  We consider the problem of secure packet routing at the maximum achievable
rate in Quantum Key Distribution (QKD) networks. Assume that a QKD protocol
generates symmetric private key pairs for secure communication over each link
in a network. The quantum key generation process is modeled using a stochastic
counting process. Packets are first encrypted with the quantum keys available
for each hop and then transmitted on a point-to-point basis over the links. A
fundamental problem in this setting is the design of a secure and
capacity-achieving routing policy that takes into account the time-varying
availability of the encryption keys and finite link capacities. In this paper,
we propose a new secure throughput-optimal policy called Tandem Queue
Decomposition (TQD). The TQD policy is derived by combining the QKD process
with the Universal Max Weight routing policy, proposed earlier by Sinha and
Modiano. We show that the TQD policy solves the problem of secure and efficient
packet routing for a broad class of traffic, including unicast, broadcast,
multicast, and anycast. The proposed decomposition reduces the problem to the
generalized network flow problem without the key availability constraints over
a transformed network. The proof of the throughput-optimality of the TQD policy
uses the Lyapunov stability theory for analyzing the interdependent packet
queueing process and the key-storage dynamics. Finally, we demonstrate the
competitiveness of the TQD policy over the existing algorithms by numerically
comparing them on a simulator that we build on top of the state-of-the-art
OMNeT++ network simulator platform.


  We find that a big gap between indicators for the breaking strengths of the
global chiral SU(2) and U(1) axial symmetries in QCD of the Standard Model (SM)
can be interpreted as a new fine-tuning problem. This may thus imply calling
for a class of Beyond the SM, which turns out to favor having a new chiral
symmetry and the associated massless new quark insensitive to the chiral SU(2)
symmetry for the lightest up and down quarks, so that the fine-tuning is
relaxed. Our statistical estimate shows that QCD of the SM is by more than 300
standard deviations off the desired parameter space, which is free from the
fine-tuning, and the significance will be greater as the lattice measurements
on the QCD hadron observables get more accurate. As one viable candidate, we
introduce a dark QCD model with massless new quarks, which can survive current
experimental, cosmological, and astrophysical limits, and also leave various
phenomenological and cosmological consequences, to be probed in the future.
This is a new indication from QCD, which gives a new avenue to deeper
understand QCD, and provides a new guideline to consider going beyond the SM.


  We propose a novel, to the best of our knowledge, approach to superresolution
optical imaging by combining quantum optics and near-field optics. Our concept
involves the utilization of single-photon quantum emitters to generate a
stand-alone evanescent wave. We demonstrate that the quantum interference
effects of single-photon emitters, in conjunction with their near-field, result
in a higher resolution of subwavelength structures than systems that are only
quantum enhanced or only near-field enhanced. We believe that nano-sized
emitters could be employed to accomplish the goals of this research, taking
into account the current progress in nanophotonics and quantum optics
technology.


  Oscillatory gene circuits are ubiquitous to biology and are involved in
fundamental processes of cell cycle, circadian rhythms and developmental
systems. The synthesis of small, non-natural oscillatory genetic circuits have
been increasingly used to test fundamental principles of genetic network
dynamics. A recently developed fast, tunable genetic oscillator by Stricker et
al.[23] has demonstrated robustness and tunability of oscillatory behavior by
combining positive and negative feedback loops. This oscillator combining lacI
(negative) and araC (positive) feedback loops, was however modeled using
multiple layers of differential equations to capture the molecular complexity
of regulation, in order to explain the experimentally measured oscillations. We
have developed a reduced model based on delay differential equations (DDEs) of
this dual feedback loop oscillator, that reproduces the tunability of
oscillator period and amplitude based on the concentration of the two inducers
isopropyl b-D-1-thiogalactopyranoside (IPTG) and arabinose. Previous work had
predicted a need for an asymmetry in copy numbers of activator (araC) and
repressor (lacI) genes encoded on plasmids. We use our reduced model to
redesign the network by comparing the effect of asymmetry in gene expression at
the level of (a) DNA copy numbers and the rates of (b) mRNA translation and (c)
degradation. We find the minimal period of the oscillator is sensitive to DNA
copy number asymmetry, but translation rate asymmetry has an identical effect
as plasmid copy numbers, while modulating the asymmetry in mRNA degradation can
improve the tunability of period of the oscillator, together with increased
robustness to replication 'noise' and influence of the host cell cycle. Thus,
our model predicts experimentally testable principles to redesign a potentially
more robust oscillatory genetic network.


  This paper characterizes the precision of index estimation as it carries over
into precision of matching. In a model assuming Gaussian covariates and making
best-case assumptions about matching quality, it sharply characterizes average
and worst-case discrepancies between paired differences of true versus
estimated index values. In this optimistic setting, worst-case true and
estimated index differences decline to zero if $p=o[n/(\log n)]$, the same
restriction on model size that is needed for consistency of common index
models. This remains so as the Gaussian assumption is relaxed to sub-gaussian,
if in that case the characterization of paired index errors is less sharp. The
formula derived under Gaussian assumptions is used as the basis for a matching
caliper. Matching such that paired differences on the estimated index fall
below this caliper brings the benefit that after matching, worst-case
differences onan underlying index tend to 0 if $p = o\{[n/(\log n)]^{2/3}\}$.
(With a linear index model, $p=o[n/(\log n)]$ suffices.) A proposed refinement
of the caliper condition brings the same benefits without the sub-gaussian
condition on covariates. When strong ignorability holds and the index is a
well-specified propensity or prognostic score, ensuring in this way that
worst-case matched discrepancies on it tend to 0 with increasing $n$ also
ensures the consistency of matched estimators of the treatment effect.


  Time series forecasting is essential for decision making in many domains. In
this work, we address the challenge of predicting prices evolution among
multiple potentially interacting financial assets. A solution to this problem
has obvious importance for governments, banks, and investors. Statistical
methods such as Auto Regressive Integrated Moving Average (ARIMA) are widely
applied to these problems. In this paper, we propose to approach economic time
series forecasting of multiple financial assets in a novel way via video
prediction. Given past prices of multiple potentially interacting financial
assets, we aim to predict the prices evolution in the future. Instead of
treating the snapshot of prices at each time point as a vector, we spatially
layout these prices in 2D as an image, such that we can harness the power of
CNNs in learning a latent representation for these financial assets. Thus, the
history of these prices becomes a sequence of images, and our goal becomes
predicting future images. We build on a state-of-the-art video prediction
method for forecasting future images. Our experiments involve the prediction
task of the price evolution of nine financial assets traded in U.S. stock
markets. The proposed method outperforms baselines including ARIMA, Prophet,
and variations of the proposed method, demonstrating the benefits of harnessing
the power of CNNs in the problem of economic time series forecasting.


  We include a fully coupled treatment of metal and dust enrichment into the
Delphi semi-analytic model of galaxy formation to explain the dust content of
13 Lyman Break Galaxies (LBGs) detected by the Atacama Large millimetre Array
(ALMA) REBELS Large Program at $z\simeq 7$. We find that the galaxy dust mass,
$M_d$, is regulated by the combination of SNII dust production, astration,
shock destruction, and ejection in outflows; grain growth (with a standard
timescale $\tau_0= 30$ Myr) plays a negligible role. The model predicts a
dust-to-stellar mass ratio of $\sim 0.07-0.1\%$ and a UV-to-total star
formation rate relation such that $log (\psi_{\rm UV}) = -0.05 ~[log
(\psi)]^{2} + 0.86 ~log(\psi) -0.05$ (implying that 55-80\% of the star
formation is obscured) for REBELS galaxies with stellar mass $M_* = 10^{9-10}
M_\odot$. This relation reconciles the intrinsic UV luminosity of LBGs with
their observed luminosity function at $z=7$. However, 2 out of the 13 systems
show dust-to-stellar mass ratios ($\sim 0.94-1.1\%$) that are up to $18\times$
larger than expected from the fiducial relation. Due to the physical coupling
between dust and metal enrichment, even decreasing $\tau_0$ to very low values
(0.3 Myr) only increases the dust-to-stellar mass ratio by a factor $ \sim 2$.
Given that grain growth is not a viable explanation for such high observed
ratios of the dust-to-stellar mass, we propose alternative solutions.


  Let $X$ and $Z$ be random vectors, and $Y=g(X,Z)$. In this paper, on the one
hand, for the case that $X$ and $Z$ are continuous, by using the ideas from the
total variation and the flux of $g$, we develop a point of view in causal
inference capable of dealing with a broad domain of causal problems. Indeed, we
focus on a function, called Probabilistic Easy Variational Causal Effect
(PEACE), which can measure the direct causal effect of $X$ on $Y$ with respect
to continuously and interventionally changing the values of $X$ while keeping
the value of $Z$ constant. PEACE is a function of $d\ge 0$, which is a degree
managing the strengths of probability density values $f(x|z)$. On the other
hand, we generalize the above idea for the discrete case and show its
compatibility with the continuous case. Further, we investigate some properties
of PEACE using measure theoretical concepts. Furthermore, we provide some
identifiability criteria and several examples showing the generic capability of
PEACE. We note that PEACE can deal with the causal problems for which
micro-level or just macro-level changes in the value of the input variables are
important. Finally, PEACE is stable under small changes in $\partial
g_{in}/\partial x$ and the joint distribution of $X$ and $Z$, where $g_{in}$ is
obtained from $g$ by removing all functional relationships defining $X$ and
$Z$.


  Combined effects of interactions and disorder are investigated using a finite
temperature quantum Monte Carlo technique for the three-dimensional Hubbard
model with random potentials of a finite range. Temperature dependence of the
charge compressibility shows that the Mott gap collapses beyond a finite
disorder strength. This is a quantum phase transition from an incompressible
phase to a compressible phase driven by disorder. We calculate the
antiferromagnetic structure factor in the presence of disorder as well. Strong
antiferromagnetic correlation, which is characteristic of the Mott insulator,
is destroyed by a finite amount of disorder.


  We study the heavy-heavy-light quark ($QQq$) potential in SU(3) quenched
lattice QCD, and discuss one of the roles of the finite-mass valence quark in
the inter-quark potential. Monte Carlo simulations are performed with the
standard gauge action on the $16^4$ lattice at $\beta =6.0$ and the
$O(a)$-improved Wilson fermion action at four hopping parameters. For
statistical improvement, the gauge configuration is fixed with the Coulomb
gauge. We calculate the potential energy of $QQq$ systems as a function of the
inter-heavy-quark distance $R$ in the range of $R \le$ 0.8 fm. The $QQq$
potential is well described with a Coulomb plus linear potential, and the
effective string tension between the two heavy quarks is significantly smaller
than the string tension $\sigma \simeq 0.89$ GeV/fm. It would generally hold
that the effect of the finite-mass valence quark reduces the inter-two-quark
confinement force in baryons.


  A Deza graph $G$ with parameters $(n,k,b,a)$ is a $k$-regular graph with $n$
vertices such that any two distinct vertices have $b$ or $a$ common neighbours.
The children $G_A$ and $G_B$ of a Deza graph $G$ are defined on the vertex set
of $G$ such that every two distinct vertices are adjacent in $G_A$ or $G_B$ if
and only if they have $a$ or $b$ common neighbours, respectively. A strongly
Deza graph is a Deza graph with strongly regular children. In this paper we
give a spectral characterisation of strongly Deza graphs, show relationships
between eigenvalues, and study strongly Deza graphs which are distance-regular.


  The effect of atomic disorder induced by neutrons irradiation on
superconducting and normal state properties of polycrystalline LaFeAsO_0.9F_0.1
was investigated. The irradiation of the sample by a moderate neutron fluence F
= 1.6*1019 cm^-2 at Tirr = 50 +- 10 C leads to the suppression of
superconductivity which recovers almost completely after annealing at
temperatures Tann < 750 C. It is shown that the reduction of superconducting
transition temperature Tc under atomic disordering is not determined solely by
the value of Hall concentration nH, i.e. doping level, but is governed by the
reduction of electronic relaxation time. This behavior can be described
qualitatively by universal Abrikosov-Gorkov equation which presents evidence on
the anomalous type of electrons pairing in Fe-based superconductors.


  We report on electrical transport measurements through a carbon nanotube
quantum dot coupled to a normal and a superconducting lead. The ratio of Kondo
temperature and superconducting gap $T_{K}/\Delta$ is identified to govern the
transport properties of the system. In the case of $T_{K}<\Delta$ the
conductance resonance splits into two resonances at $\pm \Delta$. For the
opposite scenario $T_{K}>\Delta$ the conductance resonance persists, however
the conductance is not enhanced compared to the normal state due to a relative
asymmetry of the lead-dot couplings. Within this limit the data is in agreement
with a simple model of a resonant SN-interface.


  Suppose we are given two graphs on $n$ vertices. We define an observable in
the Hilbert space $\Co[(S_n \wr S_2)^m]$ which returns the answer ``yes'' with
certainty if the graphs are isomorphic and ``no'' with probability at least
$1-n!/2^m$ if the graphs are not isomorphic. We do not know if this observable
is efficiently implementable.


  We present various relations among Versions A, B and C of the Segal-Bargmann
transform. We get results for the Segal-Bargmann transform associated to a
Coxeter group acting on a finite dimensional Euclidean space. Then analogous
results are shown for the Segal-Bargmann transform of a connected, compact Lie
group for all except one of the identities established in the Coxeter case. A
counterexample is given to show that the remaining identity from the Coxeter
case does not have an analogous identity for the Lie group case. A major result
is that in both contexts the Segal-Bargmann transform for Version C is
determined by that for Version A.


  An expression is proposed for determining the error caused on entropy
estimates by finite sample effects. This expression is based on the Ansatz that
the ranked distribution of probabilities tends to follow an empirical Zipf law.


  We determine the class of $p$-forms $F$ which possess vanishing scalar
invariants (VSI) at arbitrary order in a $n$-dimensional spacetime. Namely, we
prove that $F$ is VSI if and only if it is of type N, its multiple null
direction $l$ is "degenerate Kundt", and $\nabla_{l}F=0$. The result is
theory-independent. Next, we discuss the special case of Maxwell fields, both
at the level of test fields and of the full Einstein-Maxwell equations. These
describe electromagnetic non-expanding waves propagating in various Kundt
spacetimes. We further point out that a subset of these solutions possesses a
universal property, i.e., they also solve (virtually) any generalized
(non-linear and with higher derivatives) electrodynamics, possibly also coupled
to Einstein's gravity.


  We report a first-principles projector augmented wave (PAW) study on
Na$_{0.5}$CoO$_2$. With the sodium ion ordered insulating phase being
identified in experiments, pure density functional calculations fail to predict
an insulating ground state, which indicates that Na ordering alone can not
produce accompanying Co charge ordering, if additional correlation is not
properly considered. At this level of theory, the most stable phase presents
ferromagnetic ordering within the CoO$_2$ layer and antiferromagnetic coupling
between these layers. When the on-site Coulomb interaction for Co 3d orbitals
is included by an additional Hubbard parameter $U$, charge ordered insulating
ground state can be obtained. The effect of on-site interaction magnitude on
electronic structure is studied. At a moderate value of $U$ (4.0 eV for
example), the ground state is antiferromagnetic, with a Co$^{4+}$ magnetic
moment about 1.0 $\mu_B$ and a magnetic energy of 0.12 eV/Co. The
rehybridization process is also studied in the DFT+U point of view.


  In this paper we elaborate on the idea [Lohse et al., Phys. Rev. Lett. 78,
1359-1362 (1997)] that (single) sonoluminescing air bubbles rectify argon. The
reason for the rectification is that nitrogen and oxygen dissociate and their
reaction products dissolve in water. We give further experimental and
theoretical evidence and extend the theory to other gas mixtures. We show that
in the absence of chemical reactions (e.g., for inert gas mixtures) gas
accumulation in strongly acoustically driven bubbles can also occur.


  In addition to the second-order Einstein equations on four-dimensional
homogeneous isotropic background universe filled with the single perfect fluid,
we also derived the second-order perturbations of the continuity equation and
the Euler equation for a perfect fluid in gauge-invariant manner without
ignoring any mode of perturbations. The consistency of all equations of the
second-order Einstein equation and the equations of motion for matter fields is
confirmed. Due to this consistency check, we may say that the set of all
equations of the second-order are self-consistent and they are correct in this
sense.


  An important task in building regression models is to decide which regressors
should be included in the final model. In a Bayesian approach, variable
selection can be performed using mixture priors with a spike and a slab
component for the effects subject to selection. As the spike is concentrated at
zero, variable selection is based on the probability of assigning the
corresponding regression effect to the slab component. These posterior
inclusion probabilities can be determined by MCMC sampling. In this paper we
compare the MCMC implementations for several spike and slab priors with regard
to posterior inclusion probabilities and their sampling efficiency for
simulated data. Further, we investigate posterior inclusion probabilities
analytically for different slabs in two simple settings. Application of
variable selection with spike and slab priors is illustrated on a data set of
psychiatric patients where the goal is to identify covariates affecting
metabolism.


  We study existence and stability properties of ground-state standing waves
for two-dimensional nonlinear Schr\"odinger equation with a point interaction
and a focusing power nonlinearity. The Schr\"odinger operator with a point
interaction describes a one-parameter family of self-adjoint realizations of
the Laplacian with delta-like perturbation. The perturbed Laplace operator
always has a unique simple negative eigenvalue. We prove that if the frequency
of the standing wave is close to the negative eigenvalue, it is stable.
Moreover, if the frequency is sufficiently large, we have the stability in the
$L^2$-subcritical or critical case, while the instability in the
$L^2$-supercritical case.


  Let $G$ be a u.s.c decomposition of $S^n$, $H_G$ denote the set of
nondegenerate elements and $\pi$ be the projection of $S^n$ onto $S^n/G$.
Suppose that each point in the decomposition space has arbitrarily small
neighborhoods with ($n-1$)-sphere frontiers which miss $\pi(H_G)$, and such
frontiers satisfies the Mismatch Property. Then this paper shows that this
condition implies $S^n/G$ is homeomorphic to $S^n$ ($n\geq 4$). This answers a
weakened form of a conjecture asked by Daverman [3, p. 61]. In the case $n=3$,
the strong form of the conjecture has an affirmative answer from Woodruff [12].


  Motivated by demand-responsive parking pricing systems, we consider
posted-price algorithms for the online metric matching problem. We give an
$O(\log n)$-competitive posted-price randomized algorithm in the case that the
metric space is a line. In particular, in this setting we show how to implement
the ubiquitous guess-and-double technique using prices.


  A biophysical issue how the nuclear size dynamically scales with the cellular
size remains mysterious. We develop a theoretical framework in which the
interactions between polydisperse biomolecules and the mechanical elasticity of
the cell are precisely integrated to investigate dynamics of the
nuclear-to-cellular volume ratio (N/C ratio). We surprisingly find that the N/C
ratio varies nonmonotonically with time, instead of maintaining a constant as
normally known, during a period of osmotic shocks. Combining simulations and
analytical argument, we identify that this nontrivial dynamics can be
phenomenally predicted by the formed segregation configurations in the
concentrations of the biomolecules, and essentially, all these observed
phenomena can be further rationalized by the resultant of the excluded volume
interactions between the polydisperse biomolecules and the spatial constraint
from the nuclear envelope upon the macromolecule diffusions. Our results agree
well with the published experiments for the cellular and nuclear size controls
of the protoplasts.


  We present temporal evolution of the spin Seebeck effect in a YIG|Pt bilayer
system. Our findings reveal that this effect is a sub-microseconds fast
phenomenon governed by the temperature gradient and the thermal magnons
diffusion in the magnetic materials. A comparison of experimental results with
the thermal-driven magnon-diffusion model shows that the temporal behavior of
this effect depends on the time development of the temperature gradient in the
vicinity of the YIG|Pt interface. The effective thermal-magnon diffusion length
for YIG|Pt systems is estimated to be around 700nm.


  The orbital-Hall effect (OHE), similarly to the spin-Hall effect (SHE),
refers to the creation of a transverse flow of orbital angular momentum that is
induced by a longitudinally applied electric field. For systems in which the
spin-orbit coupling (SOC) is sizeable, the orbital and spin angular momentum
degrees of freedom are coupled, and an interrelationship between charge, spin
and orbital angular momentum excitations is naturally established. The OHE has
been explored mostly in metallic systems, where it can be quite strong.
However, several of its features remain unexplored in two-dimensional (2D)
materials. Here, we investigate the role of orbital textures for the OHE
displayed by multi-orbital 2D materials. We predict the appearance of a rather
large orbital Hall effect in these systems both in their metallic and
insulating phases. In some cases, the orbital Hall currents are larger than the
spin Hall ones, and their use as information carriers widens the development
possibilities of novel spin-orbitronic devices.


  De-bordering is the task of proving that a border complexity measure is
bounded from below, by a non-border complexity measure. This task is at the
heart of understanding the difference between Valiant's determinant vs
permanent conjecture, and Mulmuley and Sohoni's Geometric Complexity Theory
(GCT) approach to settle the P \neq NP conjecture. Currently, very few
de-bordering results are known.
  In this work, we study the question of de-bordering the border Waring rank of
polynomials. Waring and border Waring rank are very well studied measures, in
the context of invariant theory, algebraic geometry and matrix multiplication
algorithms. For the first time, we obtain a Waring rank upper bound that is
exponential in the border Waring rank and only *linear* in the degree. All
previous results were known to be exponential in the degree.
  According to Kumar's recent surprising result (ToCT'20), a small border
Waring rank implies that the polynomial can be approximated as a sum of a
constant and a small product of linear polynomials. We prove the converse of
Kumar's result, and in this way we de-border Kumar's complexity, and obtain a
new formulation of border Waring rank, up to a factor of the degree. We phrase
this new formulation as the orbit closure problem of the product-plus-power
polynomial, and we successfully de-border this orbit closure. We fully
implement the GCT approach against the power sum, and we generalize the ideas
of Ikenmeyer-Kandasamy (STOC'20) to this new orbit closure. In this way, we
obtain new multiplicity obstructions that are constructed from just the
symmetries of the points and representation theoretic branching rules, rather
than explicit multilinear computations.
  Furthermore, we realize that the generalization of our converse of Kumar's
theorem to square matrices gives a homogeneous formulation of Ben-Or and Cleve
(SICOMP'92). This results ...


  In the present work ferromagnetic ordering in the Hubbard model generalized
by taking into account the inter-atomic exchange interaction and correlated
hopping in partially filled narrow band is considered. In the case of weak
electron-electron interaction the ground state energy and condition of
ferromagnetic state realization are found using the Green function technique.
The obtained results indicate the important role of correlated hopping.


  We establish an isomorphism between the moduli space of parabolic Higgs
bundles on the projective line and quiver variety of star-shaped quiver. As
applications, we can solve the nilpotent case of the Deligne-Simpson problem in
a geometrical way; and we can show that there is an algebraically completely
integrable system structure on the moduli space as well as quiver variety we
concerned.


  Density-functional theory requires an extra variable besides the electron
density in order to properly incorporate magnetic-field effects. In a
time-dependent setting, the gauge-invariant, total current density takes that
role. A peculiar feature of the static ground-state setting is, however, that
the gauge-dependent paramagnetic current density appears as the additional
variable instead. An alternative, exact reformulation in terms of the total
current density has long been sought but to date a work by Diener is the only
available candidate. In that work, an unorthodox variational principle was used
to establish a ground-state density-functional theory of the total current
density as well as an accompanying Hohenberg-Kohn-like result. We here
reinterpret and clarify Diener's formulation based on a maximin variational
principle. Using simple facts about convexity implied by the resulting
variational expressions, we prove that Diener's formulation is unfortunately
not capable of reproducing the correct ground-state energy and, furthermore,
that the suggested construction of a Hohenberg-Kohn map contains an irreparable
mistake.


  In the context of testing general relativity with gravitational waves,
constraints obtained with multiple events are typically combined either through
a hierarchical formalism or though a combined multiplicative Bayes factor. We
show that the well-known dependence of Bayes factors on the analysis priors in
regions of the parameter space without likelihood support can lead to strong
confidence in favor of incorrect conclusions when one employs the
multiplicative Bayes factor. Bayes factors $\mathcal{O}(1)$ are ambivalent as
they depend sensitively on the analysis priors, which are rarely set in a
principled way; additionally, combined Bayes factors $>\mathcal{O}(10^3)$ can
be obtained in favor of the incorrect conclusion depending on the analysis
priors when many $\mathcal{O}(1)$ Bayes factors are multiplied, and
specifically when the priors are much wider than the underlying population. The
hierarchical analysis that instead infers the ensemble distribution of the
individual beyond-general-relativity constraints does not suffer from this
problem, and generically converges to favor the correct conclusion. Rather than
a naive multiplication, a more reliable Bayes factor can be computed from the
hierarchical analysis. We present a number of toy models showing that the
practice of multiplying Bayes Factors can lead to incorrect conclusions.


  We suggest a series of transport experiments on spin precession in quantum
dots coupled to one or two ferromagnetic leads. Dot spin states are created by
spin injection and analyzed via the linear conductance through the dot, while
an applied magnetic field gives rise to the Hanle effect. Such a Hanle
experiment can be used to determine the spin lifetime in the quantum dot, to
measure the spin injection efficiency into the dot, as well as proving the
existence of intrinsic spin precession which is driven by the Coulomb
interaction.


  We present TESS photometry of the triple star system V1031 Ori (AB)C, which
exhibits short-period oscillations superimposed on an eclipsing light curve.
The high-quality data were analyzed in detail and combined with the published
spectroscopic measurements to obtain the fundamental stellar parameters of the
program target. The masses and radii of the eclipsing pair (AB) were determined
to about 0.5 \% and 0.7 \% precision, respectively. We found 23 significant
frequencies in two ranges of $<$ 2 day$^{-1}$ and 10.9$-$12.7 day$^{-1}$ from
the eclipse-subtracted residuals. Among them, sixteen in the gravity ($g$)-mode
region may be aliases and artefacts due to imperfect removal of the systematic
trends and the binary effects from the TESS data. Seven frequencies in the
pressure ($p$)-mode region were separated by the orbital frequency and split by
the average offset of 0.042 $\pm$ 0.003 day$^{-1}$ from their adjacent
harmonics. Further, the pulsation amplitudes are clearly modulated with the
binary star orbit. The results indicate that the $p$-mode frequencies are
tidally perturbed pulsations from the secondary component and the pulsation
axis could be aligned with the tidal axis.


  We investigate the relativistic breakout of a shock wave from the surface of
a star. In this process, each fluid shell is endowed with some kinetic and
thermal energy by the shock, and then continues to accelerate adiabatically by
converting thermal energy into kinetic energy. This problem has been previously
studied for a mildly relativistic breakout, where the acceleration ends close
to the surface of the star. The current work focuses on the case where the
acceleration ends at distances much greater than the radius of the star. We
derive an analytic description for the hydrodynamic evolution of the ejecta in
this regime, and validate it using a numerical simulation. We also provide
predictions for the expected light curves and spectra from such an explosion.
The relevance to astrophysical explosions is discussed, and it is shown that
such events require more energy than is currently believed to result from
astrophysical explosions.


  We prove local H\"older regularity for a nonlocal parabolic equations of the
form \begin{align*}
  \partial_t u + \text{P.V.}\int_{\mathbb{R}^N}
\frac{|u(x,t)-u(y,t)|^{p-2}(u(x,t)-u(y,t))}{|x-y|^{N+sp}}\,dy=0, \end{align*}
for $p\in (1,\infty)$ and $s \in (0,1)$.


  We define a 3-point Virasoro algebra, and construct a representation of it on
a previously defined Fock space for the 3-point affine algebra
$\mathfrak{sl}(2, \mathcal R) \oplus\left( \Omega_{\mathcal R}/d{\mathcal
R}\right)$.


  In the present paper, we define the sheath by a monotone stationary solution
to the nonisentropic Euler-Poisson system under a condition known as the Bohm
criterion and consider a situation in which charged particles accumulate on the
boundary due to the flux from the inner region. Under this fluid-boundary
interactive setting, we prove the large time asymptotic stability of the sheath
provided that the initial perturbation is sufficiently small in some weighted
Sobolev spaces. Moreover, the convergence rate of the solution toward the
sheath is obtained. The proof is based on the weighted energy method.


  An essential property of magnetic devices is the relaxation rate in magnetic
switching which strongly depends on the energy dissipation and magnetic inertia
of the magnetization dynamics. Both parameters are commonly taken as a
phenomenological entities. However very recently, a large effort has been
dedicated to obtain Gilbert damping from first principles. In contrast, there
is no ab initio study that so far has reproduced measured data of magnetic
inertia in magnetic materials. In this letter, we present and elaborate on a
theoretical model for calculating the magnetic moment of inertia based on the
torque-torque correlation model. Particularly, the method has been applied to
bulk bcc Fe, fcc Co and fcc Ni in the framework of the tight-binding
approximation and the numerical values are comparable with recent experimental
measurements. The theoretical results elucidate the physical origin of the
moment of inertia based on the electronic structure. Even though the moment of
inertia and damping are produced by the spin-orbit coupling, our analysis shows
that they are caused by undergo different electronic structure mechanisms.


  In the recent definition of Hom-Hopf algebras the antipode S is the relative
Hominverse of the identity map with respect to the convolution product. We
observe that some fundamental properties of the antipode of Hopf algebras and
Hom-Hopf algebras, with the original definition, do not hold generally in the
new setting. We show that the antipode is a relative Hom-anti algebra and a
relative anti-coalgebra morphism. It is also relative Hom-unital, and relative
Hom-counital. Furthermore if the twisting maps of multiplications and
comultiplications are invertible then S is an anti-algebra and an
anti-coalgebra map. We show that any Hom-bialgebra map between two Hom-Hopf
algebras is a relative Hom-morphism of Hom-Hopf alegbras. Specially if the
corresponding twisting maps are all invertible then it is a Hom-Hopf algebra
map. If the Hom-Hopf algebra is commutative or cocommutative we observe that
S^2 is equal to the identity map in some sense. At the end we study the images
of primitive and group-like elements under the antipode.


  Young stars typically form in star clusters, so the supernovae (SNe) they
produce are clustered in space and time. This clustering of SNe may alter the
momentum per SN deposited in the interstellar medium (ISM) by affecting the
local ISM density, which in turn affects the cooling rate. We study the effect
of multiple SNe using idealized 1D hydrodynamic simulations which explore a
large parameter space of the number of SNe, and the background gas density and
metallicity. The results are provided as a table and an analytic fitting
formula. We find that for clusters with up to ~100 SNe the asymptotic momentum
scales super-linearly with the number of SNe, resulting in a momentum per SN
that can be an order of magnitude larger than for a single SN, with a maximum
efficiency for clusters with 10-100 SNe. We argue that additional physical
processes not included in our simulations -- self-gravity, breakout from a
galactic disk, and galactic shear -- can slightly reduce the momentum
enhancement from clustering, but the average momentum per SN still remains a
factor of 4 larger than the isolated SN value when averaged over a realistic
cluster mass function for a star-forming galaxy. We conclude with a discussion
of the possible role of mixing between hot and cold gas, induced by
multi-dimensional instabilities or preexisting density variations, as a
limiting factor in the buildup of momentum by clustered SNe, and suggest future
numerical experiments to explore these effects.


  Residential and commercial buildings, equipped with systems such as heat
pumps, hot water tanks, or stationary energy storage, have a large potential to
offer their consumption flexibility as grid services. In this work, we leverage
this flexibility to react to consumption requests related to maximizing
self-consumption and reducing peak loads. We present a general characterization
of consumption flexibility in the form of flexibility envelopes and discuss a
data-driven battery model formulation for modeling individual buildings. These
models are used to predict the available consumption flexibility while
incorporating a description of uncertainty and being risk-aware with a
pre-defined risk level. A Mixed-integer Linear Program (MILP) is formulated to
schedule the activation of the buildings in order to best respond to an
external consumption request. An aggregated consumption request is dispatched
to the active individual buildings by an algorithm, based on the previously
determined schedule. The effectiveness of the approach is demonstrated by
coordinating up to 500 simulated buildings using the Energym Python library and
observing about 1.5 times peak power reduction in comparison with a baseline
approach while maintaining comfort more robustly. We demonstrate the
scalability of the approach, with solving times being approximately linear in
the number of considered assets in the scheduling problem.


  We develop a one-dimensional model for the unsteady fluid--structure
interaction (FSI) between a soft-walled microchannel and viscous fluid flow
within it. A beam equation, which accounts for both transverse bending rigidity
and nonlinear axial tension, is coupled to a one-dimensional fluid model
obtained from depth-averaging the two-dimensional incompressible Navier--Stokes
equations across the channel height. Specifically, the Navier--Stokes equations
are scaled in the viscous lubrication limit relevant to microfluidics. The
resulting set of coupled nonlinear partial differential equations is solved
numerically through a segregated approach employing fully-implicit time
stepping. We explore both the static and dynamic FSI behavior of this example
microchannel system by varying a reduced Reynolds number $Re$, which
necessarily changes the Strouhal number $St$, while we keep the geometry and a
modified dimensionless Young's modulus $\Sigma$ fixed. At steady state, an
order-of-magnitude analysis (balancing argument) shows that the
axially-averaged pressure in the flow, $\langle P\rangle$, exhibits two
different scaling regimes, while the maximum deformation of the top wall of the
channel, $H_{\mathrm{max}}$, can fall into four different regimes, depending on
the magnitudes of $Re$ and $\Sigma$. These regimes are physically explained as
resulting from the competition between the inertial and viscous forces in the
fluid flow as well as the bending resistance and tension in the elastic wall.
Finally, the linear stability of the steady inflated microchannel shape is
assessed via a modal analysis, showing the existence of many highly oscillatory
but stable modes, which further highlights the computational challenge of
simulating unsteady FSIs.


  Although the study of weak convergence of superpositions of point processes
to the Poisson process dates back to the work of Grigelionis in 1963, it was
only recently that Schuhmacher [Stochastic Process. Appl. 115 (2005)
1819--1837] obtained error bounds for the weak convergence. Schuhmacher
considered dependent superposition, truncated the individual point processes to
0--1 point processes and then applied Stein's method to the latter. In this
paper, we adopt a different approach to the problem by using Palm theory and
Stein's method, thereby expressing the error bounds in terms of the mean
measures of the individual point processes, which is not possible with
Schuhmacher's approach. We consider locally dependent superposition as a
generalization of the locally dependent point process introduced in Chen and
Xia [Ann. Probab. 32 (2004) 2545--2569] and apply the main theorem to the
superposition of thinned point processes and of renewal processes.


  Precision measurements together with exact theoretical calculations have led
to steady progress in fundamental physics. A brief survey is given on recent
developments and current achievements in the field of perturbative precision
calculations in the Standard Model of the Elementary Particles and their
application in current high energy collider data analyses.


  Coreference resolution is essential for natural language understanding and
has been long studied in NLP. In recent years, as the format of Question
Answering (QA) became a standard for machine reading comprehension (MRC), there
have been data collection efforts, e.g., Dasigi et al. (2019), that attempt to
evaluate the ability of MRC models to reason about coreference. However, as we
show, coreference reasoning in MRC is a greater challenge than earlier thought;
MRC datasets do not reflect the natural distribution and, consequently, the
challenges of coreference reasoning. Specifically, success on these datasets
does not reflect a model's proficiency in coreference reasoning. We propose a
methodology for creating MRC datasets that better reflect the challenges of
coreference reasoning and use it to create a sample evaluation set. The results
on our dataset show that state-of-the-art models still struggle with these
phenomena. Furthermore, we develop an effective way to use naturally occurring
coreference phenomena from existing coreference resolution datasets when
training MRC models. This allows us to show an improvement in the coreference
reasoning abilities of state-of-the-art models. The code and the resulting
dataset are available at https://github.com/UKPLab/coref-reasoning-in-qa.


  Understanding transition paths between meta-stable states in molecular
systems is fundamental for material design and drug discovery. However,
sampling these paths via unbiased molecular dynamics simulations is
computationally prohibitive due to the high energy barriers between the
meta-stable states. Recent machine learning approaches are often restricted to
simple systems or rely on collective variables (CVs) extracted from expensive
domain knowledge. In this work, we propose to leverage generative flow networks
(GFlowNets) to sample transition paths without relying on CVs. We reformulate
the problem as amortized energy-based sampling over transition paths and train
a neural bias potential by minimizing the squared log-ratio between the target
distribution and the generator, derived from the flow matching objective of
GFlowNets. Our evaluation on three proteins (Alanine Dipeptide, Polyproline
Helix, and Chignolin) demonstrates that our approach, called TPS-GFN, generates
more realistic and diverse transition paths than the previous CV-free machine
learning approach.


  Event-based cameras record an asynchronous stream of per-pixel brightness
changes. As such, they have numerous advantages over the standard frame-based
cameras, including high temporal resolution, high dynamic range, and no motion
blur. Due to the asynchronous nature, efficient learning of compact
representation for event data is challenging. While it remains not explored the
extent to which the spatial and temporal event "information" is useful for
pattern recognition tasks. In this paper, we focus on single-layer
architectures. We analyze the performance of two general problem formulations:
the direct and the inverse, for unsupervised feature learning from local event
data (local volumes of events described in space-time). We identify and show
the main advantages of each approach. Theoretically, we analyze guarantees for
an optimal solution, possibility for asynchronous, parallel parameter update,
and the computational complexity. We present numerical experiments for object
recognition. We evaluate the solution under the direct and the inverse problem
and give a comparison with the state-of-the-art methods. Our empirical results
highlight the advantages of both approaches for representation learning from
event data. We show improvements of up to 9 % in the recognition accuracy
compared to the state-of-the-art methods from the same class of methods.


  Linear Temporal Logic (LTL) interpreted on finite traces is a robust
specification framework popular in formal verification. However, despite the
high interest in the logic in recent years, the topic of their quantitative
extensions is not yet fully explored. The main goal of this work is to study
the effect of adding weak forms of percentage constraints (e.g. that most of
the positions in the past satisfy a given condition, or that sigma is the
most-frequent letter occurring in the past) to fragments of LTL. Such
extensions could potentially be used for the verification of influence networks
or statistical reasoning. Unfortunately, as we prove in the paper, it turns out
that percentage extensions of even tiny fragments of LTL have undecidable
satisfiability and model-checking problems. Our undecidability proofs not only
sharpen most of the undecidability results on logics with arithmetics
interpreted on words known from the literature, but also are fairly simple. We
also show that the undecidability can be avoided by restricting the allowed
usage of the negation, and briefly discuss how the undecidability results
transfer to first-order logic on words.


  The absorption of surface acoustic waves (SAW's) by an array of quantum dots
in which the mean level spacing Delta is larger than the sound frequency omega,
the temperature T, and the phase breaking rate tau^{-1}_phi is considered. The
direct and the intra-level (Debye) contributions to the SAW attenuation
coefficient Gamma are evaluated, and it is shown that the sensitivity to weak
magnetic fields and spin-orbit scattering (``weak localization effects'') is
dramatically enhanced as compared to the case of a continuous spectrum, Delta <
tau^{-1}_phi. It is argued that the non-invasive measurement of Gamma
represents a new tool for the investigation of the temperature dependence of
the energy relaxation rate, tau^{-1}_epsilon, and the phase breaking rate,
tau^{-1}_phi$, of isolated electronic systems.


  We report first-time reverberation mapping results for 14 AGNs from the
ongoing Monitoring AGNs with H$\beta$ Asymmetry campaign (MAHA). These results
utilize optical spectra obtained with the Long Slit Spectrograph on the Wyoming
Infrared 2.3m Telescope between 2017 November-2023 May. MAHA combines
long-duration monitoring with high cadence. We report results from multiple
observing seasons for 9 of the 14 objects. These results include H$\beta$ time
lags, supermassive black hole masses, and velocity-resolved time lags. The
velocity-resolved lags allow us to investigate the kinematics of the broad-line
region.


  We report the discovery of a new dwarf spheroidal satellite of M31, Andromeda
IX, based on resolved stellar photometry from the Sloan Digital Sky Survey
(SDSS). Using both SDSS and public archival data we have estimated its distance
and other physical properties, and compared these to the properties of a
previously known dwarf spheroidal companion, Andromeda V, also observed by
SDSS. Andromeda IX is the lowest surface brightness galaxy found to date
(mu_{V} ~ 26.8 mag arcsec^-2), and at the distance we estimate from the
position of the tip of Andromeda IX's red giant branch, (m - M)_{0} ~ 24.5 (805
kpc), Andromeda IX would also be the faintest galaxy known (M_{V} ~ -8.3).


  We present a novel method to estimate the dominant eigenvalue and eigenvector
pair of any non-negative real matrix via graph infection. The key idea in our
technique lies in approximating the solution to the first-order matrix ordinary
differential equation (ODE) with the Euler method. Graphs, which can be
weighted, directed, and with loops, are first converted to its adjacency matrix
A. Then by a naive infection model for graphs, we establish the corresponding
first-order matrix ODE, through which A's dominant eigenvalue is revealed by
the fastest growing term. When there are multiple dominant eigenvalues of the
same magnitude, the classical power iteration method can fail. In contrast, our
method can converge to the dominant eigenvalue even when same-magnitude
counterparts exist, be it complex or opposite in sign. We conduct several
experiments comparing the convergence between our method and power iteration.
Our results show clear advantages over power iteration for tree graphs,
bipartite graphs, directed graphs with periods, and Markov chains with
spider-traps. To our knowledge, this is the first work that estimates dominant
eigenvalue and eigenvector pair from the perspective of a dynamical system and
matrix ODE. We believe our method can be adopted as an alternative to power
iteration, especially for graphs.


  Geochemical studies of planetary accretion and evolution have invoked various
degrees of collisional erosion to explain differences in bulk composition
between planets and chondrites. Here we undertake a full, dynamical evaluation
of 'crustal stripping' during accretion and its key geochemical consequences.
We present smoothed particle hydrodynamics simulations of collisions between
differentiated rocky planetesimals and planetary embryos. We find that the
crust is preferentially lost relative to the mantle during impacts, and we have
developed a scaling law that approximates the mass of crust that remains in the
largest remnant. Using this scaling law and a recent set of N-body simulations,
we have estimated the maximum effect of crustal stripping on incompatible
element abundances during the accretion of planetary embryos. We find that on
average one third of the initial crust is stripped from embryos as they
accrete, which leads to a reduction of ~20% in the budgets of the heat
producing elements if the stripped crust does not reaccrete. Erosion of crusts
can lead to non-chondritic ratios of incompatible elements, but the magnitude
of this effect depends sensitively on the details of the crust-forming melting
process. The Lu/Hf system is fractionated for a wide range of crustal formation
scenarios. Using eucrites (the products of planetesimal silicate melting,
thought to represent the crust of Vesta) as a guide to the Lu/Hf of
planetesimal crust partially lost during accretion, we predict the Earth could
evolve to a superchondritic 176-Hf/177-Hf (3-5 parts per ten thousand) at
present day. Such values are in keeping with compositional estimates of the
bulk Earth. Stripping of planetary crusts during accretion can lead to
detectable changes in bulk composition of lithophile elements, but the
fractionation is relatively subtle, and sensitive to the efficiency of
reaccretion.


  We compute the radiative heat transfer between nanostructured gold plates in
the framework of the scattering theory. We predict an enhancement of the heat
transfer as we increase the depth of the corrugations while keeping the
distance of closest approach fixed. We interpret this effect in terms of the
evolution of plasmonic and guided modes as a function of the grating's
geometry.


  We provide a full quantum description of the optomechanical system formed by
a Fabry-Perot cavity with a movable micro-mechanical mirror whose
center-of-mass and internal elastic modes are coupled to the driven cavity mode
by both radiation pressure and photothermal force. Adopting a quantum Langevin
description, we investigate simultaneous cooling of the micromirror elastic and
center-of-mass modes, and also the entanglement properties of the
optomechanical multipartite system in its steady state.


  In this paper we lay out an argument that generically the psychological arrow
of time should align with the thermodynamic arrow of time where that arrow is
well-defined. This argument applies to any physical system that can act as a
memory, in the sense of preserving a record of the state of some other system.
This result follows from two principles: the robustness of the thermodynamic
arrow of time to small perturbations in the state, and the principle that a
memory should not have to be fine-tuned to match the state of the system being
recorded. This argument applies even if the memory system itself is completely
reversible and non-dissipative. We make the argument with a paradigmatic
system, then formulate it more broadly for any system that can be considered a
memory. We illustrate these principles for a few other example systems, and
compare our criteria to earlier treatments of this problem.


  Cosmological simulations of Population (Pop) III star formation suggest that
the primordial initial mass function may have extended to sub-solar masses. If
Pop III stars with masses < 0.8 M_Sun did form, then they should still be
present in the Galaxy today as either main sequence or red giant stars. Despite
broad searches, however, no primordial stars have yet been identified. It has
long been recognized that the initial metal-free nature of primordial stars
could be masked due to accretion of metal-enriched material from the
interstellar medium (ISM). Here we point out that while gas accretion from the
ISM may readily occur, the accretion of dust from the ISM can be prevented due
to the pressure of the radiation emitted from low-mass stars. This implies a
possible unique chemical signature for stars polluted only via accretion,
namely an enhancement in gas phase elements relative to those in the dust
phase. Using Pop III stellar models, we outline the conditions in which this
signature could be exhibited, and we derive the expected signature for the case
of accretion from the local ISM. Intriguingly, due to the large fraction of
iron depleted into dust relative to that of carbon and other elements, this
signature is similar to that observed in many of the so-called carbon-enhanced
metal-poor (CEMP) stars. We therefore suggest that some fraction of the
observed CEMP stars may, in fact, be accretion-polluted Pop III stars.


  We present a theoretical scheme for ground state cooling of a mechanical
resonator in a membrane-in-middle optomechanical system (OMS) driven by two
red-detuned drive fields. The details of dynamical evolution of OMS are
provided, and the effect of system conditions on cooling results are
systematically studied. Most importantly, the setups with two drives are found
to be capable of achieving better cooling results than the theoretical cooling
limit with single cavity. Even an improvement by one order of thermal phonon
number is possible with proper combination of the cavity damping rate and drive
intensity.


  The mass formulae for the baryon octet and decuplet are calculated. These
formulae are function of constituent quark masses and spin spin interaction
terms for the quarks inside the baryons. The coefficients in the mass formulae
is estimated by the statistical model for J/P=1/2+, J/P=3/2+, incorporating the
contributions from \sea" containing uu; dd; ss pairs and gluons . The measured
masses are presented and found to be matching good with some of the
experimental and theoretical data.


  We discuss some relations of moduli of sheaves on rational surfaces by using
universal extensions. These are a generalization of Maruyama's method to
construct Uhlenbeck compactification of moduli of vector bundles.


  In this paper we describe the twisted Hall algebra of bound quiver with small
homological dimension. The description is given in the terms of the quadratic
form associated with the corresponding bound quiver.


  The spontaneous transformations associated with symmetry-breaking phase
transitions generate domain structures and defects that may be topological in
nature. The formation of these defects can be described according to the
Kibble-Zurek mechanism, which provides a generic relation that applies from
cosmological to interatomic lengthscales. Its verification is challenging,
however, in particular at the cosmological scale where experiments are
impractical. While it has been demonstrated for selected condensed-matter
systems, major questions remain regarding e.g. its degree of universality. Here
we develop a global Kibble-Zurek picture from the condensed-matter level. We
show theoretically that a transition between two fluctuation regimes (Ginzburg
and mean-field) can lead to an intermediate region with reversed scaling, and
we verify experimentally this behavior for the structural transition in the
series of multiferroic hexagonal manganites. Trends across the series allow us
to identify additional intrinsic features of the defect formation beyond the
original Kibble-Zurek paradigm.


  We give an explicit description of the full asymptotic expansion of the
Schwartz kernel of the complex powers of $m$-Laplace type operators $L$ on
compact Riemannian manifolds in terms of Riesz distributions. The constant term
in this asymptotic expansion turns turns out to be given by the local zeta
function of $L$. In particular, the constant term in the asymptotic expansion
of the Green's function $L^{-1}$ is often called the mass of $L$, which (in
case that $L$ is the Yamabe operator) is an important invariant, namely a
positive multiple of the ADM mass of a certain asymptotically flat manifold
constructed out of the given data. We show that for general conformally
invariant $m$-Laplace operators $L$ (including the GJMS operators), this mass
is a conformal invariant in the case that the dimension of $M$ is odd and that
$\ker L = 0$, and we give a precise description of the failure of the conformal
invariance in the case that these conditions are not satisfied.


  Demonstrations are commonly used to speed up the learning process of Deep
Reinforcement Learning algorithms. To cope with the difficulty of accessing
multiple demonstrations, some algorithms have been developed to learn from a
single demonstration. In particular, the Divide & Conquer Imitation Learning
algorithms leverage a sequential bias to learn a control policy for complex
robotic tasks using a single state-based demonstration. The latest version,
DCIL-II demonstrates remarkable sample efficiency. This novel method operates
within an extended Goal-Conditioned Reinforcement Learning framework, ensuring
compatibility between intermediate and subsequent goals extracted from the
demonstration. However, a fundamental limitation arises from the assumption
that the system can be reset to specific states along the demonstrated
trajectory, confining the application to simulated systems. In response, we
introduce an extension called Single-Reset DCIL (SR-DCIL), designed to overcome
this constraint by relying on a single initial state reset rather than
sequential resets. To address this more challenging setting, we integrate two
mechanisms inspired by the Learning from Demonstrations literature, including a
Demo-Buffer and Value Cloning, to guide the agent toward compatible success
states. In addition, we introduce Approximate Goal Switching to facilitate
training to reach goals distant from the reset state. Our paper makes several
contributions, highlighting the importance of the reset assumption in DCIL-II,
presenting the mechanisms of SR-DCIL variants and evaluating their performance
in challenging robotic tasks compared to DCIL-II. In summary, this work offers
insights into the significance of reset assumptions in the framework of DCIL
and proposes SR-DCIL, a first step toward a versatile algorithm capable of
learning control policies under a weaker reset assumption.


  We present a general formalism that uses the point form of relativistic
Hamiltonian dynamics to describe the electroweak structure of heavy-light
mesons within constituent quark models. We study the heavy quark limit (i.e.
$m_Q\to \infty$) and check that the predictions of heavy quark symmetry are
satisfied. A simple analytic expressions is given for the Isgur-Wise function.
In addition, cluster properties and the relation of our approach to front form
calculations are discussed.


  We provide proofs of the following theorems by considering the entropy of
random walks: Theorem 1.(Alon, Hoory and Linial) Let G be an undirected simple
graph with n vertices, girth g, minimum degree at least 2 and average degree d:
Odd girth: If g=2r+1,then n \geq 1 + d*(\Sum_{i=0}^{r-1}(d-1)^i) Even girth: If
g=2r,then n \geq 2*(\Sum_{i=0}^{r-1} (d-1)^i) Theorem 2.(Hoory) Let G =
(V_L,V_R,E) be a bipartite graph of girth g = 2r, with n_L = |V_L| and n_R =
|V_R|, minimum degree at least 2 and the left and right average degrees d_L and
d_R. Then, n_L \geq \Sum_{i=0}^{r-1}(d_R-1)^{i/2}(d_L-1)^{i/2} n_R \geq
\Sum_{i=0}^{r-1}(d_L-1)^{i/2}(d_R-1)^{i/2}


  The capacity achieving probability mass function (PMF) of a finite signal
constellation with an average power constraint is in most cases non-uniform. A
common approach to generate non-uniform input PMFs is Huffman shaping, which
consists of first approximating the capacity achieving PMF by a sampled
Gaussian density and then to calculate the Huffman code of the sampled Gaussian
density. The Huffman code is then used as a prefix-free modulation code. This
approach showed good results in practice, can however lead to a significant gap
to capacity. In this work, a method is proposed that efficiently constructs
optimal prefix-free modulation codes for any finite signal constellation with
average power constraint in additive noise. The proposed codes operate as close
to capacity as desired. The major part of this work elaborates an analytical
proof of this property. The proposed method is applied to 64-QAM in AWGN and
numeric results are given, which show that, opposed to Huffman shaping, by
using the proposed method, it is possible to operate very close to capacity
over the whole range of parameters.


  We design a high dynamic range electric field sensor based on domain inverted
electro-optic (E-O) polymer Y-fed directional coupler for electromagnetic wave
detection. This electrode-less, all optical, wideband electrical field sensor
is fabricated using standard processing for E-O polymer photonic devices.
Experimental results demonstrate effective detection of electric field from
16.7V/m to 750KV/m at a frequency of 1GHz, and spurious free measurement range
of 70dB.


  One of the oldest outstanding problems in dynamical algebraic combinatorics
is the following conjecture of P. Cameron and D. Fon-Der-Flaass (1995).
Consider a plane partition $P$ in an $a \times b \times c$ box ${\sf B}$. Let
$\Psi(P)$ denote the smallest plane partition containing the minimal elements
of ${\sf B} - P$. Then if $p= a+b+c-1$ is prime, Cameron and Fon-Der-Flaass
conjectured that the cardinality of the $\Psi$-orbit of $P$ is always a
multiple of $p$.
  This conjecture was established for $p \gg 0$ by Cameron and Fon-Der-Flaass
(1995) and for slightly smaller values of $p$ in work of K. Dilks, J. Striker,
and the second author (2017). Our main theorem specializes to prove this
conjecture in full generality.


  This study extends the Bayesian nonparametric instrumental variable
regression model to determine the structural effects of covariates on the
conditional quantile of the response variable. The error distribution is
nonparametrically modelled using a Dirichlet mixture of bivariate normal
distributions. The mean functions include the smooth effects of the covariates
represented using the spline functions in an additive manner. The conditional
variance of the second-stage error is also modelled using the spline functions
such that it varies smoothly with the covariates. Accordingly, the proposed
model allows for considerable flexibility in the shape of the quantile function
while correcting for an endogeneity effect. The posterior inference for the
proposed model is based on the Markov chain Monte Carlo method that requires no
Metropolis-Hastings update. The approach is demonstrated using simulated and
real data on the death rate in Japan during the inter-war period.


  We present the magnetization energy and magnetic moments of 3d monowires
aligned along the step edges of Pt (533) and (322) vicinal substrates. We
employ an electronic structure method which scales linearly with the size of
the system. This allows us to treat with ease both ferromagnetic and
antiferromagnetic solutions, and in principle the method should allow for the
evaluation of more complex systems, such as wires deposited on rough step
edges. We find that Co, Fe, and Mn are almost perfect Heisenberg systems, with
almost no change in the moment between antiferromagnetic and ferromagnetic
solutions. A large polarisation of the Pt substrate is also observed. Our
results are in close agreement w ith recent experimental results obtained for
the case of a Co monowire. As expected the trend is for the late d series to be
stabalised by ferromagnetic long range order and the middle of the d series by
antiferromagnetic order. Since our method is only \emph{locally} self
consistent we discuss as some length the convergence of the results with
respect to the size of the region which is treated self-consistently.


  We introduce multiplicative differential forms on Lie groupoids with values
in VB-groupoids. Our main result gives a complete description of these objects
in terms of infinitesimal data. By considering split VB-groupoids, we are able
to present a Lie theory for differential forms on Lie groupoids with values in
2-term representations up to homotopy. We also define a differential complex
whose 1-cocycles are exactly the multiplicative forms with values in
VB-groupoids and study the Morita invariance of its cohomology.


  Recent advances in generative diffusion models have enabled the previously
unfeasible capability of generating 3D assets from a single input image or a
text prompt. In this work, we aim to enhance the quality and functionality of
these models for the task of creating controllable, photorealistic human
avatars. We achieve this by integrating a 3D morphable model into the
state-of-the-art multi-view-consistent diffusion approach. We demonstrate that
accurate conditioning of a generative pipeline on the articulated 3D model
enhances the baseline model performance on the task of novel view synthesis
from a single image. More importantly, this integration facilitates a seamless
and accurate incorporation of facial expression and body pose control into the
generation process. To the best of our knowledge, our proposed framework is the
first diffusion model to enable the creation of fully 3D-consistent,
animatable, and photorealistic human avatars from a single image of an unseen
subject; extensive quantitative and qualitative evaluations demonstrate the
advantages of our approach over existing state-of-the-art avatar creation
models on both novel view and novel expression synthesis tasks. The code for
our project is publicly available.


  Stochastic Gradient Descent (SGD) is among the simplest and most popular
methods in optimization. The convergence rate for SGD has been extensively
studied and tight analyses have been established for the running average
scheme, but the sub-optimality of the final iterate is still not
well-understood. shamir2013stochastic gave the best known upper bound for the
final iterate of SGD minimizing non-smooth convex functions, which is $O(\log
T/\sqrt{T})$ for Lipschitz convex functions and $O(\log T/ T)$ with additional
assumption on strongly convexity. The best known lower bounds, however, are
worse than the upper bounds by a factor of $\log T$. harvey2019tight gave
matching lower bounds but their construction requires dimension $d= T$. It was
then asked by koren2020open how to characterize the final-iterate convergence
of SGD in the constant dimension setting.
  In this paper, we answer this question in the more general setting for any
$d\leq T$, proving $\Omega(\log d/\sqrt{T})$ and $\Omega(\log d/T)$ lower
bounds for the sub-optimality of the final iterate of SGD in minimizing
non-smooth Lipschitz convex and strongly convex functions respectively with
standard step size schedules. Our results provide the first general dimension
dependent lower bound on the convergence of SGD's final iterate, partially
resolving a COLT open question raised by koren2020open. We also present further
evidence to show the correct rate in one dimension should be
$\Theta(1/\sqrt{T})$, such as a proof of a tight $O(1/\sqrt{T})$ upper bound
for one-dimensional special cases in settings more general than koren2020open.


  In this paper, we look at the complexity of designing algorithms without any
bank conflicts in the shared memory of Graphical Processing Units (GPUs). Given
input of size $n$, $w$ processors and $w$ memory banks, we study three
fundamental problems: sorting, permuting and $w$-way partitioning (defined as
sorting an input containing exactly $n/w$ copies of every integer in $[w]$).
  We solve sorting in optimal $O(\frac{n}{w} \log n)$ time. When $n \ge w^2$,
we solve the partitioning problem optimally in $O(n/w)$ time. We also present a
general solution for the partitioning problem which takes $O(\frac{n}{w}
\log^3_{n/w} w)$ time. Finally, we solve the permutation problem using a
randomized algorithm in $O(\frac{n}{w} \log\log\log_{n/w} n)$ time. Our results
show evidence that when working with banked memory architectures, there is a
separation between these problems and the permutation and partitioning problems
are not as easy as simple parallel scanning.


  Weighted voting games (WVG) are coalitional games in which an agent's
contribution to a coalition is given by his it weight, and a coalition wins if
its total weight meets or exceeds a given quota. These games model
decision-making in political bodies as well as collaboration and surplus
division in multiagent domains. The computational complexity of various
solution concepts for weighted voting games received a lot of attention in
recent years. In particular, Elkind et al.(2007) studied the complexity of
stability-related solution concepts in WVGs, namely, of the core, the least
core, and the nucleolus. While they have completely characterized the
algorithmic complexity of the core and the least core, for the nucleolus they
have only provided an NP-hardness result. In this paper, we solve an open
problem posed by Elkind et al. by showing that the nucleolus of WVGs, and, more
generally, k-vector weighted voting games with fixed k, can be computed in
pseudopolynomial time, i.e., there exists an algorithm that correctly computes
the nucleolus and runs in time polynomial in the number of players and the
maximum weight. In doing so, we propose a general framework for computing the
nucleolus, which may be applicable to a wider of class of games.


  We explore topological manipulations in one spatial dimension, which are
defined for a system with a global symmetry and map the system to another one
with a dual symmetry. In particular, we discuss fusion category symmetries
enhanced by the invariance of the actions of topological manipulations, i.e.,
self-$G$-alities for topological manipulations. Based on the self-$G$-ality
conditions, we provide LSM-type constraints on the ground states of many-body
Hamiltonians. We clarify the relationship between different enhanced symmetries
and introduce the notion of $\textit{codimension-two transitions}$. We explore
concrete lattice models for such self-$G$-alities and find how the
self-$G$-ality structures match the IR critical theories.


  This paper derives most of the formulas in the MKN (Maung-Kahana-Norbury)
Theory of bound states which incorporates the Lande Subtraction method to
remove the singularities of the Cornell potential.


  We address the scattering cross sections, and their consequences, for
submicrometer Germanium spheres. It is shown that there is a wide window in the
near infrared where light scattering by these particles is fully described by
their induced electric and magnetic dipoles. In this way, we observe remarkable
anisotropic scattering angular distributions, as well as zero forward or
backward scattered intensities, which until recently was theoretically
demonstrated only for hypothetically postulated magnetodielectric spheres.
Also, interesting new effects of the optical forces exerted on these objects
are now obtained.


  For the quantum kinetic system modelling the Bose-Einstein Condensate that
accounts for interactions between condensate and excited atoms, we use the
Chapman-Enskog expansion to derive its hydrodynamic approximations, include
both Euler and Navier-Stokes approximations. The hydrodynamic approximations
describe not only the macroscopic behavior of the BEC but also its coupling
with the non-condensates, which agrees with Landau's two fluid theory.


  Kastor-Traschen (KT) type solution in a cosmological set up is studied in
this article. We examine a hybrid of a KT metric and a
Friedmann-Robertson-Walker-Lemaitre (FRWL) solution. The problem is treated in
a general number of dimensions D>=4 and we include the cosmological constant
Lambda parameter into the Einstein-Maxwell equations.
  The matter source consists of two fluids - charged dust and neutral fluid
with non-vanishing pressure.
  The equations of motion for the fluid and electromagnetic (EM) field are
written down and an exact solution generalising extremely charged
Reissner-Nordstr\"{o}m black hole to arbitrary spatial curvature parameter is
presented. We examine metric and curvature scalars singularities, trapped
horizons as well as energy conditions.


  Monte Carlo Tree Search (MCTS)-based algorithms, such as MuZero and its
derivatives, have achieved widespread success in various decision-making
domains. These algorithms employ the reanalyze process to enhance sample
efficiency from stale data, albeit at the expense of significant wall-clock
time consumption. To address this issue, we propose a general approach named
ReZero to boost tree search operations for MCTS-based algorithms. Specifically,
drawing inspiration from the one-armed bandit model, we reanalyze training
samples through a backward-view reuse technique which obtains the value
estimation of a certain child node in advance. To further adapt to this design,
we periodically reanalyze the entire buffer instead of frequently reanalyzing
the mini-batch. The synergy of these two designs can significantly reduce the
search cost and meanwhile guarantee or even improve performance, simplifying
both data collecting and reanalyzing. Experiments conducted on Atari
environments and board games demonstrate that ReZero substantially improves
training speed while maintaining high sample efficiency. The code is available
as part of the LightZero benchmark at https://github.com/opendilab/LightZero.


  We compute the total radiated momentum carried by gravitational waves during
the scattering of two spinless black holes at the lowest order in Newton's
constant, $\mathcal O(G^3)$, and all orders in velocity. By analytic
continuation into the bound state regime, we obtain the ${\cal O}(G^3)$ energy
loss in elliptic orbits. This provides an essential step towards the complete
understanding of the third-post-Minkowskian binary dynamics. We employ the
formalism of Kosower, Maybee, and O'Connell (KMOC) which relates classical
observables to quantum scattering amplitudes and derive the relevant integrands
using generalized unitarity. The subsequent phase-space integrations are
performed via the reverse unitarity method familiar from collider physics,
using differential equations to obtain the exact velocity dependence from
near-static boundary conditions.


  We present a novel method for implementing massive neutrinos in N-body
simulations. Instead of sampling the neutrino velocity distribution by
individual point particles we take neutrino free-streaming into account by
treating it as an effective redshift dependent sound speed in a perfect
isothermal fluid, and assume a relation between the sound speed and velocity
dispersion of the neutrinos. Although the method fails to accurately model the
true neutrino power spectrum, it is able to calculate the total matter power
spectrum to the same accuracy as more complex hybrid neutrino methods, except
on very small scales. We also present an easy way to update the publicly
available Gadget-2 version with this neutrino approximation.


  We propose a general framework called Network Dissection for quantifying the
interpretability of latent representations of CNNs by evaluating the alignment
between individual hidden units and a set of semantic concepts. Given any CNN
model, the proposed method draws on a broad data set of visual concepts to
score the semantics of hidden units at each intermediate convolutional layer.
The units with semantics are given labels across a range of objects, parts,
scenes, textures, materials, and colors. We use the proposed method to test the
hypothesis that interpretability of units is equivalent to random linear
combinations of units, then we apply our method to compare the latent
representations of various networks when trained to solve different supervised
and self-supervised training tasks. We further analyze the effect of training
iterations, compare networks trained with different initializations, examine
the impact of network depth and width, and measure the effect of dropout and
batch normalization on the interpretability of deep visual representations. We
demonstrate that the proposed method can shed light on characteristics of CNN
models and training methods that go beyond measurements of their discriminative
power.


  We report new results about the two-time dynamics of an anomalously diffusing
classical particle, as described by the generalized Langevin equation with a
frequency-dependent noise and the associated friction. The noise is defined by
its spectral density proportional to $\omega^{\delta-1}$ at low frequencies,
with $0<\delta<1$ (subdiffusion) or $1<\delta<2$ (superdiffusion). Using
Laplace analysis, we derive analytic expressions in terms of Mittag-Leffler
functions for the correlation functions of the velocity and of the
displacement. While the velocity thermalizes at large times (slowly, in
contrast to the standard Brownian motion case $\delta=1$), the displacement
never attains equilibrium: it ages. We thus show that this feature of normal
diffusion is shared by a subdiffusive or superdiffusive motion. We provide a
closed form analytic expression for the fluctuation-dissipation ratio
characterizing aging.


  We give a geometrical construction of Connes spectral triples or
noncommutative Dirac operators $D$ starting with a bimodule connection on the
proposed spinor bundle. The theory is applied to the example of $M_2(\Bbb C)$,
and also applies to the standard $q$-sphere and the $q$-disk with the right
classical limit and all properties holding except for $\mathcal J$ now being a
twisted isometry. We also describe a noncommutative Chern construction from
holomorphic bundles which in the $q$-sphere case provides the relevant bimodule
connection.


  This paper proposes a two-level distributed algorithmic framework for solving
the AC optimal power flow (OPF) problem with convergence guarantees. The
presence of highly nonconvex constraints in OPF poses significant challenges to
distributed algorithms based on the alternating direction method of multipliers
(ADMM). In particular, convergence is not provably guaranteed for nonconvex
network optimization problems like AC OPF. In order to overcome this
difficulty, we propose a new distributed reformulation for AC OPF and a
two-level ADMM algorithm that goes beyond the standard framework of ADMM. We
establish the global convergence and iteration complexity of the proposed
algorithm under mild assumptions. Extensive numerical experiments over some
largest test cases from NESTA and PGLib-OPF (up to 30,000-bus systems)
demonstrate advantages of the proposed algorithm over existing ADMM variants in
terms of convergence, scalability, and robustness. Moreover, under appropriate
parallel implementation, the proposed algorithm exhibits fast convergence
comparable to or even better than the state-of-the-art centralized solver.


  We argue that the late time behavior of horizon fluctuations in large anti-de
Sitter (AdS) black holes is governed by the random matrix dynamics
characteristic of quantum chaotic systems. Our main tool is the
Sachdev-Ye-Kitaev (SYK) model, which we use as a simple model of a black hole.
We use an analytically continued partition function $|Z(\beta +it)|^2$ as well
as correlation functions as diagnostics. Using numerical techniques we
establish random matrix behavior at late times. We determine the early time
behavior exactly in a double scaling limit, giving us a plausible estimate for
the crossover time to random matrix behavior. We use these ideas to formulate a
conjecture about general large AdS black holes, like those dual to 4D
super-Yang-Mills theory, giving a provisional estimate of the crossover time.
We make some preliminary comments about challenges to understanding the late
time dynamics from a bulk point of view.


  We present a novel approach to generating photo-realistic images of a face
with accurate lip sync, given an audio input. By using a recurrent neural
network, we achieved mouth landmarks based on audio features. We exploited the
power of conditional generative adversarial networks to produce
highly-realistic face conditioned on a set of landmarks. These two networks
together are capable of producing a sequence of natural faces in sync with an
input audio track.


  The dominant dielectric used currently in silicon devices is silicon oxide.
Its application for future devices will be impeded by several fundamental
limitations which lead to low reliability of semiconductor devices and to the
necessity of alternative dielectrics. Amorphous silicon nitride and oxynitride
are considered now as alternative to silicon oxide in future devices. One of
the unique property of amorphous silicon nitride is the electron and hole
capture by the deep traps with extremely long life time (10 years) in the
captured state (the memory effect). This property is employed in memory devices
and microprocessors in computers. Despite numerous efforts the nature of traps
responsible for the memory effect in this material is so far unclear. In this
paper we discuss the nature of such traps using the quantum-chemical
simulation. The calculations show that the defects responsible for the electron
and hole capture in amorphous silicon nitride can be the Si-Si defects created
by excess silicon atoms.


  We present a type theory dealing with non-linear, "ordinary" dependent types
(which we will call cartesian) and linear types, where both constructs may
depend on terms of the former. In the interplay between these, we find new type
formers $\sqcap_{x:A}B$ and $\sqsubset_{x:A}B$, akin to $\Pi$ and $\Sigma$, but
where the dependent type $B$, (and therefore the resulting construct) is a
linear type. These can be seen as internalizing universal and existential
quantification of linear predicates. We also consider two modalities, $M$ and
$L$, transforming linear types into cartesian types and vice versa. The theory
is interpreted in a split comprehension category
$\pi:\mathcal{T}\to\mathcal{C}^\to$ accompanied by a split symmetric monoidal
fibration, $\pi: \mathcal{L}\to\mathcal{C}$. This structure determines, for any
context $\Gamma$, fibers $\mathcal{T}_\Gamma$ and $\mathcal{L}_\Gamma$; the
category of cartesian types and the monoidal category of linear types over
$\Gamma$, respectively. Here, the type formers $\sqcap_{x:A}$ and
$\sqsubset_{x:A}$ are understood as right and left adjoints of the monoidal
reindexing functor $\pi_A^*:\mathcal{L}_\Gamma\to\mathcal{L}_{\Gamma.A}$. The
operators $M$ and $L$ induce a fiberwise adjunction $L \dashv M$ between
$\mathcal{L}$ and $\mathcal{T}$, where the traditional exponential modality is
understood as the comonad $! = LM$. We provide a model of this theory called
the Diagram model, which extends the groupoid model of dependent type theory to
accommodate linear types. Here, cartesian types are interpreted as a family of
groupoids, while linear types are interpreted as diagrams
$A:\Gamma\to\mathcal{V}$ in any symmetric monoidal category $\mathcal{V}$. We
show that the diagrams model can under certain conditions support a linear
analogue of the univalence axiom, and provide some discussion on the
higher-dimensional nature of linear dependent types.


  We propose to probe the quantum ground state of a spin-1 Bose-Einstein
condensate with the transmission spectra of an optical cavity. By choosing a
circularly polarized cavity mode with an appropriate frequency, we can realize
coupling between the cavity mode and the magnetization of the condensate. The
cavity transmission spectra then contain information of the magnetization
statistics of the condensate and thus can be used to distinguish the
ferromagnetic and antiferromagnetic quantum ground states. This technique may
also be useful for continuous observation of the spin dynamics of a spinor
Bose-Einstein condensate.


  We discuss various mechanisms of catalysis of black holes/wormholes (BH/WH)
formation in particles collisions. The current paradigm suggests that BH/WH
formation in particles collisions will happen when center of mass energies of
colliding particles is sufficiently above the Planck scale (the transplanckian
region). To estimate the BH/WH production we use the classical geometrical
cross section. We confirm the classical geometrical cross section of the BH
production reconsidering the process of two transplanckian particles collision
in the rest frame of one of incident particles. This consideration permits to
use the standard Thorne's hoop conjecture for a matter compressed into a region
to prove a variant of the conjecture dealing with a total amount of compressed
energy in the case of colliding particles. We calculate geometrical cross
sections for different processes and for different background, in particular,
for (A)dS. We show that results are in agreement with closed trapped surface
(CTS) estimations though there are no general theorems providing that the BH
formation follows from CTS's formation. We show that the process of BH
formation is catalyzed by the negative cosmological constant and by a
particular scalar matter, namely dilaton, while it is relaxed by the positive
cosmological constant and at a critical value just turns off. Also we note that
the cross section is sensible to the compactification of extra dimensions and
to the particular brane model.


  The heterogeneous and distributed nature of the Internet of Things (IoT) is
driving the need for extremely fast and fine-grained service provisioning in
5/5+G architectures and beyond. To meet these needs, it is critical to enable
efficient and flexible computation and networking fabrics, that can be rapidly
reconfigured to meet the computation and communication tasks at hand. In this
article, we propose a novel Fog Computing architecture that translates IoT
communications into service transactions, provisioned over a fast and efficient
networking fabric. Service matching is provided by a network function designed
using principles from Information-Centric Networks (ICN) research, routing edge
requests directly to the nearest service points without expensive and slow DNS
redirects. The proposed Fog substrate reduces the networking complexity and
overhead while being architecturally simple. We evaluate the architecture
through a comparison with how Fog might be established over existing networking
fabrics and quantify the performance benefits. Evaluation results illustrate
the superiority of the proposed architecture in reducing the required backhaul
capacity and the path length.


  We survey results on the topological complexity of classical configuration
spaces of distinct ordered points in orientable surfaces and related spaces,
including certain orbit configuration spaces and Eilenberg-Mac Lane spaces
associated to certain discrete groups.


  The number of domino tilings of a region with reflective symmetry across a
line is combinatorially shown to depend on the number of domino tilings of
particular subregions, modulo 4. This expands upon previous congruency results
for domino tilings, modulo 2, and leads to a variety of corollaries, including
that the number of domino tilings of a k x 2k rectangle is congruent to 1 mod
4.


  Previous molecular gas observations at arcsecond-scale resolution of the
Seyfert 2 galaxy M51 suggest the presence of a dense circumnuclear rotating
disk, which may be the reservoir for fueling the active nucleus and obscures it
from direct view in the optical. However, our recent interferometric CO(3-2)
observations show a hint of a velocity gradient perpendicular to the rotating
disk, which suggests a more complex structure than previously thought. To image
the putative circumnuclear molecular gas disk at sub-arcsecond resolution to
better understand both the spatial distribution and kinematics of the molecular
gas. We carried out CO(2-1) and CO(1-0) line observations of the nuclear region
of M51 with the new A configuration of the IRAM Plateau de Bure Interferometer,
yielding a spatial resolution lower than 15 pc. The high resolution images show
no clear evidence of a disk, aligned nearly east-west and perpendicular to the
radio jet axis, as suggested by previous observations, but show two separate
features located on the eastern and western sides of the nucleus. The western
feature shows an elongated structure along the jet and a good velocity
correspondence with optical emission lines associated with the jet, suggesting
that this feature is a jet-entrained gas. The eastern feature is elongated
nearly east-west ending around the nucleus. A velocity gradient appears in the
same direction with increasingly blueshifted velocities near the nucleus. This
velocity gradient is in the opposite sense of that previously inferred for the
putative circumnuclear disk. Possible explanations for the observed molecular
gas distribution and kinematics are that a rotating gas disk disturbed by the
jet, gas streaming toward the nucleus, or a ring with another smaller counter-
or Keplarian-rotating gas disk inside.


  Gaussian processes are used in machine learning to learn input-output
mappings from observed data. Gaussian process regression is based on imposing a
Gaussian process prior on the unknown regressor function and statistically
conditioning it on the observed data. In system identification, Gaussian
processes are used to form time series prediction models such as non-linear
finite-impulse response (NFIR) models as well as non-linear autoregressive
(NARX) models. Gaussian process state-space models (GPSS) can be used to learn
the dynamic and measurement models for a state-space representation of the
input-output data. Temporal and spatio-temporal Gaussian processes can be
directly used to form regressor on the data in the time domain. The aim of this
article is to briefly outline the main directions in system identification
methods using Gaussian processes.


  In this paper we formulate a weighted version of minimum problem (1.4) on the
sphere and we show that, for $K\le L$, if $\set{\phi_k}^K_{k=1}$ consists of
the spherical functions with degree less than $N$ we can localize the points
$(\xi_1,...,\xi_L)$ on the sphere so that the solution of this problem is the
simplest possible. This localization is connected to the discrete orthogonality
of the spherical functions which was proved in [3]. Using these points we
construct a frame system and a wavelet system on the sphere and we study the
properties of these systems. For $K>L$ a similar construction was made in paper
[4], but in that case the solution of the minimum problem (1.4) is not as
efficient as it is in our case. The analogue of Fej\'er and de la
Val\'ee-Poussin summation methods introduced in [3] can be expressed by the
frame system introduced in this paper.


  The Neptunian satellite system is unusual. The major satellites of Jupiter,
Saturn, and Uranus are all in prograde, low-inclination orbits. Neptune on the
other hand, has the fewest satellites, and most of the system's mass is within
one irregular satellite, Triton. Triton was most likely captured by Neptune and
destroyed the primordial regular satellite system. We investigate the
interactions between a newly captured Triton and a prior Neptunian satellite
system. We find that a prior satellite system with a mass ratio similar to the
Uranian system or smaller has a substantial likelihood of reproducing the
current Neptunian system, while a more massive system has a low probability of
leading to the current configuration. Moreover, Triton's interaction with a
prior satellite system may offer a mechanism to decrease its high initial
semimajor axis fast enough to preserve small irregular satellites (Nereid-like)
that might otherwise be lost during a prolonged Triton circularization via
tides alone.


  Event detection (ED), a sub-task of event extraction, involves identifying
triggers and categorizing event mentions. Existing methods primarily rely upon
supervised learning and require large-scale labeled event datasets which are
unfortunately not readily available in many real-life applications. In this
paper, we consider and reformulate the ED task with limited labeled data as a
Few-Shot Learning problem. We propose a Dynamic-Memory-Based Prototypical
Network (DMB-PN), which exploits Dynamic Memory Network (DMN) to not only learn
better prototypes for event types, but also produce more robust sentence
encodings for event mentions. Differing from vanilla prototypical networks
simply computing event prototypes by averaging, which only consume event
mentions once, our model is more robust and is capable of distilling contextual
information from event mentions for multiple times due to the multi-hop
mechanism of DMNs. The experiments show that DMB-PN not only deals with sample
scarcity better than a series of baseline models but also performs more
robustly when the variety of event types is relatively large and the instance
quantity is extremely small.


  Clusters of galaxies are thought to contain about ten times as much dark
matter as baryonic matter. The dark component therefore dominates the
gravitational potential of the cluster, and the baryons confined by this
potential radiate X-rays with a luminosity that depends mainly on the gas
density in the cluster's core. Predictions of the X-rays' properties based on
models of cluster formation do not, however, agree with the observations. If
the models ignore the condensation of cooling gas into stars and feedback from
the associated supernovae, they overestimate the X-ray luminosity because the
density of the core gas is too high. An early episode of uniformly distributed
supernova feedback could rectify this by heating the uncondensed gas and
therefore making it harder to compress into the core, but such a process seems
to require an implausibly large number of supernovae. Here we show how
radiative cooling of intergalactic gas and subsequent supernova heating
conspire to eliminate highly compressible low-entropy gas from the intracluster
medium. This brings the core entropy and X-ray luminosities of clusters into
agreement with the observations, in a way that depends little on the efficiency
of supernova heating in the early Universe.


  We consider the ensemble of curves
$\{\gamma_{\alpha,N}:\alpha\in(0,1],N\in\N\}$ obtained by linearly
interpolating the values of the normalized theta sum
$N^{-1/2}\sum_{n=0}^{N'-1}\exp(\pi i n^2\alpha)$, $0\leq N'<N$. We prove the
existence of limiting finite-dimensional distributions for such curves as
$N\to\infty$, with respect to an absolutely continuous probability measure
$\mu_R$ on $(0,1]$. Our Main Theorem generalizes a result by Marklof and Jurkat
and van Horne. Our proof relies on the analysis of the geometric structure of
such curves, which exhibit spiral-like patterns (curlicues) at different
scales. We exploit a renormalization procedure constructed by means of the
continued fraction expansion of $\alpha$ with even partial quotients and a
renewal-type limit theorem for the denominators of such continued fraction
expansions.


  Stochastic approximation algorithm is a useful technique which has been
exploited successfully in probability theory and statistics for a long time.
The step sizes used in stochastic approximation are generally taken to be
deterministic and same is true for the drift. However, the specific application
of urn models with random replacement matrices motivates us to consider
stochastic approximation in a setup where both the step sizes and the drift are
random, but the sequence is uniformly bounded. The problem becomes interesting
when the negligibility conditions on the errors hold only in probability. We
first prove a result on stochastic approximation in this setup, which is new in
the literature. Then, as an application, we study urn models with random
replacement matrices.
  In the urn model, the replacement matrices need neither be independent, nor
identically distributed. We assume that the replacement matrices are only
independent of the color drawn in the same round conditioned on the entire
past. We relax the usual second moment assumption on the replacement matrices
in the literature and require only first moment to be finite. We require the
conditional expectation of the replacement matrix given the past to be close to
an irreducible matrix, in an appropriate sense. We do not require any of the
matrices to be balanced or nonrandom. We prove convergence of the proportion
vector, the composition vector and the count vector in $L^1$, and hence in
probability. It is to be noted that the related differential equation is of
Lotka-Volterra type and can be analyzed directly.


  We study the spectrum of an impurity coupled to a Fermi sea (e.g., minority
atom in an ultracold gas, exciton in a solid) by attraction strong enough to
form a molecule/trion. We introduce a diagrammatic scheme which allows treating
a finite mass impurity while reproducing the Fermi edge singularity in the
immobile limit. For large binding energies the spectrum is characterized by a
semi-coherent repulsive polaron and an incoherent molecule-hole continuum,
which is the lowest-energy feature in the single-particle spectrum. The
previously predicted attractive polaron seems not to exist for strong binding.