  We study mechanisms of control of charge state and concentration of different
point defects in doped insulating crystals. The approach is based on the
density functional theory calculations. We apply it to the problem of obtaining
of Ti-doped sapphire crystals with high figure-of-merit (FOM). The FOM of a
given sample is defined as the ratio of the coefficient of absorption at the
pump frequency to the coefficient of absorption at the working frequency of
Ti:sapphire laser. It is believed that FOM is proportional to the ratio of the
concentration of isolated Ti$^{3+}$ ions to the concentration of
Ti$^{3+}$-Ti$^{4+}$ pairs. We find that generally this ratio is in inverse
proportion to the concentration of Ti$^{4+}$ isolated substitutional defects
with the coefficient of proportionality that depends on the temperature at
which the thermodynamically equilibrium concentration of defects is reached. We
argue that in certain cases the inverse proportion between concentrations of
Ti$^{3+}$-Ti$^{4+}$ and Ti$^{4+}$ may be violated. We show that codopants that
form positively (negatively) charged defects may decrease (increase) the
concentration of positively charged defects formed by the main dopants. To
evaluate the effect of codoping it is important to take into account not only
isolated defects but defect complexes formed by codopants, as well. In
particular, we show that codoping of Ti:sapphire with nitrogen results in an
essential increase of the concentration of Ti$^{4+}$ and in a decrease of the
FOM, and, consequently, growth or annealing in the presence of nitrogen or its
compounds is unfavorable for producing Ti:sapphire laser crystals. The approach
developed can be used for determining appropriate growth and annealing
conditions for obtaining doped crystals with the required characteristics.


  For both the cubic Nonlinear Schr\"odinger Equation (NLS) as well as the
  modified Korteweg-de Vries (mKdV) equation in one space dimension we consider
the set ${\bf M}_N$ of pure $N$-soliton states, and their associated
multisoliton solutions. We prove that (i) the set ${\bf M}_N$ is a uniformly
smooth manifold, and (ii) the ${\bf M}_N$ states are uniformly stable in $H^s$,
for each $s>-\frac12$.
  One main tool in our analysis is an iterated Backlund transform, which allows
us to nonlinearly add a multisoliton to an existing soliton free state (the
soliton addition map) or alternatively to remove a multisoliton from a
multisoliton state (the soliton removal map). The properties and the regularity
of these maps are extensively studied.


  We use resonant inelastic x-ray scattering (RIXS) at the O $K$- and Cu
$K$-edges to investigate the doping- and temperature dependence of low-energy
plasmon excitations in La$_{2-x}$Sr$_{x}$CuO$_4$. We observe a monotonic
increase of the energy scale of the plasmons with increasing doping $x$ in the
underdoped regime, whereas a saturation occurs above optimal doping $x \gtrsim
0.16$ and persists at least up to $x = 0.4$. Furthermore, we find that the
plasmon excitations show only a marginal temperature dependence, and possible
effects due to the superconducting transition and the onset of strange metal
behavior are either absent or below the detection limit of our experiment.
Taking into account the strongly correlated character of the cuprates, we show
that layered $t$-$J$-$V$ model calculations accurately capture the increase of
the plasmon energy in the underdoped regime. However, the computed plasmon
energy continues to increase even for doping levels above $x \gtrsim 0.16$,
which is distinct from the experimentally observed saturation, and reaches a
broad maximum around $x = 0.55$. We discuss whether possible lattice disorder
in overdoped samples, a renormalization of the electronic correlation strength
at high dopings, or an increasing relevance of non-planar Cu and O orbitals
could be responsible for the discrepancy between experiment and theory for
doping levels above $x = 0.16$.


  The problem of generating random quantum states is of a great interest from
the quantum information theory point of view. In this paper we present a
package for Mathematica computing system harnessing a specific piece of
hardware, namely Quantis quantum random number generator (QRNG), for
investigating statistical properties of quantum states. The described package
implements a number of functions for generating random states, which use
Quantis QRNG as a source of randomness. It also provides procedures which can
be used in simulations not related directly to quantum information processing.


  The author proposes a new geometry in this book. The author named this new
geometry Intercenter Geometry. Intercenter Geometry is different from
traditional Euclidean geometry and analytic geometry (coordinate geometry). The
idea of Intercenter Geometry is that the geometric quantities on a plane will
be expressed by the lengths of the three sides of a given triangle. The
geometric quantities in space will be expressed by the lengths of the six edges
of a given tetrahedron. In Intercenter Geometry, a unified approach is used to
deal with the calculation of geometric quantities of triangles and
tetrahedrons. Many new theorems and formulas on geometry and geometric
inequalities have been obtained. In particular, Intercenter Geometry has solved
some problems that have not been solved in Euclidean geometry and analytical
geometry (coordinate geometry) for a long time, such as the distance between
the centroid and the incenter of a given tetrahedron, etc. Intercenter Geometry
enriches geometry, which is not only of theoretical significance to open up the
field of mathematical research, to explore new ideas and methods of
mathematical research, but also of positive significance to promote the spirit
of innovation. The fruitful achievements of Intercenter Geometry also have
practical application value.


  Experiments and computer simulation studies have revealed existence of rich
dynamics in the orientational relaxation of molecules in confined systems such
as water in reverse micelles, cyclodextrin cavities and nano-tubes. Here we
introduce a novel finite length one dimensional Ising model to investigate the
propagation and the annihilation of dynamical correlations in finite systems
and to understand the intriguing shortening of the orientational relaxation
time that has been reported for small sized reverse micelles. In our finite
sized model, the two spins at the two end cells are oriented in the opposite
directions, to mimic the effects of surface that in real system fixes water
orientation in the opposite directions. This produces opposite polarizations to
propagate inside from the surface and to produce bulk-like condition at the
centre. This model can be solved analytically for short chains. For long chains
we solve the model numerically with Glauber spin flip dynamics (and also with
Metropolis single-spin flip Monte Carlo algorithm). We show that model nicely
reproduces many of the features observed in experiments. Due to the destructive
interference among correlations that propagate from the surface to the core,
one of the rotational relaxation time components decays faster than the bulk.
In general, the relaxation of spins is non-exponential due to the interplay
between various interactions. In the limit of strong coupling between the spins
or in the limit of low temperature, the nature of relaxation of the spins
undergoes a qualitative change with the emergence of a homogeneous dynamics
where decay is predominantly exponential, again in agreement with experiments.


  We prove that the extremal process of branching Brownian motion, in the limit
of large times, converges weakly to a cluster point process. The limiting
process is a (randomly shifted) Poisson cluster process, where the positions of
the clusters is a Poisson process with exponential density. The law of the
individual clusters is characterized as branching Brownian motions conditioned
to perform "unusually large displacements", and its existence is proved. The
proof combines three main ingredients. First, the results of Bramson on the
convergence of solutions of the Kolmogorov-Petrovsky-Piscounov equation with
general initial conditions to standing waves. Second, the integral
representations of such waves as first obtained by Lalley and Sellke in the
case of Heaviside initial conditions. Third, a proper identification of the
tail of the extremal process with an auxiliary process, which fully captures
the large time asymptotics of the extremal process. The analysis through the
auxiliary process is a rigorous formulation of the cavity method developed in
the study of mean field spin glasses.


  The Empirical Mode Decomposition (EMD) provides a tool to characterize time
series in terms of its implicit components oscillating at different
time-scales. We apply this decomposition to intraday time series of the
following three financial indices: the S\&P 500 (USA), the IPC (Mexico) and the
VIX (volatility index USA), obtaining time-varying multidimensional
cross-correlations at different time-scales. The correlations computed over a
rolling window are compared across the three indices, across the components at
different time-scales, at different lags and over time. We uncover a rich
heterogeneity of interactions which depends on the time-scale and has important
led-lag relations which can have practical use for portfolio management, risk
estimation and investments.


  Ultra-wideband 3D imaging spectrometry in the millimeter-submillimeter
(mm-submm) band is an essential tool for uncovering the dust-enshrouded portion
of the cosmic history of star formation and galaxy evolution. However, it is
challenging to scale up conventional coherent heterodyne receivers or
free-space diffraction techniques to sufficient bandwidths ($\geq$1 octave) and
numbers of spatial pixels (>$10^2$). Here we present the design and first
astronomical spectra of an intrinsically scalable, integrated superconducting
spectrometer, which covers 332-377 GHz with a spectral resolution of $F/\Delta
F \sim 380$. It combines the multiplexing advantage of microwave kinetic
inductance detectors (MKIDs) with planar superconducting filters for dispersing
the signal in a single, small superconducting integrated circuit. We
demonstrate the two key applications for an instrument of this type: as an
efficient redshift machine, and as a fast multi-line spectral mapper of
extended areas. The line detection sensitivity is in excellent agreement with
the instrument design and laboratory performance, reaching the atmospheric
foreground photon noise limit on sky. The design can be scaled to bandwidths in
excess of an octave, spectral resolution up to a few thousand and frequencies
up to $\sim$1.1 THz. The miniature chip footprint of a few $\mathrm{cm^2}$
allows for compact multi-pixel spectral imagers, which would enable
spectroscopic direct imaging and large volume spectroscopic surveys that are
several orders of magnitude faster than what is currently possible.


  Temporal stream logic (TSL) extends LTL with updates and predicates over
arbitrary function terms. This allows for specifying data-intensive systems for
which LTL is not expressive enough. In the semantics of TSL, functions and
predicates are left uninterpreted. In this paper, we extend TSL with
first-order theories, enabling us to specify systems using interpreted
functions and predicates such as incrementation or equality. We investigate the
satisfiability problem of TSL modulo the standard underlying theory of
uninterpreted functions as well as with respect to Presburger arithmetic and
the theory of equality: For all three theories, TSL satisfiability is highly
undecidable. Nevertheless, we identify three fragments of TSL for which the
satisfiability problem is (semi-)decidable in the theory of uninterpreted
functions. Despite the high undecidability, we present an algorithm - which is
not guaranteed to terminate - for checking the satisfiability of a TSL formula
in the theory of uninterpreted functions and evaluate it: It scales well and is
able to validate assumptions in a real-world system design.


  Efficient utility of radio spectrum has been a hot topic as the wireless
communication spectrum is a precious resource. The past decade has witnessed
intensive research in spectrum sharing techniques. Most of the techniques are
based on cognitive radio networks (CRNs) because cognitive capabilities are
essential for optimizing spectrum efficiency and guaranteeing safe coexistence
in the presence of the spectrum uncertainty. However, due to the high
complexity of the problem, most research has been limited to theoretical
analysis. It is non-trivial to build a simulator that is capable of carrying
out a comprehensive experimental study. In this paper, a survey is conducted to
provide a big picture of the available simulators in CRNs research. By
illustrating their major functionalities, the insight enables researchers to
select tools that match their needs. In addition, with a better understanding
of the advantages and constraints, this survey aims at providing a guideline
for simulator designers who have been trying to meet the requirements from the
CRN research community.


  We analyze the ground state of the two--component gas of trapped ultracold
fermionic atoms. We neglect the forces between atoms in the same hyperfine
state (the same component). For the case when the forces between
distinguishable atoms (i.e., atoms in different hyperfine states) are repulsive
(positive mutual scattering length), we find the existence of critical
interaction strength above which one atomic fraction expels the other from the
center of the trap. When atoms from different components attract each other
(negative mutual scattering length) the ground state of the system dramatically
changes its structure for strong enough attraction -- the Cooper pairs built of
atoms in different hyperfine states appear.


  We investigate the effect of equilibrium topology on the statistics of
non-equilibrium work performed during the subsequent unitary evolution,
following a sudden quench of the Semenoff mass of the Haldane model. We show
that the resulting work distribution function for quenches performed on the
Haldane Hamiltonian with broken time reversal symmetry (TRS) exhibits richer
universal characteristics as compared to those performed on the time-reversal
symmetric massive graphene limit whose work distribution function we have also
evaluated for comparison. Importantly, our results show that the work
distribution function exhibits different universal behaviors following the
non-equilibrium dynamics of the system for small $\phi$ (argument of complex
next nearest neighbor hopping) and large $\phi$ limits, although the two limits
belong to the same equilibrium universality class.


  Data intensive applications on clusters often require requests quickly be
sent to the node managing the desired data. In many applications, one must look
through a sorted tree structure to determine the responsible node for accessing
or storing the data.
  Examples include object tracking in sensor networks, packet routing over the
internet, request processing in publish-subscribe middleware, and query
processing in database systems. When the tree structure is larger than the CPU
cache, the standard implementation potentially incurs many cache misses for
each lookup; one cache miss at each successive level of the tree. As the
CPU-RAM gap grows, this performance degradation will only become worse in the
future.
  We propose a solution that takes advantage of the growing speed of local area
networks for clusters. We split the sorted tree structure among the nodes of
the cluster. We assume that the structure will fit inside the aggregation of
the CPU caches of the entire cluster. We then send a word over the network (as
part of a larger packet containing other words) in order to examine the tree
structure in another node's CPU cache. We show that this is often faster than
the standard solution, which locally incurs multiple cache misses while
accessing each successive level of the tree.


  The baseline configuration of the International Linear Collider requires 2
beam dumps per interaction region, each rated to 18MW of beam power, together
with additional beam dumps for tuning purposes and machine protection. The
baseline design uses high pressure moving water dumps, first developed for the
SLC and used in the TESLA design, although a gas based dump is also being
considered. In this paper we discuss the progress made by the international
community on both physics and engineering studies for the beam dumps.


  In this paper we prove the logarithmically improved Serrin's criteria to the
three-dimensional incompressible Navier-Stokes equations.


  Model-independent distance constraints to binary millisecond pulsars (MSPs)
are of great value to both the timing observations of the radio pulsars, and
multiwavelength observations of their companion stars. Very Long Baseline
Interferometry (VLBI) astrometry can be employed to provide these
model-independent distances with very high precision via the detection of
annual geometric parallax. Using the Very Long Baseline Array, we have observed
two binary millisecond pulsars, PSR J1022+1001 and J2145-0750, over a two-year
period and measured their distances to be 700 +14 -10 pc and 613 +16 -14 pc
respectively. We use the well-calibrated distance in conjunction with revised
analysis of optical photometry to tightly constrain the nature of their massive
(M ~ 0.85 Msun) white dwarf companions. Finally, we show that several
measurements of their parallax and proper motion of PSR J1022+1001 and PSR
J2145-0750 obtained by pulsar timing array projects are incorrect, differing
from the more precise VLBI values by up to 5 sigma. We investigate possible
causes for the discrepancy, and find that imperfect modeling of the solar wind
is a likely candidate for the timing model errors given the low ecliptic
latitude of these two pulsars.


  Although there is a wide use of technical trading rules in stock markets, the
profitability of them still remains controversial. This paper first presents
and proves the upper bound of cumulative return, and then introduces many of
conventional technical trading rules. Furthermore, with the help of bootstrap
methodology, we investigate the profitability of technical trading rules on
different international stock markets, including developed markets and emerging
markets. At last, the results show that the technical trading rules are hard to
beat the market, and even less profitable than the random trading strategy.


  The aim of this paper is to give a corrected bijective proof of Vershik's
relations for the Kostka numbers. Our proof uses insertion and reverse
insertion algorithms, as in the combinatorial proof of the Pieri rule.


  Cognitive radios have been studied recently as a means to utilize spectrum in
a more efficient manner. This paper focuses on the fundamental limits of
operation of a MIMO cognitive radio network with a single licensed user and a
single cognitive user. The channel setting is equivalent to an interference
channel with degraded message sets (with the cognitive user having access to
the licensed user's message). An achievable region and an outer bound is
derived for such a network setting. It is shown that under certain conditions,
the achievable region is optimal for a portion of the capacity region that
includes sum capacity.


  A systematic study, based on the third-moment structure function, of Sgr A*'s
variability finds an exponential rise time
$\tau_{1,\rm{obs}}=14.8^{+0.4}_{-1.5}~\mathrm{minutes}$ and decay time
$\tau_{2,\rm{obs}}=13.1^{+1.3}_{-1.4}~\mathrm{minutes}$. This symmetry of the
flux-density variability is consistent with earlier work, and we interpret it
as caused by the dominance of Doppler boosting, as opposed to gravitational
lensing, in Sgr~A*'s light curve. A relativistic, semi-physical model of Sgr~A*
confirms an inclination angle $i<45$ degrees. The model also shows that the
emission of the intrinsic radiative process can have some asymmetry even though
the observed emission does not. The third-moment structure function, which is a
measure of the skewness of the light-curve increments, may be a useful summary
statistic in other contexts of astronomy because it senses only temporal
asymmetry, i.e., it averages to zero for any temporally symmetric signal.


  By applying the basic concept of the density matrix in an open quantum system
and modification of quantum mechanics, we derive Kossakowski-Lindblad equation
and different properties of this equation are reviewed. Next, a pedagogical
approach is used to present Ramsey's trick for linear modification of the
quantum mechanics. We discuss how an open quantum mechanics or its modification
changes the fraction of excited states in Ramsey Interferometers.


  Inelastic transport of electrons through a two-impurity chain is studied
theoretically with account of intersite Coulomb interaction, U. Both limits of
ohmic transport (at low bias) and strongly non-ohmic transport (at high bias)
are considered. We demonstrate that correlations, induced by a finite U, in
conjunction with conventional Hubbard correlations, give rise to a distinct
transport regime, with current governed by two-electron hops. This regime
realizes when a single-electron hop onto the chain and a single-electron hop
out of the chain are both ``blocked'' due to the finite U, so that conventional
correlated sequential transport is impossible. The regime of two-electron hops
manifests itself in the form of an additional step in the current-voltage
characteristics, I(V).


  The Markovian dynamics of a qubit is investigated in the scheme of random
unitary dynamics, where Kraus operators are changed by an extra noise. The
behavior of Markovianity is explored in the perturbed scenario. We provide a
new algorithm for checking CP-divisibility (Markovianity) of a dynamical map.


  From analysis of a big variety of different knots we conclude that at q which
is an root of unity, q^{2m}=1, HOMFLY polynomials in symmetric representations
[r] satisfy recursion identity: H_{r+m} = H_r H_m for any A, which is a
generalization of the property H_r = (H_1)^r for special polynomials at q=1. We
conjecture a natural generalization to arbitrary representation R, which,
however, is checked only for torus knots. Next, Kashaev polynomial, which
arises from H_R at q=exp(i\pi/|R|), turns equal to the special polynomial with
A substituted by A^|R|, provided R is a single-hook representations (e.g.
arbitrary symmetric) -- what provides a q-A dual to the similar property of
Alexander polynomial. All this implies non-trivial relations for the
coefficients of the differential expansions, which are believed to provide
reasonable coordinates in the space of knots -- existence of such universal
relations means that these variables are still not unconstrained.


  Attack paths are the potential chain of malicious activities an attacker
performs to compromise network assets and acquire privileges through exploiting
network vulnerabilities. Attack path analysis helps organizations to identify
new/unknown chains of attack vectors that reach critical assets within the
network, as opposed to individual attack vectors in signature-based attack
analysis. Timely identification of attack paths enables proactive mitigation of
threats. Nevertheless, manual analysis of complex network configurations,
vulnerabilities, and security events to identify attack paths is rarely
feasible. This work proposes a novel transferable graph neural network-based
model for shortest path identification. The proposed shortest path detection
approach, integrated with a novel holistic and comprehensive model for
identifying potential network vulnerabilities interactions, is then utilized to
detect network attack paths. Our framework automates the risk assessment of
attack paths indicating the propensity of the paths to enable the compromise of
highly-critical assets (e.g., databases) given the network configuration,
assets' criticality, and the severity of the vulnerabilities in-path to the
asset. The proposed framework, named SPGNN-API, incorporates automated threat
mitigation through a proactive timely tuning of the network firewall rules and
zero-trust policies to break critical attack paths and bolster cyber defenses.
Our evaluation process is twofold; evaluating the performance of the shortest
path identification and assessing the attack path detection accuracy. Our
results show that SPGNN-API largely outperforms the baseline model for shortest
path identification with an average accuracy >= 95% and successfully detects
100% of the potentially compromised assets, outperforming the attack graph
baseline by 47%.


  This article provides a complete description of the differential Gerstenhaber
algebras of all nilpotent complex structures on any real six-dimensional
nilpotent algebra. As an application, we classify all pseudo-K\"ahlerian
complex structures on six-dimensional nilpotent algebras such that the
differential Gerstenhaber algebra of its complex structure is quasi-isomorphic
to that of its symplectic structure. In a weak sense of mirror symmetry, it is
a classification of pseudo-K\"ahler structures on six-dimensional nilpotent
algebras whose mirror images are themselves.


  The renormalized pion-nucleon Lagrangian is calculated to O(p^3) in heavy
baryon chiral perturbation theory. By suitably chosen transformations of the
nucleon field, the Lagrangian is brought to a standard form.


  We introduce a spin-interference device that comprises a quantum ring (QR)
with three embedded quantum point contacts (QPCs) and study theoretically its
spin transport properties in the presence of Rashba spin-orbit interaction. Two
of the QPCs conform the lead-to-ring junctions while a third one is placed
symmetrically in the upper arm of the QR. Using an appropriate scattering model
for the QPCs and the $\mathbb{S}$-matrix scattering approach, we analyze the
role of the QPCs on the Aharonov-Bohm (AB) and Aharonov-Casher (AC) conductance
oscillations of the QR-device. Exact formulas are obtained for the
spin-resolved conductances of the QR-device as a function of the confinement of
the QPCs and the AB/AC phases. Conditions for the appearance of resonances and
anti-resonances in the spin-conductance are derived and discussed. We predict
very distinctive variations of the QR-conductance oscillations not seen in
previous QR proposals. In particular we find that the interference pattern in
the QR can be manipulated to a large extend by varying electrically the
lead-to-ring topological parameters. The latter can be used to modulate the AB
and AC phases by applying gate voltage only. We have shown also that the
conductance oscillations exhibits a crossover to well-defined resonances as the
lateral QPC confinement strength is increased, mapping the eigenenergies of the
QR. In addition, unique features of the conductance arises by varying the
aperture of the upper-arm QPC and the Rashba spin-orbit coupling. Our results
may be of relevance for promising spin-orbitonics devices based in quantum
interference mechanisms.


  We show that associating the Euclidean cell decomposition due to Cooper and
Long to each point of the moduli space of framed strictly convex real
projective structures of finite volume on the once-punctured torus gives this
moduli space a natural cell decomposition. The proof makes use of coordinates
due to Fock and Goncharov, the action of the mapping class group as well as
algorithmic real algebraic geometry. We also show that the decorated moduli
space of framed strictly convex real projective structures of finite volume on
the thrice-punctured sphere has a natural cell decomposition.


  Imagine a map of your home with all of your connected devices (computers,
TVs, voice control devices, printers, security cameras, etc.), in their
location. You could then easily group devices into user-profiles, monitor Wi-Fi
quality and activity in different areas of your home, and even locate a lost
tablet in your home. MapiFi is a method to generate that map of the devices in
a home. The first part of MapiFi involves the user (either a technician or the
resident) walking around the home with a mobile device that listens to Wi-Fi
radio channels. The mobile device detects Wi-Fi packets that come from all of
the home's devices that connect to the gateway and measures their signal
strengths (ignoring the content of the packets). The second part is an
algorithm that uses all the signal-strength measurements to estimate the
locations of all the devices in the home. Then, MapiFi visualizes the home's
space as a coordinate system with devices marked as points in this space. A
patent has been filed based on this technology. This paper was published in
SCTE Technical Journal (see published paper at
https://wagtail-prod-storage.s3.amazonaws.com/documents/SCTE_Technical_Journal_V1N3.pdf).


  Ultrashort time-domain spectroscopy and field-resolved spectroscopy of
molecular fingerprints are gold standards for detecting samples' constituents
and internal dynamics. However, they are hindered by the Nyquist criterion,
leading to prolonged data acquisition, processing times, and sizable data
volumes. In this work, we present the first experimental demonstration of
compressed sensing on field-resolved molecular fingerprinting by employing
random scanning. Our measurements enable pinpointing the primary absorption
peaks of atmospheric water vapor in response to terahertz light transients
while sampling beyond the Nyquist limit. By drastically undersampling the
electric field of the molecular response at a Nyquist frequency of 0.8 THz, we
could successfully identify water absorption peaks up to 2.5 THz with a mean
squared error of 12 * 10^-4. To our knowledge, this is the first experimental
demonstration of time-domain compressed sensing, paving the path towards
real-time field-resolved fingerprinting and acceleration of advanced
spectroscopic techniques.


  Raman spectroscopy is a powerful analytical tool with applications ranging
from quality control to cutting edge biomedical research. One particular area
which has seen tremendous advances in the past decade is the development of
powerful handheld Raman spectrometers. They have been adopted widely by first
responders and law enforcement agencies for the field analysis of unknown
substances. Field detection and identification of unknown substances with Raman
spectroscopy rely heavily on the spectral matching capability of the devices on
hand. Conventional spectral matching algorithms (such as correlation, dot
product, etc.) have been used in identifying unknown Raman spectrum by
comparing the unknown to a large reference database. This is typically achieved
through brute-force summation of pixel-by-pixel differences between the
reference and the unknown spectrum. Conventional algorithms have noticeable
drawbacks. For example, they tend to work well with identifying pure compounds
but less so for mixture compounds. For instance, limited reference spectra
inaccessible databases with a large number of classes relative to the number of
samples have been a setback for the widespread usage of Raman spectroscopy for
field analysis applications. State-of-the-art deep learning methods
(specifically convolutional neural networks CNNs), as an alternative approach,
presents a number of advantages over conventional spectral comparison algorism.
With optimization, they are ideal to be deployed in handheld spectrometers for
field detection of unknown substances. In this study, we present a
comprehensive survey in the use of one-dimensional CNNs for Raman spectrum
identification. Specifically, we highlight the use of this powerful deep
learning technique for handheld Raman spectrometers taking into consideration
the potential limit in power consumption and computation ability of handheld
systems.


  Nearest neighbor-based similarity searching is a common task in chemistry,
with notable use cases in drug discovery. Yet, some of the most commonly used
approaches for this task still leverage a brute-force approach. In practice
this can be computationally costly and overly time-consuming, due in part to
the sheer size of modern chemical databases. Previous computational
advancements for this task have generally relied on improvements to hardware or
dataset-specific tricks that lack generalizability. Approaches that leverage
lower-complexity searching algorithms remain relatively underexplored. However,
many of these algorithms are approximate solutions and/or struggle with typical
high-dimensional chemical embeddings. Here we evaluate whether a combination of
low-dimensional chemical embeddings and a k-d tree data structure can achieve
fast nearest neighbor queries while maintaining performance on standard
chemical similarity search benchmarks. We examine different dimensionality
reductions of standard chemical embeddings as well as a learned,
structurally-aware embedding -- SmallSA -- for this task. With this framework,
searches on over one billion chemicals execute in less than a second on a
single CPU core, five orders of magnitude faster than the brute-force approach.
We also demonstrate that SmallSA achieves competitive performance on chemical
similarity benchmarks.


  In this paper, we determine new characterizations of nested and nested
GVZ-groups, including character-free characterizations, but we additionally
show that nested groups and nested GVZ-groups can be defined in terms of the
existence of certain normal series.


  In this paper, we consider discrete-time infinite horizon problems of optimal
control to a terminal set of states. These are the problems that are often
taken as the starting point for adaptive dynamic programming. Under very
general assumptions, we establish the uniqueness of solution of Bellman's
equation, and we provide convergence results for value and policy iteration.


  Deep neural networks are a very powerful tool for many computer vision tasks,
including image restoration, exhibiting state-of-the-art results. However, the
performance of deep learning methods tends to drop once the observation model
used in training mismatches the one in test time. In addition, most deep
learning methods require vast amounts of training data, which are not
accessible in many applications. To mitigate these disadvantages, we propose to
combine two image restoration approaches: (i) Deep Image Prior (DIP), which
trains a convolutional neural network (CNN) from scratch in test time using the
given degraded image. It does not require any training data and builds on the
implicit prior imposed by the CNN architecture; and (ii) a backprojection (BP)
fidelity term, which is an alternative to the standard least squares loss that
is usually used in previous DIP works. We demonstrate the performance of the
proposed method, termed BP-DIP, on the deblurring task and show its advantages
over the plain DIP, with both higher PSNR values and better inference run-time.


  A primary goal of the STAR Spin program at RHIC is the measurement of the
polarized gluon distribution function $\Delta G$, which can be obtained from a
global analysis incorporating measurements of the double spin asymmetry A_{LL}
in various final state channels of polarized p+p collisions. Final states with
large production cross sections such as inclusive jet and hadron production are
analyzed as the program moves towards the measurement of A_{LL} in the
theoretically clean channel of prompt photon production. The channels p+p ->
pi^{+/-} + X are unique in that the ordering of the measurements of A_{LL} in
these two channels is sensitive to the sign of Delta G. Moreover, STAR has
already established the procedure for the identification of charged pions and
the calculation of their production cross-sections over a broad kinematic
range. This contribution will present first measurements of double longitudinal
spin asymmetries for inclusive charged pion production extracted from 3 pb^{-1}
of data at sqrt{s}=200 GeV and 50% beam polarizations. The asymmetries are
calculated over the transverse momentum region 2<p_T<10 GeV/c and compared with
theoretical predictions incorporating several gluon polarization scenarios. A
systematic bias introduced by the selection of charged pions from events
satisfying electromagnetic energy triggers will be discussed and estimated
using Monte Carlo.


  Based on electron positron collision data collected with the BESIII detector
operating at the BEPCII storage rings, the differential cross sections of
inclusive $\pi^0$ and $K^0_S$ production as a function of hadron momentum,
normalized by the total cross section of the $e^{+}e^{-} \to$ hadrons process,
are measured at six center-of-mass energies from 2.2324 to 3.6710 GeV. Our
results with a relative hadron energy coverage from 0.1 to 0.9 significantly
deviate from several theoretical calculations based on existing fragmentation
functions, especially at lower energies.


  We consider stationary ergodic processes indexed by $\mathbb Z$ or $\mathbb
Z^n$ whose finite dimensional marginals have laws which are absolutely
continuous with respect to Lebesgue measure. We define an entropy theory for
these continuous processes, prove an analog of the Shannon Breiman Mac Millan
theorem and study more precisely the particular example of Gaussian processes.


  A search is conducted for a low-mass charged Higgs boson produced in a top
quark decay and subsequently decaying into a charm and a strange quark. The
data sample was recorded in proton-proton collisions at $\sqrt{s} =$ 13 TeV by
the CMS experiment at the LHC and corresponds to an integrated luminosity of
35.9 fb$^{-1}$. The search is performed in the process of top quark pair
production, where one top quark decays to a bottom quark and a charged Higgs
boson, and the other to a bottom quark and a W boson. With the W boson decaying
to a charged lepton (electron or muon) and a neutrino, the final state
comprises an isolated lepton, missing transverse momentum, and at least four
jets, of which two are tagged as b jets. To enhance the search sensitivity, one
of the jets originating from the charged Higgs boson is required to satisfy a
charm tagging selection. No significant excess beyond standard model
predictions is found in the dijet invariant mass distribution. An upper limit
in the range 1.68-0.25% is set on the branching fraction of the top quark decay
to the charged Higgs boson and bottom quark for a charged Higgs boson mass
between 80 and 160 GeV.


  The major challenges to fabricate quantum processors and future nano solid
state devices are material modification techniques with nanometre resolution
and suppression of statistical fluctuations of dopants or qubit carriers. Based
on a segmented ion trap with mK laser cooled ions we have realized a
deterministic single ion source which could operate with a huge range of
sympathetically cooled ion species, isotopes or ionic molecules. We have
deterministically extracted a predetermined number of ions on demand and have
measured a longitudinal velocity uncertainty of 6.3m/s and a spatial beam
divergence of 0.6 mrad. We show in numerical simulations that if the ions are
cooled to the motional ground state (Heisenberg limit) nanometre spatial
resolution can be achieved.


  We analyze transport through a quantum point contact in fractional quantum
Hall states with counter-propagating neutral edge modes. We show that both the
noise (as expected and previously calculated by other authors) and (perhaps
surprisingly) the average transmitted current are affected by downstream
perturbations within the standard edge state model. We consider two different
scenarios for downstream perturbations. We argue that the change in transmitted
current should be observable in experiments that have observed increased noise.


  We use data from the first epoch of observations with the IRAC/Spitzer for
the GOODS to detect and study a collection of LBGs at z ~ 6 to 5 in the HUDF,
six of which have spectroscopic confirmation. At these redshifts, IRAC samples
rest-frame optical light in the range 0.5 to 0.8 um, where the effects of dust
extinction are smaller and the sensitivity to light from evolved stars is
greater than at shorter, rest-frame UV observable from the ground or with the
HST. As such, it provides useful constraints on the ages and masses of these
galaxies' stellar populations. We find that the SEDs for many of these galaxies
are best fitted by models of stellar populations with masses of a few x 1e10
M_sun, and with ages of a few hundred Myrs, values quite similar to those
derived for typical LBGs at z ~ 3. When the universe was only 1 Gyr old, some
galaxies had already formed a mass of stars approaching that of the present-day
Milky Way, and that they started forming those stars at z > 7, and in some
cases much earlier. We find that the lower limits to the space density for
galaxies in this mass range are consistent with predictions from recent
hydrodynamic simulations of structure formation in a LCDM universe. All objects
in our samples are consistent with having solar metallicity, suggesting that
they might have already been significantly polluted by metals. The values for
dust reddening derived from the model fitting are low or zero, and we find that
some of the galaxies have rest-frame UV colors that are even bluer than those
predicted by the stellar population models to which we compare them. These
colors might be attributed to the presence of very massive stars (> 100 M_sun),
or by weaker intergalactic HI absorption than what is commonly assumed.


  We argue that a key reasoning skill that any advanced AI, say GPT-4, should
master in order to qualify as 'thinking machine', or AGI, is
hypothetic-deductive reasoning. Problem-solving or question-answering can quite
generally be construed as involving two steps: hypothesizing that a certain set
of hypotheses T applies to the problem or question at hand, and deducing the
solution or answer from T - hence the term hypothetic-deductive reasoning. An
elementary proxy of hypothetic-deductive reasoning is causal reasoning. We
propose simple tests for both types of reasoning, and apply them to ChatGPT.
Our study shows that, at present, the chatbot has a limited capacity for either
type of reasoning, as soon as the problems considered are somewhat complex.
However, we submit that if an AI would be capable of this type of reasoning in
a sufficiently wide range of contexts, it would be an AGI.


  We perform first-principles calculations of multiferroic Ca$_3$CoMnO$_6$ and
evaluate the exchange coupling constants using the Green's function method. We
clarify the effect of intra-chain and inter-chain exchange interactions on
magnetic stability. We find that inter-chain exchange coupling constants are
antiferromagnetic and that there are geometrical frustrations in the triangular
lattices of magnetic chains in Ca$_3$CoMnO$_6$. The magnetic transition
temperature is evaluated using effective Hamiltonian with calculated exchange
coupling constants. We obtain the transition temperature 5.80K. The value has
the same order as that of experimentally observed.


  If Gamma-ray Bursts (GRBs) are generally associated with supernovae like
1998bw, a relatively wide intrinsic luminosity function is implied, which
indicates the existence of a large amount of undetected dim bursts, and a much
higher event-rate than is often assumed. If it is assumed that the intrinsic
luminosity function of GRBs is a power-law: ${\phi (L)} \propto {L^{-\beta}}$
($\beta > 0$, $L_{min} \leq L \leq L_{max}$), data from the BATSE 4B catalog
can be used to constrain slope index $\beta$ and the dynamic range width Log
${L_{max}\over L_{min}}$. Using a K-S test comparison with the observational
Log $N$ - Log $P$, we find constraints on the GRB fireball model, GRB jets, and
the possible GRB contribution to cosmic gamma-ray background. We find the
acceptable dynamic range for $10^2<L_{max}/L_{min} < 10^7$.Our results show
that jet model is more likely to be related more highly energetic explosion
than fireball model.Our studies also show that the luminosity function provided
by a purely special relativistic effect on a jet is outside of the K-S test
acceptable range. Were intrinsic beaming to confine the jet to $\theta_{max} <
1/\gamma$ however, the effects of relativistic beaming would not dominate.


  In practical application, the performance of recognition network usually
decreases when being applied on super-resolution images. In this paper, we
propose a feature-based recognition network combined with GAN (FGAN). Our
network improves the recognition accuracy by extracting more features that
benefit recognition from SR images. In the experiment, we build three datasets
using three different super-resolution algorithm, and our network increases the
recognition accuracy by more than 6% comparing with ReaNet50 and DenseNet121.


  In [15], the algebraico-tree-theoretic simplicity hierarchical structure of
J. H. Conway's ordered field No of surreal numbers was brought to the fore and
employed to provide necessary and sufficient conditions for an ordered field to
be isomorphic to an initial subfield of No, i.e. a subfield of No that is an
initial subtree of No. In this sequel to [15], analogous results for ordered
abelian groups and ordered domains are established which in turn are employed
to characterize the convex subgroups and convex subdomains of initial subfields
of No that are themselves initial. It is further shown that an initial
subdomain of No is discrete if and only if it is an initial subdomain of No's
canonical integer part Oz of omnifc integers. Finally, extending results of
[15], the theories of divisible ordered abelian groups and real-closed ordered
fields are shown to be the sole theories of ordered abelian groups and ordered
fields all of whose models are isomorphic to initial subgroups and initial
subfields of No.


  This paper extends our recent theoretical work concerning the feasibility of
stable and accurate computation of turbulence using a large eddy simulation
[Ida and Taniguchi, Phys. Rev. E 68, 036705 (2003)]. In our previous paper, it
was shown, based on a simple assumption regarding the instantaneous streamwise
velocity, that the application of the Gaussian filter to the incompressible
Navier-Stokes equations can result in the appearance of a numerically unstable
term that can be decomposed into positive and negative viscosities. That result
raises the question as to whether an accurate solution can be achieved by a
numerically stable subgrid-scale model. In the present paper, based on
assumptions regarding the statistically averaged velocity, we present similar
theoretical investigations to show that in several situations, the shears
appearing in the statistically averaged velocity field numerically destabilize
the fluctuation components because of the derivation of a numerically unstable
term that represents negative diffusion in a fixed direction. This finding can
explain the problematic numerical instability that has been encountered in
large eddy simulations of wall-bounded flows. The present result suggests that
this numerical problem is universal in large eddy simulations, and that if
there is no failure in modeling, the resulting subgrid-scale model can still
have unstable characteristics; that is, the known instability problems of
several existing subgrid-scale models are not something that one may remove
simply by an artificial technique, but must be taken seriously so as to treat
them accurately.


  Let $k$ be a field of positive characteristic. We prove that the only linear
relations between the Hodge numbers $h^{i,j}(X) = \dim H^j(X,\Omega_X^i)$ that
hold for every smooth proper variety $X$ over $k$ are the ones given by Serre
duality. We also show that the only linear combinations of Hodge numbers that
are birational invariants of $X$ are given by the span of the $h^{i,0}(X)$ and
the $h^{0,j}(X)$ (and their duals $h^{i,n}(X)$ and $h^{n,j}(X)$). The
corresponding statements for compact K\"ahler manifolds were proven by
Kotschick and Schreieder.


  The axial form factor as well as the axial charge of octet baryons are
studied in the perturbative chiral quark model (PCQM) with the quark wave
functions predetermined by fitting the theoretical results of the proton charge
form factor to experimental data. The theoretical results are found, based on
the predetermined quark wave functions, in good agreement with experimental
data and lattice values. This may indicate that the electric charge and axial
charge distributions of the constituent quarks are the same. The study reveals
that the meson cloud plays an important role in the axial charge of octet
baryons, contributing 30%-40% to the total values, and strange sea quarks have
a considerable contribution to the axial charge of the $\Sigma$ and $\Xi$.


  We study D=3 field theories on the D3-branes stretched between two NS5-branes
with NS B-field background. The theory is a noncommutative gauge theory. The
mirror symmetry and S-duality of the theory are discussed. A new feature is
that the mirror of the noncommutative gauge theory is not a field theory but an
open string decoupled from the closed string. We also consider brane creation
phenomena and use the result to discuss the analogue of the Seiberg duality. A
noncommutative soliton is interpreted as a D1-brane induced on D3-brane.


  The main idea in the present work is the definition of an experimental
proposal for the detection of the number of extra{compact dimensions contained
as a core feature in String Theory. This goal will be achieved as a consequence
of the fact that the density of states of a bosonic gas does depend upon the
number and geometry of the involved space{like dimensions. In particular our
idea concerns the detection of the discontinuity of the specific heat at the
condensation temperature as a function of the number of particles present in
the gas. It will be shown that the corresponding function between these two
variables defines a segment of a straight line whose slope depends upon the
number of extra{compact dimensions. Resorting to some experiments in the
detection of the specific heat of a rubidium condensate the feasibility of this
proposal using this kind of atom is also analyzed.


  In this paper the author presents four methods to treat retinitis related
diseases using quantum dot technology.


  To O(1/N) we derive, purely from CFT data, the bulk equations of motion for
interacting scalar fields and for scalars coupled to gauge fields and gravity.
We first uplift CFT operators to mimic local AdS fields by imposing bulk
microcausality. This requires adding an infinite tower of smeared
higher-dimension double-trace operators to the CFT definition of a bulk field,
with coefficients that we explicitly compute. By summing the contribution of
the higher-dimension operators we derive the equations of motion satisfied by
these uplifted CFT operators and show that we precisely recover the expected
bulk equations of motion. We exhibit the freedom in the CFT construction which
corresponds to bulk field redefinitions.


  Using the Baum-Connes conjecture with coefficients, we develop a K-theory
formula for reduced C*-algebras of strongly $0$-$E$-unitary inverse semigroups,
or equivalently, for certain reduced partial crossed products. In the case of
semigroup C*-algebras, we obtain a generalization of previous K-theory results
of Cuntz, Echterhoff and the author without having to assume the Toeplitz
condition. As applications, we discuss semigroup C*-algebras of Artin monoids,
Baumslag-Solitar monoids, one-relator monoids, C*-algebras generated by right
regular representations of semigroups from number theory, and C*-algebras of
inverse semigroups arising in the context of tilings.


  We give a precise estimate of the Bergman kernel for the model domain defined
by $\Omega_F=\{(z,w)\in \mathbb{C}^{n+1}:{\rm Im}w-|F(z)|^2>0\},$ where
$F=(f_1,...,f_m)$ is a holomorphic map from $\mathbb{C}^n$ to $\mathbb{C}^m$,
in terms of the complex singularity exponent of $F$.


  Let $R$ be a commutative ring and $\Gamma(R)$ denote its zero-divisor graph.
In this paper, we investigate the genus number of the compact Riemann surface
which $\Gamma(R)$ can be embedded and illustrate all finite commutative rings
$R$ (up to isomorphism) such that $\Gamma(R)$ is either toroidal or planar.


  The gaseous media of galaxy clusters and cosmic filaments, which constitute
most of the baryonic matter in the universe, is highly dynamic. It is also
probably turbulent, although the turbulence properties are poorly known. The
gas is highly rarefied, essentially fully ionized plasma. Observational
evidence suggests intracluster media (ICMs) are magnetized at some level. There
are several possible origins for ICM seed fields; the observed fields are
likely the result of turbulence in the ICM. We are engaged in a simulation
study designed to understand in this context how very weak initial magnetic
fields evolve in driven turbulence. We find that the magnetic fields eventually
evolve towards equipartition levels with the vortical, solenoidal kinetic
energy in the turbulence. As they do so the topology of the field structures
transition from filamentary forms into ribbon-like structures in which the
field orientations are laminated with vorticity structures.


  Recent observations show the presence of metals in low-density Ly$\alpha$
forest absorbers at high redshift ($z\sim 3$). It remains still far from being
clearly understood what mechanisms spread metals over Mpc scales from the
parent galaxies, whether metals are homogeneously distributed in the
intergalactic medium (IGM), how metallicity of the IGM does evolve. These
questions are briefly addressed in this review.


  As main result we prove strong convergence theorems of Vilenkin-Fej\'er means
when $0<p\leq 1/2.$


  Accurate breast cancer diagnosis through mammography has the potential to
save millions of lives around the world. Deep learning (DL) methods have shown
to be very effective for mass detection in mammograms. Additional improvements
of current DL models will further improve the effectiveness of these methods. A
critical issue in this context is how to pick the right hyperparameters for DL
models. In this paper, we present GA-E2E, a new approach for tuning the
hyperparameters of DL models for brest cancer detection using Genetic
Algorithms (GAs). Our findings reveal that differences in parameter values can
considerably alter the area under the curve (AUC), which is used to determine a
classifier's performance.


  We prove a global logarithmic stability estimate for the Gel'fand-Calderon
inverse problem on a two-dimensional domain.


  In this paper, we establish the Gevrey regularity of solutions for a class of
degenerate Monge-Amp\`ere equations in the plane, under the assumption that one
principle entry of the Hessian is strictly positive and an appropriately finite
type degeneracy.


  Electrocardiography (ECG), an electrical measurement which captures cardiac
activities, is the gold standard for diagnosing cardiovascular disease (CVD).
However, ECG is infeasible for continuous cardiac monitoring due to its
requirement for user participation. By contrast, photoplethysmography (PPG)
provides easy-to-collect data, but its limited accuracy constrains its clinical
usage. To combine the advantages of both signals, recent studies incorporate
various deep learning techniques for the reconstruction of PPG signals to ECG;
however, the lack of contextual information as well as the limited abilities to
denoise biomedical signals ultimately constrain model performance. In this
research, we propose Performer, a novel Transformer-based architecture that
reconstructs ECG from PPG and combines the PPG and reconstructed ECG as
multiple modalities for CVD detection. This method is the first time that
Transformer sequence-to-sequence translation has been performed on biomedical
waveform reconstruction, combining the advantages of both PPG and ECG. We also
create Shifted Patch-based Attention (SPA), an effective method to
encode/decode the biomedical waveforms. Through fetching the various sequence
lengths and capturing cross-patch connections, SPA maximizes the signal
processing for both local features and global contextual representations. The
proposed architecture generates a state-of-the-art performance of 0.29 RMSE for
the reconstruction of PPG to ECG on the BIDMC database, surpassing prior
studies. We also evaluated this model on the MIMIC-III dataset, achieving a
95.9% accuracy in CVD detection, and on the PPG-BP dataset, achieving 75.9%
accuracy in related CVD diabetes detection, indicating its generalizability. As
a proof of concept, an earring wearable named PEARL (prototype), was designed
to scale up the point-of-care (POC) healthcare system.


  This paper studies random walks in i.i.d. random environments on
$\mathbb{Z}^d$ when there are two basic types of vertices, which we call "blue"
and "red," with drifts in different directions. We introduce a method of
studying these walks that compares the expected amount of time spent at a
specific site on the event that the site is red with the expected amount of
time spent there on the event that the site is blue. An advantage of this
method is that it produces explicit bounds on the asymptotic velocity of the
walk. We use the method to recover an early result of Kalikow, but with new
explicit bounds on the asymptotic velocity. Next, we consider a model where the
vast majority of sites are blue, and blue sites satisfy a non-nestling
assumption, but red sites break the non-nestling assumption and are permitted
to be highly pathological (for instance, red sites are allowed to give the walk
zero probability of stepping in all but two directions). We show that if the
red sites satisfy a certain uniform ellipticity assumption in two fixed
directions, then making red sites unlikely enough can push the asymptotic
velocity of the walk arbitrarily close to the bounds that come from the
non-nestling assumption on the blue sites, if all sites were blue.
Significantly, the required proportion $p^*$ of blue sites does not depend on
the distribution of red sites, except through the uniform ellipticity
assumption in two directions. Our proof is based on a coupling technique, where
two walks run in environments that are the same everywhere except at one
vertex. They decouple when they hit that vertex, and our proof is driven by
bounds on how long it takes to recouple. We then show that the i.i.d.
assumption in the theorem is necessary by providing a counterexample to the
statement of the theorem with the i.i.d. assumption removed. We conclude with
open questions.


  We aim to learn to temporally localize object state changes and the
corresponding state-modifying actions by observing people interacting with
objects in long uncurated web videos. We introduce three principal
contributions. First, we explore alternative multi-task network architectures
and identify a model that enables efficient joint learning of multiple object
states and actions such as pouring water and pouring coffee. Second, we design
a multi-task self-supervised learning procedure that exploits different types
of constraints between objects and state-modifying actions enabling end-to-end
training of a model for temporal localization of object states and actions in
videos from only noisy video-level supervision. Third, we report results on the
large-scale ChangeIt and COIN datasets containing tens of thousands of long
(un)curated web videos depicting various interactions such as hole drilling,
cream whisking, or paper plane folding. We show that our multi-task model
achieves a relative improvement of 40% over the prior single-task methods and
significantly outperforms both image-based and video-based zero-shot models for
this problem. We also test our method on long egocentric videos of the
EPIC-KITCHENS and the Ego4D datasets in a zero-shot setup demonstrating the
robustness of our learned model.


  We review the status of heavy neutral gauge bosons, Z', with emphasis on
constraints that arise in supersymmetric models, especially those motivated
from superstring compactifications. We first summarize the current
phenomenological constraints and the prospects for Z' detection and diagnostics
at the LHC and NLC. After elaborating on the status and (lack of) predictive
power for general models with an additional Z', we concentrate on motivations
and successes for Z' physics in supersymmetric theories in general and in a
class of superstring models in particular. We review phenomenologically viable
scenarios with the Z' mass in the electroweak or in the intermediate scale
region.


  We introduce Diffusion Augmented Agents (DAAG), a novel framework that
leverages large language models, vision language models, and diffusion models
to improve sample efficiency and transfer learning in reinforcement learning
for embodied agents. DAAG hindsight relabels the agent's past experience by
using diffusion models to transform videos in a temporally and geometrically
consistent way to align with target instructions with a technique we call
Hindsight Experience Augmentation. A large language model orchestrates this
autonomous process without requiring human supervision, making it well-suited
for lifelong learning scenarios. The framework reduces the amount of
reward-labeled data needed to 1) finetune a vision language model that acts as
a reward detector, and 2) train RL agents on new tasks. We demonstrate the
sample efficiency gains of DAAG in simulated robotics environments involving
manipulation and navigation. Our results show that DAAG improves learning of
reward detectors, transferring past experience, and acquiring new tasks - key
abilities for developing efficient lifelong learning agents. Supplementary
material and visualizations are available on our website
https://sites.google.com/view/diffusion-augmented-agents/


  Recently, Siamese networks have drawn great attention in visual tracking
community because of their balanced accuracy and speed. However, features used
in most Siamese tracking approaches can only discriminate foreground from the
non-semantic backgrounds. The semantic backgrounds are always considered as
distractors, which hinders the robustness of Siamese trackers. In this paper,
we focus on learning distractor-aware Siamese networks for accurate and
long-term tracking. To this end, features used in traditional Siamese trackers
are analyzed at first. We observe that the imbalanced distribution of training
data makes the learned features less discriminative. During the off-line
training phase, an effective sampling strategy is introduced to control this
distribution and make the model focus on the semantic distractors. During
inference, a novel distractor-aware module is designed to perform incremental
learning, which can effectively transfer the general embedding to the current
video domain. In addition, we extend the proposed approach for long-term
tracking by introducing a simple yet effective local-to-global search region
strategy. Extensive experiments on benchmarks show that our approach
significantly outperforms the state-of-the-arts, yielding 9.6% relative gain in
VOT2016 dataset and 35.9% relative gain in UAV20L dataset. The proposed tracker
can perform at 160 FPS on short-term benchmarks and 110 FPS on long-term
benchmarks.


  The mean-field approximation predicts pairing and shape phase transitions in
nuclei as a function of temperature or excitation energy. However, in the
finite nucleus the singularities of these phase transitions are smoothed out by
quantal and thermal fluctuations. An interesting question is whether signatures
of these transitions survive despite the large fluctuations. The shell model
Monte Carlo (SMMC) approach enables us to calculate the statistical properties
of nuclei beyond the mean-field approximation in model spaces that are many
orders of magnitude larger than spaces that can be treated by conventional
diagonalization methods. We have extended the SMMC method to heavy nuclei and
used it to study the transition from vibrational (spherical) to rotational
(deformed) nuclei in families of rare-earth isotopes. We have calculated
collective enhancement factors of level densities as a function of excitation
energy and found that the decay of the vibrational and rotational enhancements
is well correlated with the pairing and shape phase transitions, respectively.


  Spin pumping in ferromagnets provides a source of pure spin currents. Via the
inverse spin Hall effect a spin current is converted into a charge current and
a corresponding detectable DC-voltage. The ratio of injected spin current to
resulting charge current is given by the spin Hall angle. However, the number
of experiments more or less equals the number of different values for spin Hall
angles, even for the most studied normal metal platinum. This publication
provides a full study of inverse spin Hall effect and anisotropic
magnetoresistance for different NiFe(Py) / normal metal bilayers using a
coplanar waveguide structure. Angle and frequency dependent measurements
strongly suggest that spin pumping and inverse spin Hall effect can be used to
quantify spin Hall angles only if certain conditions are met. Ruling out the
anisotropic magnetoresistance as a parasitic voltage generating effect
measurements of the inverse spin Hall effect in Py/Pt and Py/Au yield spin Hall
angles of 0.09 and 0.008 respectively. Furthermore, DC-voltages at
ferromagnetic resonance for Py/Pt are studied as a function of temperature and
the results are compared to theoretical models.


  We propose a scheme to generate robust stationary continuous-variable
entanglement in optomechanical systems, based on geometrical nonlinearity that
occurs for large mechanical displacements. Such nonlinearity is often used to
correct the dynamics of the systems in the strong coupling regime. It appears
that geometrical nonlinearity enhances the entanglement and shifts its maximum
towards high detuning values. Using the experimental parameters, we find that
such a scheme generates a very robust entanglement against thermal decoherence
even at room temperature. Our results show that geometrical nonlinearity
affects entanglement as the optomechanical quantum interface.


  We study the time evolution of the entanglement entropy of a one-dimensional
nonintegrable spin chain, starting from random nonentangled initial pure
states. We use exact diagonalization of a nonintegrable quantum Ising chain
with transverse and longitudinal fields to obtain the exact quantum dynamics.
We show that the entanglement entropy increases linearly with time before
finite-size saturation begins, demonstrating a ballistic spreading of the
entanglement, while the energy transport in the same system is diffusive. Thus
we explicitly demonstrate that the spreading of entanglement is much faster
than the energy diffusion in this nonintegrable system.


  We use energetic considerations to deduce the form of a previously uncertain
coupling term in the shear-transformation-zone (STZ) theory of plastic
deformation in amorphous solids. As in the earlier versions of the STZ theory,
the onset of steady deformation at a yield stress appears here as an exchange
of dynamic stability between jammed and plastically deforming states. We show
how an especially simple ``quasilinear'' version of this theory accounts
qualitatively for many features of plasticity such as yielding, strain
softening, and strain recovery. We also show that this minimal version of the
theory fails to describe certain other phenomena, and argue that these
limitations indicate needs for additional internal degrees of freedom beyond
those included here.


  We discuss the recently observed "loophole free" violation of Bell's
inequalities in the framework of a physically realist view of quantum
mechanics, which requires that physical properties are attributed jointly to a
system, and to the context in which it is embedded. This approach is clearly
different from classical realism, but it does define a meaningful "quantum
realism" from a general philosophical point of view. Consistently with Bell
test experiments, this quantum realism embeds some form of non-locality, but
does not contain any action at a distance, in agreement with quantum mechanics.


  The reconstruction efficiency of photons and neutral pions is measured using
the relative yields of reconstructed $B^+ \to J/\psi K^{*+} (\to K^+ \pi^{0})$
and $B^+ \to J/\psi K^{+}$ decays. The efficiency is studied using the data
set, corresponding to an integrated luminosity of $3~\mathrm{fb}^{-1}$,
collected by the LHCb experiment in proton-proton collisions at the
centre-of-mass energies of 7 and 8 TeV.


  We consider a set up where a file of size M is stored in n distributed
storage nodes, using an (n,k) minimum storage regenerating (MSR) code, i.e., a
maximum distance separable (MDS) code that also allows efficient exact-repair
of any failed node. The problem of interest in this paper is to minimize the
repair bandwidth B for exact regeneration of a single failed node, i.e., the
minimum data to be downloaded by a new node to replace the failed node by its
exact replica. Previous work has shown that a bandwidth of B=[M(n-1)]/[k(n-k)]
is necessary and sufficient for functional (not exact) regeneration. It has
also been shown that if k < = max(n/2, 3), then there is no extra cost of exact
regeneration over functional regeneration. The practically relevant setting of
low-redundancy, i.e., k/n>1/2 remains open for k>3 and it has been shown that
there is an extra bandwidth cost for exact repair over functional repair in
this case. In this work, we adopt into the distributed storage context an
asymptotically optimal interference alignment scheme previously proposed by
Cadambe and Jafar for large wireless interference networks. With this scheme we
solve the problem of repair bandwidth minimization for (n,k) exact-MSR codes
for all (n,k) values including the previously open case of k > \max(n/2,3). Our
main result is that, for any (n,k), and sufficiently large file sizes, there is
no extra cost of exact regeneration over functional regeneration in terms of
the repair bandwidth per bit of regenerated data. More precisely, we show that
in the limit as M approaches infinity, the ratio B/M = (n-1)/(k(n-k))$.


  This paper accompanies a new dataset of non-linear real arithmetic problems
for the SMT-LIB benchmark collection. The problems come from an automated proof
procedure of Gerhold--Kauers, which is well suited for solution by SMT. The
problems of this type have not been tackled by SMT-solvers before. We describe
the proof technique and give one new such proof to illustrate it. We then
describe the dataset and the results of benchmarking. The benchmarks on the new
dataset are quite different to the existing ones. The benchmarking also brings
forward some interesting debate on the use/inclusion of rational functions and
algebraic numbers in the SMT-LIB.


  Neutral $B$ meson mixing matrix elements and $B$ meson decay constants are
calculated. Static approximation is used for $b$ quark and domain-wall fermion
formalism is employed for light quarks. The calculations are carried out on
$2+1$ flavor dynamical ensembles generated by RBC/UKQCD Collaborations with
lattice spacings $0.086$fm ($a^{-1}\sim 2.3$GeV) and $0.11$fm ($1.7$GeV), and a
fixed physical spatial volume of about $(2.7{\rm fm})^3$. In the static quark
action, link-smearings are used to improve the signal-to-noise ratio. We employ
two kinds of link-smearings, HYP1 and HYP2, and their results are combined in
taking the continuum limit. For the matching between the lattice and the
continuum theory, one-loop perturbative $O(a)$ improvements are made to reduce
discretization errors. As the most important quantity of this work, we obtain
SU(3) breaking ratio $\xi=1.208(60)$, where the error includes statistical and
systematic one. (Uncertainty from infinite $b$ quark mass is not included.) We
also find other neutral $B$ meson mixing quantities
$f_B\sqrt{\hat{B}_B}=240(22)$MeV, $f_{B_s}\sqrt{\hat{B}_{B_s}}=290(22)$MeV,
$\hat{B}_B=1.17(22)$, $\hat{B}_{B_s}=1.22(13)$ and $B_{B_s}/B_B=1.028(74)$, $B$
meson decay constants $f_B=219(17)$MeV, $f_{B_s}=264(19)$MeV and
$f_{B_s}/f_B=1.193(41)$, in the static limit of $b$ quark, which do not include
infinite $b$ quark mass uncertainty.


  We describe a compression-aware method to compute all-vs-all maximal exact
matches (MEM) among strings of a repetitive collection $\mathcal{T}$. The key
concept in our work is the construction of a fully-balanced grammar
$\mathcal{G}$ from $\mathcal{T}$ that meets a property that we call
\emph{fix-free}: the expansions of the nonterminals that have the same height
in the parse tree form a fix-free set (i.e., prefix-free and suffix-free). The
fix-free property allows us to compute the MEMs of $\mathcal{T}$ incrementally
over $\mathcal{G}$ using a standard suffix-tree-based MEM algorithm, which runs
on a subset of grammar rules at a time and does not decompress nonterminals. By
modifying the locally-consistent grammar of Christiansen et al 2020., we show
how we can build $\mathcal{G}$ from $\mathcal{T}$ in linear time and space. We
also demonstrate that our MEM algorithm runs on top of $\mathcal{G}$ in $O(G
+occ)$ time and uses $O(\log G(G+occ))$ bits, where $G$ is the grammar size,
and $occ$ is the number of MEMs in $\mathcal{T}$. In the conclusions, we
discuss how our idea can be modified to implement approximate pattern matching
in compressed space.


  I report observations of unusually strong photospheric and chromospheric
velocity oscillations in and near the leading sunspot of NOAA 10781 on 03 July
2005. I investigate an impinging wave as a possible origin of the velocity
pattern, and the changes of the wave after the passage through the magnetic
fields of the sunspot. The wave pattern found consists of a wave with about 3
Mm apparent wavelength that propagates towards the sunspot. This wave seems to
trigger oscillations inside the sunspot's umbra, which originate from a
location inside the penumbra on the side of the impinging wave. The wavelength
decreases and the velocity amplitude increases by an order of magnitude in the
chromospheric layers inside the sunspot. On the side of the sunspot opposite to
the impinging plane wave, circular wave fronts centered on the umbra are seen
propagating away from the sunspot outside its outer white-light boundary. They
lead to a peculiar ring structure around the sunspot, which is visible in both
velocity and intensity maps. The fact that only weak photospheric velocity
oscillations are seen in the umbra - contrary to the chromosphere where they
peak there - highlights the necessity to include the upper solar atmosphere in
calculations of wave propagation through spatially and vertically extended
magnetic field concentrations like sunspots.


  Let $\Lambda$ be an Artin algebra and ${\mathsf{mod}}\mbox{-}
({\underline{\mathsf{Gprj}}}\mbox{-}\Lambda)$ the category of finitely
presented functors over the stable category
${\underline{\mathsf{Gprj}}}\mbox{-}\Lambda$ of finitely generated Gorenstein
projective $\Lambda$-modules. This paper deals with those algebras $\Lambda$ in
which ${\mathsf{mod}}\mbox{-} ({\underline{\mathsf{Gprj}}}\mbox{-}\Lambda)$ is
a semisimple abelian category, and we call G-semisimple algebras. We study some
basic properties of such algebras. In particular, it will be observed that the
class of G-semisimple algebras contains important classes of algebras,
including gentle algebras and more generally quadratic monomial algebras. Next,
we construct an epivalence from the stable category of Gorenstein projective
representations $\underline{{\mathsf{Gprj}}}(\mathcal{Q}, \Lambda)$ of a finite
acyclic quiver $\mathcal{Q}$ to the category of representations ${\rm
rep}(\mathcal{Q}, \underline{{\mathsf{Gprj}}}\mbox{-} \Lambda)$ over
$\underline{{\mathsf{Gprj}}}\mbox{-} \Lambda)$, provided $\Lambda$ is a
G-semisimple algebra over an algebraic closed field. Using this, we will show
that the path algebra $\Lambda\mathcal{Q}$ of the G-semisimple algebra
$\Lambda$ is Cohen-Macaulay finite if and only if $\mathcal{Q}$ is Dynkin. In
the last part, we provide a complete classification of indecomposable
Gorenstein projective representations within ${\mathsf{Gprj}}(A_n, \Lambda)$ of
the linear quiver $A_n$ over a G-semisimple algebra $\Lambda$. We also
determine almost split sequences in ${\mathsf{Gprj}}(A_n, \Lambda)$ with
certain ending terms. We apply these results to obtain insights into the
cardinality of the components of the stable Auslander-Reiten quiver
${\mathsf{Gprj}}(A_n, \Lambda)$.


  We present the results of a search for pair production of a fourth-generation
charge -1/3 quark (b') in sqrt(s)=1.8 TeV ppbar collisions using 88 pb^(-1) of
data obtained with the Collider Detector at Fermilab. We assume that both
quarks decay via the flavor-changing neutral current process b' -> bZ and that
the b' mass is greater than m_Z + m_b. We studied the decay mode b'b'bar -> ZZ
b bbar where one Z0 decays into e^+e^- or mu^+ mu^- and the other decays
hadronically, giving a signature of two leptons plus jets. An upper limit on
the cross section of ppbar -> b'b'bar times [BR (b' -> bZ)]^2 is established as
a function of the b' mass. We exclude at 95% confidence level a b' quark with
mass between 100 and 199 GeV/c^2 for BR(b' -> bZ) = 100%.


  Using recent results on the occurrence times of a string of symbols in a
stochastic process with mixing properties, we present a new method for the
search of rare words in biological sequences generally modelled by a Markov
chain. We obtain a bound on the error between the distribution of the number of
occurrences of a word in a sequence (under a Markov model) and its Poisson
approximation. A global bound is already given by a Chen-Stein method. Our
approach, the psi-mixing method, gives local bounds. Since we only need the
error in the tails of distribution, the global uniform bound of Chen-Stein is
too large and it is a better way to consider local bounds. We search for two
thresholds on the number of occurrences from which we can regard the studied
word as an over-represented or an under-represented one. A biological role is
suggested for these over- or under-represented words. Our method gives such
thresholds for a panel of words much broader than the Chen-Stein method.
Comparing the methods, we observe a better accuracy for the psi-mixing method
for the bound of the tails of distribution. We also present the software PANOW
(available at http://stat.genopole.cnrs.fr/software/panowdir/) dedicated to the
computation of the error term and the thresholds for a studied word.


  We study the dynamics of a chiral SU(2) gauge theory with a Weyl fermion in
the I=3/2 representation and of its supersymmetric generalization. In the
former, we find a new and exotic mechanism of confinement, induced by
topological excitations that we refer to as magnetic quintets. The
supersymmetric version was examined earlier in the context of dynamical
supersymmetry breaking by Intriligator, Seiberg, and Shenker, who showed that
if this gauge theory confines at the origin of moduli space, one may break
supersymmetry by adding a tree level superpotential. We examine the dynamics by
deforming the theory on S^1 x R^3, and show that the infrared behavior of this
theory is an interacting CFT at small S^1. We argue that this continues to hold
at large S^1, and if so, that supersymmetry must remain unbroken. Our methods
also provide the microscopic origin of various superpotentials in SQCD on S^1 x
R^3 - which were previously obtained by using symmetry and holomorphy - and
resolve a long standing interpretational puzzle concerning a flux operator
discovered by Affleck, Harvey, and Witten. It is generated by a topological
excitation, a "magnetic bion", whose stability is due to fermion pair exchange
between its constituents. We also briefly comment on composite monopole
operators as leading effects in two dimensional anti-ferromagnets.


  We revisit the host galaxy of GRB031203 using a set of spectra obtained with
VLT. Assuming a Galactic color excess E(B-V)=0.72 (mag)in the direction of the
burst,we derive an internal extinction of about 0.4 (mag). After correcting for
reddening, we find an electronic density of 156 cm^{-3} and a temperature of
12443(K). With an ISM dominated by photo-ionization, we estimate a metallicity
of 12+Log[O/H]=8.12 and a star formation rate of 12.3 (M_{o}yr^{-1}). This
galaxy does not host a clearly detectable population of WR stars.


  We study various aspects of the renormalization of the Resonance Chiral
Theory at the one-loop level using a spin-one resonance propagator as a
concrete example. We calculate explicitly the one-loop self-energy within the
antisymmetric tensor field formalism, briefly discuss the general structure of
the corresponding propagator obtained by means of the Dyson re-summation and
give a classification of the propagating degrees of freedom. We find that
additional pathological poles (negative norm ghosts or tachyons) are
unavoidably generated and various scenarios according to their position are
possible. We also briefly comment on the eventual dynamical generation of the
opposite parity resonances which are frozen at the tree level and discuss the
role of appropriate symmetry which could prevent such a scenario.


  Recently, some papers in the literature have shown that, from a bimetric
theory of gravity, it is possible to produce massive gravitational waves which
generate a longitudinal component in a particular polarization of the wave.
After a review of previous works, in this paper the longitudinal response
function of interferometers for this particular polarization of the wave is
computed in two different gauges, showing the gauge invariance, and in its full
frequency dependence, with specific application to the Virgo and LIGO
interferometers.


  We discuss conformal properties of TMD operators and present the result of
the conformal rapidity evolution of TMD operators in the Sudakov region.


  We use renormalization group to calculate the reunion and survival exponents
of a set of random walkers interacting with a long range $1/r^2$ and a short
range interaction. These exponents are used to study the binding-unbinding
transition of polymers and the behavior of several quantum problems.


  A set valued representation of the Kronecker quiver is nothing but a quiver.
We apply the forgetful functor from vector spaces to sets and compare linear
with set valued representations of the Kronecker quiver.


  We introduce GSimCNN (Graph Similarity Computation via Convolutional Neural
Networks) for predicting the similarity score between two graphs. As the core
operation of graph similarity search, pairwise graph similarity computation is
a challenging problem due to the NP-hard nature of computing many graph
distance/similarity metrics. We demonstrate our model using the Graph Edit
Distance (GED) as the example metric. Experiments on three real graph datasets
demonstrate that our model achieves the state-of-the-art performance on graph
similarity search.


  We study the ground state properties and nonequilibrium dynamics of two
spinor bosonic impurities immersed in a one-dimensional bosonic gas upon
applying an interspecies interaction quench. For the ground state of two
non-interacting impurities we reveal signatures of attractive induced
interactions in both cases of attractive or repulsive interspecies
interactions, while a weak impurity-impurity repulsion forces the impurities to
stay apart. Turning to the quench dynamics we inspect the time-evolution of the
contrast unveiling the existence, dynamical deformation and the orthogonality
catastrophe of Bose polarons. We find that for an increasing postquench
repulsion the impurities reside in a superposition of two distinct two-body
configurations while at strong repulsions their corresponding two-body
correlation patterns show a spatially delocalized behavior evincing the
involvement of higher excited states. For attractive interspecies couplings,
the impurities exhibit a tendency to localize at the origin and remarkably for
strong attractions they experience a mutual attraction on the two-body level
that is imprinted as a density hump on the bosonic bath.


  We investigate the dynamics of the randomly pinned Fredrickson-Andersen model
on the Bethe lattice. We find a line of random pinning dynamical transitions
whose dynamical critical properties are in the same universality class of the
$A_2$ and $A_3$ transitions of Mode Coupling Theory. The $A_3$ behavior appears
at the terminal point, where the relaxation becomes logarithmic and the
relaxation time diverges exponentially. We explain the critical behavior in
terms of self-induced disorder and avalanches, strengthening the relationship
discussed in recent works between glassy dynamics and Random Field Ising Model.


  The modeling of users' behaviors is crucial in modern recommendation systems.
A lot of research focuses on modeling users' lifelong sequences, which can be
extremely long and sometimes exceed thousands of items. These models use the
target item to search for the most relevant items from the historical sequence.
However, training lifelong sequences in click through rate (CTR) prediction or
personalized search ranking (PSR) is extremely difficult due to the
insufficient learning problem of ID embedding, especially when the IDs in the
lifelong sequence features do not exist in the samples of training dataset.
Additionally, existing target attention mechanisms struggle to learn the
multi-modal representations of items in the sequence well. The distribution of
multi-modal embedding (text, image and attributes) output of user's interacted
items are not properly aligned and there exist divergence across modalities. We
also observe that users' search query sequences and item browsing sequences can
fully depict users' intents and benefit from each other. To address these
challenges, we propose a unified lifelong multi-modal sequence model called
SEMINAR-Search Enhanced Multi-Modal Interest Network and Approximate Retrieval.
Specifically, a network called Pretraining Search Unit (PSU) learns the
lifelong sequences of multi-modal query-item pairs in a pretraining-finetuning
manner with multiple objectives: multi-modal alignment, next query-item pair
prediction, query-item relevance prediction, etc. After pretraining, the
downstream model restores the pretrained embedding as initialization and
finetunes the network. To accelerate the online retrieval speed of multi-modal
embedding, we propose a multi-modal codebook-based product quantization
strategy to approximate the exact attention calculati


  Prompt Tuning is emerging as a scalable and cost-effective method to
fine-tune Pretrained Language Models (PLMs), which are often referred to as
Large Language Models (LLMs). This study benchmarks the performance and
computational efficiency of Prompt Tuning and baselines for multi-label text
classification. This is applied to the challenging task of classifying
companies into an investment firm's proprietary industry taxonomy, supporting
their thematic investment strategy. Text-to-text classification is frequently
reported to outperform task-specific classification heads, but has several
limitations when applied to a multi-label classification problem where each
label consists of multiple tokens: (a) Generated labels may not match any label
in the label taxonomy; (b) The fine-tuning process lacks permutation invariance
and is sensitive to the order of the provided labels; (c) The model provides
binary decisions rather than appropriate confidence scores. Limitation (a) is
addressed by applying constrained decoding using Trie Search, which slightly
improves classification performance. All limitations (a), (b), and (c) are
addressed by replacing the PLM's language head with a classification head,
which is referred to as Prompt Tuned Embedding Classification (PTEC). This
improves performance significantly, while also reducing computational costs
during inference. In our industrial application, the training data is skewed
towards well-known companies. We confirm that the model's performance is
consistent across both well-known and less-known companies. Our overall results
indicate the continuing need to adapt state-of-the-art methods to
domain-specific tasks, even in the era of PLMs with strong generalization
abilities. We release our codebase and a benchmarking dataset at
https://github.com/EQTPartners/PTEC.


  The Organic Materials Database (OMDB) is an open database hosting about
22,000 electronic band structures, density of states and other properties for
stable and previously synthesized 3-dimensional organic crystals. The web
interface of the OMDB offers various search tools for the identification of
novel functional materials such as band structure pattern matching and density
of states similarity search. In this work the OMDB is extended to include
magnetic excitation properties. For inelastic neutron scattering we focus on
the dynamical structure factor $S(\mathbf{q},\omega)$ which contains
information on the excitation modes of the material. We introduce a new dataset
containing atomic magnetic moments and Heisenberg exchange parameters for which
we calculate the spin wave spectra and dynamic structure factor with linear
spin wave theory and atomistic spin dynamics. We thus develop the materials
informatics tools to identify novel functional organic and metalorganic
magnets.


  The generalized density matrix (GDM) method is used to calculate
microscopically the parameters of the collective Hamiltonian. Higher order
anharmonicities are obtained consistently with the lowest order results, the
mean field [Hartree-Fock-Bogoliubov (HFB) equation] and the harmonic potential
[quasiparticle random phase approximation (QRPA)]. The method is applied to
soft spherical nuclei, where the anharmonicities are essential for restoring
the stability of the system, as the harmonic potential becomes small or
negative. The approach is tested in three models of increasing complexity: the
Lipkin model, model with factorizable forces, and the quadrupole plus pairing
model.


  Theories of physics can be considered viable if the initial value problem and
the energy conditions are formulated self-consistently. The former allow a
uniquely determined dynamical evolution of the system, and the latter guarantee
that causality is preserved and that "plausible" physical sources have been
considered. In this work, we consider the further degrees of freedom related to
curvature invariants and scalar fields in Extended Theories of Gravity (ETG).
These new degrees of freedom can be recast as effective perfect fluids that
carry different meanings with respect to the standard matter fluids generally
adopted as sources of the field equations. It is thus somewhat misleading to
apply the standard general relativistic energy conditions to this effective
energy-momentum, as the latter contains the matter content and a geometrical
quantity, which arises from the ETG considered. Here, we explore this subtlety,
extending on previous work, in particular, to cases with the contracted Bianchi
identities with diffeomorphism invariance and to cases with generalized
explicit curvature-matter couplings, which imply the non-conservation of the
energy-momentum tensor. Furthermore, we apply the analysis to specific ETGs,
such as scalar-tensor gravity, $f(R)$ gravity and modified Gauss-Bonnet
gravity. Interesting results appear such as matter that may exhibit unusual
thermodynamical features, for instance, and gravity that retains its attractive
character in the presence of negative pressures; or alternatively, we verify
that repulsive gravity may occur for standard matter.


  Let $G= (V,E)$ be a finite graph. For $d_0>0$ we say that $G$ is
$d_0$-regular, if every $v\in V$ has degree $d_0$. We say that $G$ is $(d_0,
d_1)$-regular, for $0<d_1<d_0$, if $G$ is $d_0$ regular and for every $v\in V$,
the subgraph induced on $v$'s neighbors is $d_1$-regular. Similarly, $G$ is
$(d_0, d_1,\ldots, d_{n-1})$-regular for $0<d_{n-1}<\ldots<d_1<d_0$, if $G$ is
$d_0$ regular and for every $1\leq i\leq n-1$, the joint neighborhood of every
clique of size $i$ is $d_i$-regular; In that case, we say that $G$ is an
$n$-dimensional hyper-regular graph (HRG). Here we define a new kind of graph
product, through which we build examples of infinite families of
$n$-dimensional HRG such that the joint neighborhood of every clique of size at
most $n-1$ is connected. In particular, relying on the work of Kaufman and
Oppenheim, our product yields an infinite family of $n$-dimensional HRG for
arbitrarily large $n$ with good expansion properties. This answers a question
of Dinur regarding the existence of such objects.


  The maximal Orlicz space such that the mixed logarithmic means of multiple
Fourier series for the functions from this space converge in $L_{1}$-norm is
found.


  We study time-dependent quantum transport in a correlated model system by
means of time-propagation of the Kadanoff-Baym equations for the nonequilibrium
many-body Green function. We consider an initially contacted equilibrium system
of a correlated central region coupled to tight-binding leads. Subsequently a
time-dependent bias is switched on after which we follow in detail the
time-evolution of the system. Important features of the Kadanoff-Baym approach
are 1) the possibility of studying the ultrafast dynamics of transients and
other time-dependent regimes and 2) the inclusion of exchange and correlation
effects in a conserving approximation scheme. We find that initial correlation
and memory terms due to many-body interactions have a large effect on the
transient currents. Furthermore the value of the steady state current is found
to be strongly dependent on the approximation used to treat the electronic
interactions.


  We study signals for the production of superparticles at the Tevatron in
supergravity scenarios based on the Grand Unified group SO(10). The breaking of
this group introduces extra contributions to the masses of all scalars,
described by a single new parameter. We find that varying this parameter can
considerably change the size of various expected signals studied in the
literature, with different numbers of jets and/or charged leptons in the final
state. The ratios of these signal can thus serve as a diagnostic to detect or
constrain deviations from the much--studied scenario where all scalar masses
are universal at the GUT scale. Moreover, under favorable circumstances some of
these signals, and/or new signals involving hard $b-$jets, should be observable
at the next run of the Tevatron collider even if the average scalar mass lies
well above the gluino mass.


  Let $D$ be a division ring with center $F$. We say that $D$ is a {\em
division ring of type $2$} if for every two elements $x, y\in D,$ the division
subring $F(x, y)$ is a finite dimensional vector space over $F$. In this paper
we investigate multiplicative subgroups in such a ring.


  In this work, Fe100-xNix nanoparticle systems in the invar region (x = 29,
32, and 37) were prepared by the method of chemical co-precipitation. X-Ray
Diffraction (XRD) patterns confirmed the coexistence of both bcc and fcc phases
for x = 29 and 32. However, only fcc phase was observed for x = 37. Scanning
Electron Microscope (SEM) images indicated that the particle size is ~ 120-500
nm, and is almost independent of x. M\"ossbauer spectroscopy (MS) on the
prepared nanoparticles indicated the development of a paramagnetic phase
characteristic of the low-spin (antitaenite) fcc phase, in addition to the
magnetic components characteristic of the bcc phase and the high-spin fcc
phases. Since it is not possible to resolve the low- spin fcc phase from the
high-spin fcc phase in XRD patterns, MS proves to be an effective tool for
studying the prepared nanoparticle systems.


  We examine the velocity width of cool X-ray emitting material using
XMM-Newton Reflection Grating Spectrometer (RGS) spectra of a sample of
clusters and group of galaxies and elliptical galaxies. Improving on our
previous analyses, we apply a spectral model which accounts for broadening due
to the spatial extent of the source. With both conventional and Markov Chain
Monte Carlo approaches we obtain limits, or in a few cases measurements, of the
velocity broadening of the coolest X-ray material. In our sample, we include
new observations targeting objects with compact, bright, line-rich cores. One
of these, MACSJ2229.7-2755, gives a velocity limit of 280 km/s at the 90 per
cent confidence level. Other systems with limits close to 300 km/s include
A1835, NGC4261 and NGC4472. For more than a third of the targets we find limits
better than 500 km/s. HCG62, NGC1399 and A3112 show evidence for ~400 km/s
velocity broadening. For a smaller sample of objects, we use
continuum-subtracted emission line surface brightness profiles to account for
the spatial broadening. Although there are significant systematic errors
associated with the technique (~150 km/s), we find broadening at the level of
280 to 500 km/s in A3112, NGC1399 and NGC4636.


  We present a non-linear Langevin model to investigate the early-stage
dynamics of electrified polymer jets in electrospinning experiments. In
particular, we study the effects of air drag force on the uniaxial elongation
of the charged jet, right after ejection from the nozzle. Numerical simulations
show that the elongation of the jet filament close to the injection point is
significantly affected by the non-linear drag exerted by the surrounding air.
These result provide useful insights for the optimal design of current and
future electrospinning experiments.


  We give a natural construction and a direct proof of the Adams isomorphism
for equivariant orthogonal spectra. More precisely, for any finite group G, any
normal subgroup N of G, and any orthogonal G-spectrum X, we construct a natural
map A of orthogonal G/N-spectra from the homotopy N-orbits of X to the derived
N-fixed points of X, and we show that A is a stable weak equivalence if X is
cofibrant and N-free. This recovers a theorem of Lewis, May, and Steinberger in
the equivariant stable homotopy category, which in the case of suspension
spectra was originally proved by Adams. We emphasize that our Adams map A is
natural even before passing to the homotopy category. One of the tools we
develop is a replacement-by-Omega-spectra construction with good functorial
properties, which we believe is of independent interest.