  It is known that perturbative expansions in powers of the coupling in quantum
mechanics (QM) and quantum field theory (QFT) are asymptotic series. This can
be useful at weak coupling but fails at strong coupling. In this work, we
present two types of series expansions valid at strong coupling. We apply the
series to a basic integral as well as a QM path integral containing a quadratic
and quartic term with coupling constant $\lambda$. The first series is the
usual asymptotic one, where the quartic interaction is expanded in powers of
$\lambda$. The second series is an expansion of the quadratic part where the
interaction is left alone. This yields an absolutely convergent series in
inverse powers of $\lambda$ valid at strong coupling. For the basic integral,
we revisit the first series and identify what makes it diverge even though the
original integral is finite. We fix the problem and obtain, remarkably, a
series in powers of the coupling which is absolutely convergent and valid at
strong coupling. We explain how this series avoids Dyson's argument on
convergence. We then consider the QM path integral (discretized with time
interval divided into $N$ equal segments). As before, the second series is
absolutely convergent and we obtain analytical expressions in inverse powers of
$\lambda$ for the $n$th order terms by taking functional derivatives of
generalized hypergeometric functions. The expressions are functions of $N$ and
we work them out explicitly up to third order. The general procedure has been
implemented in a Mathematica program that generates the expressions at any
order $n$. We present numerical results at strong coupling for different values
of $N$ starting at $N=2$. The series matches the exact numerical value for a
given $N$ (up to a certain accuracy). The continuum is formally reached when
$N\to \infty$ but in practice this can be reached at small $N$.


  In this paper we prove some Ramanujan-type formulas for $1/\pi$ but without
using the theory of modular forms. Instead we use the WZ-method created by H.
Wilf and D. Zeilberger and find some hypergeometric functions in two variables
which are second components of WZ-pairs that can be certified using
Zeilberger's EKHAD package. These certificates have an additional property
which allows us to get generalized Ramanujan-type series which are routinely
proven by computer. We call these second hypergeometric components of the
WZ-pairs generators. Finding generators seems a hard task but using a kind of
experimental research (explained below), we have succeeded in finding some of
them. Unfortunately we have not found yet generators for the most impressive
Ramanujan's formulas. We also prove some interesting binomial sums for the
constant $1/\pi^2$. Finally we rewrite many of the obtained series using
pochhammer symbols and study the rate of convergence.


  In this short article, we study the extremal behavior $F_\Gamma(n)$ of
divisibility functions $D_\Gamma$ introduced by the first author for finitely
generated groups $\Gamma$. We show finitely generated subgroups of $\GL(m,K)$
for an infinite field $K$ have at most polynomial growth for the function
$F_\Gamma(n)$. Consequently, we obtain a dichotomy for the growth rate of $\log
F_\Gamma(n)$ for finitely generated subgroups of $\GL(n,\C)$. We also show that
if $F_\Gamma(n) \preceq \log \log n$, then $\Gamma$ is finite. In contrast,
when $\Gamma$ contains an element of infinite order, $\log n \preceq
F_\Gamma(n)$. We end with a brief discussion of some geometric motivation for
this work.


  Creative coding is a rapidly expanding domain for both artistic expression
and computational education. Numerous libraries and IDEs support creative
coding, however there has been little consideration of how the environments
themselves might be designed to serve these twin goals. To investigate this
gap, we implemented and used an experimental editor to teach a sequence of
college and high-school creative coding courses. In the first year, we
conducted a log analysis of student work (n=39) and surveys regarding
prospective features (n=25). These guided our implementation of common
enhancements (e.g. color pickers) as well as uncommon ones (e.g. bidirectional
shape editing). In the second year, we studied the effects of these features
through logging (n=39+) and survey (n=23) studies. Reflecting on the results,
we identify opportunities to improve creativity- and novice-focused IDEs and
highlight tensions in their design -- as in tools that augment artistry or
efficiency but may be perceived as hindering learning.


  We derive a nonperturbative transverse momentum distribution for partons
using a potential model to describe the quark-quark interaction inside the
proton. We use this distribution to calculate the diferential cross-section of
$\pi^0$-production for intermediate values of transverse momentum in $p-p$
collisions at high energies. Assuming a variable string tension constant for
the quark-quark potential we obtain a very good description of the experimental
data at different energies. The corresponding values of the mean transverse
momentum of the partons are essentially lower than those obtained using a
Gaussian transverse momentum parton distribution.


  The discrete cosine transform (DCT) is a widely-used and important signal
processing tool employed in a plethora of applications. Typical fast algorithms
for nearly-exact computation of DCT require floating point arithmetic, are
multiplier intensive, and accumulate round-off errors. Recently proposed fast
algorithm arithmetic cosine transform (ACT) calculates the DCT exactly using
only additions and integer constant multiplications, with very low area
complexity, for null mean input sequences. The ACT can also be computed
non-exactly for any input sequence, with low area complexity and low power
consumption, utilizing the novel architecture described. However, as a
trade-off, the ACT algorithm requires 10 non-uniformly sampled data points to
calculate the 8-point DCT. This requirement can easily be satisfied for
applications dealing with spatial signals such as image sensors and biomedical
sensor arrays, by placing sensor elements in a non-uniform grid. In this work,
a hardware architecture for the computation of the null mean ACT is proposed,
followed by a novel architectures that extend the ACT for non-null mean
signals. All circuits are physically implemented and tested using the Xilinx
XC6VLX240T FPGA device and synthesized for 45 nm TSMC standard-cell library for
performance assessment.


  We classify the time complexities of three important decoding problems for
quantum stabilizer codes. First, regardless of the channel model, quantum
bounded distance decoding is shown to be NP-hard, like what Berlekamp, McEliece
and Tilborg did for classical binary linear codes in 1978. Then over the
depolarizing channel, the decoding problems for finding a most likely error and
for minimizing the decoding error probability are also shown to be NP-hard. Our
results indicate that finding a polynomial-time decoding algorithm for general
stabilizer codes may be impossible, but this, on the other hand, strengthens
the foundation of quantum code-based cryptography.


  "Mayer waves" are long-period (6 to 12 seconds) oscillations in arterial
blood pressure, which have been observed and studied for more than 100 years in
the cardiovascular system of humans and other mammals. A mathematical model of
the human cardiovascular system is presented, incorporating parameters
relevantto the onset of Mayer waves. The model is analyzed using methods of
Lyapunov stability and Hopf bifurcation theory. The analysis shows that
increase in the gain of the baroreflex feedback loop controlling venous volume
may lead to the onset of oscillations, while changes in the other parameters
considered do not affect stability of the equilibrium state. The results agree
with clinical observations of Mayer waves in human subjects, both in the period
of the oscillations and in the observed age-dependence of Mayer waves. This
leads to a proposed explanation of their occurrence, namely that Mayer waves
are a "gain-induced instability".


  We report on a series of twenty ~10^5 c/s, 0.125 msec time-resolution RXTE
observations of the Z source and low-mass X-ray binary Scorpius X-1. Twin
kilohertz quasi-periodic oscillation (QPO) peaks are obvious in nearly all
observations. We find that the peak separation is not constant, as expected in
some beat-frequency models, but instead varies from ~310 to ~230 Hz when the
centroid frequency of the higher-frequency peak varies from ~875 to ~1085 Hz.
We detect none of the additional QPO peaks at higher frequencies predicted in
the photon bubble model (PBM), with best-case upper limits on the peaks' power
ratio of 0.025. We do detect, simultaneously with the kHz QPO, additional QPO
peaks near 45 and 90 Hz whose frequency increases with mass accretion rate. We
interpret these as first and second harmonics of the so-called
horizontal-branch oscillations well known from other Z sources and usually
interpreted in terms of the magnetospheric beat-frequency model (BFM). We
conclude that the magnetospheric BFM and the PBM are now unlikely to explain
the kHz QPO in Sco X-1. In order to succeed in doing so, any BFM involving the
neutron star spin (unseen in Sco X-1) will have to postulate at least one
additional unseen frequency, beating with the spin to produce one of the kHz
peaks.


  The giant planets of the solar system likely played a large role in shaping
the architecture of the terrestrial planets. Using an updated collision model,
we conduct a suite of high resolution N-body integrations to probe the
relationship between giant planet mass, and terrestrial planet formation and
system architecture. We vary the mass of the planets that reside at Jupiter's
and Saturn's orbit and examine the effects on the interior terrestrial system.
We find a correlation between the mass of the exterior giant planets and the
collision history of the resulting planets, which holds implications for the
planet's properties. More massive giants also produce terrestrial planets that
are on smaller, more circular orbits. We do not find a strong correlation
between exterior giant planet mass and the number of Earth-analogs (analogous
in mass and semi-major axis) produced in the system. These results allow us to
make predictions on the nature of terrestrial planets orbiting distant Sun-like
star systems that harbor giant planet companions on long orbits---systems which
will be a priority for NASA's upcoming Wide-Field Infrared Space Telescope
(WFIRST) mission.


  We analyze microscopically the valence and impurity band models of
ferromagnetic (Ga,Mn)As. We find that the tight-binding Anderson approach with
conventional parameterization and the full potential LDA+U calculations give a
very similar picture of states near the Fermi energy which reside in an
exchange-split sp-d hybridized valence band with dominant orbital character of
the host semiconductor; this microscopic spectral character is consistent with
the physical premise of the k.p kinetic-exchange model. On the other hand, the
various models with a band structure comprising an impurity band detached from
the valence band assume mutually incompatible microscopic spectral character.
By adapting the tight-binding Anderson calculations individually to each of the
impurity band pictures in the single Mn impurity limit and then by exploring
the entire doping range we find that a detached impurity band does not persist
in any of these models in ferromagnetic (Ga,Mn)As.


  In this paper we prove bilinear Strichartz estimates for a solution to the
Schr{\"o}dinger map problem whose size is small in the critical Strichartz
space $| |\nabla|^{\frac{d - 2}{2}} \psi_{x} |_{L_{t,x}^{\frac{2(d + 2)}{d}}}$.
These estimates will be useful in an upcoming paper in proving a local well -
posedness result. Bilinear estimates make use of an argument similar to the
argument found in Planchon and Vega (2009). We use the same gauges as in
Bejenaru, Ionescu and Kenig (2007), Bejenaru et al. (2011), and Smith.


  We investigate the problem of pure gravitational localization of matter
fields within the 5D standing wave braneworld generated by gravity coupled to a
phantom-like scalar field. We show that in the case of increasing warp factor
there exist normalizable zero modes of spin-0, -1/2, -1, and -2 fields on the
brane.


  A general theory of homeoidally striated density profiles where no divergence
occurs, is adapted to cuspy density profiles, with a suitable choice of the
scaling density and the scaling radius. A general formulation of some physical
parameters, such as angular-momentum vector, rotational-energy tensor (both
calculated in connection with a special class of rotational velocity fields),
inertia tensor, and self potential-energy tensor, is performed. Other
potential-energy tensors involving two density profiles where the boundaries
are similar and similarly placed, are also expressed. Explicit results are
attained for three special cases of physical interest which fit to a good
extent the results of high-resolution simulations for dark matter haloes, and a
class of density profiles, which closely approximate the de Vaucouleurs
$r^{1/4}$ law for elliptical galaxies. The virial theorem in tensor form for
two-component systems is written for each subsystem, and applied to giant
elliptical galaxies. The predicted velocity dispersion along the line of sight,
in the limiting case where a principal axis points towards the observer, is
found to be consistent with observations except for (intrinsic) $E7$
configurations where the major axis points towards the observer. If dark matter
haloes host an amount of undetected baryons about twice as massive as the
stellar subsystem, and undetected baryons trace non baryonic matter therein,
two main consequences arise, namely (i) velocity dispersions along the line of
sight are lower than in absence of undetected baryons, and (ii) dark matter
haloes are dynamically ``hotter'' than stellar ellipsoids, the transition
occurring when the amount of undetected baryons is about one and a half times
that of the stellar subsystem.


  Kundt spacetimes are of great importance to General Relativity. We show that
a Kundt spacetime is a Lorentz manifold with a non-singular isotropic geodesic
vector field having its orthogonal distribution integrable and determining a
totally geodesic foliation. We give the local structure of Kundt spacetimes and
some properties of left invariant Kundt structures on Lie groups. Finally, we
classify all left invariant Kundt structures on three dimensional simply
connected unimodular Lie groups.


  Dispersion coefficients between the alkali metal atoms (Li-Rb) and
alkaline-earth metal atoms (Be-Sr) are evaluated using matrix elements computed
from frozen core configuration interaction calculations. Besides dispersion
coefficients with both atoms in their respective ground states, dispersion
coefficients are also given for the case where one atom is in its ground state
and the other atom is in a low lying excited state.


  Far-infrared and optical [O III] lines are useful temeprature-density
diagnostics of nebular as well as dust obscured astrophysical sources. Fine
structure transitions among the ground state levels 1s^22s^22p^3 \ ^3P_{0,1,2}
give rise to the 52 and 88 micron lines, whereas transitions among the
$^3P_{0,1,2}, ,^1D_2, ^1S_0$ levels yield the well-known optical lines 4363,
4959 and 5007 Angstroms. These lines are excited primarily by electron impact
excitation. But despite their importance in nebular diagnostics collision
strengths for the associated fine structure transitions have not been computed
taking full account of relativistic effects. We present Breit-Pauli R-matrix
calculations for the collision strengths with highly resolved resonance
structures. We find significant differences of up to 20% in the Maxwellian
averaged rate coefficients from previous works. We also tabulate these to lower
temperatures down to 100 K to enable determination of physical conditions in
cold dusty environments such photo-dissociation regions and ultra-luminous
infrared galaxies observed with the Herschel space observatory. We also examine
the effect of improved collision strengths on temperature and density sensitive
line ratios.


  To use heterogeneous hardware, programmers needed sufficient technical skills
such as OpenMP, CUDA, and OpenCL. Therefore, I have proposed
environment-adaptive software that enables high-performance operation by
automatically converting and configuring the code once written, and have been
working on automatic conversion and proper placement. However, until now, where
to initially place the converted application has been considered, but the
overall optimal placement has not been considered in consideration of the
placement status of other users. In this paper, as a new element of
environment-adaptive software, I study the relocation during operation, which
improves the overall user satisfaction by considering the placement of other
users, using a linear programming method. It was confirmed that it can be
properly rearranged through simulation experiments.


  For small-scale liquid rockets, pressure-fed systems are commonly favoured
due to their simplicity and low weight. In such systems, accurate regulation of
both tank and injector pressures over a wide range of upstream pressures is
critical $-$ more accurate regulation allows for higher engine efficiency and
minimal tank mass, thus improving flight performance. However, existing methods
such as dome-loaded pressure regulators are inflexible, or require extensive
characterization to function accurately. These methods also suffer from limited
orifice size, droop, and slow reaction times, making them unsuitable for
throttling by adjusting pressures in flight, which are increasingly important
as propulsively landing rockets become more common. To overcome these
challenges, we designed an electronic pressure regulator (eReg), a multi-input
multi-output system utilising closed loop feedback to accurately control
downstream pressures. Our design is simple, low-cost and robust: with a single
ball valve actuated by a motor, we regulate both gaseous pressurant and
cryogenic liquid propellant at high flow rates (1.14 kg/s of liquid; 0.39 kg/s
of gas) and upstream pressures (310 bar). Using 2 eRegs to regulate propellant
tank pressures, and 2 eRegs for regulating propellant flow to the engine, we
demonstrated our system's ability, in a static fire test, to regulate pressures
accurately (within 0.2 bar) while simultaneously throttling our engine. To the
best of our knowledge, this is the first time any undergraduate team has
successfully throttled a liquid bipropellant engine.


  We started a multi-scale analysis of G202.3+2.5, an intertwined filamentary
region of Monoceros OB1. In Paper I, we examined the distributions of dense
cores and protostars and found enhanced star formation (SF) activity in the
junction region of the filaments. In this second paper, we aim to unveil the
connections between the core and filament evolutions, and between the filament
dynamics and the global evolution of the cloud. We characterise the gas
dynamics and energy balance using Herschel and WISE observations and molecular
tracers observed with the IRAM 30m and TRAO 14m telescopes. The velocity field
of the cloud is examined and velocity-coherent structures are put in
perspective with the cloud environment. Two main velocity components (VCs) are
revealed, well separated in the north and merged around the location of intense
N2H+ emission where Paper I found the peak of SF activity. The relative
position of the two VCs along the sightline, and the velocity gradient in N2H+
emission imply that the VCs have been undergoing collision for ~10^5 yrs. The
dense gas where N2H+ is detected is interpreted as the compressed region
between the two filaments, which corresponds to a high mass inflow rate of
~1e-3 Msun/yr and possibly leads to an increase in its SF efficiency. We
identify a protostar in the junction region that possibly powers two crossed
intermittent outflows. We show that the HII region around the nearby cluster
NCG 2264 is still expanding and its role in the collision is examined. However,
we cannot rule out the idea that the collision arises mostly from the global
collapse of the cloud. The (sub-)filament-scale observables examined in this
paper reveal a collision between G202.3+2.5 sub-structures and its probable
role in feeding the cores in the junction region. One must now characterise the
cloud morphology, its fragmentation, and magnetic field, all at high
resolution.


  We have searched for the pair production of first generation scalar
leptoquarks using the full data set (123 pb**-1) collected with the D0 detector
at the Fermilab Tevatron during 1992-1996. We observe no candidates, consistent
with the expected background. We combine these new results from the ee + jets
and enu + jets channels with the published nunu + jets result to obtain a 95%
CL upper limits on the LQ pair production cross section as a function of mass
and beta, the branching ratio to a charged lepton and a quark. Comparing to the
NLO theory predictions, we set 95% CL lower limits on the LQ mass of 225, 204,
and 79 GeV/c**2 for beta=1, 1/2, and 0, respectively. The results of this
analysis rule out an interpretation of the excess of high Q**2 events at HERA
as leptoquarks with LQ mass below 200 GeV/c**2 for values of beta > 0.4.


  Towards better unsupervised domain adaptation (UDA). Recently, researchers
propose various domain-conditioned attention modules and make promising
progresses. However, considering that the configuration of attention, i.e., the
type and the position of attention module, affects the performance
significantly, it is more generalized to optimize the attention configuration
automatically to be specialized for arbitrary UDA scenario. For the first time,
this paper proposes EvoADA: a novel framework to evolve the attention
configuration for a given UDA task without human intervention. In particular,
we propose a novel search space containing diverse attention configurations.
Then, to evaluate the attention configurations and make search procedure
UDA-oriented (transferability + discrimination), we apply a simple and
effective evaluation strategy: 1) training the network weights on two domains
with off-the-shelf domain adaptation methods; 2) evolving the attention
configurations under the guide of the discriminative ability on the target
domain. Experiments on various kinds of cross-domain benchmarks, i.e.,
Office-31, Office-Home, CUB-Paintings, and Duke-Market-1510, reveal that the
proposed EvoADA consistently boosts multiple state-of-the-art domain adaptation
approaches, and the optimal attention configurations help them achieve better
performance.


  Searching for network width is an effective way to slim deep neural networks
with hardware budgets. With this aim, a one-shot supernet is usually leveraged
as a performance evaluator to rank the performance \wrt~different width.
Nevertheless, current methods mainly follow a manually fixed weight sharing
pattern, which is limited to distinguish the performance gap of different
width. In this paper, to better evaluate each width, we propose a locally free
weight sharing strategy (CafeNet) accordingly. In CafeNet, weights are more
freely shared, and each width is jointly indicated by its base channels and
free channels, where free channels are supposed to loCAte FrEely in a local
zone to better represent each width. Besides, we propose to further reduce the
search space by leveraging our introduced FLOPs-sensitive bins. As a result,
our CafeNet can be trained stochastically and get optimized within a min-min
strategy. Extensive experiments on ImageNet, CIFAR-10, CelebA and MS COCO
dataset have verified our superiority comparing to other state-of-the-art
baselines. For example, our method can further boost the benchmark NAS network
EfficientNet-B0 by 0.41\% via searching its width more delicately.


  Plasmonics, the science and technology of the interaction of light with
metallic objects, is fundamentally changing the way we can detect, generate and
manipulate light. Although the field is progressing swiftly, thanks to the
availability of nanoscale manufacturing and analysis methods, fundamental
properties such as the plasmonic excitations' symmetries cannot be accessed
directly, leading to a partial, sometimes incorrect, understanding of their
properties. Here we overcome this limitation by deliberately shaping the wave
function of an electron beam to match a plasmonic excitations' symmetry in a
modified transmission electron microscope. We show experimentally and
theoretically that this offers selective detection of specific plasmon modes
within metallic nanoparticles, while excluding modes with other symmetries.
This method resembles the widespread use of polarized light for the selective
excitation of plasmon modes with the advantage of locally probing the response
of individual plasmonic objects and a far wider range of symmetry selection
criteria.


  A mean-field monomer-dimer model which includes an attractive interaction
among both monomers and dimers is introduced and its exact solution rigorously
derived. The Heilmann-Lieb method for the pure hard-core interacting case is
used to compute upper and lower bounds for the pressure. The bounds are shown
to coincide in the thermodynamic limit for a suitable choice of the monomer
density m. The consistency equation characterising m is studied in the phase
space (h, J), where h tunes the monomer potential and J the attractive
potential. The critical point and exponents are computed and show that the
model is in the mean-field ferromagnetic universality class.


  We study the reionization of Helium II by quasars using a numerical approach
that combines 3D radiative transfer calculations with cosmological
hydrodynamical simulations. Sources producing the ionizing radiation are
selected according to an empirical quasar luminosity function and are assigned
luminosities according to their intrinsic masses. We present models in which
these parameters are varied and examine characteristics of the resultant
reionization process that distinguish the various cases. In addition, we
extract artificial spectra from the simulations and quantify statistical
properties of the spectral features in each model. We find that the most
important factor affecting the evolution of He II reionization is the
cumulative number of ionizing photons that are produced by the sources.
Comparisons between He II opacities measured observationally and those obtained
by our analysis reveal that the available ranges in plausible values for the
parameters provide enough leeway to provide a satisfactory match. However, one
property common to all our calculations is that the epoch of Helium II
reionization must have occurred at a redshift between 3 < z < 4. If so, future
observational programs will be able to directly trace the details of the
ionization history of helium and probe the low density phase of the
intergalactic medium during this phase of the evolution of the Universe.


  A Banach space X is said to have the Tsirelson property if it does not
contain subspaces that are isomorphic to l_{p}, p in [1,infty) or c_{0}. The
article contains a quite simple method to producing Banach spaces with the
Tsirelson property.


  We define a new notion of entropy for operators on Fock spaces and positive
definite multi-Toeplitz kernels on free semigroups. This is studied in
connection with factorization theorems for (multi-Toeplitz, multi-analytic,
etc.) operators on Fock spaces. These results lead to entropy inequalities and
entropy formulas for positive definite multi-Toeplitz kernels on free
semigroups (resp.multi-Toeplitz operators) and consequences concerning the
extreme points of the unit ball of the noncommutative analytic Toeplitz algebra
F_n^\infty.
  We obtain several geometric characterizations of the multivariable central
intertwining lifting, a maximum principle, and a permanence principle for the
noncommutative commutant lifting theorem. Under certain natural conditions, we
find explicit forms for the maximal entropy solution (and its entropy) for this
multivariable commutant lifting theorem.
  All these results are used to solve maximal entropy interpolation problems in
several variables. We obtain explicit forms for the maximal entropy solution
(as well as its entropy) of the Sarason, Caratheodory-Schur, and
Nevanlinna-Pick type interpolation problems for the noncommutative
(resp.commutative) analytic Toeplitz algebra F_n^\infty (resp.W_n^\infty)and
their tensor products with B(H,K). In particular, we provide explicit forms for
the maximal entropy solutions of several interpolation (resp.optimization)
problems on the unit ball of C^n.


  We calculate the complete three-loop O(alpha_s^3) anomalous dimension matrix
for the dimension-five dipole operators that arise in the Standard Model after
integrating out the top quark and the heavy electroweak bosons. Our computation
completes the three-loop anomalous dimension matrix of operators that govern
low-energy |Delta F| = 1 flavor-changing processes, and represents an important
ingredient of the next-to-next-to-leading order QCD analysis of the Bbar -> X_s
gamma decay.


  Aims: We study the fragmentation and dynamical properties of a massive
starless gas clump at the onset of high-mass star formation. Methods: Based on
Herschel continuum data we identify a massive gas clump that remains
far-infrared dark up to 100mum wavelengths. The fragmentation and dynamical
properties are investigated by means of Plateau de Bure Interferometer and
Nobeyama 45m single-dish spectral line and continuum observations. Results: The
massive gas reservoir fragments at spatial scales of ~18000AU in four cores.
Comparing the spatial extent of this high-mass region with intermediate- to
low-mass starless cores from the literature, we find that linear sizes do not
vary significantly over the whole mass regime. However, the high-mass regions
squeeze much more gas into these similar volumes and hence have orders of
magnitude larger densities. The fragmentation properties of the presented
low-to high-mass regions are consistent with gravitational instable Jeans
fragmentation. Furthermore, we find multiple velocity components associated
with the resolved cores. Recent radiative transfer hydrodynamic simulations of
the dynamic collapse of massive gas clumps also result in multiple velocity
components along the line of sight because of the clumpy structure of the
regions. This result is supported by a ratio between viral and total gas mass
for the whole region <1. Conclusions: This apparently still starless high-mass
gas clump exhibits clear signatures of early fragmentation and dynamic collapse
prior to the formation of an embedded heating source. A comparison with regions
of lower mass reveals that the linear size of star-forming regions does not
necessarily have to vary much for different masses, however, the mass
reservoirs and gas densities are orders of magnitude enhanced for high-mass
regions compared to their lower-mass siblings.


  We generate by computer a basis of invariants for the fundamental
representations of the exceptional Lie groups E(6) and E(7), up to degree 18.
We discuss the relevance of this calculation for the study of supersymmetric
gauge theories, and revisit the self-dual exceptional models. We study the
chiral ring of G(2) to degree 13, as well as a few classical groups. The
homological dimension of a ring is a natural estimator of its complexity and
provides a guideline for identifying theories that have a good chance to be
amenable to a solution.


  We discuss three closely related questions; i)~Given a conformal field
theory, how may we deform it? ii)~What are the symmetries of string theory? and
iii)~Does string theory have free parameters? We show that there is a distinct
deformation of the stress tensor for every solution to the linearised covariant
equations of motion for the massless modes of the Bosonic string, and use this
result to discuss the symmetries of the string. We also find an additional
finite dimensional space of deformations which may correspond to free
parameters of string theory, or alternatively may be interpreted as topological
degrees of freedom, perhaps analogous to the isolated states found in two
dimensions.


  Fast and accurate evaluation of free energy has broad applications from drug
design to material engineering. Computing the absolute free energy is of
particular interest since it allows the assessment of the relative stability
between states without the use of intermediates. In this letter, we introduce a
general framework for calculating the absolute free energy of a state. A key
step of the calculation is the definition of a reference state with tractable
deep generative models using locally sampled configurations. The absolute free
energy of this reference state is zero by design. The free energy for the state
of interest can then be determined as the difference from the reference. We
applied this approach to both discrete and continuous systems and demonstrated
its effectiveness. It was found that the Bennett acceptance ratio method
provides more accurate and efficient free energy estimations than approximate
expressions based on work. We anticipate the method presented here to be a
valuable strategy for computing free energy differences.


  Large language models (LLMs) show their powerful automatic reasoning and
planning capability with a wealth of semantic knowledge about the human world.
However, the grounding problem still hinders the applications of LLMs in the
real-world environment. Existing studies try to fine-tune the LLM or utilize
pre-defined behavior APIs to bridge the LLMs and the environment, which not
only costs huge human efforts to customize for every single task but also
weakens the generality strengths of LLMs. To autonomously ground the LLM onto
the environment, we proposed the Self-Driven Grounding (SDG) framework to
automatically and progressively ground the LLM with self-driven skill learning.
SDG first employs the LLM to propose the hypothesis of sub-goals to achieve
tasks and then verify the feasibility of the hypothesis via interacting with
the underlying environment. Once verified, SDG can then learn generalized
skills with the guidance of these successfully grounded subgoals. These skills
can be further utilized to accomplish more complex tasks which fail to pass the
verification phase. Verified in the famous instruction following task
set-BabyAI, SDG achieves comparable performance in the most challenging tasks
compared with imitation learning methods that cost millions of demonstrations,
proving the effectiveness of learned skills and showing the feasibility and
efficiency of our framework.


  We present a new dispersion relation for photons that are nonlinearly
interacting with a radiation gas of arbitrary intensity due to photon-photon
scattering. It is found that the photon phase velocity decreases with
increasing radiation intensity, it and attains a minimum value in the limit of
super-intense fields. By using Hamilton's ray equations, a self-consistent
kinetic theory for interacting photons is formulated. The interaction between
an electromagnetic pulse and the radiation gas is shown to produce pulse
self-compression and nonlinear saturation. Implications of our new results are
discussed.


  We consider the curvatures 2 form asociated with AdSL4 valued one-form gauge
connetion, and then we construct a four-dimensional action that generalize the
Einstein-Hilbert gravity. It is shown that the Maxwell extension of Einstein
gravity can be obtained from AdSL4-gravity making use of the Inonu-Wigner
contraction method. In the same way, by gauging the AdSL5 spacetime algebra,
the Einstein-Hilbert gravity is extended including the vector fields kab and ha
which are associated with non-Abelian tensors and non Abelian vectors charges
in the AdSL5 algebra. The B5 extension of Einstein gravity can be obtained from
AdSL5 gravity using of the above mentioned contraction procedure. Some aspects
of a gravity based on the algebra AdSL6 are considered in an appendix.


  This literature review will discuss the use of deep learning methods for
image reconstruction using fMRI data. More specifically, the quality of image
reconstruction will be determined by the choice in decoding and reconstruction
architectures. I will show that these structures can struggle with adaptability
to various input stimuli due to complicated objects in images. Also, the
significance of feature representation will be evaluated. This paper will
conclude the use of deep learning within visual decoding and reconstruction is
highly optimal when using variations of deep neural networks and will provide
details of potential future work.


  A program is outlined, and first results described, in which fully
three-dimensional, time dependent simulations of hydrodynamic turbulence are
used as a basis for theoretical investigation of the physics of turbulence in
stars. The inadequacy of the treatment of turbulent convection as a diffusive
process is discussed. A generalization to rotation and magnetohydrodynamics is
indicated, as are connection to simulations of 3D stellar atmospheres.


  The bolometric luminosity of active galactic nuclei (AGN) is difficult to
determine and various approximations have been used to calibrate it against
different observed properties. Here I combine theoretical calculations of
optically thick, geometrically thin accretion disks, and observed X-ray
properties of AGN, to provide new bolometric correction factors (\kbol) over a
large range of black hole (BH) mass, accretion rate, and spin. This is
particularly important in cases where the mass accretion rate cannot be
determined from the observed spectral energy distribution, and in cases where
luminosity-independent correction factors have been used. Simple powerlaw
approximations of \kbol\ are provided for L(5100\AA), L(3000\AA), L(1400\AA),
L(2-10 keV) and L(narrow \hb). In all cases the uncertainties are large mostly
due to the unknown BH spin. Prior knowledge of the BH mass reduces the
uncertainty considerably.


  Various structures are visible within Spectro-Polarimetric High-contrast
Exoplanet REsearch instrument (SPHERE) images that are not always
straightforward to interpret. In this article we present a review of these
features and demonstrate their origin using simulations. We also identify which
expected or unexpected features are limiting the contrast reached by the
instrument and how they may be tackled. This vision paves the way to designing
a future upgrade of the SPHERE instrument and the next generation of
high-contrast instruments such as those planned for the Extremely Large
Telescope (ELT).


  In many cases the correct theoretical description of flexoelectricity
requires the consideration of the finite size of a body and is reduced to the
solution of boundary problems for partial differential equations. Generally
speaking, in this case one should solve jointly the equations of polarization
equilibrium and equations of elastic equilibrium. However, due to the fact that
typically flexoelectric moduli are very small, usually one can consider the
solution of polarization equilibrium equations at a given elastic strain
(direct flexoelectric effect) or the solution of elastic equilibrium equations
at given polarization (converse flexoelectric effect). Derivation of the
polarization equilibrium equations and boundary conditions for them can be made
in the quite usual way. Solution of these equations usually is not too
difficult problem. On the contrary description of converse flexoelectric effect
is more complicated problem. Inter alia effective solution of corresponded
boundary problems requires the development of special mathematical methods. The
subject of this paper is a detailed discussion of the relevant theory focuses
on the converse flexoelectric effect. It is also considered some particular
examples illustrating the application of the general theory.


  We consider first order perturbation theory for a non-minimally coupled
inflaton field without assuming an adiabatic equation of state. In general
perturbations in non-minimally coupled theory may be non-adiabatic. However
under the slow-roll assumptions the perturbation theory may look like adiabatic
one. We show in the frame-work of perturbation theory, that our results of
spectral index and bound on no-minimal coupling parameter agree with the
results obtained using the adiabatic equation of state by the earlier authors.


  We calculate the cross section of the deeply virtual Compton scattering at
large energies and intermediate momentum transfers.


  Locally recoverable (LRC) codes have recently been a focus point of research
in coding theory due to their theoretical appeal and applications in
distributed storage systems. In an LRC code, any erased symbol of a codeword
can be recovered by accessing only a small number of other symbols. For LRC
codes over a small alphabet (such as binary), the optimal rate-distance
trade-off is unknown. We present several new combinatorial bounds on LRC codes
including the locality-aware sphere packing and Plotkin bounds. We also develop
an approach to linear programming (LP) bounds on LRC codes. The resulting LP
bound gives better estimates in examples than the other upper bounds known in
the literature. Further, we provide the tightest known upper bound on the rate
of linear LRC codes with a given relative distance, an improvement over the
previous best known bounds.


  The development of scalable, representative, and widely adopted benchmarks
for graph data systems have been a question for which answers has been sought
for decades. We conduct an in-depth study of the existing literature on
benchmarks for graph data management and processing, covering 20 different
benchmarks developed during the last 15 years. We categorize the benchmarks
into three areas focusing on benchmarks for graph processing systems, graph
database benchmarks, and bigdata benchmarks with graph processing workloads.
This systematic approach allows us to identify multiple issues existing in this
area, including i) few benchmarks exist which can produce high workload
scenarios, ii) no significant work done on benchmarking graph stream processing
as well as graph based machine learning, iii) benchmarks tend to use
conventional metrics despite new meaningful metrics have been around for years,
iv) increasing number of big data benchmarks appear with graph processing
workloads. Following these observations, we conclude the survey by describing
key challenges for future research on graph data systems benchmarking.


  We consider monoids equipped with a compatible quantale valued relation, to
which we call quantale enriched monoids, and study semidirect products of such
structures. It is well-known that semidirect products of monoids are closely
related to Schreier split extensions which, in the setting of monoids, play the
role of split extensions of groups. We will thus introduce certain split
extensions of quantale enriched monoids, which generalize the classical
Schreier split extensions of monoids, and investigate their connections with
semidirect products. We then restrict our study to a class of quantale enriched
monoids whose behavior mimics the fact that the preorder on a preordered group
is completely determined by its cone of positive elements. Finally, we
instantiate our results for preordered monoids and compare them with existing
literature.


  In this paper, we deal with (angular cut-off) Boltzmann equation with soft
potential ($-3<\gamma<0$). In particular, we construct a unique global solution
in $L^\infty_{x,v}$ which converges to global equilibrium asymptotically
provided that initial data has a large amplitude but with sufficiently small
relative entropy. Because frequency multiplier is not uniformly positive
anymore, unlike hard potential case, time-involved velocity weight will be used
to derive sub-exponential decay of the solution. Motivated by recent
development of $L^2\mbox{-}L^\infty$ approach also, we introduce some modified
estimates of quadratic nonlinear terms. Linearized collision kernel will be
treated in a subtle manner to control singularity of soft potential kernel.


  This paper describes the determination of the direct CP observables R_cp and
A_cp, related to the CKM angle gamma, using B- to D0 K- decays in 1.0 inverse
fb of data collected with the CDF II detector. This is the first measurement of
these CP observables made at a hadron collider in this decay mode. The results
presented are consistent with the measurements of these quantities made by the
Belle and BABAR collaborations.


  Hysteresis is studied for a two-dimensional, spin-1/2, nearest-neighbor,
kinetic Ising ferromagnet in an oscillating field, using Monte Carlo
simulations and analytical theory. Attention is focused on large systems and
strong field amplitudes at a temperature below T_c. In this parameter regime,
the magnetization switches through random nucleation and subsequent growth of
many droplets of spins aligned with the applied field. Using a time-dependent
extension of the Kolmogorov-Johnson-Mehl-Avrami (KJMA) theory of metastable
decay, we analyze the statistical properties of the hysteresis-loop area and
the correlation between the magnetization and the applied field. This analysis
enables us to accurately predict the results of extensive Monte Carlo
simulations. The average loop area exhibits an extremely slow approach to an
asymptotic, logarithmic dependence on the product of the amplitude and the
frequency of the applied field. This may explain the inconsistent exponent
estimates reported in previous attempts to fit experimental and numerical data
for the low-frequency behavior of this quantity to a power law. At higher
frequencies we observe a dynamic phase transition. Applying standard
finite-size scaling techniques from the theory of second-order equilibrium
phase transitions to this nonequilibrium phase transition, we obtain estimates
for the transition frequency and the critical exponents (beta/nu \approx 0.11,
gamma/nu \approx 1.84 and nu \approx 1.1). In addition to their significance
for the interpretation of recent experiments on switching in ferromagnetic and
ferroelectric nanoparticles and thin films, our results provide evidence for
the relevance of universality and finite-size scaling to dynamic phase
transitions in spatially extended nonstationary systems.


  We develop an automated technique for detecting damped Lyman-$\alpha$
absorbers (DLAs) along spectroscopic lines of sight to quasi-stellar objects
(QSOs or quasars). The detection of DLAs in large-scale spectroscopic surveys
such as SDSS-III sheds light on galaxy formation at high redshift, showing the
nucleation of galaxies from diffuse gas. We use nearly 50 000 QSO spectra to
learn a novel tailored Gaussian process model for quasar emission spectra,
which we apply to the DLA detection problem via Bayesian model selection. We
propose models for identifying an arbitrary number of DLAs along a given line
of sight. We demonstrate our method's effectiveness using a large-scale
validation experiment, with excellent performance. We also provide a catalog of
our results applied to 162 858 spectra from SDSS-III data release 12.


  Clusters of galaxies generally form by the gravitational merger of smaller
clusters and groups. Mergers drive shocks in the intracluster gas which heat
the intracluster gas. Mergers disrupt cluster cooling cores. Mergers produce
large, temporary increases in the X-ray luminosities and temperatures of
cluster; such merger boost may bias estimates of cosmological parameters from
clusters. Chandra observations of the X-ray signatures of mergers, particularly
"cold fronts," will be discussed. X-ray observations of shocks can be used to
determine the kinematics of the merger. As a result of particle acceleration in
shocks and turbulent acceleration following mergers, clusters of galaxies
should contain very large populations of relativistic electrons and ions.
Observations and models for the radio, extreme ultraviolet, hard X-ray, and
gamma-ray emission from nonthermal particles accelerated in these shocks are
described.


  Neuroscientists frequently use a certain statistical reasoning to establish
the existence of distinct neuronal processes in the brain. We show that this
reasoning is flawed and that the large corresponding literature needs
reconsideration. We illustrate the fallacy with a recent study that received an
enormous press coverage because it concluded that humans detect deceit better
if they use unconscious processes instead of conscious deliberations. The study
was published under a new open-data policy that enabled us to reanalyze the
data with more appropriate methods. We found that unconscious performance was
close to chance - just as the conscious performance. This illustrates the flaws
of this widely used statistical reasoning, the benefits of open-data practices,
and the need for careful reconsideration of studies using the same rationale.


  We obtain an interesting realization of the de Rham cohomological operators
of differential geometry in terms of the noncommutative q-superoscillators for
the supersymmetric quantum group GL_{qp} (1|1). In particular, we show that a
unique superalgebra, obeyed by the bilinears of fermionic and bosonic
noncommutative q-(super)oscillators of GL_{qp} (1|1), is exactly identical to
that obeyed by the de Rham cohomological operators. A set of discrete symmetry
transformation for a set of GL_{qp} (1|1) covariant superalgebras turns out to
be the analogue of the Hodge duality * operation of differential geometry. A
connection with an extended BRST algebra obeyed by the nilpotent (anti-)BRST
and (anti-)co-BRST charges, the ghost charge and a bosonic charge (which is
equal to the anticommutator of (anti-)BRST and (anti-)co-BRST charges) is also
established.


  In this paper we study an index of a critical orbit, defined in terms of the
degree for invariant strongly indefinite functionals. We establish a
relationship of this index with the index of a critical point of the mapping
restricted to the space normal to the orbit. The second aim of the article is
to use the index of a critical orbit to prove the bifurcation of nontrivial
solutions of nonlinear elliptic systems with Neumann boundary conditions. We
consider also the existence of unbounded sets of solutions of such systems.


  In this paper we investigate the existence of multiple solutions for the
following two fractional problems \begin{equation*} \left\{\begin{array}{ll}
(-\Delta_{\Omega})^{s} u-\lambda u= f(x, u) &\mbox{in} \Omega \\ u=0 &\mbox{in}
\partial \Omega \end{array} \right. \end{equation*} and \begin{equation*}
\left\{\begin{array}{ll} (-\Delta_{\mathbb{R}^{N}})^{s} u-\lambda u= f(x, u)
&\mbox{in} \Omega \\ u=0 &\mbox{in} \mathbb{R}^{N}\setminus \Omega, \end{array}
\right. \end{equation*} where $s\in (0,1)$, $N>2s$, $\Omega$ is a smooth
bounded domain of $\mathbb{R}^{N}$, and $f:\bar{\Omega}\times
\mathbb{R}\rightarrow \mathbb{R}$ is a superlinear continuous function which
does not satisfy the well-known Ambrosetti-Rabinowitz condition. Here
$(-\Delta_{\Omega})^{s}$ is the spectral Laplacian and
$(-\Delta_{\mathbb{R}^{N}})^{s}$ is the fractional Laplacian in
$\mathbb{R}^{N}$. By applying variational theorems of mixed type due to Marino
and Saccon and Linking Theorem, we prove the existence of multiple solutions
for the above problems.


  For a closed subgroup of a locally compact group the Rieffel induction
process gives rise to a $C^*$-correspondence over the $C^*$-algebra of the
subgroup. We study the associated Cuntz-Pimsner algebra and show that, by
varying the subgroup to be open, compact, or discrete, there are connections
with the Exel-Pardo correspondence arising from a cocycle, and also with graph
algebras.


  Efficient and accurate low-rank approximations of multiple data sources are
essential in the era of big data. The scaling of kernel-based learning
algorithms to large datasets is limited by the O(n^2) computation and storage
complexity of the full kernel matrix, which is required by most of the recent
kernel learning algorithms.
  We present the Mklaren algorithm to approximate multiple kernel matrices
learn a regression model, which is entirely based on geometrical concepts. The
algorithm does not require access to full kernel matrices yet it accounts for
the correlations between all kernels. It uses Incomplete Cholesky
decomposition, where pivot selection is based on least-angle regression in the
combined, low-dimensional feature space. The algorithm has linear complexity in
the number of data points and kernels. When explicit feature space induced by
the kernel can be constructed, a mapping from the dual to the primal Ridge
regression weights is used for model interpretation.
  The Mklaren algorithm was tested on eight standard regression datasets. It
outperforms contemporary kernel matrix approximation approaches when learning
with multiple kernels. It identifies relevant kernels, achieving highest
explained variance than other multiple kernel learning methods for the same
number of iterations. Test accuracy, equivalent to the one using full kernel
matrices, was achieved with at significantly lower approximation ranks. A
difference in run times of two orders of magnitude was observed when either the
number of samples or kernels exceeds 3000.


  The nonthermal particle acceleration during magnetic reconnection remains a
fundamental topic in several astrophysical phenomena, such as solar flares,
pulsar wind, magnetars, etc, for more than half a century, and one of the
unresolved questions is its efficiency. Recently, nonthermal particle
acceleration mechanisms during reconnection have been extensively studied by
particle-in-cell simulations, yet it is an intriguing enigma as to how the
magnetic field energy is divided into thermally heated plasmas and nonthermal
particles. Here we study both non-relativistic and relativistic magnetic
reconnections using large-scale particle-in-cell simulation for a pair plasma,
and indicate that the production of the nonthermal particle becomes efficient
with increasing the plasma temperature. In the relativistic hot plasma case, we
determine that the heated plasmas by reconnection can be approximated by a
kappa distribution function with the kappa index of approximately 3 or less
(equivalent to 2 or less for the power-law index), and the nonthermal energy
density of reconnection is approximately over 95% of the total internal energy
in the downstream exhaust.


  High-quality recordings of radio frequency (RF) emissions from commercial
communication hardware in realistic environments are often needed to develop
and assess spectrum-sharing technologies and practices, e.g., for training and
testing spectrum sensing algorithms and for interference testing.
Unfortunately, the time-consuming, expensive nature of such data collections
together with data-sharing restrictions pose significant challenges that limit
data set availability. Furthermore, developing accurate models of real-world RF
emissions from first principles is often very difficult because system
parameters and implementation details are at best only partially known, and
complex system dynamics are difficult to characterize. Hence, there is a need
for flexible, data-driven methods that can leverage existing data sets to
synthesize additional similar waveforms. One promising machine-learning
approach is unsupervised deep generative modeling with generative adversarial
networks (GANs). To date, GANs for RF communication signals have not been
studied thoroughly. In this paper, we present the first in-depth investigation
of generated signal fidelity for GANs trained with baseband orthogonal
frequency-division multiplexing (OFDM) signals, where each subcarrier is
digitally modulated with quadrature amplitude modulation (QAM). Building on
prior GAN methods, we developed two novel GAN models and evaluated their
performance using simulated data sets with known ground truth. Specifically, we
investigated model performance with respect to increasing data set complexity
over a range of OFDM parameters and conditions, including fading channels. The
findings presented here inform the feasibility of use cases and provide a
foundation for further investigations into deep generative models for RF
communication signals.


  We present 69 new mid-eclipse times of the young post-common envelope binary
(PCEB) NN Ser, which was previously suggested to possess two circumbinary
planets. We have interpreted the observed eclipse-time variations in terms of
the light-travel time effect caused by two planets, exhaustively covering the
multi-dimensional parameter space by fits in the two binary and ten orbital
parameters. We supplemented the fits by stability calculations for all models
with an acceptable chi-square. An island of secularly stable 2:1 resonant
solutions exists, which coincides with the global chi-square minimum. Our
best-fit stable solution yields current orbital periods P_o = 15.47 yr and P_i
= 7.65 yr and eccentricities e_o = 0.14 and e_i = 0.22 for the outer (o) and
inner (i) planets, respectively. The companions qualify as giant planets, with
masses of 7.0 M_Jup and 1.7 M_Jup for the case of orbits coplanar with that of
the binary. The two-planet model that starts from the present system parameters
has a lifetime greater than 10^8 yr, which significantly exceeds the age of NN
Ser of 10^6 yr as a PCEB. The resonance is characterized by libration of the
resonant variable Theta_1 and circulation of omega_i-omega_o, the difference
between the arguments of periapse of the two planets. No stable non-resonant
solutions were found, and the possibility of a 5:2 resonance suggested
previously by us is now excluded at the 99.3% confidence level.


  Bayesian networks are probabilistic graphical models often used in big data
analytics. The problem of exact structure learning is to find a network
structure that is optimal under certain scoring criteria. The problem is known
to be NP-hard and the existing methods are both computationally and memory
intensive. In this paper, we introduce a new approach for exact structure
learning. Our strategy is to leverage relationship between a partial network
structure and the remaining variables to constraint the number of ways in which
the partial network can be optimally extended. Via experimental results, we
show that the method provides up to three times improvement in runtime, and
orders of magnitude reduction in memory consumption over the current best
algorithms.


  Confinement processes arranging small polarons into insulating periodic
structures above certain conversion tempereture are considered. Vibronic
(Jahn-Teller) polarons associating inherent electric & magnetic dipoles coupled
to external fields lead to colossal field effects. Confinement modes based on
Poisson-Boltzmann equations of electrostatic strings and plates are deduced.


  We have incorporated the oblate distortion of the shape of the star due to
the stellar rotation, which modifies the finite disk correction factor (f_D) in
the m-CAK hydrodynamical model. We implement a simplified version for the f_D
allowing us to solve numerically the non-linear m- CAK momentum equation.We
solve this model for a classical Be star in the polar and equatorial
directions. The star's oblateness modifies the polar wind, which is now much
faster than the spherical one, mainly because the wind receives radiation from
a larger (than the spherical) stellar surface. In the equatorial direction we
obtain slow solutions, which are even slower and denser than the spherical
ones. For the case when the stellar rotational velocity is about the critical
velocity, the most remarkable result of our calculations is that the density
contrast between the equatorial density and the polar one, is about 100. This
result could explain a long-standing problem on Be stars.


  We consider a mechanical system which is controlled by means of moving
constraints. Namely, we assume that some of the coordinates can be directly
assigned as functions of time by means of frictionless constraints. This leads
to a system of ODE's whose right hand side depends quadratically on the time
derivative of the control. In this paper we introduce a simplified dynamics,
described by a differential inclusion. We prove that every trajectory of the
differential inclusion can be uniformly approximated by a trajectory of the
original system, on a sufficiently large time interval, starting at rest. Under
a somewhat stronger assumption, we show this second trajectory reaches exactly
the same terminal point.


  The decay K_L -> pi0 gamma e+ e- occurs at a it higher rate than the
nonradiative process K_L -> pi0 e+ e-, and hence can be a background to CP
violation studies using the latter reaction. It also has an interest in its own
right in the context of chiral perturbation theory, through its relation to the
decay K_L -> pi0 gamma gamma. The leading order chiral loop contribution to K_L
-> pi0 gamma e+ e-, including the [q(e+) + q(e-)]^2/m^2(pi) dependence, is
completely calculable. We present this result and also include the higher order
modifications which are required in the analysis of K_L -> pi0 gamma gamma.


  The accelerated digitalisation of society along with technological evolution
have extended the geographical span of cyber-physical systems. Two main threats
have made the reliable and real-time control of these systems challenging: (i)
uncertainty in the communication infrastructure induced by scale, and
heterogeneity of the environment and devices; and (ii) targeted attacks
maliciously worsening the impact of the above-mentioned communication
uncertainties, disrupting the correctness of real-time applications. This paper
addresses those challenges by showing how to build distributed protocols that
provide both real-time with practical performance, and scalability in the
presence of network faults and attacks, in probabilistic synchronous
environments. We provide a suite of real-time Byzantine protocols, which we
prove correct, starting from a reliable broadcast protocol, called PISTIS, up
to atomic broadcast and consensus. This suite simplifies the construction of
powerful distributed and decentralized monitoring and control applications,
including state-machine replication. Extensive empirical simulations showcase
PISTIS's robustness, latency, and scalability. For example, PISTIS can
withstand message loss (and delay) rates up to 50% in systems with 49 nodes and
provides bounded delivery latencies in the order of a few milliseconds.


  In a recent article [1], the FEAST algorithm has been presented as a general
purpose eigenvalue solver which is ideally suited for addressing the numerical
challenges in electronic structure calculations. Here, FEAST is presented
beyond the "black-box" solver as a fundamental modeling framework which can
naturally address the original numerical complexity of the electronic structure
problem as formulated by Slater in 1937 [2]. The non-linear eigenvalue problem
arising from the muffin-tin decomposition of the real-space domain is first
derived and then reformulated to be solved exactly within the FEAST framework.
This new framework is presented as a fundamental and practical solution for
performing both accurate and scalable electronic structure calculations,
bypassing the various issues of using traditional approaches such as
linearization and pseudopotential techniques. A finite element implementation
of this FEAST framework along with simulation results for various molecular
systems are also presented and discussed.


  The transient response from a transmitter-receiver coil system inside a
multi-layer cylindrical conductive configuration is obtained. The particular
set-up applies to well logging as well as to eddy current tube testing. In this
work, a number of improvements are presented to existing models for an
efficient calculation of the induced voltage. These include: domain truncation,
novel treatment of arbitrary number of layers in order to avoid computational
overflows and efficient time response calculation. The latter is based on a
combination of Laplace inversion techniques for short- and long-time transient
responses. This article is part of the theme issue 'Advanced electromagnetic
non-destructive evaluation and smart monitoring'.


  The quantum kinetic evolution of neutrinos in dense environments, such as the
core-collapse supernovae or the neutron star mergers, can result in fast flavor
conversion (FFC), presenting a significant challenge to achieving robust
astrophysical modeling of these systems. Recent works that directly simulate
the quantum kinetic transport of neutrinos in localized domains have suggested
that the asymptotic outcome of FFCs can be modeled by simple analytical
prescriptions. In this Letter, we incorporate the analytical prescriptions into
global simulations that solve the classical neutrino transport equation
including collisions and advection under spherical symmetry. We demonstrate
excellent agreement between results obtained using this approach and those
directly from the corresponding global quantum kinetic simulations. In
particular, this effective method can also precisely capture the collisional
feedback effect for cases where the FFC happens inside the neutrinosphere. Our
work highlights that a robust integration of FFCs in classical neutrino
transport used in astrophysical simulation can be feasible.


  Support vector machines (SVMs) have been successful in solving many computer
vision tasks including image and video category recognition especially for
small and mid-scale training problems. The principle of these non-parametric
models is to learn hyperplanes that separate data belonging to different
classes while maximizing their margins. However, SVMs constrain the learned
hyperplanes to lie in the span of support vectors, fixed/taken from training
data, and this reduces their representational power and may lead to limited
generalization performances. In this paper, we relax this constraint and allow
the support vectors to be learned (instead of being fixed/taken from training
data) in order to better fit a given classification task. Our approach,
referred to as deep total variation support vector machines, is parametric and
relies on a novel deep architecture that learns not only the SVM and the kernel
parameters but also the support vectors, resulting into highly effective
classifiers. We also show (under a particular setting of the activation
functions in this deep architecture) that a large class of kernels and their
combinations can be learned. Experiments conducted on the challenging task of
skeleton-based action recognition show the outperformance of our deep total
variation SVMs w.r.t different baselines as well as the related work.


  Since the beginning of the past century, the nature of HD 108 has been a
subject of intense debate. One after another, astronomers explored its
variability and attributed it either to binarity, or to changes in the stellar
wind of a single star. In this article, we analyse a 30 years long campaign of
spectroscopic observations of this star with special emphasis on the last 15
years during which photographic plates have been replaced by CCD detectors. Our
investigation of the radial velocities of HD 108 yields no significant short-
or long-term period and does not confirm the published periodicities either.
Though the radial velocity of HD 108 appears clearly variable, the variations
cannot be explained by the orbital motion in a spectroscopic binary. However,
our data reveal spectacular changes in the H I Balmer lines and some He I
profiles over the years. These lines continuously evolved from P Cygni profiles
to `pure' absorption lines. A similar behaviour was already observed in the
past, suggesting that these changes are recurrent. HD 108 seems to share
several characteristics of Oe stars and we discuss different hypotheses for the
origin of the observed long-term variations. As we are now in a transition
period, a continuous monitoring of HD 108 should be considered for the next few
years.


  We consider generalized interval exchange transformations, or briefly GIETs,
that is bijections of the interval which are piecewise increasing
homeomorphisms with finite branches. When all continuous branches are
translations, such maps are classical interval exchange transformations, or
briefly IETs. The well-known Rauzy renormalization procedure extends to a given
GIET and a Rauzy renormalization path is defined, provided that the map is
infinitely renormalizable. We define full families of GIETs, that is optimal
finite dimensional parameter families of GIETs such that any prescribed Rauzy
renormalization path is realized by some map in the family. In particular, a
GIET and a IET with the same Rauzy renormalization path are semi-conjugated.
This extends a classical result of Poincar\'e relating circle homeomorphisms
and irrational rotations.


  We investigate the matter distribution of a spiral galaxy with a
counter-rotating stellar core, SDSS J1331+3628 (J1331), independently with
gravitational lensing and stellar dynamical modelling. By fitting a
gravitational potential model to a quadruplet of lensing images around J1331's
bulge, we tightly constrain the mass inside the Einstein radius R_ein = (0.91
+/- 0.02)'' (~= 1.83 +/- 0.04 kpc) to within 4%: M_ein = (7.8 +/- 0.3) x 10^10
M_Sun. We model observed long-slit major axis stellar kinematics in J1331's
central regions by finding Multi-Gaussian Expansion (MGE) models for the
stellar and dark matter distribution that solve the axisymmetric Jeans
equations. The lens and dynamical model are independently derived, but in very
good agreement with each other around ~R_ein. We find that J1331's center
requires a steep total mass-to-light ratio gradient. A dynamical model
including an NFW halo (with virial velocity v_200 ~= 240 +/- 40 km/s and
concentration c_200 ~= 8 +/- 2) and moderate tangential velocity anisotropy
(beta_z ~= -0.4 +/- 0.1) can reproduce the signatures of J1331's
counter-rotating core and predict the stellar and gas rotation curve at larger
radii. However, our models do not agree with the observed velocity dispersion
at large radii. We speculate that the reason could be a non-trivial change in
structure and kinematics due to a possible merger event in J1331's recent past.


  Facial Attribute Classification (FAC) has attracted increasing attention in
computer vision and pattern recognition. However, state-of-the-art FAC methods
perform face detection/alignment and FAC independently. The inherent
dependencies between these tasks are not fully exploited. In addition, most
methods predict all facial attributes using the same CNN network architecture,
which ignores the different learning complexities of facial attributes. To
address the above problems, we propose a novel deep multi-task multi-label CNN,
termed DMM-CNN, for effective FAC. Specifically, DMM-CNN jointly optimizes two
closely-related tasks (i.e., facial landmark detection and FAC) to improve the
performance of FAC by taking advantage of multi-task learning. To deal with the
diverse learning complexities of facial attributes, we divide the attributes
into two groups: objective attributes and subjective attributes. Two different
network architectures are respectively designed to extract features for two
groups of attributes, and a novel dynamic weighting scheme is proposed to
automatically assign the loss weight to each facial attribute during training.
Furthermore, an adaptive thresholding strategy is developed to effectively
alleviate the problem of class imbalance for multi-label learning. Experimental
results on the challenging CelebA and LFWA datasets show the superiority of the
proposed DMM-CNN method compared with several state-of-the-art FAC methods.


  In this paper, we propose a Boltzmann-type kinetic model of the spreading of
an infectious disease on a network. The latter describes the connections among
countries, cities or districts depending on the spatial scale of interest. The
disease transmission is represented in terms of the viral load of the
individuals and is mediated by social contacts among them, taking into account
their displacements across the nodes of the network. We formally derive the
hydrodynamic equations for the density and the mean viral load of the
individuals on the network and we analyse the large-time trends of these
quantities with special emphasis on the cases of blow-up or eradication of the
infection. By means of numerical tests, we also investigate the impact of
confinement measures, such as quarantine or localised lockdown, on the
diffusion of the disease on the network.


  Accreting millisecond X-ray pulsars are an important subset of low-mass X-ray
binaries in which coherent X-ray pulsations can be observed during occasional,
bright outbursts (X-ray luminosity $L_X\sim 10^{36}$ erg s$^{-1}$). These
pulsations show that matter is being channeled onto the neutron star's magnetic
poles. However, such sources spend most of their time in a low-luminosity,
quiescent state ($L_X\lesssim 10^{34}$ erg s$^{-1}$), where the nature of the
accretion flow onto the neutron star (if any) is not well understood. Here we
report that the millisecond pulsar/low-mass X-ray binary transition object PSR
J1023+0038 intermittently shows coherent X-ray pulsations at luminosities
nearly 100 times fainter than observed in any other accreting millisecond X-ray
pulsar. We conclude that in spite of its low luminosity PSR J1023+0038
experiences episodes of channeled accretion, a discovery that challenges
existing models for accretion onto magnetized neutron stars.


  We calculate the one-loop corrections to the Higgs boson masses within the
context of the MSSM with Non-Minimal Flavor Violation in the squark sector. We
take into account all the relevant restrictions from BR(B -> X_s gamma), BR(B_s
-> mu^+ mu^-) and \Delta M_{B_s}. We find sizable corrections to the lightest
Higgs boson mass that are considerably larger than the expected ILC precision
for acceptable values of the mixing parameters deltas. We find delta^{LR}_{ct}
and delta^{RL}_{ct} specially relevant, mainly at low tan beta.


  We theoretically discuss the preservation of squeezing and continuous
variable entanglement of two mode squeezed light when the two modes are
subjected to unequal transmission. One of the modes is transmitted through a
slow light medium while the other is sent through an optical fiber of unit
transmission. Balanced homodyne detection is used to check the presence of
squeezing. It is found that loss of squeezing occurs when the mismatch in the
transmission of the two modes is greater than 40% while near ideal squeezing is
preserved when the transmissions are equal. We also discuss the effect of this
loss on continuous variable entanglement using strong and weak EPR criteria and
possible applications for this experimental scheme.


  In this letter, we propose enhanced factored three way restricted Boltzmann
machines (EFTW-RBMs) for speech detection. The proposed model incorporates
conditional feature learning by multiplying the dynamical state of the third
unit, which allows a modulation over the visible-hidden node pairs. Instead of
stacking previous frames of speech as the third unit in a recursive manner, the
correlation related weighting coefficients are assigned to the contextual
neighboring frames. Specifically, a threshold function is designed to capture
the long-term features and blend the globally stored speech structure. A
factored low rank approximation is introduced to reduce the parameters of the
three-dimensional interaction tensor, on which non-negative constraint is
imposed to address the sparsity characteristic. The validations through the
area-under-ROC-curve (AUC) and signal distortion ratio (SDR) show that our
approach outperforms several existing 1D and 2D (i.e., time and time-frequency
domain) speech detection algorithms in various noisy environments.


  We focus on eventually non-linear abstract Cauchy problems with a generalized
fractional derivative in time. First we prove a local existence and uniqueness
result, then we focus on a generalized Gr\"onwall inequality. Before addressing
the inequality, we study some properties of eigenvalues and eigenfunctions of
the generalized fractional derivatives. Finally, we prove some consequences of
the generalized Gr\"onwall inequality.


  The grand canonical thermodynamics of a bosonic system is studied in order to
identify the footprint of its own high-density quantum phase transition. The
phases displayed by the system at zero temperature establish recognizable
patterns at finite temperature that emerged in the proximity of the boundary of
the equilibrium diagram. The gaped phase induces a state of
collectivism/condensation at finite temperature in which population cumulates
into the ground state in spite of interacting attractively. The work sets the
foundation to approach the effect of attraction in the formation of a molecular
condensate.


  A method of simulation of particle cascades induced by ultra-high (>10$^{15}$
eV) and extremely high (>10$^{18}$ eV) energy neutrinos in water or other dense
medium has been elaborated. The lateral spread of high-energy particles in
cascades due to Coulomb scattering is negligible. So it is possible to use an
approximation of the one-dimensional development of the UHE (or EHE) cascade if
energies of particles in it higher than 10-100 GeV. An original program of the
one-dimensional development of UHE and EHE cascades in dense media taking into
account fluctuations and the Landau-Pomeranchuk-Migdal effect has been
elaborated. The GEANT4 package has been used when particle energies are below
1000 GeV, for example, or less to calculate correctly the longitudinal
distribution of an energy deposition by charge particles in a cascade. In
advance the library of longitudinal characteristics of cascades was calculated.
When a particle with the energy E which is below the threshold energy (E<1000
GeV or E<10$^6$ GeV) appears in the basic Monte Carlo program, the longitudinal
distribution of an energy deposition induced by it was taken from the library
and was added into the corresponding places of the basic distribution. The
results of simulation of cascades in a dense medium can be used for
calculations of acoustical or radio signals.


  While analyzing scanned documents, handwritten text can overlap with printed
text. This overlap causes difficulties during the optical character recognition
(OCR) and digitization process of documents, and subsequently, hurts downstream
NLP tasks. Prior research either focuses solely on the binary classification of
handwritten text or performs a three-class segmentation of the document, i.e.,
recognition of handwritten, printed, and background pixels. This approach
results in the assignment of overlapping handwritten and printed pixels to only
one of the classes, and thus, they are not accounted for in the other class.
Thus, in this research, we develop novel approaches to address the challenges
of handwritten and printed text segmentation. Our objective is to recover text
from different classes in their entirety, especially enhancing the segmentation
performance on overlapping sections. To support this task, we introduce a new
dataset, SignaTR6K, collected from real legal documents, as well as a new model
architecture for the handwritten and printed text segmentation task. Our best
configuration outperforms prior work on two different datasets by 17.9% and
7.3% on IoU scores. The SignaTR6K dataset is accessible for download via the
following link: https://forms.office.com/r/2a5RDg7cAY.


  We discuss the recently published numerical computations of the vortex free
energy. They dramatically demonstrate that the excitation probability for a
sufficiently thick vortex approaches unity at large beta, i.e. that thick
vortices `condense' in the vacuum. This is known to imply confinement. An
analytical approach for exploring this phenomenon is also outlined.


  Let $(M, g)$ be a complete Riemannian manifold without focal points and
curvature bounded below. We prove that when the average of the sectional
curvature in tangent planes along geodesics is negative and uniformly away from
zero, then the geodesic flow is of Anosov type. We use this result to construct
a non-compact manifold of non-positive curvature with the geodesic flow of
Anosov type.


  This paper studies collective motion optimization of a fleet of UAVs flying
over a populated and geometrically constrained area. The paper treats UAVs as
particles of a deformable body, thus, UAV coordination is defined by a
homeomorphic continuum deformation function. Under continuum deformation, the
distance between individual UAVs can significantly change while assuring the
UAVs dont collide, enabling a swarm to travel through the potentially cluttered
environment. To ensure inter-agent and obstacle collision avoidance, the paper
formulates safety requirements as inequality constraints of the coordination
optimization problem. The main objective of the paper is then to optimize
continuum deformation of the UAV team satisfying all continuum deformation
inequality constraints. Given initial and target configurations, the cost is
defined as a weighted sum of the travel distance and distributed cost
proportional to the likelihood of the human presence


  Femtosecond PTHB spectroscopy was expected to demonstrate the existence of
distinct s-p absorption subbands originating from the three nondegenerate
p-like excited states of hydrated electron in anisotropic solvation cavity. Yet
no conclusive experimental evidence either for this subband structure or the
reorientation of the cavity on the picosecond time scale has been obtained. We
demonstrate that rapid reorientation of s-p transition dipole moments in
response to small scale motion of water molecules is the likely culprit. The
polarized bleach is shown to be too small and too short lived to be observed
reliably on the sub-picosecond time scale.


  The Riccati equation method is used to establish some new stability criteria
for systems of two linear first-order ordinary differential equations. It is
shown that two of these criteria in the two dimensional case imply the Routh -
Hurwitz's criterion.


  We consider the dispersion interaction between two ground-state hydrogen
atoms, interacting with the quantum electromagnetic field in the vacuum state,
in the presence of an external static electric field, both in the nonretarded
and in the retarded Casimir-Polder regime. We show that the presence of the
external field strongly modifies the dispersion interaction between the atoms,
changing its space dependence. Moreover, we find that, for specific geometrical
configurations of the two atoms with respect to the external field and/or the
relative orientation of the fields acting on the two atoms, it is possible to
change the character of the dispersion force, turning it from attractive to
repulsive, or even make it vanishing. This new finding clearly shows the
possibility to control and tailor interatomic dispersion interactions through
external actions. By a numerical estimate of the field-modified interaction, we
show that at typical interatomic distances the change of the interaction's
strength can match or even outmatch the unperturbed interaction; this can be
obtained for values of the external field that can be currently achieved in the
laboratory, and sufficiently weak to be taken into account perturbatively.


  We discuss the generalization of the local renormalization group approach to
theories in which Weyl symmetry is gauged. These theories naturally correspond
to scale invariant - rather than conformal invariant - models in the flat space
limit. We argue that this generalization can be of use when discussing the
issue of scale vs conformal invariance in quantum and statistical field
theories. The application of Wess-Zumino consistency conditions constrains the
form of the Weyl anomaly and the beta functions in a nonperturbative way. In
this work we concentrate on two dimensional models including also the
contributions of the boundary. Our findings suggest that the renormalization
group flow between scale invariant theories differs from the one between
conformal theories because of the presence of a new charge that appears in the
anomaly. It does not seem to be possible to find a general scheme for which the
new charge is zero, unless the theory is conformal in flat space. Two
illustrative examples involving flat space's conformal and scale invariant
models that do not allow for a naive application of the standard local
treatment are given.


  We investigate the nonlinear evolution of structure in variants of the
standard cosmological model which display damped density fluctuations relative
to cold dark matter (e.g. in which cold dark matter is replaced by warm or
interacting DM). Using N-body simulations, we address the question of how much
information is retained from different scales in the initial linear power
spectrum following the nonlinear growth of structure. We run a suite of N-body
simulations with different initial linear matter power spectra to show that,
once the system undergoes nonlinear evolution, the shape of the linear power
spectrum at high wavenumbers does not affect the non-linear power spectrum,
while it still matters for the halo mass function. Indeed, we find that linear
power spectra which differ from one another only at wavenumbers larger than
their half-mode wavenumber give rise to (almost) identical nonlinear power
spectra at late times, regardless of the fact that they originate from
different models with damped fluctuations. On the other hand, the halo mass
function is more sensitive to the form of the linear power spectrum. Exploiting
this result, we propose a two parameter model of the transfer function in
generic damped scenarios, and show that this parametrisation works as well as
the standard three parameter models for the scales on which the linear spectrum
is relevant.


  This paper is a detailed account of the recent progress in understanding the
statistical properties of complex eigenvalues of random non-Hermitian matrices
reported earlier in our two short communications: Physics Letters A v.226, 46
(1997) and Phys. Rev. Lett., v.79, 557 (1997)


  For the identification of switched systems with a measured switching signal,
this work aims to analyze the effect of switching strategies on the estimation
error. The data for identification is assumed to be collected from globally
asymptotically or marginally stable switched systems under switches that are
arbitrary or subject to an average dwell time constraint. Then the switched
system is estimated by the least-squares (LS) estimator. To capture the effect
of the parameters of the switching strategies on the LS estimation error,
finite-sample error bounds are developed in this work. The obtained error
bounds show that the estimation error is logarithmic of the switching
parameters when there are only stable modes; however, when there are unstable
modes, the estimation error bound can increase linearly as the switching
parameter changes. This suggests that in the presence of unstable modes, the
switching strategy should be properly designed to avoid the significant
increase of the estimation error.


  We describe three in-field data collection efforts yielding a large database
of RSSI values vs. time or distance from vehicles communicating with each other
via DSRC. We show several data processing schemes we have devised to develop
Vehicle-to-Vehicle (V2V) propagation models from such data. The database is
limited in several important ways, not least, the presence of a high noise
floor that limits the distance over which good modeling is feasible. Another is
the presence of interference from multiple active transmitters. Our methodology
makes it possible to obtain, despite these limitations, accurate models of
median path loss vs. distance, shadow fading, and fast fading caused by
multipath. We aim not to develop a new V2V model, but to show the methods
enabling such a model to be obtained from in-field RSSI data.


  One Monad to Prove Them All is a modern fairy tale about curiosity and
perseverance, two important properties of a successful PhD student. We follow
the PhD student Mona on her adventure of proving properties about Haskell
programs in the proof assistant Coq. On the one hand, as a PhD student in
computer science Mona observes an increasing demand for correct software
products. In particular, because of the large amount of existing software,
verifying existing software products becomes more important. Verifying programs
in the functional programming language Haskell is no exception. On the other
hand, Mona is delighted to see that communities in the area of theorem proving
are becoming popular. Thus, Mona sets out to learn more about the interactive
theorem prover Coq and verifying Haskell programs in Coq. To prove properties
about a Haskell function in Coq, Mona has to translate the function into Coq
code. As Coq programs have to be total and Haskell programs are often not, Mona
has to model partiality explicitly in Coq. In her quest for a solution Mona
finds an ancient manuscript that explains how properties about Haskell
functions can be proven in the proof assistant Agda by translating Haskell
programs into monadic Agda programs. By instantiating the monadic program with
a concrete monad instance the proof can be performed in either a total or a
partial setting. Mona discovers that the proposed transformation does not work
in Coq due to a restriction in the termination checker. In fact the
transformation does not work in Agda anymore as well, as the termination
checker in Agda has been improved. We follow Mona on an educational journey
through the land of functional programming where she learns about concepts like
free monads and containers as well as basics and restrictions of proof
assistants like Coq. These concepts are well-known individually, but their
interplay gives rise to a solution for Mona's problem based on the originally
proposed monadic tranformation that has not been presented before. When Mona
starts to test her approach by proving a statement about simple Haskell
functions, she realizes that her approach has an additional advantage over the
original idea in Agda. Mona's final solution not only works for a specific
monad instance but even allows her to prove monad-generic properties. Instead
of proving properties over and over again for specific monad instances she is
able to prove properties that hold for all monads representable by a
container-based instance of the free monad. In order to strengthen her
confidence in the practicability of her approach, Mona evaluates her approach
in a case study that compares two implementations for queues. In order to share
the results with other functional programmers the fairy tale is available as a
literate Coq file. If you are a citizen of the land of functional programming
or are at least familiar with its customs, had a journey that involved
reasoning about functional programs of your own, or are just a curious soul
looking for the next story about monads and proofs, then this tale is for you.


  We have studied the alpha decays of 214Po into 210Pb and of 212Po into 208Pb
tagged by the coincidence with the preceding beta decays from 214Bi and 212Bi,
respectively. The employed 222Rn, 232Th, and 220Rn sources were sealed inside
quartz vials and inserted in the Counting Test Facility at the underground Gran
Sasso National Laboratory in Italy. We find that the mean lifetime of 214Po is
(236.00 +- 0.42(stat) +- 0.15(syst)) \mu s and that of 212Po is (425.1 +-
0.9(stat) +- 1.2(syst)) ns. Our results, obtained from data with
signal-to-background ratio larger than 1000, reduce the overall uncertainties
and are compatible with previous measurements.


  VAEs are probabilistic graphical models based on neural networks that allow
the coding of input data in a latent space formed by simpler probability
distributions and the reconstruction, based on such latent variables, of the
source data. After training, the reconstruction network, called decoder, is
capable of generating new elements belonging to a close distribution, ideally
equal to the original one. This article has been written in Spanish to
facilitate the arrival of this scientific knowledge to the Spanish-speaking
community.


  We continue the analysis of non-Gaussianities in the CMB by means of the
scaling index method (SIM, Raeth, Schuecker & Banday 2007) by applying this
method on the 5-year WMAP data. We compare each of the results with 1000 Monte
Carlo simulations mimicing the Gaussian properties of the best fit $\Lambda
CDM$-model. Based on the scaling indices, scale-dependent empirical probability
distributions, moments of these distributions and $\chi^2$-combinations of them
are calculated, obtaining similar results as in the former analysis of the
3-year data: We derive evidence for non-Gaussianity with a probability of up to
97.3% for the mean when regarding the KQ75-masked full sky and summing up over
all considered length scales by means of a diagonal $\chi^2$-statistics.
Looking at only the northern or southern hemisphere, we obtain up to 98.5% or
96.6%, respectively. For the standard deviation, these results appear as 95.6%
for the full sky (99.7% north, 89.4% south) and for a $\chi^2$-combination of
both measurements as 97.4% (99.1% north, 95.5% south). By performing an
analysis of rotated hemispheres, we detect an obvious asymmetry in the data. In
addition to these investigations, we present a method of filling the mask with
Gaussian noise to eliminate boundary effects caused by the mask. With the help
of this technique, we identify several local features on the map, of which the
most significant one turns out to be the well-known cold spot. When excluding
all these spots from the analysis, the deviation from Gaussianity increases,
which shows that the discovered local anomalies are not the reason of the
global detection of non-Gaussianity, but actually were damping the deviations
on average. Our analyses per band and per year suggest, however, that it is
very unlikely that the detected anomalies are due to foreground effects.


  It is well known in the field of machine learning that committee models
improve accuracy, provide generalization error estimates, and enable active
learning strategies. In this work, we adapt these concepts to interatomic
potentials based on artificial neural networks. Instead of a single model,
multiple models that share the same atomic environment descriptors yield an
average that outperforms its individual members as well as a measure of the
generalization error in the form of the committee disagreement. We not only use
this disagreement to identify the most relevant configurations to build up the
model's training set in an active learning procedure, but also monitor and bias
it during simulations to control the generalization error. This facilitates the
adaptive development of committee neural network potentials and their training
sets, while keeping the number of ab initio calculations to a minimum. To
illustrate the benefits of this methodology, we apply it to the development of
a committee model for water in the condensed phase. Starting from a single
reference ab initio simulation, we use active learning to expand into new state
points and to describe the quantum nature of the nuclei. The final model,
trained on 814 reference calculations, yields excellent results under a range
of conditions, from liquid water at ambient and elevated temperatures and
pressures to different phases of ice, and the air-water interface - all
including nuclear quantum effects. This approach to committee models will
enable the systematic development of robust machine learning models for a broad
range of systems.


  The hamiltonian structures for quartic oscillator are considered. All
structures admitting quadratic hamiltonians are classified.


  Unsupervised Domain Adaptation (UDA) methods facilitate knowledge transfer
from a labeled source domain to an unlabeled target domain, navigating the
obstacle of domain shift. While Convolutional Neural Networks (CNNs) are a
staple in UDA, the rise of Vision Transformers (ViTs) provides new avenues for
domain generalization. This paper presents an innovative method to bolster ViT
performance in source-free target adaptation, beginning with an evaluation of
how key, query, and value elements affect ViT outcomes. Experiments indicate
that altering the key component has negligible effects on Transformer
performance. Leveraging this discovery, we introduce Domain Representation
Images (DRIs), feeding embeddings through the key element. DRIs act as
domain-specific markers, effortlessly merging with the training regimen. To
assess our method, we perform target adaptation tests on the Cross Instance DRI
source-only (SO) control. We measure the efficacy of target adaptation with and
without DRIs, against existing benchmarks like SHOT-B* and adaptations via
CDTrans. Findings demonstrate that excluding DRIs offers limited gains over
SHOT-B*, while their inclusion in the key segment boosts average precision
promoting superior domain generalization. This research underscores the vital
role of DRIs in enhancing ViT efficiency in UDA scenarios, setting a precedent
for further domain adaptation explorations.


  In this article we prove level raising for cuspidal eigenforms modulo prime
powers (for odd primes) of weight $k\geq 2$ and arbitrary character, extending
the result in weight two established by the work of Tsaknias and Wiese and
generalizing (partially) Diamond-Ribet's celebrated level raising theorems.