  Driving quantum phase transitions in the 3D topological insulators offers
pathways to tuning the topological states and their properties. We use
DFT-based calculations to systematically investigate topological phase
transitions in Bi$_2$Se$_3$, Sb$_2$Se$_3$, Bi$_2$Te$_3$ and Sb$_2$Te$_3$ by
varying the $c/a$ ratio of lattice constants. This ensures no net hydrostatic
pressure under anisotropic stress and strain and allows a clear identification
of the physics leading to the transition. As a function of $c/a$, all of these
materials exhibit structural and electronic stability of the quintuple layers
(QLs), and quasi-linear behavior of both the inter-quintuple layer distance and
the energy gap near the topological transition. Our results show that the
transition is predominantly controlled by the inter-QL physics, namely by
competing Coulomb and van der Waals interactions between the outer atomic
sheets in neighboring quintuple layers. We discuss the implications of our
results for topological tuning by alloying.


  The Gravitational wave high-energy Electromagnetic Counterpart All-sky
Monitor (GECAM) , composed of two small satellites, is a new mission to monitor
the Gamma-Ray Bursts (GRBs) coincident with Gravitational Wave (GW) events with
a FOV of 100% all-sky.Each GECAM satellite detects and localizes GRBs using 25
compact and novel Gamma-Ray Detectors (GRDs) in 6 keV-5 MeV. Each GRD module is
comprised of LaBr3:Ce scintillator, SiPM array and preamplifier. A large
dynamic range of GRD is achieved by the high gain and low gain channels of the
preamplifier. The energy response of GRD prototype was evaluated using
radioactive sources in the range of 5.9-1332.5 keV. A energy resolution of 5.3%
at 662 keV was determined from the 137Cs pulse height spectra, which meets the
GECAM requirement (< 8% at 662 keV). Energy to channel conversion was evaluated
and a nonlinearity correction was performed to reduce the residuals (< 1.5%).
Also, a Geant4-based simulated in-flight background and a measured GRD LaBr3:Ce
intrinsic activity were used to evaluate the capability of in-flight
calibration. These results demonstrate the design of GRD.


  We generalized the construction of deformations of affine toric varieties of
K. Altmann and our previous construction of deformations of weak Fano toric
varieties to the case of arbitrary toric varieties by introducing the notion of
Minkowski sum decompositions of polyhedral complexes. Our construction embeds
the original toric variety into a higher dimensional toric variety where the
image is given by a prime binomial complete intersection ideal in Cox
homogeneous coordinates. The deformations are realized by families of complete
intersections. For compact simplicial toric varieties with at worst Gorenstein
terminal singularities, we show that our deformations span the infinitesimal
space of deformations by Kodaira-Spencer map. For Fano toric varieties, we show
that their deformations can be constructed in higher-dimensional Fano toric
varieties related to the Batyrev-Borisov mirror symmetry construction.


  In this paper we study mixed sums of primes and linear recurrences. We show
that if m=2(mod 4) and m+1 is a prime then $(m^{2^n-1}-1)/(m-1)\not=m^n+p^a$
for any n=3,4,... and prime power p^a. We also prove that if a>1 is an integer,
u_0=0, u_1=1 and u_{i+1}=au_i+u_{i-1} for i=1,2,3,..., then all the sums
u_m+au_n (m,n=1,2,3,...) are distinct. One of our conjectures states that any
integer n>4 can be written as the sum of an odd prime, an odd Fibonacci number
and a positive Fibonacci number.


  In this paper two identities involving a function defined by the complete
elliptic integrals of the first and second kinds are proved. Some functional
inequalities and elementary estimates for this function are also derived from
the properties of monotonicity and convexity of this function. As applications,
some functional inequalities and the growth of the exterior modulus of a
rectangle are studied.


  Topological semimetals, including Dirac semimetals, Weyl semimetals, and
nodal line semimetals, receive enormous research interest due to their
intrinsic topological nature and fascinating properties. In present work, with
the help of density functional theory (DFT), we find that nodal line semimetals
and Dirac semimetals can coexist in the low energy electron of two dimensional
(2D) monolayer B2C. Intriguingly, besides type-I and type-II Dirac fermions, a
kind of open nodal line appears around the Fermi level. The low energy
electronic nature of B2C sheet can be described by a tight-binding (TB) model
relied on the basis of B-py, pz and C-py, pz states. One of the most merit of
the system is that the energy windows of these four types topological
semimetals are different that can be easily distinguished in experiments.
Moreover, the system provides an excellent platform for studying the interplay
between different type semimetals.


  Strassen (Strassen, J. Reine Angew. Math., 375/376, 1987) introduced the
subrank of a tensor as a natural extension of matrix rank to tensors. Subrank
measures the largest diagonal tensor that can be obtained by applying linear
operations to the different indices (legs) of the tensor (just like the matrix
rank measures the largest diagonal matrix that can be obtained using row and
column operations). Motivated by problems in combinatorics and complexity
theory we introduce the new notion of symmetric subrank of tensors by
restricting these linear operations to be the same for each index.
  We prove precise relations and separations between subrank and symmetric
subrank. We prove that for symmetric tensors the subrank and the symmetric
subrank are asymptotically equal. This proves the asymptotic subrank analogon
of a conjecture known as Comon's conjecture in the theory of tensors. This
result allows us to prove a strong connection between the general and symmetric
version of an asymptotic duality theorem of Strassen. We introduce a
representation-theoretic method to asymptotically bound the symmetric subrank
called the symmetric quantum functional in analogy with the quantum functionals
(Christandl, Vrana, Zuiddam, J. Amer. Math. Soc., 2021), and we study the
relations between these functionals.


  In this paper we prove a duality for constructible sheaves on conically
smooth stratified spaces. Here we consider sheaves with values in a stable and
bicomplete $\infty$-category equipped with a closed symmetric monoidal
structure, and in this setting constructible means locally constant along
strata and with dualizable stalks. The crucial point where we need to employ
the geometry of conically smooth structures is in showing that Lurie's version
of Verdier duality restricts to an equivalence between constructible sheaves
and cosheaves: this requires a computation of the exit path $\infty$-category
of a compact stratified space, that we obtain via resolution of singularities.


  The Galactic center (GC) is the densest region of the Milky Way. Variability
surveys towards the GC potentially provide the largest number of variable stars
per square degree within the Galaxy. However, high stellar density is also a
drawback due to blending. Moreover, the GC is affected by extreme reddening,
therefore near infrared observations are needed. We plan to detect new variable
stars towards the GC, focusing on type II Cepheids (T2Cs) which have the
advantage of being brighter than RR Lyrae stars. We perform parallel
Lomb-Scargle and Generalized Lomb-Scargle periodogram analysis of the
$K_s$-band time series of the VISTA variables in the Via Lactea survey, to
detect periodicities. We employ statistical parameters to clean our sample. We
take account of periods, light amplitudes, distances, and proper motions to
provide a classification of the candidate variables. We detected 1,019 periodic
variable stars, of which 164 are T2Cs, 210 are Miras and 3 are classical
Cepheids. We also found the first anomalous Cepheid in this region. We compare
their photometric properties with overlapping catalogs and discuss their
properties on the color-magnitude and Bailey diagrams. We present the most
extensive catalog of T2Cs in the GC region to date. Offsets in E($J-K_s$) and
in the reddening law cause very large ($\sim$1-2 kpc) uncertainties on
distances in this region. We provide a catalog which will be the starting point
for future spectroscopic surveys in the innermost regions of the Galaxy.


  Silicon T centers present the promising possibility to generate optically
active spin qubits in an all-silicon device. However, these color centers
exhibit long excited state lifetimes and a low Debye-Waller factor, making them
dim emitters with low efficiency into the zero-phonon line. Nanophotonic
cavities can solve this problem by enhancing radiative emission into the
zero-phonon line through the Purcell effect. In this work we demonstrate
cavity-enhanced emission from a single T center in a nanophotonic cavity. We
achieve a two-orders of magnitude increase in brightness of the zero-phonon
line relative to waveguide-coupled emitters, a 23% collection efficiency from
emitter to fiber, and an overall emission efficiency into the zero-phonon line
of 63.4%. We also observe a lifetime enhancement of 5, corresponding to a
Purcell factor exceeding 18 when correcting for the emission to the phonon
sideband. These results pave the way towards efficient spin-photon interfaces
in silicon photonics.


  The paper is devoted to the development of a methodology for evaluating the
scalability of compute-intensive iterative algorithms used in simulating
complex physical processes on supercomputer systems. The proposed methodology
is based on the BSF (Bulk Synchronous Farm) parallel computation model, which
makes it possible to predict the upper scalability bound of an iterative
algorithm in early phases of its design. The BSF model assumes the
representation of the algorithm in the form of operations on lists using
high-order functions. Two classes of representations are considered: BSF-M (Map
BSF) and BSF-MR (Map-Reduce BSF). The proposed methodology is described by the
example of the solution of the system of linear equations by the Jacobi method.
For the Jacobi method, two iterative algorithms are constructed: Jacobi-M based
on the BSF-M representation and Jacobi-MR based on the BSF-MR representation.
Analytical estimations of the speedup, parallel efficiency and upper
scalability bound are constructed for these algorithms using the BSF cost
metrics on multiprocessor computing systems with distributed memory. An
information about the implementation of these algorithms in C++ language using
the BSF program skeleton and MPI parallel programming library are given. The
results of large-scale computational experiments performed on a cluster
computing system are demonstrated. Based on the experimental results, an
analysis of the adequacy of estimations obtained analytically by using the cost
metrics of the BSF model is made.


  We present the analysis of the binary-lens microlensing event
OGLE-2013-BLG-0911. The best-fit solutions indicate the binary mass ratio of
q~0.03 which differs from that reported in Shvartzvald+2016. The event suffers
from the well-known close/wide degeneracy, resulting in two groups of solutions
for the projected separation normalized by the Einstein radius of s~0.15 or
s~7. The finite source and the parallax observations allow us to measure the
lens physical parameters. The lens system is an M-dwarf orbited by a massive
Jupiter companion at very close (M_{host}=0.30^{+0.08}_{-0.06} M_{Sun},
M_{comp}=10.1^{+2.9}_{-2.2} M_{Jup}, a_{exp}=0.40^{+0.05}_{-0.04} au) or wide
(M_{host}=0.28^{+0.10}_{-0.08} M_{Sun}, M_{comp}=9.9^{+3.8}_{-3.5}M_{Jup},
a_{exp}=18.0^{+3.2}_{-3.2} au) separation. Although the mass ratio is slightly
above the planet-brown dwarf (BD) mass-ratio boundary of q=0.03 which is
generally used, the median physical mass of the companion is slightly below the
planet-BD mass boundary of 13M_{Jup}. It is likely that the formation
mechanisms for BDs and planets are different and the objects near the
boundaries could have been formed by either mechanism. It is important to probe
the distribution of such companions with masses of ~13M_{Jup} in order to
statistically constrain the formation theories for both BDs and massive
planets. In particular, the microlensing method is able to probe the
distribution around low-mass M-dwarfs and even BDs which is challenging for
other exoplanet detection methods.


  Neural avalanches are collective firings of neurons that exhibit emergent
scale-free behavior. Understanding the nature and distribution of these
avalanches is an important element in understanding how the brain functions. We
study a model of neural avalanches for which the dynamics are governed by
neutral theory. The neural avalanches are defined using causal connections
between the firing neurons. We analyze the scaling of causal neural avalanches
as the critical point is approached from the absorbing phase. By using cluster
analysis tools from percolation theory, we characterize the critical properties
of the neural avalanches. We identify the tuning parameters consistent with
experiments. The scaling hypothesis provides a unified explanation of the power
laws which characterize the critical point. The critical exponents
characterizing the avalanche distributions and divergence of the response
functions are consistent with the predictions of the scaling hypothesis. We use
a universal scaling function for the avalanche profile to find that the firing
rates for avalanches of different durations show data collapse after
appropriate rescaling. We also find data collapse for the avalanche
distribution functions, which is stronger evidence of criticality than just the
existence of power laws. Critical slowing-down and power law relaxation of
avalanches is observed as the system is tuned to its critical point. We discuss
how our results motivate future empirical studies of criticality in the brain.


  The notion of trees plays an important role in Butcher's B-series. More
recently, a refined understanding of algebraic and combinatorial structures
underlying the Magnus expansion has emerged thanks to the use of rooted trees.
We follow these ideas by further developing the observation that the logarithm
of the solution of a lihear first-order finite-difference equation can be
written in terms of the Magnus expansion taking place in a pre-Lie algebra. By
using basic combinatorics on planar reduced trees we derive a closed formula
for the Magnus expansion in the context of free tridendriform algebra. The
tridendriform algebra structure on word quasi-symmetric functions permits us to
derive a discrete analogue of the Mielnik-Plebanski-Strichartz formula for this
logarithm.


  We present a new technique for obtaining model fittings to VLBI images of
astrophysical jets. The method minimizes a performance function proportional to
the sum of the squared difference between the model and observed images. The
model image is constructed by summing elliptical Gaussian sources characterized
by six parameters: two-dimensional peak position, peak intensity, eccentricity,
amplitude and orientation angle of the major axis. We present results for the
fitting of two main benchmark jets: the first, constructed from three
individual Gaussian sources, the second formed by five Gaussian sources. Both
jets were analyzed by our cross-entropy technique in finite and infinite
signal-to-noise regimes, the background noise chosen to mimic that found in
interferometric radio maps. We show that our technique is capable of recovering
the parameters of the sources with a similar accuracy to that obtained from the
traditional AIPS task IMFIT when the image is relatively simple (e.g., few
components). For more complex maps, our method displays superior performance in
recovering the parameters of the jet components. Our methodology is also able
to show quantitatively the number of individual components present in an image.
An additional application of the cross-entropy technique to a real image of a
BL Lac object is shown and discussed. Our results indicate that our
cross-entropy technique must be used in situations involving the analysis of
complex emission regions having more than three sources, even though it is
substantially slower than current model fitting tasks (at least 10,000 times
slower for a single processor, depending on the number of sources to be
optimized). As in the case of any model fitting performed in the image plane,
caution is required in analyzing images constructed from a poorly sampled (u,v)
plane.


  In this paper we continue the study of the simulated stock market framework
defined by the driving sentiment processes. We focus on the market environment
driven by the buy/sell trading sentiment process of the Markov chain type. We
apply the methodology of the Hidden Markov Models and the Recurrent Neural
Networks to reconstruct the transition probabilities matrix of the Markov
sentiment process and recover the underlying sentiment states from the observed
stock price behavior.


  We observe sharp peaks and strong hysteresis in the electronic transport of a
two-dimensional electron gas (2DEG) in the region of the integral quantum Hall
effect. The peaks decay on time scales ranging from several minutes to more
than an hour. Momentary grounding of some of the contacts can vastly modify the
strength of the peaks. All these features disappear under application of a
negative bias voltage to the backside of the specimen. We conclude, that a
conduction channel parallel to the high mobility 2DEG is the origin for the
peaks and their hysteretic behavior.


  To explain the differentiation of stem cells in terms of dynamical systems
theory, models of interacting cells with intracellular protein expression
dynamics are analyzed and simulated. Simulations were carried out for all
possible protein expression networks consisting of two genes under cell--cell
interactions mediated by the diffusion of a protein. Networks that show cell
differentiation are extracted and two forms of symmetric differentiation based
on Turing's mechanism and asymmetric differentiation are identified. In the
latter network, the intracellular protein levels show oscillatory dynamics at a
single-cell level, while cell-to-cell synchronicity of the oscillation is lost
with an increase in the number of cells. Differentiation to a fixed-point type
behavior follows with a further increase in the number of cells. The cell type
with oscillatory dynamics corresponds to a stem cell that can both proliferate
and differentiate, while the latter fixed-point type only proliferates. This
differentiation is analyzed as a saddle-node bifurcation on an invariant
circle, while the number ratio of each cell type is shown to be robust against
perturbations due to self-consistent determination of the effective bifurcation
parameter as a result of the cell--cell interaction. Complex cell
differentiation is designed by combing these simple two-gene networks. The
generality of the present differentiation mechanism, as well as its biological
relevance, is discussed.


  Some binary quadratic operads are endowed with anticyclic structures and
their characteristic functions as anticyclic operads are determined, or
conjectured in one case.


  In a chromomagnetic model, we analyse the properties of the newly observed
$P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ states. We estimate the masses
of the $(uud)_{8_c}(c\bar{c})_{8_c}$ and $(uds)_{8_c}(c\bar{c})_{8_c}$
pentaquark states by considering the isospin breaking effects. Their values are
determined by calculating mass distances from the $\Sigma_c^{++}D^-$ and
$\Xi_c^{\prime+}D^-$ thresholds, respectively. It is found that the isospin
breaking effects on the spectrum are small. From the uncertainty consideration
and the rearrangement decay properties in a simple model, we find that it is
possible to assign the $P_c(4457)^+$, $P_c(4440)^+$, and $P_c(4312)^+$ as
$J^P=3/2^-$, $1/2^-$, and $3/2^-$ pentaquark states, respectively. The
assignment in the molecule picture can be different, in particular for the
$P_c(4312)^+$. The information from open-charm channels, e.g. ${\cal
B}[P_c\to\Sigma_c^{++}D^-]/{\cal B}[P_c\to J/\psi p]$, will play an important
role in distinguishing the inner structures of the $P_c$ states. Discussions
and predictions based on the calculations are also given.


  We show by simulation that the test for an unknown threshold in models with
endogenous regressors - proposed in Caner and Hansen (2004) - can exhibit
severe size distortions both in small and in moderately large samples,
pertinent to empirical applications. We propose three new tests that rectify
these size distortions. The first test is based on GMM estimators. The other
two are based on unconventional 2SLS estimators, that use additional
information about the linearity (or lack of linearity) of the first stage. Just
like the test in Caner and Hansen (2004), our tests are non-pivotal, and we
prove their bootstrap validity. The empirical application revisits the question
in Ramey and Zubairy (2018) whether government spending multipliers are larger
in recessions, but using tests for an unknown threshold. Consistent with Ramey
and Zubairy (2018), we do not find strong evidence that these multipliers are
larger in recessions.


  Let $f$ be a Hochschild $2$-cocycle and let $A_f$ be an infinitesimal
deformation of an associative finite dimensional algebra $A$ over an
algebraically closed field $\Bbbk$. We investigate the algebra structure of the
Ext-algebra of $A_f$ and, under some conditions on $f$, we describe it in terms
of the Ext-algebra of $A$. We achieve this description by getting an explicit
construction of minimal projective resolutions in $\mod A_f$.


  Influence maximization (IM) has garnered a lot of attention in the literature
owing to applications such as viral marketing and infection containment. It
aims to select a small number of seed users to adopt an item such that adoption
propagates to a large number of users in the network. Competitive IM focuses on
the propagation of competing items in the network. Existing works on
competitive IM have several limitations. (1) They fail to incorporate economic
incentives in users' decision making in item adoptions. (2) Majority of the
works aim to maximize the adoption of one particular item, and ignore the
collective role that different items play. (3) They focus mostly on one aspect
of competition -- pure competition. To address these concerns we study
competitive IM under a utility-driven propagation model called UIC, and study
social welfare maximization. The problem in general is not only NP-hard but
also NP-hard to approximate within any constant factor. We, therefore, devise
instant dependent efficient approximation algorithms for the general case as
well as a $(1-1/e-\epsilon)$-approximation algorithm for a restricted setting.
Our algorithms outperform different baselines on competitive IM, both in terms
of solution quality and running time on large real networks under both
synthetic and real utility configurations.


  We investigate a stochastic program with expected value constraints,
addressing the problem in a general context through Distributionally Robust
Optimization (DRO) approach using Wasserstein distances, where the ambiguity
set depends on the decision variable. We demonstrate that this approach can be
reformulated into a finite-dimensional optimization problem, which, in certain
instances, can be convex. Moreover, we establish criteria for determining the
feasibility of the problem concerning the Wasserstein radius and the parameter
governing the constraint. Finally, we present numerical results within the
context of portfolio optimization. In particular, we highlight the distinctions
between our approach and several existing non-robust methods, using both
simulated data and real financial market data.


  Variational Bayesian (VB) methods produce posterior inference in a time frame
considerably smaller than traditional Markov Chain Monte Carlo approaches.
Although the VB posterior is an approximation, it has been shown to produce
good parameter estimates and predicted values when a rich classes of
approximating distributions are considered. In this paper we propose Updating
VB (UVB), a recursive algorithm used to update a sequence of VB posterior
approximations in an online setting, with the computation of each posterior
update requiring only the data observed since the previous update. An extension
to the proposed algorithm, named UVB-IS, allows the user to trade accuracy for
a substantial increase in computational speed through the use of importance
sampling. The two methods and their properties are detailed in two separate
simulation studies. Two empirical illustrations of the proposed UVB methods are
provided, including one where a Dirichlet Process Mixture model with a novel
posterior dependence structure is repeatedly updated in the context of
predicting the future behaviour of vehicles on a stretch of the US Highway 101.


  We have performed detailed numerical calculations of the non-conservative
evolution of close X-ray binary systems with intermediate-mass (2.0-6.0 M_sun)
donor stars and a 1.3 M_sun accreting neutron star. We calculated the thermal
response of the donor star to mass loss, in order to determine its stability
and follow the evolution of the mass transfer. Under the assumption of the
"isotropic re-emission model" we demonstrate that in many cases it is possible
for the binary to prevent a spiral-in and survive a highly super-Eddington
mass-transfer phase (1 << M_dot/M_Edd < 10^5) on a sub-thermal timescale, if
the convective envelope of the donor star is not too deep. These systems thus
provide a new formation channel for binary millisecond pulsars with heavy CO
white dwarfs and relatively short orbital periods (3-50 days). However, we
conclude that to produce a binary pulsar with a O-Ne-Mg white dwarf or P_orb ~1
day (e.g. PSR B0655+64) the above scenario does not work, and a spiral-in phase
is still considered the most plausible scenario for the formation of such a
system.


  The study of patterns in permutations associated with forests of binary
shrubs was initiated by D. Bevan et al.. In this paper, we study five different
types of rise statistics that can be associated with such permutations and find
the generating functions for the distribution of such rise statistics.


  Possible single productions of fourth family u_{4} and d_{4} quarks via
anomalous q_{4}qV interactions at Tevatron are studied. Signature of such
processes are discussed and compared with the recent results from Tevatron.


  A family of sets $F$ is said to satisfy the $(p,q)$ property if among any $p$
sets in $F$, some $q$ have a non-empty intersection. Hadwiger and Debrunner
(1957) conjectured that for any $p \geq q \geq d+1$ there exists $c=c_d(p,q)$,
such that any family of compact convex sets in $\mathbb{R}^d$ that satisfies
the $(p,q)$ property, can be pierced by at most $c$ points. In a celebrated
result from 1992, Alon and Kleitman proved the conjecture. However, obtaining
sharp bounds on $c_d(p,q)$, called `the Hadwiger-Debrunner numbers', is still a
major open problem in discrete and computational geometry. The best currently
known lower bound on the Hadwiger-Debrunner numbers in the plane is $c_2(p,q) =
\Omega( \frac{p}{q}\log(\frac{p}{q}))$ while the best known upper bound is
$O(p^{(1.5+\delta)(1+\frac{1}{q-2})})$.
  In this paper we improve the lower bound significantly by showing that
$c_2(p,q) \geq p^{1+\Omega(1/q)}$. Furthermore, the bound is obtained by a
family of lines, and is tight for all families that have a bounded
VC-dimension. Unlike previous bounds on the Hadwiger-Debrunner numbers which
mainly used the weak epsilon-net theorem, our bound stems from a surprising
connection of the $(p,q)$ problem to an old problem of Erd\H{o}s on points in
general position in the plane. We use a novel construction for the Erd\H{o}s'
problem, obtained recently by Balogh and Solymosi using the hypergraph
container method, to get the lower bound on $c_2(p,3)$. We then generalize the
bound to $c_2(p,q)$ for any $q \geq 3$.


  We present a re-analysis of cosmic shear and galaxy clustering from
first-year Dark Energy Survey data (DES Y1), making use of a Hybrid Effective
Field Theory (HEFT) approach to model the galaxy-matter relation on weakly
non-linear scales, initially proposed in Modi et al. (2020) (arXiv:1910.07097).
This allows us to explore the enhancement in cosmological constraining power
enabled by extending the galaxy clustering scale range typically used in
projected large-scale structure analyses. Our analysis is based on a recomputed
harmonic-space data vector and covariance matrix, carefully accounting for all
sources of mode-coupling, non-Gaussianity and shot noise, which allows us to
provide robust goodness-of-fit measures. We use the \textsc{AbacusSummit} suite
of simulations to build an emulator for the HEFT model predictions. We find
that this model can explain the galaxy clustering and shear data up to
wavenumbers $k_{\rm max}\sim 0.6\, {\rm Mpc}^{-1}$. We constrain
$(S_8,\Omega_m) = (0.786\pm 0.020,0.273^{+0.030}_{-0.036})$ at the fiducial
$k_{\rm max}\sim 0.3\, {\rm Mpc}^{-1}$, improving to $(S_8,\Omega_m) =
(0.786^{+0.015}_{-0.018},0.266^{+0.024}_{-0.027})$ at $k_{\rm max}\sim 0.5\,
{\rm Mpc}^{-1}$. This represents a $\sim10\%$ and $\sim35\%$ improvement on the
constraints derived respectively on both parameters using a linear bias
relation on a reduced scale range ($k_{\rm max}\lesssim0.15\,{\rm Mpc}^{-1}$),
in spite of the 15 additional parameters involved in the HEFT model. We
investigate whether HEFT can be used to constrain the Hubble parameter and find
$H_0= 70.7_{-3.5}^{+3.0}\,{\rm km}\,s^{-1}\,{\rm Mpc}^{-1}$. Our constraints
are investigative and subject to certain caveats discussed in the text.


  Mergers between a massive galaxy and a small gas-rich companion (minor
mergers) have been proposed as a viable mechanism for triggering radio emission
in an active galaxy. Until now the problem has been catching this sequence of
events as they occur. With MRC B1221$-$423 we have an active radio galaxy that
has only recently been triggered, and a companion galaxy that provides the
"smoking gun". Using spectroscopic data taken with the VIMOS Integral Field
Unit detector on the European Southern Observatory's Very Large Telescope, we
have examined the distribution, ionization state and kinematics of ionized gas
in this interacting system. We have also modelled the stellar continuum with
synthesised spectra of stellar populations of different ages. From our study of
the ionized gas, we have derived preliminary models for the geometry of the
interaction, analysed the kinematic behaviour of the ionized gas, and examined
the ionization mechanisms at work throughout the system. Our modelling of the
stellar continuum allowed us to identify and date distinct stellar populations
within the galaxy pair. We find evidence of multiple episodes of widespread
starburst activity, and by dating these populations, we provide tentative
insight into the history of the interaction.


  We study electronic states of semi-infinite graphene with a corner edge,
focusing on the stability of edge localized states at zero energy. The
60{\deg}, 90{\deg}, 120{\deg} and 150{\deg} corner edges are examined. The
60{\deg} and 120{\deg} corner edges consist of two zigzag edges, while 90{\deg}
and 150{\deg} corner edges consist of one zigzag edge and one armchair edge. We
numerically obtain the local density of states (LDOS) on the basis of a
nearest-neighbor tight-binding model by using Haydock's recursion method. We
show that edge localized states appear along a zigzag edge of each corner edge
structure except for the 120{\deg} case. To provide insight into this behavior,
we analyze electronic states at zero energy within the framework of an
effective mass equation. The result of this analysis is consistent with the
behavior of the LDOS.


  There is a universal constant $0<r_0<1$ with the following property. Suppose
that $f$ is an analytic function on the unit disk $\D$, and suppose that there
exists a constant $M>0$ so that the Euclidean area, counting multiplicity, of
the portion of $f(\D)$ which lies over the disk $D(f(0),M)$, centered at $f(0)$
and of radius $M$, is strictly less than the area of $D(f(0),M)$. Then $f$ must
send $r_0\bar{\D}$ into $D(f(0),M)$. This answers a conjecture of Don Marshall.


  In the development of science, accurate and reproducible documentation of the
experimental process is crucial. Automatic recognition of the actions in
experiments from videos would help experimenters by complementing the recording
of experiments. Towards this goal, we propose FineBio, a new fine-grained video
dataset of people performing biological experiments. The dataset consists of
multi-view videos of 32 participants performing mock biological experiments
with a total duration of 14.5 hours. One experiment forms a hierarchical
structure, where a protocol consists of several steps, each further decomposed
into a set of atomic operations. The uniqueness of biological experiments is
that while they require strict adherence to steps described in each protocol,
there is freedom in the order of atomic operations. We provide hierarchical
annotation on protocols, steps, atomic operations, object locations, and their
manipulation states, providing new challenges for structured activity
understanding and hand-object interaction recognition. To find out challenges
on activity understanding in biological experiments, we introduce baseline
models and results on four different tasks, including (i) step segmentation,
(ii) atomic operation detection (iii) object detection, and (iv)
manipulated/affected object detection. Dataset and code are available from
https://github.com/aistairc/FineBio.


  The HIV-1 integrase (IN) is a major target for the design of novel anti-HIV
inhibitors. Among these, three inhibitors which embody a halobenzene ring
derivative (HR) in their structures are presently used in clinics.
High-resolution X-ray crystallography of the complexes of the IN-viral DNA
transient complex bound to each of the three inhibitors showed in all cases the
HR ring to interact within a confined zone of the viral DNA. The extension of
its extracyclic CX bond is electron-depleted, owing to the existence of the
"sigma-hole". It interacts favorably with the electron-rich rings of base G4.
We have sought to increase the affinity of HR derivatives for the G4/C16 base
pair. We thus designed thirteen novel derivatives and computed their Quantum
Chemistry (QC) intermolecular interaction energies (delta(E)) with this
base-pair. Most compounds had DE values significantly more favorable than those
of the HR of the most potent halobenzene drug presently used in clinics,
Dolutegravir. This should enable the improvement in a modular piece-wise
fashion, the affinities of halogenated inhibitors for viral DNA (vDNA). In view
of large scale polarizable molecular dynamics simulations on the entirety of
the IN-vDNA-inhibitor complexes, validations of the SIBFA polarizable method
are also reported, in which the evolution of each delta(SIBFA) contribution is
compared to its QC counterpart along this series of derivatives.


  Given an undirected graph $G=(V,E)$ and an integer $\ell$, the Eccentricity
Shortest Path (ESP) asks to find a shortest path $P$ such that for every vertex
$v\in V(G)$, there is a vertex $w\in P$ such that $d_G(v,w)\leq \ell$, where
$d_G(v,w)$ represents the distance between $v$ and $w$ in $G$. Dragan and
Leitert [Theor. Comput. Sci. 2017] showed that the optimization version of this
problem, which asks to find the minimum $\ell$ for the ESP problem, is NP-hard
even on planar bipartite graphs with maximum degree 3. They also showed that
ESP is W[2]-hard when parameterized by $\ell$. On the positive side, Ku\v cera
and Such\'y [IWOCA 2021] showed that the problem exhibits fixed parameter
tractable (FPT) behavior when parameterized by modular width, cluster vertex
deletion set, maximum leaf number, or the combined parameters disjoint paths
deletion set and $\ell$. It was asked as an open question in the above paper,
if ESP is FPT parameterized by disjoint paths deletion set or feedback vertex
set. We answer these questions partially and obtain the following results: -
ESP is FPT when parameterized by disjoint paths deletion set, split vertex
deletion set or the combined parameters feedback vertex set and eccentricity of
the graph. - We design a $(1+\epsilon)$-factor FPT approximation algorithm when
parameterized by the feedback vertex set number. - ESP is W[2]-hard when
parameterized by the chordal vertex deletion set.


  Understanding conditions for the synchronization of a network of
interconnected oscillators is a challenging problem. Typically, only sufficient
conditions are reported for the synchronization problem. Here, we adopted the
Lyapunov-Floquet theory and the Master Stability Function approach in order to
derive the synchronization conditions for a set of coupled nonlinear
oscillators. We found that the positivity of the coupling constant is a
necessary and sufficient condition for synchronizing linearly full-state
coupled identical oscillators. Moreover, in the case of partial state coupling,
the asymptotic convergence of volume in state space is ensured by a positive
coupling constant. The numerical calculation of the Master Stability Function
for a benchmark two-dimensional oscillator validates the synchronization
corresponding to the positive coupling. The results are illustrated using
numerical simulations and experimentation on benchmark oscillators.


  The measurement and analysis of electron scattering from He-3 and He-4 by
Sick and collaborators reported 20 years ago remains a matter of current
interest. By unfolding the measured free-proton charge distribution, they
deduced a depression in the central point nucleon density, which is not found
in few-body calculations based on realistic potentials. We find that using wave
functions from such calculations we can obtain good fits to the He charge
distributions under the assumption that the proton charge size expands toward
the center of the nucleus. The relationship to 6-quark Chromo-Dielectric Model
calculations, is discussed. The expansion is larger than than the predictions
of mean field bag calculations by others or our CDM calculations in the
independent pair approximation. There is interest here in the search for a
"smoking gun" signal of quark substructure.


  The elliptic flow of prompt and non-prompt $J/\psi$ was measured in the
dimuon decay channel in Pb+Pb collisions at $\sqrt{s_{_\text{NN}}}=5.02$ TeV
with an integrated luminosity of $0.42~\mathrm{nb}^{-1}$ with the ATLAS
detector at the LHC. The prompt and non-prompt signals are separated using a
two-dimensional simultaneous fit of the invariant mass and pseudo-proper decay
time of the dimuon system from the $J/\psi$ decay. The measurement is performed
in the kinematic range of dimuon transverse momentum and rapidity
$9<p_\mathrm{T}<30$ GeV, $|y|<2$, and 0-60% collision centrality. The elliptic
flow coefficient, $v_2$, is evaluated relative to the event plane and the
results are presented as a function of transverse momentum, rapidity and
centrality. It is found that prompt and non-prompt $J/\psi$ mesons have
non-zero elliptic flow. Prompt $J/\psi$ $v_2$ decreases as a function of
$p_\mathrm{T}$, while non-prompt $J/\psi$ it is, with limited statistical
significance, consistent with a flat behaviour over the studied kinematic
region. There is no observed dependence on rapidity or centrality.


  Existing HST UV data offer many previously neglected clues to eta Car's
behavior since 2000. Here we examine a subset of observations with diverse
results. (1) The star's rapid change of state is confirmed by major changes in
UV absorption lines, circumstellar extinction, and other features. (2) N III]
1750 is one of the two most luminous emission features in eta Car's observable
spectrum, comparable to H-alpha. This and other semi-forbidden lines are useful
because they have no P Cyg absorption. (3) N III] multiplet ratios provide the
first direct diagnostic of gas densities in eta Car's outflow. They strongly
suggest that high-excitation lines originate in condensations within the
colliding-wind shocked region. The parameters imply that published models have
not adequately represented the essential small size scales. (4) In 2002-2004, a
very large amount of N III] emission had anomalous Doppler velocities from +400
to +1200 km/s. This is a mystery; we conjecture that it may have resulted from
a burst of mass ejection in the 2003.5 periastron event. Various other effects
are also difficult to explain and merit further investigation.


  Stein Variational Gradient Descent (SVGD) is a popular particle-based method
for Bayesian inference. However, its convergence suffers from the variance
collapse, which reduces the accuracy and diversity of the estimation. In this
paper, we study the isotropy property of finite particles during the
convergence process and show that SVGD of finite particles cannot spread across
the entire sample space. Instead, all particles tend to cluster around the
particle center within a certain range and we provide an analytical bound for
this cluster. To further improve the effectiveness of SVGD for high-dimensional
problems, we propose the Augmented Message Passing SVGD (AUMP-SVGD) method,
which is a two-stage optimization procedure that does not require sparsity of
the target distribution, unlike the MP-SVGD method. Our algorithm achieves
satisfactory accuracy and overcomes the variance collapse problem in various
benchmark problems.


  A collective flashing ratchet transports Brownian particles using a spatially
periodic, asymmetric, and time-dependent on-off switchable potential. The net
current of the particles in this system can be substantially increased by
feedback control based on the particle positions. Several feedback policies for
maximizing the current have been proposed, but optimal policies have not been
found for a moderate number of particles. Here, we use deep reinforcement
learning (RL) to find optimal policies, with results showing that policies
built with a suitable neural network architecture outperform the previous
policies. Moreover, even in a time-delayed feedback situation where the on-off
switching of the potential is delayed, we demonstrate that the policies
provided by deep RL provide higher currents than the previous strategies.


  We derive formulae for some ratios of the Macdonald functions, which are
simpler and easier to treat than known formulae. The result gives two
applications in probability theory. One is the formula for the L{\'e}vy measure
of the distribution of the first hitting time of a Bessel process and the other
is an explicit form for the expected volume of the Wiener sausage for an even
dimensional Brownian motion. Moreover, the result enables us to write down the
algebraic equations whose roots are the zeros of Macdonald functions.


  Recently, Sophie Grivaux showed that there exists a rank one perturbation of
a unitary operator in a Hilbert space which is hypercyclic. We give a similar
construction using a functional model for rank one perturbations of singular
unitary operators.


  An intrinsic curvature model is investigated using the canonical Monte Carlo
simulations on dynamically triangulated spherical surfaces of size upto N=4842
with two fixed-vertices separated by the distance 2L. We found a first-order
transition at finite curvature coefficient \alpha, and moreover that the order
of the transition remains unchanged even when L is enlarged such that the
surfaces become sufficiently oblong. This is in sharp contrast to the known
results of the same model on tethered surfaces, where the transition weakens to
a second-order one as L is increased. The phase transition of the model in this
paper separates the smooth phase from the crumpled phase. The surfaces become
string-like between two point-boundaries in the crumpled phase. On the
contrary, we can see a spherical lump on the oblong surfaces in the smooth
phase. The string tension was calculated and was found to have a jump at the
transition point. The value of \sigma is independent of L in the smooth phase,
while it increases with increasing L in the crumpled phase. This behavior of
\sigma is consistent with the observed scaling relation \sigma \sim (2L/N)^\nu,
where \nu\simeq 0 in the smooth phase, and \nu=0.93\pm 0.14 in the crumpled
phase. We should note that a possibility of a continuous transition is not
completely eliminated.


  Local and inter-area oscillations in bulk power systems are typically
identified using spatial profiles of poorly damped modes, and they are
mitigated via carefully tuned decentralized controllers. In this paper, we
employ non-modal tools to analyze and control inter-area oscillations. Our
input-output analysis examines power spectral density and variance
amplification of stochastically forced systems and offers new insights relative
to modal approaches. To improve upon the limitations of conventional wide-area
control strategies, we also study the problem of signal selection and optimal
design of sparse and block-sparse wide-area controllers. In our design, we
preserve rotational symmetry of the power system by allowing only relative
angle measurements in the distributed controllers. For the IEEE 39 New England
model, we examine performance tradeoffs and robustness of different control
architectures and show that optimal retuning of fully-decentralized control
strategies can effectively guard against local and inter-area oscillations.


  This paper focuses on the undecidability of translational tiling of
$n$-dimensional space $\mathbb{Z}^n$ with a set of $k$ tiles. It is known that
tiling $\mathbb{Z}^2$ with translated copies with a set of $8$ tiles is
undecidable. Greenfeld and Tao gave strong evidence in a series of works that
for sufficiently large dimension $n$, the translational tiling problem for
$\mathbb{Z}^n$ might be undecidable for just one tile. This paper shows the
undecidability of translational tiling of $\mathbb{Z}^3$ with a set of $6$
tiles.


  Recapturing attack can be employed as a simple but effective anti-forensic
tool for digital document images. Inspired by the document inspection process
that compares a questioned document against a reference sample, we proposed a
document recapture detection scheme by employing Siamese network to compare and
extract distinct features in a recapture document image. The proposed algorithm
takes advantages of both metric learning and image forensic techniques. Instead
of adopting Euclidean distance-based loss function, we integrate the forensic
similarity function with a triplet loss and a normalized softmax loss. After
training with the proposed triplet selection strategy, the resulting feature
embedding clusters the genuine samples near the reference while pushes the
recaptured samples apart. In the experiment, we consider practical domain
generalization problems, such as the variations in printing/imaging devices,
substrates, recapturing channels, and document types. To evaluate the
robustness of different approaches, we benchmark some popular off-the-shelf
machine learning-based approaches, a state-of-the-art document image detection
scheme, and the proposed schemes with different network backbones under various
experimental protocols. Experimental results show that the proposed schemes
with different network backbones have consistently outperformed the
state-of-the-art approaches under different experimental settings.
Specifically, under the most challenging scenario in our experiment, i.e.,
evaluation across different types of documents that produced by different
devices, we have achieved less than 5.00% APCER (Attack Presentation
Classification Error Rate) and 5.56% BPCER (Bona Fide Presentation
Classification Error Rate) by the proposed network with ResNeXt101 backbone at
5% BPCER decision threshold.


  It is proved that the wave operators corresponding to Schroedinger operators
with Aharonov-Bohm type magnetic fields can be rewritten in terms of explicit
functions of the generator of dilations and of the Laplacian.


  After 20 years of research the low energy physics of cuprates remains a
mystery. It is generally accepted that a three band Hamiltonian with Cu's and
O's orbitals should contain the essential physics so we can say that there is
consensus at the length scale of the Cu-O distance but there is disagreement
when it comes to describe higher length scales or to set up a low energy model.
Here we present computations of cuprates which accurately describe the physics
arising at scales of up to several lattice constants. We review the comparison
of our results with different proves as resonant X-ray scattering, scanning
tunneling microscopy, optical conductivity and magnetic neutron scattering.


  For a graph $G$, let $\mu_k(G):=\min~\{\max_{x\in S}d_G(x):~S\in
\mathcal{S}_k\}$, where $\mathcal{S}_k$ is the set consisting of all
independent sets $\{u_1,\ldots,u_k\}$ of $G$ such that some vertex, say $u_i$
($1\leq i\leq k$), is at distance two from every other vertex in it. A graph
$G$ is $1$-tough if for each cut set $S\subseteq V(G)$, $G-S$ has at most $|S|$
components. Recently, Shi and Shan \cite{Shi} conjectured that for each integer
$k\geq 4$, being $2k$-connected is sufficient for $1$-tough $(P_2\cup
kP_1)$-free graphs to be hamiltonian, which was confirmed by Xu et al.
\cite{Xu} and Ota and Sanka \cite{Ota2}, respectively. In this article, we
generalize the above results through the following Fan-type theorem: Let $k$ be
an integer with $k\geq 2$ and let $G$ be a $1$-tough and $k$-connected
$(P_2\cup kP_1)$-free graph with $\mu_{k+1}(G)\geq\frac{7k-6}{5}$, then $G$ is
hamiltonian or the Petersen graph.


  Since the 1930s, theories of skin-friction drag from plates with rough
surfaces have been based by analogy to turbulent flow in pipes with rough
interiors. Failure of this analogy at slow velocities has frustrated attempts
to create a comprehensive theory.
  Utilizing the concept of a self-similar roughness which disrupts the boundary
layer at all scales, this investigation derives formulas for a rough or smooth
plate's skin-friction coefficient and forced convection heat transfer given its
characteristic length, root-mean-squared (RMS) height-of-roughness, isotropic
spatial period, Reynolds number, and the fluid's Prandtl number.
  This novel theory was tested with 456 heat transfer and friction measurements
in 32 data-sets from one book, six peer-reviewed studies, and the present
apparatus. Compared with the present theory, the RMS relative error (RMSRE)
values of the 32 data-sets span 0.75% through 8.2%, with only four data-sets
exceeding 6%. Prior work formulas have smaller RMSRE on only four of the
data-sets.


  In this paper, we generalize construction of Seidel's long exact sequence of
Lagrangian Floer cohomology to that of compact Lagrangian submanifolds with
vanishing Malsov class on general Calabi-Yau manifolds. We use the framework of
anchored Lagrangian submanifolds developed in \cite{fooo:anchor} and some
compactness theorem of \emph{smooth} $J$-holomorphic sections of Lefschetz
Hamiltonian fibration for a generic choice of $J$. The proof of the latter
compactness theorem involves a study of proper pseudoholomorphic curves in the
setting of noncompact symplectic manifolds with cylindrical ends.


  The effectiveness and performance of artificial neural networks, particularly
for visual tasks, depends in crucial ways on the receptive field of neurons.
The receptive field itself depends on the interplay between several
architectural aspects, including sparsity, pooling, and activation functions.
In recent literature there are several ad hoc proposals trying to make
receptive fields more flexible and adaptive to data. For instance, different
parameterizations of convolutional and pooling layers have been proposed to
increase their adaptivity. In this paper, we propose the novel theoretical
framework of density-embedded layers, generalizing the transformation
represented by a neuron. Specifically, the affine transformation applied on the
input is replaced by a scalar product of the input, suitably represented as a
piecewise constant function, with a density function associated with the
neuron. This density is shown to describe directly the receptive field of the
neuron. Crucially, by suitably representing such a density as a linear
combination of a parametric family of functions, we can efficiently train the
densities by means of any automatic differentiation system, making it adaptable
to the problem at hand, and computationally efficient to evaluate. This
framework captures and generalizes recent methods, allowing a fine tuning of
the receptive field. In the paper, we define some novel layers and we
experimentally validate them on the classic MNIST dataset.


  Domain decomposition methods are widely used to solve sparse linear systems
from scientific problems, but they are not suited to solve sparse linear
systems extracted from integrated circuits. The reason is that the sparse
linear system of integrated circuits may be non-diagonal-dominant, and domain
decomposition method might be unconvergent for these non-diagonal-dominant
matrices. In this paper, we propose a mini-step strategy to do the circuit
transient analysis. Different from the traditional large-step approach, this
strategy is able to generate diagonal-dominant sparse linear systems. As a
result, preconditioned domain decomposition methods can be used to simulate the
large integrated circuits on the supercomputers and clouds.


  We summarize measurements of b and c jet production at the LHC, which are an
important signature and background for decays of massive particles such as
H-to-b-bbar. These include measurements of the inclusive and dijet production
of heavy quark jets, b and c jets produced in association with vector bosons Z
and W, and decays of boosted Z bosons into pairs of b-bbar. The current status
of b tagging and b jet energy scale is also reviewed. These measurements test
perturbative QCD in the four and five-flavor number schemes, and provide
insight into the relative importance of heavy flavor production through flavor
creation, flavor excitation and gluon splitting channels. The W+c measurement
provides additionally a powerful way to probe the strange quark and antiquark
sea in the proton. The recent studies looking separately at production of one
and two b jets find generally good agreement with theory predictions for two
b-jet production, while some discrepancies are observed for singly produced b
jets, particularly at large b-jet pT , where gluon splitting becomes dominant.


  We review some recent results on the norm approximation to the Schr\"odinger
dynamics. We consider $N$ bosons in $\mathbb{R}^3$ with an interaction
potential of the form $N^{3\beta-1}w(N^{\beta}(x-y))$ with $0\le \beta<1/2$,
and show that in the large $N$ limit, the fluctuations around the condensate
can be effectively described using Bogoliubov approximation.


  Digital image sensors are ubiquitous in astronomical instrumentation and it
is well known that they suffer from issues that must be corrected for data to
be scientifically useful. I present discussion on errors resulting from
digitization and characterization of nonlinearity and ADC errors of the
PhotonFocus MV-D1024E cameras selected for the K-Coronagraph of the Coronal
Solar Magnetism Observatory. I derive an analytic expression for quantization
errors. The MV-D1024E camera has adequate bit depth for which quantization
error is not an issue. I show that this is not the case for all cameras,
particularly those with deep wells and low read noise. The impact of
nonlinearity and ADC errors on science observations of the K-Coronagraph is
analyzed using a simplified telescope model. Errors caused by the camera ADCs
result in systematic errors in the measurement of the polarimetric signal of
several times $10^{-9}~B_\odot$, which is about an order of magnitude above the
desired sensitivity. I demonstrate a method for post-facto data correction
using a lookup table and derive parameters from camera characterization
measurements that were made with a lab setup. Nonlinearity is traditionally
addressed with a global correction. I show through analysis of calibration data
that for the MV-D1024E this correction leaves residual systematic errors after
dark and gain correction of up to 1% of the signal. I demonstrate that a
pixel-wise correction of nonlinearity reduces the errors to below 0.1%. These
corrections are necessary for the K-Coronagraph data products to meet the
science requirements. They have been implemented in the instrument data
acquisition system and data reduction pipeline. While no other instruments
besides the K-Coronagraph or cameras besides the MV-D1024E are discussed here,
the results are illustrative for all instruments and cameras.


  Joint registration of a stack of 2D histological sections to recover 3D
structure (``3D histology reconstruction'') finds application in areas such as
atlas building and validation of \emph{in vivo} imaging. Straightforward
pairwise registration of neighbouring sections yields smooth reconstructions
but has well-known problems such as ``banana effect'' (straightening of curved
structures) and ``z-shift'' (drift). While these problems can be alleviated
with an external, linearly aligned reference (e.g., Magnetic Resonance (MR)
images), registration is often inaccurate due to contrast differences and the
strong nonlinear distortion of the tissue, including artefacts such as folds
and tears. In this paper, we present a probabilistic model of spatial
deformation that yields reconstructions for multiple histological stains that
that are jointly smooth, robust to outliers, and follow the reference shape.
The model relies on a spanning tree of latent transforms connecting all the
sections and slices of the reference volume, and assumes that the registration
between any pair of images can be see as a noisy version of the composition of
(possibly inverted) latent transforms connecting the two images. Bayesian
inference is used to compute the most likely latent transforms given a set of
pairwise registrations between image pairs within and across modalities. The
framework is used for accurate 3D reconstruction of two stains (Nissl and
parvalbumin) from the Allen human brain atlas, showing its benefits on real
data with severe distortions. Moreover, we also provide the registration of the
reconstructed volume to MNI space, bridging the gaps between two of the most
widely used atlases in histology and MRI. The 3D reconstructed volumes and
atlas registration can be downloaded from
https://openneuro.org/datasets/ds003590. The code is freely available at
https://github.com/acasamitjana/3dhirest.


  The Auslander correspondence is a fundamental result in Auslander-Reiten
theory. In this paper we introduce the category
$\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ of admissibly finitely
presented functors and use it to give a version of Auslander correspondence for
any exact category $\mathcal{E}$. An important ingredient in the proof is the
localization theory of exact categories. We also investigate how properties of
$\mathcal{E}$ are reflected in
$\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$, for example being (weakly)
idempotent complete or having enough projectives or injectives. Furthermore, we
describe $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ as a subcategory of
$\operatorname{mod}(\mathcal{E})$ when $\mathcal{E}$ is a resolving subcategory
of an abelian category. This includes the category of Gorenstein projective
modules and the category of maximal Cohen-Macaulay modules as special cases.
Finally, we use $\operatorname{mod_{\mathsf{adm}}}(\mathcal{E})$ to give a
bijection between exact structures on an idempotent complete additive category
$\mathcal{C}$ and certain resolving subcategories of
$\operatorname{mod}(\mathcal{C})$.


  We present an analytic study of the phase diagram of the one-dimensional t-J
model and a couple of its cousins. To deal with the interactions induced by the
no double occupancy constraints, we introduce a deformation of the Hubbard
operators. When the deformation parameter $\Delta$ is small, the induced
interactions are softened, accessible by perturbation theory. We combine
bososnization with renormalization group techniques to map out the phase
diagram of the system. We argue that when $\Delta\to 1$, there is no essential
change in the phase diagram. Comparison with the existing results in the
literature obtained by other methods justifies our deformation approach.


  We consider a quantum key expansion (QKE) protocol based on
entanglement-assisted quantum error-correcting codes (EAQECCs). In these
protocols, a seed of a previously shared secret key is used in the
post-processing stage of a standard quantum key distribution protocol like the
Bennett-Brassard 1984 protocol, in order to produce a larger secret key. This
protocol was proposed by Luo and Devetak, but codes leading to good performance
have not been investigated. We look into a family of EAQECCs generated by
classical finite geometry (FG) low-density parity-check (LDPC) codes, for which
very efficient iterative decoders exist. A critical observation is that almost
all errors in the resulting secret key result from uncorrectable block errors
that can be detected by an additional syndrome check and an additional sampling
step. Bad blocks can then be discarded. We make some changes to the original
protocol to avoid the consumption of the preshared key when the protocol fails.
This allows us to greatly reduce the bit error rate of the key at the cost of a
minor reduction in the key production rate, but without increasing the
consumption rate of the preshared key. We present numerical simulations for the
family of FG LDPC codes, and show that this improved QKE protocol has a good
net key production rate even at relatively high error rates, for appropriate
choices of these codes.


  In this paper, we study the morphologic interaction between graphene and Si
nanowires on a SiO2 substrate, using molecular mechanics simulations. Two cases
are considered: 1) a graphene nanoribbon intercalated by a single Si nanowire
on a SiO2 substrate and 2) a blanket graphene flake intercalated by an array of
Si nanowires evenly patterned in parallel on a SiO2 substrate. Various graphene
morphologies emerge from the simulation results of these two cases, which are
shown to depend on both geometric parameters (e.g., graphene nanoribbon width,
nanowire diameter, and nanowire spacing) and material properties (e.g.,
graphene-nanowire and graphene-substrate bonding strength). While the
quantitative results at the atomistic resolution in this study can be further
used to determine the change of electronic properties of graphene under
morphologic regulation, the qualitative understandings from this study can be
extended to help exploring graphene morphology in other material systems.


  We report quantum-mechanical close-coupling calculations for rotational state
resolved cross sections for p-H2+HD collisions. The low temperature limit of
p-H2+HD is investigated, which is of significant astrophysical interest in
regard to the cooling of primordial gas and the interstellar media. Sharp
resonances have been reproduced in the cross sections of some transition states
at very low kinetic energies, E< 0.00001 eV.


  We will argument how infalling information can be chaotized inside realistic
quantum black holes.


  Motion planning under differential constraints, kinodynamic motion planning,
is one of the canonical problems in robotics. Currently, state-of-the-art
methods evolve around kinodynamic variants of popular sampling-based
algorithms, such as Rapidly-exploring Random Trees (RRTs). However, there are
still challenges remaining, for example, how to include complex dynamics while
guaranteeing optimality. If the open-loop dynamics are unstable, exploration by
random sampling in control space becomes inefficient. We describe a new
sampling-based algorithm, called CL-RRT#, which leverages ideas from the RRT#
algorithm and a variant of the RRT algorithm that generates trajectories using
closed-loop prediction. The idea of planning with closed-loop prediction allows
us to handle complex unstable dynamics and avoids the need to find
computationally hard steering procedures. The search technique presented in the
RRT# algorithm allows us to improve the solution quality by searching over
alternative reference trajectories. Numerical simulations using a nonholonomic
system demonstrate the benefits of the proposed approach.


  We propose a discrete lattice version of the Fokker-Planck kinetic equation
along lines similar to the Lattice-Boltzmann scheme. Our work extends an
earlier one-dimensional formulation to arbitrary spatial dimension $D$. A
generalized Hermite-Gauss procedure is used to construct a discretized kinetic
equation and a Chapman-Enskog expansion is applied to adapt the scheme so as to
correctly reproduce the macroscopic continuum equations. The stability of the
algorithm with respect to the finite time-step $\Delta t$ is characterized by
the eigenvalues of the collision matrix. A heuristic second-order algorithm in
$\Delta t$ is applied to investigate the time evolution of the distribution
function of simple model systems, and compared to known analytical solutions.
Preliminary investigations of sedimenting Brownian particles subjected to an
orthogonal centrifugal force illustrate the numerical efficiency of the
Lattice-Fokker-Planck algorithm to simulate non-trivial situations.
Interactions between Brownian particles may be accounted for by adding a
standard BGK collision operator to the discretized Fokker-Planck kernel.


  Certain quantum many-body ground states can be prepared by a large-depth
quantum circuit consisting of geometrically local gates. In the presence of
noise, local expectation values deviate from the correct value at most by an
amount comparable to the noise rate. This happens if the action of the
noiseless circuit, restricted to certain subsystems, rapidly mixes local
observables up to a small correction. The encoding circuit for the surface code
is given as an example.


  MXenes are a family of 2D transition metal carbides and nitrides with
remarkable properties and great potential for energy storage and catalysis
applications. However, their oxidation behavior is not yet fully understood,
and there are still open questions regarding the spatial distribution and
precise quantification of surface terminations, intercalated ions, and possible
uncontrolled impurities incorporated during synthesis and processing. Here,
atom probe tomography analysis of as-synthesized Ti$_3$C$_2$T$_x$ MXenes
reveals the presence of alkali (Li, Na) and halogen (Cl, F) elements as well as
unetched Al. Following oxidation of the colloidal solution of MXenes, it is
observed that the alkalies enriched in TiO$_2$ nanowires. Although these
elements are tolerated through the incorporation by wet chemical synthesis,
they are often overlooked when the activity of these materials is considered,
particularly during catalytic testing. This work demonstrates how the
capability of atom probe tomography to image these elements in 3D at the
near-atomic scale can help to better understand the activity and degradation of
MXenes, in order to guide their synthesis for superior functional properties.


  The constraints from the measurements of the $B\to X_s\gamma$ decay rate on
the parameter space of 3-Higgs Doublet Models (3HDMs), where all the doublets
have non-zero vacuum expectation values, are studied at the next-to-leading
order in QCD. In order to naturally avoid the presence of flavour changing
neutral currents at the tree level, we impose two softly-broken discrete $Z_2$
symmetries. This gives rise to five independent types of 3HDMs that differ in
their Yukawa couplings. We show that in all these 3HDMs (including the case of
type-II-like Yukawa interactions) both masses of the two charged Higgs bosons
$m_{H_1^\pm}$ and $m_{H_2^\pm}$ can be smaller than the top mass $m_t$ while
complying with the constraints from $B\to X_s\gamma$. As an interesting
phenomenological consequence, the branching ratios of the charged Higgs bosons
decay into the $cb$ final states can be as large as $80\%$ when their masses
are taken to be below $m_t$ in two of the five 3HDMs (named as Type-Y and
Type-Z). This light charged Higgs boson scenario provides a hallmark 3HDM
signature that cannot be realised in $Z_2$ symmetric 2-Higgs doublet models. We
find that in the Type-Y and Type-Z 3HDMs the scenario with $90\,{\rm GeV}<
m_{H^\pm_1}^{}\,, m_{H^\pm_2}^{}<m_t$ is ruled out by the direct searches at
the LHC, but in the Type-Y 3HDM $80~\text{GeV}<m_{H_1^\pm}^{}<90~\text{GeV}$
and $90~\text{GeV}<m_{H_2^\pm}^{}<m_t$ is allowed by $B\to X_s\gamma$ and
direct searches at LEP2, Tevatron and LHC due to the reduced sensitivity of
these searches to the degenerate case $m_{H_1^\pm}\approx m_{W^\pm}$. The cases
where only one or both charged Higgs bosons are above the top quark mass are
also naturally allowed in the both Type-Y and Type-Z 3HDMs.


  Williamson's theorem is well known for symmetric matrices. In this paper, we
state and re-derive some of the cases of Williamson's theorem for symmetric
positive-semi definite matrices and symmetric matrices having negative index 1,
due to H\"ormander. We prove theorems that guarantee conditions under which two
symmetric positive-definite matrices can be simultaneously diagonalized in the
sense of Williamson's theorem and their corollaries. Finally, we provide an
application of this result to physical systems and another connecting the
decompositions for the degenerate and non-degenerate cases, involving phase
space constraints that we later apply to phase space cylinders and ellipsoids
via symplectic capacities.


  The radiation of twisted photons by charged particles traversing a
cholesteric plate is studied in the framework of quantum electrodynamics in an
anisotropic inhomogeneous dispersive medium. The complete set of solutions to
the Maxwell equations in the cholesteric plate is constructed in the paraxial
and small anisotropy approximations. The explicit expressions for the average
numbers of plane-wave and twisted photons created by a charged point particle
crossing the cholesteric plate are derived. The selection rules for the twisted
photons radiated at the harmonic $n\in \mathbb{Z}$ are established. In the
paraxial regime, the projection of the orbital angular momentum of a radiated
twisted photon obeys the selection rule $l=\pm(2n+1)$. In the approximation of
a small anisotropy of the permittivity tensor, the selection rule becomes
$m=\pm 2n$, where $m$ is the projection of the total angular momentum of a
radiated twisted photon. The sign "$\pm$" in these selection rules is related
to the choice of the forward or reflected waves in the cholesteric and is
realized at the different energies of radiated photons. As the examples, the
radiation of optical twisted photons by electrons with the Lorentz factors
$\gamma=235$ and $\gamma=500$ and by uranium nuclei with $\gamma=2$ are
considered. It is shown that charged particles traversing normally a
cholesteric plate can be used as a pure source of twisted photons.


  In this paper we deal with Drinfeld modular forms, defined and taking values
in complete fields of positive characteristic. Our aim is to study a sequence
of families of Drinfeld modular forms depending on a parameter t that produces,
for certain values of t, several kinds of Eisenstein series considered by
Gekeler. We obtain formulas involving these functions. To obtain our results,
we introduce and discuss tau-linear recurrent sequences and deformations of
vectorial modular forms in this setting.


  Surface curvature of magnetic systems can lead to many static and dynamic
effects which are not present in flat systems of the same material. These
emergent magnetochiral effects can lead to frequency nonreciprocity of spin
waves, which has been shown to be a bulk effect of dipolar origin and is
related to a curvature-induced symmetry breaking in the magnetic volume
charges. So far, such effects have been investigated theoretically mostly for
thin shells, where the spatial profiles of the spin waves can be assumed to be
homogeneous along the thickness. Here, using a finite-element dynamic-matrix
approach, we investigate the transition of the spin-wave spectrum from thin to
thick curvilinear shells, at the example of magnetic nanotubes in the vortex
state. With increasing thickness, we observe the appearance of higher-order
radial modes which are strongly hybridized and resemble the
perpendicular-standing-waves (PSSWs) in flat films. Along with an increasing
dispersion asymmetry, we uncover the curvature-induced non-reciprocity of the
mode profiles. This is explained in a very simple picture general for thick
curvilinear shells, considering the inhomogeneity of the emergent geometric
volume charges along the thickness of the shell. Such curvature-induced
mode-profile asymmetry also leads to non-reciprocal hybridization which can
facilitate unidirectional spin-wave propagation. With that, we also show how
curvature allows for nonlinear three-wave splitting of a higher-order radial
mode into secondary modes which can also propagate unidirectionally. We believe
that our study provides a significant contribution to the understanding of the
spin-wave dynamics in curvilinear magnetic systems, but also advertises these
for novel magnonic applications.


  The $(1+(\lambda,\lambda))$ genetic algorithm is a bright example of an
evolutionary algorithm which was developed based on the insights from
theoretical findings. This algorithm uses crossover, and it was shown to
asymptotically outperform all mutation-based evolutionary algorithms even on
simple problems like OneMax. Subsequently it was studied on a number of other
problems, but all of these were pseudo-Boolean.
  We aim at improving this situation by proposing an adaptation of the
$(1+(\lambda,\lambda))$ genetic algorithm to permutation-based problems. Such
an adaptation is required, because permutations are noticeably different from
bit strings in some key aspects, such as the number of possible mutations and
their mutual dependence. We also present the first runtime analysis of this
algorithm on a permutation-based problem called Ham whose properties resemble
those of OneMax. On this problem, where the simple mutation-based algorithms
have the running time of $\Theta(n^2 \log n)$ for problem size $n$, the
$(1+(\lambda,\lambda))$ genetic algorithm finds the optimum in $O(n^2)$ fitness
queries. We augment this analysis with experiments, which show that this
algorithm is also fast in practice.


  We show that the stellar surface-brightness profiles in disc
galaxies---observed to be approximately exponential---can be explained if
radial migration efficiently scrambles the individual stars' angular momenta
while conserving the circularity of the orbits and the total mass and angular
momentum. In this case the disc's distribution of specific angular momenta $j$
should be near a maximum-entropy state and therefore approximately exponential,
$dN\propto\exp(-j/\langle j\rangle)dj$. This distribution translates to a
surface-density profile that is generally not an exponential function of
radius: $\Sigma(R)\propto\exp[-R/R_e(R)]/(RR_e(R))(1+d\log v_c(R)/d\log R)$,
for a rotation curve $v_c(R)$ and $R_e(R)\equiv\langle j\rangle/v_c(R)$. We
show that such a profile matches the observed surface-brightness profiles of
disc-dominated galaxies as well as the empirical exponential profile. Disc
galaxies that exhibit population gradients cannot have fully reached a
maximum-entropy state but appear to be close enough that their
surface-brightness profiles are well-fit by this idealized model.


  We discuss theoretical predictions for the thermal Casimir force and compare
them with available experimental data. Special attention is paid to the recent
claim of the observation of that effect, as predicted by the Drude model
approach. We show that this claim is in contradiction with a number of
experiments reported so far. We suggest that the experimental errors, as
reported in support of the observation of the thermal Casimir force, are
significantly underestimated. Furthermore, the experimental data at separations
above $3\,\mu$m are shown to be in agreement not with the Drude model approach,
as is claimed, but with the plasma model. The seeming agreement of the data
with the Drude model at separations below $3\,\mu$m is explained by the use of
an inadequate formulation of the proximity force approximation.


  This paper is about a sequence of quadratic functions that enumerate the
total number of ON cells up to and including generation $n$ of the
Ulam-Warburton cellular automaton, where $n$ has the form $n_m=m\cdot2^k$


  We use transport techniques to calculate the trispectrum produced in
multiple-field inflationary models with canonical kinetic terms. Our method
allows the time evolution of the local trispectrum parameters, tauNL and gNL,
to be tracked throughout the inflationary phase. We illustrate our approach
using examples. We give a simplified method to calculate the superhorizon part
of the relation between field fluctuations on spatially flat hypersurfaces and
the curvature perturbation on uniform density slices, and obtain its
third-order part for the first time. We clarify how the 'backwards' formalism
of Yokoyama et al. relates to our analysis and other recent work. We supply
explicit formulae which enable each inflationary observable to be computed in
any canonical model of interest, using a suitable first-order ODE solver.


  Significant computational cost and memory requirements for deep neural
networks (DNNs) make it difficult to utilize DNNs in resource-constrained
environments. Binary neural network (BNN), which uses binary weights and binary
activations, has been gaining interests for its hardware-friendly
characteristics and minimal resource requirement. However, BNN usually suffers
from accuracy degradation. In this paper, we introduce "BitSplit-Net", a neural
network which maintains the hardware-friendly characteristics of BNN while
improving accuracy by using multi-bit precision. In BitSplit-Net, each bit of
multi-bit activations propagates independently throughout the network before
being merged at the end of the network. Thus, each bit path of the BitSplit-Net
resembles BNN and hardware friendly features of BNN, such as bitwise binary
activation function, are preserved in our scheme. We demonstrate that the
BitSplit version of LeNet-5, VGG-9, AlexNet, and ResNet-18 can be trained to
have similar classification accuracy at a lower computational cost compared to
conventional multi-bit networks with low bit precision (<= 4-bit). We further
evaluate BitSplit-Net on GPU with custom CUDA kernel, showing that BitSplit-Net
can achieve better hardware performance in comparison to conventional multi-bit
networks.


  In 1972, Chvatal gave a well-known sufficient condition for a graphical
sequence to be forcibly hamiltonian, and showed that in some sense his
condition is best possible. Nash-Williams gave examples of forcibly hamiltonian
n-sequences that do not satisfy Chvatla's condition for every n at least 5. In
this note we generalize the Nash-Williams examples, and use this generalization
to generate \Omega(2^n/n^.5) forcibly hamiltonian n-sequences that do not
satisfy Chvatal's condition


  We consider a Black-Scholes market in which a number of stocks and an index
are traded. The simplified Capital Asset Pricing Model is the conjunction of
the usual Capital Asset Pricing Model, or CAPM, and the statement that the
appreciation rate of the index is equal to its squared volatility plus the
interest rate. (The mathematical statement of the conjunction is simpler than
that of the usual CAPM.) Our main result is that either we can outperform the
index or the simplified CAPM holds.


  In this paper, the incremental nonlinear dynamic inversion (INDI) method is
applied to the control system design of coaxial rotor UAVs. The aerodynamic
uncertainty and anti-disturbance problems are solved in the control system
design. The designed controller gives the UAV excellent flight performance and
control robustness. An incremental gain method (IGM) is proposed for the delay
problem of the state derivative. This method has the advantages of less
calculation load and simple parameter adjustment, which provides excellent
convenience for applying INDI controllers to coaxial rotor UAVs. The principle
of IGM is demonstrated by the stability analysis method of the discrete system,
and the parameter selection strategy of the IGM is analyzed in detail by
simulation. The advantages of the controller design method are verified by
comparative flight tests of nonlinear dynamic inversion (NDI) and INDI. The
experimental results show that the average trajectory tracking error of INDI is
only 58.3% of that of NDI under the same wind speed. When the angular
acceleration delay is less than 0.06 s, IGM can easily keep the system stable.
In addition, INDI has better robustness under obvious model errors and strong
input disturbance.


  The scaling of observable properties of galaxy clusters with mass evolves
with time. Assessing the role of the evolution is crucial to study the
formation and evolution of massive halos and to avoid biases in the
calibration. We present a general method to infer the mass and the redshift
dependence, and the time-evolving intrinsic scatter of the mass-observable
relations. The procedure self-calibrates the redshift dependent completeness
function of the sample. The intrinsic scatter in the mass estimates used to
calibrate the relation is considered too. We apply the method to the scaling of
mass M_Delta versus line of sight galaxy velocity dispersion sigma_v, optical
richness, X-ray luminosity, L_X, and Sunyaev-Zel'dovich signal. Masses were
calibrated with weak lensing measurements. The measured relations are in good
agreement with time and mass dependencies predicted in the self-similar
scenario of structure formation. The lone exception is the L_X-M_Delta relation
whose time evolution is negative in agreement with formation scenarios with
additional radiative cooling and uniform preheating at high redshift. The
intrinsic scatter in the sigma_v-M_Delta relation is notably small, of order of
14 per cent. Robust predictions on the observed properties of the galaxy
clusters in the CLASH sample are provided as cases of study. Catalogs and
scripts are publicly available at http://pico.bo.astro.it/~sereno/CoMaLit/.


  Video super-resolution (VSR) technology excels in reconstructing low-quality
video, avoiding unpleasant blur effect caused by interpolation-based
algorithms. However, vast computation complexity and memory occupation hampers
the edge of deplorability and the runtime inference in real-life applications,
especially for large-scale VSR task. This paper explores the possibility of
real-time VSR system and designs an efficient and generic VSR network, termed
EGVSR. The proposed EGVSR is based on spatio-temporal adversarial learning for
temporal coherence. In order to pursue faster VSR processing ability up to 4K
resolution, this paper tries to choose lightweight network structure and
efficient upsampling method to reduce the computation required by EGVSR network
under the guarantee of high visual quality. Besides, we implement the batch
normalization computation fusion, convolutional acceleration algorithm and
other neural network acceleration techniques on the actual hardware platform to
optimize the inference process of EGVSR network. Finally, our EGVSR achieves
the real-time processing capacity of<EMAIL_ADDRESS>Compared with TecoGAN, the
most advanced VSR network at present, we achieve 85.04% reduction of
computation density and 7.92x performance speedups. In terms of visual quality,
the proposed EGVSR tops the list of most metrics (such as LPIPS, tOF, tLP,
etc.) on the public test dataset Vid4 and surpasses other state-of-the-art
methods in overall performance score. The source code of this project can be
found on https://github.com/Thmen/EGVSR.


  We study remarkable connections between twistor-string formulas for tree
amplitudes in ${\cal N}=4$ SYM and ${\cal N}=6$ ABJM, and the corresponding
momentum amplituhedron in the kinematic space of $D=4$ and $D=3$, respectively.
Based on the Veronese map to positive Grassmannians, we define a twistor-string
map from $G_{+}(2,n)$ to a $(2n{-}4)$-dimensional subspace of the 4d kinematic
space where the momentum amplituhedron of SYM lives. We provide strong evidence
that the twistor-string map is a diffeomorphism from $G_+(2,n)$ to the interior
of momentum amplituhedron; the canonical form of the latter, which is known to
give tree amplitudes of SYM, can be obtained as pushforward of that of former.
We then move to three dimensions: based on Veronese map to orthogonal positive
Grassmannian, we propose a similar twistor-string map from the moduli space
${\cal M}_{0,n}^+$ to a $(n{-}3)$-dimensional subspace of 3d kinematic space.
The image gives a new positive geometry which conjecturally serves as the
momentum amplituhedron for ABJM; its canonical form gives the tree amplitude
with reduced supersymmetries in the theory. We also show how boundaries of
compactified ${\cal M}_{0,n}^+$ map to boundaries of momentum amplituhedra for
SYM and ABJM corresponding to factorization channels of amplitudes, and in
particular for ABJM case the map beautifully excludes all unwanted channels.


  The algorithm of Tutte for constructing convex planar straight-line drawings
and the algorithm of Floater and Gotsman for constructing planar straight-line
morphs are among the most popular graph drawing algorithms. Quite surprisingly,
little is known about the resolution of the drawings produced by these
algorithms. In this paper, focusing on maximal plane graphs, we prove tight
bounds on the resolution of the planar straight-line drawings produced by
Floater's algorithm, which is a broad generalization of Tutte's algorithm.
Further, we use such a result in order to prove a lower bound on the resolution
of the drawings of maximal plane graphs produced by Floater and Gotsman's
morphing algorithm. Finally, we show that such a morphing algorithm might
produce drawings with exponentially-small resolution, even when transforming
drawings with polynomial resolution.


  In this review we concentrate on the work of K. Alex M\"uller in connection
with his activities on oxide perovskites and ferroelectrics which were central
to his research career long before he successfully discovered the first high
temperature superconductor (HTSC) together with J. G. Bednorz in 1986. Not
accidentally, but taking his long experience in perovskite ferroelectrics into
account, the first HTSC was an oxide perovskite which had never been considered
before to be superconducting.


  We present multi-colour time-series CCD photometry of the solar-age galactic
open cluster M67 (NGC 2682). About 3600 frames spread over 28 nights were
obtained with the 1.5 m Russian-Turkish and 1.2 m Mercator telescopes.
High-precision observations of the close binary stars AH Cnc, EV Cnc, ES Cnc,
the $\delta$ Scuti type systems EX Cnc and EW Cnc, and some long-period
variables belonging to M67 are presented. Three full multi-colour light curves
of the overcontact binary AH Cnc were obtained during three observing seasons.
Likewise we gathered three light curves of EV Cnc, an EB-type binary, and two
light curves of ES Cnc, a blue straggler binary. Parts of the light change of
long-term variables S1024, S1040, S1045, S1063, S1242, and S1264 are obtained.
Period variation analysis of AH Cnc, EV Cnc, and ES Cnc were done using all
times of mid-eclipse available in the literature and those obtained in this
study. In addition, we analyzed multi-colour light curves of the close binaries
and also determined new frequencies for the $\delta$ Scuti systems. The
physical parameters of the close binary stars were determined with simultaneous
solutions of multi-colour light and radial velocity curves. Finally we
determined the distance of M67 as 857(33) pc via binary star parameters, which
is consistent with an independent method from earlier studies.


  We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined
in a d-dimensional domain. The object of interest is the time-independent Green
function G_z(r,r') = < r | (z-H)^{-1} | r' >. Recently, in one dimension (1D),
the Green's function problem was solved explicitly in inverse form, with
diagonal elements of Green's function as prescribed variables. The first aim of
this paper is to extract from the 1D inverse solution such information about
Green's function which cannot be deduced directly from its definition. Among
others, this information involves universal, i.e. u(r)-independent, behavior of
Green's function close to the domain boundary. The second aim is to extend the
inverse formalism to higher dimensions, especially to 3D, and to derive the
universal form of Green's function for various shapes of the confining domain
boundary.


  In this paper, we implement an application-aware scheduler that
differentiates users running real-time applications and delay-tolerant
applications while allocating resources. This approach ensures that the
priority is given to real-time applications over delay-tolerant applications.
In our system model, we include realistic channel effects of Long Term
Evolution (LTE) system. Our application-aware scheduler runs in two stages, the
first stage is resource block allocation and the second stage is power
allocation. In the optimal solution of resource block allocation problem, each
user is inherently guaranteed a minimum Quality of Experience (QoE) while
ensuring priority given to users with real-time applications. In the power
allocation problem, a new power allocation method is proposed which utilizes
the optimal solution of the application-aware resource block scheduling
problem. As a proof of concept, we run a simulation comparison between a
conventional proportional fairness scheduler and the application-aware
scheduler. The simulation results show better QoE with the application-aware
scheduler.


  Let $f: \CN \rightarrow \C $ be a reduced polynomial map, with $D=f^{-1}(0)$,
$\U=\CN \setminus D$ and boundary manifold $M=\partial \U$. Assume that $f$ is
transversal at infinity and $D$ has only isolated singularities. Then the only
interesting non-trivial Alexander modules of $\U$ and resp. $M$ appear in the
middle degree $n$. We revisit the mixed Hodge structures on these Alexander
modules and study their associated spectral pairs (or equivariant mixed Hodge
numbers). We obtain upper bounds for the spectral pairs of the $n$-th Alexander
module of $\U$, which can be viewed as a Hodge-theoretic refinement of
Libgober's divisibility result for the corresponding Alexander polynomials. For
the boundary manifold $M$, we show that the spectral pairs associated to the
non-unipotent part of the $n$-th Alexander module of $M$ can be computed in
terms of local contributions (coming from the singularities of $D$) and
contributions from "infinity".


  We consider the tentative indication of flavor-violating Higgs boson decay
$h\to\mu\tau$ recently reported in the CMS experiment within the framework of
minimal flavor violation. Specifically, we adopt the standard model extended
with the seesaw mechanism involving right-handed neutrinos plus effective
dimension-six operators satisfying the minimal flavor violation principle in
the lepton sector. We find that it is possible to accommodate the CMS
$h\to\mu\tau$ signal interpretation provided that the right-handed neutrinos
couple to the Higgs boson in some nontrivial way. We take into account
empirical constraints from other lepton-flavor-violating processes and discuss
how future searches for the $\mu\to e\gamma$ decay and $\mu\to e$ conversion in
nuclei may further probe the lepton-flavor-violating Higgs couplings.


  In this paper we formulate embedding maps into time-frequency space related
to the Carleson operator and its variational counterpart. We prove bounds for
these embedding maps by iterating the outer measure theory of [DT15].
Introducing iterated outer $L^p$ spaces is a main novelty of this paper.
  [DT15] Yen Do and Christoph Thiele. "$L^p$ theory for outer measures and two
themes of Lennart Carleson united". In: Bulletin of the American Mathematical
Society 52.2 (2015), pp. 249-296.


  We explore the application of U-KAN, a U-Net based network enhanced with
Kolmogorov-Arnold Network (KAN) layers, for 3D brain tumor segmentation using
multi-modal MRI data. We adapt the original 2D U-KAN model to the 3D task, and
introduce a variant called UKAN-SE, which incorporates Squeeze-and-Excitation
modules for global attention. We compare the performance of U-KAN and UKAN-SE
against existing methods such as U-Net, Attention U-Net, and Swin UNETR, using
the BraTS 2024 dataset. Our results show that U-KAN and UKAN-SE, with
approximately 10.6 million parameters, achieve exceptional efficiency,
requiring only about 1/4 of the training time of U-Net and Attention U-Net, and
1/6 that of Swin UNETR, while surpassing these models across most evaluation
metrics. Notably, UKAN-SE slightly outperforms U-KAN.


  We have developed a new methodology and a time-domain software package for
the estimation of the oscillation frequency and the phase noise spectrum of
non-linear noisy microwave circuits based on the direct integration of the
system of stochastic differential equations representing the circuit. Our
theoretical evaluations can be used in order to make detailed comparisons with
the experimental measurements of phase noise spectra in selected oscillating
circuits.


  In this short note a differential version of the classical Weil descent is
established in all characteristics. This yields a ready-to-deploy tool of
differential restriction of scalars for differential varieties over finite
differential field extensions.


  Adult learning is increasingly recognized as a crucial way for personal
development and societal progress. It however is challenging, and adult
learners face unique challenges such as balancing education with other life
responsibilities. Collecting feedback from adult learners is effective in
understanding their concerns and improving learning experiences, and social
networks provide a rich source of real-time sentiment data from adult learners.
Machine learning technologies especially large language models (LLMs) perform
well in automating sentiment analysis. However, none of such models is
specialized for adult learning with accurate sentiment understanding. In this
paper, we present A-Learn, which enhances adult learning sentiment analysis by
customizing existing general-purpose LLMs with domain-specific datasets for
adult learning. We collect adult learners' comments from social networks and
label the sentiment of each comment with an existing LLM to form labelled
datasets tailored for adult learning. The datasets are used to customize
A-Learn from several base LLMs. We conducted experimental studies and the
results reveal A-Learn's competitive sentiment analysis performance, achieving
up to 91.3% accuracy with 20% improvement over the base LLM. A-Learn is also
employed for word cloud analysis to identify key concerns of adult learners.
The research outcome of this study highlights the importance of applying
machine learning with educational expertise for teaching improvement and
educational innovations that benefit adult learning and adult learners.


  We present new high spatial resolution HST/ACS imaging of NGC 1140 and high
spectral resolution VLT/UVES spectroscopy of its central star-forming region.
The central region contains several clusters, the two brightest of which are
clusters 1 and 6 from Hunter, O'Connell & Gallagher, located within
star-forming knots A and B, respectively. Nebular analysis indicates that the
knots have an LMC-like metallicity of 12 + log(O/H) = 8.29 +/- 0.09. According
to continuum subtracted H alpha ACS imaging, cluster 1 dominates the nebular
emission of the brighter knot A. Conversely, negligible nebular emission in
knot B originates from cluster 6. Evolutionary synthesis modelling implies an
age of 5 +/- 1 Myr for cluster 1, from which a photometric mass of (1.1 +/-
0.3) x 10^6 Msun is obtained. For this age and photometric mass, the modelling
predicts the presence of ~5900 late O stars within cluster 1. Wolf-Rayet
features are observed in knot A, suggesting 550 late-type WN and 200 early-type
WC stars. Therefore, N(WR)/N(O) ~ 0.1, assuming that all the WR stars are
located within cluster 1. The velocity dispersions of the clusters were
measured from constituent red supergiants as sigma ~ 23 +/- 1 km/s for cluster
1 and sigma ~ 26 +/- 1 km/s for cluster 6. Combining sigma with half-light
radii of 8 +/- 2 pc and 6.0 +/- 0.2 pc measured from the F625W ACS image
implies virial masses of (10 +/- 3) x 10^6 Msun and (9.1 +/- 0.8) x 10^6 Msun
for clusters 1 and 6, respectively. The most likely reason for the difference
between the dynamical and photometric masses of cluster 1 is that the velocity
dispersion of knot A is not due solely to cluster 1, as assumed, but has an
additional component associated with cluster 2.


  The identification of nodes occupying important positions in a network
structure is crucial for the understanding of the associated real-world system.
Usually, betweenness centrality is used to evaluate a node capacity to connect
different graph regions. However, we argue here that this measure is not
adapted for that task, as it gives equal weight to "local" centers (i.e. nodes
of high degree central to a single region) and to "global" bridges, which
connect different communities. This distinction is important as the roles of
such nodes are different in terms of the local and global organisation of the
network structure. In this paper we propose a decomposition of betweenness
centrality into two terms, one highlighting the local contributions and the
other the global ones. We call the latter bridgeness centrality and show that
it is capable to specifically spot out global bridges. In addition, we
introduce an effective algorithmic implementation of this measure and
demonstrate its capability to identify global bridges in air transportation and
scientific collaboration networks.