  Primordial stars are key to primeval structure formation as the first stellar
components of primeval galaxies, the sources of cosmic chemical enrichment and
likely cosmic reionization, and they possibly gave rise to the supermassive
black holes residing at the centres of galaxies today. While the direct
detection of individual Pop III stars will likely remain beyond reach for
decades to come, we show their supernova remnants may soon be detectable in the
radio. We calculate radio synchrotron signatures between 0.5 - 35 GHz from
hydrodynamical computations of the supernova remnants of Pop III stars in
minihaloes. We find that hypernovae yield the brightest systems, with observed
radio fluxes as high as 1 - 10 muJy. Less energetic Type II supernovae yield
remnants about a factor of 30 dimmer and pair-instability supernova remnants
are dimmer by a factor of more than 10,000. Because of the high gas densities
of the progenitor environments, synchrotron losses severely limit the maximum
emission frequencies, producing a distinctive peaked radio spectrum
distinguishable from normal galactic supernova remnant spectra. Hypernovae
radio remnants should be detectable by existing radio facilities like eVLA and
eMERLIN while Type II supernova remnants will require the Square Kilometre
Array. The number counts of hypernova remnants at z > 20 with fluxes above 1
muJy are expected to be one per hundred square degree field, increasing to a
few per square degree if they form down to z = 10. The detection of a z > 20
Type II supernova remnant brighter than 1 nJy would require a 100 - 200 square
degree field, although only a 1 - 2 square degree field for those forming down
to z = 10. Hypernova and Type II supernova remnants are easily separated from
one another by their light curves, which will enable future surveys to use them
to constrain the initial mass function of Pop III stars.


  Interstellar C IV absorption line studies of the hot gaseous halo of the
Large Magellanic Cloud (LMC) have been hindered by non-ideal selections of
early-type probe stars in regions where C+3 can be produced locally via
photoionization, fast stellar winds, or supernovae. To observe stars outside
such regions, precise spectral classifications of OB stars in the field are
needed. Therefore, we have obtained medium-dispersion spectra of 42 early-type
stars in the LMC that are distributed outside superbubbles or supergiant
shells. The spectral classification of these stars is presented in this paper.
Nineteen of these program stars have spectral types between B1 and O7, and are
thus suitable probes for interstellar C IV absorption line studies of the hot
gaseous halo of the LMC.


  The exponential growth of multimedia information and the development of
various communication media generated new problems at various levels including
the rate of flow of information, problems of storage and management. The
difficulty which arises is no longer the existence of information but rather
the access to this information. When designing multimedia information retrieval
system, it is appropriate to bear in mind the potential users and their
information needs. We assumed that multimedia information representation which
takes into account explicitly the users' needs and the cases of use could
contribute to the adaptation potentials of the system for the end-users. We
believe also that responses of multimedia information system would be more
relevant to the users' needs if the types of results to be used from the system
were identified before the design and development of the system. We propose the
integration of the users' information needs. More precisely integrating usage
contexts of resulting information in an information system (during creation and
feedback) should enhance more pertinent users' need. The first section of this
study is dedicated to traditional multimedia information systems and
specifically the approaches of representing multimedia information. Taking into
account the dynamism of users, these approaches do not permit the explicit
integration of the users' information needs. In this paper, we will present our
proposals based on economic intelligence approach. This approach emphasizes the
importance of starting any process of information retrieval witch the user
information need.


  Discovering distinct features and their relations from data can help us
uncover valuable knowledge crucial for various tasks, e.g., classification. In
neuroimaging, these features could help to understand, classify, and possibly
prevent brain disorders. Model introspection of highly performant
overparameterized deep learning (DL) models could help find these features and
relations. However, to achieve high-performance level DL models require
numerous labeled training samples ($n$) rarely available in many fields. This
paper presents a pre-training method involving graph convolutional/neural
networks (GCNs/GNNs), based on maximizing mutual information between two
high-level embeddings of an input sample. Many of the recently proposed
pre-training methods pre-train one of many possible networks of an
architecture. Since almost every DL model is an ensemble of multiple networks,
we take our high-level embeddings from two different networks of a model --a
convolutional and a graph network--. The learned high-level graph latent
representations help increase performance for downstream graph classification
tasks and bypass the need for a high number of labeled data samples. We apply
our method to a neuroimaging dataset for classifying subjects into healthy
control (HC) and schizophrenia (SZ) groups. Our experiments show that the
pre-trained model significantly outperforms the non-pre-trained model and
requires $50\%$ less data for similar performance.


  We first consider various methods for the indirect implementation of unitary
gates. We apply these methods to rederive the universality of 4-qubit
measurements based on a scheme much simpler than Nielsen's original
construction [quant-ph/0108020]. Then, we prove the universality of simple
discrete sets of 2-qubit measurements, again using a scheme simplifying the
initial construction [quant-ph/0111122]. Finally, we show how to use a single
4-qubit measurement to achieve universal quantum computation, and outline a
proof for the universality of almost all maximally entangling 4-qubit
measurements.


  We quantify the baryon anti-baryon production generated by a metastable
cosmic string, similar to the embedded pion string. More precisely, we study
skyrmion production mediated by instantons generated by a pion-like metastable
string in contact with a thermal bath, and interpret these Skyrmions as
baryons. As shown in a previous work, the core of such a metastable string can
melt due to quantum tunneling in the charged field direction. The specific
configuration of our string containing 4 scalar fields out of equilibrium in
contact with a thermal bath is shown to yield skyrmion production with partial
or integer winding number. In this work, we describe and quantify this skyrmion
production per unit length of the string. We also evaluate the skyrmion-anti
skyrmions production by a dense string network by invoking similarity with the
Skyrmion production in a phase transition.


  The paper demonstrates the use of variational autoencoders for graphical
representation of a large database containing process-microstructure
relationships. Correlating microstructural features to processing is an
essential first step to answer the difficult problem of process sequence
design. In this paper, a large database of 346,200 orientation distribution
functions resulting from a variety of process sequences is constructed, where
each sequence comprises up to four stages of tension, compression and rolling
along different directions in various permutations. This opensource database is
constructed for collaborative development of process design algorithms. The
paper demonstrates a novel application of the large database: graphical
representation of texture-process relationships. A variational autoencoder is
used to reduce the entire database to a two dimensional latent space where
variations in processes and properties can be visualized. Using proximity
analysis in this latent space, we can quickly unearth multiple process
solutions to the problem of texture or property design.


  We consider the solution of nonlinear programs with nonlinear
semidefiniteness constraints. The need for an efficient exploitation of the
cone of positive semidefinite matrices makes the solution of such nonlinear
semidefinite programs more complicated than the solution of standard nonlinear
programs. In particular, a suitable symmetrization procedure needs to be chosen
for the linearization of the complementarity condition. The choice of the
symmetrization procedure can be shifted in a very natural way to certain linear
semidefinite subproblems, and can thus be reduced to a well-studied problem.
The resulting sequential semidefinite programming (SSP) method is a
generalization of the well-known SQP method for standard nonlinear programs. We
present a sensitivity result for nonlinear semidefinite programs, and then
based on this result, we give a self-contained proof of local quadratic
convergence of the SSP method. We also describe a class of nonlinear
semidefinite programs that arise in passive reduced-order modeling, and we
report results of some numerical experiments with the SSP method applied to
problems in that class.


  Protostellar jets and outflows are pointers of star-formation and serve as
important sources of momentum and energy transfer to the interstellar medium.
Radio emission from ionized jets have been detected towards a number of
protostellar objects. In few cases, negative spectral indices and polarized
emission have also been observed suggesting the presence of synchrotron
emission from relativistic electrons. In this work, we develop a numerical
model that incorporates both thermal free-free and non-thermal synchrotron
emission mechanisms in the jet geometry. The flux densities include
contribution from an inner thermal jet, and a combination of emission from
thermal and non-thermal distributions along the edges and extremities, where
the jet interacts with the interstellar medium. We also include the effect of
varying ionization fraction laterally across the jet. An investigation of radio
emission and spectra along the jet shows the dependence of the emission process
and optical depth along the line of sight. We explore the effect of various
parameters on the turnover frequencies and the radio spectral indices (between
10 MHz and 300 GHz) associated with them.


  The paper gives some criteria for partial sums of rational number sequences
to be not rational functions and to be not algebraic functions. As an
application, we study partial sums of some famous rational number sequences in
mathematical analysis with relevance to number theory.


  We study the back-reaction of fermion fields on the kink solution in one
space and one time dimension. We employ a variational procedure to determine an
upper limit for the minimum of the total energy. This energy has three
contributions: the classical kink energy, the energy of valence fermions and
the fermion vacuum polarization energy. The latter arises from the interaction
of the kink with the Dirac sea and is required for consistency of the
semi-classical expansion for the fermions. Earlier studies only considered the
valence part and observed a substantial back-reaction. This was reflected by a
sizable distortion of the kink profile. We find that this distortion is
strongly mitigated when the Dirac sea is properly accounted for. As a result
the back-reaction merely produces a slight squeeze or stretch of the kink
profile.


  The behavior of the iterative/subdivision hybrid algorithm for curve/curve
intersection proposed in [20] depends on the choice of the domain for their
convergence test. Using either too small or too large test domain may cause the
test to fail to detect cases where Newton's method in fact converges to a
solution, which results in unnecessary additional subdivisions and consequently
more computation time. We propose a modification to the algorithm to adaptively
adjust the test domain size according to what happens during the test of the
parent region. This is in contrast to the original algorithm whose test domain
is always a fixed multiple of the input domain under consideration.
Computational results show that the proposed algorithm is slightly more
efficient than the original algorithm.


  We study a model of random graphs where each edge is drawn independently (but
not necessarily identically distributed) from the others, and then assigned a
random weight. When the mean degree of such a graph is low, it is known that
the spectrum of the adjacency matrix $A$ deviates significantly from that of
its expected value $\mathbb E A$. In contrast, we show that over a wide range
of parameters the top eigenvalues of the non-backtracking matrix $B$ -- a
matrix whose powers count the non-backtracking walks between two edges -- are
close to those of $\mathbb E A$, and all other eigenvalues are confined in a
bulk with known radius. We also obtain a precise characterization of the scalar
product between the eigenvectors of $B$ and their deterministic counterparts
derived from the model parameters. This result has many applications, in
domains ranging from (noisy) matrix completion to community detection, as well
as matrix perturbation theory. In particular, we establish as a corollary that
a result known as the Baik-Ben Arous-P\'ech\'e phase transition, previously
established only for rotationally invariant random matrices, holds more
generally for matrices $A$ as above under a mild concentration hypothesis.


  We have performed an extensive ab initio LDA and LSDA+U calculations of
electronic structure of newly discovered high-temperature superconducting
series ReO(1-x)F(x)FeAs (Re=La,Ce, Pr, Nd, Sm and hypothetical case of Re=Y).
In all cases we obtain almost identical electronic spectrum (both energy
dispersions and the densities of states) in rather wide energy interval (about
2 eV) around the Fermi level. We also debate that this fact is unlikely to be
changed by the account of strong correlations. It leads inevitably to the same
critical temperature Tc of superconducting transition in any theoretical
BCS-like mechanism of Cooper pair formation. We argue that the experimentally
observed variations of Tc for different rare-earth substitutions are either due
to disorder effects or less probably because of possible changes in
spin-fluctuation spectrum of FeAs layers caused by magnetic interactions with
rare-earth spins in ReO layers.


  One of the most common problems that any technique encounters is the high
dimensionality of the input data. This yields several problems in the
subsequently statistical methods due to so called "curse of dimensionality".
Several dimension reduction methods have been proposed in the literature, until
now, to accomplish the goal of having smaller dimension space. The most popular
among them, is the so called Principal Component Analysis (PCA). One of the
extensions of PCA is Probabilistic PCA (known as PPCA). In PPCA, a
probabilistic model is used to perform the dimension reduction. By convention,
there are cases in applied sciences, e.g. Bioinformatics, Biology and Geology
that the data at hand are in non Euclidean space. Elaborating further, an
important situation is when each variable poses a direction so that a data
point is lying on a torus. According to its importance, the extension of the
PCA to such data is being under attention during last decades. In this paper,
we introduce a Probabilistic PCA for data on torus (TPPCA), assuming a
Multivariate Wrapped Normal distribution as the underline model. Furthermore,
we present certain appropriate algorithms to compute this dimension reduction
technique and then, we compare our proposal with other dimension reduction
techniques using examples based on real datasets and a small Monte Carlo
simulation.


  This paper presents a novel deep learning framework for human trajectory
prediction and detecting social group membership in crowds. We introduce a
generative adversarial pipeline which preserves the spatio-temporal structure
of the pedestrian's neighbourhood, enabling us to extract relevant attributes
describing their social identity. We formulate the group detection task as an
unsupervised learning problem, obviating the need for supervised learning of
group memberships via hand labeled databases, allowing us to directly employ
the proposed framework in different surveillance settings. We evaluate the
proposed trajectory prediction and group detection frameworks on multiple
public benchmarks, and for both tasks the proposed method demonstrates its
capability to better anticipate human sociological behaviour compared to the
existing state-of-the-art methods.


  Complex systems are embedded in our everyday experience. Stochastic modelling
enables us to understand and predict the behaviour of such systems, cementing
its utility across the quantitative sciences. Accurate models of highly
non-Markovian processes -- where the future behaviour depends on events that
happened far in the past -- must track copious amounts of information about
past observations, requiring high-dimensional memories. Quantum technologies
can ameliorate this cost, allowing models of the same processes with lower
memory dimension than corresponding classical models. Here we implement such
memory-efficient quantum models for a family of non-Markovian processes using a
photonic setup. We show that with a single qubit of memory our implemented
quantum models can attain higher precision than possible with any classical
model of the same memory dimension. This heralds a key step towards applying
quantum technologies in complex systems modelling.


  Consider a discrete finite-dimensional, Markovian market model. In this
setting, discretely sampled American options can be priced using the so-called
``non-recombining'' tree algorithm. By successively increasing the number of
exercise times, the American option price itself can be computed; for
combinatorial reasons, we shall consider a recursive algorithm that doubles the
number of exercise times at each recursion step. First we prove, by elementary
arguments, error bounds for the first order differences in this recursive
algorithm. From this, bounds on the higher order differences can be obtained
using combinatorial arguments that are motivated by the theory of rough paths.
We shall obtain an explicit $L^1(C)$ convergence estimate for the recursive
algorithm that prices a discretely sampled American $\max$-put option (on a
basket of size $d$) at each recursion step, $C$ belonging to a certain class of
compact subset of $\RR^d$, in under the assumption of sufficiently small
volatilities. In case $d=1$, $L^1(C)$-bounds for an even more natural choice of
$C$ will be derived.


  Exact and asymptotic lineshape expressions are derived from the
semi-classical density matrix representation describing a set of closed
three-level atomic or molecular states including decoherences, relaxation rates
and light-shifts. An accurate analysis of the exact steady-state Dark Resonance
profile describing the Autler-Townes doublet, the Electromagnetically Induced
Transparency or Coherent Population Trapping resonance and the Fano-Feshbach
lineshape, leads to the linewidth expression of the two-photon Raman transition
and frequency-shifts associated to the clock transition. From an adiabatic
analysis of the dynamical Optical Bloch Equations in the weak field limit, a
pumping time required to efficiently trap a large number of atoms into a
coherent superposition of long-lived states is established. For a highly
asymmetrical configuration with different decay channels, a strong two-photon
resonance based on a lower states population inversion is established when the
driving continuous-wave laser fields are greatly unbalanced. When time
separated resonant two-photon pulses are applied in the adiabatic pulsed regime
for atomic or molecular clock engineering, where the first pulse is long enough
to reach a coherent steady-state preparation and the second pulse is very short
to avoid repumping into a new dark state, Dark Resonance fringes mixing
continuous-wave lineshape properties and coherent Ramsey oscillations are
created. Those fringes allow interrogation schemes bypassing the power
broadening effect. Frequency-shifts affecting the central clock fringe computed
from asymptotic profiles and related to Raman decoherence process, exhibit
non-linear shapes with the three-level observable used for quantum measurement.
We point out that different observables experience different shifts on the
lower-state clock transition.


  The ubiquitous ADE classification has induced many proposals of often
mysterious correspondences both in mathematics and physics. The mathematics
side includes quiver theory and the McKay Correspondence which relates finite
group representation theory to Lie algebras as well as crepant resolutions of
Gorenstein singularities. On the physics side, we have the graph-theoretic
classification of the modular invariants of WZW models, as well as the relation
between the string theory nonlinear $\sigma$-models and Landau-Ginzburg
orbifolds. We here propose a unification scheme which naturally incorporates
all these correspondences of the ADE type in two complex dimensions. An
intricate web of inter-relations is constructed, providing a possible guideline
to establish new directions of research or alternate pathways to the standing
problems in higher dimensions.


  Multidimensional cosmological, static spherically symmetric and Euclidean
configurations are described in a unified way for gravity interacting with
several dilatonic fields and antisymmetric forms, associated with electric and
magnetic p-branes. Exact solutions are obtained when certain vectors, built
from the input parameters of the model, are either orthogonal in the
minisuperspace, or form mutually orthogonal subsystems. Some properties of
black-hole solutions are indicated, in particular, a no-hair-type theorem and
restrictions emerging in models with multiple times. From the non-existence of
Lorentzian wormholes, a universal restriction is obtained, applicable to
orthogonal or block-orthogonal subsystems of any p-brane systems. Euclidean
wormhole solutions are found, their actions and radii are explicitly
calculated.


  We consider the quantum effects of matter fields in scalar-tensor theories
and clarify the role of trace anomaly when switching between conformally
related `frames'. We exploit the property that the couplings between the scalar
and the gauge fields are not frame-invariant in order to define a `QCD-frame',
where the scalar is not coupled to the gluons. We show that this frame is a
natural generalization of the `Jordan frame' in the case of non-metric theories
and that it is particularly convenient for gravitational phenomenology: test
bodies have trajectories that are as close as possible to geodesics with
respect to such a metric and equivalence principle violations are directly
proportional to the scalar coupling parameters written in this frame. We show
how RG flow and decoupling work in metric and non-metric theories. RG-running
commutes with the operation of switching between frames at different scales.
When only matter loops are considered, our analysis confirms that metricity is
stable under radiative corrections and shows that approximate metricity is
natural in a technical sense.


  It was recently discovered that for a boundary system in the presence of a
background magnetic field, the quantum fluctuation of the vacuum would create a
non-uniform magnetization density for the vacuum and a magnetization current is
induced in the vacuum. It was also shown that this magnetic Casimir effect of
the vacuum is closely related to another quantum effect of the vacuum, the Weyl
anomaly. Furthermore, the phenomena can be understood in terms of the
holography of the boundary system. In this article, we review the derivation of
this phenomena from QFT as well as the derivation of it using AdS/BCFT. We then
generalize this four dimensional effect to six-dimensions. We use the AdS/BCFT
holography to show that in the presence of a 3-form magnetic field strength
$H$, a string current is induced in a six-dimensional boundary conformal field
theory. This allows us to determine the gauge field contribution to the Weyl
anomaly in six-dimensional conformal field theory in a $H$-flux background. For
the (2,0) superconformal field theory of $N$ M5-branes, the current has a
magnitude proportional to $N^3$ for large $N$. This suggests that the degree of
freedoms scales as $N^3$ in the (2,0) superconformal theory of $N$ multiple
M5-branes. Our result for the Weyl anomaly is a new prediction for the (2,0)
theory.


  When humidified at different moisture conditions, restrained spider silk
fibers can exhibit a very high supercontraction phenomenon. The hydration water
molecules induce a Hydrogen-bonds disruption process that, due to entropic
effects, decreases the natural -- zero force -- end-to-end chains length. By
considering a bundle of macromolecules, we describe supercontraction as a
possible actuation system and determine the maximum actuation force depending
on the silk properties at the molecular scale and on the constraining system
representing other silk threads or the actuated device. The comparison with
experimental results of Argiope trifasciata silk fibers show the effectiveness
of the proposed model in quantitatively predicting the experimental actuation
properties. The considered historical case study of obelisk rescue in Saint
Peter's Square (Rome) through ropes hydration is discussed evidencing the
optimal performances of this natural material adopted as moisture powered
actuator: we obtain a work density of 2.19 kJ/m3 making spider silk the most
performant hydration driven active material. Moreover we obtain a power density
of the order of 730 W/kg about three times the most performant carbon nanotube
actuators making such material very competitive as compared with all types of
actuator. The analytic description of the macroscopic actuation parameters from
microscale properties shows the possibility of adopting our approach also in
the field of bioinspired artificial silks design, possibly considering also
important non-linear effects in the actuated system.


  Phasor measurement units (PMUs) have the advantage of providing direct
measurements of power states. However, as the number of PMUs in a power system
is limited, the traditional supervisory control and data acquisition (SCADA)
system cannot be replaced by the PMU-based system overnight. Therefore, hybrid
power state estimation taking advantage of both systems is important. As
experiments show that sampling phase errors among PMUs are inevitable in
practical deployment, this paper proposes a distributed power state estimation
algorithm under PMU phase errors. The proposed distributed algorithm only
involves local computations and limited information exchange between
neighboring areas, thus alleviating the heavy communication burden compared to
the centralized approach. Simulation results show that the performance of the
proposed algorithm is very close to that of centralized optimal hybrid state
estimates without sampling phase error.


  In this paper, downlink (DL) precoding and power allocation strategies are
identified for a time-division-duplex (TDD) multi-cell multi-user massive
Full-Dimension MIMO (FD-MIMO) network. Utilizing channel reciprocity, DL
channel state information (CSI) feedback is eliminated and the DL multi-user
MIMO precoding is linked to the uplink (UL) direction of arrival (DoA)
estimation through estimation of signal parameters via rotational invariance
technique (ESPRIT). Assuming non-orthogonal/non-ideal spreading sequences of
the UL pilots, the performance of the UL DoA estimation is analytically
characterized and the characterized DoA estimation error is incorporated into
the corresponding DL precoding and power allocation strategy. Simulation
results verify the accuracy of our analytical characterization of the DoA
estimation and demonstrate that the introduced multi-user MIMO precoding and
power allocation strategy outperforms existing zero-forcing based massive MIMO
strategies.


  The tight upper bound $\operatorname{pt}_+(G) \leq \left\lceil
\frac{\left\vert \operatorname{V}(G) \right\vert - \operatorname{Z}_+(G)}{2}
\right\rceil$ is established for the positive semidefinite propagation time of
a graph in terms of its positive semidefinite zero forcing number. To prove
this bound, two methods of transforming one positive semidefinite zero forcing
set into another and algorithms implementing these methods are presented.
Consequences of the bound, including a tight Nordhaus-Gaddum sum upper bound on
positive semidefinite propagation time, are established.


  Event-based sensors are well suited for real-time processing due to their
fast response times and encoding of the sensory data as successive temporal
differences. These and other valuable properties, such as a high dynamic range,
are suppressed when the data is converted to a frame-based format. However,
most current methods either collapse events into frames or cannot scale up when
processing the event data directly event-by-event. In this work, we address the
key challenges of scaling up event-by-event modeling of the long event streams
emitted by such sensors, which is a particularly relevant problem for
neuromorphic computing. While prior methods can process up to a few thousand
time steps, our model, based on modern recurrent deep state-space models,
scales to event streams of millions of events for both training and
inference.We leverage their stable parameterization for learning long-range
dependencies, parallelizability along the sequence dimension, and their ability
to integrate asynchronous events effectively to scale them up to long event
streams.We further augment these with novel event-centric techniques enabling
our model to match or beat the state-of-the-art performance on several event
stream benchmarks. In the Spiking Speech Commands task, we improve
state-of-the-art by a large margin of 6.6% to 87.1%. On the DVS128-Gestures
dataset, we achieve competitive results without using frames or convolutional
neural networks. Our work demonstrates, for the first time, that it is possible
to use fully event-based processing with purely recurrent networks to achieve
state-of-the-art task performance in several event-based benchmarks.


  Results for the frequencies of zero-sound excitations in the isospin
asymmetric nuclear matter are presented for the different parameters of
asymmetry -1\leq\beta\leq 1. The dispersion equations are constructed within
the random phase approximation. We use the effective Landau-Migdal
quasiparticle interaction with the special isospin dependence of the phase
volume in the normalization factor C_0. In the paper we present zero-sound
branches of the dispersion equation solutions in the symmetric, asymmetric and
neutron matter. The branches correspond to the different channels of decay of
the zero-sound excitation in the nuclear matter or nuclei. In the asymmetric
nuclear matter we obtain three branches of solutions on the physical and
unphysical sheets of the complex frequency plane, \omega_{s\,\tau}(k,\beta),
\tau=p,n,np. We demonstrate the change of branches with \beta and conversion of
the three branches into two branches in symmetric nuclear matter (\beta=0) and
into one branch in the neutron matter (\beta=1).


  We study active structure learning of Bayesian networks in an observational
setting, in which there are external limitations on the number of variable
values that can be observed from the same sample. Random samples are drawn from
the joint distribution of the network variables, and the algorithm iteratively
selects which variables to observe in the next sample. We propose a new active
learning algorithm for this setting, that finds with a high probability a
structure with a score that is $\epsilon$-close to the optimal score. We show
that for a class of distributions that we term stable, a sample complexity
reduction of up to a factor of $\widetilde{\Omega}(d^3)$ can be obtained, where
$d$ is the number of network variables. We further show that in the worst case,
the sample complexity of the active algorithm is guaranteed to be almost the
same as that of a naive baseline algorithm. To supplement the theoretical
results, we report experiments that compare the performance of the new active
algorithm to the naive baseline and demonstrate the sample complexity
improvements. Code for the algorithm and for the experiments is provided at
https://github.com/noabdavid/activeBNSL.


  In this short article I introduce the frab package which provides an
alternative interpretation of named vectors in the R programming language; it
is available on CRAN. The underlying mathematical object is the free Abelian
group.


  Energy efficiency solutions are more vital for Green Mesh Network (GMN)
campuses. Today students are benefited using these e-learning methodologies.
Renewable energies such as solar, wind, hydro has tremendous applications on
energy efficient wireless networks for sustaining the ever growing traffic
demands. One of the major issues in designing a GMN is minimizing the number of
deployed mesh routers and gateways and satisfying the sustainable QOS based
energy constraints. During low traffic periods the mesh routers are switched to
power save or sleep mode. In this paper we have mathematically formulated a
single objective function with multi constraints to optimize the energy. The
objective is to place minimum number of Mesh routers and gateways in a set of
candidate location. The mesh nodes are powered using the solar energy to meet
the traffic demands. Two global optimisation algorithms are compared in this
paper to optimize the energy sustainability, to guarantee seamless
connectivity.


  Accreting black holes on all mass scales (from stellar to supermassive)
appear to follow a nonlinear relation between X-ray luminosity, radio
luminosity and BH mass, indicating that similar physical processes drive the
central engines in X-ray binaries and active galactic nuclei (AGN). However, in
recent years an increasing number of BH systems have been identified that do
not fit into this scheme. These outliers may be the key to understand how BH
systems are powered by accretion. Here we present results from EVN observations
of a sample of low-luminosity AGN (LLAGN) with known mass that have unusually
high radio powers when compared with their X-ray luminosity.


  In the context of time-series forecasting, we propose a LSTM-based recurrent
neural network architecture and loss function that enhance the stability of the
predictions. In particular, the loss function penalizes the model, not only on
the prediction error (mean-squared error), but also on the predicted variation
error.
  We apply this idea to the prediction of future glucose values in diabetes,
which is a delicate task as unstable predictions can leave the patient in doubt
and make him/her take the wrong action, threatening his/her life. The study is
conducted on type 1 and type 2 diabetic people, with a focus on predictions
made 30-minutes ahead of time.
  First, we confirm the superiority, in the context of glucose prediction, of
the LSTM model by comparing it to other state-of-the-art models (Extreme
Learning Machine, Gaussian Process regressor, Support Vector Regressor).
  Then, we show the importance of making stable predictions by smoothing the
predictions made by the models, resulting in an overall improvement of the
clinical acceptability of the models at the cost in a slight loss in prediction
accuracy.
  Finally, we show that the proposed approach, outperforms all baseline
results. More precisely, it trades a loss of 4.3\% in the prediction accuracy
for an improvement of the clinical acceptability of 27.1\%. When compared to
the moving average post-processing method, we show that the trade-off is more
efficient with our approach.


  Very Long Baseline Interferometry (VLBI) observations can provide the
position of compact radio sources with an accuracy of order 50
micro-arcseconds. This is sufficient to measure the trigonometric parallax and
proper motions of any object within 500 pc of the Sun to better than a few
percent. Because they are magnetically active, young stars are often associated
with compact radio emission detectable using VLBI techniques. Here we will show
how VLBI observations have already constrained the distance to the most often
studied nearby regions of star-formation (Taurus, Ophiuchus, Orion, etc.) and
have started to provide information on their internal structure and kinematics.
We will then briefly describe a large project (called The Gould's Belt Distance
Survey) designed to provide a detailed view of star-formation in the Solar
neighborhood using VLBI observations.


  Dealing with a generic time-local non-Markovian master equation, we define
current and power to be process-dependent as in classical thermodynamics. Each
process is characterized by a symmetry transformation, a gauge of the master
equation, and is associated with different amounts of heat and/or work. Once
the symmetry requirement fixes the thermodynamical quantities, a consistent
gauge interpretation of the laws of thermodynamics emerges. We also provide the
necessary and sufficient conditions for a system to have a gauge-independent
thermodynamical behavior and show that systems satisfying Quantum Detailed
Balance conditions are gauge-independent. Applying the theory to quantum
thermal engines, we show that gauge transformations can change the machine
efficiency, however, yet constrained by the classical Carnot bound.


  Limits for the applicability of the equivalence principle are considered in
the context of low-energy effective field theories. In particular, we find a
class of higher-derivative interactions for the gravitational and
electromagnetic fields which produce dispersive photon propagation. The latter
is illustrated by calculating the energy-dependent contribution to the
deflection of light rays.


  Dedicated detector simulations are very important for the success of high
energy physics experiments. They not only bring benefits to the optimization of
the detectors, but can also improve the precision of the physics results. To
design a Multi-gap Resistive Plate Chamber (MRPC) with a very good time
resolution, a detailed monte-carlo simulation of the detector is needed and
described in this paper. The simulation can produce detector signal waveforms
which contain a complete information about the events. The detector performance
filled with different gas mixtures is studied, and comparison between
simulation and experimental results show a good agreement.


  The non-Gaussian operation can be used not only to enhance and distill the
entanglement between Gaussian entangled states, but also to improve quantum
communications. In this paper, we propose an non-Gaussian continuous-variable
quantum key distribution (CVQKD) by using quantum catalysis (QC), which is an
intriguing non-Gaussian operation in essence that can be implemented with
current technologies. We perform quantum catalysis on both ends of the
Einstein-Podolsky-Rosen (EPR) pair prepared by a sender, Alice, and find that
for the single-photon QC-CVQKD, the bilateral symmetrical quantum catalysis
(BSQC) performs better than the single-side quantum catalysis (SSQC).
Attributing to characteristics of integral within an ordered product (IWOP) of
operators, we find that the quantum catalysis operation can improve the
entanglement property of Gaussian entangled states by enhancing the success
probability of non-Gaussian operation, leading to the improvement of the
QC-CVQKD system. As a comparison, the QC-CVQKD system involving zero-photon and
single-photon quantum catalysis outperforms the previous non-Gaussian CVQKD
scheme via photon subtraction in terms of secret key rate, maximal transmission
distance and tolerable excess noise.


  In this paper, we study the problem of physical layer security in the uplink
of millimeter-wave massive multiple-input multiple-output (MIMO) networks and
propose a jamming detection and suppression method. The proposed method is
based on directional information of the received signals at the base station
antenna array. The proposed jamming detection method can accurately detect both
the existence and direction of the jammer using the received pilot signals in
the training phase. The obtained information is then exploited to develop a
channel estimator that excludes the jammer's angular subspace from received
training signals. The estimated channel information is then used for designing
a combiner at the base station that is able to effectively cancel out the
deliberate interference of the jammer. By numerical simulations, we evaluate
the performance of the proposed jamming detection method in terms of correct
detection probability and false alarm probability and show its effectiveness
when the jammer's power is substantially lower than the user's power. Also, our
results show that the proposed jamming suppression method can achieve a very
close spectral efficiency as the case of no jamming in the network


  We show that every member of an infinite family of symplectic manifolds
constructed by R. Inanc Baykur, Kenta Hayano, and Naoyuki Monden
(arXiv:1903:02906) is diffeomorphic to an elliptic surface. As a result: (1)
the symplectic Calabi-Yau 4-manifolds among their family are diffeomorphic to
the standard K3 surface; (2) each elliptic surface E(n) admits a genus g
Lefschetz pencil, for all g greater than or equal to n; and (3) each elliptic
surface E(n) blown up once admits a pair of inequivalent genus g Lefschetz
pencils, for all g greater than or equal to n.


  The statistical problem of estimating the effective dimension-reduction (EDR)
subspace in the multi-index regression model with deterministic design and
additive noise is considered. A new procedure for recovering the directions of
the EDR subspace is proposed. Under mild assumptions, $\sqrt n$-consistency of
the proposed procedure is proved (up to a logarithmic factor) in the case when
the structural dimension is not larger than 4. The empirical behavior of the
algorithm is studied through numerical simulations.


  This chapter will primarily focus on the studies of quantum optics with
semiconductor, epitaxially grown quantum dots embedded in photonic crystal
cavities. We will start by giving brief introductions into photonic crystals
and quantum dots, then proceed with the introduction to cavity quantum
electrodynamics (QED) effects, with a particular emphasis on the demonstration
of these effects on the quantum dot-photonic crystal platform. Finally, we will
focus on the applications of such cavity QED effects.


  We present the most complete list of mirror pairs of Calabi-Yau complete
intersections in toric ambient varieties and develop the methods to solve the
topological string and to calculate higher genus amplitudes on these compact
Calabi-Yau spaces. These symplectic invariants are used to remove redundancies
in examples. The construction of the B-model propagators leads to compatibility
conditions, which constrain multi-parameter mirror maps. For K3 fibered
Calabi-Yau spaces without reducible fibers we find closed formulas for all
genus contributions in the fiber direction from the geometry of the fibration.
If the heterotic dual to this geometry is known, the higher genus invariants
can be identified with the degeneracies of BPS states contributing to
gravitational threshold corrections and all genus checks on string duality in
the perturbative regime are accomplished. We find, however, that the BPS
degeneracies do not uniquely fix the non-perturbative completion of the
heterotic string. For these geometries we can write the topological partition
function in terms of the Donaldson-Thomas invariants and we perform a
non-trivial check of S-duality in topological strings. We further investigate
transitions via collapsing D5 del Pezzo surfaces and the occurrence of free Z2
quotients that lead to a new class of heterotic duals.


  We describe the propagation of charm quarks in the quark-gluon plasma (QGP)
by means of a Boltzmann transport approach. Non-perturbative interaction
between heavy quarks and light quarks have been taken into account through a
quasi-particle approach in which light partons are dressed with thermal masses
tuned to lQCD thermodynamics. Such a model is able to describe the main feature
of the non-perturbative dynamics: the enhancement of the interaction strength
near $T_c$. We show that the resulting charm in-medium evolution is able to
correctly predict simultaneously the nuclear suppression factor, $R_{AA}$, and
the elliptic flow, $v_2$, at both RHIC and LHC energies and at different
centralities. The hadronization of charm quarks is described by mean of an
hybrid model of fragmentation plus coalescence and plays a key role toward the
agreeement with experimental data.
  We also performed calculations within the Langevin approach which can lead to
very similar $R_{AA}(p_T)$ as Boltzmann, but the charm drag coefficient as to
be reduced by about a $30\%$ and also generates an elliptic flow $v_2(p_T)$ is
about a $15\%$ smaller. We finally compare the space diffusion coefficient
$2\pi TD_s$ extracted by our phenomenological approach to lattice QCD results,
finding a satisfying agreement within the present systematic uncertainties. Our
analysis implies a charm thermalization time, in the $p\rightarrow 0$ limit, of
about $4-6 \, fm/c$ which is smaller than the QGP lifetime at LHC energy.


  Let $(A, \oplus, *, 0)$ be an MV-algebra, $(A, \odot, 0)$ be the associated
commutative semigroup, and $I$ be an ideal of $A$. Define the ideal-based
zero-divisor graph $\Gamma_{I}(A)$ of $A$ with respect to $I$ to be a simple
graph with the set of vertices $V(\Gamma_{I}(A))=\{x\in A\backslash I ~|~
(\exists~ y\in A\backslash I) ~x\odot y\in I\},$ and two distinct vertices $x$
and $y$ are joined by an edge if and only if $x\odot y\in I$.
  We prove that $\Gamma_{I}(A)$ is connected and its diameter is less than or
equal to $3$. Also, some relationship between the diameter (the girth) of
$\Gamma_{I}(A)$ and the diameter (the girth) of the zero-divisor graph of $A/I$
are investigated. And using the girth of zero-divisor graphs (resp. ideal-based
zero-divisor graphs) of MV-algebras, we classify all MV-algebras into
$2~($resp. $3)$ types.


  The two-tensor-pomeron model proposed previously to describe low $x$ DIS data
is applied to real and virtual Compton scattering on a proton. The model
includes two tensor pomerons, a soft and a hard one, and tensor reggeons. We
include contributions of both transverse and longitudinal virtual photons. We
show that this model gives a very good description of experimental data at
small Bjorken $x$ on deeply virtual Compton scattering (DVCS) from HERA. The
reggeon exchange term is particularly relevant for describing the
real-photon-proton scattering measured at lower $\gamma p$ energies at FNAL. We
present two fits which differ somewhat in the strength of the hard pomeron
contribution. In both fits we find that the interference between soft- and
hard-pomeron exchange plays an important role. We find that in DVCS the
soft-pomeron contribution is considerable up to $Q^{2} \sim 20$ GeV$^{2}$. Our
model allows to study the transition from the small-$Q^{2}$ regime, including
the photoproduction ($Q^{2} = 0$) limit, to the large-$Q^{2}$ regime, the DIS
limit. We also discuss the ratio of cross sections for longitudinally and
transversely polarized virtual photons in $\gamma^{*} p \to \gamma p$ as a
function of $|t|$ and $Q^2$. The ratio $\tilde{R}(Q^{2},W^{2},t) =
(d\sigma_{\rm L} / dt) / (d\sigma_{\rm T} / dt)$ strongly increases with $t$.
Our findings may be checked in future lepton-nucleon scattering experiments in
the low-$x$ regime, for instance, at a future Electron-Ion Collider at the BNL
(EIC), and, if LHeC is realized, at the LHC.


  We consider quantum channels with two senders and one receiver. For an
arbitrary such channel, we give multi-letter characterizations of two different
two-dimensional capacity regions. The first region is comprised of the rates at
which it is possible for one sender to send classical information, while the
other sends quantum information. The second region consists of the rates at
which each sender can send quantum information. For each region, we give an
example of a channel for which the corresponding region has a single-letter
description. One of our examples relies on a new result proved here, perhaps of
independent interest, stating that the coherent information over any degradable
channel is concave in the input density operator. We conclude with connections
to other work and a discussion on generalizations where each user
simultaneously sends classical and quantum information.


  Two taxonomies of money that include cryptocurrencies are analyzed. A
definition of the term cryptocurrency is given and a taxonomy of them is
presented, based on how its price is fixed. The characteristics of the use of
current fiat money and the operation of two-level banking systems are
discussed. Cryptocurrencies are compared with fiat money and the aspects in
which the latter cannot be overcome are indicated. The characteristics of
blockchains and databases are described. The possible cases of use of both
technologies are compared, and it is noted that blockchains, in addition to
cryptocurrencies and certain records, have not yet shown their usefulness,
while databases constitute the foundation of most of the automated systems in
operation.


  We discover a pressure induced quantum phase transition from the
superconducting state to the non-superconducting Kondo screened phase
associated with a 2% volume collapse in CeFeAsO0.7F0.3 through measurements of
high-pressure resistance, synchrotron x-ray diffraction, and x-ray absorption
spectroscopy (XAS) in a diamond anvil cell. Our XAS data of Ce-L3 in
CeFeAsO0.7F0.3 clearly show a spectral weight transfer from the main line to
the satellite line after the transition, demonstrating the formation of the
Kondo singlets under pressure in CeFeAsO1-xFx. Our results have revealed a
physical picture of a pressure-induce competition between Kondo singlets and
BCS singlets in the Ce-pnictide superconductors.


  New physics and detector concepts for a future pp and heavy ion program at
the RHIC-II accelerator facility will be discussed. I will focus on hadronic
observables which enable us to gain a better understanding on the hadronization
from a sQGP and the chiral symmetry restoration in a sQGP. The ultimate
question of how matter acquires mass can be addressed by this program in a
complementary way to the Higgs search in high energy physics. The contributions
of the RHIC program to the study of QCD will be discussed in detail.


  Convolutional neural networks excel in image recognition tasks, but this
comes at the cost of high computational and memory complexity. To tackle this
problem, [1] developed a tensor factorization framework to compress
fully-connected layers. In this paper, we focus on compressing convolutional
layers. We show that while the direct application of the tensor framework [1]
to the 4-dimensional kernel of convolution does compress the layer, we can do
better. We reshape the convolutional kernel into a tensor of higher order and
factorize it. We combine the proposed approach with the previous work to
compress both convolutional and fully-connected layers of a network and achieve
80x network compression rate with 1.1% accuracy drop on the CIFAR-10 dataset.


  Developing the calculation techniques to fivefold heavy hadrons, we perform
the study of novel fully-heavy $QQQQ\bar{Q}$ pentaquark states by the QCD sum
rule approach that is firmly based on the QCD basic theory. Numerically, masses
of fully-heavy pentaquark states are calculated to be
$7.41^{+0.27}_{-0.31}~\mbox{GeV}$ for $cccc\bar{c}$ and
$21.60^{+0.73}_{-0.22}~\mbox{GeV}$ for $bbbb\bar{b}$, respectively. In
experiment, these predicted all-heavy pentaquark states could be searched for
in the $\Omega_{QQQ}\eta_{Q}$ invariant mass spectrum.


  In this paper we study a quench protocol on thermofield double states in the
presence of time-reversal symmetry that is inspired by the work of Gao,
Jafferis and Wall.
  The deformation is a product of hermitian operators on the left and right
systems that are identical to each other and that lasts for a small amount of
time.
  We study the linear dependence on the quench to the properties of the
deformation under time reversal. If the quench is time symmetric, then the
linear response after the quench of all T-even operators vanishes. This
includes the response of the energy on the left system and all the
thermodynamic expectation values (the time averaged expectation values of the
operators). Also, we show under an assumption of non-degeneracy of the
Hamiltonian that the entanglement entropy between left and right is not
affected to this order. We also study a variation of the quench where an
instantaneous deformation is given by an operator of fixed T-parity and it's
time derivative. It is shown that the sign of the response of the Hamiltonian
is correlated with the T-parity of the operator. We can then choose the sign of
the amplitude of the quench to result in a reduction in the energy. This
implies a reduction of the entanglement entropy between both sides.


  The Brown-Resnick max-stable process has proven to be well-suited for
modeling extremes of complex environmental processes, but in many applications
its likelihood function is intractable and inference must be based on a
composite likelihood, thereby preventing the use of classical Bayesian
techniques. In this paper we exploit a case in which the full likelihood of a
Brown-Resnick process can be calculated, using componentwise maxima and their
partitions in terms of individual events, and we propose two new approaches to
inference. The first estimates the partitions using declustering, while the
second uses random partitions in a Markov chain Monte Carlo algorithm. We use
these approaches to construct a Bayesian hierarchical model for extreme low
temperatures in northern Fennoscandia.


  We construct an integral model for Lubin-Tate curves as moduli of finite
subgroups of formal deformations over complete Noetherian local rings. They are
p-adic completions of the modular curves X_0(p) at a mod-p supersingular point.
Our model is semistable in the sense that the only singularities of its special
fiber are normal crossings. Given this model, we obtain a uniform presentation
for the Dyer-Lashof algebra of Morava E-theories at height 2 as local moduli of
power operations in elliptic cohomology.


  Machine Learning (ML) techniques can facilitate the automation of malicious
software (malware for short) detection, but suffer from evasion attacks. Many
studies counter such attacks in heuristic manners, lacking theoretical
guarantees and defense effectiveness. In this paper, we propose a new
adversarial training framework, termed Principled Adversarial Malware Detection
(PAD), which offers convergence guarantees for robust optimization methods. PAD
lays on a learnable convex measurement that quantifies distribution-wise
discrete perturbations to protect malware detectors from adversaries, whereby
for smooth detectors, adversarial training can be performed with theoretical
treatments. To promote defense effectiveness, we propose a new mixture of
attacks to instantiate PAD to enhance deep neural network-based measurements
and malware detectors. Experimental results on two Android malware datasets
demonstrate: (i) the proposed method significantly outperforms the
state-of-the-art defenses; (ii) it can harden ML-based malware detection
against 27 evasion attacks with detection accuracies greater than 83.45%, at
the price of suffering an accuracy decrease smaller than 2.16% in the absence
of attacks; (iii) it matches or outperforms many anti-malware scanners in
VirusTotal against realistic adversarial malware.


  In this paper we study the problem of determining the largest degree of
stability that can be achieved for SISO systems using negative imaginary state
feedback control. A state feedback result is given for synthesising a
controller for a plant such that a given closed-loop transfer function is
strictly negative imaginary with a prescribed degree of stability. By varying a
parameter, the placement of the closed-loop system poles can be adjusted to
give a prescribed degree of stability. We show the achievable degree of
stability is related to the zero locations of the transfer function from the
control input to the disturbance output of the nominal plant being controlled.
Moreover, we offer results that outline the largest degree of stability that
can be achieved for systems with distinct eigenvalues.


  Polydispersity is found to have a significant effect on the potential energy
landscape; the the average inherent structure energy with temperature decreases
with polydispersity. Increasing polydispersity at fixed volume fraction
decreases the glass transition temperature and the fragility of glass formation
analogous to the antiplasticization seen in some polymeric melts. An
interesting temperature dependent crossover of heterogeneity with
polydispersity is observed at low temperature due to the faster build-up of
dynamic heterogeneity at lower polydispersity.


  New optical spectra of 28 H II regions in the M101 disk have been obtained,
yielding 10 new detections of the [O III]{\lambda}4363 auroral line. The oxygen
abundance gradient measured from these data, combined with previous
observations, displays a local scatter of 0.15+/-0.03 dex along an arc in the
west side of the galaxy, compared with a smaller scatter of 0.08+/-0.01 dex in
the rest of the disk. One of the H I I regions in our sample (H27) has a
significantly lower oxygen abundance than surrounding nebulae at a similar
galactocentric distance, while an additional, relatively nearby one (H128) was
already known to have a high oxygen abundance for its position in the galaxy.
These results represent marginal evidence for the existence of moderate
deviations from chemical abundance homogeneity in the interstellar medium of
M101. Using a variety of strong-line abundance indicators, we find no evidence
for significant large-scale azimuthal variations of the oxygen abundance across
the whole disk of the galaxy.


  Zeckendorf proved that every positive integer has a unique representation as
a sum of non-consecutive Fibonacci numbers. A natural generalization of this
theorem is to look at the sequence defined as follows: for $n\ge 2$, let
$F_{n,1} = F_{n,2} = \cdots = F_{n,n} = 1$ and $F_{n, m+1} = F_{n, m} + F_{n,
m+1-n}$ for all $m\ge n$. It is known that every positive integer has a unique
representation as a sum of $F_{n,m}$'s where the indexes of summands are at
least $n$ apart. We call this the $n$-decomposition. Griffiths showed an
interesting relationship between the Zeckendorf decomposition and the golden
string. In this paper, we continue the work to show a relationship between the
$n$-decomposition and the generalized golden string.


  A relation is found between pulsed measurements of the excited state
probability of a two-level atom illuminated by a driving laser, and a
continuous measurement by a second laser coupling the excited state to a third
state which decays rapidly and irreversibly. We find the time between pulses to
achieve the same average detection time than a given continuous measurement in
strong, weak, or intermediate coupling regimes, generalizing the results in L.
S. Schulman, Phys. Rev. A 57, 1509 (1998).


  Although nonperturbative functional methods are often associated with low
energy Quantum Chromodynamics, contemporary studies indicate that they provide
reliable tools to characterize a much wider spectrum of strongly interacting
many-body systems. In this review, we aim to provide a modest overview on a few
notable applications of Dyson-Schwinger equations to QCD and condensed matter
physics. After a short introduction, we lay out some formal considerations and
proceed by addressing the confinement problem. We discuss in some detail the
heavy quark limit of Coulomb gauge QCD, in particular the simple connection
between the nonperturbative Green's functions of Yang-Mills theory and the
confinement potential. Landau gauge results on the infrared Yang-Mills
propagators are also briefly reviewed. We then focus on less common
applications, in graphene and high-temperature superconductivity. We discuss
recent developments, and present theoretical predictions that are supported by
experimental findings.


  In this paper we consider the cubic regularization (CR) method for minimizing
a twice continuously differentiable function. While the CR method is widely
recognized as a globally convergent variant of Newton's method with superior
iteration complexity, existing results on its local quadratic convergence
require a stringent non-degeneracy condition. We prove that under a local error
bound (EB) condition, which is much weaker a requirement than the existing
non-degeneracy condition, the sequence of iterates generated by the CR method
converges at least Q-quadratically to a second-order critical point. This
indicates that adding a cubic regularization not only equips Newton's method
with remarkable global convergence properties but also enables it to converge
quadratically even in the presence of degenerate solutions. As a byproduct, we
show that without assuming convexity, the proposed EB condition is equivalent
to a quadratic growth condition, which could be of independent interest. To
demonstrate the usefulness and relevance of our convergence analysis, we focus
on two concrete nonconvex optimization problems that arise in phase retrieval
and low-rank matrix recovery, respectively, and prove that with overwhelming
probability, the sequence of iterates generated by the CR method for solving
these two problems converges at least Q-quadratically to a global minimizer. We
also present numerical results of the CR method when applied to solve these two
problems to support and complement our theoretical development.


  Cosmic voids are underdense regions filling up most of the volume in the
Universe. They are expected to emerge in regions comprising negative initial
density fluctuations, and subsequently expand as the matter around them
collapses and forms walls, filaments and clusters. We report results from the
analysis of a cosmological simulation specially designed to accurately describe
low-density regions, such as cosmic voids. Contrary to the common expectation,
we find that voids also experience significant mass inflows over cosmic
history. On average, $10\%$ of the mass of voids in the sample at $z \sim 0$ is
accreted from overdense regions, reaching values beyond $35\%$ for a
significant fraction of voids. More than half of the mass entering the voids
lingers on periods of time $\sim 10 \, \mathrm{Gyr}$ well inside them, reaching
inner radii. This would imply that part of the gas lying inside voids at a
given time proceeds from overdense regions (e.g., clusters or filaments), where
it could have been pre-processed, thus challenging the scenario of galaxy
formation in voids, and dissenting from the idea of being pristine
environments.


  We prove nonexistence of nontrivial, possibly sign changing, stable solutions
to a class of quasilinear elliptic equations with a potential on Riemannian
manifolds, under suitable weighted volume growth conditions on geodesic balls.


  Invariant object recognition is one of the most fundamental cognitive tasks
performed by the brain. In the neural state space, different objects with
stimulus variabilities are represented as different manifolds. In this
geometrical perspective, object recognition becomes the problem of linearly
separating different object manifolds. In feedforward visual hierarchy, it has
been suggested that the object manifold representations are reformatted across
the layers, to become more linearly separable. Thus, a complete theory of
perception requires characterizing the ability of linear readout networks to
classify object manifolds from variable neural responses.
  A theory of the perceptron of isolated points was pioneered by E. Gardner who
formulated it as a statistical mechanics problem and analyzed it using replica
theory. In this thesis, we generalize Gardner's analysis and establish a theory
of linear classification of manifolds synthesizing statistical and geometric
properties of high dimensional signals. [..] Next, we generalize our theory
further to linear classification of general perceptual manifolds, such as point
clouds. We identify that the capacity of a manifold is determined that
effective radius, R_M, and effective dimension, D_M. Finally, we show
extensions relevant for applications to real data, incorporating correlated
manifolds, heterogenous manifold geometries, sparse labels and nonlinear
classifications. Then, we demonstrate how object-based manifolds transform in
standard deep networks.
  This thesis lays the groundwork for a computational theory of neuronal
processing of objects, providing quantitative measures for linear separability
of object manifolds. We hope this theory will provide new insights into the
computational principles underlying processing of sensory representations in
biological and artificial neural networks.


  A new approach to prove weak convergence of random polytopes on the space of
compact convex sets is presented. This is used to show that the profile of the
rescaled Schl\"afli random cone of a random conical tessellation generated by
$n$ independent and uniformly distributed random linear hyperplanes in
$\mathbb{R}^{d+1}$ weakly converges to the typical cell of a stationary and
isotropic Poisson hyperplane tessellation in $\mathbb{R}^d$, as $n \to \infty$.


  Error-correcting codes are efficient methods for handling \emph{noisy}
communication channels in the context of technological networks. However, such
elaborate methods differ a lot from the unsophisticated way biological entities
are supposed to communicate. Yet, it has been recently shown by Feinerman,
Haeupler, and Korman {[}PODC 2014{]} that complex coordination tasks such as
\emph{rumor spreading} and \emph{majority consensus} can plausibly be achieved
in biological systems subject to noisy communication channels, where every
message transferred through a channel remains intact with small probability
$\frac{1}{2}+\epsilon$, without using coding techniques. This result is a
considerable step towards a better understanding of the way biological entities
may cooperate. It has been nevertheless be established only in the case of
2-valued \emph{opinions}: rumor spreading aims at broadcasting a single-bit
opinion to all nodes, and majority consensus aims at leading all nodes to adopt
the single-bit opinion that was initially present in the system with (relative)
majority. In this paper, we extend this previous work to $k$-valued opinions,
for any $k\geq2$.
  Our extension requires to address a series of important issues, some
conceptual, others technical. We had to entirely revisit the notion of noise,
for handling channels carrying $k$-\emph{valued} messages. In fact, we
precisely characterize the type of noise patterns for which plurality consensus
is solvable. Also, a key result employed in the bivalued case by Feinerman et
al. is an estimate of the probability of observing the most frequent opinion
from observing the mode of a small sample. We generalize this result to the
multivalued case by providing a new analytical proof for the bivalued case that
is amenable to be extended, by induction, and that is of independent interest.


  Research into the efficiency of photosynthetic light harvesting has focused
on two factors: (1) entanglement of chromophores, and (2) environmental noise.
While chromophores are conjugated $\pi$-bonding molecules with strongly
correlated electrons, previous models have treated this correlation implicitly
without a mathematical variable to gauge correlation-enhanced efficiency. Here
we generalize the single-electron/exciton models to a multi-electron/exciton
model that explicitly shows the effects of enhanced electron correlation within
chromophores on the efficiency of energy transfer. The model provides more
detailed insight into the interplay of electron correlation within chromophores
and electron entanglement between chromophores. Exploiting this interplay is
assisting in the design of new energy-efficient materials, which are just
beginning to emerge.


  This work addresses two important questions pertinent to Relation Extraction
(RE). First, what are all possible relations that could exist between any two
given entity types? Second, how do we define an unambiguous taxonomical (is-a)
hierarchy among the identified relations? To address the first question, we use
three resources Wikipedia Infobox, Wikidata, and DBpedia. This study focuses on
relations between person, organization and location entity types. We exploit
Wikidata and DBpedia in a data-driven manner, and Wikipedia Infobox templates
manually to generate lists of relations. Further, to address the second
question, we canonicalize, filter, and combine the identified relations from
the three resources to construct a taxonomical hierarchy. This hierarchy
contains 623 canonical relations with highest contribution from Wikipedia
Infobox followed by DBpedia and Wikidata. The generated relation list subsumes
an average of 85% of relations from RE datasets when entity types are
restricted.


  We consider a mechanism of spin decay for an electron spin in a quantum dot
due to coupling to a nearby quantum point contact (QPC) with and without an
applied bias voltage. The coupling of spin to charge is induced by the
spin-orbit interaction in the presence of a magnetic field. We perform a
microscopic calculation of the effective Hamiltonian coupling constants to
obtain the QPC-induced spin relaxation and decoherence rates in a realistic
system. This rate is shown to be proportional to the shot noise of the QPC in
the regime of large bias voltage and scales as $a^{-6}$ where $a$ is the
distance between the quantum dot and the QPC. We find that, for some specific
orientations of the setup with respect to the crystallographic axes, the
QPC-induced spin relaxation and decoherence rates vanish, while the charge
sensitivity of the QPC is not changed. This result can be used in experiments
to minimize QPC-induced spin decay in read-out schemes.


  We present a variational study of the 2D and 3D Wigner crystal phase of large
polarons. The method generalizes that introduced by S. Fratini,P.\
Qu{\'{e}}merais [Mod. Phys. Lett. B {\bf 12} 1003 (1998)]. We take into account
the Wigner crystal normal modes rather than a single mean frequency in the
minimization procedure of the variational free energy. We calculate the
renormalized modes of the crystal as well as the charge polarization
correlation function and polaron radius. The solid phase boundaries are
determined via a Lindemann criterion, suitably generalized to take into account
the classical-to-quantum cross-over.
  In the weak electron-phonon coupling limit, the Wigner crystal parameters are
renormalized by the electron-phonon interaction leading to a stabilization of
the solid phase for low polarizability of the medium. Conversely, at
intermediate and strong coupling, the behavior of the system depends strongly
on the polarizability of the medium.
  For weakly polarizable media, a density crossover occurs inside the solid
phase when the renormalized plasma frequency approaches the phonon frequency.
At low density, we have a renormalized polaron Wigner crystal, while at higher
densities the electron-phonon interaction is weakened irrespective of the {\it
bare} electron-phonon coupling.
  For strongly polarizable media, the system behaves as a Lorentz lattice of
dipoles. The abrupt softening of the internal polaronic frequency predicted by
Fratini and Quemerais is observed near the actual melting point only at very
strong coupling, leading to a possible liquid polaronic phase for a wider range
of parameters.


  We present a pragmatic approach to the sparse identification of nonlinear
dynamics for systems with discrete delays. It relies on approximating the
underlying delay model with a system of ordinary differential equations via
pseudospectral collocation. To minimize the reconstruction error, the new
strategy avoids optimizing all possible multiple unknown delays, identifying
only the maximum one. The computational burden is thus greatly reduced,
improving the performance of recent implementations that work directly on the
delay system.


  Reflexive functors of modules naturally appear in Algebraic Geometry. In this
paper we define a wide and elementary family of reflexive functors of modules,
closed by tensor products and homomorphisms, in which Algebraic Geometry can be
developed.


  We prove that over any perfect field the plane Cremona group is generated by
involutions.


  We completely describe the Brill-Noether theory of pencils on general
primitive covers of elliptic curves of any degree.


  To understand the dynamics on complex networks, measurement of correlations
is indispensable. In a motorway network, it is not sufficient to collect
information on fluxes and velocities on all individual links, i.e. parts of the
freeways between ramps and highway crosses. The interdependencies and mutual
connections are also of considerable interest. We analyze correlations in the
complete motorway network in North Rhine-Westphalia, the most populous state in
Germany. We view the motorway network as a complex system consisting of road
sections which interact via the motion of vehicles, implying structures in the
corresponding correlation matrices. In particular, we focus on collective
behavior, i.e. coherent motion in the whole network or in large parts of it. To
this end, we study the eigenvalue and eigenvector statistics and identify
significant sections in the motorway network. We find collective behavior in
these significant sections and further explore its causes. We show that
collectivity throughout the network cannot directly be related to the traffic
states (free, synchronous and congested) in Kerner's three-phase theory. Hence,
the degree of collectivity provides a new, complementary observable to
characterize the motorway network.


  The radio galaxy 3C 66B has been hypothesized to host a supermassive black
hole binary (SMBHB) at its center based on electromagnetic observations. Its
apparent 1.05-year period and low redshift ($\sim0.02$) make it an interesting
testbed to search for low-frequency gravitational waves (GWs) using Pulsar
Timing Array (PTA) experiments. This source has been subjected to multiple
searches for continuous GWs from a circular SMBHB, resulting in progressively
more stringent constraints on its GW amplitude and chirp mass. In this paper,
we develop a pipeline for performing Bayesian targeted searches for eccentric
SMBHBs in PTA data sets, and test its efficacy by applying it on simulated data
sets with varying injected signal strengths. We also search for a realistic
eccentric SMBHB source in 3C 66B using the NANOGrav 12.5-year data set
employing PTA signal models containing Earth term-only as well as Earth+Pulsar
term contributions using this pipeline. Due to limitations in our PTA signal
model, we get meaningful results only when the initial eccentricity $e_0<0.5$
and the symmetric mass ratio $\eta>0.1$. We find no evidence for an eccentric
SMBHB signal in our data, and therefore place 95% upper limits on the PTA
signal amplitude of $88.1\pm3.7$ ns for the Earth term-only and $81.74\pm0.86$
ns for the Earth+Pulsar term searches for $e_0<0.5$ and $\eta>0.1$. Similar 95%
upper limits on the chirp mass are $(1.98 \pm 0.05) \times 10^9\,M_{\odot}$ and
$(1.81 \pm 0.01) \times 10^9\,M_{\odot}$. These upper limits, while less
stringent than those calculated from a circular binary search in the NANOGrav
12.5-year data set, are consistent with the SMBHB model of 3C 66B developed
from electromagnetic observations.


  Motivated by vision-based control of autonomous vehicles, we consider the
problem of controlling a known linear dynamical system for which partial state
information, such as vehicle position, is extracted from complex and nonlinear
data, such as a camera image. Our approach is to use a learned perception map
that predicts some linear function of the state and to design a corresponding
safe set and robust controller for the closed loop system with this sensing
scheme. We show that under suitable smoothness assumptions on both the
perception map and the generative model relating state to complex and nonlinear
data, parameters of the safe set can be learned via appropriately dense
sampling of the state space. We then prove that the resulting
perception-control loop has favorable generalization properties. We illustrate
the usefulness of our approach on a synthetic example and on the self-driving
car simulation platform CARLA.


  Training deep reinforcement learning agents complex behaviors in 3D virtual
environments requires significant computational resources. This is especially
true in environments with high degrees of aliasing, where many states share
nearly identical visual features. Minecraft is an exemplar of such an
environment. We hypothesize that interactive machine learning IML, wherein
human teachers play a direct role in training through demonstrations, critique,
or action advice, may alleviate agent susceptibility to aliasing. However,
interactive machine learning is only practical when the number of human
interactions is limited, requiring a balance between human teacher effort and
agent performance. We conduct experiments with two reinforcement learning
algorithms which enable human teachers to give action advice, Feedback
Arbitration and Newtonian Action Advice, under visual aliasing conditions. To
assess potential cognitive load per advice type, we vary the accuracy and
frequency of various human action advice techniques. Training efficiency,
robustness against infrequent and inaccurate advisor input, and sensitivity to
aliasing are examined.


  The goal of this paper is to prove an equivalence between the
$(\infty,2)$-category of cartesian factorization systems of $\infty$-categories
and that of pointed cartesian fibrations of $\infty$-categories. This
generalizes a similar result known for ordinary categories and sheds some light
on the interplay between these two seemingly distant concepts.


  We describe a fault-tolerant one-way quantum computer on cluster states in
three dimensions. The presented scheme uses methods of topological error
correction resulting from a link between cluster states and surface codes. The
error threshold is 1.4% for local depolarizing error and 0.11% for each source
in an error model with preparation-, gate-, storage- and measurement errors.


  Using S(pacelike)-branes defined through rolling tachyon solutions, we show
how the dynamical formation of D(irichlet)-branes and strings in tachyon
condensation can be understood. Specifically we present solutions of S-brane
actions illustrating the classical confinement of electric and magnetic flux
into fundamental strings and D-branes. The role of S-branes in string theory is
further clarified and their RR charges are discussed. In addition, by examining
``boosted'' S-branes, we find what appears to be a surprising dual S-brane
description of strings and D-branes, which also indicates that the critical
electric field can be considered as a self-dual point in string theory. We also
introduce new tachyonic S-branes as Euclidean counterparts to non-BPS branes.


  Similarly to the linear Harbourne constant recently defined, we study the
elliptic $H$-constants of $\mathbb{P}^{2}$ and Abelian surfaces. We exhibit
configurations of smooth plane cubic curves whose Harbourne index is
arbitrarily close to $-4$. As a Corollary, we obtain that the global
$H$-constant of any surface $X$ is less or equal to $-4$. Related to these
problems, we moreover give a new inequality for the number and multiplicities
of singularities of elliptic curves arrangements on Abelian surfaces,
inequality which has a close similarity to the one of Hirzebruch for
arrangements of lines in the plane.


  The non-centrosymmetric Weyl semimetal candidate, MoTe$_2$ was investigated
through neutron diffraction and transport measurements at pressures up to 1.5
GPa and at temperatures down to 40 mK. Centrosymmetric and non-centrosymmetric
structural phases were found to coexist in the superconducting state. Density
Functional Theory (DFT) calculations reveal that the strength of the
electron-phonon coupling is similar for both crystal structures. Furthermore,
it was found that by controlling non-hydrostatic components of stress, it is
possible to mechanically control the ground state crystal structure. This
allows for the tuning of crystal symmetry in the superconducting phase from
centrosymmetric to non-centrosymmetric. DFT calculations support this strain
control of crystal structure. This mechanical control of crystal symmetry gives
a route to tuning the band topology of MoTe$_2$ and possibly the topology of
the superconducting state.


  Nanoparticles tethered with DNA strands are promising building blocks for
bottom-up nanotechnology, and a theoretical understanding is important for
future development. Here we build on approaches developed in polymer physics to
provide theoretical descriptions for the equilibrium clustering and dynamics,
as well as the self-assembly kinetics of DNA-linked nanoparticles. Striking
agreement is observed between the theory and molecular modeling of DNA tethered
nanoparticles.


  The panel data regression models have become one of the most widely applied
statistical approaches in different fields of research, including social,
behavioral, environmental sciences, and econometrics. However, traditional
least-squares-based techniques frequently used for panel data models are
vulnerable to the adverse effects of the data contamination or outlying
observations that may result in biased and inefficient estimates and misleading
statistical inference. In this study, we propose a minimum density power
divergence estimation procedure for panel data regression models with random
effects to achieve robustness against outliers. The robustness, as well as the
asymptotic properties of the proposed estimator, are rigorously established.
The finite-sample properties of the proposed method are investigated through an
extensive simulation study and an application to climate data in Oman. Our
results demonstrate that the proposed estimator exhibits improved performance
over some traditional and robust methods in the presence of data contamination.


  A local gauge invariant interaction Lagrangian for two gauge fields of spin
$\ell$ and $\ell-2$ $(\ell>2)$ and the scalar field is defined. It gives rise
to one-loop corrections to the gauge field propagator. The loop function
contains the Goldstone boson propagator for gauge symmetry breaking. The
proportionality factor in front of this propagator is the mass squared of the
gauge boson.


  Double-stranded DNA `overstretches' at a pulling force of about 65 pN,
increasing in length by a factor of 1.7. The nature of the overstretched state
is unknown, despite its considerable importance for DNA's biological function
and technological application. Overstretching is thought by some to be a
force-induced denaturation, and by others to consist of a transition to an
elongated, hybridized state called S-DNA. Within a statistical mechanical model
we consider the effect upon overstretching of extreme sequence heterogeneity.
`Chimeric' sequences possessing halves of markedly different AT composition
elongate under fixed external conditions via distinct, spatially segregated
transitions. The corresponding force-extension data display two plateaux at
forces whose difference varies with pulling rate in a manner that depends
qualitatively upon whether the hybridized S-form is accessible. This
observation implies a test for S-DNA that could be performed in experiment. Our
results suggest that qualitatively different, spatially segregated
conformational transitions can occur at a single thermodynamic state within
single molecules of DNA.


  The large scale structure of the present Universe is determined by the growth
of dark matter density fluctuations and by the dynamical action of dark energy
and dark matter. While much progress has been made in recent years in
constraining the cosmological parameters, and in reconstructing the evolution
in the large--scale structure of the dark matter distribution, we still lack an
understanding of the evolution of the baryonic component of the Universe.
  Located at nodes of the cosmic web, clusters of galaxies are the largest
collapsed structures in the Universe with total masses up to 10$^{15}$
M$_{\sun}$. Over 80% of their mass resides in the form of dark matter. The
remaining mass is composed of baryons, most of which (about 85%) is a diffuse,
hot plasma that radiates primarily in X-rays. X-ray observations of the
evolving cluster population provide a unique opportunity to address such open
and fundamental questions as: How do hot diffuse baryons dynamically evolve in
dark matter potentials? How and when was the excess energy which we observe in
the intergalactic medium generated? What is the cosmic history of heavy-element
production and circulation?
  Our current knowledge comes primarily from detailed studies of clusters in
the relatively nearby Universe (z$<$0.5). Major advances will come from high
throughput, high spectral and spatial resolution X-ray observations that
measure the thermodynamical properties and metal content of the first low mass
clusters emerging at z $\sim$ 2 and directly trace their evolution into today's
massive clusters.


  Let $K$ be a square Cantor set, i.e. the Cartesian product $K=E\times E$ of
two linear Cantor sets. Let $\delta_n$ denote the proportion of the intervals
removed in the $n$th stage of the construction of $E$. It is shown that if
$\delta_n=o(\frac1{\log\log n})$ then the corona theorem holds on the domain
$\Omega=\mathbb C^\ast\setminus K$.


  Leveraging 2.5D interposer technology, we advocate the integration of
untrusted commodity components/chiplets with physically separate, entrusted
logic components. Such organization provides a modern root of trust for secure
system-level integration. We showcase our scheme by utilizing industrial ARM
components that are interconnected via a security-providing active interposer,
and thoroughly evaluate the achievable security via different threat scenarios.
Finally, we provide detailed end-to-end physical design results to demonstrate
the efficacy of our proposed methodology.


  We present a global analysis of the trans-helicity worm-gear distribution
function, $g_{1T}^\perp$, by fitting the longitudinal-transverse double spin
asymmetry data of the semi-inclusive deep inelastic scattering. The analysis is
performed within the framework of transverse momentum dependent factorization
and evolution. It is found that the $u$-quark favors a positive distribution
and the $d$-quark favors a negative distribution, which is consistent with
previous model calculations and phenomenological extractions. Based on the fit
to existing world data, we also study the impact of the proposed electron-ion
collider in China and conclude that it can significantly improve the precision
of the worm-gear distribution function and hence enhance our understanding of
nucleon spin structures.


  We propose to enhance the training of physics-informed neural networks
(PINNs). To this aim, we introduce nonlinear additive and multiplicative
preconditioning strategies for the widely used L-BFGS optimizer. The nonlinear
preconditioners are constructed by utilizing the Schwarz domain-decomposition
framework, where the parameters of the network are decomposed in a layer-wise
manner. Through a series of numerical experiments, we demonstrate that both,
additive and multiplicative preconditioners significantly improve the
convergence of the standard L-BFGS optimizer, while providing more accurate
solutions of the underlying partial differential equations. Moreover, the
additive preconditioner is inherently parallel, thus giving rise to a novel
approach to model parallelism.


  We present new, simple, fully distributed, practical algorithms with linear
time communication cost for irregular gather and scatter operations in which
processors contribute or consume possibly different amounts of data. In a
linear cost transmission model with start-up latency $\alpha$ and cost per unit
$\beta$, the new algorithms take time $3|{\log_2 p}|\alpha+\beta \sum_{i\neq
r}m_i$ where $p$ is the number of processors, $m_i$ the amount of data for
processor $i, 0\leq i<p$, and processor $r, 0\leq r<p$ a root processor
determined by the algorithm. For a fixed, externally given root processor $r$,
there is an additive penalty of at most $\beta(M_{d'}-m_{r_{d'}}-\sum_{0\leq
j<d'}M_j)$ time steps where each $M_j$ is the total amount of data in a tree of
$2^j$ different processors with roots $r_j$ as constructed by the algorithm.
The worst-case penalty is less than $\beta \sum_{i\neq r}m_i$ time steps. The
algorithms have attractive properties for implementing the operations for MPI
(the Message-Passing Interface). Standard algorithms using fixed trees take
time either $|{\log_2 p}|(\alpha+\beta \sum_{i\neq r} m_i)$ in the worst case,
or $\sum_{i\neq r}(\alpha+\beta m_i)$. We have used the new algorithms to give
prototype implementations for the MPI_Gatherv and MPI_Scatterv collectives of
MPI, and present benchmark results from a small and a medium-large InfiniBand
cluster. In order to structure the experimental evaluation we formulate new
performance guidelines for irregular collectives that can be used to assess the
performance in relation to the corresponding regular collectives. We show that
the new algorithms can fulfill these performance expectations with a large
margin, and that standard implementations do not.


  Detecting molecular line emission from classical nova remnants has the
potential of revealing information on the composition of the ejecta, in
particular, it can deliver accurate isotopic ratios in the matter processed by
a thermonuclear runaway. We conducted searches toward more than 100 classical
novae for emission in lines of the CO or HCN molecules using single-dish
telescopes and interferometric arrays at millimeter and submillimeter
wavelengths. The survey demonstrates that classical novae, young or old, are
not strong sources of molecular emission at submillimeter and millimeter
wavelengths. Additionally, we mapped CO emission around Nova Persei 1901 (GK
Per), earlier claimed to be circumstellar in origin. Our measurements indicate
that the observed emission is from the interstellar medium. Although no
molecular emission at millimeter and submillimeter wavelengths has been found
in classical novae, it is still likely that some will be detected with
high-sensitivity interferometers such as ALMA.


  This article is a contribution to the project of classifying the torsion
growth of elliptic curve upon base-change. In this article we treat the case of
elliptic curve defined over the rationals with complex multiplication. For this
particular case, we give a description of the possible torsion growth over
cubic fields and a completely explicit description of this growth in terms of
some invariants attached to a given elliptic curve.


  We have studied the doping-driven orbital-selective Mott transition in
multi-band Hubbard models with equal band width in the presence of crystal
field splitting. Crystal field splitting lifts one of the bands while leaving
the others degenerate. We use single-site dynamical mean-field theory combined
with continuous time quantum Monte Carlo impurity solver to calculate a phase
diagram as a function of total electron filling $N$ and crystal field splitting
$\Delta$. We find a large region of orbital-selective Mott phase in the phase
diagram when the doping is large enough. Further analysis indicates that the
large region of orbital-selective Mott phase is driven and stabilized by
doping. Such models may account for the orbital-selective Mott transition in
some doped realistic strongly correlated materials.


  We present S. Todorcevic's method of forcing with a coherent Souslin tree
over restricted iteration axioms as a black box usable by those who wish to
avoid its complexities but still access its power.


  According to the honing theory of creativity, creative thought works not on
individually considered, discrete, predefined representations but on a
contextually-elicited amalgam of items which exist in a state of potentiality
and may not be readily separable. This leads to the prediction that analogy
making proceeds not by mapping correspondences from candidate sources to
target, as predicted by the structure mapping theory of analogy, but by weeding
out non-correspondences, thereby whittling away at potentiality. Participants
were given an analogy problem, interrupted before they had time to solve it,
and asked to write down what they had by way of a solution. Na\"ive judges
categorized responses as significantly more supportive of the predictions of
honing theory than those of structure mapping.


  One X-ray short burst accompanied by a Galactic fast radio burst has been
detected so far, and its X-ray cut-off energy was significantly higher than
that of other X-ray short bursts. Such X-ray bursts are thought to be emitted
from a fireball in the magnetosphere of magnetars. If a fireball is formed
around a magnetic pole, it expands and is accelerated under its radiation
pressure, later producing photon emission and plasma outflow, which can be
responsible for radio bursts. We numerically study the radiative acceleration
of this outflowing fireball, which consists of electron-positron pairs and
radiation, and obtain the spectrum of the escaped X-ray photons. We
consistently take into account cyclotron resonant scattering, which enhances
the scattering cross section resulting in a strong radiative force and high
optical depth. Our results show that similar spectra to the observed X-ray
spectrum in the Galactic fast radio burst are realized in outflowing fireballs
and that the plasma outflow is simultaneously accelerated to a high Lorentz
factor owing to cyclotron resonant scattering.


  We study the equation $u_t +uu_x +u-K*u=0$ in the case of an arbitrary $K
\geq 0$, which is a generalization of a model for radiating gas, in which
$K(y)={1/2}e^{-|y|}$. Using a monotone iteration scheme argument we establish
the existence of traveling waves, which gives a solution to an open question
raised by Denis Serre.


  The microcanonical ensemble is a natural starting point of statistical
mechanics. However, when it comes to perturbation theory in statistical
mechanics, traditionally only the canonical and grand canonical ensembles have
been used. In this article we show how the microcanonical ensemble can be
directly used to carry out perturbation theory for both non-interacting and
interacting systems. We obtain the first non-trivial order answers for the
specific heat of anharmonic oscillators and for the virial expansion in real
gases. They are in exact agreement with the results obtained from the canonical
ensemble. In addition, we show how crossover functions for the specific heat of
anharmonic oscillators can be constructed using a microcanonical ensemble and
also how the subsequent terms of the virial expansion can be obtained. However,
we find that if we consider quantum free particles in a one-dimensional box of
extension L, then the two ensembles give strikingly different answers for the
first correction to the specific heat in the high temperature limit.


  Supermassive black hole (SMBH) binaries form due to galaxy mergers and minor
accretion events. When the SMBHs are accreting, they form dual or binary AGN
and can give rise to double-peaked emission lines in the optical spectra of the
merger remnant. The double-peaked emission lines could also be due to jet-ISM
interaction or rotating disks. One of the best ways to confirm dual/binary AGN
in double-peaked AGN (DPAGN) is by using high resolution radio observations. We
have observed a sample of 20 DPAGN at two or more frequencies using the Karl G.
Jansky Very Large Array (VLA), of which one source is already published and the
remaining 19 are presented in this paper. We have detected dual radio
structures at separation of $\lesssim$ 10 kpc in three of our sample galaxies.
Using the spectral index maps and optical spectra of the sources, we have
confirmed that one of them is a dual AGN (DAGN), while the other two can be
dual AGN or AGN+ star-forming nuclei pairs. Of the remaining sources, one has a
clear core-jet structure and another source could be a core-jet structure or a
DAGN. The remaining 13 sources are single cores while one source is not
detected at any frequency. We find that for our dual AGN detection, the DPAGN
emission lines do not originate from the dual/binary AGN. Instead, they could
be due to outflows or jets. Hence, we conclude that DPAGN identified in low
resolution SDSS spectra are not good indicators of dual/binary AGN. On the
other hand, closely interacting galaxies or merger remnants are good candidates
for detecting dual/binary AGN.


  Before cosmic reionization, hydrogen atoms acquire a spin polarization
quadrupole through interaction with the anisotropic 21-cm radiation field. The
interaction of this quadrupole with anisotropies in the cosmic microwave
background (CMB) radiation field gives a net spin orientation to the hydrogen
atoms. The 21-cm radiation emitted by these spin-oriented hydrogen atoms is
circularly polarized. Here, we reformulate succinctly the derivation of the
expression for this circular polarization in terms of Cartesian (rather than
spherical) tensors. We then compute the angular power spectrum of the observed
Stokes-$V$ parameter in the standard $\Lambda$CDM cosmological model and show
how it depends on redshift, or equivalently, the observed frequency.