  We present multi-frequency radio observations from the afterglow of GRB
980519 beginning 7.2 hours after the gamma-ray burst and ending 63 days later.
The fast decline in the optical and X-ray light curves for this burst has been
interpreted either as afterglow emission originating from a collimated outflow
-- a jet -- or the result of a blast wave propagating into a medium whose
density is shaped by the wind of an evolved massive star. These two models
predict divergent behavior for the radio afterglow, and therefore, radio
observations are capable, in principle, of discriminating between the two. We
show that a wind model describes the subsequent evolution of the radio
afterglow rather well. However, we see strong modulation of the light curve,
which we interpret as diffractive scintillation. These variations prevent us
from decisively rejecting the jet model.


  We study the impact of tunable parameters on computational intensity (i.e.,
inverse code balance) and energy consumption of multicore-optimized wavefront
diamond temporal blocking (MWD) applied to different stencil-based update
schemes. MWD combines the concepts of diamond tiling and multicore-aware
wavefront blocking in order to achieve lower cache size requirements than
standard single-core wavefront temporal blocking. We analyze the impact of the
cache block size on the theoretical and observed code balance, introduce loop
tiling in the leading dimension to widen the range of applicable diamond sizes,
and show performance results on a contemporary Intel CPU. The impact of code
balance on power dissipation on the CPU and in the DRAM is investigated and
shows that DRAM power is a decisive factor for energy consumption, which is
strongly influenced by the code balance. Furthermore we show that highest
performance does not necessarily lead to lowest energy even if the clock speed
is fixed.


  The strong decays of the $D_{s1}(2710)$ and $D_{sJ}(2860)$ are investigated
in the framework of the $^3P_0$ model. Its decay properties newly reported by
the BaBar Collaboration can be reasonably accounted for in the presence of the
$D_{s1}(2710)$ being a mixture of the $D_s(2 ^3S_1)$ and $D_s(1 ^3D_1)$. The
orthogonal partner of the $D_{s1}(2710)$ is expected to have a mass of about
$2.66\sim 2.9$ GeV in quark models and a width of about $40\sim 60$ MeV in the
$^3P_0$ model. The predicted decay properties turn out to be consistent with
the BaBar's new data in both the orthogonal partner of the $D_{s1}(2710)$ and
the $D_s(1 ^3D_3)$ interpretations for the $D_{sJ}(2860)$. The available
experimental information is not enough to distinguish these two possibilities.
The $E1$ radiative transitions of the $D_{s1}(2710)$ and $D_{sJ}(2860)$ are
also studied. We tend to conclude that the $D_{s1}(2710)$ can be identified as
a mixture of the $D_s(2 ^3S_1)$ and $D_s(1 ^3D_1)$, and the $D_{sJ}(2860)$
could be either the orthogonal partner of the $D_{s1}(2710)$ or the $D_s(1
^3D_3)$. Further experimental information on the $D_{sJ}(2860)$ in the
$D_s\eta$, $D^\ast_s\eta$, and $DK^\ast$ channels is needed.


  Modern software systems become too complex to be tested and validated.
Detecting software partial failures in complex systems at runtime assist to
handle software unintended behaviors, avoiding catastrophic software failures
and improving software runtime availability. These detection techniques aim to
find the manifestation of faults before they finally lead to unavoidable
failures, thus supporting following runtime fault tolerant techniques. We
review the state of the art articles and find that the content failures account
for the majority of all kinds of software failures, but its detection methods
are rarely studied. In this work, we propose a novel failure detection
indicator based on the software runtime dynamic execution information for
software content failures. The runtime information is recorded during software
execution, then transformed to a measure named runtime entropy and finally fed
into machine learning models. The machine learning models are built to classify
the intended and unintended behaviors of the objected software systems. A
series of controlled experiments on several open source projects are conducted
to prove the feasibility of the method. We also evaluate the accuracy of
machine learning models built in this work.


  Stars like our Sun form in self-gravitating dense and cold structures within
interstellar clouds, called pre-stellar cores. Although much is known about the
physical structure of dense clouds just before and soon after the switch-on of
a protostar, the central few thousand astronomical units (au) of pre-stellar
cores are unexplored. It is within these central regions that stellar systems
assemble and fragmentation may take place, with the consequent formation of
binaries and multiple systems. We present ALMA Band 6 observations (ACA and 12m
array) of the dust continuum emission of the 8 Msun pre-stellar core L1544,
with angular resolution of 2'' x 1.6'' (linear resolution 270 au x 216 au).
Within the primary beam, a compact region of 0.1 Msun, which we call a
"kernel", has been unveiled. The kernel is elongated, with a central flat zone
with radius Rker ~ 10'' (~ 1400 au). The average number density within Rker is
~1 x 10^6 cm^{-3}, with possible local density enhancements. The region within
Rker appears to have fragmented, but detailed analysis shows that similar
substructure can be reproduced by synthetic interferometric observations of a
smooth centrally concentrated dense core with a similar central flat zone. The
presence of a smooth kernel within a dense core is in agreement with non-ideal
magneto-hydro-dynamical simulations of a contracting cloud core with a peak
number density of 1 x 10^7 cm^{-3}. Dense cores with lower central densities
are completely filtered out when simulated 12m-array observations are carried
out. These observations demonstrate that the kernel of dynamically evolved
dense cores can be investigated at high angular resolution with ALMA.


  The Wiener index W(G) of a graph G is the sum of distances between all
unordered pairs of its vertices. Dobrynin and Mel'nikov [in: Distance in
Molecular Graphs - Theory, 2012, p. 85-121] propose the study of estimates for
extremal values of the ratio R_k(G) = W(L^k(G))/W(G) where L^k(G) denotes the
k-th iterated line graph of G. Hri\v{n}\'akov\'a, Knor and \v{S}krekovski [Art
Discrete Appl. Math. 1 (2018) #P1.09] prove that for each k>2, the path P_n has
the smallest value of the ratio R_k among all trees of large order n, and they
conjecture that the same holds for the case k=2. We give a counterexample of
every order n>21 to this conjecture.


  The 3d Heisenberg model is studied from a dual point of view. It is shown
that the disordered phase corresponds to condensation of vortices in the
vacuum, and the critical indices are computed from the corresponding disorder
parameter.


  In the field of holomorphic dynamics in one complex variable, hedgehog is the
local invariant set arising about a Cremer point and endowed with a very
complicate shape as well as relating to very weak numerical conditions. We give
a solution to the open problem of its digital visualization, featuring either a
time saving approach and a far-reaching insight.


  We present HotStuff, a leader-based Byzantine fault-tolerant replication
protocol for the partially synchronous model. Once network communication
becomes synchronous, HotStuff enables a correct leader to drive the protocol to
consensus at the pace of actual (vs. maximum) network delay--a property called
responsiveness--and with communication complexity that is linear in the number
of replicas. To our knowledge, HotStuff is the first partially synchronous BFT
replication protocol exhibiting these combined properties. HotStuff is built
around a novel framework that forms a bridge between classical BFT foundations
and blockchains. It allows the expression of other known protocols (DLS, PBFT,
Tendermint, Casper), and ours, in a common framework.
  Our deployment of HotStuff over a network with over 100 replicas achieves
throughput and latency comparable to that of BFT-SMaRt, while enjoying linear
communication footprint during leader failover (vs. quadratic with BFT-SMaRt).


  Scheduling communication traffic in networks of event-triggered control (ETC)
systems is challenging, as their sampling times are unknown, hindering
application of ETC in networks. In previous work, finite-state abstractions
were created, capturing the sampling behaviour of LTI ETC systems with
quadratic triggering functions. Offering an infinite-horizon look to all
sampling patterns of an ETC system, such abstractions can be used for
scheduling of ETC traffic. Here we significantly extend this framework, by
abstracting perturbed uncertain nonlinear ETC systems with general triggering
functions. To construct an ETC system's abstraction: a) the state space is
partitioned into regions, b) for each region an interval is determined,
containing all intersampling times of points in the region, and c) the
abstraction's transitions are determined through reachability analysis. To
determine intervals and transitions, we devise algorithms based on reachability
analysis. For partitioning, we propose an approach based on isochronous
manifolds, resulting into tighter intervals and providing control over them,
thus containing the abstraction's non-determinism. Simulations showcase our
developments.


  Shortcuts to adiabaticity (STA) are fast methods to realize the same final
state evolution of quantum adiabatic process. We develop a general theory to
construct a new kind of STA by solely sampling the points of the adiabatic path
of the original adiabatic Hamiltonian. In contrast to previous methods, our
approach does not require any additional control resources, has inherent
robustness, and does not use any complicated unitary transformation. Based on
path sampling, the resulting STA protocols are simple and can avoid points of
adiabatic path that are challenging to implement. As applications of our
theory, we demonstrate reduction of the effects of both dissipation and
dephasing noise by a novel robust three-level control, as well as reliable and
fast ground state evolution in an adiabatic quantum computing model. Our theory
offers a new route to design robust and fast control methods for general
quantum systems.


  We present observations of two new hydrogen-poor superluminous supernovae
(SLSN-I), iPTF15esb and iPTF16bad, showing late-time H-alpha emission with line
luminosities of (1-3)e+41 erg/s and velocity widths of (4000-6000) km/s.
Including the previously published iPTF13ehe, this makes up a total of three
such events to date. iPTF13ehe is one of the most luminous and the slowest
evolving SLSNe-I, whereas the other two are less luminous and fast decliners.
We interpret this as a result of the ejecta running into a neutral H-shell
located at a radius of ~ 1.0e+16cm. This implies that violent mass loss must
have occurred several decades before the supernova explosion. Such a short time
interval suggests that eruptive mass loss could be common shortly prior to the
death of a massive star as a SLSN. And more importantly, helium is unlikely to
be completely stripped off the progenitor stars and could be present in the
ejecta. It is a mystery why helium features are not detected, even though
non-thermal energy sources, capable of ionizing He atoms, may exist as
suggested by the O II absorption series in the early time spectra. At late
times (+240d), our spectra appear to have intrinsically lower [O I]6300A
luminosities than that of SN2015bn and SN2007bi, possibly an indication of
smaller oxygen masses (<10-30Msun). The blue-shifted H-alpha emission relative
to the hosts for all three events may be in tension with the binary star model
proposed for iPTF13ehe. Finally, iPTF15esb has a peculiar light curve with
three peaks separated from one another by ~ 22 days. The LC undulation is
higher in bluer bands. One possible explanation is eject-CSM interaction.


  Experimentation with software prototypes plays a fundamental role in software
engineering research. In contrast to many other scientific disciplines,
however, explicit support for this key activity in software engineering is
relatively small. While some approaches to improve this situation have been
proposed by the software engineering community, experiments are still very
difficult and sometimes impossible to replicate. In this paper, we propose the
concept of an experimentation workbench as a means of explicit support for
experimentation in software engineering research. In particular, we discuss
core requirements that an experimentation workbench should satisfy in order to
qualify as such and to offer a real benefit for researchers. Beyond their core
benefits for experimentation, we stipulate that experimentation workbenches
will also have benefits in regard to reproducibility and repeatability of
software engineering research. Further, we illustrate this concept with a
scenario and a case study, and describe relevant challenges as well as our
experience with experimentation workbenches.


  We demonstrate that the profile of the space-resolved spectral function at
finite temperature provides a signature of Wigner localization for electrons in
quantum wires and semiconducting carbon nanotubes. Our numerical evidence is
based on the exact diagonalization of the microscopic Hamiltonian of few
particles interacting in gate-defined quantum dots. The minimal temperature
required to suppress residual exchange effects in the spectral function image
of (nanotubes) quantum wires lies in the (sub-) Kelvin range.


  The operation of superconducting coplanar waveguide cavities, as used for
circuit quantum electrodynamics and kinetic inductance detectors, in
perpendicular magnetic fields normally leads to a reduction of the device
performance due to energy dissipating Abrikosov vortices. We experimentally
investigate the vortex induced energy losses in such Nb resonators with
different spatial distributions of micropatterned pinning sites (antidots) by
transmission spectroscopy measurements at 4.2 K. In comparison to resonators
without antidots we find a significant reduction of vortex induced losses and
thus increased quality factors over a broad range of frequencies and applied
powers in moderate fields.


  We extend the paraunitary (PU) theory for complementary pairs to comple-
mentary sets and complete complementary codes (CCC) by proposing a new PU
construction. A special, but very important case of complementary sets (and CC-
C), based on standard delays, is analyzed in details and a new 'Radix-M
generator' (RM-G) is presented. The RM-G can be viewed as a generalization of
the Boolean generator for complementary pairs. An efficient correlator for
standard complemen- tary sets and CCC is also presented. Finally, examples of
polyphase, QAM and hexagonal PU sets of three sequences are given.


  The NA62 experiment at CERN, configured in beam-dump mode, has searched for
dark photon decays in flight to electron-positron pairs using a sample of
$1.4\times 10^{17}$ protons on dump collected in 2021. No evidence for a dark
photon signal is observed. The combined result for dark photon searches in
lepton-antilepton final states is presented and a region of the parameter space
is excluded at 90% CL, improving on previous experimental limits for dark
photon mass values between 50 and 600 MeV$/c^2$ and coupling values in the
range $10^{-6}$ to $4\times10^{-5}$. An interpretation of the $e^+ e^-$ search
result in terms of the emission and decay of an axion-like particle is also
presented.


  The spontaneous spreading of non-volatile liquid droplets on solid substrates
poses a classic problem in the context of wetting phenomena. It is well known
that the spreading of a macroscopic droplet is in many cases accompanied by a
thin film of macroscopic lateral extent, the so-called precursor film, which
emanates from the three-phase contact line region and spreads ahead of the
latter with a much higher speed. Such films have been usually associated with
liquid-on-solid systems, but in the last decade similar films have been
reported to occur in solid-on-solid systems. While the situations in which the
thickness of such films is of mesoscopic size are rather well understood, an
intriguing and yet to be fully understood aspect is the spreading of
microscopic, i.e., molecularly thin films. Here we review the available
experimental observations of such films in various liquid-on-solid and
solid-on-solid systems, as well as the corresponding theoretical models and
studies aimed at understanding their formation and spreading dynamics. Recent
developments and perspectives for future research are discussed.


  Multifractal properties of wave functions in a disordered system can be
derived from self-consistent theory of localization by Vollhardt and Woelfle. A
diagrammatic interpretation of results allows to obtain all scaling relations
used in numerical experiments. The arguments are given that the one-loop Wegner
result for a space dimension d=2+\epsilon may appear to be exact, so the
multifractal spectrum is strictly parabolical. The \sigma-models are shown to
be deficient at the four-loop level and the possible reasons of that are
discussed. The extremely slow convergence to the thermodynamic limit is
demonstrated. The open question on the relation between multifractality and a
spatial dispersion of the diffusion coefficient D(\omega,q) is resolved in the
compromise manner due to ambiguity of the D(\omega,q) definition. Comparison is
made with the extensive numerical material.


  Bursting is a phenomenon found in a variety of physical and biological
systems. For example, in neuroscience, bursting is believed to play a key role
in the way information is transferred in the nervous system. In this work, we
propose a model that, appropriately tuned, can display several types of
bursting behaviors. The model contains two subsystems acting at different
timescales. For the fast subsystem we use the planar unfolding of a high
codimension singularity. In its bifurcation diagram, we locate paths that
underly the right sequence of bifurcations necessary for bursting. The slow
subsystem steers the fast one back and forth along these paths leading to
bursting behavior. The model is able to produce almost all the classes of
bursting predicted for systems with a planar fast subsystems. Transitions
between classes can be obtained through an ultra-slow modulation of the model's
parameters. A detailed exploration of the parameter space allows predicting
possible transitions. This provides a single framework to understand the
coexistence of diverse bursting patterns in physical and biological systems or
in models.


  The combined use of multiple modalities enables accurate pedestrian detection
under poor lighting conditions by using the high visibility areas from these
modalities together. The vital assumption for the combination use is that there
is no or only a weak misalignment between the two modalities. In general,
however, this assumption often breaks in actual situations. Due to this
assumption's breakdown, the position of the bounding boxes does not match
between the two modalities, resulting in a significant decrease in detection
accuracy, especially in regions where the amount of misalignment is large. In
this paper, we propose a multi-modal Faster-RCNN that is robust against large
misalignment. The keys are 1) modal-wise regression and 2) multi-modal IoU for
mini-batch sampling. To deal with large misalignment, we perform bounding box
regression for both the RPN and detection-head with both modalities. We also
propose a new sampling strategy called "multi-modal mini-batch sampling" that
integrates the IoU for both modalities. We demonstrate that the proposed
method's performance is much better than that of the state-of-the-art methods
for data with large misalignment through actual image experiments.


  Effective resistance is an important metric that measures the similarity of
two vertices in a graph. It has found applications in graph clustering,
recommendation systems and network reliability, among others. In spite of the
importance of the effective resistances, we still lack efficient algorithms to
exactly compute or approximate them on massive graphs.
  In this work, we design several \emph{local algorithms} for estimating
effective resistances, which are algorithms that only read a small portion of
the input while still having provable performance guarantees. To illustrate,
our main algorithm approximates the effective resistance between any vertex
pair $s,t$ with an arbitrarily small additive error $\varepsilon$ in time
$O(\mathrm{poly}(\log n/\varepsilon))$, whenever the underlying graph has
bounded mixing time. We perform an extensive empirical study on several
benchmark datasets, validating the performance of our algorithms.


  We investigate the transverse momentum dependent (TMD) quark and gluon
distribution functions in the modified chiral quark model ($\chi QM$).
Calculations of the TMD quark and gluon densities, using the modified $\chi QM$
are done for the first time in this article. For this propose we first
formulate the TMD interactions that occur in the $\chi QM$ at low $Q^2$ scale
($Q^2=0.35~ GeV^2$) and then obtain the TMD parton distributions inside the
proton, considering the interactions. To this end, we need to compute the TMD
bare quark distributions. These TMD bare densities are calculated, using the
solution of Dirac equation with a squared radial symmetry potential . It is
shown that our results consist appropriate behavior which are expecting for the
TMD parton distributions.


  Satellite aerosol products have been widely used to retrieve ground PM2.5
concentration because of its wide coverage and continuously spatial
distribution. While more and more studies focus on the retrieval algorithm, we
find that the relationship between PM2.5 concentration and satellite AOD has
not been fully discussed in China. Is satellite AOD always a good indicator for
PM2.5 in different regions and can AOD still be employed to retrieve PM2.5 with
pollution conditions changing in these years remain unclear. In this study, the
relationships between PM2.5 and AOD were investigated in 368 cities in China
for a continuous period from February 2013 to December 2017, at different time
and regional scales. Pearson correlation coefficients and PM2.5/AOD ratio were
used as the indicator. Firstly, we concluded the relationship of PM2.5 and AOD
in terms of spatiotemporal variations. Then the impact of meteorological
factors, aerosol size and topography were discussed. Finally, a GWR retrieval
experiment was conducted to find out how was the retrieval accuracy changing
with the varying of PM2.5-AOD relationship. We found that spatially the
correlation is higher in Beijing-Tianjin-Hebei and Chengyu region and weaker in
coastal areas such as Yangtze River Delta and Pearl River Delta. The PM2.5/AOD
ratio has obvious North-South difference with a high ratio in north China and a
lower ratio in south China. Temporally, PM2.5/AOD ratio is higher in winter and
lower in summer, the correlation coefficient tends to be higher in May and
September. As for interannual variations from 2013 to 2017, we detected a
declining tendency on PM2.5/AOD ratio. The accuracy of GWR retrievals were
decreasing too, which may imply that AOD may not be a good indicator for PM2.5
in the future.


  We discuss a phase transition in spin glass models which have been rarely
considered in the past, namely the phase transition that may take place when
two real replicas are forced to be at a larger distance (i.e. at a smaller
overlap) than the typical one. In the first part of the work, by solving
analytically the Sherrington-Kirkpatrick model in a field close to its critical
point, we show that even in a paramagnetic phase the forcing of two real
replicas to an overlap small enough leads the model to a phase transition where
the symmetry between replicas is spontaneously broken. More importantly, this
phase transition is related to the de Almeida-Thouless (dAT) critical line. In
the second part of the work, we exploit the phase transition in the overlap
between two real replicas to identify the critical line in a field in
finite-dimensional spin glasses. This is a notoriously difficult computational
problem, because of huge finite-size corrections. We introduce a new method of
analysis of Monte Carlo data for disordered systems, where the overlap between
two real replicas is used as a conditioning variate. We apply this analysis to
equilibrium measurements collected in the paramagnetic phase in a field, $h>0$
and $T_c(h)<T<T_c(h=0)$, of the $d=1$ spin glass model with long-range
interactions decaying fast enough to be outside the regime of validity of the
mean-field theory. We thus provide very reliable estimates for the
thermodynamic critical temperature in a field.


  We show how to construct $(1+\varepsilon)$-spanner over a set $P$ of $n$
points in $\mathbb{R}^d$ that is resilient to a catastrophic failure of nodes.
Specifically, for prescribed parameters $\vartheta,\varepsilon \in (0,1)$, the
computed spanner $G$ has $ O\bigl(\varepsilon^{-c} \vartheta^{-6} n \log n
(\log\log n)^6 \bigr) $ edges, where $c= O(d)$. Furthermore, for any $k$, and
any deleted set $B \subseteq P$ of $k$ points, the residual graph $G \setminus
B$ is $(1+\varepsilon)$-spanner for all the points of $P$ except for
$(1+\vartheta)k$ of them. No previous constructions, beyond the trivial clique
with $O(n^2)$ edges, were known such that only a tiny additional fraction
(i.e., $\vartheta$) lose their distance preserving connectivity.
  Our construction works by first solving the exact problem in one dimension,
and then showing a surprisingly simple and elegant construction in higher
dimensions, that uses the one-dimensional construction in a black box fashion.


  We employ values of the colour dipole cross section extracted from
electroproduction and photoproduction data to show that gluon saturation
effects are not required by the current HERA data but will become important in
the THERA energy region.


  Optically detected magnetic resonance (ODMR) is a way to characterize the NV
centers. Recently, a remarkably sharp dip was observed in the ODMR with a
high-density ensemble of NV centers, and this was reproduced by a theoretical
model in [Zhu et al., Nature Communications 5, 3424 (2014)], showing that the
dip is a consequence of the spin-1 properties of the NV centers. Here, we
present much more details of analysis to show how this model can be applied to
investigate the properties of the NV centers. By using our model, we have
reproduced the ODMR with and without applied magnetic fields. Also, we
theoretically investigate how the ODMR is affected by the typical parameters of
the ensemble NV centers such as strain distributions, inhomogeneous magnetic
fields, and homogeneous broadening width. Our model could provide a way to
estimate these parameters from the ODMR, which would be crucial to realize
diamond-based quantum information processing.


  The paper considers some concepts of nonuniform asymptotic stability for
skew-evolution semiflows on Banach spaces. The obtained results clarify
differences between the uniform and nonuniform cases. Some examples are
included to illustrate the results.


  We develop a new scheme of proofs for spectral theory of the $N$-body
Schr\"odinger operators, reproducing and extending a series of sharp results
under minimum conditions. Our main results include Rellich's theorem, limiting
absorption principle bounds, microlocal resolvent bounds, H\"older continuity
of the resolvent and a microlocal Sommerfeld uniqueness result. We present a
new proof of Rellich's theorem which is unified with exponential decay
estimates studied previously only for $L^2$-eigenfunctions. Each pair-potential
is a sum of a long-range term with first order derivatives, a short-range term
without derivatives and a singular term of operator- or form-bounded type, and
the setup includes hard-core interaction. Our proofs consist of a systematic
use of commutators with `zeroth order' operators. In particular they do not
rely on Mourre's differential inequality technique.


  Phylogenetics has seen an steady increase in substitution model complexity,
which requires increasing amounts of computational power to compute
likelihoods. This model complexity motivates strategies to approximate the
likelihood functions for branch length optimization and Bayesian sampling. In
this paper, we develop an approximation to the one-dimensional likelihood
function as parametrized by a single branch length. This new method uses a
four-parameter surrogate function abstracted from the simplest phylogenetic
likelihood function, the binary symmetric model. We show that it offers a
surrogate that can be fit over a variety of branch lengths, that it is
applicable to a wide variety of models and trees, and that it can be used
effectively as a proposal mechanism for Bayesian sampling. The method is
implemented as a stand-alone open-source C library for calling from
phylogenetics algorithms; it has proven essential for good performance of our
online phylogenetic algorithm sts.


  In this paper, we first study one-dimensional quadratic backward stochastic
differential equations driven by $G$-Brownian motions ($G$-BSDEs) with
unbounded terminal values. With the help of a $\theta$-method of Briand and Hu
[4] and nonlinear stochastic analysis techniques, we propose an approximation
procedure to prove existence and uniqueness result when the generator is convex
(or concave) and terminal value is of exponential moments of arbitrary order.
Finally, we also establish the well-posedness of multi-dimensional G-BSDEs with
diagonally quadratic generators.


  We discuss the general form of the mass terms that can appear in the
effective field theories of coordinate-dependent compactifications a la
Scherk-Schwarz. As an illustrative example, we consider an interacting
five-dimensional theory compactified on the orbifold S^1/Z_2, with a fermion
subject to twisted periodicity conditions. We show how the same physics can be
described by equivalent effective Lagrangians for periodic fields, related by
field redefinitions and differing only in the form of the five-dimensional mass
terms. In a suitable limit, these mass terms can be localized at the orbifold
fixed points. We also show how to reconstruct the twist parameter from any
given mass terms of the allowed form. Finally, after mentioning some possible
generalizations of our results, we re-discuss the example of brane-induced
supersymmetry breaking in five-dimensional Poincare' supergravity, and comment
on its relation with gaugino condensation in M-theory.


  We present new additive results for DMP elements in a Banach algebra with
involution. The necessary and sufficient conditions under which the sum of two
DMP elements is DMP are investigated.


  In this paper, we review two related aspects of field theory: the modeling of
the fields by means of exterior algebra and calculus, and the derivation of the
field dynamics, i.e., the Euler-Lagrange equations, by means of the stationary
action principle. In contrast to the usual tensorial derivation of these
equations for field theories, that gives separate equations for the field
components, two related coordinate-free forms of the Euler-Lagrange equations
are derived. These alternative forms of the equations, reminiscent of the
formulae of vector calculus, are expressed in terms of vector derivatives of
the Lagrangian density. The first form is valid for a generic Lagrangian
density that only depends on the first-order derivatives of the field. The
second form, expressed in exterior algebra notation, is specific to the case
when the Lagrangian density is a function of the exterior and interior
derivatives of the multivector field. As an application, a Lagrangian density
for generalized electromagnetic multivector fields of arbitrary grade is
postulated and shown to have, by taking the vector derivative of the Lagrangian
density, the generalized Maxwell equations as Euler--Lagrange equations.


  We present the explicit expressions in N=8 supergravity for the bosonic
4-particle tree and 1-loop amplitudes including vectors and scalars. We also
present the candidate 4-point UV divergences in a form of helicity amplitudes,
corresponding to 3-loop manifestly N=8 supersymmetric and Lorentz covariant
counterterm. This may shed some light on the 3-loop finiteness of N=8 SG and on
a conjectured higher loop finiteness. We perform a supersymmetric deformation
to complex momentum of the 4-point generating function including higher-loop
counterterms and the 1-loop UV finite amplitudes. Using the explicit form of
the scalar part of the 3-loop counterterm and of the 1-loop UV finite scalar
4-point amplitudes we find that they both have an unbroken E7 symmetry. We
derive from E7 symmetry the low-energy theorem for the 1-loop n-point
amplitudes.


  Under certain general conditions in an expanding universe, the luminosity
distance (d_L) and angular diameter distance (d_A) are connected by the
Etherington relation as d_L = d_A (1 + z)^2. The Tolman test suggests the use
of objects of known surface brightness, to test this relation. In this letter,
we propose the use of redshifted 21 cm signal from disk galaxies, where neutral
hydrogen (HI) masses are seen to be almost linearly correlated with surface
area, to conduct a new Tolman test. We construct simulated catalogs of
galaxies, with the observed size-luminosity relation and realistic redshift
evolution of HI mass functions, likely to be detected with the planned Square
Kilometer Array (SKA). We demonstrate that these observations may soon provide
the best implementation of the Tolman test to detect any violation of the
Etherington relation.


  We present maps of 7 young massive molecular clumps within 5 target regions
in the C18O (J=1-0) line emission, using the Nobeyama 45m telescope. These
clumps, which are not associated with clusters, lie at distances between 0.7 to
2.1 kpc. We find C18O clumps with radii of 0.5-1.7 pc, masses of 470-4200 Msun,
and velocity widths of 1.4-3.3 km/s. All of the clumps are massive and
approximately in virial equilibrium, suggesting they will potentially form
clusters. Three of our target regions are associated with H II regions ("CWHRs"
from Clump with H II Regions), and the other two are without H II regions
(CWOHRs). The C18O clumps can be classified into two morphological types: CWHRs
shape a filamentary or shell-like structure, CWOHRs are spherical. The two
CWOHRs have systematic velocity gradients. Using the publicly released WISE
database, Class I and Class II protostellar candidates were identified within
the C18O clumps. The fraction of the Class I candidates among all YSO
candidates (Class I+Class II) is > 50 % in CWHRs, and < 50 % in CWOHRs. We
conclude that effects from the H II regions can be seen in (1) spatial
distributions of the clumps: filamentary or shell-like structure running along
the H II regions, (2) velocity structures of the clumps: large velocity
dispersion along shells, and (3) small age spreads of YSOs. The small spread in
age of the YSOs show that the presence of H II regions tend to trigger coeval
cluster formation.


  Computing entanglement entropy and its cousins is often challenging even in
the simplest continuum and lattice models, partly because such entropies depend
nontrivially on all geometric characteristics of the entangling region. Quantum
information measures between two or more regions are even more complicated, but
contain more, and universal, information. In this paper, we focus on R\'{e}nyi
entropy and information of the order $n=2$. For a free field theory, we show
that these quantities are mapped to the change of the thermodynamic free energy
by introducing boundaries subject to Dirichlet and Neumann boundary conditions
in one higher dimension. This mapping allows us to exploit the powerful tools
available in the context of thermal Casimir effect, specifically a multipole
expansion suited for computing the R\'{e}nyi information between
arbitrarily-shaped regions. In particular, we compute the R\'{e}nyi information
between two disk-shaped regions at an arbitrary separation distance. We provide
an alternative representation of the R\'{e}nyi information as a sum over
closed-loop polymers, which establishes a connection to purely entropic
effects, and proves useful in deriving information inequalities. Finally, we
discuss extensions of our results beyond free field theories.


  In this paper, we prove that if $M_t\subset \mathbb{R}^{n+1}$, $2\leq n\leq
6$, is the $n$-dimensional closed embedded $\mathcal{F}-$stable solution to
mean curvature flow with mean curvature of $M_t$ is uniformly bounded on
$[0,T)$ for $T<\infty$, then the flow can be smoothly extended over time $T$.


  The BCS-BEC crossover and phase diagram for asymmetric nuclear superfluid
with pairings in isospin I = 0 and I = 1 channels are investigated at mean
field level, by using a density dependent nucleon-nucleon potential. Induced by
the in-medium nucleon mass and density dependent coupling constants,
neutron-proton Cooper pairs could be in BEC state at sufficiently low density,
but there is no chance for the BEC formation of neutron-neutron and
proton-proton pairs at any density and asymmetry. We calculate the phase
diagram in asymmetry-temperature plane for weakly interacting nuclear
superfluid, and find that including the I = 1 channel changes significantly the
phase structure at low temperature. There appears a new phase with both I = 0
and I = 1 pairings at low temperature and low asymmetry, and the gapless state
in any phase with I = 1 pairing is washed out and all excited nucleons are
fully gapped.


  We construct finitely generated nil algebras with prescribed growth rate. In
particular, any increasing submultiplicative function is realized as the growth
function of a nil algebra up to a polynomial error term and an arbitrarily slow
distortion. We then move on to examples of nil algebras and domains with
strongly oscillating growth functions and construct primitive algebras for
which the Gelfand-Kirillov dimension is strictly sub-additive with respect to
tensor products, thus answering a question raised by Krempa-Okninski and
Krause-Lenagan.


  Robust multi-level spin memory with the ability to write information
electrically is a long-sought capability in spintronics, with great promise for
applications. Here we achieve nonvolatile and highly energy-efficient
magnetization switching in a single-material device formed of van-der-Waals
topological ferromagnet Fe3GeTe2, whose magnetic information can be readily
controlled by a tiny current. Furthermore, the switching current density and
power dissipation are about 400 and 4000 times smaller than those of the
existing spin-orbit-torque magnetic random access memory based on conventional
magnet/heavy-metal systems. Most importantly, we also demonstrate multi-level
states, switched by electrical current, which can dramatically enhance the
information capacity density and reduce computing costs. Thus, our observations
combine both high energy efficiency and large information capacity density in
one device, showcasing the potential applications of the emerging field of
van-der-Waals magnets in the field of spin memory and spintronics.


  One popular way to compute the CANDECOMP/PARAFAC (CP) decomposition of a
tensor is to transform the problem into a sequence of overdetermined least
squares subproblems with Khatri-Rao product (KRP) structure involving factor
matrices. In this work, based on choosing the factor matrix randomly, we
propose a mini-batch stochastic gradient descent method with importance
sampling for those special least squares subproblems. Two different sampling
strategies are provided. They can avoid forming the full KRP explicitly and
computing the corresponding probabilities directly. The adaptive step size
version of the method is also given. For the proposed method, we present its
detailed theoretical properties and comprehensive numerical performance. The
results on synthetic and real data show that our method performs better than
the corresponding one in the literature.


  To what extent do the characteristic features of a chemical reaction network
reflect its purpose and function? In general, one argues that correlations
between specific features and specific functions are key to understanding a
complex structure. However, specific features may sometimes be neutral and
uncorrelated with any system-specific purpose, function or causal chain. Such
neutral features are caused by chance and randomness. Here we compare two
classes of chemical networks: one that has been subjected to biological
evolution (the chemical reaction network of metabolism in living cells) and one
that has not (the atmospheric planetary chemical reaction networks). Their
degree distributions are shown to share the very same neutral
system-independent features. The shape of the broad distributions is to a large
extent controlled by a single parameter, the network size. From this
perspective, there is little difference between atmospheric and metabolic
networks; they are just different sizes of the same random assembling network.
In other words, the shape of the degree distribution is a neutral
characteristic feature and has no functional or evolutionary implications in
itself; it is not a matter of life and death.


  Recently, GRAVITY onboard the Very Large Telescope Interferometer (VLTI)
first spatially resolved the structure of the quasar 3C 273 with an
unprecedented resolution of $\sim 10\mu$as. A new method of measuring parallax
distances has been successfully applied to the quasar through joint analysis of
spectroastrometry (SA) and reverberation mapping (RM) observation of its broad
line region (BLR). The uncertainty of this SA and RM (SARM) measurement is
about $16\%$ from real data, showing its great potential as a powerful tool for
precision cosmology. In this paper, we carry out detailed analyses of mock data
to study impacts of data qualities of SA observations on distance measurements
and establish a quantitative relationship between statistical uncertainties of
distances and relative errors of differential phases. We employ a circular disk
model of BLR for the SARM analysis. We show that SARM analyses of observations
generally generate reliable quasar distances, even for relatively poor SA
measurements with error bars of $40\%$ at peaks of phases. Inclinations and
opening angles of BLRs are the major parameters governing distance
uncertainties. It is found that BLRs with inclinations $\gtrsim 10^{\circ}$ and
opening angles $\lesssim 40^{\circ}$ are the most reliable regimes from SARM
analysis for distance measurements. Through analysis of a mock sample of AGNs
generated by quasar luminosity functions, we find that if the GRAVITY/GRAVITY+
can achieve a phase error of $0.1^{\circ}$ per baseline for targets with
magnitudes $K \lesssim 11.5$, the SARM campaign can constrain $H_0$ to an
uncertainty of $2\%$ by observing $60$ targets.


  Recent advancements in large language models have opened new possibilities
for generative molecular drug design. We present Chemlactica and Chemma, two
language models fine-tuned on a novel corpus of 110M molecules with computed
properties, totaling 40B tokens. These models demonstrate strong performance in
generating molecules with specified properties and predicting new molecular
characteristics from limited samples. We introduce a novel optimization
algorithm that leverages our language models to optimize molecules for
arbitrary properties given limited access to a black box oracle. Our approach
combines ideas from genetic algorithms, rejection sampling, and prompt
optimization. It achieves state-of-the-art performance on multiple molecular
optimization benchmarks, including an 8% improvement on Practical Molecular
Optimization compared to previous methods. We publicly release the training
corpus, the language models and the optimization algorithm.


  Making use of the isospectrality of Supersymmetry transformations, we propose
a general and high-fidelity method to prepare gapped topological modes in
discrete systems from a single-site excitation. The method consists of
adiabatically connecting two superpartner structures, deforming the input state
into the desired mode. We demonstrate the method by pumping topological states
of the Su-Schrieffer-Heeger model in an optical waveguide array, where the
adiabatic deformation is performed along the propagation direction. We obtain
fidelities above $F=0.99$ for a wide range of coupling strengths when pumping
edge and interface states.


  Shock tubes create simulated blast waves which can be directed and measured
to study blast wave effects under laboratory conditions. It is desirable to
increase available peak pressure from ~1 MPa to ~5 MPa to simulate closer blast
sources and facilitate development and testing of personal and vehicle armors.
Three methods were investigated to increase peak simulated blast pressure
produced by an oxy-acetylene driven shock tube while maintaining suitability
for laboratory studies. The first method is the addition of a Shchelkin spiral
priming section which works by increasing the turbulent flow of the
deflagration wave, thus increasing its speed and pressure. This approach
increased the average peak pressure from 1.17 MPa to 5.33 MPa while maintaining
a relevant pressure-time curve (Friedlander waveform). The second method is a
bottleneck between the driving and driven sections. Coupling a 79 mm diameter
driving section to a 53 mm driven section increased the peak pressure from 1.17
MPa to 2.25 MPa. Using a 103 mm driving section increased peak pressure to 2.64
MPa. The third method, adding solid fuel to the driving section with the
oxy-acetylene, resulted in a peak pressure increase to 1.70 MPa.


  The Calkin-Wilf tree is an infinite binary tree whose vertices are the
positive rational numbers. Each such number occurs in the tree exactly once and
in the form $a/b$, where are $a$ and $b$ are relatively prime positive
integers. This tree is associated with the matrices $L_1 = \left(
\begin{matrix} 1 & 0 \\ 1 & 1 \end{matrix} \right)$ and $R_1 = \left(
\begin{matrix} 1 & 1 \\ 0 & 1 \end{matrix} \right)$, which freely generate the
monoid $SL_2(\mathbf{N}_0)$ of $2 \times 2$ matrices with determinant 1 and
nonnegative integral coordinates. For other pairs of matrices $L_u$ and $R_v$
that freely generate submonoids of $GL_2(\mathbf{N}_0)$, there are forests of
infinitely many rooted infinite binary trees that partition the set of positive
rational numbers, and possess a remarkable symmetry property.


  3D shape is a crucial but heavily underutilized cue in today's computer
vision systems, mostly due to the lack of a good generic shape representation.
With the recent availability of inexpensive 2.5D depth sensors (e.g. Microsoft
Kinect), it is becoming increasingly important to have a powerful 3D shape
representation in the loop. Apart from category recognition, recovering full 3D
shapes from view-based 2.5D depth maps is also a critical part of visual
understanding. To this end, we propose to represent a geometric 3D shape as a
probability distribution of binary variables on a 3D voxel grid, using a
Convolutional Deep Belief Network. Our model, 3D ShapeNets, learns the
distribution of complex 3D shapes across different object categories and
arbitrary poses from raw CAD data, and discovers hierarchical compositional
part representations automatically. It naturally supports joint object
recognition and shape completion from 2.5D depth maps, and it enables active
object recognition through view planning. To train our 3D deep learning model,
we construct ModelNet -- a large-scale 3D CAD model dataset. Extensive
experiments show that our 3D deep representation enables significant
performance improvement over the-state-of-the-arts in a variety of tasks.


  We extend the traditional worst-case, minimax analysis of stochastic convex
optimization by introducing a localized form of minimax complexity for
individual functions. Our main result gives function-specific lower and upper
bounds on the number of stochastic subgradient evaluations needed to optimize
either the function or its "hardest local alternative" to a given numerical
precision. The bounds are expressed in terms of a localized and computational
analogue of the modulus of continuity that is central to statistical minimax
analysis. We show how the computational modulus of continuity can be explicitly
calculated in concrete cases, and relates to the curvature of the function at
the optimum. We also prove a superefficiency result that demonstrates it is a
meaningful benchmark, acting as a computational analogue of the Fisher
information in statistical estimation. The nature and practical implications of
the results are demonstrated in simulations.


  We present a new application and implementation of the so-called Pound
locking technique for the interrogation of superconducting microresonators. We
discuss how by comparing against stable frequency sources this technique can be
used to characterize properties of resonators that can not be accessed using
traditional methods. Specifically, by analyzing the noise spectra and the Allan
deviation we obtain valuable information about the nature of the noise in
superconducting planar resonators. This technique also greatly improves the
read-out accuracy and measurement throughput compared to conventional methods.


  The problem of distributed data compression for function computation is
considered, where (i) the function to be computed is not necessarily
symbol-wise function and (ii) the information source has memory and may not be
stationary nor ergodic. We introduce the class of smooth sources and give a
sufficient condition on functions so that the achievable rate region for
computing coincides with the Slepian-Wolf region (i.e., the rate region for
reproducing the entire source) for any smooth sources. Moreover, for
symbol-wise functions, the necessary and sufficient condition for the
coincidence is established. Our result for the full side-information case is a
generalization of the result by Ahlswede and Csiszar to sources with memory;
our dichotomy theorem is different from Han and Kobayashi's dichotomy theorem,
which reveals an effect of memory in distributed function computation. All
results are given not only for fixed-length coding but also for variable-length
coding in a unified manner. Furthermore, for the full side-information case,
the error probability in the moderate deviation regime is also investigated.


  Let $\A_0, \A_1, \ldots, \A_n$ be given square matrices of size $m$ with
rational coefficients. The paper focuses on the exact computation of one point
in each connected component of the real determinantal variety $\{\X \in\RR^n \:
:\: \det(\A_0+x_1\A_1+\cdots+x_n\A_n)=0\}$. Such a problem finds applications
in many areas such as control theory, computational geometry, optimization,
etc. Using standard complexity results this problem can be solved using
$m^{O(n)}$ arithmetic operations. Under some genericity assumptions on the
coefficients of the matrices, we provide an algorithm solving this problem
whose runtime is essentially quadratic in ${{n+m}\choose{n}}^{3}$. We also
report on experiments with a computer implementation of this algorithm. Its
practical performance illustrates the complexity estimates. In particular, we
emphasize that for subfamilies of this problem where $m$ is fixed, the
complexity is polynomial in $n$.


  We consider the problem of learning from a similarity matrix (such as
spectral clustering and lowd imensional embedding), when computing pairwise
similarities are costly, and only a limited number of entries can be observed.
We provide a theoretical analysis using standard notions of graph
approximation, significantly generalizing previous results (which focused on
spectral clustering with two clusters). We also propose a new algorithmic
approach based on adaptive sampling, which experimentally matches or improves
on previous methods, while being considerably more general and computationally
cheaper.


  The microwave photoresistance of a two-dimensional topological insulator in a
HgTe quantum well with an inverted spectrum has been experimentally studied
under irradiation at frequencies of 110-169 GHz. Two mechanisms of formation of
this photoresistance have been revealed. The first mechanism is due to
transitions between the dispersion branches of edge current states, whereas the
second mechanism is caused by the action of radiation on the bulk of the
quantum well.


  This work focuses on Rayleigh-Taylor instability (RTI)driven by acceleration
with power-law time-dependence. We review the existing theoretical approaches,
apply the group theory approach to solve this long-standing problem, and yield
the unified framework for the scale-dependent dynamics of Rayleigh-Taylor (RT)
bubbles and RT spikes. For the early-time linear dynamics we provide the
dependence of RTI evolution on the acceleration parameters and the initial
conditions. For the late-time nonlinear dynamics, we find a continuous family
of asymptotic solutions, directly link the interface velocity to the interface
morphology and the interfacial shear, derive solutions for the regular bubbles
and for the singular spikes, and study stability of these solutions. The
properties of special nonlinear solutions in the RT family are scrupulously
described, including the critical, the Taylor, the Layzer-drag, and the Atwood
solutions. It is shown that the fastest Atwood bubble is regular and stable,
and the fastest Atwood spike is singular and unstable. The essentially
multi-scale and interfacial character of RT dynamics is demonstrated. The
former can be understood by viewing RT coherent structure of bubbles and spikes
as a standing wave with the growing amplitude. The latter implies that RT flow
has effectively no motion of the fluids away from the interface and has intense
motion of the fluids near the interface, with shear-driven vortical structures
appearing at the interface. Our theory agrees with available observations, and
elaborates extensive benchmarks for future research and for better
understanding of RT driven phenomena in plasmas.


  Based on two assumptions, the surface layer is flexible, and the internal
energy of the latent heat of vaporization is completely utilized by the atoms
for overcoming on the surface resistance of the liquid, the enthalpy of
vaporization was calculated for 45 elements. The theoretical values were tested
against experiments with positive result.


  Compressive Sensing (CS) is a new paradigm for the efficient acquisition of
signals that have sparse representation in a certain domain. Traditionally, CS
has provided numerous methods for signal recovery over an orthonormal basis.
However, modern applications have sparked the emergence of related methods for
signals not sparse in an orthonormal basis but in some arbitrary, perhaps
highly overcomplete, dictionary, particularly due to their potential to
generate different kinds of sparse representation of signals. To this end, we
apply a signal space greedy method, which relies on the ability to optimally
project a signal onto a small number of dictionary atoms, to address signal
recovery in this setting. We describe a generalized variant of the iterative
recovery algorithm called Signal space Subspace Pursuit (SSSP) for this more
challenging setting. Here, using the Dictionary-Restricted Isometry Property
(D-RIP) rather than classical RIP, we derive a low bound on the number of
measurements required and then provide the proof of convergence for the
algorithm. The algorithm in noisy and noise-free measurements has low
computational complexity and provides high recovery accuracy. Simulation
results show that the algorithm outperforms best compared with the existing
recovery algorithms.


  Elementary cellular automata are the simplest form of cellular automata,
studied extensively by Wolfram in the 1980s. He discovered complex behavior in
some of these automata and developed a classification for all cellular automata
based on their phenomenology. In this paper, we present an algorithm to
classify them more effectively by measuring difference patterns using the
Hamming distance. Our classification aligns with Wolfram's and further
categorizes them into additional subclasses.


  The classifying space of the embedded cobordism category has been identified
in by Galatius, Tillmann, Madsen, and Weiss as the infinite loop space of a
certain Thom spectrum. This identifies the set of path components with the
classical cobordism group. In this paper, we give a geometric interpretation of
the higher homotopy groups as certain cobordism groups where all manifolds are
now equipped with a set of orthonormal sections in the tangent bundle. We also
give a description of the fundamental group as a free group with a set of
geometrically intuitive relations.


  Eight experiments were conducted to test an oregano-essential-oil-based
product (PRO) on performance, gut health, and nutrient absorption capacity in
broilers. The first three, up to 14d and without specific challenges, tested
the effects on intestinal histology, skeletal integrity, and growth. Other two
experiments, up to 28d birds were challenged to induce feed passage syndrome
(STR) and test the effect on the antioxidant status and performance,
contrasting later the results under a natural challenge in commercial
conditions. Finally, in two other experiments, up to 21 d, birds challenged
with coccidia were tested to determine the effects on coccidiosis, nutrient
digestibility, and feed efficiency (FCR). Corn-soybean-fish meal diets were
used. Under healthy conditions, PRO effects were observed on intestinal villus
height and surface area, mucosa density and structure, villus to crypt ratio,
goblet cells density, mucus production, body weight gain, and FCR (P<0.04), and
carcass yield and bone density (P<0.08). Birds affected by STR showed effects
(P<0.05) on superoxide dismutase activity, bodyweight gain, FCRE, non-normal
feces frequency, bursal diameter, and dysbacteriosis. Birds affected by
coccidia showed effects on cocci-positive ratio, cocci microscopic score,
oocysts count, bursal diameter, body weight gain, FCR, apparent digestibility
of dry matter and crude protein, protein and energy efficiencies (P<0.01), and
nitrogen apparent retention (P<0.07). Results showed PRO added value to the
diet favoring feed efficiency and performance.


  Current models of the effect of spontaneous emission on the electron beam
dynamics neglect the discreteness of electron recoil associated with photon
emission. We present a novel, one-dimensional model of the effect of
spontaneous emission on the electron beam dynamics in an undulator both in the
classical regime where discrete electron recoil is negligible, and the quantum
regime where it is significant. It is shown that in the classical regime,
continuous decrease of the average electron energy and diffusive growth of the
electron energy spread occurs, in agreement with previous classical models. In
the quantum regime, it is shown that the evolution of the electron momentum
distribution occurs as discrete momentum groups according to a Poisson
distribution. The narrow momentum features of the quantum regime may be useful
for generation of coherent radiation, which relies on electron beams having
sufficiently narrow momentum/energy distributions.


  We present the Mathematica package DREAM for arbitrarily high precision
computation of multiloop integrals within the DRA (Dimensional Recurrence &
Analyticity) method as solutions of dimensional recurrence relations. Starting
from these relations, the package automatically constructs the inhomogeneous
solutions and reduces the manual efforts to setting proper homogeneous
solutions. DREAM also provides means to define the homogeneous solutions of the
higher-order recurrence relations (and can construct those of the first-order
recurrence relations automatically). Therefore, this package can be used to
apply the DRA method to the topologies with sectors having more than one master
integral. Two nontrivial examples are presented: four-loop fully massive
tadpole diagrams of cat-eye topology and three-loop cut diagrams which are
necessary for computation of the width of the para-positronium decay into four
photons. The analytical form of this width is obtained here for the first time
to the best of our knowledge.


  Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) infectivity is a
major concern in coronavirus disease 2019 (COVID-19) prevention and economic
reopening. However, rigorous determination of SARS-COV-2 infectivity is
essentially impossible owing to its continuous evolution with over 13752 single
nucleotide polymorphisms (SNP) variants in six different subtypes. We develop
an advanced machine learning algorithm based on the algebraic topology to
quantitatively evaluate the binding affinity changes of SARS-CoV-2 spike
glycoprotein (S protein) and host angiotensin-converting enzyme 2 (ACE2)
receptor following the mutations. Based on mutation-induced binding affinity
changes, we reveal that five out of six SARS-CoV-2 subtypes have become either
moderately or slightly more infectious, while one subtype has weakened its
infectivity. We find that SARS-CoV-2 is slightly more infectious than SARS-CoV
according to computed S protein-ACE2 binding affinity changes. Based on a
systematic evaluation of all possible 3686 future mutations on the S protein
receptor-binding domain (RBD), we show that most likely future mutations will
make SARS-CoV-2 more infectious. Combining sequence alignment, probability
analysis, and binding affinity calculation, we predict that a few residues on
the receptor-binding motif (RBM), i.e., 452, 489, 500, 501, and 505, have very
high chances to mutate into significantly more infectious COVID-19 strains.


  We show that the problem of communication in a quantum computer reduces to
constructing reliable quantum channels by distributing high-fidelity EPR pairs.
We develop analytical models of the latency, bandwidth, error rate and resource
utilization of such channels, and show that 100s of qubits must be distributed
to accommodate a single data communication. Next, we show that a grid of
teleportation nodes forms a good substrate on which to distribute EPR pairs. We
also explore the control requirements for such a network. Finally, we propose a
specific routing architecture and simulate the communication patterns of the
Quantum Fourier Transform to demonstrate the impact of resource contention.


  Recently, there have been numerous analyses of the redshift space power
spectrum of rich clusters of galaxies. Some of these analyses indicate a "bump"
in the Abell/ACO cluster power spectrum around k= 0.05hMpc^-1. Such a feature
in the power spectrum excludes most standard formation models and indicates
possible periodicity in the distribution of large-scale structure. However, the
data used in detecting this peak include clusters with estimated redshifts
and/or clusters outside of Abell's (1958) statistical sample, i.e. R=0
clusters. Here, we present estimations of the redshift-space power spectrum for
a newly expanded sample of 637 R >= 1 Abell/ACO clusters which has a constant
number density to z = 0.10 in the Southern Hemisphere and a nearly constant
number density to z = 0.14 in the Northern Hemisphere. The volume sampled,
\~10^8h^{-3}Mpc^{3}, is large enough to accurately calculate the power per mode
to scales approaching 10^3h^{-1}Mpc. We find the shape of the power spectrum is
is a power-law on scales 0.02 <= k <= 0.10hMpc^{-1}, with enhanced power over
less rare clusters, such as APM clusters. The slope of this power-law is n=
-1.4. The power spectrum is essentially featureless, although we do see a dip
near $k = 0.04h$Mpc$^{-1}$ which cannot be considered statistically significant
based on this data alone. We do not detect a narrow peak at $k \sim
0.05h$Mpc$^{-1}$ and there is no evidence for a turn-over in the power spectrum
as has been previously reported. We compare the shape of the Abell/ACO rich
cluster power spectrum to various linear models.


  Let $F(z)$ be a $k$-regular series in $\mathbb{Z}[[z]]$ and $b$ be an integer
with $b\ge2$. Bell, Bugeaud and Coons [BelBC] proved that $F(\frac{1}{b})$ is
either rational or transcendental. In [Mi], we introduce a generalized
$k$-regular sequence as a unification of several kinds of important sequences
including $k$-regular, $k$-additive and $k$-multiplicative sequences. In this
paper, we give a generalization of the result of Bell, Bugeaud and Coons for
certain generalized $k$-regular series. Especially, we show that the values of
irrational generating functions of certain sum of $k$-additive sequences and
certain $k$-multiplicative sequences are either rational or transcendental.
Moreover, we also give a partly generalization of a result obtained by
Tachiya[Ta]. Especially, we show that the values of irrational generating
functions of certain $k$-additive sequences and certain $k$-multiplicative
sequences give transcendental numbers.


  Theoretical predictions of top-quark cross sections depend on the values of
the parameters of the quantum chromodynamics Lagrangian, such as the strong
coupling constant and the mass of the top quark, but also on parameters of the
electroweak sector of the standard model and parton distribution functions.
Comparisons between state-of-the-art calculations and recent measurements at
the ATLAS and CMS experiments at the CERN LHC allow for the precise
determination of these parameters. In this proceeding, the most recent results
by the two collaborations are summarized and discussed.


  Some varieties of groupoids and quasigroups generated by linear-bivariate
polynomials $P(x,y)=a+bx+cy$ over the ring $\mathbb{Z}_n$ are studied.
Necessary and sufficient conditions for such groupoids and quasigroups to obey
identities which involve one, two, three (e.g. Bol-Moufang type) and four
variables w.r.t. $a$, $b$ and $c$ are established. Necessary and sufficient
conditions for such groupoids and quasigroups to obey some inverse properties
w.r.t. $a$, $b$ and $c$ are also established. This class of groupoids and
quasigroups are found to belong to some varieties of groupoids and quasigroups
such as medial groupoid(quasigroup), F-quasigroup, semi automorphic inverse
property groupoid(quasigroup) and automorphic inverse property
groupoid(quasigroup).


  Integrating machine learning techniques into RDBMSs is an important task
since there are many real applications that require modeling (e.g., business
intelligence, strategic analysis) as well as querying data in RDBMSs. In this
paper, we provide an SQL solution that has the potential to support different
machine learning modelings. As an example, we study how to support unsupervised
probabilistic modeling, that has a wide range of applications in clustering,
density estimation and data summarization, and focus on
Expectation-Maximization (EM) algorithms, which is a general technique for
finding maximum likelihood estimators. To train a model by EM, it needs to
update the model parameters by an E-step and an M-step in a while-loop
iteratively until it converges to a level controled by some threshold or
repeats a certain number of iterations. To support EM in RDBMSs, we show our
answers to the matrix/vectors representations in RDBMSs, the relational algebra
operations to support the linear algebra operations required by EM, parameters
update by relational algebra, and the support of a while-loop. It is important
to note that the SQL'99 recursion cannot be used to handle such a while-loop
since the M-step is non-monotonic. In addition, assume that a model has been
trained by an EM algorithm, we further design an automatic in-database model
maintenance mechanism to maintain the model when the underlying training data
changes.We have conducted experimental studies and will report our findings in
this paper.


  Modern surveys of gravitational microlensing events have progressed to
detecting thousands per year. Surveys are capable of probing Galactic
structure, stellar evolution, lens populations, black hole physics, and the
nature of dark matter. One of the key avenues for doing this is studying the
microlensing Einstein radius crossing time distribution ($t_E$). However,
systematics in individual light curves as well as over-simplistic modeling can
lead to biased results. To address this, we developed a model to simultaneously
handle the microlensing parallax due to Earth's motion, systematic instrumental
effects, and unlensed stellar variability with a Gaussian Process model. We
used light curves for nearly 10,000 OGLE-III and IV Milky Way bulge
microlensing events and fit each with our model. We also developed a forward
model approach to infer the timescale distribution by forward modeling from the
data rather than using point estimates from individual events. We find that
modeling the variability in the baseline removes a source of significant bias
in individual events, and previous analyses over-estimated the number of long
timescale ($t_E>100$ days) events due to their over simplistic models ignoring
parallax effects and stellar variability. We use our fits to identify hundreds
of events that are likely black holes.


  We construct a lattice gauge theory using reduced staggered fermions and
gauge fields which provides a non-perturbative realization of a {\it complete}
technicolor model; one which treats both strong and weakly coupled gauge
sectors on an equal footing. We show that the model is capable of developing a
Higgs phase at non zero lattice spacing via the formation of fermion
condensates. We further show that while the broken symmetry associated with
this phase has a vector character in the lattice theory it is realized as an
axial symmetry in the continuum limit in agreement with the Vafa Witten
theorem. We discuss our result in the context of universality


  We discuss the close relation between shadowing in deep-inelastic
lepton-nucleus scattering and diffractive photo- and leptoproduction of hadrons
from free nucleons. We show that the magnitude of nuclear shadowing at small
Bjorken-x, as measured by the E665 and NMC collaborations, is directly related
to HERA data on the amount of diffraction in the scattering from free nucleons.


  It is becoming common to hear teaching advice about spending more time on the
"physics of the problem" so that students will get more physical insight and
develop a stronger intuition that can be very helpful when thinking about
physics problems. Based on this type of justification, mathematical skills such
as the ability to compute moments of inertia, center of mass, or gravitational
fields from mass distributions, and electrical fields from charge distributions
are considered "distracting mathematics" and therefore receive less attention.
We argue a) that this approach can have a negative influence on student
reasoning when dealing with questions of rotational dynamics, a highly
non-intuitive subject where even instructors may fail to provide correct
answers, and b) that exposure of students to mathematical reasoning and to a
wide range of computational techniques to obtain the moment of inertia of
different mass distributions will make students more comfortable with the
subject of rotational dynamics, thus improving their physical insight on the
topic.


  We show that the Connes-Marcolli $GL_{2}$-system can be represented on the
Big Picture, a combinatorial gadget introduced by Conway in order to understand
various results about congruence subgroups pictorially. In this representation
the time evolution of the system is implemented by Conway's distance between
projective classes of commensurable lattices. We exploit these results in order
to associate quantum statistical mechanical systems to congruence subgroups in
a way appropriate for the study of monstrous moonshine.


  Heterogeneous graphs, which contain nodes and edges of multiple types, are
prevalent in various domains, including bibliographic networks, social media,
and knowledge graphs. As a fundamental task in analyzing heterogeneous graphs,
relevance measure aims to calculate the relevance between two objects of
different types, which has been used in many applications such as web search,
recommendation, and community detection. Most of existing relevance measures
focus on homogeneous networks where objects are of the same type, and a few
measures are developed for heterogeneous graphs, but they often need the
pre-defined meta-path. Defining meaningful meta-paths requires much domain
knowledge, which largely limits their applications, especially on schema-rich
heterogeneous graphs like knowledge graphs. Recently, the Graph Neural Network
(GNN) has been widely applied in many graph mining tasks, but it has not been
applied for measuring relevance yet. To address the aforementioned problems, we
propose a novel GNN-based relevance measure, namely GSim. Specifically, we
first theoretically analyze and show that GNN is effective for measuring the
relevance of nodes in the graph. We then propose a context path-based graph
neural network (CP-GNN) to automatically leverage the semantics in
heterogeneous graphs. Moreover, we exploit CP-GNN to support relevance measures
between two objects of any type. Extensive experiments demonstrate that GSim
outperforms existing measures.


  The classical approach to inverse problems is based on the optimization of a
misfit function. Despite its computational appeal, such an approach suffers
from many shortcomings, e.g., non-uniqueness of solutions, modeling prior
knowledge, etc. The Bayesian formalism to inverse problems avoids most of the
difficulties encountered by the optimization approach, albeit at an increased
computational cost. In this work, we use information theoretic arguments to
cast the Bayesian inference problem in terms of an optimization problem. The
resulting scheme combines the theoretical soundness of fully Bayesian inference
with the computational efficiency of a simple optimization.


  Style is an integral component of text that expresses a diverse set of
information, including interpersonal dynamics (e.g. formality) and the author's
emotions or attitudes (e.g. disgust). Humans often employ multiple styles
simultaneously. An open question is how large language models can be explicitly
controlled so that they weave together target styles when generating text: for
example, to produce text that is both negative and non-toxic. Previous work
investigates the controlled generation of a single style, or else controlled
generation of a style and other attributes. In this paper, we expand this into
controlling multiple styles simultaneously. Specifically, we investigate
various formulations of multiple style rewards for a reinforcement learning
(RL) approach to controlled multi-style generation. These reward formulations
include calibrated outputs from discriminators and dynamic weighting by
discriminator gradient magnitudes. We find that dynamic weighting generally
outperforms static weighting approaches, and we explore its effectiveness in 2-
and 3-style control, even compared to strong baselines like plug-and-play
model. All code and data for RL pipelines with multiple style attributes will
be publicly available.


  Using derivative expansion applied to the Wigner transform of the two - point
Green function we analyse the anomalous quantum Hall effect (AQHE), and the
chiral magnetic effect (CME). The corresponding currents are proportional to
the momentum space topological invariants. We reproduce the conventional
expression for the Hall conductivity in $2+1$ D. In $3+1$ D our analysis allows
to explain systematically the AQHE in topological insulators and Weyl
semimetals. At the same time using this method it may be proved, that the
equilibrium CME is absent in the wide class of solids, as well as in the
properly regularized relativistic quantum field theory.


  For a multipartite quantum system of the dimension $d_1\otimes d_2\otimes...
d_n$, $d_1\ge d_2\ge...\ge d_n$, is there an entangled state {\em maximum} in
the sense that all other states in the system can be obtained from the state
through local quantum operations and classical communications (LOCC)? When
$d_1\ge\Pi_{i=2}^n d_i$, such state exists. We show that this condition is also
necessary. Our proof, somewhat surprisingly, uses results from algebraic
complexity theory.


  We develop a microscopic approach to the kinetic theory of many-particle
systems with dissipative and potential interactions in presence of active
fluctuations. The approach is based on a generalization of
Bogolyubov--Peletminsky reduced description method applied to the systems of
many active particles. It is shown that the microscopic approach developed
allows to construct the kinetic theory of two- and three-dimensional systems of
active particles in presence of non-linear friction (dissipative interaction)
and an external random field with active fluctuations. The kinetic equations
for these systems in case of a weak interaction between the particles (both
potential and dissipative) and low-intensity active fluctuations are obtained.
We demonstrate particular cases in which the derived kinetic equations have
solutions that match the results known in the literature. It is shown that the
display of the head-tail asymmetry and self-propelling even in the case of a
linear friction, is one of the consequences of the local nature of the active
fluctuations.


  We give examples of Lie-Rinehart algebras whose enveloping algebra is not a
full Hopf algebroid in the sense of Bohm and Szlachanyi. We construct these
examples as quotients of a canonical Lie-Rinehart algebra over a Jacobi algebra
which does admit an antipode.


  We study the linear stability of Plane Poiseuille flow of an
elastoviscoplastic fluid using a revised version of the model proposed by Putz
and Burghelea (Rheol. Acta (2009)48:673-689). The evolution of the
microstructure upon a gradual increase of the external forcing is governed by a
structural variable (the concentration of solid material elements) which decays
smoothly from unity to zero as the stresses are gradually increased beyond the
yield point. Stability results are in close conformity with the ones of a
pseudo-plastic fluid. Destabilizing effects are related to the presence of an
intermediate transition zone where elastic solid elements coexist with fluid
elements. This region brings an elastic contribution which does modify the
stability of the flow.


  The present status of the Roper resonance in lattice QCD is reviewed. Some of
the latest lattice results are discussed with particular emphasis on a large
systematic error stemming from the finite size effect. These results suggest
that the Roper resonance can be described by the simple three quark excitation
of sizable extent.


  For the muon spectrometer of the ATLAS detector at the large hadron collider
(LHC), large drift chambers consisting of 6 to 8 layers of pressurized drift
tubes are used for precision tracking covering an active area of 5000 m2 in the
toroidal field of superconducting air core magnets. The chambers have to
provide a spatial resolution of 41 microns with Ar:CO2 (93:7) gas mixture at an
absolute pressure of 3 bar and gas gain of 2?104. The environment in which the
chambers will be operated is characterized by high neutron and background with
counting rates of up to 100 per square cm and second. The resolution and
efficiency of a chamber from the serial production for ATLAS has been
investigated in a 100 GeV muon beam at photon irradiation rates as expected
during LHC operation. A silicon strip detector telescope was used as external
reference in the beam. The spatial resolution of a chamber is degraded by 4 ?m
at the highest background rate. The detection efficiency of the drift tubes is
unchanged under irradiation. A tracking efficiency of 98% at the highest rates
has been demonstrated.


  We present stellar kinematics of 22 nearby early-type galaxies (ETGs), based
on two-dimensional (2D) absorption line stellar spectroscopy out to ~2-4 R_e
(effective radii), as part of the ongoing SLUGGS Survey. The galaxies span a
factor of 20 in intrinsic luminosity, as well as a full range of environment
and ETG morphology. Our data consist of good velocity resolution (sigma_inst ~
25 km/s) integrated stellar-light spectra extracted from the individual
slitlets of custom made Keck/DEIMOS slitmasks. We extract stellar kinematics
measurements (V, sigma, h_3, and h_4) for each galaxy. Combining with
literature values from smaller radii, we present 2D spatially resolved maps of
the large-scale kinematic structure in each galaxy. We find that the kinematic
homogeneity found inside 1 R_e often breaks down at larger radii, where a
variety of kinematic behaviors are observed. While central slow rotators remain
slowly rotating in their halos, central fast rotators show more diversity,
ranging from rapidly increasing to rapidly declining specific angular momentum
profiles in the outer regions. There are indications that the outer trends
depend on morphological type, raising questions about the proposed unification
of the elliptical and lenticular (S0) galaxy families in the ATLAS^3D survey.
Several galaxies in our sample show multiple lines of evidence for distinct
disk components embedded in more slowly rotating spheroids, and we suggest a
joint photometric-kinematic approach for robust bulge-disk decomposition. Our
observational results appear generally consistent with a picture of two-phase
(in-situ plus accretion) galaxy formation.


  We consider a nonlinear elliptic Dirichlet equation driven by a nonlinear
nonhomogeneous differential operator involving a Carath\'{e}odory reaction
which is $(p-1)$-superlinear but does not satisfy the Ambrosetti-Rabinowitz
condition. First we prove a three-solutions-theorem extending an earlier
classical result of Wang (Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire 8
(1991), no. 1, 43--57). Subsequently, by imposing additional conditions on the
reaction $f(x,\cdot)$, we produce two more nontrivial constant sign solutions
and a nodal solution for a total of five nontrivial solutions. In the special
case of $(p,2)$-equations we prove the existence of a second nodal solution for
a total of six nontrivial solutions given with complete sign information.
Finally, we study a nonlinear eigenvalue problem and we show that the problem
has at least two nontrivial positive solutions for all parameters $\lambda>0$
sufficiently small where one solution vanishes in the Sobolev norm as $\lambda
\to 0^+$ and the other one blows up (again in the Sobolev norm) as $\lambda \to
0^+$.


  The electronic band structures of BeSiN$_2$ and BeGeN$_2$ compounds are
calculated using the quasiparticle self-consistent $GW$ method. The lattice
parameters are calculated for the wurtzite based crystal structure commonly
found in other II-IV-N$_2$ compounds with the $Pbn$2$_1$ space group. They are
determined both in the local density approximation (LDA) and generalized
gradient approximation (GGA), which provide lower and upper limits. At the GGA
lattice constants, which gives lattice constants closer to the experimental
ones, BeSiN$_2$ is found to have an indirect band gap of 6.88 eV and its direct
gap at $\Gamma$ is 7.77 eV, while in BeGeN$_2$ the gap is direct at $\Gamma$
and equals 5.03 eV. To explain the indirect gap in BeSiN$_2$, comparisons are
made with the parent III-N compound w-BN band structure. The effective mass
parameters are also evaluated and found to decrease from BeSiN$_2$ to
BeGeN$_2$.


  Higher-order recursion schemes (HORS) have received much attention as a
useful abstraction of higher-order functional programs with a number of new
verification techniques employing HORS model-checking as their centrepiece. We
give an account of the C-SHORe tool, which contributed to the ongoing quest for
a truly scalable model-checker for HORS by offering a different, automata
theoretic perspective. C-SHORe implements the first practical model-checking
algorithm that acts on a generalisation of pushdown automata equi-expressive
with HORS called collapsible pushdown systems (CPDS). At its core is a
backwards saturation algorithm for CPDS. Additionally, it is able to use
information gathered from an approximate forward reachability analysis to guide
its backward search. Moreover, it uses an algorithm that prunes the CPDS prior
to model-checking and a method for extracting counter-examples in negative
instances. We provide an up-to-date comparison of C-SHORe with the
state-of-the-art verification tools for HORS. The tool and additional material
are available from http://cshore.cs.rhul.ac.uk.


  A new version is proposed for the universal empirical formula, EPAX, which
describes fragmentation cross sections in high-energy heavy-ion reactions. The
new version, EPAX 3, can be shown to yield cross sections that are in better
agreement with experimental data for the most neutron-rich fragments than the
previous version. At the same time, the very good agreement of EPAX 2 with data
on the neutron-deficient side has been largely maintained. Comparison with
measured cross sections show that the bulk of the data is reproduced within a
factor of about 2, for cross sections down to the pico-barn range.


  The Sierpinski gasket is known to support an exotic stochastic process called
the asymptotically one-dimensional diffusion. This process displays local
anisotropy, as there is a preferred direction of motion which dominates at the
microscale, but on the macroscale we see global isotropy in that the process
will behave like the canonical Brownian motion on the fractal. In this paper we
analyse the microscale behaviour of such processes, which we call non-fixed
point diffusions, for a class of fractals and show that there is a natural
limit diffusion associated with the small scale asymptotics. This limit process
no longer lives on the original fractal but is supported by another fractal,
which is the Gromov-Hausdorff limit of the original set after a shorting
operation is performed on the dominant microscale direction of motion. We
establish the weak convergence of the rescaled diffusions in a general setting
and use this to answer a question raised in Hattori (1994) about the
ultraviolet limit of the asymptotically one-dimensional diffusion process on
the Sierpinski gasket.


  We study the out-of-equilibrium dynamics of quantum systems with long-range
interactions. Two different models describing, respectively, interacting
lattice bosons and spins are considered. Our study relies on a combined
approach based on accurate many-body numerical calculations as well as on a
quasiparticle microscopic theory. For sufficiently fast decaying long-range
potentials, we find that the quantum speed limit set by the long-range
Lieb-Robinson bounds is never attained and a purely ballistic behavior is
found. For slowly decaying potentials, a radically different scenario is
observed. In the bosonic case, a remarkable local spreading of correlations is
still observed, despite the existence of infinitely fast traveling excitations
in the system. This is in marked contrast to the spin case, where locality is
broken. We finally provide a microscopic justification of the different regimes
observed and of the origin of the protected locality in the bosonic model.


  We present the results of a set of radiation magnetohydrodynamic simulations
of turbulent molecular clouds in which we vary the initial strength of the
magnetic field within a range ($1 \lesssim \mu \lesssim 5$) consistent with
observations of local giant molecular clouds (GMCs). We find that as we
increase the strength of the magnetic field, star formation transitions from
unimodal (the baseline case, $\mu=5$, with a single burst of star formation and
Salpeter IMF) to bimodal. This effect is clearest in the most strongly
magnetized GMCs ($\mu=1$): a first burst of star formation with duration,
intensity and IMF comparable to the baseline case, is followed by a second star
formation episode in which only low-mass stars are formed. Overall, due to the
second burst of star formation, the strongly magnetized case results in a
longer star formation period and a higher efficiency of star formation. The
second burst is produced by gas that is not expelled by radiative feedback,
instead remaining trapped in the GMC by the large-scale B-field, producing a
nearly one-dimensional flow of gas along the field lines. The trapped gas has a
turbulent and magnetic topology that differs from that of the first phase and
strongly suppresses gas accretion onto protostellar cores, reducing their
masses. We speculate that this star formation bimodality may be an important
ingredient to understand the origin of multiple stellar populations observed in
massive globular clusters.


  Thermodiffusive instabilities can have a leading order effect on flame
propagation for lean premixed hydrogen flames. Many simulation studies have
been performed to study this effect, but almost exclusively in two-dimensional
(2D) or domain sizes too small to support the characteristic large-scale
features of the instability. The main purpose of this study is to quantify the
differences of 3D and 2D flames using simulations on sufficiently large
domains. To this end, direct numerical simulations (DNS) of thermodiffusively
unstable laminar premixed hydrogen flames stabilized in 3D domains were
performed. The effects of confinement on the flame dynamics are rigorously
investigated by varying the domain size. The flame burning velocity shows a
strong dependence on the domain size when the lateral domain width is less than
50 laminar flame thicknesses. The characteristic patterns of the
thermodiffusively unstable flame are analyzed in detail, including the
instantaneous flame structure, global burning velocity, flame surface area,
stretch factor, curvature distribution, and the cell size. The effects of the
computational setup (2D vs. 3D) on the local flame front curvature and the
distributions of the thermo-chemical quantities are quantified through a
conditional analysis. The formation and destruction mechanisms of the distinct
cellular structures observed in the 3D domain are analyzed focusing on the
interactions between the flame dynamics and the flow field, and the
contributions of the production of flame surface density, kinematic
restoration, and curvature dissipation are quantified. Compared with the
corresponding 2D simulation, the flame surface area in the cut plane of the 3D
configuration is similar, yet the burning velocity and the stretch factor are
increased. The reason for this is the difference in curvature statistics in 2D
and 3D.


  Motivated from option and derivative pricing, this note develops Edgeworth
expansions both in the Kolmogorov and Wasserstein metric for many different
types of discrete time volatility models and their possible transformations.
This includes, among others, H\"{o}lder-type functions of (augmented) Garch
processes of any order, iterated random functions or Volterra-processes.


  Low-rank factorization is used in many areas of computer science where one
performs spectral analysis on large sensitive data stored in the form of
matrices. In this paper, we study differentially private low-rank factorization
of a matrix with respect to the spectral norm in the turnstile update model. In
this problem, given an input matrix $\mathbf{A} \in \mathbb{R}^{m \times n}$
updated in the turnstile manner and a target rank $k$, the goal is to find two
rank-$k$ orthogonal matrices $\mathbf{U}_k \in \mathbb{R}^{m \times k}$ and
$\mathbf{V}_k \in \mathbb{R}^{n \times k}$, and one positive semidefinite
diagonal matrix $\textbf{\Sigma}_k \in \mathbb{R}^{k \times k}$ such that
$\mathbf{A} \approx \mathbf{U}_k \textbf{\Sigma}_k \mathbf{V}_k^\mathsf{T}$
with respect to the spectral norm.
  Our main contributions are two computationally efficient and sub-linear space
algorithms for computing a differentially private low-rank factorization. We
consider two levels of privacy. In the first level of privacy, we consider two
matrices neighboring if their difference has a Frobenius norm at most $1$. In
the second level of privacy, we consider two matrices as neighboring if their
difference can be represented as an outer product of two unit vectors. Both
these privacy levels are stronger than those studied in the earlier papers such
as Dwork {\it et al.} (STOC 2014), Hardt and Roth (STOC 2013), and Hardt and
Price (NIPS 2014).
  As a corollary to our results, we get non-private algorithms that compute
low-rank factorization in the turnstile update model with respect to the
spectral norm. We note that, prior to this work, no algorithm that outputs
low-rank factorization with respect to the spectral norm in the turnstile
update model was known; i.e., our algorithm gives the first non-private
low-rank factorization with respect to the spectral norm in the turnstile
update mode.


  We give criteria for R-equivalence of torsors under finite constant group
schemes over a field. In paticular, using bitorsors, we obtain a Galois
devissage result which formalises and generalises a theorem of Philippe Gille
in the case of local fields; for instance, Gille's theorem is shown to extend
to higher local fields.


  Radio frequency-orbital angular momentum (RF-OAM) is a novel approach of
multiplexing a set of orthogonal modes on the same frequency channel to achieve
high spectrum efficiencies. Since OAM requires precise alignment of the
transmit and the receive antennas, the electronic beam steering approach has
been proposed for the uniform circular array (UCA)-based OAM communication
system to circumvent large performance degradation induced by small antenna
misalignment in practical environment. However, in the case of large-angle
misalignment, the OAM channel capacity can not be effectively compensated only
by the electronic beam steering. To solve this problem, we propose a hybrid
mechanical and electronic beam steering scheme, in which mechanical rotating
devices controlled by pulse width modulation (PWM) signals as the execution
unit are utilized to eliminate the large misalignment angle, while electronic
beam steering is in charge of the remaining small misalignment angle caused by
perturbations. Furthermore, due to the interferometry, the receive
signal-to-noise ratios (SNRs) are not uniform at the elements of the receive
UCA. Therefore, a rotatable UCA structure is proposed for the OAM receiver to
maximize the channel capacity, in which the simulated annealing algorithm is
adopted to obtain the optimal rotation angle at first, then the servo system
performs mechanical rotation, at last the electronic beam steering is adjusted
accordingly. Both mathematical analysis and simulation results validate that
the proposed hybrid mechanical and electronic beam steering scheme can
effectively eliminate the effect of diverse misalignment errors of any
practical OAM channel and maximize the OAM channel capacity.


  We explicitly construct the extension of the N=2 super Virasoro algebra by
two super primary fields of dimension two and three with vanishing u(1)-charge.
Using a super covariant formalism we obtain two different solutions both
consistent for generic values of the central charge c. The first one can be
identified with the super W_4-algebra - the symmetry algebra of the CP(3)
Kazama-Suzuki model. With the help of unitarity arguments we predict the
self-coupling constant of the field of dimension two for all super
W_n-algebras. The second solution is special in the sense that it does not have
a finite classical limit c->infinity and generic null fields appear. In the
spirit of recent results in the N=0 case it can be understood as a unifying N=2
super W-algebra for all CP(n) coset models. It does not admit any unitary
representation.


  In this paper we study the ring $\mathcal{P}$ of combinatorial convex
polytopes. We introduce the algebra of operators $\mathcal{D}$ generated by the
operators $d_k$ that send an $n$-dimensional polytope $P^n$ to the sum of all
its $(n-k)$-dimensional faces. It turns out that $\mathcal{D}$ is isomorphic to
the universal Leibnitz-Hopf algebra with the antipode $\chi(d_k)=(-1)^kd_k$.
Using the operators $d_k$ we build the generalized $f$-polynomial, which is a
ring homomorphism from $\mathcal{P}$ to the ring $\Qsym[t_1,t_2,...][\alpha]$
of quasi-symmetric functions with coefficients in $\mathbb Z[\alpha]$. The
images of two polytopes coincide if and only if their flag $f$-vectors are
equal. We describe the image of this homomorphism over the integers and prove
that over the rationals it is a free polynomial algebra with dimension of the
$n$-th graded component equal to the $n$-th Fibonacci number. This gives a
representation of the Fibonacci series as an infinite product. The homomorphism
is an isomorphism on the graded group $BB$ generated by the polytopes
introduced by Bayer and Billera to find the linear span of flag $f$-vectors of
convex polytopes. This gives the group $BB$ a structure of the ring isomorphic
to $f(\mathcal{P})$. We show that the ring of polytopes has a natural Hopf
comodule structure over the Rota-Hopf algebra of posets. As a corollary we
build a ring homomorphism $l_{\alpha}\colon\mathcal{P}\to\mathcal{R}[\alpha]$
such that $F(l_{\alpha}(P))=f(P)^*$, where $F$ is the Ehrenborg quasi-symmetric
function.


  The popularity of content management software (CMS) is growing vastly to the
web developers and the business people because of its capacity for easy
accessibility, manageability and usability of the distributed website contents.
As per the statistics of Built with, 32% of the web applications are developed
with WordPress(WP) among all other CMSs [1]. It is obvious that quite a good
number of web applications were built with WP in version 4.7.0 and 4.7.1. A
recent research reveals that content injection vulnerability was found
available in the above two versions of WP [2]. Unauthorized content injection
by an intruder in a CMS managed application is one of the serious problems for
the business as well as for the web owner.Therefore, detection of the
vulnerability becomes a critical issue for this time. In this paper, we have
discussed about the root cause of WP content injection of the above versions
and have also proposed a detection model for the given vulnerability. A tool,
SAISAN has been implemented as per our anticipated model and conducted an
examination on 176 WP developed web applications using SAISAN. We achieved the
accuracy of 92% of the result of SAISAN as compared to manual black box testing
outcome.