  Order strengthening in nickel-based superalloys is associated with the extra
stress required for dislocations to bypass the $\gamma'$ precipitates
distributed in the $\gamma$ matrix. A rich variety of bypass mechanism has been
identified, with various shearing and Orowan looping processes giving way to
climb bypass as the operating conditions change from the low/intermediate
temperatures and high stress regime, to the high temperature and low stress
regime. When anti phase boundary (APB) shearing and Orowan looping mechanisms
operate, the bypass mechanism changes from shearing to looping with increased
particle size and within a broad coexistence size window. Another possibility,
supported by indirect experimental evidence, is that a third "hybrid"
transition mechanism may operate. In this paper we use discrete dislocation
dynamics (DDD) simulations to study dislocation bypass mechanisms in Ni-based
superalloys. We develop a new method to compute generalized stacking fault
forces in DDD simulations. We use this method to study the mechanisms of bypass
of a square lattice of spherical $\gamma'$ precipitates by
$a/2\langle110\rangle\{111\}$ edge dislocations, as a function of the
precipitates volume fraction and size. We show that the hybrid mechanism is
possible and it operates as a transition mechanism between the shearing and
looping regimes over a large range of precipitates volume fraction and radii.
We also consider the effects of a $\gamma/\gamma'$ lattice misfit on the bypass
mechanisms, which we approximate by an additional precipitate stress computed
according to Eshelby's inclusion theory. We show that in the shearing and
hybrid looping-shearing regimes, a lattice misfit generally results in an
increased bypass stress. For sufficiently high lattice misfit, the bypass
stress is controlled by the pinning of the trailing dislocation on the exit
side of the precipitates.


  We investigate extremal problems for quasirandom hypergraphs. We say that a
$3$-uniform hypergraph $H=(V,E)$ is $(d,\eta)$-quasirandom if for any subset
$X\subseteq V$ and every set of pairs $P\subseteq V\times V$ the number of
pairs $(x,(y,z))\in X\times P$ with $\{x,y,z\}$ being a hyperedge of $H$ is in
the interval $d|X||P|\pm\eta|V|^3$. We show that for any $\varepsilon>0$ there
exists $\eta>0$ such that every sufficiently large
$(1/2+\varepsilon,\eta)$-quasirandom hypergraph contains a tetrahedron, i.e.,
four vertices spanning all four hyperedges. A known random construction shows
that the density $1/2$ is best possible. This result is closely related to a
question of Erd\H{o}s, whether every weakly quasirandom $3$-uniform hypergraph
$H$ with density bigger than $1/2$, i.e., every large subset of vertices
induces a hypergraph with density bigger than $1/2$, contains a tetrahedron.


  We consider the inverse problem of determining different type of information
about a diffusion process, described by ordinary or fractional diffusion
equations stated on a bounded domain, like the density of the medium or the
velocity field associated with the moving quantities from a single boundary
measurement. This properties will be associated with some general class of time
independent coefficients that we recover from a single Neumann boundary
measurement, on some parts of the boundary, of the solution of our diffusion
equation with a suitable boundary input, located on some parts of the boundary.


  An intriguing link between a wide range of problems occurring in physics and
financial engineering is presented. These problems include the evolution of
small perturbations of linear flows in hydrodynamics, the movements of
particles in random fields described by the Kolmogorov and Klein-Kramers
equations, the Ornstein-Uhlenbeck and Feller processes, and their
generalizations. They are reduced to affine differential and
pseudo-differential equations and solved in a unified way by using Kelvin waves
and developing a comprehensive math framework for calculating transition
probabilities and expectations. Kelvin waves are instrumental for studying the
well-known Black-Scholes, Heston, and Stein-Stein models and more complex
path-dependent volatility models, as well as the pricing of Asian options,
volatility and variance swaps, bonds, and bond options. Kelvin waves help to
solve several cutting-edge problems, including hedging the impermanent loss of
Automated Market Makers for cryptocurrency trading. This title is also
available as Open Access on Cambridge Core.


  In this work we study the magnetic remanence exhibited by Josephson junction
arrays in response to an excitation with an AC magnetic field. The effect,
predicted by numerical simulations to occur in a range of temperatures, is
clearly seen in our tridimensional disordered arrays. We also discuss the
influence of the critical current distribution on the temperature interval
within which the array develops a magnetic remanence. This effect can be used
to determine the critical current distribution of an array.


  One of the cornerstones of the field of signal processing on graphs are graph
filters, direct analogues of classical filters, but intended for signals
defined on graphs. This work brings forth new insights on the distributed graph
filtering problem. We design a family of autoregressive moving average (ARMA)
recursions, which (i) are able to approximate any desired graph frequency
response, and (ii) give exact solutions for tasks such as graph signal
denoising and interpolation. The design philosophy, which allows us to design
the ARMA coefficients independently from the underlying graph, renders the ARMA
graph filters suitable in static and, particularly, time-varying settings. The
latter occur when the graph signal and/or graph are changing over time. We show
that in case of a time-varying graph signal our approach extends naturally to a
two-dimensional filter, operating concurrently in the graph and regular time
domains. We also derive sufficient conditions for filter stability when the
graph and signal are time-varying. The analytical and numerical results
presented in this paper illustrate that ARMA graph filters are practically
appealing for static and time-varying settings, as predicted by theoretical
derivations.


  Superconductivity in a crystalline lattice without inversion is subject to
complex spin-orbit-coupling effects, which can lead to mixed-parity pairing and
an unusual magnetic response. In this study, the properties of a layered
superconductor with alternating Rashba spin-orbit coupling in the stacking of
layers, hence (globally) possessing a center of inversion, is analyzed in an
applied magnetic field, using a generalized Ginzburg-Landau model. The
superconducting order parameter consists of an even- and an odd-parity pairing
component which exchange their roles as dominant pairing channel upon
increasing the magnetic field. This leads to an unusual kink feature in the
upper critical field and a first-order phase transition within the mixed phase.
We investigate various signatures of this internal phase transition. The
physics we discuss here could explain the recently found $H$--$T$ phase diagram
of the heavy Fermion superconductor CeRh$_2$As$_2$.


  We construct a rank one infinite measure preserving transformation $T$ such
that for all sequences of nonzero integers $\{k_{1},..., k_{r}\}$,
$T^{k_{1}}\times...\times T^{k_{r}}$ is ergodic.


  We study strongly interacting two component Fermi gas near a Feshbach
resonance. By using a ground state energy functional constructed based on
asymptotic limits and Monte Carlo calculations, we calculate the contact,
structure factor, and collective oscillation frequencies in the BCS-BEC
crossover region. The calculated contact and structure factor show excellent
agreements with recent experiments. We compare these results with a standard
mean-field theory and find that the contact is proportional to the square of
superfluid order parameter. Further, we present the chemical potential and the
polytropic index in terms of homogenous energy and the contact.


  This study examines multilevel channel polarization for a certain class of
erasure channels that the input alphabet size is an arbitrary composite number.
We derive limiting proportions of partially noiseless channels for such a
class. The results of this study are proved by an argument of convergent
sequences, inspired by Alsan and Telatar's simple proof of polarization, and
without martingale convergence theorems for polarization process.


  Motivated by the observation that the Standard Model of particle physics
(plus a right-handed neutrino) has precisely 16 Weyl fermions per generation,
we search for $(3+1)$-dimensional chiral fermionic theories and chiral gauge
theories that can be regularized on a 3 dimensional spatial lattice when and
only when the number of flavors is an integral multiple of 16. All these
results are based on the observation that local interactions reduce the
classification of certain $(4+1)$-dimensional topological superconductors from
$\mathbb{Z}$ to $\mathbb{Z}_{8}$, which means that one of their
$(3+1)$-dimensional boundaries can be gapped out by interactions without
breaking any symmetry when and only when the number of boundary chiral fermions
is an integral multiple of $16$.


  We apply (Fractional) Analytic Perturbation Theory (FAPT) to the QCD analysis
of the nonsinglet nucleon structure function $F_2(x,Q^2)$ in deep inelastic
scattering up to the next leading order and compare the results with ones
obtained within the standard perturbation QCD. Based on a popular
parameterization of the corresponding parton distribution we perform the
analysis within the Jacobi Polynomial formalism and under the control of the
numerical inverse Mellin transform. To reveal the main features of the FAPT
two-loop approach, we consider a wide range of momentum transfer from high
$Q^2\sim 100 {\rm GeV}^2$ to low $Q^2\sim 0.3 {\rm GeV}^2$ where the approach
still works.


  We speculate about the possible interpretations of the recently observed
excess in the $h \to \tau \mu$ decay. We derive a robust lower bound on the
Higgs boson coupling strength to a tau and a muon, even in presence of the most
general new physics affecting other Higgs properties. Then we reevaluate
complementary indirect constraints coming from low energy observables as well
as from theoretical considerations. In particular, the tentative signal should
lead to $\tau \to \mu \gamma$ at rates which could be observed at Belle II. In
turn we show that, barring fine-tuned cancellations, the effect can only be
accommodated within models with an extended scalar sector. These general
conclusions are demonstrated using a number of explicit new physics models.
Finally we show how, given the $h \to \tau \mu$ signal, the current and future
searches for $\mu \to e \gamma$ and $\mu \to e$ nuclear conversions
unambiguously constrain the allowed rates for $h \to \tau e$.


  Acoustic scattering of waves by bounded inhomogeneities in an unbounded
homogeneous domain is considered. A symmetric coupled system of time-domain
boundary integral equations and the second order formulation of the wave
equation is described. A fully discrete system consists of spatial
discretization by boundary and finite element methods (BEM/FEM), leapfrog
time-stepping in the interior, and convolution quadrature for the boundary
integral equations. Convolution quadrature is based on BDF2, trapezoidal rule,
or a newly introduced truncated trapezoidal rule that has some favourable
properties for both the implementation and quality of approximate solution. We
give a stability and convergence analysis under a CFL conditon of the fully
discrete system. The theoretical results are illustrated by numerical
experiments in two dimensions.


  We investigate the $K$-theoretic Gysin map for type $A$ partial flag bundles
from the viewpoint of integrability. We introduce several types of partition
functions for one version of $q=0$ degeneration of $U_q(\widehat{sl_n})$ vertex
models on rectangular grids which differ by boundary conditions and sizes, and
can be viewed as Grothendieck classes of the Grothendieck group of a
nonsingular variety and partial flag bundles. By deriving multiple commutation
relations for the $q=0$ $U_q(\widehat{sl_n})$ Yang-Baxter algebra and combining
with the description of the $K$-theoretic Gysin map for partial flag bundles
using symmetrizing operators, we show that the $K$-theoretic Gysin map of the
first type of partition functions on a rectangular grid is given by the second
type whose boundary conditions on one side are reversed from the first type.
This generalizes the author's previous result from Grassmann bundles to partial
flag bundles. We also discuss the inhomogenous version of the partition
functions and applications to the $K$-theoretic Gysin map.


  The classical Ritt's Theorems state several properties of univariate
polynomial decomposition. In this paper we present new counterexamples to
Ritt's first theorem, which states the equality of length of decomposition
chains of a polynomial, in the case of rational functions. Namely, we provide
an explicit example of a rational function with coefficients in Q and two
decompositions of different length.
  Another aspect is the use of some techniques that could allow for other
counterexamples, namely, relating groups and decompositions and using the fact
that the alternating group A_4 has two subgroup chains of different lengths;
and we provide more information about the generalizations of another property
of polynomial decomposition: the stability of the base field. We also present
an algorithm for computing the fixing group of a rational function providing
the complexity over Q.


  We consider semilinear higher order (in time) evolution inequalities posed in
an exterior domain of the half-space $\mathbb{R}_+^N$, $N\geq 2$, and involving
differential operators of the form $\mathcal{L}_\lambda =-\Delta
+\lambda/|x|^2$, where $\lambda\geq -N^2/4$. A potential function of the form
$|x|^\tau$, $\tau\in \mathbb{R}$, is allowed in front of the power
nonlinearity. Under inhomogeneous Dirichlet-type boundary conditions, we show
that the dividing line with respect to existence or nonexistence is given by a
Fujita-type critical exponent that depends on $\lambda, N$ and $\tau$, but
independent of the order of the time derivative.


  Radio and optical images of the M87 jet show bright filaments, twisted into
an apparent double helix, extending from HST-1 to knot A. Proper motions within
the jet suggest a decelerating jet flow passing through a slower, accelerating
wave pattern. We use these observations to develop a mass and energy flux
conserving model describing the jet flow and conditions along the jet. We
determine the cocoon conditions required if the twisted filaments are the
result of the Kelvin-Helmholtz (KH) unstable elliptical mode. We find that the
cocoon must be cooler than the jet at HST-1 but must be about as hot as the jet
at knot A. Under these conditions we find that the observed filament wavelength
is near the elliptical mode maximum growth rate and growth is rapid enough for
the filaments to develop and saturate well before HST-1. We generate a
pseudo-synchrotron image of a model jet carrying a combination of normal modes
of the KH instability. The pseudo-synchrotron image of the jet reveals: (1)
that a slow decline in the model jet's surface brightness is still about five
times faster than the real jet; (2) that KH produced dual helically twisted
filaments can appear qualitatively similar to those on the real jet if any
helical perturbation to the jet is very small or nonexistent inside knot A; (3)
that the knots in the real jet cannot be associated with the twisted
filamentary features and are unlikely to be the result of a KH instability. The
existence of the knots in the real jet, the limb brightening of the real jet in
the radio, and the slower decline of the surface brightness of the real jet
indicate that additional processes --- such as unsteady jet flow and internal
particle acceleration --- are occurring within the jet. Disruption of the real
jet beyond knot A by KH instability is consistent with the jet and cocoon
conditions we find at knot A.


  We present an evolution equation which simultaneously sums the leading BFKL
and DGLAP logarithms for the integrated gluon distribution in terms of a single
variable, namely the emission angle of the gluon. This form of evolution is
appropriate for Monte Carlo simulations of events of high energy pp (and
p\bar{p}) interactions, particularly where small x events are sampled.


  We show that complete cotangent lifts of vector fields, their decomposition
into vertical representative and holonomic part provide a geometrical framework
underlying Eulerian equations of continuum mechanics. We discuss Euler
equations for ideal incompressible fluid and Vlasov equations of plasma
dynamics in connection with the lifts of divergence-free and Hamiltonian vector
fields, respectively. As a further application, we obtain kinetic equations of
particles moving with the flow of contact vector fields both from Lie-Poisson
reductions and with the techniques of present framework.


  Abstract Covariance matrix estimation is a challenging problem in cosmology.
Recent work has shown that model covariance matrices can be precise, and that
at relatively large scales they can also be accurate. We introduce a
data-driven method that can identify features from a mock covariance matrix
that are missing from a corresponding model, then incorporate them into the
model without significantly degrading the model's precision. We apply this
method to a BOSS-like survey and extend a model covariance to be valid at
scales relevant for measurements of Redshift Space Distortions (8-40 Mpc/h),
where the galaxy field is significantly non-Gaussian.


  We study a doubly-bottomed tetra-quark state $(bb\bar{u}\bar{d})$ with
quantum number $I(J^P)=0(1^+)$, denoted by $T_{bb}$, in lattice QCD with the
Non-Relativistic QCD (NRQCD) quark action for $b$ quarks. Employing
$(2+1)$-flavor gauge configurations at $a \approx 0.09$ {fm} on $32^3\times 64$
lattices, we have extracted the coupled channel potential between
$\bar{B}\bar{B}^*$ and $\bar{B}^* \bar{B}^*$ in the HAL QCD method, which
predicts an existence of a bound $T_{bb}$ below the $\bar{B}\bar{B}^*$
threshold. By extrapolating results at $m_\pi\approx 410,\, 570,\, 700$ {MeV}
to the physical pion mass $m_\pi\approx140$ {MeV}, we obtain a biding energy
with its statistical error as $E_{\rm binding}^{\rm (single)} = 155(17)$ MeV
and $E_{\rm binding}^{\rm (coupled)} = 83(10)$ MeV, where ``coupled" means that
effects due to virtual $\bar{B}^* \bar{B}^*$ states are included through the
coupled channel potential, while only a potential for a single
$\bar{B}\bar{B}^*$ channel is used in the analysis for ``single". A comparison
shows that the effect from virtual $\bar{B}^* \bar{B}^*$ states is quite
sizable to the binding energy of $T_{bb}$. We estimate systematic errors to be
$\pm 20$ MeV at most, which are mainly caused by the NRQCD approximation for
$b$ quarks.


  Despite tremendous progress in the research on self-assembled
nanotechnological building blocks such as macromolecules, nanowires, and
two-dimensional materials, synthetic self-assembly methods bridging nanoscopic
to macroscopic dimensions remain unscalable and inferior to biological
self-assembly. In contrast, planar semiconductor technology has had an immense
technological impact owing to its inherent scalability, yet it appears unable
to reach the atomic dimensions enabled by self-assembly. Here we use surface
forces including Casimir-van der Waals interactions to deterministically
self-assemble and self-align suspended silicon nanostructures with void
features well below the length scales possible with conventional lithography
and etching, despite using nothing more than conventional lithography and
etching. The method is remarkably robust and the threshold for self-assembly
depends monotonically on all governing parameters across thousands of measured
devices. We illustrate the potential of these concepts by fabricating
nanostructures, which are impossible to make with any other known method:
Waveguide-coupled high-Q silicon photonic cavities that confine telecom photons
to 2 nm air gaps with an aspect ratio of 100, corresponding to mode volumes
more than 100 times below the diffraction limit. Scanning transmission electron
microscopy measurements confirm the ability to build devices even with
subnanometer dimensions. Our work constitutes the first steps towards a new
generation of fabrication technology that combines the atomic dimensions
enabled by self-assembly with the scalability of planar semiconductors.


  Dispatching policies such as the join shortest queue (JSQ), join smallest
work (JSW) and their power of two variants are used in load balancing systems
where the instantaneous queue length or workload information at all queues or a
subset of them can be queried. In situations where the dispatcher has an
associated memory, one can minimize this query overhead by maintaining a list
of idle servers to which jobs can be dispatched. Recent alternative approaches
that do not require querying such information include the cancel on start and
cancel on complete based replication policies. The downside of such policies
however is that the servers must communicate the start or completion of each
service to the dispatcher and must allow cancellation of redundant copies. In
practice, the requirements of query messaging, memory, and replica cancellation
pose challenges in their implementation and their advantages are not clear. In
this work, we consider load balancing policies that do not query load
information, do not have a memory, and do not cancel replicas. Surprisingly, we
were able to identify operating regimes where such policies have better
performance when compared to some of the popular policies that utilize server
feedback information. Our policies allow the dispatcher to append a timer to
each job or its replica. A job or a replica is discarded if its timer expires
before it starts receiving service. We analyze several variants of this policy
which are novel, simple to implement, and also have remarkably good performance
in some operating regimes, despite no feedback from servers to the dispatcher.


  We develop an effective algorithm to compute the derivative of a Bianchi
modular form with respect to weight space as it varies in a $p$-adic family.
This method is entirely local at the modular form, and does not compute the
family anywhere outside an infinitesimal neighbourhood. We numerically verify
some conjectures surrouding smoothness of the eigenvariety (equivalently,
uniqueness of families) and the ``direction over weight space'' of the family.
The methods are also applied to study elliptic modular forms and their
$\mathcal{L}$-invariants.


  The one-loop electroweak radiative correction of the lowest order to lepton
current for deep inelastic scattering of longitudinally polarized leptons by
polarized nucleons is obtained in model independent way. The detailed numerical
analysis within kinematical requirements of future polarization collider
experiments is performed. The possibility to reduce radiative effects by
detection of hard photons is studied.


  In this work, a new constrained hybrid variational deblurring model is
developed by combining the non-convex first- and second-order total variation
regularizers. Moreover, a box constraint is imposed on the proposed model to
guarantee high deblurring performance. The developed constrained hybrid
variational model could achieve a good balance between preserving image details
and alleviating ringing artifacts. In what follows, we present the
corresponding numerical solution by employing an iteratively reweighted
algorithm based on alternating direction method of multipliers. The
experimental results demonstrate the superior performance of the proposed
method in terms of quantitative and qualitative image quality assessments.


  Both the intrinsic anisotropic optical materials and fullerene-assembled 2D
materials have attracted a lot of interests in fundamental science and
potential applications. The synthesis of a monolayer (ML) fullerene makes the
combination of these two features plausible. In this work, using
first-principles calculations, we systematically study the electronic
structure, optical properties of quasi-hexagonal phase (qHP) ML and
quasi-tetragonal phase (qTP) ML fullerenes. The calculations of qHP ML show
that it is a semi-conductor with small anisotropic optical absorption, which
agrees with the recent experimental measurements. However, the results for qTP
ML reveal that it is a semimetal with highly in-plane anisotropic absorption.
The dichroic ratio, namely the absorption ratio of $x$- and $y$-polarized light
$\alpha$$_x$$_x$/$\alpha$$_y$$_y$, is around 12 at photon energy of 0.29 eV.
This anisotropy is much more pronounced when the photon energy is between 0.7
and 1.4 eV, where $\alpha$$_x$$_x$ becomes nearly zero while $\alpha$$_y$$_y$
is more than two orders of magnitude larger. This indicates qTP ML as a
candidate for long-pursuit lossless metal and a potential material for
atomically thin polarizer. We hope this will stimulate further experimental
efforts in the study of qTP ML and other fullerene-assembled 2D materials.


  We consider the following $(p, q)$-Laplacian Kirchhoff type problem
\begin{align*} \begin{split} &-\left(a+b\int_{\mathbb{R}^{3}}|\nabla u|^{p}\,
dx \right)\Delta_{p}u - \left(c+d\int_{\mathbb{R}^{3}}|\nabla u|^{q}\, dx
\right ) \Delta_{q}u
  + V(x) (|u|^{p-2}u + |u|^{q-2}u)= K(x) f(u) \quad \mbox{ in } \mathbb{R}^{3},
\end{split} \end{align*} where $a, b, c, d>0$ are constants, $\frac{3}{2}< p<
q<3$, $V: \mathbb{R}^{3}\rightarrow \mathbb{R}$ and $K:
\mathbb{R}^{3}\rightarrow \mathbb{R}$ are positive continuous functions allowed
vanishing behavior at infinity, and $f$ is a continuous function with
quasicritical growth. Using a minimization argument and a quantitative
deformation lemma we establish the existence of nodal solutions.


  Policymakers often require information on programs' long-term impacts that is
not available when decisions are made. We demonstrate how data fusion methods
may be used address the problem of missing final outcomes and predict long-run
impacts of interventions before the requisite data are available. We implement
this method by concatenating data on an intervention with auxiliary long-term
data and then imputing missing long-term outcomes using short-term surrogate
outcomes while approximating uncertainty with replication methods. We use
simulations to examine the performance of the methodology and apply the method
in a case study. Specifically, we fuse data on the Oregon Health Insurance
Experiment with data from the National Longitudinal Mortality Study and
estimate that being eligible to apply for subsidized health insurance will lead
to a statistically significant improvement in long-term mortality.


  Evidence is provided from experiment, for the hypothesis that defect
organization (internal friction) is a means for operation of a phonon maser.


  We study the classical dynamics of black holes during a nonsingular
cosmological bounce. Taking a simple model of a nonsingular bouncing cosmology
driven by the combination of a ghost and ordinary scalar field, we use
nonlinear evolutions of the Einstein equations to follow rotating and
non-rotating black holes of different sizes through the bounce. The violation
of the null energy condition allows for a shrinking black hole event horizon
and we find that for sufficiently large black holes (relative to the minimum
Hubble radius) the black hole apparent horizon can disappear during the
contraction phase. Despite this, we show that most of the local cosmological
evolution remains largely unaffected by the presence of the black hole. We find
that, independently of the black hole's initial mass, the black hole's event
horizon persists throughout the bounce, and the late time dynamics consists of
an expanding universe with a black hole of mass comparable to its initial
value.


  Segregation induced by a thermal gradient of an impurity in a driven
low-density granular gas is studied. The system is enclosed between two
parallel walls from which we input thermal energy to the gas. We study here
steady states occurring when the inelastic cooling is exactly balanced by some
external energy input (stochastic force or viscous heating), resulting in a
uniform heat flux. A segregation criterion based on Navier-Stokes granular
hydrodynamics is written in terms of the tracer diffusion transport
coefficients, whose dependence on the parameters of the system (masses, sizes
and coefficients of restitution) is explicitly determined from a solution of
the inelastic Boltzmann equation. The theoretical predictions are validated by
means of Monte Carlo and molecular dynamics simulations, showing that
Navier-Stokes hydrodynamics produces accurate segregation criteria even under
strong shearing and/or inelasticity.


  The method of the effective action for the composite operators $\Phi^2(x)$
and $\Phi^4(x)$ is applied to the termodynamics of the scalar quantum field
with $\lambda\Phi^4$ interaction. An expansion of the finite temperature
effective potential in powers of $\hbar$ provides successive approximations to
the free energy with an effective mass and an effective coupling determined by
the gap equations. The numerical results are studied in the space-time of one
dimension, when the theory is equivalent to the quantum mechanics of an
anharmonic oscillator. The approximations to the free energy show quick
convergence to the exact result.


  We call a Lebesgue-Feynman measure (LFM) any generalized measure
(distribution in the sense of Sobolev and Schwartz) on a locally convex
topological vector space E which is translation invariant. In the present
paper, we investigate transformations of the LFM generated by transformations
of the domain and also discuss the connections of these transformations of the
LFM with so-called quantum anomalies, improving some recent results of teh
authors and co-workers. We revisit the contradiction between the points of view
on quantum anomalies presented in the books of Fujikawa and Suzuki on the one
hand, and of Cartier and DeWitt-Morette on the other.


  Semi-inclusive deep inelastic Scattering (SIDIS) has been a very successful
tool to investigate the partonic structure of the nucleon over the last decade.
Compared to inclusive DIS, information about the quantum numbers of the struck
quark can be inferred from the identity, distribution and polarization of the
final state hadrons. Up to now, virtually all knowledge about the quark-gluon
structure of the nucleon from SIDIS has been gained from distributions of
independently observed scalar hadrons. However, given the amount of data
current and future experiments at JLab, RHIC, KEK and the EIC will collect, new
paradigms have to be explored to leverage the statistical power of the data.
Similar to other felds in nuclear and particle physics, it is natural to move
towards the exploration of more complex correlations in the observed fi nal
state. This contribution will discuss recent results and future prospects of
using di-hadron correlations and polarized hyperon probes to study QCD in
SIDIS, pp and e+e- annihilation. Both of these probes exploit additional
degrees of freedom in the final state, given by the relative momentum of the
di-hadron pair and the hyperon polarization, respectively. This contribution
will focus on recent results and opportunities opened by these probes to study
nucleon structure, hadronization and QCD in novel ways. The focus will be on
planned SIDIS measurements at CLAS12 at JLab and e+e- at Belle II.


  A roadmap for an algebraic set $V$ defined by polynomials with coefficients
in some real field, say $\mathbb{R}$, is an algebraic curve contained in $V$
whose intersection with all connected components of $V\cap\mathbb{R}^{n}$ is
connected. These objects, introduced by Canny, can be used to answer
connectivity queries over $V\cap \mathbb{R}^{n}$ provided that they are
required to contain the finite set of query points $\mathcal{P}\subset V$; in
this case,we say that the roadmap is associated to $(V, \mathcal{P})$.
  In this paper, we make effective a connectivity result we previously proved,
to design a Monte Carlo algorithm which, on input (i) a finite sequence of
polynomials defining $V$ (and satisfying some regularity assumptions) and (ii)
an algebraic representation of finitely many query points $\mathcal{P}$ in $V$,
computes a roadmap for $(V, \mathcal{P})$. This algorithm generalizes the
nearly optimal one introduced by the last two authors by dropping a boundedness
assumption on the real trace of $V$.
  The output size and running times of our algorithm are both polynomial in
$(nD)^{n\log d}$, where $D$ is the maximal degree of the input equations and
$d$ is the dimension of $V$. As far as we know, the best previously known
algorithm dealing with such sets has an output size and running time polynomial
in $(nD)^{n\log^2 n}$.


  We calculate magnetization in magnetically doped semiconductors assuming a
local exchange model of carrier-mediated ferromagnetic mechanism and using a
number of complementary theoretical approaches. In general, we find that the
results of our mean-field calculations, particularly the dynamical mean field
theory results, give excellent qualitative agreement with the experimentally
observed magnetization in systems with itinerant charge carriers, such as
Ga_{1-x}Mn_xAs with 0.03 < x < 0.07, whereas our percolation-theory-based
calculations agree well with the existing data in strongly insulating
materials, such as Ge_{1-x}Mn_x. We comment on the issue of non-mean-field like
magnetization curves and on the observed incomplete saturation magnetization
values in diluted magnetic semiconductors from our theoretical perspective. In
agreement with experimental observations, we find the carrier density to be the
crucial parameter determining the magnetization behavior. Our calculated
dependence of magnetization on external magnetic field is also in excellent
agreement with the existing experimental data.


  A matter self-interacting model with N=1-supersymmetry in 3D is discussed in
connection with the appearance of a central charge in the algebra of the
supersymmetry generators. The result is extended to include gauge fields with a
Chern-Simons term. The main result is that, for a simple supersymmetry, only
the matter sector contributes to the central charge in contrast to what occurs
in the N=2 case.


  The fastest possible collective response of a quantum many-body system is
related to its excitations at the highest possible energy. In condensed-matter
systems, the corresponding timescale is typically set by the Fermi energy.
Taking advantage of fast and precise control of interactions between ultracold
atoms, we report on the observation of ultrafast dynamics of impurities coupled
to an atomic Fermi sea. Our interferometric measurements track the
non-perturbative quantum evolution of a fermionic many-body system, revealing
in real time the formation dynamics of quasiparticles and the quantum
interference between attractive and repulsive states throughout the full depth
of the Fermi sea. Ultrafast time-domain methods to manipulate and investigate
strongly interacting quantum gases open up new windows on the dynamics of
quantum matter under extreme non-equilibrium conditions.


  Stationary perfect-fluid configurations of Einstein's theory of gravity are
studied. It is assumed that the 4-velocity of the fluid is parallel to the
stationary Killing field, and also that the norm and the twist potential of the
stationary Killing field are functionally independent. It has been pointed out
earlier by one of us (I.R.) that for these perfect-fluid geometries some of the
basic field equations are invariant under an $SL(2,R)$ transformation. Here it
is shown that this transformation can be applied to generate possibly new
perfect-fluid solutions from existing known ones only for the case of
barotropic equation of state $\rho+3p=0$. In order to study the effect of this
transformation, its application to known perfect-fluid solutions is presented.
In this way, different previously known solutions could be written in a singe
compact form. A new derivation of all Petrov type D stationary axisymmetric
rigidly rotating perfect-fluid solutions with an equation of state
$\rho+3p=constant$ is given in an appendix.


  Studies of solar wind turbulence traditionally employ high-resolution
magnetic field data, but high-resolution measurements of ion and electron
moments have been possible only recently. We report the first turbulence
studies of ion and electron velocity moments accumulated in pristine solar wind
by the Fast Particle Investigation instrument onboard the Magnetospheric
Multiscale (MMS) Mission. Use of these data is made possible by a novel
implementation of a frequency domain Hampel filter, described herein. After
presenting procedures for processing of the data, we discuss statistical
properties of solar wind turbulence extending into the kinetic range. Magnetic
field fluctuations dominate electron and ion velocity fluctuation spectra
throughout the energy-containing and inertial ranges. However, a
multi-spacecraft analysis indicates that at scales shorter than the
ion-inertial length, electron velocity fluctuations become larger than ion
velocity and magnetic field fluctuations. The kurtosis of ion velocity peaks
around few ion-inertial lengths and returns to near gaussian value at sub-ion
scales.


  In the paper it is demonstrated that the particular form of CHSH,
S=E{A(1)[B(1)-B(2)]-A(2)[B(1)+B(2)]} with, S maximally 2 and minimally -2,for A
and B functions in {-1,1}, is not generally valid. The nonzero probability that
local hidden extra parameters violate the CHSH, is not eliminated with basic
principles derived from the CHSH.


  Several observational and theoretical indications suggest that the initial
mass function (IMF) becomes increasingly top-heavy (i.e., overabundant in
high-mass stars with mass $m > 1M_{\odot}$) with decreasing metallicity and
increasing gas density of the forming object. This affects the evolution of
globular clusters (GCs) owing to the different mass-loss rates and the number
of black holes formed. Previous numerical modeling of GCs usually assumed an
invariant canonical IMF. Using the state-of-the-art $NBODY6$ code, we perform a
comprehensive series of direct $N$-body simulations to study the evolution of
star clusters, starting with a top-heavy IMF and undergoing early gas
expulsion. Utilizing the embedded cluster mass-radius relation of Marks &
Kroupa (2012) for initializing the models, and by varying the degree of
top-heaviness, we calculate the minimum cluster mass needed for the cluster to
survive longer than 12 Gyr. We document how the evolution of different
characteristics of star clusters such as the total mass, the final size, the
density, the mass-to-light ratio, the population of stellar remnants, and the
survival of GCs is influenced by the degree of top-heaviness. We find that the
lifetimes of clusters with different IMFs moving on the same orbit are
proportional to the relaxation time to a power of $x$ that is in the range of
0.8 to 1. The observed correlation between concentration and the mass function
slope in Galactic GCs can be accounted for excellently in models starting with
a top-heavy IMF and undergoing an early phase of rapid gas expulsion.


  We numerically study the crossing symmetry constraints in 4D CFTs, using
previously introduced algorithms based on semidefinite programming. We study
bounds on OPE coefficients of tensor operators as a function of their scaling
dimension and extend previous studies of bounds on OPE coefficients of
conserved vector currents to the product groups SO(N)xSO(M). We also analyze
the bounds on the OPE coefficients of the conserved vector currents associated
with the groups SO(N), SU(N) and SO(N)xSO(M) under the assumption that in the
singlet channel no scalar operator has dimension less than four, namely that
the CFT has no relevant deformations. This is motivated by applications in the
context of composite Higgs models, where the strongly coupled sector is assumed
to be a spontaneously broken CFT with a global symmetry.


  We consider the three-loop corrections to the static potential which are
induced by a closed fermion loop. For the reduction of the occurring integrals
a combination of the Gr\"obner and Laporta algorithm has been used and the
evaluation of the master integrals has been performed with the help of the
Mellin-Barnes technique. The fermionic three-loop corrections amount to 2% of
the tree-level result for top quarks, 8% for bottom quarks and 27% for the
charm quark system.


  We investigate the formation of jellyfish galaxies using
radiation-hydrodynamic simulations of gas-rich dwarf galaxies with a
multi-phase interstellar medium (ISM). We find that the ram-pressure-stripped
(RPS) ISM is the dominant source of molecular clumps in the near wake within 10
kpc from the galactic plane, while in-situ formation is the major channel for
dense gas in the distant tail of the gas-rich galaxy. Only 20% of the molecular
clumps in the near wake originate from the intracluster medium (ICM); however,
the fraction reaches 50% in the clumps located at $80\,{\rm kpc}$ from the
galactic center since the cooling time of the RPS gas tends to be short due to
the ISM--ICM mixing ($\lesssim$ 10 Myr). The tail region exhibits a star
formation rate of $0.001-0.01\,{\rm M_{\odot}\,yr^{-1}}$, and most of the tail
stars are born in the stripped wake within 10 kpc from the galactic plane.
These stars induce bright H$\alpha$ blobs in the tail, while H$\alpha$ tails
fainter than $6\times10^{38}\,{\rm erg\,s^{-1}\,kpc^{-2}}$ are mostly formed
via collisional radiation and heating due to mixing. We also find that the
stripped tails have intermediate X-ray to H$\alpha$ surface brightness ratios
(1.5$\lesssim F_{\rm X}/F_{\rm H\alpha}\lesssim$20), compared to the ISM
($\lesssim$1.5) or pure ICM ($\gg$20). Our results suggest that jellyfish
features emerge when the ISM from gas-rich galaxies is stripped by strong ram
pressure, mixes with the ICM, and enhances the cooling in the tail.


  Planar black holes in AdS, which are holographically dual to compressible
relativistic fluids, have a long-lived phonon mode that captures the physics of
attenuated sound propagation and transports energy in the plasma. We describe
the open effective field theory of this fluctuating phonon degree of freedom.
The dynamics of the phonon is encoded in a single scalar field whose
gravitational coupling has non-trivial spatial momentum dependence. This
description fits neatly into the paradigm of classifying gravitational modes by
their Markovianity index, depending on whether they are long-lived. The sound
scalar is a non-Markovian field with index (3-d) for a d-dimensional fluid. We
reproduce (and extend) the dispersion relation of the holographic sound mode to
quartic order in derivatives, constructing in the process the effective field
theory governing its attenuated dynamics and associated stochastic
fluctuations. We also remark on the presence of additional spatially
homogeneous zero modes in the gravitational problem, which remain disconnected
from the phonon Goldstone mode.


  Although the driving mechanism acting in beta Cephei pulsators is well known
(e.g. Dziembowski & Pamyatnykh 1993), problems concerning identification of
amplitude limitation mechanism and non-uniform filling of the theoretical
instability strip, remain to be solved. In the present analysis, these problems
are addressed by non-linear modelling of radial pulsations of these stars. In
this approach radial modes are treated as representative for all acoustic
oscillations.
  Several models of different masses and metallicities were converged to limit
cycles through Stellingwerf (1974) relaxation technique. Resulting peak-to-peak
amplitudes are of order of DeltaV=0.3 mag. Such amplitudes are significantly
larger than those observed in beta Cephei pulsators. Assuming that all acoustic
modes are similar, we show that collective saturation of the driving mechanism
by several acoustic modes can easily lower predicted saturation amplitudes to
the observed level. Our calculations predict significant decrease of saturation
amplitudes as we go to high mass/high luminosity models. However, this effect
is not strong enough to explain scarcity of high mass beta Cephei variables.
  We also discuss robust double-mode behaviour, encountered in our radiative
models. On a single evolutionary track we identify two double-mode domains with
two different mechanisms resposible for double-mode behaviour. The non-resonant
double-mode domain separates first overtone and fundamental mode pulsation
domains. The resonant double-mode domain appears in the middle of the first
overtone pulsation domain. Its origin can be traced to the
2omega_1=omega_0+omega_2 parametric resonance, which destabilizes the first
overtone limit cycle.


  We present the first detailed analysis of three extragalactic fields (IRAC
Dark Field, ELAIS-N1, ADF-S) observed by the infrared satellite, AKARI, using
an optimised data analysis toolkit specifically for the processing of
extragalactic point sources. The InfraRed Camera (IRC) on AKARI complements the
Spitzer space telescope via its comprehensive coverage between 8-24 microns
filling the gap between the Spitzer IRAC and MIPS instruments. Source counts in
the AKARI bands at 3.2, 4.1, 7, 11, 15 and 18 microns are presented. At
near-infrared wavelengths, our source counts are consistent with counts made in
other AKARI fields and in general with Spitzer/IRAC (except at 3.2 microns
where our counts lie above). In the mid-infrared (11 - 18 microns) we find our
counts are consistent with both previous surveys by AKARI and the Spitzer
peak-up imaging survey with the InfraRed Spectrograph (IRS). Using our counts
to constrain contemporary evolutionary models we find that although the models
and counts are in agreement at mid-infrared wavelengths there are
inconsistencies at wavelengths shortward of 7 microns, suggesting either a
problem with stellar subtraction or indicating the need for refinement of the
stellar population models. We have also investigated the AKARI/IRC filters, and
find an AGN selection criteria out to $z<2$ on the basis of AKARI 4.1, 11, 15
and 18 microns colours.


  In order to exploit the intriguing optical properties of graphene it is
essential to gain a better understanding of the light-matter interaction in the
material on ultrashort timescales. Exciting the Dirac fermions with intense
ultrafast laser pulses triggers a series of processes involving interactions
between electrons, phonons and impurities. Here we study these interactions in
epitaxial graphene supported on silicon carbide (semiconducting) and iridium
(metallic) substrates using ultrafast time- and angle-resolved photoemission
spectroscopy (TR-ARPES) based on high harmonic generation. For the
semiconducting substrate we reveal a complex hot carrier dynamics that
manifests itself in an elevated electronic temperature and an increase in
linewidth of the $\pi$ band. By analyzing these effects we are able to
disentangle electron relaxation channels in graphene. On the metal substrate
this hot carrier dynamics is found to be severely perturbed by the presence of
the metal, and we find that the electronic system is much harder to heat up
than on the semiconductor due to screening of the laser field by the metal.


  Solving the road congestion problem is one of the most pressing issues in
moderncities since it causes time wasting, pollution, higher industrial costs
and huge roadmaintenance costs. Advances in ITS technologies and the advent of
autonomousvehicles are changing mobility dramatically. They enable the
implementation of acoordination mechanism, called coordinated traffic
assignment, among the sat-navdevices aiming at assigning paths to drivers to
eliminate congestion and to re-duce the total travel time in traffic networks.
Among possible congestion avoidance methods, coordinated traffic assignment is
a valuable choice since it does not involvehuge investments to expand the road
network. Traffic assignments are traditionally devoted to two main perspectives
on which the well-known Wardropian principlesare inspired: the user equilibrium
and the system optimum. User equilibrium is a user-driven traffic assignment in
which each user chooses the most convenientpath selfishly. It guarantees that
fairness among users is respected since, whenthe equilibrium is reached, all
users sharing the same origin and destination willexperience the same travel
time. The main drawback in a user equilibrium is thatthe system total travel
time is not minimized and, hence, the so-called Price ofAnarchy is paid. On the
other hand, the system optimum is an efficient system-wide traffic assignment
in which drivers are routed on the network in such a waythe total travel time
is minimized but users might experience travel times that arehigher than the
other users travelling from the same origin to the same destina-tion affecting
the compliance. Thus, drawbacks in implementing one of the two assignments can
be overcome by hybridizing the two approaches aiming at bridging users'
fairness to system-wide efficiency. The survey reviews the state-of-the-art of
these trade-off approaches


  A simple and testable necessary condition for the gauge independence of the
Pinch Technique self-energies at two loops is discussed. It is then shown that,
in the case of the $Z$ and $W$ self-energies, the condition is indeed satisfied
by the Papavassiliou-Pilaftsis formulation.


  The LIGO-Virgo Collaboration has so far detected around 90 black holes, some
of which have masses larger than what were expected from the collapse of stars.
The mass distribution of LIGO-Virgo black holes appears to have a peak at
$\sim30M_{\odot}$ and two tails on the ends. By assuming that they all have a
primordial origin, we analyze the GWTC-1 (O1\&O2) and GWTC-2 (O3a) datasets by
performing maximum likelihood estimation on a broken power law mass function
$f(m)$, with the result $f\propto m^{1.2}$ for $m<35M_{\odot}$ and $f\propto
m^{-4}$ for $m>35M_{\odot}$. This appears to behave better than the popular
log-normal mass function. Surprisingly, such a simple and unique distribution
can be realized in our previously proposed mechanism of PBH formation, where
the black holes are formed by vacuum bubbles that nucleate during inflation via
quantum tunneling. Moreover, this mass distribution can also provide an
explanation to supermassive black holes formed at high redshifts.


  We give a complete classification of irreducible symmetric spaces for which
there exist proper SL(2,R)-actions as isometries, using the criterion for
proper actions by T. Kobayashi [Math. Ann. '89] and combinatorial techniques of
nilpotent orbits. In particular, we classify irreducible symmetric spaces that
admit surface groups as discontinuous groups, combining this with Benoist's
theorem [Ann. Math. '96].


  We consider continuous state branching processes that are perturbed by a
Brownian motion. These processes are constructed as the unique strong solution
of a stochastic differential equation. The long-term extinction and explosion
behaviours are studied. In the stable case, the extinction and explosion
probabilities are given explicitly. We find three regimes for the asymptotic
behaviour of the explosion probability and, as in the case of branching
processes in random environment, we find five regimes for the asymptotic
behaviour of the extinction probability. In the supercritical regime, we study
the process conditioned on eventual extinction where three regimes for the
asymptotic behaviour of the extinction probability appear. Finally, the process
conditioned on non-extinction and the process with immigration are given.


  The determination of the mechanical properties of soils containing particles
larger than the allowable size of standard laboratory equipments is complex. It
is indeed necessary to remove the coarsest fraction to carry out the tests.
This scalping poses a problem of reliability of the results at the scale of the
structure. Parallel gradation is the method commonly used for estimating the
shear strength of heterogeneous granular soils from tests on their finer
fraction. However, the effect of high fines content on the estimation of shear
strength by this method is not well understood. The results of this study
showed that the parallel gradation method could predict the friction angle of
the initial soil with high fines content when the modelled soil had a similar
skeleton as the initial soil. However, the cohesion of the initial soil was
overestimated.


  We present a greedy algorithm for solving binary classification problems in
situations where the dataset is either too small or not fully representative of
the problem being solved, and obtaining more data is not possible. This
algorithm is of particular interest when training small models that have
trouble generalizing. It relies on a trained model with loose accuracy
constraints, an iterative hyperparameter pruning procedure, and a function used
to generate new data. Analysis on correctness and runtime complexity under
ideal conditions and an extension to deep neural networks is provided. In the
former case we obtain an asymptotic bound of
$O\left(|\Theta^2|\left(\log{|\Theta|} + |\theta^2| + T_f\left(|
D|\right)\right) + \bar{S}|\Theta||{E}|\right)$, where $|{\Theta}|$ is the
cardinality of the set of hyperparameters $\theta$ to be searched; $|{E}|$ and
$|{D}|$ are the sizes of the evaluation and training datasets, respectively;
$\bar{S}$ and $\bar{f}$ are the inference times for the trained model and the
candidate model; and $T_f({|{D}|})$ is a polynomial on $|{D}|$ and $\bar{f}$.
Under these conditions, this algorithm returns a solution that is $1 \leq r
\leq 2(1 - {2^{-|{\Theta}|}})$ times better than simply enumerating and
training with any $\theta \in \Theta$. As part of our analysis of the
generating function we also prove that, under certain assumptions, if an open
cover of $D$ has the same homology as the manifold where the support of the
underlying probability distribution lies, then $D$ is learnable, and viceversa.


  The development of high-density magnetic recording media is limited by the
superparamagnetism in very small ferromagnetic crystals. Hard magnetic
materials with strong perpendicular anisotropy offer stability and high
recording density. To overcome the difficulty of writing media with a large
coercivity, heat assisted magnetic recording (HAMR) has been developed, rapidly
heating the media to the Curie temperature Tc before writing, followed by rapid
cooling. Requirements are a suitable Tc, coupled with anisotropic thermal
conductivity and hard magnetic properties. Here we introduce Rh2CoSb as a new
hard magnet with potential for thin film magnetic recording. A
magnetocrystalline anisotropy of 3.6 MJm-3 is combined with a saturation
magnetization of {\mu}0Ms = 0.52 T at 2 K (2.2 MJm-3 and 0.44 T at
room-temperature). The magnetic hardness parameter of 3.7 at room temperature
is the highest observed for any rare-earth free hard magnet. The anisotropy is
related to an unquenched orbital moment of 0.42 {\mu}B on Co, which is
hybridized with neighbouring Rh atoms with a large spin-orbit interaction.
Moreover, the pronounced temperature-dependence of the anisotropy that follows
from its Tc of 450 K, together with a high thermal conductivity of 20 Wm-1K-1,
makes Rh2CoSb a candidate for development for heat assisted writing with a
recording density in excess of 10 Tb/in2.


  We propose a model of suppression of $\pi^0$'s based on two different
effects: at low $p_T$ we take into account the shadowing corrections, while at
large $p_T$ the suppression is produced due to the interaction of the large
$p_T$ pion with the dense medium created in the collision. The main features of
the data on $AuAu$ and $dAu$ collisions are reproduced both at mid and at
forward rapidities.


  The strength of the nonlinearity is measured in decaying two-dimensional
turbulence, by comparing its value to that found in a Gaussian field. It is
shown how the nonlinearity drops following a two-step process. First a fast
relaxation is observed on a timescale comparable to the time of for-mation of
vortical structures, then at long times the nonlinearity relaxes further during
the phase when the eddies merge to form the final dynamic state of decay. Both
processes seem roughly independent of the value of the Reynolds number.


  The Widom line identifies the locus in the phase diagram where a
supercritical gas crosses over from gas-like to a more liquid-like behavior. A
similar transition exists in correlated electron liquids, where the interplay
of Coulomb repulsion, bandwidth and temperature triggers between the Mott
insulating state and an incoherent conduction regime. Here we explore the
electrodynamic response of three organic quantum spin liquids with different
degrees of effective correlation, where the absence of magnetic order enables
unique insight into the nature of the genuine Mott state down to the most
relevant low-temperature region. Combining optical spectroscopy with
pressure-dependent dc transport and theoretical calculations, we succeeded to
construct a phase diagram valid for all Mott insulators on a quantitative
scale. In the vicinity of the low-temperature phase boundary, we discover
metallic fluctuations within the Mott gap, exhibiting enhanced absorption upon
cooling that is not present in antiferromagnetic Mott insulators. Our findings
reveal the phase coexistence region and Pomeranchuk-like anomaly of the Mott
transition, previously predicted but never observed.


  We demonstrate that the `microscopic' field theory representation, directly
derived from the corresponding master equation, fails to adequately capture the
continuous nonequilibrium phase transition of the Pair Contact Process with
Diffusion (PCPD). The ensuing renormalization group (RG) flow equations do not
allow for a stable fixed point in the parameter region that is accessible by
the physical initial conditions. There exists a stable RG fixed point outside
this regime, but the resulting scaling exponents, in conjunction with the
predicted particle anticorrelations at the critical point, would be in
contradiction with the positivity of the equal-time mean-square particle number
fluctuations. We conclude that a more coarse-grained effective field theory
approach is required to elucidate the critical properties of the PCPD.


  We consider entanglement entropy in the context of gauge/gravity duality for
conformal field theories in even dimensions. The holographic prescription due
to Ryu and Takayanagi (RT) leads to an equation describing how the entangling
surface extends into the bulk geometry. We show that setting to zero the
time-time component of the Brown-York stress tensor evaluated on the
co-dimension one entangling surface, leads to the same equation. By considering
a spherical entangling surface as an example, we observe that Euclidean action
methods in AdS/CFT will lead to the RT area functional arising as a counterterm
needed to regularize the stress tensor. We present arguments leading to a
justification for the minimal area prescription.


  We observe that emerging artificial intelligence, high-performance computing,
and storage workloads pose new challenges for large-scale datacenter
networking. RDMA over Converged Ethernet (RoCE) was an attempt to adopt modern
Remote Direct Memory Access (RDMA) features into existing Ethernet
installations. Now, a decade later, we revisit RoCE's design points and
conclude that several of its shortcomings must be addressed to fulfill the
demands of hyperscale datacenters. We predict that both the datacenter and
high-performance computing markets will converge and adopt modernized
Ethernet-based high-performance networking solutions that will replace TCP and
RoCE within a decade.


  This paper reviews the first challenge on high-dynamic range (HDR) imaging
that was part of the New Trends in Image Restoration and Enhancement (NTIRE)
workshop, held in conjunction with CVPR 2021. This manuscript focuses on the
newly introduced dataset, the proposed methods and their results. The challenge
aims at estimating a HDR image from one or multiple respective low-dynamic
range (LDR) observations, which might suffer from under- or over-exposed
regions and different sources of noise. The challenge is composed by two
tracks: In Track 1 only a single LDR image is provided as input, whereas in
Track 2 three differently-exposed LDR images with inter-frame motion are
available. In both tracks, the ultimate goal is to achieve the best objective
HDR reconstruction in terms of PSNR with respect to a ground-truth image,
evaluated both directly and with a canonical tonemapping operation.


  The leptons are viewed as composite objects, exhibiting anomalous magnetic
moments and anomalous flavor-changing transition moments. The decay \mu \to e
\gamma is expected to occur with a branching ratio of the same order as the
present experimental limit. The first order QED radiative correction is
considered.


  The conventional approach to nanophotonic metasurface design and optimization
for a targeted electromagnetic response involves exploring large geometry and
material spaces, which is computationally costly, time consuming and a highly
iterative process based on trial and error. Moreover, the non-uniqueness of
structural designs and high non-linearity between electromagnetic response and
design makes this problem challenging. To model this non-intuitive relationship
between electromagnetic response and metasurface structural design as a
probability distribution in the design space, we introduce a cyclical deep
learning (DL) based framework for inverse design of nanophotonic metasurfaces.
The proposed framework performs inverse design and optimization mechanism for
the generation of meta-atoms and meta-molecules as metasurface units based on
DL models and genetic algorithm. The framework includes consecutive DL models
that emulate both numerical electromagnetic simulation and iterative processes
of optimization, and generate optimized structural designs while simultaneously
performing forward and inverse design tasks. A selection and evaluation of
generated structural designs is performed by the genetic algorithm to construct
a desired optical response and design space that mimics real world responses.
Importantly, our cyclical generation framework also explores the space of new
metasurface topologies. As an example application of utility of our proposed
architecture, we demonstrate the inverse design of gap-plasmon based half-wave
plate metasurface for user-defined optical response. Our proposed technique can
be easily generalized for designing nanophtonic metasurfaces for a wide range
of targeted optical response.


  We propose a novel approach to address the problem of Simultaneous Detection
and Segmentation introduced in [Hariharan et al 2014]. Using the hierarchical
structures first presented in [Arbel\'aez et al 2011] we use an efficient and
accurate procedure that exploits the feature information of the hierarchy using
Locality Sensitive Hashing. We build on recent work that utilizes convolutional
neural networks to detect bounding boxes in an image [Ren et al 2015] and then
use the top similar hierarchical region that best fits each bounding box after
hashing, we call this approach C&Z Segmentation. We then refine our final
segmentation results by automatic hierarchical pruning. C&Z Segmentation
introduces a train-free alternative to Hypercolumns [Hariharan et al 2015]. We
conduct extensive experiments on PASCAL VOC 2012 segmentation dataset, showing
that C&Z gives competitive state-of-the-art segmentations of objects.


  We show that in the grounded conducting sphere image problem, all the
necessary information about the image charge can be found from a mirror
equation and a magnification formula. Then, we propose a method to solve the
image problem for an extended charge distribution near a grounded conducting
sphere.


  This paper is a continuation of the work done in \cite{sal-yas} and
\cite{may-pat-rob}. We deal with the Vietoris hyperspace of all nontrivial
convergent sequences $\mathcal{S}_c(X)$ of a space $X$. We answer some
questions in \cite{sal-yas} and generalize several results in
\cite{may-pat-rob}. We prove that: The connectedness of $X$ implies the
connectedness of $\mathcal{S}_c(X)$; the local connectedness of $X$ is
equivalent to the local connectedness of $\mathcal{S}_c(X)$; and the path-wise
connectedness of $\mathcal{S}_c(X)$ implies the path-wise connectedness of $X$.
We also show that the space of nontrivial convergent sequences on the Warsaw
circle has $\mathfrak{c}$-many path-wise connected components, and provide a
dendroid with the same property.


  An arc-colored tournament is said to be $k$-spanning for an integer $k\geq 1$
if the union of its arc-color classes of maximal valency at most $k$ is the arc
set of a strongly connected digraph. It is proved that isomorphism testing of
$k$-spanning tournaments is fixed-parameter tractable.


  In this work we present a new approach for the combination of electroweak
(EW) corrections at high energies, the so-called EW Sudakov logarithms (EWSL),
and next-to-leading-order QCD predictions matched to parton-shower simulations
(NLO+PS). Our approach is based on a reweighting procedure of NLO+PS events. In
particular, both events with and without an extra hard emission from matrix
elements are consistently reweighted via the inclusion of the corresponding
EWSL contribution. We describe the technical details and the implementation in
the MadGraph5_aMC@NLO framework. Via a completely automated procedure, events
at this new level of accuracy can be obtained for a vast class of
hadroproduction processes. As a byproduct we provide results for
phenomenologically relevant physical distributions from top-quark pair and
Higgs boson associated production ($t\overline{t}H$) and from the associated
production of three $Z$ gauge bosons ($ZZZ$).


  Renewable energy has attracted significant attention over the last decade,
conceivably due to its environmental benefits and the recent drops in the
development and deployment cost of the technology. The increase in renewable
generation, however, has resulted in new challenges in supply-load balancing,
owing to its intermittent, non-predictable and volatile generation features.
Several methods have been introduced to cope with negative impacts of the
renewable generation deployment. In this paper, a novel method, i.e., the
application of microgrids in capturing the variabilities of distributed
renewable generation in distribution networks is proposed and investigated.
Utilizing available flexibility of microgrids represents a local and viable
solution which leads to lower investments from electric utilities for
increasing their flexibility and providing more reserved power. It is
investigated that how the system flexibility requirements can be integrated
into the microgrid optimal scheduling model to enable microgrids in supporting
the grid operators by offering flexibility services. Using the proposed
flexibility constraints, intra-hour and inter-hour variabilities at the
distribution feeder will be efficiently captured. Numerical simulations on a
test distribution feeder, with one microgrid and several renewable-equipped
consumers, show the effectiveness of the proposed model.


  Exploring the complementary information of multi-view data to improve
clustering effects is a crucial issue in multi-view clustering. In this paper,
we propose a novel model based on information theory termed Informative
Multi-View Clustering (IMVC), which extracts the common and view-specific
information hidden in multi-view data and constructs a clustering-oriented
comprehensive representation. More specifically, we concatenate multiple
features into a unified feature representation, then pass it through a encoder
to retrieve the common representation across views. Simultaneously, the
features of each view are sent to a encoder to produce a compact view-specific
representation, respectively. Thus, we constrain the mutual information between
the common representation and view-specific representations to be minimal for
obtaining multi-level information. Further, the common representation and
view-specific representation are spliced to model the refined representation of
each view, which is fed into a decoder to reconstruct the initial data with
maximizing their mutual information. In order to form a comprehensive
representation, the common representation and all view-specific representations
are concatenated. Furthermore, to accommodate the comprehensive representation
better for the clustering task, we maximize the mutual information between an
instance and its k-nearest neighbors to enhance the intra-cluster aggregation,
thus inducing well separation of different clusters at the overall aspect.
Finally, we conduct extensive experiments on six benchmark datasets, and the
experimental results indicate that the proposed IMVC outperforms other methods.


  Let $X=\{X_j , j\ge 1\}$ be a sequence of independent, square integrable
variables taking values in a common lattice $\mathcal L(v_{ 0},D )= \{v_{
k}=v_{ 0}+D k , k\in \Z\}$.
  Let $S_n=X_1+\ldots +X_n$, $a_n= {\mathbb E\,} S_n$, and $\s_n^2={\rm
Var}(S_n)\to \infty$ with $n$. Assume that for each $j$, $\t_{X_j} =\sum_{k\in
\Z}{\mathbb P}\{X_j=v_k\}\wedge{\mathbb P}\{X_j=v_{k+1}\}>0$. Using the
Bernoulli part, we prove a general sharp correlation inequality extending the
one we obtained in the i.i.d.\,case in \cite{W3}: Let $0<\t_j\le \t_{X_j}$ and
assume that $ \nu_n =\sum_{j=1}^n \t_j \, \uparrow \infty$, $n\to \infty$.
  Let $\k_j\in \mathcal L(jv_0,D)$, $j=1,2,\ldots$ be a sequence of integers
such that
  \begin{equation*} {\rm(1)}\qquad\frac{\kappa_j-a_j}{\s_j}=\mathcal O(1 ),
\qq\quad {\rm(2)}\qquad \s_j \,{\mathbb P}\{S_j=\kappa_j\} ={\mathcal O}(1).
  \end{equation*}
  Then there exists a constant $C $
  such that for all $1\le m<n$, \begin{align*}
  \s_n&\s_m \, \Big|{\mathbb P}\{S_n=\k_n, S_m=\k_m\}- {\mathbb P}\{S_n=\k_n
\}{\mathbb P}\{ S_m=\k_m\} \Big|
  \cr & \,\le \, \frac{C}{D^2}\, \max \Big(\frac{\s_n
}{\sqrt{\nu_n}},\frac{\s_m }{\sqrt {\nu_m}} \Big)^3 \,\bigg\{ \nu_n^{1/2}
\prod_{j=m+1}^n\vartheta_j + {\nu_n^{1/2} \over
  (\nu_n-\nu_m) ^{3/2}}+{ 1\over \sqrt{{\nu_n\over \nu_m}}-1} \bigg\}.
  \end{align*} We derive a sharp almost sure local limit theorem


  In this paper we establish new Calabi-Bernstein results for maximal surfaces
immersed into a Lorentzian product space of the form $M^2\times\mathbb{R}_1$,
where $M^2$ is a connected Riemannian surface and $M^2\times\mathbb{R}_1$ is
endowed with the Lorentzian metric $<,>=<,>_{M}-dt^2$. In particular, when $M$
is a Riemannian surface with non-negative Gaussian curvature $K_M$, we prove
that any complete maximal surface in $M^2\times\mathbb{R}_1$ must be totally
geodesic. Besides, if $M$ is non-flat we conclude that it must be a slice
$M\times\{t_0\}$, $t_0\in\mathbb{R}$ (here by "complete" it is meant, as usual,
that the induced Riemannian metric on the maximal surface from the ambient
Lorentzian metric is complete). We prove that the same happens if the maximal
surface is complete with respect to the metric induced from the Riemannian
product $M^2\times\mathbb{R}$. This allows us to give also a non-parametric
version of the Calabi-Bernstein theorem for entire maximal graphs in
$M^2\times\mathbb{R}_1$, under the same assumptions on $K_M$. Moreover, we also
construct counterexamples which show that our Calabi-Bernstein results are no
longer true without the hypothesis $K_M\geq 0$. These examples are constructed
via a duality result between minimal and maximal graphs.


  Using a 13.7 fb-1 data sample collected with the CLEO II and II.V detectors,
we report new branching fraction measurements for two Cabibbo-suppressed decay
modes of the D+ meson: BR(D+ -> pi+ pi0) = (1.31 +/- 0.17 +/- 0.09 +/- 0.09) x
10^(-3)and BR(D+ -> K+ K0bar) = (5.24 +/- 0.43 +/- 0.20 +/- 0.34) x 10^(-3)
which are significant improvements over past measurements. The errors reflect
statistical and systematical uncertainties as well as the uncertainty in the
absolute D+ branching fraction scale. We also set the first 90% confidence
level upper limit on the branching fraction of the doubly Cabibbo-suppressed
decay mode BR(D+ -> K+ pi0) < 4.2 x 10^(-4).


  In electrochemical systems, an understanding of the underlying transport
processes is required to aid in their better design. This includes knowledge of
possible near-electrode convective mixing that can enhance measured currents.
Here, for a binary acidic electrolyte in contact with a platinum electrode, we
provide evidence of electroconvective instability during electrocatalytic
proton reduction. The current-voltage characteristics indicate that
electroconvection, visualized with a fluorescent dye, drives current densities
larger than the diffusion transport limit. The onset and transition times of
the instability do not follow the expected inverse-square dependence on the
current density, but, above a bulk-reaction-limited current density are delayed
by the water dissociation reaction. The dominant size of the electroconvective
patterns is also measured and found to vary as the diffusion length scale,
confirming previous predictions on the size of electroconvective vortices.


  In dialogue state tracking, dialogue history is a crucial material, and its
utilization varies between different models. However, no matter how the
dialogue history is used, each existing model uses its own consistent dialogue
history during the entire state tracking process, regardless of which slot is
updated. Apparently, it requires different dialogue history to update different
slots in different turns. Therefore, using consistent dialogue contents may
lead to insufficient or redundant information for different slots, which
affects the overall performance. To address this problem, we devise DiCoS-DST
to dynamically select the relevant dialogue contents corresponding to each slot
for state updating. Specifically, it first retrieves turn-level utterances of
dialogue history and evaluates their relevance to the slot from a combination
of three perspectives: (1) its explicit connection to the slot name; (2) its
relevance to the current turn dialogue; (3) Implicit Mention Oriented
Reasoning. Then these perspectives are combined to yield a decision, and only
the selected dialogue contents are fed into State Generator, which explicitly
minimizes the distracting information passed to the downstream state
prediction. Experimental results show that our approach achieves new
state-of-the-art performance on MultiWOZ 2.1 and MultiWOZ 2.2, and achieves
superior performance on multiple mainstream benchmark datasets (including
Sim-M, Sim-R, and DSTC2).


  This paper investigates the closed-loop $\mathcal{L}_2$ stability of
two-dimensional (2-D) feedback systems across a digital communication network
by introducing the tool of dissipativity. First, sampling of a continuous 2-D
system is considered and an analytical characterization of the
$QSR$-dissipativity of the sampled system is presented. Next, the
input-feedforward output-feedback passivity (IF-OFP), a simplified form of
$QSR$-dissipativity, is utilized to study the framework of feedback
interconnection of two 2-D systems over networks. Then, the effects of signal
quantization in communication links on dissipativity degradation of the 2-D
feedback quantized system is analyzed. Additionally, an event-triggered
mechanism is developed for 2-D networked control systems while maintaining
$\mathcal{L}_2$ stability of the closed-loop system. In the end, an
illustrative example is provided.


  The aim of this paper is to introduce models and algorithms for the
Participatory Budgeting problem when projects can interact with each other. In
this problem, the objective is to select a set of projects that fits in a given
budget. Voters express their preferences over the projects and the goal is then
to find a consensus set of projects that does not exceed the budget. Our goal
is to detect such interactions thanks to the preferences expressed by the
voters. Through the projects selected by the voters, we detect positive and
negative interactions between the projects by identifying projects that are
consistently chosen together. In presence of project interactions, it is
preferable to select projects that interact positively rather than negatively,
all other things being equal. We introduce desirable properties that utility
functions should have in presence of project interactions and we build a
utility function which fulfills the desirable properties introduced. We then
give axiomatic properties of aggregation rules, and we study three classical
aggregation rules: the maximization of the sum of the utilities, of the product
of the utilities, or of the minimal utility. We show that in the three cases
the problems solved by these rules are NP-hard, and we propose a branch and
bound algorithm to solve them. We conclude the paper by experiments.


  For the interacting Feynman propagator $ \Delta_{F,int}(x,y) $ of scalar
electrodynamics, we show that the sign property, $ \operatorname{Re}
i\Delta_{F,int} \geq 0 $, hinges on the reversibility of time evolution. In
contrast, $ \operatorname{Im} i\Delta_{F,int} $ is indeterminate. When we
switch to reduced dynamics under the weak coupling approximation, the positive
semidefinite sign of $ \operatorname{Re} i\Delta_{F,int} $ is generally lost,
unless we impose severe restrictions on the Kraus operators that govern time
evolution. With another approximation, the rotating wave approximation, we may
recover the sign by restricting the test functions to exponentials under
certain conditions.


  In a $\Lambda$ system with two nearly degenerate ground states and one
excited state in an atom or quantum dot, spontaneous radiative decay can lead
to a range of phenomena, including electron-photon entanglement, spontaneously
generated coherence, and two-pathway decay. We show that a treatment of the
radiative decay as a quantum evolution of a single physical system composed of
a three-level electron subsystem and photons leads to a range of consequences
depending on the electron-photon interaction and the measurement. Different
treatments of the emitted photon channel the electron-photon system into a
variety of final states. The theory is not restricted to the three-level
system.


  In the field of out-of-distribution (OOD) detection, a previous method that
use auxiliary data as OOD data has shown promising performance. However, the
method provides an equal loss to all auxiliary data to differentiate them from
inliers. However, based on our observation, in various tasks, there is a
general imbalance in the distribution of the auxiliary OOD data across classes.
We propose a balanced energy regularization loss that is simple but generally
effective for a variety of tasks. Our balanced energy regularization loss
utilizes class-wise different prior probabilities for auxiliary data to address
the class imbalance in OOD data. The main concept is to regularize auxiliary
samples from majority classes, more heavily than those from minority classes.
Our approach performs better for OOD detection in semantic segmentation,
long-tailed image classification, and image classification than the prior
energy regularization loss. Furthermore, our approach achieves state-of-the-art
performance in two tasks: OOD detection in semantic segmentation and
long-tailed image classification. Code is available at
https://github.com/hyunjunChhoi/Balanced_Energy.


  We analyse the spectrum of non-BPS branes in the type I theory on the
orbifold $T^4/{\cal I}_4$. We present a detailed analysis of the action of the
worldsheet parity $\Omega$ on the different D-brane boundary state sectors of
type IIB on $T^4/{\cal I}_4$, using the covariant formulation. Using these
results we derive the spectrum of branes in the type I orbifold. We find
$\Z_2$- and $\Z$- charged non-BPS branes. A study of the stability of these
branes in the type I orbifold is also presented. We find that the type I
non-BPS D-particle and D-instanton remain stable in the orbifold. The
D-particle carries no charge whereas the non-BPS D-instanton can carry twisted
R-R charge.


  For a surjective self-morphism on a projective variety defined over a number
field, we study the preimages question, which asks if the set of rational
points on the iterated preimages of an invariant closed subscheme eventually
stabilize. We prove the answer is positive for self-morphisms on $\mathbb{P}^1
\times \mathbb{P}^1$. We also prove that the answer is positive even if we
allow finite extension of the number field by a bounded degree if the morphism
is \'etale or the invariant subscheme is $0$-dimensional. We prove certain
uniformity of the stabilization for self-morphisms on abelian varieties. When
the subscheme is not invariant, we provide counterexamples and a result in a
positive direction for products of polynomial maps on $\mathbb{P}^1 \times
\mathbb{P}^1$.


  Using deep infrared observations conducted with the MOIRCS on the Subaru
Telescope in GOODS-N combined with public surveys in GOODS-S, we investigate
the dependence on stellar mass, M_*, and galaxy type of the close pair fraction
(5 kpc < r < 20 kpc) and implied merger rate. In common with some recent
studies we find that the fraction of paired systems that could result in major
mergers is low (~4%) and does not increase significantly with redshift to
z~1.2, with (1+z)^{1.6 \pm 1.6}. Our key finding is that massive galaxies with
M_* > 1E11 Msun are more likely to host merging companions than less massive
systems (M_* ~ 1E10 Msun). We find evidence for a higher pair fraction for red,
spheroidal hosts compared to blue, late-type systems, in line with expectations
based on clustering at small scales. So-called "dry" mergers between early-type
galaxies represent nearly 50% of close pairs with M_* > 3E10 Msun at z~0.5, but
less than 30% at z~1. This result can be explained by the increasing abundance
of red, early-type galaxies at these masses. We compare the volumetric merger
rate of galaxies with different masses to mass-dependent trends in galaxy
evolution, finding that major mergers cannot fully account for the formation of
spheroidal galaxies since z~1. In terms of mass assembly, major mergers
contribute little to galaxy growth below M_* ~ 3E10 Msun but are more
significant among galaxies with M_* > 1E11 Msun, 30% of which have undergone
mostly dry mergers over the observed redshift range. Overall, the relatively
more rapid coalescence of high mass galaxies mirrors the expected hierarchical
growth of halos and is consistent with recent model predictions, even if the
downsizing of star formation and morphological evolution involves additional
physical processes.


  Using scanning probe microscopy and spectroscopy, we explore the spatial
symmetry of the electronic wavefunctions of twisted bilayer graphene at the
"magic angle" of 1.1 degrees. This small twist angle leads to a long wavelength
moir\'e unit cell on the order of 13 nm and the appearance of two flat bands.
As the twist angle is decreased, correlation effects increase until they are
maximized at the magic angle. At this angle, the wavefunctions at the charge
neutrality point show only C2 symmetry due to the emergence of a charge ordered
state. As the system is doped, the symmetry of the wavefunctions change at each
commensurate filling of the moir\'e unit cell pointing to the correlated nature
of the spin and valley degeneracy broken states.


  In this paper we extend dyadic shifts and the dyadic representation theorem
to an operator-valued setting: We first define operator-valued dyadic shifts
and prove that they are bounded. We then extend the dyadic representation
theorem, which states that every scalar-valued Calder\'on-Zygmund operator can
be represented as a series of dyadic shifts and paraproducts averaged over
randomized dyadic systems, to operator-valued Calder\'on-Zygmund operators. As
a corollary, we obtain another proof of the operator-valued, global T(1)
theorem.
  We work in the setting of integral operators that have R-bounded
operator-valued kernels and act on functions taking values in UMD-spaces. The
domain of the functions is the Euclidean space equipped with the Lebesgue
measure.
  In addition, we give new proofs for the following known theorems: Boundedness
of the dyadic (operator-valued) paraproduct, a variant of Pythagoras' theorem
for (vector-valued) functions adapted to a sparse collection of dyadic cubes,
and a decoupling inequality for (UMD-valued) martingale differences.


  Intelligence Quotient (IQ) Test is a set of standardized questions designed
to evaluate human intelligence. Verbal comprehension questions appear very
frequently in IQ tests, which measure human's verbal ability including the
understanding of the words with multiple senses, the synonyms and antonyms, and
the analogies among words. In this work, we explore whether such tests can be
solved automatically by artificial intelligence technologies, especially the
deep learning technologies that are recently developed and successfully applied
in a number of fields. However, we found that the task was quite challenging,
and simply applying existing technologies (e.g., word embedding) could not
achieve a good performance, mainly due to the multiple senses of words and the
complex relations among words. To tackle these challenges, we propose a novel
framework consisting of three components. First, we build a classifier to
recognize the specific type of a verbal question (e.g., analogy,
classification, synonym, or antonym). Second, we obtain distributed
representations of words and relations by leveraging a novel word embedding
method that considers the multi-sense nature of words and the relational
knowledge among words (or their senses) contained in dictionaries. Third, for
each type of questions, we propose a specific solver based on the obtained
distributed word representations and relation representations. Experimental
results have shown that the proposed framework can not only outperform existing
methods for solving verbal comprehension questions but also exceed the average
performance of the Amazon Mechanical Turk workers involved in the study. The
results indicate that with appropriate uses of the deep learning technologies
we might be a further step closer to the human intelligence.


  Continuous-wave-driven Kerr nonlinear microresonators give rise to
self-organization in terms of dissipative Kerr solitons, which constitute
optical frequency combs that can be used to generate low-noise microwave
signals. Here, by applying either amplitude or phase modulation to the driving
laser we create an intracavity potential trap, to discipline the repetition
rate of the solitons. We demonstrate that this effect gives rise to a novel
spectral purification mechanism of the external microwave signal frequency,
leading to reduced phase noise of the output signal. We experimentally observe
that the microwave signal generated from disciplined solitons follows the
external drive at long time scales, but exhibits an unexpected suppression of
the fast timing jitter. Counter-intuitively, this filtering takes place for
frequencies that are substantially lower than the cavity decay rate. As a
result, while the long-time-scale stability of the Kerr frequency comb
repetition rate is improved by more than 4 orders of magnitude as a result of
locking to the external microwave signal, the soliton stream shows a reduction
of the phase noise by 30 dB at offset frequencies above 10 kHz.


  An R_2-move is a homotopy of wrinkled fibrations which deforms images of
indefinite fold singularities like Reidemeister move of type II. Variants of
this move are contained in several important deformations of wrinkled
fibrations, flip and slip for example. In this paper, we first investigate how
monodromies are changed by this move. For a given fibration and its vanishing
cycles, we then give an algorithm to obtain vanishing cycles in one reference
fiber of a fibration, which is obtained by applying flip and slip to the
original fibration, in terms of mapping class groups. As an application of this
algorithm, we give several examples of diagrams which were introduced by
Williams to describe smooth 4-manifolds by simple closed curves of closed
surfaces.


  For the water waves equations, the existence of splat singularities has been
shown in [3], i.e., the interface self-intersects along an arc in finite time.
The aim of this paper is to show the absence of splat singularities for the
incompressible fluid dynamics in porous media.


  We generalise our previous results of universal linear manipulations [Phys.
Rev. A63, 032304 (2001)] to investigate three types of nonlinear qubit
transformations using measurement and quantum based schemes. Firstly, nonlinear
rotations are studied. We rotate different parts of a Bloch sphere in opposite
directions about the z-axis. The second transformation is a map which sends a
qubit to its orthogonal state (which we define as ORTHOG). We consider the case
when the ORTHOG is applied to only a partial area of a Bloch sphere. We also
study nonlinear general transformation, i.e. (theta,phi)->(theta-alpha,phi),
again, applied only to part of the Bloch sphere. In order to achieve these
three operations, we consider different measurement preparations and derive the
optimal average (instead of universal) quantum unitary transformations. We also
introduce a simple method for a qubit measurement and its application to other
cases.


  Providing natural language instructions in prompts is a useful new paradigm
for improving task performance of large language models in a zero-shot setting.
Recent work has aimed to improve such prompts via manual rewriting or
gradient-based tuning. However, manual rewriting is time-consuming and requires
subjective interpretation, while gradient-based tuning can be extremely
computationally demanding for large models and may not be feasible for
API-based models. In this work, we introduce Gradient-free Instructional Prompt
Search (GrIPS), a gradient-free, edit-based search approach for improving task
instructions for large language models. GrIPS takes in instructions designed
for humans and automatically returns an improved, edited prompt, while allowing
for API-based tuning. With InstructGPT models, GrIPS improves the average task
performance by up to 4.30 percentage points on eight classification tasks from
the Natural Instructions dataset (with similar improvements for OPT, BLOOM, and
FLAN-T5). We see improvements for both instruction-only prompts and instruction
+ k-shot examples prompts. Notably, GrIPS outperforms manual rewriting and
purely example-based prompts while controlling for the available compute and
data budget. Further, performance of GrIPS is comparable to select
gradient-based tuning approaches. Qualitatively, we show our edits can simplify
instructions and at times make them incoherent but nonetheless improve
accuracy. Our code is available at: https://github.com/archiki/GrIPS


  The formation of self assembled structures such as micelles has been
intensively studied and is well understood. The ability of a solution of
amphiphilic molecules to develop micelles is depending on the concentration and
characterized by the critical micelle concentration (cmc), above which micelle
formation does occur. Recent studies use a lattice approach in order to
determine cmc and show that the correct modelling and analysis of cluster
formations is highly non-trivial. We developed a minimalistic coarse grained
model for amphiphilic molecules in the continuum and simulated the time
evolution via dynamic Monte Carlo simulations in the canonical (NVT) ensemble.
Starting from a homogeneous system we observed and characterized how the
initial fluctuations, yielding small aggregates of amphiphilic molecules, end
up in the growth of complete micelles. Our model is sufficiently versatile to
account for different structures of surfactant systems such as membranes,
micelles of variable radius and tubes at high particle densities by adjusting
particle density and potential properties. Particle densities and micellization
rates are investigated and an order parameter is introduced, so that the
dependence of the micellization process on temperature and surfactant density
can be studied. The constant density of free particles for concentrations above
cmc, e. g. as expected from theoretical considerations, can be reproduced when
choosing a careful definition of free volumes. In the cmc regime at low
temperatures different non-equilibrium effects are reported, occurring even for
very long time-scales.


  Shapley-related techniques have gained attention as both global and local
interpretation tools because of their desirable properties. However, their
computation using conditional expectations is computationally expensive.
Approximation methods suggested in the literature have limitations. This paper
proposes the use of a surrogate model-based tree to compute Shapley and SHAP
values based on conditional expectation. Simulation studies show that the
proposed algorithm provides improvements in accuracy, unifies global Shapley
and SHAP interpretation, and the thresholding method provides a way to
trade-off running time and accuracy.


  A notable aspect of high-temperature superconductivity in the copper oxides
is the unconventional nature of the underlying paired-electron state. A direct
manifestation of the unconventional state is a pairing energy - that is, the
energy required to remove one electron from the superconductor - that varies
(between zero and a maximum value) as a function of momentum or wavevector: the
pairing energy for conventional superconductors is wavevector-independent. The
wavefunction describing the superconducting state will include not only the
pairing of charges, but also of the spins of the paired charges. Each pair is
usually in the form of a spin singlet, so there will also be a pairing energy
associated with transforming the spin singlet into the higher energy spin
triplet form without necessarily unbinding the charges. Here we use inelastic
neutron scattering to determine the wavevector-dependence of spin pairing in
La_{2-x}Sr_xCuO_4, the simplest high-temperature superconductor. We find that
the spin pairing energy (or 'spin gap') is wavevector independent, even though
superconductivity significantly alters the wavevector dependence of the spin
fluctuations at higher energies.


  Comment: Monitoring Networked Applications With Incremental Quantile
Estimation [arXiv:0708.0302]


  We explore the range of wide field multi-object instrument concepts taking
advantage of the unique capabilities of the Starbug focal plane positioning
concept. Advances to familiar instrument concepts, such as fiber positioners
and deployable fiber-fed IFUs, are discussed along with image relays and
deployable active sensors. We conceive deployable payloads as components of
systems more traditionally regarded as part of telescope systems rather than
instruments - such as adaptive optics and ADCs. Also presented are some of the
opportunities offered by the truly unique capabilities of Starbug, such as
microtracking to apply intra-field distortion correction during the course of
an observation.


  A vacuum instability due to a massless ghost in a hidden sector can lead to
an effective equation of state for dark energy that changes smoothly from
$w=-3/2$ at large redshifts, to $w\approx-1.2$ today, to $w=-1$ in the future.
We discuss how this ghost can be the Goldstone boson of Lorentz symmetry
breaking, and we find that this breaking in the hidden sector should occur at a
scale below $\sim$10 KeV. The normal particles that are produced along with the
ghosts are then predominantly neutrinos.


  We give a new lower bound on the number of connected components of the space
of representations of a surface group into the group of orientation preserving
homeomorphisms of the circle. Precisely, for the fundamental group of a genus g
surface, we show there are at least k^(2g) + 1 connected components containing
representations with Euler number (2g-2)/(k). We also show that certain
representations are rigid, meaning that all deformations lie in the same
semiconjugacy class. Our methods apply to representations of surface groups
into finite covers of PSL(2,R) and into Diff+(S^1) as well, in which case we
recover theorems of W. Goldman and J. Bowden.
  The key technique is an investigation of local maximality phenomena for
rotation numbers of products of circle homeomorphisms, using techniques of
Calegari-Walker. This is a new approach to studying deformation classes of
group actions on the circle, and may be of independent interest.


  In this work we are going to study the dynamics of the linear automorphisms
of a measure convolution algebra over a finite group, $T(\mu)=\nu * \mu$. In
order to understand an classify the asymptotic behavior of this dynamical
system we provide an alternative to classical results, a very direct way to
understand convergence of the sequence $\{\nu^{n}\}_{n\in\mathbb{N}}$, where
$G$ is a finite group, $\nu\in\mathcal{P}(G)$ and
$\nu^n=\underbrace{\nu\ast...\ast\nu}_n$, trough the subgroup generated by his
support.


  In this paper, we study the memory properties of transformations of linear
processes. Dittmann and Granger (2002) studied the polynomial transformations
of Gaussian FARIMA(0,d,0) processes by applying the orthonormality of the
Hermite polynomials under the measure for the standard normal distribution.
Nevertheless, the orthogonality does not hold for transformations of
non-Gaussian linear processes. Instead, we use the decomposition developed by
Ho and Hsing (1996, 1997) to study the memory properties of nonlinear
transformations of linear processes, which include the FARIMA(p,d,q) processes,
and obtain consistent results as in the Gaussian case. In particular, for
stationary processes, the transformations of short-memory time series still
have short-memory and the transformation of long-memory time series may have
different weaker memory parameters which depend on the power rank of the
transformation. On the other hand, the memory properties of transformations of
non-stationary time series may not depend on the power ranks of the
transformations. This study has application in econometrics and financial data
analysis when the time series observations have non-Gaussian heavy tails. As an
example, the memory properties of call option processes at different strike
prices are discussed in details.