  Extracting as much information as possible about an object when probing with
a limited number of photons is an important goal with applications from biology
and security to metrology. Imaging with a few photons is a challenging task as
the detector noise and stray light are then predominant, which precludes the
use of conventional imaging methods. Quantum correlations between photon pairs
has been exploited in a so called 'heralded imaging scheme' to eliminate this
problem. However these implementations have so-far been limited to intensity
imaging and the crucial phase information is lost in these methods. In this
work, we propose a novel quantum-correlation enabled Fourier Ptychography
technique, to capture high-resolution amplitude and phase images with a few
photons. This is enabled by the heralding of single photons combined with
Fourier ptychographic reconstruction. We provide experimental validation and
discuss the advantages of our technique that include the possibility of
reaching a higher signal to noise ratio and non-scanning Fourier Ptychographic
acquisition.


  Based on simple scale arguments we argue that any thermalized fireball
evolution scenario which is in agreement with the observed Hanbury-Brown Twiss
(HBT) correlation radii at RHIC and reproduces the measured total multiplicity
cannot reflect the distribution of matter at or close to a phase transition
temperature of ~170 MeV and any scenario which assumes that HBT reflects these
properties cannot be reached by a sensible choice of evolution parameters while
agreeing with all correlation radii. We investigate this question in more
detail using a parametrized version of the fireball evolution which has been
shown to reproduce particle spectra and HBT for a separate chemical and kinetic
freeze-out.


  FIRSTv2 (Fibered Imager foR a Single Telescope version 2) is the upgrade of a
post-AO spectro-interferometer (FIRST) that enables high contrast imaging and
spectroscopy at spatial scales below the diffraction limit of a single
telescope. FIRST is currently installed, and routinely used, on the Subaru
telescope as a module of the Subaru Extreme AO (SCExAO) platform. It achieves
sensitivity and accuracy by a unique combination of sparse aperture masking,
spatial filtering by single-mode fibers and cross-dispersion in the visible
(600-900nm). The ongoing upgrade aims at using a photonic chip beam combiner,
allowing the measurement of the complex visibility for every baseline
independently. Using the integrated optics technology will increase the
stability and sensitivity, and thus improve the dynamic range. Integrated
optics chips working in the visible wavelength range are challenging (in terms
of throughput and polarization). Several photonic chips are under
characterization in our laboratory and we have installed a first prototype chip
in the FIRSTv2 instrument at the Subaru Telescope. I will thus report on the
on-sky results obtained with this kind of device, for the first time in the
visible. This is the first step towards the full upgrade of FIRSTv2, that will
ultimately provide unique capabilities to detect and characterize close
companions such as exoplanets, by combining high angular resolution and
spectral resolution in the visible.


  We propose the existence of a lower bound on the energy of pure neutron
matter (PNM) on the basis of unitary-gas considerations. We discuss its
justification from experimental studies of cold atoms as well as from
theoretical studies of neutron matter. We demonstrate that this bound results
in limits to the density-dependent symmetry energy, which is the difference
between the energies of symmetric nuclear matter and PNM. In particular, this
bound leads to a lower limit to the volume symmetry energy parameter $S_0$. In
addition, for assumed values of $S_0$ above this minimum, this bound implies
both upper and lower limits to the symmetry energy slope parameter $L$, which
describes the lowest-order density dependence of the symmetry energy. A lower
bound on the neutron-matter incompressibility is also obtained. These bounds
are found to be consistent with both recent calculations of the energies of PNM
and constraints from nuclear experiments. Our results are significant because
several equations of state that are currently used in astrophysical simulations
of supernovae and neutron star mergers, as well as in nuclear physics
simulations of heavy-ion collisions, have symmetry energy parameters that
violate these bounds. Furthermore, below the nuclear saturation density, the
bound on neutron-matter energies leads to a lower limit to the
density-dependent symmetry energy, which leads to upper limits to the nuclear
surface symmetry parameter and the neutron-star crust-core boundary. We also
obtain a lower limit to the neutron-skin thicknesses of neutron-rich nuclei.
Above the nuclear saturation density, the bound on neutron-matter energies also
leads to an upper limit to the symmetry energy, with implications for
neutron-star cooling via the direct Urca process.


  A general method for deriving maximally informative sigmoidal tuning curves
for neural systems with small normalized variability is presented. The optimal
tuning curve is a nonlinear function of the cumulative distribution function of
the stimulus and depends on the mean-variance relationship of the neural
system. The derivation is based on a known relationship between Shannon's
mutual information and Fisher information, and the optimality of Jeffrey's
prior. It relies on the existence of closed-form solutions to the converse
problem of optimizing the stimulus distribution for a given tuning curve. It is
shown that maximum mutual information corresponds to constant Fisher
information only if the stimulus is uniformly distributed. As an example, the
case of sub-Poisson binomial firing statistics is analyzed in detail.


  In recent years, we have seen significant steps taken in the development of
self-driving cars. Multiple companies are starting to roll out impressive
systems that work in a variety of settings. These systems can sometimes give
the impression that full self-driving is just around the corner and that we
would soon build cars without even a steering wheel. The increase in the level
of autonomy and control given to an AI provides an opportunity for new modes of
human-vehicle interaction. However, surveys have shown that giving more control
to an AI in self-driving cars is accompanied by a degree of uneasiness by
passengers. In an attempt to alleviate this issue, recent works have taken a
natural language-oriented approach by allowing the passenger to give commands
that refer to specific objects in the visual scene. Nevertheless, this is only
half the task as the car should also understand the physical destination of the
command, which is what we focus on in this paper. We propose an extension in
which we annotate the 3D destination that the car needs to reach after
executing the given command and evaluate multiple different baselines on
predicting this destination location. Additionally, we introduce a model that
outperforms the prior works adapted for this particular setting.


  The BL Lac object Mrk 421 was observed in optical bands from 2009 April to
2012 May with the 1.0 m telescope at Weihai Observatory of Shandong University.
Microvariability was analysed by C and F tests, but no significant
microvariability was detected during our observations.


  With the goal of elucidating the effects of low metallicity on the star
formation activity, feedback and interstellar medium of low metallicity
environments, SOFIA has observed a 40' x 20' (60 pc x 30 pc) area of our
neighboring metal-poor Large Magellanic Cloud in 158 micron [CII] and 88 micron
[OIII], targeting the southern molecular ridge just south of 30Doradus. We find
extensive [CII] emission over the region, which encompasses a wide variety of
local physical conditions, from bright compact star forming regions to lower
density environments beyond, much of which does not correspond to CO
structures. Preliminary analyses indicates that most of the molecular hydrogen
is in a CO-dark gas component.


  Magnetoquantum oscillations of resistance as functions of the potential
difference applied across the contact are studied for metallic point contacts
made of $Al$ and $Be$. The amplitude of resistance oscillations in a magnetic
field increases with voltage and is identical to the EPI spectrum of the point
contact for one group of contacts, and with the bias voltage across the contact
for another. The increase in the oscillation amplitude as well as its decrease
has a nonmonotonic dependence on energy. The scattering of electrons by
nonequilibrium phonons and the Fermi-liquid effects in the nonequilibrium
electron system are considered as the possible reasons behind the observed
effects.


  The nonlinear and nonlocal PDE $$ |v_t|^{p-2}v_t+(-\Delta_p)^sv=0 \, , $$
where $$ (-\Delta_p)^s v\, (x,t)=2 \,\text{PV}
\int_{\mathbb{R}^n}\frac{|v(x,t)-v(x+y,t)|^{p-2}(v(x,t)-v(x+y,t))}{|y|^{n+sp}}\,
dy, $$ has the interesting feature that an associated Rayleigh quotient is
non-increasing in time along solutions. We prove the existence of a weak
solution of the corresponding initial value problem which is also unique as a
viscosity solution. Moreover, we provide H\"older estimates for viscosity
solutions and relate the asymptotic behavior of solutions to the eigenvalue
problem for the fractional $p$-Laplacian.


  In this paper we construct non-simply connected contact manifolds $M$ of
dimension $\geq5$ such that $M\times S^1$ does not admit a symplectic
structure.


  A comparative study is performed of a deformed mean field theory, represented
by the cranked Nilsson-Strutinsky (CNS) model, and the spherical shell model.
Energy spectra, occupation numbers, B(E2)-values, and spectroscopic quadrupole
moments in the light pf shell nuclei are calculated in the two models and
compared. The result is also compared to available experimental data which are
generally well described by the shell model. Although the Nilsson-Strutinsky
calculation does not include pairing, both the subshell occupation numbers and
quadrupole properties are found to be rather similar in the two models. It is
also shown that ``unpaired'' shell model calculations produce very similar
energies as the CNS at all spins. The role of the pairing energy in the
description of backbending and signature splitting in odd-mass nuclei is also
discussed.


  An important question that discrete approaches to quantum gravity must
address is how continuum features of spacetime can be recovered from the
discrete substructure. Here, we examine this question within the causal set
approach to quantum gravity, where the substructure replacing the spacetime
continuum is a locally finite partial order. A new topology on causal sets
using ``thickened antichains'' is constructed. This topology is then used to
recover the homology of a globally hyperbolic spacetime from a causal set which
faithfully embeds into it at sufficiently high sprinkling density. This implies
a discrete-continuum correspondence which lends support to the fundamental
conjecture or ``Hauptvermutung'' of causal set theory.


  By the Pieri rule, the tensor product of an exterior power and a
finite-dimensional irreducible representation of a general linear group has a
multiplicity-free decomposition. The embeddings of the constituents are called
Pieri inclusions and were first studied by Weyman in his thesis and described
explicitly by Olver. More recently, these maps have appeared in the work of
Eisenbud, Fl{\o}stad, and Weyman and of Sam and Weyman to compute pure free
resolutions for classical groups.
  In this paper, we give a new closed form, non-recursive description of Pieri
inclusions. For partitions with a bounded number of distinct parts, the
resulting algorithm has polynomial time complexity whereas the previously known
algorithm has exponential time complexity.


  Electromagnetic interactions are incorporated into Heavy Hadron Chiral
Perturbation Theory. Short and long distance magnetic moment contributions to
the chiral Lagrangian are identified, and $M1$ radiative decays of heavy vector
mesons and sextet baryons are studied. Using recent CLEO $D^*$ branching
fraction ratio data, we fit the meson coupling to the axial vector Goldstone
current and find $g_1^2 = 0.34 \pm 0.48$ for $\mc = 1700 \MeV$. Finally, we
obtain model independent predictions for total and partial widths of charm and
bottom vector mesons.


  In this paper we introduce and study some mathematical structures on top of
transitive Lie algebroids in order to formulate gauge theories in terms of
generalized connections and their curvature: metrics, Hodge star operator and
integration along the algebraic part of the transitive Lie algebroid (its
kernel). Explicit action functionals are given in terms of global objects and
in terms of their local description as well. We investigate applications of
these constructions to Atiyah Lie algebroids and to derivations on a vector
bundle. The obtained gauge theories are discussed with respect to ordinary and
to similar non-commutative gauge theories.


  More than 90% of matter in the Universe could be composed of heavy particles,
which were non-relativistic, or 'cold', when they froze-out from the primordial
soup. I will review current searches for these hypothetical particles, both via
interactions with nuclei in deep underground detectors, and via the observation
of their annihilation products in the Sun, galactic halo and galactic center.


  We prove operator-norm resolvent convergence estimates for one-dimensional
periodic differential operators with rapidly oscillating coefficients in the
non-uniformly elliptic high-contrast setting, which has been out of reach of
the existing homogenisation techniques. Our asymptotic analysis is based on a
special representation of the resolvent of the operator in terms of the
$M$-matrix of an associated boundary triple ("Krein resolvent formula''). The
resulting asymptotic behaviour is shown to be described, up to a unitary
equivalent transformation, by a non-standard version of the Kronig-Penney model
on $\mathbb R$.


  Conventional synchronous machines are gradually replaced by converter-based
renewable resources. As a result, synchronous inertia, an important
time-varying quantity, has substantially more impact on modern power systems
stability. The increasing integration of renewable energy resources imports
different dynamics into traditional power systems; therefore, the estimation of
system inertia using mathematical model becomes more difficult. In this paper,
we propose a novel learning-assisted inertia estimation model based on
long-term recurrent convolutional network (LRCN) that uses system wide
frequency and phase voltage measurements. The proposed approach uses a
non-intrusive probing signal to perturb the system and collects ambient
measurements with phasor measurement units (PMU) to train the proposed LRCN
model. Case studies are conducted on the IEEE 24-bus system. Under a
signal-to-noise ratio (SNR) of 60dB condition, the proposed LRCN based inertia
estimation model achieves an accuracy of 97.56% with a mean squared error (MSE)
of 0.0552. Furthermore, with a low SNR of 45dB, the proposed learning-assisted
inertia estimation model is still able to achieve a high accuracy of 93.07%.


  We offer a model to describe the intrinsic nonlinear response of surface
plasmon polaritons (SPPs). Relation of the complex nonlinear coefficient of
SPPs to the third-order nonlinear susceptibility of the metal is provided. As
reported in a recent study, gold is highly lossy and simultaneously highly
nonlinear due to interband absorption and interband thermo-modulation at a
wavelength shorter than 700 nm. The effect of the high loss of the metal on the
SPP nonlinear propagation is taken into account in our model. With the model we
show difference in sign of real and imaginary parts between the nonlinear
propagation coefficient and the nonlinear susceptibility of component material
for the first time to our knowledge. Our model could have practical importance
in studying plasmonic devices utilizing the nonlinear phase modulation and the
nonlinear absorption of SPPs. For example, it allows one to extract the complex
nonlinear susceptibility of gold through a measurement of SPP nonlinear
propagation at the visible range.


  The quantum Fourier transform (QFT) brings efficiency in many respects,
especially usage of resource, for most operations on quantum computers. In this
study, the existing QFT-based and non-QFT-based quantum arithmetic operations
are examined. The capabilities of QFT-based addition and multiplication are
improved with some modifications. The proposed operations are compared with the
nearest quantum arithmetic operations. Furthermore, novel QFT-based
subtraction, division and exponentiation operations are presented. The proposed
arithmetic operations can perform nonmodular operations on all signed numbers
without any limitation by using less resources. In addition, novel quantum
circuits of two's complement, absolute value and comparison operations are also
presented by using the proposed QFT-based addition and subtraction operations.


  We study the interplay of disorder and Heisenberg interactions in Kitaev
model on honeycomb lattice. The effect of disorder on the transition between
Kitaev spin liquid and magnetic ordered states as well as the stability of
magnetic ordering is investigated. Using Lanczos exact diagonalization we
discuss the consequences of two types of disorder: (i) random-coupling disorder
and (ii) singular-coupling disorder. They exhibit qualitatively similar effects
in the pure Kitaev-Heisenberg model without long-range interactions. The range
of spin liquid phases is reduced and the transition to magnetic ordered phases
becomes more crossover-like. Furthermore, the long-range zigzag and stripy
orderings in the clean system are replaced by their three domains with
different ordering direction. Especially in the crossover range the coexistence
of magnetically ordered and Kitaev spin-liquid domains is possible. With
increasing the disorder strength the area of domains becomes smaller and the
system goes into a spin-glass state. However, the disorder effect is different
in magnetically ordered phases caused by long-range interactions. The stability
of such magnetic ordering is diminished by singular-coupling disorder, and
accordingly, the range of spin-liquid regime is extended. This mechanism may be
relevant to materials like $\alpha$-RuCl$_3$ and H$_3$LiIr$_2$O$_6$ where the
zigzag ground state is stabilized by weak long-range interactions. We also find
that the flux gap closes at a critical disorder strength and vortices appears
in the flux arrangement. Interestingly, the vortices tend to form kinds of
commensurate ordering.


  We predict the existence of an anomalous crossover between thermal and shot
noise in macroscopic diffusive conductors. We first show that, besides thermal
noise, these systems may also exhibit shot noise due to fluctuations of the
total number of carriers in the system. Then we show that at increasing
currents the crossover between the two noise behaviors is anomalous, in the
sense that the low frequency current spectral density displays a region with a
superlinear dependence on the current up to a cubic law. The anomaly is due to
the non-trivial coupling in the presence of the long range Coulomb interaction
among the three time scales relevant to the phenomenon, namely, diffusion,
transit and dielectric relaxation time.


  Domain Adaptation (DA) aims to leverage the knowledge learned from a source
domain with ample labeled data to a target domain with unlabeled data only.
Most existing studies on DA contribute to learning domain-invariant feature
representations for both domains by minimizing the domain gap based on
convolution-based neural networks. Recently, vision transformers significantly
improved performance in multiple vision tasks. Built on vision transformers, in
this paper we propose a Bidirectional Cross-Attention Transformer (BCAT) for DA
with the aim to improve the performance. In the proposed BCAT, the attention
mechanism can extract implicit source and target mixup feature representations
to narrow the domain discrepancy. Specifically, in BCAT, we design a
weight-sharing quadruple-branch transformer with a bidirectional
cross-attention mechanism to learn domain-invariant feature representations.
Extensive experiments demonstrate that the proposed BCAT model achieves
superior performance on four benchmark datasets over existing state-of-the-art
DA methods that are based on convolutions or transformers.


  This paper deals with cellular (e.g. LTE) networks that selectively offload
the mobile data traffic onto WiFi (IEEE 802.11) networks to improve network
performance. We propose the Seamless Internetwork Flow Mobility (SIFM)
architecture that provides seamless flow-mobility support using concepts of
Software Defined Networking (SDN). The SDN paradigm decouples the control and
data plane, leading to a centralized network intelligence and state. The SIFM
architecture utilizes this aspect of SDN and moves the mobility decisions to a
centralized Flow Controller (FC). This provides a global network view while
making mobility decisions and also reduces the complexity at the PGW. We
implement and evaluate both basic PMIPv6 and the SIFM architectures by
incorporating salient LTE and WiFi network features in the ns-3 simulator.
Performance experiments validate that seamless mobility is achieved. Also, the
SIFM architecture shows an improved network performance when compared to the
base PMIPv6 architecture. A proof-of-concept prototype of the SIFM architecture
has been implemented on an experimental testbed. The LTE network is emulated by
integrating USRP B210x with the OpenLTE eNodeB and OpenLTE EPC. The WiFi
network is emulated using hostapd and dnsmasq daemons running on Ubuntu 12.04.
An off-the-shelf LG G2 mobile phone running Android 4.2.2 is used as the user
equipment. We demonstrate seamless mobility between the LTE network and the
WiFi network with the help of ICMP ping and a TCP chat application.


  The black hole information paradox is the incompatibility of quantum
mechanics with the semi-classical picture of Hawking radiation. Hawking
radiation appears thermal and eventually leads to the complete disappearance of
a black hole. However, black holes could be formed from a pure quantum state.
The transition from such an initial state to the final state of pure Hawking
radiation cannot be described by unitary time evolution. In this paper, we
present an analysis in quantum gravity that shows how boundary conditions in
the future prevent a loss of quantum mechanical information from the spacetime.
In classical physics, the future boundary of the spacetime in the black hole
interior is a singularity. Realistic gravitational collapse results in a BKL
type of approach to the singularity. But, solving the Wheeler-DeWitt equation
reveals that the singularity does not form and can be replaced by specifying a
final state density matrix. Such a condition is natural within the context of
consistent histories version of quantum mechanics. We provide a self-contained
treatment of these issues. How information escapes from the black hole will be
treated elsewhere.


  "Quantum trajectories" are solutions of stochastic differential equations
also called Belavkin or Stochastic Schr\"odinger Equations. They describe
random phenomena in quantum measurement theory. Two types of such equations are
usually considered, one is driven by a one-dimensional Brownian motion and the
other is driven by a counting process. In this article, we present a way to
obtain more advanced models which use jump-diffusion stochastic differential
equations. Such models come from solutions of martingale problems for
infinitesimal generators. These generators are obtained from the limit of
generators of classical Markov chains which describe discrete models of quantum
trajectories. Furthermore, stochastic models of jump-diffusion equations are
physically justified by proving that their solutions can be obtained as the
limit of the discrete trajectories.


  We propose an ontology enhanced model for sentence based claim detection. We
fused ontology embeddings from a knowledge base with BERT sentence embeddings
to perform claim detection for the ClaimBuster and the NewsClaims datasets. Our
ontology enhanced approach showed the best results with these small-sized
unbalanced datasets, compared to other statistical and neural machine learning
models. The experiments demonstrate that adding domain specific features
(either trained word embeddings or knowledge graph metadata) can improve
traditional ML methods. In addition, adding domain knowledge in the form of
ontology embeddings helps avoid the bias encountered in neural network based
models, for example the pure BERT model bias towards larger classes in our
small corpus.


  Generalization error bounds are essential to understanding machine learning
algorithms. This paper presents novel expected generalization error upper
bounds based on the average joint distribution between the output hypothesis
and each input training sample. Multiple generalization error upper bounds
based on different information measures are provided, including Wasserstein
distance, total variation distance, KL divergence, and Jensen-Shannon
divergence. Due to the convexity of the information measures, the proposed
bounds in terms of Wasserstein distance and total variation distance are shown
to be tighter than their counterparts based on individual samples in the
literature. An example is provided to demonstrate the tightness of the proposed
generalization error bounds.


  This paper is concerned with the construction of graded meshes for
approximating so-called singular solutions of elliptic boundary value problems
by means of multipatch discontinuous Galerkin Isogeometric Analysis schemes.
Such solutions appear, for instance, in domains with re-entrant corners on the
boundary of the computational domain, in problems with changing boundary
conditions, in interface problems, or in problems with singular source terms.
Making use of the analytic behavior of the solution, we construct the graded
meshes in the neighborhoods of such singular points following a multipatch
approach.
  We prove that appropriately graded meshes lead to the same convergence rates
as in the case of smooth solutions with approximately the same number of
degrees of freedom. Representative numerical examples are studied in order to
confirm the theoretical convergence rates and to demonstrate the efficiency of
the mesh grading technology in Isogeometric Analysis.


  We investigate liquid layers adsorbed at spherical and corrugated cylindrical
substrates. The effective Hamiltonians for the liquid-gas interfaces
fluctuating in the presence of such curved substrates are derived via the
mean-field density functional theory. Their structure is compared with the
Helfrich Hamiltonian which is parametrized by the bending and Gaussian rigidity
coefficients. For long-ranged interparticle interactions of van der Waals type
these coefficients turn out to be non-universal functions of interfacial
curvatures; their form varies from one interface to another. We discuss
implications of the structure of these functions on the effective Hamiltonian.


  The asteroseismology of rapidly rotating pulsating stars is hindered by our
poor knowledge of the effect of the rotation on the oscillation properties.
Here we present an asymptotic analysis of high-frequency acoustic modes in
rapidly rotating stars. We study the Hamiltonian dynamics of acoustic rays in
uniformly rotating polytropic stars and show that the phase space structure has
a mixed character, regions of chaotic trajectories coexisting with stable
structures like island chains or invariant tori. In order to interpret the ray
dynamics in terms of acoustic mode properties, we then use tools and concepts
developed in the context of quantum physics. Accordingly, the high-frequency
acoustic spectrum is a superposition of frequency subsets associated with
dynamically independent phase space regions. The sub-spectra associated with
stable structures are regular and can be modelled through EBK quantization
methods while those associated with chaotic regions are irregular but with
generic statistical properties. The results of this asymptotic analysis are
successfully confronted with the properties of numerically computed
high-frequency acoustic modes. The implications for the asteroseismology of
rapidly rotating stars are discussed.


  Natural Language Inference (NLI) aims to determine the logic relationships
(i.e., entailment, neutral and contradiction) between a pair of premise and
hypothesis. Recently, the alignment mechanism effectively helps NLI by
capturing the aligned parts (i.e., the similar segments) in the sentence pairs,
which imply the perspective of entailment and contradiction. However, these
aligned parts will sometimes mislead the judgment of neutral relations.
Intuitively, NLI should rely more on multiple perspectives to form a holistic
view to eliminate bias. In this paper, we propose the Multi-Perspective
Inferrer (MPI), a novel NLI model that reasons relationships from multiple
perspectives associated with the three relationships. The MPI determines the
perspectives of different parts of the sentences via a routing-by-agreement
policy and makes the final decision from a holistic view. Additionally, we
introduce an auxiliary supervised signal to ensure the MPI to learn the
expected perspectives. Experiments on SNLI and MultiNLI show that 1) the MPI
achieves substantial improvements on the base model, which verifies the
motivation of multi-perspective inference; 2) visualized evidence verifies that
the MPI learns highly interpretable perspectives as expected; 3) more
importantly, the MPI is architecture-free and compatible with the powerful
BERT.


  We relate the relative nerve $\mathrm{N}_f(\mathcal{D})$ of a diagram of
simplicial sets $f \colon \mathcal{D} \to \mathsf{sSet}$ with the Grothendieck
construction $\mathsf{Gr} F$ of a simplicial functor $F \colon \mathcal{D} \to
\mathsf{sCat}$ in the case where $f = \mathrm{N} F$. We further show that any
strict monoidal simplicial category $\mathcal{C}$ gives rise to a functor
$\mathcal{C}^\bullet \colon \Delta^\mathrm{op} \to \mathsf{sCat}$, and that the
relative nerve of $\mathrm{N} \mathcal{C}^\bullet$ is the operadic nerve
$\mathrm{N}^\otimes(\mathcal{C})$. Finally, we show that all the above
constructions commute with appropriately defined opposite functors.


  We present a novel method to perform a direct T (time reversal) symmetry test
in the neutral kaon system, independent of any CP and/or CPT symmetry tests.
This is based on the comparison of suitable transition probabilities, where the
required interchange of in <-> out states for a given process is obtained
exploiting the Einstein-Podolsky-Rosen correlations of neutral kaon pairs
produced at a $\phi$-factory. In the time distribution between the two decays,
we compare a reference transition like the one defined by the time ordered
decays $(\ell^-,\pi\pi)$ with the T -conjugated one defined by $(3\pi^0,
\ell^+)$. With the use of this and other T conjugated comparisons, the KLOE-2
experiment at DA$\Phi$NE could make a significant test.


  This paper proposes a non-computational method of counteracting the effect of
image degradation introduced by the diffraction phenomenon in lensless
microscopy. All the optical images (whether focused by lenses or not) are
diffraction patterns, which preserve the visual information upto a certain
extent determined by the size of the point spread functions, like airy disks in
some cases. A highly diverging beam can be exploited to reduce the spatial
extent of these point spread functions relatively in the transformed projective
space, which can help us in the spatial unmixing of the visual information. The
principle has been experimentally validated by the lensless imaging of red
blood cells of diameter ~6-9 micrometers and a photolithography mask with
features in micrometer scale. The important advantages of the proposed approach
of non-computational shadow microscopy are the improved depth of field and a
drastic increase in the sensor to sample working distance. The imaging method
can also be used as a projection technique in the multi-angle optical computed
tomography (CT).


  We discuss information-theoretic properties of low-energy photons and
gravitons in the S-matrix. Given an incoming n-particle momentum eigenstate, we
demonstrate that unobserved soft photons decohere nearly all outgoing momentum
superpositions of charged particles, while the universality of gravity implies
that soft gravitons decohere nearly all outgoing momentum superpositions of all
the hard particles. Using this decoherence, we compute the entanglement entropy
of the soft bosons and show that it is infrared-finite when the leading
divergences are re-summed a la Bloch and Nordsieck.


  We perform a variational calculation in the SU(N) Yang Mills theory in 3+1
dimensions. Our trial variational states are explicitly gauge invariant, and
reduce to simple Gaussian states in the zero coupling limit. Our main result is
that the energy is minimized for the value of the variational parameter away
form the perturbative value. The best variational state is therefore
characterized by a dynamically generated mass scale $M$. This scale is related
to the perturbative scale $\Lambda_{QCD}$ by the following relation:
$\alpha_{QCD}(M)={\pi\over 4}{1\over N}$. Taking the one loop QCD $\beta$-
function and $\Lambda_{QCD}=150 Mev$ we find (for N=3) the vacuum condensate
${\alpha\over \pi}<F^2>= 0.008 Gev^4$.


  Symmetric Teleparallel Gravity is an exceptional theory of gravity that is
consistent with the vanishing affine connection. This theory is an alternative
and a simpler geometrical formulation of general relativity, where the
non-metricity $Q$ drives the gravitational interaction. Our interest lies in
exploring the cosmological bouncing scenarios in a flat
Friedmann-Lima\^itre-Robertson-Walker (FLRW) spacetime within this framework.
We explore bouncing scenarios with two different Lagrangian forms of $f(Q)$
such as a linearly and non-linearly dependence on $Q$. We have successfully
examined all the energy conditions and stability analysis for both models to
present a matter bounce.


  The ANAIS (Annual modulation with NaI(Tl) Scintillators) experiment aims at
the confirmation of the DAMA/LIBRA positive annual modulation signal using the
same target and technique at the Canfranc Underground Laboratory (LSC). A first
step, named ANAIS-25 (two 12.5 kg NaI(Tl) modules) taking data from December
2012 to February 2015, provided interesting outcomes: very high light
collection efficiency, that could allow to lower the analysis energy threshold
down to the level of 1 keVee, and a good understanding of the different
background components, in particular the cosmogenic activated isotopes in the
crystal bulk and other radioactive contaminations of the NaI crystal/powder.
But those prototypes clearly pointed to the need for improved crystal
radiopurity, in particular for $^{210}$Pb contamination. Since then,
improvements in the purification and growing procedures in order to reduce
background in the very low energy region have been implemented and a new 12.5
kg module has been constructed and installed between the former two crystals,
forming the ANAIS-37 setup. Very preliminary results of this setup evidence the
improvement on radiopurity of the new crystal and are presented here. In
addition, background simulations and prospects for the full experiment are
discussed.


  Feedback is an essential composition operator in many classes of reactive and
other systems. This paper studies feedback in the context of compositional
theories with refinement. Such theories allow to reason about systems on a
component-by-component basis, and to characterize substitutability as a
refinement relation. Although compositional theories of feedback do exist, they
are limited either to deterministic systems (functions) or input-receptive
systems (total relations). In this work we propose a compositional theory of
feedback which applies to non-deterministic and non-input-receptive systems
(e.g., partial relations). To achieve this, we use the semantic frameworks of
predicate and property transformers, and relations with fail and unknown
values. We show how to define instantaneous feedback for stateless systems and
feedback with unit delay for stateful systems. Both operations preserve the
refinement relation, and both can be applied to non-deterministic and
non-input-receptive systems.


  We give a proof of perturbative renormalizability of SU(2) Yang--Mills theory
in four-dimensional Euclidean space which is based on the Flow Equations of the
renormalization group. The main motivation is to present a proof which does not
make appear mathematically undefined objects (as for example dimensionally
regularized generating functionals), which permits to parametrize the theory in
terms of {\it physical} renormalization conditions, and which allows to control
the singularities of the correlation functions of the theory in the infrared
domain. Thus a large part of the proof is dedicated to bounds on massless
correlation functions.


  We present the first numerical construction of the scalar Schwarzschild Green
function in the time-domain, which reveals several universal features of wave
propagation in black hole spacetimes. We demonstrate the trapping of energy
near the photon sphere and confirm its exponential decay. The trapped wavefront
propagates through caustics resulting in echoes that propagate to infinity. The
arrival times and the decay rate of these caustic echoes are consistent with
propagation along null geodesics and the large l-limit of quasinormal modes. We
show that the four-fold singularity structure of the retarded Green function is
due to the well-known action of a Hilbert transform on the trapped wavefront at
caustics. A two-fold cycle is obtained for degenerate source-observer
configurations along the caustic line, where the energy amplification increases
with an inverse power of the scale of the source. Finally, we discuss the tail
piece of the solution due to propagation within the light cone, up to and
including null infinity, and argue that, even with ideal instruments, only a
finite number of echoes can be observed. Putting these pieces together, we
provide a heuristic expression that approximates the Green function with a few
free parameters. Accurate calculations and approximations of the Green function
are the most general way of solving for wave propagation in curved spacetimes
and should be useful in a variety of studies such as the computation of the
self-force on a particle.


  Convolutional Neural Networks (CNNs), architectures consisting of
convolutional layers, have been the standard choice in vision tasks. Recent
studies have shown that Vision Transformers (VTs), architectures based on
self-attention modules, achieve comparable performance in challenging tasks
such as object detection and semantic segmentation. However, the image
processing mechanism of VTs is different from that of conventional CNNs. This
poses several questions about their generalizability, robustness, reliability,
and texture bias when used to extract features for complex tasks. To address
these questions, we study and compare VT and CNN architectures as feature
extractors in object detection and semantic segmentation. Our extensive
empirical results show that the features generated by VTs are more robust to
distribution shifts, natural corruptions, and adversarial attacks in both
tasks, whereas CNNs perform better at higher image resolutions in object
detection. Furthermore, our results demonstrate that VTs in dense prediction
tasks produce more reliable and less texture-biased predictions.


  Calibration ab initio (direct coupled cluster) calculations including basis
set extrapolation, relativistic effects, inner-shell correlation, and an
anharmonic zero-point energy, predict the total atomization energy at 0 K of
SO$_3$ to be 335.96 (observed 335.92$\pm$0.19) kcal/mol. Inner polarization
functions make very large (40 kcal/mol with $spd$, 10 kcal/mol with $spdfg$
basis sets) contributions to the SCF part of the binding energy. The molecule
presents an unusual hurdle for less computationally intensive theoretical
thermochemistry methods and is proposed as a benchmark for them. A slight
modification of Weizmann-1 (W1) theory is proposed that appears to
significantly improve performance for second-row compounds.


  Correlation-based techniques used for frame synchronization can suffer
significant performance degradation over multi-path frequency-selective
channels. In this paper, we propose a joint frame synchronization and channel
estimation (JFSCE) framework as a remedy to this problem. This framework,
however, increases the size of the resulting combined channel vector which
should capture both the channel impulse response (CIR) vector and the frame
boundary offset and, therefore, its estimation becomes more challenging. On the
other hand, because the combined channel vector is sparse, sparse channel
estimation methods can be applied. We propose several JFSCE methods using
popular sparse signal recovery (SSR) algorithms which exploit the sparsity of
the combined channel vector. Subsequently, the sparse channel vector estimate
is used to design a sparse equalizer. Our simulation results and experimental
measurements using software defined radios (SDRs) show that in some scenarios
our proposed method improves the overall system performance significantly, in
terms of the mean square error (MSE) between the transmitted and the equalized
symbols compared to the conventional method.


  This letter focuses on exploring a new decoding order to resolve the secrecy
issue among untrusted nonorthogonal multiple access users. In this context,
firstly, we identify the total number of possible decoding orders analytically.
Then, we propose a decoding order strategy ensuring positive secrecy rate for
all users, and obtain the number of feasible secure decoding orders based on
this proposed strategy numerically. Thereafter, we present a suboptimal policy
to avoid the computational complexity involved in finding the best secure
decoding order. Numerical results illustrate that the suboptimal solution
provides a performance gain of about 137% over therelevant benchmark.


  We report on an analysis of RXTE data of the transient neutron star low-mass
X-ray binary (NS-LMXB) XTE J1701-462, obtained during its 2006-2007 outburst.
The X-ray properties of the source changed between those of various types of
NS-LMXB subclasses. At high luminosities the source switched between two types
of Z source behavior and at low luminosities we observed a transition from Z
source to atoll source behavior. These transitions between subclasses primarily
manifest themselves as changes in the shapes of the tracks in X-ray color-color
and hardness-intensity diagrams, but they are accompanied by changes in the kHz
quasi-periodic oscillations, broad-band variability, burst behavior, and/or
X-ray spectra. We find that the low-energy X-ray flux is a good parameter to
track the gradual evolution of the tracks in color-color and hardness-intensity
diagrams, allowing us to resolve the evolution of the source in greater detail
than before and relate the observed properties to other NS-LMXBs. We further
find that during the transition from Z to atoll, characteristic behavior known
as the atoll upper banana can equivalently be described as the final stage of a
weakening Z source flaring branch, thereby blurring the line between the two
subclasses. Our findings strongly suggest that the wide variety in behavior
observed in NS-LXMBs with different luminosities can be linked through changes
in a single variable parameter, namely the mass accretion rate, without the
need for additional differences in the neutron star parameters or viewing
angle. We briefly discuss the implications of our findings for the spectral
changes observed in NS LMXBs and suggest that, contrary to what is often
assumed, the position along the color-color tracks of Z sources is not
determined by the instantaneous mass accretion rate.


  The minimization of Gibbs free energy is based on the changes in work and
free energy that occur in a physical or chemical system. The maximization of
mutual information, the capacity, of a noisy channel is determined based on the
marginal probabilities and conditional entropies associated with a
communications system. As different as the procedures might first appear,
through the exploration of a simple, "dual use" Ising model, it is seen that
the two concepts are in fact the same. In particular, the case of a binary
symmetric channel is calculated in detail.


  In this paper, we establish the Gr\"{o}bner-Shirshov bases theory for
metabelian Lie algebras. As applications, we find the Gr\"{o}bner-Shirshov
bases for partial commutative metabelian Lie algebras related to circuits,
trees and some cubes.


  High-dimensional quantum key distribution (QKD) allows to achieve
information-theoretic secure communications, providing high key generation
rates which cannot in principle be obtained by QKD protocols with binary
encoding. Nonetheless, the amount of experimental resources needed increases as
the quantum states to be detected belong to a larger Hilbert space, thus
raising the costs of practical high-dimensional systems. Here, we present a
novel scheme for fiber-based 4-dimensional QKD, with time and phase encoding
and one-decoy state technique. Quantum states transmission is tested over
different channel lengths up to 145 km of standard single-mode fiber,
evaluating the enhancement of the secret key rate in comparison to the
three-state 2-dimensional BB84 protocol, which is tested with the same
experimental setup. Our scheme allows to measure the 4-dimensional states with
a simplified and compact receiver, where only two single-photon detectors are
necessary, thus making it a cost-effective solution for practical and
fiber-based QKD.


  Using the well-known low-energy effective Lagrangian of QCD --valid for small
(non-vanishing) quark masses and a large number of colors-- we study in detail
the regions of parameter space where $CP$ is spontaneously broken/unbroken for
a vacuum angle $\theta= \pi$. In the $CP$-broken region there are first order
phase transitions as one crosses $\theta=\pi$, while on the (hyper)surface
separating the two regions, there are second order phase transitions signaled
by the vanishing of the mass of a pseudo Nambu-Goldstone boson and by a
divergent QCD topological susceptibility. The second order point sits at the
end of a first order line associated with the $CP$ spontaneous breaking, in the
appropriate complex parameter plane. When the effective Lagrangian is extended
by the inclusion of an axion these features of QCD imply that standard
calculations of the axion potential have to be revised when the QCD parameters
fall in the above mentioned $CP$-broken region, in spite of the fact that the
axion solves the strong-$CP$ problem. These latter results could be of interest
for axionic dark matter calculations if the topological susceptibility of pure
Yang-Mills theory falls off sufficiently fast when temperature is increased
towards the QCD deconfining transition.


  The noise-type completion C of a noise-type Boolean algebra B is generally
not the same as the closure of B. As shown in Part I (Introduction, Theorem 2),
C consists of all complemented elements of the closure. It appears that C is
the whole closure if and only if B is classical (as defined in Part II, Sect.
1a), which is the main result of this Part III.


  A discussion of the field content of quadratic higher-derivative gravitation
is presented, together with a new example of a massless spin-two field
consistently coupled to gravity. The full quadratic gravity theory is shown to
be equivalent to a canonical second-order theory of a massive scalar field, a
massive spin-two symmetric tensor field and gravity. The conditions showing
that the tensor field describes only spin-two degrees of freedom are derived. A
limit of the second-order theory provides a new example of massless spin-two
field consistently coupled to gravity. A restricted set of vacua of the
second-order theory is also discussed. It is shown that flat-space is the only
stable vacuum of this type, and that the spin-two field around flat space is
unfortunately always ghost-like.


  Radar as a remote sensing technology has been used to analyze human activity
for decades. Despite all the great features such as motion sensitivity, privacy
preservation, penetrability, and more, radar has limited spatial degrees of
freedom compared to optical sensors and thus makes it challenging to sense
crowded environments without prior information. In this paper, we develop a
novel dual-sensing system, in which a vision sensor is leveraged to guide
digital beamforming in a multiple-input multiple-output (MIMO) radar. Also, we
develop a calibration algorithm to align the two types of sensors and show that
the calibrated dual system achieves about two centimeters precision in
three-dimensional space within a field of view of $75^\circ$ by $65^\circ$ and
for a range of two meters. Finally, we show that the proposed approach is
capable of detecting the vital signs simultaneously for a group of closely
spaced subjects, sitting and standing, in a cluttered environment, which
highlights a promising direction for vital signs detection in realistic
environments.


  In this work, we extensively study the problem of broadcasting of
entanglement. In the first part of the work, we reconceptualize the idea of
state dependent quantum cloning machine, and in that process we introduce
different types of state dependent cloners like static and dynamic state
dependent cloners. We derive the conditions under which we can make these
cloners independent of the input state. In the broadcasting part, as our
resource initial state, we start with general two qubit state and consider
specific examples like, non maximally entangled state (NME), Werner like state
(WS), and Bell diagonal state (BDS). We apply both state dependent/ state
independent cloners, both locally and non-locally, in each of these cases.
Incidentally, we find several instances where state dependent cloners
outperform state independent cloners in broadcasting. This work gives us a
holistic view on the broadcasting of entanglement in various two qubit states,
when we have an almost exhaustive sets of cloning machines in our arsenal


  The effectiveness of the NonRelativistic Quark Model of hadrons can be
explained by Bohm's quantum theory applied to a fermion confined in a box, in
which the fermion is at rest because its kinetic energy is transformed into
PSI-field potential energy. Since that aspect of Bohm's quantum theory is not a
property of most other formulations of quantum theory, the effectiveness of the
NonRelativistic Quark Model confirms Bohm's quantum theory as opposed to those
others.


  Aerosols exhibit periodic or cyclic variations depending on natural and
anthropogenic sources over a region, which can get modulated by synoptic
meteorological parameters such as winds, rainfall and relative humidity, and
long-range transport. Information on periodicity and phase in aerosol
properties assumes significance in prediction as well as to examine the
radiative and climate effects of aerosols including its association with
changes in cloud properties and rainfall. Periodicity in aerosol optical depth,
which is a columnar measure of aerosol distribution, is determined using
continuous wavelet transform over 35 locations in India. Continuous wavelet
transform is used in the study because it is better suited to extract the
periodic and local modulations present at various frequency ranges, as these
features are invisible in conventional methods such as Fourier Transform.
Monthly mean aerosol optical depths (AODs) from MODerate Resolution Imaging
Spectroradiometer (MODIS) on board the Terra satellite from January 2001 to
December 2012 are used. Annual and quasi-biennial oscillations (QBO) in AOD are
evident in addition to the weak semi-annual and quasi-triennial. The
semi-annual and annual oscillations are consistent with the seasonal and yearly
cycle of variations in AODs. The 40-month periodicity indicates the presence of
long term correlations in AOD. The observed periodicities in MODIS Terra AODs
are also evident in the ground-based AOD measurements made over Kanpur in the
Indo-Gangetic Plain. The phase of the periodicity in AOD is stable in the
mid-frequency range, while local disturbances in the high-frequency range and
long term changes in the atmospheric composition give rise to unstable phases
in low-frequency range. That modulations in AOD over one location/region can
influence the other is revealed by the presence of phase relation among
different locations.


  We address the intractable multi-armed bandit problem with switching costs,
for which Asawa and Teneketzis introduced in [M. Asawa and D. Teneketzis. 1996.
Multi-armed bandits with switching penalties. IEEE Trans. Automat. Control, 41
328-348] an index that partially characterizes optimal policies, attaching to
each project state a ``continuation index'' (its Gittins index) and a
``switching index.'' They proposed to jointly compute both as the Gittins index
of a project with $2 n$ states -- when the original project has $n$ states --
resulting in an eight-fold increase in $O(n^3)$ arithmetic operations relative
to those to compute the continuation index. We present a faster decoupled
computation method, which in a first stage computes the continuation index and
then, in a second stage, computes the switching index an order of magnitude
faster in at most $n^2 + O(n)$ arithmetic operations, achieving overall a
four-fold reduction in arithmetic operations and substantially reduced memory
operations. The analysis exploits the fact that the Asawa and Teneketzis index
is the marginal productivity index of the project in its restless
reformulation, using methods introduced by the author. Extensive computational
experiments are reported, which demonstrate the dramatic runtime speedups
achieved by the new algorithm, as well as the near-optimality of the resultant
index policy and its substantial gains against the benchmark Gittins index
policy across a wide range of randomly generated two- and three-project
instances.


  The Nambu-Goldstone (NG) mode in a Bose-Einstein condensate (BEC) transmits a
potential barrier with probability 1 in the zero-energy limit, which is known
as the anomalous tunneling. In this paper, we investigate the tunneling
properties of quasiparticles in a dynamically unstable BEC. We prepare a
multi-component BEC (binary and spin-1 BEC) in a dynamically unstable state and
solve the tunneling problem of the spin-wave excitation from the condensate. We
find that the perfect transmission occurs even when the BEC is dynamically
unstable if the spin-wave is the NG mode. Here, the mode that exhibits the
perfect transmission is the dynamically unstable spin-wave mode, which is a
pure-imaginary-eigenvalue solution of the Bogoliubov-de Gennes equation. Hence,
we should take the zero-energy limit along not the real axis but the imaginary
axis. We also demonstrate the existence of the perfect reflection of a
dynamically unstable mode at the point where the imaginary part of the
eigenvalue takes its maximum. In this case, the incident and reflected waves
destructively interfere, and the amplitude of the quasiparticle wave function
is strongly suppressed. We numerically confirm that the perfect reflection is a
generic nature of dynamically unstable modes and not related to the NG mode.


  An automatic image segmentation procedure is an inevitable part of many image
analyses and computer vision which deeply affect the rest of the system;
therefore, a set of interactive segmentation evaluation methods can
substantially simplify the system development process. This entry presents the
state of the art of quantitative evaluation metrics for color image
segmentation methods by performing an analytical and comparative review of the
measures. The decision-making process in selecting a suitable evaluation metric
is still very serious because each metric tends to favor a different
segmentation method for each benchmark dataset. Furthermore, a conceptual
comparison of these metrics is provided at a high level of abstraction and is
discussed for understanding the quantitative changes in different image
segmentation results.


  This paper proposes near-optimal algorithms for the pure-exploration linear
bandit problem in the fixed confidence and fixed budget settings. Leveraging
ideas from the theory of suprema of empirical processes, we provide an
algorithm whose sample complexity scales with the geometry of the instance and
avoids an explicit union bound over the number of arms. Unlike previous
approaches which sample based on minimizing a worst-case variance (e.g.
G-optimal design), we define an experimental design objective based on the
Gaussian-width of the underlying arm set. We provide a novel lower bound in
terms of this objective that highlights its fundamental role in the sample
complexity. The sample complexity of our fixed confidence algorithm matches
this lower bound, and in addition is computationally efficient for
combinatorial classes, e.g. shortest-path, matchings and matroids, where the
arm sets can be exponentially large in the dimension. Finally, we propose the
first algorithm for linear bandits in the the fixed budget setting. Its
guarantee matches our lower bound up to logarithmic factors.


  The project of Super Tau-Charm Facility (STCF) proposed in China, as a
new-generation high-luminosity $e^+e^-$ collider in the low-energy region with
the center-of-mass energy of 2-7 GeV, is well underway. The luminosity is
targeted at $1.0\times10^{35} cm^{-2}s^{-1}$ at the optimized beam energy of 2
GeV. Longitudinal beam dynamics becomes of great importance for the STCF due to
the constraints from the novel beam-beam effect called coherent X-Z instability
and severe beam collective effects. In this paper, we will develop an iterative
optimization model for the STCF longitudinal beam dynamics design, which takes
into account the influence of transverse dynamics, coherent X-Z instability,
and collective effects.


  In this paper we study the non-unitary deformations of the two-dimensional
Tricritical Ising Model obtained by coupling its two spin Z2 odd operators to
imaginary magnetic fields. Varying the strengths of these imaginary magnetic
fields and adjusting correspondingly the coupling constants of the two spin Z2
even fields, we establish the presence of two universality classes of infrared
fixed points on the critical surface. The first class corresponds to the
familiar Yang-Lee edge singularity, while the second class to its tricritical
version. We argue that these two universality classes are controlled by the
conformal non-unitary minimal models M(2,5) and M(2,7) respectively, which is
supported by considerations based on PT symmetry and the corresponding
extension of Zamolodchikov's c-theorem, and also verified numerically using the
truncated conformal space approach. Our results are in agreement with a
previous numerical study of the lattice version of the Tricritical Ising Model
[1]. We also conjecture the classes of universality corresponding to higher
non-unitary multicritical points obtained by perturbing the conformal unitary
models with imaginary coupling magnetic fields.


  The effects on the spin state of an electron in a time independent electric
field are examined. The probability of spin flipping is calculated, and other
effects are studied using the minimally coupled Dirac equation.


  There is a quickly increasing wealth of experimental data on so-called dusty
plasmas i. e. ionized gases or usual plasmas that contain micron sized charged
particles. Interest in these structures is driven both by their importance in
many astrophysical as well as commercial situations. Among them are linear and
nonlinear wave phenomena. We consider the influence of dust charge fluctuations
on stability of the ion-acoustic waves when the stream of particles is present.
It is assumed that all grains of dust have equal masses but charges are not
constant in time-they may fluctuate in time. The dust charges are not really
independent of the variations of the plasma potentials. All modes will
influence the charging mechanism, and feedback will lead to several new
interesting and unexpected phenomena. The charging of the grains depends on
local plasma characteristics. If the waves disturb these characteristic, then
charging of the grains is affected and the grain charge is modified, with a
resulting feedback on the wave mode. In case considering here, when temperature
of electrons is much greater then the temperature of the ions and temperature
of electrons is not great enough for further ionization of the ions, we show
that stability of the acoustic wave depends only one phenomenological
coefficient.


  We give three new algorithms for efficient in-place estimation, without using
ancilla qubits, of average fidelity of a quantum logic gate acting on a
d-dimensional system using much fewer random bits than what was known so far.
Previous approaches for efficient estimation of average gate fidelity replaced
Haar random unitaries in the naive estimation algorithm by approximate unitary
2-designs, and sampled them uniformly and independently. In contrast, in our
first algorithm we sample the unitaries of the approximate unitary 2-design
uniformly using a limited independence pseudorandom generator, a powerful tool
from derandomisation theory. This algorithm uses the same number of basic
operations as previous efficient algorithms but much fewer number of random
bits. Reducing the requirement of classical random bits increases the
reliability of estimation as often, high quality random bits are an expensive
computational resource.
  Our second efficient algorithm, based on a 4-quantum tensor product expander,
works if the gate dimension d is large. It uses even lesser random bits than
the first algorithm, and has the added advantage that it needs to implement
only one unitary versus potentially all the unitaries of an approximate
2-design in the first algorithm.
  Our third efficient algorithm, based on an l-quantum tensor product expander
for moderately large values of l, works for all values of the parameters. It
uses slightly more random bits than the other algorithms but has the advantage
that it needs to implement only a small number of unitaries versus potentially
all the unitaries of an approximate 2-design in the first algorithm. This
advantage is of great importance to experimental implementations in the near
future.


  A geometrically exact dimensionally reduced order model for the nonlinear
deformation of thin magnetoelastic shells is presented. The Kirchhoff-Love
assumptions for the mechanical fields are generalised to the magnetic variables
to derive a consistent two-dimensional theory based on a rigorous variational
approach. The general deformation map, as opposed to the mid-surface
deformation, is considered as the primary variable resulting in a more accurate
description of the nonlinear deformation. The commonly used plane stress
assumption is discarded due to the Maxwell stress in the surrounding free-space
requiring careful treatment on the upper and lower shell surfaces. The
complexity arising from the boundary terms when deriving the Euler-Lagrange
governing equations is addressed via a unique application of Green's
theorem.The governing equations are solved analytically for the problem of an
infinite cylindrical magnetoelastic shell. This clearly demonstrates the
model's capabilities and provides a physical interpretation of the new
variables in the modified variational approach. This novel formulation for
magnetoelastic shells serves as a valuable tool for the accurate design of thin
magneto-mechanically coupled devices.


  The functional ANOVA expansion of a multivariate mapping plays a fundamental
role in statistics. The expansion is unique once a unique distribution is
assigned to the covariates. Recent investigations in the environmental and
climate sciences show that analysts may not be in a position to assign a unique
distribution in realistic applications. We offer a systematic investigation of
existence, uniqueness, orthogonality, monotonicity and ultramodularity of the
functional ANOVA expansion of a multivariate mapping when a multiplicity of
distributions is assigned to the covariates. In particular, we show that a
multivariate mapping can be associated with a core of probability measures that
guarantee uniqueness. We obtain new results for variance decomposition and
dimension distribution under mixtures. Implications for the global sensitivity
analysis of computer experiments are also discussed.


  We present analytic techniques for parametric integrations of massive
two-loop four-point Feynman integrals at high energies, and their
implementation in the toolbox AsyInt. In the high-energy region, the Feynman
integrals involving external and internal massive particles, such as the top
quark, Higgs and vector bosons, can be asymptotically expanded and directly
calculated in the small-mass limit. With this approach, analytic results for
higher orders in the expansion parameter and the dimensional regulator can be
obtained with AsyInt. These results are important ingredients for the two-loop
electroweak and QCD corrections for $2 \to 2$ scattering processes in the large
transverse momenta region, which is relevant to both precision collider
phenomenology and new physics searches at the LHC. In this paper, analytic
results of representative planar and non-planar Feynman integrals are
presented.


  The practice of luminosity levelling with an offset beam has been used as a
routine operation in the LHC since 2011. This paper will describe how it has
been implemented and what has been the operational experience with the system.


  We study the impact of rotation on the multimessenger signals of
core-collapse supernovae (CCSNe) with the occurrence of a first-order
hadron-quark phase transition (HQPT). We simulate CCSNe with the \texttt{FLASH}
code starting from a 20~$M_\odot$ progenitor with different rotation rates, and
using the RDF equation of state from \textit{Bastian} 2021 that prescribes the
HQPT. Rotation is found to delay the onset of the HQPT and the resulting
dynamical collapse of the protocompact star (PCS) due to the centrifugal
support. All models with the HQPT experience a second bounce shock which leads
to a successful explosion. The oblate PCS as deformed by rotation gives rise to
strong gravitational-wave (GW) emission around the second bounce with a peak
amplitude larger by a factor of $\sim10$ than that around the first bounce. The
breakout of the second bounce shock at the neutrinosphere produces a
$\bar{\nu}_e$-rich neutrino burst with a luminosity of serveral
10$^{53}$~erg~s$^{-1}$. In rapidly rotating models the PCS pulsation following
the second bounce generates oscillations in the neutrino signal after the
burst. In the fastest rotating model with the HQPT, a clear correlation is
found between the oscillations in the GW and neutrino signals immediately after
the second bounce. In addition, the HQPT-induced collapse leads to a jump in
the ratio of rotational kinetic energy to gravitational energy ($\beta$) of the
PCS, for which persistent GW emission may arise due to secular nonaxisymmetric
instabilities.


  We show that networks of topological nanowires can realize the physics of
exactly solvable Kitaev spin models with two-body interactions. This connection
arises from the description of the low-energy theory of both systems in terms
of a tight-binding model of Majorana modes. In Kitaev spin models the Majorana
description provides a convenient representation to solve the model, whereas in
an array of topological nanowires it arises, because the physical Majorana
modes localized at wire ends permit tunnelling between wire ends and across
different Josephson junctions. We explicitly show that an array of junctions of
three wires -- a setup relevant to topological quantum computing with nanowires
-- can realize the Yao-Kivelson model, a variant of Kitaev spin models on a
decorated honeycomb lattice. Translating the results from the latter, we show
that the network can be constructed to give rise to collective states
characterized by Chern numbers \nu = 0, +/-1 and +/-2, and that defects in an
array can be associated with vortex-like quasi-particle excitations. Finally,
we analyze the stability of the collective states as well as that of the
network as a quantum information processor. We show that decoherence inducing
instabilities, be them due to disorder or phase fluctuations, can be understood
in terms of proliferation of the vortex-like quasi-particles.


  We present a study of the spin-1/2 Heisenberg chain with alternating ferro-
and antiferromagnetic exchange, focusing on the role of the exchange couplings
to cover both, dimer and Haldane limit. Employing a complementary combination
of perturbation theory and quantum Monte Carlo simulation, we report results
for the magnetic susceptibility as well as the dynamic structure factor over a
wide range of coupling constants and for different temperatures to extract the
spin gap. For a small ferromagnetic coupling, we find good agreement between
perturbation theory and quantum Monte Carlo. For arbitrary exchange couplings
we show that the dynamic structure factor, obtained from quantum Monte Carlo,
scales between triplons and a Haldane chain spectrum. Finally, we contrast our
findings for the spin gap versus the exchange couplings against existing
literature.


  Amplification was regarded, since the early days of quantum theory, as a
mysterious ingredient that endows quantum microstates with macroscopic
consequences, key to the "collapse of the wavepacket", and a way to avoid
embarrassing problems exemplified by Schr\"odinger's cat. Such a bridge between
the quantum microworld and the classical world of our experience was postulated
ad hoc in the Copenhagen Interpretation. Quantum Darwinism views amplification
as replication, in many copies, of the information about quantum states. We
show that such amplification is a natural consequence of a broad class of
models of decoherence, including the photon environment we use to obtain most
of our information. This leads to objective reality via the presence of robust
and widely accessible records of selected quantum states. The resulting
redundancy (the number of copies deposited in the environment) follows from the
Quantum Chernoff Information that quantifies the information transmitted by a
typical elementary subsystem of the environment.


  The Fast Bunch Integrator is a bunch intensity monitor designed around the
measurements made from Resistive Wall Current Monitors. During the Run II
period these were used in both Tevatron and Main Injector for single and
multiple bunch intensity measurements. This paper presents an overview of the
design and use of these systems during this period.


  For a $p$-group of order $p^n$, it is known that the order of $2$-nilpotent
multiplier is equal to $|\mathcal{M}^{(2)}(G)|=p^{\f12n(n-1)(n-2)+3-s_2(G)}$
for an integer $s_2(G)$. In this article, we characterize all of non abelian
$p$-groups satisfying in $s_2(G)\in\{1,2,3\}.


  Loop quantum gravity inspired partial polymer quantization in
four-dimensional spacetime leads to a globally regular black hole with a single
horizon. The polymerized black hole metric is characterized by the minimum
length parameter $k$, and mimics the Schwarzschild black hole in the weak-field
limit. We present an analytic and numerical investigation of the strong
gravitational lensing and shadow morphology to determine the observational
impacts of quantum effects. Interestingly, the light deflection angle, the
angular separation between the outermost relativistic image, and magnification
are significantly larger than those for the Schwarzschild black hole. Using the
ray-tracing technique, we simulate the black hole shadows under three distinct
optically thin accretion models: static spherical accretion, radially infalling
spherical accretion, and the thin accretion disk model. Polymerized black
holes' shadow morphology strongly depends on $k$. We derive constraints on $k$
from the M87* and Sgr A* black hole shadow observations from the Event Horizon
Telescope.


  We discuss the response of an rf-SQUID formed by anomalous Josephson
junctions embedded in a superconducting ring with a non-negligible inductance.
We demonstrate that a properly sweeping in-plane magnetic field can cause both
the total flux and the current circulating in the device to modulate and to
behave hysteretically. The bistable response of the system is analyzed as a
function of the anomalous phase shift at different values of the screening
parameter, in order to highlight the parameter range within which a hysteretic
behavior can be observed. The magnetic flux piercing the SQUID ring is
demonstrated to further modulate the hysteretical response of the system.
Moreover, we show that the anomalous phase shift can be conveniently determined
through the measurement of the out-of-plane magnetic field at which the device
switches to the voltage state and the number of trapped flux quanta changes.
Finally, we compare the response of two different device configurations,
namely, a SQUID including only one or two anomalous junctions. In view of these
results, the proposed device can be effectively used to detect and measure the
anomalous Josephson effect.


  We give an explicit component Lagrangian construction of massive higher spin
on-shell $N=1$ supermultiplets in four-dimensional Anti-de Sitter space
$AdS_4$. We use a frame-like gauge invariant description of massive higher spin
bosonic and fermionic fields. For the two types of the supermultiplets (with
integer and half-integer superspins) each one containing two massive bosonic
and two massive fermionic fields we derive the supertransformations leaving the
sum of four their free Lagrangians invariant such that the algebra of these
supertransformations is closed on-shell.


  Transistors are the fundamental building block of modern electronic devices.
So far, all transistors are based on various types of semiconductor junctions.
The most common bipolar-junction transistors and metal-oxide-semiconductor
field-effect transistors contain p-n junctions to control the current,
depending on applied biases across the junctions. Thin-film transistors need
metal-semiconductor junctions for injecting and extracting electrons from their
channels. Here, by coating a heavily-doped thin indium-tin-oxide (ITO) film
through a shadow mask onto a biopolymer chitosan/ITO/glass substrate, we can
have a high-performance junctionless transparent organic-inorganic hybrid thin
film transistor. This could be the simplest transistor in the world, to our
knowledge, not only in its structure, but also its fabrication process. In
addition, the device performance is found to be greatly enhanced using a
reinforced chitosan/SiO2 hybrid bilayer dielectric stack. Our results clearly
show that this architecture can lead to a new class of low-cost transistors.


  Recent measurements by the NA48 at CERN of selected $K_L$ decays are
presented. These are the branching ratios and form factors for channels $K_L\to
\pi^{\pm}\pi^0\e^{\mp}\nu_e$ (final result), $K_L\to\pi^{\pm}e^{\mp}\nu_e$ and
$K_L\to e^+e^-e^+e^-$ (preliminary results).


  In this lecture we introduce from basic principles the main concepts of beam
focusing and transport in modern accelerators using the beam envelope
equationas a convenient mathematical tool. Matching conditions suitable for
preserving beam quality are derived from the model for significant beam
dynamics regimes. An extension of the model to the case of plasma accelerators
is introduced. The understanding of similarities and differences with respect
to traditionalaccelerators is also emphasized.


  Task-based distributed frameworks (e.g., Ray, Dask, Hydro) have become
increasingly popular for distributed applications that contain asynchronous and
dynamic workloads, including asynchronous gradient descent, reinforcement
learning, and model serving. As more data-intensive applications move to run on
top of task-based systems, collective communication efficiency has become an
important problem. Unfortunately, traditional collective communication
libraries (e.g., MPI, Horovod, NCCL) are an ill fit, because they require the
communication schedule to be known before runtime and they do not provide fault
tolerance.
  We design and implement Hoplite, an efficient and fault-tolerant collective
communication layer for task-based distributed systems. Our key technique is to
compute data transfer schedules on the fly and execute the schedules
efficiently through fine-grained pipelining. At the same time, when a task
fails, the data transfer schedule adapts quickly to allow other tasks to keep
making progress. We apply Hoplite to a popular task-based distributed
framework, Ray. We show that Hoplite speeds up asynchronous stochastic gradient
descent, reinforcement learning, and serving an ensemble of machine learning
models that are difficult to execute efficiently with traditional collective
communication by up to 7.8x, 3.9x, and 3.3x, respectively.


  Networks are ubiquitous in biology where they encode connectivity patterns at
all scales of organization, from molecular to the biome. However, biological
networks are noisy due to the limitations of measurement technology and
inherent natural variation, which can hamper discovery of network patterns and
dynamics. We propose Network Enhancement (NE), a method for improving the
signal-to-noise ratio of undirected, weighted networks. NE uses a doubly
stochastic matrix operator that induces sparsity and provides a closed-form
solution that increases spectral eigengap of the input network. As a result, NE
removes weak edges, enhances real connections, and leads to better downstream
performance. Experiments show that NE improves gene function prediction by
denoising tissue-specific interaction networks, alleviates interpretation of
noisy Hi-C contact maps from the human genome, and boosts fine-grained
identification accuracy of species. Our results indicate that NE is widely
applicable for denoising biological networks.


  We point out the high physical correctness of the use and the concept of the
crystal-field approach, even if is used to metallic magnetic materials of
transition-metal 3d/4f/5f compounds. We discuss the place of the crystal-field
theory in modern solid-state physics and we point out the necessity to consider
the crystal-field approach with the spin-orbit coupling and strong electron
correlations, as a contrast to the single-electron version of the crystal field
customarily used for 3d electrons. We have extended the strongly-correlated
crystal-field theory to a Quantum Atomistic Solid-State Theory (QUASST) to
account for the translational symmetry and inter-site spin-dependent
interactions indispensable for formation of magnetically-ordered state. We have
correlated macroscopic magnetic and electronic properties with the atomic-scale
electronic structure for ErNi5, UPd2Al3, FeBr2, LaCoO3 and LaMnO3. In QUASST we
have made unification of 3d and rare-earth compounds in description of the
low-energy electronic structures and magnetism of open 3d-/4f-/5f-shell
electrons. QUASST offers consistent description of zero-temperature properties
and thermodynamic properties of 4f-/5f-/3d-atom containing compounds. Our
studies indicate that it is the highest time to unquench the orbital magnetism
in 3d oxides.


  We revisit the problem of extraordinary transmission of acoustic
(electromagnetic) waves through a slit in a rigid (perfectly conducting) wall.
We use matched asymptotic expansions to study the pertinent limit where the
slit width is small compared to the wall thickness, the latter being
commensurate with the wavelength. Our analysis focuses on near-resonance
frequencies, furnishing elementary formulae for the field enhancement,
transmission efficiency, and deviations of the resonances from the Fabry-Perot
frequencies of the slit. We find that the apertures' near fields play a
dominant role, in contrast with the prevalent approximate theory of Takakura
[Physical Review Letters, 86 5601 (2001)]. Our theory agrees remarkably well
with numerical solutions and electromagnetic experiments [Suckling et al.,
Physical Review Letters, 92 147401 (2004)], thus providing a paradigm for
analyzing a wide range of wave propagation problems involving small holes and
slits.


  The chiral magnetic effect (CME) is a novel transport phenomenon, arising
from the interplay between quantum anomalies and strong magnetic fields in
chiral systems. In high-energy nuclear collisions, the CME may survive the
expansion of the quark-gluon plasma fireball and be detected in experiments.
Over the past decade, the experimental searches for the CME have aroused
extensive interest at the Relativistic Heavy Ion Collider (RHIC) and the Large
Hadron Collider (LHC). The main goal of this article is to investigate three
pertinent experimental approaches: the $\gamma$ correlator, the $R$ correlator
and the signed balance functions. We will exploit both simple Monte Carlo
simulations and a realistic event generator (EBE-AVFD) to verify the
equivalence in the kernel-component observables among these methods and to
ascertain their sensitivities to the CME signal for the isobaric collisions at
RHIC.


  We provide a lower bound on the expected discovery time of one-way neighbor
discovery in multi antenna system. We assume that the scheme allows to use
different directional transmission probabilities, which result in different
probability of successful discovery between nodes. The proof shows that the
lower bound to the expected discovery time, that node $i$ takes to discover its
neighbors, is given by the reciprocal of the average probabilities of
successful discovery.


  In the current era of noisy intermediate-scale quantum (NISQ) devices,
research in the theory of open system dynamics has a crucial role to play. In
particular, understanding and quantifying memory effects in quantum systems is
critical to gain a better handle on the effects of noise in quantum devices.
The main focus of this review is to address the fundamental question of
defining and characterizing such memory effects -- broadly referred to as
quantum non-Markovianity -- from various approaches. We first discuss the
two-time-parameter maps approach to open system dynamics and review the various
notions of quantum non-Markovianity that arise in this paradigm. We then
discuss an alternate approach to quantum stochastic processes based on the
quantum combs framework, which accounts for multi-time correlations. We discuss
the interconnections and differences between these two paradigms, and conclude
with a discussion on necessary and sufficient conditions for quantum
non-Markovianity.


  We introduce a proper multi-type display calculus for bilattice logic (with
conflation) for which we prove soundness, completeness, conservativity,
standard subformula property and cut-elimination. Our proposal builds on the
product representation of bilattices and applies the guidelines of the
multi-type methodology in the design of display calculi.


  We derive exact expressions for so-called ``void'' bounds on the trapping
constant $\gamma$ and fluid permeability $k$ for coated-spheres and
coated-cylinders models of porous media. We find that in some cases the bounds
are optimal, i.e., the void bounds coincide with the corresponding exact
solutions of $\gamma$ and $k$ for these coated-inclusions models. In these
instances, exact expressions are obtained for the relevant length scale that
arises in the void bounds, which depends on a two-point correlation function
that characterizes the porous medium. In contrast to bounds on the effective
conductivity and elastic moduli of composite media, this is the first time that
model microstructures have been found that exactly realize bounds on either the
trapping constant or fluid permeability.


  Human Activity Recognition (HAR) plays a crucial role in various applications
such as human-computer interaction and healthcare monitoring. However,
challenges persist in HAR models due to the data distribution differences
between training and real-world data distributions, particularly evident in
cross-user scenarios. This paper introduces a novel framework, termed
Diffusion-based Noise-centered Adversarial Learning Domain Adaptation
(Diff-Noise-Adv-DA), designed to address these challenges by leveraging
generative diffusion modeling and adversarial learning techniques. Traditional
HAR models often struggle with the diversity of user behaviors and sensor data
distributions. Diff-Noise-Adv-DA innovatively integrates the inherent noise
within diffusion models, harnessing its latent information to enhance domain
adaptation. Specifically, the framework transforms noise into a critical
carrier of activity and domain class information, facilitating robust
classification across different user domains. Experimental evaluations
demonstrate the effectiveness of Diff-Noise-Adv-DA in improving HAR model
performance across different users, surpassing traditional domain adaptation
methods. The framework not only mitigates distribution mismatches but also
enhances data quality through noise-based denoising techniques.


  Quark-hadron duality is a key concept in QCD, allowing for the description of
physical hadronic observables in terms of quark-gluon degrees of freedom. The
modern theoretical framework for its implementation is Wilson's operator
product expansion (OPE), supplemented by analytic extrapolation from large
Euclidean momenta, where the OPE is defined, to the Minkowski axis, where
observable quantities are defined. Recently, the importance of additional terms
in the expansion of QCD correlators near the Minkowski axis, responsible for
quark-hadron duality violations (DVs), was emphasized. In this paper we
introduce a mathematical tool that might be useful for the study of DVs in QCD.
It is based on finding the minimal distance, measured in the $L^\infty$ norm
along a contour in the complex momentum plane, between a class of admissible
functions containing the physical amplitude and the asymptotic expansion
predicted by the OPE. This minimal distance is given by the norm of a Hankel
matrix that can be calculated exactly, using as input the experimental spectral
function on a finite interval of the timelike axis. We also comment on the
relation between the new functional tool and the more commonly used
$\chi^2$-based analysis. The approach is illustrated on a toy model for the QCD
polarization function recently proposed in the literature.


  Let $P$ be a unital subsemigroup of a group $G$. We propose an approach to
$\mathrm{C}^*$-algebras associated to product systems over $P$. We call the
$\mathrm{C}^*$-algebra of a given product system $\mathcal{E}$ its covariance
algebra and denote it by $A\times_{\mathcal{E}}P$, where $A$ is the coefficient
$\mathrm{C}^*$-algebra. We prove that our construction does not depend on the
embedding $P\hookrightarrow G$ and that a representation of
$A\times_{\mathcal{E}}P$ is faithful on the fixed-point algebra for the
canonical coaction of $G$ if and only if it is faithful on $A$. We compare this
with other constructions in the setting of irreversible dynamical systems, such
as Cuntz--Nica--Pimsner algebras, Fowler's Cuntz--Pimsner algebra, semigroup
$\mathrm{C}^*$-algebras of Xin Li and Exel's crossed products by interaction
groups.


  From personal experience, I report about the development of sheaf
representations for algebraic structures between the years 1966 and 1976.
Starting with rings, lattice-ordered groups and rings it turns to general
algebraic structures.


  We construct an infinite family of hyperbolic, homologically thin knots that
are not quasi-alternating. To establish the latter, we argue that the branched
double-cover of each knot in the family does not bound a negative definite
4-manifold with trivial first homology and bounded second betti number. This
fact depends in turn on information from the correction terms in Heegaard Floer
homology, which we establish by way of a relationship to, and calculation of,
the Turaev torsion.


  Given a generalized $e$-block $B$ of a symmetric group and an $e$-regular
conjugacy class $C$, we study the number of irreducible characters in $B$ which
do not vanish on $C$ and find lower bounds for it.


  Transport properties of molecular junctions are notoriously expensive to
calculate with ab initio methods, primarily due to the semi-infinite
electrodes. This has led to the introduction of different approximation schemes
for the electrodes. For the most popular metals used in experiments, such as
gold, the wide-band limit (WBL) is a particularly efficient choice. In this
paper we investigate the performance of different WBL schemes relative to more
sophisticated approaches including the fully self-consistent non-equilibrium
Green's function (NEGF) method. We find reasonably good agreement between all
schemes for systems in which the molecule (and not the metal-molecule
interface) dominates the transport properties. Moreover, our implementation of
the WBL requires negligible computational effort compared to the ground state
DFT calculation of a molecular junction. We also present a new approximate but
efficient scheme for calculating transport with a finite bias. Provided the
voltage drop occurs primarily inside the molecule, this method provides results
in reasonable agreement with fully self-consistent calculations.


  By applying a slow curing process, we show that biomolecules can be
incorporated via a simple process as liquid stable phases inside a
polydimethylsiloxane (PDMS) matrix. The process is carried out under mild
conditions with regards to temperature, pH and relative humidity, and is thus
suitable for application to biological entities. Fluorescence and enzymatic
activity measurements, show that the biochemical properties of the proteins and
enzyme tested are preserved, without loss due to adsorption at the
liquid-polymer interface. Protected from external stimuli by the PDMS matrix,
these soft liquid composite materials are new tools of interest for robotics,
microfluidics, diagnostics and chemical microreactors.


  The cosmic first order phase transition from quarks to hadrons, occurring a
few microseconds after the Big Bang, would lead to the formation of quark
nuggets which would be stable on a cosmological time scale, if the associated
baryon number is larger than a critical value. We examine the possibility that
these surviving quark nuggets may not only be viable candidates for cold dark
matter but even close the universe.


  [Devito] is an open-source Python project based on domain-specific language
and compiler technology. Driven by the requirements of rapid HPC applications
development in exploration seismology, the language and compiler have evolved
significantly since inception. Sophisticated boundary conditions, tensor
contractions, sparse operations and features such as staggered grids and
sub-domains are all supported; operators of essentially arbitrary complexity
can be generated. To accommodate this flexibility whilst ensuring performance,
data dependency analysis is utilized to schedule loops and detect
computational-properties such as parallelism. In this article, the generation
and simulation of MPI-parallel propagators (along with their adjoints) for the
pseudo-acoustic wave-equation in tilted transverse isotropic media and the
elastic wave-equation are presented. Simulations are carried out on industry
scale synthetic models in a HPC Cloud system and reach a performance of
28TFLOP/s, hence demonstrating Devito's suitability for production-grade
seismic inversion problems.


  We consider Baxter Q-operators for various versions of quantum affine Toda
chain. The interpretation of eigenvalues of the finite Toda chain Baxter
operators as local Archimedean L-functions proposed recently is generalized to
the case of affine Lie algebras. We also introduce a simple generalization of
Baxter operators and local L-functions compatible with this identification.
This gives a connection of the Toda chain Baxter Q-operators with an
Archimedean version of the Polya-Hilbert operator proposed by Berry-Kitting. We
also elucidate the Dorey-Tateo spectral interpretation of eigenvalues of
Q-operators. Using explicit expressions for eigenfunctions of
affine/relativistic Toda chain we obtain an Archimedean analog of
Casselman-Shalika-Shintani formula for Whittaker function in terms of
characters.


  An accurate and systematic equation of state for the hard-core one-component
plasma (HCOCP) is obtained. The result is based on the Hubbard-Schofield
transformation which yields the field-theoretical Hamiltonian, with
coefficients expressed in terms of equilibrium correlation functions of the
reference hard-core fluid. Explicit calculations were performed using the
Gaussian approximation for the effective Hamiltonian and known thermodynamic
and structural properties of the reference hard-core fluid. For small values of
the plasma parameter G and packing fraction the Debye-Huckel result is
recovered, while for G>>1, the excess free energy F_ex and internal U_{ex}
energy depend linearly on G. The obtained expression for U_ex is in a good
agreement with the available Monte Carlo data for the HCOCP. We also analyse
the validity of the widely used approximation, which represents the free energy
as a sum of the hard-core and electrostatic part.


  We present a robust theoretical framework for the characterisation and
manipulation of optical flow, i.e 2D vector fields, in the context of their use
in motion estimation algorithms and beyond. The definition of two frames of
reference guides the mathematical derivation of flow field application,
inversion, evaluation, and composition operations. This structured approach is
then used as the foundation for an implementation in Python 3, with the fully
differentiable PyTorch version oflibpytorch supporting back-propagation as
required for deep learning. We verify the flow composition method empirically
and provide a working example for its application to optical flow ground truth
in synthetic training data creation. All code is publicly available.


  For any fixed coprime positive integers $a,b$ and $c$ with $\min\{a,b,c\}>1$,
we prove that the equation $a^x+b^y=c^z$ has at most two solutions in positive
integers $x,y$ and $z$, except for one specific case which exactly gives three
solutions. Our result is essentially sharp in the sense that there are
infinitely many examples allowing the equation to have two solutions in
positive integers. From the viewpoint of a well-known generalization of
Fermat's equation, it is also regarded as a 3-variable generalization of the
celebrated theorem of Bennett [M.A.Bennett, On some exponential equations of
S.S.Pillai, Canad. J. Math. 53(2001), no.2, 897--922] which asserts that
Pillai's type equation $a^x-b^y=c$ has at most two solutions in positive
integers $x$ and $y$ for any fixed positive integers $a,b$ and $c$ with
$\min\{a,b\}>1$.


  The theory of moduli of morphisms on P^n generalizes the study of rational
maps on P^1. This paper proves three results about the space of morphisms on
P^n of degree d > 1, and its quotient by the conjugation action of PGL(n+1).
First, we prove that this quotient is geometric, and compute the stable and
semistable completions of the space of morphisms. This strengthens previous
results of Silverman, as well as of Petsche, Szpiro, and Tepper. Second, we
bound the size of the stabilizer group in PGL(n+1) of every morphism in terms
of only n and d. Third, we specialize to the case where n = 1, and show that
the quotient space is rational for all d > 1; this partly generalizes a result
of Silverman about the case d = 2.


  We show that the search for supersymmetry at LHC will be very problematic for
the particular case of nonuniversal relations among gaugino masses. Namely, if
gluino, first chargino and LSP masses are closed to each other it would be very
difficult to discover supersymmetry even if sparticle masses are lighter than 1
TeV.


  Generalized susceptibilities of the net quark number have been proposed to be
good probes for the transitions in the QCD phase diagram and for the search of
a possible critical end point. In this article we explore a new strategy for
computing quark number susceptibilities from lattice QCD via an expansion in
the fugacity parameter $e^{\mu\beta}$. All quark number related bulk
observables are particularly easy to access in this approach and we present
results for generalized quark number susceptibilities up to 4-th order. Ratios
of these quantities are studied and compared with model calculations for the
high- and low temperature regions up to a chemical potential of
$\mu\beta\approx1.0$.


  Let $G$ be a reductive complex Lie group acting holomorphically on normal
Stein spaces $X$ and $Y$, which are locally $G$-biholomorphic over a common
categorical quotient $Q$. When is there a global $G$-biholomorphism $X\to Y$?
  If the actions of $G$ on $X$ and $Y$ are what we, with justification, call
generic, we prove that the obstruction to solving this local-to-global problem
is topological and provide sufficient conditions for it to vanish. Our main
tool is the equivariant version of Grauert's Oka principle due to Heinzner and
Kutzschebauch.
  We prove that $X$ and $Y$ are $G$-biholomorphic if $X$ is $K$-contractible,
where $K$ is a maximal compact subgroup of $G$, or if $X$ and $Y$ are smooth
and there is a $G$-diffeomorphism $\psi:X\to Y$ over $Q$, which is holomorphic
when restricted to each fibre of the quotient map $X\to Q$. We prove a similar
theorem when $\psi$ is only a $G$-homeomorphism, but with an assumption about
its action on $G$-finite functions. When $G$ is abelian, we obtain stronger
theorems. Our results can be interpreted as instances of the Oka principle for
sections of the sheaf of $G$-biholomorphisms from $X$ to $Y$ over $Q$. This
sheaf can be badly singular, even for a low-dimensional representation of
$\mathrm{SL}_2(\C)$.
  Our work is in part motivated by the linearisation problem for actions on
$\C^n$. It follows from one of our main results that a holomorphic $G$-action
on $\C^n$, which is locally $G$-biholomorphic over a common quotient to a
generic linear action, is linearisable.