  Let $n$ and $t$ be positive integers with $t<n$, and let $q$ be a prime
power. A partial $(t-1)$-spread of ${\rm PG}(n-1,q)$ is a set of
$(t-1)$-dimensional subspaces of ${\rm PG}(n-1,q)$ that are pairwise disjoint.
Let $r\equiv n\pmod{t}$ with $0\leq r<t$, and let ${\theta}_i=(q^i-1)/(q-1)$.
We essentially prove that if $2\leq r<t\leq {\theta}_r$, then the maximum size
of a partial $(t-1)$-spread of ${\rm PG}(n-1,q)$ is bounded from above by
$({\theta}_n-{\theta}_{t+r})/{\theta}_t+q^r-(q-1)(t-3)+1$. We actually give
tighter bounds when certain divisibility conditions are satisfied. These bounds
improve on the previously known upper bound for the maximum size partial
($t-1$)-spreads of ${\rm PG}(n-1,q)$; for instance, when
$\lceil\frac{{\theta}_r}{2}\rceil+4\leq t\leq {\theta}_r$ and $q>2$. The exact
value of the maximum size partial $(t-1)$-spread has been recently determined
for $t>{\theta}_r$ by the authors of this paper (see N\u{a}stase-Sissokho
[21]).


  Large Language Models (LLMs) are not only resource-intensive to train but
even more costly to deploy in production. Therefore, recent work has attempted
to prune blocks of LLMs based on cheap proxies for estimating block importance,
effectively removing 10% of blocks in well-trained LLaMa-2 and Mistral 7b
models without any significant degradation of downstream metrics. In this
paper, we explore different block importance metrics by considering adaptive
metrics such as Shapley value in addition to static ones explored in prior
work. We show that adaptive metrics exhibit a trade-off in performance between
tasks i.e., improvement on one task may degrade performance on the other due to
differences in the computed block influences. Furthermore, we extend this
analysis from a complete block to individual self-attention and feed-forward
layers, highlighting the propensity of the self-attention layers to be more
amendable to pruning, even allowing removal of upto 33% of the self-attention
layers without incurring any performance degradation on MMLU for Mistral 7b
(significant reduction in costly maintenance of KV-cache). Finally, we look at
simple performance recovery techniques to emulate the pruned layers by training
lightweight additive bias or low-rank linear adapters. Performance recovery
using emulated updates avoids performance degradation for the initial blocks
(up to 5% absolute improvement on MMLU), which is either competitive or
superior to the learning-based technique.


  In a recent paper [S. Abe and N. Suzuki, Europhys. Lett., 65 (2004) 581], the
concept of earthquake network has been introduced in order to describe
complexity of seismicity. There, the cell size, which is the scale of coarse
graining needed for constructing an earthquake network, has remained as a free
parameter. Here, a method is presented for determining it based on the scaling
behavior of the network. Quite remarkably, both the exponent of the power-law
connectivity distribution and the clustering coefficient are found to approach
the respective universal values and remain invariant as the cell size becomes
larger than a certain value, $l_*$, which depends on the number of events
contained in the analysis, in general. This $l_*$ fixes the scale of coarse
graining. Universality of the result is demonstrated for all of the networks
constructed from the data independently taken from California, Japan and Iran.


  There is a class of single trace operators in ${\cal N}=4$ Yang-Mills theory
which are related by the AdS/CFT correspondence to classical string solutions.
Interesting examples of such solutions corresponding to periodic trajectories
of the Neumann system were studied recently. In our paper we study a
generalization of these solutions. We consider strings moving with large
velocities. We show that the worldsheet of the fast moving string can be
considered as a perturbation of the degenerate worldsheet, with the small
parameter being the relativistic factor $\sqrt{1-v^2}$. The series expansion in
this relativistic factor should correspond to the perturbative expansion in the
dual Yang-Mills theory. The operators minimizing the anomalous dimension in the
sector with given charges correspond to periodic trajectories in the mechanical
system which is closely related to the product of two Neumann systems.


  Geometric conditions are given so that the leafwise reduced cohomology is of
infinite dimension, specially for foliations with dense leaves on closed
manifolds. The main new definition involved is the intersection number of
subfoliations with "appropriate coefficients". The leafwise reduced cohomology
is also described for homogeneous foliations with dense leaves on closed
nilmanifolds.


  The small-world property in the context of complex networks implies
structural benefits to the processes taking place within a network, such as
optimal information transmission and robustness. In this paper, we study a
model network of integrate-and-fire neurons that are subject to
activity-dependent synaptic plasticity. We find the learning rule that gives
rise to a small-world structure when the collective dynamics of the system
reaches a critical state which is characterised by power-law distributions of
activity clusters. Moreover, by analysing the motif profile of the networks, we
observe that bidirectional connectivity is impaired by the effects of this type
of plasticity.


  The use of Wake-Up Radio (WUR) in Internet of Things (IoT) networks can
significantly improve their energy efficiency: battery-powered sensors can
remain in a low-power (sleep) mode while listening for wake-up messages using
their WUR and reactivate only when polled, saving energy. However,
polling-based Time Division Multiple Access (TDMA) may significantly increase
data transmission delay if packets are generated sporadically, as nodes with no
information still need to be polled. In this paper, we examine the effect of
multicast polling for WUR-enabled wireless nodes. The idea is to assign nodes
to multicast groups so that all nodes in the same group can be solicited by a
multicast polling message. This may cause collisions, which can be solved by
requesting retransmissions from the involved nodes. We analyze the performance
of different multicast polling and retransmission strategies, showing that the
optimal approach can significantly reduce the delay over TDMA and ALOHA in
low-traffic scenarios while keeping good energy efficiency.


  Two results support the idea that the scalar and vector potentials in the
Lorenz gauge can be considered to be physical quantities: (i) they separately
satisfy the properties of causality and propagation at the speed of light and
not imply spurious terms and (ii) they can naturally be written in a manifestly
covariant form. In this paper we introduce expressions for the Lorenz-gauge
potentials at the present time in terms of electric and magnetic fields at the
retarded time. These expressions provide a third result in favor of a physical
interpretation of the Lorenz-gauge potentials: (iii) they can be regarded as
causal effects of the observed electric and magnetic fields.


  Exoplanetary systems host giant planets on substantially non-circular,
close-in orbits. We propose that these eccentricities arise in a phase of giant
impacts, analogous to the final stage of Solar System assembly that formed
Earth's Moon. In this scenario, the planets scatter each other and collide,
with corresponding mass growth as they merge. We numerically integrate an
ensemble of systems with varying total planet mass, allowing for collisional
growth, to show that (1) the high-eccentricity giants observed today may have
formed preferentially in systems of higher initial total planet mass, and (2)
the upper bound on the observed giant planet eccentricity distribution is
consistent with planet-planet scattering. We predict that mergers will produce
a population of high-mass giant planets between 1 and 8 au from their stars.


  We present a detailed analysis of the class of regression decision tree
algorithms which employ a regulized piecewise-linear node-splitting criterion
and have regularized linear models at the leaves. From a theoretic standpoint,
based on Rademacher complexity framework, we present new high-probability upper
bounds for the generalization error for the proposed classes of regularized
regression decision tree algorithms, including LASSO-type, and $\ell_{2}$
regularization for linear models at the leaves. Theoretical result are further
extended by considering a general type of variable selection procedure.
Furthermore, in our work we demonstrate that the class of piecewise-linear
regression trees is not only numerically stable but can be made tractable via
an algorithmic implementation, presented herein, as well as with the help of
modern GPU technology. Empirically, we present results on multiple datasets
which highlight the strengths and potential pitfalls, of the proposed tree
algorithms compared to baselines which grow trees based on piecewise constant
models.


  We identify the scaling region of a width O(n^{-1}) in the vicinity of the
accumulation points $t=\pm 1$ of the real roots of a random Kac-like polynomial
of large degree n. We argue that the density of the real roots in this region
tends to a universal form shared by all polynomials with independent,
identically distributed coefficients c_i, as long as the second moment
\sigma=E(c_i^2) is finite. In particular, we reveal a gradual (in contrast to
the previously reported abrupt) and quite nontrivial suppression of the number
of real roots for coefficients with a nonzero mean value \mu_n = E(c_i) scaled
as \mu_n\sim n^{-1/2}.


  Regular Kadomtsev-Petviashvili II (KPII) line solitons have been investigated
and classified successfully by the Grassmannians. The inverse scattering method
provides a promising and powerful approach to study the stability properties of
$\textrm{Gr}(N, M)_{> 0}$ KP solitons. In this paper, we complete rigorous
analysis for the direct scattering problem of perturbed $\textrm{Gr}(N, M)_{>
0}$ KP solitons}.


  While the composite fermion picture is so effective as to describe the
excitation spectra including the spin wave for Laughlin's quantum liquid, ``how
heavy and how strongly-interacting" remains a formidable question for the
composite fermions, to which this article first addresses. The effective mass
(purely interaction originated) defined from the excitation spectrum and
obtained for various even- as well as odd-fractions exhibits a curious,
step-like filling dependence basically determined by the number of flux quanta
attached to each fermion, where the non-monotonic behaviour indicates a strong
effect of gauge-field fluctuations. The excitation spectrum fits a Fermi
liquid, but again a large effect of inter-composite fermion interaction appears
as anomalous Landau's parameters. We have then moved on to see how the
introduction of three-dimensionality (where the shape of the Fermi surface
becomes relevant) affects the interacting electron system, and propose the
magnetic-field induced SDW in three-dimensional systems. This should be a good
candidate, in entirely realistic magnetic fields, for the integer QHE recently
predicted by Koshino et al to occur in 3D on the fractal energy spectrum
similar to Hofstadter's. The mechanism for the field-induced phase is an effect
of interaction in Landau's quantisation on incompletely-nested (i.e.,
multiply-connected) Fermi surfaces, so the interplay of many-body physics and
the magnetic quantisation on various Fermi surfaces may provide an interesting
future avenue for 3D systems.


  We introduce the notion of Rota-Baxter coalgebra which can be viewed as the
dual notion of Rota-Baxter algebra. We provide some concrete examples and
establish various properties of this new object. We also consider comodules
over Rota-Baxter coalgebras.


  In this paper, we investigate the controlled system described by
forward-backward stochastic differential equations with the control contained
in drift, diffusion and generator of BSDE. A new verification theorem is
derived within the framework of viscosity solutions without involving any
derivatives of the value functions. It is worth to pointing out that this
theorem has wider applicability than the restrictive classical verification
theorems. As a relevant problem, the optimal stochastic feedback controls for
forward-backward system are discussed as well.


  We apply a proposal of Yuen and Tombesi, for treating stochastic problems
with negative diffusion, to the analytically soluble problem of the single-mode
anharmonic oscillator. We find that the associated stochastic realizations
include divergent trajectories. It is possible, however, to solve the
stochastic problem exactly, but the averaging must be performed with great
care.


  We express notions of K-stability of polarized spherical varieties in terms
of combinatorial data, vastly generalizing the case of toric varieties. We then
provide a combinatorial sufficient condition of G-uniform K-stability by
studying the corresponding convex geometric problem. Thanks to recent work of
Chi Li and a remark by Yuji Odaka, this provides an explicitly checkable
sufficient condition of existence of constant scalar curvature Kahler metrics.
As a side effect, we show that, on several families of spherical varieties,
G-uniform K-stability is equivalent to K-polystability with respect to
G-equivariant test configurations for polarizations close to the anticanonical
bundle.


  The main statement of the nucleon constituent quark model with a fixed number
of particles as basic ansatz are considered in a framework of the single-time
(quasipotential) approach to the bound state problem. The scaling law breacking
for the proton form factor is investigated for Q^2 = 0 -- 2 Gev^2.


  We studied autoassociative networks in which synapses are noisy on a time
scale much shorter that the one for the neuron dynamics. In our model a
presynaptic noise causes postsynaptic depression as recently observed in
neurobiological systems. This results in a nonequilibrium condition in which
the network sensitivity to an external stimulus is enhanced. In particular, the
fixed points are qualitatively modified, and the system may easily scape from
the attractors. As a result, in addition to pattern recognition, the model is
useful for class identification and categorization.


  The search or design of silicon nanostructures similar to their carbon
analogues has attracted great interest recently. In this work, density
functional calculations are performed to systematically study a series of
finite and infinite hydrogenated cluster-assembled silicon nanotubes (SiNTs).
It is found that stable one-dimensional SiNTs with formula
$Si_{m(3k+1)}H_{2m(k+1)}$ can be constructed by proper assembly of hydrogenated
fullerene-like silicon clusters $Si_{4m}H_{4m}$. The stability is first
demonstrated by the large cohesive energies and HOMO-LUMO gaps. Among all such
silicon nanotubes, the ones built from $Si_{20}H_{20}$($m=5$) and
$Si_{24}H_{24}$($m=6$) are the most stable due to the silicon bond angles that
are most close to the bulk $sp^{3}$ type in these structures. Thermostability
analysis further verifies that such tubes may well exist at room temperature.
Finally, both finite nanotubes and infinite nanotubes show a large energy gap.
A direct-indirect-direct band gap transition has been revealed with the
increase of the tube radius. The existence of direct band gap may make them
potential building blocks for electronic and optoelectronic devices.


  Existing deep learning real denoising methods require a large amount of
noisy-clean image pairs for supervision. Nonetheless, capturing a real
noisy-clean dataset is an unacceptable expensive and cumbersome procedure. To
alleviate this problem, this work investigates how to generate realistic noisy
images. Firstly, we formulate a simple yet reasonable noise model that treats
each real noisy pixel as a random variable. This model splits the noisy image
generation problem into two sub-problems: image domain alignment and noise
domain alignment. Subsequently, we propose a novel framework, namely
Pixel-level Noise-aware Generative Adversarial Network (PNGAN). PNGAN employs a
pre-trained real denoiser to map the fake and real noisy images into a nearly
noise-free solution space to perform image domain alignment. Simultaneously,
PNGAN establishes a pixel-level adversarial training to conduct noise domain
alignment. Additionally, for better noise fitting, we present an efficient
architecture Simple Multi-scale Network (SMNet) as the generator. Qualitative
validation shows that noise generated by PNGAN is highly similar to real noise
in terms of intensity and distribution. Quantitative experiments demonstrate
that a series of denoisers trained with the generated noisy images achieve
state-of-the-art (SOTA) results on four real denoising benchmarks. Part of
codes, pre-trained models, and results are available at
https://github.com/caiyuanhao1998/PNGAN for comparisons.


  One of the key science goals of advanced gravitational-wave detectors is to
observe a stochastic gravitational-wave background. However, recent work
demonstrates that correlated magnetic fields from Schumann resonances can
produce correlated strain noise over global distances, potentially limiting the
sensitivity of stochastic background searches with advanced detectors. In this
paper, we estimate the correlated noise budget for the worldwide Advanced LIGO
network and conclude that correlated noise may affect upcoming measurements. We
investigate the possibility of a Wiener filtering scheme to subtract correlated
noise from Advanced LIGO searches, and estimate the required specifications. We
also consider the possibility that residual correlated noise remains following
subtraction, and we devise an optimal strategy for measuring astronomical
parameters in the presence of correlated noise. Using this new formalism, we
estimate the loss of sensitivity for a broadband, isotropic stochastic
background search using 1 yr of LIGO data at design sensitivity. Given our
current noise budget, the uncertainty with which LIGO can estimate energy
density will likely increase by a factor of ~4--if it is impossible to achieve
significant subtraction. Additionally, narrowband cross-correlation searches
may be severely affected at low frequencies f < 45 Hz without effective
subtraction.


  We consider the numerical approximation of different ordinary differential
equations (ODEs) and partial differential equations (PDEs) with periodic
boundary conditions involving a one-dimensional random parameter, comparing the
intrusive and non-intrusive polynomial chaos expansion (PCE) method. We
demonstrate how to modify two schemes for intrusive PCE (iPCE) which are highly
efficient in solving nonlinear reaction-diffusion equations: A second-order
exponential time differencing scheme (ETD-RDP-IF) as well as a spectral
exponential time differencing fourth-order Runge-Kutta scheme (ETDRK4). In
numerical experiments, we show that these schemes show superior accuracy to
simpler schemes such as the EE scheme for a range of model equations and we
investigate whether they are competitive with non-intrusive PCE (niPCE)
methods. We observe that the iPCE schemes are competitive with niPCE for some
model equations, but that iPCE breaks down for complex pattern formation models
such as the Gray-Scott system.


  In this paper we study analogues of the perfect splines for weighted Sobolev
classes of functions defined on the half-line. Maximally oscillating splines
play important role in the solution of certain extremal problems. In
particular, using these splines, we characterize the modulus of continuity of
the differential operator.


  (Abridged) Electron-molecule interaction is a fundamental process in
radiation-driven chemistry in space, from the interstellar medium to comets.
Therefore, knowledge of interaction cross-sections is key. While there has been
a plethora of studies of total ionization cross-sections, data is often spread
over many sources, or not public or readily available. We introduce the
Astrochemistry Low-energy Electron Cross-Section (ALeCS) database, a public
database for electron interaction cross-sections and ionization rates for
molecules of astrochemical interest. In this work, we present the first data
release comprising total ionization cross-sections and ionization rates for
over 200 neutral molecules. We include optimized geometries and molecular
orbital energies at various levels of theory, and for a subset of the
molecules, the ionization potentials. We compute total ionization
cross-sections using the binary-encounter Bethe model and screening-corrected
additivity rule, and ionization rates and reaction network coefficients for
molecular cloud environments for $>$200 neutral molecules ranging from
diatomics to complex organics. We demonstrate that our binary-encounter Bethe
cross-sections agree well with experimental data. We show that the ionization
rates scale roughly linearly with the number of constituent atoms in the
molecule. We introduce and describe the public ALeCS database. For the initial
release, we include total ionization cross-sections for $>$200 neutral
molecules and several cations and anions calculated with different levels of
quantum chemistry theory, the chemical reaction rates for the ionization, and
network files in the formats of the two most popular astrochemical networks,
the KIDA and UMIST. The database will be continuously updated for more
molecules and interactions.


  The effect of vacuum birefringence in a magnetic field generated by a
laser-driven capacitor-coil generator as well as in field of an electromagnetic
wave in a radioguide has been theoretically considered. The resulting
ellipticity of a linearly polarized laser beam propagating in the considered
field configuration is calculated. The obtained results are compared to the
parameters of the PVLAS experiment which aims to observe the effect of magnetic
vacuum birefringence experimentally.


  Skillful subseasonal forecasts are crucial for various sectors of society but
pose a grand scientific challenge. Recently, machine learning based weather
forecasting models outperform the most successful numerical weather predictions
generated by the European Centre for Medium-Range Weather Forecasts (ECMWF),
but have not yet surpassed conventional models at subseasonal timescales. This
paper introduces FuXi Subseasonal-to-Seasonal (FuXi-S2S), a machine learning
model that provides global daily mean forecasts up to 42 days, encompassing
five upper-air atmospheric variables at 13 pressure levels and 11 surface
variables. FuXi-S2S, trained on 72 years of daily statistics from ECMWF ERA5
reanalysis data, outperforms the ECMWF's state-of-the-art
Subseasonal-to-Seasonal model in ensemble mean and ensemble forecasts for total
precipitation and outgoing longwave radiation, notably enhancing global
precipitation forecast. The improved performance of FuXi-S2S can be primarily
attributed to its superior capability to capture forecast uncertainty and
accurately predict the Madden-Julian Oscillation (MJO), extending the skillful
MJO prediction from 30 days to 36 days. Moreover, FuXi-S2S not only captures
realistic teleconnections associated with the MJO, but also emerges as a
valuable tool for discovering precursor signals, offering researchers insights
and potentially establishing a new paradigm in Earth system science research.


  The relation between the heavy-quark field in QCD and the corresponding field
in HQET is derived up to three loops, and to all orders in the large-$\beta_0$
limit. The corresponding relation between the QED electron field and the
Bloch--Nordsieck one is gauge invariant to all orders. We also prove that the
$\bar{\text{MS}}$ anomalous dimension of the QED electron field depends on the
gauge parameter only at one loop.


  A theory of spin relaxation in graphene including intrinsic, Bychkov-Rashba,
and ripple spin-orbit coupling is presented. We find from spin relaxation data
by Tombros et al. [Nature 448, 571 (2007).] that intrinsic spin-orbit coupling
dominates over other contributions with a coupling constant of 3.7 meV.
Although it is 1-3 orders of magnitude larger than those obtained from first
principles, we show that comparable values are found for other honeycomb
systems, MgB2 and LiC6; the latter is studied herein by electron spin resonance
(ESR). We predict that spin coherence is longer preserved for spins
perpendicular to the graphene plane, which is beneficial for spintronics. We
identify experimental conditions when bulk ESR is realizable on graphene.


  We present a general prescription for the holographic computation of
real-time n-point functions in non-trivial states. In QFT such real-time
computations involve a choice of a time contour in the complex time plane. The
holographic prescription amounts to ``filling in'' this contour with bulk
solutions: real segments of the contour are filled in with Lorentzian solutions
while imaginary segments are filled in with Riemannian solutions and
appropriate matching conditions are imposed at the corners of the contour. We
illustrate the general discussion by computing the 2-point function of a scalar
operator using this prescription and by showing that this leads to an
unambiguous answer with the correct i epsilon insertions.


  Using several cosmological observations, i.e. the cosmic microwave background
anisotropies (WMAP), the weak gravitational lensing (CFHTLS), the measurements
of baryon acoustic oscillations (SDSS+WiggleZ), the most recent observational
Hubble parameter data, the Union2.1 compilation of type Ia supernovae, and the
HST prior, we impose constraints on the sum of neutrino masses ($\mnu$), the
effective number of neutrino species ($\neff$) and dark energy equation of
state ($w$), individually and collectively. We find that a tight upper limit on
$\mnu$ can be extracted from the full data combination, if $\neff$ and $w$ are
fixed. However this upper bound is severely weakened if $\neff$ and $w$ are
allowed to vary. This result naturally raises questions on the robustness of
previous strict upper bounds on $\mnu$, ever reported in the literature. The
best-fit values from our most generalized constraint read
$\mnu=0.556^{+0.231}_{-0.288}\rm eV$, $\neff=3.839\pm0.452$, and
$w=-1.058\pm0.088$ at 68% confidence level, which shows a firm lower limit on
total neutrino mass, favors an extra light degree of freedom, and supports the
cosmological constant model. The current weak lensing data are already helpful
in constraining cosmological model parameters for fixed $w$. The dataset of
Hubble parameter gains numerous advantages over supernovae when $w=-1$,
particularly its illuminating power in constraining $\neff$. As long as $w$ is
included as a free parameter, it is still the standardizable candles of type Ia
supernovae that play the most dominant role in the parameter constraints.


  The origin of nonclassicality in quantum mechanics (QM) has been investigated
recently by a number of authors with a view to identifying axioms that would
single out quantum mechanics as a special theory within a broader framework
such as convex operational theories. In these studies, the axioms tend to be
logically independent in the sense that no specific ordering of the axioms is
implied. Here, we identify a hierarchy of five nonclassical features that
separate QM from a classical theory: (Q1) Incompatibility and indeterminism;
(Q2) Contextuality; (Q3) Entanglement; (Q4) Nonlocality and (Q5)
Indistinguishability of identical particles. Such a hierarchy isn't obvious
when viewed from within the quantum mechanical framework, but, from the
perspective of generalized probability theories (GPTs), the later axioms can be
regarded as further structure introduced on top of earlier axioms. Relevant toy
GPTs are introduced at each layer when useful to illustrate the action of the
nonclassical features associated with the particular layer.


  We study the effects of the spacial structure of localized losses in
weakly-interacting fermionic quantum wires. We show that multiple dissipative
impurities give rise to resonant effects visible in the transport properties
and the particles' momentum distribution. These resonances can enhance or
suppress the effective particle losses in the wire. Moreover, we investigate
the interplay between interactions and the impurity shape and find that,
differently from the coherent scatterer case, the impurity shape modifies the
scaling of the scattering probabilities close to the Fermi momentum. We show
that, while the fluctuation-induced quantum Zeno effect is robust against the
shape of the impurities, the fluctuation-induced transparency is lifted
continuously. This is reflected in the emergence of a continuous line of fixed
points in the renormalization group flow of the scattering probabilities.


  The particle spectrum of the supersymmetric extension of the standard model
with a gauge singlet is studied. Soft supersymmetry breaking terms are
explicitly chosen to be non-universal according to orbifold string theory. they
depend on modular weights of chiral fields and on an angle $\theta$ specifying
the supersymmetry breaking sector. Imposing radiative weak symmetry breaking
and requiring that standard model Yukawa couplings should be allowed yield
constraints on modular weights and almost specifies the angle $\theta$. We then
perform a numerical anlysis of the low energy spectrum. It turns out that the
spectrum is very constrained, revealing salient features such as light Higgses
and neutralinos. The latter turns out to be essentially gaugino-like.


  In this paper, we develop an interior-point method for solving a class of
convex optimization problems with time-varying objective and constraint
functions. Using log-barrier penalty functions, we propose a continuous-time
dynamical system for tracking the (time-varying) optimal solution with an
asymptotically vanishing error. This dynamical system is composed of two terms:
(i) a correction term consisting of a continuous-time version of Newton's
method, and (ii) a prediction term able to track the drift of the optimal
solution by taking into account the time-varying nature of the objective and
constraint functions. Using appropriately chosen time-varying slack and barrier
parameters, we ensure that the solution to this dynamical system globally
asymptotically converges to the optimal solution at an exponential rate. We
illustrate the applicability of the proposed method in two practical
applications: a sparsity promoting least squares problem and a collision-free
robot navigation problem.


  High-resolution imaging has revealed an unusually high binary fraction
amongst objects spanning the transition between the L dwarf and T dwarf
spectral classes. In an attempt to reproduce and unravel the origins of this
apparent binary excess, I present a series of Monte Carlo mass function and
multiplicity simulations of field brown dwarfs in the vicinity of the Sun.
These simulations are based on the solar metallicity brown dwarf evolutionary
models and incorporate empirical luminosity and absolute magnitude scales,
measured multiplicity statistics and observed spectral templates in the
construction and classification of composite binary spectra. In addition to
providing predictions on the number and surface density distributions of L and
T dwarfs for volume-limited and magnitude-limited samples, these simulations
successfully reproduce the observed binary fraction distribution assuming an
intrinsic (resolved) binary fraction of 11(+6)(-3)% (95% confidence interval),
consistent with prior determinations. However, the true binary fraction may be
as high as 40% if, as suggested by Liu et al., a significant fraction of L/T
transition objects (~66%) are tightly-bound, unresolved multiples. The
simulations presented here demonstrate that the binary excess amongst L/T
transition objects arises primarily from the flattening of the luminosity scale
over these spectral types and is not inherently the result of selection effects
incurred in current magnitude-limited imaging samples. Indeed, the existence of
a binary excess can be seen as further evidence that brown dwarfs traverse the
L/T transition rapidly, possibly driven by a nonequilibrium submergence of
photospheric condensates.


  A new approach to modelling the behaviour of simple fluids is presented.
Starting from the usual expression of the partition function of N molecules, a
Fourier transformation is performed. It is argued that the N(N-1)/2 dynamical
variables kpq in the reciprocal space featuring the link between 2 molecules p
and q can reasonably be considered independent in the thermodynamical limit.
Treated as a set of effective independent particles, their statistical
behaviour is analogous to a Bose-Einstein gas. Expressions of the partition
function, of the radial pair correlation function and of the pressure are
derived, and a special attention is given to the mathematical inter-consistency
of those quantities. The results, which are independent of the exact shape of
the intermolecular potential, are applied to the simple case of hard sphere
fluids. An analytical expression of the radial pair correlation function is
derived as well as of the equation of state. The model predicts a qualitatively
satisfactory behaviour for g(R), and it provides numerically correct values for
the equation of state at low and medium densities, although at higher densities
the contact value of g(R)is underestimated. Quite interestingly it predicts for
the maximum random close packing density the correct value 0.637 .


  Real-time time-dependent density functional theory, in conjunction with the
Ehrenfest molecular dynamics scheme, is becoming a popular methodology to
investigate ultrafast phenomena on the nanoscale. Thanks to recent
developments, it is also possible to explicitly include in the simulations a
time-dependent laser pulse, thereby accessing the transient excitation regime.
However, the complexity entailed in these calculations calls for in-depth
analysis of the accessible and yet approximate (either "dressed" or "bare")
quantities, in order to evaluate their ability to provide us with a realistic
picture of the simulated processes. In this work, we analyze the ultrafast
dynamics of three small molecules (ethylene, benzene, and thiophene) excited by
a resonant laser pulse in the framework of the adiabatic local-density
approximation. The electronic response to the laser perturbation in terms of
induced dipole moment and excited-state population is compared to the results
given by an exactly solvable two-level model. In this way, we can interpret the
charge-carrier dynamics in terms of simple estimators, such as the number of
excited electrons. From the computed transient absorption spectra we unravel
the appearance of nonlinear effects such as excited-state absorption and
vibronic coupling. In this way, we observe that the laser excitation affects
the vibrational spectrum by enhancing the anharmonicities therein while the
coherent vibrational motion contributes to stabilize the electronic excitation
already within a few tens of femtoseconds.


  We have calculated a grid of photospheric phase atmospheres of Type Ia
supernovae (SNe Ia) with metallicities from ten times to one thirtieth the
solar metallicity in the C+O layer of the deflagration model, W7. We have
modeled the spectra using the multi-purpose NLTE model-atmosphere and
spectrum-synthesis code, PHOENIX. We show models for the epochs 7, 10, 15, 20,
and 35 days after explosion. When compared to observed spectra obtained at the
approximately corresponding epochs these synthetic spectra fit reasonably well.
The spectra show variation in the overall level of the UV continuum with lower
fluxes for models with higher metallicity in the unburned C+O layer. This is
consistent with the classical surface cooling and line blocking effect due to
metals in the outer layers of C+O. The UV features also move consistently to
the blue with higher metallicity, demonstrating that they are forming at
shallower and faster layers in the atmosphere. The potentially most useful
effect is the blueward movement of the Si II feature at 6150 Angstrom with
increasing C+O layer metallicity. We also demonstrate the more complex effects
of metallicity variations by modifying the 54Fe content of the incomplete
burning zone in W7 at maximum light. We briefly address some shortcomings of
the W7 Finally, we identify that the split in the Ca H+K feature produced in W7
and observed in some SNe Ia is due to a blending effect of Ca II and Si II and
does not necessarily represent a complex abundance or ionization effect in Ca
II. amodel when compared to observations.


  Constitutive models for concrete based on the microplane concept have
repeatedly proven their ability to well-reproduce its non-linear response on
material as well as structural scales. The major obstacle to a routine
application of this class of models is, however, the calibration of
microplane-related constants from macroscopic data. The goal of this paper is
two-fold: (i) to introduce the basic ingredients of a robust inverse procedure
for the determination of dominant parameters of the M4 model proposed by Bazant
and co-workers based on cascade Artificial Neural Networks trained by
Evolutionary Algorithm and (ii) to validate the proposed methodology against a
representative set of experimental data. The obtained results demonstrate that
the soft computing-based method is capable of delivering the searched response
with an accuracy comparable to the values obtained by expert users.


  A method of obtaining the critical temperature from within a supercritical
mesophase bounded by percolation transition loci is described. We report
thermodynamic pressures from MD simulations for more than 2000 state points
along 7 near-critical isotherms of a Lennard-Jones fluid. Direct evaluation of
Gibbs chemical potential along the critical isotherm reaffirms the existence of
a supercritical mesophaseand a line of critical states and non-existence of van
der Waals critical point.


  The concept of lasers based on the frozen mode regime in active periodic
optical waveguides with a 3rd-order exceptional point of degeneracy (EPD) is
advanced. The frozen mode regime in a lossless and gainless waveguide is
associated with a stationary inflection point (SIP) in the Bloch dispersion
relation, where three Bloch eigenmodes coalesce forming the frozen mode. As a
practical example, we consider an asymmetric serpentine optical waveguide
(ASOW). An ASOW operating near the SIP frequency displays a large group delay
of a non-resonant nature that scales as the cube of the waveguide length,
leading to a strong gain enhancement when active material is included.
Therefore, a laser operating in the close vicinity of an SIP has a gain
threshold that scales as a negative cube of the waveguide length. We determine
that this scaling law is maintained in the presence of small distributed
losses, such as radiation associated with waveguide bends and roughness. In
addition, we show that although gain causes a distortion in the modes
coalescing at the SIP, the properties of the frozen mode are relatively
resistant to such small perturbations and we still observe a large degree of
exceptional degeneracy for gain values that bring the system above threshold.
Finally, our study also reveals that lasing near an SIP is favored over lasing
near a photonic band edge located in close proximity to the SIP. In particular,
we observe that an SIP-induced lasing in an ASOW displays lower gain threshold
compared to lasing near the photonic regular band edge (RBE), even though the
SIP resonance has a lower quality factor than the RBE resonance.


  Adopting the setting for the study of existence and scale locality of the
energy cascade in 3D viscous flows in physical space recently introduced by the
authors to 3D inviscid flows, it is shown that the anomalous dissipation is --
in the case of decaying turbulence -- indeed capable of triggering the cascade
which then continues ad infinitum, confirming Onsager's predictions.


  Raman spectroscopy is an integral part of graphene research. It is used to
determine the number and orientation of layers, the quality and types of edge,
and the effects of perturbations, such as electric and magnetic fields, strain,
doping, disorder and functional groups. This, in turn, provides insight into
all $sp^2$-bonded carbon allotropes, because graphene is their fundamental
building block. Here we review the state of the art, future directions and open
questions in Raman spectroscopy of graphene. We describe essential physical
processes whose importance has only recently been recognized, such as the
various types of resonance at play, and the role of quantum interference. We
update all basic concepts and notations, and propose a terminology that is able
to describe any result in literature. We finally highlight the potential of
Raman spectroscopy for layered materials other than graphene.


  The cosmological evolution of the string landscape is expected to consist of
multiple stages of old inflation with large cosmological constant ending by
tunnelling. Old inflation has a well known graceful exit problem as the
observable universe becomes empty, devoid of any entropy. Simultaneously, in
the quest for reheating the right degrees of freedom, it is important that the
final stage of inflation reheat Standard Model sector. It is known that
inflation can occur naturally along a flat direction of the Minimal
Supersymmetric Standard Model (MSSM), solving the reheating problem, but the
initial conditions require a large degree of fine-tuning. In this paper, we
study how inflation of a MSSM flat direction can be embedded into the string
theory landscape to solve both the graceful exit problem of old inflation and
the fine-tuning problem of MSSM inflation, elaborating on ideas of Bousso and
Polchinski. The fluctuations of the MSSM flat direction during old inflation
create regions with initial conditions favorable for eternal inflation, which
also allows the cosmological constant to continue to relax. This final phase of
inflation also provides all the usual benefits of MSSM inflation, including
straightforward reheating into Standard Model degrees of freedom.


  Location sharing applications are becoming increasingly common. These
applications allow users to share their own locations and view contacts'
current locations on a map. Location applications are commonly used by friends
and family members to view Global Positioning System (GPS) location of an
individual, but valuable forensic evidence may exist in this data when stored
locally on smartphones. This paper aims to discover forensic artifacts from two
popular third-party location sharing applications on iOS and Android devices.
Industry standard mobile forensic suites are utilized to discover if any
locally stored data could be used to assist investigations reliant on knowing
the past location of a suspect. Security issues raised regarding the artifacts
found during our analysis is also discussed.


  After defining cohomologically higher order BRST and anti-BRST operators for
a compact simple algebra {\cal G}, the associated higher order Laplacians are
introduced and the corresponding supersymmetry algebra $\Sigma$ is analysed.
These operators act on the states generated by a set of fermionic ghost fields
transforming under the adjoint representation. In contrast with the standard
case, for which the Laplacian is given by the quadratic Casimir, the higher
order Laplacians $W$ are not in general given completely in terms of the
Casimir-Racah operators, and may involve the ghost number operator. The higher
order version of the Hodge decomposition is exhibited. The example of su(3) is
worked out in detail, including the expression of its higher order Laplacian W.


  Training Large Language Models (LLMs) is memory-intensive due to the large
number of parameters and associated optimization states. GaLore, a recent
method, reduces memory usage by projecting weight gradients into a low-rank
subspace without compromising performance. However, GaLore relies on
time-consuming Singular Value Decomposition (SVD) operations to identify the
subspace, and the frequent subspace updates lead to significant training time
overhead. Moreover, GaLore offers minimal improvements in accuracy and
efficiency compared to LoRA in more accessible fine-tuning scenarios. To
address these limitations, we introduce Q-Galore, a novel approach that
substantially reduces memory usage by combining quantization and low-rank
projection, surpassing the benefits of GaLore. Our method is based on two key
observations: (i) the gradient subspace exhibits diverse properties, with some
layers converging early in training while others are subject to frequent
changes; (ii) the projection matrices are highly resilient to low-bit
quantization. Leveraging these insights, Q-GaLore adaptively updates the
gradient subspace based on its convergence statistics, achieving comparable
performance while significantly reducing the number of SVD operations. We
maintain the projection matrices in INT4 format and weights in INT8 format,
incorporating stochastic rounding to capture accumulated gradient information.
This approach enables a high-precision training trajectory using only
low-precision weights. We demonstrate that Q-GaLore achieves highly competitive
performance with exceptional memory efficiency. At pre-training, Q-GaLore
facilitates training a LLaMA-7B model from scratch on a single NVIDIA RTX 4060
Ti with only 16 GB memory. At fine-tuning, it reduces memory consumption by up
to 50% compared to LoRA and GaLore, while consistently outperforming QLoRA at
the same memory cost.


  Optimal selection of a subset of items from a given set is a hard problem
that requires combinatorial optimization. In this paper, we propose a subset
selection algorithm that is trainable with gradient-based methods yet achieves
near-optimal performance via submodular optimization. We focus on the task of
identifying a relevant set of sentences for claim verification in the context
of the FEVER task. Conventional methods for this task look at sentences on
their individual merit and thus do not optimize the informativeness of
sentences as a set. We show that our proposed method which builds on the idea
of unfolding a greedy algorithm into a computational graph allows both
interpretability and gradient-based training. The proposed differentiable
greedy network (DGN) outperforms discrete optimization algorithms as well as
other baseline methods in terms of precision and recall.


  Quorum based mutual exclusion algorithms enjoy many advantages such as low
message complexity and high failure resiliency. The use of quorums is a well
known approach to achieving mutual exclusion in distributed environments.
Several distributed based quorum mutual exclusion was presented.


  An approximate scaling relation is found for the transition temperature to a
charge-density-wave instability in the anharmonic electron-phonon problem,
which maps a wide range of interaction strengths, anharmonicities, and phonon
frequencies onto a common functional form. The relation employs the
wave-function renormalization parameter and is valid even for systems that are
not Fermi liquids.


  This paper introduces a novel unsupervised learning paradigm inspired by
Gerald Edelman's theory of neuronal group selection ("Neural Darwinism"). The
presented automaton learns to recognize arbitrary symbols (e.g., letters of an
alphabet) when they are presented repeatedly, as they are when children learn
to read. On a second hierarchical level, the model creates abstract categories
representing the learnt symbols. The fundamental computational unit are simple
McCulloch-Pitts neurons arranged into fully-connected groups (Hopfield networks
with randomly initialized weights), which are "selected", in an evolutionary
sense, through symbol presentation. The learning process is fully tractable and
easily interpretable for humans, in contrast to most neural network
architectures. Computational properties of Hopfield networks enabling pattern
recognition are discussed. In simulations, the model achieves high accuracy in
learning the letters of the Latin alphabet, presented as binary patterns on a
grid. This paper is a proof of concept with no claims to state-of-the-art
performance in letter recognition, but hopefully inspires new thinking in
bio-inspired machine learning.


  With a large band gap and a single Dirac cone responsible for the topological
surface states, Bi2Se3 is widely regarded as a prototypical 3D topological
insulator. Further applications of the bulk material has, however, been
hindered by inherent structural defects that donate electrons and make the bulk
conductive. Consequently, controlling these defects is of great interest for
future technological applications, and while past literature has focused on
adding external doping elements to the mixture, a complete study on undoped
Bi2Se3 was still lacking. In this work, we use the self-flux method to obtain
high-quality Bi2Se3 single-crystals in the entire concentration range available
on the phase-diagram for the technique. By combining basic structural
characterization with measurements of the resistivity, Hall effect and
Shubnikov-de Haas (SdH) quantum oscillations, the effects of these impurities
on the bulk transport are investigated in samples with electron densities
ranging from 10^17 cm^-3 to 10^19 cm^-3, from Se-rich to Bi-rich mixtures,
respectively, evidencing the transition into a degenerate semiconductor regime.
We find that electron-donor impurities, likely Se vacancies, unavoidably shift
the Fermi level up to 200 meV inside the conduction band. Other impurities,
like interstitial Bi and Se, are shown to play a significant role as scattering
centres, specially at low temperatures and in the decoherence of the SdH
oscillations. Previous open questions on Bi2Se3, such as the upturn in
resistivity below 30 K, the different scattering times in transport and quantum
oscillations, and the presence of additional low mobility bands, are addressed.
The results outlined here provide a concise picture on the bulk conducting
states in flux-grown Bi2Se3 single crystals, enabling better control of the
structural defects and electronic properties.


  Distributed systems address the increasing demand for fast access to
resources and fault tolerance for data. However, due to scalability
requirements, software developers need to trade consistency for performance.
For certain data, consistency guarantees may be weakened if application
correctness is unaffected. In contrast, data flow from data with weak
consistency to data with strong consistency requirements is problematic, since
application correctness may be broken. In this paper, we propose lattice-based
consistency types for replicated data (CTRD), a higher-order static
consistency-typed language with replicated data types. The type system of CTRD
supports shared data among multiple clients, and statically enforces
noninterference between data types with weaker consistency and data types with
stronger consistency. The language can be applied to many distributed
applications and guarantees that updates of weakly-consistent data can never
affect strongly-consistent data. We also extend the basic CTRD with an
optimization that reduces synchronization for generating reference graphs.


  For many transcendental entire functions, the escaping set has the structure
of a Cantor bouquet, consisting of uncountably many disjoint curves. Rippon and
Stallard showed that there are many functions for which the escaping set has a
new connected structure known as an infinite spider's web. We investigate a
connection between these two topological structures for a certain class of sums
of exponentials.


  We develop a novel computational framework to approximate solution operators
of evolution partial differential equations (PDEs). By employing a general
nonlinear reduced-order model, such as a deep neural network, to approximate
the solution of a given PDE, we realize that the evolution of the model
parameter is a control problem in the parameter space. Based on this
observation, we propose to approximate the solution operator of the PDE by
learning the control vector field in the parameter space. From any initial
value, this control field can steer the parameter to generate a trajectory such
that the corresponding reduced-order model solves the PDE. This allows for
substantially reduced computational cost to solve the evolution PDE with
arbitrary initial conditions. We also develop comprehensive error analysis for
the proposed method when solving a large class of semilinear parabolic PDEs.
Numerical experiments on different high-dimensional evolution PDEs with various
initial conditions demonstrate the promising results of the proposed method.


  We study the Hamiltonian formulation of the Ashtekar-Olmedo-Singh model for
the description of the interior geometry of non-rotating, uncharged black
holes. This model incorporates loop quantum effects through the introduction of
two regularization parameters. We consider an extended phase space formalism
proposed by the creators of the model that includes such parameters as
configuration variables, constrained to be functions of the black hole mass. We
generalize this restriction, allowing for an off-shell phase space dependence.
We then introduce a gauge fixing procedure and reduce the system, proving that
the reduced symplectic structure cannot reproduce the standard relativistic one
in terms of the densitized triad and the Ashtekar-Barbero connection. Actually,
the reduced structure precisely compensates the modifications that arise in the
Hamilton equations when the regularization parameters are treated as phase
space functions, rather than as numbers, attaining a consistent Hamiltonian
derivation of the dynamics. We then choose the extended phase space formalism
as starting point to address the loop quantization of the model. Taking the
definition of certain geometric operators as the only basic ingredient and
adopting prescriptions that have proven successful in loop quantum cosmology,
we construct a polymer representation of all the constraints and deduce the
formal expression of the physical states, assuming reasonable spectral
properties for the constraint operators. The physical states turn out to be
characterized by a wave function of the black hole mass with support on a very
specific set. We finally discuss conditions that guarantee the existence of
physical states in the region of large black hole masses. This is a first step
in the development of a new loop quantum theory of black holes.


  We present two end-to-end models: Audio-to-Byte (A2B) and Byte-to-Audio
(B2A), for multilingual speech recognition and synthesis. Prior work has
predominantly used characters, sub-words or words as the unit of choice to
model text. These units are difficult to scale to languages with large
vocabularies, particularly in the case of multilingual processing. In this
work, we model text via a sequence of Unicode bytes, specifically, the UTF-8
variable length byte sequence for each character. Bytes allow us to avoid large
softmaxes in languages with large vocabularies, and share representations in
multilingual models. We show that bytes are superior to grapheme characters
over a wide variety of languages in monolingual end-to-end speech recognition.
Additionally, our multilingual byte model outperform each respective single
language baseline on average by 4.4% relatively. In Japanese-English
code-switching speech, our multilingual byte model outperform our monolingual
baseline by 38.6% relatively. Finally, we present an end-to-end multilingual
speech synthesis model using byte representations which matches the performance
of our monolingual baselines.


  The translocation of double-stranded DNA through a solid-state nanopore may
either decrease or increase the ionic current depending on the ionic
concentration of the surrounding solution. Below a certain crossover ionic
concentration, the current change inverts from a current blockade to current
enhancement. In this paper, we show that the crossover concentration for
bundled DNA nanostructures composed of multiple connected DNA double-helices is
lower than that of double-stranded DNA. Our measurements suggest that
counterion mobility in the vicinity of DNA is reduced depending on the
three-dimensional structure of the molecule. We further demonstrate that
introducing neutral polymers such as polyethylene glycol into the measurement
solution reduces electroosmotic outflow from the nanopore, allowing
translocation of large DNA structures at low salt concentrations. Our
experiments contribute to an improved understanding of ion transport in
confined DNA environments, which is critical for the development of nanopore
sensing techniques as well as synthetic membrane channels. Our salt-dependent
measurements of model DNA nanostructures will guide the development of
computational models of DNA translocation through nanopores.


  In this talk we report on a recent lattice investigation of the Landau gauge
gluon and ghost propagators in pure SU(3) lattice gauge theory with a special
emphasis on the Gribov copy problem. In the (infrared) region of momenta $q^2
\le 0.3 \mathrm{GeV}^2$ we find the corresponding MOM scheme running coupling
$\alpha_s(q^2)$ to rise in $q$. We also report on a first SU(3) computation of
the ghost-gluon vertex function showing that it deviates only weakly from being
constant. In addition we study the spectrum of low-lying eigenvalues and
eigenfunctions of the Faddeev-Popov operator as well as the spectral
representation of the ghost propagator.


  We introduce a stochastic model for the determination of phase noise in
optoelectronic oscillators. After a short overview of the main results for the
phase diffusion approach in autonomous oscillators, an extension is proposed
for the case of optoelectronic oscillators where the microwave is a limit-cycle
originated from a bifurcation induced by nonlinearity and time-delay. This
Langevin approach based on stochastic calculus is also successfully confronted
with experimental measurements.


  Kolmogorov-Sinai entropy is an invariant of measure-preserving actions of the
group of integers that is central to classification theory. There are two
recently developed invariants, sofic entropy and Rokhlin entropy, that
generalize classical entropy to actions of countable groups. These new theories
have counterintuitive properties such as factor maps that increase entropy.
This survey article focusses on examples, many of which have not appeared
before, that highlight the differences and similarities with classical theory.


  We construct a link in the $3$-space that is not isotopic to any PL link
(non-ambiently). In fact, there exist uncountably many $I$-equivalence classes
of links.
  The paper also includes some observations on Cochran's invariants $\beta_i$.


  Temporal difference (TD) learning is a policy evaluation in reinforcement
learning whose performance can be enhanced by variance reduction methods.
Recently, multiple works have sought to fuse TD learning with Stochastic
Variance Reduced Gradient (SVRG) method to achieve a geometric rate of
convergence. However, the resulting convergence rate is significantly weaker
than what is achieved by SVRG in the setting of convex optimization. In this
work we utilize a recent interpretation of TD-learning as the splitting of the
gradient of an appropriately chosen function, thus simplifying the algorithm
and fusing TD with SVRG. Our main result is a geometric convergence bound with
predetermined learning rate of $1/8$, which is identical to the convergence
bound available for SVRG in the convex setting. Our theoretical findings are
supported by a set of experiments.


  We investigate a class of constrained sparse regression problem with
cardinality penalty, where the feasible set is defined by box constraint, and
the loss function is convex, but not necessarily smooth. First, we put forward
a smoothing fast iterative hard thresholding (SFIHT) algorithm for solving such
optimization problems, which combines smoothing approximations, extrapolation
techniques and iterative hard thresholding methods. The extrapolation
coefficients can be chosen to satisfy $\sup_k \beta_k=1$ in the proposed
algorithm. We discuss the convergence behavior of the algorithm with different
extrapolation coefficients, and give sufficient conditions to ensure that any
accumulation point of the iterates is a local minimizer of the original
cardinality penalized problem. In particular, for a class of fixed
extrapolation coefficients, we discuss several different update rules of the
smoothing parameter and obtain the convergence rate of $O(\ln k/k)$ on the loss
and objective function values. Second, we consider the case in which the loss
function is Lipschitz continuously differentiable, and develop a fast iterative
hard thresholding (FIHT) algorithm to solve it. We prove that the iterates of
FIHT converge to a local minimizer of the problem that satisfies a desirable
lower bound property. Moreover, we show that the convergence rate of loss and
objective function values are $o(k^{-2})$. Finally, some numerical examples are
presented to illustrate the theoretical results.


  Distributed training of $l_1$ regularized classifiers has received great
attention recently. Most existing methods approach this problem by taking steps
obtained from approximating the objective by a quadratic approximation that is
decoupled at the individual variable level. These methods are designed for
multicore and MPI platforms where communication costs are low. They are
inefficient on systems such as Hadoop running on a cluster of commodity
machines where communication costs are substantial. In this paper we design a
distributed algorithm for $l_1$ regularization that is much better suited for
such systems than existing algorithms. A careful cost analysis is used to
support these points and motivate our method. The main idea of our algorithm is
to do block optimization of many variables on the actual objective function
within each computing node; this increases the computational cost per step that
is matched with the communication cost, and decreases the number of outer
iterations, thus yielding a faster overall method. Distributed Gauss-Seidel and
Gauss-Southwell greedy schemes are used for choosing variables to update in
each step. We establish global convergence theory for our algorithm, including
Q-linear rate of convergence. Experiments on two benchmark problems show our
method to be much faster than existing methods.


  We show that Lusztig's homomorphism from an affine Hecke algebra to the
direct summand of its asymptotic Hecke algebra corresponding to the lowest
two-sided cell is related to the homomorphism constructed by Chriss and
Ginzburg using equivariant K-theory by a matrix over the representation ring of
the associated algebraic group.


  Excitons are pairs of electrons and holes bound together by the Coulomb
interaction. At low temperatures, excitons can form a Bose-Einstein condensate
(BEC), enabling macroscopic phase coherence and superfluidity. An electronic
double layer (EDL), in which two parallel conducting layers are separated by an
insulator, is an ideal platform to realize a stable exciton BEC. In an EDL
under strong magnetic fields, electron-like and hole-like quasi-particles from
partially filled Landau levels (LLs) bind into excitons and condense. However,
in semiconducting double quantum wells, this magnetic-field-induced exciton BEC
has been observed only in sub-Kelvin temperatures due to the relatively strong
dielectric screening and large separation of the EDL. Here we report exciton
condensation in bilayer graphene EDL separated by a few atomic layers of
hexagonal boron nitride (hBN). Driving current in one graphene layer generates
a quantized Hall voltage in the other layer, signifying coherent superfluid
exciton transport. Owing to the strong Coulomb coupling across the atomically
thin dielectric, we find that quantum Hall drag in graphene appears at a
temperature an order of magnitude higher than previously observed in GaAs EDL.
The wide-range tunability of densities and displacement fields enables
exploration of a rich phase diagram of BEC across Landau levels with different
filling factors and internal quantum degrees of freedom. The observed robust
exciton superfluidity opens up opportunities to investigate various quantum
phases of the exciton BEC and design novel electronic devices based on
dissipationless transport.


  We consider the frequency response problem and derive a posteriori error
estimates for the discrete error in a reduced finite element model obtained
using the component mode synthesis (CMS) method. We provide estimates in a
linear quantity of interest and the energy norm. The estimates reflect to what
degree each CMS subspace influence the overall error in the reduced solution.
This enables automatic error control through adaptive algorithms that determine
suitable dimensions of each subspace. We illustrate the theoretical results by
including several numerical examples.


  We prove that the maximal number of directed edges in a vertex-critical
strongly connected simple digraph on n vertices is n(n-1)/2 - n +4.


  The dynamics of vortices in type II superconductors exhibit a variety of
patterns whose origin is poorly understood. This is partly due to the
nonlinearity of the vortex mobility which gives rise to singular behavior in
the vortex densities. Such singular behavior complicates the application of
standard linear stability analysis. In this paper, as a first step towards
dealing with these dynamical phenomena, we analyze the dynamical stability of a
front between vortices and antivortices. In particular we focus on the question
of whether an instability of the vortex front can occur in the absence of a
coupling to the temperature. Borrowing ideas developed for singular bacterial
growth fronts, we perform an explicit linear stability analysis which shows
that, for sufficiently large front velocities and in the absence of coupling to
the temperature, such vortex fronts are stable even in the presence of in-plane
anisotropy. This result differs from previous conclusions drawn on the basis of
approximate calculations for stationary fronts. As our method extends to more
complicated models, which could include coupling to the temperature or to other
fields, it provides the basis for a more systematic stability analysis of
nonlinear vortex front dynamics.


  Estimating the Domain of Attraction (DA) of non-polynomial systems is a
challenging problem. Taylor expansion is widely adopted for transforming a
nonlinear analytic function into a polynomial function, but the performance of
Taylor expansion is not always satisfactory. This paper provides solvable ways
for estimating the DA via Chebyshev approximation. Firstly, for Chebyshev
approximation without the remainder, higher order derivatives of Lyapunov
functions are used for estimating the DA, and the largest estimate is obtained
by solving a generalized eigenvalue problem. Moreover, for Chebyshev
approximation with the remainder, an uncertain polynomial system is
reformulated, and a condition is proposed for ensuring the convergence to the
largest estimate with a selected Lyapunov function. Numerical examples
demonstrate that both accuracy and efficiency are improved compared to Taylor
approximation.


  We present infrared (IR) to X-ray spectral energy distributions (SEDs) for 44
red AGN selected from the 2MASS survey on the basis of their red J-K$_S$ color
(>2 mag) and later observed by Chandra. In comparison with optically-, radio-,
and X-ray selected AGN, their median SEDs are red in the optical and near-IR
with little/no blue bump. It thus seems that near-IR color selection isolates
the reddest subset of AGN that can be classified optically. The shape of the
SEDs is generally consistent with modest absorption by gas (in the X-ray) and
dust (in the optical-IR). The levels of obscuration, estimated from X-rays,
far-IR and our detailed optical/near-IR color modeling are all consistent
implying N_H < few*10^{22} cm^{-2}. We present SED models that show how the AGN
optical/near-IR colors change due to differing amounts of reddening, AGN to
host galaxy ratio, redshift and scattered light emission and apply them to the
sources in the sample. We find that the 2MASS AGN optical color, B-R, and to a
lesser extent the near-IR color, J-K$_S$, are strongly affected by reddening,
host galaxy emission, redshift, and in few, highly polarized objects, also by
scattered AGN light. The obscuration/inclination of the AGN allows us to see
weaker emission components which are generally swamped by the AGN.


  We report on pulse profile decomposition analysis of a bright transient X-ray
pulsar 1A 0535+262 using the broadband Insight-HXMT observations during a giant
outburst of the source in 2020. We show that the observed pulse profile shape
can be described in terms of a combination of two symmetric single-pole
contributions for wide range of energies and luminosities for a fixed geometry
defining basic geometry of the pulsar. This corresponds to a slightly distorted
dipole magnetic field, i.e., one pole has to be offset by $\sim 12^{\circ}$
from the antipodal position of the other pole. We reconstruct the intrinsic
beam patterns of the pulsar assuming the geometry recovered from the
decomposition analysis, and find evidence for a transition between "pencil" and
"fan" beams in energy ranges above the cyclotron line energy which can be
interpreted as transition from sub- to super-critical accretion regimes
associated with onset of an accretion column. At lower energies the beam
pattern appears, however, to be more complex, and contains substantial "fan"
beam and an additional "pencil" beam component at all luminosities. The latter
is not related to the accretion rate and is stronger in the fading phase of the
outburst. We finally discuss results in context of other observational and
theoretical findings earlier reported for the source in the literature.


  Feature selection is a crucial preprocessing step in data analytics and
machine learning. Classical feature selection algorithms select features based
on the correlations between predictive features and the class variable and do
not attempt to capture causal relationships between them. It has been shown
that the knowledge about the causal relationships between features and the
class variable has potential benefits for building interpretable and robust
prediction models, since causal relationships imply the underlying mechanism of
a system. Consequently, causality-based feature selection has gradually
attracted greater attentions and many algorithms have been proposed. In this
paper, we present a comprehensive review of recent advances in causality-based
feature selection. To facilitate the development of new algorithms in the
research area and make it easy for the comparisons between new methods and
existing ones, we develop the first open-source package, called CausalFS, which
consists of most of the representative causality-based feature selection
algorithms (available at https://github.com/kuiy/CausalFS). Using CausalFS, we
conduct extensive experiments to compare the representative algorithms with
both synthetic and real-world data sets. Finally, we discuss some challenging
problems to be tackled in future causality-based feature selection research.


  The self-duality of Dirichlet $3$-brane action under the $SL(2,R)$ duality
transformation of type IIB superstring theory is shown in the Hamiltonian form
of the path integral for the partition function by performing the direct
integration with respect to the boundary gauge field. Through the integration
in the phase space the canonical momentum conjugate to the boundary gauge field
can be effectively replaced by the dual gauge field.


  The 19th century Aether died with Special Relativity but was resurrected by
General Relativity in the form of dark energy; a tensile material with tension
equal to its energy density. Such a material is provided by the D-branes of
string-theory; these can support the fields of supersymmetric particle-physics,
although their energy density is cancelled by orientifold singularities upon
compactification. Dark energy can still arise from supersymmetry-breaking
anti-D-branes but it is probably time-dependent. Recent results on
time-dependent compactifications to an FLRW universe with late-time accelerated
expansion are reviewed.


  We have studied $\Delta(54)\times Z_2$ flavor model for leptons and sleptons.
The tri-bimaximal mixing can be reproduced for arbitrary neutrino masses if
vacuum alignments of scalar fields are guaranteed. The deviation from the
tri-bimaximal mixing of leptons is predicted. The predicted upper bound for
$\sin\theta_{13}$ is 0.06. The magnitude of $\sin\theta_{23}$ could be deviated
from the maximal mixing considerably, but $\sin\theta_{12}$ is hardly deviated
from the tri-maximal mixing. We have also studied SUSY breaking terms in the
slepton sector. Three families of left-handed and right-handed slepton masses
are degenerate. Even although flavor symmetry breaking effects are taken into
account, our model leads to smaller values of flavor changing neutral currents
than the present experimental bounds.


  We consider a dynamics of Higgs' field in the framework of cosmological
models involving the scalar field from Nonsymmetric Kaluza-Klein (Jordan-Thiry)
Theory. The field plays here a role of a quintessence field. We consider phase
transition in cosmological models of the second and of the first order due to
evolution of Higgs' field. We developed inflationary models including
calculation of an amount of inflation. We match some cosmological models,
calculating a Hubble parameter and an age of the Universe.


  We describe the state of analysis of the MIPP experiment, its plans to
upgrade the experiment and the impact such an upgraded experiment will have on
hypernuclear physics.


  The Cheeger inequalities give an upper and lower bound on the spectral gap of
discrete Laplacians defined on a graph in terms of the geometric
characteristics of the graph. We generalise this approach and we employ it to
determine if a given discrete Hamiltonian with non-positive elements is gapped
or not in the thermodynamic limit. First, we define the graph that corresponds
to such a generic Hamiltonian. Then we present a suitable generalisation of the
Cheeger inequalities that overcomes scaling deficiencies of the original
version. By employing simple examples we illustrate how the generalised Cheeger
inequalities can successfully identify gapped or gapless phases and we comment
on the computational complexity of this approach.


  Thorough characterization of the thermo-mechanical properties of materials
requires difficult and time-consuming experiments. This severely limits the
availability of data and it is one of the main obstacles for the development of
effective accelerated materials design strategies. The rapid screening of new
potential systems requires highly integrated, sophisticated and robust
computational approaches. We tackled the challenge by surveying more than 3,000
crystalline solids within the AFLOW framework with the newly developed
"Automatic Elasticity Library" combined with the previously implemented GIBBS
method. The first extracts the mechanical properties from automatic
self-consistent stress-strain calculations, while the latter employs those
mechanical properties to evaluate the thermodynamics within the Debye model.
The new thermo-elastic library is benchmarked against a set of 74
experimentally characterized systems to pinpoint a robust computational
methodology for the evaluation of bulk and shear moduli, Poisson ratios, Debye
temperatures, Gr\"uneisen parameters, and thermal conductivities of a wide
variety of materials. The effect of different choices of equations of state is
examined and the optimum combination of properties for the
Leibfried-Schl\"omann prediction of thermal conductivity is identified, leading
to improved agreement with experimental results than the GIBBS-only approach.


  Thompson sampling is an efficient algorithm for sequential decision making,
which exploits the posterior uncertainty to address the
exploration-exploitation dilemma. There has been significant recent interest in
integrating Bayesian neural networks into Thompson sampling. Most of these
methods rely on global variable uncertainty for exploration. In this paper, we
propose a new probabilistic modeling framework for Thompson sampling, where
local latent variable uncertainty is used to sample the mean reward.
Variational inference is used to approximate the posterior of the local
variable, and semi-implicit structure is further introduced to enhance its
expressiveness. Our experimental results on eight contextual bandit benchmark
datasets show that Thompson sampling guided by local uncertainty achieves
state-of-the-art performance while having low computational complexity.


  Hybrid reconfigurable intelligent surfaces (HRIS) are RIS architectures
having both active and passive elements. The received signal-to-noise ratio
(SNR) in HRIS-assisted communication systems depends on the placement of active
elements. In this paper, we show that received SNR can be improved with a
channel-aware placement of the active elements. We jointly design the transmit
precoder, the RIS coefficients, and the location of active and passive elements
of the HRIS to maximize the SNR. We solve the underlying combinatorial
nonconvex optimization problem using alternating optimization and propose a
low-complexity solver, which is provably nearly optimal. Through numerical
simulations, we demonstrate that the proposed method offers significantly
improved performance compared to communication systems having a fully passive
RIS array or a hybrid RIS array with channel agnostic active element placement
and performance comparable to that of communication systems with a fully active
RIS array.


  We show that one-loop corrections to the large-scale power spectrum from
small-scale modes in non-slow-roll dynamics are always negligible, namely they
are volume suppressed by the ratio of the short to long distance scales.
One-loop contributions proportional to the long wavelength tree-level power
spectrum, and not sharing this suppression, appear only when considering a
subset of vertexes, but they cancel exactly when all relevant interactions are
taken into account. We prove the previous statement in two different ways, i.e.
by using two equivalent forms of the interaction Hamiltonian. Contributions
from boundary terms to equal time correlators are included when necessary.


  We study the gravitational lensing in the weak field approximation assuming
the presence of a plasma and of a magnetic field around a compact gravitational
source. The external magnetic field causes the split of the image, as the
counterpart of the Zeeman effect. The magnetic field affects the magnification
of images, creating additional components. We also study the time delay of an
electromagnetic signal due to the geometry and the gravitational field around
the source. We show that the time delay strongly depends on the plasma
parameters. Lastly, we consider the effects of the presence of an inhomogeneous
plasma on the gravitational lensing.


  Neutron stars provide a natural laboratory to test some unique implications
of Quantum Chromodynamics (QCD)- the underlying theory of strong interactions-
at extreme conditions of very high baryon density. It has been suggested that
the true ground state of QCD is strange quark matter, and, consequently,
neutron stars should convert to strange quark stars under suitable conditions.
Substantial efforts have been, and are being, spent in studying the details of
such conversion. In this letter, we show that the presence of high magnetic
field, an essential feature of neutron stars, strongly inhibits the conversion
of neutron stars to bare quark stars.


  In recent decades, the main focus of computer modeling has been on supporting
the design and development of engineering prototyes, but it is now ubiquitous
in non-traditional areas such as medical rehabilitation. Conventional modeling
approaches like the finite element~(FE) method are computationally costly when
dealing with complex models, making them of limited use for purposes like
real-time simulation or deployment on low-end hardware, if the model at hand
cannot be simplified in a useful manner. Consequently, non-traditional
approaches such as surrogate modeling using data-driven model order reduction
are used to make complex high-fidelity models more widely available anyway.
They often involve a dimensionality reduction step, in which the
high-dimensional system state is transformed onto a low-dimensional subspace or
manifold, and a regression approach to capture the reduced system behavior.
While most publications focus on one dimensionality reduction, such as
principal component analysis~(PCA) (linear) or autoencoder (nonlinear), we
consider and compare PCA, kernel PCA, autoencoders, as well as variational
autoencoders for the approximation of a structural dynamical system. In detail,
we demonstrate the benefits of the surrogate modeling approach on a complex FE
model of a human upper-arm. We consider both the models deformation and the
internal stress as the two main quantities of interest in a FE context. By
doing so we are able to create a computationally low cost surrogate model which
captures the system behavior with high approximation quality and fast
evaluations.


  Let $X$ be a very general degree $d\geq 5$ hypersurface in $\mathbb{P}^3$. We
compute the ample cone of the Hilbert scheme $X^{[n]}$ of $n$ points on $X$ for
various small values of $n$ (the answer is already known for large $n$). We
obtain complete answers in some cases and find lower bounds in certain others.
We also observe that in the case of $X^{[2]}$ for quintic hypersurfaces $X$,
the existence (or absence) of hyperplane sections with points of high
multiplicity also plays a role in the answer to the question at hand, in
contrast with cases known earlier. Finally, in the case that a degree $d\geq3$
smooth hypersurface $X$ contains a line, we compute the nef cone of $X^{[n]}$
in a slice of the N\'eron-Severi space.


  We present an experiment performed to understand the polarization convention
adopted for band 4 (550--900 MHz) of the upgraded Giant Metrewave Radio
Telescope (uGMRT). For that we observed the pulsar B1702--19 in this band, both
in interferometry and pulsar modes, and compare the results with its already
known Stokes $I$, $Q$, $U$, $V$ profiles obtained with the Lovell telescope. We
find that the results obtained from interferometry and pulsar modes of the
uGMRT agree with each other. However, although the Stokes $U$ profile obtained
with the uGMRT match with that obtained by the Lovell telescope, Stokes $Q$ and
$V$ do not. This can be explained if the $X$ and $Y$ dipoles in this band, from
which $R$ and $L$ are derived, are swapped w.r.t. the IAU convention. The
swapping makes $RR^*$ and $LL^*$ of the uGMRT band 4 to be $LL^*$ and $RR^*$
respectively according to the IEEE convention. This implies that if we need to
compare polarization measurements obtained in band 4 of the uGMRT with
telescopes like Lovell, Parkes, Very Large Array etc. (all follow IEEE
convention for defining right and left hand circular polarization), we must
interchange $RR^*$ and $LL^*$, and change the sign of Stokes $Q$ for the uGMRT
data. Note that this is the current convention for uGMRT band 4, and is likely
to change in future once the swapping of the dipoles is taken care of. Once it
is done, it will be notified in another technical report.


  In many hierarchical inverse problems, not only do we want to estimate high-
or infinite-dimensional model parameters in the parameter-to-observable maps,
but we also have to estimate hyperparameters that represent critical
assumptions in the statistical and mathematical modeling processes. As a joint
effect of high-dimensionality, nonlinear dependence, and non-concave structures
in the joint posterior posterior distribution over model parameters and
hyperparameters, solving inverse problems in the hierarchical Bayesian setting
poses a significant computational challenge. In this work, we aim to develop
scalable optimization-based Markov chain Monte Carlo (MCMC) methods for solving
hierarchical Bayesian inverse problems with nonlinear parameter-to-observable
maps and a broader class of hyperparameters. Our algorithmic development is
based on the recently developed scalable randomize-then-optimize (RTO) method
[4] for exploring the high- or infinite-dimensional model parameter space. By
using RTO either as a proposal distribution in a Metropolis-within-Gibbs update
or as a biasing distribution in the pseudo-marginal MCMC [2], we are able to
design efficient sampling tools for hierarchical Bayesian inversion. In
particular, the integration of RTO and the pseudo-marginal MCMC has sampling
performance robust to model parameter dimensions. We also extend our methods to
nonlinear inverse problems with Poisson-distributed measurements. Numerical
examples in PDE-constrained inverse problems and positron emission tomography
(PET) are used to demonstrate the performance of our methods.


  {\bf Abstract.} We show that two hierarchies of spin Hamilton operators admit
the same spectrum. Both Hamilton operators play a central role for quantum
gates in particular for the case spin-$\frac12$ and the case spin-1. The
spin-$\frac12$, spin-1, spin-$\frac32$ and spin-2 cases are studied in detail.
Entanglement and mutually unbiased bases of the eigenvectors is discussed. Two
triple Hamilton operators are also investigated. Both are also admitting the
same spectrum.


  Intersection graphs are well-studied in the area of graph algorithms. Some
intersection graph classes are known to have algorithms enumerating all
unlabeled graphs by reverse search. Since these algorithms output graphs one by
one and the numbers of graphs in these classes are vast, they work only for a
small number of vertices. Binary decision diagrams (BDDs) are compact data
structures for various types of data and useful for solving optimization and
enumeration problems. This study proposes enumeration algorithms for five
intersection graph classes, which admit $\mathrm{O}(n)$-bit string
representations for their member graphs. Our algorithm for each class
enumerates all unlabeled graphs with $n$ vertices over BDDs representing the
binary strings in time polynomial in $n$. Moreover, our algorithms are extended
to enumerate those with constraints on the maximum (bi)clique size and/or the
number of edges.


  Multipolar interactions are derived in the orbitally degenerate Anderson
lattice with a spherical Fermi surface and one conduction electron per unit
cell of the simple cubic lattice. As the crystalline-electric-field (CEF)
ground state of $f^1$ configuration, the four-fold degenerate $\Gamma_8$ is
mainly studied. Intersite interactions up to a sufficiently distant pair are
Fourier transformed to the wavenumber space. For the $\Gamma_8$ case,
quadrupolar and octupolar interactions favor the staggered order with $\mib{q}
= (1/2,1/2,1/2)$, while the dipolar interaction favors an incommensurate
magnetic structure with a long modulation period. The latter is due to a Kohn
anomaly which is found to be sharply peaked for interaction channels with large
angular momenta. Implications of results are discussed for multipole orders in
CeB$_6$, and the incommensurate magnetic structure in a quasi-cubic system
CeB$_2$C$_2$.


  Studying the transformation of cluster galaxies contributes a lot to have a
clear picture of evolution of the universe. Towards that we are studying
different properties (morphology, star formation, AGN contribution and
metallicity) of galaxies in clusters up to $z\sim1.0$ taking three different
clusters: ZwCl0024+1652 at $z\sim0.4$, RXJ1257+4738 at $z\sim0.9$ and Virgo at
$z\sim0.0038$. For ZwCl0024+1652 and RXJ1257+4738 clusters we used tunable
filters data from GLACE survey taken with GTC 10.4 m telescope and other public
data, while for Virgo we used public data. We did the morphological
classification of 180 galaxies in ZwCl0024+1652 using galSVM, where 54\% and
46\% of galaxies were classified as early-type (ET) and late-type (LT)
respectively. We did a comparison between the three clusters within the
clustercentric distance of 1Mpc and found that ET proportion (decreasing with
redshift) dominates over the LT (increasing with redshift) throughout. We
finalized the data reduction for ZwCl0024+1652 cluster and identified 46 [OIII]
and 73 H$\beta$ emission lines. For this cluster we have classified 22 emission
line galaxies (ELGs) using BPT-NII diagnostic diagram resulting with 14
composite, 1 AGN and 7 star forming (SF) galaxies. We are using these results,
together with the public data, for further analysis of the variations of
properties in relation to redshift within $z<1.0$.


  We consider the $n$-dimensional Chaplygin sphere under the assumption that
the mass distribution of the sphere is axisymmetric. We prove that for initial
conditions whose angular momentum about the contact point is vertical, the
dynamics is quasi-periodic. For $n=4$ we perform the reduction by the
associated $SO(3)$ symmetry and show that the reduced system is integrable by
the Euler-Jacobi theorem.


  Hydrogen decrepitation process has been applied for the first time for the
direct recycling of SmCo5 magnets. Industrially produced sintered SmCo5 magnets
were decrepitated by hydrogen gas at a pressure of 1 bar to 9.5 bar at room
temperature in a planetary rotating jar. After decrepitation, the starting
sintered magnets were reduced to a powder with a particle size of less than 200
microns. The produced powder was used for the preparation of recycled SmCo5
magnets. Scanning electron microscopy, energy-dispersive X-ray spectroscopy,
X-ray diffraction studies and magnetic measurements were used to follow the
decrepitation and the sintering processes. The measured remanence and maximum
energy product of the recycled magnet are 0.94 T and 171.1 kJ/m3, respectively,
in comparison with 0.91 T and 156.8 kJ/m3, respectively for the original magnet
before recycling. It was also observed that, there is refinement in the
microstructure after recycling in comparison to the original magnet.


  We study some jumping SDE and the corresponding Fokker-Planck (or Kolmogorov
forward) equation, which is a non-local PDE. We assume only some measurability
and growth conditions on the coefficients. We prove that for any weak solution
$(f_t)_{t\in [0,T]}$ of the PDE, there exists a weak solution to the SDE of
which the time marginals are given by $(f_t)_{t\in[0,T]}$. As a corollary, we
deduce that for any given initial condition, existence for the PDE is
equivalent to weak existence for the SDE and uniqueness in law for the SDE
implies uniqueness for the PDE. This extends some ideas of Figalli [5]
concerning continuous SDEs and local PDEs.


  The increasing size of large language models (LLMs) traditionally requires
low-precision integer formats to meet strict latency and power demands. Yet
recently, alternative formats such as Normal Float (NF4) have increased model
accuracy at the cost of increased chip area. In this work, we first conduct a
large-scale analysis of LLM weights and activations across 30 networks and
conclude that most distributions follow a Student's t-distribution. We then
derive a new theoretically optimal format, Student Float (SF4), that improves
over NF4 across modern LLMs, for example increasing the average accuracy on
LLaMA2-7B by 0.76% across tasks. Using this format as a high-accuracy
reference, we then propose augmenting E2M1 with two variants of supernormal
support for higher model accuracy. Finally, we explore the quality and
efficiency frontier across 11 datatypes by evaluating their model accuracy and
hardware complexity. We discover a Pareto curve composed of INT4, E2M1, and
E2M1 with supernormal support, which offers a continuous tradeoff between model
accuracy and chip area. For example, E2M1 with supernormal support increases
the accuracy of Phi-2 by up to 2.19% with 1.22% area overhead, enabling more
LLM-based applications to be run at four bits. The supporting code is hosted at
https://github.com/cornell-zhang/llm-datatypes.


  Thanks to its unique capabilities the ALICE experiment can measure the
production of identified particles and resonances over a wide momentum range
both in pp and Pb-Pb collisions at the LHC. In this report,
particle-identification detectors and techniques, as well as achieved
performance, are shortly reviewed. The current results on hadron transverse
momentum spectra measured in pp collisions at $\sqrt{s}$ = 0.9 TeV and 7 TeV,
and in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV are shown. In
particular, proton-proton results on particle production yields, spectral
shapes and particle ratios are presented as a function of the collision energy
and compared to previous experiments and commonly-used Monte Carlo models.
Particle spectra, yields and ratios in Pb-Pb are measured as a function of the
collision centrality and the results are compared with published RHIC data in
Au-Au collisions at $\sqrt{s_{\rm NN}}$ = 0.2 TeV and predictions for the LHC.


  A dominating induced matching, also called an efficient edge domination, of a
graph $G=(V,E)$ with $n=|V|$ vertices and $m=|E|$ edges is a subset $F
\subseteq E$ of edges in the graph such that no two edges in $F$ share a common
endpoint and each edge in $E\setminus F$ is incident with exactly one edge in
$F$. It is NP-hard to decide whether a graph admits a dominating induced
matching or not. In this paper, we design a $1.1467^nn^{O(1)}$-time exact
algorithm for this problem, improving all previous results. This problem can be
redefined as a partition problem that is to partition the vertex set of a graph
into two parts $I$ and $F$, where $I$ induces an independent set (a 0-regular
graph) and $F$ induces a perfect matching (a 1-regular graph). After giving
several structural properties of the problem, we show that the problem always
contains some "good vertices", branching on which by including them to either
$I$ or $F$ we can effectively reduce the graph. This leads to a fast exact
algorithm to this problem.


  We construct a reflexive Banach space $X$ with a subspace isometric to $X$,
which is not complemented in $X$.


  If the twist $Poincar\acute{e}$ transformation is imposed on the
noncommutative spacetime, then $Lorentz$ invariance cannot be applied on QFT.
To data, noncommutative theory is one of the best candidates to modify
$Lorentz$ transformation. In this paper, we argue parity violation under the
process of $e^{+}e^{-}\to\gamma \gamma$ and make a detailed analysis of the
difference behavior of each helicity state on noncommutative spacetime. The
effect arises from the production of spin and magnetic fields. We check the
energy momentum conservation for all used couplings and discover that if the
electric field changes particle energy spectrum, there is no symmetry violation
as the field produces a longitudinal state on the finial triple boson
couplings.


  We consider the prediction problem of a continuous-time stochastic process on
an entire time-interval in terms of its recent past. The approach we adopt is
based on functional kernel nonparametric regression estimation techniques where
observations are segments of the observed process considered as curves. These
curves are assumed to lie within a space of possibly inhomogeneous functions,
and the discretized times series dataset consists of a relatively small,
compared to the number of segments, number of measurements made at regular
times. We thus consider only the case where an asymptotically non-increasing
number of measurements is available for each portion of the times series. We
estimate conditional expectations using appropriate wavelet decompositions of
the segmented sample paths. A notion of similarity, based on wavelet
decompositions, is used in order to calibrate the prediction. Asymptotic
properties when the number of segments grows to infinity are investigated under
mild conditions, and a nonparametric resampling procedure is used to generate,
in a flexible way, valid asymptotic pointwise confidence intervals for the
predicted trajectories. We illustrate the usefulness of the proposed functional
wavelet-kernel methodology in finite sample situations by means of three
real-life datasets that were collected from different arenas.


  We present an analysis of new and archival data to the 20.506-minute LISA
verification binary J052610.42$+$593445.32 (J0526$+$5934). Our joint
spectroscopic and photometric analysis finds that the binary contains an unseen
$M_1=0.89\pm0.11~{\rm M_\odot}$ CO-core white dwarf primary with an
$M_2=0.38\pm0.07~{\rm M_\odot}$ post-core-burning subdwarf, or low-mass white
dwarf, companion. Given the short orbital period and relatively large total
binary mass, we find that LISA will detect this binary with signal-to-noise
ratio $44$ after 4 years of observations. J0526$+$5934 is expected to merge
within $1.8\pm0.3~{\rm Myr}$ and likely result in a ${\rm D}^6$ scenario Type
Ia supernova or form a He-rich star which will evolve into a massive single
white dwarf.


  This article discusses the positive impact metro cell antennas with narrow
vertical beamwidth and electrical downtilt can have on heterogeneous cellular
networks. Using a model of random cell placement based on Poisson distribution,
along with an innovative 3D building model that quantifies blockage due to
shadowing, it is demonstrated that network spectral efficiency and average user
throughput both increase as vertical beamwidth is decreased and downtilt is
applied to metro cell transmission. Moreover, the network becomes more energy
efficient. Importantly, these additional gains in network performance can be
achieved without any cooperation or exchange of information between macro cell
base stations and metro cells.


  We measure the fractal dimension of loop-erased random walk (LERW) in 3
dimensions, and estimate that it is 1.62400 +- 0.00005. LERW is closely related
to the uniform spanning tree and the abelian sandpile model. We simulated LERW
on both the cubic and face-centered cubic lattices; the corrections to scaling
are slightly smaller for the face-centered cubic lattice.