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The classical Fundamental Theorem of Affine Geometry states that for $n\geq
2$, any bijection of $n$-dimensional Euclidean space that maps lines to lines
(as sets) is given by an affine map. We consider an analogous characterization
of affine automorphisms for compact quotients, and establish it for tori: A
bijection of an n-dimensional torus ($n\geq 2$) is affine if and only if it
maps lines to lines.
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We summarize some observational comparison concerning the features of
globular clusters (GCs) population in connection to the evolution of King
models. We also make a comparison with some extragalactic GCs systems, in order
to underline the effects of the main body on the dynamical evolution.
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We present a complete analysis of the neutral fermion sector of
supersymmetric E_6-inspired low energy models containing an extra SU(2),
concentrating on the Alternate Left-Right and Inert models. We show that the
R-parity conserving scenario always exhibits a large Dirac mass for \nu_L with
maximal mixing with an isosinglet neutrino, and that R-parity violating
scenarios do not change the picture other than allowing further mixing with
another isosinglet. In order to recover Standard Model phenomenology,
additional assumptions in the form of discrete symmetries and/or new
interactions are needed. We introduce and investigate Discrete Symmetry method
and Higher Dimensional Operators as mechanisms for solving the neutrino mass
and mixing problems in these models.
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Two players take it turn to claim empty cells from an $n\times n$ grid. The
first player (if any) to occupy a transversal (a set of $ n $ cells having no
two cells in the same row or column) is the winner. What is the outcome of the
game given optimal play? Our aim in this paper is to show that for $n\ge 4$ the
first player has a winning strategy. This answers a question of Erickson.
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Despite the remarkable progress made by learning based stereo matching
algorithms, one key challenge remains unsolved. Current state-of-the-art stereo
models are mostly based on costly 3D convolutions, the cubic computational
complexity and high memory consumption make it quite expensive to deploy in
real-world applications. In this paper, we aim at completely replacing the
commonly used 3D convolutions to achieve fast inference speed while maintaining
comparable accuracy. To this end, we first propose a sparse points based
intra-scale cost aggregation method to alleviate the well-known edge-fattening
issue at disparity discontinuities. Further, we approximate traditional
cross-scale cost aggregation algorithm with neural network layers to handle
large textureless regions. Both modules are simple, lightweight, and
complementary, leading to an effective and efficient architecture for cost
aggregation. With these two modules, we can not only significantly speed up
existing top-performing models (e.g., $41\times$ than GC-Net, $4\times$ than
PSMNet and $38\times$ than GA-Net), but also improve the performance of fast
stereo models (e.g., StereoNet). We also achieve competitive results on Scene
Flow and KITTI datasets while running at 62ms, demonstrating the versatility
and high efficiency of the proposed method. Our full framework is available at
https://github.com/haofeixu/aanet .
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Recently Fayers introduced a large family of combinatorial realizations of
the fundamental crystal for affine sl(n), where the vertices are indexed by
certain partitions. He showed that special cases of this construction agree
with the Misra-Miwa realization and with Berg's ladder crystal. Here we show
that another special case is naturally isomorphic to a realization using
Nakajima's monomial crystal.
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We classify all products of flag varieties with finitely many orbits under
the diagonal action of the general linear group. We also classify the orbits in
each case and construct explicit representatives. This generalizes the
classical Schubert decompostion, which states that the GL(n)-orbits on a
product of two flag varieties correspond to permutations. Our main tool is the
theory of quiver representations.
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A generalized version of the TKNN-equations computing Hall conductances for
generalized Dirac-like Harper operators is derived. Geometrically these
equations relate Chern numbers of suitable (dual) bundles naturally associated
to spectral projections of the operators.
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The ability of continual learning systems to transfer knowledge from
previously seen tasks in order to maximize performance on new tasks is a
significant challenge for the field, limiting the applicability of continual
learning solutions to realistic scenarios. Consequently, this study aims to
broaden our understanding of transfer and its driving forces in the specific
case of continual reinforcement learning. We adopt SAC as the underlying RL
algorithm and Continual World as a suite of continuous control tasks. We
systematically study how different components of SAC (the actor and the critic,
exploration, and data) affect transfer efficacy, and we provide recommendations
regarding various modeling options. The best set of choices, dubbed ClonEx-SAC,
is evaluated on the recent Continual World benchmark. ClonEx-SAC achieves 87%
final success rate compared to 80% of PackNet, the best method in the
benchmark. Moreover, the transfer grows from 0.18 to 0.54 according to the
metric provided by Continual World.
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Electronic spins associated with the Nitrogen-Vacancy (NV) center in diamond
offer an opportunity to study spin-related phenomena with extremely high
sensitivity owing to their high degree of optical polarization. Here, we study
both single- and double-quantum transitions (SQT and DQT) in NV centers between
spin-mixed states, which arise from magnetic fields that are non-collinear to
the NV axis. We demonstrate the amplification of the ESR signal from both these
types of transition under laser illumination. We obtain hyperfine-resolved
X-band ESR signal as a function of both excitation laser power and misalignment
of static magnetic field with the NV axis. This combined with our analysis
using a seven-level model that incorporates thermal polarization and double
quantum relaxation allows us to comprehensively analyze the polarization of NV
spins under off-axis fields. Such detailed understanding of spin-mixed states
in NV centers under photo-excitation can help greatly in realizing NV-diamond
platform's potential in sensing correlated magnets and biological samples, as
well as other emerging applications, such as masing and nuclear
hyperpolarization.
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Similarity search is a fundamental task for exploiting information in various
applications dealing with graph data, such as citation networks or knowledge
graphs. While this task has been intensively approached from heuristics to
graph embeddings and graph neural networks (GNNs), providing explanations for
similarity has received less attention. In this work we are concerned with
explainable similarity search over graphs, by investigating how GNN-based
methods for computing node similarities can be augmented with explanations.
Specifically, we evaluate the performance of two prominent approaches towards
explanations in GNNs, based on the concepts of mutual information (MI), and
gradient-based explanations (GB). We discuss their suitability and empirically
validate the properties of their explanations over different popular graph
benchmarks. We find that unlike MI explanations, gradient-based explanations
have three desirable properties. First, they are actionable: selecting inputs
depending on them results in predictable changes in similarity scores. Second,
they are consistent: the effect of selecting certain inputs overlaps very
little with the effect of discarding them. Third, they can be pruned
significantly to obtain sparse explanations that retain the effect on
similarity scores.
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Spatial chaos as a phenomenon of ultimate complexity requires the efficient
numerical algorithms. For this purpose iterative low-dimensional maps have
demonstrated high efficiency. Natural generalization of Feigenbaum and Ikeda
maps may include convolution integrals with kernel in a form of Green function
of a relevant linear physical system. It is shown that such iterative
$nonlocal$ $nonlinear$ $maps$ are equivalent to ubiquitous class of nonlinear
partial differential equations of Ginzburg-Landau type. With a Green functions
relevant to generic optical resonators these $nonlocal$ $maps$ emulate the
basic spatiotemporal phenomena as spatial solitons, vortex eigenmodes breathing
via relaxation oscillations mediated by noise, vortex-vortex and
vortex-antivortex lattices with periodic location of vortex cores. The smooth
multimode noise addition facilitates the selection of stable entities and
elimination of numerical artifacts.
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In the marine environment biological processes are strongly affected by
oceanic currents, particularly by eddies (vortices) formed by the hydrodynamic
flow field. Employing a kinematic flow field coupled to a population dynamical
model for plankton growth, we study the impact of an intermittent upwelling of
nutrients on triggering harmful algal blooms (HABs). Though it is widely
believed that additional nutrients boost the formation of HABs or algal blooms
in general, we show that the response of the plankton to nutrient plumes
depends crucially on the mesoscale hydrodynamic flow structure. In general
nutrients can either be quickly washed out from the observation area, or can be
captured by the vortices in the flow. The occurrence of either scenario depends
on the relation between the time scales of the vortex formation and nutrient
upwelling as well as the time instants at which upwelling pulse occurs and how
long do they last. We show that these two scenarios result in very different
responses in plankton dynamics which makes it very difficult to predict,
whether nutrient upwelling will lead to a HAB or not. This explains, why
observational data are sometimes inconclusive establishing a correlation
between upwelling events and plankton blooms.
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Let ($X,Y)$ be a random vector with distribution function $F(x,y),$ and
$(X_{1},Y_{1}),(X_{2},Y_{2}),...,(X_{n},Y_{n})$ are independent copies of
($X,Y).$ Let $X_{i:n}$ be the $i$th order statistics constructed from the
sample $X_{1},X_{2},...,X_{n}$ of the first coordinate of the bivariate sample
and $Y_{[i:n]}$ be the concomitant of $X_{i:n}.$ Denote $F_{i:n}%
(x,y)=P\{X_{i:n}\leq x,Y_{[i:n]}\leq y\}.$ Using majorization theory we write
upper and lower bounds for $F$ expressed in terms of mixtures of joint
distributions of order statistics and their concomitants, i.e. ${\dsum
\limits_{i=1}^{n}}% {\sum\limits_{i=1}^{n}} p_{i}F_{i:n}(x,y)$ and ${\dsum
\limits_{i=1}^{n}}% {\sum\limits_{i=1}^{n}} p_{i}F_{n-i+1:n}(x,y).$ It is shown
that these bounds converge to $F$ for a particular sequence
$(p_{1}(m),p_{2}(m),...,p_{n}(m)),m=1,2,..$ as $m\rightarrow\infty.$
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This paper is devoted to the Hamiltonian analysis of bimetric gravity in
vierbein formulation. We identify all constraints and determine their nature.
We also show an existence of additional constraint so that the scalar mode can
be eliminated.
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We point out that, when the dimension of the Hilbert space is greater than
two, Bell's operators entering the Bell-CHSH inequality exhibit unitarily
inequivalent representations. Although the Bell-CHSH inequality turns out to be
violated, the size of the violation is different for different representations,
the maximum violation being given by Tsirelson's bound. The feature relies on a
pairing mechanism between the modes of the Hilbert space of the system.
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At about 70 solar masses, the recently-discovered dark object orbited by a
B-type star in the system LB-1 is difficult to understand as the end point of
standard stellar evolution, except as a binary black hole (BBH). LB-1 shows a
strong, broad H-alpha emission line that is best attributed to a gaseous disk
surrounding the dark mass. We use the observed H-alpha line shape, particularly
its wing extension, to constrain the inner radius of the disk and thereby the
separation of a putative BBH. The hypothesis of a current BBH is effectively
ruled out on the grounds that its merger time must be a small fraction of the
current age of the B star. The hypothesis of a previous BBH that merged to
create the current dark mass is also effectively ruled out by the low orbital
eccentricity, due to the combination of mass loss and kick resulted from
gravitational wave emission in any past merger. We conclude that the current
dark mass is a single black hole produced by the highly mass-conserving,
monolithic collapse of a massive star.
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Music tone quality evaluation is generally performed by experts. It could be
subjective and short of consistency and fairness as well as time-consuming. In
this paper we present a new method for identifying the clarinet reed quality by
evaluating tone quality based on the harmonic structure and energy
distribution. We first decouple the quality of reed and clarinet pipe based on
the acoustic harmonics, and discover that the reed quality is strongly relevant
to the even parts of the harmonics. Then we construct a features set consisting
of the even harmonic envelope and the energy distribution of harmonics in
spectrum. The annotated clarinet audio data are recorded from 3 levels of
performers and the tone quality is classified by machine learning. The results
show that our new method for identifying low and medium high tones
significantly outperforms previous methods.
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This paper concerns the maximum-likelihood channel estimation for MIMO
systems with orthogonal space-time block codes when the finite alphabet
constraint of the signal constellation is relaxed. We study the channel
coefficients estimation subspace generated by this method. We provide an
algebraic characterisation of this subspace which turns the optimization
problem into a purely algebraic one and more importantly, leads to several
interesting analytical proofs. We prove that with probability one, the
dimension of the estimation subspace for the channel coefficients is
deterministic and it decreases by increasing the number of receive antennas up
to a certain critical number of receive antennas, after which the dimension
remains constant. In fact, we show that beyond this critical number of receive
antennas, the estimation subspace for the channel coefficients is isometric to
a fixed deterministic invariant space which can be easily computed for every
specific OSTB code.
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Simultaneous spectral differential imaging is a high contrast technique by
which subtraction of simultaneous images reduces noise from atmospheric
speckles and optical aberrations. Small non-common wave front errors between
channels can seriously degrade its performance. We present a new concept, a
multicolor detector assembly (MCDA), which can eliminate this problem. The
device consists of an infrared detector and a microlens array onto the flat
side of which a checkerboard pattern of narrow-band micro-filters is deposited,
each micro-filter coinciding with a microlens. Practical considerations for
successful implementation of the technique are mentioned. Numerical simulations
predict a noise attenuation of 10^-3 at 0.5" for a 10^5 seconds integration on
a mH=5 star of Strehl ratio 0.9 taken with an 8-m telescope. This reaches a
contrast of 10^-7 at an angular distance of 0.5" from the center of the star
image.
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We investigate gas accretion flow onto a circumplanetary disk from a
protoplanetary disk in detail by using high-resolution three-dimensional
nested-grid hydrodynamic simulations, in order to provide a basis of formation
processes of satellites around giant planets. Based on detailed analyses of gas
accretion flow, we find that most of gas accretion onto circumplanetary disks
occurs nearly vertically toward the disk surface from high altitude, which
generates a shock surface at several scale heights of the circumplanetary disk.
The gas that has passed through the shock surface moves inward because its
specific angular momentum is smaller than that of the local Keplerian rotation,
while gas near the midplane in the protoplanetary disk cannot accrete to the
circumplanetary disk. Gas near the midplane within the planet's Hill sphere
spirals outward and escapes from the Hill sphere through the two Lagrangian
points L$_1$ and L$_2$. We also analyze fluxes of accreting mass and angular
momentum in detail and find that the distributions of the fluxes onto the disk
surface are well described by power-law functions and that a large fraction of
gas accretion occurs at the outer region of the disk, i.e., at about 0.1 times
the Hill radius. The nature of power-law functions indicates that, other than
the outer edge, there is no specific radius where gas accretion is
concentrated. These source functions of mass and angular momentum in the
circumplanetary disk would provide us with useful constraints on the structure
and evolution of the circumplanetary disk, which is important for satellite
formation.
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Revealing phase transitions of solids through mechanical anomalies in the
friction of nanotips sliding on their surfaces is an unconventional and
instructive tool for continuous transitions, unexplored for first-order ones.
Owing to slow nucleation, first-order structural transformations generally do
not occur at the precise crossing of free energies, but hysteretically, near
the spinodal temperatures where, below and above the thermodynamic transition
temperature, one or the other metastable free energy branches terminates. The
spinodal transformation, a collective one-shot event with no heat capacity
anomaly, is easy to trigger by a weak external perturbations. Here we propose
that even the gossamer mechanical action of an AFM tip may locally act as a
surface trigger, narrowly preempting the spontaneous spinodal transformation,
and making it observable as a nanofrictional anomaly. Confirming this
expectation, the CCDW-NCCDW first-order transition of the important layer
compound 1T-TaS$_2$ is shown to provide a demonstration of this effect.
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We define and characterize multi-time Lagrangian structure functions using
data stemming from two swirling flows with mean flow and turbulent
fluctuations: A Taylor-Green numerical flow, and a von K\'arm\'an laboratory
experiment. Data is obtained from numerical integration of tracers in the
former case, and from three-dimensional particle tracking velocimetry
measurements in the latter. Multi-time statistics are shown to decrease the
contamination of large scales in the inertial range scaling. A time scale at
which contamination from the mean flow becomes dominant is identified, with
this scale separating two different Lagrangian scaling ranges. The results from
the multi-time structure functions also indicate that Lagrangian intermittency
is not a result of large-scale flow effects. The multi-time Lagrangian
structure functions can be used without prior knowledge of the forcing
mechanisms or boundary conditions, allowing their application in different flow
geometries.
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We develop an approximation approach to infinite dimensional quantum channels
based on detailed investigation of the continuity properties of entropic
characteristics of quantum channels and operations (trace-nonincreasing
completely positive maps) as functions of a pair ``channel, input state''. The
obtained results are then applied to the following problems: continuity of the
$\chi$-capacity as function of a channel; strong additivity of the
$\chi$-capacity for infinite dimensional channels; the analytical expression
for the convex closure of the output entropy of arbitrary quantum channel.
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An AVL tree is the original type of balanced binary search tree. An insertion
in an $n$-node AVL tree takes at most two rotations, but a deletion in an
$n$-node AVL tree can take $\Theta(\log n)$. A natural question is whether
deletions can take many rotations not only in the worst case but in the
amortized case as well. A sequence of $n$ successive deletions in an $n$-node
tree takes $O(n)$ rotations, but what happens when insertions are intermixed
with deletions? Heaupler, Sen, and Tarjan conjectured that alternating
insertions and deletions in an $n$-node AVL tree can cause each deletion to do
$\Omega(\log n)$ rotations, but they provided no construction to justify their
claim. We provide such a construction: we show that, for infinitely many $n$,
there is a set $E$ of {\it expensive} $n$-node AVL trees with the property
that, given any tree in $E$, deleting a certain leaf and then reinserting it
produces a tree in $E$, with the deletion having done $\Theta(\log n)$
rotations. One can do an arbitrary number of such expensive deletion-insertion
pairs. The difficulty in obtaining such a construction is that in general the
tree produced by an expensive deletion-insertion pair is not the original tree.
Indeed, if the trees in $E$ have even height $k$, $2^{k/2}$ deletion-insertion
pairs are required to reproduce the original tree.
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Being spontaneous, micro-expressions are useful in the inference of a
person's true emotions even if an attempt is made to conceal them. Due to their
short duration and low intensity, the recognition of micro-expressions is a
difficult task in affective computing. The early work based on handcrafted
spatio-temporal features which showed some promise, has recently been
superseded by different deep learning approaches which now compete for the
state of the art performance. Nevertheless, the problem of capturing both local
and global spatio-temporal patterns remains challenging. To this end, herein we
propose a novel spatio-temporal transformer architecture -- to the best of our
knowledge, the first purely transformer based approach (i.e. void of any
convolutional network use) for micro-expression recognition. The architecture
comprises a spatial encoder which learns spatial patterns, a temporal
aggregator for temporal dimension analysis, and a classification head. A
comprehensive evaluation on three widely used spontaneous micro-expression data
sets, namely SMIC-HS, CASME II and SAMM, shows that the proposed approach
consistently outperforms the state of the art, and is the first framework in
the published literature on micro-expression recognition to achieve the
unweighted F1-score greater than 0.9 on any of the aforementioned data sets.
|
By applying suitable centrality condition to non-commutative non-isospectral
lattice modified Gel'fand-Dikii type systems we obtain the corresponding
non-autonomous equations. Then we derive non-commutative q-discrete Painleve VI
equation with full range of parameters as the (2,2) similarity reduction of the
non-commutative, non-isospectral and non-autonomous lattice modified
Korteweg-de Vries equation. We also comment on the fact that in making the
analogous reduction starting from Schwarzian Korteweg-de Vries equation no such
"non-isospectral generalization" is needed.
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The dynamical aspects of the phonoriton state in highly-photoexcited
semiconductors is studied theoretically. The effect of the exciton-exciton
interaction and nonbosonic character of high-density excitons are taken into
account. Using Green's function method and within the Random Phase
Approximation it is shown that the phonoriton dispersion and damping are very
sensitive to the exciton density, characterizing the excitation degree of
semiconductors.
|
The nature of quantum correlations in strongly correlated systems has been a
subject of intense research. In particular, it has been realized that
entanglement and quantum discord are present at quantum phase transitions and
able to characterize it. Surprisingly, it has been shown for a number of
different systems that qubit pairwise states, even when highly entangled, do
not violate Bell's inequalities, being in this sense local. Here we show that
such a local character of quantum correlations is in fact general for
translation invariant systems and has its origins in the monogamy trade-off
obeyed by tripartite Bell correlations. We illustrate this result in a quantum
spin chain with a soft breaking of translation symmetry. In addition, we extend
the monogamy inequality to the $N$-qubit scenario, showing that the bound
increases with $N$ and providing examples of its saturation through uniformly
generated random pure states.
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I review the advancements of atomic scale nanoelectronics towards quantum
neuromorphics. First, I summarize the key properties of elementary combinations
of few neurons, namely long-- and short--term plasticity, spike-timing
dependent plasticity (associative plasticity), quantumness and stochastic
effects, and their potential computational employment. Next, I review several
atomic scale device technologies developed to control electron transport at the
atomic level, including single atom implantation for atomic arrays and CMOS
quantum dots, single atom memories, Ag$_2$S and Cu$_2$S atomic switches,
hafnium based RRAMs, organic material based transistors, Ge$_2$Sb$_2$Te$_5$
synapses. Each material/method proved successful in achieving some of the
properties observed in real neurons. I compare the different methods towards
the creation of a new generation of naturally inspired and biophysically
meaningful artificial neurons, in order to replace the rigid CMOS based
neuromorphic hardware. The most challenging aspect to address appears to obtain
both the stochastic/quantum behavior and the associative plasticity, which are
currently observed only below and above 20 nm length scale respectively, by
employing the same material.
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The phase diagram of isotropically expanded graphene cannot be correctly
predicted by ignoring either electron correlations, or mobile carbons, or the
effect of applied stress, as was done so far. We calculate the ground state
enthalpy (not just energy) of strained graphene by an accurate off-lattice
Quantum Monte Carlo (QMC) correlated ansatz of great variational flexibility.
Following undistorted semimetallic graphene (SEM) at low strain,
multi-determinant Heitler-London correlations stabilize between $\simeq$8.5%
and $\simeq$15% strain an insulating Kekule-like dimerized (DIM) state. Closer
to a crystallized resonating-valence bond than to a Peierls state, the DIM
state prevails over the competing antiferromagnetic insulating (AFI) state
favored by density-functional calculations which we conduct in parallel. The
DIM stressed graphene insulator, whose gap is predicted to grow in excess of 1
eV before failure near 15% strain, is topological in nature, implying under
certain conditions 1D metallic interface states lying in the bulk energy gap.
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We devise and demonstrate a method to search for non-gravitational couplings
of ultralight dark matter to standard model particles using space-time
separated atomic clocks and cavity-stabilized lasers. By making use of
space-time separated sensors, which probe different values of an oscillating
dark matter field, we can search for couplings that cancel in typical local
experiments. We demonstrate this method using existing data from a frequency
comparison of lasers stabilized to two optical cavities connected via a 2220 km
fiber link [Nat. Commun. 13, 212 (2022)]. The absence of significant
oscillations in the data results in constraints on the coupling of scalar dark
matter to electrons, d_me, for masses between 1e-19 eV and 2e-15 eV. These are
the first constraints on d_me alone in this mass range, and improve the dark
matter constraints on any scalar-Fermion coupling by up to two orders of
magnitude.
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The nuclei of galaxies often host small stellar discs with scale-lengths of a
few tens of parsecs and luminosities up to 10^7 Lsun. To investigate the
formation and properties of nuclear stellar discs (NSDs), we look for their
presence in a set of N-body simulations studying the dissipationless merging of
multiple star clusters in galactic nuclei. A few tens of star clusters with
sizes and masses comparable to those of globular clusters observed in the Milky
Way are accreted onto a pre-existing nuclear stellar component: either a
massive super star cluster or a rapidly rotating, compact disc with a
scale-length of a few parsecs, mimicing the variety of observed nuclear
structures. Images and kinematic maps of the simulation time-steps are then
built and analysed as if they were real and at the distance of the Virgo
cluster. We use the Scorza-Bender method to search for the presence of disc
structures via photometric decomposition. In one case the merger remnant has
all the observed photometric and kinematic properties of NSDs observed in real
galaxies. This shows that current observations are consistent with most of the
NSD mass being assembled from the migration and accretion of star clusters into
the galactic centre. In the other simulation instead, we detect an elongated
structure from the unsharp masked image, that does not develop the photometric
or kinematic signature of a NSD. Thus, in the context of searches for a disc
structure, the Scorza-Bender method is a robust and necessary tool.
|
The intriguing choice to treat alternative theories of gravity by means of
the Palatini approach, namely elevating the affine connection to the role of
independent variable, contains the seed of some interesting (usually
under-explored) generalizations of General Relativity, the metric-affine
theories of gravity. The peculiar aspect of these theories is to provide a
natural way for matter fields to be coupled to the independent connection
through the covariant derivative built from the connection itself. Adopting a
procedure borrowed from the effective field theory prescriptions, we study the
dynamics of metric-affine theories of increasing order, that in the complete
version include invariants built from curvature, nonmetricity and torsion. We
show that even including terms obtained from nonmetricity and torsion to the
second order density Lagrangian, the connection lacks dynamics and acts as an
auxiliary field that can be algebraically eliminated, resulting in some extra
interactions between metric and matter fields.
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We present a study of the structure, the electric resistivity, the magnetic
susceptibility, and the thermal expansion of La$_{1-x}$Eu$_x$CoO$_3$. LaCoO$_3$
shows a temperature-induced spin-state transition around 100 K and a
metal-insulator transition around 500 K. Partial substitution of La$^{3+}$ by
the smaller Eu$^{3+}$ causes chemical pressure and leads to a drastic increase
of the spin gap from about 190 K in LaCoO$_3$ to about 2000 K in EuCoO$_3$, so
that the spin-state transition is shifted to much higher temperatures. A
combined analysis of thermal expansion and susceptibility gives evidence that
the spin-state transition has to be attributed to a population of an
intermediate-spin state with orbital order for $x<0.5$ and without orbital
order for larger $x$. In contrast to the spin-state transition, the
metal-insulator transition is shifted only moderately to higher temperatures
with increasing Eu content, showing that the metal-insulator transition occurs
independently from the spin-state distribution of the Co$^{3+}$ ions. Around
the metal-insulator transition the magnetic susceptibility shows a similar
increase for all $x$ and approaches a doping-independent value around 1000 K
indicating that well above the metal-insulator transition the same spin state
is approached for all $x$.
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We develop the resonant mode coupling approximation to calculate the optical
spectra of a stack of two photonic crystal slabs. The method is based on a
derivation of the input and output resonant vectors in each slab in terms of
the Fourier modal method in the scattering matrix form. We show that using the
resonant mode coupling approximation of the scattering matrices of the upper
and lower slabs, one can construct the total scattering matrix of the stack.
The formation of the resonant output and input vectors of the stacked system is
rigorously derived by means of an effective Hamiltonian. We demonstrate that
the proposed procedure dramatically decreases the computation time without
sufficient loss of accuracy. We believe that the proposed technique can be a
powerful tool for fast solving inverse scattering problems using stochastic
optimization methods such as genetic algorithms or machine learning.
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We have analyzed a sample of 27,258 fundamental-mode RR Lyrae variable stars
(type RRab) detected recently toward the Galactic bulge by the Optical
Gravitational Lensing Experiment (OGLE) survey. The data support our earlier
claim that these metal-poor stars trace closely the barred structure formed of
intermediate-age red clump giants. The distance to the Galactic center (GC)
inferred from the bulge RR Lyrae stars is R_0=8.27+/-0.01(stat)+/-0.40(sys)
kpc. We show that their spatial distribution has the shape of a triaxial
ellipsoid with an major axis located in the Galactic plane and inclined at an
angle of i=20+/-3 deg to the Sun-GC line of sight. The obtained scale-length
ratio of the major axis to the minor axis in the Galactic plane and to the axis
vertical to the plane is 1:0.49(2):0.39(2). We do not see the evidence for the
bulge RR Lyrae stars forming an X-shaped structure. Based on the light curve
parameters, we derive metallicities of the RRab variables and show that there
is a very mild but statistically significant radial metallicity gradient. About
60% of the bulge RRab stars form two very close sequences on the
period-amplitude (or Bailey) diagram, which we interpret as two major old bulge
populations: A and B. Their metallicities likely differ. Population A is about
four times less abundant than the slightly more metal-poor population B. Most
of the remaining stars seem to represent other, even more metal-poor
populations of the bulge. The presence of multiple old populations indicates
that the Milky Way bulge was initially formed through mergers.
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Answering a question of A. Vershik we construct two non-weakly isomorphic
ergodic automorphisms for which the associated unitary (Koopman)
representations are Markov quasi-similar. We also discuss metric invariants of
Markov quasi-similarity in the class of ergodic automorphisms.
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As Nature's version of machine learning, evolution has solved many
extraordinarily complex problems, none perhaps more remarkable than learning to
harness an increase in chemical entropy (disorder) to generate directed
chemical forces (order). Using muscle as a model system, here I unpack the
basic mechanism by which life creates order from disorder. In short, evolution
tuned the physical properties of certain proteins to contain changes in
chemical entropy. As it happens, these are the "sensible" properties Gibbs
postulated were needed to solve his paradox.
|
A mechanism to construct asymptotically flat, isolated, stationary black hole
(BH) spacetimes with no $\mathbb{Z}_2$ (No$\mathbb{Z}$) isometry is described.
In particular, the horizon geometry of such No$\mathbb{Z}$ BHs does not have
the usual north-south (reflection) symmetry. We discuss two explicit families
of models wherein No$\mathbb{Z}$ BHs arise. In one of these families, we
exhibit the intrinsic horizon geometry of an illustrative example by
isometrically embedding it in Euclidean 3-space, resulting in an "egg-like"
shaped horizon. This asymmetry leaves an imprint in the No$\mathbb{Z}$ BH
phenomenology, for instance in its lensing of light; but it needs not be
manifest in the BH shadow, which in some cases can be analytically shown to
retain a $\mathbb{Z}_2$ symmetry. Light absorption and scattering due to an
isotropic source surrounding a No$\mathbb{Z}$ BH endows it with a non-zero
momentum, producing an asymmetry triggered BH rocket effect.
|
This paper provides a behavioral analysis of conservatism in beliefs. I
introduce a new axiom, Dynamic Conservatism, that relaxes Dynamic Consistency
when information and prior beliefs "conflict." When the agent is a subjective
expected utility maximizer, Dynamic Conservatism implies that conditional
beliefs are a convex combination of the prior and the Bayesian posterior.
Conservatism may result in belief dynamics consistent with confirmation bias,
representativeness, and the good news-bad news effect, suggesting a deeper
behavioral connection between these biases. An index of conservatism and a
notion of comparative conservatism are characterized. Finally, I extend
conservatism to the case of an agent with incomplete preferences that admit a
multiple priors representation.
|
We implement a decision procedure for answering questions about a class of
infinite words that might be called (for lack of a better name)
"Fibonacci-automatic". This class includes, for example, the famous Fibonacci
word f = 01001010..., the fixed point of the morphism 0 -> 01 and 1 -> 0. We
then recover many results about the Fibonacci word from the literature (and
improve some of them), such as assertions about the occurrences in f of
squares, cubes, palindromes, and so forth. As an application of our method we
prove a new result: there exists an aperiodic infinite binary word avoiding the
pattern x x x^R. This is the first avoidability result concerning a nonuniform
morphism proven purely mechanically.
|
We report on fluctuations in the electron system, Cooper pairs and
quasiparticles, of a superconducting aluminium film. The superconductor is
exposed to pair-breaking photons (1.54 THz), which are coupled through an
antenna. The change in the complex conductivity of the superconductor upon a
change in the quasiparticle number is read out by a microwave resonator. A
large range in radiation power can be chosen by carefully filtering the
radiation from a blackbody source. We identify two regimes. At high radiation
power, fluctuations in the electron system caused by the random arrival rate of
the photons are resolved, giving a straightforward measure of the optical
efficiency (48%). At low radiation power fluctuations are dominated by excess
quasiparticles, the number of which is measured through their recombination
lifetime.
|
The classical Lippmann-Schwinger equation plays an important role in the
scattering theory (non-relativistic case, Schr\"odinger equation). In the
present paper we consider the relativistic analogue of the Lippmann-Schwinger
equation. We represent the corresponding equation in the integral form. Using
this integral equation we investigate the stationary scattering problems
(relativistic case, Dirac equation). We consider the dynamical scattering
problems (relativistic case, Dirac equation) as well.
|
The constrained-search formulation of Levy and Lieb, which formally defines
the exact Hohenberg-Kohn functional for any N-representable electron density,
is here shown to be equivalent to the minimization of the correlation
functional with respect to the N-1 conditional probability density, where N is
number of electrons of the system. The consequences and implications of such a
result are here analyzed and discussed via a practical example.
|
We study the dynamical evolution of a phase interface or bubble in the
context of a \lambda \phi^4 + g \phi^6 scalar quantum field theory. We use a
self-consistent mean-field approximation derived from a 2PI effective action to
construct an initial value problem for the expectation value of the quantum
field and two-point function. We solve the equations of motion numerically in
(1+1)-dimensions and compare the results to the purely classical evolution. We
find that the quantum fluctuations dress the classical profile, affecting both
the early time expansion of the bubble and the behavior upon collision with a
neighboring interface.
|
We present Herschel far-infrared and submillimeter maps of the debris disk
associated with the HR 8799 planetary system. We resolve the outer disk
emission at 70, 100, 160 and 250 um and detect the disk at 350 and 500 um. A
smooth model explains the observed disk emission well. We observe no obvious
clumps or asymmetries associated with the trapping of planetesimals that is a
potential consequence of planetary migration in the system. We estimate that
the disk eccentricity must be <0.1. As in previous work by Su et al. (2009), we
find a disk with three components: a warm inner component and two outer
components, a planetesimal belt extending from 100 - 310 AU, with some
flexibility (+/- 10 AU) on the inner edge, and the external halo which extends
to ~2000 AU. We measure the disk inclination to be 26 +/- 3 deg from face-on at
a position angle of 64 deg E of N, establishing that the disk is coplanar with
the star and planets. The SED of the disk is well fit by blackbody grains whose
semi-major axes lie within the planetesimal belt, suggesting an absence of
small grains. The wavelength at which the spectrum steepens from blackbody, 47
+/- 30 um, however, is short compared to other A star debris disks, suggesting
that there are atypically small grains likely populating the halo. The PACS
longer wavelength data yield a lower disk color temperature than do MIPS data
(24 and 70 um), implying two distinct halo dust grain populations.
|
Today, all types of digital signature schemes emphasis on secure and best
verification methods. Different digital signature schemes are used in order for
the websites, security organizations, banks and so on to verify user's
validity. Digital signature schemes are categorized to several types such as
proxy, on-time, batch and so on. In this paper, different types of schemes are
compared based on security level, efficiency, difficulty of algorithm and so
on. Results show that best scheme depends on security, complexity and other
important parameters. We tried simply to define the schemes and review them in
practice.
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Learning the distribution of natural images is one of the hardest and most
important problems in machine learning. The problem remains open, because the
enormous complexity of the structures in natural images spans all length
scales. We break down the complexity of the problem and show that the hierarchy
of structures in natural images fuels a new class of learning algorithms based
on the theory of critical phenomena and stochastic processes. We approach this
problem from the perspective of the theory of critical phenomena, which was
developed in condensed matter physics to address problems with infinite
length-scale fluctuations, and build a framework to integrate the criticality
of natural images into a learning algorithm. The problem is broken down by
mapping images into a hierarchy of binary images, called bitplanes. In this
representation, the top bitplane is critical, having fluctuations in structures
over a vast range of scales. The bitplanes below go through a gradual
stochastic heating process to disorder. We turn this representation into a
directed probabilistic graphical model, transforming the learning problem into
the unsupervised learning of the distribution of the critical bitplane and the
supervised learning of the conditional distributions for the remaining
bitplanes. We learnt the conditional distributions by logistic regression in a
convolutional architecture. Conditioned on the critical binary image, this
simple architecture can generate large, natural-looking images, with many
shades of gray, without the use of hidden units, unprecedented in the studies
of natural images. The framework presented here is a major step in bringing
criticality and stochastic processes to machine learning and in studying
natural image statistics.
|
We have developed a wide-field mosaic CCD camera, MOA-cam3, mounted at the
prime focus of the Microlensing Observations in Astrophysics (MOA) 1.8-m
telescope. The camera consists of ten E2V CCD4482 chips, each having 2kx4k
pixels, and covers a 2.2 deg^2 field of view with a single exposure. The
optical system is well optimized to realize uniform image quality over this
wide field. The chips are constantly cooled by a cryocooler at -80C, at which
temperature dark current noise is negligible for a typical 1-3 minute exposure.
The CCD output charge is converted to a 16-bit digital signal by the GenIII
system (Astronomical Research Cameras Inc.) and readout is within 25 seconds.
Readout noise of 2--3 ADU (rms) is also negligible. We prepared a wide-band red
filter for an effective microlensing survey and also Bessell V, I filters for
standard astronomical studies. Microlensing studies have entered into a new
era, which requires more statistics, and more rapid alerts to catch exotic
light curves. Our new system is a powerful tool to realize both these
requirements.
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We present GausSN, a Bayesian semi-parametric Gaussian Process (GP) model for
time-delay estimation with resolved systems of gravitationally lensed
supernovae (glSNe). GausSN models the underlying light curve non-parametrically
using a GP. Without assuming a template light curve for each SN type, GausSN
fits for the time delays of all images using data in any number of wavelength
filters simultaneously. We also introduce a novel time-varying magnification
model to capture the effects of microlensing alongside time-delay estimation.
In this analysis, we model the time-varying relative magnification as a sigmoid
function, as well as a constant for comparison to existing time-delay
estimation approaches. We demonstrate that GausSN provides robust time-delay
estimates for simulations of glSNe from the Nancy Grace Roman Space Telescope
and the Vera C. Rubin Observatory's Legacy Survey of Space and Time
(Rubin-LSST). We find that up to 43.6% of time-delay estimates from Roman and
52.9% from Rubin-LSST have fractional errors of less than 5%. We then apply
GausSN to SN Refsdal and find the time delay for the fifth image is consistent
with the original analysis, regardless of microlensing treatment. Therefore,
GausSN maintains the level of precision and accuracy achieved by existing
time-delay extraction methods with fewer assumptions about the underlying shape
of the light curve than template-based approaches, while incorporating
microlensing into the statistical error budget rather than requiring
post-processing to account for its systematic uncertainty. GausSN is scalable
for time-delay cosmography analyses given current projections of glSNe
discovery rates from Rubin-LSST and Roman.
|
The complementary DNA (cDNA) sequence is considered to be the magic biometric
technique for personal identification. In this paper, we present a new method
for cDNA recognition based on the artificial neural network (ANN). Microarray
imaging is used for the concurrent identification of thousands of genes. We
have segmented the location of the spots in a cDNA microarray. Thus, a precise
localization and segmenting of a spot are essential to obtain a more accurate
intensity measurement, leading to a more precise expression measurement of a
gene. The segmented cDNA microarray image is resized and it is used as an input
for the proposed artificial neural network. For matching and recognition, we
have trained the artificial neural network. Recognition results are given for
the galleries of cDNA sequences . The numerical results show that, the proposed
matching technique is an effective in the cDNA sequences process. We also
compare our results with previous results and find out that, the proposed
technique is an effective matching performance.
|
We present an action for a six-dimensional superconformal field theory
containing a non-abelian tensor multiplet. All of the ingredients of this
action have been available in the literature. We bring these pieces together by
choosing the string Lie 2-algebra as a gauge structure, which we motivated in
previous work. The kinematical data contains a connection on a categorified
principal bundle, which is the appropriate mathematical description of the
parallel transport of self-dual strings. Our action can be written down for
each of the simply laced Dynkin diagrams, and each case reduces to a
four-dimensional supersymmetric Yang--Mills theory with corresponding gauge Lie
algebra. Our action also reduces nicely to an M2-brane model which is a
deformation of the ABJM model. While this action is certainly not the desired
M5-brane model, we regard it as a key stepping stone towards a potential
construction of the (2,0)-theory.
|
Burr and Erd\H{o}s conjectured that for each $k,\ell \in \mathbb Z^+$ such
that $k \mathbb Z + \ell$ contains even integers, there exists $c_k(\ell)$ such
that any graph of average degree at least $c_k(\ell)$ contains a cycle of
length $\ell$ mod $k$. This conjecture was proved by Bollob\'{a}s, and many
successive improvements of upper bounds on $c_k(\ell)$ appear in the
literature. In this short note, for $1 \leq \ell \leq k$, we show that
$c_k(\ell)$ is proportional to the largest average degree of a $C_{\ell}$-free
graph on $k$ vertices, which determines $c_k(\ell)$ up to an absolute constant.
In particular, using known results on Tur\'{a}n numbers for even cycles, we
obtain $c_k(\ell) = O(\ell k^{2/\ell})$ for all even $\ell$, which is tight for
$\ell \in \{4,6,10\}$. Since the complete bipartite graph $K_{\ell - 1,n - \ell
+ 1}$ has no cycle of length $2\ell$ mod $k$, it also shows $c_k(\ell) =
\Theta(\ell)$ for $\ell = \Omega(\log k)$.
|
The effective detection of evidence of financial anomalies requires
collaboration among multiple entities who own a diverse set of data, such as a
payment network system (PNS) and its partner banks. Trust among these financial
institutions is limited by regulation and competition. Federated learning (FL)
enables entities to collaboratively train a model when data is either
vertically or horizontally partitioned across the entities. However, in
real-world financial anomaly detection scenarios, the data is partitioned both
vertically and horizontally and hence it is not possible to use existing FL
approaches in a plug-and-play manner.
Our novel solution, PV4FAD, combines fully homomorphic encryption (HE),
secure multi-party computation (SMPC), differential privacy (DP), and
randomization techniques to balance privacy and accuracy during training and to
prevent inference threats at model deployment time. Our solution provides input
privacy through HE and SMPC, and output privacy against inference time attacks
through DP. Specifically, we show that, in the honest-but-curious threat model,
banks do not learn any sensitive features about PNS transactions, and the PNS
does not learn any information about the banks' dataset but only learns
prediction labels. We also develop and analyze a DP mechanism to protect output
privacy during inference. Our solution generates high-utility models by
significantly reducing the per-bank noise level while satisfying distributed
DP. To ensure high accuracy, our approach produces an ensemble model, in
particular, a random forest. This enables us to take advantage of the
well-known properties of ensembles to reduce variance and increase accuracy.
Our solution won second prize in the first phase of the U.S. Privacy Enhancing
Technologies (PETs) Prize Challenge.
|
The study of multi-type Protein-Protein Interaction (PPI) is fundamental for
understanding biological processes from a systematic perspective and revealing
disease mechanisms. Existing methods suffer from significant performance
degradation when tested in unseen dataset. In this paper, we investigate the
problem and find that it is mainly attributed to the poor performance for
inter-novel-protein interaction prediction. However, current evaluations
overlook the inter-novel-protein interactions, and thus fail to give an
instructive assessment. As a result, we propose to address the problem from
both the evaluation and the methodology. Firstly, we design a new evaluation
framework that fully respects the inter-novel-protein interactions and gives
consistent assessment across datasets. Secondly, we argue that correlations
between proteins must provide useful information for analysis of novel
proteins, and based on this, we propose a graph neural network based method
(GNN-PPI) for better inter-novel-protein interaction prediction. Experimental
results on real-world datasets of different scales demonstrate that GNN-PPI
significantly outperforms state-of-the-art PPI prediction methods, especially
for the inter-novel-protein interaction prediction.
|
The rapid growth of connected devices has led to the proliferation of novel
cyber-security threats known as zero-day attacks. Traditional behaviour-based
IDS rely on DNN to detect these attacks. The quality of the dataset used to
train the DNN plays a critical role in the detection performance, with
underrepresented samples causing poor performances. In this paper, we develop
and evaluate the performance of DBN on detecting cyber-attacks within a network
of connected devices. The CICIDS2017 dataset was used to train and evaluate the
performance of our proposed DBN approach. Several class balancing techniques
were applied and evaluated. Lastly, we compare our approach against a
conventional MLP model and the existing state-of-the-art. Our proposed DBN
approach shows competitive and promising results, with significant performance
improvement on the detection of attacks underrepresented in the training
dataset.
|
We prove linearly repetitive Delone systems have finitely many Delone system
factors up to conjugacy. This result is also applicable to linearly repetitive
tiling systems.
|
(abridged) We investigate the quark deconfinement phase transition in the
context of binary neutron star (BNS) mergers. We employ a new
finite-temperature composition-dependent equation of state (EOS) with a first
order phase transition between hadrons and deconfined quarks to perform
numerical relativity simulations of BNS mergers. The softening of the EOS due
to the phase transition causes the merger remnants to be more compact and to
collapse to a black hole (BH) at earlier times. The phase transition is
imprinted on the postmerger gravitational wave (GW) signal duration, amplitude,
and peak frequency. However, this imprint is only detectable for binaries with
sufficiently long-lived remnants. Moreover, the phase transition does not
result in significant deviations from quasi-universal relations for the
postmerger GW peak frequency. We also study the impact of the phase transition
on dynamical ejecta, remnant accretion disk masses, r-process nucleosynthetic
yields and associated electromagnetic (EM) counterparts. While there are
differences in the EM counterparts and nucleosynthesis yields between the
purely hadronic models and the models with phase transitions, these can be
primarily ascribed to the difference in remnant collapse time between the two.
An exception is the non-thermal afterglow caused by the interaction of the
fastest component of the dynamical ejecta and the interstellar medium, which is
systematically boosted in the binaries with phase transition as a consequence
of the more violent merger they experience.
|
This paper presents the latest optical design for the MOONS triple-arm
spectrographs. MOONS will be a Multi-Object Optical and Near-infrared
Spectrograph and will be installed on one of the European Southern Observatory
(ESO) Very Large Telescopes (VLT). Included in this paper is a trade-off
analysis of different types of collimators, cameras, dichroics and filters.
|
The varying-coefficient model is an important nonparametric statistical model
that allows us to examine how the effects of covariates vary with exposure
variables. When the number of covariates is big, the issue of variable
selection arrives. In this paper, we propose and investigate marginal
nonparametric screening methods to screen variables in ultra-high dimensional
sparse varying-coefficient models. The proposed nonparametric independence
screening (NIS) selects variables by ranking a measure of the nonparametric
marginal contributions of each covariate given the exposure variable. The sure
independent screening property is established under some mild technical
conditions when the dimensionality is of nonpolynomial order, and the
dimensionality reduction of NIS is quantified. To enhance practical utility and
the finite sample performance, two data-driven iterative NIS methods are
proposed for selecting thresholding parameters and variables: conditional
permutation and greedy methods, resulting in Conditional-INIS and Greedy-INIS.
The effectiveness and flexibility of the proposed methods are further
illustrated by simulation studies and real data applications.
|
The processional switching mechanism governs magnetic switching in magnetic
tunnel junctions (MTJs) in the sub-nanosecond range, which limits the
application of spin transfer torque magnetic random access memory (STT-MRAM) in
the ultrafast region. In this paper, we propose a new picosecond magnetic
switching mechanism in a synthetic antiferromagnetic (SAF) structure using the
adjustable Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction controlled by an
external electric field (E-field). It is shown that along with the sign change
of the RKKY interaction in the SAF structure with an external E-field, the
critical switching current density can be significantly reduced by one order of
magnitude compared to that of a normal MTJ design at 100 ps; thus, this novel
STT-MRAM can be written with a very low switching current density to avoid the
MTJ breakdown problem and reduce the writing energy. To understand the physical
origin of this abnormal phenomenon, a toy model is proposed in which the
external-E-field-controlled sign change of the RKKY interaction in the SAF
structure provides an extra contribution to the total energy that helps
thespins overcome the energy barrier and break the processional switching
mechanism.
|
We predict the range of proper motions of 19 satellite galaxies of M31 that
would rotationally stabilise the M31 plane of satellites consisting of 15-20
members as identified by Ibata et al. (2013). Our prediction is based purely on
the current positions and line-of-sight velocities of these satellites and the
assumption that the plane is not a transient feature. These predictions are
therefore independent of the current debate about the formation history of this
plane. We further comment on the feasibility of measuring these proper motions
with future observations by the THEIA satellite mission as well as the
currently planned observations by HST and JWST.
|
In this article, we study the simultaneous sign changes of the Fourier
coefficients of two Hilbert cusp forms of different integral weights. We also
study the simultaneous non-vanishing of Fourier coefficients, of two distinct
non-zero primitive Hilbert cuspidal non-CM eigenforms of integral weights, at
powers of a fixed prime ideal.
|
Certain star shaped quivers exhibit a pattern of symmetry enhancement on the
Coulomb branch of $3d$ $\mathcal{N}=4$ supersymmetric gauge theories. This
paper studies a subclass of theories where such global symmetry enhancement
occurs through a computation of the Highest Weight Generating Function (HWG)
and of the corresponding Hilbert Series (HS), providing a further test of the
Coulomb branch formula. This special subclass has a feature in which the HWG
takes a particularly simple form, as a simple rational function which is either
a product of simple poles (termed freely generated) or a simple PE (termed
complete intersection). Out of all possible star shaped quivers, this is a
particularly simple subclass. The present study motivates a further study of
identifying all star shaped quivers for which their HWG is of this simple form.
|
Let G be a finite group. The Plesken Lie algebra L[G] is a subalgebra of the
complex group algebra C[G] and admits a direct-sum decomposition into simple
Lie algebras based on the ordinary character theory of G. In this paper we
review the known results on L[G] and related Lie algebras, as well as introduce
a conjecture on a characteristic p analog L_p[G], with a focus on when p
divides the order of G.
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We confirm the following conjecture which has been proposed in [{\em Linear
Algebra and its Applications}, {\bf 436} (2012), No. 5, 1425-1435.]: $$
0.945\approx\displaystyle\lim_{n\longrightarrow
\infty}\sigma(P_n,Z_n)=\displaystyle\lim_{n\longrightarrow
\infty}\sigma(W_n,Z_n)=\frac{1}{2}\displaystyle\lim_{n\longrightarrow
\infty}\sigma(P_n,W_n);\ \displaystyle\lim_{n\longrightarrow
\infty}\sigma(C_{2n},Z_{2n})=2,$$ where $\sigma(G_1,G_2)=\sum_{i=1}^n
|\lambda_i(G_1)-\lambda_i(G_2)|$ is the spectral distance between $n$ vertex
non-isomorphic graphs $G_1$ and $G_2$ with adjacency spectra $\lambda_1(G_i)
\geq \lambda_2(G_i) \geq \cdots \geq \lambda_n(G_i)$ for $i=1,2$, and $P_n$ and
$C_n$ denote the path and cycle on $n$ vertices, respectively; $Z_n$ denotes
the coalescence of $P_{n-2}$ and $P_3$ on one of the vertices of degree 1 of
$P_{n-2}$ and the vertex of degree $2$ of $P_3$; and $W_n$ denotes the
coalescence of $Z_{n-2}$ and $P_3$ on the vertex of degree 1 of $Z_{n-2}$ which
is adjacent to a vertex of degree $2$ and the vertex of degree $2$ of $P_3$.
|
Entanglement in the ground state of the XY model on the infinite chain can be
measured by the von Neumann entropy of a block of neighboring spins. We study a
double scaling limit: the size of the block is much larger then 1 but much
smaller then the length of the whole chain. In this limit, the entropy of the
block approaches a constant. The limiting entropy is a function of the
anisotropy and of the magnetic field. The entropy reaches minima at product
states and increases boundlessly at phase transitions.
|
We present an experimental study of spin-torque driven vortex
self-oscillations in magnetic nanocontacts. We find that above a certain
threshold in applied currents, the vortex gyration around the nanocontact is
modulated by relaxation oscillations, which involve periodic reversals of the
vortex core. This modulation leads to the appearance of commensurate but also
more interestingly here, incommensurate states, which are characterized by
devil's staircases in the modulation frequency. We use frequency- and
time-domain measurements together with advanced time-series analyses to provide
experimental evidence of chaos in incommensurate states of vortex oscillations,
in agreement with theoretical predictions.
|
Radiative emissions from electrons and positrons generated by dark matter
(DM) annihilation or decay are one of the most investigated signals in indirect
searches of WIMPs. Ideal targets must have large ratio of DM to baryonic
matter. However, such ``dark'' systems have a poorly known level of magnetic
turbulence, which determines the residence time of the electrons and positrons
and therefore also the strength of the expected signal. This typically leads to
significant uncertainties in the derived DM bounds. In a novel approach, we
compute the self-confinement of the DM-induced electrons and positrons. Indeed,
they themselves generate irregularities in the magnetic field, thus setting a
lower limit on the presence of the magnetic turbulence. We specifically apply
this approach to dwarf spheroidal galaxies. Finally, by comparing the expected
synchrotron emission with radio data from the direction of the Draco galaxy
collected at the Giant Metre Radio Telescope, we show that the proposed
approach can be used to set robust and competitive bounds on WIMP DM.
|
The first observation of the decay $\eta_{c}(2S) \to p \bar p$ is reported
using proton-proton collision data corresponding to an integrated luminosity of
$3.0\rm \, fb^{-1}$ recorded by the LHCb experiment at centre-of-mass energies
of 7 and 8 TeV. The $\eta_{c}(2S)$ resonance is produced in the decay $B^{+}
\to [c\bar c] K^{+}$. The product of branching fractions normalised to that for
the $J/\psi$ intermediate state, ${\cal R}_{\eta_{c}(2S)}$, is measured to be
\begin{align*} {\cal R}_{\eta_{c}(2S)}\equiv\frac{{\mathcal B}(B^{+} \to
\eta_{c}(2S) K^{+}) \times {\mathcal B}(\eta_{c}(2S) \to p \bar p)}{{\mathcal
B}(B^{+} \to J/\psi K^{+}) \times {\mathcal B}(J/\psi\to p \bar p)} =~& (1.58
\pm 0.33 \pm 0.09)\times 10^{-2}, \end{align*} where the first uncertainty is
statistical and the second systematic. No signals for the decays $B^{+} \to
X(3872) (\to p \bar p) K^{+}$ and $B^{+} \to \psi(3770) (\to p \bar p) K^{+}$
are seen, and the 95\% confidence level upper limits on their relative
branching ratios are % found to be ${\cal R}_{X(3872)}<0.25\times10^{-2}$ and
${\cal R}_{\psi(3770))}<0.10$. In addition, the mass differences between the
$\eta_{c}(1S)$ and the $J/\psi$ states, between the $\eta_{c}(2S)$ and the
$\psi(2S)$ states, and the natural width of the $\eta_{c}(1S)$ are measured as
\begin{align*} M_{J/\psi} - M_{\eta_{c}(1S)} =~& 110.2 \pm 0.5 \pm 0.9 \rm \,
MeV, M_{\psi(2S)} -M_{\eta_{c}(2S)} =~ & 52.5 \pm 1.7 \pm 0.6 \rm \, MeV,
\Gamma_{\eta_{c}(1S)} =~& 34.0 \pm 1.9 \pm 1.3 \rm \, MeV. \end{align*}
|
Large-scale dynamics of the oceans and the atmosphere are governed by
primitive equations (PEs). Due to the nonlinearity and nonlocality, the
numerical study of the PEs is generally challenging. Neural networks have been
shown to be a promising machine learning tool to tackle this challenge. In this
work, we employ physics-informed neural networks (PINNs) to approximate the
solutions to the PEs and study the error estimates. We first establish the
higher-order regularity for the global solutions to the PEs with either full
viscosity and diffusivity, or with only the horizontal ones. Such a result for
the case with only the horizontal ones is new and required in the analysis
under the PINNs framework. Then we prove the existence of two-layer tanh PINNs
of which the corresponding training error can be arbitrarily small by taking
the width of PINNs to be sufficiently wide, and the error between the true
solution and its approximation can be arbitrarily small provided that the
training error is small enough and the sample set is large enough. In
particular, all the estimates are a priori, and our analysis includes
higher-order (in spatial Sobolev norm) error estimates. Numerical results on
prototype systems are presented to further illustrate the advantage of using
the $H^s$ norm during the training.
|
In order to meet the increasing demands of high data rate and low latency
cellular broadband applications, plans are underway to roll out the Fifth
Generation (5G) cellular wireless system by the year 2020. This paper proposes
a novel method for adapting the Third Generation Partnership Project (3GPP)'s
5G architecture to the principles of Software Defined Networking (SDN). We
propose to have centralized network functions in the 5G network core to control
the network, end-to-end. This is achieved by relocating the control
functionality present in the 5G Radio Access Network (RAN) to the network core,
resulting in the conversion of the base station known as the gNB into a pure
data plane node. This brings about a significant reduction in signaling costs
between the RAN and the core network. It also results in improved system
performance. The merits of our proposal have been illustrated by evaluating the
Key Performance Indicators (KPIs) of the 5G network, such as network attach
(registration) time and handover time. We have also demonstrated improvements
in attach time and system throughput due to the use of centralized algorithms
for mobility management with the help of ns-3 simulations.
|
Recent progress in the text-driven 3D stylization of a single object has been
considerably promoted by CLIP-based methods. However, the stylization of
multi-object 3D scenes is still impeded in that the image-text pairs used for
pre-training CLIP mostly consist of an object. Meanwhile, the local details of
multiple objects may be susceptible to omission due to the existing supervision
manner primarily relying on coarse-grained contrast of image-text pairs. To
overcome these challenges, we present a novel framework, dubbed TeMO, to parse
multi-object 3D scenes and edit their styles under the contrast supervision at
multiple levels. We first propose a Decoupled Graph Attention (DGA) module to
distinguishably reinforce the features of 3D surface points. Particularly, a
cross-modal graph is constructed to align the object points accurately and noun
phrases decoupled from the 3D mesh and textual description. Then, we develop a
Cross-Grained Contrast (CGC) supervision system, where a fine-grained loss
between the words in the textual description and the randomly rendered images
are constructed to complement the coarse-grained loss. Extensive experiments
show that our method can synthesize high-quality stylized content and
outperform the existing methods over a wide range of multi-object 3D meshes.
Our code and results will be made publicly available
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Given an integer k, we consider the parallel k-stripping process applied to a
hypergraph H: removing all vertices with degree less than k in each iteration
until reaching the k-core of H. Take H as H_r(n,m): a random r-uniform
hypergraph on n vertices and m hyperedges with the uniform distribution. Fixing
k,r\ge 2 with (k,r)\neq (2,2), it has previously been proved that there is a
constant c_{r,k} such that for all m=cn with constant c\neq c_{r,k}, with high
probability, the parallel k-stripping process takes O(\log n) iterations. In
this paper we investigate the critical case when c=c_{r,k}+o(1). We show that
the number of iterations that the process takes can go up to some power of n,
as long as c approaches c_{r,k} sufficiently fast. A second result we show
involves the depth of a non-k-core vertex v: the minimum number of steps
required to delete v from H_r(n,m) where in each step one vertex with degree
less than k is removed. We will prove lower and upper bounds on the maximum
depth over all non-k-core vertices.
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Some markers of oxidative injury were measured in different rat brain areas
(hippocampus, cerebral cortex, striatum, hypothalamus, amygdala/piriform cortex
and cerebellum) after the systemic administration of an excitotoxic dose of
kainic acid (KA, 9 mg kg(-1) i.p.) at two different sampling times (24 and 48
h). Kainic acid was able to lower markedly (P < 0.05) the glutathione (GSH)
levels in hippocampus, cerebellum and amygdala/piriform cortex (maximal
reduction at 24 h). In a similar way, lipid peroxidation, as assessed by
malonaldehyde and 4-hydroxyalkenal levels, significantly increased (P < 0.05)
in hippocampus, cerebellum and amygdala/piriform cortex mainly at 24 h after
KA. In addition, hippocampal superoxide dismutase (SOD) activity decreased
significantly (P < 0.05) with respect to basal levels by 24 h after KA
application. On the other hand, brain areas such as hypothalamus, striatum and
cerebral cortex seem to be less susceptible to KA excitotoxicity. According to
these findings, the pattern of oxidative injury induced by systemically
administered KA seems to be highly region-specific. Further, our results have
shown that a lower antioxidant status (GSH and SOD) seems not to play an
important role in the selective vulnerability of certain brain regions because
it correlates poorly with increases in markers of oxidative damage.
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The pursuit of explaining and improving generalization in deep learning has
elicited efforts both in regularization techniques as well as visualization
techniques of the loss surface geometry. The latter is related to the intuition
prevalent in the community that flatter local optima leads to lower
generalization error. In this paper, we harness the state-of-the-art "filter
normalization" technique of loss-surface visualization to qualitatively
understand the consequences of using adversarial training data augmentation as
the explicit regularization technique of choice. Much to our surprise, we
discover that this oft deployed adversarial augmentation technique does not
actually result in "flatter" loss-landscapes, which requires rethinking
adversarial training generalization, and the relationship between
generalization and loss landscapes geometries.
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We consider dilaton gravity theories in four spacetime dimensions
parametrised by a constant $a$, which controls the dilaton coupling, and
construct new exact solutions. We first generalise the C-metric of
Einstein-Maxwell theory ($a=0$) to solutions corresponding to oppositely
charged dilaton black holes undergoing uniform acceleration for general $a$. We
next develop a solution generating technique which allows us to ``embed" the
dilaton C-metrics in magnetic dilaton Melvin backgrounds, thus generalising the
Ernst metric of Einstein-Maxwell theory. By adjusting the parameters
appropriately, it is possible to eliminate the nodal singularities of the
dilaton C-metrics. For $a<1$ (but not for $a\ge 1$), it is possible to further
restrict the parameters so that the dilaton Ernst solutions have a smooth
euclidean section with topology $S^2\times S^2-{\rm\{pt\}}$, corresponding to
instantons describing the pair production of dilaton black holes in a magnetic
field. A different restriction on the parameters leads to smooth instantons for
all values of $a$ with topology $S^2\times \R^2$.
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The Complex Axis theorem states that any endomorphism of a finite-dimensional
complex vector space affords an eigen-vector (or "invariant axis"). A geometric
proof of this geometric result was given by A. de Medeiros, transforming the
endomorphism into a topological self-map with Lefschetz number not equal to
zero. We give a dual version of this proof, which may be more uniform, and does
not rely on the need to do any calculation of an Euler characteristic or
Lefschetz number. A vector field on Projective space is read off directly from
the coordinates ("entries") of the given endomorphism (complex square matrix).
A bordism is defined between such vector fields by means of Stokes' Theorem
applied to a real manifold-with-boundary. This is the principle behind Hopf's
lemma relating the Gauss map and the index of a vector field. All vector fields
of the de Medeiros type are co-bordant to the Milnor-Hopf vector field. This
latter comes from a non-derogatory, real diagonal endomorphism, so clearly
possesses an eigen-vector. Therefore so has the given arbitrary endomorphism.
The main theorem on complex polynomials naturally follows, using the companion
matrix, secular polynomial reciprocity. The geometric Complex Axis derivation
is meant to avoid determinants or "general position" arguments.
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In this paper, we present our numerical simulation results on the Stimulated
Brillouin Scattering (SBS) with injection of an ordinary mode (O-mode)
electromagnetic wave (our pump wave) with frequencies 70 GHz and 110 GHz.
Solving the Fourier transformed Vlasov equation in the velocity space, creates
a profile for distribution function. Time evolution of the distribution
function is investigated as well. Considering an average density for plasma
fusion (n_{0} ~ 10^{19} m^{-3}), we gain a profile for density. Then
two-dimensional instability rate for SBS is obtained. So, the fluctuation of
distribution function affects density and again density affects instability
rate. Increasing the incident light wave frequency causes the instability
growth rate to decrease. Time evolution shows a clear damping for instability
rate since the pump wave's energy is absorbed in plasma (plasma heating).
Furthermore, changing Landau damping for ion acoustic waves (IAW) by changing
ion-to-electron temperature ratio is presented as well, because this damping is
more dominant in high temperatures.
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The oxygen-exchange behavior has been studied in half-doped manganese and
cobalt perovskite oxides. We have found that the oxygen diffusivity in
Gd_{0.5}Ba_{0.5}MnO_{3-\delta} can be enhanced by orders of magnitude by
inducing crystallographic ordering among lanthanide and alkali-earth ions in
the A-site sublattice. Transformation of a simple cubic perovskite, with
randomly occupied A-sites, into a layered crystal GdBaMn_2O_{5+x} (or
isostructural GdBaCo_2O_{5+x} for cobalt oxide) with alternating lanthanide and
alkali-earth planes reduces the oxygen bonding strength and provides
disorder-free channels for ion motion, pointing to an efficient way to design
new ionic conductors.
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We study the consequences for top-quark physics of having electron and
positron beams available at the LHeC and FCC-he, as was the case in HERA. We
show that the asymmetry between top production in $pe^+$ collisions and antitop
production in $pe^-$ reactions is sensitive to $|V_{td}|$. By means of detailed
parton-level Monte Carlo simulations of single $t$ and $\bar{t}$ production and
its backgrounds, we parametrize the asymmetry dependence on $|V_{td}|$ and
estimate its uncertainties. We thus obtain limits on $|V_{td}|$ that are
substantially stronger than current ones, and also smaller than current
projections for the HL-LHC. We have $|V_{td}| < 1.6\times
|V_{td}^\mathrm{PDG}|$ at the LHeC, at 68\% C.L.\ with $L_\mathrm{int}=2$/ab.
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Every closed oriented PL 4-manifold is a branched cover of the 4-sphere
branched over a PL-surface with finitely many singularities by Piergallini
[Topology 34(3):497-508, 1995]. This generalizes a long standing result by
Hilden and Montesinos to dimension four. Izmestiev and Joswig [Adv. Geom.
3(2):191-225, 2003] gave a combinatorial equivalent of the Hilden and
Montesinos result, constructing closed oriented combinatorial 3-manifolds as
simplicial branched covers of combinatorial 3-spheres. The construction of
Izmestiev and Joswig is generalized and applied to the result of Piergallini,
obtaining closed oriented combinatorial 4-manifolds as simplicial branched
covers of simplicial 4-spheres.
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We establish the Hasse Principle for systems of r simultaneous diagonal cubic
equations whenever the number of variables exceeds 6r and the associated
coefficient matrix contains no singular r x r submatrix, thereby achieving the
theoretical limit of the circle method for such systems.
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Consider a proper, isometric action by a unimodular locally compact group $G$
on a Riemannian manifold $M$ with boundary, such that $M/G$ is compact. Then an
equivariant Dirac-type operator $D$ on $M$ under a suitable boundary condition
has an equivariant index $\operatorname{index}_G(D)$ in the $K$-theory of the
reduced group $C^*$-algebra $C^*_rG$ of $G$. This is a common generalisation of
the Baum-Connes analytic assembly map and the (equivariant)
Atiyah-Patodi-Singer index. In part I of this series, a numerical index
$\operatorname{index}_g(D)$ was defined for an element $g \in G$, in terms of a
parametrix of $D$ and a trace associated to $g$. An Atiyah-Patodi-Singer type
index formula was obtained for this index. In this paper, we show that, under
certain conditions, $\tau_g(\operatorname{index}_G(D)) =
\operatorname{index}_g(D)$, for a trace $\tau_g$ defined by the orbital
integral over the conjugacy class of $g$. This implies that the index theorem
from part I yields information about the $K$-theoretic index
$\operatorname{index}_G(D)$. It also shows that $\operatorname{index}_g(D)$ is
a homotopy-invariant quantity.
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Current methods for measuring magnetic flux are based on performing many
measurements over a large ensemble of electrons. We propose a novel method
based on wavefunction "revival" for measuring the flux modulo hc/2e using only
a single electron. A preliminary analysis of the feasibility of the experiment
is provided.
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We report results from the experiment NA57 at CERN SPS on hyperon production
at midrapidity in Pb-Pb collisions at 158 $A$ GeV/$c$ and 40 $A$ GeV/$c$.
$\Lambda$, $\Xi$ and $\Omega$ yields are compared with those from the STAR
experiment at the higher energy of the BNL RHIC. $\Lambda$, $\Xi$, $\Omega$\
and preliminary $K_S^0$ transverse mass spectra are presented and interpreted
within the framework of a hydro-dynamical blast wave model.
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Gaze behavior is an important non-verbal cue in social signal processing and
human-computer interaction. In this paper, we tackle the problem of person- and
head pose-independent 3D gaze estimation from remote cameras, using a
multi-modal recurrent convolutional neural network (CNN). We propose to combine
face, eyes region, and face landmarks as individual streams in a CNN to
estimate gaze in still images. Then, we exploit the dynamic nature of gaze by
feeding the learned features of all the frames in a sequence to a many-to-one
recurrent module that predicts the 3D gaze vector of the last frame. Our
multi-modal static solution is evaluated on a wide range of head poses and gaze
directions, achieving a significant improvement of 14.6% over the state of the
art on EYEDIAP dataset, further improved by 4% when the temporal modality is
included.
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Generic matrix multiplication (GEMM) and one-dimensional
convolution/cross-correlation (CONV) kernels often constitute the bulk of the
compute- and memory-intensive processing within image/audio recognition and
matching systems. We propose a novel method to scale the energy and processing
throughput of GEMM and CONV kernels for such error-tolerant multimedia
applications by adjusting the precision of computation. Our technique employs
linear projections to the input matrix or signal data during the top-level GEMM
and CONV blocking and reordering. The GEMM and CONV kernel processing then uses
the projected inputs and the results are accumulated to form the final outputs.
Throughput and energy scaling takes place by changing the number of projections
computed by each kernel, which in turn produces approximate results, i.e.
changes the precision of the performed computation. Results derived from a
voltage- and frequency-scaled ARM Cortex A15 processor running face recognition
and music matching algorithms demonstrate that the proposed approach allows for
280%~440% increase of processing throughput and 75%~80% decrease of energy
consumption against optimized GEMM and CONV kernels without any impact in the
obtained recognition or matching accuracy. Even higher gains can be obtained if
one is willing to tolerate some reduction in the accuracy of the recognition
and matching applications.
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Neutron scattering measurements of the lowest-energy TO phonons in the
relaxor Pb(Mg1/3Nb2/3)O3 (PMN) are reported for 10<=T<=750 K. The soft mode,
which is overdamped by the polar nanoregions below the Burns temperature T_d =
620 K, surprisingly recovers below 220 K. The square of the soft mode energy
hw0^2 increases linearly with decreasing temperature, and is consistent with
the behavior of a ferroelectric soft mode. At 10 K, hw0 reaches 11 meV, the
same value observed in ferroelectric Pb(Zn1/3Nb2/3)O3 at low-T. An unusual
broadening of the TA phonon starts at T_d and disappears at 220 K, coincident
with the recovery of the TO mode. These dynamics suggest that a well-developed
ferroelectric state is established below 220 K.
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Consider a finite inhomogeneous random graph running in continuous time,
where each vertex has a mass, and the edge that links any pair of vertices
appears with a rate equal to the product of their masses. The simultaneous
breadth-first-walk introduced by Limic (2019) is extended in order to account
for the surplus edge data in addition to the spanning edge data. Two different
graph-based representations of the multiplicative coalescent, with different
advantages and drawbacks, are discussed in detail. A canonical multi-graph from
Bhamidi, Budhiraja and Wang (2014) naturally emerges. The presented framework
will facilitate the understanding of scaling limits with surplus edges for
near-critical random graphs in the domain of attraction of general (not
necessarily standard) eternal augmented multiplicative coalescent.
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We solve the boson normal ordering problem for (q(a*)a + v(a*))^n with
arbitrary functions q and v and integer n, where a and a* are boson
annihilation and creation operators, satisfying [a,a*]=1. This leads to
exponential operators generalizing the shift operator and we show that their
action can be expressed in terms of substitutions. Our solution is naturally
related through the coherent state representation to the exponential generating
functions of Sheffer-type polynomials. This in turn opens a vast arena of
combinatorial methodology which is applied to boson normal ordering and
illustrated by a few examples.
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Based on the convex force-motion polynomial model for quasi-static sliding,
we derive the kinematic contact model to determine the contact modes and
instantaneous object motion on a supporting surface given a position controlled
manipulator. The inherently stochastic object-to-surface friction distribution
is modelled by sampling physically consistent parameters from appropriate
distributions, with only one parameter to control the amount of noise. Thanks
to the high fidelity and smoothness of convex polynomial models, the mechanics
of patch contact is captured while being computationally efficient without mode
selection at support points. The motion equations for both single and multiple
frictional contacts are given. Simulation based on the model is validated with
robotic pushing and grasping experiments.
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In this work, we propose a model-agnostic instance-based post-hoc
explainability method for time series classification. The proposed algorithm,
namely Time-CF, leverages shapelets and TimeGAN to provide counterfactual
explanations for arbitrary time series classifiers. We validate the proposed
method on several real-world univariate time series classification tasks from
the UCR Time Series Archive. The results indicate that the counterfactual
instances generated by Time-CF when compared to state-of-the-art methods,
demonstrate better performance in terms of four explainability metrics:
closeness, sensibility, plausibility, and sparsity.
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We aim to constrain the temperature and velocity structures, and H2O
abundances in the winds of a sample of M-type AGB stars. We further aim to
determine the effect of H2O line cooling on the energy balance in the inner
circumstellar envelope. We use two radiative-transfer codes to model molecular
emission lines of CO and H2O towards four M-type AGB stars. We focus on
spectrally resolved observations of CO and H2O from HIFI. The observations are
complemented by ground-based CO observations, and spectrally unresolved CO and
H2O observations with PAC. The observed line profiles constrain the velocity
structure throughout the circumstellar envelopes (CSEs), while the CO
intensities constrain the temperature structure in the CSEs. The H2O
observations constrain the o-H2O and p-H2O abundances relative to H2. Finally,
the radiative-transfer modelling allows to solve the energy balance in the CSE,
in principle including also H2O line cooling. The fits to the line profiles
only set moderate constraints on the velocity profile, indicating shallower
acceleration profiles in the winds of M-type AGB stars than predicted by
dynamical models, while the CO observations effectively constrain the
temperature structure. Including H2O line cooling in the energy balance was
only possible for the low-mass-loss-rate objects in the sample, and required an
ad hoc adjustment of the dust velocity profile in order to counteract extreme
cooling in the inner CSE. H2O line cooling was therefore excluded from the
models. The constraints set on the temperature profile by the CO lines
nevertheless allowed us to derive H2O abundances. The derived H2O abundances
confirm previous estimates and are consistent with chemical models. However,
the uncertainties in the derived abundances are relatively large, in particular
for p-H2O, and consequently the derived o/p-H2O ratios are not well
constrained.
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This document lists a set of (refereed and unrefereed) scientific
publications based on data taken with the instruments of the Italian Telescopio
Nazionale Galileo (TNG, mainly from the year 2000 onward) and the technical
papers describing the development of the TNG project from the "phase A" (late
'80s) until the end of year 2005. The collection is compiled by searching for
publications on the internet. In particular, the search engines of the NASA
Astrophysics Data System and Google Scholar are used. This work represents the
first attempt to probe the scientific production of the TNG and will be updated
regularly from year to year. Comments and suggestions are welcome.
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The main target of retrosynthesis is to recursively decompose desired
molecules into available building blocks. Existing template-based
retrosynthesis methods follow a template selection stereotype and suffer from
limited training templates, which prevents them from discovering novel
reactions. To overcome this limitation, we propose an innovative retrosynthesis
prediction framework that can compose novel templates beyond training
templates. As far as we know, this is the first method that uses machine
learning to compose reaction templates for retrosynthesis prediction. Besides,
we propose an effective reactant candidate scoring model that can capture
atom-level transformations, which helps our method outperform previous methods
on the USPTO-50K dataset. Experimental results show that our method can produce
novel templates for 15 USPTO-50K test reactions that are not covered by
training templates. We have released our source implementation.
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The supercharacter theory is constructed for the parabolic subgroups of
$\mathrm{GL}(n,\Fq)$ with blocks of orders less or equal to two. The author
formulated the hypotheses on construction of a supercharacter theory for an
arbitrary parabolic subgroup in $\mathrm{GL}(n,\Fq)$.
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We prove the existence of complexified real arrangements with the same
combinatorics but different embeddings in the complex projective plane. Such
pair of arrangements has an additional property: they admit conjugated
equations on the ring of polynomials over the number field ${\mathbb
Q}(\sqrt{5})$.
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This paper explores the possibility that asset prices, especially those
traded in large volume on public exchanges, might comply with specific physical
laws of motion and probability. The paper first examines the basic dynamics of
asset price displacement and finds one can model this dynamic as a harmonic
oscillator at local "slices" of elapsed time. Based on this finding, the paper
theorizes that price displacements are constrained, meaning they have extreme
values beyond which they cannot go when measured over a large number of
sequential periods. By assuming price displacements are also subject to the
principle of stationary action, the paper explores a method for measuring
specific probabilities of future price displacements based on prior historical
data. Testing this theory with two prevalent stock indices suggests it can make
accurate forecasts as to constraints on extreme price movements during market
"crashes" and probabilities of specific price displacements at other times.
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Subsets and Splits