  A key scientific challenge during the outbreak of novel infectious diseases
is to predict how the course of the epidemic changes under different
countermeasures that limit interaction in the population. Most epidemiological
models do not consider the role of mutations and heterogeneity in the type of
contact events. However, pathogens have the capacity to mutate in response to
changing environments, especially caused by the increase in population immunity
to existing strains and the emergence of new pathogen strains poses a continued
threat to public health. Further, in light of differing transmission risks in
different congregate settings (e.g., schools and offices), different mitigation
strategies may need to be adopted to control the spread of infection. We
analyze a multi-layer multi-strain model by simultaneously accounting for i)
pathways for mutations in the pathogen leading to the emergence of new pathogen
strains, and ii) differing transmission risks in different congregate settings,
modeled as network-layers. Assuming complete cross-immunity among strains,
namely, recovery from any infection prevents infection with any other (an
assumption that will need to be relaxed to deal with COVID-19 or influenza), we
derive the key epidemiological parameters for the proposed multi-layer
multi-strain framework. We demonstrate that reductions to existing
network-based models that discount heterogeneity in either the strain or the
network layers can lead to incorrect predictions for the course of the
outbreak. In addition, our results highlight that the impact of
imposing/lifting mitigation measures concerning different contact network
layers (e.g., school closures or work-from-home policies) should be evaluated
in connection with their effect on the likelihood of the emergence of new
pathogen strains.


  We present an algorithm for selecting an uniform sample of gravitationally
lensed quasar candidates from low-redshift (0.6<z<2.2) quasars brighter than
i=19.1 that have been spectroscopically identified in the SDSS. Our algorithm
uses morphological and color selections that are intended to identify small-
and large-separation lenses, respectively. Our selection algorithm only relies
on parameters that the SDSS standard image processing pipeline generates,
allowing easy and fast selection of lens candidates. The algorithm has been
tested against simulated SDSS images, which adopt distributions of field and
quasar parameters taken from the real SDSS data as input. Furthermore, we take
differential reddening into account. We find that our selection algorithm is
almost complete down to separations of 1'' and flux ratios of 10^-0.5. The
algorithm selects both double and quadruple lenses. At a separation of 2'',
doubles and quads are selected with similar completeness, and above (below) 2''
the selection of quads is better (worse) than for doubles. Our morphological
selection identifies a non-negligible fraction of single quasars: To remove
these we fit images of candidates with a model of two point sources and reject
those with unusually small image separations and/or large magnitude differences
between the two point sources. We estimate the efficiency of our selection
algorithm to be at least 8% at image separations smaller than 2'', comparable
to that of radio surveys. The efficiency declines as the image separation
increases, because of larger contamination from stars. We also present the
magnification factor of lensed images as a function of the image separation,
which is needed for accurate computation of magnification bias.


  We present a large-scale study of stellar rotation for T Tauri stars in the
Orion Star-Forming Complex. We use the projected rotational velocity
($v\sin(i)$) estimations reported by the APOGEE-2 collaboration as well as
individual masses and ages derived from the position of the stars in the HR
diagram, considering Gaia-EDR3 parallaxes and photometry plus diverse
evolutionary models. We find an empirical trend for $v\sin(i)$ decreasing with
age for low-mass stars ($0.4 M_{\odot} < M_{\ast} < 1.2 M_{\odot}$). Our
results support the existence of a mechanism linking $v\sin(i)$ to the presence
of accreting protoplanetary disks, responsible for regulating stellar rotation
in timescales of about 6 Myr, which is the timescale in which most of the T
Tauri stars lose their inner disk. Our results provide important constraints to
models of rotation in the early phases of evolution of young stars and their
disks.


  Image blending is an integral part of many multi-image applications such as
panorama stitching or remote image acquisition processes. In such scenarios,
multiple images are connected at predefined boundaries to form a larger image.
A convincing transition between these boundaries may be challenging, since each
image might have been acquired under different conditions or even by different
devices.
  We propose the first blending approach based on osmosis filters. These
drift-diffusion processes define an image evolution with a non-trivial steady
state. For our blending purposes, we explore several ways to compose drift
vector fields based on the derivatives of our input images. These vector fields
guide the evolution such that the steady state yields a convincing blended
result. Our method benefits from the well-founded theoretical results for
osmosis, which include useful invariances under multiplicative changes of the
colour values. Experiments on real-world data show that this yields better
quality than traditional gradient domain blending, especially under challenging
illumination conditions.


  The detection of a spatial variation of the fine-structure constant, alpha,
based on study of quasar absorption systems has recently been reported. The
physics that causes this alpha-variation should have other observable
manifestations, and this motivates us to look for complementary astrophysical
effects. In this paper we propose a method to test whether spatial variation of
fundamental constants existed during the epoch of big bang nucleosynthesis.
Using existing measurements of primordial deuterium abundance we find very weak
indications that such a signature might exist, but the paucity of measurements
precludes any firm conclusion. We also examine existing quasar absorption
spectra data that are sensitive to variation of the electron-to-proton mass
ratio, mu, and x = (alpha^2 mu g_p) for spatial variation.


  New trial wave functions corresponding to half filling quantum Hall states
are proposed. These wave functions are constructed by first pairing up the
quasielectrons of the 1/3 Laughlin quantum Hall state, with the same relative
angular momentum for each pair, and then making the paired quasielectrons
condense into a 1/4 Laughlin state. The quasiparticle excitations of the
proposed wave functions carry $\pm1/4$ of electron charge, and obey Abelian
fractional statistics. In the spherical geometry, the total flux quanta
$N_{\phi}$ is shown to be related to the number of electrons $N$ by $N_{\phi} =
2N-(5-q)$ with $q$ being the relative angular momentum between the
quasielectrons in each pair which takes values of non-negative even integers.
The overlaps are calculated between the proposed trial wave functions,
including the ground state, quasiexciton states, and quasihole states, and the
exact states of the finite size systems at $N_{\phi} = 2N-3$. The near unity
overlaps are obtained in the lowest Landau level, while the moderate overlaps
are obtained in the second Landau level. The relevance of the wave functions to
the yet to be discovered fractional quantum Hall effect in the lowest Landau
level, as well as the 5/2 quantum Hall effect is also discussed.


  Using a temporally weighted norm we first establish a result on the global
existence and uniqueness of solutions for Caputo fractional stochastic
differential equations of order $\alpha\in(\frac{1}{2},1)$ whose coefficients
satisfy a standard Lipschitz condition. For this class of systems we then show
that the asymptotic distance between two distinct solutions is greater than
$t^{-\frac{1-\alpha}{2\alpha}-\eps}$ as $t \to \infty$ for any $\eps>0$. As a
consequence, the mean square Lyapunov exponent of an arbitrary non-trivial
solution of a bounded linear Caputo fractional stochastic differential equation
is always non-negative.


  Recently reported measurements of specific heat on the compound Mn-formate
di-Urea (Mn-f-2U) by Takeda et al. [Phys. Rev. B 63, 024425 (2001)] are
considered. As a model to describe the overall thermodynamic behavior of such
compound, the easy-axis two-dimensional Heisenberg antiferromagnet is proposed
and studied by means of the 'pure quantum self-consistent harmonic
approximation' (PQSCHA). In particular it is shown that, when the temperature
decreases, the compound exhibits a crossover from 2D-Heisenberg to 2D-Ising
behavior, followed by a 2D-Ising-like phase transition, whose location allows
to get a reliable estimate of the easy-axis anisotropy driving the transition
itself. Below the critical temperature T_N=3.77 K, the specific heat is well
described by the two-dimensional easy-axis model down to a temperature T*=1.47
K where a T^3-law sets in, possibly marking a low-temperature crossover of
magnetic fluctuations from two to three dimensions.


  The pseudo entropy is a promising recent generalization of the entanglement
entropy to the situations in which both the initial and final state are
involved, with the density matrix promoted to the transition matrix. However,
in contrast to the non-Hermiticity of the generic transition matrix, the
holographic pseudo entropy formulated via the Euclidean AdS/CFT turns out to be
always real-valued, which potentially conceals the crucial natures of this
novel quantity. In this note, we make the first attempt to formulate a
real-time prescription for computations to incorporate naturally the pseudo
entropy, as a generally complex-valued entanglement measure, into the AdS/CFT
context. It is then conjectured that the holographic pseudo entropy is dual to
the extremal codimension-2 area surface in the generally time-dependent
Lorentzian asymptotically AdS spacetime, but may also receive imaginary
contribution from the regularized extrinsic curvature term of the area surface,
which is not included in the covariant holographic entanglement entropy. In
this real-time prescription, the holographic pseudo entropy can be considered
as a generalization of the covariant holographic entanglement entropy, as well.


  We investigate the potentiality of using strong lensing clusters to constrain
the cosmological parameters Omega_m and Omega_lambda. The existence of a
multiple image system with known redshift allows, for a given (Omega_m,
Omega_lambda) cosmology, absolute calibration of the total mass deduced from
lens modelling. Recent Hubble Space Telescope (HST) observations of galaxy
clusters reveal a large number of multiple images, which are predicted to be at
different redshifts. If it is possible to measure spectroscopically the
redshifts of many multiple images then one can in principle constrain
(Omega_m,Omega_lambda) through ratios of angular diameter distances,
independently of any external assumptions. For a regular/relaxed cluster
observed by HST with 3 multiple image systems, each with different
spectroscopic redshifts, we show by analytic calculation that the following
uncertainties can be expected: Omega_m=0.30 +/- 0.11, Omega_lambda=0.70 +/-
0.23 or Omega_m=1.00 +/- 0.17, Omega_lambda=0.00 +/- 0.48 for the two most
popular world models. Numerical tests on simulated data confirm these good
constraints, even in the case of more realistic cluster potentials, such as
bimodal clusters, or when including perturbations by galaxies. To investigate
the sensitivity of the method to different mass profiles, we also use an
analytic ``pseudo-elliptical'' Navarro, Frenk & White profile in the
simulations. These constraints can be improved if more than 3 multiple images
with spectroscopic redshifts are observed, or by combining the results from
different clusters. Some prospects on the determination of the cosmological
parameters with gravitational lensing are given.


  A new mechanism for spontaneous breaking of flavour symmetry is demonstrated.
An exactly flavour symmetric model with degenerate bare nonets and with
sufficiently strong tri-linear meson couplings is shown to lead to
self-consistency equations which are unstable. Instead there exists a stable
solution, which break flavour symmetry spontaneously in the mass spectrum. For
a C-degenerate meson spectrum the stable mass spectrum obeys the
Okubo-Zweig-Iizuka (OZI) rule and the approximate equal spacing rule.


  Let $G\subseteq GL(n)$ be a finite group without pseudo-reflections. We
present an algorithm to compute and verify a candidate for the Cox ring of a
resolution $X\rightarrow \mathbb{C}^n/G$, which is based just on the geometry
of the singularity $\mathbb{C}^n/G$, without further knowledge of its
resolutions. We explain the use of our implementation of the algorithms in
Singular. As an application, we determine the Cox rings of resolutions
$X\rightarrow \mathbb{C}^3/G$ for all $G\subseteq GL(3)$ with the
aforementioned property and of order $|G|\leq 12$. We also provide examples in
dimension 4.


  Flat density cores have been obtained for a limited number of clusters of
galaxies by strong gravitational lensing. This paper explores the possibility
that the degeneracy pressure of fermionic dark matter accounts for the flat top
density profiles. This is a case study of A1689 for which the density profile
has been obtained from the inner region out to 1Mpc by the combination of
strong and weak lensing. In the case that the dark matter consists of the
mixture of degenerate relic neutrinos and collisionless cold dark matter
particles, the acceptable mass range for relic neutrinos is between 1 and 2 eV,
if the ratio of the two kinds of dark matter particles is fixed to its cosmic
value.


  We examine the uplink spectral efficiency of a massive MIMO base station
employing a one-bit Sigma-Delta sampling scheme implemented in the spatial
rather than the temporal domain. Using spatial rather than temporal
oversampling, and feedback of the quantization error between adjacent antennas,
the method shapes the spatial spectrum of the quantization noise away from an
angular sector where the signals of interest are assumed to lie. It is shown
that, while a direct Bussgang analysis of the Sigma-Delta approach is not
suitable, an alternative equivalent linear model can be formulated to
facilitate an analysis of the system performance. The theoretical properties of
the spatial quantization noise power spectrum are derived for the Sigma-Delta
array, as well as an expression for the spectral efficiency of maximum ratio
combining (MRC). Simulations verify the theoretical results and illustrate the
significant performance gains offered by the Sigma-Delta approach for both MRC
and zero-forcing receivers.


  Replica field theory is used to study the n-dependent free energy of the
Ising spin glass in a first order perturbative treatment. Large
sample-to-sample deviations of the free energy from its quenched average prove
to be Gaussian, independently of the special structure of the order parameter.
The free energy difference between the replica symmetric and (infinite level)
replica symmetry broken phases is studied in details: the line n(T) where it is
zero coincides with the Almeida-Thouless line for d>8. The dimensional domain
6<d<8 is more complicated, and several scenarios are possible.


  We study the high-energy eigenfunctions of the Laplacian on a compact
Riemannian manifold with Anosov geodesic flow. The localization of a
semiclassical measure associated with a sequence of eigenfunctions is
characterized by the Kolmogorov-Sinai entropy of this measure. We show that
this entropy is necessarily bounded from below by a constant which, in the case
of constant negative curvature, equals half the maximal entropy. In this sense,
high-energy eigenfunctions are at least half-delocalized.


  We undertake herein to derive the Wigner-Wilkins [W-W] neutron/nucleus
scattering kernel, a foundation stone in neutron thermalization theory, on the
basis of a self-contained calculation in quantum mechanics. Indeed, a
quantum-mechanical derivation of the W-W kernel is available in the literature,
cited below, but it is, in our opinion, robbed of conviction by being couched
in terms of an excessive generality. Here, by contrast, we proceed along a
self-contained route relying on the Fermi pseudopotential and a first-order
term in a time-dependent Born approximation series. Our calculations are fully
explicit at every step and, in particular, we tackle in its every detail a
final integration whose result is merely stated in the available literature.
Furthermore, and perhaps the most important point of all, we demonstrate that
the quantum-mechanical W-W kernel outcome is identical down to the last iota
with its classical antecedent, classical not only by virtue of historical
precedence but also by being based on classical Newtonian mechanics.


  We have used R_C I_C CCD photometry from the Isaac Newton telescope and
intermediate resolution spectroscopy from the Gemini North telescope to
identify and characterise low-mass (0.15<M/M_sun<1.3) pre-main sequence stars
in the young open cluster NGC 2169. Isochrone fitting to the high- and low-mass
populations yields an intrinsic distance modulus of 10.13{+0.06}{-0.09} mag and
a model-dependent age of 9+/-2 Myr. Compared with the nearby, kinematically
defined groups of a similar age, NGC 2169 has a large low-mass population which
potentially offers a more precise statistical investigation of several aspects
of star formation and early stellar evolution. By modelling the distribution of
low-mass stars in the I_C versus R_C-I_C diagram we find that any age spread
among cluster members has a Gaussian full width at half maximum <=2.5 Myr. A
young age and small age spread (<10 Myr) are supported by the lack of
significant lithium depletion in the vast majority of cluster members. There is
no clear evidence for accretion or warm circumstellar dust in the low-mass
members of NGC 2169, bolstering the idea that strong accretion has ceased and
inner discs have dispersed in almost all low-mass stars by ages of 10 Myr.


  This paper addresses an open problem in the area of linear quadratic optimal
control. We consider the regular, infinite-horizon,
stability-modulo-a-subspace, indefinite linear quadratic problem under the
assumption that the dynamics are stabilizable. Our result generalizes previous
works dealing with the same problem in the case of controllable dynamics. We
explicitly characterize the unique solution of the algebraic Riccati equation
that gives the optimal cost and optimal feedback control, as well as necessary
and sufficient conditions for the existence of optimal controls.


  We study the feasibility of probing a region of Natural Supersymmetry where
the stop and higgsino masses are compressed. Although this region is most
effectively searched for in the mono-jet channel, this signature is present in
many other non-supersymmetric frameworks. Therefore, another channel that
carries orthogonal information is required to confirm the existence of the
light stop and higgsinos. We show that a supersymmetric version of the $t \bar
t H$ process, $pp \to t \tilde t_1 \tilde \chi^0_{1(2)}$, can have observably
large rate when both the stop and higgsinos are significantly light, and it
leads to a distinctive mono-top signature in the compressed mass region. We
demonstrate that the hadronic channel of the mono-top signature can effectively
discriminate the signal from backgrounds by tagging a hadronic top-jet. We show
that the hadronic channel of mono-top signature offers a significant
improvement over the leptonic channel and the sensitivity reaches $m_{\tilde
t_1} \simeq 420$ GeV at the 13 TeV LHC with 3 ab$^{-1}$ luminosity.


  Schmidt's game is a powerful tool for studying properties of certain sets
which arise in Diophantine approximation theory, number theory, and dynamics.
Recently, many new results have been proven using this game. In this paper we
address determinacy and indeterminacy questions regarding Schmidt's game and
its variations, as well as more general games played on complete metric spaces
(e.g. fractals). We show that except for certain exceptional cases, these games
are undetermined on Bernstein sets.


  Preliminary trigonometric parallaxes and BVI photometry are presented for two
dwarf carbon stars, LP765-18 (= LHS1075) and LP328-57 (= CLS96). The data are
combined with the literature values for a third dwarf carbon star, G77-61 (=
LHS1555). All three stars have very similar luminosities (9.6<M_V<10.0) and
very similar broadband colors across the entire visual-to-near IR (BVIJHK)
wavelength range. Their visual (BVI) colors differ from all known red dwarfs,
subdwarfs, and white dwarfs. In the M_V versus V-I color-magnitude diagram they
are approximately 2 magnitudes subluminous compared with normal disk dwarfs
with solar-like metallicities, occupying a region also populated by O-rich
subdwarfs with -1.5<[m/H]<-1.0. The kinematics indicate that they are members
of the Galactic spheroid population. The subluminosity of all three stars is
due to an as-yet-unknown combination of (undoubtedly low) metallicity, possibly
enhanced helium abundance, and unusual line-blanketing in the bandpasses
considered. The properties of the stars are compared with models for the
production of dwarf carbon stars.


  For a graph $G$, let $\chi (G)$ denote the chromatic number. In graph theory,
the following famous conjecture posed by Hedetniemi has been studied: For two
graphs $G$ and $H$, $\chi (G\times H)=\min\{\chi (G),\chi (H)\}$, where $G
\times H$ is the tensor product of $G$ and $H$. In this paper, we give a
reduction of Hedetniemi's conjecture to an inclusion relation problem on ideals
of polynomial rings, and we demonstrate computational experiments for partial
solutions of Hedetniemi's conjecture along such a strategy using Gr\"{o}bner
basis.


  We discuss the impact of the recent KamLAND constraint on the solar
anti-neutrino flux on the analysis of solar neutrino data in the presence of
Majorana neutrino transition magnetic moments and solar magnetic fields. We
consider different stationary solar magnetic field models, both regular and
random, highlighting the strong enhancement in the anti-neutrino production
rates that characterize turbulent solar magnetic field models. Moreover, we
show that for such magnetic fields inside the Sun, one can constrain the
intrinsic neutrino magnetic moment down to the level of mu_nu lessthan few
times 10^-12 x mu_B irrespective of details of the underlying turbulence model.
This limit is more stringent than all current experimental sensitivities, and
similar to the most stringent bounds obtained from stellar cooling. We also
comment on the robustness of this limit and show that at most it might be
weakened by one order of magnitude, under very unlikely circumstances.


  We study the properties of a two-body random matrix ensemble for
distinguishable spins. We require the ensemble to be invariant under the group
of local transformations and analyze a parametrization in terms of the group
parameters and the remaining parameters associated with the "entangling" part
of the interaction. We then specialize to a spin chain with nearest neighbour
interactions and numerically find a new type of quantum phase transition
related to the strength of a random external field i.e. the time reversal
breaking one body interaction term.


  Study of eye-movement is being employed in Human Computer Interaction (HCI)
research. Eye - gaze tracking is one of the most challenging problems in the
area of computer vision. The goal of this paper is to present a review of
latest research in this continued growth of remote eye-gaze tracking. This
overview includes the basic definitions and terminologies, recent advances in
the field and finally the need of future development in the field.


  The motivation for this thesis is to find a fluctuating hydrodynamic
description of quantum coherent effects in mesoscopic quantum systems with
diffusive transport properties. Coherent effects are inscribed into the
coherences (two-point Green's function) on which we focus as the building
blocks of such a theory. Our approach is rather mathematical and not related to
concrete experiments. We study the quantum symmetric simple exclusion process
(QSSEP), a potentially iconic model describing transport of noisy free fermions
on a 1D lattice, which has the minimal structure to capture what we are
interested in: Long-ranged coherences and diffusive transport. In mean, QSSEP
reduces to the symmetric simple exclusion process (SSEP), a classical toy model
that was important in the development of the macroscopic fluctuation theory, a
fluctuating hydrodynamic description of diffusive transport in classical
systems. Studying QSSEP we hope to make progress towards a quantum coherent
extension of the macroscopic fluctuation theory.
  The thesis summarizes many results we have obtained about QSSEP in the last
three years, such as the dynamical equation and an exact stationary solution
for correlation functions of coherences at hydrodynamic scales, the
distribution of entanglement in QSSEP and an argument why QSSEP might be an
effective noisy description for more generic mesoscopic quantum systems. Many
of these results are due to a relation between the statistical properties of
coherences in QSSEP and free probability theory. We devote a whole chapter to
this relation and present, as a by-product, a method to characterize the
spectrum of subblocks of a large class of structured random matrices.


  The composition dependence of the Yb valence and of the thermal expansion
have been studied in the YbGa$_x$Ge$_{2-x}$ system. X-ray diffraction reveals
that single-phased samples isostructural to YbGaGe are obtained in the range of
0.9 <= x <= 1.5. The magnetic susceptibility shows that the systems are almost
nonmagnetic below room temperature, indicating a stable Yb2+ state for the x
range 0.9 <= x <= 1.5. The lattice constants as well as the lattice volume of
these systems are found to decrease monotonically with decreasing temperature,
suggesting the absence of zero thermal-expansion previously reported for
YbGaGe.


  The case for a future high-energy collider based on muon beams is briefly
reviewed.


  The basic analytical forms of the deuteron wave function (DWF) in a
coordinate representation have been reviewed. The asymptotic behaviour of DWF
near the origin of coordinates has been analyzed. New analytical forms of DWF
as a product of the exponential function r^n and the sum of the exponential
terms Ai*exp(-ai*r3) are applied for the calculation of the polarization
characteristics of the deuteron. Numerical calculations have been done for
realistic phenomenological potential of Nijmegen groups, Reid93. In the paper,
the results of the angular asymmetry for deuteron vector t10, t11 and tensor
t20, t21, t22 polarizations are described. Along with the angular asymmetry,
the momentum asymmetry for deuteron vector t1i polarizations is described too.
The influence of DWF approximation in a coordinate representation on the
subsequent results of the calculations of the tensor polarization t20 is
investigated. A comparison of values t20 is made at 70 degree if to apply four
different DWF approximations to the same NN-potential Reid93. When the received
theoretical values t20 are compared with the experimental data of world
collaborations and reviews, a good coordination for the area of values momentum
p=1-4fm-1 is observed. Using the method of invariant amplitude, spin
observables in backward elastic dp-scattering-tensor analyzing power T20 and
polarization transfer K0 have been calculated. The values of K0 and correlation
K0-T20 are compared with experimental data. In a wide range of momentums p and
scattering angles, the asymmetry for the tensor analyzing power T20 and T22 has
been presented, which characterizes the photoproduction of negative pi- meson
from deuteron in reaction g(d, pi-)pp. A symmetry of values T20 and T22
concerning a 90 angle is observed. The ratio R for the vector Px and tensor Pxz
polarizations is characterized by angular asymmetry....


  The main goal of the future MPD experiment at NICA is to explore the QCD
phase diagram in the region of highly compressed and hot baryonic matter in the
energy range corresponding to the highest chemical potential. Properties of
such dense matter can be studied using azimuthal anisotropy which is
categorized by the Fourier coefficients of the azimuthal distribution
decomposition. Performance of the detector response based on simulations with
realistic reconstruction procedure is presented for centrality determination,
reaction plane estimation, directed and elliptic flow coefficients.


  In this paper we study quasi-homogeneous affine algebraic varieties, that is,
varieties obtained as closures of orbits of suitable group representations. We
also discuss one interesting case that has links with the Orthogonal
Grassmannian OGr(5,10). The main aim is to write the tangent bundle and the
canonical class of quasi-homogeneous affine algebraic varieties in terms of
group representations.


  In the last few years, brane tilings have proven to be an efficient and
convenient way of studying supersymmetric gauge theories living on D3-branes or
M2-branes. In these pages we present a quick and simple introduction to the
subject, hoping this could tickle the reader's curiosity to learn more on this
extremely fascinating subject.


  Although the energetic phenomena of the Sun (flares, coronal mass injections
etc.) exhibit intermittent stochastic behavior in their rate of occurrence,
they are well correlated to the variations of the solar cycle. In this work we
study the spatial and temporal characteristics of transient solar activity in
an attempt to statistically interpret the evolution of these phenomena through
the solar cycle, in terms of the self-organized criticality theory.


  Vacuum birefringence is governed by the amplitude for a photon to flip
helicity or polarisation state in an external field. Here we calculate the flip
and non-flip amplitudes in arbitrary plane wave backgrounds, along with the
induced spacetime-dependent refractive indices of the vacuum. We compare the
behaviour of the amplitudes in the low energy and high energy regimes, and
analyse the impact of pulse shape and energy. We also provide the first
lightfront-QED derivation of the coefficients in the Heisenberg-Euler effective
action.


  We theoretically study long-term trends in the statistics of record-breaking
daily temperatures and validate these predictions using Monte Carlo simulations
and data from the city of Philadelphia, for which 126 years of daily
temperature data is available. Using extreme statistics, we derive the number
and the magnitude of record temperature events, based on the observed Gaussian
daily temperatures distribution in Philadelphia, as a function of the number of
elapsed years from the start of the data. We further consider the case of
global warming, where the mean temperature systematically increases with time.
We argue that the current warming rate is insufficient to measurably influence
the frequency of record temperature events over the time range of the
observations, a conclusion that is supported by numerical simulations and the
Philadelphia temperature data.


  The estimation of a sparse vector in the linear model is a fundamental
problem in signal processing, statistics, and compressive sensing. This paper
establishes a lower bound on the mean-squared error, which holds regardless of
the sensing/design matrix being used and regardless of the estimation
procedure. This lower bound very nearly matches the known upper bound one gets
by taking a random projection of the sparse vector followed by an $\ell_1$
estimation procedure such as the Dantzig selector. In this sense, compressive
sensing techniques cannot essentially be improved.


  Let $N$ be an odd perfect number. Let $\omega(N)$ be the number of distinct
prime factors of $N$ and let $\Omega(N)$ be the total number of prime factors
of $N$. We prove that if $(3,N)=1$, then $ \frac{302}{113}\omega -
\frac{286}{113} \leq \Omega. $
  If $3|N$, then $\frac{66}{25}\omega-5\leq\Omega.$ This is an improvement on
similar prior results by the author which was an improvement of a result of
Ochem and Rao. We also establish new lower bounds on $\omega(N)$ in terms of
the smallest prime factor of $N$ and establish new lower bounds on $N$ in terms
of its smallest prime factor.


  The recent observation of a Higgs boson at the LHC and experimental
confirmation of nonvanishing neutrino-mixing parameter sin(theta_13) offer
important means to test physics beyond the standard model. We explore this
within the context of the scotogenic model, in which neutrinos acquire mass
radiatively via one-loop interactions with dark matter. Starting with a
two-parameter neutrino-mixing matrix which is consistent with the latest
neutrino-oscillation data at the one-sigma level, we derive different sets of
solutions for the Yukawa couplings of the nonstandard particles in the model
and use the results to consider the Higgs decays into final states involving
the new particles. Assuming that the lightest one of them serves as fermionic
cold dark matter, we show that such decays are allowed by various experimental
and theoretical constraints to have substantial rates that are already
restricted by the current LHC data. We also look at their correlations with the
Higgs decays into gamma gamma and gamma Z. Upcoming LHC measurements of the
Higgs boson can therefore either detect scotogenic signals or place further
constraints on the model.


  We show that for a quantum wire with a local asymmetric scattering potential
the principal channels for charge and heat rectification decouple and
renormalise differently under electron interactions, with heat rectification
generally being more relevant. The polarisation of the rectification results
from quantum interference and is tuneable through external gating. Furthermore,
for spin polarised or helical electrons and sufficiently strong interactions a
regime can be obtained in which heat transport is strongly rectified but charge
rectification is very weak.


  In hyperspectral image (HSI) classification, spatial context has demonstrated
its significance in achieving promising performance. However, conventional
spatial context-based methods simply assume that spatially neighboring pixels
should correspond to the same land-cover class, so they often fail to correctly
discover the contextual relations among pixels in complex situations, and thus
leading to imperfect classification results on some irregular or inhomogeneous
regions such as class boundaries. To address this deficiency, we develop a new
HSI classification method based on the recently proposed Graph Convolutional
Network (GCN), as it can flexibly encode the relations among arbitrarily
structured non-Euclidean data. Different from traditional GCN, there are two
novel strategies adopted by our method to further exploit the contextual
relations for accurate HSI classification. First, since the receptive field of
traditional GCN is often limited to fairly small neighborhood, we proposed to
capture long range contextual relations in HSI by performing successive graph
convolutions on a learned region-induced graph which is transformed from the
original 2D image grids. Second, we refine the graph edge weight and the
connective relationships among image regions by learning the improved adjacency
matrix and the 'edge filter', so that the graph can be gradually refined to
adapt to the representations generated by each graph convolutional layer. Such
updated graph will in turn result in accurate region representations, and vice
versa. The experiments carried out on three real-world benchmark datasets
demonstrate that the proposed method yields significant improvement in the
classification performance when compared with some state-of-the-art approaches.


  We present a new method for the generation of atmospheric turbulence phase
screens based on the frequency shift property of the Fourier transform. This
method produces low spatial frequency distortions without additional
computation time penalties associated with methods using subharmonic subgrids.
It is demonstrated that for simulations of atmospheric turbulence with finite
outer scales, the performance of our method with respect to the statistical
phase structure function of the screen meets or exceeds other methods with
respect to agreement with theory. We outline small-scale accuracy issues
associated with modelling non-Kolmogorov spectral power laws using existing
techniques, and propose a solution. For simulations of long-range propagation
through atmospheric optical turbulence, our method provides various advantages
over standard methods.


  We consider the classical theta operator $\theta$ on modular forms modulo
$p^m$ and level $N$ prime to $p$ where $p$ is a prime greater than 3. Our main
result is that $\theta$ mod $p^m$ will map forms of weight $k$ to forms of
weight $k+2+2p^{m-1}(p-1)$ and that this weight is optimal in certain cases
when $m$ is at least 2. Thus, the natural expectation that $\theta$ mod $p^m$
should map to weight $k+2+p^{m-1}(p-1)$ is shown to be false.
  The primary motivation for this study is that application of the $\theta$
operator on eigenforms mod $p^m$ corresponds to twisting the attached Galois
representations with the cyclotomic character. Our construction of the
$\theta$-operator mod $p^m$ gives an explicit weight bound on the twist of a
modular mod $p^m$ Galois representation by the cyclotomic character.


  Let $b_k$ be strictly decreasing sequence of real numbers such that $b_0 = 1$
and $f_k$ be decreasing, linear functions such that $f_k(b_k) = 1$ and
$f_k(b_{k-1}) = 0$, $k = 1, 2, \dots$. We define iterated function system (IFS)
$S_n$ by limiting the collection of functions $f_k$ to first n, meaning $S_n =
\{f_k \}_{k=1}^n$. Let $J_n$ denote the limit set of $S_n$. We show that if
$S_n$ fulfills the following two conditions: (1)~$\lim\limits_{n \to \infty}
\left(1-h_n\right) \ln{n} = 0 $ where $h_n$ is the Hausdorff dimension of
$J_n$, and (2)~$\sup \limits_{k\in \mathbb{N}} \left
\{\frac{b_k-b_{k+1}}{b_{k+1}} \right \} < \infty $, then $\lim\limits_{n\to
\infty} H_{h_n}(J_n) = 1 = H_1(J)$, where $h_n$ is the Hausdorff dimension of
$J_n$ and $H_{h_n}$ is the corresponding Hausdorff measure. We also show
examples of families of IFSes fulfilling those properties.


  The Transformer-based models with the multi-head self-attention mechanism are
widely used in natural language processing, and provide state-of-the-art
results. While the pre-trained language backbones are shown to implicitly
capture certain linguistic knowledge, explicitly incorporating structure-aware
features can bring about further improvement on the downstream tasks. However,
such enhancement often requires additional neural components and increases
training parameter size. In this work, we investigate the attention head
selection and manipulation strategy for feature injection from a network
pruning perspective, and conduct a case study on dialogue summarization. We
first rank attention heads in a Transformer-based summarizer with layer-wise
importance. We then select the underused heads through extensive analysis, and
inject structure-aware features by manipulating the selected heads.
Experimental results show that the importance-based head selection is effective
for feature injection, and dialogue summarization can be improved by
incorporating coreference information via head manipulation.


  The baseband-up centralization architecture of radio access networks (C-RAN)
has recently been proposed to support efficient cooperative communications and
reduce deployment and operational costs. However, the massive fronthaul
bandwidth required to aggregate baseband samples from remote radio heads (RRHs)
to the central office incurs huge fronthauling cost, and existing baseband
compression algorithms can hardly solve this issue. In this paper, we propose a
graphbased framework to effectively reduce fronthauling cost through properly
splitting and placing baseband processing functions in the network. Baseband
transceiver structures are represented with directed graphs, in which nodes
correspond to baseband functions, and edges to the information flows between
functions. By mapping graph weighs to computational and fronthauling costs, we
transform the problem of finding the optimum location to place some baseband
functions into the problem of finding the optimum clustering scheme for graph
nodes. We then solve this problem using a genetic algorithm with customized
fitness function and mutation module. Simulation results show that proper
splitting and placement schemes can significantly reduce fronthauling cost at
the expense of increased computational cost. We also find that cooperative
processing structures and stringent delay requirements will increase the
possibility of centralized placement.


  The strong dependence of the neutrino annihilation mechanism on the mass
accretion rate makes it difficult to explain the LGRBs with duration in excess
of 100 seconds as well as the precursors separated from the main gamma-ray
pulse by few hundreds of seconds. Even more difficult is to explain the Swift
observations of the shallow decay phase and X-ray flares, if they indeed
indicate activity of the central engine for as long as 10,000 seconds. These
data suggest that some other, most likely magnetic mechanisms have to be
considered. The magnetic models do not require the development of accretion
disk within the first few seconds of the stellar collapse and hence do not
require very rapidly rotating stellar cores at the pre-supernova state. This
widens the range of potential LGRB progenitors. In this paper, we re-examine
the close binary scenario allowing for the possibility of late development of
accretion disks in the collapsar model and investigate the available range of
mass accretion rates, black hole masses, and spins. A particularly interesting
version of the binary progenitor involves merger of a WR star with an
ultra-compact companion, neutron star or black hole. In this case we expect the
formation of very long-lived accretion disks, that may explain the phase of
shallow decay and X-ray flares observed by Swift. Similarly long-lived magnetic
central engines are expected in the current single star models of LGRB
progenitors due to their assumed exceptionally fast rotation.


  We introduce a simple model for DNA-cationic-lipid complexes in which
galleries between planar bilayer lipid lamellae contain DNA 2D smectic lattices
that couple orientationally and positionally to lattices in neighboring
galleries. We identify a new equilibrium phase in which there are long-range
orientational but not positional correlations between DNA lattices. We discuss
properties of this new phase such as its X-ray structure factor S(r), which
exhibits unusual exp(- const.ln^2 r) behavior as a function of in-plane
separation r.


  We establish some geometrical properties of the space of idempotent
probability measures. In particular, for a compact $X$ it is established that
if the space $I_{3}(X)\backslash X$ is hereditary normally, then $X$ is
metrizable; some subsets allocate of the space of idempotent probability
measures which are, respectively, $Z$-sets, $\max$-$\mbox{plus}$-convex
subsets, $G_\delta$-sets.


  Successfully training deep neural networks often requires either batch
normalization, appropriate weight initialization, both of which come with their
own challenges. We propose an alternative, geometrically motivated method for
training. Using elementary results from linear programming, we introduce Farkas
layers: a method that ensures at least one neuron is active at a given layer.
Focusing on residual networks with ReLU activation, we empirically demonstrate
a significant improvement in training capacity in the absence of batch
normalization or methods of initialization across a broad range of network
sizes on benchmark datasets.


  We proved that under quantum mechanics a momentum-energy and a space-time are
dual vector spaces on an almost complex manifold in position representation,
and the minimal uncertainty relations are equivalent to the inner-product
relations of their bases. In a microscopic sense, there exist locally a
momentum-energy conservation and a space-time conservation. The minimal
uncertainty relations refer to a local equilibrium state for a stable system,
and the relations will be invariable in the special relativity. A supposition
about something having dark property is proposed, which relates to a breakdown
of time symmetry.


  We study signals at the Large Hadron Collider (LHC) for the Kaluza-Klein (KK)
excitations of electroweak charged gauge bosons in the framework of the
Standard Model (SM) fields propagating in the bulk of a warped extra dimension.
Such a scenario can solve both the Planck-weak and flavor hierarchy problems of
the SM. There are two such charged states in this scenario with couplings to
light quarks and leptons being suppressed relative to those in the SM, whereas
the couplings to top/bottom quarks are enhanced, similar to the case of
electroweak neutral gauge bosons previously studied. However, unlike the case
of electroweak neutral gauge bosons, there is no irreducible QCD background
(including pollution from possibly degenerate KK gluons) for decays to top +
bottom final state so that this channel is useful for the discovery of the
charged states. Moreover, decays of electroweak charged gauge bosons to
longitudinal W, Z and Higgs are enhanced just as for the neutral bosons.
However, unlike for the neutral gauge bosons, the purely leptonic (and hence
clean) decay mode of the WZ are fully reconstructible so that the ratio of the
signal to the SM (electroweak) background can potentially be enhanced by
restricting to the resonance region more efficiently. We show that such final
states can give sensitivity to 2 (3) TeV masses with an integrated luminosity
of 100 (300) inverse fb. We emphasize that improvements in discriminating a
QCD-jet from a highly boosted hadronically decaying W, and a highly boosted
top-jet from a bottom-jet will enhance the reach for these KK particles, and
that the signals we study for the warped extra dimensional model might actually
be applicable also to a wider class of non-supersymmetric models of electroweak
symmetry breaking.


  The canonical answer to the question posed is "Yes." -- tacitly assuming that
quantum theory and the concept of spacetime are to be unified by `quantizing' a
theory of gravitation. Yet, instead, one may ponder: Could quantum mechanics
arise as a coarse-grained reflection of the atomistic nature of spacetime? --
We speculate that this may indeed be the case. We recall the similarity between
evolution of classical and quantum mechanical ensembles, according to Liouville
and von Neumann equation, respectively. The classical and quantum mechanical
equations are indistinguishable for objects which are free or subject to
spatially constant but possibly time dependent, or harmonic forces, if
represented appropriately. This result suggests a way to incorporate anharmonic
interactions, including fluctuations which are tentatively related to the
underlying discreteness of spacetime. Being linear and local at the quantum
mechanical level, the model offers a decoherence and natural localization
mechanism. However, the relation to primordial deterministic degrees of freedom
is nonlocal.


  We introduce a hybrid model combining a quantum-inspired tensor network and a
variational quantum circuit to perform supervised learning tasks. This
architecture allows for the classical and quantum parts of the model to be
trained simultaneously, providing an end-to-end training framework. We show
that compared to the principal component analysis, a tensor network based on
the matrix product state with low bond dimensions performs better as a feature
extractor for the input data of the variational quantum circuit in the binary
and ternary classification of MNIST and Fashion-MNIST datasets. The
architecture is highly adaptable and the classical-quantum boundary can be
adjusted according the availability of the quantum resource by exploiting the
correspondence between tensor networks and quantum circuits.


  The results of tunnelling studies of the energy spectrum of two-dimensional
(2D) states in a surface quantum well in a semiconductor with inverted band
structure are presented. The energy dependence of quasimomentum of the 2D
states over a wide energy range is obtained from the analysis of tunnelling
conductivity oscillations in a quantizing magnetic field. The spin-orbit
splitting of the energy spectrum of 2D states, due to inversion asymmetry of
the surface quantum well, and the broadening of 2D states at the energies, when
they are in resonance with the heavy hole valence band, are investigated in
structures with different strength of the surface quantum well. A quantitative
analysis is carried out within the framework of the Kane model of the energy
spectrum. The theoretical results are in good agreement with the tunnelling
spectroscopy data.


  We propose a size effect which leads to the negative magnetoresistance in
granular metal-insulator materials in which the hopping between two nearest
neighbor clusters is the main transport mechanism. We show that the hopping
probability increases with magnetic field. This is originated from the level
crossing in a few-electron cluster. Thus, the overlap of electronic states of
two neighboring clusters increases, and the negative magnetoresistance is
resulted.


  Despite decades of research, understanding human manipulation activities is,
and has always been, one of the most attractive and challenging research topics
in computer vision and robotics. Recognition and prediction of observed human
manipulation actions have their roots in the applications related to, for
instance, human-robot interaction and robot learning from demonstration. The
current research trend heavily relies on advanced convolutional neural networks
to process the structured Euclidean data, such as RGB camera images. These
networks, however, come with immense computational complexity to be able to
process high dimensional raw data.
  Different from the related works, we here introduce a deep graph autoencoder
to jointly learn recognition and prediction of manipulation tasks from symbolic
scene graphs, instead of relying on the structured Euclidean data. Our network
has a variational autoencoder structure with two branches: one for identifying
the input graph type and one for predicting the future graphs. The input of the
proposed network is a set of semantic graphs which store the spatial relations
between subjects and objects in the scene. The network output is a label set
representing the detected and predicted class types. We benchmark our new model
against different state-of-the-art methods on two different datasets, MANIAC
and MSRC-9, and show that our proposed model can achieve better performance. We
also release our source code https://github.com/gamzeakyol/GNet.


  We study the inverse boundary value problem for the Helmholtz equation using
the Dirichlet-to-Neumann map at selected frequencies as the data. A conditional
Lipschitz stability estimate for the inverse problem holds in the case of
wavespeeds that are a linear combination of piecewise constant functions
(following a domain partition) and gives a framework in which the scheme
converges. The stability constant grows exponentially as the number of
subdomains in the domain partition increases. We establish an order optimal
upper bound for the stability constant. We eventually realize computational
experiments to demonstrate the stability constant evolution for three
dimensional wavespeed reconstruction.


  Let $G$ be a compact Lie group and $T$ its maximal torus. In this paper, we
try to compute $gr_{\gamma}^*(G/T)$ the graded ring associated with the gamma
filtration of the complex $K$-theory $K^0(G/T)$ for $G=Spin(n)$. In particular,
we give a counterexample for a conjecture by Karpenko when $G=Spin(17)$. The
arguments for $E_7$ in $\S 11$ of the old version were not correct, and they
are deleted in this version.


  A microscopic treatment of cumulative phenomena based on perturbative QCD
calculations of the corresponding quark diagrams near the threshold is
presented. To sum all diagrams like these the special technique based on the
recurrence relations was developed. The x-behaviour of the nuclear structure
function $F_{2}(x)$ in the cumulative region x>1 was found to be roughly
exponential, governed by an effective coupling constant, which depends on the
QCD coupling constant and quark mass. Two mechanisms for cumulative particle
production, direct and spectator ones, were analysed. It was shown that due to
final state interactions the leading terms of the direct mechanism contribution
are cancelled and the spectator mechanism is the dominant one. It leads to a
smaller slope of the particle production rates compared to the slope of the
nuclear structure function in the cumulative region, in agreement with the
recent experimental data. The slope difference is due to additional multiple
interactions between nuclear and projectile partons which enter the spectator
mechanism for the cumulative production. The different versions of
hadronization mechanisms of the produced cumulative quarks into hadrons are
also discussed.


  This paper proposes a distributed controller synthesis framework for safe
navigation of multi-agent systems. We leverage control barrier functions to
formulate collision avoidance with obstacles and teammates as constraints on
the control input for a state-dependent network optimization problem that
encodes team formation and the navigation task. Our algorithmic solution is
valid for general nonlinear control dynamics and optimization problems. The
resulting controller is distributed, satisfies the safety constraints at all
times, and is asymptotically optimal. We illustrate its performance in a team
of differential-drive robots in a variety of complex environments, both in
simulation and in hardware.


  The field of Deep Learning is rich with empirical evidence of human-like
performance on a variety of prediction tasks. However, despite these successes,
the recent Predicting Generalization in Deep Learning (PGDL) NeurIPS 2020
competition suggests that there is a need for more robust and efficient
measures of network generalization. In this work, we propose a new framework
for evaluating the generalization capabilities of trained networks. We use
perturbation response (PR) curves that capture the accuracy change of a given
network as a function of varying levels of training sample perturbation. From
these PR curves, we derive novel statistics that capture generalization
capability. Specifically, we introduce two new measures for accurately
predicting generalization gaps: the Gi-score and Pal-score, which are inspired
by the Gini coefficient and Palma ratio (measures of income inequality), that
accurately predict generalization gaps. Using our framework applied to intra
and inter-class sample mixup, we attain better predictive scores than the
current state-of-the-art measures on a majority of tasks in the PGDL
competition. In addition, we show that our framework and the proposed
statistics can be used to capture to what extent a trained network is invariant
to a given parametric input transformation, such as rotation or translation.
Therefore, these generalization gap prediction statistics also provide a useful
means for selecting optimal network architectures and hyperparameters that are
invariant to a certain perturbation.


  We show that Massive Black Holes of AGNs follow the same approximately linear
relation with the luminosity of the host spheroid (bulge) found in normal
(quiescent) galaxies, with the black hole mass being ~0.002 that of the bulge.
We also demonstrate that Narrow line AGNs seem to have a significantly lower
Mbh/Lbulge ratio, which implies a new strong correlation between Mbh/Lbulge and
the width of the broad emission lines of AGNs. Combining existing data, new
observations and extrapolation schemes based on the Faber-Jackson relation, the
relation between the BH mass and the stellar velocity dispersion in the host
bulge of AGNs is constructed. It too agrees with the relation found in
quiescent galaxies.


  Higher-order interactions play a key role for the stability and function of a
complex system. However, how to identify them is still an open problem. Here,
we propose a method to fully reconstruct the structural connectivity of a
system of coupled dynamical units, identifying both pairwise and higher-order
interactions from the system time evolution. Our method works for any dynamics,
and allows the reconstruction of both hypergraphs and simplicial complexes,
either undirected or directed, unweighted or weighted. With two concrete
applications, we show how the method can help understanding the ecosystemic
complexity of bacterial systems, or the microscopic mechanisms of interaction
underlying coupled chaotic oscillators.


  We present experimental constraints on the spin-dependent WIMP-nucleon
elastic cross sections from the total 129.5 kg-year exposure acquired by the
Large Underground Xenon experiment (LUX), operating at the Sanford Underground
Research Facility in Lead, South Dakota (USA). A profile likelihood ratio
analysis allows 90% CL upper limits to be set on the WIMP-neutron (WIMP-proton)
cross section of $\sigma_n$ = 1.6$\times 10^{-41}$ cm$^{2}$ ($\sigma_p$ =
5$\times 10^{-40}$ cm$^{2}$) at 35 GeV$c^{-2}$, almost a sixfold improvement
over the previous LUX spin-dependent results. The spin-dependent WIMP-neutron
limit is the most sensitive constraint to date.


  Diffusion models have achieved state-of-the-art performance in generating
many different kinds of data, including images, text, and videos. Despite their
success, there has been limited research on how the underlying diffusion
process and the final convergent prior can affect generative performance; this
research has also been limited to continuous data types and a score-based
diffusion framework. To fill this gap, we explore how different discrete
diffusion kernels (which converge to different prior distributions) affect the
performance of diffusion models for graphs. To this end, we developed a novel
formulation of a family of discrete diffusion kernels which are easily
adjustable to converge to different Bernoulli priors, and we study the effect
of these different kernels on generative performance. We show that the quality
of generated graphs is sensitive to the prior used, and that the optimal choice
cannot be explained by obvious statistics or metrics, which challenges the
intuitions which previous works have suggested.


  We investigate the formation of rashbon bound states and strong-coupling
effects in an ultracold Fermi gas with a spherical spin-orbit interaction,
$H_{\rm so}=\lambda{\bf p}\cdot{\bf \sigma}$ (where ${\bf
\sigma}=(\sigma_x,\sigma_y,\sigma_z)$ are Pauli matrices). Extending the
strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR) to
include this spin-orbit coupling, we determine the superfluid phase transition
temperature $T_{\rm c}$, as functions of the strength of a pairing interaction
$U_s$, as well as the spin-orbit coupling strength $\lambda$. Evaluating poles
of the NSR particle-particle scattering matrix describing fluctuations in the
Cooper channel, we clarify the region where rashbon bound states dominate the
superfluid phase transition in the $U_{s}$-$\lambda$ phase diagram. Since the
antisymmetric spin-orbit interaction $H_{\rm so}$ breaks the inversion symmetry
of the system, rashbon bound states naturally have, not only a spin-singlet and
even-parity symmetry, but also a spin-triplet and odd-parity symmetry. Thus,
our results would be also useful for the study of this parity mixing effect in
the BCS-BEC crossover regime of a spin-orbit coupled Fermi gas.


  The successful explanation of fermion mixing and of the fermion mass
hierarchy by the Dualized Standard Model (DSM) scheme is based on the premises
of a fermion mass matrix rotating in generation space with changing scales at a
certain speed, which could in principle lead to sizeable flavour-violation
observable in high sensitivity experiments such as BaBar. However, a full
perturbative calculation to 1-loop order reported here shows that this
kinematical, flavour-violating effect of a rotating mass matrix is off-set in
the DSM by parallel effects from rotating wave functions and vertices giving in
the end only very small flavour-violations which are unlikely to be detectable
by present experiments. The result means that at least for the present the DSM
scheme has survived yet another threat to its validity, which is indeed its
most stringent and dangerous to-date. It also provides some clarification of
certain concepts connected with the rotating mass matrix which had previously
been found puzzling.


  In this paper, we study the uniqueness of the differential-difference
polynomials of entire functions on $\mathbb{C}^{n}$. We prove the following
result: Let $f(z)$ be a transcendental entire function on $\mathbb{C}^{n}$ of
hyper-order less than $1$ and
$g(z)=b_{-1}+\sum_{i=0}^{n}b_{i}f^{(k_{i})}(z+\eta_{i})$, where $b_{-1}$ and
$b_{i} (i=0\ldots,n)$ are small meromorphic functions of $f$ on
$\mathbb{C}^{n}$, $k_{i}\geq0 (i=0\ldots,n)$ are integers, and $\eta_{i}
(i=0\ldots,n)$ are finite values. Let $a_{1}(z)\not\equiv\infty,
a_{2}(z)\not\equiv\infty$ be two distinct small meromorphic functions of $f(z)$
on $\mathbb{C}^{n}$. If $f(z)$ and $g(z)$ share $a_{1}(z)$ CM, and $a_{2}(z)$
IM. Then either $f(z)\equiv g(z)$ or $a_{1}=2a_{2}=2$, $$f(z)\equiv
e^{2p}-2e^{p}+2,$$ and $$g(z)\equiv e^{p},$$ where $p(z)$ is a non-constant
entire function on $\mathbb{C}^{n}$. Especially, in the case of
$g(z)=(\Delta_{\eta}^{n}f(z))^{k}$, we obtain $f(z)\equiv
(\Delta_{\eta}^{n}f(z))^{k}$.


  Apart from assessing individual asset performance, investors in financial
markets also need to consider how a set of firms performs collectively as a
portfolio. Whereas traditional Markowitz-based mean-variance portfolios are
widespread, network-based optimisation techniques have built upon these
developments. However, most studies do not contain firms at risk of default and
remove any firms that drop off indices over a certain time. This is the first
study to incorporate risky firms and use all the firms in portfolio
optimisation. We propose and empirically test a novel method that leverages
Graph Attention networks (GATs), a subclass of Graph Neural Networks (GNNs).
GNNs, as deep learning-based models, can exploit network data to uncover
nonlinear relationships. Their ability to handle high-dimensional features and
accommodate customised layers for specific purposes makes them particularly
appealing for large-scale problems such as mid- and small-cap portfolio
optimization. This study utilises 30 years of data on mid-cap firms, creating
graphs of firms using distance correlation and the Triangulated Maximally
Filtered Graph approach. These graphs are the inputs to a GAT model that we
train using custom layers which impose weight and allocation constraints and a
loss function derived from the Sharpe ratio, thus directly maximising portfolio
risk-adjusted returns. This new model is benchmarked against a network
characteristic-based portfolio, a mean variance-based portfolio, and an
equal-weighted portfolio. The results show that the portfolio produced by the
GAT-based model outperforms all benchmarks and is consistently superior to
other strategies over a long period while also being informative of market
dynamics.


  Search is a central problem in artificial intelligence, and breadth-first
search (BFS) and depth-first search (DFS) are the two most fundamental ways to
search. In this paper we derive estimates for average BFS and DFS runtime. The
average runtime estimates can be used to allocate resources or judge the
hardness of a problem. They can also be used for selecting the best graph
representation, and for selecting the faster algorithm out of BFS and DFS. They
may also form the basis for an analysis of more advanced search methods. The
paper treats both tree search and graph search. For tree search, we employ a
probabilistic model of goal distribution; for graph search, the analysis
depends on an additional statistic of path redundancy and average branching
factor. As an application, we use the results to predict BFS and DFS runtime on
two concrete grammar problems and on the N-puzzle. Experimental verification
shows that our analytical approximations come close to empirical reality.


  In chapter VIII of Introductio in analysin infinitorum, Euler derives a
series for sine, cosine, and the formula $e^{iv}=\cos v+i\sin v$ His arguments
employ infinitesimal and infinitely large numbers and some strange equalities.
We interpret these seemingly inconsistent objects within the field of hyperreal
numbers. We show that any non-Archimedean field provides a framework for such
an interpretation. Yet, there is one implicit lemma underlying Euler's proof,
which requires specific techniques of non-standard analysis. Analyzing chapter
III of Institutiones calculi differentialis reveals Euler's appeal to the rules
of an ordered field which includes infinitesimals -- the same ones he applies
deriving series for $\sin v$, $\cos v$, and $e^{v}$.


  Several sages wearing colored hats occupy the vertices of a graph. Each sage
tries to guess the color of his own hat merely on the basis of observing the
hats of his neighbours without exchanging any information. Each hat can have
one of three colors. A predetermined guessing strategy is winning if it
guarantees at least one correct individual guess for every assignment of
colors. We completely solve the problem of describing graphs for which the
sages win.


  Proper scoring rules are an essential tool to assess the predictive
performance of probabilistic forecasts. However, propriety alone does not
ensure an informative characterization of predictive performance and it is
recommended to compare forecasts using multiple scoring rules. With that in
mind, interpretable scoring rules providing complementary information are
necessary. We formalize a framework based on aggregation and transformation to
build interpretable multivariate proper scoring rules.
Aggregation-and-transformation-based scoring rules are able to target specific
features of the probabilistic forecasts; which improves the characterization of
the predictive performance. This framework is illustrated through examples
taken from the literature and studied using numerical experiments showcasing
its benefits. In particular, it is shown that it can help bridge the gap
between proper scoring rules and spatial verification tools.


  Air transport systems are highly dynamic at temporal scales from minutes to
years. This dynamic behavior not only characterizes the evolution of the system
but also affect the system's functioning. Understanding the evolutionary
mechanisms is thus fundamental in order to better design optimal air transport
networks that benefits companies, passengers and the environment. In this
review, we briefly present and discuss the state-of-art on time-evolving air
transport networks. We distinguish the structural analysis of sequences of
network snapshots, ideal for long-term network evolution (e.g. annual
evolution), and temporal paths, preferred for short-term dynamics (e.g. hourly
evolution). We emphasize that most previous research focused on the first
modeling approach (i.e. long-term) whereas only a few studies look at
high-resolution temporal paths. We conclude the review highlighting that much
research remains to be done, both to apply already available methods and to
develop new measures for temporal paths on air transport networks. In
particular, we identify that the study of delays, network resilience and
optimization of resources (aircraft and crew) are critical topics that can
benefit of temporal network analysis.


  In this Letter we model the chemistry of DCO$^{+}$ in protoplanetary disks.
We find that the overall distribution of the DCO$^{+}$ abundance is
qualitatively similar to that of CO but is dominated by thin layer located at
the inner disk surface. To understand its distribution, we investigate the
different key gas-phase deuteration pathways that can lead to the formation of
DCO$^{+}$. Our analysis shows that the recent update in the exothermicity of
the reaction involving CH$_2$D$^{+}$ as a parent molecule of DCO$^{+}$ favors
deuterium fractionation in warmer conditions. As a result the formation of
DCO$^{+}$ is enhanced in the inner warm surface layers of the disk where X-ray
ionization occurs. Our analysis points out that DCO$^{+}$ is not a reliable
tracer of the CO snow line as previously suggested. We thus predict that
DCO$^{+}$ is a tracer of active deuterium and in particular X-ray ionization of
the inner disk.


  This work presents Arcula, a new design for hierarchical deterministic
wallets that brings identity-based addresses to the blockchain. Arcula is built
on top of provably secure cryptographic primitives. It generates all its
cryptographic secrets from a user-provided seed and enables the derivation of
new public keys based on the identities of users, without requiring any secret
information. Unlike other wallets, it achieves all these properties while being
secure against privilege escalation. We formalize the security model of
hierarchical deterministic wallets and prove that an attacker compromising an
arbitrary number of users within an Arcula wallet cannot escalate his
privileges and compromise users higher in the access hierarchy. Our design
works out-of-the-box with any blockchain that enables the verification of
signatures on arbitrary messages. We evaluate its usage in a real-world
scenario on the Bitcoin Cash network.


  We present time-resolved measurements of spin-flip photon-assisted tunneling
and spin-flip relaxation in a doubly occupied double quantum dot. The
photon-assisted excitation rate as a function of magnetic field indicates that
spin-orbit coupling is the dominant mechanism behind the spin-flip under the
present conditions. We are able to extract the resulting effective `spin-flip
tunneling' energy, which is found to be three orders of magnitude smaller than
the regular spin-conserving tunneling energy. We also measure the relaxation
and dephasing times of a qubit formed out of two two-electron states with
different spin and charge configurations.


  This paper investigates a source coding problem in which two terminals
communicating through a relay wish to estimate one another's source within some
distortion constraint. The relay has access to side information that is
correlated with the sources. Two different schemes based on the order of
communication, \emph{distributed source coding/delivery} and \emph{two cascaded
rounds}, are proposed and inner and outer bounds for the resulting
rate-distortion regions are provided. Examples are provided to show that
neither rate-distortion region includes the other one.


  Numerical treatment of the problem of two-dimensional viscous fluid flow in
and around circular porous inclusions is considered. The mathematical model is
described by Navier-Stokes equation in the free flow domain $\Omega_f$ and
nonlinear convective Darcy-Brinkman-Forchheimer equations in porous subdomains
$\Omega_p$. It is well-known that numerical solutions of the problems in such
heterogeneous domains require a very fine computational mesh that resolve
inclusions on the grid level. The size alteration of the relevant system
requires model reduction techniques. Here, we present a multiscale model
reduction technique based on the Generalized Multiscale Finite Element Method
(GMsFEM). We discuss construction of the multiscale basis functions for the
velocity fields based on the solution of the local problems with and without
oversampling strategy. Three test cases are considered for a given choice of
the three key model parameters, namely, the Reynolds number ($Re$), the
Forchheimer coefficient ($C$) and the Darcy number ($Da$). For the test runs,
the Reynolds number values are taken to be $Re = 1, 10, 100$ while the
Forchheimer coefficient and Darcy number are chosen as $C= 1, 10$ and $Da =
10^{-5}, 10^{-4}, 10^{-3}$, respectively. We numerically study the convergence
of the method as we increase the number of multiscale basis functions in each
domain, and observe good performance of the multiscale method.


  The deflection, potential, shear and magnification of a gravitational lens
following an elliptical power law mass model are investigated. This mass model
is derived from the circular power law profile through a rescaling of the axes,
similar to the case of a singular isothermal ellipsoid. The resulting
deflection can be calculated explicitly and given in terms of the Gaussian
hypergeometric function. Analytic expressions for the remaining lensing
properties are found as well. Because the power law profile lens contains a
number of well-known lens models as special cases, the equivalence of the new
expressions with known results is checked. Finally, it is shown how these
results naturally lead to a fast and accurate numerical scheme for computing
the deflection and other lens quantities, making this method a useful tool for
realistically modelling observed lenses.


  Heat management is crucial in the design of nanoscale devices as the
operating temperature determines their efficiency and lifetime. Past
experimental and theoretical works exploring nanoscale heat transport in
semiconductors addressed known deviations from Fourier's law modeling by
including effective parameters, such as a size-dependent thermal conductivity.
However, recent experiments have qualitatively shown new behavior that cannot
be modeled in this way. Here, we combine advanced experiment and theory to show
that the cooling of 1D- and 2D-confined nanoscale hot spots on silicon can be
described using a general hydrodynamic heat transport model, contrary to
previous understanding of heat flow in bulk silicon. We use a comprehensive set
of extreme ultraviolet scatterometry measurements of non-diffusive transport
from transiently heated nanolines and nanodots to validate and generalize our
ab initio model, that does not need any geometry-dependent fitting parameters.
This allows us to uncover the existence of two distinct timescales and heat
transport mechanisms: an interface resistance regime that dominates on short
time scales, and a hydrodynamic-like phonon transport regime that dominates on
longer timescales. Moreover, our model can predict the full thermomechanical
response on nanometer length scales and picosecond time scales for arbitrary
geometries, providing an advanced practical tool for thermal management of
nanoscale technologies. Furthermore, we derive analytical expressions for the
transport timescales, valid for a subset of geometries, supplying a route for
optimizing heat dissipation.


  In the particle acceleration by stimulated emission of radiation (PASER), the
efficient interaction occurs when a train of micro-bunches whose periodicity
being identical to the resonance frequency of the medium. The previous
theoretical calculations based on the simplified model consider only the energy
exchange in the boundless condition, under the experimental condition, however,
the gas active medium must be guided by the metal waveguide. In this paper, we
have developed the model of energy exchange between a train of micro-bunches
and gas mixture active medium in waveguide boundary for the first time based on
the Theory of Electromagnetic Fields, and made detailed analysis and
calculations with MathCAD. The results show that the energy density could be
optimized to a certain value to get the maximum energy exchange.


  A function on the real line is called regulated if it has a left limit and a
right limit at each point. If $f$ is a Schwartz distribution on the real line
such that $f=F'$ (distributional or weak derivative) for a regulated function
$F$ then the regulated primitive integral of $f$ is
$\int_{(a,b)}f=F(b-)-F(a+)$, with similar definitions for other types of
intervals. The space of integrable distributions is a Banach space and Banach
lattice under the Alexiewicz norm. It contains the spaces of Lebesgue and
Henstock--Kurzweil integrable functions as continuous embeddings. It is the
completion of the space of signed Radon measures in the Alexiewicz norm.
Functions of bounded variation form the dual space and the space of
multipliers. The integrable distributions are a module over the functions of
bounded variation. Properties such as integration by parts, change of
variables, H\"older inequality, Taylor's theorem and convergence theorems are
proved.


  This work provides new insights and constructs to the field of computer
architecture and systems, and these insights are expected to be useful for the
broad software stack. First, this work introduces Functionality Locality: this
form of Functionality Locality shows that functionalities can be changed with a
single piece of information, by solely changing the access order. This broadens
the scope of ``principle of locality", which originally includes spatial and
temporal locality. Second, this work coins the term Mixture, by incorporating
the layout-directed functionalities with the original quantifiers such as
scalar and vector. The implications of Mixture significantly expands new
understanding of quantifiers, and this work identifies several important ones
(from the author perspective). Third, with Functionality and Mixture, this work
identifies the principle ``Control = Logic = Memory", and provides a revisit to
Von Neumann architectures and Harvard architectures. This centers the focus on
the memory, and brings further guidelines on memory-centric architectures with
a new analytic framework. Fourth, this work discusses several important
implications from this work in a variety of aspects.


  We prove the convergence of a class of high frequency path-functionals of a
sticky diffusion to its local time. First, we prove this for the sticky
Brownian motion. Then, we extend the result to sticky stochastic differential
equations. We combine the local time approximation with an approximation of the
occupation time to set up a consistent stickiness estimator. Last, we perform
numerical experiments to assess the properties of the stickiness estimator and
the local time approximation.


  Microarray data come from many steps of production and have been known to
contain noise. The pre-processing is implemented to reduce the noise, where the
background is corrected. Prior to further analysis, many Illumina BeadArrays
users had applied the convolution model, a model which had been adapted from
when it was first developed on the Affymetrix platform, to adjust the intensity
value: corrected background intensity value.
  Several models based on different underlying distributions and or parameters
estimation methods have been proposed and applied. For instance : the
exponential-gamma, the normal-gamma and the exponential-normal convolutions
with a maximum likelihood estimation, non-parametric, Bayesian and moment
methods of the parameters estimation, including two recent
exponential-lognormal and gamma-lognormal convolutions.
  In this paper, we propose models and derive the corrected background
intensity based on the generalized betas and the generalized beta-normal
convolutions as a generalization of the existing models.


  In a continuous-time model with multiple assets described by c\`{a}dl\`{a}g
processes, this paper characterizes superhedging prices, absence of arbitrage,
and utility maximizing strategies, under general frictions that make execution
prices arbitrarily unfavorable for high trading intensity. Such frictions
induce a duality between feasible trading strategies and shadow execution
prices with a martingale measure. Utility maximizing strategies exist even if
arbitrage is present, because it is not scalable at will.


  We review results obtained from recent neutron scattering studies of the
lead-oxide class of perovskite relaxors PMN and PZN. A ferroelectric soft mode
has been identified in PMN at 1100 K that becomes overdamped near 620 K. This
is the same temperature at which polar nanoregions (PNR) begin to form, denoted
by Td, and suggests that a direct connection exists between the soft mode and
the PNR. The appearance of diffuse scattering intensity at Td reported by
Naberezhnov et al. lends further support to this picture. At lower temperature
the soft mode in PMN reappears close to Tc = 213 K (defined only for E > Ec).
These results are provocative because the dynamics below Tc are characteristic
of an ordered ferroelectric state, yet they occur in a system that remains
cubic on average at all temperatures. We discuss a coupled-mode model that
successfully describes these data as well as those from earlier lattice
dynamical studies of other perovskites such as BaTiO3.


  In a recent result by the authors (ref. [1]) it was proved that solutions of
the self-similar fragmentation equation converge to equilibrium exponentially
fast. This was done by showing a spectral gap in weighted $L^2$ spaces of the
operator defining the time evolution. In the present work we prove that there
is also a spectral gap in weighted $L^1$ spaces, thus extending exponential
convergence to a larger set of initial conditions. The main tool is an
extension result in ref. [4].


  As we move to distribute High Energy Physics computing tasks throughout the
global Grid, we are encountering ever more severe difficulties installing and
selecting appropriate versions of the supporting products. Problems show up at
every level: the base operating systems and tools, general purpose utilities
like root, and specific releases of application code. I will discuss some
specific examples, including what we've learned in commissioning the SAM
software for use by CDF. I will show why revision control can be a truly
difficult problem, and will discuss what we've been doing to measure and
control the situation.


  In the context of a cosmological string model describing the propagation of
strings in a time-dependent Robertson-Walker background space-time, we show
that the asymptotic acceleration of the Universe can be identified with the
square of the string coupling. This allows for a direct measurement of the
ten-dimensional string coupling using cosmological data. We conjecture that
this is a generic feature of a class of non-critical string models that
approach asymptotically a conformal (critical) sigma model whose target space
is a four-dimensional space-time with a dilaton background that is linear in
sigma-model time. The relation between the cosmic acceleration and the string
coupling does not apply in critical strings with constant dilaton fields in
four dimensions.


  This work deals with the homogenization of functionals with linear growth in
the context of $\mathcal{A}$-quasiconvexity. A representation theorem is
proved, where the new integrand function is obtained by solving a cell problem
where the coupling between homogenization and the $\mathcal{A}$-free condition
plays a crucial role. This result extends some previous work to the linear
case, thus allowing for concentration effects.


  We introduce a numerical method for extracting minimal geodesics along the
group of volume preserving maps, equipped with the L2 metric, which as observed
by Arnold solve Euler's equations of inviscid incompressible fluids. The method
relies on the generalized polar decomposition of Brenier, numerically
implemented through semi-discrete optimal transport. It is robust enough to
extract non-classical, multi-valued solutions of Euler's equations, for which
the flow dimension is higher than the domain dimension, a striking and
unavoidable consequence of this model. Our convergence results encompass this
generalized model, and our numerical experiments illustrate it for the first
time in two space dimensions.


  We prove an arithmetic analogue of the typical structure theorem for graph
hereditary properties due to Alon, Balogh, Bollob\'as and Morris.


  In this work we propose an extension of physics informed supervised learning
strategies to parametric partial differential equations. Indeed, even if the
latter are indisputably useful in many applications, they can be
computationally expensive most of all in a real-time and many-query setting.
Thus, our main goal is to provide a physics informed learning paradigm to
simulate parametrized phenomena in a small amount of time. The physics
information will be exploited in many ways, in the loss function (standard
physics informed neural networks), as an augmented input (extra feature
employment) and as a guideline to build an effective structure for the neural
network (physics informed architecture). These three aspects, combined
together, will lead to a faster training phase and to a more accurate
parametric prediction. The methodology has been tested for several equations
and also in an optimal control framework.


  Recent experiments in graphene heterostructures have observed Chern
insulators - integer and fractional Quantum Hall states made possible by a
periodic substrate potential. Here we study theoretically the competition
between different Chern insulators, which can be tuned by the amplitude of the
periodic potential, leads to a new family of quantum critical points described
by QED$_3$-Chern-Simons theory. At these critical points, $N_f$ flavors of
Dirac fermions interact through an emergent U$(1)$ gauge theory at Chern-Simons
level $K$, and remarkably, the entire family (with any $N_f$ or $K$) can be
realized at special values of the external magnetic field. Transitions between
particle-hole conjugate Jain states realize "pure" QED$_3$ in which multiple
flavors of Dirac fermion interact with a Maxwell U$(1)$ gauge field. The
multi-flavor nature of the critical point leads to an emergent SU$(N_f)$
symmetry. Specifically, at the transition from a $\nu=$1/3 to 2/3 quantum Hall
state, the emergent SU(3) symmetry predicts an octet of charge density waves
with enhanced susceptibilities, which is verified by DMRG numerical simulations
on microscopic models applicable to graphene heterostructures. We propose
experiments on Chern insulators that could resolve open questions in the study
of 2+1 dimensional conformal field theories and test recent duality inspired
conjectures.


  We study a nonhierarchical tritrophic system, whose predator-prey
interactions are described by the rock-paper-scissors game rules. In our
stochastic simulations, individuals may move strategically towards the
direction with more conspecifics to form clumps instead of moving aimlessly on
the lattice. Considering that the conditioning to move gregariously depends on
the organism's physical and cognitive abilities, we introduce a maximum
distance an individual can perceive the environment and a minimum conditioning
level to perform the gregarious movement. We investigate the pattern formation
and compute the average size of the single-species spatial domains emerging
from the grouping behaviour. The results reveal that the defence tactic reduces
the predation risk significantly, being more profitable if individuals perceive
further distances, thus creating bigger groups. Our outcomes show that the
species with more conditioned organisms dominate the cyclic spatial game,
controlling most of the territory. On the other hand, the species with fewer
individuals ready to perform aggregation strategy gives its predator the chance
to fill the more significant fraction of the grid. The spatial interactions
assumed in our numerical experiments constitute a data set that may help
biologists and data scientists understand how local interactions influence
ecosystem dynamics.


  Maintaining literature databases and online bibliographies is a core
responsibility of metadata aggregators such as digital libraries. In the
process of monitoring all the available data sources the question arises which
data source should be prioritized. Based on a broad definition of information
quality we are looking for different ways to find the best fitting and most
promising conference candidates to harvest next. We evaluate different
conference ranking features by using a pseudo-relevance assessment and a
component-based evaluation of our approach.


  We demonstrate that the Discrete Persistent Source Extractor (DisPerSE) can
be used with spectroscopic redshifts to define the cosmic web and its distance
to galaxies in small area deepfields. Here we analyze the use of DisPerSE to
identify structure in observational data. We apply DisPerSE to the distribution
of galaxies in the COSMOS field and find the best parameters to identify
filaments. We compile a catalog of 11500 spectroscopic redshifts from the
Galaxy and Mass Assembly (GAMA) G10 data release. We analyze two-dimensional
slices, extract filaments and calculate the distance for each galaxy to its
nearest filament. We find that redder and more massive galaxies are closer to
filaments. To study the growth of galaxies across cosmic time, and environment,
we are carrying out an HI survey covering redshifts z = 0 - 0.45, the COSMOS HI
Large Extragalactic Survey (CHILES). In addition we present the predicted HI
mass fraction as a function of distance to filaments for the spectroscopically
known galaxies in CHILES. Lastly, we discuss the cold gas morphology of a few
individual galaxies and their positions with respect to the cosmic web. The
identification of the cosmic web, and the ability of CHILES to study the
resolved neutral hydrogen morphologies and kinematics of galaxies, will allow
future studies of the properties of neutral hydrogen in different cosmic web
environments across the redshift range z = 0.1 - 0.45.


  In this paper we try to bridge breakthroughs in quantitative
sociology/econometrics pioneered during the last decades by Mac Fadden,
Brock-Durlauf, Granovetter and Watts-Strogats through introducing a minimal
model able to reproduce essentially all the features of social behavior
highlighted by these authors. Our model relies on a pairwise Hamiltonian for
decision maker interactions which naturally extends the multi-populations
approaches by shifting and biasing the pattern definitions of an Hopfield model
of neural networks. Once introduced, the model is investigated trough graph
theory (to recover Granovetter and Watts-Strogats results) and statistical
mechanics (to recover Mac-Fadden and Brock-Durlauf results). Due to internal
symmetries of our model, the latter is obtained as the relaxation of a proper
Markov process, allowing even to study its out of equilibrium properties. The
method used to solve its equilibrium is an adaptation of the Hamilton-Jacobi
technique recently introduced by Guerra in the spin glass scenario and the
picture obtained is the following: just by assuming that the larger the amount
of similarities among decision makers, the stronger their relative influence,
this is enough to explain both the different role of strong and weak ties in
the social network as well as its small world properties. As a result,
imitative interaction strengths seem essentially a robust request (enough to
break the gauge symmetry in the couplings), furthermore, this naturally leads
to a discrete choice modelization when dealing with the external influences and
to imitative behavior a la Curie-Weiss as the one introduced by Brock and
Durlauf.


  We use simulations to demonstrate that photometric redshift "errors" can be
greatly reduced by using the photometric redshift probability distribution p(z)
rather than a one-point estimate such as the most likely redshift. In principle
this involves tracking a large array of numbers rather than a single number for
each galaxy. We introduce a very simple estimator that requires tracking only a
single number for each galaxy, while retaining the systematic-error-reducing
properties of using the full p(z) and requiring only very minor modifications
to existing photometric redshift codes. We find that using this redshift
estimator (or using the full p(z)) can substantially reduce systematics in dark
energy parameter estimation from weak lensing, at no cost to the survey.


  We refine a technique used in a paper by Schur on real-rooted polynomials.
This amounts to an extension of a theorem of Wagner on Hadamard products of
Toeplitz matrices. We also apply our results to polynomials for which the
Neggers-Stanley Conjecture is known to hold. More precisely, we settle
interlacing properties for $E$-polynomials of series-parallel posets and
column-strict labelled Ferrers posets.


  Several measurements, including the data from the laser spectrometer in the
Sample Analysis at Mars instrument suite on the Curiosity Rover in Gale crater,
have measured seasonal variations in atmospheric methane at the 0.7 ppbv (parts
per billion volume) level. As a result, models have been proposed to understand
the methane production including novel chemical, geological, meteorological,
and biological mechanisms. Biological models often rely on methanogenic
extremophile archaea which might be similar to some Earth based organisms which
can be studied exhaustively in a laboratory setting. Such organisms might
thrive in a subsurface ecosystem involving water and methane and as such could
leave a unique biosignature in the Martian regolith that could be preserved
over extended periods of time. The resulting mixture of carboxyl, acetyl and
hydroxyl groups blended with the metallic sulfates and regolith constituents
could produce a Raman signature detectable on the next rover mission if the
concentration is high enough. Here we measure the 532 nm and the 780 nm Raman
spectra of a variety of molar concentrations of several hydrated metallic
sulfates mixed with JSC-1 Martian regolith simulant to identify the signature
concentration thresholds for the isolated C=O Raman peak from acetic acid. We
find a Raman peak removed from most fragmented molecular Raman bands near 1608
cm-1 using the 532 nm laser for the Fe and Mg sulfates to yield a threshold in
the 120 - 160 ppmv range for a cutoff S/N of 2.


  We present a parallelized bijective graph matching algorithm that leverages
seeds and is designed to match very large graphs. Our algorithm combines
spectral graph embedding with existing state-of-the-art seeded graph matching
procedures. We justify our approach by proving that modestly correlated, large
stochastic block model random graphs are correctly matched utilizing very few
seeds through our divide-and-conquer procedure. We also demonstrate the
effectiveness of our approach in matching very large graphs in simulated and
real data examples, showing up to a factor of 8 improvement in runtime with
minimal sacrifice in accuracy.


  Binary decision diagrams can compactly represent vast sets of states,
mitigating the state space explosion problem in model checking. Probabilistic
systems, however, require multi-terminal diagrams storing rational numbers.
They are inefficient for models with many distinct probabilities and for
iterative numeric algorithms like value iteration. In this paper, we present a
new "symblicit" approach to checking Markov chains and related probabilistic
models: We first generate a decision diagram that symbolically collects all
reachable states and their predecessors. We then concretise states one-by-one
into an explicit partial state space representation. Whenever all predecessors
of a state have been concretised, we eliminate it from the explicit state space
in a way that preserves all relevant probabilities and rewards. We thus keep
few explicit states in memory at any time. Experiments show that very large
models can be model-checked in this way with very low memory consumption.


  A Laplacian eigenfunction on a two-dimensional Riemannian manifold provides a
natural partition into Neumann domains (a.k.a. a Morse--Smale complex). This
partition is generated by gradient flow lines of the eigenfunction, which bound
the so-called Neumann domains. We prove that the Neumann Laplacian defined on a
Neumann domain is self-adjoint and has a purely discrete spectrum. In addition,
we prove that the restriction of an eigenfunction to any one of its Neumann
domains is an eigenfunction of the Neumann Laplacian. By comparison, similar
statements about the Dirichlet Laplacian on a nodal domain of an eigenfunction
are basic and well-known. The difficulty here is that the boundary of a Neumann
domain may have cusps and cracks, so standard results about Sobolev spaces are
not available.
  Another very useful common fact is that the restricted eigenfunction on a
nodal domain is the first eigenfunction of the Dirichlet Laplacian. This is no
longer true for a Neumann domain. Our results enable the investigation of the
resulting spectral position problem for Neumann domains, which is much more
involved than its nodal analogue.


  We evaluate the performance of small error-correcting codes, which we tailor
to hardware platforms of very different connectivity and coherence: on a
superconducting processor based on transmon qubits and a spintronic quantum
register consisting of a nitrogen-vacancy center in diamond. Taking the
hardware-specific errors and connectivity into account, we investigate the
dependence of the resulting logical error rate on the platform features such as
the native gates, native connectivity, gate times, and coherence times. Using a
standard error model parameterized for the given hardware, we simulate the
performance and benchmark these predictions with experimental results when
running the code on the superconducting quantum device. The results indicate
that for small codes, the quasi-linear layout of the superconducting device is
advantageous. Yet, for codes involving multi-qubit controlled operations, the
central-spin connectivity of the color centers enables lower error rates.