  Particle production from an expanding classical color electromagnetic field
is extensively studied, motivated by the early stage dynamics of
ultra-relativistic heavy ion collisions. We develop a formalism at one-loop
order to compute the particle spectra by canonically quantizing quark, gluon
and ghost fluctuations under the presence of such an expanding classical color
background field; the canonical quantization is done in the $\tau$-$\eta$
coordinates in order to take into account manifestly the expanding geometry. As
a demonstration, we model the expanding classical color background field by a
boost-invariantly expanding homogeneous color electric field with lifetime $T$,
for which we obtain analytically the quark and gluon production spectra by
solving the equations of motion of QCD non-perturbatively with respect to the
color electric field. In this paper we study (i) finite lifetime effect which
is found to modify significantly the particle spectra from those expected from
the Schwinger formula; (ii) the difference between the quark and gluon
production; and (iii) the quark mass dependence of the production spectra.
Implications of these results to ultra-relativistic heavy ion collisions are
also discussed.


  We propose to apply an "effective boundary condition" method to the problem
of chiral propulsion. For the case of a rotating helix moving through a fluid
at a low Reynolds number, the method amounts to replacing the original helix
(in the limit of small pitch) by a cylinder, but with a special kind of partial
slip boundary conditions replacing the non-slip boundary conditions on the
original helix. These boundary conditions are constructed to reproduce
far-field velocities of the original problem, and are defined by a few
parameters (slipping lengths) that can be extracted from a problem in planar
rather than cylindrical geometry. We derive the chiral propulsion coefficients
for spirals, helicoids, helically modulated cylinders, and some of their
generalizations using the introduced method. In the case of spirals, we compare
our results with the ones derived by Lighthill and find a very good agreement.
The proposed method is general and can be applied to any helical shape in the
limit of a small pitch. We have established that for a broad class of helical
surfaces the dependence of the chiral propulsion on the helical angle $\theta$
is universal, $\chi\sim \cos\theta\sin 2\theta$ with the maximal propulsion
achieved at the universal angle $\theta_m = \tan^{-1}(1/\sqrt{2})\approx
35.26^\circ$.


  Nonlinear Floquet states associated with a symmetry-breaking driving field
are exploited to control the dynamics of a Bose-Einstein condensate in a
double-well potential. The population imbalance between the two wells is shown
to be controllable by slowly tuning system parameters along a closed path. The
results extend symmetry-breaking-based quantum control to many-body systems and
extend navigation of linear Floquet states to navigation of nonlinear Floquet
states.


  With the increased pervasiveness of Lithium-ion batteries, there is growing
concern for the amount of retired batteries that will be entering the waste
stream. Although these batteries no longer meet the demands of their first
application, many still have a significant portion of their initial capacity
remaining for use in secondary applications. Yet, direct repurposing is
generally not possible and each cell in a battery must be evaluated, increasing
the cost of the repurposed packs due to the time intensive screening process.
In this paper, a rapid assessment of the internal resistance of a cell is
proposed. First, this method of measuring the resistance is completed on cells
from twelve retired battery packs and one fresh pack using a hybrid pulse power
characterization (HPPC) test as a benchmark for the analysis. Results from
these tests show relatively constant resistance measurements across mid to high
terminal voltages, allowing this metric to be independent of state of charge
(SOC). Then, the relation between internal resistance and capacity across the
various packs is discussed. Initial experimental results from this study show a
correlation between internal resistance and capacity which can be approximated
with a linear fit, suggesting internal resistance measurements taken above a
threshold cell terminal voltage may be a suitable initial screening metric for
the capacity of retired cells without knowledge of the SOC.


  As the number of Human-Centered Internet of Things (HCIoT) applications
increases, the self-adaptation of its services and devices is becoming a
fundamental requirement for addressing the uncertainties of the environment in
decision-making processes. Self-adaptation of HCIoT aims to manage run-time
changes in a dynamic environment and to adjust the functionality of IoT objects
in order to achieve desired goals during execution. SMASH is a semantic-enabled
multi-agent system for self-adaptation of HCIoT that autonomously adapts IoT
objects to uncertainties of their environment. SMASH addresses the
self-adaptation of IoT applications only according to the human values of
users, while the behavior of users is not addressed. This article presents
Q-SMASH: a multi-agent reinforcement learning-based approach for
self-adaptation of IoT objects in human-centered environments. Q-SMASH aims to
learn the behaviors of users along with respecting human values. The learning
ability of Q-SMASH allows it to adapt itself to the behavioral change of users
and make more accurate decisions in different states and situations.


  This paper discusses a generalized model for compact stars, assumed to be
anisotropic in nature due to the spherical symmetry and high density. After
embedding the four-dimensional spacetime in a five-dimensional flat spacetime,
which may be treated as an alternative to Karmarkar's condition of embedding
class 1 spacetime, the Einstein field equations were solved by employing a
class of physically acceptable metric functions proposed by Lake
\cite{Lake2003}. The physical properties determined include the anisotropic
factor showing that the anisotropy is zero at the center and maximal at the
surface. Other boundary conditions yielded the values of various parameters
needed for rendering the numerous plots and also led to the EOS parameters. It
was further determined that the usual energy conditions are satisfied and that
the compact structures are stable, based on several criteria, starting with the
TOV equation. The calculation of the effective gravitational mass shows that
the models satisfy the Buchdahl condition. Finally, the values of the numerous
constants and physical parameters were determined specifically for the strange
star LMCX-4. It is shown that the present generalized model can justify most
off the compact stars including white dwarfs and ultra dense compact stars for
a suitable tuning of the parametric values of $n$.


  Contrastive learning has emerged as a prominent branch of self-supervised
learning for several years. Especially, CLIP, which applies contrastive
learning to large sets of captioned images, has garnered significant attention.
Recently, SigLIP, a variant of CLIP, has been proposed, which uses the sigmoid
loss instead of the standard InfoNCE loss. SigLIP achieves the performance
comparable to CLIP in a more efficient manner by eliminating the need for a
global view. However, theoretical understanding of using the sigmoid loss in
contrastive learning is underexplored. In this paper, we provide a theoretical
analysis of using the sigmoid loss in contrastive learning, in the perspective
of the geometric structure of learned embeddings. First, we propose the
double-Constant Embedding Model (CCEM), a framework for parameterizing various
well-known embedding structures by a single variable. Interestingly, the
proposed CCEM is proven to contain the optimal embedding with respect to the
sigmoid loss. Second, we mathematically analyze the optimal embedding
minimizing the sigmoid loss for contrastive learning. The optimal embedding
ranges from simplex equiangular-tight-frame to antipodal structure, depending
on the temperature parameter used in the sigmoid loss. Third, our experimental
results on synthetic datasets coincide with the theoretical results on the
optimal embedding structures.


  A kinetic description of lattice-gas automaton models for reaction-diffusion
systems is presented. It provides corrections to the mean-field rate equations
in the diffusion-limited regime. When applied to the two-species Maginu model,
the theory gives an excellent quantitative prediction of the effect of slow
diffusion on the periodic oscillations of the average concentrations in a
spatially homogeneous state.


  Schramm Loewner Evolutions (SLE) are random increasing hulls defined through
the Loewner equation driven by Brownian motion. It is known that the increasing
hulls are generated by continuous curves. When the driving process is of the
form \sqrt{\kappa} B+\theta^{1/\alpha}S for a Brownian motion B and a symmetric
\alpha-stable process S with \kappa not equal to 4 and 8, we prove that the
corresponding increasing hulls are generated by Cadlag curves.


  We propose a mew picture for superconductivity in $\kappa-(BEDT-TTF)_2X$
salts arguing that small-{\bf q} electron-phonon scattering dominates the
pairing. We reproduce the distinct X-shaped d-wave gap reported recently by
magnetooptic measurements and we argue that the softness of the momentum
structure of the gap and the near degeneracy of s- and d-wave gap states may be
at the origin of the experimental controversy about the gap symmetry. We show
that a magnetic field applied parallel to the planes may induce extended
gapless-regions on the FS accounting for the experimental signatures of a
Fulde-Ferrel-Larkin-Ovchinikov state and it may induce gap symmetry transitions
as well.


  The demand of fast and power efficient spintronics devices with flexibility
requires additional energy for magnetization manipulation. Stress/and strain
have shown their potentials for tuning magnetic properties to the desired
level. Here, we report a systematic study for the effect of both tensile and
compressive stresses on the magnetic anisotropy (MA). Further the effect of
stress on the domain structure and magnetization relaxation mechanism in a
perpendicularly magnetized Co/Pt film has been studied. It is observed that a
minimal in-plane tensile strain has increased the coercivity of the film by
38$\%$ of its initial value, while a very small change of coercivity has been
found under compressive strain. The size of ferromagnetic domains decreases
under tensile strain, while no change is observed under the compressive strain.
Magnetization relxation measured at sub-coercive fields yields longer
relaxation time in the strained state.


  Traveling wave solutions of (2 + 1)-dimensional Zoomeron equation(ZE) are
developed in terms of exponential functions involving free parameters. It is
shown that the novel Lie group of transformations method is a competent and
prominent tool in solving nonlinear partial differential equations(PDEs) in
mathematical physics. The similarity transformation method(STM) is applied
first on (2 + 1)-dimensional ZE to find the infinitesimal generators.
Discussing the different cases on these infinitesimal generators, STM reduce (2
+ 1)-dimensional ZE into (1 + 1)-dimensional PDEs, later it reduces these PDEs
into various ordinary differential equations(ODEs) and help to find exact
solutions of (2 + 1)-dimensional ZE.


  We study the problem of jointly reasoning about language and vision through a
navigation and spatial reasoning task. We introduce the Touchdown task and
dataset, where an agent must first follow navigation instructions in a
real-life visual urban environment, and then identify a location described in
natural language to find a hidden object at the goal position. The data
contains 9,326 examples of English instructions and spatial descriptions paired
with demonstrations. Empirical analysis shows the data presents an open
challenge to existing methods, and qualitative linguistic analysis shows that
the data displays richer use of spatial reasoning compared to related
resources.


  We study heavy tailed random variables obtained by sampling an observable
with a power singularity along an orbit of an expanding map on the circle. In
the regime where the observables have infinite variance, we show that the set
of limit points of the ergodic sum process, rescaled by $N^{1/s} (\ln
N)^\alpha$, where $s$ is the index of limiting stable law, equals to the set of
piecewise constant increasing functions with finitely many jumps. The proof
relies on the multiple Borel-Cantelli Lemma proven in Dolgopyat, Fayad and Liu
[J. Mod. Dyn. 18 (2022) 209--289].


  The properties of the ground state of two-color QCD at non-zero baryon
chemical potential $\mu$ present an interesting problem in strongly-interacting
gauge theory; in particular the nature of the physically-relevant degrees of
freedom in the superfluid phase in the post-onset regime $\mu>m_\pi/2$ still
needs clarification. In this study we present evidence for in-medium effects at
high $\mu$ by studying the wavefunctions of mesonic and diquark states using
orthodox lattice simulation techniques, made possible by the absence of a Sign
Problem for the model with $N_f=2$. Our results show that beyond onset the
spatial extent of hadrons decreases as $\mu$ grows, and that the wavefunction
profiles are consistent with the existence of a dynamically-gapped Fermi
surface in this regime.


  One of the most promising routes to non-fermi liquids and strange metals has
been through SYK models \cite{Sachdev:2010um}, which necessarily involve large
flavor degrees of freedom and interactions with imposed disorder. We introduce
an interacting model of nonlocal spinless fermions in which large flavor and
effective disorder emerge spontaneously in the extreme nonlocal limit. This
model may be thought of as an expansion in a dimensionless "locality scale,"
$\alpha$, with the limit $\alpha \rightarrow 0$ recovering a conventional local
action. For finite $\alpha$, the resulting interacting nonlocal action exhibits
a large number of low-energy degrees of freedom -- proportional to $\alpha$ --
and the structure factor mediating the local interactions between these
fermions is effectively random for large $\alpha$. In one dimension, with
finite $\alpha$, we show that interactions are marginal to the one loop level
(as they are in the conventional local case), preserving a gapless phase. At
large $\alpha$ the interaction strength becomes comparable to the bandwidth and
we analyze this large flavor limit in a manner similar to the diagrammatic
approach to SYK. As $\alpha$ is increased we argue that the gapless phase
established by conventional RG possibly crosses over to a gapless SYK phase,
although the "melon" diagrams are not exclusively dominant. We speculate on how
this model might arise physically from an S-matrix connecting pure excited
states -- rather than the vacuum -- to access finite temperature interacting
fermions.


  We present specific heat and resistivity study of CeIrIn5 in magnetic fields
up to 17 T and temperature down to 50 mK. Both quantities were measured with
the magnetic field parallel to the c-axis (H || [001]) and within the a-b plane
(H \perp [001]). Non-Fermi-liquid (NFL) behavior develops above 12 T for H ||
[001]. The Fermi liquid state is much more robust for H \perp [001] and is
suppressed only moderately at the highest applied field. Based on the observed
trends and the proximity to a metamagnetic phase transition, which exists at
fields above 25 T for H || [001], we suggest that the observed NFL behavior in
CeIrIn5 is a consequence of a metamagnetic quantum critical point.


  The success of the quantum level predictions of the Standard Model on the $Z$
boson properties, on $\mw$ and on $\mt$, which makes use of the muon lifetime
as an input, implies a stringent constraint on new physics contributions to the
$V-A$ charged-current interactions among leptons. Observed unitarity of the CKM
matrix elements then implies constraints on non-standard contributions to the
lepton-quark charged-current interactions. By using the recent electroweak data
as inputs, we find the 95%~CL limits for the corresponding contact
interactions: $\Lambda_{CC,+}^{\ell\ell}>7.5$ TeV and
$\Lambda_{CC,-}^{\ell\ell}>10.2$ TeV for the purely leptonic terms, and
$\Lambda_{CC,+}^{\ell q}>5.8$ TeV and $\Lambda_{CC,-}^{\ell q}>10.1$~TeV for
the lepton-quark contact interactions.


  Existing NeRF-based inverse rendering methods suppose that scenes are
exclusively illuminated by distant light sources, neglecting the potential
influence of emissive sources within a scene. In this work, we confront this
limitation using LDR multi-view images captured with emissive sources turned on
and off. Two key issues must be addressed: 1) ambiguity arising from the
limited dynamic range along with unknown lighting details, and 2) the expensive
computational cost in volume rendering to backtrace the paths leading to final
object colors. We present a novel approach, ESR-NeRF, leveraging neural
networks as learnable functions to represent ray-traced fields. By training
networks to satisfy light transport segments, we regulate outgoing radiances,
progressively identifying emissive sources while being aware of reflection
areas. The results on scenes encompassing emissive sources with various
properties demonstrate the superiority of ESR-NeRF in qualitative and
quantitative ways. Our approach also extends its applicability to the scenes
devoid of emissive sources, achieving lower CD metrics on the DTU dataset.


  We study F-theory duals of heterotic line bundle models on elliptically
fibered Calabi-Yau threefolds. These models necessarily contain NS5-branes
which are geometrised in the dual F-theory compactifications. We initiate a
systematic study of the correspondence between various configurations of
NS5-branes and the dual geometries in F-theory and perform several checks of
the duality. Furthermore, we discuss the singular transitions between different
configurations of NS5-branes.


  In this article, we will briefly review the recent progress on hydrodynamic
modeling and the extraction of the quark-gluon plasma (QGP) specific shear
viscosity with an emphasis on results obtained from the hybrid model VISHNU
that couples viscous hydrodynamics for the macroscopic expansion of the QGP to
the hadron cascade model for the microscopic evolution of the late hadronic
stage.


  We investigate the effects of spin fluctuations on the tunneling spectra of
the NS junction. In the high junction resistance limit, the dip/hump structure
observed in ARPES data for the high Tc superconductors is reproduced in a RPA
treatment of the t-t'-J model. It is shown that the dip/hump structure weakens
as doping increases as reflected in the data. In the other limit, we predict
that the zero bias Andreev peak can coexist with the dip/hump structure.
Furthermore, the c-axis tunneling spectra is found to be very similar to a
recent STM data once these fluctuations are included.


  Recently, the configuration using atomic interferometers (AIs) had been
suggested for the detection of gravitational waves. A new AI with some
additional laser pulses for implementing large momentum transfer was also put
forward, in order to improve the influence of shot noise and laser frequency
noise. In the paper, we use the sensitivity function to analyze all possible
configurations of the new AI and to distinguish how many momenta are
transferred in a specific configuration. With the analysis for the new
configuration, we explore the detection scheme of gravitational wave further,
in particular, for the amelioration of the laser frequency noise. We find that
the amelioration is definite in such scheme, but novelly, in some cases the
frequency noise can be canceled completely by using a proper data processing
method.


  Three-dimensional convex bodies can be classified in terms of the number and
stability types of critical points on which they can balance at rest on a
horizontal plane. For typical bodies these are nondegenerate maxima, minima,
and saddle-points, the numbers of which provide a primary classification.
Secondary and tertiary classifications use graphs to describe orbits connecting
these critical points in the gradient vector field associated with each body.
In previous work it was shown that these classifications are complete in that
no class is empty. Here we construct 1- and 2-parameter families of convex
bodies connecting members of adjacent primary and secondary classes and show
that transitions between them can be realized by codimension 1 saddle-node and
saddle-saddle (heteroclinic) bifurcations in the gradient vector fields. Our
results indicate that all combinatorially possible transitions can be realized
in physical shape evolution processes, e.g. by abrasion of sedimentary
particles.


  A time-dependent completely integrable Hamiltonian system is quantized with
respect to time-dependent action-angle variables near an instantly compact
regular invariant manifold. Its Hamiltonian depends only on action variables,
and has a time-independent countable energy spectrum.


  We perform the finite-temperature determinant quantum Monte Carlo simulation
for the attractive Hubbard model on the half-filled bilayer square lattice.
Recent progress on optical lattice experiments lead us to investigate various
single-particle properties such as momentum distribution and double occupancies
which should be easily measured in cold-atom experiments. The pair-pair and the
density-density correlations have been studied in detail, and through
finite-size scaling, we show that there is no competing charge density wave
order in the bilayer band-insulator model and that the superfluid phase is the
stable phase for the interaction range $\abs{U}/t = 5-10$. We show the
existence of two energy scales in the system as we increase the attractive
interaction, one governing the phase coherence and the other one corresponding
to the molecule formation. In the end, we map out the full $T-U$ phase diagram
and compare the $T_c$ obtained through the mean-field analysis. We observe that
the maximum $T_c/t(= 0.27)$ occurs for $\abs{U}/t = 6$, which is roughly twice
the reported $T_c$ of the single-layer attractive Hubbard model.


  In autonomous driving, radar systems play an important role in detecting
targets such as other vehicles on the road. Radars mounted on different cars
can interfere with each other, degrading the detection performance. Deep
learning methods for automotive radar interference mitigation can succesfully
estimate the amplitude of targets, but fail to recover the phase of the
respective targets. In this paper, we propose an efficient and effective
technique based on unfolded robust Principal Component Analysis (RPCA) that is
able to estimate both amplitude and phase in the presence of interference. Our
contribution consists in introducing residual overcomplete auto-encoder
(ROC-AE) blocks into the recurrent architecture of unfolded RPCA, which results
in a deeper model that significantly outperforms unfolded RPCA as well as other
deep learning models.


  In the article by M. G. Mustafa published in Phys. Rev. C {\bf 72}, 014905
(2005) the author has estimated the total energy loss of a charm quark and
quenching of hadron spectra due to the collisional energy loss of energetic
partons in an expanding quark-gluon plasma employing Fokker-Planck equation. We
wish to point out through this Comment that some of conceptual and numerical
results of the said paper are unreliable. For the sake of clarity our
discussion will focus on the massless case (although a few remarks on the
$m\neq 0$ case are also made).


  Throughout the past decade, research in HCI has identified numerous instances
of dark patterns in digital interfaces. These efforts have led to a
well-fostered typology describing harmful strategies users struggle to
navigate. However, an in-depth understanding of the underlying mechanisms that
deceive, coerce, or manipulate users is missing. We explore the interplay
between cognitive biases and dark patterns to address this gap. To that end, we
conducted four focus groups with experts (N=15) in psychology and dark pattern
scholarship, inquiring how they conceptualise the relation between cognitive
biases and dark patterns. Based on our results, we constructed the
"Relationship Model of Cognitive Biases and Dark Patterns" which illustrates
how cognitive bias and deceptive design patterns relate and identifies
opportune moments for ethical reconsideration and user protection mechanisms.
Our insights contribute to the current discourse by emphasising ethical design
decisions and their implications in the field of HCI.


  We establish existence of solutions in a scale of classes weaker than the
finite energy Leray class and stronger than the infinite energy
Lemari\'e-Rieusset class. The new classes are based on the $L^2$ Wiener amalgam
spaces. Solutions in the classes closer to the Leray class are shown to satisfy
some properties known in the Leray class but not the Lemari\'e-Rieusset class,
namely eventual regularity and long time estimates on the growth of the local
energy. In this sense, these solutions bridge the gap between Leray's original
solutions and Lemari\'e-Rieusset's solutions and help identify scalings at
which certain properties may break down.


  The influence of the temperature and its fluctuations on the ion saturation
current and the floating potential, which are typical quantities measured by
Langmuir probes in the turbulent edge region of fusion plasmas, is analysed by
global nonlinear gyrofluid simulations for two exemplary parameter regimes. The
numerical simulation facilitates a direct access to densities, temperatures and
the plasma potential at different radial positions around the separatrix. This
allows a comparison between raw data and the calculated ion saturation current
and floating potential within the simulation. Calculations of the
fluctuation-induced radial particle flux and its statistical properties reveal
significant differences to the actual values at all radial positions of the
simulation domain, if the floating potential and the temperature averaged
density inferred from the ion saturation current is used.


  We present recent progress in the lattice calculation of leptonic decay
constants for $B_{(s)}$ and $D_{(s)}$ mesons using the Oktay-Kronfeld (OK)
action for charm and bottom valence quarks, whose masses are tuned
non-perturbatively. The calculations are done on 6 HISQ ensembles generated by
the MILC collaboration with $N_f=2+1+1$ flavors. We also use the HISQ action
for the light spectator quarks. Results are presented for the ratios
$f_{B_s}/f_B$ and $f_{D_s}/f_D$, which reflect $SU(3)$ flavor symmetry
breaking, and are independent of the renormalization constants of the axial
currents.


  We present ZeroRF, a novel per-scene optimization method addressing the
challenge of sparse view 360{\deg} reconstruction in neural field
representations. Current breakthroughs like Neural Radiance Fields (NeRF) have
demonstrated high-fidelity image synthesis but struggle with sparse input
views. Existing methods, such as Generalizable NeRFs and per-scene optimization
approaches, face limitations in data dependency, computational cost, and
generalization across diverse scenarios. To overcome these challenges, we
propose ZeroRF, whose key idea is to integrate a tailored Deep Image Prior into
a factorized NeRF representation. Unlike traditional methods, ZeroRF
parametrizes feature grids with a neural network generator, enabling efficient
sparse view 360{\deg} reconstruction without any pretraining or additional
regularization. Extensive experiments showcase ZeroRF's versatility and
superiority in terms of both quality and speed, achieving state-of-the-art
results on benchmark datasets. ZeroRF's significance extends to applications in
3D content generation and editing. Project page:
https://sarahweiii.github.io/zerorf/


  The graph of a Hecke operator encodes all information about the action of
this operator on automorphic forms. Let $X$ be a curve over $\mathbb{F}_q$, $F$
its function field and $\mathbb{A}$ the adele ring of $F$. In this paper we
will exhibit the first properties for the graph of Hecke operators for
$\mathrm{GL}_n(\mathbb{A}),$ for every $n \geq 1.$ This includes a description
of the graph in terms of coherent sheaves on $X.$ We provide a numerical
condition for two vertices to be connected by an edge. Moreover, we describe
how to calculate these graphs in the case of the projective line $X =
\mathbb{P}^1(\mathbb{F}_q).$


  Hercules is a dwarf spheroidal satellite of the Milky Way, found at a
distance of about 138 kpc, and showing evidence of tidal disruption. It is very
elongated and exhibits a velocity gradient of 16 +/- 3 km/s/kpc. Using this
data a possible orbit of Hercules has previously been deduced in the
literature. In this study we make use of a novel approach to find a best fit
model that follows the published orbit. Instead of using trial and error, we
use a systematic approach in order to find a model that fits multiple
observables simultaneously. As such, we investigate a much wider parameter
range of initial conditions and ensure we have found the best match possible.
Using a dark matter free progenitor that undergoes tidal disruption, our
best-fit model can simultaneously match the observed luminosity, central
surface brightness, effective radius, velocity dispersion, and velocity
gradient of Hercules. However, we find it is impossible to reproduce the
observed elongation and the position angle of Hercules at the same time in our
models. This failure persists even when we vary the duration of the simulation
significantly, and consider a more cuspy density distribution for the
progenitor. We discuss how this suggests that the published orbit of Hercules
is very likely to be incorrect.


  By the use of a point charge model based on the Judd-Ofelt transition theory,
the luminescence from Eu3+ ions embedded in Gd2O3 clusters is calculated and
compared to the experimental data. The main result of the numerical study is
that without invoking any other mechanisms such as crystal disorder, the pure
geometrical argument of the symmetry breaking induced by the particle surface
has influence on the energy level splitting. The modifications are also
predicted to be observable in realistic conditions where unavoidable size
dispersion has to be taken into account. The emission spectrum results from the
contribution of three distinct regions, a cluster core, a cluster shell and a
very surface, the latter being almost completely quenched in realistic
conditions. Eventually, by detailing the spectra of the ions embedded at
different positions in the cluster we get an estimate of about 0.5 nm for the
extent of the crystal field induced Stark effect. Due to the similarity between
Y2O3 and Gd2O3, these results apply also to Eu3+ doped Y2O3 nanoparticles.


  We prove that a compact contact threefold which is bimeromorphically
equivalent to a Kaehler manifold and not rationally connected is the
projectivised tangent bundle of a Kaehler surface.


  In this paper, we study the stochastic resonance (SR) effect in an
optomechanical system driven by a strong coupling field and two weak signals in
both semiclassical and quantum frameworks. In the semiclassical description,
the SR phenomena are found at the cooperation of input signals and system
noises. When two signals co-act on our system, the interference effect between
the optically induced SR and the mechanically induced SR can be generated. In
particular, a unique beating effect, which makes the SR effect robust against
the initial phase difference of two signals, appears in the SR synchronization
process with unsynchronized signals. In addition, the quantum stochastic
resonance effect is numerically observed in the full quantum framework induced
by pure quantum fluctuations.


  A geometric braid $B$ can be interpreted as a loop in the space of monic
complex polynomials with distinct roots. This loop defines a function
$g:\mathbb{C}\times S^1\to\mathbb{C}$ that vanishes on $B$. We define the set
of P-fibered braids as those braids that can be represented by loops of
polynomials such that the corresponding function $g$ induces a fibration $\arg
g:(\mathbb{C}\times S^1)\backslash B\to S^1$. We show that a certain satellite
operation produces new P-fibered braids from known ones. We also prove that any
braid $B$ with $n$ strands, $k_-$ negative and $k_+$ positive crossings can be
turned into a P-fibered braid (and hence also into a braid whose closure is
fibered) by adding at least $\tfrac{k_-+1}{n}$ negative or $\tfrac{k_+ +1}{n}$
positive full twists to it.


  Let $\mathcal{H}$ denote the class of harmonic functions $f$ in $\mathbb{D}:=
\{z\in \mathbb{C}:|z| < 1\}$ normalized by $f(0) = 0 = f_z(0) -1$. For $\alpha
\geq 0$, we consider the following class
$$\mathcal{W}^0_{\mathcal{H}}(\alpha):= \{f = h + \overline{g}\in\mathcal{H}:
{\rm Re\,}(h'(z) + \alpha z h''(z)) >|g'(z) + \alpha z g''(z)|, \quad z\in
\mathbb{D}\}. $$ In this paper, we first prove the coefficient conjecture of
Clunie and Sheil-Small for functions in the class
$\mathcal{W}^0_{\mathcal{H}}(\alpha)$. We also prove growth theorem,
convolution, convex combination properties for functions in the class
$\mathcal{W}^0_{\mathcal{H}}(\alpha)$. Finally, we determine the value of $r$
so that the partial sums of functions in the class
$\mathcal{W}^0_{\mathcal{H}}(\alpha)$ are close-to-convex in $|z|<r$.


  Within the performance-based earthquake engineering (PBEE) framework, the
fragility model plays a pivotal role. Such a model represents the probability
that the engineering demand parameter (EDP) exceeds a certain safety threshold
given a set of selected intensity measures (IMs) that characterize the
earthquake load. The-state-of-the art methods for fragility computation rely on
full non-linear time-history analyses. Within this perimeter, there are two
main approaches: the first relies on the selection and scaling of recorded
ground motions; the second, based on random vibration theory, characterizes the
seismic input with a parametric stochastic ground motion model (SGMM). The
latter case has the great advantage that the problem of seismic risk analysis
is framed as a forward uncertainty quantification problem. However, running
classical full-scale Monte Carlo simulations is intractable because of the
prohibitive computational cost of typical finite element models. Therefore, it
is of great interest to define fragility models that link an EDP of interest
with the SGMM parameters -- which are regarded as IMs in this context. The
computation of such fragility models is a challenge on its own and, despite few
recent studies, there is still an important research gap in this domain. This
study tackles this computational challenge by using stochastic polynomial chaos
expansions to represent the statistical dependence of EDP on IMs. More
precisely, this surrogate model estimates the full conditional probability
distribution of EDP conditioned on IMs. We compare the proposed approach with
some state-of-the-art methods in two case studies. The numerical results show
that the new method prevails its competitors in estimating both the conditional
distribution and the fragility functions.


  By using the scaling method we derive the virial theorem for the relativistic
mean field model of nuclei treated in the Thomas-Fermi approach. The
Thomas-Fermi solutions statisfy the stability condition against scaling. We
apply the formalism to study the excitation energy of the breathing mode in
finite nuclei with several relativistic parameter sets of common use.


  Autonomous discovery and direct instruction are two distinct sources of
learning in children but education sciences demonstrate that mixed approaches
such as assisted discovery or guided play result in improved skill acquisition.
In the field of Artificial Intelligence, these extremes respectively map to
autonomous agents learning from their own signals and interactive learning
agents fully taught by their teachers. In between should stand teachable
autotelic agents (TAA): agents that learn from both internal and teaching
signals to benefit from the higher efficiency of assisted discovery. Designing
such agents will enable real-world non-expert users to orient the learning
trajectories of agents towards their expectations. More fundamentally, this may
also be a key step to build agents with human-level intelligence. This paper
presents a roadmap towards the design of teachable autonomous agents. Building
on developmental psychology and education sciences, we start by identifying key
features enabling assisted discovery processes in child-tutor interactions.
This leads to the production of a checklist of features that future TAA will
need to demonstrate. The checklist allows us to precisely pinpoint the various
limitations of current reinforcement learning agents and to identify the
promising first steps towards TAA. It also shows the way forward by
highlighting key research directions towards the design or autonomous agents
that can be taught by ordinary people via natural pedagogy.


  Presented here is a description of the ionization of hydrogen and hydrogenic
ions by antiproton-impact, based on very large scale numerical solutions of the
time-dependent Schr\"odinger equation in three spatial dimensions and on
analysis of the topology of the electronic eigenenergy surfaces in the plane of
complex internuclear distance. Comparison is made with other theories and very
recent measurements.


  A non-commutative, planar, Hopf algebra of rooted trees was proposed in L.
Foissy, Bull. Sci. Math. 126 (2002) 193-239. In this paper we propose such a
non-commutative Hopf algebra for graphs. In order to define a non-commutative
product we use a quantum field theoretical (QFT) idea, namely the one of
introducing discrete scales on each edge of the graph (which, within the QFT
framework, corresponds to energy scales of the associated propagators).


  We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove
existence of the infinite volume addition operator, almost surely with respect
to the infinite volume limit mu of the uniform measures on recurrent
configurations. We prove the existence of a Markov process with stationary
measure mu, and study ergodic properties of this process. The main techniques
we use are a connection between the statistics of waves and uniform
two-component spanning trees and results on the uniform spanning tree measure
on Z^d.


  The recently discovered Parrondo's paradox claims that two losing games can
result, under random or periodic alternation of their dynamics, in a winning
game: "losing+losing=winning". In this paper we follow Parrondo's philosophy of
combining different dynamics and we apply it to the case of one-dimensional
quadratic maps. We prove that the periodic mixing of two chaotic dynamics
originates an ordered dynamics in certain cases. This provides an explicit
example (theoretically and numerically tested) of a different Parrondian
paradoxical phenomenon: "chaos+chaos=order"


  Three deep flux minima were observed with nearly the same time-scales and
intervals for the blazar PKS 1510-089 in the past few years. A binary black
hole system was proposed to be at the nucleus of this object, and a new minimum
was predicted to occur in 2002 March. We monitored this source with a 60/90 cm
Schmidt telescope from 2002 February to April. In combination with the data
obtained by Xie et al. (2004) in the same period, we presented for the 2002
minimum a nearly symmetric light curve, which would be required by an eclipsing
model of a binary black hole system. We also constrained the time-scale of the
minimum to be 35 min, which is more consistent with the time-scales ~42 min of
the three previous minima than the 89 min time-scale given by the same authors.
The wiggling miniarcsecond radio jet observed in this object is taken as a
further evidence for the binary black hole system. The `coupling' of the
periodicity in light curve and the helicity in radio jet is discussed in the
framework of a binary black hole system.


  This paper is concerned with the approximation of the solution of partial
differential equations by means of artificial neural networks. Here a
feedforward neural network is used to approximate the solution of the partial
differential equation. The learning problem is formulated as a least squares
problem, choosing the residual of the partial differential equation as a loss
function, whereas a multilevel Levenberg-Marquardt method is employed as a
training method. This setting allows us to get further insight into the
potential of multilevel methods. Indeed, when the least squares problem arises
from the training of artificial neural networks, the variables subject to
optimization are not related by any geometrical constraints and the standard
interpolation and restriction operators cannot be employed any longer. A
heuristic, inspired by algebraic multigrid methods, is then proposed to
construct the multilevel transfer operators. Numerical experiments show
encouraging results related to the efficiency of the new multilevel
optimization method for the training of artificial neural networks, compared to
the standard corresponding one-level procedure.


  Neuromorphic chip refers to an unconventional computing architecture that is
modelled on biological brains. It is ideally suited for processing sensory data
for intelligence computing, decision-making or context cognition. Despite rapid
development, conventional artificial synapses exhibit poor connection
flexibility and require separate data acquisition circuitry, resulting in
limited functionalities and significant hardware redundancy. Here we report a
novel light-stimulated artificial synapse based on a graphene-nanotube hybrid
phototransistor that can directly convert optical stimuli into a "neural image"
for further neuronal analysis. Our optically-driven synapses involve multiple
steps of plasticity mechanisms and importantly exhibit flexible tuning of both
short- and long-term plasticity. Furthermore, our neuromorphic phototransistor
can take multiple pre-synaptic light stimuli via wavelength-division
multiplexing and allows advanced optical processing through
charge-trap-mediated optical coupling. The capability of complex neuromorphic
functionalities in a simple silicon-compatible device paves the way for novel
neuromorphic computing architectures involving photonics.


  Reliable and efficient trajectory generation methods are a fundamental need
for autonomous dynamical systems of tomorrow. The goal of this article is to
provide a comprehensive tutorial of three major convex optimization-based
trajectory generation methods: lossless convexification (LCvx), and two
sequential convex programming algorithms known as SCvx and GuSTO. In this
article, trajectory generation is the computation of a dynamically feasible
state and control signal that satisfies a set of constraints while optimizing
key mission objectives. The trajectory generation problem is almost always
nonconvex, which typically means that it is not readily amenable to efficient
and reliable solution onboard an autonomous vehicle. The three algorithms that
we discuss use problem reformulation and a systematic algorithmic strategy to
nonetheless solve nonconvex trajectory generation tasks through the use of a
convex optimizer. The theoretical guarantees and computational speed offered by
convex optimization have made the algorithms popular in both research and
industry circles. To date, the list of applications includes rocket landing,
spacecraft hypersonic reentry, spacecraft rendezvous and docking, aerial motion
planning for fixed-wing and quadrotor vehicles, robot motion planning, and
more. Among these applications are high-profile rocket flights conducted by
organizations like NASA, Masten Space Systems, SpaceX, and Blue Origin. This
article aims to give the reader the tools and understanding necessary to work
with each algorithm, and to know what each method can and cannot do. A publicly
available source code repository supports the provided numerical examples. By
the end of the article, the reader should be ready to use the methods, to
extend them, and to contribute to their many exciting modern applications.


  We present a simple algebraic construction of all the small resolutions for
the SU(5) Weierstrass model. Each resolution corresponds to a subchamber on the
Coulomb branch of the five-dimensional N=1 SU(5) gauge theory with matter
fields in the fundamental and two-index antisymmetric representations. This
construction unifies all previous resolutions found in the literature in a
single framework.


  Direct numerical simulation (DNS), mostly used in fundamental turbulence
research, is limited to low turbulent intensities due the current and future
computer resources. Standard turbulence models, like RaNS (Reynolds averaged
Navier-Stokes) and LES (Large Eddy Simulation), are applied to flows in
engineering, but they miss small scale effects, which are frequently of
importance, see e.g. the whole area of reactive flows, flows with apparent
Prandtl or Schmidt number effects, or even wall bounded flows. A recent
alternative to these standard approaches is the one-dimensional turbulence
(ODT) model, which is limited to 1D sub-domains. In two papers we will provide
a generalized filter strategy, called XLES (extended LES), including a formal
theory (part I) and one special approach in the XLES family of models, called
ODTLES (in part II (see Glawe et al. (2015))). ODTLES uses an ODT sub-grid
model to describe all turbulent scales not represented by XLES, which leaves
the larger scales to be simulated in 3D. This allows a turbulence modeling
approach with a 3D resolution mainly independent of the turbulent intensity.
Thus ODTLES is able to compute highly turbulent flows in domains of moderate
complexity affordably and including the full range of turbulent and diffusive
scales. The convergence of XLES to DNS is shown and the unconventional XLES
advection approach is investigated in basic numerical tests. In part II, highly
turbulent channel and duct flow results are discussed and show the future
potential of XLES and ODTLES.


  The land-use map is an important data that can reflect the use and
transformation of human land, and can provide valuable reference for land-use
planning. For the traditional image classification method, producing a high
spatial resolution (HSR), land-use map in large-scale is a big project that
requires a lot of human labor, time, and financial expenditure. The rise of the
deep learning technique provides a new solution to the problems above. This
paper proposes a fast and precise method that can achieve large-scale land-use
classification based on deep convolutional neural network (DCNN). In this
paper, we optimize the data tiling method and the structure of DCNN for the
multi-channel data and the splicing edge effect, which are unique to remote
sensing deep learning, and improve the accuracy of land-use classification. We
apply our improved methods in the Guangdong Province of China using GF-1
images, and achieve the land-use classification accuracy of 81.52%. It takes
only 13 hours to complete the work, which will take several months for human
labor.


  Complex fluid-fluid interfaces featuring mesoscale structures with adsorbed
particles are key components of newly designed materials which are continuously
enriching the field of soft matter. Simulation tools which are able to cope
with the different scales characterizing these systems are fundamental
requirements for efficient theoretical investigations. In this paper we present
a novel simulation method, based on the approach of Ahlrichs and D\"unweg
[Ahlrichs and D\"unweg, Int. J. Mod. Phys. C, 1998, 9, 1429], that couples the
"Shan-Chen" multicomponent Lattice Boltzmann technique to off-lattice molecular
dynamics to simulate efficiently complex fluid-fluid interfaces.
  We demonstrate how this approach can be used to study a wide class of
challenging problems. Several examples are given, with an accent on
bicontinuous phases formation in polyelectrolyte solutions and ferrofluid
emulsions. We also show that the introduction of solvation free energies in the
particle-fluid interaction unveils the hidden, multiscale nature of the
particle-fluid coupling, allowing to treat symmetrically (and interchangeably)
the on-lattice and off-lattice components of the system.


  As the amount and complexity of data grows, retrieving it has become a more
difficult task that requires greater knowledge and resources. This is
especially true for the logistics industry, where new technologies for data
collection provide tremendous amounts of interconnected real-time data. The
Intelligent Query and Learning System (IQLS) simplifies the process by allowing
natural language use to simplify data retrieval . It maps structured data into
a framework based on the available metadata and available data models. This
framework creates an environment for an agent powered by a Large Language
Model. The agent utilizes the hierarchical nature of the data to filter
iteratively by making multiple small context-aware decisions instead of
one-shot data retrieval. After the Data filtering, the IQLS enables the agent
to fulfill tasks given by the user query through interfaces. These interfaces
range from multimodal transportation information retrieval to route planning
under multiple constraints. The latter lets the agent define a dynamic object,
which is determined based on the query parameters. This object represents a
driver capable of navigating a road network. The road network is depicted as a
graph with attributes based on the data. Using a modified version of the
Dijkstra algorithm, the optimal route under the given constraints can be
determined. Throughout the entire process, the user maintains the ability to
interact and guide the system. The IQLS is showcased in a case study on the
Canadian logistics sector, allowing geospatial, visual, tabular and text data
to be easily queried semantically in natural language.


  X-ray absorption spectroscopy (XAS) is an element-specific materials
characterization technique that is sensitive to structural and electronic
properties. First-principles simulated XAS has been widely used as a powerful
tool to interpret experimental spectra and draw physical insights. Recently,
there has also been growing interest in building computational XAS databases to
enable data analytics and machine learning applications. However, there are
non-trivial differences among commonly used XAS simulation codes, both in
underlying theoretical formalism and in technical implementation. Reliable and
reproducible computational XAS databases require systematic benchmark studies.
In this work, we benchmarked Ti K-edge XAS simulations of ten representative
Ti-O binary compounds, which we refer to as the Ti-O-10 dataset, using three
state-of-the-art codes: xspectra, ocean and exciting. We systematically studied
the convergence behavior with respect to the input parameters and developed a
workflow to automate and standardize the calculations to ensure converged
spectra. Our benchmark comparison shows: (1) the two Bethe-Salpeter equation
(BSE) codes (ocean and exciting) have excellent agreement in the energy range
studied (up to 35 eV above the onset) with an average Spearman's rank
correlation score of 0.998; (2) good agreement is obtained between the
core-hole potential code (xspectra) and BSE codes (ocean and exciting) with an
average Spearman's rank correlation score of 0.990. Our benchmark study
provides important standards for first-principles XAS simulations with broad
impact in data-driven XAS analysis.


  We present a new method for finding isolated exact solutions of a class of
non-adiabatic Hamiltonians of relevance to quantum optics and allied areas.
Central to our approach is the use of Bogoliubov transformations of the bosonic
fields in the models. We demonstrate the simplicity and efficiency of this
method by applying it to the Rabi Hamiltonian.


  We study the two-baryon system with two units of charm looking for the
possible existence of a loosely bound state resembling the $H$ dibaryon. We
make use of a chiral constituent quark model tuned in the description of the
baryon and meson spectra as well as the $NN$ interaction. The presence of the
heavy quarks makes the interaction simpler than in light baryon systems. We
analyze possible quark-Pauli effects that would be present in spin-isospin
saturated channels. Our results point to the non-existence of a charmed
$H$-like dibaryon, although it may appear as a resonance above the
$\Lambda_c\Lambda_c$ threshold.


  Due to the trial-and-error nature, it is typically challenging to apply RL
algorithms to safety-critical real-world applications, such as autonomous
driving, human-robot interaction, robot manipulation, etc, where such errors
are not tolerable. Recently, safe RL (i.e. constrained RL) has emerged rapidly
in the literature, in which the agents explore the environment while satisfying
constraints. Due to the diversity of algorithms and tasks, it remains difficult
to compare existing safe RL algorithms. To fill that gap, we introduce GUARD, a
Generalized Unified SAfe Reinforcement Learning Development Benchmark. GUARD
has several advantages compared to existing benchmarks. First, GUARD is a
generalized benchmark with a wide variety of RL agents, tasks, and safety
constraint specifications. Second, GUARD comprehensively covers
state-of-the-art safe RL algorithms with self-contained implementations. Third,
GUARD is highly customizable in tasks and algorithms. We present a comparison
of state-of-the-art safe RL algorithms in various task settings using GUARD and
establish baselines that future work can build on.


  We study galaxy populations and search for possible merging substructures in
the rich galaxy cluster A2142. Normal mixture modelling revealed in A2142
several infalling galaxy groups and subclusters. The projected phase space
diagram was used to analyse the dynamics of the cluster and study the
distribution of various galaxy populations in the cluster and subclusters. The
cluster, supercluster, BCGs, and one infalling subcluster are aligned. Their
orientation is correlated with the alignment of the radio and X-ray haloes of
the cluster. Galaxies in the centre of the main cluster at the clustercentric
distances $0.5~h^{-1}Mpc$ have older stellar populations (with the median age
of $10 - 11$~Gyrs) than galaxies at larger clustercentric distances.
Star-forming and recently quenched galaxies are located mostly in the infall
region at the clustercentric distances $D_{\mathrm{c}} \approx 1.8~h^{-1}Mpc$,
where the median age of stellar populations of galaxies is about $2$~Gyrs.
Galaxies in A2142 have higher stellar masses, lower star formation rates, and
redder colours than galaxies in other rich groups. The total mass in infalling
groups and subclusters is $M \approx 6\times10^{14}h^{-1}M_\odot$,
approximately half of the mass of the cluster, sufficient for the mass growth
of the cluster from redshift $z = 0.5$ (half-mass epoch) to the present. The
cluster A2142 may have formed as a result of past and present mergers and
infallen groups, predominantly along the supercluster axis. Mergers cause
complex radio and X-ray structure of the cluster and affect the properties of
galaxies in the cluster, especially in the infall region. Explaining the
differences between galaxy populations, mass, and richness of A2142, and other
groups and clusters may lead to better insight about the formation and
evolution of rich galaxy clusters.


  Epidermal growth factor (EGF), a potent cytokine, is known to promote tumor
invasion both in vivo and in vitro. Previously, we observed that single breast
tumor cells (MDA-MB-231 cell line) embedded within a 3D collagen matrix
displayed enhanced motility but no discernible chemotaxis in the presence of
linear EGF gradients using a microfluidic platform. Inspired by a recent
theoretical development that clustered mammalian cells respond differently to
chemical gradients than single cells, we studied tumor spheroid invasion within
a 3D extracellular matrix (ECM) in the presence of EGF gradients. We found that
EGF gradients promoted tumor cell detachment from the spheroid core, and the
position of the tumor spheroid core showed a mild chemotactic response towards
the EGF gradients. For those tumor cells detached from the spheroids, they
showed an enhanced chemokinesis response in contrast to previous experimental
results using single cells embedded within an ECM. No discernible chemotactic
response towards the EGF gradients was found for the cells outside the spheroid
core. This work demonstrates that a cluster of tumor cells responds differently
than single tumor cells towards EGF gradients and highlights the importance of
a tumor spheroid platform for chemotaxis studies.


  We report the detection of quantum confinement in single InAs-InP core-shell
nanowires. The wires having an InAs core with ~25 nm diameter are characterized
by emission spectra in which two peaks are identified under high excitation
intensity conditions. The peaks are caused by emission from the ground and
excited quantized levels, due to the quantum confinement in the plane
perpendicular to the nanowire axis. We have identified in the emission spectra
different energy contributions related to the wurtzite structure of the wires,
the strain between the wurtzite core and shell, and the confinement energy of
the InAs core. Calculations based on 6-band strain-dependent k.p theory allow
the theoretical estimation of the confined energy states in such materials and
we found these results to be in good agreement with those from the
photoluminescence studies.


  We construct examples of Tonelli Hamiltonians on $\T^n$ (for any $n\geq 2$)
such that the hypersurfaces corresponding to the Ma\~n\'e critical value are
stable (i.e. geodesible). We also provide a criterion for instability in terms
of closed orbits in free homotopy classes and we show that any stable energy
level of a Tonelli Hamiltonian must contain a closed orbit.


  Let $X$ be an arbitrary continuous random variable and $Z$ be an independent
Gaussian random variable with zero mean and unit variance. For $t~>~0$, Costa
proved that $e^{2h(X+\sqrt{t}Z)}$ is concave in $t$, where the proof hinged on
the first and second order derivatives of $h(X+\sqrt{t}Z)$. Specifically, these
two derivatives are signed, i.e., $\frac{\partial}{\partial t}h(X+\sqrt{t}Z)
\geq 0$ and $\frac{\partial^2}{\partial t^2}h(X+\sqrt{t}Z) \leq 0$. In this
paper, we show that the third order derivative of $h(X+\sqrt{t}Z)$ is
nonnegative, which implies that the Fisher information $J(X+\sqrt{t}Z)$ is
convex in $t$. We further show that the fourth order derivative of
$h(X+\sqrt{t}Z)$ is nonpositive. Following the first four derivatives, we make
two conjectures on $h(X+\sqrt{t}Z)$: the first is that
$\frac{\partial^n}{\partial t^n} h(X+\sqrt{t}Z)$ is nonnegative in $t$ if $n$
is odd, and nonpositive otherwise; the second is that $\log J(X+\sqrt{t}Z)$ is
convex in $t$. The first conjecture can be rephrased in the context of
completely monotone functions: $J(X+\sqrt{t}Z)$ is completely monotone in $t$.
The history of the first conjecture may date back to a problem in mathematical
physics studied by McKean in 1966. Apart from these results, we provide a
geometrical interpretation to the covariance-preserving transformation and
study the concavity of $h(\sqrt{t}X+\sqrt{1-t}Z)$, revealing its connection
with Costa's EPI.


  Understanding the underlying mechanism of crystal nucleation during
solidification is a fundamental aspect in the prediction and control of
materials properties. Classical nucleation theory (CNT) assumes that
homogeneous nucleation occurs via random fluctuations within the supercooled
liquid, that the structure of the growing clusters resembles the most stable
bulk phase, and that the nucleus size is the sole reaction coordinate (RC) of
the process. Many materials are, however, known to exhibit multiple steps
during crystallization, forming different polymorphs. As a consequence, more
complex RCs are often required to capture all relevant information about the
process. In this work, we employ transition path sampling together with a
maximum likelihood analysis of candidate order parameters to identify suitable
reaction coordinates for the nucleation mechanism during solidification in Ni.
In contrast to CNT, the analysis of the reweighted path ensemble shows that a
pre-structured liquid region that surrounds the crystal cluster is a relevant
order parameter that enhances the RC and therefore plays a key role in the
description of the growing nucleus and the interfacial free energy. We
demonstrate that pre-structured liquid clusters that emerge within the liquid
act as precursors of the crystallization in a non-classical two-step mechanism
which predetermines the coordination of the polymorphs that are being selected.


  The voltage-spectral density SV(f) of the 2-dimensional electron gas formed
at the interface of LaAlO3 /SrTiO3 has been thoroughly investigated. The
low-frequency component has a clear 1/f behavior with a quadratic bias current
dependence, attributed to resistance fluctuations. However, its temperature
dependence is inconsistent with the classical Hooge model, based on
carrier-mobility fluctuations. The experimental results are, instead, explained
in terms of carrier-number fluctuations, due to an excitation-trapping
mechanism of the 2-dimensional electron gas.


  Network (or matrix) reconstruction is a general problem which occurs if the
margins of a matrix are given and the matrix entries need to be predicted. In
this paper we show that the predictions obtained from the iterative
proportional fitting procedure (IPFP) or equivalently maximum entropy (ME) can
be obtained by restricted maximum likelihood estimation relying on augmented
Lagrangian optimization. Based on the equivalence we extend the framework of
network reconstruction towards regression by allowing for exogenous covariates
and random heterogeneity effects. The proposed estimation approach is compared
with different competing methods for network reconstruction and matrix
estimation. Exemplary, we apply the approach to interbank lending data,
provided by the Bank for International Settlement (BIS). This dataset provides
full knowledge of the real network and is therefore suitable to evaluate the
predictions of our approach. It is shown that the inclusion of exogenous
information allows for superior predictions in terms of $L_1$ and $L_2$ errors.
Additionally, the approach allows to obtain prediction intervals via bootstrap
that can be used to quantify the uncertainty attached to the predictions.


  We study H\"older continuity for solutions of the $p$-Laplace equation. This
is established through a method involving an ordinary differential inequality,
in contrast to the classical proof of the De Giorgi-Nash-Moser Theorem which
uses iteration of an inequality through concentric balls.


  The theoretical properties of active inference agents are impressive, but how
do we realize effective agents in working hardware and software on edge
devices? This is an interesting problem because the computational load for
policy exploration explodes exponentially, while the computational resources
are very limited for edge devices. In this paper, we discuss the necessary
features for a software toolbox that supports a competent non-expert engineer
to develop working active inference agents. We introduce a toolbox-in-progress
that aims to accelerate the democratization of active inference agents in a
similar way as TensorFlow propelled applications of deep learning technology.


  We discuss the role of the extra force $$ \mathbf f_{\rm e}=-\frac 1
2(\nabla\cdot\mathbf v)\mathbf v $$ in the system of partial differential
equations \begin{equation*} \left\{ \begin{aligned} &\frac{\partial\mathbf
v}{\partial \rm t}+(\mathbf v\cdot\nabla)\mathbf v+\nabla \mathrm p-\frac 1
{\rm Re}\Delta\mathbf v=\mathbf f+\mathbf f_{\rm e},\\ &\frac 1 {\mathrm
K}\frac{\partial \mathrm p}{\partial \rm t}+\nabla\cdot\mathbf v=0,\qquad
\mathrm K>>1, \end{aligned}\right. \end{equation*} whose weak solution has been
proved in [Arch. Rat. Mech. Analysis, 32:135-153] to approximate, in the limit
$\mathrm K\to\infty$, the weak solution of the incompressible Navier-Stokes
system. Taking the cue from [Ann. Mat. Pura Appl. 172:103-124], we provide a
physical interpretation of the extra force $\mathbf f_{\rm e}$, showing that it
is a manifestation of inertia.


  Following the Mellin and inverse Mellin transform techniques presented in our
paper arXiv:1606.02150 (NT), we have established close forms of Laurent series
expansions of products of bi- and trigamma functions /psi(z)*/psi(-z) and
/psi_(1)(z)*/psi_(1)(-z). These series were used to find summation rules which
include generalized harmonic numbers of first, second and third powers and
values of the Riemann zeta-functions at integers / Bernoulli numbers, for
example 2*Sum_(k-1)^(infinity)(H_(k)^((2))/k^3)=6*/zeta(2)*/zeta(3)-9*/zeta(5).
Some of these rules were tested numerically.


  The slicing degree of a knot $K$ is defined as the smallest integer $k$ such
that $K$ is $k$-slice in $\#^n \overline{\mathbb{CP}^2}$ for some $n$. In this
paper, we establish bounds for the slicing degrees of knots using Rasmussen's
$s$-invariant, knot Floer homology and singular instanton homology. We compute
the slicing degrees for many small knots (with crossing numbers up to $9$) and
for some families of torus knots.


  We explore the cohomological structure for the (possibly singular) moduli of
$\mathrm{SL}_n$-Higgs bundles for arbitrary degree on a genus g curve with
respect to an effective divisor of degree >2g-2. We prove a support theorem for
the $\mathrm{SL}_n$-Hitchin fibration extending de Cataldo's support theorem in
the nonsingular case, and a version of the Hausel-Thaddeus topological mirror
symmetry conjecture for intersection cohomology. This implies a generalization
of the Harder-Narasimhan theorem concerning semistable vector bundles for any
degree.
  Our main tool is an Ng\^{o}-type support inequality established recently
which works for possibly singular ambient spaces and intersection cohomology
complexes.


  We present a class of models in which the dark matter stabilization symmetry
is generated by spontaneous symmetry breaking. These models naturally correlate
the dark and electroweak symmetry breaking scales. The result is a generic
mechanism linking the annihilation cross section for thermally populated dark
matter with the weak scale. The thermal relic abundance, sensitivity to major
precision electroweak observables and additional LHC signatures are also
presented.


  We have carried out a model calculation of the flux noise produced by vortex
avalanches in a Type-II superconductor, using a simple kinetic model proposed
by Bassler and Paczuski. Over a broad range of frequencies, we find that the
flux noise $S_{\Phi}(\omega)$ has a power-law dependence on frequency,
$S_{\Phi}(\omega) \sim \omega^{-s}$, with $s \sim 1.4$ in reasonable agreement
with experiment. In addition, for small lattices, the calculated
$S_{\Phi}(\omega)$ has a high-frequency knee, which is seen in some
experiments, and which is due to the finite lattice size. Deviations between
calculation and experiment are attributed mostly to uncertainties in the
measured critical current densities and pinning strengths of the experimental
samples.


  We elaborate on the idea that loop corrections to belief propagation could be
dealt with in a systematic way on pairwise Markov random fields, by using the
elements of a cycle basis to define region in a generalized belief propagation
setting. The region graph is specified in such a way as to avoid dual loops as
much as possible, by discarding redundant Lagrange multipliers, in order to
facilitate the convergence, while avoiding instabilities associated to minimal
factor graph construction. We end up with a two-level algorithm, where a belief
propagation algorithm is run alternatively at the level of each cycle and at
the inter-region level. The inverse problem of finding the couplings of a
Markov random field from empirical covariances can be addressed region wise. It
turns out that this can be done efficiently in particular in the Ising context,
where fixed point equations can be derived along with a one-parameter log
likelihood function to minimize. Numerical experiments confirm the
effectiveness of these considerations both for the direct and inverse MRF
inference.


  The structural and magnetic properties of a series of superlattices
consisting of two ferromagnetic metals La$_{0.7}$Sr$_{0.3}$MnO$_3$ (LSMO) and
SrRuO$_3$ (SRO) grown on (001) oriented SrTiO$_3$ are studied. Superlattices
with a fixed LSMO layer thickness of 20 unit cells (u.c.) and varying SRO layer
thickness show a sudden drop in magnetization on cooling through temperature
where both LSMO and SRO layers are ferromagnetic. This behavior suggests an
antiferromagnetic coupling between the layers. In addition, the samples having
thinner SRO layers (n \TEXTsymbol{<} 6) exhibit enhanced saturation
magnetization at 10 K. These observations are attributed to the possible
modification in the stereochemistry of the Ru and Mn ions in the interfacial
region.


  We adapt the notion of Jacobi diagrams on surfaces (considered by
Andersen-Mattes-Reshetikhin), and construct a LMO-like map that we use to
compare some functoriality properties of WRT and LMO invariants.


  Design of experiments and estimation of treatment effects in large-scale
networks, in the presence of strong interference, is a challenging and
important problem. Most existing methods' performance deteriorates as the
density of the network increases. In this paper, we present a novel strategy
for accurately estimating the causal effects of a class of treatments in a
dense large-scale network. First, we design an approximate randomized
controlled experiment by solving an optimization problem to allocate treatments
in the presence of competition among neighboring nodes. Then we apply an
importance sampling adjustment to correct for any leftover bias (from the
approximation) in estimating average treatment effects. We provide theoretical
guarantees, verify robustness in a simulation study, and validate the
scalability and usefulness of our procedure in a real-world experiment on a
large social network.


  A single atom in a cavity is the model system of cavity quantum
electrodynamics (CQED). The strong coupling regime between the atom and
cavity-confined photon corresponds to the reversible exchange of energy between
the two modes, and underpins a wide range of CQED phenomena with applications
in quantum information science, including for example as quantum logic gates
and as sources of entangled states. An important advance was achieved recently
when strong coupling between excitons and cavity photons was reported for the
first time for localized quantum dots (QDs) in micron-size solid state
cavities. This has significance in terms of scalability and integration with
other optical devices, and could lead to the emergence of "quantum optics on a
chip" technology. However the results presented so far for quantum dots are in
the linear regime, corresponding to coupling to the vacuum field (vacuum Rabi
splitting); they are not a true QED effect and can equally well be described by
classical physics as the coupling between two oscillators. In this paper, we
present evidence for a purely quantum phenomenon for the QD/cavity photon
system, namely the increase in splitting of the levels when the mean number of
photons in the cavity is increased. This corresponds to non-linearities on the
single-photon scale: the presence of a single excitation in the cavity changes
the level structure, affecting the emission energies for a second photon. Such
results are a first step in demonstrating the promise of quantum dots for CQED
applications.


  The BMV conjecture states that for $n\times n$ Hermitian matrices $A$ and $B$
the function $f_{A,B}(t)=trace{\, } e^{tA+B}$ is exponentially convex. Recently
the BMV conjecture was proved by Herbert Stahl. The proof of Herbert Stahl is
based on ingenious considerations related to Riemann surfaces of algebraic
functions. In the present paper we give a purely "matrix" proof of the BMV
conjecture for the special case $rank\,A=1$. This proof is based on the Lie
product formula for the exponential of the sum of two matrices and does not
require complex analysis.


  We propose a generalized method for boosting the generalization ability of
pre-trained vision-language models (VLMs) while fine-tuning on downstream
few-shot tasks. The idea is realized by exploiting out-of-distribution (OOD)
detection to predict whether a sample belongs to a base distribution or a novel
distribution and then using the score generated by a dedicated competition
based scoring function to fuse the zero-shot and few-shot classifier. The fused
classifier is dynamic, which will bias towards the zero-shot classifier if a
sample is more likely from the distribution pre-trained on, leading to improved
base-to-novel generalization ability. Our method is performed only in test
stage, which is applicable to boost existing methods without time-consuming
re-training. Extensive experiments show that even weak distribution detectors
can still improve VLMs' generalization ability. Specifically, with the help of
OOD detectors, the harmonic mean of CoOp and ProGrad increase by 2.6 and 1.5
percentage points over 11 recognition datasets in the base-to-novel setting.


  Using a tight-binding atomistic simulation, we simulate the recent
atomic-force microscopy experiments probing the slipperiness of graphene flakes
made slide against a graphite surface. Compared to previous theoretical models,
where the flake was assumed to be geometrically perfect and rigid, while the
substrate is represented by a static periodic potential, our fully-atomistic
model includes quantum mechanics with the chemistry of bond breaking and bond
formation, and the flexibility of the flake. These realistic features, include
in particular the crucial role of the flake rotation in determining the static
friction, in qualitative agreement with experimental observations.


  To investigate the Hall resistivity rH of systems with non-trivial spin
structures, transport and magnetic properties of the oxygen deficient
perovskite system TbBaCo2O5.53 with non-trivial magnetic structures have been
adopted. As has been already known, the system exhibits, with decreasing
temperature T, a transition to a ferromagnetic (FM) phase with non-collinear
magnetic structure at TC 280 K in zero magnetic field and with further
decreasing T, the spontaneous magnetization begins to decrease at T1~260 K and
becomes zero at TN 245 K, where an antiferromagnetic (AFM) phase with
non-collinear magnetic structure is realized. The metamagnetic behavior is
induced by the relatively small magnetic field H (< 5 T) in the T region
between ~200 K and T1. In this T region, unusual H dependence of rH has been
observed. By analyzing the observed rH and magnetization M, the H dependence of
the anomalous Hall coefficients Rs has been obtained at various fixed
temperatures. Based on the magnetic structure reported previously by our group,
the possible relevance of the non-trivial magnetic structure to the observed
unusual behavior of rH is pointed out.


  A study covering some aspects of the Einstein--Rosen metric is presented. The
electric and magnetic parts of the Weyl tensor are calculated. It is shown that
there are no purely magnetic E--R spacetimes, and also that a purely electric
E--R spacetime is necessarily static. The geodesics equations are found and
circular ones are analyzed in detail. The super--Poynting and the
``Lagrangian'' Poynting vectors are calculated and their expressions are found
for two specific examples. It is shown that for a pulse--type solution, both
expressions describe an inward radially directed flow of energy, far behind the
wave front. The physical significance of such an effect is discussed.


  High-speed machinery is often designed to pass several $"$critical$"$ speeds,
where vibration levels can be very high. To reduce vibrations, rotors usually
undergo a mass balancing process, where the machine is rotated at its full
speed range, during which the dynamic response near critical speeds can be
measured. High sensitivity, which is required for a successful balancing
process, is achieved near the critical speeds, where a single deflection mode
shape becomes dominant, and is excited by the projection of the imbalance on
it. The requirement to rotate the machine at high speeds is an obstacle in many
cases, where it is impossible to perform measurements at high speeds, due to
harsh conditions such as high temperatures and inaccessibility (e.g., jet
engines). $\\$ This paper proposes a novel balancing method of flexible rotors,
which does not require the machine to be rotated at high speeds. With this
method, the rotor is spun at low speeds, while subjecting it to a set of
externally controlled forces. The external forces comprise a set of tuned,
response dependent, parametric excitations, and nonlinear stiffness terms. The
parametric excitation can isolate any desired mode, while keeping the response
directly linked to the imbalance. A software controlled nonlinear stiffness
term limits the response, hence preventing the rotor to become unstable. These
forces warrant sufficient sensitivity required to detect the projection of the
imbalance on any desired mode without rotating the machine at high speeds.
Analytical, numerical and experimental results are shown to validate and
demonstrate the method.


  We consider the general open system problem of a charged quantum oscillator
confined in a harmonic trap, whose frequency can be arbitrarily modulated in
time, that interacts with both an incoherent quantized (blackbody) radiation
field and with an arbitrary coherent laser field. We assume that the oscillator
is initially in thermodynamic equilibrium with its environment, a
non-factorized initial density matrix of the system and the environment, and
that at $t=0$ the modulation of the frequency, the coupling to the incoherent
and the coherent radiation are switched on. The subsequent dynamics, induced by
the presence of the blackbody radiation and the laser field, is studied in the
framework of the influence functional approach. This approach allows
incorporating, in \emph{analytic closed formulae}, the non-Markovian character
of the oscillator-environment interaction at any temperature as well the
non-Markovian character of the blackbody radiation and its zero-point
fluctuations. Expressions for the time evolution of the covariance matrix
elements of the quantum fluctuations and the reduced density-operator are
obtained.


  Liver diseases pose a significant global health burden, impacting a
substantial number of individuals and exerting substantial economic and social
consequences. Rising liver problems are considered a fatal disease in many
countries, such as Egypt, Molda, etc. The objective of this study is to
construct a predictive model for liver illness using Basic Formal Ontology
(BFO) and detection rules derived from a decision tree algorithm. Based on
these rules, events are detected through batch processing using the Apache Jena
framework. Based on the event detected, queries can be directly processed using
SPARQL. To make the ontology operational, these Decision Tree (DT) rules are
converted into Semantic Web Rule Language (SWRL). Using this SWRL in the
ontology for predicting different types of liver disease with the help of the
Pellet and Drool inference engines in Protege Tools, a total of 615 records are
taken from different liver diseases. After inferring the rules, the result can
be generated for the patient according to the DT rules, and other
patient-related details along with different precautionary suggestions can be
obtained based on these results. Combining query results of batch processing
and ontology-generated results can give more accurate suggestions for disease
prevention and detection. This work aims to provide a comprehensive approach
that is applicable for liver disease prediction, rich knowledge graph
representation, and smart querying capabilities. The results show that
combining RDF data, SWRL rules, and SPARQL queries for analysing and predicting
liver disease can help medical professionals to learn more about liver diseases
and make a Decision Support System (DSS) for health care.


  This paper studies the possibility of upper bounding the position error of an
estimate for range based positioning algorithms in wireless sensor networks. In
this study, we argue that in certain situations when the measured distances
between sensor nodes are positively biased, e.g., in non-line-of-sight
conditions, the target node is confined to a closed bounded convex set (a
feasible set) which can be derived from the measurements. Then, we formulate
two classes of geometric upper bounds with respect to the feasible set. If an
estimate is available, either feasible or infeasible, the worst-case position
error can be defined as the maximum distance between the estimate and any point
in the feasible set (the first bound). Alternatively, if an estimate given by a
positioning algorithm is always feasible, we propose to get the maximum length
of the feasible set as the worst-case position error (the second bound). These
bounds are formulated as nonconvex optimization problems. To progress, we relax
the nonconvex problems and obtain convex problems, which can be efficiently
solved. Simulation results indicate that the proposed bounds are reasonably
tight in many situations.


  The authors recently presented new values for the octet baryon sigma terms.
These were extracted using the Feynman-Hellman theorem from a chiral
perturbation theory fit to octet baryon mass data from the PACS-CS
collaboration. Of particular interest is the precise determination of the
strangeness sigma term $\sigma_s = 21 \pm 6$ MeV. In this work, we elaborate on
the critical effect which the choice of scale setting has on this value. We
discuss the prospect that the comparison of direct and 'spectrum'
determinations of the sigma terms from the lattice can provide insight not only
into scale setting on the lattice, but into QCD itself.


  We demonstrate a silicon photonic dual-polarization phase retrieval receiver.
The receiver recovers phase from intensity-only measurements without a local
oscillator or transmitted carrier. We design silicon waveguides providing long
delays and microring resonators with large dispersion to enable
symbol-to-symbol interference and dispersive projection in the phase retrieval
algorithm. We retrieve the full field of a polarization-division multiplexed
30-GBd QPSK and 20-GBd 8QAM signals over 80 km of SSMF.


  Conventional cell tracking methods detect multiple cells in each frame
(detection) and then associate the detection results in successive time-frames
(association). Most cell tracking methods perform the association task
independently from the detection task. However, there is no guarantee of
preserving coherence between these tasks, and lack of coherence may adversely
affect tracking performance. In this paper, we propose the Motion and Position
Map (MPM) that jointly represents both detection and association for not only
migration but also cell division. It guarantees coherence such that if a cell
is detected, the corresponding motion flow can always be obtained. It is a
simple but powerful method for multi-object tracking in dense environments. We
compared the proposed method with current tracking methods under various
conditions in real biological images and found that it outperformed the
state-of-the-art (+5.2\% improvement compared to the second-best).


  Inversion symmetry is a key symmetry in unconventional superconductors and
even its local breaking can have profound implications. For inversion-symmetric
systems, there is a competition on a microscopic level between the spin-orbit
coupling associated with the local lack of inversion and hybridizing terms that
`restore' inversion. Investigating a layered system with alternating
mirror-symmetry breaking, we study this competition considering the spin
response of different superconducting order parameters for the case of strong
spin-orbit coupling. We find that signatures of the local non-centrosymmetry,
such as an increased spin susceptibility in spin-singlet superconductors for
$T\rightarrow 0$, persist even into the quasi-three-dimensional regime. This
leads to a direction dependent spin response which allows to distinguish
different superconducting order parameters. Furthermore, we identify several
regimes with possible topological superconducting phases within a
symmetry-indicator analysis. Our results may have direct relevance for the
recently reported Ce-based superconductor CeRh$_2$As$_2$ and beyond.


  We present ALICE results on strange and multi-strange hadron production as a
function of centrality in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
at the LHC. Their transverse momentum spectra, yields and particle ratios are
compared to the corresponding measurements in pp collisions to address
strangeness enhancement and high $p_{\rm T}$ particle suppression. The results
are also compared to measurements at RHIC and SPS energies.


  Starting from the Bethe ansatz solution we derive a set of coupled non-linear
integral equations for the fully packed double loop model (FPL^2) on the square
lattice. As an application we find exact expressions for the central charge and
for the scaling dimension corresponding to the simplest charge excitation. We
study numerically the low-lying excitations corresponding to more general
perturbations of the ground state and discover that the corresponding scaling
dimensions are well described by the Cartan matrix of sl_4.


  Despite the fact that Solid State Disk (SSD) data storage media had offered a
revolutionary property storages community, but the unavailability of a
comprehensive allocation strategy in SSDs storage media, leads to consuming the
available space, random writing processes, time-consuming reading processes,
and system resources consumption. In order to overcome these challenges, an
efficient allocation algorithm is a desirable option. In this paper, we had
executed an intensive investigation on the SSD-based allocation algorithms that
had been proposed by the knowledge community. An explanatory comparison had
been made between these algorithms. We reviewed these algorithms in order to
building advanced knowledge armature that would help in inventing new
allocation algorithms for this type of storage media.


  We present a semi-supervised learning framework based on graph embeddings.
Given a graph between instances, we train an embedding for each instance to
jointly predict the class label and the neighborhood context in the graph. We
develop both transductive and inductive variants of our method. In the
transductive variant of our method, the class labels are determined by both the
learned embeddings and input feature vectors, while in the inductive variant,
the embeddings are defined as a parametric function of the feature vectors, so
predictions can be made on instances not seen during training. On a large and
diverse set of benchmark tasks, including text classification, distantly
supervised entity extraction, and entity classification, we show improved
performance over many of the existing models.


  We report the forbidden $6s^{2} ^{1}S_{0}\longrightarrow6s5d ^{3}D_{1}$
magnetic-dipole transition amplitude computed using multi-reference Fock-space
coupled-cluster theory. Our computed transition matrix element
($1.34\times10^{-4}\mu_{B}$) is in excellent agreement with the experimental
value ($1.33\times10^{-4}$ $\mu_{B}$). This value in combination with other
known quantities will be helpful to determine the parity non-conserving
amplitude for the $6s^{2} ^{1}S_{0}\longrightarrow6s5d ^{3}D_{1}$ transition in
atomic Yb. To our knowledge our calculation is the most accurate to date and
can be very important in the search of physics beyond the standard model. We
further report the $6s6p ^{3}P_{0}\longrightarrow6s6p ^{1}P_{1}$ and $6s5d
^{3}D_{1}\longrightarrow6s6p ^{3}P_{0}$ transition matrix elements which are
also in good agreement with the earlier theoretical estimates.


  We study the formation of finite time singularities of the Kahler-Ricci flow
in relation to high codimensional birational surgery in algebraic geometry. We
show that the Kahler-Ricci flow on an n-dimensionl Kahler manifold contracts a
complex submanifold $\mathbb{P}^m$ with normal bundle
$\oplus_{j=1}^{n-m}\mathcal{O}_{\mathbb{P}^m}(-a_j)$ for $a_j\in\mathbb{Z}^+$
and $\sum_{j=1}^{n-m} a_j \leq m$ in Gromov-Hausdorff topology with suitable
initial Kahler class. We also show that the Kahler-Ricci flow resolves a family
of isolated singularities uniquely in Gromov-Hausdorff topology. In particular,
we construct global and local examples of metric flips by the Kahler-Ricci flow
as a continuous path in Gromov-Hausdorff topology.


  Einstein's field equations are solved exactly for static charged dust
distributions. These solutions generalize the Majumdar Papapetrou metrics.
Maxwell's equations lead to the equality of charge and mass densities of the
dust distribution. Einstein's equatins reduce to a nonlinear version of
Poisson's equation.


  Magnetars are an extreme, highly magnetized class of isolated neutron stars
whose large X-ray luminosity is believed to be driven by their high magnetic
field. In this work we study for the first time the possible very high energy
gamma-ray emission above 100 GeV from magnetars, observing the sources 4U
0142+61 and 1E 2259+586. We observed the two sources with atmospheric Cherenkov
telescopes in the very high energy range (E > 100 GeV). 4U 0142+61 was observed
with the MAGIC I telescope in 2008 for ~25 h and 1E 2259+586 was observed with
the MAGIC stereoscopic system in 2010 for ~14 h. The data were analyzed with
the standard MAGIC analysis software. Neither magnetar was detected. Upper
limits to the differential and integral flux above 200 GeV were computed using
the Rolke algorithm. We obtain integral upper limits to the flux of
1.52*10^-12cm^-2 s^-1 and 2.7*10^-12cm^-2 s^-1 with a confidence level of 95%
for 4U 0142+61 and 1E 2259+586, respectively. The resulting differential upper
limits are presented together with X-ray data and upper limits in the GeV
energy range.


  We present a single crystal study of low temperature magnetism and transport
in Sm$Tr_2$Al$_{20}$ ($Tr =$ Ti, V and Cr). Strong valence fluctuation is
manifested as Kondo effects including a large Sommerfeld coefficient $\gamma$,
a weak temperature dependence of magnetic susceptibility and a $-\ln T$
dependent resistivity. All the systems order antiferromagnetically at $T_{\rm
N}=$ 6.4 K (Ti), 2.3 K (V) and 1.8 K (Cr). Systematic change in the
susceptibility, specific heat, and resistivity indicates that stronger $c$-$f$
hybridization in SmV$_2$Al$_{20}$ and SmCr$_2$Al$_{20}$ than in
SmTi$_2$Al$_{20}$ suppresses $T_{\rm N}$ and induces the valence fluctuations
and moreover field insensitive heavy fermion states.


  The emergence of active regions on the Sun is an integral feature of the
solar dynamo mechanism. However, details about the generation of
active-region-scale magnetism and the journey of this magnetic flux to the
photosphere are still in question. Shifting paradigms are now developing for
the source depth of the Sun's large-scale magnetism, the organization of this
magnetism into fibril flux tubes, and the role of convection in shaping
active-region observables. Here we review the landscape of flux emergence
theories and simulations, highlight the role flux emergence plays in the global
dynamo process, and make connections between flux emergence on the Sun and
other cool stars. As longer-term and higher fidelity observations of both solar
active regions and their associated flows are amassed, it is now possible to
place new constraints on models of emerging flux. We discuss the outcomes of
statistical studies which provide observational evidence that flux emergence
may be a more passive process (at least in the upper convection zone);
dominated to a greater extent by the influence of convection and to a lesser
extent by buoyancy and the Coriolis force acting on rising magnetic flux tubes
than previously thought. We also discuss how the relationship between stellar
rotation, fractional convection zone depth, and magnetic activity on other
stars can help us better understand flux emergence processes. Looking forward,
we identify open questions regarding magnetic flux emergence that we anticipate
can be addressed in the next decade with further observations and simulations.


  We present the direct-imaging discovery of a substellar companion in orbit
around a Sun-like star member of the Hyades open cluster. So far, no other
substellar companions have been unambiguously confirmed via direct imaging
around main-sequence stars in Hyades. The star HIP 21152 is an accelerating
star as identified by the astrometry from the Gaia and Hipparcos satellites. We
have detected the companion, HIP 21152 B, in multi-epoch using the
high-contrast imaging from SCExAO/CHARIS and Keck/NIRC2. We have also obtained
the stellar radial-velocity data from the Okayama 188cm telescope. The CHARIS
spectroscopy reveals that HIP 21152 B's spectrum is consistent with the L/T
transition, best fit by an early T dwarf. Our orbit modeling determines the
semi-major axis and the dynamical mass of HIP 21152 B to be
17.5$^{+7.2}_{-3.8}$ au and 27.8$^{+8.4}_{-5.4}$ $M_{\rm{Jup}}$, respectively.
The mass ratio of HIP 21152 B relative to its host is $\approx$2\%, near the
planet/brown dwarf boundary suggested from recent surveys. Mass estimates
inferred from luminosity evolution models are slightly higher (33--42
$M_{\rm{Jup}}$). With a dynamical mass and a well-constrained age due to the
system's Hyades membership, HIP 21152 B will become a critical benchmark in
understanding the formation, evolution, and atmosphere of a substellar object
as a function of mass and age. Our discovery is yet another key
proof-of-concept for using precision astrometry to select direct imaging
targets.


  We use the method of maximum entropy to model physical space as a curved
statistical manifold. It is then natural to use information geometry to explain
the geometry of space. We find that the resultant information metric does not
describe the full geometry of space but only its conformal geometry -- the
geometry up to local changes of scale. Remarkably, this is precisely what is
needed to model "physical" space in general relativity.


  Sparse signal representations based on linear combinations of learned atoms
have been used to obtain state-of-the-art results in several practical signal
processing applications. Approximation methods are needed to process
high-dimensional signals in this way because the problem to calculate optimal
atoms for sparse coding is NP-hard. Here we study greedy algorithms for
unsupervised learning of dictionaries of shift-invariant atoms and propose a
new method where each atom is selected with the same probability on average,
which corresponds to the homeostatic regulation of a recurrent convolutional
neural network. Equiprobable selection can be used with several greedy
algorithms for dictionary learning to ensure that all atoms adapt during
training and that no particular atom is more likely to take part in the linear
combination on average. We demonstrate via simulation experiments that
dictionary learning with equiprobable selection results in higher entropy of
the sparse representation and lower reconstruction and denoising errors, both
in the case of ordinary matching pursuit and orthogonal matching pursuit with
shift-invariant dictionaries. Furthermore, we show that the computational costs
of the matching pursuits are lower with equiprobable selection, leading to
faster and more accurate dictionary learning algorithms.


  We present an analysis of seven flares detected from five RS CVn-type
binaries (UZ Lib, \sigma Gem, \lambda And, V711 Tau and EI Eri) observed with
XMM-Newton observatory. The quiescent state X-ray luminosities in the energy
band of 0.3-10.0 keV of these stars were found to be 10^{30.7-30.9} erg/s. The
exponential decay time in all the sample of flares range from ~ 1 to 8 hrs. The
luminosity at peak of the flares in the energy band of 0.3-10.0 keV were found
to be in the range of 10^{30.8} - 10^{31.8} erg/s. The great sensitivity of the
XMM-EPIC instruments allowed us to perform time resolved spectral analysis
during the flares and also in the subsquent quiescent phases. The derived metal
abundances of coronal plasma were found to vary during the flares observed from
\sigma Gem, V771 Tau and EI Eri. In these flares elemental abundances found to
be enhanced by factors of ~ 1.3-1.5 to the quiescent states. In most of the
flares, the peak temperature was found to be more than 100 MK whereas emission
measure increased by factors of 1.5 - 5.5. Significant sustained heating was
present in the majority of flares. The loop lengths (L) derived for flaring
structure were found to be of the order of 10^{10 -11} cm and are smaller than
the stellar radii (R*) i.e. L/R* \lesssim 1. The flare from \sigma Gem showed a
high and variable absorption column density during the flare.


  How long people live depends on their health, and how it changes with age.
Individual health can be tracked by the accumulation of age-related health
deficits. The fraction of age-related deficits is a simple quantitative measure
of human aging. This quantitative frailty index (F) is as good as chronological
age in predicting mortality. In this paper, we use a dynamical network model of
deficits to explore the effects of interactions between deficits, deficit
damage and repair processes, and the connection between the F and mortality.
With our model, we qualitatively reproduce Gompertz's law of increasing human
mortality with age, the broadening of the F distribution with age, the
characteristic non-linear increase of the F with age, and the increased
mortality of high-frailty individuals. No explicit time-dependence in damage or
repair rates is needed in our model. Instead, implicit time-dependence arises
through deficit interactions -- so that the average deficit damage rates
increases, and deficit repair rates decreases, with age . We use a simple
mortality criterion, where mortality occurs when the most connected node is
damaged.