text
stringlengths 6
128k
|
|---|
Platelet products are both expensive and have very short shelf lives. As
usage rates for platelets are highly variable, the effective management of
platelet demand and supply is very important yet challenging. The primary goal
of this paper is to present an efficient forecasting model for platelet demand
at Canadian Blood Services (CBS). To accomplish this goal, four different
demand forecasting methods, ARIMA (Auto Regressive Moving Average), Prophet,
lasso regression (least absolute shrinkage and selection operator) and LSTM
(Long Short-Term Memory) networks are utilized and evaluated. We use a large
clinical dataset for a centralized blood distribution centre for four hospitals
in Hamilton, Ontario, spanning from 2010 to 2018 and consisting of daily
platelet transfusions along with information such as the product
specifications, the recipients' characteristics, and the recipients' laboratory
test results. This study is the first to utilize different methods from
statistical time series models to data-driven regression and a machine learning
technique for platelet transfusion using clinical predictors and with different
amounts of data. We find that the multivariate approaches have the highest
accuracy in general, however, if sufficient data are available, a simpler time
series approach such as ARIMA appears to be sufficient. We also comment on the
approach to choose clinical indicators (inputs) for the multivariate models.
|
The structural properties of NaxCoO2 and NaxCoO2yH2O have been investigated.
The NaxCoO2yH2O samples in general show up the superconducting transitions at
around 3.5K. EDAX analyses suggest our samples have the average composition of
Na0.65CoO2 for the parent compound and Na0.26CoO2yH2O for the superconducting
crystals. TEM observation reveals a superstructure with wave vector q=<1/2,0,
0> in the parent Na0.65CoO2 materials. This superstructure becomes very weak in
the superconducting oxyhydrates. EELS analyses show that the Co ions have the
valence state of around +3.3 in the Na0.65CoO2 materials and around +3.7 in the
superconducting materials.
|
We study the excited random walk, in which a walk that is at a site that
contains cookies eats one cookie and then hops to the right with probability p
and to the left with probability q=1-p. If the walk hops onto an empty site,
there is no bias. For the 1-excited walk on the half-line (one cookie initially
at each site), the probability of first returning to the starting point at time
t scales as t^{-(2-p)}. Although the average return time to the origin is
infinite for all p, the walk eats, on average, only a finite number of cookies
until this first return when p<1/2. For the infinite line, the probability
distribution for the 1-excited walk has an unusual anomaly at the origin. The
positions of the leftmost and rightmost uneaten cookies can be accurately
estimated by probabilistic arguments and their corresponding distributions have
power-law singularities near the origin. The 2-excited walk on the infinite
line exhibits peculiar features in the regime p>3/4, where the walk is
transient, including a mean displacement that grows as t^{nu}, with nu>1/2
dependent on p, and a breakdown of scaling for the probability distribution of
the walk.
|
The Spitzer Space Telescope, born as the Shuttle Infrared Telescope Facility
(SIRTF) and later the Space Infrared Telescope Facility (still SIRTF), was
under discussion and development within NASA and the scientific community for
more than 30 years prior to its launch in 2003. This brief history chronicles a
few of the highlights and the lowlights of those 30 years from the authors
personal perspective. A much more comprehensive history of SIRTF/Spitzer has
been written by George Rieke (2006).
|
We have measured electron-ion recombination for Fe$^{9+}$ forming Fe$^{8+}$
and for Fe$^{10+}$ forming Fe$^{9+}$ using merged beams at the TSR heavy-ion
storage-ring in Heidelberg. The measured merged beams recombination rate
coefficients (MBRRC) for relative energies from 0 to 75 eV are presented,
covering all dielectronic recombination (DR) resonances associated with 3s->3p
and 3p->3d core transitions in the spectroscopic species Fe X and Fe XI,
respectively. We compare our experimental results to multi-configuration
Breit-Pauli (MCBP) calculations and find significant differences. From the
measured MBRRC we have extracted the DR contributions and transform them into
plasma recombination rate coefficients (PRRC) for astrophysical plasmas with
temperatures from 10^2 to 10^7 K. This spans across the regimes where each ion
forms in photoionized or in collisionally ionized plasmas. For both temperature
regimes the experimental uncertainties are 25% at a 90% confidence level. The
formerly recommended DR data severely underestimated the rate coefficient at
temperatures relevant for photoionized gas. At the temperatures relevant for
photoionized gas, we find agreement between our experimental results and MCBP
theory. At the higher temperatures relevant for collisionally ionized gas, the
MCBP calculations yield a Fe XI DR rate coefficent which is significantly
larger than the experimentally derived one. We present parameterized fits to
our experimentally derived DR PRRC.
|
Let $\chi$ be a Dirichlet character (mod $n$) with conductor $d$. In a quite
recent paper Zhao and Cao deduced the identity $\sum_{k=1}^n (k-1,n) \chi(k)=
\varphi(n)\tau(n/d)$, which reduces to Menon's identity if $\chi$ is the
principal character (mod $n$). We generalize the above identity by considering
even functions (mod $n$), and offer an alternative approach to proof. We also
obtain certain related formulas concerning Ramanujan sums.
|
Motivated by Hubert's segmentation procedure we discuss the application of
hidden Markov models (HMM) to the segmentation of hydrological and enviromental
time series. We use a HMM algorithm which segments time series of several
hundred terms in a few seconds and is computationally feasible for even longer
time series. The segmentation algorithm computes the Maximum Likelihood
segmentation by use of an expectation / maximization iteration. We rigorously
prove algorithm convergence and use numerical experiments, involving
temperature and river discharge time series, to show that the algorithm usually
converges to the globally optimal segmentation. The relation of the proposed
algorithm to Hubert's segmentation procedure is also discussed.
|
The correspondence between gyrofluid and low frequency fluid equations is
examined. The lowest order conservative effects in ExB advection, parallel
dynamics, and curvature match trivially. The principal concerns are
polarisation fluxes, and dissipative parallel viscosity and parallel heat
fluxes. The emergence of the polarisation heat flux in the fluid model and its
contribution to the energy theorem is reviewed. It is shown that gyroviscosity
and the polarisation fluxes are matched by the finite gyroradius corrections to
advection in the long wavelength limit, provided that the differences between
gyrocenter and particle representations is taken into account. The dissipative
parallel viscosity is matched by the residual thermal anisotropy in the
gyrofluid model in the collision dominated limit. The dissipative parallel heat
flux is matched by the gyrofluid parallel heat flux variables in the collision
dominated limit. Hence, the gyrofluid equations are a complete superset of the
low frequency fluid equations.
|
We describe the various types of singularities that can arise for second
order rational mappings and we discuss the historical and present-day,
practical, role the singularity confinement property plays as an integrability
detector. In particular, we show how singularity analysis can be used to
calculate explicitly the dynamical degree for such mappings.
|
In model-based reinforcement learning, the agent interleaves between model
learning and planning. These two components are inextricably intertwined. If
the model is not able to provide sensible long-term prediction, the executed
planner would exploit model flaws, which can yield catastrophic failures. This
paper focuses on building a model that reasons about the long-term future and
demonstrates how to use this for efficient planning and exploration. To this
end, we build a latent-variable autoregressive model by leveraging recent ideas
in variational inference. We argue that forcing latent variables to carry
future information through an auxiliary task substantially improves long-term
predictions. Moreover, by planning in the latent space, the planner's solution
is ensured to be within regions where the model is valid. An exploration
strategy can be devised by searching for unlikely trajectories under the model.
Our method achieves higher reward faster compared to baselines on a variety of
tasks and environments in both the imitation learning and model-based
reinforcement learning settings.
|
In a point cloud sequence, 3D object tracking aims to predict the location
and orientation of an object in the current search point cloud given a template
point cloud. Motivated by the success of transformers, we propose Point
Tracking TRansformer (PTTR), which efficiently predicts high-quality 3D
tracking results in a coarse-to-fine manner with the help of transformer
operations. PTTR consists of three novel designs. 1) Instead of random
sampling, we design Relation-Aware Sampling to preserve relevant points to
given templates during subsampling. 2) Furthermore, we propose a Point Relation
Transformer (PRT) consisting of a self-attention and a cross-attention module.
The global self-attention operation captures long-range dependencies to enhance
encoded point features for the search area and the template, respectively.
Subsequently, we generate the coarse tracking results by matching the two sets
of point features via cross-attention. 3) Based on the coarse tracking results,
we employ a novel Prediction Refinement Module to obtain the final refined
prediction. In addition, we create a large-scale point cloud single object
tracking benchmark based on the Waymo Open Dataset. Extensive experiments show
that PTTR achieves superior point cloud tracking in both accuracy and
efficiency.
|
This paper demonstrates cooling of the center-of-mass motion of 10
$\mu$m-diameter optically levitated silica spheres to an effective temperature
of $50\pm22 \mu$K, achieved by minimizing the technical pointing noise of the
trapping laser. This low noise leads to an acceleration and force sensitivity
of $95\pm41$ n$g/\sqrt{\mathrm{Hz}}$ ($g = 9.8$ m/s$^2$) and $0.95\pm0.11$
aN$/\sqrt{\mathrm{Hz}}$, respectively, at frequencies near 50 Hz. This force
sensitivity is comparable to that demonstrated for optically levitated
nanospheres that are $10^4$ times less massive, corresponding to an
acceleration sensitivity that is several orders of magnitude better. It is
further shown that under these conditions the spheres remain stably trapped at
pressures of $\sim 10^{-7}$ mbar with no active cooling for periods longer than
a day. Feedback cooling is still necessary in the moderate-pressure regime,
motivating a comprehensive study of the loss mechanisms of the microspheres and
providing better understanding of the requirements for feedback-free optical
trapping in vacuum. This work can enable high-sensitivity searches for
accelerations and forces acting on micron-sized masses, including those that
could be produced by new physics beyond the Standard Model.
|
Using ultraviolet spectra obtained with the Cosmic Origins Spectrograph on
the Hubble Space Telescope, we extend our previous ground-based optical
determinations of the composition of the extrasolar asteroids accreted onto two
white dwarfs, GD 40 and G241-6. Combining optical and ultraviolet spectra of
these stars with He-dominated atmospheres, 13 and 12 polluting elements are
confidently detected in GD 40 and G241-6, respectively. For the material
accreted onto GD 40, the volatile elements C and S are deficient by more than a
factor of 10 and N by at least a factor of 5 compared to their mass fractions
in primitive CI chondrites and approach what is inferred for bulk Earth. A
similar pattern is found for G241-6 except that S is undepleted. We have also
newly detected or placed meaningful upper limits for the amount of Cl, Al, P,
Ni and Cu in the accreted matter. Extending results from optical studies, the
mass fractions of refractory elements in the accreted parent bodies are similar
to what is measured for bulk Earth and chondrites. Thermal processing, perhaps
interior to a snow line, appears to be of central importance in determining the
elemental compositions of these particular extrasolar asteroids.
|
Uncovering the formation process that reproduces the distinct properties of
compact super-Earth exoplanet systems is a major goal of planet formation
theory. The most successful model argues that non-resonant systems begin as
resonant chains of planets that later experience a dynamical instability.
However, both the boundary of stability in resonant chains and the mechanism of
the instability itself are poorly understood. Previous work postulated that a
secondary resonance between the fastest libration frequency and a difference in
synodic frequencies destabilizes the system. Here, we use that hypothesis to
produce a simple and general criterion for resonant chain stability that
depends only on planet orbital periods and masses. We show that the criterion
accurately predicts the maximum mass of planets in synthetic resonant chains up
to six planets. More complicated resonant chains produced in population
synthesis simulations are found to be less stable than expected, although our
criterion remains useful and superior to machine learning models.
|
Recent demonstrations of controlled switching between different ordered
macroscopic states by impulsive electromagnetic perturbations in complex
materials have opened some fundamental questions on the mechanisms responsible
for such remarkable behavior. Here we experimentally address the question of
whether two-dimensional (2D) Mott physics can be responsible for unusual
switching between states of different electronic order in the layered
dichalcogenide 1T-TaS2, or it is a result of subtle inter-layer orbitronic
re-ordering of its helical stacking structure. We report on the switching
properties both in-plane and perpendicular to the layers by current-pulse
injection, the anisotropy of electronic transport in the commensurate ground
state, and relaxation properties of the switched metastable state. Contrary to
recent theoretical calculations, which predict a uni-directional metal
perpendicular to the layers, we observe a large resistivity in this direction,
with a temperature-dependent anisotropy. Remarkably, large resistance ratios
are observed in the memristive switching both in-plane (IP) and out-of-plane
(OP). The relaxation dynamics of the metastable state for both IP and OP
electron transport are seemingly governed by the same mesoscopic quantum
re-ordering process. We conclude that 1T-TaS2 shows resistance switching
arising from an interplay of both IP and OP correlations.
|
Emulsions are common in many natural and industrial settings. Recently, much
attention has been put on understanding the dynamics of turbulent emulsions.
This paper reviews some recent studies of emulsions in turbulent Taylor-Couette
flow, mainly focusing on the statistics of the dispersed phase and the global
momentum transport of the system. We first study the size distribution and the
breakup mechanism of the dispersed droplets for turbulent emulsions with a low
volume-fraction (dilute) of the dispersed phase. For systems with a high
volume-fraction of the dispersed phase (dense), we address the detailed
response of the global transport (effective viscosity) of the turbulent
emulsion and its connection to the droplet statistics. Finally, we will discuss
catastrophic phase inversions, which can happen when the volume fraction of the
dispersed phase exceeds a critical value during dynamic emulsification. We end
the manuscript with a summary and an outlook including some open questions for
future research. This article is part of the theme issue `Taylor-Couette and
Related Flows on the Centennial of Taylor's Seminal Philosophical Transactions
Paper'.
|
Flatness measurement of a surface plate is an intensive and old research
topic. However ISO definition related and other measurement methods seem uneasy
in measuring and/ or complicated in data analysis. Especially in reality, the
mentioned methods don't take a clear and straightforward care on the inclining
angle which is always included in any given flatness measurement. In this
report a novel simple and accurate flatness measurement method was introduced
to overcome this prevailing feature in the available methods. The mathematical
modeling for this method was also presented making the underlying nature of the
method transparent. The applying examples show consistent results.
|
We present an elegant design of the core language in a dependently-typed
lambda calculus with $\delta$-reduction and an elaboration algorithm.
|
We introduce Wilson-It\^o diffusions, a class of random fields on
$\mathbb{R}^d$ that change continuously along a scale parameter via a Markovian
dynamics with local coefficients. Described via forward-backward stochastic
differential equations, their observables naturally form a pre-factorization
algebra \`a la Costello-Gwilliam. We argue that this is a new non-perturbative
quantization method applicable also to gauge theories and independent of a
path-integral formulation. Whenever a path-integral is available, this approach
reproduces the setting of Wilson-Polchinski flow equations.
|
The influence of an impurity atom on the electrostatic behaviour of a Single
Molecular Transistor (SMT) was investigated through Ab-initio calculations in a
double-gated geometry. The charge stability diagram carries unique signature of
the position of the impurity atom in such devices which together with the
charging energy of the molecule could be utilised as an electronic fingerprint
for the detection of such impurity states in a nano-electronic device. The two
gated geometry allows additional control over the electrostatics as can be seen
from the total energy surfaces (for a specific charge state) which is sensitive
to the positions of the impurity. These devices which are operational at room
temperature can provide significant advantages over the conventional Silicon
based single dopant devices functional at low temperature. The present approach
could be a very powerful tool for the detection and control of individual
impurity atoms in a single molecular device and for applications in future
molecular electronics.
|
Using properties of diffusion according to a quantum heat kernel constructed
as an expectation over classical heat kernels on $S^1$, we probe the
non-manifold-like nature of quantized space in a model of (1+1)-dimensional
quantum gravity. By computing the mean squared displacement of a diffusing
particle, we find that diffusion is anomalous, behaving similarly to that on a
porous substrate, network, or fractal over short distances. The walk dimension
of the path for a particle diffusing in quantized space is calculated to have
an infimum of 4, rising to arbitrarily large values depending on a parameter
labeling the choice of factor ordering in the quantum Hamiltonian for our model
and figuring in the asymptotic behavior of the wavefunction used to construct
the quantum heat kernel. Additionally, we derive an expansion for return
probability of a diffusing particle, whose modifications from the classical
power-series form depend on the factor-ordering parameter.
|
Top-down instance segmentation framework has shown its superiority in object
detection compared to the bottom-up framework. While it is efficient in
addressing over-segmentation, top-down instance segmentation suffers from
over-crop problem. However, a complete segmentation mask is crucial for
biological image analysis as it delivers important morphological properties
such as shapes and volumes. In this paper, we propose a region proposal
rectification (RPR) module to address this challenging incomplete segmentation
problem. In particular, we offer a progressive ROIAlign module to introduce
neighbor information into a series of ROIs gradually. The ROI features are fed
into an attentive feed-forward network (FFN) for proposal box regression. With
additional neighbor information, the proposed RPR module shows significant
improvement in correction of region proposal locations and thereby exhibits
favorable instance segmentation performances on three biological image datasets
compared to state-of-the-art baseline methods. Experimental results demonstrate
that the proposed RPR module is effective in both anchor-based and anchor-free
top-down instance segmentation approaches, suggesting the proposed method can
be applied to general top-down instance segmentation of biological images.
|
We investigate two stochastic models of a growing population subject to
selection and mutation. In our models each individual carries a fitness which
determines its mean offspring number. Many of these offspring inherit their
parent's fitness, but some are mutants and obtain a fitness randomly sampled
from a distribution in the domain of attraction of the Fr\'echet distribution.
We give a rigorous proof for the precise rate of superexponential growth of
these stochastic processes and support the argument by a heuristic and
numerical study of the mechanism underlying this growth.
|
We calculate the angular momentum and energy of a vortex dipole in a trapped
atomic Bose-Einstein condensate. Fully analytic expressions are obtained. We
apply the results to understand a novel phenomenon in the MIT group experiment,
an excellent agreement is achieved, and further experimental investigation is
proposed to confirm this vortex dipole mechanism. We then suggest an effective
generation and detection of vortex dipole for experimental realization.
Application of the sum rule to calculate collective mode frequency splitting is
also discussed.
|
Background: Network Analysis (NA) is a method that has been used in various
disciplines such as Social sciences and Ecology for decades. So far, NA has not
been used extensively in studies of medication use. Only a handful of papers
have used NA in Drug Prescription Networks (DPN). We provide an introduction to
NA terminology alongside a guide to creating and extracting results from the
medication networks. Objective: To introduce the readers to NA as a tool to
study medication use by demonstrating how to apply different NA measures on 3
generated medication networks. Methods: We used the Norwegian Prescription
Database (NorPD) to create a network that describes the co-medication in
elderly persons in Norway on January 1, 2013. We used the Norwegian Electronic
Prescription Support System (FEST) to create another network of severe
drug-drug interactions (DDIs). Lastly, we created a network combining the two
networks to show the actual use of drugs with severe DDIs. We used these
networks to elucidate how to apply and interpret different network measures in
medication networks. Results: Interactive network graphs are made available
online, Stata and R syntaxes are provided. Various useful network measures for
medication networks were applied such as network topological features,
modularity analysis and centrality measures. Edge lists data used to generate
the networks are openly available for readers in an open data repository to
explore and use. Conclusion: We believe that NA can be a useful tool in
medication use studies. We have provided information and hopefully inspiration
for other researchers to use NA in their own projects. While network analyses
are useful for exploring and discovering structures in medication use studies,
it also has limitations. It can be challenging to interpret and it is not
suitable for hypothesis testing.
|
Radiative corrections to an atom are calculated near a half-space that has
arbitrarily-shaped small depositions upon its surface. The method is based on
calculation of the classical Green's function of the macroscopic Maxwell
equations near an arbitrarily perturbed half-space using a Born series
expansion about the bare half-space Green's function. The formalism of
macroscopic quantum electrodynamics is used to carry this over into the quantum
picture. The broad utility of the calculated Green's function is demonstrated
by using it to calculate two quantities --- the spontaneous decay rate of an
atom near a sharp surface feature, and the Casimir-Polder potential of a finite
grating deposited on a substrate. Qualitatively new behaviour is found in both
cases, most notably in the latter where it is observed that the periodicity of
the Casimir-Polder potential persists even outside the immediate vicinity of
the grating.
|
A sample of field early-type galaxies (E/S0) at intermediate redshift
($z\sim0.1-0.6$) is selected, based on morphology and colours from HST-WFPC2
parallel images. Photometric structural parameters (effective radius
$R_{\tx{e}}$ and effective surface brightness $SB_{\tx{e}}$) are derived
through the F606W and F814W filters, using luminosity profile fitting and
two-dimensional fitting techniques. The combined parameter that enters the
Fundamental Plane ($\log R_{\tx{e}}-\beta SB_{\tx{e}}$, with
$\beta\approx0.32$) is shown to suffer from significantly smaller uncertainties
(r.m.s. 0.03) than the individual structural parameters (e.g. $\sim 15$ per
cent r.m.s. on the effective radius).
High signal-to-noise intermediate resolution spectra, taken at the ESO-3.6m,
yield redshifts for 35 galaxies and central velocity dispersions for 22
galaxies. Central velocity dispersions are derived using a library of stellar
templates covering a wide range of spectral types, in order to study the
effects of templates mismatches. The average random error on the central
velocity dispersion is found to be 8 per cent and the average systematic error
due to template mismatch is found to be 5 per cent. The errors on velocity
dispersion measurement and the effects of template mismatches are studied by
means of extensive Montecarlo simulations. In addition, we investigate whether
the determination of the velocity dispersion is sensitive to the spectral range
used, finding that the value of velocity dispersion is unchanged when the
spectral regions that include the absorption features Ca HK and NaD are masked
out during the fit.
|
Panoramic Dental Radiography (PDR) image processing is one of the most
extensively used manual methods for gender determination in forensic medicine.
With the assistance of the PDR images, a person's biological gender
determination can be performed through analyzing skeletal structures expressing
sexual dimorphism. Manual approaches require a wide range of mandibular
parameter measurements in metric units. Besides being time-consuming, these
methods also necessitate the employment of experienced professionals. In this
context, deep learning models are widely utilized in the auto-analysis of
radiological images nowadays, owing to their high processing speed, accuracy,
and stability. In our study, a data set consisting of 24,000 dental panoramic
images was prepared for binary classification, and the transfer learning method
was used to accelerate the training and increase the performance of our
proposed DenseNet121 deep learning model. With the transfer learning method,
instead of starting the learning process from scratch, the existing patterns
learned beforehand were used. Extensive comparisons were made using deep
transfer learning (DTL) models VGG16, ResNet50, and EfficientNetB6 to assess
the classification performance of the proposed model in PDR images. According
to the findings of the comparative analysis, the proposed model outperformed
the other approaches by achieving a success rate of 97.25% in gender
classification.
|
It is generally known that linear (free) field theories are one of the few
QFT that are exactly soluble. In the Schroedinger functional description of a
scalar field on flat Minkowski spacetime and for flat embeddings, it is known
that the usual Fock representation is described by a Gaussian measure. In this
paper, arbitrary globally hyperbolic space-times and embeddings of the Cauchy
surface are considered. The classical structures relevant for quantization are
used for constructing the Schroedinger representation in the general case. It
is shown that in this case, the measure is also Gaussian. Possible implications
for the program of canonical quantization of midisuperspace models are pointed
out.
|
Production of $\Upsilon$ mesons in proton-lead collisions at a
nucleon-nucleon centre-of-mass energy $\sqrt{s_{NN}}=5 \mathrm{TeV}$ is studied
with the LHCb detector. The analysis is based on a data sample corresponding to
an integrated luminosity of $1.6 \mathrm{nb}^{-1}$. The $\Upsilon$ mesons of
transverse momenta up to $15 \mathrm{GeV}/c$ are reconstructed in the dimuon
decay mode. The rapidity coverage in the centre-of-mass system is $1.5<y<4.0$
(forward region) and $-5.0<y<-2.5$ (backward region). The forward-backward
production ratio and the nuclear modification factor for $\Upsilon(1S)$ mesons
are determined. The data are compatible with the predictions for a suppression
of $\Upsilon(1S)$ production with respect to proton-proton collisions in the
forward region, and an enhancement in the backward region. The suppression is
found to be smaller than in the case of prompt $J/\psi$ mesons.
|
Disordered noninteracting quasiparticles that are governed by a Majorana-type
Hamiltonian -- prominent examples are dirty superconductors with broken
time-reversal and spin-rotation symmetry, or the fermionic representation of
the 2d Ising model with fluctuating bond strengths -- are called class D. In
two dimensions, weakly disordered systems of this kind may possess a metallic
phase beyond the insulating phases expected for strong disorder. We show that
the 2d metal phase emanates from the free Majorana fermion point, in the
direction of the RG trajectory of a perturbed WZW model. To establish this
result, we develop a supersymmetric extension of the method of nonabelian
bosonization. On the metallic side of the metal-insulator transition, the
density of states becomes nonvanishing at zero energy, by a mechanism akin to
dynamical mass generation. This feature is explored in a model of N species of
disordered Dirac fermions, via the mapping on a nonlinear sigma model, which
encapsulates a Z_2 spin degree of freedom. We compute the density of states in
a finite system, and obtain agreement with the random-matrix prediction for
class D, in the ergodic limit. Vortex disorder, which is a relevant
perturbation at the free-fermion point, changes the density of states at low
energy and suppresses the local Z_2 degree of freedom, thereby leading to a
different symmetry class, BD.
|
Kernel methods provide an elegant framework for developing nonlinear learning
algorithms from simple linear methods. Though these methods have superior
empirical performance in several real data applications, their usefulness is
inhibited by the significant computational burden incurred in large sample
situations. Various approximation schemes have been proposed in the literature
to alleviate these computational issues, and the approximate kernel machines
are shown to retain the empirical performance. However, the theoretical
properties of these approximate kernel machines are less well understood. In
this work, we theoretically study the trade-off between computational
complexity and statistical accuracy in Nystr\"om approximate kernel principal
component analysis (KPCA), wherein we show that the Nystr\"om approximate KPCA
matches the statistical performance of (non-approximate) KPCA while remaining
computationally beneficial. Additionally, we show that Nystr\"om approximate
KPCA outperforms the statistical behavior of another popular approximation
scheme, the random feature approximation, when applied to KPCA.
|
(This is not the abstract): The language is Japanese. If your printer does
not have fonts for Japases characters, the characters in figures will not be
printed out correctly. Dissertation for Bachelor's degree at Kyoto
University(Nagao lab.),March 1994.
|
Sexually reproducing populations with small number of individuals may go
extinct by stochastic fluctuations in sex determination, causing all their
members to become male or female in a generation. In this work we calculate the
time to extinction of isolated populations with fixed number $N$ of individuals
that are updated according to the Moran birth and death process. At each time
step, one individual is randomly selected and replaced by its offspring
resulting from mating with another individual of opposite sex; the offspring
can be male or female with equal probability. A set of $N$ time steps is called
a generation, the average time it takes for the entire population to be
replaced. The number k of females fluctuates in time, similarly to a random
walk, and extinction, which is the only asymptotic possibility, occurs when k=0
or k=N. We show that it takes only one generation for an arbitrary initial
distribution of males and females to approach the binomial distribution. This
distribution, however, is unstable and the population eventually goes extinct
in 2^N/N generations. We also discuss the robustness of these results against
bias in the determination of the sex of the offspring, a characteristic
promoted by infection by the bacteria Wolbachia in some arthropod species or by
temperature in reptiles.
|
We analyze the Bombay stock exchange (BSE) price index over the period of
last 12 years. Keeping in mind the large fluctuations in last few years, we
carefully find out the transient, non-statistical and locally structured
variations. For that purpose, we make use of Daubechies wavelet and
characterize the fractal behavior of the returns using a recently developed
wavelet based fluctuation analysis method. the returns show a fat-tail
distribution as also weak non-statistical behavior. We have also carried out
continuous wavelet as well as Fourier power spectral analysis to characterize
the periodic nature and correlation properties of the time series.
|
The local Minkowski tensors are valuations on the space of convex bodies in
Euclidean space with values in a space of tensor measures. They generalize at
the same time the intrinsic volumes, the curvature measures and the isometry
covariant Minkowski tensors that were introduced by McMullen and characterized
by Alesker. In analogy to the characterization theorems of Hadwiger and
Alesker, we give here a complete classification of all locally defined tensor
measures on convex bodies that share with the local Minkowski tensors the basic
geometric properties of isometry covariance and weak continuity.
|
The concept of time reversal (TR) of scalar wave is reexamined from basic
principles. Five different time reversal mirrors (TRM) are introduced and their
relations are analyzed. For the boundary behavior, it is shown that for
paraxial wave only the monopole TR scheme satisfies the exact boundary
condition while for spherical wave only one of the mixed mode TR scheme, after
multiplication by two, satisfies the exact boundary condition. The asymptotic
analysis of the near-field focusing property is presented. It is shown that to
have a subwavelength focal spot the TRM should involve dipole fields. The
monopole TR is extremely ineffective to focus below wavelength as the focal
spot size decreases logarithmically with the distance between the source and
TRM. Contrary to the matched field processing and the phase processor, both of
which resemble TR, TR in a weak- or non-scattering medium is usually biased in
the longitudinal direction, especially when TR is carried out on a {\em single}
plane with a {finite} aperture. This is true for all five TR schemes. On the
other hand, the TR focal spot has been shown repeatedly in the literature, both
theoretically and experimentally, to be centered at the source point when the
medium is multiply scattering. A reconciliation of the two seemingly
conflicting results is found in the random fluctuations in the intensity of the
Green function for a multiply scattering medium and the notion of
scattering-enlarged effective aperture.
|
Segmentation of the developing fetal brain is an important step in
quantitative analyses. However, manual segmentation is a very time-consuming
task which is prone to error and must be completed by highly specialized
indi-viduals. Super-resolution reconstruction of fetal MRI has become standard
for processing such data as it improves image quality and resolution. However,
dif-ferent pipelines result in slightly different outputs, further complicating
the gen-eralization of segmentation methods aiming to segment super-resolution
data. Therefore, we propose using transfer learning with noisy multi-class
labels to automatically segment high resolution fetal brain MRIs using a single
set of seg-mentations created with one reconstruction method and tested for
generalizability across other reconstruction methods. Our results show that the
network can auto-matically segment fetal brain reconstructions into 7 different
tissue types, regard-less of reconstruction method used. Transfer learning
offers some advantages when compared to training without pre-initialized
weights, but the network trained on clean labels had more accurate
segmentations overall. No additional manual segmentations were required.
Therefore, the proposed network has the potential to eliminate the need for
manual segmentations needed in quantitative analyses of the fetal brain
independent of reconstruction method used, offering an unbiased way to quantify
normal and pathological neurodevelopment.
|
This is a long introduction to the theory of "branch groups": groups acting
on rooted trees which exhibit some self-similarity features in their lattice of
subgroups.
|
We present a quantum Monte Carlo method which allows calculations on
many-fermion systems at finite temperatures without any sign decay. This
enables simulations of the grand-canonical ensemble at large system sizes and
low temperatures. Both diagonal and off-diagonal expectations can be computed
straightforwardly. The sign decay is eliminated by a constraint on the fermion
determinant. The algorithm is approximate. Tests on the Hubbard model show that
accurate results on the energy and correlation functions can be obtained.
|
We study steady axisymmetric water waves with general vorticity and swirl,
subject to the influence of surface tension. Explicit solutions to such a water
wave problem are static configurations where the surface is an unduloid, that
is, a periodic surface of revolution with constant mean curvature. We prove
that to any such configuration there connects a global continuum of non-static
solutions by means of a global implicit function theorem. To prove this, the
key is strict monotonicity of a certain function describing the mean curvature
of an unduloid and involving complete elliptic integrals. From this point of
view, this paper is an interesting interplay between water waves, geometry, and
properties of elliptic integrals.
|
In analogy with classical submanifold theory, we introduce morphisms of real
metric calculi together with noncommutative embeddings. We show that basic
concepts, such as the second fundamental form and the Weingarten map, translate
into the noncommutative setting and, in particular, we prove a noncommutative
analogue of Gauss equations for the curvature of a submanifold. Moreover, the
mean curvature of an embedding is readily introduced, giving a natural
definition of a noncommutative minimal embedding, and we illustrate the novel
concepts by considering the noncommutative torus as a minimal surface in the
noncommutative 3-sphere.
|
The efficiencies of the gratings in the High Energy Transmission Grating
Spectrometer (HETGS) were updated using in-flight observations of bright
continuum sources. The procedure first involved verifying that fluxes obtained
from the +1 and -1 orders match, which checks that the contaminant model and
the CCD quantum efficiencies agree. Then the fluxes derived using the high
energy gratings (HEGs) were compared to those derived from the medium energy
gratings (MEGs). The flux ratio was fit to a low order polynomial, which was
allocated to the MEGs above 1 keV or the HEGs below 1 keV. The resultant
efficiencies were tested by examining fits to blazar spectra.
|
Previous research has shown that fully-connected networks with small
initialization and gradient-based training methods exhibit a phenomenon known
as condensation during training. This phenomenon refers to the input weights of
hidden neurons condensing into isolated orientations during training, revealing
an implicit bias towards simple solutions in the parameter space. However, the
impact of neural network structure on condensation has not been investigated
yet. In this study, we focus on the investigation of convolutional neural
networks (CNNs). Our experiments suggest that when subjected to small
initialization and gradient-based training methods, kernel weights within the
same CNN layer also cluster together during training, demonstrating a
significant degree of condensation. Theoretically, we demonstrate that in a
finite training period, kernels of a two-layer CNN with small initialization
will converge to one or a few directions. This work represents a step towards a
better understanding of the non-linear training behavior exhibited by neural
networks with specialized structures.
|
We present a search for variable stars in the Fornax dwarf galaxy covering an
area of 1/2 a square degree. We have ~30 epochs of VI data. We found and
determined periods for more than 500 RR Lyrae, 17 anomalous Cepheids, 6
Population II Cepheids. In addition we have 85 candidate Long Period Variables,
the majority of which were previously unknown. We estimated that the average
metal abundance of RR Lyrae stars is [Fe/H] ~ -1.6 dex.
|
Solar flares are explosive releases of magnetic energy. Hard X-ray (HXR)
flare emission originates from both hot (millions of Kelvin) plasma and
nonthermal accelerated particles, giving insight into flare energy release. The
Nuclear Spectroscopic Telescope ARray (NuSTAR) utilizes direct focusing optics
to attain much higher sensitivity in the HXR range than that of previous
indirect imagers. This paper presents eleven NuSTAR microflares from two active
regions (AR 12671 on 2017 August 21, and AR 12712 on 2018 May 29). The
temporal, spatial, and energetic properties of each are discussed in context
with previously published HXR brightenings. They are seen to display several
'large-flare' properties, such as impulsive time profiles and earlier peaktimes
in higher energy HXRs. For two events where active region background could be
removed, microflare emission did not display spatial complexity: differing
NuSTAR energy ranges had equivalent emission centroids. Finally, spectral
fitting showed a high energy excess over a single thermal model in all events.
This excess was consistent with additional higher-temperature plasma volumes in
10/11 microflares, and consistent only with an accelerated particle
distribution in the last. Previous NuSTAR studies focused on one or a few
microflares at a time, making this the first to collectively examine a sizable
number of events. Additionally, this paper introduces an observed variation in
the NuSTAR gain unique to the extremely low-livetime (<1%) regime, and
establishes a correction method to be used in future NuSTAR solar spectral
analysis.
|
With advances in geo-positioning technologies and geo-location services,
there are a rapidly growing massive amount of spatio-temporal data collected in
many applications such as location-aware devices and wireless communication, in
which an object is described by its spatial location and its timestamp.
Consequently, the study of spatio-temporal search which explores both
geo-location information and temporal information of the data has attracted
significant concern from research organizations and commercial communities.
This work study the problem of spatio-temporal \emph{k}-nearest neighbors
search (ST$k$NNS), which is fundamental in the spatial temporal queries. Based
on HBase, a novel index structure is proposed, called \textbf{H}ybrid
\textbf{S}patio-\textbf{T}emporal HBase \textbf{I}ndex (\textbf{HSTI} for
short), which is carefully designed and takes both spatial and temporal
information into consideration to effectively reduce the search space. Based on
HSTI, an efficient algorithm is developed to deal with spatio-temporal
\emph{k}-nearest neighbors search. Comprehensive experiments on real and
synthetic data clearly show that HSTI is three to five times faster than the
state-of-the-art technique.
|
Using the quasinormal modes of a massless scalar perturbation, we investigate
the small/large black hole phase transition in the Lorentz symmetry breaking
massive gravity. We mainly focus on two issues: i) the sign change of slope of
the quasinormal mode frequencies in the complex-$\omega$ diagram; ii) the
behaviors of the imaginary part of the quasinormal mode frequencies along the
isobaric or isothermal processes. For the first issue, our result shows that,
at low fixed temperature or pressure, the phase transition can be probed by the
sign change of slope. While increasing the temperature or pressure to some
certain values near the critical point, there will appear the deflection point,
which indicates that such method may not be appropriate to test the phase
transition. In particular, the behavior of the quasinormal mode frequencies for
the small and large black holes tend to the same at the critical point. For the
second issue, it is shown that the non-monotonic behavior is observed only when
the small/large black hole phase transition occurs. Therefore, this property
can provide us with an additional method to probe the phase transition through
the quasinormal modes.
|
Lottery Ticket Hypothesis (LTH) raises keen attention to identifying sparse
trainable subnetworks, or winning tickets, which can be trained in isolation to
achieve similar or even better performance compared to the full models. Despite
many efforts being made, the most effective method to identify such winning
tickets is still Iterative Magnitude-based Pruning (IMP), which is
computationally expensive and has to be run thoroughly for every different
network. A natural question that comes in is: can we "transform" the winning
ticket found in one network to another with a different architecture, yielding
a winning ticket for the latter at the beginning, without re-doing the
expensive IMP? Answering this question is not only practically relevant for
efficient "once-for-all" winning ticket finding, but also theoretically
appealing for uncovering inherently scalable sparse patterns in networks. We
conduct extensive experiments on CIFAR-10 and ImageNet, and propose a variety
of strategies to tweak the winning tickets found from different networks of the
same model family (e.g., ResNets). Based on these results, we articulate the
Elastic Lottery Ticket Hypothesis (E-LTH): by mindfully replicating (or
dropping) and re-ordering layers for one network, its corresponding winning
ticket could be stretched (or squeezed) into a subnetwork for another deeper
(or shallower) network from the same family, whose performance is nearly the
same competitive as the latter's winning ticket directly found by IMP. We have
also extensively compared E-LTH with pruning-at-initialization and dynamic
sparse training methods, as well as discussed the generalizability of E-LTH to
different model families, layer types, and across datasets. Code is available
at https://github.com/VITA-Group/ElasticLTH.
|
Context: The cross-covariance of solar oscillations observed at pairs of
points on the solar surface is a fundamental ingredient in time-distance
helioseismology. Wave travel times are extracted from the cross-covariance
function and are used to infer the physical conditions in the solar interior.
Aims: Understanding the statistics of the two-point cross-covariance function
is a necessary step towards optimizing the measurement of travel times.
Methods: By modeling stochastic solar oscillations, we evaluate the variance of
the cross-covariance function as function of time-lag and distance between the
two points. Results: We show that the variance of the cross-covariance is
independent of both time-lag and distance in the far field, i.e., when they are
large compared to the coherence scales of the solar oscillations. Conclusions:
The constant noise level for the cross-covariance means that the
signal-to-noise ratio for the cross-covariance is proportional to the amplitude
of the expectation value of the cross-covariance. This observation is important
for planning data analysis efforts.
|
Stellar loci are widely used for selection of interesting outliers, reddening
determinations, and calibrations. However, hitherto the dependence of stellar
loci on metallicity has not been fully explored and their intrinsic widths are
unclear. In this paper, by combining the spectroscopic and re-calibrated
imaging data of the SDSS Stripe 82, we have built a large, clean sample of
dwarf stars with accurate colors and well determined metallicities to
investigate the metallicity dependence and intrinsic widths of the SDSS stellar
loci. Typically, one dex decrease in metallicity causes 0.20 and 0.02 mag
decrease in colors u-g and g-r, and 0.02 and 0.02 mag increase in colors r-i
and i-z, respectively. The variations are larger for metal-rich stars than for
metal-poor ones, and for F/G/K stars than for A/M ones. Using the sample, we
have performed two dimensional polynomial fitting to the u-g, g-r, r-i, and i-z
colors as a function of color g-i and metallicity [Fe/H]. The residuals, at the
level of 0.029, 0.008, 0.008 and 0.011 mag for the u-g, g-r, r-i, and i-z
colors, respectively can be fully accounted for by the photometric errors and
metallicity uncertainties, suggesting that the intrinsic widths of the loci are
at maximum a few mmag. The residual distributions are asymmetric, revealing
that a significant fraction of stars are binaries. In a companion paper, we
will present an unbiased estimate of the binary fraction for field stars. Other
potential applications of the metallicity dependent stellar loci are briefly
discussed.
|
The issue of whether the quantum critical point (QCP) is hidden inside
unconventional superconductors is a matter of hot debate. Although a prominent
experiment on London penetration depth has demonstrated the existence of the
QCP in the isovalent-doped iron-based superconductor
BaFe$_2$(As$_{1-x}$P$_x$)$_2$, with the observation of a sharp peak in the
penetration depth in the vicinity of the disappearance of magnetic order at
zero temperature, the nature of such an emerging QCP remains unclear. Here, we
provide a unique picture to understand well the phenomena of the QCP based on
the framework of linear response theory. Evidence from the density of states
and superfluid density calculations suggests the nodeless-to-nodal pairing
transition accompanied the appearance of a sharp peak in the penetration depth
in BaFe$_2$(As$_{1-x}$P$_x$)$_2$. Such a pairing transition originates from the
three-dimensional electronic properties with a strong interlayer
superconducting pairing. This finding provides a significant insight into the
understanding of the QCP observed in experiment in
BaFe$_2$(As$_{1-x}$P$_x$)$_2$.
|
We present a catalog of 1750 massive stars in the Large Magellanic Cloud,
with accurate spectral types compiled from the literature, and a photometric
catalog for a subset of 1268 of these stars, with the goal of exploring their
infrared properties. The photometric catalog consists of stars with infrared
counterparts in the Spitzer SAGE survey database, for which we present uniform
photometry from 0.3-24 microns in the UBVIJHKs+IRAC+MIPS24 bands. The resulting
infrared color-magnitude diagrams illustrate that the supergiant B[e], red
supergiant and luminous blue variable (LBV) stars are among the brightest
infrared point sources in the Large Magellanic Cloud, due to their intrinsic
brightness, and at longer wavelengths, due to dust. We detect infrared excesses
due to free-free emission among ~900 OB stars, which correlate with luminosity
class. We confirm the presence of dust around 10 supergiant B[e] stars, finding
the shape of their spectral energy distributions (SEDs) to be very similar, in
contrast to the variety of SED shapes among the spectrally variable LBVs. The
similar luminosities of B[e] supergiants (log L/Lo>=4) and the rare, dusty
progenitors of the new class of optical transients (e.g. SN 2008S and NGC 300
OT), plus the fact that dust is present in both types of objects, suggests a
common origin for them. We find the infrared colors for Wolf-Rayet stars to be
independent of spectral type and their SEDs to be flatter than what models
predict. The results of this study provide the first comprehensive roadmap for
interpreting luminous, massive, resolved stellar populations in nearby galaxies
at infrared wavelengths.
|
Using data obtained in a laboratory thermal convection experiment at high
Rayleigh numbers, it is shown that the multiscaling properties of the observed
mean wind reversals are quantitatively consistent with analogous multiscaling
properties of the Bak-Tang-Wiesenfeld prototype model of self-organized
criticality in two dimensions.
|
Endowing a dialogue system with particular personality traits is essential to
deliver more human-like conversations. However, due to the challenge of
embodying personality via language expression and the lack of large-scale
persona-labeled dialogue data, this research problem is still far from
well-studied. In this paper, we investigate the problem of incorporating
explicit personality traits in dialogue generation to deliver personalized
dialogues.
To this end, firstly, we construct PersonalDialog, a large-scale multi-turn
dialogue dataset containing various traits from a large number of speakers. The
dataset consists of 20.83M sessions and 56.25M utterances from 8.47M speakers.
Each utterance is associated with a speaker who is marked with traits like Age,
Gender, Location, Interest Tags, etc. Several anonymization schemes are
designed to protect the privacy of each speaker. This large-scale dataset will
facilitate not only the study of personalized dialogue generation, but also
other researches on sociolinguistics or social science.
Secondly, to study how personality traits can be captured and addressed in
dialogue generation, we propose persona-aware dialogue generation models within
the sequence to sequence learning framework. Explicit personality traits
(structured by key-value pairs) are embedded using a trait fusion module.
During the decoding process, two techniques, namely persona-aware attention and
persona-aware bias, are devised to capture and address trait-related
information. Experiments demonstrate that our model is able to address proper
traits in different contexts. Case studies also show interesting results for
this challenging research problem.
|
In this paper we study differential operators of the form \begin{align*}
\left[\mathcal{L}_\infty v \right](x) = A\triangle v(x) + \left\langle
Sx,\nabla v(x) \right\rangle - Bv(x), \,x \in \mathbb{R}^d, \,d \geqslant 2,
\end{align*} for matrices $A,B\in\mathbb{C}^{N,N}$, where the eigenvalues of
$A$ have positive real parts. The sum $A\triangle v(x) + \left\langle Sx,
\nabla v(x) \right\rangle$ is known as the Ornstein-Uhlenbeck operator with an
unbounded drift term defined by a skew-symmetric matrix $S\in\mathbb{R}^{d,d}$.
Differential operators such as $\mathcal{L}_{\infty}$ arise as linearizations
at rotating waves in time-dependent reaction diffusion systems. The results of
this paper serve as foundation for proving exponential decay of such waves.
Under the assumption that $A$ and $B$ can be diagonalized simultaneously we
construct a heat kernel matrix $H(x,\xi,t)$ of $\mathcal{L}_{\infty}$ that
solves the evolution equation $v_t=\mathcal{L}_{\infty}v$. In the following we
study the Ornstein-Uhlenbeck semigroup \begin{align*} \left[ T(t)v\right](x) =
\int_{\mathbb{R}^d} H(x,\xi,t) v(\xi) d\xi,\,x \in \mathbb{R}^d,\, t>0,
\end{align*} in exponentially weighted function spaces. This is used to derive
resolvent estimates for $\mathcal{L}_{\infty}$ in exponentially weighted
$L^p$-spaces $L^p_{\theta} (\mathbb{R}^d,\mathbb{C}^N)$, $1\leqslant p<\infty$,
as well as in exponentially weighted $C_{\mathrm{b}}$-spaces
$C_{\mathrm{b},\theta}(\mathbb{R}^d,\mathbb{C}^N)$.
|
There is a theorem known as a Virial theorem that restricts the possible
existence of non-trivial static solitary waves with scalar fields in a flat
space-time with 3 or more spatial dimensions. This raises the following
question: Does the analogous curved space-time version hold?. We investigate
the possibility of solitons in a 4-D curved space-time with a simple model
using numerical analysis. We found that there exists a static solution of the
proposed non linear wave equation. This proves that in curved space-time the
possibilities of solitonic solutions is enhanced relative to the flat
space-time case.
|
A new low-order discretization scheme for the identity operator in the
magnetic field integral equation (MFIE) is discussed. Its concept is derived
from the weak-form representation of combined sources which are discretized
with Rao-Wilton-Glisson (RWG) functions. The resulting MFIE overcomes the
accuracy problem of the classical MFIE while it maintains fast iterative solver
convergence. The improvement in accuracy is verified with a mesh refinement
analysis and with near- and far-field scattering results. Furthermore,
simulation results for a combined field integral equation (CFIE) involving the
new MFIE show that this CFIE is interior-resonance free and well-conditioned
like the classical CFIE, but also accurate as the EFIE.
|
We construct and analyze first- and second-order implicit-explicit (IMEX)
schemes based on the scalar auxiliary variable (SAV) approach for the
magneto-hydrodynamic equations. These schemes are linear, only require solving
a sequence of linear differential equations with constant coefficients at each
time step, and are unconditionally energy stable. We derive rigorous error
estimates for the velocity, pressure and magnetic field of the first-order
scheme in the two dimensional case without any condition on the time step.
Numerical examples are presented to validate the proposed schemes.
|
We introduce a constrained energy functional to describe dielectric response.
We demonstrate that the local functional is a generalization of the long ranged
Marcus energy. Our re-formulation is used to implement a cluster Monte Carlo
algorithm for the simulation of dielectric media. The algorithm avoids solving
the Poisson equation and remains efficient in the presence of spatial
heterogeneity, nonlinearity and scale dependent dielectric properties.
|
Message passing algorithms are popular in many combinatorial optimization
problems. For example, experimental results show that {\em survey propagation}
(a certain message passing algorithm) is effective in finding proper
$k$-colorings of random graphs in the near-threshold regime. In 1962 Gallager
introduced the concept of Low Density Parity Check (LDPC) codes, and suggested
a simple decoding algorithm based on message passing. In 1994 Alon and Kahale
exhibited a coloring algorithm and proved its usefulness for finding a
$k$-coloring of graphs drawn from a certain planted-solution distribution over
$k$-colorable graphs. In this work we show an interpretation of Alon and
Kahale's coloring algorithm in light of Gallager's decoding algorithm, thus
showing a connection between the two problems - coloring and decoding. This
also provides a rigorous evidence for the usefulness of the message passing
paradigm for the graph coloring problem. Our techniques can be applied to
several other combinatorial optimization problems and networking-related
issues.
|
We consider the possibility that ultra-high energy cosmic rays originate from
the annihilation of relic superheavy dark-matter particles. We find that a
cross section of <sigma_A v> ~ 10^{-26}cm^2 (M_X/10^{12}GeV)^{3/2} is required
to account for the observed rate of super-GZK events if the superheavy dark
matter follows a Navarro-Frenk-White density profile. This would require
extremely large-l contributions to the annihilation cross section. We also
calculate the possible signature from annihilation in sub-galactic clumps of
dark matter and find that the signal from sub-clumps dominates and may explain
the observed flux with a much smaller cross section than if the superheavy dark
matter is smoothly distributed. Finally, we discuss the expected anisotropy in
the arrival directions of the cosmic rays, which is a characteristic signature
of this scenario.
|
In this article, we compute the mod 2 representarion of the symmetric group
of order 2 over the singular cohomology groups of orderd 2-configuration space
$C_{2}(T^{d})$ of the $d$-torus $T^{d}$ for $d\geq 1$. As applications of the
computation, we determine the Stiefel-Whitney height of $C_{2}(T^{d})$ for any
$d$, and determine $\mathbb{F}_{2}[{\Sigma}_{2}]$-module structure of the
cohomology groups of the unordered 2-configuration space of the $d$-torus for
$d=2,3$ using the Serre spectral sequence.
|
Visual Place Recognition (VPR) is a crucial component of 6-DoF localization,
visual SLAM and structure-from-motion pipelines, tasked to generate an initial
list of place match hypotheses by matching global place descriptors. However,
commonly-used CNN-based methods either process multiple image resolutions after
training or use a single resolution and limit multi-scale feature extraction to
the last convolutional layer during training. In this paper, we augment NetVLAD
representation learning with low-resolution image pyramid encoding which leads
to richer place representations. The resultant multi-resolution feature pyramid
can be conveniently aggregated through VLAD into a single compact
representation, avoiding the need for concatenation or summation of multiple
patches in recent multi-scale approaches. Furthermore, we show that the
underlying learnt feature tensor can be combined with existing multi-scale
approaches to improve their baseline performance. Evaluation on 15
viewpoint-varying and viewpoint-consistent benchmarking datasets confirm that
the proposed MultiRes-NetVLAD leads to state-of-the-art Recall@N performance
for global descriptor based retrieval, compared against 11 existing techniques.
Source code is publicly available at
https://github.com/Ahmedest61/MultiRes-NetVLAD.
|
We present a theory of ultrafast photo-induced dynamics in a spin-charge
coupled system, motivated by pump-probe experiments in perovskite manganites. A
microscopic picture for multiple dynamics in spin and charge degrees is focused
on. Real-time simulations are carried out by two complimentary methods. Our
calculation demonstrates that electron motion governs a short-time scale where
charge and spin dynamics are combined strongly, while, in a long-time scale
controlled by spin relaxation, charge sector does not follow remarkable change
in spin sector. Present results are in contrast to a conventional
double-exchange picture in equilibrium states.
|
In this paper we study the question of determining when an irreducible
admissible representation of ${\rm GL}_n(D)$ admits a symplectic model, that is
when such a representation has a linear functional invariant under ${\rm
Sp}_n(D)$, where $D$ is a quaternion division algebra over a non-Archimedian
local field $k$ and ${\rm Sp}_{n}(D)$ is the unique non-split inner form of the
symplectic group ${\rm Sp}_{2n}(k)$. We show that if a representation has a
symplectic model it is necessarily unique. For ${\rm GL}_2(D)$ we completely
classify those representations which have a symplectic model. Globally, we show
that if a discrete automorphic representation of ${\rm GL}_{n}(D_\mathbb{A})$
has a non-zero period for ${\rm Sp}_{n}(D_\mathbb{A})$, then its
Jacquet-Langlands lift also has a non-zero symplectic period. A somewhat
striking difference between distinction question for ${\rm GL}_{2n}(k)$, and
${\rm GL}_n(D)$(with respect to ${\rm Sp}_{2n}(k)$ and ${\rm Sp}_n(D)$ resp.)
is that there are supercuspidal representations of ${\rm GL}_n(D)$ which are
distinguished by ${\rm Sp}_n(D)$. The paper ends by formulating a general
question classifying all unitary distinguished representations of ${\rm
GL}_n(D)$, and proving a part of the local conjectures through a global
conjecture.
|
We present the complete one-loop effective action up to dimension eight after
integrating out degenerate scalars using the Heat-Kernel method. The result is
provided without assuming any specific form of either UV or low energy
theories, i.e., universal. In this paper, we consider the effects of only heavy
scalar propagators in the loops. We also verify part of the results using the
covariant diagram technique.
|
Given a sextuple of distinct points $A, B, C, D, E, F$ on a conic, arranged
into an array $\left[\begin{array}{ccc} A & B & C F & E & D
\end{array}\right]$, Pascal's theorem says that the points $AE \cap BF, BD \cap
CE, AD \cap CF$ are collinear. The line containing them is called the Pascal of
the array, and one gets altogether sixty such lines by permuting the points. In
this paper we prove that the initial sextuple can be explicitly reconstructed
from four specifically chosen Pascals. The reconstruction formulae are encoded
by some transvectant identities which are proved using the graphical calculus
for binary forms.
|
Single-photon wave packets can carry quantum information between nodes of a
quantum network. An important general operation in photon-based quantum
information systems is blind reversal of a photon's temporal wave-packet
envelope, that is, the ability to reverse an envelope without knowing the
temporal state of the photon. We present an all-optical means for doing so,
using nonlinear-optical frequency conversion driven by a short pump pulse. This
scheme allows for quantum operations such as a temporal-mode parity sorter. We
also verify that the scheme works for arbitrary states (not only single-photon
ones) of an unknown wave packet.
|
The practical implementation of free-space quantum information tasks requires
entanglement to be sustained over long distances and in the presence of
turbulent and noisy environments. The transverse position-momentum entanglement
of photon pairs produced by parametric down-conversion has found several uses
in quantum information science, however, it is not suitable for applications
involving long-distance propagation as the entanglement decays very rapidly
when photons propagate away from their source. Entanglement is lost after a few
centimetres of propagation, and the effect becomes even more pronounced in
turbulent environments. In contrast, in this article, we show that entanglement
in the angle-orbital angular momentum (OAM) bases exhibits a remarkably
different behaviour. As with the position-momentum case, initially, the
angle-OAM entanglement decays with propagation, but as the photons continue to
travel further from the source, the photons regain their strongly correlated
behaviour, and the entanglement returns. We theoretically and experimentally
demonstrate this behaviour and show that entanglement returns even in the
presence of strong turbulence. The only effect of turbulence is to increase the
propagation distance for revival, but once revived, the two photons remain
entangled up to an arbitrary propagation distance. This work highlights the
role that OAM-angle entanglement will play in applications where quantum
information is shared over long distances.
|
We prove that there is no 1-complemented subspace of finite codimension in
separable rearrangament-invariant function spaces.
|
Through solving pretext tasks, self-supervised learning leverages unlabeled
data to extract useful latent representations replacing traditional input
features in the downstream task. In audio/speech signal processing, a wide
range of features where engineered through decades of research efforts. As it
turns out, learning to predict such features (a.k.a pseudo-labels) has proven
to be a particularly relevant pretext task, leading to useful self-supervised
representations which prove to be effective for downstream tasks. However,
methods and common practices for combining such pretext tasks for better
performance on the downstream task have not been explored and understood
properly. In fact, the process relies almost exclusively on a computationally
heavy experimental procedure, which becomes intractable with the increase of
the number of pretext tasks. This paper introduces a method to select a group
of pretext tasks among a set of candidates. The method we propose estimates
calibrated weights for the partial losses corresponding to the considered
pretext tasks during the self-supervised training process. The experiments
conducted on automatic speech recognition, speaker and emotion recognition
validate our approach, as the groups selected and weighted with our method
perform better than classic baselines, thus facilitating the selection and
combination of relevant pseudo-labels for self-supervised representation
learning.
|
We present an approach for analyzing initial-boundary value problems which is
formulated on the finite interval ($0\le x\le L$, where $L$ is a positive
constant) for integrable equations whose Lax pairs involve $3\times 3$
matrices. Boundary value problems for integrable nonlinear evolution PDEs can
be analyzed by the unified method introduced by Fokas and developed by him and
his collaborators. In this paper, we show that the solution can be expressed in
terms of the solution of a $3\times 3$ Riemann-Hilbert problem. The relevant
jump matrices are explicitly given in terms of the three matrix-value spectral
functions $s(k)$,$S(k)$ and $S_L(k)$, which in turn are defined in terms of the
initial values, boundary values at $x=0$ and boundary values at $x=L$,
respectively. However, these spectral functions are not independent, they
satisfy a global relation. Here, we show that the characterization of the
unknown boundary values in terms of the given initial and boundary data is
explicitly described for a nonlinear evolution PDE defined on the interval.
Also, we show that in the limit when the length of the interval tends to
infity, the relevant formulas reduce to the analogous formulas obtained for the
case of boundary value problems formulated on the half-line.
|
In this communication, we present an efficient method for computation of
energy and wave function of weakly bound nuclei by the application of
supersymmetric quantum mechanics (SSQM) and bound states in continuum (BIC)
technique. As a case study the scheme is implemented to the two-body ($^{30}$Ne
+ n) cluster model calculation of neutron-rich nucleus $^{31}$Ne. Woods-Saxon
central potential with spin-orbit component is used as the core-nucleon
interaction. The two-body Schr\"{o}dinger equation in relative coordinate is
solved numerically to get the energy and wave function of the low-lying bound
states. A one-parameter family of isospectral potential (IP) is constructed
from the bound state solutions following algebra of SSQM to find energies and
wave functions of the resonance states. In addition to the 2p$_{3/2^-}$ (-0.33
MeV) ground state, two bound excited states: s$_{1/2}$ (-0.30 MeV), $p_{1/2}$
(-0.15 MeV) are also obtained. Few low-lying resonance states: f$_{7/2_1}$
(2.57 MeV), f$_{7/2_2}$ (4.59 MeV), f$_{5/2_1}$ (5.58 MeV), p$_{1/2_1}$(1.432
MeV), p$_{1/2_2}$ (4.165 MeV), p$_{3/2_1}$ (1.431 MeV), p$_{3/2_2}$ (4.205 MeV)
are predicted. Among the predicted resonance states, the f$_{7/2^{-}}$ state
having resonance energy $E_R \simeq 4.59$ MeV is in excellent agreement with
the one found in the literature.
|
Self-supervised learning representations (SSLR) have resulted in robust
features for downstream tasks in many fields. Recently, several SSLRs have
shown promising results on automatic speech recognition (ASR) benchmark
corpora. However, previous studies have only shown performance for solitary
SSLRs as an input feature for ASR models. In this study, we propose to
investigate the effectiveness of diverse SSLR combinations using various fusion
methods within end-to-end (E2E) ASR models. In addition, we will show there are
correlations between these extracted SSLRs. As such, we further propose a
feature refinement loss for decorrelation to efficiently combine the set of
input features. For evaluation, we show that the proposed 'FeaRLESS learning
features' perform better than systems without the proposed feature refinement
loss for both the WSJ and Fearless Steps Challenge (FSC) corpora.
|
The ultra-violet (UV) high-resolution spectropolarimeter Pollux is being
studied in Europe under CNES leadership for the LUVOIR space mission. LUVOIR is
a projected 15-m telescope equipped with a suite of instruments proposed to
NASA. Pollux will perform spectropolarimetric measurements from 90 to 400 nm
with a resolution of 120000. The spectrograph will be divided in three
channels, each with its own polarimeter: far UV (FUV, 90-124.5 nm), mid UV
(MUV, 118.5-195 nm), and near UV (NUV, 190-390 nm). We present here our FUV
prototype and our investigation to optimize this polarimeter (angle, materials,
coating...).
|
The amount of data generated in the modern society is increasing rapidly. New
problems and novel approaches of data capture, storage, analysis and
visualization are responsible for the emergence of the Big Data research field.
Machine Learning algorithms can be used in Big Data to make better and more
accurate inferences. However, because of the challenges Big Data imposes, these
algorithms need to be adapted and optimized to specific applications. One
important decision made by software engineers is the choice of the language
that is used in the implementation of these algorithms. Therefore, this
literature survey identifies and describes domain-specific languages and
frameworks used for Machine Learning in Big Data. By doing this, software
engineers can then make more informed choices and beginners have an overview of
the main languages used in this domain.
|
We consider an expanding boost-invariant plasma at strong coupling using the
AdS/CFT correspondence for N=4 SYM. We determine the relaxation time in second
order viscous hydrodynamics and find that it is around thirty times shorter
than weak coupling expectations. We find that the nonsingularity of the dual
geometry in the string frame necessitates turning on the dilaton which leads to
a nonvanishing expectation value for tr F^2 behaving like tau^(-10/3).
|
Inconsistency in prediction problems occurs when instances that relate in a
certain way on condition attributes, do not follow the same relation on the
decision attribute. For example, in ordinal classification with monotonicity
constraints, it occurs when an instance dominating another instance on
condition attributes has been assigned to a worse decision class. It typically
appears as a result of perturbation in data caused by incomplete knowledge
(missing attributes) or by random effects that occur during data generation
(instability in the assessment of decision attribute values). Inconsistencies
with respect to a crisp preorder relation (expressing either dominance or
indiscernibility between instances) can be handled using symbolic approaches
like rough set theory and by using statistical/machine learning approaches that
involve optimization methods. Fuzzy rough sets can also be seen as a symbolic
approach to inconsistency handling with respect to a fuzzy relation. In this
article, we introduce a new machine learning method for inconsistency handling
with respect to a fuzzy preorder relation. The novel approach is motivated by
the existing machine learning approach used for crisp relations. We provide
statistical foundations for it and develop optimization procedures that can be
used to eliminate inconsistencies. The article also proves important properties
and contains didactic examples of those procedures.
|
We propose a mechanism to use inelastic tunneling spectrosopy STM to detect a
single spin in a d-wave superconductor and in a pseudogap state, based on a
direct exchange coupling J between the surface electrons and the local spin S
in a magnetic field. This coupling will produce a kink in a dI/dV
characteristic at Zeeman energy of the spin \omega_0. We find that for relevant
values of parameters signal scales as dI^2/dV^2 \simeq (JN_0)^2 \Theta(eV -
\omega_0) and could be in the range of 10^{-2} of the bare density of states
where N_0 is the density of states for surface electrons. Scattering in
superconductor with the coherence peak at gap maximum \Delta leads also to
strong features at \Delta + \omega_0. This suggests a new technique for a
detection of a local spin excitation with STM. We also consider a detection of
a local vibrational mode as a simple extension of the spin case.
|
AI algorithms at the edge demand smaller model sizes and lower computational
complexity. To achieve these objectives, we adopt a green learning (GL)
paradigm rather than the deep learning paradigm. GL has three modules: 1)
unsupervised representation learning, 2) supervised feature learning, and 3)
supervised decision learning. We focus on the second module in this work. In
particular, we derive new discriminant features from proper linear combinations
of input features, denoted by x, obtained in the first module. They are called
complementary and raw features, respectively. Along this line, we present a
novel supervised learning method to generate highly discriminant complementary
features based on the least-squares normal transform (LNT). LNT consists of two
steps. First, we convert a C-class classification problem to a binary
classification problem. The two classes are assigned with 0 and 1,
respectively. Next, we formulate a least-squares regression problem from the
N-dimensional (N-D) feature space to the 1-D output space, and solve the
least-squares normal equation to obtain one N-D normal vector, denoted by a1.
Since one normal vector is yielded by one binary split, we can obtain M normal
vectors with M splits. Then, Ax is called an LNT of x, where transform matrix A
in R^{M by N} by stacking aj^T, j=1, ..., M, and the LNT, Ax, can generate M
new features. The newly generated complementary features are shown to be more
discriminant than the raw features. Experiments show that the classification
performance can be improved by these new features.
|
Finite difference methods are traditionally used for modelling the time
domain in numerical weather prediction (NWP). Time-spectral solution is an
attractive alternative for reasons of accuracy and efficiency and because time
step limitations associated with causal, CFL-like critera are avoided. In this
work, the Lorenz 1984 chaotic equations are solved using the time-spectral
algorithm GWRM. Comparisons of accuracy and efficiency are carried out for both
explicit and implicit time-stepping algorithms. It is found that the efficiency
of the GWRM compares well with these methods, in particular at high accuracy.
For perturbative scenarios, the GWRM was found to be as much as four times
faster than the finite difference methods. A primary reason is that the GWRM
time intervals typically are two orders of magnitude larger than those of the
finite difference methods. The GWRM has the additional advantage to produce
analytical solutions in the form of Chebyshev series expansions. The results
are encouraging for pursuing further studies, including spatial dependence, of
the relevance of time-spectral methods for NWP modelling.
|
Quantum coherent superpositions of states with different energies, i.e.,
states with coherence with respect to energy basis, are important resource for
modern quantum technologies. States with small coherence can be obtained either
autonomously, due to the effect of a weak coherent drive or, potentially, due
to the presence of an environment. In this paper, we propose a
measurement-based protocol for quantum coherence synthesis from individual
systems (with low initial coherence) into a global (and higher) coherence of
the joint system. As an input, it uses $N$ non-interacting copies of two-level
systems (TLS), with low initial energy and coherence. These can be supplied by,
e.g., a weak external drive or can result from an interaction with a bath. This
protocol conditionally synthesizes an output state with higher energy and
coherence than the initial state had, representing an universal process whose
rules have not been well studied, yet. In addition to energy and coherence, we
study the quantity called mutual coherence, showing increase after the protocol
application, as well. This approach is based on application of sequential
pairwise projective measurements on TLS pairs (conditionally removing their
ground states), that are diagonal in the TLS energy basis. The functionality of
the coherence synthesis is robust with respect to dephasing effects of the TLS
environment on the system. Our approach may show its benefits in quantum
sensing, quantum batteries charging, or other applications where synthesis of a
larger coherent system from smaller (weaker) resources is useful.
|
While astrochemical models are successful in reproducing many of the observed
interstellar species, they have been struggling to explain the observed
abundances of complex organic molecules. Current models tend to privilege grain
surface over gas phase chemistry in their formation. One key assumption of
those models is that radicals trapped in the grain mantles gain mobility and
react on lukewarm (>30 K) dust grains. Thus, the recent detections of methyl
formate (MF) and dimethyl ether (DME) in cold objects represent a challenge and
may clarify the respective role of grain surface and gas phase chemistry. We
propose here a new model to form DME and MF with gas phase reactions in cold
environments, where DME is the precursor of MF via an efficient reaction
overlooked by previous models. Furthermore, methoxy, a precursor of DME, is
also synthetized in the gas phase from methanol, which is desorbed by a
non-thermal process from the ices. Our new model reproduces fairy well the
observations towards L1544. It also explains, in a natural way, the observed
correlation between DME and MF. We conclude that gas phase reactions are major
actors in the formation of MF, DME and methoxy in cold gas. This challenges the
exclusive role of grain-surface chemistry and favours a combined grain-gas
chemistry.
|
In the universal extra dimensions models, Kaluza Klein excitations of matter
are generaly produced in pairs. However, if matter lives on a fat brane
embedded in a larger space, gravity-matter interactions do not obey KK number
conservation, thus making possible the production of single KK excitations at
colliders. We evaluate the production rates for such excitations at the
Tevatron and LHC colliders, and look for ways to detect them.
|
One of the most interesting application scenarios in anomaly detection is
when sequential data are targeted. For example, in a safety-critical
environment, it is crucial to have an automatic detection system to screen the
streaming data gathered by monitoring sensors and to report abnormal
observations if detected in real-time. Oftentimes, stakes are much higher when
these potential anomalies are intentional or goal-oriented. We propose an
end-to-end framework for sequential anomaly detection using inverse
reinforcement learning (IRL), whose objective is to determine the
decision-making agent's underlying function which triggers his/her behavior.
The proposed method takes the sequence of actions of a target agent (and
possibly other meta information) as input. The agent's normal behavior is then
understood by the reward function which is inferred via IRL. We use a neural
network to represent a reward function. Using a learned reward function, we
evaluate whether a new observation from the target agent follows a normal
pattern. In order to construct a reliable anomaly detection method and take
into consideration the confidence of the predicted anomaly score, we adopt a
Bayesian approach for IRL. The empirical study on publicly available real-world
data shows that our proposed method is effective in identifying anomalies.
|
The interpolant existence problem (IEP) for a logic L is to decide, given
formulas P and Q, whether there exists a formula I, built from the shared
symbols of P and Q, such that P entails I and I entails Q in L. If L enjoys the
Craig interpolation property (CIP), then the IEP reduces to validity in L.
Recently, the IEP has been studied for logics without the CIP. The results
obtained so far indicate that even though the IEP can be computationally harder
than validity, it is decidable when L is decidable. Here, we give the first
examples of decidable fragments of first-order logic for which the IEP is
undecidable. Namely, we show that the IEP is undecidable for the two-variable
fragment with two equivalence relations and for the two-variable guarded
fragment with individual constants and two equivalence relations. We also
determine the corresponding decidable Boolean description logics for which the
IEP is undecidable.
|
We study the Darboux and Laplace transformations for the
Boiti-Leon-Pempinelli equations (BLP). These equations are the (1+2)
generalization of the sinh-Gordon equation. In addition, the BLP equations
reduced to the Burgers (and anti-Burgers) equation in a one-dimensional limit.
Localized nonsingular solutions in both spatial dimensions and (anti) "blow-up"
solutions are constructed. The Burgers equation's "dressing" procedure is
suggested. This procedure allows us to construct such solutions of the BLP
equations which are reduced to the solutions of the dissipative Burgers
equations when $t\to \infty$. These solutions we call the BLP dissipative
structures.
|
Inspired by Naor et al.'s visual secret sharing (VSS) scheme, a novel n out
of n quantum visual secret sharing (QVSS) scheme is proposed, which consists of
two phases: sharing process and recovering process. In the first process, the
color information of each pixel from the original secret image is encoded into
an n-qubit superposition state by using the strategy of quantum expansion
instead of classical pixel expansion, and then these n qubits are distributed
as shares to n participants, respectively. During the recovering process, all
participants cooperate to collect these n shares of each pixel together, then
perform the corresponding measurement on them, and execute the n-qubit XOR
operation to recover each pixel of the secret image. The proposed scheme has
the advantage of single-pixel parallel processing that is not available in the
existing analogous quantum schemes and perfectly solves the problem that in the
classic VSS schemes the recovered image has the loss in resolution. Moreover,
its experiment implementation with the IBM Q is conducted to demonstrate the
practical feasibility.
|
Accretion disks in white dwarf systems are believed to be tilted. In a recent
publication, the lift force has been suggested to be a source to disk tilt, a
source that is likely relevant to all accretion disk systems. Lift is generated
by slightly different supersonic gas stream speeds flowing over and under the
disk at the bright spot. In this conference proceeding, we focus on whether a
brown dwarf donor star accreting onto a white dwarf primary has enough mass to
contribute to disk tilt. We also would like to obtain whether a white dwarf -
brown dwarf close binary system has enough mass to induce and maintain a disk
tilt of four degrees. We adopt SDSS 103533.03+055158.4 as our model system
which has a mass transfer rate of ((10\pm2) \times 10^{-12}) M$_{\odot}$
yr$^{-1}$. We find that the brown dwarf in SDSS 1035 does not have enough mass
to contribute to disk tilt. We find a gross magnitude of the minimum mass
transfer rate to be $\sim10^{-10}$M$_{\odot}$yr$^{-1}$. We conclude that SDSS
1035 does not seem to have a high enough mass transfer rate to induce and
maintain an observable disk tilt. Hence one reason why brown dwarf donor
systems may be so difficult to find could be due to their low mass transfer
rates which do not induce observable dynamical effects that is typical in white
dwarf-red dwarf CVs.
|
We consider the low energy effective chiral theory of QCD mesons and the
electroweak Goldstone bosons. In this effective theory the pion sector
contributes to the gauge boson masses and the Yukawa couplings of the fermions.
Consequently the Yukawa sector of quarks and leptons can have a $SU(2)_L\times
U(1)_Y\times U(1)_A$ global symmetry even with nonvanishing fermion masses. The
extra chiral $U(1)_A$ symmetry can be used to rotate the CP violating $\bar
\theta G\tilde G $ term away which therefore makes no contribution to low
energy CP violating effects like the neutron electric dipole momment. The
Goldstone mode associated with this $U(1)_A$ symmetry may be identified with
the $SU(2)$ singlet meson $\eta_0$.
|
This review describes the physics of spins in quantum dots containing one or
two electrons, from an experimentalist's viewpoint. Various methods for
extracting spin properties from experiment are presented, restricted
exclusively to electrical measurements. Furthermore, experimental techniques
are discussed that allow for: (1) the rotation of an electron spin into a
superposition of up and down, (2) the measurement of the quantum state of an
individual spin and (3) the control of the interaction between two neighbouring
spins by the Heisenberg exchange interaction. Finally, the physics of the
relevant relaxation and dephasing mechanisms is reviewed and experimental
results are compared with theories for spin-orbit and hyperfine interactions.
All these subjects are directly relevant for the fields of quantum information
processing and spintronics with single spins (i.e. single-spintronics).
|
We determined the crystal-field split Hund's rule ground state of the
non-centrosymmetric heavy fermion superconductor CePt3Si with polarization
dependent soft X-ray absorption spectroscopy (XAS) and polarized neutron
scattering. We are also able to give the sequence of the crystal-field states
from the temperature evolution of the linear dichroic signal in the XAS. The
quantitative analysis of the XAS temperature dependence together with the
neutron transition energies complete the identification of the crystal-field
level scheme.
|
We present novel previously unexplored periodic solutions, expressed in terms
of Jacobi elliptic functions, for both a coupled $\phi^4$ model and a coupled
nonlinear Schr\"odinger equation (NLS) model. Remarkably, these solutions can
be elegantly reformulated as a linear combination of periodic kinks and
antikinks, or as a combination of two periodic kinks or two periodic pulse
solutions. However, we also find that for $m=0$ and a specific value of the
periodicity (or at a nonzero value of the elliptic modulus $m$) this
superposition does not hold. These results demonstrate that the notion of
superposed solutions extends to the coupled nonlinear equations as well.
|
A simplified polycrystalline model (the so-called RL model) is proposed to
simulate the anisotropic viscoplastic behavior of metallic materials. A generic
method is presented that makes it possible to build a simplified anisotropic
material texture, based on the principal features of the pole figures. The
method is applied to a recrystallized zirconium alloy, used as clad material in
the fuel rods of nuclear power plants. An important database consisting in
mechanical tests performed on Zircaloy tubes is collected. Only a small number
of tests (pure tension, pure shear) are used to identify the material
parameters, and the texture parameters. It is shown that six crystallographic
orientations (6 "grains") are sufficient to describe the large anisotropy of
such hcp alloy. The identified crystallographic orientations match the
experimental pole figures of the material, not used in the identification
procedure. Special attention is paid to the predictive ability of the model,
i.e., its ability to simulate correctly experimental tests not belonging to the
identification database. These predictive results are good, thanks to an
identification procedure that enables to consider the contribution of each slip
system in each crystallographic orientation.
|
The semi-simple unification model based on SU(5)_GUT \times U(3)_H gauge
group is an interesting extension of the minimal SU(5)_GUT grand unification
theory (GUT), since it solves the two serious problems in the standard GUT: the
triplet-doublet splitting problem and the presence of dangerous dimension five
operators for proton decay. Here, the extra U(3)_H gauge interaction plays a
crucial role on the GUT breaking. In this paper, we show that the full
multiplet structure of the U(3)_H sector required for the desired GUT breaking
is reproduced naturally on T^6/Z_12 orientifold in the type IIB supergravity
with a D3-D7 system. The SU(5)_GUT vector multiplet lives on D7-branes and the
U(3)_H sector resides on D3-branes. We also show that various interesting
features in the original SU(5)_GUT \times U(3)_H model are explained in the
present brane-world scenario. A possible extension to the type IIB string
theory is also discussed.
|
For a finite set $\cal F$ of polynomials over fixed finite prime field of
size $p$ containing all polynomials $x^2 - x$ a Nullstellensatz proof of the
unsolvability of the system $$
f = 0\ ,\ \mbox{ all } f \in {\cal F} $$ in the field is a linear combination
$\sum_{f \in {\cal F}} \ h_f \cdot f$ that equals to $1$ in the ring of
polynomails. The measure of complexity of such a proof is its degree: $\max_f
deg(h_f f)$.
We study the problem to establish degree lower bounds for some {\em extended}
NS proof systems: these systems prove the unsolvability of $\cal F$ by proving
the unsolvability of a bigger set ${\cal F}\cup {\cal E}$, where set $\cal E$
may use new variables $r$ and contains all polynomials $r^p - r$, and satisfies
the following soundness condition: -- - Any $0,1$-assignment $\overline a$ to
variables $\overline x$ can be appended by an assignment $\overline b$ to
variables $\overline r$ such that for all $g \in {\cal E}$ it holds that
$g(\overline a, \overline b) = 0$.
We define a notion of pseudo-solutions of $\cal F$ and prove that the
existence of pseudo-solutions with suitable parameters implies lower bounds for
two extended NS proof systems ENS and UENS defined in Buss et al. (1996/97).
Further we give a combinatorial example of $\cal F$ and candidate
pseudo-solutions based on the pigeonhole principle.
|
Inspired by a Blaschke's work about analytic convex surfaces, we study {\em
shadow boundaries} of Riemannian submanifolds $M$, which are defined by a
parallel vector field along $M$. Since a shadow boundary is just a closed
subset of $M$, first, we will give a condition that guarantee its smoothness.
It depends on the second fundamental form of the submanifold. It is natural to
search for what kind of properties might have such submanifolds of $M$? Could
they be totally geodesic or minimal? Answers to these and related questions are
given in this work.
|
The anisotropies in the galaxy two-point correlation function measured from
redshift surveys exhibits deviations from the predictions of the linear theory
of redshift space distortion on scales as large 20 Mpc/h where we expect linear
theory to hold in real space. Any attempt at analyzing the anisotropies in the
redshift correlation function and determining the linear distortion parameter
\beta requires these deviations to be correctly modeled and taken into account.
These deviations are usually attributed to galaxy random motions and these are
incorporated in the analysis through a phenomenological model where the linear
redshift correlation is convolved with the random pairwise velocity
distribution function along the line of sight. We show that a substantial part
of the deviations arise from non-linear effects in the mapping from real to
redshift space caused by the coherent flows. Models which incorporate this
effect provide a better fit to N-body results as compared to the
phenomenological model which has only the effect of random motions. We find
that the pairwise velocity dispersion predicted by all the models that we have
considered are in excess of the values determined directly from the N-body
simulations. This indicates a shortcoming in our understanding of the
statistical properties of peculiar velocities and their relation to redshift
distortion.
|
Frustrated quantum magnets not only provide exotic ground states and unusual
magnetic structures, but also support unconventional excitations in many cases.
Using a physically relevant spin model for a breathing pyrochlore lattice, we
discuss the presence of topological linear band crossings of magnons in
antiferromagnets. These are the analogs of Weyl fermions in electronic systems,
which we dub Weyl magnons. The bulk Weyl magnon implies the presence of chiral
magnon surface states forming arcs at finite energy. We argue that such
antiferromagnets present a unique example in which Weyl points can be
manipulated in situ in the laboratory by applied fields. We discuss their
appearance specifically in the breathing pyrochlore lattice, and give some
general discussion of conditions to find Weyl magnons and how they may be
probed experimentally. Our work may inspire a re-examination of the magnetic
excitations in many magnetically ordered systems.
|
Subsets and Splits