a
significant reduction of the magnetic-field error up to a factor of four. The
residual error is explained via numerical simulations, accounting for the
geometrical imperfections in the HTS screens, thus achieving satisfactory
agreement with experimental results. Simulations show that if screens are
increased in width and thickness, and operated at 4.5 Kelvin, field errors may
be eliminated almost entirely for the typical excitation cycles of accelerator
magnets.


  The main aim of this report is to provide an introductory tutorial on the
Abstract State Machines (ASM) specification method for software engineering to
an audience already familiar with the Temporal Logic of Actions (TLA$^+$)
method. The report asks to what extent the ASM and TLA$^+$ methods are
complementary in checking specifications against stated requirements and
proposes some answers. A second aim is to provide a comparison between
different executable frameworks that have been developed for the same
specification languages. Thus, the ASM discussion is complemented by executable
Corinthian ASM (CASM) and CoreASM models. Similarly, the two TLA$^+$
specifications presented, which rely on the TLC and Apalache model checkers,
respectively, are complemented by a Quint specification, a new language
developed by Informal Systems to serve as a user-friendly syntax layer for
TLA$^+$. For the basis of comparison we use the specification of the
Alternating Bit (AB) protocol because it is a simple and well-understood
protocol already extensively analysed in the literature. While the models
reported here and developed with the two methods are semantically equivalent,
ASMs and Quint are better suited for top-down specification from abstract
requirements by iterative refinement. TLA$^+$ seems to be more easily used
bottom-up, to build abstractions on top of verified components in spite of the
fact that it, too, emphasizes iterative refinement. In the final section, the
report begins to scope out the possibility of a homomorphism between the
specification of the AB protocol and its finite-state machine (FSM) through
state space visualizations, motivated by a search for a formal decomposition
method.


  Recently, in a number of papers it was understood that results on sampling
discretization and on the universal sampling discretization can be successfully
used in the problem of sampling recovery. Moreover, it turns out that it is
sufficient to only have a one-sided discretization inequality for some of those
applications. This motivates us to write the present paper as a survey/research
paper with the focus on the one-sided discretization inequalities and their
applications in the sampling recovery. In this sense the paper complements the
two existing survey papers on sampling discretization.


  In this paper, we present an algorithm to construct the qT distribution at
NLO accuracy to arbitrary power precision, including the assembly of suitable
zero-bin subtrahends, in a mathematically well-defined way for a generic choice
of rapidity-divergence regularisation prescription. In its derivation, we
divide the phase space into two sectors, the interior of the integration domain
as well as the integration boundary, which we include here for the first time.
To demonstrate the applicability and usefulness of our algorithm, we calculate
the NNLP corrections for Higgs hadroproduction for the first time. We observe
that our approximate NNLP-accurate qT spectra replicate the asymptotic
behaviour of the full QCD calculation to a much better degree than the
previously available results, both within the $q_{\mathrm{T}}\to 0$ limit and
in the large-qT domain for all the involved partonic processes. While playing a
minor role at larger transverse momenta, we show that the newly incorporated
boundary contribution plays a vital role in the $q_{\mathrm{T}}\to 0$ limit,
where any subleading power accuracy would be lost without them. In particular,
our NNLP-accurate qT expansion can approximate the exact qT distribution up to
$q_{\mathrm{T}}\sim30\,\text{GeV}$ at the percent level for rapidities
$|Y_H|\lesssim 3$.


  Many physical systems are governed by ordinary or partial differential
equations (see, for example, Chapter ''Differential equations'', ''System of
Differential Equations''). Typically the solution of such systems are functions
of time or of a single space variable (in the case of ODE's), or they depend on
multidimensional space coordinates or on space and time (in the case of PDE's).
In some cases, the solutions may depend on several time or space scales. An
example governed by ODE's is the damped harmonic oscillator, in the two extreme
cases of very small or very large damping, the cardiovascular system, where the
thickness of the arteries and veins varies from centimeters to microns, shallow
water equations, which are valid when water depth is small compared to typical
wavelength of surface waves, and sorption kinetics, in which the range of
interaction of a surfactant with an air bubble is much smaller than the size of
the bubble itself. In all such cases a detailed simulation of the models which
resolves all space or time scales is often inefficient or intractable, and
usually even unnecessary to provide a reasonable description of the behavior of
the system. In the Chapter ''Multiscale modeling with differential equations''
we present examples of systems described by ODE's and PDE's which are
intrinsically multiscale, and illustrate how suitable modeling provide an
effective way to capture the essential behavior of the solutions of such
systems without resolving the small scales.


  Combining the Su-Schrieffer-Heeger model and the non-equilibrium Green's
function formalism, we investigate the negative differential resistance effect
in organic spintronics at low temperature and interprete it with a self-doping
picture. A giant negative magnetoresistance exceeding 300% is theoretically
predicted as the results of the negative differential resistance effects.


  We propose a new, two-stage approach to the vertebrae centroid detection and
localization problem. The first stage detects where the vertebrae appear in the
scan using 3D samples, the second identifies the specific vertebrae within that
region-of-interest using 2D slices. Our solution utilizes new techniques to
improve the accuracy of the algorithm such as a revised approach to dense
labelling from sparse centroid annotations and usage of large anisotropic
kernels in the base level of a U-net architecture to maximize the receptive
field. Our method improves the state-of-the-art's mean localization accuracy by
0.87mm on a publicly available spine CT benchmark.


  Brain-Like Stochastic Search (BLiSS) refers to this task: given a family of
utility functions U(u,A), where u is a vector of parameters or task
descriptors, maximize or minimize U with respect to u, using networks (Option
Nets) which input A and learn to generate good options u stochastically. This
paper discusses why this is crucial to brain-like intelligence (an area funded
by NSF) and to many applications, and discusses various possibilities for
network design and training. The appendix discusses recent research, relations
to work on stochastic optimization in operations research, and relations to
engineering-based approaches to understanding neocortex.


  Curved fluid interfaces are investigated on the nanometre length scale by
molecular dynamics simulation. Thereby, droplets surrounded by a metastable
vapour phase are stabilized in the canonical ensemble. Analogous simulations
are conducted for cylindrical menisci separating vapour and liquid phases under
confinement in planar nanopores. Regarding the emergence of nanodroplets during
nucleation, a non-equilibrium phenomenon, both the non-steady dynamics of
condensation processes and stationary quantities related to supersaturated
vapours are considered. Results for the truncated and shifted Lennard-Jones
fluid and for mixtures of quadrupolar fluids confirm the applicability of the
capillarity approximation and the classical nucleation theory.


  Our environment is filled with rich and dynamic acoustic information. When we
walk into a cathedral, the reverberations as much as appearance inform us of
the sanctuary's wide open space. Similarly, as an object moves around us, we
expect the sound emitted to also exhibit this movement. While recent advances
in learned implicit functions have led to increasingly higher quality
representations of the visual world, there have not been commensurate advances
in learning spatial auditory representations. To address this gap, we introduce
Neural Acoustic Fields (NAFs), an implicit representation that captures how
sounds propagate in a physical scene. By modeling acoustic propagation in a
scene as a linear time-invariant system, NAFs learn to continuously map all
emitter and listener location pairs to a neural impulse response function that
can then be applied to arbitrary sounds. We demonstrate that the continuous
nature of NAFs enables us to render spatial acoustics for a listener at an
arbitrary location, and can predict sound propagation at novel locations. We
further show that the representation learned by NAFs can help improve visual
learning with sparse views. Finally, we show that a representation informative
of scene structure emerges during the learning of NAFs.


  We perform a Wigner analysis of Fourier integral operators (FIOs), whose main
examples are Schr\"odinger propagators arising from quadratic Hamiltonians with
bounded perturbations. The perturbation is given by a pseudodifferential
operator $\sigma(x,D)$ with symbol in the H\"ormander class
$S^0_{0,0}(\mathbb{R}^{2d})$. We compute and study the Wigner kernel of these
operators. They are special instances of a more general class of FIOs named
$FIO(S)$, with $S$ the symplectic matrix representing the classical symplectic
map. We shall show the algebra and the Wiener's property of this class. The
algebra will be the fundamental tool to represent the Wigner kernel of the
Schr\"odinger propagator for every $t\in\mathbb{R}^d$, also in the caustic
points. This outcome underlines the validity of the Wigner analysis for the
study of Schr\"odinger equations.


  We investigate the superconformal index of four-dimensional N=1
superconformal field theories that arise on coincident M5 branes wrapping a
holomorphic curve in a local Calabi-Yau three-fold. The structure of the index
is very similar to that which appears in the special case preserving N=2
supersymmetry. We first compute the index for the fixed points that admit a
known four-dimensional ultraviolet description and prove infrared equivalence
at the level of the index for all such constructions. These results suggest a
formulation of the index as a two-dimensional topological quantum field theory
that generalizes the one that computes the N=2 index. The TQFT structure leads
to an expression for the index of all class S fixed points in terms of the
index of the N=2 theories. Calculations of spectral data using the index
suggests a connection between these families of fixed points and the
mathematics of SU(2) Yang-Mills theory on the wrapped curve.


  Freshness of status update packets is essential for enabling services where a
destination needs the most recent measurements of various sensors. In this
paper, we study the information freshness of single-server multi-source
queueing models under a first-come first-served (FCFS) serving policy. In the
considered model, each source independently generates status update packets
according to a Poisson process. The information freshness of the status updates
of each source is evaluated by the average age of information (AoI). We derive
an exact expression for the average AoI for the case with exponentially
distributed service time, i.e., for a multi-source M/M/1 queueing model.
Moreover, we derive three approximate expressions for the average AoI for a
multi-source M/G/1 queueing model having a general service time distribution.
Simulation results are provided to validate the derived exact average AoI
expression, to assess the tightness of the proposed approximations, and to
demonstrate the AoI behavior for different system parameters.


  We study surface superconductivity involving the `drumhead' surface states of
(doped) Weyl loop materials. The leading weak coupling instability in the bulk
is toward a chiral superconducting order, which fully gaps the Fermi surface.
In this state the surface also becomes superconducting, with $p+ip$ symmetry.
We show that the surface SC state is "topological" as long as it is fully
gapped, and the system traps Majoarana modes wherever a vortex line enters or
exits the bulk. In contrast to true 2D $p+ip$ superconductors, these Majorana
zero modes arise even in the "strong pairing" regime where the chemical
potential is entirely above/below the drumhead. We also consider conventional
$s$-wave pairing, and show that in this case the surface hosts a flat band of
charge neutral Majorana fermions, whose momentum range is given by the
projection of the bulk Fermi surface. Weyl loop materials thus provide access
to new forms of topological superconductivity.


  Recent advancements in machine learning research, i.e., deep learning,
introduced methods that excel conventional algorithms as well as humans in
several complex tasks, ranging from detection of objects in images and speech
recognition to playing difficult strategic games. However, the current
methodology of machine learning research and consequently, implementations of
the real-world applications of such algorithms, seems to have a recurring
HARKing (Hypothesizing After the Results are Known) issue. In this work, we
elaborate on the algorithmic, economic and social reasons and consequences of
this phenomenon. We present examples from current common practices of
conducting machine learning research (e.g. avoidance of reporting negative
results) and failure of generalization ability of the proposed algorithms and
datasets in actual real-life usage. Furthermore, a potential future trajectory
of machine learning research and development from the perspective of
accountable, unbiased, ethical and privacy-aware algorithmic decision making is
discussed. We would like to emphasize that with this discussion we neither
claim to provide an exhaustive argumentation nor blame any specific institution
or individual on the raised issues. This is simply a discussion put forth by
us, insiders of the machine learning field, reflecting on us.


  A unified mathematical language for medicine and science will be presented.
Using this language, models for DNA replication, protein synthesis, chemical
reactions, neurons and a cardiac cycle of a heart have been built. Models for
Turing machines, cellular automaton, fractals and physical systems are also
represented with the use of this language. Interestingly, the language comes
with a way to represent probability theory concepts and also programming
statements. With this language, questions and processes in medicine can be
represented as systems of equations; and solutions to these equations are
viewed as treatments or previously unknown processes. This language can serve
as the framework for the creation of a large interactive open-access scientific
database that allows extensive mathematical medicine computations. It can also
serve as a basis for exploring ideas related to what could be called
metascience.


  The spectacular metal-to-insulator transition of V2O3 can be progressively
suppressed in thin film samples. Evidence for phase separation was observed
using microbridges as a mesoscopic probe of transport properties where the same
film possesses domains that exhibit a metal-to-insulator transition with clear
first order features or remain metallic down to low temperatures. A simple
model consisting of two parallel resistors can be used to quantify a phase
coexistence scenario explaining the measured macroscopic transport properties.
The interaction between film and substrate is the most plausible candidate to
explain this extended phase coexistence as shown by a correlation between the
transport properties and the structural data.


  Two-way quantum key distribution protocols utilize bi-directional quantum
communication to establish a shared secret key. Due to the increased attack
surface, security analyses remain challenging. Here we investigate a
high-dimensional variant of the Ping Pong protocol and perform an information
theoretic security analysis in the finite-key setting. Our methods may be
broadly applicable to other QKD protocols, especially those relying on two-way
channels. Along the way, we show some fascinating benefits to high-dimensional
quantum states applied to two-way quantum communication.


  The gravitationally lensing clusters A370, A2218, A1689 and CL0024+1654 were
observed with the Infrared Space Observatory (ISO) using ISOCAM at 6.7 and 14.3
microns (hereafter 7 and 15 microns respectively). A total of 178 sources were
detected in the whole set, 70 of them being cluster objects. The spectral
energy distribution of a subset of sources was calculated using GRASIL. The
results for the total infrared luminosity and the estimation of the star
formation rate are presented for the non stellar objects for which the SED has
been determined. The majority of the cluster galaxies in A2218 are best fit by
models of quiescent ellipticals. In Cl0024+1654, most of the galaxies lying on
the Butcher-Oemler region of the colour-magnitude diagram are best fit by disk
galaxies, while those on the main sequence area have in general SEDs
corresponding to post-starburst galaxies. The population of each cluster is
compared with the field population, as well as with the population of other
clusters. A significant number of Luminous IR Galaxies (LIRGs) is detected in
CL0024+1654, while only one LIRG has been observed in total in A370, A1689, and
A2218. This result supports the link between LIRGs in clusters and recent or
ongoing cluster merger activity as well as the need for extending the
observations to the outer parts of clusters.


  We present a systematic theoretical study of spin-dependent recombination and
its effect on optical orientation of photoelectron spins in semiconductors with
deep paramagnetic centers. For this aim we generalize the Shockley-Read theory
of recombination of electrons and holes through the deep centers with allowance
for optically-induced spin polarization of free and bound electrons. Starting
from consideration of defects with three charge states we turn to the
two-charge-state model possessing nine parameters and show that it is
compatible with available experimental data on undoped GaAsN alloys. In the
weak- and strong-pumping limits, we derive simple analytic equations which are
useful in prediction and interpretation of experimental results. Experimental
and theoretical dependencies of the spin-dependent-recombination ratio and
degree of photoluminescence circular polarization on the pumping intensity and
the transverse magnetic field are compared and discussed.


  In this paper, we give some stability estimates for the Faber-Krahn
inequality relative to the eigenvalues of Hessian operators


  Catastrophic forgetting is a problem faced by many machine learning models
and algorithms. When trained on one task, then trained on a second task, many
machine learning models "forget" how to perform the first task. This is widely
believed to be a serious problem for neural networks. Here, we investigate the
extent to which the catastrophic forgetting problem occurs for modern neural
networks, comparing both established and recent gradient-based training
algorithms and activation functions. We also examine the effect of the
relationship between the first task and the second task on catastrophic
forgetting. We find that it is always best to train using the dropout
algorithm--the dropout algorithm is consistently best at adapting to the new
task, remembering the old task, and has the best tradeoff curve between these
two extremes. We find that different tasks and relationships between tasks
result in very different rankings of activation function performance. This
suggests the choice of activation function should always be cross-validated.


  The process $ep \to e^{\prime}p^{\prime}\pi^0$ has been measured at $Q^2$ =
6.4 and 7.7 GeV/c$^2$)$^2$ in Jefferson Lab's Hall C. Unpolarized differential
cross sections are reported in the virtual photon-proton center of mass frame
considering the process $\gamma^{\ast}p \to p^{\prime}\pi^0$. Various details
relating to the background subtractions, radiative corrections and systematic
errors are discussed. The usefulness of the data with regard to the measurement
of the electromagnetic properties of the well known $\Delta(1232)$ resonance is
covered in detail. Specifically considered are the electromagnetic and
scalar-magnetic ratios $R_{EM}$ and $R_{SM}$ along with the magnetic transition
form factor $G_M^{\ast}$. It is found that the rapid fall off of the
$\Delta(1232)$ contribution continues into this region of momentum transfer and
that other resonances


  Let $X$ be an algebraic variety defined over a field of characteristic zero,
and let $\xi \in \mathrm{\underline{Max}\; mult}(X)$ be a point in the closed
subset of maximum multiplicity of $X$. We provide a criterion, given in terms
of arcs, to determine whether $\xi $ is isolated in $\mathrm{\underline{Max}\;
mult}(X)$. More precisely, we use invariants of arcs derived from the Nash
multiplicity sequence to characterize when $\xi $ is an isolated point in
$\mathrm{\underline{Max}\; mult}(X)$.


  We simulated both the matter and light (galaxy) distributions in a wedge of
the universe and calculated the gravitational lensing magnification caused by
the mass along the line of sight of galaxies and galaxy groups identified in
sky surveys. A large volume redshift cone containing cold dark matter particles
mimics the expected cosmological matter distribution in a flat universe with
low matter density and a cosmological constant. We generate a mock galaxy
catalogue from the matter distribution and identify thousands of galaxy groups
in the luminous sky projection. We calculate the expected magnification around
galaxies and galaxy groups and then the induced QSO-lens angular correlation
due to magnification bias. This correlation is an observable and can be used to
estimate the average mass of the lens population and also make cosmological
inferences. We also use analytic calculations and various analysis to compare
the observational results with theoretical expectations for the
cross-correlation between faint QSOs from the 2dF Survey and nearby galaxies
and groups from the APM and SDSS EDR. The observed QSO-lens anti-correlations
are stronger than the predictions for the cosmological model used. This
suggests that there could be unknown systematic errors in the observations and
data reduction, or that the model used is not adequate. If the observed signal
is assumed to be solely due to gravitational lensing then the lensing is
stronger than expected, due to more massive galactic structures or more
efficient lensing than simulated.


  From the analysis of the measurement process we make the hypothesis that we
have to add to the quantum state psi a label z and a special function alpha in
order to describe completely the preparation of a (pure) quantum system . Given
such a terne every observable A receives a univocal value . Therefore all
physical quantities of the system are well defined independently from the
measuring process. Making the unknown parameter z to vary in its space we get
the probabilities prescribed by quantum mechanics.We show also that every
evolution of quantum states can be extended to an evolution of the ternes.


  We propose a unified approach to the formal long-wave reduction of several
fluid models for thin-layer incompressible homogeneous flows driven by a
constant external force like gravity. The procedure is based on a mathematical
coherence property that univoquely defines one reduced model given one rheology
and one thin-layer regime. For the first time, as far as we know, various known
reduced models can thus be investigated within a single mathematical framework,
for various rheologies (viscous and viscoelastic) and various limit regimes
(fast inertial flows and slow viscous flows). Furthermore, our systematic
procedure also produces new reduced models for viscoelastic non-Newtonian
fluids and improves on our previous work [Bouchut & Boyaval, M3AS (23) 8,
2013].


  A new learning algorithm proposed by Brandt and Lin for neural network [1],
[2] has been shown to be mathematically equivalent to the conventional
back-propagation learning algorithm, but has several advantages over the
backpropagation algorithm, including feedback-network-free implementation and
biological plausibility. In this paper, we investigate the convergence of the
new algorithm. A necessary and sufficient condition for the algorithm to
converge is derived. A convergence measure is proposed to measure the
convergence rate of the new algorithm. Simulation studies are conducted to
investigate the convergence of the algorithm with respect to the number of
neurons, the connection distance, the connection density, the ratio of
excitatory/inhibitory synapses, the membrane potentials, and the synapse
strengths.


  Far-field super-resolution fluorescence microscopy has been rapidly developed
for applications ranging from cell biology to nanomaterials. However, it
remains a significant challenge to achieve super-resolution imaging at depth in
opaque materials. In this study, we present a super-resolution microscopy
technique for imaging hidden fluorescent objects through scattering media,
started by exploiting the inherent object replica generation arising from the
memory effect, i.e. the seemingly informationless emission speckle can be
regarded as a random superposition of multiple object copies. Inspired by the
concept of super-resolution optical fluctuation imaging, we use
temporally-fluctuating speckles to excite fluorescent signals and perform
high-order cumulant analysis on the fluctuation, which can not only improve the
image resolution, but also increase the speckle contrast to isolate only the
bright object replicas. A super-resolved image can be finally retrieved by
simply unmixing the sparsely distributed replicas with their location map. This
methodology allows to overcome scattering and achieve robust super-resolution
fluorescence imaging, circumventing the need of heavy computational steps.


  Gaussian multiplicative noise is commonly used as a stochastic regularisation
technique in training of deterministic neural networks. A recent paper
reinterpreted the technique as a specific algorithm for approximate inference
in Bayesian neural networks; several extensions ensued. We show that the
log-uniform prior used in all the above publications does not generally induce
a proper posterior, and thus Bayesian inference in such models is ill-posed.
Independent of the log-uniform prior, the correlated weight noise approximation
has further issues leading to either infinite objective or high risk of
overfitting. The above implies that the reported sparsity of obtained solutions
cannot be explained by Bayesian or the related minimum description length
arguments. We thus study the objective from a non-Bayesian perspective, provide
its previously unknown analytical form which allows exact gradient evaluation,
and show that the later proposed additive reparametrisation introduces minima
not present in the original multiplicative parametrisation. Implications and
future research directions are discussed.


  There has been considerable attention devoted to models that learn to jointly
infer an expression's syntactic structure and its semantics. Yet,
\citet{NangiaB18} has recently shown that the current best systems fail to
learn the correct parsing strategy on mathematical expressions generated from a
simple context-free grammar. In this work, we present a recursive model
inspired by \newcite{ChoiYL18} that reaches near perfect accuracy on this task.
Our model is composed of two separated modules for syntax and semantics. They
are cooperatively trained with standard continuous and discrete optimization
schemes. Our model does not require any linguistic structure for supervision
and its recursive nature allows for out-of-domain generalization with little
loss in performance. Additionally, our approach performs competitively on
several natural language tasks, such as Natural Language Inference or Sentiment
Analysis.


  Let $\sigma$ be the involution of the Roe algebra $\Roe{\RR}$ which is
induced from the reflection $\RR\to\RR; x\mapsto -x$. A graded Fredholm module
over a separable $C^*$-algebra $A$ gives rise to a homomorphism
$\tilde{\rho}:A\to\Roe{\RR}^\sigma$ to the fixed-point subalgebra. We use this
observation to give an even-dimensional analogue of a result of Roe. Namely, we
show that the $K$-theory of this symmetric Roe algebra is
$K_0(\Roe{\RR}^\sigma)\cong\ZZ$, $K_1(\Roe{\RR})=0$, and that the induced map
$\tilde{\rho}_*:K_0(A) \to \ZZ$ on $K$-theory gives the index pairing of
$K$-homology with $K$-theory.


  High resolution (lambda / Delta-lambda = 50,000) K-band spectra of massive,
embedded, young stellar objects are presented. The present sample consists of
four massive young stars located in nascent clusters powering Galactic giant H
II regions. Emission in the 2.3 micron 2--0 vibrational--rotational bandhead of
CO is observed. A range of velocity broadened profiles seen in three of the
objects is consistent with the emission arising from a circumstellar disk seen
at various inclination angles. Br gamma spectra of the same spectral and
spatial resolution are also presented which support an accretion disk or torus
model for massive stars. In the fourth object, Br emission suggesting a
rotating torus is observed, but the CO profile is narrow, indicating that there
may be different CO emission mechanisms in massive stars and this is consistent
with earlier observations of the BN object and MWC 349. To--date, only young
massive stars of late O or early B types have been identified with clear
accretion disk signatures in such embedded clusters. Often such stars are found
in the presence of other more massive stars which are revealed by their
photospheric spectra but which exhibit no disk signatures. This suggests the
timescale for dissipating their disks is much faster than the less massive OB
stars or that the most massive stars do not form with accretion disks.


  While deep learning has enabled tremendous progress on text and image
datasets, its superiority on tabular data is not clear. We contribute extensive
benchmarks of standard and novel deep learning methods as well as tree-based
models such as XGBoost and Random Forests, across a large number of datasets
and hyperparameter combinations. We define a standard set of 45 datasets from
varied domains with clear characteristics of tabular data and a benchmarking
methodology accounting for both fitting models and finding good
hyperparameters. Results show that tree-based models remain state-of-the-art on
medium-sized data ($\sim$10K samples) even without accounting for their
superior speed. To understand this gap, we conduct an empirical investigation
into the differing inductive biases of tree-based models and Neural Networks
(NNs). This leads to a series of challenges which should guide researchers
aiming to build tabular-specific NNs: 1. be robust to uninformative features,
2. preserve the orientation of the data, and 3. be able to easily learn
irregular functions. To stimulate research on tabular architectures, we
contribute a standard benchmark and raw data for baselines: every point of a 20
000 compute hours hyperparameter search for each learner.


  In many real-world scenarios where extrinsic rewards to the agent are
extremely sparse, curiosity has emerged as a useful concept providing intrinsic
rewards that enable the agent to explore its environment and acquire
information to achieve its goals. Despite their strong performance on many
sparse-reward tasks, existing curiosity approaches rely on an overly holistic
view of state transitions, and do not allow for a structured understanding of
specific aspects of the environment. In this paper, we formulate curiosity
based on grounded question answering by encouraging the agent to ask questions
about the environment and be curious when the answers to these questions
change. We show that natural language questions encourage the agent to uncover
specific knowledge about their environment such as the physical properties of
objects as well as their spatial relationships with other objects, which serve
as valuable curiosity rewards to solve sparse-reward tasks more efficiently.


  In the present paper we prove uniqueness results for solutions to a class of
Neumann boundary value problems whose prototype is --div((1 + |$\nabla$u| 2)
(p--2)/2 $\nabla$u) -- div(c(x)|u| p--2 u) = f in $\Omega$, (1 + |$\nabla$u| 2)
(p--2)/2 $\nabla$u + c(x)|u| p--2 u $\times$ n = 0 on $\partial$$\Omega$,


  For an affine algebra of nonexceptional type in the large rank we show the
fermionic formula depends only on the attachment of the node 0 of the Dynkin
diagram to the rest, and the fermionic formula of not type A can be expressed
as a sum of that of type A with Littlewood-Richardson coefficients. Combining
this result with math.CO/9901037 and arXiv:1002.3715 we settle the X=M
conjecture under the large rank hypothesis.


  The spectral fluctuations of a quantum Hamiltonian system with time-reversal
symmetry are studied in the semiclassical limit by using periodic-orbit theory.
It is found that, if long periodic orbits are hyperbolic and uniformly
distributed in phase space, the spectral form factor agrees with the GOE
prediction of random-matrix theory up to second order included in the time
measured in units of the Heisenberg time (leading off-diagonal approximation).
Our approach is based on the mechanism of periodic-orbit correlations
discovered recently by Sieber and Richter (Phys. Scr. T 90, 128, 2001). By
reformulating the theory of these authors in phase space, their result on the
free motion on a Riemann surface with constant negative curvature is extended
to general Hamiltonian hyperbolic systems with two degrees of freedom.


  In this article, we prove that the average rank of elliptic curves over
$\mathbb{Q}$, when ordered by height, is less than $1$ (in fact, less than
$.885$). As a consequence of our methods, we also prove that at least four
fifths of all elliptic curves over $\mathbb{Q}$ have rank either 0 or 1;
furthermore, at least one fifth of all elliptic curves in fact have rank 0. The
primary ingredient in the proofs of these theorems is a determination of the
average size of the $5$-Selmer group of elliptic curves over $\mathbb{Q}$; we
prove that this average size is $6$. Another key ingredient is a new lower
bound on the equidistribution of root numbers of elliptic curves; we prove that
there is a family of elliptic curves over $\mathbb{Q}$ having density at least
$55\%$ for which the root number is equidistributed.


  We investigate the dynamics of a space-charge limited, photoinjected,
electron beam in a microscopic vacuum diode. Due to the small nature of the
system it is possible to conduct high-resolution simulations where the number
of simulated particles is equal to the number of electrons within the system.
In a series of simulations of molecular dynamics type, where electrons are
treated as point-charges, we address and analyze space-charge effects in a
$\mu$m-scale vacuum diode. We have been able to reproduce breakup of a single
pulse injected with a current density beyond the Child-Langmuir limit, and we
find that continuous injection of current into the diode gap results in a well
defined train of electron bunches corresponding to THz frequency. A simple
analytical explanation of this behavior is given.


  Based on a dataset acquired by the BaBar experiment running on and near the
$\Upsilon(4S)$ resonance from 1999-2002, limits are set on the rate of $D^0$--
$\kern 0.2em\bar{\kern -0.2em D}{}^0$ mixing using the decay mode $D^{*+} \to
D^0 \pi^{+}$, followed by a semi-leptonic decay of the $D^0$. Results are
compared to previous BaBar analysis using hadronic decays. We also report on a
search for the flavor-changing neutral current decays $D^0 \to e^{+} e^{-}$
($\mu^{+} \mu^{-}$) and the lepton-flavor violation decays $D^0 \to e^{\pm}
\mu^{\mp}$.


  We establish linear convergence rates for a certain class of extrapolated
fixed point algorithms which are based on dynamic string-averaging methods in a
real Hilbert space. This applies, in particular, to the extrapolated
simultaneous and cyclic cutter methods. Our analysis covers the cases of both
metric and subgradient projections.


  The magnetorotational instability (MRI) is a fundamental process of accretion
disk physics, but its saturation mechanism remains poorly understood despite
considerable theoretical and computational effort. We present a multiple scales
analysis of the non-ideal MRI in the weakly nonlinear regime -- that is, when
the most unstable MRI mode has a growth rate asymptotically approaching zero
from above. Here, we develop our theory in a local, Cartesian channel. Our
results confirm the finding by Umurhan et al. (2007) that the perturbation
amplitude follows a Ginzburg-Landau equation. We further find that the
Ginzburg-Landau equation will arise for the local MRI system with
shear-periodic boundary conditions when the effects of ambipolar diffusion are
considered. A detailed force balance for the saturated azimuthal velocity and
vertical magnetic field demonstrates that even when diffusive effects are
important, the bulk flow saturates via the combined processes of reducing the
background shear and rearranging and strengthening the background vertical
magnetic field. We directly simulate the Ginzburg-Landau amplitude evolution
for our system and demonstrate the pattern formation our model predicts on long
length and time scales. We compare the weakly nonlinear theory results to a
direct numerical simulation of the MRI in a thin-gap Taylor Couette flow.


  Using the narrow clustering of the geometrically corrected gamma-ray energies
released by gamma-ray bursts, we investigate the possibility of using these
sources as standard candles to probe cosmological parameters such as the matter
density Omega_m and the cosmological constant energy density Omega_Lambda. By
simulating different samples of gamma-ray bursts, we find that Omega_m can be
determined with accuracy ~7% with data from 300 sources. We also show that, if
Omega = 1 is due to a quintessence field, some of the models proposed in the
literature may be discriminated from a Universe with cosmological constant, by
a similar-sized sample of gamma-ray bursts.


  This work contains two main contributions concerning the asymmetric broadcast
channel. The first is an analysis of the exact random coding error exponents
for both users, and the second is the derivation of universal decoders for both
users. These universal decoders are certain variants of the maximum mutual
information (MMI) universal decoder, which achieve the corresponding random
coding exponents of optimal decoding. In addition, we introduce some lower
bounds, which involve optimization over very few parameters, unlike the
original, exact exponents, which involve minimizations over auxiliary
probability distributions. Numerical results for the binary symmetric broadcast
channel show improvements over previously derived error exponents for the same
model.


  For deuteron electroweak disintegration, parity violating effects are
investigated which arise from the interference of $\gamma$ and $Z$ exchange as
well as from the hadronic sector via a small parity violating component in the
deuteron. The general formalism for the differential cross section and
polarization observables of electromagnetic deuteron disintegration is extended
to incorporate parity violating contributions. Formal expressions for the
additional structure functions are derived. Results are presented for these
parity violating structure functions for quasifree kinematics neglecting final
state interaction and two-body effects. Both types of parity violating
contributions to the asymmetry of the inclusive reaction with respect to
longitudinally polarized electrons are evaluated. The one from parity violating
deuteron components is negligible over the whole range of momentum transfers
considered.


  Distances between sequences based on their $k$-mer frequency counts can be
used to reconstruct phylogenies without first computing a sequence alignment.
Past work has shown that effective use of k-mer methods depends on 1)
model-based corrections to distances based on $k$-mers and 2) breaking long
sequences into blocks to obtain repeated trials from the sequence-generating
process. Good performance of such methods is based on having many high-quality
blocks with many homologous sites, which can be problematic to guarantee a
priori.
  Nature provides natural blocks of sequences into homologous regions---namely,
the genes. However, directly using past work in this setting is problematic
because of possible discordance between different gene trees and the underlying
species tree. Using the multispecies coalescent model as a basis, we derive
model-based moment formulas that involve the divergence times and the
coalescent parameters. From this setting, we prove identifiability results for
the tree and branch length parameters under the Jukes-Cantor model of sequence
mutations.


  We present high resolution 4.7 micron CO fundamental spectroscopy of V836
Tau, a young star with properties that are between those of classical and weak
T Tauri stars and which may be dissipating its circumstellar disk. We find that
the CO line profiles of V836 Tau are unusual in that they are markedly
double-peaked, even after correcting for stellar photospheric absorption in the
spectrum. This suggests that the CO emission arises from a restricted range of
disk radii (< 0.5 AU), in contrast to the situation for most classical T Tauri
stars where the CO emission extends out to much larger radii (~ 1-2 AU). We
discuss whether the outer radius of the emission in V836 Tau results from the
physical truncation of the disk or an excitation effect. We also explore how
either of these hypotheses may bear on our understanding of disk dissipation in
this system.