  In this paper, we prove a Hardy--Moser--Trudinger inequality in the unit ball
$\mathbb B^n$ in $\mathbb R^n$ which improves both the classical singular
Moser--Trudinger inequality and the classical Hardy inequality at the same
time. More precisely, we show that for any $\beta \in [0,n)$ there exists a
constant $C>0$ depending only on $n$ and $\beta$ such that \[ \sup_{u\in
W^{1,n}_0(\mathbb B^n), \mathcal H(u) \leq 1}\int_{\mathbb B^n}
e^{(1-\frac\beta n)\alpha_n |u|^{\frac n{n-1}}} |x|^{-\beta} dx \leq C \] where
$\alpha_n = n \omega_{n-1}^{\frac1{n-1}}$ with $\omega_{n-1}$ being the surface
area of the unit sphere $S^{n-1} = \partial \mathbb B^n$, and \[ \mathcal H(u)
= \int_{\mathbb B^n} |\nabla u|^n dx -\left(\frac{2(n-1)}n\right)^n
\int_{\mathbb B^n} \frac{|u|^n}{(1-|x|^2)^n} dx. \] This extends an inequality
of Wang and Ye in dimension two to higher dimensions and to the singular case
as well. The proof is based on the method of transplantation of Green's
functions and without using the blow-up analysis method. As a consequence, we
obtain a singular Moser--Trudinger inequality in the hyperbolic spaces which
confirms affirmatively a conjecture by Mancini, Sandeep and Tintarev
\cite[Conjecture $5.2$]{MST}. We also propose an inequality which extends the
singular Hardy--Moser--Trudinger inequality to any bounded convex domain in
$\mathbb R^n$ which is analogue of the conjecture of Wang and Ye in higher
dimensions.


  We describe bases for the morphism spaces of the Frobenius Heisenberg
categories associated to a symmetric graded Frobenius algebra, proving several
open conjectures. Our proof uses a categorical comultiplication and generalized
cyclotomic quotients of the category. We use our basis theorem to prove that
the Grothendieck ring of the Karoubi envelope of the Frobenius Heisenberg
category recovers the lattice Heisenberg algebra associated to the Frobenius
algebra.


  A 2+1 dimensional fermion field theory is proposed as a model for the
low-energy electronic excitations in monolayer graphene. The model consists of
N=2 four-component Dirac fermions moving in the plane and interacting via a
contact interaction between charge densities. For strong couplings there is a
continuous transition to a Mott insulting phase. We present results of an
extensive numerical study of the model's critical region, including the order
parameter, its associated susceptibility, and for the first time the
quasiparticle propagator. The data enables an extraction of the critical
exponents at the transition, including the dynamical critical exponent, which
are hypothesised to be universal features of a quantum critical point. The
relation of our model with others in the literature is discussed, along with
the implications for physical graphene following from our value of the critical
coupling.


  For semilinear stochastic evolution equations whose coefficients are more
general than the classical global Lipschitz, we present results on the strong
convergence rates of numerical discretizations. The proof of them provides a
new approach to strong convergence analysis of numerical discretizations for a
large family of second order parabolic stochastic partial differential
equations driven by space-time white noises. We apply these results to the
stochastic advection-diffusion-reaction equation with a gradient term and
multiplicative white noise, and show that the strong convergence rate of a
fully discrete scheme constructed by spectral Galerkin approximation and
explicit exponential integrator is exactly $\frac12$ in space and $\frac14$ in
time. Compared with the optimal regularity of the mild solution, it indicates
that the spetral Galerkin approximation is superconvergent and the convergence
rate of the exponential integrator is optimal. Numerical experiments support
our theoretical analysis.


  We introduce a novel method for identifying the modular structures of a
network based on the maximization of an objective function: the ratio
association. This cost function arises when the communities detection problem
is described in the probabilistic autoencoder frame. An analogy with kernel
k-means methods allows to develop an efficient optimization algorithm, based on
the deterministic annealing scheme. The performance of the proposed method is
shown on a real data set and on simulated networks.


  We propose a method to enhance lysozyme trapping and supported-Copper
catalysis when confined in organosilica materials. The direct synthesis
presented here allows the control of the silica surface hydrophobicity by
uniform introduction of methyl or phenyl groups. As a result, the lysozyme
trapping is observed to be 3.2 times more efficient with the
phenyl-functionalized material than MCM-41. For heterogeneous catalysis, Copper
was immobilized on the new organosilica surface. In this case, the presence of
methyl groups significantly enhanced the product yield for the catalyzed
synthesis of a triazole derivative. This method opens a new route of synthesis
where the material properties can be adjusted and dedicated to a specific
application.


  Abstract reasoning, i.e., inferring complicated patterns from given
observations, is a central building block of artificial general intelligence.
While humans find the answer by either eliminating wrong candidates or first
constructing the answer, prior deep neural network (DNN)-based methods focus on
the former discriminative approach. This paper aims to design a framework for
the latter approach and bridge the gap between artificial and human
intelligence. To this end, we propose logic-guided generation (LoGe), a novel
generative DNN framework that reduces abstract reasoning as an optimization
problem in propositional logic. LoGe is composed of three steps: extract
propositional variables from images, reason the answer variables with a logic
layer, and reconstruct the answer image from the variables. We demonstrate that
LoGe outperforms the black box DNN frameworks for generative abstract reasoning
under the RAVEN benchmark, i.e., reconstructing answers based on capturing
correct rules of various attributes from observations.


  The nonlinear magneto-optical Kerr-effect (NOLIMOKE) is determined for
freestanding Fe monolayers with several in-plane structures from first
principles. Based on the theory of nonlinear magneto-optics by H\"ubner and
Bennemann [Phys. Rev. B, {\bf 40}, 5973 (1989)] we calculate the nonlinear
susceptibilities of the monolayers using the ab initio FLAPW-method WIEN95 with
the additional implementation of spin-orbit coupling and the calculation of the
dipole transition matrix elements appropriate for freestanding monolayers. We
present results for the spectral dependence of the nonlinear susceptibility
tensor elements and the resulting intensities and Kerr angles. Special
emphasize is put on the effects of structural changes such as the variation of
the lattice constant and different surface orientations. The influence of
spin-orbit coupling on the tensor elements for different magnetization
directions is presented as well as the azimuthal dependence of the intensities
generated by several low index surfaces, showing the pronounced sensitivity of
second harmonic generation to lateral structural changes as well as magnetic
properties even in the monolayer range.


  We consider the influence of Faraday rotation in chaotic magnetic field on
the intensity and linear polarization of multiple scattered radiation.
  All fluctuations are assumed as Gaussian type and isotropic. The values of
magnetic field are less than $10^5$Gauss. In this case the parameter $
\omega_B/\omega=(eB/m_ec)/\omega\simeq 0.93\cdot
10^{-8}\lambda$($\mu$m)$B($G$)$ is small and the radiation scatterings are the
usual scatterings on free electrons. Only the Faraday rotation influences on
the intensity and polarization of radiation. We consider the Milne problem in
the electron magnetized atmosphere without the mean magnetic field. We found
that chaotic magnetic field does not increase the number of H-functions,
describing the Milne problem. There are four H-functions as in the Milne
problem for non-magnetized case. The calculations demonstrate that the
polarization of outgoing radiation diminishes strongly with the increasing of
the level of magnetic fluctuations. The calculations can be used for
estimations of inclination angle $i$ of accretion discs and the level of
magnetic fluctuations.


  For distributed sensor/relay networks, high reliability and power efficiency
are often required. However, several implementation issues arise in practice.
One such problem is that all the distributed transmitters have limited power
supply since the power source of the transmitters cannot be recharged
continually. To resolve this, distributed beamforming has been proposed as a
viable solution where all distributed transmitters seek to align in phase at
the receiver end. However, it is difficult to implement such transmit
beamforming in a distributed fashion in practice since perfect channel state
information (CSI) need to be made available at all distributed transmitters,
requiring tremendous overhead to feed back CSI from the receiver to all
distributed transmitters.
  In this paper, we propose a novel algorithm that belongs to the category of
deterministic phase adjustment algorithm: the Deterministic Differential Search
Algorithm (DDSA), where the differences between the measured received signal
strength (RSS) are utilized judiciously to help us predict the deterministic
phase adjustment done at distributed transmitters. Numerical simulations
demonstrate rapid convergence to a pre-determined threshold.


  This review article discusses limit distributions and variance bounds for
particle current in several dynamical stochastic systems of particles on the
one-dimensional integer lattice: independent particles, independent particles
in a random environment, the random average process, the asymmetric simple
exclusion process, and a class of totally asymmetric zero range processes. The
first three models possess linear macroscopic flux functions and lie in the
Edwards-Wilkinson universality class with scaling exponent 1/4 for current
fluctuations. For these we prove Gaussian limits for the current process. The
latter two systems belong to the Kardar-Parisi-Zhang class. For these we prove
the scaling exponent 1/3 in the form of upper and lower variance bounds.


  It has been a longstanding problem whether every amenable operator algebra is
isomorphic to a (necessarily nuclear) C*-algebra. In this note, we give a
nonseparable counterexample. The existence of a separable counterexample
remains an open problem. We also initiate a general study of unitarizability of
representations of amenable groups in C*-algebras and show that our method
cannot produce a separable counterexample.


  A simple and convenient procedure for single-shot, single-spot ablation
threshold measurement has been developed. It is based on the employment of
cylindrical lens to obtain elliptical Gaussian laser spot. The ablated spot
chords which are parallel to the minor axis were measured across the spot major
axis which is proportional to the fluence cross-section thus providing wide
range dependence of damaged spot size versus fluence in one spot measurement.
For both conventional and new-developed procedures the ablation threshold for
typical Nd:YAG laser parameters (1064 nm, 10 ns) has been measured as 50 mJ/cm2
which is one order of magnitude lower than that for a bulk graphite.


  We reformulate the agent-based opinion dynamics models of Weisbuch-Deffuant
and Hegselmann-Krause as interactive Markov chains. So we switch the scope from
a finite number of n agents to a finite number of n opinion classes. Thus, we
will look at an infinite population distributed to opinion classes instead of
agents with real number opinions. The interactive Markov chains show similar
dynamical behavior as the agent-based models: stabilization and clustering. Our
framework leads to a discrete bifurcation diagram for each model which gives a
good view on the driving forces and the attractive states of the system. The
analysis shows that the emergence of minor clusters in the Weisbuch-Deffuant
model and of meta-stable states with very slow convergence to consensus in the
Hegselmann Krause model are intrinsic to the dynamical behavior.


  We present a version of GMI (Gomory mixed-integer) cuts in a way so that they
are derived with respect to a "dual form" mixed-integer optimization problem
and applied on the standard-form primal side as columns, using the primal
simplex algorithm. This follows the general scheme of He and Lee, who did the
case of Gomory pure-integer cuts.
  Our input mixed-integer problem is not in standard form, and so our cuts are
derived rather differently from how they are normally derived. A convenient way
to develop GMI cuts is from MIR (mixed-integer rounding) cuts, which are
developed from 2-dimensional BMI (basic mixed integer) cuts, which involve a
nonnegative continuous variable and an integer variable. The nonnegativity of
the continuous variable is not the right tool for us, as our starting point
(the "dual form" mixed-integer optimization problem) has no nonnegativity. So
we work out a different 2-dimensional starting point, a pair of somewhat
arbitrary inequalities in one continuous and one integer variable. In the end,
we follow the approach of He and Lee, getting now a finitely converging
primal-simplex column-generation algorithm for mixed-integer optimization
problems.


  The poorly-ionized interior of the protoplanetary disk is the location where
dust coagulation processes may be most efficient. However even here,
planetesimal formation may be limited by the loss of solid material through
radial drift, and by collisional fragmentation of the particles. Our aim is to
investigate the possibility that solid particles are trapped at local pressure
maxima in the dynamically evolving disk. We perform the first 3-D global
non-ideal MHD calculations of the disk treating the turbulence driven by the
magneto-rotational instability. The domain contains an inner MRI-active region
near the young star and an outer midplane dead zone, with the transition
between the two modeled by a sharp increase in the magnetic diffusivity. The
azimuthal magnetic fields generated in the active zone oscillate over time,
changing sign about every 150 years. We thus observe the radial structure of
the `butterfly pattern' seen previously in local shearing-box simulations. The
mean magnetic field diffuses from the active zone into the dead zone, where the
Reynolds stress nevertheless dominates. The greater total accretion stress in
the active zone leads to a net reduction in the surface density, so that after
800 years an approximate steady state is reached in which a local radial
maximum in the midplane pressure lies near the transition radius. We also
observe the formation of density ridges within the active zone. The dead zone
in our models possesses a mean magnetic field, significant Reynolds stresses
and a steady local pressure maximum at the inner edge, where the outward
migration of planetary embryos and the efficient trapping of solid material are
possible.


  Convexity and convex functions play an important role in theoretical physics.
To initiate a study of the possible uses of convex functions in General
Relativity, we discuss the consequences of a spacetime $(M,g_{\mu \nu})$ or an
initial data set $(\Sigma, h_{ij}, K_{ij})$ admitting a suitably defined convex
function. We show how the existence of a convex function on a spacetime places
restrictions on the properties of the spacetime geometry.


  We propose a low cost and effective way to combine a free simulation software
and free CAD models for modeling human-object interaction in order to improve
human & object segmentation. It is intended for research scenarios related to
safe human-robot collaboration (SHRC) and interaction (SHRI) in the industrial
domain. The task of human and object modeling has been used for detecting
activity, and for inferring and predicting actions, different from those works,
we do human and object modeling in order to learn interactions in RGB-D data
for improving segmentation. For this purpose, we define a novel density
function to model a three dimensional (3D) scene in a virtual environment
(VREP). This density function takes into account various possible
configurations of human-object and object-object relationships and interactions
governed by their affordances. Using this function, we synthesize a large,
realistic and highly varied synthetic RGB-D dataset that we use for training.
We train a random forest classifier, and the pixelwise predictions obtained is
integrated as a unary term in a pairwise conditional random fields (CRF). Our
evaluation shows that modeling these interactions improves segmentation
performance by ~7\% in mean average precision and recall over state-of-the-art
methods that ignore these interactions in real-world data. Our approach is
computationally efficient, robust and can run real-time on consumer hardware.


  The recent observation of superconducting state at atomic scale has motivated
the pursuit of exotic condensed phases in two-dimensional (2D) systems. Here we
report on a superconducting phase in two-monolayer crystalline Ga films
epitaxially grown on wide band-gap semiconductor GaN(0001). This phase exhibits
a hexagonal structure and only 0.552 nm in thickness, nevertheless, brings
about a superconducting transition temperature Tc as high as 5.4 K, confirmed
by in situ scanning tunneling spectroscopy, and ex situ electrical
magneto-transport and magnetization measurements. The anisotropy of critical
magnetic field and Berezinski-Kosterlitz-Thouless-like transition are observed,
typical for the 2D superconductivity. Our results demonstrate a novel platform
for exploring atomic-scale 2D superconductor, with great potential for
understanding of the interface superconductivity.


  Actor-critic methods, a type of model-free reinforcement learning (RL), have
achieved state-of-the-art performances in many real-world domains in continuous
control. Despite their success, the wide-scale deployment of these models is
still a far cry. The main problems in these actor-critic methods are
inefficient exploration and sub-optimal policies. Soft Actor-Critic (SAC) and
Twin Delayed Deep Deterministic Policy Gradient (TD3), two cutting edge such
algorithms, suffer from these issues. SAC effectively addressed the problems of
sample complexity and convergence brittleness to hyper-parameters and thus
outperformed all state-of-the-art algorithms including TD3 in harder tasks,
whereas TD3 produced moderate results in all environments. SAC suffers from
inefficient exploration owing to the Gaussian nature of its policy which causes
borderline performance in simpler tasks. In this paper, we introduce
Opportunistic Actor-Critic (OPAC), a novel model-free deep RL algorithm that
employs better exploration policy and lesser variance. OPAC combines some of
the most powerful features of TD3 and SAC and aims to optimize a stochastic
policy in an off-policy way. For calculating the target Q-values, instead of
two critics, OPAC uses three critics and based on the environment complexity,
opportunistically chooses how the target Q-value is computed from the critics'
evaluation. We have systematically evaluated the algorithm on MuJoCo
environments where it achieves state-of-the-art performance and outperforms or
at least equals the performance of TD3 and SAC.


  This Letter reports a new wave phenomenon. We show that wave energy can be
stored in random media. Associated with such energy storage is a global
collective behavior. The features depicted are so general that they may be
observed in many random systems.


  In computational biology, biological entities such as genes or proteins are
usually annotated with terms extracted from Gene Ontology (GO). The functional
similarity among terms of an ontology is evaluated by using Semantic Similarity
Measures (SSM). More recently, the extensive application of SSMs yielded to the
Semantic Similarity Networks (SSNs). SSNs are edge-weighted graphs where the
nodes are concepts (e.g. proteins) and each edge has an associated weight that
represents the semantic similarity among related pairs of nodes. The analysis
of SSNs may reveal biologically meaningful knowledge. For these aims, the need
for the introduction of tool able to manage and analyze SSN arises.
Consequently we developed SSN-Analyzer a web based tool able to build and
preprocess SSN. As proof of concept we demonstrate that community detection
algorithms applied to filtered (thresholded) networks, have better performances
in terms of biological relevance of the results, with respect to the use of raw
unfiltered networks.


  We study supersymmetric domain wall solutions in four dimensions arising from
the compactification of type II supergravity on a SU(3)xSU(3) structure
manifold. Using a pure spinor approach, we show that the supersymmetry
variations can be reinterpreted as a generalisation of the Hitchin flow
equations and describe the embedding of a SU(3)xSU(3) structure manifold into a
G_2xG_2 structure manifold. We find a precise agreement between the four- and
ten-dimensional supergravity results. The flow equations derived here should
have applications in constructing the gravity duals of Chern-Simons-matter
conformal field theories.


  If the Standard Model (SM) Higgs is weakly coupled to the inflationary
sector, the Higgs is expected to be universally in the form of a condensate
towards the end of inflation. The Higgs decays rapidly after inflation - via
non-perturbative effects - into an out-of-equilibrium distribution of SM
species, which thermalize soon afterwards. If the post-inflationary equation of
state of the universe is stiff, $w \simeq +1$, the SM species eventually
dominate the total energy budget. This provides a natural origin for the
relativistic thermal plasma of SM species, required for the onset of the `hot
Big Bang' era. The viability of this scenario requires the inflationary Hubble
scale $H_*$ to be lower than the instability scale for Higgs vacuum decay, the
Higgs not to generate too large curvature perturbations at cosmological scales,
and the SM dominance to occur before Big Bang Nucleosynthesis. We show that
successful reheating into the SM can only be obtained in the presence of a
non-minimal coupling to gravity $\xi \gtrsim 1$, with a reheating temperature
of $T_{\rm RH} \gtrsim \mathcal{O}(10^{10})\xi^{3/2}(H_*/10^{14}{\rm
GeV})^2~{\rm GeV}$.


  In this paper we study a model of the two-dimensional quantum harmonic
oscillator in a 3-dimensional anti-de Sitter background. We use a generalized
Schr\"odinger picture in which the analogs of the Schr\"odinger operators of
the particle are independent of both the time and the space coordinates in
different representations. The spacetime independent operators of the particle
induce the Lie algebra of Killing vector fields of the $AdS_3$ spacetime. In
this picture, we have a metamorphosis of the Heisenberg's uncertainty
relations.


  For the past few decades, man has been trying to create an intelligent
computer which can talk and respond like he can. The task of creating a system
that can talk like a human being is the primary objective of Automatic Speech
Recognition. Various Speech Recognition techniques have been developed in
theory and have been applied in practice. This paper discusses the problems
that have been encountered in developing Speech Recognition, the techniques
that have been applied to automate the task, and a representation of the core
problems of present day Speech Recognition by using Fuzzy Mathematics.


  This paper proposes an optimization strategy to assist utility operators to
recover power distribution systems after large outages. Specifically, a
mixed-integer linear programming (MILP) model is developed for co-optimizing
crews, resources, and network operations. The MILP model coordinates damage
isolation, network reconfiguration, distributed generator re-dispatch, and
crew/resource logistics. In addition, a framework for integrating different
types of photovoltaic (PV) systems in the restoration process is developed.} We
consider two different types of crews, namely, line crews for damage repair and
tree crews for obstacle removal. We also model the repair resource logistic
constraints. Furthermore, a new algorithm is developed for solving the
distribution system repair and restoration problem (DSRRP). The algorithm
starts by solving DSRRP using an assignment-based method, then a neighborhood
search method is designed to iteratively improve the solution. The proposed
method is validated on modified IEEE 123- and 8500-bus distribution test
systems.


  We use lookup tables to design faster algorithms for important algebraic
problems over finite fields. These faster algorithms, which only use arithmetic
operations and lookup table operations, may help to explain the difficulty of
determining the complexities of these important problems. Our results over a
constant-sized finite field are as follows.
  The Walsh-Hadamard transform of a vector of length $N$ can be computed using
$O(N \log N / \log \log N)$ bit operations. This generalizes to any transform
defined as a Kronecker power of a fixed matrix. By comparison, the Fast
Walsh-Hadamard transform (similar to the Fast Fourier transform) uses $O(N \log
N)$ arithmetic operations, which is believed to be optimal up to constant
factors.
  Any algebraic algorithm for multiplying two $N \times N$ matrices using
$O(N^\omega)$ operations can be converted into an algorithm using $O(N^\omega /
(\log N)^{\omega/2 - 1})$ bit operations. For example, Strassen's algorithm can
be converted into an algorithm using $O(N^{2.81} / (\log N)^{0.4})$ bit
operations. It remains an open problem with practical implications to determine
the smallest constant $c$ such that Strassen's algorithm can be implemented to
use $c \cdot N^{2.81} + o(N^{2.81})$ arithmetic operations; using a lookup
table allows one to save a super-constant factor in bit operations.


  We study the total (dynamical plus geometrical (Berry)) phase of cyclic
quantum motion for coherent states over homogeneous K\"ahler manifolds X=G/H,
which can be considered as the phase spaces of classical systems and which are,
in particular cases, coadjoint orbits of some Lie groups G. When the
Hamiltonian is linear in the generators of a Lie group, both phases can be
calculated exactly in terms of {\em classical} objects. In particular, the
geometric phase is given by the symplectic area enclosed by the (purely
classical) motion in the space of coherent states.


  Measurements are reported of the cross-correlation of spectra of differential
position signals from the Fermilab Holometer, a pair of co-located 39 m long,
high power Michelson interferometers with flat, broadband frequency response in
the MHz range. The instrument obtains sensitivity to high frequency correlated
signals far exceeding any previous measurement in a broad frequency band
extending beyond the 3.8 MHz inverse light crossing time of the apparatus. The
dominant but uncorrelated shot noise is averaged down over $2\times 10^8$
independent spectral measurements with 381 Hz frequency resolution to obtain
$2.1\times 10^{-20} \ \mathrm{m}/\sqrt{\mathrm{Hz}}$ sensitivity to stationary
signals. For signal bandwidths $\Delta f > 11$ kHz, the sensitivity to strain
$h$ or shear power spectral density of classical or exotic origin surpasses a
milestone $PSD_{\delta h} < t_p$ where $t_p= 5.39\times 10^{-44}/\mathrm{Hz}$
is the Planck time.


  In this study, the charged Higgs pair production is analyzed for the minimal
extension of the standard model called two-higgs-doublet model. The process
$\gamma\gamma\rightarrow H^+H^-$ is calculated at the tree level for the ILC
and the numerical analysis is presented for various parameters. The production
rate of the charged Higgs boson pair as a function of center-of-mass (CM)
energy and the differential cross section as a function of angle between photon
and positive charged Higgs boson is presented. The cross section gets high at
the low charged Higgs mass and low CM energies. The total integrated cross
section of the process is also calculated at a $e^+e^-$-collider by convoluting
the $\gamma\gamma\rightarrow H^+H^-$ subprocess with the photon luminosity of
the backscattered photons. The total integrated cross section peaks around
$\sqrt{s}=650 \;\text{GeV}$ and have a value of $1.4 \;\text{pb}$ for
$m_{H^\pm}=100\;\text{GeV/c}^2$. Charged Higgs detection is very important sign
for the new physics and the results shows the potential of the ILC for the
search of the new physics signals.


  We study von Neumann measurement-related matrices, and the nullity condition
of quantum correlation. We investigate the properties of these matrices that
are related to a von Neumann measurement. It is shown that these (m^2-1)*
(m^2-1) matrices are idempotent, and have rank m-1. These properties give rise
to necessary conditions for the nullity of quantum correlations in bipartite
systems. Finally, as an example we discuss quantum correlation in Bell diagonal
states.


  In this work, we present a collection of new results on two fundamental
problems in geometric data structures: orthogonal point location and rectangle
stabbing.
  -We give the first linear-space data structure that supports 3-d point
location queries on $n$ disjoint axis-aligned boxes with optimal $O\left( \log
n\right)$ query time in the (arithmetic) pointer machine model. This improves
the previous $O\left( \log^{3/2} n \right)$ bound of Rahul [SODA 2015]. We
similarly obtain the first linear-space data structure in the I/O model with
optimal query cost, and also the first linear-space data structure in the word
RAM model with sub-logarithmic query time.
  -We give the first linear-space data structure that supports 3-d $4$-sided
and $5$-sided rectangle stabbing queries in optimal $O(\log_wn+k)$ time in the
word RAM model. We similarly obtain the first optimal data structure for the
closely related problem of 2-d top-$k$ rectangle stabbing in the word RAM
model, and also improved results for 3-d 6-sided rectangle stabbing.
  For point location, our solution is simpler than previous methods, and is
based on an interesting variant of the van Emde Boas recursion, applied in a
round-robin fashion over the dimensions, combined with bit-packing techniques.
For rectangle stabbing, our solution is a variant of Alstrup, Brodal, and
Rauhe's grid-based recursive technique (FOCS 2000), combined with a number of
new ideas.


  Full-duplex systems are expected to achieve 100% rate improvement over
half-duplex systems if the self-interference signal can be significantly
mitigated. In this paper, we propose the first full-duplex system utilizing
Multi-Reconfigurable Antenna (MRA) with ?90% rate improvement compared to
half-duplex systems. MRA is a dynamically reconfigurable antenna structure,
that is capable of changing its properties according to certain input
configurations. A comprehensive experimental analysis is conducted to
characterize the system performance in typical indoor environments. The
experiments are performed using a fabricated MRA that has 4096 configurable
radiation patterns. The achieved MRA-based passive self-interference
suppression is investigated, with detailed analysis for the MRA training
overhead. In addition, a heuristic-based approach is proposed to reduce the MRA
training overhead. The results show that at 1% training overhead, a total of
95dB self-interference cancellation is achieved in typical indoor environments.
The 95dB self-interference cancellation is experimentally shown to be
sufficient for 90% full-duplex rate improvement compared to half-duplex
systems.


  In 1907, Oskar Perron showed that a positive square matrix has a unique
largest positive eigenvalue with a positive eigenvector. This result was
extended to irreducible nonnegative matrices by Geog Frobenius in 1912, and to
irreducible nonnegative tensors and weakly irreducible nonnegative tensors
recently. This result is a fundamental result in matrix theory and has found
wide applications in probability theory, internet search engines, spectral
graph and hypergraph theory, etc. In this paper, we give a necessary and
sufficient condition for the existence of such a positive eigenvector, i.e., a
positive Perron vector, for a nonnegative tensor. We show that every
nonnegative tensor has a canonical nonnegative partition form, from which we
introduce strongly nonnegative tensors. A tensor is called strongly
nonnegative, if the spectral radius of each genuine weakly irreducible block is
equal to the spectral radius of the tensor, which is strictly larger than the
spectral radius of any other block. We prove that a nonnegative tensor has a
positive Perron vector if and only if it is strongly nonnegative. The proof is
nontrivial. Numerical results for finding a positive Perron vector are
reported.


  The uplink where both the transmitter and receiver can use a large antenna
array is considered. This is proposed as a method of antenna offloading and
connecting small cell access points (SCAP) in a Two-Tier cellular network. Due
to having a limited number of RF-chains, hybrid beamformers are designed where
phase-only processing is done at the RF-band, followed by digital processing at
the baseband. The proposed receiver is a row combiner that clusters
sufficiently correlated antenna elements, and its' performance is compared
against random projection via a Discrete Fourier Transform (DFT) matrix. The
analogue to the row combiner is a column spreader, which is dependent on the
transmit correlation, and repeats the transmitted signal over antenna elements
that are correlated. A key benefit of this approach is to reduce the number of
phase shifters used, while outperforming the DFT scheme. When only the
transmitter has correlation and is RF-chain limited, the baseband precoding
vectors are shown to be the eigenvectors of the effective transmit correlation
matrix. Depending on the channel correlation, this matrix can be approximated
to have a tridiagonal Toeplitz structure with the proposed column spreader
(CS). The resulting eigenvalues have a closed form solution which allows us to
characterize the sum rate of the system. Most interestingly, the associated
eigenvectors do not require knowledge of the effective transmit correlation
matrix to be calculated using an Eigenvalue Decomposition (EVD) method.


  The extended BMS group includes supertranslation, dual supertranslation and
Lorentz transformations. The generators of these symmetries can be classified
according to their parity into "electric" and "magnetic" types. Using a
multipole expansion of gravitational sources in the Newman-Penrose formalism,
we associate each one of these charges with a particular moment. At leading
order, the "electric" and "magnetic" monopole moments correspond respectively
to supertranslations and dual supertranslations. At the first subleading order,
the "electric" and "magnetic" dipole moments correspond respectively to boosts
and rotations, therefore comprising the entire Lorentz group. Electric-magnetic
type of duality then rotates the boost and rotation generators into each other.


  Recent measurements of the properties of W+W- events produced in e+e-
collisions at Ecm=183 GeV at LEP are reviewed. The data are used to investigate
the predicted effects of final state interactions, specifically "colour
reconnection".


  The notion of the orbifold Euler characteristic came from physics at the end
of 80's. There were defined higher order versions of the orbifold Euler
characteristic and generalized ("motivic") versions of them. In a previous
paper the authors defined a notion of the Grothendieck ring $K_0^{\rm
fGr}(Var)$ of varieties with actions of finite groups on which the orbifold
Euler characteristic and its higher order versions are homomorphisms to the
ring of integers. Here we define the generalized orbifold Euler characteristic
and higher order versions of it as ring homomorphisms from $K_0^{\rm fGr}(Var)$
to the Grothendieck ring $K_0(Var)$ of complex quasi-projective varieties and
give some analogues of the classical Macdonald equations for the generating
series of the Euler characteristics of the symmetric products of a space.


  We show that common choices of kernel functions for a highly accurate and
massively scalable nearest-neighbour based GP regression model (GPnn:
\cite{GPnn}) exhibit gradual convergence to asymptotic behaviour as
dataset-size $n$ increases. For isotropic kernels such as Mat\'{e}rn and
squared-exponential, an upper bound on the predictive MSE can be obtained as
$O(n^{-\frac{p}{d}})$ for input dimension $d$, $p$ dictated by the kernel (and
$d>p$) and fixed number of nearest-neighbours $m$ with minimal assumptions on
the input distribution. Similar bounds can be found under model
misspecification and combined to give overall rates of convergence of both MSE
and an important calibration metric. We show that lower bounds on $n$ can be
given in terms of $m$, $l$, $p$, $d$, a tolerance $\varepsilon$ and a
probability $\delta$. When $m$ is chosen to be $O(n^{\frac{p}{p+d}})$ minimax
optimal rates of convergence are attained. Finally, we demonstrate empirical
performance and show that in many cases convergence occurs faster than the
upper bounds given here.


  Primordial magnetic fields can change the recombination history of the
universe by inducing clumping in the baryon density at small scales. They were
recently proposed as a candidate model to relieve the Hubble tension. We
investigate the consistency of the constraints on a clumping factor parameter
$b$ in a simplistic model, using the latest CMB data from Planck, ACT DR4 and
SPT-3G 2018. For the combined CMB data alone, we find no evidence for clumping
being different from zero, though when adding a prior on $H_0$ based on the
latest distance-ladder analysis of the SH0ES team, we report a weak detection
of $b$. Our analysis of simulated datasets shows that ACT DR4 has more
constraining power with respect to SPT-3G 2018 due to the degeneracy breaking
power of the TT band powers (not included in SPT). Simulations also suggest
that the TE,EE power spectra of the two datasets should have the same
constraining power. However, the ACT DR4 TE,EE constraint is tighter than
expectations, while the SPT-3G 2018 one is looser. While this is compatible
with statistical fluctuations, we explore systematic effects which may account
for such deviations. Overall, the ACT results are only marginally consistent
with Planck or SPT-3G, at the $2-3\sigma$ level within $\Lambda$CDM+$b$ and
$\Lambda$CDM, while Planck and SPT-3G are in good agreement. Combining the CMB
data together with BAO and SNIa provides an upper limit of b<0.4 at 95\% c.l.
(b<0.5 without ACT). Adding a SH0ES-based prior on the Hubble constant gives $b
= 0.31^{+0.11}_{-0.15}$ and $H_0=69.28 \pm 0.56$ km/s/Mpc ($b =
0.41^{+0.14}_{-018}$ and $H_0=69.70 \pm 0.63$ km/s/Mpc without ACT). Finally,
we forecast constraints on $b$ for the full SPT-3G survey, Simons Observatory,
and CMB-S4, finding improvements by factors of 1.5 (2.7 with Planck), 5.9 and
7.8, respectively, over Planck alone.


  Most methods for decision-theoretic online learning are based on the Hedge
algorithm, which takes a parameter called the learning rate. In most previous
analyses the learning rate was carefully tuned to obtain optimal worst-case
performance, leading to suboptimal performance on easy instances, for example
when there exists an action that is significantly better than all others. We
propose a new way of setting the learning rate, which adapts to the difficulty
of the learning problem: in the worst case our procedure still guarantees
optimal performance, but on easy instances it achieves much smaller regret. In
particular, our adaptive method achieves constant regret in a probabilistic
setting, when there exists an action that on average obtains strictly smaller
loss than all other actions. We also provide a simulation study comparing our
approach to existing methods.


  Vision-based segmentation in forested environments is a key functionality for
autonomous forestry operations such as tree felling and forwarding. Deep
learning algorithms demonstrate promising results to perform visual tasks such
as object detection. However, the supervised learning process of these
algorithms requires annotations from a large diversity of images. In this work,
we propose to use simulated forest environments to automatically generate 43 k
realistic synthetic images with pixel-level annotations, and use it to train
deep learning algorithms for tree detection. This allows us to address the
following questions: i) what kind of performance should we expect from deep
learning in harsh synthetic forest environments, ii) which annotations are the
most important for training, and iii) what modality should be used between RGB
and depth. We also report the promising transfer learning capability of
features learned on our synthetic dataset by directly predicting bounding box,
segmentation masks and keypoints on real images. Code available on GitHub
(https://github.com/norlab-ulaval/PercepTreeV1).


  We study nuclear shadowing at small Bjorken x < 0.01 in the color dipole
approach. Such a light-cone quantum-chromodynamics formalism based on the Green
function technique incorporates naturally color transparency and coherence
length effects. The nuclear shadowing for the barq-q Fock component of the
photon is calculated using exact numerical solution of the evolution equation
for the Green function. At x < 0.01 we demonstrate that a contribution of
higher Fock states containing gluons to overall nuclear shadowing becomes
effective. Numerical results for nuclear shadowing are compared with available
data from the E665 and NMC collaborations. Model calculations are finally
tested with the results obtained from other models.


  The aim of this work is to extend the knowledge about Quasinormal Modes
(QNMs) and the equilibration of strongly coupled systems, specifically of a
quark gluon plasma (which we consider to be in a strong magnetic background
field) by using the duality between $\mathcal{N}=4$ Super Yang-Mills (SYM)
theory and type IIb Super Gravity (SUGRA) and including higher derivative
corrections. The behaviour of the equilibrating system can be seen as the
response of the system to tiny excitations. A quark gluon plasma in a strong
magnetic background field, as produced for very short times during an actual
heavy ion collision, is described holographically by certain metric solutions
to $5\text{D}$ Einstein-Maxwell-(Chern-Simons) theory, which can be obtained
from type IIb SUGRA. We are going to compute higher derivative corrections to
this metric and consider $\alpha'^3$ corrections to tensor-quasinormal modes in
this background geometry. We find indications for a strong influence of the
magnetic background field on the equilibration behaviour also and especially
when we include higher derivative corrections.


  During the periods of sudden transition to online education, the opportunity
to make applications that might attract students' attention to the course has
decreased even more. Although this deficiency was tried to be eliminated with
videos and simulations, it was not possible to ensure active participation of
students in some cases. In this study, the Algodoo program, which can increase
the efficiency of the teaching environment by ensuring active participation of
students in online lessons and the applications that can be done about Impulse
and momentum are explained in detail. A total of 6 different applications were
carried out, 1 related to the subject of impulse, 1 related to the momentum, 2
related to the relationship between impulse and momentum change, and 2 related
to momentum conservation. At the same time, while developing these
applications, the adjustments made on the simulation and the reasons are
explained in detail. In this way, both the introduction of the program and the
sample application suggestion were presented. The values obtained as a result
of the applications were calculated and compared both theoretically and on
simulation in different ways. As a result, it has been observed that the values
have internal consistency with each other and are also compatible with
theoretical calculations. Algodoo program, which allows many interactive
applications and can be downloaded for free, is a program that can be used both
in lecturing and evaluation processes in physics lessons while online education
process.


  The elementary optical excitations of a two-dimensional electron or hole
system have been identified as exciton-Fermi-polarons. Nevertheless, the
connection between the bound state of an exciton and an electron, termed trion,
and exciton-polarons is subject of ongoing debate. Here, we use an analogy to
the Tavis-Cummings model of quantum optics to show that an exciton-polaron can
be understood as a hybrid quasiparticle -- a coherent superposition of a bare
exciton in an unperturbed Fermi sea and a bright collective excitation of many
trions. The analogy is valid to the extent that the Chevy Ansatz provides a
good description of dynamical screening of excitons and provided the Fermi
energy is much smaller than the trion binding energy. We anticipate our results
to bring new insight that could help to explain the striking differences
between absorption and emission spectra of two-dimensional semiconductors.


  Recently Abe (arXiv:cond-mat/1005.5110v1) claimed that the q-entropy of
nonextensive statistical mechanics cannot be generalized for the continuous
variables and therefore can be used only in the discrete case. In this letter,
we show that the discrete q-entropy can be generalized to continuous variables
exactly in the same manner as Boltzmann-Gibbs entropy, contrary to the claim by
Abe, so that q-entropy can be used with discrete as well as continuous
variables.


  Understanding and modeling plasma-surface interactions frame a multi-scale as
well as multi-physics problem. Scale-bridging machine learning surface
surrogate models have been demonstrated to perceive the fundamental atomic
fidelity for the physical vapor deposition of pure metals. However, the immense
computational cost of the data-generating simulations render a practical
application with predictions on relevant timescales impracticable. This issue
is resolved in this work for the sputter deposition of AlN in Ar/N$_2$
discharges by developing a scheme that populates the parameter spaces
effectively. Hybrid reactive molecular dynamics / time-stamped force-bias Monte
Carlo simulations of randomized plasma-surface interactions / diffusion
processes are used to setup a physics-separating artificial neural network. The
application of this generic machine learning model to a specific experimental
reference case study enables the systematic analysis of the particle flux
emission as well as underlying system state (e.g., composition, mass density,
stress, point defect structure) evolution within process times of up to 45
minutes.


  Multimode nonlinear optics offers to overcome a long-standing limitation of
fiber optics, tightly phase locking several spatial modes and enabling the
coherent transport of a wavepacket through a multimode fiber. A similar problem
is encountered in the temporal compression of multi-mJ pulses to few-cycle
duration in hollow gas-filled fibers. Scaling the fiber length to up to six
meters, hollow fibers have recently reached 1 TW of peak power. Despite the
remarkable utility of the hollow fiber compressor and its widespread
application, however, no analytical model exists to enable insight into the
scaling behavior of maximum compressibility and peak power. Here we extend a
recently introduced formalism for describing mode-locking to the spatially
analogue scenario of locking spatial fiber modes together. Our formalism
unveils the coexistence of two soliton branches for anomalous modal dispersion
and indicates the formation of stable spatio-temporal light bullets that would
be unstable in free space, similar to the temporal cage solitons in
mode-locking theory. Our model enables deeper understanding of the physical
processes behind the formation of such light bullets and predict the existence
of multimode solitons in a much wider range of fiber types than previously
considered possible.


  Psychophysical experiments suggested a relative importance of a narrow band
of spatial frequencies for recognition of face identity in humans. There
exists, however, no conclusive evidence of why it is that such frequencies are
preferred. To address this question, I examined the amplitude spectra of a
large number of face images, and observed that face spectra generally fall off
steeper with spatial frequency compared to ordinary natural images. When
external face features (like hair) are suppressed, then whitening of the
corresponding mean amplitude spectra revealed higher response amplitudes at
those spatial frequencies which are deemed important for processing face
identity. The results presented here therefore provide support for that face
processing characteristics match corresponding stimulus properties.


  With the rapid development of cloud computing, virtual machine scheduling has
become one of the most important but challenging issues for the cloud computing
community, especially for practical heterogeneous request sequences. By
analyzing the impact of request heterogeneity on some popular heuristic
schedulers, it can be found that existing scheduling algorithms can not handle
the request heterogeneity properly and efficiently. In this paper, a
plug-and-play virtual machine scheduling intensifier, called Resource Assigner
(ReAssigner), is proposed to enhance the scheduling efficiency of any given
scheduler for heterogeneous requests. The key idea of ReAssigner is to
pre-assign roles to physical resources and let resources of the same role form
a virtual cluster to handle homogeneous requests. ReAssigner can cooperate with
arbitrary schedulers by restricting their scheduling space to virtual clusters.
With evaluations on the real dataset from Huawei Cloud, the proposed ReAssigner
achieves significant scheduling performance improvement compared with some
state-of-the-art scheduling methods.


  The three-in-a-tree algorithm of Chudnovsky and Seymour decides in time
$O(n^4)$ whether three given vertices of a graph belong to an induced tree.
Here, we study four-in-a-tree for triangle-free graphs. We give a structural
answer to the following question: what does a triangle-free graph look like if
no induced tree covers four given vertices? Our main result says that any such
graph must have the "same structure", in a sense to be defined precisely, as a
square or a cube.
  We provide an $O(nm)$-time algorithm that given a triangle-free graph $G$
together with four vertices outputs either an induced tree that contains them
or a partition of $V(G)$ certifying that no such tree exists. We prove that the
problem of deciding whether there exists a tree $T$ covering the four vertices
such that at most one vertex of $T$ has degree at least 3 is NP-complete.


  We present a possible Cepheid-like luminosity estimator for the long
gamma-ray bursts based on the variability of their light curves. To construct
the luminosity estimator, we use CGRO/BATSE data for 13 bursts, Wind/KONUS data
for 5 bursts, Ulysses/GRB data for 1 burst, and NEAR/XGRS data for 1 burst.
Spectroscopic redshifts, peak fluxes, and high resolution light curves are
available for 11 of these bursts; partial information is available for the
remaining 9 bursts. We find that the isotropic-equivalent luminosities L of
these bursts positively correlate with a rigorously-constructed measure V of
the variability of their light curves. We fit a model to these data that
accommodates both intrinsic scatter (statistical variance) and extrinsic
scatter (sample variance). If one excludes GRB 980425 from the fit on the
grounds that its association with SN 1998bw at a redshift of z = 0.0085 is not
secure, the luminosity estimator spans approx. 2.5 orders of magnitude in L,
and the slope of the correlation between L and V is positive with a probability
of 1 - 1.4 x 10^-4 (3.8 sigma). Although GRB 980425 is excluded from this fit,
its L and V values are consistent with the fitted model, which suggests that
GRB 980425 may well be associated with SN 1998bw, and that GRB 980425 and the
cosmological bursts may share a common physical origin. If one includes GRB
980425 in the fit, the luminosity estimator spans approx. 6.3 orders of
magnitude in L, and the slope of the correlation is positive with a probability
of 1 - 9.3 x 10^-7 (4.9 sigma). Independently of whether or not GRB 980425
should be included in the fit, its light curve is unique in that it is much
less variable than the other approx. 17 light curves in our sample for which
the signal-to-noise is reasonably good.


  Monte Carlo simulations have been performed in order to evaluate the
efficiencies of several light ions identification techniques. The detection
system was composed with layers of scintillating material to measure either the
deposited energy or the time-of-flight of ions produced by nuclear reactions
between 12C projectiles and a PMMA target. Well known techniques such as
(DELTA) E--Range, (DELTA) E--E--ToF and (DELTA)E--E are presented and their
particle identification efficiencies are compared one to another regarding the
generated charge and mass of the particle to be identified. The simulations
allowed to change the beam energy matching the ones proposed in an hadron
therapy facility, namely from 95 to 400 MeV/A.


  We investigate the stability and critical velocity of a weakly interacting
Bose gas flowing in a random potential. By applying the Bogoliubov theory to a
disordered Bose system with a steady flow, the condensate density and the
superfluid density are determined as functions of the disorder strength, flow
velocity, and temperature. The critical velocity, at which the steady flow
becomes unstable, is calculated from the spectrum of hydrodynamic excitation.
We also show that in two dimensions the critical velocity strongly depends on
the system size.


  Albertson has defined the irregularity of a simple undirected graph $G=(V,E)$
as $ \irr(G) = \sum_{uv\in E}|d_G(u)-d_G(v)|,$ where $d_G(u)$ denotes the
degree of a vertex $u \in V$. Recently, this graph invariant gained interest in
the chemical graph theory, where it occured in some bounds on the first and the
second Zagreb index, and was named the third Zagreb index Fath-Tabar. For
general graphs with $n$ vertices, Albertson has obtained an asymptotically
tight upper bound on the irregularity of $4 n^3 /27.$ Here, by exploiting a
different approach than in Albertson, we show that for general graphs with $n$
vertices the upper bound $\lfloor \frac{n}{3} \rfloor \lceil \frac{2 n}{3}
\rceil (\lceil \frac{2 n}{3} \rceil -1)$ is sharp. Next, we determine
$k$-cyclic graphs with maximal irregularity. We also present some bounds on the
maximal/minimal irregularity of graphs with fixed minimal and/or maximal vertex
degrees, and consider an approximate computation of the irregularity of a
graph.


  ISO provides a key new far-infrared window through which to observe the
multi-wavelength spectral energy distributions (SEDs) of quasars and active
galactic nuclei (AGN). It allows us, for the first time, to observe a
substantial fraction of the quasar population in the far-IR, and to obtain
simultaneous, multi-wavelength observations from 5--200 microns. With these
data we can study the behavior of the IR continuum in comparison with
expectations from competing thermal and non-thermal models. A key to
determining which mechanism dominates, is the measurement of the peak
wavelength of the emission and the shape of the far-IR--mm turnover. Turnovers
which are steeper than frequency^2.5 indicate thermal dust emission in the
far-IR.
  Preliminary results from our ISO data show broad, fairly smooth, IR continuum
emission with far-IR turnovers generally too steep to be explained by
non-thermal synchrotron emission. Assuming thermal emission throughout leads to
a wide inferred temperature range of 50-1000 K. The hotter material, often
called the AGN component, probably originates in dust close to and heated by
the central source, e.g. the ubiquitous molecular torus. The cooler emission is
too strong to be due purely to cool, host galaxy dust, and so indicates either
the presence of a starburst in addition to the AGN or AGN-heated dust covering
a wider range of temperatures than present in the standard, optically thick
torus models.


  The separation assurance task will be extremely challenging for air traffic
controllers in a complex and high density airspace environment. Deep
reinforcement learning (DRL) was used to develop an autonomous separation
assurance framework in our previous work where the learned model advised speed
maneuvers. In order to improve the safety of this model in unseen environments
with uncertainties, in this work we propose a safety module for DRL in
autonomous separation assurance applications. The proposed module directly
addresses both model uncertainty and state uncertainty to improve safety. Our
safety module consists of two sub-modules: (1) the state safety sub-module is
based on the execution-time data augmentation method to introduce state
disturbances in the model input state; (2) the model safety sub-module is a
Monte-Carlo dropout extension that learns the posterior distribution of the DRL
model policy. We demonstrate the effectiveness of the two sub-modules in an
open-source air traffic simulator with challenging environment settings.
Through extensive numerical experiments, our results show that the proposed
sub-safety modules help the DRL agent significantly improve its safety
performance in an autonomous separation assurance task.


  Packet routing is a fundamental problem in communication networks that
decides how the packets are directed from their source nodes to their
destination nodes through some intermediate nodes. With the increasing
complexity of network topology and highly dynamic traffic demand, conventional
model-based and rule-based routing schemes show significant limitations, due to
the simplified and unrealistic model assumptions, and lack of flexibility and
adaption. Adding intelligence to the network control is becoming a trend and
the key to achieving high-efficiency network operation. In this paper, we
develop a model-free and data-driven routing strategy by leveraging
reinforcement learning (RL), where routers interact with the network and learn
from the experience to make some good routing configurations for the future.
Considering the graph nature of the network topology, we design a multi-agent
RL framework in combination with Graph Neural Network (GNN), tailored to the
routing problem. Three deployment paradigms, centralized, federated, and
cooperated learning, are explored respectively. Simulation results demonstrate
that our algorithm outperforms some existing benchmark algorithms in terms of
packet transmission delay and affordable load.


  We present an effective field theory method to determine secondary massive
quark effects in jet production taking the thrust distribution for e+ e-
collisions in the dijet limit as a concrete example. The method is based on the
field theoretic treatment of collinear and soft mass modes which have to be
separated coherently from the collinear and ultrasoft modes related to massless
quarks and gluons. For thrust the structure of the conceptual setup is closely
related to the production of massive gauge bosons and involves four different
effective field theories to describe all possible kinematic situations. The
effective field theories merge into each other continuously and thus allow for
a continuous description from infinitely heavy to arbitrarily small masses
keeping the exact mass dependence of the most singular terms treated through
factorization. The mass mode field theory method we present here is in the
spirit of the variable fermion number scheme originally proposed by Aivazis,
Collins, Olness and Tung and can also be applied in hadron collisions.


  With the increasing use of autonomous unmanned aerial vehicles (UAVs), it is
critical to ensure that they are continuously tracked and controlled,
especially when UAVs operate beyond the communication range of ground stations
(GSs). Conventional surveillance methods for UAVs, such as satellite
communications, ground mobile networks and radars are subject to high costs and
latency. The automatic dependent surveillance-broadcast (ADS-B) emerges as a
promising method to monitor UAVs, due to the advantages of real-time
capabilities, easy deployment and affordable cost. Therefore, we employ the
ADS-B for UAV trajectory tracking in this work. However, the inherent noise in
the transmitted data poses an obstacle for precisely tracking UAVs. Hence, we
propose the algorithm of recurrent neural network-enhanced interacting multiple
model-Kalman filter (RNN-enhanced IMM-KF) for UAV trajectory filtering.
Specifically, the algorithm utilizes the RNN to capture the maneuvering
behavior of UAVs and the noise level in the ADS-B data. Moreover, accurate UAV
tracking is achieved by adaptively adjusting the process noise matrix and
observation noise matrix of IMM-KF with the assistance of the RNN. The proposed
algorithm can facilitate GSs to make timely decisions during trajectory
deviations of UAVs and improve the airspace safety. Finally, via comprehensive
simulations, the total root mean square error of the proposed algorithm
decreases by 28.56%, compared to the traditional IMM-KF.


  We discuss exact renormalization group (RG) in $R^2$-gravity using effective
average action formalism. The truncated evolution equation for such a theory on
De Sitter background leads to the system of nonperturbative RG equations for
cosmological and gravitational coupling constants. Approximate solution of
these RG equations shows the appearence of antiscreening and screening
behaviour of Newtonian coupling what depends on higher derivative coupling
constants.


  The computation of approximating e^tA B, where A is a large sparse matrix and
B is a rectangular matrix, serves as a crucial element in numerous scientific
and engineering calculations. A powerful way to consider this problem is to use
Krylov subspace methods. The purpose of this work is to approximate the matrix
exponential and some Cauchy-Stieltjes functions on a block vectors B of R^n*p
using a rational block Lanczos algorithm. We also derive some error estimates
and error bound for the convergence of the rational approximation and finally
numerical results attest to the computational efficiency of the proposed
method.


  We investigate the behavior of equilibria in an $M/M/1$ feedback queue where
price and time sensitive customers are homogeneous with respect to service
valuation and cost per unit time of waiting. Upon arrival, customers can
observe the number of customers in the system and then decide to join or to
balk. Customers are served in order of arrival. After being served, each
customer either successfully completes the service and departs the system with
probability $q$, or the service fails and the customer immediately joins the
end of the queue to wait to be served again until she successfully completes
it.
  We analyse this decision problem as a noncooperative game among the
customers. We show that there exists a unique symmetric Nash equilibrium
threshold strategy. We then prove that the symmetric Nash equilibrium threshold
strategy is evolutionarily stable. Moreover, if we relax the strategy
restrictions by allowing customers to renege, in the new Nash equilibrium,
customers have a greater incentive to join. However, this does not necessarily
increase the equilibrium expected payoff, and for some parameter values, it
decreases it.


  Guided wave optics, including most prominently fiber optics and integrated
photonics, very often considers only one or very few spatial modes of the
waveguides. Despite being known and utilized for decades, multi-mode guided
wave optics is currently rapidly increasing in parallel with technological
improvements and better simulation tools. The physics of multi-mode
interactions are usually driven by some initial energy distribution in a number
of spatial modes. In this work we introduce how, with free-space input beams
having space-time couplings, the different modes can be excited with different
complex frequency or time profiles. We cover fundamentals, the coupling with a
few simple space-time aberrations, different waveguides, and a number of
technical nuances. This concept of space-time initial conditions in multi-mode
waveguides will provide yet another tool to study the rich nonlinear
interactions in such systems.


  CLIPStyler demonstrated image style transfer with realistic textures using
only a style text description (instead of requiring a reference style image).
However, the ground semantics of objects in the style transfer output is lost
due to style spill-over on salient and background objects (content mismatch) or
over-stylization. To solve this, we propose Semantic CLIPStyler (Sem-CS), that
performs semantic style transfer. Sem-CS first segments the content image into
salient and non-salient objects and then transfers artistic style based on a
given style text description. The semantic style transfer is achieved using
global foreground loss (for salient objects) and global background loss (for
non-salient objects). Our empirical results, including DISTS, NIMA and user
study scores, show that our proposed framework yields superior qualitative and
quantitative performance. Our code is available at
github.com/chandagrover/sem-cs.


  We study Laplacians on graphs and networks via regular Dirichlet forms. We
give a sufficient geometric condition for essential selfadjointness and
explicitly determine the generators of the associated semigroups on all
$\ell^p$, $1\leq p < \infty$, in this case. We characterize stochastic
completeness thereby generalizing all earlier corresponding results for graph
Laplacians. Finally, we study how stochastic completeness of a subgraph is
related to stochastic completeness of the whole graph.


  1H RAMPS solid state NMR and 13C CP/MAS spectra of D- and L- alanine crystals
were measured at temperature ranging from 220K to 295K. Some major points are
as follows: (1)alpha-H and protons in the methyl group showed a spin-spin
coupling effect as temperature went down in the 1H- MAS spectra of D-alanine.
(2) In the 1H CRAMPS spectra, peak widths of alpha-H and beta-H showed a
different trend between alanine enantiomers when temperature varied.(3) The
dynamic behavior of 13C spectra showed an obvious change around 250K, which was
supposed as a phase transition in alanine crystal. In the discussion section,
we give these experimental phenomena a possible explanation related to
chirality.


  Within the k_t-factorization framework, we study diffractive production of
orbitally excited vector mesons and compare it with the production of radial
excitations, focusing on the rho(1450)/rho(1700) case. At small Q^2, orbital
excitation of light quarkonia is found to dominate over radial excitations in
diffractive production. We predict strong suppression of the production of
orbital excitations by longitudinal photons, which leads to very small
sigma_L/sigma_T ratio. At small Q^2, the s-channel helicity violating
transitions contribute \sim 10-15% of the transverse cross section and \sim 50%
of the longitudinal cross section. We also study mixing between radial and
orbital excitations and determine strategies towards clarification of
S-wave/D-wave assignment to rho(1450) and rho(1700) mesons. The results are
compared with the experimental data available, and predictions for future
experiments are given.


  In this paper, we show that our proposed hybrid optoelectronic correlator
(HOC), which correlates images using spatial light modulators (SLM), detectors
and field programmable gate arrays (FPGAs), is capable of detecting objects in
a scale and rotation invariant manner, along with the shift invariance feature,
by incorporating polar mellin transform (PMT). We also illustrate a key
limitation of the ideas presented in previous papers on performing PMT and
present a solution to circumvent this limitation by cutting out a small circle
at the center of the Fourier Transform which precedes PMT. Furthermore, we show
how to carry out shift, rotation and scale invariant detection of multiple
matching objects simultaneously, a process previously thought to be
incompatible with PMT based correlators. We present results of numerical
simulations to validate the concepts.


  We calculate the next-to-next-to-next-to-leading-order (N$^3$LO) QCD
corrections to inclusive vector-boson fusion (VBF) Higgs production at proton
colliders, in the limit in which there is no colour exchange between the
hadronic systems associated with the two colliding protons. We also provide
differential cross sections for the Higgs transverse momentum and rapidity
distributions. We find that the corrections are at the 1-2 permille level, well
within the scale-uncertainty of the next-to-next-to-leading-order (NNLO)
calculation. The associated scale-uncertainty of the N$^3$LO calculation is
typically found to be below the 2 permille level. We also consider theoretical
uncertainties due to missing higher order parton distribution functions, and
provide an estimate of their importance.


  With the beginning of the COVID-19 pandemic, we became aware of the need for
comprehensive data collection and its provision to scientists and experts for
proper data analyses. In Germany, the Robert Koch Institute (RKI) has tried to
keep up with this demand for data on COVID-19, but there were (and still are)
relevant data missing that are needed to understand the whole picture of the
pandemic. In this paper, we take a closer look at the severity of the course of
COVID-19 in Germany, for which ideal information would be the number of
incoming patients to ICU units. This information was (and still is) not
available. Instead, the current occupancy of ICU units on the district level
was reported daily. We demonstrate how this information can be used to predict
the number of incoming as well as released COVID-19 patients using a stochastic
version of the Expectation Maximisation algorithm (SEM). This in turn, allows
for estimating the influence of district-specific and age-specific infection
rates as well as further covariates, including spatial effects, on the number
of incoming patients. The paper demonstrates that even if relevant data are not
recorded or provided officially, statistical modelling allows for
reconstructing them. This also includes the quantification of uncertainty which
naturally results from the application of the SEM algorithm.


  We investigate the communication of supersymmetry breaking to the Standard
Model in theories of gauge mediated supersymmetry breaking with general weakly
coupled messenger sectors. We calculate the one loop gaugino and two loop soft
scalar masses for nonvanishing Str M^2 of the messenger sector. The soft scalar
masses are sensitive to physics at scales higher than the messenger scale, in
contrast to models with vanishing messenger supertrace. We discuss the
implications of this ultraviolet sensitivity in theories with renormalizable
and nonrenormalizable supersymmetry breaking sectors. We note that the standard
relation, in minimal gauge mediation, between soft scalar and gaugino masses is
altered in models with nonvanishing messenger supertrace.


  We apply Koide's mass relation of charged leptons to neutrinos and quarks,
with both the normal and inverted mass schemes of neutrinos discussed. We
introduce the parameters $k_{\nu}$, $k_u$ and $k_d$ to describe the deviations
of neutrinos and quarks from Koide's relation, and suggest a quark-lepton
complementarity of masses such as $ k_{l}+k_{d} \approx k_{\nu}+k_{u} \approx
2$. The masses of neutrinos are determined from the improved relation, and they
are strongly hierarchical (with the different orders of magnitude of $10^{-5}
eV$, $10^{-3} eV$, and $10^{-2} eV$).


  In modern scientific studies, it is often imperative to determine whether a
set of phenotypes is affected by a single factor. If such an influence is
identified, it becomes essential to discern whether this effect is contingent
upon categories such as sex or age group, and importantly, to understand
whether this dependence is rooted in purely non-environmental reasons. The
exploration of such dependencies often involves studying pleiotropy, a
phenomenon wherein a single genetic locus impacts multiple traits. This
heightened interest in uncovering dependencies by pleiotropy is fueled by the
growing accessibility of summary statistics from genome-wide association
studies (GWAS) and the establishment of thoroughly phenotyped sample
collections. This advancement enables a systematic and comprehensive
exploration of the genetic connections among various traits and diseases.
additive genetic correlation illuminates the genetic connection between two
traits, providing valuable insights into the shared biological pathways and
underlying causal relationships between them. In this paper, we present a novel
method to analyze such dependencies by studying additive genetic correlations
between pairs of traits under consideration. Subsequently, we employ matrix
comparison techniques to discern and elucidate sex-specific or
age-group-specific associations, contributing to a deeper understanding of the
nuanced dependencies within the studied traits. Our proposed method is
computationally handy and requires only GWAS summary statistics. We validate
our method by applying it to the UK Biobank data and present the results.


  Biosensors are frequently used nowadays for the sake of their attractive
capabilities. Because of their high accuracy and precision, they are more and
more used in the medical sector. Natural receptors are mostly used, but their
use have some specific drawbacks. Therefore, new read-out methods are being
developed where there is no need for these receptors. Via a Transient Plane
Source (TPS) sensor, the thermal properties of a fluid can be determined. These
sensors can detect the capability of a fluid to absorb heat i.e. the thermal
effusivity. By the way of monitoring this property, many potential bioprocesses
can be monitored. The use of this promising technique was further developed in
this research for later use of detecting cell growth and protein
concentrations. Firstly, the thermal properties of growth medium and yeast
cells were determined. Here, it became clear that the thermal properties change
in different concentrations. Also, measurements were performed on protein
concentration. No unambiguously results were obtained from these tests. But,
the overall results from the use of this sensor are very promising, especially
in the cell detection compartment. However, further research will tell about
the applicability and sensitivity of this type of sensor.


  We study the well-posedness of the biological models with AHL-dependent cell
mobility on engineered Escherichia coli populations. For the kinetic model
proposed by Xue-Xue-Tang recently, the local existence for large initial data
is proved first. Furthermore, the positivity and local conservation laws for
density $\rho (t,x,z)$ and nutrient $n(t,x)$ with initial assumptions are
justified. Based on these properties, it can be extended globally in time near
the equilibrium $(0,0,0)$. Considering the asymptotic behaviors of faster
response CheZ turnover rate (i.e.,$\varepsilon\rightarrow 0$), one formally
derives an anisotropic diffusion engineered Escherichia coli populations model
(in short, AD-EECP) for which we find a key extra a priori estimate to overcome
the difficulties coming from the nonlinearity of the diffusion structure. The
local well-posedness and the positivity and local conservation laws for density
and nutrient of the AD-EECP are justified. Furthermore, the global existence
around the steady state $(\varrho_a, h_a, 0)$ with $\varrho_a \in [0,
\Lambda_b)$ is obtained.


  Autonomous camera systems are often subjected to an optimization/filtering
operation to smoothen and stabilize the rough trajectory estimates. Most common
filtering techniques do reduce the irregularities in data; however, they fail
to mimic the behavior of a human cameraman. Global filtering methods modeling
human camera operators have been successful; however, they are limited to
offline settings. In this paper, we propose two online filtering methods called
Cinefilters, which produce smooth camera trajectories that are motivated by
cinematographic principles. The first filter (CineConvex) uses a sliding
window-based convex optimization formulation, and the second (CineCNN) is a CNN
based encoder-decoder model. We evaluate the proposed filters in two different
settings, namely a basketball dataset and a stage performance dataset. Our
models outperform previous methods and baselines on both quantitative and
qualitative metrics. The CineConvex and CineCNN filters operate at about 250fps
and 1000fps, respectively, with a minor latency (half a second), making them
apt for a variety of real-time applications.


  We classify all real hypersurfaces with three distinct constant principal
curvatures in complex hyperbolic spaces of dimension greater than two.


  Creating virtual models of real spaces and objects is cumbersome and time
consuming. This paper focuses on the problem of geometric reconstruction from
sparse data obtained from certain image-based modeling approaches. A number of
elegant and simple-to-state problems arise concerning when the geometry can be
reconstructed. We describe results and counterexamples, and list open problems.


  It is shown that the transformations of the charge conjugation in classical
electrodynamics and in quantum theory can be interpreted as the consequences of
the symmetry of Maxwell and Dirac equations with respect to the inversion of
the speed of light: c to -c; t to t; (x,y,z) to (x,y,z), where c is the speed
of light; t is the time; x, y, z are the spatial variables.
  The elements of physical interpretation are given.


  Model-Agnostic Meta-Learning (MAML) and its variants are popular few-shot
classification methods. They train an initializer across a variety of sampled
learning tasks (also known as episodes) such that the initialized model can
adapt quickly to new tasks. However, current MAML-based algorithms have
limitations in forming generalizable decision boundaries. In this paper, we
propose an approach called MetaMix. It generates virtual feature-target pairs
within each episode to regularize the backbone models. MetaMix can be
integrated with any of the MAML-based algorithms and learn the decision
boundaries generalizing better to new tasks. Experiments on the mini-ImageNet,
CUB, and FC100 datasets show that MetaMix improves the performance of
MAML-based algorithms and achieves state-of-the-art result when integrated with
Meta-Transfer Learning.


  We present new Gemini spectra of 14 new objects found within the HI tails of
Hickson Compact Groups 92 and 100. Nine of them are GALEX Far-UV (FUV) and
Near-UV (NUV) sources. The spectra confirm that these objects are members of
the compact groups and have metallicities close to solar, with an average value
of 12+log(O/H)~8.5. They have average FUV luminosities 7 x 10^40 erg/s, very
young ages (< 100 Myr) and two of them resemble tidal dwarf galaxies (TDGs)
candidates. We suggest that they were created within gas clouds that were
ejected during galaxy-galaxy interactions into the intergalactic medium, which
would explain the high metallicities of the objects, inherited from the parent
galaxies from which the gas originated. We conduct a search for similar objects
in 6 interacting systems with extended HI tails, NGC 2623, NGC 3079, NGC 3359,
NGC 3627, NGC 3718, NGC 4656. We found 35 UV sources with ages < 100 Myr,
however most of them are on average less luminous/massive than the UV sources
found around HCG 92 and 100. We speculate that this might be an environmental
effect and that compact groups of galaxies are more favorable to TDG formation
than other interacting systems.


  Collaborative Filtering (CF) has emerged as one of the most prominent
implementation strategies for building recommender systems. The key idea is to
exploit the usage patterns of individuals to generate personalized
recommendations. CF techniques, especially for newly launched platforms, often
face a critical issue known as the data sparsity problem, which greatly limits
their performance. Several approaches in the literature have been proposed to
tackle the problem of data sparsity, among which cross-domain collaborative
filtering (CDCF) has gained significant attention in the recent past. In order
to compensate for the scarcity of available feedback in a target domain, the
CDCF approach utilizes information available in other auxiliary domains.
Traditional CDCF approaches primarily focus on finding a common set of entities
(users or items) across the domains, which then act as a conduit for knowledge
transfer. Nevertheless, most real-world datasets are collected from different
domains, so they often lack information about anchor points or reference
information for entity alignment. This paper introduces a domain adaptation
technique to align the embeddings of entities across the two domains. Our
approach first exploits the available textual and visual information to
independently learn a multi-view latent representation for each entity in the
auxiliary and target domains. The different representations of the entity are
then fused to generate the corresponding unified representation. A domain
classifier is then trained to learn the embedding for the domain alignment by
fixing the unified features as the anchor points. Experiments on two publicly
benchmark datasets indicate the effectiveness of our proposed approach.


  The initial boundary value problem for a class of scalar non autonomous
conservation laws in one space dimension is proved to be well posed and stable
with respect to variations in the flux. Targeting applications to traffic, the
regularity assumptions on the flow are extended to a merely
$\mathbf{L}^{\infty}$ dependence on time. These results ensure, for instance,
the well posedness of a class of vehicular traffic models with time dependent
speed limits. A traffic management problem is then shown to admit an optimal
solution.


  Based on possible albeit tiny, admixtures of mirror matter in ordinary mesons
we study the K_L \to \gamma\gamma transition. We find that this process can be
described with a small SU(3) symmetry breaking of only 3%. We also determine
the eta-eta' mixing angle and the pseudoscalar decay constants. The results for
these parameters are consistent with some obtained in the literature. They
favor two recent determinations; one based on two analytical constraints, and
another one based on next-to-leading order power corrections.


  Age of Information (AoI) and Peak AoI (PAoI) and their analytical models have
recently drawn substantial amount of attention in information theory and
wireless communications disciplines, in the context of qualitative assessment
of information freshness in status update systems. We take a queueing-theoretic
approach and study a probabilistically preemptive bufferless $M/PH/1/1$
queueing system with arrivals stemming from $N$ separate information sources,
with the aim of modeling a generic status update system. In this model, a new
information packet arrival from source $m$ is allowed to preempt a packet from
source $n$ in service, with a probability depending on $n$ and $m$. To make the
model even more general than the existing ones, for each of the information
sources, we assume a distinct PH-type service time distribution and a distinct
packet error probability. Subsequently, we obtain the exact distributions of
the AoI and PAoI for each of the information sources using matrix-analytical
algorithms and in particular the theory of Markov fluid queues and sample path
arguments. This is in contrast with existing methods that rely on Stochastic
Hybrid Systems (SHS) which obtain only the average values and in less general
settings. Numerical examples are provided to validate the proposed approach as
well as to give engineering insight on the impact of preemption probabilities
on certain AoI and PAoI performance figures.


  Let $\alpha>0$ and $0<\gamma<1$. Define
$g_{\alpha,\gamma}:\mathbb{N}\rightarrow\mathbb{N}$ by
$g_{\alpha,\gamma}\left(n\right)=\lfloor\alpha n+\gamma\rfloor$. The set
$\left\{ g_{\alpha,\gamma}\left(n\right):n\in\mathbb{N}\right\} $ is called the
nonhomogeneous spectrum of $\alpha$ and $\gamma$. We refer to the maps
$g_{\alpha,\gamma}$ as nonhomogeneous spectra. In \cite{BHK}, Bergelson,
Hindman and Kra showed that if $A$ is an $IP$-set, a central set, an
$IP^{\star}$-set, or a central$^{\star}$-set, then
$g_{\alpha,\gamma}\left[A\right]$ is the corresponding objects. Hindman and
Johnsons extended this result to include several other notions of largeness:
$C$-sets, $J$-sets, strongly central sets, piecwise syndetic sets, $AP$-sets
syndetic set, $C^{\star}$-sets, strongly central$^{\star}$- sets . In
\cite{DHS}, De, Hindman and Strauss introduced $C$-set and $J$-set and showed
that $C$-sets satisfy the conclusion of the Central Sets Theorem. To prepare
this article, we have been strongly motivated by the fact that $C$-sets are
essential $\mathcal{J}$-sets. In this article, we prove some new results
regarding nonhomogeneous spectra of essential $\mathcal{F}$-sets for shift
invariant $\mathcal{F}$-sets. We have a special interest in the family
$\mathcal{HSD}=\left\{ A\subseteq\mathbb{N}:\sum_{n\in
A}\frac{1}{n}=\infty\right\} $ as this family is directly connected with the
famous Erd\H{o}s sum of reciprocal conjecture and as a consequence we get
$g_{\alpha,\gamma}\left[\mathbb{P}\right]\in\mathcal{HSD}$, where $\mathbb{P}$
is the set of prime numbers in $\mathbb{N}$. Throughout this article, we use
some elementary techniques and algebra of the Stone-\v{C}ech compactifications
of discrete semigroups.


  In this paper, we consider the Minimum-Load $k$-Clustering/Facility Location
(MLkC) problem where we are given a set $P$ of $n$ points in a metric space
that we have to cluster and an integer $k$ that denotes the number of clusters.
Additionally, we are given a set $F$ of cluster centers in the same metric
space. The goal is to select a set $C\subseteq F$ of $k$ centers and assign
each point in $P$ to a center in $C$, such that the maximum load over all
centers is minimized. Here the load of a center is the sum of the distances
between it and the points assigned to it.
  Although clustering/facility location problems have a rich literature, the
minimum-load objective is not studied substantially, and hence MLkC has
remained a poorly understood problem. More interestingly, the problem is
notoriously hard even in some special cases including the one in line metrics
as shown by Ahmadian et al. [ACM Trans. Algo. 2018]. They also show
APX-hardness of the problem in the plane. On the other hand, the best-known
approximation factor for MLkC is $O(k)$, even in the plane.
  In this work, we study a fair version of MLkC inspired by the work of
Chierichetti et al. [NeurIPS, 2017], which generalizes MLkC. Here the input
points are colored by one of the $\ell$ colors denoting the group they belong
to. MLkC is the special case with $\ell=1$. Considering this problem, we are
able to obtain a $3$-approximation in $f(k,\ell)\cdot n^{O(1)}$ time. Also, our
scheme leads to an improved $(1 + \epsilon)$-approximation in case of Euclidean
norm, and in this case, the running time depends only polynomially on the
dimension $d$. Our results imply the same approximations for MLkC with running
time $f(k)\cdot n^{O(1)}$, achieving the first constant approximations for this
problem in general and Euclidean metric spaces.


  Broadcast consensus protocols (BCPs) are a model of computation, in which
anonymous, identical, finite-state agents compute by sending/receiving global
broadcasts. BCPs are known to compute all number predicates in
$\mathsf{NL}=\mathsf{NSPACE}(\log n)$ where $n$ is the number of agents. They
can be considered an extension of the well-established model of population
protocols. This paper investigates execution time characteristics of BCPs. We
show that every predicate computable by population protocols is computable by a
BCP with expected $\mathcal{O}(n \log n)$ interactions, which is asymptotically
optimal. We further show that every log-space, randomized Turing machine can be
simulated by a BCP with $\mathcal{O}(n \log n \cdot T)$ interactions in
expectation, where $T$ is the expected runtime of the Turing machine. This
allows us to characterise polynomial-time BCPs as computing exactly the number
predicates in $\mathsf{ZPL}$, i.e. predicates decidable by log-space bounded
randomised Turing machine with zero-error in expected polynomial time where the
input is encoded as unary.


  Melody estimation or melody extraction refers to the extraction of the
primary or fundamental dominant frequency in a melody. This sequence of
frequencies obtained represents the pitch of the dominant melodic line from
recorded music audio signals. The music signal may be monophonic or polyphonic.
The melody extraction problem from audio signals gets complicated when we start
dealing with polyphonic audio data. This is because in generalized audio
signals,the sounds are highly correlated over both frequency and time domains.
This complex overlap of many sounds, makes identification of predominant
frequency challenging.


  All state-of-the-art (SOTA) differentially private machine learning (DP ML)
methods are iterative in nature, and their privacy analyses allow publicly
releasing the intermediate training checkpoints. However, DP ML benchmarks, and
even practical deployments, typically use only the final training checkpoint to
make predictions. In this work, for the first time, we comprehensively explore
various methods that aggregate intermediate checkpoints to improve the utility
of DP training. Empirically, we demonstrate that checkpoint aggregations
provide significant gains in the prediction accuracy over the existing SOTA for
CIFAR10 and StackOverflow datasets, and that these gains get magnified in
settings with periodically varying training data distributions. For instance,
we improve SOTA StackOverflow accuracies to 22.7% (+0.43% absolute) for
$\epsilon=8.2$, and 23.84% (+0.43%) for $\epsilon=18.9$. Theoretically, we show
that uniform tail averaging of checkpoints improves the empirical risk
minimization bound compared to the last checkpoint of DP-SGD. Lastly, we
initiate an exploration into estimating the uncertainty that DP noise adds in
the predictions of DP ML models. We prove that, under standard assumptions on
the loss function, the sample variance from last few checkpoints provides a
good approximation of the variance of the final model of a DP run. Empirically,
we show that the last few checkpoints can provide a reasonable lower bound for
the variance of a converged DP model.


  We point out that the quantum dynamical map of an open quantum system can be
generated by an effective Liouville operator. The effective Liouville shows the
dynamical breaking of time reversibility. This breaking of reversibility is
expressed by the effective Liouville's discrete spectrum having negative
imaginary parts. This generated dynamics of open quantum systems is capable of
memory effects described by a frequency dependence of the spectrum. When memory
effects can be neglected or smoothed out, the effective Liouville generates the
well known semi-group dynamics of open systems in the Markov approximation. The
spectral analysis of the effective Liouville -with or without memory- allows to
represent the quantum dynamical map and expectation values of physical
quantities by metric expressions using complex eigenvalues and bi-orthonormal
eigenmodes. The long time dynamics is dominated by the zero-mode, which forms
the stationary state of the open system. The relaxation time scale $\tau$ is
set by the inverse of the smallest negative imaginary part of the non-vanishing
effective eigenvalues of the effective Liouville. In generic cases of
system-environment-coupling this time scale $\tau$ is the relevant scale for
both, the relaxation of diagonal elements (populations) and the decay of
off-diagonal elements (coherences) of an initial density matrix in the
stationary state's diagonal representation. It also sets the time scale after
which the entropy tends to its stationary value. The effective Liouville and
its spectral content thus give a framework to study the dynamic breaking of
time reversibility, memory effects, decoherence, relaxation to a stationary
state and the role of entropy in open quantum systems.


  The subtleties of human perception, as measured by vision scientists through
the use of psychophysics, are important clues to the internal workings of
visual recognition. For instance, measured reaction time can indicate whether a
visual stimulus is easy for a subject to recognize, or whether it is hard. In
this paper, we consider how to incorporate psychophysical measurements of
visual perception into the loss function of a deep neural network being trained
for a recognition task, under the assumption that such information can enforce
consistency with human behavior. As a case study to assess the viability of
this approach, we look at the problem of handwritten document transcription.
While good progress has been made towards automatically transcribing modern
handwriting, significant challenges remain in transcribing historical
documents. Here we describe a general enhancement strategy, underpinned by the
new loss formulation, which can be applied to the training regime of any deep
learning-based document transcription system. Through experimentation, reliable
performance improvement is demonstrated for the standard IAM and RIMES datasets
for three different network architectures. Further, we go on to show
feasibility for our approach on a new dataset of digitized Latin manuscripts,
originally produced by scribes in the Cloister of St. Gall in the the 9th
century.


  In this article we used supersymmetry quantum mechanics and factorization
methods to study the bound and scattering state of Klein-Gordon equation with
deformed Hulthen plus deformed hyperbolical potential for arbitrary state in
D-dimensions. The analytic relativistic bound state eigenvalues and the
scattering phase factor are found in closed form. We reported on the numerical
results for the bound state energy in D-dimensions.


  We present a model predictive controller (MPC) that automatically discovers
collision-free locomotion while simultaneously taking into account the system
dynamics, friction constraints, and kinematic limitations. A relaxed barrier
function is added to the optimization's cost function, leading to collision
avoidance behavior without increasing the problem's computational complexity.
Our holistic approach does not require any heuristics and enables legged robots
to find whole-body motions in the presence of static and dynamic obstacles. We
use a dynamically generated euclidean signed distance field for static
collision checking. Collision checking for dynamic obstacles is modeled with
moving cylinders, increasing the responsiveness to fast-moving agents.
Furthermore, we include a Kalman filter motion prediction for moving obstacles
into our receding horizon planning, enabling the robot to anticipate possible
future collisions. Our experiments demonstrate collision-free motions on a
quadrupedal robot in challenging indoor environments. The robot handles complex
scenes like overhanging obstacles and dynamic agents by exploring motions at
the robot's dynamic and kinematic limits.


  Model predictive control (MPC) is a promising approach for the lateral and
longitudinal control of autonomous vehicles. However, the parameterization of
the MPC with respect to high-level requirements such as passenger comfort as
well as lateral and longitudinal tracking is a challenging task. Numerous
tuning parameters as well as conflicting requirements need to be considered.
This contribution formulates the MPC tuning task as a multi-objective
optimization problem. Solving it is challenging for two reasons: First,
MPC-parameterizations are evaluated on an computationally expensive simulation
environment. As a result, the used optimization algorithm needs to be as
sampleefficient as possible. Second, for some poor parameterizations the
simulation cannot be completed and therefore useful objective function values
are not available (learning with crash constraints). In this contribution, we
compare the sample efficiency of multi-objective particle swarm optimization
(MOPSO), a genetic algorithm (NSGA-II) and multiple versions of Bayesian
optimization (BO). We extend BO, by introducing an adaptive batch size to limit
the computational overhead and by a method on how to deal with crash
constraints. Results show, that BO works best for a small budget, NSGA-II is
best for medium budgets and for large budgets none of the evaluated optimizers
is superior to random search. Both proposed BO extensions are shown to be
beneficial.


  LaCasa is a type system and programming model to enforce the object
capability discipline in Scala, and to provide affine types. One important
application of LaCasa's type system is software isolation of concurrent
processes. Isolation is important for several reasons including security and
data-race freedom. Moreover, LaCasa's affine references enable efficient,
by-reference message passing while guaranteeing a "deep-copy" semantics. This
deep-copy semantics enables programmers to seamlessly port concurrent programs
running on a single machine to distributed programs running on large-scale
clusters of machines.
  This paper presents an integration of LaCasa with actors in Scala,
specifically, the Akka actor-based middleware, one of the most widely-used
actor systems in industry. The goal of this integration is to statically ensure
the isolation of Akka actors. Importantly, we present the results of an
empirical study investigating the effort required to use LaCasa's type system
in existing open-source Akka-based systems and applications.