  Biological units such as macromolecules, organelles, and cells are directed
to a proper location under gradients of relevant chemicals. By considering a
macroscopic element that has binding sites for a chemical adsorption reaction
to occur on its surface, we show the existence of a thermodynamic force that is
generated by the gradient and exerted on the element. By assuming local
equilibrium and adopting the grand potential from thermodynamics, we derive a
formula for such a thermodynamic force, which depends on the chemical potential
gradient and Langmuir isotherm. The conditions under which the formula can be
applied are demonstrated to hold in intracellular reactions. The role of the
force in the partitioning of bacterial chromosome/plasmid during cell division
is discussed.


  We study several-matrix models and show that when the potential is convex and
a small perturbation of the Gaussian potential, the first order correction to
the free energy can be expressed as a generating function for the enumeration
of maps of genus one. In order to do that, we prove a central limit theorem for
traces of words of the weakly interacting random matrices defined by these
matrix models and show that the variance is a generating function for the
number of planar maps with two vertices with prescribed colored edges.


  Adversarial training is one of the most popular methods for training methods
robust to adversarial attacks, however, it is not well-understood from a
theoretical perspective. We prove and existence, regularity, and minimax
theorems for adversarial surrogate risks. Our results explain some empirical
observations on adversarial robustness from prior work and suggest new
directions in algorithm development. Furthermore, our results extend previously
known existence and minimax theorems for the adversarial classification risk to
surrogate risks.


  Molecular dynamics simulations were performed to study the effects of Si
solute on the glass formation and crystallization of Pd liquid. Pure Pd sample
prepared by quenching process with cooling rate of $10^{13}$ K/s can be in an
amorphous state but the structural analysis indicates there is nearly no
glass-forming motif in the sample. However, doping a small amount Si (Si
concentration ~ 4%) the sample can be vitrified at a cooling rate of $10^{12}$
K/s. The glass-forming motifs such as Pd-centered Z13, Si-centered Z9-like and
Mixed-ICO-Cube clusters with 5-fold local symmetry are found to be the dominant
short-range orders in the glassy samples. With the increasing of the Si-doping
concentration, these glass-forming motifs tend to aggregate and connect with
each other forming a network structure. Our calculated results revealed that Si
solutes in liquid Pd can significantly enhance the glass-forming ability.


  We consider constant scalar curvature K\"{a}hler metrics on a smooth minimal
model of general type in a neighborhood of the canonical class, which is the
perturbation of the canonical class by a fixed K\"{a}hler metric. We show that
sequences of such metrics converge smoothly on compact subsets away from a
subvariety to the singular K\"{a}hler Einstein metric in the canonical class.
This confirms partially a conjecture of Jian-Shi-Song about the convergence
behavior of such sequences.


  We present a method to infer a dense depth map from a color image and
associated sparse depth measurements. Our main contribution lies in the design
of an annealing process for determining co-visibility (occlusions,
disocclusions) and the degree of regularization to impose on the model. We show
that regularization and co-visibility are related via the fitness (residual) of
model to data and both can be unified into a single framework to improve the
learning process. Our method is an adaptive weighting scheme that guides
optimization by measuring the residual at each pixel location over each
training step for (i) estimating a soft visibility mask and (ii) determining
the amount of regularization. We demonstrate the effectiveness our method by
applying it to several recent unsupervised depth completion methods and
improving their performance on public benchmark datasets, without incurring
additional trainable parameters or increase in inference time. Code available
at: https://github.com/alexklwong/adaframe-depth-completion.


  We calculate the ferroelectric polarization dynamics induced by a femtosecond
midinfrared pulse as measured in the recent experiment by R. Mankowsky et al.,
Phys. Rev. Lett. 118, 197601 (2017). It is due to the nonlinear coupling of the
excited infrared-active phonon with the ferroelectric mode or to the excitation
of the ferroelectric mode itself depending on the pulse frequency. To begin
with, we write the LiNbO$_3$ crystal symmetry invariant thermodynamic potential
including electric field and nonlinear phonon coupling terms. We solve the
equations of motion determined by this potential for phonon coordinates
numerically in classical approximation. We explain the transient polarization
reversal observed in the experiment by action of the depolarizing electric
field which is due to bound charges at the polarization domain boundaries and
give a reasonable estimate for its value. We argue that the polarization could
be ultimately reversed when this field is screened.


  Knowledge regarding the coronal magnetic field is important for the
understanding of many phenomena, like flares and coronal mass ejections.
Because of the low plasma beta in the solar corona the coronal magnetic field
is often assumed to be force-free and we use photospheric vector magnetograph
data to extrapolate the magnetic field into the corona with the help of a
non-linear force-free optimization code. Unfortunately the measurements of the
photospheric magnetic field contain inconsistencies and noise. In particular
the transversal components (say Bx and By) of current vector magnetographs have
their uncertainties. Furthermore the magnetic field in the photosphere is not
necessary force-free and often not consistent with the assumption of a
force-free field above. We develop a preprocessing procedure to drive the
observed non force-free data towards suitable boundary conditions for a
force-free extrapolation. As a result we get a data set which is as close as
possible to the measured data and consistent with the force-free assumption.


  We show that chirping gravitational waves in the LIGO frequency band $f=1 -
5000$ Hz can be gravitationally diffracted by the Sun, due to the coincidence
of its Fresnel length $r_F \propto \sqrt{1\, {\rm AU}/f}$ and the solar radius
$r_\odot$. This solar diffraction is detectable through its frequency-dependent
amplification of the wave, albeit with low event rates. We also advocate that
solar diffraction allows probing the inner solar profile with the chirping
evolution of frequencies. Along the course, we develop diffractive lensing in
terms of simple convergence and shear of a lens and emphasize the relevance of
high-frequency regimes including merger and ringdown phases for detection. This
work not only presents an interesting opportunity with ongoing and future
LIGO-band missions but also develops the diffractive lensing of long-wavelength
waves in the universe. A similar phenomenon can also help discover
non-relativistic wave dark matter, as studied in a sequel.


  A low energy bound in a class of chiral solitonic field theories related the
infrared physics of the SU(N) Yang-Mills theory is established.


  A tree-based network on a set $X$ of $n$ leaves is said to be universal if
any rooted binary phylogenetic tree on $X$ can be its base tree. Francis and
Steel showed that there is a universal tree-based network on $X$ in the case of
$n=3$, and asked whether such a network exists in general. We settle this
problem by proving that there are infinitely many universal tree-based networks
for any $n>1$.


  We use machine learning to study the locus ${\mathcal L}_n$ of genus two
curves with $(n, n)$-split Jacobian. More precisely we design a transformer
model which given values for the Igusa invariants determines if the
corresponding genus two curve is in the locus ${\mathcal L}_n$, for $n=2, 3, 5,
7$. Such curves are important in isogeny based cryptography.
  During this study we discover that there are no rational points ${\mathfrak
p} \in {\mathcal L}_n$ with weighted moduli height $\leq 2$ in any of
${\mathcal L}_2$, ${\mathcal L}_3$, and ${\mathcal L}_5$. This extends on
previous work of the authors to use machine learning methods to study the
moduli space of genus 2 algebraic curves.


  We present an imaging technique particularly suited to the detection of a
target embedded in a strongly scattering medium. Classical imaging techniques
based on the Born approximation fail in this kind of configuration because of
multiply scattered echoes and aberration distortions. The experimental set up
we consider uses an array of programmable transmitters/receivers. A target is
placed behind a scattering medium. The impulse responses between all array
elements are measured and form a matrix. The core of the method is to separate
the single-scattered echo of the target from the multiple scattering
background. This is possible because of a deterministic coherence along the
antidiagonals of the array response matrix, which is typical of single
scattering. Once this operation is performed, target detection is achieved by
applying the DORT method (French acronym for decomposition of the time reversal
operator). Experimental results are presented in the case of wide-band
ultrasonic waves around 3 MHz. A 125-element array is placed in front of a
collection of randomly distributed steel rods (diameter 0.8mm). The slab
thickness is three times the scattering mean free path. The target is a larger
steel cylinder (diameter 15 mm) that we try to detect and localize. The quality
of detection is assessed theoretically based on random matrix theory and is
shown to be significantly better than what is obtained with classical imaging
methods. Aside from multiple scattering, the technique is also shown to reduce
the aberrations induced by an heterogeneous layer.


  We present the results of an XMM-Newton observation of the radio-quiet X-ray
pulsar 1E 1207-5209 located at the center of the shell-like supernova remnant
G296.5+10.0. The X-ray spectrum is characterized by the presence of two
phase-dependent absorption lines at energies ~0.7 keV and ~1.4 keV. Moreover,
these broad spectral features have significant substructure, suggesting that
they are due to the blending of several narrower lines. We interpret such
features as evidence for an atmosphere containing metals and a magnetic field
value of a few 10^12 G, consistent with the observed spin-down rate
P_dot=(1.98+/-0.83)*10^(-14) s/s. Since 1E 1207-5209 is the only X-ray emitting
pulsar showing evidence of such features, we tentatively link them to the
unique combination of age and energetics that characterize this object. We
suggest that a young age and a low level of magnetospheric activity are
favorable conditions for the detection of atomic spectral features from metals
in neutron star atmospheres, which would be either blanketed by a thin layer of
accreted hydrogen in older objects or masked by non-thermal processes in young
energetic pulsars.


  The four-roll mill, wherein four identical cylinders undergo rotation of
identical magnitude but alternate signs, was originally proposed by GI Taylor
to create local extensional flows and study their ability to deform small
liquid drops. Since an extensional flow has an unstable eigendirection, a drop
located at the flow stagnation point will have a tendency to escape. This
unstable dynamics can however be stabilised using, e.g., a modulation of the
rotation rates of the cylinders. Here we use Reinforcement Learning, a branch
of Machine Learning devoted to the optimal selection of actions based on
cumulative rewards, in order to devise a stabilisation algorithm for the
four-roll mill flow. The flow is modelled as the linear superposition of four
two-dimensional rotlets and the drop is treated as a rigid spherical particle
smaller than all other length scales in the problem. Unlike previous attempts
to devise control, we take a probabilistic approach whereby speed adjustments
are drawn from a probability density function whose shape is improved over time
via a form of gradient ascent know as Actor-Critic method. With enough
training, our algorithm is able to precisely control the drop and keep it close
to the stagnation point for as long as needed. We explore the impact of the
physical and learning parameters on the effectiveness of the control and
demonstrate the robustness of the algorithm against thermal noise. We finally
show that Reinforcement Learning can provide a control algorithm effective for
all initial positions and that can be adapted to limit the magnitude of the
flow extension near the position of the drop.


  The Cauchy problem for the 1-dimensional Zakharov system is shown to be
globally well-posed for large data which not necessarily have finite energy.
The proof combines the local well-posedness result of Ginibre, Tsutsumi, Velo
and a general method introduced by Bourgain to prove a similar result for
nonlinear Schr\"odinger equations.


  We propose a simple ansatz that allows to generate new exactly solvable
multi-state Landau-Zener models. It is based on a system of two decoupled
two-level atoms whose levels vary with time and cross at some moments. Then we
consider multiparticle systems with Heisenberg equations for annihilation
operators having similar structure with Shr\"odinger equation for amplitudes in
multistate Landau-Zener models and show that the corresponding Shr\"odinger
equation in multiparticle sector belongs to the multistate Landau-Zener class.
This observation allows to generate new exactly solvable models from already
known ones.
  We discuss possible applications of the new solutions in the problem of the
driven charge transport in quantum dots.


  High dynamic range (HDR) imaging involves capturing a series of frames of the
same scene, each with different exposure settings, to broaden the dynamic range
of light. This can be achieved through burst capturing or using staggered HDR
sensors that capture long and short exposures simultaneously in the camera
image signal processor (ISP). Within camera ISP pipeline, illuminant estimation
is a crucial step aiming to estimate the color of the global illuminant in the
scene. This estimation is used in camera ISP white-balance module to remove
undesirable color cast in the final image. Despite the multiple frames captured
in the HDR pipeline, conventional illuminant estimation methods often rely only
on a single frame of the scene. In this paper, we explore leveraging
information from frames captured with different exposure times. Specifically,
we introduce a simple feature extracted from dual-exposure images to guide
illuminant estimators, referred to as the dual-exposure feature (DEF). To
validate the efficiency of DEF, we employed two illuminant estimators using the
proposed DEF: 1) a multilayer perceptron network (MLP), referred to as
exposure-based MLP (EMLP), and 2) a modified version of the convolutional color
constancy (CCC) to integrate our DEF, that we call ECCC. Both EMLP and ECCC
achieve promising results, in some cases surpassing prior methods that require
hundreds of thousands or millions of parameters, with only a few hundred
parameters for EMLP and a few thousand parameters for ECCC.


  Through dedicated measurements in the optical regime we demonstrate that
ptychography can be applied to reconstruct complex-valued object functions that
vary with time from a sequence of spectral measurements. A probe pulse of
approximately 1 ps duration, time delayed in increments of 0.25 ps is shown to
recover dynamics on a ten times faster time scale with an experimental limit of
approximately 5 fs.


  We consider two examples of a fully decodable combinatorial encoding of
Bernoulli schemes: the encoding via Weyl simplices and the much more
complicated encoding via the RSK (Robinson--Schensted--Knuth) correspondence.
In the first case, the decodability is a quite simple fact, while in the second
case, this is a nontrivial result obtained by D.~Romik and P.~\'Sniady and
based on the papers~ \cite{KV}, \cite{VK}, and others. We comment on the proofs
from the viewpoint of the theory of measurable partitions; another proof, using
representation theory and generalized Schur--Weyl duality, will be presented
elsewhere. We also study a new dynamics of Bernoulli variables on $P$-tableaux
and find the limit 3D-shape of these tableaux.


  The vertex distortion of a lattice knot is the supremum of the ratio of the
distance between a pair of vertices along the knot and their distance in the
l1-norm. We show analogous results to those of Gromov, Pardon and
Blair-Campisi-Taylor-Tomova about the distortion of smooth knots hold for
vertex distortion: the vertex distortion of a lattice knot is 1 only if it is
the unknot, and that there are minimal lattice-stick number knot conformations
with arbitrarily high distortion.


  This paper extends the key concept of persistence within Topological Data
Analysis (TDA) in a new direction. TDA quantifies topological shapes hidden in
unorganized data such as clouds of unordered points. In the 0-dimensional case
the distance-based persistence is determined by a single-linkage (SL)
clustering of a finite set in a metric space. Equivalently, the 0D persistence
captures only edge-lengths of a Minimum Spanning Tree (MST). Both SL dendrogram
and MST are unstable under perturbations of points. We define the new
stable-under-noise mergegram, which outperforms previous isometry invariants on
a classification of point clouds by PersLay.


  Efficient representation of quantum many-body states on classical computers
is a problem of enormous practical interest. An ideal representation of a
quantum state combines a succinct characterization informed by the system's
structure and symmetries, along with the ability to predict the physical
observables of interest. A number of machine learning approaches have been
recently used to construct such classical representations [1-6] which enable
predictions of observables [7] and account for physical symmetries [8].
However, the structure of a quantum state gets typically lost unless a
specialized ansatz is employed based on prior knowledge of the system [9-12].
Moreover, most such approaches give no information about what states are easier
to learn in comparison to others. Here, we propose a new generative
energy-based representation of quantum many-body states derived from Gibbs
distributions used for modeling the thermal states of classical spin systems.
Based on the prior information on a family of quantum states, the energy
function can be specified by a small number of parameters using an explicit
low-degree polynomial or a generic parametric family such as neural nets, and
can naturally include the known symmetries of the system. Our results show that
such a representation can be efficiently learned from data using exact
algorithms in a form that enables the prediction of expectation values of
physical observables. Importantly, the structure of the learned energy function
provides a natural explanation for the hardness of learning for a given class
of quantum states.


  Let $p_n$ be a polynomial of degree $n$ having all its roots on the real line
distributed according to a smooth function $u(0,x)$. One could wonder how the
distribution of roots behaves under iterated differentation of the function,
i.e. how the density of roots of $p_n^{(k)}$ evolves. We derive a nonlinear
transport equation with nonlocal flux $$ u_t + \frac{1}{\pi}\left( \arctan{
\left( \frac{Hu}{ u}\right)} \right)_x = 0,$$ where $H$ is the Hilbert
transform. This equation has three very different compactly supported
solutions: (1) the arcsine distribution $u(t,x) = (1-x^2)^{-1/2}
\chi_{(-1,1)}$, (2) the family of semicircle distributions $$ u(t,x) =
\frac{2}{\pi} \sqrt{(T-t) - x^2}$$ and (3) a family of solutions contained in
the Marchenko-Pastur law.


  An identifying code in a graph is a dominating set that also has the property
that the closed neighborhood of each vertex in the graph has a distinct
intersection with the set. The minimum cardinality of an identifying code, or
ID code, in a graph $G$ is called the ID code number of $G$ and is denoted
$\gid(G)$. In this paper, we give upper and lower bounds for the ID code number
of the prism of a graph, or $G\Box K_2$. In particular, we show that $\gid(G
\Box K_2) \ge \gid(G)$ and we show that this bound is sharp. We also give upper
and lower bounds for the ID code number of grid graphs and a general upper
bound for $\gid(G\Box K_2)$.


  In this paper, a new concept, radial coverage strength, is first proposed to
characterize the visual sensing performance when the orientation of the target
pose is considered. In particular, the elevation angle of the optical pose of
the visual sensor is taken to decompose the visual coverage strength into
effective and ineffective components, motivated by the imaging intuition. An
optimization problem is then formulated for a multi-camera network to maximize
the coverage of the object area based on the strength information fusion along
the effective coverage strength direction through the deployment of the angle
between radial coverage vector of the camera optical pose. Both simulation and
experiments are conducted to validate the proposed approach and comparison with
existing methods is also provided.


  Faraday's Law of induction is often stated as "a change in magnetic flux
causes an EMF"; or, more cautiously, "a change in magnetic flux is associated
with an EMF"; It is as well that the more cautious form exists, because the
first "causes" form is incompatible with the usual expression $V = - \partial_t
\Phi$. This is not, however, to deny the causality as reasonably inferred from
experimental observation - it is the equation for Faraday's Law of induction
which does not represent the claimed cause-and-effect relationship. Here I
investigate a selection of different approaches, trying to see how an
explicitly causal mathematical equation, which attempts to encapsulate the "a
change in magnetic flux causes ..." idea, might arise.


  Given a reaction-diffusion system interacting via a complex network, we
propose two different techniques to modify the network topology while
preserving its dynamical behaviour. In the region of parameters where the
homogeneous solution gets spontaneously destabilized, perturbations grow along
the unstable directions made available across the networks of connections,
yielding irregular spatio-temporal patterns. We exploit the spectral properties
of the Laplacian operator associated to the graph in order to modify its
topology, while preserving the unstable manifold of the underlying equilibrium.
The new network is isodynamic to the former, meaning that it reproduces the
dynamical response (pattern) to a perturbation, as displayed by the original
system. The first method acts directly on the eigenmodes, thus resulting in a
general redistribution of link weights which, in some cases, can completely
change the structure of the original network. The second method uses
localization properties of the eigenvectors to identify and randomize a
subnetwork that is mostly embedded only into the stable manifold. We test both
techniques on different network topologies using the Ginzburg-Landau system as
a reference model. Whereas the correlation between patterns on isodynamic
networks generated via the first recipe is larger, the second method allows for
a finer control at the level of single nodes. This work opens up a new
perspective on the multiple possibilities for identifying the family of
discrete supports that instigate equivalent dynamical responses on a
multispecies reaction-diffusion system.


  A new method is developed for estimating photometric redshifts, using
realistic template SEDs, extending over four decades in wavelength (i.e from
0.05 $\mu m$ to 1 mm). The SEDs are constructed for four different spectral
types of galaxies (elliptical, spiral, irregular and starburst) and satisfy the
following characteristics: a). they are optimised to produce the observed
colours of galaxies at $z\sim 0$; b). incorporate the chemo-photometric
spectral evolution of galaxies of different types, in agreement with
observations; c). allow treatment of dust contribution and its evolution with
redshift, consistent with the spectral evolution model; d). include absorption
and re-emission of radiation by dust and hence, realistic estimates of the
far-infrared radiation; e). include correction for inter-galactic absorption by
Lyman continuum and Lyman forest.
  Using these template SEDs, the photometric redshifts are estimated to an
accuracy of $\Delta z = 0.11$. The degeneracy in the method and hence, the
redshifts and spectral types, are explored via Monte Carlo simulations. The
consistency of the technique is demonstrated by applying it on a UV selected
sample of HDF galaxies and comparing the statistical results with those from
other independent studies.


  Motivated by Burillo, Cleary and Roever's summary on obstructions of
subgroups of Thompson's group $V,$ we explored the higher dimensional version
of the groups, Brin-Thompson groups $nV$ and $SV,$ a class of infinite
dimensional Brin-Thompson groups and an easy class of the twisted version of
the Brin-Thompson groups $SV_G$ with some certain condition. We found that they
have similar obstructions as Thompson's group $V$ on the torsion subgroups and
a selection of the interesting Baumslag-Solitor groups are excluded as the
subgroups of $SV$ and $SV_G.$ We also discuss a little on the group
$\mathscr{S}V,$ an even larger class relaxing some of the "finiteness
condition" and observe that some of the restrictions on subgroups disappear.


  We propose a practical Bayesian optimization method using Gaussian process
regression, of which the marginal likelihood is maximized where the number of
model selection steps is guided by a pre-defined threshold. Since Bayesian
optimization consumes a large portion of its execution time in finding the
optimal free parameters for Gaussian process regression, our simple, but
straightforward method is able to mitigate the time complexity and speed up the
overall Bayesian optimization procedure. Finally, the experimental results show
that our method is effective to reduce the execution time in most of cases,
with less loss of optimization quality.


  The radio bright zone (RBZ) at the Galactic center has been observed with the
JVLA in the A, B and C array configurations at 5.5 and 9 GHz. With a procedure
for high-dynamic range imaging developed on CASA, we constructed deep images a
resolution up to 0.2", achieving rms noises of a few $\mu$Jy/beam. From the
high-resolution and high-dynamics range images at 5.5 and 9 GHz, a population
of compact radio sources ranging from a few mJy to a few tens $\mu$Jy in flux
density is revealed. The steep-spectrum radio sources in RBZ are likely the
candidates of high-energy objects that are associated with neutron stars and/or
stellar mass black holes at the Galactic center. We report new results of the
Cannonball and Galactic center transient (GCT).


  The open-shell reference relativistic equation-of-motion coupled-cluster
method within its four-component description is successfully implemented with
the consideration of single- and double- excitation approximation. The one-body
and two-body matrix elements required for the correlation calculation are
generated using Dirac-Coulomb Hamiltonian. As a first attempt, the implemented
method is employed to calculate a few of the low-lying ionized states of heavy
atomic (Ag, Cs, Au, Fr, Lr) and valence ionization potential of molecular (HgH,
PbF) systems, where the effect of relativity does really matter to obtain
highly accurate results. Not only the relativistic effect, but also the effect
of electron correlation is crucial in these heavy atomic and molecular systems.
To justify the fact, we have taken two further approximations in the
four-component relativistic equation-of-motion framework to quantify how the
effect of electron correlation plays a role in the calculated values at
different level of the approximation. All these calculated results are compared
with the available experimental data as well as with other theoretically
calculated values to judge the extent of accuracy obtained in our calculations.
A nice agreement is achieved for all the considered systems which validates the
performance of the open-shell reference relativistic equation-of-motion
coupled-cluster method.


  The construction of a novel surgical instrument is considered, which is also
a probing device providing a signal to the measuring equipment, which after its
interpretation allows to obtain useful information about the section quality
and the biomaterial properties. We propose here some formalized considerations
on the possibility of its implementation for different variables registration.
The idea is also extrapolated into the field of micrurgy which refers to the
microelectrode techniques and the local potential registration in situ.


  We investigate "chimera" states in a ring of identical phase oscillators
coupled in a time-delayed and spatially non-local fashion. We find novel
"clustered chimera" states that have spatially distributed phase coherence
separated by incoherence with adjacent coherent regions in anti-phase. The
existence of such time-delay induced phase clustering is further supported
through solutions of a generalized functional self-consistency equation of the
mean field. Our results highlight an additional mechanism for cluster formation
that may find wider practical applications.


  We present the first Swift Ultraviolet/Optical Telescope Serendipitous Source
Catalogue (UVOTSSC). The catalogue was compiled from 23,059 Swift datasets
taken within the first five years of observations with the Swift UVOT. A
purpose-built processing pipeline, based around the standard Swift processing
tools, was employed. The catalogue contains positions, photometry in three UV
and three optical bands, morphological information and data quality flags. In
total, the catalogue contains 6,200,016 unique sources of which more than 2
million have multiple observations in the catalogue.


  The fundamental gap of an interacting many-electron system is given by the
sum of the single-particle Kohn-Sham gap and the derivative discontinuity. The
latter can be generated by advanced approximations to the exchange-correlation
(XC) energy and is the key quantity to capture strong correlation with density
functional theory (DFT). In this work we derive an expression for the
derivative discontinuity in terms of the XC kernel of time-dependent density
functional theory and demonstrate the crucial role of a discontinuity in the XC
kernel itself. By relating approximate XC kernels to approximate local vertex
corrections we then generate beyond-GW self-energies that include a
discontinuity in the local vertex function. The quantitative importance of this
result is illustrated with a numerical study of the local exchange vertex on
model systems.


  We study and constrain the parameter space of the vector color-octet model
from observed data at Tevatron by studying top quark pair production and
associated observables afbt and spin-correlation. In particular we study
invariant mass and rapidity dependence of afbt at Tevatron. In addition to FC
couplings we extend our study to include FV coupling involving first & third
generation quarks for both these processes. In order to ensure that we remain
within the constraints imposed by LHC data, we analyze the charge asymmetry,
p_T spectrum & invariant mass in t\bar t production data at LHC. The
constraints from dijet resonance searches performed by LHC are also considered.
We also explore the contribution of this model to single top quark production
mediated by charged & neutral color-octet vector bosons. FV couplings
introduced then induce same-sign top-pair production process which is analyzed
for both hadron colliders. We have incorporated effect of finite decay width of
color octets on these processes. We find that it is possible to explain the
observed afbt anomaly in color-octet vector model without transgressing
production cross sections of all these processes both through FC and FV
couplings at Tevatron. We predict best point sets in model parameter space for
specific choices of color-octet masses corresponding to chi^2_min evaluated
using mttb and dyy spectrum of afbt from observed data set at Tevatron (8.7
fb-1). We find that single top quark production is more sensitive to FC and FV
couplings in comparison to top-pair production. We provide 95% exclusion
contours on the plane of FV chiral couplings from recent data at Tevatron, CMS
and ATLAS corresponding to nonobservability of large same-sign dilepton events.
The four observed point sets are consistent with the cross section, charge
asymmetry and spin-correlation measurements for t\bar t production & dijet
searches at LHC.


  In this note, we prove the uniqueness of the Neumann matrices of the
open-closed vertex in plane-wave light-cone string-field theory, first derived
for all values of the mass parameter mu in hep-th/0311231. We also prove the
existence and uniqueness of the inverse of an infinite dimensional matrix
necessary for the cubic vertex Neumann matrices, and give an explicit
expression for it in terms of mu-deformed Gamma functions. Methods of complex
analysis are used together with the analytic properties of the mu-deformed
Gamma functions. One of the implications of these results is that the
geometrical continuity conditions suffice to determine the bosonic part of the
vertices as in flat space.


  We first present a short overview of X-ray probes of the black hole region of
active galaxies (AGN) and then concentrate on the X-ray search for supermassive
black holes (SMBHs) in optically non-active galaxies.
  The first part focuses on recent results from the X-ray observatories Chandra
and XMM-Newton which detected a wealth of new spectral features which originate
in the nuclear region of AGN.
  In the last few years, giant-amplitude, non-recurrent X-ray flares have been
observed from several non-active galaxies. All of them share similar
properties, namely: extreme X-ray softness in outburst, huge peak luminosity
(up to ~10^{44} erg/s), and the absence of optical signs of Seyfert activity.
Tidal disruption of a star by a supermassive black hole is the favored
explanation of these unusual events. The second part provides a review of the
initial X-ray observations, follow-up studies,and the relevant aspects of tidal
disruption models studied in the literature.


  In this master thesis, we give a new proof on the pointwise asymptotic
expansion for Bergman kernel of a hermitian holomorphic line bundle on the
points where the curvature of the line bundle is positive and satisfy local
spectral gap condition. The main point is to introduce a suitable
semi-classical symbol space and related symbolic calculus inspired from recent
work of Hsiao and Savale. Particularly, we establish the existence of pointwise
asymptotic expansion on the positive part for certain semi-positive line
bundles.


  Breakup cross sections are determined for the Borromean nucleus 22C by using
a four-body eikonal model, including Coulomb corrections. Bound and continuum
states are constructed within a 20C + n + n three-body model in hyperspherical
coordinates. We compute continuum states with the correct asymptotic behavior
through the R-matrix method. For the n+ n potential, we use the Minnesota
interaction. As there is no precise experimental information on 21C, we define
different parameter sets for the 20C + n potentials. These parameter sets
provide different scattering lengths, and resonance energies of an expected
3/2+ excited state. Then we analyze the 22C ground-state energy and rms radius,
as well as E1 strength distributions and breakup cross sections. The E1
strength distribution presents an enhancement at low energies. Its amplitude is
associated with the low binding energy, rather than with a three-body
resonance. We show that the shape of the cross section at low energies is
sensitive to the ground-state properties. In addition, we suggest the existence
of a low-energy 2+ resonance, which should be observable in breakup
experiments.


  The proposed Iron Calorimeter (ICAL) detector at Indian Neutrino
Observatory(INO) will be a large (50 kt) magnetized detector located 1270 m
underground at Bodi West Hills in Tamilnadu. ICAL is capable of identifying the
charge of the particles. In this paper its potential for the measurement of the
muon charge ratio is explored by means of a detailed simulation-based study,
first using the CORSIKA code and then comparing it with an analytical model
(the "pika" model). The estimated muon charge ratio is in agreement with the
existing experimental observations, its measure can be extended by INO-ICAL up
to 10 TeV and up to 60 degrees.


  We review a performance of Fock space methods in calculating spectra of a
range of supersymmetric models with gauge symmetry. Examples include: a) SU(2)
Supersymmetric Yang Mills Quantum Mechanics in four euclidean dimensions, b)
Quantum Mechanics of one fermion and one boson with infinite number of colours,
and c) planar 1+1 dimensional Yang Mills theories with adjoint matter. Infrared
divergencies of the latter theories with scalars are briefly discussed and a
possible dynamical solution of the problem is suggested.


  A major question in dynamical systems is to understand the mechanisms driving
global instability in the 3 Body Problem (3BP), which models the motion of
three bodies under Newtonian gravitational interaction. The 3BP is called
restricted if one of the bodies has zero mass and the other two, the primaries,
have strictly positive masses $m_0,m_1$. We consider the Restricted Planar
Elliptic 3 Body Problem (RPE3BP) where the primaries revolve in Keplerian
ellipses. We prove that the RPE3BP exhibits topological instability: for any
values of the masses $m_0,m_1$ (except $m_0=m_1$), we build orbits along which
the angular momentum of the massless body experiences an arbitrarily large
variation provided the eccentricity of the orbit of the primaries is positive
but small enough.
  In order to prove this result we show that a degenerate Arnold Diffusion
Mechanism, which moreover involves exponentially small phenomena, takes place
in the RPE3BP. Our work extends the result obtained in \cite{MR3927089} for the
a priori unstable case $m_1/m_0\ll1$, to the case of arbitrary masses
$m_0,m_1>0$, where the model displays features of the so-called \textit{a
priori stable} setting.


  The authors establish a relation of the theory of varieties with degenerate
Gauss maps in projective spaces with the theory of congruences and
pseudocongruences of subspaces and show how these two theories can be applied
to the construction of induced connections on submanifolds of projective spaces
and other spaces endowed with a projective structure.


  Two properties of the radiation emitted by a relativistic electron in an
external field, in the classical approximation, are presented in details: 1)
spectral sum rules and their relationship with the sum rules for oscillator
strength in atomic physics. Filtered sum rules can be used to remove infrared
or ultraviolet divergences. 2) "half-naked electron" effects like the Landau-
Pomeranchuk-Migdal and Ternovskij-Shul'ga-Fomin effects. These properties are
best understood when introducing the apparent transverse velocity.


  It was observed recently by Randall and Wise that, any particle in the
Standard Model cannot decay to $e^+e^-$ and $\gamma \gamma$ final states with
comparably measurable branching ratios. This is also true for most extensions
of the Standard Model, with the Randall-Sundrum model as an outstanding
exception. In this paper, we show that two-Higgs-Doublet-Models (2HDM) yield
another possible exception if certain parameters are properly chosen. In
addition, we have checked that this model survives the tests of low energy
processes, including the anomalous magnetic moment and electric dipole moment
of leptons, lepton-flavor-violating decays $\mu^- \to e^- \gamma$ and $e^- e^+
e^-$.


  We investigated a possibility of application of liquid metal contacts for
devices based on thermotunneling. Electric and thermal characteristics of low
wetting contact Hg/Si, and high wetting contacts Hg/Cu were determined and
compared. We got tunneling I-V characteristics for Hg/Si, while for Hg/Cu, I-V
characteristics were ohmic. We explained tunneling I-V characteristics by
presence of nanogap between the contact materials. Heat conductance of high
wetting and low wetting contacts were compared, using calorimeter measurements.
Heat conductance of high wetting contact was 3-4 times more than of low wetting
contact. Both electric and thermal characteristics of liquid metal contact
indicated that it could be used for thermotunneling devices. We solved liquid
Cs in liquid Hg to reduce work function and make liquid metal more suitable for
room temperature cooling. Work function as low as 2.6 eV was obtained.


  In this paper, we focus on the nonlinear least squares:
$\mbox{min}_{\mathbf{x} \in \mathbb{H}^d}\| |A\mathbf{x}|-\mathbf{b}\|$ where
$A\in \mathbb{H}^{m\times d}$, $\mathbf{b} \in \mathbb{R}^m$ with $\mathbb{H}
\in \{\mathbb{R},\mathbb{C} \}$ and consider the uniqueness and stability of
solutions. Such problem arises, for instance, in phase retrieval and absolute
value rectification neural networks. For the case where
$\mathbf{b}=|A\mathbf{x}_0|$ for some $\mathbf{x}_0\in \mathbb{H}^d$, many
results have been developed to characterize the uniqueness and stability of
solutions. However, for the case where $\mathbf{b} \neq |A\mathbf{x}_0| $ for
any $\mathbf{x}_0\in \mathbb{H}^d$, there is no existing result for it to the
best of our knowledge. In this paper, we first focus on the uniqueness of
solutions and show for any matrix $A\in \mathbb{H}^{m \times d}$ there always
exists a vector $\mathbf{b} \in \mathbb{R}^m$ such that the solution is not
unique. But, in real case, such ``bad'' vectors $\mathbf{b}$ are negligible,
namely, if $\mathbf{b} \in \mathbb{R}_{+}^m$ does not lie in some measure zero
set, then the solution is unique. We also present some conditions under which
the solution is unique. For the stability of solutions, we prove that the
solution is never uniformly stable. But if we restrict the vectors $\mathbf{b}$
to any convex set then it is stable.


  We present a Lagrangian formulation for ${\cal N}=8$ superconformal field
theories in three spacetime dimensions that is general enough to encompass
infinite-dimensional gauge algebras that generally go beyond Lie algebras. To
this end we employ Chern-Simons theories based on Leibniz algebras, which give
rise to L$_{\infty}$ algebras and are defined on the dual space $\frak{g}^*$ of
a Lie algebra $\frak{g}$ by means of an embedding tensor map $\vartheta
:\frak{g}^*\rightarrow \frak{g}$. We show that for the Lie algebra
$\frak{sdiff}_3$ of volume-preserving diffeomorphisms on a 3-manifold there is
a natural embedding tensor defining a Leibniz algebra on the space of
one-forms. Specifically, we show that the cotangent bundle to any 3-manifold
with a volume-form carries the structure of a (generalized) Courant algebroid.
The resulting ${\cal N}=8$ superconformal field theories are shown to be
equivalent to Bandos-Townsend theories. We show that the theory based on $S^3$
is an infinite-dimensional generalization of the Bagger-Lambert-Gustavsson
model that in turn is a consistent truncation of the full theory. We also
review a Scherk-Schwarz reduction on $S^2\times S^1$, which gives the
super-Yang-Mills theory with gauge algebra $\frak{sdiff}_2$, and we construct
massive deformations.


  We calculate pionic contribution to the relativistic Fermi Liquid parameters
(RFLPs) using Chiral Effective Lagrangian. The RFLPs so determined are then
used to calculate chemical potential, exchange and nuclear symmetry energies
due to $\pi$$N$ interaction. We also evaluate two loop ring diagrams involving
$\sigma$, $\omega$ and $\pi$ meson exchanges and compare results with what one
obtains from the relativistic Fermi Liquid theory (RFLT).


  Sampling-based motion planning algorithms such as RRT* are well-known for
their ability to quickly find an initial solution and then converge to the
optimal solution asymptotically. However, the convergence rate can be slow for
highdimensional planning problems, particularly for dynamical systems where the
sampling space is not just the configuration space but the full state space. In
this paper, we introduce the idea of using a partial-final-state-free (PFF)
optimal controller in kinodynamic RRT* [1] to reduce the dimensionality of the
sampling space. Instead of sampling the full state space, the proposed
accelerated kinodynamic RRT*, called Kino-RRT*, only samples part of the state
space, while the rest of the states are selected by the PFF optimal controller.
We also propose a delayed and intermittent update of the optimal arrival time
of all the edges in the RRT* tree to decrease the computation complexity of the
algorithm. We tested the proposed algorithm using 4-D and 10-D state-space
linear systems and showed that Kino-RRT* converges much faster than the
kinodynamic RRT* algorithm.


  We give an overview of our recent integral-field-unit spectroscopy of
luminous extended emission-line regions (EELRs) around low-redshift quasars,
including new observations of 5 fields. Previous work has shown that the most
luminous EELRs are found almost exclusively around steep-spectrum radio-loud
quasars, with apparently disordered global velocity fields, and little, if any,
morphological correlation with either the host-galaxy or the radio structure.
Our new observations confirm and expand these results. The EELRs often show
some clouds with velocities exceeding 500 km/s, ranging up to 1100 km/s, but
the velocity dispersions, with few exceptions, are in the 30-100 km/s range.
Emission-line ratios show that the EELRs are clearly photoionized by the
quasars. Masses of the EELRs range up to >10^10 Msun. Essentially all of the
EELRs show relatively low metallicities, and they are associated with quasars
that, in contrast to most, show similarly low metallicities in their broad-line
regions. The two objects in our sample that do not have classical double-lobed
radio morphologies (3C48, with a compact-steep-spectrum source; Mrk1014,
radio-quiet, but with a weak compact-steep-spectrum source) are the only ones
that appear to have recent star formation. While some of the less-luminous
EELRs may have other origins, the most likely explanation for the ones in our
sample is that they are examples of gas swept out of the host galaxy by a
large-solid-angle blast wave accompanying the production of the radio jets. The
triggering of the quasar activity is almost certainly the result of the merger
of a gas-rich galaxy with a massive, gas-poor galaxy hosting the supermassive
black hole.


  The action in general relativity (GR), which is an integral over the manifold
plus an integral over the boundary, is a global object and is only well defined
when the topology is fixed. Therefore, to use the action in GR and in most
approaches to quantum gravity (QG) based on a covariant Lorentzian action,
there needs to exist a prefered (global) timelike vector, and hence a global
topology $R \times S^3$, for it to make sense. This is especially true in the
Hamiltonian formulation of QG. Therefore, in order to do canonical
quantization, we need to know the topology, appropriate boundary conditions and
(in an open manifold) the conditions at infinity, which affects the fundamental
geometrical scalar invariants of the spacetime (and especially those which may
occur in the QG action).


  An important problem in quantum computation is generation of single-qubit
quantum gates such as Hadamard ($H$) and $\pi/8$ ($T$) gates which are
components of a universal set of gates. Qubits in experimental realizations of
quantum computing devices are interacting with their environment. While the
environment is often considered as an obstacle leading to decrease of the gate
fidelity, in some cases it can be used as a resource. Here we consider the
problem of optimal generation of $H$ and $T$ gates using coherent control and
the environment as a resource acting on the qubit via incoherent control. For
this problem, we study quantum control landscape which represents the behaviour
of the infidelity as a functional of the controls. We consider three
landscapes, with infidelities defined by steering between two, three (via
Goerz-Reich-Koch approach), and four matrices in the qubit Hilbert space. We
observe that for the $H$ gate, which is Clifford gate, for all three
infidelities the distributions of minimal values obtained with gradient search
have a simple form with just one peak. However, for $T$ gate which is a
non-Clifford gate, the situation is surprisingly different - this distribution
for the infidelity defined by two matrices also has one peak, whereas
distributions for the infidelities defined by three and four matrices have two
peaks, that might indicate possible existence of two isolated minima in the
control landscape. Important is that among these three infidelities only those
defined with three and four matrices guarantee closeness of generated gate to a
target and can be used as a good measure of closeness. We study sets of
optimized solutions for this most general and not treated before case of
coherent and incoherent controls acting together, and discover that they form
submanifolds in the control space, and unexpected, in some cases two isolated
submanifolds.


  The quaternion offset linear canonical transform (QOLCT) which is time
shifted and frequency modulated version of the quaternion linear canonical
transform (QLCT) provides a more general framework of most existing signal
processing tools. For the generalized QOLCT, the classical Heisenbergs and
Liebs uncertainty principles have been studied recently. In this paper, we
first define the shorttime quaternion offset linear canonical transform
(STQOLCT) and drive its relationship with the quaternion Fourier transform
(QFT). The crux of the paper lies in the generalization of several well known
uncertainty principles for the STQOLCT, including Donoho Starks uncertainty
principle, Hardys uncertainty principle, Beurlings uncertainty principle, and
Logarithmic uncertainty principle.


  Field-orthogonal temporal modes of photonic quantum states provide a new
framework for quantum information science (QIS). They intrinsically span a
high-dimensional Hilbert space and lend themselves to integration into existing
single-mode fiber communication networks. We show that the three main
requirements to construct a valid framework for QIS -- the controlled
generation of resource states, the targeted and highly efficient manipulation
of temporal modes and their efficient detection -- can be fulfilled with
current technology. We suggest implementations of diverse QIS applications
based on this complete set of building blocks.


  Using the sunspot numbers reported during the Maunder minimum and the
empirical relations between the mode frequencies and solar activity indices,
the variations in the total solar irradiance and 10.7 cm radio flux for the
period 1645 to 1715 is estimated. We find that the total solar irradiance and
radio flux during the Maunder minimum decreased by 0.19% and 52% respectively,
as compared to the values for solar cycle 22.


  Monotonicity with respect to all arguments is fundamental to the definition
of aggregation functions. It is also a limiting property that results in many
important non-monotonic averaging functions being excluded from the theoretical
framework. This work proposes a definition for weakly monotonic averaging
functions, studies some properties of this class of functions and proves that
several families of important non-monotonic means are actually weakly monotonic
averaging functions. Specifically we provide sufficient conditions for weak
monotonicity of the Lehmer mean and generalised mixture operators. We establish
weak monotonicity of several robust estimators of location and conditions for
weak monotonicity of a large class of penalty-based aggregation functions.
These results permit a proof of the weak monotonicity of the class of
spatial-tonal filters that include important members such as the bilateral
filter and anisotropic diffusion. Our concept of weak monotonicity provides a
sound theoretical and practical basis by which (monotone) aggregation functions
and non-monotone averaging functions can be related within the same framework,
allowing us to bridge the gap between these previously disparate areas of
research.


  This paper studies traveling waves with nonzero wave speed (angular traveling
waves) of the high-dimensional Boussinesq equation that have not been studied
before. We analyze the properties of these waves and demonstrate that, unlike
the unique stationary solution, they lack positivity, radial symmetry, and
exponential decay. By employing variational and geometric approaches, along
with perturbation theory, we establish the orbital (in)stability and strong
instability of these traveling waves.


  We propose Gaussian processes for signals over graphs (GPG) using the apriori
knowledge that the target vectors lie over a graph. We incorporate this
information using a graph- Laplacian based regularization which enforces the
target vectors to have a specific profile in terms of graph Fourier transform
coeffcients, for example lowpass or bandpass graph signals. We discuss how the
regularization affects the mean and the variance in the prediction output. In
particular, we prove that the predictive variance of the GPG is strictly
smaller than the conventional Gaussian process (GP) for any non-trivial graph.
We validate our concepts by application to various real-world graph signals.
Our experiments show that the performance of the GPG is superior to GP for
small training data sizes and under noisy training.


  We give a new characterization of the class of rational string functions from
formal language theory using order-preserving interpretations with respect to a
very weak monadic programming language. This refines the known characterization
of rational functions by order-preserving MSO interpretations.


  Non-commutative crepant resolutions are algebraic objects defined by Van den
Bergh to realize an equivalence of derived categories in birational geometry.
They are motivated by tilting theory, the McKay correspondence, and the minimal
model program, and have applications to string theory and representation
theory. In this expository article I situate Van den Bergh's definition within
these contexts and describe some of the current research in the area.


  Coherent optical memories will likely play an important role in future
quantum communication networks. Among the different platforms, memories based
on ladder-type orbital transitions in atomic gasses offer high bandwidth
($>100$ MHz), continuous (on-demand) readout, and low-noise operation. Here we
report on an upgraded setup of our previously-reported fast ladder memory, with
improved efficiency and lifetime, and reduced noise. The upgrade employs a
stronger control field, wider signal beam, reduced atomic density, higher
optical depth, annular optical-pumping beam, and weak dressing of an auxiliary
orbital to counteract residual Doppler-broadening. For a 2 ns-long pulse, we
demonstrate 53% internal efficiency, 35% end-to-end efficiency, $3\times
10^{-5}$ noise photons per pulse, and a $1/e$ lifetime of 108 ns. This
combination of performances is a record for continuous-readout memories.


  Exoplanets have been observed at many stages of their host star's life,
including the main sequence (MS), subgiant and red giant branch stages. Also,
polluted white dwarfs (WDs) likely represent dynamically active systems at late
times. Here, we perform 3-body simulations which include realistic post-MS
stellar mass loss and span the entire lifetime of exosystems with two massive
planets, from the endpoint of formation to several Gyr into the WD phase of the
host star. We find that both MS and WD systems experience ejections and
star-planet collisions (Lagrange instability) even if the planet-planet
separation well-exceeds the analytical orbit-crossing (Hill instability)
boundary. Consequently, MS-stable planets do not need to be closely-packed to
experience instability during the WD phase. This instability may pollute the WD
directly through collisions, or, more likely, indirectly through increased
scattering of smaller bodies such as asteroids or comets. Our simulations show
that this instability occurs predominately between tens of Myr to a few Gyrs of
WD cooling.


  Let $F$ be a non-archimedean locally compact field of residue characteristic
$p\neq2$, let $G=\mathrm{GL}_{n}(F)$ and let $H$ be an orthogonal subgroup of
$G$. For $\pi$ a complex smooth supercuspidal representation of $G$, we give a
full characterization for the distinguished space $\mathrm{Hom}_{H}(\pi,1)$
being non-zero and we further study its dimension as a complex vector space,
which generalizes a similar result of Hakim for tame supercuspidal
representations. As a corollary, the embeddings of $\pi$ in the space of smooth
functions on the set of symmetric matrices in $G$, as a complex vector space,
is non-zero and of dimension four, if and only if the central character of
$\pi$ evaluating at $-1$ is $1$.


  We show that incompatible ``higher-order quantum theoretic testing
procedures", known as quantum testers, perform better in distinguishing causal
quantum networks than its compatible counterparts. To demonstrate our finding,
we consider a specific two-party quantum comb discrimination (QCD) game based
on the task in which a receiver gets a black-box that implements a quantum comb
and they attempt to determine which comb it implements based on prior
information. We show that the receiver does better at winning the game when
they have exclusive access to incompatible testers over compatible ones. Our
investigation generalises the earlier finding that the incompatibility of POVMs
is a {\em bona fide} resource in quantum state distinguishability. We also show
that any quantum resource in testers is useful in comb exclusion tasks using
the resource measure, {\em convex weight}.


  Conducting a systematic review (SR) is comprised of multiple tasks: (i)
collect documents (studies) that are likely to be relevant from digital
libraries (eg., PubMed), (ii) manually read and label the documents as relevant
or irrelevant, (iii) extract information from the relevant studies, and (iv)
analyze and synthesize the information and derive a conclusion of SR. When
researchers label studies, they can screen ranked documents where relevant
documents are higher than irrelevant ones. This practice, known as screening
prioritization (ie., document ranking approach), speeds up the process of
conducting a SR as the documents labelled as relevant can move to the next
tasks earlier. However, the approach is limited in reducing the manual workload
because the total number of documents to screen remains the same. Towards
reducing the manual workload in the screening process, we investigate the
quality of document ranking of SR. This can signal researchers whereabouts in
the ranking relevant studies are located and let them decide where to stop the
screening. After extensive analysis on SR document rankings from different
ranking models, we hypothesize 'topic broadness' as a factor that affects the
ranking quality of SR. Finally, we propose a measure that estimates the topic
broadness and demonstrate that the proposed measure is a simple yet effective
method to predict the qualities of document rankings for SRs.


  We introduce a one-way, one-quantum cascade, whereby a single excitation
proceeds one-directionwise in a ladder of energy levels. This makes a variation
from more famous two-way cascades where the excitation can go up and down
following its excitation or relaxation in the ladder. We provide closed-form
solutions for two-photon correlation functions between any transitions in such
circular cascades. We discuss how the rich correlations that result from what
appears to be an extremely simple implementation, are essentially those which
have been entertained from complex architectures relying on
strongly-correlated, many-body physics or cavity QED effects.


  The Laser Interferometer Space Antenna (LISA) is expected to detect N ~ 22
[x10^(+/- 1)] close white dwarf binaries in the Large Magellanic Cloud (LMC)
through their gravitational radiation with signal-to-noise ratios greater than
10 in observational durations of 3 years or more. In addition to chirp mass,
location on the sky, and other binary parameters, the distance to each binary
is an independent parameter that can be extracted from an analysis of
gravitational waves from these binaries. Using a sample of binaries, one can
establish the mean distance to the LMC as well as the variance of this
distance. Assuming no confusion noise at frequencies above 2 mHz, LISA might
determine the LMC distance to ~ 4.5 (N/22)^(1/2)% and the line of sight extent
of LMC to ~ 15 (N/22)^(1/4)$%, relative to its distance, at the one-sigma
confidence. These estimates are competitive to some of the proposed direct
geometric techniques to measure LMC distance in future with missions such as
SIM and GAIA.


  Strong cocomparability graphs are the reflexive graphs whose adjacency matrix
can be rearranged by a simultaneous row and column permutation to avoid the
submatrix with rows $01, 10$. Strong cocomparability graphs form a subclass of
cocomparability graphs (i.e., the complements of comparability graphs) and can
be recognized in polynomial time. In his seminal paper, Gallai characterized
cocomparability graphs in terms of a forbidden structure called asteroids.
Gallai proved that cocomparability graphs are precisely those reflexive graphs
which do not contain asteroids.
  In this paper, we give a characterization of strong cocomparability graphs
which is analogous to Gallai's characterization for cocomparability graphs. We
prove that strong cocomparability graphs are precisely those reflexive graphs
which do not contain weak edge-asteroids (a weaker version of asteroids). Our
characterization also leads to a polynomial time recognition algorithm for
strong cocomparability graphs.


  In this paper, we study resource allocation for a full-duplex (FD) radio base
station serving multiple half-duplex (HD) downlink and uplink users
simultaneously. The considered resource allocation algorithm design is
formulated as a non-convex optimization problem taking into account minimum
required receive signal-to-interference-plus-noise ratios (SINRs) for downlink
and uplink communication and maximum tolerable SINRs at potential
eavesdroppers. The proposed optimization framework enables secure downlink and
uplink communication via artificial noise generation in the downlink for
interfering the potential eavesdroppers. We minimize the weighted sum of the
total downlink and uplink transmit power by jointly optimizing the downlink
beamformer, the artificial noise covariance matrix, and the uplink transmit
power. We adopt a semidefinite programming (SDP) relaxation approach to obtain
a tractable solution for the considered problem. The tightness of the SDP
relaxation is revealed by examining a sufficient condition for the global
optimality of the solution. Simulation results demonstrate the excellent
performance achieved by the proposed scheme and the significant transmit power
savings enabled optimization of the artificial noise covariance matrix.


  Results from randomized experiments (trials) can be severely distorted by
outcome misclassification, such as from measurement error or reporting bias in
binary outcomes. All existing approaches to outcome misclassification rely on
some data-generating (super-population) model and therefore may not be
applicable to randomized experiments without additional assumptions. We propose
a model-free and finite-population-exact framework for randomized experiments
subject to outcome misclassification. A central quantity in our framework is
"warning accuracy," defined as the threshold such that the causal conclusion
drawn from the measured outcomes may differ from that based on the true
outcomes if the outcome measurement accuracy did not surpass that threshold. We
show how learning the warning accuracy and related concepts can benefit a
randomized experiment subject to outcome misclassification. We show that the
warning accuracy can be computed efficiently (even for large datasets) by
adaptively reformulating an integer program with respect to the randomization
design. Our framework covers both Fisher's sharp null and Neyman's weak null,
works for a wide range of randomization designs, and can also be applied to
observational studies adopting randomization-based inference. We apply our
framework to a large randomized clinical trial for the prevention of prostate
cancer.


  We introduce the notion of pie algebra for a 2-monad, these bearing the same
relationship to the flexible and semiflexible algebras as pie limits do to
flexible and semiflexible ones. We see that in many cases, the pie algebras are
precisely those "free at the level of objects" in a suitable sense; so that,
for instance, a strict monoidal category is pie just when its underlying monoid
of objects is free. Pie algebras are contrasted with flexible and semiflexible
algebras via a series of characterisations of each class; particular attention
is paid to the case of pie, flexible and semiflexible weights, these being
characterised in terms of the behaviour of the corresponding weighted limit
functors.


  The traditional approach of defining the fundamental group first and then
constructing universal coverings works well only for the class of Poincar\' e
spaces. For general spaces there were several attempts to define generalized
coverings (see \cite{BP3}, \cite{BDLM}, and \cite{FisZas}), yet there is no
general theory so far that covers all path connected spaces. In this paper we
plan to remedy that by changing the order of things: we define the universal
covering first and its group of deck transformations is the new fundamental
group of the base space.
  The basic idea is that a non-trivial loop ought to be detected by a covering
(not by extension over the unit disk): a loop is non-trivial if there is a
covering such that some lift of the loop is a non-loop.
  So it remains to define coverings: the most natural class is the class of
maps that have unique disk lifting property. To make the theory work one needs
to add the assumption that path components of pre-images of open sets form a
basis of the total space.


  The learning capability of a neural network improves with increasing depth at
higher computational costs. Wider layers with dense kernel connectivity
patterns furhter increase this cost and may hinder real-time inference. We
propose feature map and kernel level pruning for reducing the computational
complexity of a deep convolutional neural network. Pruning feature maps reduces
the width of a layer and hence does not need any sparse representation.
Further, kernel pruning converts the dense connectivity pattern into a sparse
one. Due to coarse nature, these pruning granularities can be exploited by GPUs
and VLSI based implementations. We propose a simple and generic strategy to
choose the least adversarial pruning masks for both granularities. The pruned
networks are retrained which compensates the loss in accuracy. We obtain the
best pruning ratios when we prune a network with both granularities.
Experiments with the CIFAR-10 dataset show that more than 85% sparsity can be
induced in the convolution layers with less than 1% increase in the
missclassification rate of the baseline network.


  Tunnel magnetoresistance (TMR) sensor is a highly sensitive magnetic field
sensor and is expected to be applied in various fields, such as magnetic
recording, industrial sensing, and bio-medical sensing. To improve the
detection capability of TMR sensors in low frequency regime it is necessary to
suppress the 1/f noise. We theoretically study 1/f noise of a tiny TMR sensor
using the macrospin model. Starting from the generalized Langevin equation, 1/f
noise power spectrum and the Hooge parameter are derived. The calculated Hooge
parameter of a tiny TMR sensor is much smaller than that of a conventional TMR
sensor with large junction area. The results provide a new perspective on
magnetic 1/f noise and will be useful for improvement of TMR sensors.


  Named entity recognition (NER) is a fundamental component in many
applications, such as Web Search and Voice Assistants. Although deep neural
networks greatly improve the performance of NER, due to the requirement of
large amounts of training data, deep neural networks can hardly scale out to
many languages in an industry setting. To tackle this challenge, cross-lingual
NER transfers knowledge from a rich-resource language to languages with low
resources through pre-trained multilingual language models. Instead of using
training data in target languages, cross-lingual NER has to rely on only
training data in source languages, and optionally adds the translated training
data derived from source languages. However, the existing cross-lingual NER
methods do not make good use of rich unlabeled data in target languages, which
is relatively easy to collect in industry applications. To address the
opportunities and challenges, in this paper we describe our novel practice in
Microsoft to leverage such large amounts of unlabeled data in target languages
in real production settings. To effectively extract weak supervision signals
from the unlabeled data, we develop a novel approach based on the ideas of
semi-supervised learning and reinforcement learning. The empirical study on
three benchmark data sets verifies that our approach establishes the new
state-of-the-art performance with clear edges. Now, the NER techniques reported
in this paper are on their way to become a fundamental component for Web
ranking, Entity Pane, Answers Triggering, and Question Answering in the
Microsoft Bing search engine. Moreover, our techniques will also serve as part
of the Spoken Language Understanding module for a commercial voice assistant.
We plan to open source the code of the prototype framework after deployment.


  We study root separation of reducible monic integer polynomials of odd
degree. Let h(P) be the naive height, sep(P) the minimal distance between two
distinct roots of an integer polynomial P(x) and sep(P)=h(P)^{-e(P)}. Let
e_r*(d)=limsup_{deg(P)=d, h(P)-> +infty} e(P), where the limsup is taken over
the reducible monic integer polynomials P(x) of degree d. We prove that e_r*(d)
<= d-2. We also obtain a lower bound for e_r*(d) for d odd, which improves
previously known lower bounds for e_r*(d) when d = 5, 7, 9.


  Cooperative relaying has been proposed as a promising transmission technique
that effectively creates spatial diversity through the cooperation among
spatially distributed nodes. However, to achieve efficient communications while
gaining full benefits from cooperation, more interactions at higher protocol
layers, particularly the MAC (Medium Access Control) and network layers, are
vitally required. This is ignored in most existing articles that mainly focus
on physical (PHY)-layer relaying techniques. In this paper, we propose a novel
cross-layer framework involving two levels of joint design---a MAC-network
cross-layer design for forwarder selection (or termed routing) and a MAC-PHY
for relay selection---over symbol-wise varying channels. Based on location
knowledge and contention processes, the proposed cross-layer protocol, CoopGeo,
aims at providing an efficient, distributed approach to select next hops and
optimal relays along a communication path. Simulation results demonstrate that
CoopGeo not only operates properly with varying densities of nodes, but
performs significantly better than the existing protocol BOSS in terms of
packet error rate, transmission error probability, and saturated throughput.


  Superconducting microwave cavities with ultra-high Q-factors are
revolutionizing the field of quantum computing, offering long coherence times
exceeding 1 ms, which is critical for realizing scalable multi-qubit quantum
systems with low error rates. In this work, we provide an in-depth analysis of
recent advances in ultra-high Q-factor cavities, integration of Josephson
junction-based qubits, and bosonic-encoded qubits in 3D cavities. We examine
the sources of quantum state dephasing caused by damping and noise mechanisms
in cavities and qubits, highlighting the critical challenges that need to be
addressed to achieve even higher coherence times. We critically survey the
latest progress made in implementing single 3D qubits using superconducting
materials, normal metals, and multi-qubit and multi-state quantum systems. Our
work sheds light on the promising future of this research area, including novel
materials for cavities and qubits, modes with nontrivial topological
properties, error correction techniques for bosonic qubits, and new
light-matter interaction effects.


  After carefully considering the scalability problem in Tor and exhaustively
evaluating related works on AS-level adversaries, the author proposes
ASmoniTor, which is an autonomous system monitor for mitigating correlation
attacks in the Tor network. In contrast to prior works, which often released
offline packets, including the source code of a modified Tor client and a
snapshot of the Internet topology, ASmoniTor is an online system that assists
end users with mitigating the threat of AS-level adversaries in a near
real-time fashion. For Tor clients proposed in previous works, users need to
compile the source code on their machine and continually update the snapshot of
the Internet topology in order to obtain accurate AS-path inferences. On the
contrary, ASmoniTor is an online platform that can be utilized easily by not
only technical users, but also by users without a technical background, because
they only need to access it via Tor and input two parameters to execute an
AS-aware path selection algorithm. With ASmoniTor, the author makes three key
technical contributions to the research against AS-level adversaries in the Tor
network. First, ASmoniTor does not require the users to initiate complicated
source code compilations. Second, it helps to reduce errors in AS-path
inferences by letting users input a set of suspected ASes obtained directly
from their own traceroute measurements. Third, the Internet topology database
at the back-end of ASmoniTor is periodically updated to assure near real-time
AS-path inferences between Tor exit nodes and the most likely visited websites.
Finally, in addition to its convenience, ASmoniTor gives users full control
over the information they want to input, thus preserving their privacy.


  Consider a two-person zero-sum search game between a Hider and a Searcher.
The Hider chooses to hide in one of $n$ discrete locations (or "boxes") and the
Searcher chooses a search sequence specifying which order to look in these
boxes until finding the Hider. A search at box $i$ takes $t_i$ time units and
finds the Hider - if hidden there - independently with probability $q_i$, for
$i=1,\ldots,n$. The Searcher wants to minimize the expected total time needed
to find the Hider, while the Hider wants to maximize it. It is shown in the
literature that the Searcher has an optimal search strategy that mixes up to
$n$ distinct search sequences with appropriate probabilities. This paper
investigates the existence of optimal pure strategies for the Searcher - a
single deterministic search sequence that achieves the optimal expected total
search time regardless of where the Hider hides. We identify several cases in
which the Searcher has an optimal pure strategy, and several cases in which
such optimal pure strategy does not exist. An optimal pure search strategy has
significant practical value because the Searcher does not need to randomize
their actions and will avoid second guessing themselves if the chosen search
sequence from an optimal mixed strategy does not turn out well.


  Polarized emission from polycyclic aromatic hydrocarbons (PAHs) potentially
provides a new way to test basic physics of the alignment of ultrasmall grains.
In this paper, we present a new model of polarized PAH emission that takes into
account the effect of PAH alignment with the magnetic field. We first generate
a large sample of the grain angular momentum $\bf J$ by simulating the
alignment of PAHs due to resonance paramagnetic relaxation that accounts for
various interaction processes. We then calculate the polarization level of PAH
emission features, for the different phases of the ISM, including the cold
neutral medium (CNM), reflection nebulae (RN), and photodissociation regions
(PDRs). We find that a moderate degree of PAH alignment can significantly
enhance the polarization degree of PAH emission compared to the previous
results obtained with randomly oriented $\bf J$. In particular, we find that
smallest, negatively charged PAHs in RN can be excited to slightly suprathermal
rotation due to enhanced ion collisional excitation, resulting in an increase
of the polarization with the ionization fraction. Our results suggest that RN
is the most favorable environment to observe polarized PAH emission and to test
alignment physics of nanoparticles. Finally, we present an explicit
relationship between the polarization level of PAH emission and the degree of
external alignment for the CNM and RN. The obtained relationship will be
particularly useful for testing alignment physics of PAHs by future
observations.


  The discovery of partial differential equations (PDEs) is a challenging task
that involves both theoretical and empirical methods. Machine learning
approaches have been developed and used to solve this problem; however, it is
important to note that existing methods often struggle to identify the
underlying equation accurately in the presence of noise. In this study, we
present a new approach to discovering PDEs by combining variational Bayes and
sparse linear regression. The problem of PDE discovery has been posed as a
problem to learn relevant basis from a predefined dictionary of basis
functions. To accelerate the overall process, a variational Bayes-based
approach for discovering partial differential equations is proposed. To ensure
sparsity, we employ a spike and slab prior. We illustrate the efficacy of our
strategy in several examples, including Burgers, Korteweg-de Vries, Kuramoto
Sivashinsky, wave equation, and heat equation (1D as well as 2D). Our method
offers a promising avenue for discovering PDEs from data and has potential
applications in fields such as physics, engineering, and biology.


  With the large chunks of social media data being created daily and the
parallel rise of realistic multimedia tampering methods, detecting and
localising tampering in images and videos has become essential. This survey
focusses on approaches for tampering detection in multimedia data using deep
learning models. Specifically, it presents a detailed analysis of benchmark
datasets for malicious manipulation detection that are publicly available. It
also offers a comprehensive list of tampering clues and commonly used deep
learning architectures. Next, it discusses the current state-of-the-art
tampering detection methods, categorizing them into meaningful types such as
deepfake detection methods, splice tampering detection methods, copy-move
tampering detection methods, etc. and discussing their strengths and
weaknesses. Top results achieved on benchmark datasets, comparison of deep
learning approaches against traditional methods and critical insights from the
recent tampering detection methods are also discussed. Lastly, the research
gaps, future direction and conclusion are discussed to provide an in-depth
understanding of the tampering detection research arena.


  The thermal entanglement of a two-qubit anisotropic Heisenberg $XYZ$ chain
under an inhomogeneous magnetic field b is studied. It is shown that when
inhomogeneity is increased to certain value, the entanglement can exhibit a
larger revival than that of less values of b. The property is both true for
zero temperature and a finite temperature. The results also show that the
entanglement and critical temperature can be increased by increasing
inhomogeneous exteral magnetic field.


  The construction of the *-product proposed by Fedosov is implemented in terms
of the theory of fibre bundles. The geometrical origin of the Weyl algebra and
the Weyl bundle is shown. Several properties of the product in the Weyl algebra
are proved. Symplectic and abelian connections in the Weyl algebra bundle are
introduced. Relations between them and the symplectic connection on a phase
space M are established. Elements of differential symplectic geometry are
included. Examples of the Fedosov formalism in quantum mechanics are given.


  Highway vehicular traffic is an inherently multi-agent problem. Traffic jams
can appear and disappear mysteriously. We develop a method for traffic flow
control that is applied at the vehicular level via mean-field games. We begin
this work with a microscopic model of vehicles subject to control input,
disturbances, noise, and a speed limit. We formulate a discounted-cost
infinite-horizon robust mean-field game on the vehicles, and obtain the
associated dynamic programming (DP) PDE system. We then perform approximate
dynamic programming (ADP) using these equations to obtain a sub-optimal control
for the traffic density adaptively. The sub-optimal controls are subject to an
ODE-PDE system. We show that the ADP ODE-PDE system has a unique weak solution
in a suitable Hilbert space using semigroup and successive approximation
methods. We additionally give a numerical simulation, and interpret the
results.


  We derive some integral inequalities for holomorphic maps between complex
manifolds. As applications, some rigidity and degeneracy theorems for
holomorphic maps without assuming any pointwise curvature signs for both the
domain and target manifolds are proved, in which key roles are played by total
integration of the function of the first eigenvalue of second Ricci curvature
and an almost nonpositivity notion for holomorphic sectional curvature
introduced in our previous work. We also apply these integral inequalities to
discuss the infinite-time singularity type of the K\"ahler-Ricci flow. The
equality case is characterized for some special settings.


  We have observed the steep spectrum radio source B2 0924+30 using the LOw
Frequency ARray (LOFAR) telescope. Hosted by a z=0.026 elliptical galaxy, it
has a relatively large angular size of 12' (corresponding to 360 kpc projected
linear size) and a morphology reminiscent of a remnant Fanaroff-Riley type II
(FRII) radio galaxy. We combine LOFAR and archival images to study the spectral
properties at a spatial resolution of 1'. We derive low frequency spectral
index maps and use synchrotron ageing models to infer ages for different
regions of the source. Using radiative ageing model fitting we show that the
AGN activity ceased around 50 Myr ago. We note that the outer regions of the
lobes are younger than the inner regions which is interpreted as a sign that
those regions are remnant hotspots. We demonstrate the usefulness of maps of
AGN radio remnants taken at low frequencies and suggest caution over the
interpretation of spectral ages derived from integrated flux density
measurements versus age mapping. The spectral index properties as well as the
derived ages of B2 0924+30 are consistent with it being an FRII AGN radio
remnant. LOFAR data are proving to be instrumental in extending our studies to
the lowest radio frequencies and enabling analysis of the oldest source
regions.


  Static rankings of papers play a key role in the academic search setting.
Many features are commonly used in the literature to produce such rankings,
some examples are citation-based metrics, distinct applications of PageRank,
among others. More recently, learning to rank techniques have been successfully
applied to combine sets of features producing effective results. In this work,
we propose the metric S-RCR, which is a simplified version of a metric called
Relative Citation Ratio --- both based on the idea of a co-citation network.
When compared to the classical version, our simplification S-RCR leads to
improved efficiency with a reasonable effectiveness. We use S-RCR to rank over
120 million papers in the Microsoft Academic Graph dataset. By using this
single feature, which has no parameters and does not need to be tuned, our team
was able to reach the 3rd position in the first phase of the WSDM Cup 2016.


  In this work, we introduce LokiLM, a 1.4B parameter large language model
trained on 500B tokens. Our model performs strongly in natural language
reasoning tasks and achieves state-of-the-art performance among models with
1.5B parameters or less. LokiLM is trained using multi-teacher knowledge
distillation and high-quality training data to achieve benchmark results
competitive with larger models trained on significantly more tokens. We support
these findings by introducing steps to avoid benchmark contamination and
overfitting throughout our development process. Despite its promising
performance, LokiLM exhibits a concerning amount of hallucinations and scores
poorly on the TruthfulQA benchmark, so we do not release the model publicly.


  A thorough study is performed on pair production and signatures of
supersymmetric neutralinos in the MSSM at LEP2. Particular attention is paid to
the region of the SuSy parameter space where the associated production of
lightest and next-to-lightest neutralinos is the only visible allowed
supersymmetric process. In that region, the signal is critically dependent on
the selectron masses m(e_L,R). For sqrt(s)/2 < m(e_L,R) < 200-300 GeV and
charginos above the threshold for pair production, neutralinos arising from
e+e- --> X0(1)X0(2) could be the only SuSy signal detectable at LEP2.


  We investigate the local metrizability of Finsler spaces with $m$-Kropina
metric $F = \alpha^{1+m}\beta^{-m}$, where $\beta$ is a closed null 1-form. We
show that such a space is of Berwald type if and only if the
(pseudo-)Riemannian metric $\alpha$ and 1-form $\beta$ have a very specific
form in certain coordinates. In particular, when the signature of $\alpha$ is
Lorentzian, $\alpha$ belongs to a certain subclass of the Kundt class and
$\beta$ generates the corresponding null congruence, and this generalizes in a
natural way to arbitrary signature. We use this result to prove that the affine
connection on such an $m$-Kropina space is locally metrizable by a
(pseudo-)Riemannian metric if and only if the Ricci tensor constructed form the
affine connection is symmetric. In particular we construct all counterexamples
of this type to Szabo's metrization theorem, which has only been proven for
positive definite Finsler metrics that are regular on all of the slit tangent
bundle.


  We present and analyse a space-time discontinuous Galerkin method for wave
propagation problems. The special feature of the scheme is that it is a Trefftz
method, namely that trial and test functions are solution of the partial
differential equation to be discretised in each element of the (space-time)
mesh. The method considered is a modification of the discontinuous Galerkin
schemes of Kretzschmar et al., and of Monk and Richter. For Maxwell's equations
in one space dimension, we prove stability of the method, quasi-optimality,
best approximation estimates for polynomial Trefftz spaces and (fully explicit)
error bounds with high order in the meshwidth and in the polynomial degree. The
analysis framework also applies to scalar wave problems and Maxwell's equations
in higher space dimensions. Some numerical experiments demonstrate the
theoretical results proved and the faster convergence compared to the
non-Trefftz version of the scheme.


  The increasing use of tools and solutions based on Large Language Models
(LLMs) for various tasks in the medical domain has become a prominent trend.
Their use in this highly critical and sensitive domain has thus raised
important questions about their robustness, especially in response to
variations in input, and the reliability of the generated outputs. This study
addresses these questions by constructing a textual dataset based on the
ICD-10-CM code descriptions, widely used in US hospitals and containing many
clinical terms, and their easily reproducible rephrasing. We then benchmarked
existing embedding models, either generalist or specialized in the clinical
domain, in a semantic search task where the goal was to correctly match the
rephrased text to the original description. Our results showed that generalist
models performed better than clinical models, suggesting that existing clinical
specialized models are more sensitive to small changes in input that confuse
them. The highlighted problem of specialized models may be due to the fact that
they have not been trained on sufficient data, and in particular on datasets
that are not diverse enough to have a reliable global language understanding,
which is still necessary for accurate handling of medical documents.


  A difficulty in MSE estimation occurs because we do not specify a full
distribution for the survey weights. This obfuscates the use of fully
parametric bootstrap procedures. To overcome this challenge, we develop a novel
MSE estimator. We estimate the leading term in the MSE, which is the MSE of the
best predictor (constructed with the true parameters), using the same simulated
samples used to construct the basic predictor. We then exploit the asymptotic
normal distribution of the parameter estimators to estimate the second term in
the MSE, which reflects variability in the estimated parameters. We incorporate
a correction for the bias of the estimator of the leading term without the use
of computationally intensive double-bootstrap procedures. We further develop
calibrated prediction intervals that rely less on normal theory than standard
prediction intervals. We empirically demonstrate the validity of the proposed
procedures through extensive simulation studies. We apply the methods to
predict several functions of sheet and rill erosion for Iowa counties using
data from a complex agricultural survey.


  We report the results of a spectropolarimetric observation of the C IV
mini-BAL in the quasar HS1603+3820. The observations were carried out with the
FOCAS instrument on the Subaru telescope and yielded an extremely high
polarization sensitivity of 0.1%, at a resolving power of 1500. HS1603+3820 has
been the target of a high-resolution spectroscopic monitoring campaign for more
than four years, aimed at studying its highly variable C IV mini-BAL profile.
Using the monitoring observations, in an earlier paper we were able to narrow
down the causes of the variability to the following two scenarios: (1)
scattering material of variable optical depth redirecting photons around the
absorber, and (2) a variable, highly-ionized screen between the continuum
source and the absorber which modulates the UV continuum incident on the
absorber. The observations presented here provide a crucial test of the
scattering scenario and lead us to disfavor it because (a) the polarization
level is very small (p~0.6%) throughout the spectrum, and (b) the polarization
level does not increase across the mini-BAL trough. Thus, the variable screen
scenario emerges as our favored explanation of the C IV mini-BAL variability.
Our conclusion is bolstered by recent X-ray observations of nearby mini-BAL
quasars, which show a rapidly variable soft X-ray continuum that appears to be
the result of transmission through an ionized absorber of variable ionization
parameter and optical depth.


  Graphene placed in a magnetic field possesses an extremely high
mid/far-infrared optical nonlinearity originating from its unusual band
structure and selection rules for the optical transitions near the Dirac point.
Here we study the linear and nonlinear optical response of graphene in strong
magnetic and optical fields using quantum- mechanical density-matrix formalism.
We calculate the power of coherent terahertz radiation generated as a result of
four-wave mixing in graphene. We show that even one monolayer of graphene gives
rise to appreciable nonlinear frequency conversion efficiency and Raman gain
for modest intensities of incident infrared radiation.


  Graphical chip-firing is a discrete dynamical system where chips are placed
on the vertices of a graph and exchanged via simple firing moves. Recent work
has sought to generalize chip-firing on graphs to higher dimensions, wherein
graphs are replaced by cellular complexes and chip firing becomes
flow-rerouting along the faces of the complex. Given such a system, it is
natural to ask (1) whether this firing process terminates and (2) if it
terminates uniquely (e.g. is confluent). In the graphical case, these questions
were definitively answered by Bjorner--Lovasz--Shor, who developed three
regimes which completely determine if a given system will terminate. Building
on the work of Duval--Klivans--Martin and Felzenszwalb-Klivans, we answer these
questions in a context called flow-firing, where the cellular complexes are
2-dimensional.


  Embedding diversity into knowledge discovery tasks is of crucial importance
to enhance the meaningfulness of the mined patterns with high-impact aspects
related to novelty, serendipity, and ethics. Surprisingly, in the classic
problem of influence maximization in social networks, relatively little study
has been devoted to diversity and its integration into the objective function
of an influence maximization method.
  In this work, we propose the integration of a side-information-based notion
of seed diversity into the objective function of a targeted influence
maximization problem. Starting from the assumption that side-information is
available at node level in the general form of categorical attribute values, we
design a class of monotone submodular functions specifically conceived for
determining the diversity within a set of categorical profiles associated with
the seeds to be discovered. This allows us to develop an efficient scalable
approximate method, with a constant-factor guarantee of optimality. More
precisely, we formulate the attribute-based diversity-sensitive targeted
influence maximization problem under the state-of-the-art reverse influence
sampling framework, and we develop a method, dubbed ADITUM, that ensures a
(1-1/e-\epsilon)-approximate solution under the general triggering diffusion
model. We experimentally evaluated ADITUM on five real-world networks,
including comparison with methods that exploit numerical-attribute-based
diversity and topology-driven diversity in influence maximization.


  The dispersive wave propagation in a periodic metamaterial with tetrachiral
topology and inertial local resonators is investigated. The Floquet-Bloch
spectrum of the metamaterial is compared with that of the tetrachiral beam
lattice material without resonators. The resonators can be designed to open and
shift frequency band gaps, that is, spectrum intervals in which harmonic waves
do not propagate. Therefore, an optimal passive control of the frequency band
structure can be pursued in the metamaterial. To this aim, a suitable
constrained nonlinear optimization problem on a compact set of admissible
geometrical and mechanical parameters is stated. According to functional
requirements, the particular set of parameters which determines the largest
low-frequency band gap between a pair of consecutive branches of the
Floquet-Bloch spectrum is obtained. The optimization problem is successfully
solved by means of a version of the method of moving asymptotes, combined with
a quasi-Monte Carlo multi-start technique.


  Measurement-device-independent quantum key distribution protocol, whose
security analysis does not rely on any assumption on the detection system, can
immune the attacking against detectors. We give a first composable security
analysis for continuous-variable measurement-device-independent quantum key
distribution using squeezed states against general coherent attacks. The
security analysis is derived based on the entanglement-based scheme considering
finite size effect. A version of entropic uncertainty relation is exploited to
give a lower bound on the conditional smooth min-entropy by trusting Alice's
and Bob's devices. The simulation results indicate that, in the universal
composable security framework, the protocol can tolerate 2.5 dB and 6.5 dB
channel loss against coherent attacks with direct and reverse reconciliation,
respectively.


  Ultrathin membranes have drawn much attention due to their unprecedented
spatial resolution for DNA nanopore sequencing. However, the high translocation
velocity (3000-50000 nt/ms) of DNA molecules moving across such membranes
limits their usability. To this end, we have introduced a viscosity gradient
system based on room-temperature ionic liquids (RTILs) to control the dynamics
of DNA translocation through a nanometer-size pore fabricated in an atomically
thin MoS2 membrane. This allows us for the first time to statistically identify
all four types of nucleotides with solid state nanopores. Nucleotides are
identified according to the current signatures recorded during their transient
residence in the narrow orifice of the atomically thin MoS2 nanopore. In this
novel architecture that exploits high viscosity of RTIL, we demonstrate
single-nucleotide translocation velocity that is an optimal speed (1-50 nt/ms)
for DNA sequencing, while keeping the signal to noise ratio (SNR) higher than
10. Our findings pave the way for future low-cost and rapid DNA sequencing
using solid-state nanopores.