  There have been numerous breakthroughs with reinforcement learning in the
recent years, perhaps most notably on Deep Reinforcement Learning successfully
playing and winning relatively advanced computer games. There is undoubtedly an
anticipation that Deep Reinforcement Learning will play a major role when the
first AI masters the complicated game plays needed to beat a professional
Real-Time Strategy game player. For this to be possible, there needs to be a
game environment that targets and fosters AI research, and specifically Deep
Reinforcement Learning. Some game environments already exist, however, these
are either overly simplistic such as Atari 2600 or complex such as Starcraft II
from Blizzard Entertainment. We propose a game environment in between Atari
2600 and Starcraft II, particularly targeting Deep Reinforcement Learning
algorithm research. The environment is a variant of Tower Line Wars from
Warcraft III, Blizzard Entertainment. Further, as a proof of concept that the
environment can harbor Deep Reinforcement algorithms, we propose and apply a
Deep Q-Reinforcement architecture. The architecture simplifies the state space
so that it is applicable to Q-learning, and in turn improves performance
compared to current state-of-the-art methods. Our experiments show that the
proposed architecture can learn to play the environment well, and score 33%
better than standard Deep Q-learning which in turn proves the usefulness of the
game environment.


  We prove that for a three-qubit system in the Greenberger-Horne-Zeilinger
(GHZ) state, locality per se is in conflict with the perfect GHZ correlations.
The proof does not in any way use the realism assumption and can lead to a
refutation of locality. We also provide inequalities that are imposed by
locality. The experimental confirmation of the present reasoning may imply a
genuine quantum nonlocality and will deepen our understanding of nonlocality of
nature.


  We classify the first few brane tilings on a genus 2 Riemann surface and
identify their toric Calabi-Yau moduli spaces. These brane tilings are
extensions of tilings on the 2-torus, which represent one of the largest known
classes of 4d N=1 superconformal field theories for D3-branes. The
classification consists of 16 distinct genus 2 brane tilings with up to 8
quiver fields and 4 superpotential terms. The Higgs mechanism is used to relate
the different theories.


  In a class of left-right symmetric models for linear seesaw, a neutrinoless
double beta decay induced by the left- and right-handed charged currents
together will only depend on the breaking details of left-right and electroweak
symmetries. This neutrinoless double beta decay can reach the experimental
sensitivities if the right-handed charged gauge boson is below the 100 TeV
scale.


  The increasingly neutral intergalactic gas at $z>6$ impacts the
Lyman-$\alpha$ flux observed from galaxies. One luminous galaxy, COLA1, stands
out because of its unique double-peaked Ly$\alpha$ line at $z=6.6$, unseen in
any simulation of reionization. Here we present JWST/NIRCam wide-field slitless
spectroscopy in a 21 arcmin$^2$ field centered on COLA1. We find 141 galaxies
spectroscopically-selected through the [OIII]($\lambda4969,5008$) doublet at
$5.35<z<6.95$, with 40 of these sources showing H$\beta$. For COLA1 we
additionally detect [OIII]$_{4363}$ and H$\gamma$. We measure a systemic
redshift of $z=6.5917$ for COLA1, confirming the double-peak nature of the
Ly$\alpha$ profile. This implies that it resides in a highly ionized bubble and
that it is leaking ionizing photons with a high escape fraction $f_{\rm
esc}{\rm (LyC)}=20$-$50$%, making it a prime laboratory to study Lyman
continuum escape in the Epoch of Reionization. COLA1 shows all the signs of a
prolific ionizer with a Ly$\alpha$ escape fraction of $81\pm5\%$, Balmer
decrement indicating no dust, a steep UV slope ($\beta_{\rm UV}=-3.2\pm 0.4$),
and a star-formation surface density $\gtrsim 10\times$ that of typical
galaxies at similar redshift. We detect 5 galaxies in COLA1's close environment
($\Delta z<0.02$). Exploiting the high spectroscopic completeness inherent to
grism surveys, and using mock simulations that mimic the selection function, we
show the that number of detected companions is very typical for a similarly
UV-bright ($M_{\rm{UV}}\sim-21.3$) galaxy; that is, the ionized bubble around
COLA1 is unlikely due to an excessively large over-density. Instead, the
measured ionizing properties suggest that COLA1 by itself might be powering the
bubble required to explain its double-peaked Ly$\alpha$ profile ($R_{\rm
ion}\approx0.7$ pMpc), with minor contribution from detected neighbours
($-17.5>M_{\rm UV}>-19.5$).


  Presented study concerns the possibility of evaluation of interfacial thermal
resistance (ITR) between the constituents in composite materials with the use
of flash technique. Two variants of such measurement are considered, the first
of which is the measurement of ITR between two bonded layers of different
materials which had been studied before by various researchers. The second
tested measurement method is targeted at determination of ITR in particulate
composites with low and moderate filler content based on their effective
thermal conductivity. Method of such measurement is proposed and tested on two
cases of particle-filled polymer composites. Positive verification results were
obtained for polymer/glass composite in which the difference between thermal
conductivities of matrix and filler is low. For a polymer filled with aluminum
particles the evaluation of average ITR in the samples was impossible as the
effective medium models applied in the method strongly underestimated the
thermal conductivity of that material. The investigation confirmed the need for
more accurate methods of macroscopic thermal properties prediction for
composite media with high contrast of thermal conductivities of the
constituents. Extended literature study suggests that the method can be
applicable to selected classes of engineering materials.


  The initial-boundary value problem in a bounded domain with moving boundaries
and nonhomogeneous boundary conditions for a higher order nonlinear
Schr\"odinger (HNLS) equation is considered. Existence and uniqueness of global
weak solutions are proved as well as the stability of the solution.
Additionally, a conservative numerical method of finite differences is
introduced that also verifies stability properties with respect to the
$L^2$-norm, and along with proving its convergence, some interesting numerical
examples are shown that illustrate the behavior of the solution.


  The purpose of this brief note is to understand the reason for the appearance
of a genus two Riemann surface in the expression for the microscopic degeneracy
of 1/4 BPS dyons in N=4 String Theory.


  Diffusion Limited Aggregation (DLA) is a model of fractal growth that was
introduced in 1981 and had since attained a paradigmatic status due to its
simplicity and its underlying role for a variety of pattern forming processes.
Despite tremendous efforts there is no theory to compute the fractal dimension
of DLA from first principles. In this Letter we offer such a theory for fractal
growth patterns in two dimensions, including DLA as a particular case. In this
theory the fractal dimension of the asymptotic cluster manifests iteself as a
renormalization exponent observable already at very early growth stages. Using
early stage dynamics we compute 1.6896<D<1.7135, and explain why traditional
numerical estimates converged so slowly. We discuss similar computations for
other fractal growth processes in 2-dimensions.


  The first problem we investigate is the following: given $k\in
\mathbb{R}_{\ge 0}$ and a vector $v$ of Pl\"ucker coordinates of a point in the
real Grassmannian, is the vector obtained by taking the $k$th power of each
entry of $v$ again a vector of Pl\"ucker coordinates? For $k\neq 1$, this is
true if and only if the corresponding matroid is regular. Similar results hold
over other fields. We also describe the subvariety of the Grassmannian that
consists of all the points that define a regular matroid.
  The second topic is a related problem for arithmetic matroids. Let
$\mathcal{A} = (E, rk, m)$ be an arithmetic matroid and let $k\neq 1 $ be a
non-negative integer. We prove that if $\mathcal{A}$ is representable and the
underlying matroid is non-regular, then $\mathcal{A}^k := (E, rk, m^k)$ is not
representable. This provides a large class of examples of arithmetic matroids
that are not representable. On the other hand, if the underlying matroid is
regular and an additional condition is satisfied, then $\mathcal{A}^k$ is
representable. Bajo-Burdick-Chmutov have recently discovered that arithmetic
matroids of type $\mathcal{A}^2$ arise naturally in the study of colourings and
flows on CW complexes. In the last section, we prove a family of necessary
conditions for representability of arithmetic matroids.


  This research work proposes a design of an analog ReRAM-based PIM
(processing-in-memory) architecture for fast and efficient CNN (convolutional
neural network) inference. For the overall architecture, we use the basic
hardware hierarchy such as node, tile, core, and subarray. On the top of that,
we design intra-layer pipelining, inter-layer pipelining, and batch pipelining
to exploit parallelism in the architecture and increase overall throughput for
the inference of an input image stream. We also optimize the performance of the
NoC (network-on-chip) routers by decreasing hop counts using SMART
(single-cycle multi-hop asynchronous repeated traversal) flow control. Finally,
we experiment with weight replications for different CNN layers in VGG (A-E)
for large-scale data set ImageNet. In our simulation, we achieve 40.4027 TOPS
(tera-operations per second) for the best-case performance, which corresponds
to over 1029 FPS (frames per second). We also achieve 3.5914 TOPS/W
(tera-operaions per second per watt) for the best-case energy efficiency. In
addition, the architecture with aggressive pipelining and weight replications
can achieve 14X speedup compared to the baseline architecture with basic
pipelining, and SMART flow control achieves 1.08X speedup in this architecture
compared to the baseline. Last but not least, we also evaluate the performance
of SMART flow control using synthetic traffic.


  Online ranker evaluation is one of the key challenges in information
retrieval. While the preferences of rankers can be inferred by interleaving
methods, the problem of how to effectively choose the ranker pair that
generates the interleaved list without degrading the user experience too much
is still challenging. On the one hand, if two rankers have not been compared
enough, the inferred preference can be noisy and inaccurate. On the other, if
two rankers are compared too many times, the interleaving process inevitably
hurts the user experience too much. This dilemma is known as the exploration
versus exploitation tradeoff. It is captured by the $K$-armed dueling bandit
problem, which is a variant of the $K$-armed bandit problem, where the feedback
comes in the form of pairwise preferences. Today's deployed search systems can
evaluate a large number of rankers concurrently, and scaling effectively in the
presence of numerous rankers is a critical aspect of $K$-armed dueling bandit
problems.
  In this paper, we focus on solving the large-scale online ranker evaluation
problem under the so-called Condorcet assumption, where there exists an optimal
ranker that is preferred to all other rankers. We propose Merge Double Thompson
Sampling (MergeDTS), which first utilizes a divide-and-conquer strategy that
localizes the comparisons carried out by the algorithm to small batches of
rankers, and then employs Thompson Sampling (TS) to reduce the comparisons
between suboptimal rankers inside these small batches. The effectiveness
(regret) and efficiency (time complexity) of MergeDTS are extensively evaluated
using examples from the domain of online evaluation for web search. Our main
finding is that for large-scale Condorcet ranker evaluation problems, MergeDTS
outperforms the state-of-the-art dueling bandit algorithms.


  In this paper, we study the blow-up of Willmore surfaces. By using the
3-circle theorem, we prove a decay estimate of the second fundamental form
along the neck region. This estimate provides a new perspective and streamlined
proofs to a few key results in this field, such as the energy
identity(quantization), removable singularities and gap theorem.


  A no-hair theorem for spherical black holes in scalar-tensor gravity is
presented. Contrary to the existing theorems, which are proved in the Einstein
conformal frame, this proof is performed entirely in the Jordan frame. The
theorem is limited to spherical symmetry (instead of axisymmetry) but holds for
non-constant Brans-Dicke couplings.


  Based on dispersion theory, we present a formalism for a model-independent
evaluation of the hadronic light-by-light contribution to the anomalous
magnetic moment of the muon. In particular, we comment on the definition of the
pion pole in this framework and provide a master formula that relates the
effect from pi pi intermediate states to the partial waves for the process
gamma^* gamma^* --> pi pi. All contributions are expressed in terms of on-shell
form factors and scattering amplitudes, and as such amenable to an experimental
determination.


  We propose a new summary statistic for inhomogeneous intensity-reweighted
moment stationary spatio-temporal point processes. The statistic is defined
through the n-point correlation functions of the point process and it
generalises the J-function when stationarity is assumed. We show that our
statistic can be represented in terms of the generating functional and that it
is related to the inhomogeneous K-function. We further discuss its explicit
form under some specific model assumptions and derive a ratio-unbiased
estimator. We finally illustrate the use of our statistic on simulated data.


  In this paper, we extend the maximum modulus estimate of the solutions of the
nonstationary Stokes equations in the bounded $C^2$ cylinders for the space
variables in \cite{CC} to time estimate. We show that if the boundary data is
$L^\infty$ and the normal part of the boundary data has log-Dini continuity
with respect to time, then the velocity is bounded. We emphasize that there is
no continuity assumption on space variables in the new maximum modulus
estimate. This completes the maximum modulus estimate.


  A vertex-colored graph $G$ is rainbow vertex-connected if any pair of
distinct vertices are connected by a path whose internal vertices have distinct
colors. The rainbow vertex-connection number of $G$, denoted by $rvc(G)$, is
the minimum number of colors that are needed to make $G$ rainbow
vertex-connected. In this paper we give a Nordhaus-Gaddum-type result of the
rainbow vertex-connection number. We prove that when $G$ and $\bar{G}$ are both
connected, then $2\leq rvc(G)+rvc(\bar{G})\leq n-1$. Examples are given to show
that both the upper bound and the lower bound are best possible for all $n\geq
5$.


  Spectrum sharing is one of the promising solutions to meet the spectrum
demand in 5G networks that results from the emerging services like machine to
machine and vehicle to infrastructure communication. The idea is to allow a set
of entities access the spectrum whenever and wherever it is unused by the
licensed users. In the proposed framework, different spectrum provider (SP)
networks with surplus spectrum available may rank the operators requiring the
spectrum, called spectrum users (SUs) hereafter, differently in terms of their
preference to lease spectrum, based for example on target business market
considerations of the SUs. Similarly, SUs rank SPs depending on a number of
criteria, for example based on coverage and availability in a service area.
Ideally, both SPs and SUs prefer to provide/get spectrum to/from the operator
of their first choice, but this is not necessarily always possible due to
conflicting preferences. We apply matching theory algorithms with the aim to
resolve the conflicting preferences of the SPs and SUs and quantify the effect
of the proposed matching theory approach on establishing preferred (spectrum)
provider-user network pairs. We discuss both one-to-one and many-to-one
spectrum sharing scenarios and evaluate the performance using Monte Carlo
simulations. The results show that comprehensive gains in terms of preferred
matching of the provider-user network pairs can be achieved by applying
matching theory for spectrum sharing as compared to uncoordinated spectrum
allocation of the available spectrum to the SUs.


  Interpolation techniques play a central role in Astronomy, where one often
needs to smooth irregularly sampled data into a smooth map. In a previous
article (Lombardi & Schneider 2001), we have considered a widely used smoothing
technique and we have evaluated the expectation value of the smoothed map under
a number of natural hypotheses. Here we proceed further on this analysis and
consider the variance of the smoothed map, represented by a two-point
correlation function. We show that two main sources of noise contribute to the
total error budget and we show several interesting properties of these two
noise terms. The expressions obtained are also specialized to the limiting
cases of low and high densities of measurements. A number of examples are used
to show in practice some of the results obtained.


  In this paper, we propose a novel framework for music-driven dance motion
synthesis with controllable key pose constraint. In contrast to methods that
generate dance motion sequences only based on music without any other
controllable conditions, this work targets on synthesizing high-quality dance
motion driven by music as well as customized poses performed by users. Our
model involves two single-modal transformer encoders for music and motion
representations and a cross-modal transformer decoder for dance motions
generation. The cross-modal transformer decoder achieves the capability of
synthesizing smooth dance motion sequences, which keeps a consistency with key
poses at corresponding positions, by introducing the local neighbor position
embedding. Such mechanism makes the decoder more sensitive to key poses and the
corresponding positions. Our dance synthesis model achieves satisfactory
performance both on quantitative and qualitative evaluations with extensive
experiments, which demonstrates the effectiveness of our proposed method.


  I report results on $B\to VV$ and $B\to PV$ decays. The results include the
measurements of the decay amplitudes and the branching fractions in the decays
$B\to \phi K^*$ and $B^+\to \rho^+\rho^0$, the measurements of the branching
fraction and CP asymmetry in $B^+\to \rho^+\pi^0$, and the first evidence of
the decay $B^0\to\rho^0\pi^0$.


  We propose that a certain $4d$ $\mathcal{N}=1$ $SU(2)\times SU(2)$ gauge
theory flows in the IR to an $\mathcal{N}=3$ SCFT plus a single free chiral
field. The specific $\mathcal{N}=3$ SCFT has rank $1$ and a dimension three
Coulomb branch operator. The flow is generically expected to land at the
$\mathcal{N}=3$ SCFT deformed by the marginal deformation associated with said
Coulomb branch operator. We also present a discussion about the properties
expected of various RG invariant quantities from $\mathcal{N}=3$ superconformal
symmetry, and use these to test our proposal. Finally, we discuss a
generalization to another $\mathcal{N}=1$ model that we propose is related to a
certain rank $3$ $\mathcal{N}=3$ SCFT through the turning of certain marginal
deformations.


  In this paper, we investigate the deductive inference for the interiors and
exteriors of Horn knowledge bases, where the interiors and exteriors were
introduced by Makino and Ibaraki to study stability properties of knowledge
bases. We present a linear time algorithm for the deduction for the interiors
and show that it is co-NP-complete for the deduction for the exteriors. Under
model-based representation, we show that the deduction problem for interiors is
NP-complete while the one for exteriors is co-NP-complete. As for Horn
envelopes of the exteriors, we show that it is linearly solvable under
model-based representation, while it is co-NP-complete under formula-based
representation. We also discuss the polynomially solvable cases for all the
intractable problems.


  The density and velocity fields as extracted from the Abell/ACO clusters are
compared to the corresponding fields recovered by the POTENT method from the
Mark~III peculiar velocities of galaxies. In order to minimize non-linear
effects and to deal with ill-sampled regions we smooth both fields using a
Gaussian window with radii ranging between $12 - 20\hmpc$. The density and
velocity fields within $70\hmpc$ exhibit similarities, qualitatively consistent
with gravitational instability theory and a linear biasing relation between
clusters and mass. The random and systematic errors are evaluated with the help
of mock catalogs. Quantitative comparisons within a volume containing
$\sim\!12$ independent samples yield
$\betac\equiv\Omega^{0.6}/b_c=0.22\pm0.08$, where $b_c$ is the cluster biasing
parameter at $15\hmpc$. If $b_c \sim 4.5$, as indicated by the cluster
correlation function, our result is consistent with $\Omega \sim 1$.


  This paper proves a Serrin's type blow-up criterion for the 3D
density-dependent Navier-Stokes-Korteweg equations with vacuum. It is shown
that if the density and velocity field satisfy some Serrin's type condition,
then the strong solutions to the density-dependent Navier-Stokes-Korteweg
equations can exist globally.


  We report on study of the electronic anisotropy of the newly discovered MgB2
superconductor using the in-plane resistivity measurements in magnetic field
applied perpendicular and parallel to Mg and B planes of MgB2 single crystals.
The results show temperature dependent anisotropy of the upper critical field
with anisotropy ratio increasing from 2.2 close to Tc up to about 3 below 30K.
Our estimation of the in-plane and out-of-plane coherence length of about 68A
and 23A and electronic mean-free path 240A and 60A respectively indicates MgB2
single crystal as approaching clean limit type-II superconductor.


  Textual domain is a crucial property within the Natural Language Processing
(NLP) community due to its effects on downstream model performance. The concept
itself is, however, loosely defined and, in practice, refers to any
non-typological property, such as genre, topic, medium or style of a document.
We investigate the core notion of domains via human proficiency in identifying
related intrinsic textual properties, specifically the concepts of genre
(communicative purpose) and topic (subject matter). We publish our annotations
in *TGeGUM*: A collection of 9.1k sentences from the GUM dataset (Zeldes, 2017)
with single sentence and larger context (i.e., prose) annotations for one of 11
genres (source type), and its topic/subtopic as per the Dewey Decimal library
classification system (Dewey, 1979), consisting of 10/100 hierarchical topics
of increased granularity. Each instance is annotated by three annotators, for a
total of 32.7k annotations, allowing us to examine the level of human
disagreement and the relative difficulty of each annotation task. With a
Fleiss' kappa of at most 0.53 on the sentence level and 0.66 at the prose
level, it is evident that despite the ubiquity of domains in NLP, there is
little human consensus on how to define them. By training classifiers to
perform the same task, we find that this uncertainty also extends to NLP
models.


  We introduce a new class of growth models, with a surface restructuring
mechanism in which impinging particles may dislodge suspended particles,
previously aggregated on the same column in the deposit. The flux of these
particles is controlled through a probability $p$. These systems present a
crossover, for small values of $p$, from random to correlated (KPZ) growth of
surface roughness, which is studied through scaling arguments and Monte Carlo
simulations on one- and two-dimensional substrates. We show that the crossover
characteristic time $t_{\times}$ scales with $p$ according to $t_{\times}\sim
p^{-y}$ with $y=(n+1)$ and that the interface width at saturation $W_{sat}$
scales as $W_{sat}\sim p^{-\delta}$ with $\delta = (n+1)/2$, where $n$ is
either the maximal number of broken bonds or of dislodged suspended particles.
This result shows that the sets of exponents $y=1$ and $\delta=1/2$ or $y=2$
and $\delta=1$ found in all previous works focusing on systems with this same
type of crossover are not universal. Using scaling arguments, we show that the
bulk porosity $P$ of the deposits scales as $P\sim p^{y-\delta}$ for small
values of $p$. This general scaling relation is confirmed by our numerical
simulations and explains previous results present in literature.


  We will prove that by averaging of random variables (r.v.) and random fields
(r.f.) its tails of distributions do not increase in comparison with the tails
of source variables, essentially or almost exact, under very weak conditions.


  The I-GALFA survey is mapping all the HI in the inner Galactic disk visible
to the Arecibo 305m telescope within 10 degrees of the Galactic plane
(longitudes of 32 to 77 deg at b=0 deg). The survey, which will obtain 1.3
million independent spectra, became possible with the installation of the
7-beam Arecibo L-Band Feed Array (ALFA) receiver in 2004. ALFA's 3.4 arcmin
resolution and tremendous sensitivity offer a great opportunity to observe the
fine details of HI in the Galaxy. The I-GALFA survey began in 2008 May and will
be completed in 2009 September. The data will be made publicly available when
the calibrated and gridded cubes are completed. Further information on the
I-GALFA project may be found at www.naic.edu/~galfa.


  In this paper, we propose a whole-body planning framework that unifies
dynamic locomotion and manipulation tasks by formulating a single multi-contact
optimal control problem. We model the hybrid nature of a generic multi-limbed
mobile manipulator as a switched system, and introduce a set of constraints
that can encode any pre-defined gait sequence or manipulation schedule in the
formulation. Since the system is designed to actively manipulate its
environment, the equations of motion are composed by augmenting the robot's
centroidal dynamics with the manipulated-object dynamics. This allows us to
describe any high-level task in the same cost/constraint function. The
resulting planning framework could be solved on the robot's onboard computer in
real-time within a model predictive control scheme. This is demonstrated in a
set of real hardware experiments done in free-motion, such as base or
end-effector pose tracking, and while pushing/pulling a heavy resistive door.
Robustness against model mismatches and external disturbances is also verified
during these test cases.


  We discuss constraints on so-called `varying speed of light theories' coming
from the physics of the early universe. Specifically, we consider the position
of the first acoustic peak of the CMB angular power spectrum, showing that the
recent determination of its position by various CMB experiments, in particular
BOOMERanG/NA, can be used to constrain the value of the speed of light $c$
after the epoch of last scattering. Specifically, we find that for a flat
universe and a standard density of baryonic matter a variation in $c$ of up to
4% is consistent with the current observations. The position of the Doppler
peak is fairly sensitive to changes in $c$, and future observations should
dramatically improve this bound. On the other hand, we also find that the
maximum baryonic density allowed in VSL theories is about $\Omega_B h^2\sim
0.06\Omega_0$. We comment on the significance of these results.


  We studied the room evacuation problem within the context of the Social Force
Model. We focused on a system of 225 pedestrians escaping from a room in
different anxiety levels, and analyzed the clogging delays as the relevant
magnitude responsible for the evacuation performance. We linked the delays with
the clusterization phenomenon along the "faster is slower" and the "faster is
faster" regimes. We will show that the "faster is faster" regime is
characterized by the presence of a giant cluster structure (composed by more
than 15 pedestrians), although no long lasting delays appear within this
regime. For this system, we found that the relevant structures in the "faster
is slower" regime are those blocking clusters that are somehow attached to the
two walls defining the exit. At very low desired velocities, very small
structures become relevant (composed by less than 5 pedestrians), but at
intermediate velocities (vd = 3 m/s) the pedestrians involved in the blockings
increases (not exceeding 15 pedestrians).


  Quintessence is a canonical scalar field introduced to explain the late-time
cosmic acceleration. The cosmological dynamics of quintessence is reviewed,
paying particular attention to the evolution of the dark energy equation of
state w. For the field potentials having tracking and thawing properties, the
evolution of w can be known analytically in terms of a few model parameters.
Using the analytic expression of w, we constrain quintessence models from the
observations of supernovae type Ia, cosmic microwave background, and baryon
acoustic oscillations. The tracking freezing models are hardly distinguishable
from the LCDM model, whereas in thawing models the today's field equation of
state is constrained to be w_0<-0.7 (95 % CL). We also derive an analytic
formula for the growth rate of matter density perturbations in dynamical dark
energy models, which allows a possibility to put further bounds on w from the
measurement of redshift-space distortions in the galaxy power spectrum. Finally
we review particle physics models of quintessence- such as those motivated by
supersymmetric theories. The field potentials of thawing models based on a
pseudo-Nambu-Goldstone boson or on extended supergravity theories have a nice
property that a tiny mass of quintessence can be protected against radiative
corrections.


  Random walks on simple graphs in connection with electrical resistor networks
lead to the definition of Markov chains with transition probability matrix in
terms of electrical conductances. We extend this definition to an effective
transition matrix $P_{ij}$ to account for the probability of going from vertex
$i$ to any vertex $j$ of the original connected graph $G$. Also, we present an
algorithm based on the definition of this effective transition matrix among
vertices in the network to extract a topological feature related to the manner
graph $G$ has been organized. This topological feature corresponds to the
communities in the graph.


  Neural models excel at extracting statistical patterns from large amounts of
data, but struggle to learn patterns or reason about language from only a few
examples. In this paper, we ask: Can we learn explicit rules that generalize
well from only a few examples? We explore this question using program
synthesis. We develop a synthesis model to learn phonology rules as programs in
a domain-specific language. We test the ability of our models to generalize
from few training examples using our new dataset of problems from the
Linguistics Olympiad, a challenging set of tasks that require strong linguistic
reasoning ability. In addition to being highly sample-efficient, our approach
generates human-readable programs, and allows control over the generalizability
of the learnt programs.


  Habitable zone dust levels are a key unknown that must be understood to
ensure the success of future space missions to image Earth analogues around
nearby stars. Current detection limits are several orders of magnitude above
the level of the Solar System's Zodiacal cloud, so characterisation of the
brightness distribution of exo-zodi down to much fainter levels is needed. To
this end, the large Binocular Telescope Interferometer (LBTI) will detect
thermal emission from habitable zone exo-zodi a few times brighter than Solar
System levels. Here we present a modelling framework for interpreting LBTI
observations, which yields dust levels from detections and upper limits that
are then converted into predictions and upper limits for the scattered light
surface brightness. We apply this model to the HOSTS survey sample of nearby
stars; assuming a null depth uncertainty of 10$^{-4}$ the LBTI will be
sensitive to dust a few times above the Solar System level around Sun-like
stars, and to even lower dust levels for more massive stars.


  We give an answer to Problem 9.3 stated by by Mesiar and Stupnanova (2015).
We show that the class of semicopulas solving this problem contains any
associative semicopula S such that a the function S(a,.) is continuous and
increasing on a countable number of intervals.


  This note modifies the reference encoding of Turing machines in the
$\lambda$-calculus by Dal Lago and Accattoli, which is tuned for time
efficiency, as to accommodate logarithmic space. There are two main changes:
Turing machines now have *two* tapes, an input tape and a work tape, and the
input tape is encoded differently, because the reference encoding comes with a
linear space overhead for managing tapes, which is excessive for studying
logarithmic space.


  The continuous increase of data generated provides enormous possibilities of
both public and private companies. The management of this mass of data or big
data will play a crucial role in the society of the future, as it finds
applications in different fields. There are so much potential and extremely
useful insights hidden in the huge volume of data. The advanced analysis
techniques available including predictive analytics, text mining, semantic
analysis are needed to enable organizations to create a competitive advantage
through data analyzed with different levels of sophistication, speed and
accuracy previously unavailable. Therefore, is it still possible to have that
level of sophistication with the ubiquitous numeric ocean that accompanies use
every day via connected devices that invade our lives? However, development of
big data requires a good understanding of the issues associated with it. And
this is the purpose of this paper, which focuses on giving a close-up view of
big data analysis, opportunities and challenges.


  The demand for condition-based and predictive maintenance is rising across
industries, especially for remote, high-value, and high-risk assets. In this
article, the diagnostic digital twin concept is introduced, discussed, and
implemented for a floating offshore turbine. A diagnostic digital twin is a
virtual representation of an asset that combines real-time data and models to
monitor damage, detect anomalies, and diagnose failures, thereby enabling
condition-based and predictive maintenance. By applying diagnostic digital
twins to offshore assets, unexpected failures can be alleviated, but the
implementation can prove challenging. Here, a diagnostic digital twin is
implemented for an operational floating offshore wind turbine. The asset is
monitored through measurements. Unsupervised learning methods are employed to
build a normal operation model, detect anomalies, and provide a fault
diagnosis. Warnings and diagnoses are sent through text messages, and a more
detailed diagnosis can be accessed in a virtual reality interface. The
diagnostic digital twin successfully detected an anomaly with high confidence
hours before a failure occurred. The paper concludes by discussing diagnostic
digital twins in the broader context of offshore engineering. The presented
approach can be generalized to other offshore assets to improve maintenance and
increase the lifetime, efficiency, and sustainability of offshore assets.


  We developed a new lattice Boltzmann method that allows the simulation of
two-phase flow of viscoelastic liquid mixtures. We used this new method to
simulate a bubble rising in a viscoelastic fluid and were able to reproduce the
experimentally observed cusp at the trailing end of the bubble.


  Main characteristics of Google Scholar Metrics new version (july 2013) are
presented. We outline the novelties and the weaknesses detected after a first
analysis. As main conclusion, we remark the lack of new functionalities with
respect to last editions, as the only modification is the update of the
timeframe (2008-2012). Hence, problems pointed out in our last reviews still
remain active. Finally, it seems Google Scholar Metrics will be updated in a
yearly basis


  Certifying the robustness of neural networks against adversarial attacks is
essential to their reliable adoption in safety-critical systems such as
autonomous driving and medical diagnosis. Unfortunately, state-of-the-art
verifiers either do not scale to bigger networks or are too imprecise to prove
robustness, limiting their practical adoption. In this work, we introduce
GPUPoly, a scalable verifier that can prove the robustness of significantly
larger deep neural networks than previously possible. The key technical insight
behind GPUPoly is the design of custom, sound polyhedra algorithms for neural
network verification on a GPU. Our algorithms leverage the available GPU
parallelism and inherent sparsity of the underlying verification task. GPUPoly
scales to large networks: for example, it can prove the robustness of a 1M
neuron, 34-layer deep residual network in approximately 34.5 ms. We believe
GPUPoly is a promising step towards practical verification of real-world neural
networks.


  Protein-protein interactions (PPIs) perform important roles on biological
functions. Researches of mutants on protein interactions can further understand
PPIs. In the past, many researchers have developed databases that stored
mutants on protein interactions, which are old and not updated till now. To
address the issue, we developed a kinetic and thermodynamic database of mutant
protein interactions (dbMPIKT) that can be freely accessible at our website.
This database contains 5291 mutants that integrated data from previous
databases and data from literatures for nearly three years. Furthermore, the
data were analyzed, involving mutation number, mutation type, protein pair
source and network map construction. On the whole, the database provides new
data to further improve the study on PPIs. Website:
http://210.45.212.128/lqy/index.php


  We use field-level forward models of galaxy clustering and the EFT likelihood
formalism to study, for the first time for self-consistently simulated
galaxies, the relations between the linear $b_1$ and second-order bias
parameters $b_2$ and $b_{K^2}$. The forward models utilize all of the
information available in the galaxy distribution up to a given order in
perturbation theory, which allows us to infer these bias parameters with high
signal-to-noise, even from relatively small volumes ($L_{\rm box} = 205{\rm
Mpc}/h$). We consider galaxies from the IllustrisTNG simulations, and our main
result is that the $b_2(b_1)$ and $b_{K^2}(b_1)$ relations obtained from
gravity-only simulations for total mass selected objects are broadly preserved
for simulated galaxies selected by stellar mass, star formation rate, color and
black hole accretion rate. We also find good agreement between the bias
relations of the simulated galaxies and a number of recent estimates for
observed galaxy samples. The consistency under different galaxy selection
criteria suggests that theoretical priors on these bias relations may be used
to improve cosmological constraints based on observed galaxy samples. We do
identify some small differences between the bias relations in the
hydrodynamical and gravity-only simulations, which we show can be linked to the
environmental dependence of the relation between galaxy properties and mass. We
also show that the EFT likelihood recovers the value of $\sigma_8$ to
percent-level from various galaxy samples (including splits by color and star
formation rate) and after marginalizing over 8 bias parameters. This
demonstration using simulated galaxies adds to previous works based on halos as
tracers, and strengthens further the potential of forward models to infer
cosmology from galaxy data.


  Swift J004929.5-733107 is an X-ray source in the Small Magellanic Cloud (SMC)
that has been reported several times, but the optical counterpart has been
unclear due to source confusion in a crowded region of the SMC. Previous works
proposed [MA93] 302 as the counterpart, however we show here, using data
obtained from the S-CUBED project, that the X-ray positio is inconsistent with
that object. Instead we propose a previously unclassified object which has all
the indications of being a newly identified Be star exhibiting strong HU
emission. Evidence for the presence of significant I-band variability strongly
suggest that this is, in fact, a Be type star with a large circumstellar disk.
Over 18 years worth of optical monitoring by the OGLE project reveal a periodic
modulation at a period of 413d, probably the binary period of the system. A
SALT optical spectrum shows strong Balmer emission and supports a proposed
spectral classification of B1-3 III-IVe. The X-ray data obtained from the
S-CUBED project reveal a time-averaged spectrum well fitted by a photon index =
0.93 pm 0.16. Assuming the known distance to the SMC the flux corresponds to a
luminosity 10E35 erg/s. All of these observational facts suggest that this is
confirmed as a Be star-neutron star X-ray binary (BeXRB) in the SMC, albeit one
with an unusually long binary period at the limits of the Corbet Diagram.


  We study the logarithmic entanglement negativity of symmetry-protected
topological (SPT) phases and quantum critical points (QCPs) of one-dimensional
noninteracting fermions at finite temperatures. In particular, we consider a
free fermion model that realizes not only quantum phase transitions between
gapped phases but also an exotic topological phase transition between quantum
critical states in the form of the fermionic Lifshitz transition. The bipartite
entanglement negativity between adjacent fermion blocks reveals the crossover
boundary of the quantum critical fan near the QCP between two gapped phases.
Along the critical phase boundary between the gapped phases, the sudden
decrease in the entanglement negativity signals the fermionic Lifshitz
transition responsible for the change in the topological nature of the QCPs. In
addition, the tripartite entanglement negativity between spatially separated
fermion blocks counts the number of topologically protected boundary modes for
both SPT phases and topologically nontrivial QCPs at zero temperature. However,
the long-distance entanglement between the boundary modes vanishes at finite
temperatures due to the instability of SPTs, the phases themselves.


  We solve the Dirichlet problem for Monge-Amp\`ere equation for $(n-1)$-PSH
functions possibly with degenerate right-hand side, through deriving a
quantitative version of boundary estimate under the assumption of $(n-1)$-PSH
subsolutions. In addition, we confirm the subsolution assumption on a product
of a closed balanced manifold with a compact Riemann surface with boundary.


  While the spin liquid state in the frustrated pyrochlore
Tb$_{2+x}$Ti$_{2-x}$O$_{7+y}$ has been studied both experimentally and
theoretically for more than two decades, no definite description of this
unconventional state has been achieved. Using synchrotron based THz
spectroscopy in combination with quantum numerical simulations, we highlight a
significant link between two previously unrelated features: the existence of a
quadrupolar order following an ice rule and the presence of strong
magneto-elastic coupling in the form of hybridized Tb$^{3+}$ crystal-field and
phonon modes. The magnitude of this so-called vibronic process, which involves
quadrupolar degrees of freedom, is significantly dependent on small
off-stoichiometry $x$ and favors all-in all-out like correlations between
quadrupoles. This mechanism competes with the long range ordered quadrupolar
ice, and for slightly different stoichiometry, is able to destabilize it.


  A permutation group $(X,G)$ is said to be binary, or of relational complexity
$2$, if for all $n$, the orbits of $G$ (acting diagonally) on $X^2$ determine
the orbits of $G$ on $X^n$ in the following sense: for all $\bar{x},\bar{y} \in
X^n$, $\bar{x}$ and $\bar{y}$ are $G$-conjugate if and only if every pair of
entries from $\bar{x}$ is $G$-conjugate to the corresponding pair from
$\bar{y}$. Cherlin has conjectured that the only finite primitive binary
permutation groups are $S_n$, groups of prime order, and affine orthogonal
groups $V\rtimes O(V)$ where $V$ is a vector space equipped with an anisotropic
quadratic form; recently he succeeded in establishing the conjecture for those
groups with an abelian socle. In this note, we show that what remains of the
conjecture reduces, via the O'Nan-Scott Theorem, to groups with a nonabelian
simple socle.


  One class of statistical hypothesis testing procedures is the indisputable
equivalence tests, whose main objective is to establish practical equivalence
rather than the usual statistical significant difference. These hypothesis
tests are prone in bioequivalence studies, where one would wish to show that,
for example, an existing drug and a new one under development have the same
therapeutic effect. In this article, we consider a two-stage randomized (RAND2)
p-value utilizing the uniformly most powerful (UMP) p-value in the first stage
when multiple two-one-sided hypotheses are of interest. We investigate the
behavior of the distribution functions of the two p-values when there are
changes in the boundaries of the null or alternative hypothesis or when the
chosen parameters are too close to these boundaries. We also consider the
behavior of the power functions to an increase in sample size. Specifically, we
investigate the level of conservativity to the sample sizes to see if we
control the type I error rate when using either of the two p-values for any
sample size. In multiple tests, we evaluate the performance of the two p-values
in estimating the proportion of true null hypotheses. We conduct a family-wise
error rate control using an adaptive Bonferroni procedure with a plug-in
estimator to account for the multiplicity that arises from the multiple
hypotheses under consideration. We verify the various claims in this research
using simulation study and real-world data analysis.


  Real time data acquisition systems in nuclear science often rely on
high-speed logic designs to reach the fast data rate requirements. They are
mostly coded in a hardware description language (HDL). However, in recent
years, high level synthesis (HLS) compilers have appeared, with the notable
advantage that they rely on the widespread C/C++ syntax. This paper's aim is to
outline differences between HDL and C/C++ HLS based designs for two real-time
data acquisition modules used in nuclear science. The first module is a
real-time crystal identification module, and the second is a compact event
timestamp sorting module. This evaluation was done by an experienced VHDL
programmer with no prior HLS training. For the crystal identification module,
both HDL and HLS versions have the same event processing interval, and the HLS
implementation consumes twice as many lookup tables and flip flops as the HDL
version. On the other hand, the HLS version took half the time to write and
debug. For the sorter module, the HLS version requires about 3 to 4 times more
logic resources, with a slightly longer processing interval. It was also
completed in half the time compared to the original HDL code. While different
compiler directives can still be explored to improve source code clarity,
resource usage and timing closure in these designs, this trial shows that HLS
is a compelling alternative to custom HDL implementations for real time systems
in nuclear and plasma science.


  In this paper, we consider a layer of a viscous incompressible electrically
conducting fluid interacting with the magnetic filed in a horizontally periodic
setting. The upper boundary bounded by a free boundary and below bounded by a
flat rigid interface. We prove the global well-posedness of the problem for
both the case with and without surface tension. Moreover, we show that the
global solution decays to the equilibrium exponentially in the case with
surface tension, however the global solution decays to the equilibrium at an
almost exponential rate in the case without surface tension.


  The quantum random energy model provides a mean-field description of the
equilibrium spin glass transition. We show that it further exhibits a many-body
localization - delocalization (MBLD) transition when viewed as a closed quantum
system. The mean-field structure of the model allows an analytically tractable
description of the MBLD transition using the forward-scattering approximation
and replica techniques. The predictions are in good agreement with the
numerics. The MBLD lies at energy density significantly above the equilibrium
spin glass transition, indicating that the closed system dynamics freezes well
outside of the traditional glass phase. We also observe that the structure of
the eigenstates at the MBLD critical point changes continuously with the energy
density, raising the possibility of a family of critical theories for the MBLD
transition.


  The quality of industrial components is critical to the production of special
equipment such as robots. Defect inspection of these components is an efficient
way to ensure quality. In this paper, we propose a hybrid network, SSD-Faster
Net, for industrial defect inspection of rails, insulators, commutators etc.
SSD-Faster Net is a two-stage network, including SSD for quickly locating
defective blocks, and an improved Faster R-CNN for defect segmentation. For the
former, we propose a novel slice localization mechanism to help SSD scan
quickly. The second stage is based on improved Faster R-CNN, using FPN,
deformable kernel(DK) to enhance representation ability. It fuses multi-scale
information, and self-adapts the receptive field. We also propose a novel loss
function and use ROI Align to improve accuracy. Experiments show that our
SSD-Faster Net achieves an average accuracy of 84.03%, which is 13.42% higher
than the nearest competitor based on Faster R-CNN, 4.14% better than GAN-based
methods, more than 10% higher than that of DNN-based detectors. And the
computing speed is improved by nearly 7%, which proves its robustness and
superior performance.


  The spin-1/2 kagome lattice antiferromagnet herbertsmithite,
ZnCu$_{3}$(OH)$_{6}$Cl$_{2}$, is a candidate material for a quantum spin liquid
ground state. We show that the magnetic response of this material displays an
unusual scaling relation in both the bulk ac susceptibility and the low energy
dynamic susceptibility as measured by inelastic neutron scattering. The
quantity $\chi T^\alpha$ with $\alpha \simeq 0.66$ can be expressed as a
universal function of $H/T$ or $\omega/T$. This scaling is discussed in
relation to similar behavior seen in systems influenced by disorder or by the
proximity to a quantum critical point.


  The European Far-Infrared (FIR) Space Roadmap focuses on fundamental, yet
still unresolved, astrophysical questions that can only be answered through a
far-infrared space mission and gives an overview of the technology required to
answer them. The document discusses topics ranging from Solar System and Planet
Formation, Our Galaxy and nearby Galaxies and Distant Galaxies and Galaxy
Evolution. The FIR Roadmap was open to comments from the wider astronomical
community following a presentation during EWASS 2016.


  Here we prove the convergence of the Ando-Li-Mathias and Bini-Meini-Poloni
procedures for matrix means. Actually it is proved here that for a two-variable
function which maps pairs of positive definite matrices to a positive definite
matrix and is not greater than the square mean of two positive definite
matrices, the Ando-Li-Mathias and Bini-Meini-Poloni procedure converges. In
order to be able to set up the Bini-Meini-Poloni procedure, a weighted
two-variable matrix mean is also needed. Therefore a definition of a
two-variable weighted matrix mean corresponding to every symmetric matrix mean
is also given. It is also shown here that most of the properties considered by
Ando, Li and Mathias for the $n$-variable geometric mean hold for all of these
$n$-variable maps that we obtain by this two limiting process for all
two-variable matrix means. As a consequence it also follows that the
Bini-Meini-Poloni procedure converges cubically for every matrix mean.


  In this paper we consider the problem of finding the {\em densest} subset
subject to {\em co-matroid constraints}. We are given a {\em monotone
supermodular} set function $f$ defined over a universe $U$, and the density of
a subset $S$ is defined to be $f(S)/\crd{S}$. This generalizes the concept of
graph density. Co-matroid constraints are the following: given matroid $\calM$
a set $S$ is feasible, iff the complement of $S$ is {\em independent} in the
matroid. Under such constraints, the problem becomes $\np$-hard. The specific
case of graph density has been considered in literature under specific
co-matroid constraints, for example, the cardinality matroid and the partition
matroid. We show a 2-approximation for finding the densest subset subject to
co-matroid constraints. Thus, for instance, we improve the approximation
guarantees for the result for partition matroids in the literature.


  In PT quantum mechanics a fundamental principle of quantum mechanics, that
the Hamiltonian must be hermitian, is replaced by another set of requirements,
including notably symmetry under PT, where P denotes parity and T denotes time
reversal. Here we study the role of boundary conditions in PT quantum mechanics
by constructing a simple model that is the PT symmetric analog of a particle in
a box. The model has the usual particle in a box Hamiltonian but boundary
conditions that respect PT symmetry rather than hermiticity. We find that for a
broad class of PT-symmetric boundary conditions the model respects the
condition of unbroken PT-symmetry, namely that the Hamiltonian and the symmetry
operator PT have simultaneous eigenfunctions, implying that the energy
eigenvalues are real. We also find that the Hamiltonian is self-adjoint under
the PT inner product. Thus we obtain a simple soluble model that fulfils all
the requirements of PT quantum mechanics. In the second part of this paper we
formulate a variational principle for PT quantum mechanics that is the analog
of the textbook Rayleigh-Ritz principle. Finally we consider electromagnetic
analogs of the PT-symmetric particle in a box. We show that the isolated
particle in a box may be realized as a Fabry-Perot cavity between an absorbing
medium and its conjugate gain medium. Coupling the cavity to an external
continuum of incoming and outgoing states turns the energy levels of the box
into sharp resonances. Remarkably we find that the resonances have a
Breit-Wigner lineshape in transmission and a Fano lineshape in reflection; by
contrast in the corresponding hermitian case the lineshapes always have a
Breit-Wigner form in both transmission and reflection.


  The process $(G_t)_{t\in[0,T]}$ is referred to as a fractional Gaussian
process if the first-order partial derivative of the difference between its
covariance function and that of the fractional Brownian motion
$(B^H_t)_{t\in[0,T ]}$ is a normalized bounded variation function. We quantify
the relation between the associated reproducing kernel Hilbert space of $(G)$
and that of $(B^H)$. Seven types of Gaussian processes with non-stationary
increments in the literature belong to it. In the context of applications, we
demonstrate that the Gladyshev's theorem holds for this process, and we provide
Berry-Ess\'{e}en upper bounds associated with the statistical estimations of
the ergodic fractional Ornstein-Uhlenbeck process driven by it. The second
application partially builds upon the idea introduced in \cite{BBES 23}, where
they assume that $(G)$ has stationary increments. Additionally, we briefly
discuss a variant of this process where the covariance structure is not
entirely linked to that of the fractional Brownian motion.


  It has been suggested that the peanut-shaped bulges seen in some edge-on disk
galaxies are produced when bars in these galaxies buckle. This paper reviews
the modelling which seeks to show how bars buckle, and I present a very simple
new model which captures the essential physics of this process. I then discuss
the problems in establishing observationally the connection between
peanut-shaped bulges and bars: confirmation of the link has proved difficult
because boxy bulges are only apparent in edge-on galaxies whereas bars are only
easily detectable in more face-on systems. Finally, I present a new technique
which avoids this difficulty by searching for the distinctive kinematic
signature of an edge-on bar; application of this method to spectra of
peanut-shaped bulges reveals that they are, indeed, associated with hidden
bars.


  While they have long been a subject of academic study, social virtual reality
(SVR) systems are now attracting increasingly large audiences on current
consumer virtual reality systems. The design space of SVR systems is very
large, and relatively little is known about how these systems should be
constructed in order to be usable and efficient. In this paper we present Ubiq,
a toolkit that focuses on facilitating the construction of SVR systems. We
argue for the design strategy of Ubiq and its scope. Ubiq is built on the Unity
platform. It provides core functionality of many SVR systems such as connection
management, voice, avatars, etc. However, its design remains easy to extend. We
demonstrate examples built on Ubiq and how it has been successfully used in
classroom teaching. Ubiq is open source (Apache License) and thus enables
several use cases that commercial systems cannot.


  Neutrinos play an important role in core-collapse supernova events since they
are a key piece to understand the explosion mechanisms. The analysis of the
neutrino fluxes can bring answers to neutrino's related problems e.g.: mass
hierarchy, spectral splitting, sterile neutrinos, etc. In this work we study
the impact of neutrino oscillations and the possible existence of eV sterile
neutrinos upon the supernova neutrino flux $F_\nu(E)$. We have calculated the
energy distribution of the neutrino flux from a supernova and the total number
of events which would be detected in a liquid scintillator. We also present an
analysis for the conversion probabilities as a function of the active-sterile
neutrino mixing parameters. Finally, we have carried out a statistical analysis
to extract values for the mixing parameters of the model.


  The Dirichlet eigenvalues of the Laplace-Beltrami operator are larger on a
flat disc than on any other surface of revoltuion immersed in Euclidean space
with the same boundary.


  Reachability analysis is important for studying optimal control problems and
differential games, which are powerful theoretical tools for analyzing and
modeling many practical problems in robotics, aircraft control, among other
application areas. In reachability analysis, one is interested in computing the
reachable set, defined as the set of states from which there exists a control,
despite the worst disturbance, that can drive the system into a set of target
states. The target states can be used to model either unsafe or desirable
configurations, depending on the application. Many Hamilton-Jacobi formulations
allow the computation of reachable sets; however, due to the exponential
complexity scaling in computation time and space, problems involving
approximately 5 dimensions become intractable. A number of methods that compute
an approximate solution exist in the literature, but these methods trade off
complexity for optimality. In this paper, we eliminate complexity-optimality
trade-offs for time-invariant decoupled systems using a decoupled
Hamilton-Jacobi formulation that enables the exact reconstruction of high
dimensional solutions via low dimensional solutions of the decoupled
subsystems. Our formulation is compatible with existing numerical tools, and we
show the accuracy, computation benefits, and an application of our novel
approach using two numerical examples.


  We introduce a method that dramatically reduces fine-tuning VRAM requirements
and rectifies quantization errors in quantized Large Language Models. First, we
develop an extremely memory-efficient fine-tuning (EMEF) method for quantized
models using Low-Rank Adaptation (LoRA), and drawing upon it, we construct an
error-correcting algorithm designed to minimize errors induced by the
quantization process. Our method reduces the memory requirements by up to 5.6
times, which enables fine-tuning a 7 billion parameter Large Language Model
(LLM) on consumer laptops. At the same time, we propose a Low-Rank Error
Correction (LREC) method that exploits the added LoRA layers to ameliorate the
gap between the quantized model and its float point counterpart. Our error
correction framework leads to a fully functional INT2 quantized LLM with the
capacity to generate coherent English text. To the best of our knowledge, this
is the first INT2 Large Language Model that has been able to reach such a
performance. The overhead of our method is merely a 1.05 times increase in
model size, which translates to an effective precision of INT2.1. Also, our
method readily generalizes to other quantization standards, such as INT3, INT4,
and INT8, restoring their lost performance, which marks a significant milestone
in the field of model quantization. The strategies delineated in this paper
hold promising implications for the future development and optimization of
quantized models, marking a pivotal shift in the landscape of low-resource
machine learning computations.


  Recently, we made available WeNet, a production-oriented end-to-end speech
recognition toolkit, which introduces a unified two-pass (U2) framework and a
built-in runtime to address the streaming and non-streaming decoding modes in a
single model. To further improve ASR performance and facilitate various
production requirements, in this paper, we present WeNet 2.0 with four
important updates. (1) We propose U2++, a unified two-pass framework with
bidirectional attention decoders, which includes the future contextual
information by a right-to-left attention decoder to improve the representative
ability of the shared encoder and the performance during the rescoring stage.
(2) We introduce an n-gram based language model and a WFST-based decoder into
WeNet 2.0, promoting the use of rich text data in production scenarios. (3) We
design a unified contextual biasing framework, which leverages user-specific
context (e.g., contact lists) to provide rapid adaptation ability for
production and improves ASR accuracy in both with-LM and without-LM scenarios.
(4) We design a unified IO to support large-scale data for effective model
training. In summary, the brand-new WeNet 2.0 achieves up to 10\% relative
recognition performance improvement over the original WeNet on various corpora
and makes available several important production-oriented features.


  In loving memory of Asher Peres, we discuss a most important and influential
paper written in 1935 by his thesis supervisor and mentor Nathan Rosen,
together with Albert Einstein and Boris Podolsky. In that paper, the trio known
as EPR questioned the completeness of quantum mechanics. The authors argued
that the then-new theory should not be considered final because they believed
it incapable of describing physical reality. The epic battle between Einstein
and Bohr intensified following the latter's response later the same year. Three
decades elapsed before John S. Bell gave a devastating proof that the EPR
argument was fatally flawed. The modest purpose of our paper is to give a
critical analysis of the original EPR paper and point out its logical
shortcomings in a way that could have been done 70 years ago, with no need to
wait for Bell's theorem. We also present an overview of Bohr's response in the
interest of showing how it failed to address the gist of the EPR argument.


  Spacetime geometry is supposed to be measured by identifying the trajectories
of free test particles with geodesics. In practice, this cannot be done
because, being described by Quantum Mechanics, particles do not follow
trajectories. As a first step to study how it is possible to read spacetime
geometry with quantum particles, we model these particles with classical
extended objects. We propose to represent such extended objects by its
covariant center of mass, which generically does not follow a geodesic of the
background metric. We present a scheme that allows to extract some of
components of an "effective" connection, namely, the connection that would be
obtained if the locus of the center of mass is regarded as a geodesic. We
discuss some issues that arise when trying to obtain all the components of the
effective connection and its possible implications.


  We shall study some moduli spaces of Bridgeland's semi-stable objects on
abelian surfaces and K3 surfaces with Picard number 1. Under some conditions,
we show that the moduli spaces are isomorphic to the moduli spaces of Gieseker
semi-stable sheaves. We also study the ample cone of the moduli spaces.


  We present an overall picture of the advances in the description of black
hole physics from the perspective of loop quantum gravity. After an
introduction that discusses the main conceptual issues we present some details
about the classical and quantum geometry of isolated horizons and their quantum
geometry and then use this scheme to give a natural definition of the entropy
of black holes. The entropy computations can be neatly expressed in the form of
combinatorial problems solvable with the help of methods based on number theory
and the use of generating functions. The recovery of the Bekenstein-Hawking law
and corrections to it is explained in some detail. After this, due attention is
paid to the discussion of semiclassical issues. An important point in this
respect is the proper interpretation of the horizon area as the energy that
should appear in the statistical-mechanical treatment of the black hole model
presented here. The chapter ends with a comparison between the microscopic and
semiclassical approaches to the computation of the entropy and discusses a
number of issues regarding the relation between entanglement and statistical
entropy and the possibility of comparing the subdominant (logarithmic)
corrections to the entropy obtained with the help of the Euclidean path
integral with the ones obtained in the present framework.


  Autonomous robots often rely on monocular cameras for odometry estimation and
navigation. However, the scale ambiguity problem presents a critical barrier to
effective monocular visual odometry. In this paper, we present CodedVO, a novel
monocular visual odometry method that overcomes the scale ambiguity problem by
employing custom optics to physically encode metric depth information into
imagery. By incorporating this information into our odometry pipeline, we
achieve state-of-the-art performance in monocular visual odometry with a known
scale. We evaluate our method in diverse indoor environments and demonstrate
its robustness and adaptability. We achieve a 0.08m average trajectory error in
odometry evaluation on the ICL-NUIM indoor odometry dataset.


  The theory of pictures between posets is known to encode much of the
combinatorics of symmetric group representations and related topics such as
Young diagrams and tableaux. Many reasons, com-binatorial (e.g. since
semi-standard tableaux can be viewed as double quasi-posets) and topological
(quasi-posets identify with finite topolo-gies) lead to extend the theory to
quasi-posets. This is the object of the present article.


  We study a family of posets and the associated chain and order polytopes. We
identify the order polytope as a maximal Kogan face in a Gelfand-Tsetlin
polytope of a multiple of a fundamental weight. We show that the character of
such a Kogan face equals to the character of a Demazure module which occurs in
the irreducible representation of $\mathfrak{sl}_n$ having highest weight
multiple of fundamental weight and for any such Demazure module there exists a
corresponding poset and associated maximal Kogan face. We prove that the chain
polytope parametrizes a monomial basis of the associated PBW-graded Demazure
module and further, that the Demazure module is a favourable module, e.g.
interesting geometric properties are governed by combinatorics of convex
polytopes. Thus, we obtain for any minuscule Schubert variety a flat
degeneration into a toric projective variety which is projectively normal and
arithmetically Cohen-Macaulay. We provide a necessary and sufficient condition
on the Weyl group element such that the toric variety associated to the chain
polytope and the toric variety associated to the order polytope are isomorphic.


  In this paper, we shall consider the notion of hyperbolic semi norm which on
a module $X$ to set of all positive hyperbolic numbers. We shall prove the
characterization of continuity of hyperbolic semi norm in this setup. We shall
prove Zabreiko's lemma when $X$ is a F, $\mathbb{BC}$ module, where
$\mathbb{BC}$ denotes the set of Bi complex numbers.(analogous to
completeness). This lemma shall be used to prove the fundamental theorems of
functional analysis like the Closed Graph Theorem, Open mapping Theorem,
Uniform Boundedness principle.


  Increasing greenhouse gases will change many aspects of the Earth's climate,
from its annual mean to the frequency of extremes such as heat waves and
droughts. Here we report that the current generation of climate models predicts
a delay in the seasonal cycle of global rainfall and ocean temperature in
response to increasing greenhouse gases, with important implications for the
regional monsoons. In particular, the rainy season of the semi-arid African
Sahel is projected to start later and become shorter: an undesirable change for
local rainfed agriculture and pastoralism. Previous work has highlighted the
uncertainty in this region's response to anthropogenic global warming: summer
rainfall is predicted either to decrease or increase by up to 30% depending
which model is used. The robust agreement across models on the seasonal
distribution of rainfall changes signifies that the onset date and length of
the rainy season should be more predictable than annual mean anomalies.


  We demonstrate that the inclusion of van der Waals dispersive interaction
sensibly improves the prediction of lattice constants by density functional
theory in iron-chalcogenides (FeCh) superconductor compounds, namely FeSe and
FeTe. We show how generalized gradient approximation (GGA) for the exchange
correlation potential overestimates the out-of-plane lattice constants in both
compounds when compared with experiments. In addition, GGA predicts a too weak
bonding between the neutral FeCh layers, with a sensible underestimation of the
bulk modulus. van der Waals corrected simulations completely solve both
problems, reconciling theoretical results with experiments. These findings must
be considered when dealing with theoretical predictions in FeCh compounds.


  Deep learning for unsupervised image segmentation remains challenging due to
the absence of human labels. The common idea is to train a segmentation head,
with the supervision of pixel-wise pseudo-labels generated based on the
representation of self-supervised backbones. By doing so, the model performance
depends much on the distance between the distributions of target datasets and
the pre-training dataset (e.g., ImageNet). In this work, we investigate a new
task, namely unsupervised camouflaged object segmentation (UCOS), where the
target objects own a common rarely-seen attribute, i.e., camouflage.
Unsurprisingly, we find that the state-of-the-art unsupervised models struggle
in adapting UCOS, due to the domain gap between the properties of generic and
camouflaged objects. To this end, we formulate the UCOS as a source-free
unsupervised domain adaptation task (UCOS-DA), where both source labels and
target labels are absent during the whole model training process. Specifically,
we define a source model consisting of self-supervised vision transformers
pre-trained on ImageNet. On the other hand, the target domain includes a simple
linear layer (i.e., our target model) and unlabeled camouflaged objects. We
then design a pipeline for foreground-background-contrastive self-adversarial
domain adaptation, to achieve robust UCOS. As a result, our baseline model
achieves superior segmentation performance when compared with competing
unsupervised models on the UCOS benchmark, with the training set which's scale
is only one tenth of the supervised COS counterpart.


  The exterior algebra of Minkowski space naturally has the structure of a
sixteen-dimensional Clifford algebra representation, and so can be used as the
space of spinors. We examine plane, circular, and spherical solutions to the
free Dirac equation in this extended notion of Minkowski space, and indicate
how they can be used to obtain solutions to the standard four-dimensional Dirac
equation.


  LI-LMC 1813 is a dust-enshrouded Asymptotic Giant Branch (AGB) star, located
in the small open cluster KMHK 1603 near the rim of the Large Magellanic Cloud
(LMC). Optical and infrared photometry between 0.5 and 60 micron is obtained to
constrain the spectral energy distribution of LI-LMC 1813. Near-infrared
spectra unambiguously show it to be a carbon star. Modelling with the radiation
transfer code Dusty yields accurate values for the bolometric luminosity, L=1.5
x 10^4 Lsun, and mass-loss rate, Mdot=3.7(+/-1.2) x 10^-5 Msun/yr. On the basis
of colour-magnitude diagrams, the age of the cluster KMHK 1603 is estimated to
be t=0.9-1.0 Gyr, which implies a Zero-Age Main Sequence mass for LI-LMC 1813
of M(ZAMS)=2.2+/-0.1 Msun. This makes LI-LMC 1813 arguably the object with the
most accurately and reliably determined (circum)stellar parameters amongst all
carbon stars in the superwind phase.


  A class of Laplacian growth models in the channel geometry is studied using
the formalism of tripolar Loewner evolutions, in which three points, namely,
the channel corners and infinity, are kept fixed. Initially, the problem of
fingered growth, where growth takes place only at the tips of slit-like
fingers, is revisited and a class of exact exact solutions of the corresponding
Loewner equation is presented for the case of stationary driving functions. A
model for interface growth is then formulated in terms of a generalized
tripolar Loewner equation and several examples are presented, including
interfaces with multiple tips as well as multiple growing interfaces. The model
exhibits interesting dynamical features, such as tip and finger competition.


  A search for the light pseudoscalar sgoldstino production in three-body K-
decay K- --> pi-pi0 P has been performed with the ISTRA+ detector exposed to
the 25 GeV negative secondary of the U-70 proton synchrotron. No signal is
seen. Upper limits for the branching ratio at 90% confidence level vary between
2.0 10**-5 and 0.5 10**-5 in the effective mass m(P) range from 0 up to 190
MeV. Our results improve the limits published by the E787 Collaboration in the
mass interval between 0 and 120 MeV and are the first ones at higher masses.


  We study fluid-fluid equilibrium in the simplest model of ionic solutions
where the solvent is explicitly included, i.e., a binary mixture consisting of
a restricted primitive model (RPM) and neutral hard-spheres (RPM-HS mixture).
First, using the collective variable method we find free energy, pressure and
partial chemical potentials in the random phase approximation (RPA) for a
rather general model that takes into consideration solvent-solvent and
solvent-ion interactions beyond the hard core. In the special case of a RPM-HS
mixture, we consider two regularizations of the Coulomb potential inside the
hard core, i.e., the Weeks-Chandler-Andersen (WCA) regularization leading to
the WCA approximation and the optimized regularization giving the optimized RPA
(ORPA) or the mean spherical approximation (MSA). Furthermore, we calculate the
phase coexistence using the associative mean spherical approximation (AMSA). In
general, the three approximations produce qualitatively similar phase diagrams
of the RPM-HS mixture, i.e., a fluid-fluid coexistence envelope with an upper
critical solution point, a shift of the coexistence region towards higher total
number densities and higher solvent concentrations with increasing pressure,
and a small increase of the critical temperature with an increase of pressure.
As for a pure RPM, the AMSA leads to the best agreement with the available
simulation data when the association constant proposed by Olaussen and Stell is
used. We also discuss the peculiarities of the phase diagrams in the WCA
approximation.


  The inductive dimension dim(G) of a finite undirected graph G=(V,E) is a
rational number defined inductively as 1 plus the arithmetic mean of the
dimensions of the unit spheres dim(S(x)) at vertices x primed by the
requirement that the empty graph has dimension -1. We look at the distribution
of the random variable "dim" on the Erdos-Renyi probability space G(n,p), where
each of the n(n-1)/2 edges appears independently with probability p. We show
here that the average dimension E[dim] is a computable polynomial of degree
n(n-1)/2 in p. The explicit formulas allow experimentally to explore limiting
laws for the dimension of large graphs. We also study the expectation E[X] of
the Euler characteristic X, considered as a random variable on G(n,p). We look
experimentally at the statistics of curvature K(v) and local dimension dim(v) =
1+dim(S(v)) which satisfy the Gauss-Bonnet formula X(G) = sum K(v) and by
definition dim(G) = sum dim(v)/|V|. We also look at the signature functions
f(p)=E[dim], g(p)=E[X] and matrix values functions A(p) = Cov[{dim(v),dim(w)],
B(p) = Cov[K(v),K(w)] on the probability space G(p) of all subgraphs of a host
graph G=(V,E) with the same vertex set V, where each edge is turned on with
probability p. If G is the complete graph or a union of cyclic graphs with have
explicit formulas for the signature polynomials f and g.


  We propose nearly-optimal control strategies for changing states of a quantum
system. We argue that quantum control optimization can be studied analytically
within some protocol families that depend on a small set of parameters for
optimization. This optimization strategy can be preferred in practice because
it is physically transparent and does not lead to combinatorial complexity in
multistate problems. For demonstration, we design optimized control protocols
that achieve switching between orthogonal states of a naturally biased quantum
two-level system.


  We analyze the deuteron bound state through the One Pion Exchange Potential.
We pay attention to the short distance peculiar singularity structure of the
bound state wave functions in coordinate space and the elimination of short
distance ambiguities by selecting the regular solution at the origin. We
determine the so far elusive amplitude of the converging exponential solutions
at the origin. All bound state deuteron properties can then be uniquely deduced
from the deuteron binding energy, the pion-nucleon coupling constant and pion
mass. This generates correlations among deuteron properties. Scattering phase
shifts and low energy parameters in the 3S1-3D1 channel are constructed by
requiring orthogonality of the positive energy states to the deuteron bound
state, yielding an energy independent combination of boundary conditions. We
also analyze from the viewpoint of short distance boundary conditions the weak
binding regime on the light of long distance perturbation theory and discuss
the approach to the chiral limit.


  This paper studies known indexing structures from a new point of view:
minimisation of data exchange between an IoT device acting as a blockchain
client and the blockchain server running a protocol suite that includes two Guy
Fawkes protocols, PLS and SLVP. The PLS blockchain is not a cryptocurrency
instrument; it is an immutable ledger offering guaranteed non-repudiation to
low-power clients without use of public key crypto. The novelty of the
situation is in the fact that every PLS client has to obtain a proof of absence
in all blocks of the chain to which its counterparty does not contribute, and
we show that it is possible without traversing the block's Merkle tree.
  We obtain weight statistics of a leaf path on a sparse Merkle tree
theoretically, as our ground case. Using the theory we quantify the
communication cost of a client interacting with the blockchain. We show that
large savings can be achieved by providing a bitmap index of the tree
compressed using Tunstall's method. We further show that even in the case of
correlated access, as in two IoT devices posting messages for each other in
consecutive blocks, it is possible to prevent compression degradation by
re-randomising the IDs using a pseudorandom bijective function. We propose a
low-cost function of this kind and evaluate its quality by simulation, using
the avalanche criterion.


  We point out that perturbative evolution in QCD at three loops generates a
strange-antistrange asymmetry s(x)-sbar(x) in the nucleon's sea just from the
fact that the nucleon has non-vanishing up and down quark valence densities.
The recently computed three-loop splitting functions allow for an estimate of
this effect. We find that a fairly sizable asymmetry may be generated. Results
for analogous asymmetries in the heavy-quark sector are also presented.


  Despite excellent progress in recent years, mode collapse remains a major
unsolved problem in generative adversarial networks (GANs).In this paper, we
present spectral regularization for GANs (SR-GANs), a new and robust method for
combating the mode collapse problem in GANs. Theoretical analysis shows that
the optimal solution to the discriminator has a strong relationship to the
spectral distributions of the weight matrix.Therefore, we monitor the spectral
distribution in the discriminator of spectral normalized GANs (SN-GANs), and
discover a phenomenon which we refer to as spectral collapse, where a large
number of singular values of the weight matrices drop dramatically when mode
collapse occurs. We show that there are strong evidence linking mode collapse
to spectral collapse; and based on this link, we set out to tackle spectral
collapse as a surrogate of mode collapse. We have developed a spectral
regularization method where we compensate the spectral distributions of the
weight matrices to prevent them from collapsing, which in turn successfully
prevents mode collapse in GANs. We provide theoretical explanations for why
SR-GANs are more stable and can provide better performances than SN-GANs. We
also present extensive experimental results and analysis to show that SR-GANs
not only always outperform SN-GANs but also always succeed in combating mode
collapse where SN-GANs fail. The code is available at
https://github.com/max-liu-112/SRGANs-Spectral-Regularization-GANs-.


  A simple radiation condition at infinity for time-harmonic massive Dirac
spinors is proposed. This condition allows an analogue of the Cauchy integral
formula in unbounded domains for null-solutions of the Dirac equation to be
proved. The result is obtained with the aid of methods of quaternionic
analysis.


  Single crystal antiferromagnetic USb2 was studied at 15K by angle-resolved
photoemission with an overall energy resolution of 24 meV. The measurements
unambiguously show the dispersion of extremely narrow bands situated near the
Fermi level. The peak at the Fermi level represents the narrowest feature
observed in 5f-electron photoemission to date. The natural linewidth of the
feature just below the Fermi level is not greater than 10 meV. Normal emission
data indicate a three dimensional aspect to the electronic structure of this
layered material.


  Time reversal (T) invariant topological insulator is widely recognized as one
of the fundamental discoveries in condensed matter physics, for which the most
fascinating hallmark is perhaps a spin based topological protection, the total
cancellation of scattering of conduction electrons with certain spins on matter
surface. Recently, it has created a paradigm shift for topological insulators,
from electronics to photonics, phononics as well as mechanics, bringing about
not only involved new physics but also potential applications in robust wave
transport. Despite the growing interests in realizing topologically protected
acoustic wave transport, T-invariant acoustic topological insulator has not yet
been achieved. Here, we report the first demonstration of acoustic topological
insulator: a strongly coupled metamaterial ring lattice that supports one-way
propagation of helical edge states under T-symmetry, backscattering immune to
boundary abrupt variations. The very unique thing is the formation of
spin-filtered interface states due to lattice dislocations. The mechanism
underlying the formation of topologically protected edge states and interface
states is applicable in various other wave systems or higher dimensions.


  We combine the Bondal-Uehara method for producing exceptional collections on
toric varieties with a result of the first author and Favero to expand the set
of varieties satisfying Orlov's Conjecture on derived dimension.


  Two-dimensional (2D) layered materials with diverse properties have attracted
significant interest in the past decade. The layered materials discovered so
far have covered a wide, yet discontinuous electromagnetic spectral range from
semimetallic graphene, insulating boron nitride, to semiconductors with
bandgaps from middle infrared to visible light. Here, we introduce new layered
semiconductors, black arsenic-phosphorus (b-AsP), with highly tunable chemical
compositions and electronic and optical properties. Transport and infrared
absorption studies demonstrate the semiconducting nature of b-AsP with tunable
bandgaps, ranging from 0.3 to 0.15 eV. These bandgaps fall into long-wavelength
infrared (LWIR) regime and cannot be readily reached by other layered
materials. Moreover, polarization-resolved infrared absorption and Raman
studies reveal in-plane anisotropic properties of b-AsP. This family of layered
b-AsP materials extend the electromagnetic spectra covered by 2D layered
materials to the LWIR regime, and may find unique applications for future all
2D layered material based devices.


  We formulate the string field theory in zero-dimensional target space
corresponding to the two-dimensional quantum gravity theory defined through
Causal Dynamical Triangulations. This third quantization of the quantum gravity
theory allows us in principle to calculate the transition amplitudes of
processes in which the topology of space changes in time, and to include
non-trivial topologies of space-time. We formulate the corresponding
Dyson-Schwinger equations and illustrate how they can be solved iteratively.


  The Polkadot ecosystem is a disruptive and highly complex multi-chain
architecture that poses challenges in terms of data analysis and
communicability. Currently, there is a lack of standardized and holistic
approaches to retrieve and analyze data across parachains and applications,
making it difficult for general users and developers to access ecosystem data
consistently. This paper proposes a conceptual framework that includes a domain
ontology called POnto (a Polkadot Ontology) to address these challenges. POnto
provides a structured representation of the ecosystem's concepts and
relationships, enabling a formal understanding of the platform. The proposed
knowledge-oriented approach enhances integration and communicability, enabling
a wider range of users to participate in the ecosystem and facilitating the
development of AI-based applications. The paper presents a case study
methodology to validate the proposed framework, which includes expert feedback
and insights from the Polkadot community. The POnto ontology and the roadmap
for a query engine based on a Controlled Natural Language using the ontology,
provide valuable contributions to the growth and adoption of the Polkadot
ecosystem in heterogeneous socio-technical environments.


  In this paper we consider cellular automata $(\mathfrak{G},\Phi)$ with
algebraic local rules and such that $\mathfrak{G}$ is a topological Markov
chain which has a structure compatible to this local rule. We characterize such
cellular automata and study the convergence of the Ces\`aro mean distribution
of the iterates of any probability measure with complete connections and
summable decay.


  We investigate nanoelectromechanical systems near mechanical instabilities.
We show that quite generally, the interaction between the electronic and the
vibronic degrees of freedom can be accounted for essentially exactly when the
instability is continuous. We apply our general framework to the Euler buckling
instability and find that the interaction between electronic and vibronic
degrees of freedom qualitatively affects the mechanical instability, turning it
into a discontinuous one in close analogy with tricritical points in the Landau
theory of phase transitions.


  The effects of magnetic doping on a EuB_6 single crystal were investigated
based on magnetic and transport measurements. A modest 5% Sm substitution for
Eu changes the magnetic and transport properties dramatically and gives rise to
concurrent antiferromagnetic and metal-insulator transitions (MIT) from
ferromagnetic MIT for EuB6. Magnetic doping simultaneously changes the
itinerant carrier density and the magnetic interactions. We discuss the origin
of the concurrent magnetic MIT in (Eu,Sm)B_6.


  Materials with reduced dimensionality often exhibit exceptional properties
that are different from their bulk counterparts. Here we report the emergence
of a commensurate 2 $\times$ 2 charge density wave (CDW) in monolayer and
bilayer SnSe$_2$ films by scanning tunneling microscope. The visualized spatial
modulation of CDW phase becomes prominent near the Fermi level, which is pinned
inside the semiconductor band gap of SnSe$_2$. We show that both CDW and Fermi
level pinning are intimately correlated with band bending and virtual induced
gap states at the semiconductor heterointerface. Through interface engineering,
the electron-density-dependent phase diagram is established in SnSe$_2$. Fermi
surface nesting between symmetry inequivalent electron pockets is revealed to
drive the CDW formation and to provide an alternative CDW mechanism that might
work in other compounds.


  Let $G$ be a non-abelian group and $Z(G)$ be the center of $G$. Associate a
graph $\Gamma_G$ (called non-commuting graph of $G$) with $G$ as follows: take
$G\setminus Z(G)$ as the vertices of $\Gamma_G$ and join two distinct vertices
$x$ and $y$, whenever $xy\neq yx$. Here, we prove that "the commutativity
pattern of a finite non-abelian $p$-group determine its order among the class
of groups"; this means that if $P$ is a finite non-abelian $p$-group such that
$\Gamma_P\cong \Gamma_H$ for some group $H$, then $|P|=|H|$.


  We derive, in model independent way, the spin structure of the matrix element
for the reaction of associative $\Theta^+$ pentaquark production,
$\pi^{\pm}+D\to \Theta^+ +\Sigma^{\pm}, $ in the threshold region and in
collinear kinematics. The expressions for the polarization observables in this
reaction are found assuming spin 1/2 and different parities for $\Theta^+ .$ We
have proved that such reaction can be used for a model independent
determination of the P-parity of $\Theta^+$ only by measuring the $\Theta^+$
polarization. Other polarization observables, such as the dependence of the
$\Sigma^{\pm}$ polarization on the vector and tensor deuteron polarizations,
are insensitive to the $\Theta^+$ parity in the considered kinematical
conditions. All linear and quadratic relations between polarization observables
in $\pi^{\pm}+\vec D\to \Theta^+ +\vec\Sigma^{\pm}(\Theta^+ $ is unpolarized)
do not depend on the parity of the $\Theta^+$ pentaquark.


  We use maximal periodic flats to show that on a finite volume irreducible
locally symmetric manifold of dimension $\geq 3$, no metric $g$ has more
symmetry than the locally symmetric metric. We also show that if $g$ is a
finite volume metric that is not locally symmetric, then its lift to the
universal cover has discrete isometry group.


  It was shown: 1) that the mass of the Higgs boson discovered by LHC
corresponds to the stability conditions of the SM vacua and to the Multiple
Point Principle, according to which all vacua of the SM are degenerate, or
almost degenerate; 2) that early predicted by authors new bound states (NBS) of
the 6 top and 6 anti-top quarks ("T-fireballs"), which are formed by their
intermediate interactions with the Higgs bosons, manifest themselves in the
production of multijets in pp-collisions at LHC. The CMS experiment of LHC with
the production of 10 jets can be explained by the production of pairs of these
NBS along with the production of pairs of the top-anti-top quarks. 3) Also it
was shown that the next indication of the possible existence of the NBS can be
the decay $H\to \gamma\gamma$, which was observed by CMS-collaboration of LHC.
We have considered the contributions of the one-loop diagrams to the width
$\Gamma_{H\to \gamma\gamma}$, taking into account the contributions of the
T-fireballs along the contributions of the known SM-particles.


  The classical machine-learning model for support vector regression (SVR) is
widely used for regression tasks, including weather prediction, stock-market
and real-estate pricing. However, a practically realisable quantum version for
SVR remains to be formulated. We devise annealing-based algorithms, namely
simulated and quantum-classical hybrid, for training two SVR models, and
compare their empirical performances against the SVR implementation of Python's
scikit-learn package and the SVR-based state-of-the-art algorithm for the
facial landmark detection (FLD) problem. Our method is to derive a
quadratic-unconstrained-binary formulation for the optimisation problem used
for training a SVR model and solve this problem using annealing. Using D-Wave's
Hybrid Solver, we construct a quantum-assisted SVR model, thereby demonstrating
a slight advantage over classical models regarding landmark-detection accuracy.
Furthermore, we observe that annealing-based SVR models predict landmarks with
lower variances compared to the SVR models trained by greedy optimisation
procedures. Our work is a proof-of-concept example for applying quantu-assisted
SVR to a supervised learning task with a small training dataset.


  The topological properties of non-Hermitian Hamiltonian is a hot topic, and
the theoretical studies along this research line are usually based on the
two-level non-Hermitian Hamiltonian (or, equivalently, a spin-$1/2$
non-Hermitian Hamiltonian). We are motivated to study the geometrical phases of
a three-level Lieb lattice model (or, equivalently, a spin-$1$ non-Hermitian
Hamiltonian) with the complex hopping and flat band in the context of a
polariton condensate, with the emphasis on the higher spin degree of freedom on
topological properties of non-Hermitian Hamiltonian. The topological invariants
are calculated by both winding numbers in the Brillouin zone and the
geometrical phase of Majorana stars in the Bloch sphere. Besides, we provide an
intuitive way to study the topological phase transformation in high dimensions,
and the flat band offers a platform to define the high spin topological phase
transition on the Bloch sphere. According to the trajectories of the Majorana
stars, we calculate the geometrical phases of the Majorana stars, and we find
they have a jump when the parameters change from the trivial phase to the
topological phase. Besides, the correlation phase of Majorana stars will rise
along with the increase of the imaginary parts of the hopping energy.


  Although the spread of behaviors is influenced by many social factors,
existing literature tends to study the effects of single factors -- most often,
properties of the social network -- on the final cascade. In order to move
towards a more integrated view of cascades, this paper offers the first
comprehensive investigation into the role of two social factors in the
diffusion of 1,337 popular hashtags representing the production of novel
culture on Twitter: 1) the topology of the Twitter social network and 2)
performance of each user's probable demographic identity. Here, we show that
cascades are best modeled using a combination of network and identity, rather
than either factor alone. This combined model best reproduces a composite index
of ten cascade properties across all 1,337 hashtags. However, there is
important heterogeneity in what social factors are required to reproduce
different properties of hashtag cascades. For instance, while a combined
network+identity model best predicts the popularity of cascades, a network-only
model has better performance in predicting cascade growth and an identity-only
model in adopter composition. We are able to predict what type of hashtag is
best modeled by each combination of features and use this to further improve
performance. Additionally, consistent with prior literature on the combined
network+identity model most outperforms the single-factor counterfactuals among
hashtags used for expressing racial or regional identity, stance-taking,
talking about sports, or variants of existing cultural trends with very slow-
or fast-growing communicative need. In sum, our results imply the utility of
multi-factor models in predicting cascades, in order to account for the varied
ways in which network, identity, and other social factors play a role in the
diffusion of hashtags on Twitter.