  At the Large Hadron Collider (LHC) it will become possible for the first time
to investigate experimentally the forward region in hadron-hadron collisions
via high-$p_T$ processes. In the LHC forward kinematics QCD logarithmic
corrections in the hard transverse momentum and in the large rapidity interval
may both be quantitatively significant. We analyze the hadroproduction of
forward jets in the framework of QCD high-energy factorization, which allows
one to resum consistently both kinds of corrections to higher orders in QCD
perturbation theory. We compute the short-distance matrix elements needed to
evaluate the factorization formula at fully exclusive level. We discuss
numerically dynamical features of multi-gluon emission at large angle encoded
in the factorizing high-energy amplitudes.


  In this paper, we study the receiver performance with physical layer security
in a Poisson field of interferers. We compare the performance in two deployment
scenarios: (i) the receiver is located at the corner of a quadrant, (ii) the
receiver is located in the infinite plane. When the channel state information
(CSI) of the eavesdropper is not available at the transmitter, we calculate the
probability of secure connectivity using the Wyner coding scheme, and we show
that hiding the receiver at the corner is beneficial at high rates of the
transmitted codewords and detrimental at low transmission rates. When the CSI
is available, we show that the average secrecy capacity is higher when the
receiver is located at the corner, even if the intensity of interferers in this
case is four times higher than the intensity of interferers in the bulk.
Therefore boundaries can also be used as a secrecy enhancement technique for
high data rate applications.


  Understanding cultural phenomena on Social Networks (SNs) and exploiting the
implicit knowledge about their members is attracting the interest of different
research communities both from the academic and the business side. The
community of complexity science is devoting significant efforts to define laws,
models, and theories, which, based on acquired knowledge, are able to predict
future observations (e.g. success of a product). In the mean time, the semantic
web community aims at engineering a new generation of advanced services by
defining constructs, models and methods, adding a semantic layer to SNs. In
this context, a leapfrog is expected to come from a hybrid approach merging the
disciplines above. Along this line, this work focuses on the propagation of
individual interests in social networks. The proposed framework consists of the
following main components: a method to gather information about the members of
the social networks; methods to perform some semantic analysis of the Domain of
Interest; a procedure to infer members' interests; and an interests evolution
theory to predict how the interests propagate in the network. As a result, one
achieves an analytic tool to measure individual features, such as members'
susceptibilities and authorities. Although the approach applies to any type of
social network, here it is has been tested against the computer science
research community.
  The DBLP (Digital Bibliography and Library Project) database has been elected
as test-case since it provides the most comprehensive list of scientific
production in this field.


  We report on a numerical study of optical chirality. Intertwined gold helices
illuminated with plane waves concentrate right and left circularly polarized
electromagnetic field energy to sub-wavelength regions. These spots of enhanced
chirality can be smoothly shifted in position and magnitude by varying
illumination parameters, allowing for the control of light-matter interactions
on a nanometer scale.


  ${\cal H}^2$-matrix constitutes a general mathematical framework for
efficient computation of both partial-differential-equation and
integral-equation-based operators. Existing linear-complexity ${\cal H}^2$
matrix-matrix product (MMP) algorithm lacks explicit accuracy control, while
controlling accuracy without compromising linear complexity is challenging. In
this paper, we develop an accuracy controlled ${\cal H}^2$ matrix-matrix
product algorithm by instantaneously changing the cluster bases during the
matrix product computation based on prescribed accuracy. Meanwhile, we retain
the computational complexity of the overall algorithm to be linear. Different
from the existing ${\cal H}^2$ matrix-matrix product algorithm where formatted
multiplications are performed using the original cluster bases, in the proposed
algorithm, all additions and multiplications are either exact or computed based
on prescribed accuracy. Furthermore, the original ${\cal H}^2$-matrix structure
is preserved in the matrix product. While achieving optimal complexity for
constant-rank matrices, the computational complexity of the proposed algorithm
is also minimized for variable-rank ${\cal H}^2$-matrices. The proposed work
serves as a fundamental arithmetic in the development of fast solvers for
large-scale electromagnetic analysis. Applications to both large-scale
capacitance extraction and electromagnetic scattering problems involving
millions of unknowns on a single core have demonstrated the accuracy and
efficiency of the proposed algorithm.


  Standard Patlak plot is widely used to describe FDG kinetics for dynamic PET
imaging. Whole-body Patlak parametric imaging remains constrained due to the
need for a full-time input function. Here, we demonstrate the Relative Patlak
(RP) plot, which eliminates the need for the early-time input function, for
total-body parametric imaging and its application to clinical 20-min scan
acquired in list-mode. We demonstrated that the RP intercept b' is equivalent
to a ratio of standardized uptake value relative to the blood, while the RP
slope Ki' is equal to the standard Patlak Ki multiplied by a global scaling
factor for each subject. One challenge in applying RP to a short scan duration
(20 min) is the high noise in parametric images. We applied a deep kernel
method for noise reduction. Using the standard Patlak plot as the reference,
the RP method was evaluated for lesion quantification, lesion-to-background
contrast, and myocardial visualization in total-body parametric imaging with
uEXPLORER in 22 human subjects who underwent a 1-h dynamic 18F-FDG scan. The RP
method was also applied to the dynamic data regenerated from a clinical
standard 20-min scan either at 1-h or 2-h post-injection for two cancer
patients. We demonstrated that it is feasible to obtain high-quality parametric
images from 20-min dynamic scans using the RP plot with a self-supervised
deep-kernel noise reduction strategy. The RP Ki' highly correlated with Ki in
lesions and major organs, demonstrating its quantitative potential across
subjects. Compared to conventional SUVs, the Ki' images significantly improved
lesion contrast and enabled visualization of the myocardium for potential
cardiac assessment. The application of RP parametric imaging to two clinical
scans also showed similar benefits. Total-body PET with the RP plot is feasible
to generate parametric images from the dynamic data of a 20-min clinical scan.


  We introduce a family of linear sets of $\mathrm{PG}(1,q^{2n})$ arising from
maximum scattered linear sets of pseudoregulus type of $\mathrm{PG}(3,q^{n})$.
For $n=3,4$ and for certain values of the parameters we show that these linear
sets of $\mathrm{PG}(1,q^{2n})$ are maximum scattered and they yield new
MRD-codes with parameters $(6,6,q;5)$ for $q>2$ and with parameters $(8,8,q;7)$
for $q$ odd.


  Statistics of the inverse participation ratio (IPR) at the critical point of
the localization transition is studied numerically for the power-law random
banded matrix model. It is shown that the IPR distribution function is
scale-invariant, with a power-law asymptotic ``tail''. This scale invariance
implies that the fractal dimensions $D_q$ are non-fluctuating quantities,
contrary to a recent claim in the literature. A recently proposed relation
between $D_2$ and the spectral compressibility $\chi$ is violated in the regime
of strong multifractality, with $\chi\to 1$ in the limit $D_2\to 0$.


  We show that, for $\varepsilon=\dfrac{1}{4000}$, any action of a finite
cyclic group by $(1+\varepsilon)$-bilipschitz homeomorphisms on a closed
3-manifold is conjugated to a smooth action.


  Lifetimes of the doubly heavy baryons ${\cal B}_{bb}$ and ${\cal B}_{bc}$ are
analyzed within the framework of the heavy quark expansion (HQE). Lifetime
differences arise from the spectator effects such as $W$-exchange and Pauli
interference. For doubly bottom baryons, the lifetime pattern is
$\tau(\Omega_{bb}^-)\sim \tau(\Xi_{bb}^{-})>\tau(\Xi_{bb}^0)$. The
$\Xi_{bb}^{0}$ baryon is shortest-lived owing to the $W$-exchange contribution,
while $\Xi_{bb}^{-}$ and $\Omega_{bb}^{-}$ have similar lifetimes as they both
receive contributions from destructive Pauli interference. We find the lifetime
ratio $\tau(\Xi_{bb}^{-})/\tau(\Xi_{bb}^0)=1.26$\,. The large $W$-exchange
contribution to $\Xi_{bc}^0$ through the subprocess $cd\to us\to cd$ and the
sizable destructive Pauli interference contribution to $\Xi_{bc}^+$ imply a
substantial lifetime difference between $\Xi_{bc}^+$ and $\Xi_{bc}^0$. In the
presence of subleading $1/m_c$ and $1/m_b$ corrections to the spectator
effects, we find that $\tau(\Omega_{bc}^0)$ becomes longest-lived. This is
because $\Gamma^{\rm int}_+$ and $\Gamma^{\rm semi}$ for $\Omega_{bc}^0$ are
subject to large cancellation between dimension-6 and -7 operators. This
implies that the subleading corrections are too large to justify the validity
of the HQE. Demanding that $\Gamma^{cs}_{{\rm int+}}(\Omega_{bc}^0)$,
$\Gamma^{{\rm SL},cs}_{\rm int}(\Omega_{bc}^0)$ be positive and
$\Gamma^{cu}_{{\rm int-}}(\Xi^+_{bc})$ be negative, we conjecture that
$1.68\times 10^{-13}s<\tau(\Omega_{bc}^0)< 3.70\times 10^{-13}s$ , $4.09\times
10^{-13}s<\tau(\Xi_{bc}^+)< 6.07\times 10^{-13}s$ and $0.93\times
10^{-13}s<\tau(\Xi_{bc}^0)< 1.18\times 10^{-13}s$. Hence, the lifetime
hierarchy of ${\cal B}_{bc}$ baryons is expected to be the pattern
$\tau(\Xi_{bc}^{+})>\tau(\Omega_{bc}^0)>\tau(\Xi_{bc}^0)$.


  We report finite-bias characteristics of electrical transport through
phosphorus donors in silicon nanoscale transistors, in which we observe
inelastic-cotunneling current in the Coulomb blockade region. The cotunneling
current appears like a resonant-tunneling current peak emerging from the
excited state at the crossover between blockade and non-blockade regions. These
cotunneling features are unique, since the inelastic-cotunneling currents have
so far been reported either as a broader hump or as a continuous increment of
current. This finding is ascribed purely due to excitation-related inelastic
cotunneling involving the ground and excited states. Theoretical calculations
were performed for a two-level quantum dot, supporting our experimental
observation.


  The aim of this study was to assess the extreme effects of tinted lenses on
colour vision by examining changes in chromatic sensitivity when viewing visual
displays through a slightly tinted (blue-blocking) filter and through a heavily
tinted, orange coloured filter. The CAD test was used to measure both red/green
(RG) and yellow/blue (YB) chromatic sensitivity in ten subjects when viewing
visual displays through each of the two filters. The measured RG and YB colour
thresholds were then compared with similar measurements made without coloured
filters in front of the eye. The blue-blocking filter absorbs only a small
amount of short-wavelength light whilst the orange filter attenuates
preferentially more short wavelength and some middle-wavelength light. The
results show that the blue-blocking filter does not affect significantly either
RG or YB colour vision. The orange filter, on the other hand, causes large
changes in colour discrimination. The results were analysed statistically by
comparing results obtained with the coloured filters with those measured
without any filters in front of the eye. More experimental work is now needed
to establish how much short wavelength light can be removed without affecting
significantly the subject's colour discrimination performance.


  Let G be a graph and let \Delta,\delta be the maximum and minimum degrees of
G respectively, where \Delta/\delta<c<\sqrt{2} and c is a constant. In this
paper we establish a sufficient spectral condition for the graph G to be
Hamiltonian, that is, the nontrivial eigenvalues of the normalized Laplacian of
G are sufficiently close to 1.


  If a graph $G$ can be represented by means of paths on a grid, such that each
vertex of $G$ corresponds to one path on the grid and two vertices of $G$ are
adjacent if and only if the corresponding paths share a grid edge, then this
graph is called EPG and the representation is called EPG representation. A
$k$-bend EPG representation is an EPG representation in which each path has at
most $k$ bends. The class of all graphs that have a $k$-bend EPG representation
is denoted by $B_k$. $B_\ell^m$ is the class of all graphs that have a
monotonic $\ell$-bend EPG representation, i.e. an $\ell$-bend EPG
representation, where each path is ascending in both columns and rows.
  It is trivial that $B^m_k\subseteq B_k$ for all $k$. Moreover, it is known
that $B^m_k\subsetneqq B_k$, for $k=1$. By investigating the $B_k$-membership
and the $B^m_k$-membership of complete bipartite graphs we prove that the
inclusion is also proper for $k\in \{2,3,5\}$ and for $k\geqslant 7$. In
particular, we derive necessary conditions for this membership that have to be
fulfilled by $m$, $n$ and $k$, where $m$ and $n$ are the number of vertices on
the two partition classes of the bipartite graph. We conjecture that $B_{k}^{m}
\subsetneqq B_{k}$ holds also for $k\in \{4,6\}$.
  Furthermore, we show that $B_k \not\subseteq B_{2k-9}^m$ holds for all
$k\geqslant 5$. This implies that restricting the shape of the paths can lead
to a significant increase of the number of bends needed in an EPG
representation. So far no bounds on the amount of that increase were known. We
prove that $B_1 \subseteq B_3^m$ holds, providing the first result of this
kind.


  We fabricated epitaxial thin films of hexagonal DyMnO3, which otherwise form
in a bulk perovskite structure, via deposition on Pt(111)//Al2O3 (0001) and
YSZ(111) substrates: each of which has in-plane hexagonal symmetry. The
polarization hysteresis loop demonstrated the existence of ferroelectricity in
our hexagonal DyMnO3 films at least below 70 K. The observed 2.2 uC/cm^2
remnant polarization at 25 K corresponded to a polarization enhancement by a
factor of 10 compared to that of the bulk orthorhombic DyMnO3. Interestingly,
this system showed an antiferroelectric-like feature in its hysteresis loop.
Our hexagonal DyMnO3 films showed an antiferromagnetic Neel temperature around
60 K and a spin reorientation transition around 40 K. We also found a clear
hysteresis in the temperature dependence of the magnetization, which was
measured after zero-field-cooling and field-cooling. This hysteresis may well
have been of spin glass origin, which was likely to arise from the geometric
frustration of antiferromagnetically-coupled Mn spins with an edge-sharing
triangular lattice.


  The results of studies of 2006 VV2 and 13170 (1999 HF1) binary asteroids of
NEA group, (45) Eugenia and (87) Sylvia triple asteroids, (762) Pulcova and
(90) Antiope binary asteroids of the Main Belt are presented. For the asteroid
2006 VV2, color indices (B-V, V-R, R-I), the absolute magnitude (16.7 \pm
0.2m), a taxonomy class, the density (2.71 \pm 0.04 g/cm3), the masses of
components as well as refined form of the main component and the satellite
orbit were determined. For the (45) Eugenia asteroid, refined form the main
component, simulated orbits of both satellites were determined and it was
showed that the axis of rotation of the main component undergoes a forced
precession with an angle of 10 deg and a period of 66 days. Based on a
comparison of model lightcurves with observations over a long interval of time
of (90) Antiope asteroid, reflective surface properties of its components were
investigated. For asteroid (762) Pulcova, form of the main component was
determined and the reflective properties of its surface were investigated. For
asteroid 137170 (1999 HF1), estimates of the size of the main component (a =
2.12 \pm 0.02, b = 1.77 \pm 0.01, c = 1.73 \pm 0.03 km) were made and possible
stable orbit of the satellite (with the elements of a~6.2 km, e~0.1, i~2 deg)
was identified and of component masses were estimated. For the asteroid (87)
Sylvia, form the main component was refined.


  We study the zero-temperature phase diagram of the half-filled
one-dimensional ionic Hubbard model. This model is governed by the interplay of
the on-site Coulomb repulsion and an alternating one-particle potential.
Various many-body energy gaps, the charge-density-wave and bond-order
parameters, the electric as well as the bond-order susceptibilities, and the
density-density correlation function are calculated using the density-matrix
renormalization group method. In order to obtain a comprehensive picture, we
investigate systems with open as well as periodic boundary conditions and study
the physical properties in different sectors of the phase diagram. A careful
finite-size scaling analysis leads to results which give strong evidence in
favor of a scenario with two quantum critical points and an intermediate
spontaneously dimerized phase. Our results indicate that the phase transitions
are continuous. Using a scaling ansatz we are able to read off critical
exponents at the first critical point. In contrast to a bosonization approach,
we do not find Ising critical exponents. We show that the low-energy physics of
the strong coupling phase can only partly be understood in terms of the strong
coupling behavior of the ordinary Hubbard model.


  Pre-election logic and accuracy (L&A) testing is a process in which election
officials validate the behavior of voting equipment by casting a known set of
test ballots and confirming the expected results. Ideally, such testing can
serve to detect certain forms of human error or fraud and help bolster voter
confidence. We present the first detailed analysis of L&A testing practices
across the United States. We find that while all states require L&A testing
before every election, their implementations vary dramatically in scope,
transparency, and rigorousness. We summarize each state's requirements and
score them according to uniform criteria. We also highlight best practices and
flag opportunities for improvement, in hopes of encouraging broader adoption of
more effective L&A processes.


  Categories and categorical structures are increasingly recognized as useful
abstractions for modeling in science and engineering. To uniformly implement
category-theoretic mathematical models in software, we introduce GATlab, a
domain-specific language for algebraic specification embedded in a technical
programming language. GATlab is based on generalized algebraic theories (GATs),
a logical system extending algebraic theories with dependent types so as to
encompass category theory. Using GATlab, the programmer can specify generalized
algebraic theories and their models, including both free models, based on
symbolic expressions, and computational models, defined by arbitrary code in
the host language. Moreover, the programmer can define maps between theories
and use them to declaratively migrate models of one theory to models of
another. In short, GATlab aims to provide a unified environment for both
computer algebra and software interface design with generalized algebraic
theories. In this paper, we describe the design, implementation, and
applications of GATlab.


  Uncertainty propagation software can have unknown, inadvertent biases
introduced by various means. This work is a case study in bias identification
and reduction in one such software package, the Microwave Uncertainty Framework
(MUF). The general purpose of the MUF is to provide automated multivariate
statistical uncertainty propagation and analysis on a Monte Carlo (MC) basis.
Combine is a key module in the MUF, responsible for merging data, raw or
transformed, to accurately reflect the variability in the data and in its
central tendency. In this work the performance of Combine's MC replicates is
analytically compared against its stated design goals. An alternative
construction is proposed for Combine's MC replicates and its performance is
compared, too, against Combine's design goals. These comparisons are made
within an archetypal two-stage scenario in which received data are first
transformed in conjunction with shared systematic error and then combined to
produce summary information. These comparisons reveal the limited conditions
under which Combine's uncertainty results are unbiased and the extent of these
biases when these conditions are not met. For small MC sample sizes neither
construction, current or alternative, fully meets Combine's design goals, nor
does either construction consistently outperform the other. However, for large
MC sample sizes the bias in the proposed alternative construction is
asymptotically zero, and this construction is recommended.


  In this conference paper, I review the present status and technical problems
of the Photon collider, as well as various additional applications of Compton
scattering.


  The Lusternik-Schnirelmann category $cat(X)$ is a homotopy invariant which is
a numerical bound on the number of critical points of a smooth function on a
manifold. Another similar invariant is the topological complexity $TC(X)$ (a la
Farber) which has interesting applications in Robotics, specifically, in the
robot motion planning problem. In this paper we calculate the
Lusternik-Schnirelmann category and as a consequence we calculate the
topological complexity of the two-point ordered configuration space of
$\mathbb{CP}^n$ for every $n\geq 1$.


  Malaria disease is a major global health and economic development threat. It
results in approximately 2.7 million deaths annually. There is currently no
vaccine that has been licensed for use against malaria. Studies in animal
models, especially non-human primates can lead to the revelation of possible
immunological mechanisms that can lead to protection or predisposition of the
host to malaria. Plasmodium knowlesi, a simian and human malaria parasite, is
an attractive experimental parasite for malaria research since it can infect
olive baboons (Papio anubis), non-human primates that have similar
host-pathogen interactions to humans. This study was carried out to determine
host immunological profiles provoked in olive baboons during the course of an
infection with Plasmodium knowlesi. A total of eight adult baboons were
intravenously inoculated with overnight cultured blood stage P. knowlesi H
strain parasites. Five of these baboons became acutely infected while the other
three became chronically infected. The immunological basis of this dual outcome
of the infection was determined by measuring circulating cytokine (T helper 1
and T helper 2) and antibody (immunoglobulin G and immunoglobulin M) responses
elicited in the infected baboons on a weekly basis by Enzyme Linked
Immunosorbent Assay (ELISA) for up to six weeks post infection. Generated data
for the first time indicated that acute P. knowlesi malaria is accompanied by
increased concentrations of interferon gamma (IFN gamma), tumour necrosis
factor alpha (TNF alpha) and IL 6 and reduced levels of circulating interleukin
10 (IL 10), IL 4, IL 12, immunoglobulin G (IgG) and IgM in the baboon host.
These results are largely agreeable with data from human studies, thereby
increasing the relevance of the olive baboon - P. knowlesi experimental
infection system for future malaria studies.


  In this paper we incorporate gauge fields into the tachyon field theory
models for unstable D-branes in bosonic and in Type II string theories. The
chosen couplings yield massless gauge fields and an infinite set of equally
spaced massive gauge fields on codimension one branes. A lack of a continuum
spectrum is taken as evidence that the stable tachyon vacuum does not support
conventional gauge excitations. For the bosonic string model we find two
possible solvable couplings, one closely related to Born-Infeld forms and the
other allowing a detailed comparison to the open string modes on bosonic
D-branes. We also show how to include fermions in the type II model. They
localize correctly on stable codimension one branes resulting in bose-fermi
degeneracy at the massless level. Finally, we establish the solvability of a
large class of models that include kinetic terms with more than two
derivatives.


  We introduce a notion of twisted pure spinor in order to characterize, in a
unified way, all the special Riemannian holonomy groups just as a classical
pure spinor characterizes the special K\"ahler holonomy. Motivated by certain
curvature identities satisfied by manifolds admitting parallel twisted pure
spinors, we also introduce the Clifford monopole equations as a natural
geometric generalization of the Seiberg-Witten equations. We show that they
restrict to the Seiberg-Witten equations in 4 dimensions, and that they admit
non-trivial solutions on manifolds with special Riemannian holonomy.


  We investigate the rate of thermalization of local operators in the
one-dimensional anisotropic antiferromagnetic Heisenberg model with
next-nearest neighbor interactions that break integrability. This is done by
calculating the scaling of the difference of the diagonal and canonical thermal
ensemble values as function of system size, and by directly calculating the
time evolution of the expectation values of the operators with the Chebyshev
polynomial expansion. Spatial and spin symmetry is exploited and the
Hamiltonian is divided in subsectors according to their symmetry. The rate of
thermalization depends on the proximity to the integrable limit. When
integrability is weakly broken thermalization is slow, and becomes faster the
stronger the next-nearest neighbor interaction is. Three different regimes for
the rate of thermalization with respect to the strength of the integrability
breaking parameter are identified. These are shown to be directly connected
with the relative strength of the low and higher energy difference off-diagonal
operator matrix elements in the symmetry eigenbasis of the Hamiltonian. Close
to the integrable limit the off-diagonal matrix elements peak at higher
energies and high frequency fluctuations are important and slow down
thermalization. Away from the integrable limit a strong low energy peak
gradually develops that takes over the higher frequency fluctuations and leads
to quicker thermalization.


  Phantom eye devices are designed to mimic the optical properties of the human
eye; however, the retinal structures are typically emulated with synthetic
tissues. Thus, it is currently impossible to exploit phantom eye devices for
fluorescence microscopy experiments on cultures, or ex-vivo tissues, although
these ophthalmic measurements would be of importance for many applications such
as the testing of retinal biomarkers. Here we report and describe the
development of a phantom eye designed to host biological samples, such as
retinal cultures differentiated from human induced pluripotent stem cells. We
characterized the imaging performance of the humanized phantom eye on standard
biomarkers such as Alexa Fluor 532 and Alexa fluor 594.


  Let $M$ be a complete Riemannian manifold satisfying the doubling volume
condition for geodesic balls and $L^q$ scaled Poincar\'e inequalities on
suitable remote balls for some $q<2$. We prove the inequality $\left\Vert
\Delta^{1/2}f\right\Vert_p\lesssim \left\Vert \nabla f\right\Vert_p$ for all
$p\in (q,2]$, which generalizes previous results due to Auscher and Coulhon.
Our conclusion applies, in particular, when $M$ has a finite number of
Euclidean ends. The proof strongly relies on Hardy inequalities, which are also
new in this context and of independent interest.
  The second part of this work deals with analogous questions in fractal-like
cable systems. In this framework, it was already proved by Chen, Coulhon,
Feneuil and the second author that, in the Vicsek cable system, the inequality
$\left\Vert \Delta^{1/2}f\right\Vert_p\lesssim \left\Vert \nabla
f\right\Vert_p$ may be false for all $p\in [1,2)$. Following a recent joint
work by the two authors and Yang, we examine the validity of inequalities of
the form $\left\Vert \Delta^{\gamma}e^{-\Delta}f\right\Vert_p\lesssim
\left\Vert \nabla f\right\Vert_p$. In the Vicsek case, we give the optimal
range of $p$ for which this inequality holds.


  Let $X$ be a projective toric surface of Picard number one blown up at a
general point. We bring an infinite family of examples of such $X$ whose
Kleiman-Mori cone of curves is not closed: there is no negative curve
generating one of the two boundary rays of the cone. These examples are related
to Nagata's conjecture and rationality of Seshadri constants.


  In this work, we analyze dimension reduction algorithms based on the Kac walk
and discrete variants.
  (1) For $n$ points in $\mathbb{R}^{d}$, we design an optimal
Johnson-Lindenstrauss (JL) transform based on the Kac walk which can be applied
to any vector in time $O(d\log{d})$ for essentially the same restriction on $n$
as in the best-known transforms due to Ailon and Liberty [SODA, 2008], and
Bamberger and Krahmer [arXiv, 2017]. Our algorithm is memory-optimal, and
outperforms existing algorithms in regimes when $n$ is sufficiently large and
the distortion parameter is sufficiently small. In particular, this confirms a
conjecture of Ailon and Chazelle [STOC, 2006] in a stronger form.
  (2) The same construction gives a simple transform with optimal Restricted
Isometry Property (RIP) which can be applied in time $O(d\log{d})$ for
essentially the same range of sparsity as in the best-known such transform due
to Ailon and Rauhut [Discrete Comput. Geom., 2014].
  (3) We show that by fixing the angle in the Kac walk to be $\pi/4$
throughout, one obtains optimal JL and RIP transforms with almost the same
running time, thereby confirming -- up to a $\log\log{d}$ factor -- a
conjecture of Avron, Maymounkov, and Toledo [SIAM J. Sci. Comput., 2010]. Our
moment-based analysis of this modification of the Kac walk may also be of
independent interest.


  Color centers in silicon carbide (SiC) have demonstrated significant promise
for quantum information processing. However, the undesirable ionization process
that occurs during optical manipulation frequently causes fluctuations in the
charge state and performance of these defects, thereby restricting the
effectiveness of spin-photon interfaces. Recent predictions indicate that
divacancy defects near stacking faults possess the capability to stabilize
their neutral charge states, thereby providing robustness against
photoionization effects. In this work, we present a comprehensive protocol for
the scalable and targeted fabrication of single divacancy arrays in 4H-SiC
using a high-resolution focused helium ion beam. Through photoluminescence
emission (PLE) experiments, we demonstrate long-term emission stability with
minimal linewidth shift ($\sim$ 50 MHz over 3 hours) for the single c-axis
divacancies within stacking faults. By measuring the ionization rate for
different polytypes of divacancies, we found that the divacancies within
stacking faults are more robust against resonant excitation. Additionally,
angle-resolved PLE spectra reveal their two resonant-transition lines with
mutually orthogonal polarizations. Notably, the PLE linewidths are
approximately 7 times narrower and the spin-coherent times are 6 times longer
compared to divacancies generated via carbon-ion implantation. These findings
highlight the immense potential of SiC divacancies for on-chip quantum
photonics and the construction of efficient spin-to-photon interfaces,
indicating a significant step forward in the development of quantum
technologies.


  We consider impulsive dynamical systems defined on compact metric spaces and
their respective impulsive semiflows. We establish sufficient conditions for
the existence of probability measures which are invariant by such impulsive
semiflows. We also deduce the forward invariance of their non-wandering sets
except the discontinuity points.


  Using the CLASH-VLT survey, we assembled an unprecedented sample of 1234
spectroscopically confirmed members in Abell~S1063, finding a dynamically
complex structure at z_cl=0.3457 with a velocity dispersion \sigma_v=1380 -32
+26 km s^-1. We investigate cluster environmental and dynamical effects by
analysing the projected phase-space diagram and the orbits as a function of
galaxy spectral properties. We classify cluster galaxies according to the
presence and strength of the [OII] emission line, the strength of the H$\delta$
absorption line, and colours. We investigate the relationship between the
spectral classes of galaxies and their position in the projected phase-space
diagram. We analyse separately red and blue galaxy orbits. By correlating the
observed positions and velocities with the projected phase-space constructed
from simulations, we constrain the accretion redshift of galaxies with
different spectral types. Passive galaxies are mainly located in the virialised
region, while emission-line galaxies are outside r_200, and are accreted later
into the cluster. Emission-lines and post-starbursts show an asymmetric
distribution in projected phase-space within r_200, with the first being
prominent at Delta_v/sigma <~-1.5$, and the second at Delta_v/ sigma >~ 1.5,
suggesting that backsplash galaxies lie at large positive velocities. We find
that low-mass passive galaxies are accreted in the cluster before the high-mass
ones. This suggests that we observe as passives only the low-mass galaxies
accreted early in the cluster as blue galaxies, that had the time to quench
their star formation. We also find that red galaxies move on more radial orbits
than blue galaxies. This can be explained if infalling galaxies can remain blue
moving on tangential orbits.


  We investigate the geometry of four dimensional black hole solutions in the
presence of stringy higher curvature corrections to the low energy effective
action. For certain supersymmetric two charge black holes these corrections
drastically alter the causal structure of the solution, converting seemingly
pathological null singularities into timelike singularities hidden behind a
finite area horizon. We establish, analytically and numerically, that the
string-corrected two-charge black hole metric has the same Penrose diagram as
the extremal four-charge black hole. The higher derivative terms lead to
another dramatic effect -- the gravitational force exerted by a black hole on
an inertial observer is no longer purely attractive! The magnitude of this
effect is related to the size of the compactification manifold.


  Radio Frequency Fingerprint (RFF) identification on account of deep learning
has the potential to enhance the security performance of wireless networks.
Recently, several RFF datasets were proposed to satisfy requirements of
large-scale datasets. However, most of these datasets are collected from 2.4G
WiFi devices and through similar channel environments. Meanwhile, they only
provided receiving data collected by the specific equipment. This paper
utilizes software radio peripheral as a dataset generating platform. Therefore,
the user can customize the parameters of the dataset, such as frequency band,
modulation mode, antenna gain, and so on. In addition, the proposed dataset is
generated through various and complex channel environments, which aims to
better characterize the radio frequency signals in the real world. We collect
the dataset at transmitters and receivers to simulate a real-world RFF dataset
based on the long-term evolution (LTE). Furthermore, we verify the dataset and
confirm its reliability. The dataset and reproducible code of this paper can be
downloaded from GitHub link: https://github.com/njuptzsp/XSRPdataset.


  Our first goal in this work is to study general and model-independent
properties of cyclic cosmologies. The large number of studies of bouncing
cosmologies and different cyclic scenarios published recently calls for a
proper understanding of the universal properties of cyclic models. We thus
first review and further elaborate the common physical and geometrical
properties of various classes of cyclic models and then discuss how cyclic
Universe can be treated as a dynamic system. We then discuss how two theorems
from dynamic systems analysis can be used to ensure the existence of cyclic
cosmological solutions under certain conditions on the field equations. After
this we proceed towards our second goal which is the application of the
obtained results to different frameworks of modified gravity theories: $f(R)$
gravity, dynamic dark energy and $f(T)$ gravity. We discuss the general
requirements for the existence of cyclic solutions in these theories and also
obtain various examples of cyclic cosmologies, while discussing their basic
properties.


  The paper addresses the issue of reliability of complex embedded control
systems in the safety-critical environment. In this paper, we propose a novel
approach to design controller that (i) guarantees the safety of nonlinear
physical systems, (ii) enables safe system restart during runtime, and (iii)
allows the use of complex, unverified controllers (e.g., neural networks) that
drive the physical systems towards complex specifications. We use
abstraction-based controller synthesis approach to design a formally verified
controller that provides application and system-level fault tolerance along
with safety guarantee. Moreover, our approach is implementable using
commercial-off-the-shelf (COTS) processing unit. To demonstrate the efficacy of
our solution and to verify the safety of the system under various types of
faults injected in applications and in the underlying real-time operating
system (RTOS), we implemented the proposed controller for the inverted pendulum
and three degree-of-freedom (3-DOF) helicopter.


  The author introduces a conjecture about Makar-Limanov invariants of affine
unique factorization domains over a field of characteristic zero. Then the
author finds that the conjecture does not always hold when $\mathbbm{k}$ is not
algebraically closed and gives some examples where the conjecture holds.


  It is proved that the KAM tori (thus quasi-periodic solutions) are long time
stable for infinite dimensional Hamiltonian systems generated by nonlinear wave
equation, by constructing a partial normal form of higher order around the KAM
torus and showing $p$-tame property persists under KAM iterative procedure and
normal form iterative procedure.


  We present an re-analysis of the longest timescale gravitational microlensing
event discovered to date: MACHO-99-BLG-22/OGLE-1999-BUL-32, which was
discovered by both the MACHO and OGLE microlensing alert systems. Our analysis
of this microlensing parallax event includes a likelihood analysis of the lens
position based upon a standard model of the Galactic velocity distribution, and
this implies that the lens could be a black hole of ~100 M_solar at a distance
of a few hundred parsecs in the Galactic disk or a massive stellar remnant
(black hole or neutron star) in the Galactic bulge. Our new analysis includes
data from the MACHO, GMAN, and MPS collaborations in addition to the OGLE data
used in a previous analysis by Mao et al (2002). The crucial feature that
distinguishes our analysis from that of Mao et al is an accurate constraint on
the direction of lens motion and an analysis of the implications of this
direction.


  This paper shows any non-Anosov partially hyperbolic diffeomorphism on the
3-torus which is homotopic to Anosov must be accessible.


  We present new evidence for a large deficiency in the local galaxy
distribution situated in the 4000 sq.deg. APM survey area. We use models guided
by the 2dF Galaxy Redshift Survey (2dFGRS) n(z) as a probe of the underlying
LSS. We first check the usefulness of this technique by comparing the 2dFGRS
n(z) model prediction with the K-band and B-band number counts extracted from
the 2MASS and 2dFGRS parent catalogues over the 2dFGRS Northern and Southern
declination strips, before turning to a comparison with the APM counts. We find
that the APM counts in both the B and K-bands indicate a deficiency in the
local galaxy distribution of approx. 30% to z=0.1 over the entire APM survey
area. We examine the implied significance of such a large local hole,
considering several possible forms for the real-space correlation function. We
find that such a deficiency in the APM survey area indicates an excess of power
at large scales over what is expected from the correlation function observed in
the 2dFGRS correlation function or predicted from $\Lambda$CDM Hubble Volume
mock catalogues. In order to check further the clustering at large scales in
the 2MASS data, we have calculated the angular power spectrum for 2MASS
galaxies. Although in the linear regime (l<30), LCDM models can give a good fit
to the 2MASS angular power spectrum, over a wider range (l<100) the power
spectrum from Hubble Volume mock catalogues suggests that scale-dependent bias
may be needed for LCDM to fit. However, the modest increase in large-scale
power observed in the 2MASS angular power spectrum is still not enough to
explain the local hole.


  For many patients, current ovarian cancer treatments offer limited clinical
benefit. For some therapies, it is not possible to predict patients' responses,
potentially exposing them to the adverse effects of treatment without any
therapeutic benefit. As part of the automated prediction of treatment
effectiveness in ovarian cancer using histopathological images (ATEC23)
challenge, we evaluated the effectiveness of deep learning to predict whether a
course of treatment including the antiangiogenic drug bevacizumab could
contribute to remission or prevent disease progression for at least 6 months in
a set of 282 histopathology whole slide images (WSIs) from 78 ovarian cancer
patients. Our approach used a pretrained Hierarchical Image Pyramid Transformer
(HIPT) to extract region-level features and an attention-based multiple
instance learning (ABMIL) model to aggregate features and classify whole
slides. The optimal HIPT-ABMIL model had an internal balanced accuracy of 60.2%
+- 2.9% and an AUC of 0.646 +- 0.033. Histopathology-specific model pretraining
was found to be beneficial to classification performance, though hierarchical
transformers were not, with a ResNet feature extractor achieving similar
performance. Due to the dataset being small and highly heterogeneous,
performance was variable across 5-fold cross-validation folds, and there were
some extreme differences between validation and test set performance within
folds. The model did not generalise well to tissue microarrays, with accuracy
worse than random chance. It is not yet clear whether ovarian cancer WSIs
contain information that can be used to accurately predict treatment response,
with further validation using larger, higher-quality datasets required.


  The recent discovery of two-dimensional magnetic insulators has generated a
great deal of excitement over their potential for nanoscale manipulation of
spin or magnetism. One intriguing use for these materials is to put them in
contact with graphene, with the goal of making graphene magnetic while
maintaining its unique electronic properties. Such a system could prove useful
in applications such as magnetic memories, or could serve as a host for exotic
states of matter. Proximity to a magnetic insulator will alter the spin
transport properties of graphene, and the strength of this interaction can be
probed with Hanle spin precession experiments. To aid in the analysis of such
experiments, in this work we derive an explicit expression for Hanle spin
precession in graphene interfaced with a ferromagnetic insulator whose
magnetization points perpendicular to the graphene plane. We find that this
interface results in a shifted and asymmetric Hanle response, and we discuss
how this behavior can be used to interpret measurements of spin transport in
these systems.


  In this paper we provide the first examples of arithmetic hyperbolic
3-manifolds that are rational homology spheres and bound geometrically either
compact or cusped hyperbolic 4-manifolds.


  If a sparse semidefinite program (SDP), specified over $n\times n$ matrices
and subject to $m$ linear constraints, has an aggregate sparsity graph $G$ with
small treewidth, then chordal conversion will sometimes allow an interior-point
method to solve the SDP in just $O(m+n)$ time per-iteration, which is a
significant speedup over the $\Omega(n^{3})$ time per-iteration for a direct
application of the interior-point method. Unfortunately, the speedup is not
guaranteed by an $O(1)$ treewidth in $G$ that is independent of $m$ and $n$, as
a diagonal SDP would have treewidth zero but can still necessitate up to
$\Omega(n^{3})$ time per-iteration. Instead, we construct an extended aggregate
sparsity graph $\bar{G}\supseteq G$ by forcing each constraint matrix $A_{i}$
to be its own clique in $G$. We prove that a small treewidth in $\bar{G}$ does
indeed guarantee that chordal conversion will solve the SDP in $O(m+n)$ time
per-iteration, to $\epsilon$-accuracy in at most
$O(\sqrt{m+n}\log(1/\epsilon))$ iterations. This sufficient condition covers
many successful applications of chordal conversion, including the MAX-$k$-CUT
relaxation, the Lov\'asz theta problem, sensor network localization, polynomial
optimization, and the AC optimal power flow relaxation, thus allowing theory to
match practical experience.


  We present a systematic technique to construct solutions to the Yang-Baxter
equation which depend not only on a spectral parameter but in addition on
further continuous parameters. These extra parameters enter the Yang-Baxter
equation in a similar way to the spectral parameter but in a non-additive form.
We exploit the fact that quantum non-compact algebras such as $U_q(su(1,1))$
and type-I quantum superalgebras such as $U_q(gl(1|1))$ and $U_q(gl(2|1))$ are
known to admit non-trivial one-parameter families of infinite-dimensional and
finite dimensional irreps, respectively, even for generic $q$. We develop a
technique for constructing the corresponding spectral-dependent R-matrices. As
examples we work out the the $R$-matrices for the three quantum algebras
mentioned above in certain representations.


  In this paper a measure of complexity of the system of angle-angular momentum
quantum states produced in hadronic scattering is introduced in terms of the
scattering entropies. We presented strong experimental evidence for the
saturation of the entropic optimal limits in the pion-nucleon and kaon-nucleon
scatterings. The validity of a principle of minimum complexity in hadronic
interaction is supported with high accuracy (CL>99%) by the experimental data
on pion-nucleon especially at energies higher than 2 GeV.


  Preserving contour topology during image segmentation is useful in many
practical scenarios. By keeping the contours isomorphic, it is possible to
prevent over-segmentation and under-segmentation, as well as to adhere to given
topologies. The Self-repelling Snake model (SR) is a variational model that
preserves contour topology by combining a non-local repulsion term with the
geodesic active contour model (GAC). The SR is traditionally solved using the
additive operator splitting (AOS) scheme. In our paper, we propose an
alternative solution to the SR using the Split Bregman method. Our algorithm
breaks the problem down into simpler sub-problems to use lower-order evolution
equations and a simple projection scheme rather than re-initialization. The
sub-problems can be solved via fast Fourier transform (FFT) or an approximate
soft thresholding formula which maintains stability, shortening the convergence
time, and reduces the memory requirement. The Split Bregman and AOS algorithms
are compared theoretically and experimentally.


  We define a general scheme for the evolution of fragmentation functions which
resums soft gluon logarithms in a manner consistent with fixed order evolution.
We present an explicit example of our approach in which double logarithms are
resummed using the Double Logarithmic Approximation. We show that this scheme
reproduces the Modified Leading Logarithm Approximation in certain limits, and
find that after using it to fit quark and gluon fragmentation functions to
experimental data,a good description of the data from the largest x values to
the peak region in ln (1/x) is obtained. In addition, we develop a treatment of
hadron mass effects which gives additional improvements at small x.


  The UKIDSS Large Area Survey (LAS) began in 2005, with the start of the
UKIDSS program as a 7 year effort to survey roughly 4000 deg$^2$ at high
galactic latitudes in Y, J, H and K bands. The survey also included a
significant quantity of 2-epoch J band observations, with an epoch baseline
greater than 2 years to calculate proper motions. We present a near infrared
proper motion catalogue for the 1500 deg$^2$ of the 2 epoch LAS data, which
includes 135,625 stellar sources and a further 88,324 with ambiguous
morphological classifications, all with motions detected above the 5$\sigma$
level. We developed a custom proper motion pipeline which we describe here. Our
catalogue agrees well with the proper motion data supplied for a 300 deg$^2$
subset in the current WFCAM Science Archive (WSA) tenth data release (DR10)
catalogue, and in various optical catalogues, but it benefits from a larger
matching radius and hence a larger upper proper motion detection limit. We
provide absolute proper motions, using LAS galaxies for the relative to
absolute correction. By using local 2nd order polynomial transformations, as
opposed to linear transformations in the WSA, we correct better for any local
distortions in the focal plane, not including the radial distortion that is
removed by the UKIDSS pipeline. We present the results of proper motion
searches for new brown dwarfs and white dwarfs. We discuss 41 sources in the
WSA DR10 overlap with our catalogue with proper motions $>$300 $mas yr^{-1}$,
several of which are new detections. We present 15 new candidate ultra-cool
dwarf binary systems.


  We consider the Quantum Navier-Stokes system in three space dimensions. We
prove compactness of finite energy weak solutions for large initial data. The
main novelties are that vacuum regions are included in the weak formulation and
no extra terms, like damping or cold pressure, are considered in the equations
in order to define the velocity field. Our argument uses an equivalent
formulation of the system in terms of an effective velocity, in order to
eliminate the third order terms in the new system. It allows us to derive
estimates similar to the ones available in the case of the compressible
Navier-Stokes with degenerate viscosity.


  We prove that every finite dimensional unitary representation of
$\mathrm{SL}_{4}(\mathbf{Z})$ contains a non-zero
$\mathrm{SL}_{2}(\mathbf{Z})$-invariant vector. As a consequence, there is no
sequence of finite-dimensional representations of $\mathrm{SL}_{4}(\mathbf{Z})$
that gives rise to an embedding of its reduced $C^*$-algebra into an
ultraproduct of matrix algebras.


  We have performed x-ray photoemission spectroscopy on the system of
noncentrosymmetric superconductor, Li$_2$(Pd$_x$Pt$_{1-x}$3)B. For
Li$_2$Pt$_3$B, we found 2 major peaks with 2 other weak components, and the
band calculations were in agreement with the observation. The assignment of
valence band features using the calculated partial density of states determined
that Pt 5d and B 2p contribute to the density of states at the Fermi level. The
effect of antisymmetric spin-orbit coupling on the band structure might have
been probed, and the analysis on the effect of Pt incorporation into the system
indicates the smooth evolution of electronic structures. We presented the
measurements of core levels (Pd 3d, Pt 4f, and B 1s) and discussed the chemical
bonding states and electronic structures from them.


  We consider the problem of discovering novel object categories in an image
collection. While these images are unlabelled, we also assume prior knowledge
of related but different image classes. We use such prior knowledge to reduce
the ambiguity of clustering, and improve the quality of the newly discovered
classes. Our contributions are twofold. The first contribution is to extend
Deep Embedded Clustering to a transfer learning setting; we also improve the
algorithm by introducing a representation bottleneck, temporal ensembling, and
consistency. The second contribution is a method to estimate the number of
classes in the unlabelled data. This also transfers knowledge from the known
classes, using them as probes to diagnose different choices for the number of
classes in the unlabelled subset. We thoroughly evaluate our method,
substantially outperforming state-of-the-art techniques in a large number of
benchmarks, including ImageNet, OmniGlot, CIFAR-100, CIFAR-10, and SVHN.


  Crack detection plays a key role in automated pavement inspection. Although a
large number of algorithms have been developed in recent years to further boost
performance, there are still remaining challenges in practice, due to the
complexity of pavement images. To further accelerate the development and
identify the remaining challenges, this paper conducts a comparison study to
evaluate the performance of the state of the art crack detection algorithms
quantitatively and objectively. A more comprehensive annotated pavement crack
dataset (NHA12D) that contains images with different viewpoints and pavements
types is proposed. In the comparison study, crack detection algorithms were
trained equally on the largest public crack dataset collected and evaluated on
the proposed dataset (NHA12D). Overall, the U-Net model with VGG-16 as backbone
has the best all-around performance, but models generally fail to distinguish
cracks from concrete joints, leading to a high false-positive rate. It also
found that detecting cracks from concrete pavement images still has huge room
for improvement. Dataset for concrete pavement images is also missing in the
literature. Future directions in this area include filling the gap for concrete
pavement images and using domain adaptation techniques to enhance the detection
results on unseen datasets.


  The accuracy of deep learning methods for two foundational tasks in medical
image analysis -- detection and segmentation -- can suffer from class
imbalance. We propose a `switching loss' function that adaptively shifts the
emphasis between foreground and background classes. While the existing loss
functions to address this problem were motivated by the classification task,
the switching loss is based on Dice loss, which is better suited for
segmentation and detection. Furthermore, to get the most out the training
samples, we adapt the loss with each mini-batch, unlike previous proposals that
adapt once for the entire training set. A nucleus detector trained using the
proposed loss function on a source dataset outperformed those trained using
cross-entropy, Dice, or focal losses. Remarkably, without retraining on target
datasets, our pre-trained nucleus detector also outperformed existing nucleus
detectors that were trained on at least some of the images from the target
datasets. To establish a broad utility of the proposed loss, we also confirmed
that it led to more accurate ventricle segmentation in MRI as compared to the
other loss functions. Our GPU-enabled pre-trained nucleus detection software is
also ready to process whole slide images right out-of-the-box and is usably
fast.


  Providing artificial agents with the same computational models of biological
systems is a way to understand how intelligent behaviours may emerge. We
present an active inference body perception and action model working for the
first time in a humanoid robot. The model relies on the free energy principle
proposed for the brain, where both perception and action goal is to minimise
the prediction error through gradient descent on the variational free energy
bound. The body state (latent variable) is inferred by minimising the
difference between the observed (visual and proprioceptive) sensor values and
the predicted ones. Simultaneously, the action makes sensory data sampling to
better correspond to the prediction made by the inner model. We formalised and
implemented the algorithm on the iCub robot and tested in 2D and 3D visual
spaces for online adaptation to visual changes, sensory noise and discrepancies
between the model and the real robot. We also compared our approach with
classical inverse kinematics in a reaching task, analysing the suitability of
such a neuroscience-inspired approach for real-world interaction. The algorithm
gave the robot adaptive body perception and upper body reaching with head
object tracking (toddler-like), and was able to incorporate visual features
online (in a closed-loop manner) without increasing the computational
complexity. Moreover, our model predicted involuntary actions in the presence
of sensorimotor conflicts showing the path for a potential proof of active
inference in humans.


  We use a composite gravitational galactic model consisting of a disk, a halo,
a massive nucleus and a strong nuclear bar, in order to study the connections
between global and local parameters in a realistic dynamical system. The local
model is constructed from a two-dimensional perturbed harmonic oscillator and
can be derived by expanding the global model in the vicinity of the central
stable Lagrange equilibrium point. The frequencies of oscillations are not
arbitrary, but they are connected with all the parameters involved with the
global model. Moreover, the value of the local energy is also connected with
the value of the global energy. Low and high energy stars in the global model
display chaotic motion. Comparison with previous research reveals that the
presence of the massive nucleus is responsible for the chaotic motion of the
low energy stars. In the local motion, the low energy stars show interesting
resonance phenomena, but the chaotic motion, if any, is negligible. On the
contrary, the high energy stars do not show bounded motion in the local model.
This is an indication of particular activity near the center of galaxies
possessing massive nuclei.


  Large-scale non-convex sparsity-constrained problems have recently gained
extensive attention. Most existing deterministic optimization methods (e.g.,
GraSP) are not suitable for large-scale and high-dimensional problems, and thus
stochastic optimization methods with hard thresholding (e.g., SVRGHT) become
more attractive. Inspired by GraSP, this paper proposes a new general relaxed
gradient support pursuit (RGraSP) framework, in which the sub-algorithm only
requires to satisfy a slack descent condition. We also design two specific
semi-stochastic gradient hard thresholding algorithms. In particular, our
algorithms have much less hard thresholding operations than SVRGHT, and their
average per-iteration cost is much lower (i.e., O(d) vs. O(d log(d)) for
SVRGHT), which leads to faster convergence. Our experimental results on both
synthetic and real-world datasets show that our algorithms are superior to the
state-of-the-art gradient hard thresholding methods.


  QCD sum rules are overviewed with an emphasize on the practical applications
of this method to the physics of light and heavy hadrons.


  ER UMa stars are a recently recognized small subgroup of SU UMa-type dwarf
novae, which are characterized by the extremely high outburst frequency and
short (19--48 d) supercycles. From the current thermal-tidal disk instability
scheme, they are considered to be high mass-transfer SU UMa-type dwarf novae,
and comprise a link to "permanent superhumpers" below the period gap. They do
not only provide an opportunity to test the applicability of thermal-tidal
instability model but also pose problems on the origin of high mass-transfer in
short orbital-period cataclysmic variables. A historical review of this
subgroup and recent topics of ER UMa stars, the unique pattern of superhump
evolution and the "helium ER UMa analog" (CR Boo), are also discussed.


  Let $R$ and $B$ be two disjoint sets of points in the plane where the points
of $R$ are colored red and the points of $B$ are colored blue, and let
$n=|R\cup B|$. A bichromatic spanning tree is a spanning tree in the complete
bipartite geometric graph with bipartition $(R,B)$. The minimum (respectively
maximum) bichromatic spanning tree problem is the problem of computing a
bichromatic spanning tree of minimum (respectively maximum) total edge length.
  1. We present a simple algorithm that solves the minimum bichromatic spanning
tree problem in $O(n\log^3 n)$ time. This algorithm can easily be extended to
solve the maximum bichromatic spanning tree problem within the same time bound.
It also can easily be generalized to multicolored point sets.
  2. We present $\Theta(n\log n)$-time algorithms that solve the minimum and
the maximum bichromatic spanning tree problems.
  3. We extend the bichromatic spanning tree algorithms and solve the
multicolored version of these problems in $O(n\log n\log k)$ time, where $k$ is
the number of different colors (or the size of the multipartition in a complete
multipartite geometric graph).


  We study Vafa's geometric transition and Klebanov - Strassler solution from
various points of view in M-theory. In terms of brane configurations, we show
the detailed equivalences between the two models. In some limits, both models
have an alternative realization as fourfolds in M-theory with appropriate
G-fluxes turned on. We discuss some aspects of the fourfolds including how to
see the transition and a possible extension to the non-supersymmetric case.


  We survey Lagrangian fibrations of holomorphic symplectic varieties, both
compact and non-compact, whose fibres are Jacobians and Prym varieties.


  We study laser cooling of $^{24}$Mg atoms in dipole optical trap with pumping
field resonant to narrow $(3s3s)\,^1S_0 \rightarrow \, (3s3p)\,^{3}P_1$
($\lambda = 457$ nm) optical transition. For description of laser cooling of
atoms in the optical trap with taking into account quantum recoil effects we
consider two quantum models. The first one is based on direct numerical
solution of quantum kinetic equation for atom density matrix and the second one
is simplified model based on decomposition of atom density matrix over
vibration states in the dipole trap. We search pumping field intensity and
detuning for minimum cooling energy and fast laser cooling.


  The major challenge in audio-visual event localization task lies in how to
fuse information from multiple modalities effectively. Recent works have shown
that attention mechanism is beneficial to the fusion process. In this paper, we
propose a novel joint attention mechanism with multimodal fusion methods for
audio-visual event localization. Particularly, we present a concise yet valid
architecture that effectively learns representations from multiple modalities
in a joint manner. Initially, visual features are combined with auditory
features and then turned into joint representations. Next, we make use of the
joint representations to attend to visual features and auditory features,
respectively. With the help of this joint co-attention, new visual and auditory
features are produced, and thus both features can enjoy the mutually improved
benefits from each other. It is worth noting that the joint co-attention unit
is recursive meaning that it can be performed multiple times for obtaining
better joint representations progressively. Extensive experiments on the public
AVE dataset have shown that the proposed method achieves significantly better
results than the state-of-the-art methods.


  We investigate the possibility of a fourth sequential generation in the
lepton sector. Assuming neutrinos to be Majorana particles and starting from a
recent - albeit weak - evidence for a non-zero admixture of a fourth generation
neutrino from fits to weak lepton and meson decays we discuss constraints from
neutrinoless double beta decay, radiative lepton decay and like-sign dilepton
production at hadron colliders. Also an idea for fourth generation neutrino
mass model building is briefly outlined. Here we soften the large hierarchy of
the neutrino masses within an extradimensional model that locates each
generation on different lepton number violating branes without large
hierarchies.


  Time-periodic solutions to the Navier-Stokes equations that govern the flow
of a viscous liquid past a three-dimensional body moving with a time-periodic
velocity are investigated. The net motion of the body over a full time-period
is assumed to be non-zero. In this case the appropriate linearization of the
system is constituted by the time-periodic Oseen equations in a
three-dimensional exterior domain. A priori Lp estimates are established for
this linearization. Based on these estimates, existence of a solution to the
fully non-linear Navier-Stokes problem is obtained by the contraction mapping
principle.


  The purpose of this paper is to investigate the structure of Shlyakhtenko's
free Araki-Woods factors using the framework of ultraproduct von Neumann
algebras. We first prove that all the free Araki-Woods factors
$\Gamma(H_{\mathbb R}, U_t)^{\prime \prime}$ are $\omega$-solid in the
following sense: for every von Neumann subalgebra $Q \subset \Gamma(H_{\mathbb
R}, U_t)^{\prime \prime}$ that is the range of a faithful normal conditional
expectation and such that the relative commutant $Q' \cap M^\omega$ is diffuse,
we have that $Q$ is amenable. Next, we prove that the continuous cores of the
free Araki-Woods factors $\Gamma(H_{\mathbb R}, U_t)^{\prime \prime}$
associated with mixing orthogonal representations $U : \mathbb R \to \mathcal
O(H_{\mathbb R})$ are $\omega$-solid type ${\rm II_\infty}$ factors. Finally,
when the orthogonal representation $U : \mathbb R \to \mathcal O(H_{\mathbb
R})$ is weakly mixing, we prove a dichotomy result for all the von Neumann
subalgebras $Q \subset \Gamma(H_{\mathbb R}, U_t)^{\prime \prime}$ that are
globally invariant under the modular automorphism group
$(\sigma_t^{\varphi_U})$ of the free quasi-free state $\varphi_U$.


  In this paper we point out a converse result of the celebrated Jensen
inequality for differentiable convex mappings of several variables and apply it
to counterpart well-known analytic inequalities. Applications to Shannon's and
Renyi's entropy mappings are also given.


  We revisit the well-known object-pool design pattern in Java. In the last
decade, the pattern has attracted a lot of criticism regarding its validity
when used for light-weight objects that are only meant to hold memory rather
than any other resources (database connections, sockets etc.) and in fact,
common opinion holds that is an anti-pattern in such cases. Nevertheless, we
show through several experiments in different systems that the use of this
pattern for extremely short-lived and light-weight memory objects can in fact
significantly reduce the response time of high-performance multi-threaded
applications, especially in memory-constrained environments. In certain
multi-threaded applications where high performance is a requirement and/or
memory constraints exist, we recommend therefore that the object pool pattern
be given consideration and tested for possible run-time as well as memory
footprint improvements.


  This study aims at making the architecture search process more adaptive for
one-shot or online training. It is extended from the existing study on
differentiable neural architecture search, and we made the backbone
architecture transformable rather than fixed during the training process. As is
known, differentiable neural architecture search (DARTS) requires a pre-defined
over-parameterized backbone architecture, while its size is to be determined
manually. Also, in DARTS backbone, Hadamard product of two elements is not
introduced, which exists in both LSTM and GRU cells for recurrent nets. This
study introduces a growing mechanism for differentiable neural architecture
search based on network morphism. It enables growing of the cell structures
from small size towards large size ones with one-shot training. Two modes can
be applied in integrating the growing and original pruning process. We also
implement a recently proposed two-input backbone architecture for recurrent
neural networks. Initial experimental results indicate that our approach and
the two-input backbone structure can be quite effective compared with other
baseline architectures including LSTM, in a variety of learning tasks including
multi-variate time series forecasting and language modeling. On the other hand,
we find that dynamic network transformation is promising in improving the
efficiency of differentiable architecture search.


  The LHC is a promising machine to discover new physics in the top sector.
There are several models that predict the existence of heavy colored resonances
decaying to top quarks in the TeV energy range. The production of such
resonances might generate a sizable charge asymmetry of top versus antitop
quarks. At the Tevatron, a 2 sigma discrepancy with the SM prediction for the
forward--backward asymmetry has been found, boosting a renewed interest for
this kind of models. We consider a toy model with general flavour dependent
couplings of the resonance to quarks, of both vector and axial-vector kind and
investigate the possible constraints on the coupling space from the measurement
of the asymmetry and the invariant mass distribution at the Tevatron. Then, we
define a central asymmetry in a specific kinematic region and investigate its
signature at the LHC as well as its statistical significance, for exclusive
processes.


  Disoriented chiral condensates are manifested as long wavelength pionic
oscillations and their interaction with the thermal environment can be a
significant source of dileptons. We calculate the yield of such dilepton
production within the linear sigma model and illustrate the basic features of
the dilepton spectrum in a schematic model. We find that the dilepton yield
with invariant mass near and below $2m_{\pi}$ due to the soft pion modes can be
up to two orders of magnitude larger than the corresponding equilibrium yield.
We conclude with a discussion on how this enhancement can be detected by
present dilepton experiments.


  In this paper, we study the dihedral codes, i.e. the left ideals of
$\mathbb{F}_qD_{n}$ in the case $\gcd(q, n) = 1$. An explicit algebraic
description of the dihedral codes and their duals is obtained. In addition, a
criterion for self-duality of a dihedral code is obtained. Bases, generating
and check matrices of dihedral codes are constructed. Given a dihedral code, we
consider exterior and interior codes that are induced by cyclic codes. Using
this codes, some properties of generating matrices are described and a
connection to cyclic code theory is established. In addition, some estimates of
code parameters are obtained and several illustrative examples are given.


  Although resource-limited networked autonomous systems must be able to
efficiently and effectively accomplish tasks, better conservation of resources
often results in worse task performance. We specifically address the problem of
finding strategies for managing measurement communication costs between agents.
A well understood technique for trading off communication costs with estimation
accuracy is event triggering (ET), where measurements are only communicated
when useful, e.g., when Kalman filter innovations exceed some threshold. In the
absence of measurements, agents can use implicit information to achieve results
almost as well as when explicit data is always communicated. However, there are
no methods for setting this threshold with formal guarantees on task
performance. We fill this gap by developing a novel belief space discretization
technique to abstract a continuous space dynamics model for ET estimation to a
discrete Markov decision process, which scalably accommodates
threshold-sensitive ET estimator error covariances. We then apply an existing
probabilistic trade-off analysis tool to find the set of all optimal trade-offs
between resource consumption and task performance. From this set, an ET
threshold selection strategy is extracted. Simulated results show our approach
identifies non-trivial trade-offs between performance and energy savings, with
only modest computational effort.


  We give classifications of group gradings, up to equivalence and up to
isomorphism, on the tensor product of a Cayley algebra $\mathcal{C}$ and a
Hurwitz algebra over a field of characteristic different from 2. We also prove
that the automorphism group schemes of $\mathcal{C}^{\otimes n}$ and
$\mathcal{C}^n$ are isomorphic.
  On the other hand, we prove that the automorphism group schemes of a Smirnov
algebra (a $35$-dimensional simple exceptional structurable algebra constructed
from a Cayley algebra $\mathcal{C}$) and $\mathcal{C}$ are isomorphic. This is
used to obtain classifications, up to equivalence and up to isomorphism, of the
group gradings on Smirnov algebras.


  The generating function of energy counting statistics is derived for phononic
junction systems. It is expressed in terms of the contour-ordered self-energy
of the lead with shifted arguments, $\Sigma^A(\tau, \tau') = \Sigma_L\bigl(\tau
+\hbar x(\tau), \tau' + \hbar x(\tau')\bigr) - \Sigma_L(\tau, \tau')$, where
$\Sigma_L(\tau,\tau')$ is the usual contour-ordered self-energy of the left
lead. The cumulants of the energy transferred in a given time $t_M$ from the
lead to the center is obtained by taking derivatives. A transient result of the
first four cumulants of a graphene junction is presented. It is found that
measurements cause the energy to flow into the lead.


  The geometry of the dark energy and cold dark matter dominated cosmological
model (LambdaCDM) is commonly assumed to be given by a
Friedmann-Lemaitre-Robertson-Walker (FLRW) metric, i.e. it assumes homogeneity
in the comoving spatial section. The homogeneity assumption fails most strongly
at (i) small distance scales and (ii) recent epochs, implying that the FLRW
approximation is most likely to fail at these scales. We use the virialisation
fraction to quantify (i) and (ii), which approximately coincide with each other
on the observational past light cone. For increasing time, the virialisation
fraction increases above 10% at about the same redshift (sim 1-3) at which
Omega_Lambda grows above 10% (approx 1.8). Thus, instead of non-zero
Omega_Lambda, we propose an approximate, general-relativistic correction to the
matter-dominated (Omega_m =1, Omega_Lambda=0), homogeneous metric (Einstein de
Sitter, EdS). A low-redshift effective matter-density parameter of
Omega_m^eff(0) = 0.26 pm 0.05 is inferred. Over redshifts 0 < z < 3, the
distance modulus of the virialisation-corrected EdS model approximately matches
the LambdaCDM distance modulus. This rough approximation assumes "old physics"
(general relativity), not "new physics". Thus, pending more detailed
calculations, we strengthen the claim that "dark energy" should be considered
as an artefact of emerging average curvature in the void-dominated Universe,
via a novel approach that quantifies the relation between virialisation and
average curvature evolution.


  We generalize the existence of maximal orders in a semi-simple algebra for
general ground rings. We also improve several statements in Chapter 5 and 6 of
Reiner's book concerning separable algebras by removing the separability
condition, provided the ground ring is only assumed to be Japanese, a very mild
condition. Finally, we show the existence of maximal orders as endomorphism
rings of abelian varieties in each isogeny class.


  We present high-quality aperture synthesis observations of the neutral
hydrogen distribution in a sample of five galactic systems believed to be
involved in progressive stages of merging: Arp295, NGC4676, NGC520, NGC3921,
and NGC7252. These data are supplemented by wide-field images taken through a
narrow band Halpha filter, and by deep R-band surface photometry. In the early
stages, large amounts of HI exist within the galactic disks and star formation
is widespread. The ionized gas emission often takes on the appearance of plumes
and arcs emanating from the nuclear regions, which are presumably the sites of
interaction induced starbursts. In the final stages there is little if any HI
within the remnant bodies, and tidal material is seen moving inward. This
suggests that these remnants will evolve into elliptical galaxies in their
atomic gas contents as well as their photometric properties. However the
observations of NGC520 reveal an extensive rotating gaseous disk, suggesting
that perhaps some mergers will not destroy the atomic gas disks of the
progenitors. Overall, large quantities of both gas and starlight are seen at
large radii. Since this material evolves on very long time scales, it may leave
observable signatures for many Gyr.


  We perform a cosmographic analysis using several cosmological observables
such as the luminosity distance moduli, the volume distance, the angular
diameter distance and the Hubble parameter. These quantities are determined
using different data sets: Supernovae type Ia and Gamma Ray Bursts, the
Baryonic Acoustic Oscillations, the cosmic microwave background power spectrum
and the Hubble parameter as measured from surveys of galaxies. This data set
allows to put constraints on the cosmographic expansion with unprecedented
precision. We also present forecasts for the coefficients of the kinematic
expansion using future but realistic data sets: constraints on the coefficients
of the expansions are likely to improve by a factor ten with the upcoming large
scale structure probes. Finally, we derive the set of the cosmographic
parameters for several cosmological models (including $\Lambda$CDM) and compare
them with our best fit set. While distance measurements are unable to
discriminate among these models, we show that the inclusion of the Hubble data
set leads to strong constraints on the lowest order coefficients and in
particular it is incompatible with $\Lambda$CDM at 3-$\sigma$ confidence level.
We discuss the reliability of this determination and suggest further
observations which might be of crucial importance for the viability of
cosmographic tests in the next future.


  APACIC++ is a Monte-Carlo event-generator dedicated for the simulation of
electron-positron annihilations into jets. Within the framework of APACIC++,
the emergence of jets is identified with the perturbative production of partons
as governed by corresponding matrix elements. In addition to the build-in
matrix elements describing the production of two and three jets, further
programs can be linked allowing for the simultaneous treatment of higher
numbers of jets. APACIC++ hosts a new approach for the combination of arbitrary
matrix elements for the production of jets with the parton shower, which in
turn models the evolution of these jets. For the evolution, different ordering
schemes are available, namely ordering by virtualities or by angles. At the
present state, the subsequent hadronization of the partons is accomplished by
means of the Lund-string model as provided within Pythia. An appropriate
interface is provieded.
  The program takes full advantage of the object-oriented features provided by
C++ allowing for an equally abstract and transparent programming style.


  In this paper our first goal is to give precise definition of the L\'evy
bridges with random length. Our second task is to establish the Markov property
of this process with respect to its completed natural filtration and thus with
respect to the usual augmentation of this one. This property will be crucial
for the right-continuity of completed natural filtration.


  The Korean VLBI Network (KVN) is a new mm-VLBI dedicated array with
capability for simultaneous observations at multiple frequencies, up to 129
GHz. The innovative multi-channel receivers present significant benefits for
astrometric measurements in the frequency domain. The aim of this work is to
verify the astrometric performance of the KVN using a comparative study with
the VLBA, a well established instrument. For that purpose, we carried out
nearly contemporaneous observations with the KVN and the VLBA, at 14/7 mm, in
April 2013. The KVN observations consisted of simultaneous dual frequency
observations, while the VLBA used fast frequency switching observations. We
used the Source Frequency Phase Referencing technique for the observational and
analysis strategy. We find that having simultaneous observations results in a
superior performance for compensation of all atmospheric terms in the
observables, in addition to offering other significant benefits for astrometric
analysis. We have compared the KVN astrometry measurements to those from the
VLBA. We find that the structure blending effects introduce dominant systematic
astrometric shifts and these need to be taken into account. We have tested
multiple analytical routes to characterize the impact of the low resolution
effects for extended sources in the astrometric measurements. The results from
the analysis of KVN and full VLBA datasets agree within 2-$\sigma$ of the
thermal error estimate. We interpret the discrepancy as arising from the
different resolutions. We find that the KVN provides astrometric results with
excellent agreement, within 1-$\sigma$, when compared to a VLBA configuration
which has a similar resolution. Therefore this comparative study verifies the
astrometric performance of KVN using SFPR at 14/7 mm, and validates the KVN as
an astrometric instrument.


  A cellular-connected unmanned aerial vehicle (UAV)faces several key
challenges concerning connectivity and energy efficiency. Through a
learning-based strategy, we propose a general novel multi-armed bandit (MAB)
algorithm to reduce disconnectivity time, handover rate, and energy consumption
of UAV by taking into account its time of task completion. By formulating the
problem as a function of UAV's velocity, we show how each of these performance
indicators (PIs) is improved by adopting a proper range of corresponding
learning parameter, e.g. 50% reduction in HO rate as compared to a blind
strategy. However, results reveal that the optimal combination of the learning
parameters depends critically on any specific application and the weights of
PIs on the final objective function.


  This note is an attempt to unconditionally prove the existence of weak one
way functions (OWF). Starting from a provably intractable decision problem
$L_D$ (whose existence is nonconstructively assured from the well-known
discrete time-hierarchy theorem from complexity theory), we construct another
intractable decision problem $L\subseteq \{0,1\}^*$ that has its words
scattered across $\{0,1\}^\ell$ at a relative frequency $p(\ell)$, for which
upper and lower bounds can be worked out. The value $p(\ell)$ is computed from
the density of the language within $\{0,1\}^\ell$ divided by the total word
count $2^\ell$. It corresponds to the probability of retrieving a yes-instance
of a decision problem upon a uniformly random draw from $\{0,1\}^\ell$. The
trick to find a language with known bounds on $p(\ell)$ relies on switching
from $L_D$ to $L_0:=L_D\cap L'$, where $L'$ is an easy-to-decide language with
a known density across $\{0,1\}^*$. In defining $L'$ properly (and upon a
suitable G\"odel numbering), the hardness of deciding $L_D\cap L'$ is inherited
from $L_D$, while its density is controlled by that of $L'$. The lower and
upper approximation of $p(\ell)$ then let us construct an explicit threshold
function (as in random graph theory) that can be used to efficiently and
intentionally sample yes- or no-instances of the decision problem (language)
$L_0$ (however, without any auxiliary information that could ease the decision
like a polynomial witness). In turn, this allows to construct a weak OWF that
encodes a bit string $w\in\{0,1\}^*$ by efficiently (in polynomial time)
emitting a sequence of randomly constructed intractable decision problems,
whose answers correspond to the preimage $w$.


  We present a formulation of the multiconfigurational (MC) wave function
symmetry-adapted perturbation theory (SAPT). The method is applicable to
noncovalent interactions between monomers which require a multiconfigurational
description, in particular when the interacting system is strongly correlated
or in an electronically excited state. SAPT(MC) is based on one- and
two-particle reduced density matrices of the monomers and assumes the
single-exchange approximation for the exchange energy contributions.
Second-order terms are expressed through response properties from extended
random phase approximation (ERPA) equations. SAPT(MC) is applied either with
generalized valence bond perfect pairing (GVB) or with complete active space
self consistent field (CASSCF) treatment of the monomers. We discuss two model
multireference systems: the H2-H2 dimer in out-of-equilibrium geometries and
interaction between the argon atom and excited state of ethylene. In both cases
SAPT(MC) closely reproduces benchmark results. Using the C2H4-Ar complex as an
example, we examine second-order terms arising from negative transitions in the
linear response function of an excited monomer. We demonstrate that the
negative-transition terms must be accounted for to ensure qualitative
prediction of induction and dispersion energies and develop a procedure
allowing for their computation. Factors limiting the accuracy of SAPT(MC) are
discussed in comparison with other second-order SAPT schemes on a data set of
small single-reference dimers.


  We introduce a new geometric framework for the set of symmetric
positive-definite (SPD) matrices, aimed to characterize deformations of SPD
matrices by individual scaling of eigenvalues and rotation of eigenvectors of
the SPD matrices. To characterize the deformation, the eigenvalue-eigenvector
decomposition is used to find alternative representations of SPD matrices, and
to form a Riemannian manifold so that scaling and rotations of SPD matrices are
captured by geodesics on this manifold. The problems of non-unique
eigen-decompositions and eigenvalue multiplicities are addressed by finding
minimal-length geodesics, which gives rise to a distance and an interpolation
method for SPD matrices. Computational procedures to evaluate the minimal
scaling--rotation deformations and distances are provided for the most useful
cases of $2 \times 2$ and $3 \times 3$ SPD matrices. In the new geometric
framework, minimal scaling--rotation curves interpolate eigenvalues at constant
logarithmic rate, and eigenvectors at constant angular rate. In the context of
diffusion tensor imaging, this results in better behavior of the trace,
determinant and fractional anisotropy of interpolated SPD matrices in typical
cases.


  Intrinsic volumes, which generalize both Euler characteristic and Lebesgue
volume, are important properties of $d$-dimensional sets. A random cubical
complex is a union of unit cubes, each with vertices on a regular cubic
lattice, constructed according to some probability model. We analyze and give
exact polynomial formulae, dependent on a probability, for the expected value
and variance of the intrinsic volumes of several models of random cubical
complexes. We then prove a central limit theorem for these intrinsic volumes.
For our primary model, we also prove an interleaving theorem for the zeros of
the expected-value polynomials. The intrinsic volumes of cubical complexes are
useful for understanding the shape of random $d$-dimensional sets and for
characterizing noise in applications.


  We classify the simple sheaves microsupported along the conormal bundle of a
knot. We also establish a correspondence between simple sheaves up to local
systems and augmentations, explaining the underlying reason why knot contact
homology representations detect augmentations.


  We consider the problem of assigning appearing times to the edges of a
digraph in order to maximize the (average) temporal reachability between pairs
of nodes. Motivated by the application to public transit networks, where edges
cannot be scheduled independently one of another, we consider the setting where
the edges are grouped into certain walks (called trips) in the digraph and
where assigning the appearing time to the first edge of a trip forces the
appearing times of the subsequent edges. In this setting, we show that, quite
surprisingly, it is NP-complete to decide whether there exists an assignment of
times connecting a given pair of nodes. This result allows us to prove that the
problem of maximising the temporal reachability cannot be approximated within a
factor better than some polynomial term in the size of the graph. We thus focus
on the case where, for each pair of nodes, there exists an assignment of times
such that one node is reachable from the other. We call this property strong
temporalisability. It is a very natural assumption for the application to
public transit networks. On the negative side, the problem of maximising the
temporal reachability remains hard to approximate within a factor $\sqrt$ n/12
in that setting. Moreover, we show the existence of collections of trips that
are strongly temporalisable but for which any assignment of starting times to
the trips connects at most an O(1/ $\sqrt$ n) fraction of all pairs of nodes.
On the positive side, we show that there must exist an assignment of times that
connects a constant fraction of all pairs in the strongly temporalisable and
symmetric case, that is, when the set of trips to be scheduled is such that,
for each trip, there is a symmetric trip visiting the same nodes in reverse
order. Keywords:edge labeling edge scheduled network network optimisation
temporal graph temporal path temporal reachability time assignment


  Deep reinforcement learning agents have achieved state-of-the-art results by
directly maximising cumulative reward. However, environments contain a much
wider variety of possible training signals. In this paper, we introduce an
agent that also maximises many other pseudo-reward functions simultaneously by
reinforcement learning. All of these tasks share a common representation that,
like unsupervised learning, continues to develop in the absence of extrinsic
rewards. We also introduce a novel mechanism for focusing this representation
upon extrinsic rewards, so that learning can rapidly adapt to the most relevant
aspects of the actual task. Our agent significantly outperforms the previous
state-of-the-art on Atari, averaging 880\% expert human performance, and a
challenging suite of first-person, three-dimensional \emph{Labyrinth} tasks
leading to a mean speedup in learning of 10$\times$ and averaging 87\% expert
human performance on Labyrinth.


  In this work we consider the topological analysis of symbolic formal systems
in the framework of network theory. In particular we analyse the network
extracted by Principia Mathematica of B. Russell and A.N. Whitehead, where the
vertices are the statements and two statements are connected with a directed
link if one statement is used to demonstrate the other one. We compare the
obtained network with other directed acyclic graphs, such as a scientific
citation network and a stochastic model. We also introduce a novel topological
ordering for directed acyclic graphs and we discuss its properties in respect
to the classical one. The main result is the observation that formal systems of
knowledge topologically behave similarly to self-organised systems.


  The decays eta, eta-prime --> pi+ pi- l+ l- (with l = e, mu) are investigated
within a chiral unitary approach which combines the chiral effective Lagrangian
with a coupled-channels Bethe-Salpeter equation. Predictions for the decay
widths and spectra are given.


  We present the results of radiation-magnetohydrodynamic simulations of the
expansion of HII regions and surrounding photodissociation regions in
turbulent, magnetised, molecular clouds on scales of up to 4 parsecs, including
the effects of ionising and non-ionising ultraviolet radiation and x rays from
young star clusters. We find that HII region expansion reduces the disordered
component of the B field, imposing a large-scale order on the field around its
border. The field in the neutral gas lies along the ionisation front, while the
field in the ionised gas tends to be perpendicular to this. The highest
pressure compressed neutral/molecular gas is driven towards approximate
equipartition between thermal/magnetic/turbulent energy densities, whereas
lower pressure neutral/molecular gas divides into quiescent, magnetically
dominated regions, and, on the other hand, turbulent, demagnetised regions. The
ionised gas shows approximate thermal/turbulent equipartition, but with
magnetic energy densities 1 to 3 orders of magnitude lower. A high velocity
dispersion (approx 8 km/s) is maintained in the ionised gas throughout our
simulations, despite the mean expansion velocity being significantly lower. The
B field does not significantly brake the HII region expansion on the length and
timescales accessible to our simulations, but it does tend to suppress the
small-scale fragmentation and radiation-driven implosion of neutral/molecular
gas that forms globules and pillars at the edge of the HII region. However, the
relative luminosity of ionising and non-ionising radiation has a much larger
influence than the presence or absence of the B field. When the radiation field
is relatively soft (as in the case of a lower mass cluster, with earliest
spectral type of B0.5), then fragmentation is less vigorous and a thick,
relatively smooth PDR forms. Movies available at
http://youtube.com/user/divBequals0


  Let $A$ be a set of natural numbers. A set $B$, a set of natural numbers, is
said to be an additive complement of the set $A$ if all sufficiently large
natural numbers can be represented in the form $x+y$, where $x\in A$ and $y\in
B$. This article describes various types of additive complements of the set $A$
such as those additive complement of $A$ that does not intersects $A$, additive
complements of the form of the union of disjoint infinite arithmetic
progressions, additive complement having various density etc. As an application
of this study, we also focus on the structure of sumset of arithmetic
progression and geometric progression. Apart from this, for given positive real
no. $\alpha \leq 1$ and finite set $A$, we investigate a set $B$ such that it
can be written as union of disjoint infinite arithmetic progression and density
of $A+B$ is $\alpha$.


  A general Lorentz-invariant parameterization for the short-range part of the
0vBB decay rate is derived. Combined with the long range part already published
this general parameterization in terms of effective B-L violating couplings
allows one to extract the 0vBB limits on arbitrary lepton number violating
theories.


  It has long been known that the following basic objects are obstructions to
bounded tree-width: for arbitrarily large $t$, $(1)$ the complete graph $K_t$,
$(2)$ the complete bipartite graph $K_{t,t}$, $(3)$ a subdivision of the $(t
\times t)$-wall and $(4)$ the line graph of a subdivision of the $(t \times
t)$-wall. We now add a further \emph{boundary object} to this list, a
\emph{$t$-sail}.
  These results have been obtained by studying sparse hereditary
\emph{path-star} graph classes, each of which consists of the finite induced
subgraphs of a single infinite graph whose edges can be partitioned into a path
(or forest of paths) with a forest of stars, characterised by an infinite word
over a possibly infinite alphabet. We show that a path-star class whose
infinite graph has an unbounded number of stars, each of which connects an
unbounded number of times to the path, has unbounded tree-width. In addition,
we show that such a class is not a subclass of the hereditary class of circle
graphs.
  We identify a collection of \emph{nested} words with a recursive structure
that exhibit interesting characteristics when used to define a path-star graph
class. These graph classes do not contain any of the four basic obstructions
but instead contain graphs that have large tree-width if and only if they
contain arbitrarily large $t$-sails. We show that these classes are infinitely
defined and, like classes of bounded degree or classes excluding a fixed minor,
do not contain a minimal class of unbounded tree-width.


  The performance of quantum algorithms for eigenvalue problems, such as
computing Hamiltonian spectra, depends strongly on the overlap of the initial
wavefunction and the target eigenvector. In a basis of Slater determinants, the
representation of energy eigenstates of systems with $N$ strongly correlated
electrons requires a number of determinants that scales exponentially with $N$.
On classical processors, this restricts simulations to systems where $N$ is
small. Here, we show that quantum computers can efficiently simulate strongly
correlated molecular systems by directly encoding the dominant entanglement
structure in the form of spin-coupled initial states. This avoids resorting to
expensive classical or quantum state preparation heuristics and instead
exploits symmetries in the wavefunction. We provide quantum circuits for
deterministic preparation of a family of spin eigenfunctions with ${N \choose
N/2}$ Slater determinants with depth $\mathcal{O}(N)$ and $\mathcal{O}(N^2)$
local gates. Their use as highly entangled initial states in quantum algorithms
reduces the total runtime of quantum phase estimation and related
fault-tolerant methods by orders of magnitude. Furthermore, we assess the
application of spin-coupled wavefunctions as initial states for a range of
heuristic quantum algorithms, namely the variational quantum eigensolver,
adiabatic state preparation, and different versions of quantum subspace
diagonalization (QSD) including QSD based on real-time-evolved states. We also
propose a novel QSD algorithm that exploits states obtained through adaptive
quantum eigensolvers. For all algorithms, we demonstrate that using
spin-coupled initial states drastically reduces the quantum resources required
to simulate strongly correlated ground and excited states. Our work paves the
way towards scalable quantum simulation of electronic structure for classically
challenging systems.