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LPCNet: Improving Neural Speech Synthesis Through Linear Prediction | Neural speech synthesis models have recently demonstrated the ability to
synthesize high quality speech for text-to-speech and compression applications.
These new models often require powerful GPUs to achieve real-time operation, so
being able to reduce their complexity would open the way for many new
applications. We propose LPCNet, a WaveRNN variant that combines linear
prediction with recurrent neural networks to significantly improve the
efficiency of speech synthesis. We demonstrate that LPCNet can achieve
significantly higher quality than WaveRNN for the same network size and that
high quality LPCNet speech synthesis is achievable with a complexity under 3
GFLOPS. This makes it easier to deploy neural synthesis applications on
lower-power devices, such as embedded systems and mobile phones.
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Coherent anti-Stokes Raman Scattering Lidar Using Slow Light: A Theoretical Study | We theoretically investigate a scheme in which backward coherent anti-Stokes
Raman scattering (CARS) is significantly enhanced by using slow light.
Specifically, we reduce the group velocity of the Stokes excitation pulse by
introducing a coupling laser that causes electromagnetically induced
transparency (EIT). When the Stokes pulse has a spatial length shorter than the
CARS wavelength, the backward CARS emission is significantly enhanced. We also
investigated the possibility of applying this scheme as a CARS lidar with O2 or
N2 as the EIT medium. We found that if nanosecond laser with large pulse energy
(>1 J) and a telescope with large aperture (~10 m) are equipped in the lidar
system, a CARS lidar could become much more sensitive than a spontaneous Raman
lidar.
| 0 | 1 | 0 | 0 | 0 | 0 |
Tests based on characterizations, and their efficiencies: a survey | A survey of goodness-of-fit and symmetry tests based on the characterization
properties of distributions is presented. This approach became popular in
recent years. In most cases the test statistics are functionals of
$U$-empirical processes. The limiting distributions and large deviations of new
statistics under the null hypothesis are described. Their local Bahadur
efficiency for various parametric alternatives is calculated and compared with
each other as well as with diverse previously known tests. We also describe new
directions of possible research in this domain.
| 0 | 0 | 1 | 1 | 0 | 0 |
Hyperprior on symmetric Dirichlet distribution | In this article we introduce how to put vague hyperprior on Dirichlet
distribution, and we update the parameter of it by adaptive rejection sampling
(ARS). Finally we analyze this hyperprior in an over-fitted mixture model by
some synthetic experiments.
| 1 | 0 | 0 | 0 | 0 | 0 |
On the interpretability and computational reliability of frequency-domain Granger causality | This is a comment to the paper 'A study of problems encountered in Granger
causality analysis from a neuroscience perspective'. We agree that
interpretation issues of Granger Causality in Neuroscience exist (partially due
to the historical unfortunate use of the name 'causality', as nicely described
in previous literature). On the other hand we think that the paper uses a
formulation of Granger causality which is outdated (albeit still used), and in
doing so it dismisses the measure based on a suboptimal use of it. Furthermore,
since data from simulated systems are used, the pitfalls that are found with
the used formulation are intended to be general, and not limited to
neuroscience. It would be a pity if this paper, even written in good faith,
became a wildcard against all possible applications of Granger Causality,
regardless of the hard work of colleagues aiming to seriously address the
methodological and interpretation pitfalls. In order to provide a balanced
view, we replicated their simulations used the updated State Space
implementation, proposed already some years ago, in which the pitfalls are
mitigated or directly solved.
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Artificial topological models based on a one-dimensional spin-dependent optical lattice | Topological matter is a popular topic in both condensed matter and cold atom
research. In the past decades, a variety of models have been identified with
fascinating topological features. Some, but not all, of the models can be found
in materials. As a fully controllable system, cold atoms trapped in optical
lattices provide an ideal platform to simulate and realize these topological
models. Here we present a proposal for synthesizing topological models in cold
atoms based on a one-dimensional (1D) spin-dependent optical lattice potential.
In our system, features such as staggered tunneling, staggered Zeeman field,
nearest-neighbor interaction, beyond-near-neighbor tunneling, etc. can be
readily realized. They underlie the emergence of various topological phases.
Our proposal can be realized with current technology and hence has potential
applications in quantum simulation of topological matter.
| 0 | 1 | 0 | 0 | 0 | 0 |
Ramsey expansions of metrically homogeneous graphs | We discuss the Ramsey property, the existence of a stationary independence
relation and the coherent extension property for partial isometries (coherent
EPPA) for all classes of metrically homogeneous graphs from Cherlin's
catalogue, which is conjectured to include all such structures. We show that,
with the exception of tree-like graphs, all metric spaces in the catalogue have
precompact Ramsey expansions (or lifts) with the expansion property. With two
exceptions we can also characterise the existence of a stationary independence
relation and the coherent EPPA.
Our results can be seen as a new contribution to Nešetřil's
classification programme of Ramsey classes and as empirical evidence of the
recent convergence in techniques employed to establish the Ramsey property, the
expansion (or lift or ordering) property, EPPA and the existence of a
stationary independence relation. At the heart of our proof is a canonical way
of completing edge-labelled graphs to metric spaces in Cherlin's classes. The
existence of such a "completion algorithm" then allows us to apply several
strong results in the areas that imply EPPA and respectively the Ramsey
property.
The main results have numerous corollaries on the automorphism groups of the
Fraïssé limits of the classes, such as amenability, unique ergodicity,
existence of universal minimal flows, ample generics, small index property,
21-Bergman property and Serre's property (FA).
| 1 | 0 | 1 | 0 | 0 | 0 |
Rapidly star-forming galaxies adjacent to quasars at redshifts exceeding 6 | The existence of massive ($10^{11}$ solar masses) elliptical galaxies by
redshift z~4 (when the Universe was 1.5 billion years old) necessitates the
presence of galaxies with star-formation rates exceeding 100 solar masses per
year at z>6 (corresponding to an age of the Universe of less than 1 billion
years). Surveys have discovered hundreds of galaxies at these early cosmic
epochs, but their star-formation rates are more than an order of magnitude
lower. The only known galaxies with very high star-formation rates at z>6 are,
with only one exception, the host galaxies of quasars, but these galaxies also
host accreting supermassive (more than $10^9$ solar masses) black holes, which
probably affect the properties of the galaxies. Here we report observations of
an emission line of singly ionized carbon ([CII] at a wavelength of 158
micrometres) in four galaxies at z>6 that are companions of quasars, with
velocity offsets of less than 600 kilometers per second and linear offsets of
less than 600 kiloparsecs. The discovery of these four galaxies was
serendipitous; they are close to their companion quasars and appear bright in
the far-infrared. On the basis of the [CII] measurements, we estimate
star-formation rates in the companions of more than 100 solar masses per year.
These sources are similar to the host galaxies of the quasars in [CII]
brightness, linewidth and implied dynamical masses, but do not show evidence
for accreting supermassive black holes. Similar systems have previously been
found at lower redshift. We find such close companions in four out of
twenty-five z>6 quasars surveyed, a fraction that needs to be accounted for in
simulations. If they are representative of the bright end of the [CII]
luminosity function, then they can account for the population of massive
elliptical galaxies at z~4 in terms of cosmic space density.
| 0 | 1 | 0 | 0 | 0 | 0 |
Regular irreducible characters of a hyperspecial compact group | A parametrization of irreducible unitary representations associated with the
regular adjoint orbits of a hyperspecial compact subgroup of a reductive group
over a non-dyadic non-archimedean local filed is presented. The parametrization
is given by means of (a subset of) the character group of certain finite
abelian groups arising from the reductive group. Our method is based upon
Cliffod's theory and Weil representations over finite fields. It works under an
assumption of the triviality of certain Schur multipliers defined for an
algebraic group over a finite field. The assumption of the triviality has good
evidences in the case of general linear groups and highly probable in general.
| 0 | 0 | 1 | 0 | 0 | 0 |
Active Exploration Using Gaussian Random Fields and Gaussian Process Implicit Surfaces | In this work we study the problem of exploring surfaces and building compact
3D representations of the environment surrounding a robot through active
perception. We propose an online probabilistic framework that merges visual and
tactile measurements using Gaussian Random Field and Gaussian Process Implicit
Surfaces. The system investigates incomplete point clouds in order to find a
small set of regions of interest which are then physically explored with a
robotic arm equipped with tactile sensors. We show experimental results
obtained using a PrimeSense camera, a Kinova Jaco2 robotic arm and Optoforce
sensors on different scenarios. We then demonstrate how to use the online
framework for object detection and terrain classification.
| 1 | 0 | 0 | 0 | 0 | 0 |
Doing good vs. avoiding bad in prosocial choice: A refined test and extension of the morality preference hypothesis | Prosociality is fundamental to human social life, and, accordingly, much
research has attempted to explain human prosocial behavior. Capraro and Rand
(Judgment and Decision Making, 13, 99-111, 2018) recently provided experimental
evidence that prosociality in anonymous, one-shot interactions (such as
Prisoner's Dilemma and Dictator Game experiments) is not driven by
outcome-based social preferences - as classically assumed - but by a
generalized morality preference for "doing the right thing". Here we argue that
the key experiments reported in Capraro and Rand (2018) comprise prominent
methodological confounds and open questions that bear on influential
psychological theory. Specifically, their design confounds: (i) preferences for
efficiency with self-interest; and (ii) preferences for action with preferences
for morality. Furthermore, their design fails to dissociate the preference to
do "good" from the preference to avoid doing "bad". We thus designed and
conducted a preregistered, refined and extended test of the morality preference
hypothesis (N=801). Consistent with this hypothesis, our findings indicate that
prosociality in the anonymous, one-shot Dictator Game is driven by preferences
for doing the morally right thing. Inconsistent with influential psychological
theory, however, our results suggest the preference to do "good" was as potent
as the preference to avoid doing "bad" in this case.
| 0 | 0 | 0 | 0 | 1 | 0 |
Measuring Territorial Control in Civil Wars Using Hidden Markov Models: A Data Informatics-Based Approach | Territorial control is a key aspect shaping the dynamics of civil war.
Despite its importance, we lack data on territorial control that are
fine-grained enough to account for subnational spatio-temporal variation and
that cover a large set of conflicts. To resolve this issue, we propose a
theoretical model of the relationship between territorial control and tactical
choice in civil war and outline how Hidden Markov Models (HMMs) are suitable to
capture theoretical intuitions and estimate levels of territorial control. We
discuss challenges of using HMMs in this application and mitigation strategies
for future work.
| 1 | 0 | 0 | 1 | 0 | 0 |
Virtual quandle for links in lens spaces | We construct a virtual quandle for links in lens spaces $L(p,q)$, with $q=1$.
This invariant has two valuable advantages over an ordinary fundamental quandle
for links in lens spaces: the virtual quandle is an essential invariant and the
presentation of the virtual quandle can be easily written from the band diagram
of a link.
| 0 | 0 | 1 | 0 | 0 | 0 |
Adaptation to Easy Data in Prediction with Limited Advice | We derive an online learning algorithm with improved regret guarantees for
`easy' loss sequences. We consider two types of `easiness': (a) stochastic loss
sequences and (b) adversarial loss sequences with small effective range of the
losses. While a number of algorithms have been proposed for exploiting small
effective range in the full information setting, Gerchinovitz and Lattimore
[2016] have shown the impossibility of regret scaling with the effective range
of the losses in the bandit setting. We show that just one additional
observation per round is sufficient to circumvent the impossibility result. The
proposed Second Order Difference Adjustments (SODA) algorithm requires no prior
knowledge of the effective range of the losses, $\varepsilon$, and achieves an
$O(\varepsilon \sqrt{KT \ln K}) + \tilde{O}(\varepsilon K \sqrt[4]{T})$
expected regret guarantee, where $T$ is the time horizon and $K$ is the number
of actions. The scaling with the effective loss range is achieved under
significantly weaker assumptions than those made by Cesa-Bianchi and Shamir
[2018] in an earlier attempt to circumvent the impossibility result. We also
provide a regret lower bound of $\Omega(\varepsilon\sqrt{T K})$, which almost
matches the upper bound. In addition, we show that in the stochastic setting
SODA achieves an $O\left(\sum_{a:\Delta_a>0}
\frac{K\varepsilon^2}{\Delta_a}\right)$ pseudo-regret bound that holds
simultaneously with the adversarial regret guarantee. In other words, SODA is
safe against an unrestricted oblivious adversary and provides improved regret
guarantees for at least two different types of `easiness' simultaneously.
| 0 | 0 | 0 | 1 | 0 | 0 |
Why Bohr was (Mostly) Right | After a discussion of the Frauchiger-Renner argument that no 'single- world'
interpretation of quantum mechanics can be self-consistent, I propose a
'Bohrian' alternative to many-worlds or QBism as the rational option.
| 0 | 1 | 0 | 0 | 0 | 0 |
Generalizing Distance Covariance to Measure and Test Multivariate Mutual Dependence | We propose three measures of mutual dependence between multiple random
vectors. All the measures are zero if and only if the random vectors are
mutually independent. The first measure generalizes distance covariance from
pairwise dependence to mutual dependence, while the other two measures are sums
of squared distance covariance. All the measures share similar properties and
asymptotic distributions to distance covariance, and capture non-linear and
non-monotone mutual dependence between the random vectors. Inspired by complete
and incomplete V-statistics, we define the empirical measures and simplified
empirical measures as a trade-off between the complexity and power when testing
mutual independence. Implementation of the tests is demonstrated by both
simulation results and real data examples.
| 0 | 0 | 1 | 1 | 0 | 0 |
Simultaneous Inference for High Dimensional Mean Vectors | Let $X_1, \ldots, X_n\in\mathbb{R}^p$ be i.i.d. random vectors. We aim to
perform simultaneous inference for the mean vector $\mathbb{E} (X_i)$ with
finite polynomial moments and an ultra high dimension. Our approach is based on
the truncated sample mean vector. A Gaussian approximation result is derived
for the latter under the very mild finite polynomial ($(2+\theta)$-th) moment
condition and the dimension $p$ can be allowed to grow exponentially with the
sample size $n$. Based on this result, we propose an innovative resampling
method to construct simultaneous confidence intervals for mean vectors.
| 0 | 0 | 1 | 1 | 0 | 0 |
Joint Routing, Scheduling and Power Control Providing Hard Deadline in Wireless Multihop Networks | We consider optimal/efficient power allocation policies in a single/multihop
wireless network in the presence of hard end-to-end deadline delay constraints
on the transmitted packets. Such constraints can be useful for real time voice
and video. Power is consumed in only transmission of the data. We consider the
case when the power used in transmission is a convex function of the data
transmitted. We develop a computationally efficient online algorithm, which
minimizes the average power for the single hop. We model this problem as
dynamic program (DP) and obtain the optimal solution. Next, we generalize it to
the multiuser, multihop scenario when there are multiple real time streams with
different hard deadline constraints.
| 1 | 0 | 0 | 0 | 0 | 0 |
Activation of Microwave Fields in a Spin-Torque Nano-Oscillator by Neuronal Action Potentials | Action potentials are the basic unit of information in the nervous system and
their reliable detection and decoding holds the key to understanding how the
brain generates complex thought and behavior. Transducing these signals into
microwave field oscillations can enable wireless sensors that report on brain
activity through magnetic induction. In the present work we demonstrate that
action potentials from crayfish lateral giant neuron can trigger microwave
oscillations in spin-torque nano-oscillators. These nanoscale devices take as
input small currents and convert them to microwave current oscillations that
can wirelessly broadcast neuronal activity, opening up the possibility for
compact neuro-sensors. We show that action potentials activate microwave
oscillations in spin-torque nano-oscillators with an amplitude that follows the
action potential signal, demonstrating that the device has both the sensitivity
and temporal resolution to respond to action potentials from a single neuron.
The activation of magnetic oscillations by action potentials, together with the
small footprint and the high frequency tunability, makes these devices
promising candidates for high resolution sensing of bioelectric signals from
neural tissues. These device attributes may be useful for design of
high-throughput bi-directional brain-machine interfaces.
| 0 | 1 | 0 | 0 | 0 | 0 |
Responses in Large-Scale Structure | We introduce a rigorous definition of general power-spectrum responses as
resummed vertices with two hard and $n$ soft momenta in cosmological
perturbation theory. These responses measure the impact of long-wavelength
perturbations on the local small-scale power spectrum. The kinematic structure
of the responses (i.e., their angular dependence) can be decomposed
unambiguously through a "bias" expansion of the local power spectrum, with a
fixed number of physical response coefficients, which are only a function of
the hard wavenumber $k$. Further, the responses up to $n$-th order completely
describe the $(n+2)$-point function in the squeezed limit, i.e. with two hard
and $n$ soft modes, which one can use to derive the response coefficients. This
generalizes previous results, which relate the angle-averaged squeezed limit to
isotropic response coefficients. We derive the complete expression of first-
and second-order responses at leading order in perturbation theory, and present
extrapolations to nonlinear scales based on simulation measurements of the
isotropic response coefficients. As an application, we use these results to
predict the non-Gaussian part of the angle-averaged matter power spectrum
covariance ${\rm Cov}^{\rm NG}_{\ell = 0}(k_1,k_2)$, in the limit where one of
the modes, say $k_2$, is much smaller than the other. Without any free
parameters, our model results are in very good agreement with simulations for
$k_2 \lesssim 0.06\ h/{\rm Mpc}$, and for any $k_1 \gtrsim 2 k_2$. The
well-defined kinematic structure of the power spectrum response also permits a
quick evaluation of the angular dependence of the covariance matrix. While we
focus on the matter density field, the formalism presented here can be
generalized to generic tracers such as galaxies.
| 0 | 1 | 0 | 0 | 0 | 0 |
Graph isomorphisms in quasi-polynomial time | Let us be given two graphs $\Gamma_1$, $\Gamma_2$ of $n$ vertices. Are they
isomorphic? If they are, the set of isomorphisms from $\Gamma_1$ to $\Gamma_2$
can be identified with a coset $H\cdot\pi$ inside the symmetric group on $n$
elements. How do we find $\pi$ and a set of generators of $H$?
The challenge of giving an always efficient algorithm answering these
questions remained open for a long time. Babai has recently shown how to solve
these problems -- and others linked to them -- in quasi-polynomial time, i.e.
in time $\exp\left(O(\log n)^{O(1)}\right)$. His strategy is based in part on
the algorithm by Luks (1980/82), who solved the case of graphs of bounded
degree.
| 0 | 0 | 1 | 0 | 0 | 0 |
Hardware-Aware Machine Learning: Modeling and Optimization | Recent breakthroughs in Deep Learning (DL) applications have made DL models a
key component in almost every modern computing system. The increased popularity
of DL applications deployed on a wide-spectrum of platforms have resulted in a
plethora of design challenges related to the constraints introduced by the
hardware itself. What is the latency or energy cost for an inference made by a
Deep Neural Network (DNN)? Is it possible to predict this latency or energy
consumption before a model is trained? If yes, how can machine learners take
advantage of these models to design the hardware-optimal DNN for deployment?
From lengthening battery life of mobile devices to reducing the runtime
requirements of DL models executing in the cloud, the answers to these
questions have drawn significant attention.
One cannot optimize what isn't properly modeled. Therefore, it is important
to understand the hardware efficiency of DL models during serving for making an
inference, before even training the model. This key observation has motivated
the use of predictive models to capture the hardware performance or energy
efficiency of DL applications. Furthermore, DL practitioners are challenged
with the task of designing the DNN model, i.e., of tuning the hyper-parameters
of the DNN architecture, while optimizing for both accuracy of the DL model and
its hardware efficiency. Therefore, state-of-the-art methodologies have
proposed hardware-aware hyper-parameter optimization techniques. In this paper,
we provide a comprehensive assessment of state-of-the-art work and selected
results on the hardware-aware modeling and optimization for DL applications. We
also highlight several open questions that are poised to give rise to novel
hardware-aware designs in the next few years, as DL applications continue to
significantly impact associated hardware systems and platforms.
| 0 | 0 | 0 | 1 | 0 | 0 |
On the unit distance problem | The Erd\H os unit distance conjecture in the plane says that the number of
pairs of points from a point set of size $n$ separated by a fixed (Euclidean)
distance is $\leq C_{\epsilon} n^{1+\epsilon}$ for any $\epsilon>0$. The best
known bound is $Cn^{\frac{4}{3}}$. We show that if the set under consideration
is well-distributed and the fixed distance is much smaller than the diameter of
the set, then the exponent $\frac{4}{3}$ is significantly improved.
Corresponding results are also established in higher dimensions. The results
are obtained by solving the corresponding continuous problem and using a
continuous-to-discrete conversion mechanism. The degree of sharpness of results
is tested using the known results on the distribution of lattice points dilates
of convex domains.
We also introduce the following variant of the Erd\H os unit distance
problem: how many pairs of points from a set of size $n$ are separated by an
integer distance? We obtain some results in this direction and formulate a
conjecture.
| 0 | 0 | 1 | 0 | 0 | 0 |
Ordered states in the Kitaev-Heisenberg model: From 1D chains to 2D honeycomb | We study the ground state of the 1D Kitaev-Heisenberg (KH) model using the
density-matrix renormalization group and Lanczos exact diagonalization methods.
We obtain a rich ground-state phase diagram as a function of the ratio between
Heisenberg ($J=\cos\phi)$ and Kitaev ($K=\sin\phi$) interactions. Depending on
the ratio, the system exhibits four long-range ordered states:
ferromagnetic-$z$ , ferromagnetic-$xy$, staggered-$xy$, Néel-$z$, and two
liquid states: Tomonaga-Luttinger liquid and spiral-$xy$. The two Kitaev points
$\phi=\frac{\pi}{2}$ and $\phi=\frac{3\pi}{2}$ are singular. The
$\phi$-dependent phase diagram is similar to that for the 2D honeycomb-lattice
KH model. Remarkably, all the ordered states of the honeycomb-lattice KH model
can be interpreted in terms of the coupled KH chains. We also discuss the
magnetic structure of the K-intercalated RuCl$_3$, a potential Kitaev material,
in the framework of the 1D KH model. Furthermore, we demonstrate that the
low-lying excitations of the 1D KH Hamiltonian can be explained within the
combination of the known six-vertex model and spin-wave theory.
| 0 | 1 | 0 | 0 | 0 | 0 |
Quadratic forms and Sobolev spaces of fractional order | We study quadratic functionals on $L^2(\mathbb{R}^d)$ that generate seminorms
in the fractional Sobolev space $H^s(\mathbb{R}^d)$ for $0 < s < 1$. The
functionals under consideration appear in the study of Markov jump processes
and, independently, in recent research on the Boltzmann equation. The
functional measures differentiability of a function $f$ in a similar way as the
seminorm of $H^s(\mathbb{R}^d)$. The major difference is that differences $f(y)
- f(x)$ are taken into account only if $y$ lies in some double cone with apex
at $x$ or vice versa. The configuration of double cones is allowed to be
inhomogeneous without any assumption on the spatial regularity. We prove that
the resulting seminorm is comparable to the standard one of
$H^s(\mathbb{R}^d)$. The proof follows from a similar result on discrete
quadratic forms in $\mathbb{Z}^d$, which is our second main result. We
establish a general scheme for discrete approximations of nonlocal quadratic
forms. Applications to Markov jump processes are discussed.
| 0 | 0 | 1 | 0 | 0 | 0 |
General Latent Feature Modeling for Data Exploration Tasks | This paper introduces a general Bayesian non- parametric latent feature model
suitable to per- form automatic exploratory analysis of heterogeneous datasets,
where the attributes describing each object can be either discrete, continuous
or mixed variables. The proposed model presents several important properties.
First, it accounts for heterogeneous data while can be inferred in linear time
with respect to the number of objects and attributes. Second, its Bayesian
nonparametric nature allows us to automatically infer the model complexity from
the data, i.e., the number of features necessary to capture the latent
structure in the data. Third, the latent features in the model are
binary-valued variables, easing the interpretability of the obtained latent
features in data exploration tasks.
| 1 | 0 | 0 | 1 | 0 | 0 |
The ALMA View of the OMC1 Explosion in Orion | Most massive stars form in dense clusters where gravitational interactions
with other stars may be common. The two nearest forming massive stars, the BN
object and Source I, located behind the Orion Nebula, were ejected with
velocities of $\sim$29 and $\sim$13 km s$^{-1}$ about 500 years ago by such
interactions. This event generated an explosion in the gas. New ALMA
observations show in unprecedented detail, a roughly spherically symmetric
distribution of over a hundred $^{12}$CO J=2$-$1 streamers with velocities
extending from V$_{LSR}$ =$-$150 to +145 km s$^{-1}$. The streamer radial
velocities increase (or decrease) linearly with projected distance from the
explosion center, forming a `Hubble Flow' confined to within 50 arcseconds of
the explosion center. They point toward the high proper-motion, shock-excited
H$_2$ and [Fe ii ] `fingertips' and lower-velocity CO in the H$_2$ wakes
comprising Orion's `fingers'. In some directions, the H$_2$ `fingers' extend
more than a factor of two farther from the ejection center than the CO
streamers. Such deviations from spherical symmetry may be caused by ejecta
running into dense gas or the dynamics of the N-body interaction that ejected
the stars and produced the explosion. This $\sim$10$^{48}$ erg event may have
been powered by the release of gravitational potential energy associated with
the formation of a compact binary or a protostellar merger. Orion may be the
prototype for a new class of stellar explosion responsible for luminous
infrared transients in nearby galaxies.
| 0 | 1 | 0 | 0 | 0 | 0 |
Neurology-as-a-Service for the Developing World | Electroencephalography (EEG) is an extensively-used and well-studied
technique in the field of medical diagnostics and treatment for brain
disorders, including epilepsy, migraines, and tumors. The analysis and
interpretation of EEGs require physicians to have specialized training, which
is not common even among most doctors in the developed world, let alone the
developing world where physician shortages plague society. This problem can be
addressed by teleEEG that uses remote EEG analysis by experts or by local
computer processing of EEGs. However, both of these options are prohibitively
expensive and the second option requires abundant computing resources and
infrastructure, which is another concern in developing countries where there
are resource constraints on capital and computing infrastructure. In this work,
we present a cloud-based deep neural network approach to provide decision
support for non-specialist physicians in EEG analysis and interpretation. Named
`neurology-as-a-service,' the approach requires almost no manual intervention
in feature engineering and in the selection of an optimal architecture and
hyperparameters of the neural network. In this study, we deploy a pipeline that
includes moving EEG data to the cloud and getting optimal models for various
classification tasks. Our initial prototype has been tested only in developed
world environments to-date, but our intention is to test it in developing world
environments in future work. We demonstrate the performance of our proposed
approach using the BCI2000 EEG MMI dataset, on which our service attains 63.4%
accuracy for the task of classifying real vs. imaginary activity performed by
the subject, which is significantly higher than what is obtained with a shallow
approach such as support vector machines.
| 1 | 0 | 0 | 1 | 0 | 0 |
Estimation of Low-Rank Matrices via Approximate Message Passing | Consider the problem of estimating a low-rank symmetric matrix when its
entries are perturbed by Gaussian noise, a setting that is known as `spiked
model' or `deformed Wigner matrix'. If the empirical distribution of the
entries of the spikes is known, optimal estimators that exploit this knowledge
can substantially outperform spectral approaches. Recent work characterizes the
accuracy of Bayes-optimal estimators in the high-dimensional limit. In this
paper we present a practical algorithm that can achieve Bayes-optimal accuracy
above the spectral threshold. A bold conjecture from statistical physics posits
that no polynomial-time algorithm achieves optimal error below the same
threshold (unless the best estimator is trivial). Our approach uses Approximate
Message Passing (AMP) in conjunction with a spectral initialization. AMP has
proven successful in a variety of statistical problem, and are amenable to
exact asymptotic analysis via state evolution. Unfortunately, state evolution
is uninformative when the algorithm is initialized near an unstable fixed
point, as it often happens in matrix estimation. We develop a new analysis of
AMP that allows for spectral initializations, and builds on a decoupling
between the outlier eigenvectors and the bulk in the spiked random matrix
model. Our main theorem is general and applies beyond matrix estimation.
However, we use it to derive detailed predictions for the problem of estimating
a rank-one matrix in noise. Special cases of these problem are closely related
-via universality arguments- to the network community detection problem for two
asymmetric communities. For general rank-one models, we show that AMP can be
used to construct asymptotically valid confidence intervals. As a further
illustration, we consider the example of a block-constant low-rank matrix with
symmetric blocks, which we refer to as `Gaussian Block Model'.
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Simultaneous diagonalisation of the covariance and complementary covariance matrices in quaternion widely linear signal processing | Recent developments in quaternion-valued widely linear processing have
established that the exploitation of complete second-order statistics requires
consideration of both the standard covariance and the three complementary
covariance matrices. Although such matrices have a tremendous amount of
structure and their decomposition is a powerful tool in a variety of
applications, the non-commutative nature of the quaternion product has been
prohibitive to the development of quaternion uncorrelating transforms. To this
end, we introduce novel techniques for a simultaneous decomposition of the
covariance and complementary covariance matrices in the quaternion domain,
whereby the quaternion version of the Takagi factorisation is explored to
diagonalise symmetric quaternion-valued matrices. This gives new insights into
the quaternion uncorrelating transform (QUT) and forms a basis for the proposed
quaternion approximate uncorrelating transform (QAUT) which simultaneously
diagonalises all four covariance matrices associated with improper quaternion
signals. The effectiveness of the proposed uncorrelating transforms is
validated by simulations on both synthetic and real-world quaternion-valued
signals.
| 1 | 0 | 0 | 0 | 0 | 0 |
Arithmetic Siegel-Weil formula on $X_{0}(N)$ | In this paper, we proved an arithmetic Siegel-Weil formula and the modularity
of some arithmetic theta function on the modular curve $X_0(N)$ when $N$ is
square free. In the process, we also construct some generalized Delta function
for $\Gamma_0(N)$ and proved some explicit Kronecker limit formula for
Eisenstein series on $X_0(N)$.
| 0 | 0 | 1 | 0 | 0 | 0 |
Perturbation, Non-Gaussianity and Reheating in a GB-$α$-Attractor Model | Motivated by $\alpha$-attractor models, in this paper we consider a
Gauss-Bonnet inflation with E-model type of potential. We consider the
Gauss-Bonnet coupling function to be the same as the E-model potential. In the
small $\alpha$ limit we obtain an attractor at $r=0$ as expected, and in the
large $\alpha$ limit we recover the Gauss-Bonnet model with potential and
coupling function of the form $\phi^{2n}$. We study perturbations and
non-Gaussianity in this setup and we find some constraints on the model's
parameters in comparison with PLANCK datasets. We study also the reheating
epoch after inflation in this setup. For this purpose, we seek the number of
e-folds and temperature during reheating epoch. These quantities depend on the
model's parameter and the effective equation of state of the dominating energy
density in the reheating era. We find some observational constraints on these
parameters.
| 0 | 1 | 0 | 0 | 0 | 0 |
Experimental determination of the frequency and field dependence of Specific Loss Power in Magnetic Fluid Hyperthermia | Magnetic nanoparticles are promising systems for biomedical applications and
in particular for Magnetic Fluid Hyperthermia, a promising therapy that
utilizes the heat released by such systems to damage tumor cells. We present an
experimental study of the physical properties that influences the capability of
heat release, i.e. the Specific Loss Power, SLP, of three biocompatible
ferrofluid samples having a magnetic core of maghemite with different core
diameter d= 10.2, 14.6 and 19.7 nm. The SLP was measured as a function of
frequency f and intensity of the applied alternating magnetic field H, and it
turned out to depend on the core diameter, as expected. The results allowed us
to highlight experimentally that the physical mechanism responsible for the
heating is size-dependent and to establish, at applied constant frequency, the
phenomenological functional relationship SLP=cH^x, with 2<x<3 for all samples.
The x-value depends on sample size and field frequency/ intensity, here chosen
in the typical range of operating magnetic hyperthermia devices. For the
smallest sample, the effective relaxation time Teff=19.5 ns obtained from SLP
data is in agreement with the value estimated from magnetization data, thus
confirming the validity of the Linear Response Theory model for this system at
properly chosen field intensity and frequency.
| 0 | 1 | 0 | 0 | 0 | 0 |
Training wide residual networks for deployment using a single bit for each weight | For fast and energy-efficient deployment of trained deep neural networks on
resource-constrained embedded hardware, each learned weight parameter should
ideally be represented and stored using a single bit. Error-rates usually
increase when this requirement is imposed. Here, we report large improvements
in error rates on multiple datasets, for deep convolutional neural networks
deployed with 1-bit-per-weight. Using wide residual networks as our main
baseline, our approach simplifies existing methods that binarize weights by
applying the sign function in training; we apply scaling factors for each layer
with constant unlearned values equal to the layer-specific standard deviations
used for initialization. For CIFAR-10, CIFAR-100 and ImageNet, and models with
1-bit-per-weight requiring less than 10 MB of parameter memory, we achieve
error rates of 3.9%, 18.5% and 26.0% / 8.5% (Top-1 / Top-5) respectively. We
also considered MNIST, SVHN and ImageNet32, achieving 1-bit-per-weight test
results of 0.27%, 1.9%, and 41.3% / 19.1% respectively. For CIFAR, our error
rates halve previously reported values, and are within about 1% of our
error-rates for the same network with full-precision weights. For networks that
overfit, we also show significant improvements in error rate by not learning
batch normalization scale and offset parameters. This applies to both full
precision and 1-bit-per-weight networks. Using a warm-restart learning-rate
schedule, we found that training for 1-bit-per-weight is just as fast as
full-precision networks, with better accuracy than standard schedules, and
achieved about 98%-99% of peak performance in just 62 training epochs for
CIFAR-10/100. For full training code and trained models in MATLAB, Keras and
PyTorch see this https URL .
| 0 | 0 | 0 | 1 | 0 | 0 |
IP Based Traffic Recovery: An Optimal Approach using SDN Application for Data Center Network | With the passage of time and indulgence in Information Technology, network
management has proved its significance and has become one of the most important
and challenging task in today's era of information flow. Communication networks
implement a high level of sophistication in managing and flowing the data
through secure channels, to make it almost impossible for data loss. That is
why there are many proposed solution that are currently implemented in wide
range of network-based applications like social networks and finance
applications. The objective of this research paper is to propose a very
reliable method of data flow: Choose best path for traffic using SDN
application. This is an IP based method in which our SDN application implements
provision of best possible path by filtering the requests on base of their IP
origin. We'll distinguish among source and will provide the data flow with
lowest traffic path, thus resulting in providing us minimum chances of data
loss. A request to access our test application will be generated from host and
request from each host will be distinguished by our SDN application that will
get number of active users for all available servers and will redirect the
request to server with minimum traffic load. It will also destroy sessions of
inactive users, resulting in maintaining a best responsive channel for data
flow.
| 1 | 0 | 0 | 0 | 0 | 0 |
Performance of Optimal Data Shaping Codes | Data shaping is a coding technique that has been proposed to increase the
lifetime of flash memory devices. Several data shaping codes have been
described in recent work, including endurance codes and direct shaping codes
for structured data. In this paper, we study information-theoretic properties
of a general class of data shaping codes and prove a separation theorem stating
that optimal data shaping can be achieved by the concatenation of optimal
lossless compression with optimal endurance coding. We also determine the
expansion factor that minimizes the total wear cost. Finally, we analyze the
performance of direct shaping codes and establish a condition for their
optimality.
| 1 | 0 | 0 | 0 | 0 | 0 |
Finding influential nodes for integration in brain networks using optimal percolation theory | Global integration of information in the brain results from complex
interactions of segregated brain networks. Identifying the most influential
neuronal populations that efficiently bind these networks is a fundamental
problem of systems neuroscience. Here we apply optimal percolation theory and
pharmacogenetic interventions in-vivo to predict and subsequently target nodes
that are essential for global integration of a memory network in rodents. The
theory predicts that integration in the memory network is mediated by a set of
low-degree nodes located in the nucleus accumbens. This result is confirmed
with pharmacogenetic inactivation of the nucleus accumbens, which eliminates
the formation of the memory network, while inactivations of other brain areas
leave the network intact. Thus, optimal percolation theory predicts essential
nodes in brain networks. This could be used to identify targets of
interventions to modulate brain function.
| 0 | 0 | 0 | 0 | 1 | 0 |
Automatic Music Highlight Extraction using Convolutional Recurrent Attention Networks | Music highlights are valuable contents for music services. Most methods
focused on low-level signal features. We propose a method for extracting
highlights using high-level features from convolutional recurrent attention
networks (CRAN). CRAN utilizes convolution and recurrent layers for sequential
learning with an attention mechanism. The attention allows CRAN to capture
significant snippets for distinguishing between genres, thus being used as a
high-level feature. CRAN was evaluated on over 32,000 popular tracks in Korea
for two months. Experimental results show our method outperforms three baseline
methods through quantitative and qualitative evaluations. Also, we analyze the
effects of attention and sequence information on performance.
| 1 | 0 | 0 | 1 | 0 | 0 |
On Oracle-Efficient PAC RL with Rich Observations | We study the computational tractability of PAC reinforcement learning with
rich observations. We present new provably sample-efficient algorithms for
environments with deterministic hidden state dynamics and stochastic rich
observations. These methods operate in an oracle model of computation --
accessing policy and value function classes exclusively through standard
optimization primitives -- and therefore represent computationally efficient
alternatives to prior algorithms that require enumeration. With stochastic
hidden state dynamics, we prove that the only known sample-efficient algorithm,
OLIVE, cannot be implemented in the oracle model. We also present several
examples that illustrate fundamental challenges of tractable PAC reinforcement
learning in such general settings.
| 0 | 0 | 0 | 1 | 0 | 0 |
Noise induced transition in Josephson junction with second harmonic | We show a noise-induced transition in Josephson junction with fundamental as
well as second harmonic. A periodically modulated multiplicative colored noise
can stabilize an unstable configuration in such a system. The stabilization of
the unstable configuration has been captured in the effective potential of the
system obtained by integrating out the high-frequency components of the noise.
This is a classical approach to understand the stability of an unstable
configuration due to the presence of such stochasticity in the system and our
numerical analysis confirms the prediction from the analytical calculation.
| 0 | 1 | 0 | 0 | 0 | 0 |
Distributed Estimation of Principal Eigenspaces | Principal component analysis (PCA) is fundamental to statistical machine
learning. It extracts latent principal factors that contribute to the most
variation of the data. When data are stored across multiple machines, however,
communication cost can prohibit the computation of PCA in a central location
and distributed algorithms for PCA are thus needed. This paper proposes and
studies a distributed PCA algorithm: each node machine computes the top $K$
eigenvectors and transmits them to the central server; the central server then
aggregates the information from all the node machines and conducts a PCA based
on the aggregated information. We investigate the bias and variance for the
resulting distributed estimator of the top $K$ eigenvectors. In particular, we
show that for distributions with symmetric innovation, the empirical top
eigenspaces are unbiased and hence the distributed PCA is "unbiased". We derive
the rate of convergence for distributed PCA estimators, which depends
explicitly on the effective rank of covariance, eigen-gap, and the number of
machines. We show that when the number of machines is not unreasonably large,
the distributed PCA performs as well as the whole sample PCA, even without full
access of whole data. The theoretical results are verified by an extensive
simulation study. We also extend our analysis to the heterogeneous case where
the population covariance matrices are different across local machines but
share similar top eigen-structures.
| 0 | 0 | 1 | 1 | 0 | 0 |
Invariant algebraic surfaces of the FitzHugh-Nagumo system | In this paper, we characterize all the irreducible Darboux polynomials and
polynomial first integrals of FitzHugh-Nagumo (F-N) system. The method of the
weight homogeneous polynomials and the characteristic curves is widely used to
give a complete classification of Darboux polynomials of a system. However,
this method does not work for F-N system. Here by considering the Darboux
polynomials of an assistant system associated to F-N system, we classified the
invariant algebraic surfaces of F-N system. Our results show that there is no
invariant algebraic surface of F-N system in the biological parameters region.
| 0 | 0 | 1 | 0 | 0 | 0 |
Local and global boundary rigidity and the geodesic X-ray transform in the normal gauge | In this paper we analyze the local and global boundary rigidity problem for
general Riemannian manifolds with boundary $(M,g)$ whose boundary is strictly
convex. We show that the boundary distance function, i.e., $d_g|_{\partial
M\times\partial M}$, known over suitable open sets of $\partial M$ determines
$g$ in suitable corresponding open subsets of $M$, up to the natural
diffeomorphism invariance of the problem. We also show that if there is a
function on $M$ with suitable convexity properties relative to $g$ then
$d_g|_{\partial M\times\partial M}$ determines $g$ globally in the sense that
if $d_g|_{\partial M\times\partial M}=d_{\tilde g}|_{\partial M\times \partial
M}$ then there is a diffeomorphism $\psi$ fixing $\partial M$ (pointwise) such
that $g=\psi^*\tilde g$. This global assumption is satisfied, for instance, for
the distance function from a given point if the manifold has no focal points
(from that point).
We also consider the lens rigidity problem. The lens relation measures the
point of exit from $M$ and the direction of exit of geodesics issued from the
boundary and the length of the geodesic. The lens rigidity problem is whether
we can determine the metric up to isometry from the lens relation. We solve the
lens rigidity problem under the same global assumption mentioned above. This
shows, for instance, that manifolds with a strictly convex boundary and
non-positive sectional curvature are lens rigid.
The key tool is the analysis of the geodesic X-ray transform on 2-tensors,
corresponding to a metric $g$, in the normal gauge, such as normal coordinates
relative to a hypersurface, where one also needs to allow microlocal weights.
This is handled by refining and extending our earlier results in the solenoidal
gauge.
| 0 | 0 | 1 | 0 | 0 | 0 |
Adversarial Source Identification Game with Corrupted Training | We study a variant of the source identification game with training data in
which part of the training data is corrupted by an attacker. In the addressed
scenario, the defender aims at deciding whether a test sequence has been drawn
according to a discrete memoryless source $X \sim P_X$, whose statistics are
known to him through the observation of a training sequence generated by $X$.
In order to undermine the correct decision under the alternative hypothesis
that the test sequence has not been drawn from $X$, the attacker can modify a
sequence produced by a source $Y \sim P_Y$ up to a certain distortion, and
corrupt the training sequence either by adding some fake samples or by
replacing some samples with fake ones. We derive the unique rationalizable
equilibrium of the two versions of the game in the asymptotic regime and by
assuming that the defender bases its decision by relying only on the first
order statistics of the test and the training sequences. By mimicking Stein's
lemma, we derive the best achievable performance for the defender when the
first type error probability is required to tend to zero exponentially fast
with an arbitrarily small, yet positive, error exponent. We then use such a
result to analyze the ultimate distinguishability of any two sources as a
function of the allowed distortion and the fraction of corrupted samples
injected into the training sequence.
| 1 | 0 | 0 | 1 | 0 | 0 |
Toric actions and convexity in cosymplectic geometry | We prove a convexity theorem for Hamiltonian torus actions on compact
cosymplectic manifolds. We show that compact toric cosymplectic manifolds are
mapping tori of equivariant symplectomorphisms of toric symplectic manifolds.
| 0 | 0 | 1 | 0 | 0 | 0 |
Localization and Stationary Phase Approximation on Supermanifolds | Given an odd vector field $Q$ on a supermanifold $M$ and a $Q$-invariant
density $\mu$ on $M$, under certain compactness conditions on $Q$, the value of
the integral $\int_{M}\mu$ is determined by the value of $\mu$ on any
neighborhood of the vanishing locus $N$ of $Q$. We present a formula for the
integral in the case where $N$ is a subsupermanifold which is appropriately
non-degenerate with respect to $Q$.
In the process, we discuss the linear algebra necessary to express our result
in a coordinate independent way. We also extend stationary phase approximation
and the Morse-Bott Lemma to supermanifolds.
| 0 | 0 | 1 | 0 | 0 | 0 |
An Analytical Design Optimization Method for Electric Propulsion Systems of Multicopter UAVs with Desired Hovering Endurance | Multicopters are becoming increasingly important in both civil and military
fields. Currently, most multicopter propulsion systems are designed by
experience and trial-and-error experiments, which are costly and ineffective.
This paper proposes a simple and practical method to help designers find the
optimal propulsion system according to the given design requirements. First,
the modeling methods for four basic components of the propulsion system
including propellers, motors, electric speed controls, and batteries are
studied respectively. Secondly, the whole optimization design problem is
simplified and decoupled into several sub-problems. By solving these
sub-problems, the optimal parameters of each component can be obtained
respectively. Finally, based on the obtained optimal component parameters, the
optimal product of each component can be quickly located and determined from
the corresponding database. Experiments and statistical analyses demonstrate
the effectiveness of the proposed method.
| 1 | 0 | 0 | 0 | 0 | 0 |
A Reassessment of Absolute Energies of the X-ray L Lines of Lanthanide Metals | We introduce a new technique for determining x-ray fluorescence line energies
and widths, and we present measurements made with this technique of 22 x-ray L
lines from lanthanide-series elements. The technique uses arrays of
transition-edge sensors, microcalorimeters with high energy-resolving power
that simultaneously observe both calibrated x-ray standards and the x-ray
emission lines under study. The uncertainty in absolute line energies is
generally less than 0.4 eV in the energy range of 4.5 keV to 7.5 keV. Of the
seventeen line energies of neodymium, samarium, and holmium, thirteen are found
to be consistent with the available x-ray reference data measured after 1990;
only two of the four lines for which reference data predate 1980, however, are
consistent with our results. Five lines of terbium are measured with
uncertainties that improve on those of existing data by factors of two or more.
These results eliminate a significant discrepancy between measured and
calculated x-ray line energies for the terbium Ll line (5.551 keV). The line
widths are also measured, with uncertainties of 0.6 eV or less on the
full-width at half-maximum in most cases. These measurements were made with an
array of approximately one hundred superconducting x- ray microcalorimeters,
each sensitive to an energy band from 1 keV to 8 keV. No energy-dispersive
spectrometer has previously been used for absolute-energy estimation at this
level of accuracy. Future spectrometers, with superior linearity and energy
resolution, will allow us to improve on these results and expand the
measurements to more elements and a wider range of line energies.
| 0 | 1 | 0 | 0 | 0 | 0 |
Limitations of Source-Filter Coupling In Phonation | The coupling of vocal fold (source) and vocal tract (filter) is one of the
most critical factors in source-filter articulation theory. The traditional
linear source-filter theory has been challenged by current research which
clearly shows the impact of acoustic loading on the dynamic behavior of the
vocal fold vibration as well as the variations in the glottal flow pulses
shape. This paper outlines the underlying mechanism of source-filter
interactions; demonstrates the design and working principles of coupling for
the various existing vocal cord and vocal tract biomechanical models. For our
study, we have considered self-oscillating lumped-element models of the
acoustic source and computational models of the vocal tract as articulators. To
understand the limitations of source-filter interactions which are associated
with each of those models, we compare them concerning their mechanical design,
acoustic and physiological characteristics and aerodynamic simulation.
| 1 | 0 | 0 | 0 | 0 | 0 |
Correlation between clustering and degree in affiliation networks | We are interested in the probability that two randomly selected neighbors of
a random vertex of degree (at least) $k$ are adjacent. We evaluate this
probability for a power law random intersection graph, where each vertex is
prescribed a collection of attributes and two vertices are adjacent whenever
they share a common attribute. We show that the probability obeys the scaling
$k^{-\delta}$ as $k\to+\infty$. Our results are mathematically rigorous. The
parameter $0\le \delta\le 1$ is determined by the tail indices of power law
random weights defining the links between vertices and attributes.
| 1 | 0 | 0 | 0 | 0 | 0 |
Automatic Disambiguation of French Discourse Connectives | Discourse connectives (e.g. however, because) are terms that can explicitly
convey a discourse relation within a text. While discourse connectives have
been shown to be an effective clue to automatically identify discourse
relations, they are not always used to convey such relations, thus they should
first be disambiguated between discourse-usage non-discourse-usage. In this
paper, we investigate the applicability of features proposed for the
disambiguation of English discourse connectives for French. Our results with
the French Discourse Treebank (FDTB) show that syntactic and lexical features
developed for English texts are as effective for French and allow the
disambiguation of French discourse connectives with an accuracy of 94.2%.
| 1 | 0 | 0 | 0 | 0 | 0 |
Predicting Financial Crime: Augmenting the Predictive Policing Arsenal | Financial crime is a rampant but hidden threat. In spite of this, predictive
policing systems disproportionately target "street crime" rather than white
collar crime. This paper presents the White Collar Crime Early Warning System
(WCCEWS), a white collar crime predictive model that uses random forest
classifiers to identify high risk zones for incidents of financial crime.
| 1 | 0 | 0 | 0 | 0 | 0 |
Polar codes with a stepped boundary | We consider explicit polar constructions of blocklength $n\rightarrow\infty$
for the two extreme cases of code rates $R\rightarrow1$ and $R\rightarrow0.$
For code rates $R\rightarrow1,$ we design codes with complexity order of $n\log
n$ in code construction, encoding, and decoding. These codes achieve the
vanishing output bit error rates on the binary symmetric channels with any
transition error probability $p\rightarrow 0$ and perform this task with a
substantially smaller redundancy $(1-R)n$ than do other known high-rate codes,
such as BCH codes or Reed-Muller (RM). We then extend our design to the
low-rate codes that achieve the vanishing output error rates with the same
complexity order of $n\log n$ and an asymptotically optimal code rate
$R\rightarrow0$ for the case of $p\rightarrow1/2.$
| 1 | 0 | 0 | 0 | 0 | 0 |
Resonant Scattering Characteristics of Homogeneous Dielectric Sphere | In the present article the classical problem of electromagnetic scattering by
a single homogeneous sphere is revisited. Main focus is the study of the
scattering behavior as a function of the material contrast and the size
parameters for all electric and magnetic resonances of a dielectric sphere.
Specifically, the Padé approximants are introduced and utilized as an
alternative system expansion of the Mie coefficients. Low order Padé
approximants can give compact and physically insightful expressions for the
scattering system and the enabled dynamic mechanisms. Higher order approximants
are used for predicting accurately the resonant pole spectrum. These results
are summarized into general pole formulae, covering up to fifth order magnetic
and forth order electric resonances of a small dielectric sphere. Additionally,
the connection between the radiative damping process and the resonant linewidth
is investigated. The results obtained reveal the fundamental connection of the
radiative damping mechanism with the maximum width occurring for each
resonance. Finally, the suggested system ansatz is used for studying the
resonant absorption maximum through a circuit-inspired perspective.
| 0 | 1 | 0 | 0 | 0 | 0 |
An efficient global optimization algorithm for maximizing the sum of two generalized Rayleigh quotients | Maximizing the sum of two generalized Rayleigh quotients (SRQ) can be
reformulated as a one-dimensional optimization problem, where the function
value evaluations are reduced to solving semi-definite programming (SDP)
subproblems. In this paper, we first use the dual SDP subproblem to construct
an explicit overestimation and then propose a branch-and-bound algorithm to
globally solve (SRQ). Numerical results demonstrate that it is even more
efficient than the recent SDP-based heuristic algorithm.
| 0 | 0 | 1 | 0 | 0 | 0 |
Location Dependent Dirichlet Processes | Dirichlet processes (DP) are widely applied in Bayesian nonparametric
modeling. However, in their basic form they do not directly integrate
dependency information among data arising from space and time. In this paper,
we propose location dependent Dirichlet processes (LDDP) which incorporate
nonparametric Gaussian processes in the DP modeling framework to model such
dependencies. We develop the LDDP in the context of mixture modeling, and
develop a mean field variational inference algorithm for this mixture model.
The effectiveness of the proposed modeling framework is shown on an image
segmentation task.
| 1 | 0 | 0 | 1 | 0 | 0 |
Poisson brackets symmetry from the pentagon-wheel cocycle in the graph complex | Kontsevich designed a scheme to generate infinitesimal symmetries
$\dot{\mathcal{P}} = \mathcal{Q}(\mathcal{P})$ of Poisson brackets
$\mathcal{P}$ on all affine manifolds $M^r$; every such deformation is encoded
by oriented graphs on $n+2$ vertices and $2n$ edges. In particular, these
symmetries can be obtained by orienting sums of non-oriented graphs $\gamma$ on
$n$ vertices and $2n-2$ edges. The bi-vector flow $\dot{\mathcal{P}} =
\text{Or}(\gamma)(\mathcal{P})$ preserves the space of Poisson structures if
$\gamma$ is a cocycle with respect to the vertex-expanding differential in the
graph complex.
A class of such cocycles $\boldsymbol{\gamma}_{2\ell+1}$ is known to exist:
marked by $\ell \in \mathbb{N}$, each of them contains a $(2\ell+1)$-gon wheel
with a nonzero coefficient. At $\ell=1$ the tetrahedron $\boldsymbol{\gamma}_3$
itself is a cocycle; at $\ell=2$ the Kontsevich--Willwacher pentagon-wheel
cocycle $\boldsymbol{\gamma}_5$ consists of two graphs. We reconstruct the
symmetry $\mathcal{Q}_5(\mathcal{P}) =
\text{Or}(\boldsymbol{\gamma}_5)(\mathcal{P})$ and verify that $\mathcal{Q}_5$
is a Poisson cocycle indeed:
$[\![\mathcal{P},\mathcal{Q}_5(\mathcal{P})]\!]\doteq 0$ via
$[\![\mathcal{P},\mathcal{P}]\!]=0$.
| 0 | 0 | 1 | 0 | 0 | 0 |
Shadows of characteristic cycles, Verma modules, and positivity of Chern-Schwartz-MacPherson classes of Schubert cells | Chern-Schwartz-MacPherson (CSM) classes generalize to singular and/or
noncompact varieties the classical total homology Chern class of the tangent
bundle of a smooth compact complex manifold. The theory of CSM classes has been
extended to the equivariant setting by Ohmoto. We prove that for an arbitrary
complex projective manifold $X$, the homogenized, torus equivariant CSM class
of a constructible function $\varphi$ is the restriction of the characteristic
cycle of $\varphi$ via the zero section of the cotangent bundle of $X$. This
extends to the equivariant setting results of Ginzburg and Sabbah. We
specialize $X$ to be a (generalized) flag manifold $G/B$. In this case CSM
classes are determined by a Demazure-Lusztig (DL) operator. We prove a `Hecke
orthogonality' of CSM classes, determined by the DL operator and its
Poincar{é} adjoint. We further use the theory of holonomic
$\mathcal{D}_X$-modules to show that the characteristic cycle of a Verma
module, restricted to the zero section, gives the CSM class of the
corresponding Schubert cell. Since the Verma characteristic cycles naturally
identify with the Maulik and Okounkov's stable envelopes, we establish an
equivalence between CSM classes and stable envelopes; this reproves results of
Rim{á}nyi and Varchenko. As an application, we obtain a Segre type formula
for CSM classes. In the non-equivariant case this formula is manifestly
positive, showing that the expansion in the Schubert basis of the CSM class of
a Schubert cell is effective. This proves a previous conjecture by Aluffi and
Mihalcea, and it extends previous positivity results by J. Huh in the Grassmann
manifold case. Finally, we generalize all of this to partial flag manifolds
$G/P$.
| 0 | 0 | 1 | 0 | 0 | 0 |
An Iterative Scheme for Leverage-based Approximate Aggregation | The current data explosion poses great challenges to the approximate
aggregation with an efficiency and accuracy. To address this problem, we
propose a novel approach to calculate the aggregation answers with a high
accuracy using only a small portion of the data. We introduce leverages to
reflect individual differences in the samples from a statistical perspective.
Two kinds of estimators, the leverage-based estimator, and the sketch estimator
(a "rough picture" of the aggregation answer), are in constraint relations and
iteratively improved according to the actual conditions until their difference
is below a threshold. Due to the iteration mechanism and the leverages, our
approach achieves a high accuracy. Moreover, some features, such as not
requiring recording the sampled data and easy to extend to various execution
modes (e.g., the online mode), make our approach well suited to deal with big
data. Experiments show that our approach has an extraordinary performance, and
when compared with the uniform sampling, our approach can achieve high-quality
answers with only 1/3 of the same sample size.
| 1 | 0 | 0 | 0 | 0 | 0 |
A Game of Martingales | We consider a two player dynamic game played over $T \leq \infty$ periods. In
each period each player chooses any probability distribution with support on
$[0,1]$ with a given mean, where the mean is the realized value of the draw
from the previous period. The player with the highest realization in the period
achieves a payoff of $1$, and the other player, $0$; and each player seeks to
maximize the discounted sum of his per-period payoffs over the whole time
horizon. We solve for the unique subgame perfect equilibrium of this game, and
establish properties of the equilibrium strategies and payoffs in the limit.
The solution and comparative statics thereof provide insight about
intertemporal choice with status concerns. In particular we find that patient
players take fewer risks.
| 0 | 0 | 0 | 0 | 0 | 1 |
Effects of tunnelling and asymmetry for system-bath models of electron transfer | We apply the newly derived nonadiabatic golden-rule instanton theory to
asymmetric models describing electron-transfer in solution. The models go
beyond the usual spin-boson description and have anharmonic free-energy
surfaces with different values for the reactant and product reorganization
energies. The instanton method gives an excellent description of the behaviour
of the rate constant with respect to asymmetry for the whole range studied. We
derive a general formula for an asymmetric version of Marcus theory based on
the classical limit of the instanton and find that this gives significant
corrections to the standard Marcus theory. A scheme is given to compute this
rate based only on equilibrium simulations. We also compare the rate constants
obtained by the instanton method with its classical limit to study the effect
of tunnelling and other quantum nuclear effects. These quantum effects can
increase the rate constant by orders of magnitude.
| 0 | 1 | 0 | 0 | 0 | 0 |
Self-Modifying Morphology Experiments with DyRET: Dynamic Robot for Embodied Testing | If robots are to become ubiquitous, they will need to be able to adapt to
complex and dynamic environments. Robots that can adapt their bodies while
deployed might be flexible and robust enough to meet this challenge. Previous
work on dynamic robot morphology has focused on simulation, combining simple
modules, or switching between locomotion modes. Here, we present an alternative
approach: a self-reconfigurable morphology that allows a single four-legged
robot to actively adapt the length of its legs to different environments. We
report the design of our robot, as well as the results of a study that verifies
the performance impact of self-reconfiguration. This study compares three
different control and morphology pairs under different levels of servo supply
voltage in the lab. We also performed preliminary tests in different
uncontrolled outdoor environments to see if changes to the external environment
supports our findings in the lab. Our results show better performance with an
adaptable body, lending evidence to the value of self-reconfiguration for
quadruped robots.
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Dropout is a special case of the stochastic delta rule: faster and more accurate deep learning | Multi-layer neural networks have lead to remarkable performance on many kinds
of benchmark tasks in text, speech and image processing. Nonlinear parameter
estimation in hierarchical models is known to be subject to overfitting. One
approach to this overfitting and related problems (local minima, colinearity,
feature discovery etc.) is called dropout (Srivastava, et al 2014, Baldi et al
2016). This method removes hidden units with a Bernoulli random variable with
probability $p$ over updates. In this paper we will show that Dropout is a
special case of a more general model published originally in 1990 called the
stochastic delta rule ( SDR, Hanson, 1990). SDR parameterizes each weight in
the network as a random variable with mean $\mu_{w_{ij}}$ and standard
deviation $\sigma_{w_{ij}}$. These random variables are sampled on each forward
activation, consequently creating an exponential number of potential networks
with shared weights. Both parameters are updated according to prediction error,
thus implementing weight noise injections that reflect a local history of
prediction error and efficient model averaging. SDR therefore implements a
local gradient-dependent simulated annealing per weight converging to a bayes
optimal network. Tests on standard benchmarks (CIFAR) using a modified version
of DenseNet shows the SDR outperforms standard dropout in error by over 50% and
in loss by over 50%. Furthermore, the SDR implementation converges on a
solution much faster, reaching a training error of 5 in just 15 epochs with
DenseNet-40 compared to standard DenseNet-40's 94 epochs.
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Kernel Regression with Sparse Metric Learning | Kernel regression is a popular non-parametric fitting technique. It aims at
learning a function which estimates the targets for test inputs as precise as
possible. Generally, the function value for a test input is estimated by a
weighted average of the surrounding training examples. The weights are
typically computed by a distance-based kernel function and they strongly depend
on the distances between examples. In this paper, we first review the latest
developments of sparse metric learning and kernel regression. Then a novel
kernel regression method involving sparse metric learning, which is called
kernel regression with sparse metric learning (KR$\_$SML), is proposed. The
sparse kernel regression model is established by enforcing a mixed $(2,1)$-norm
regularization over the metric matrix. It learns a Mahalanobis distance metric
by a gradient descent procedure, which can simultaneously conduct
dimensionality reduction and lead to good prediction results. Our work is the
first to combine kernel regression with sparse metric learning. To verify the
effectiveness of the proposed method, it is evaluated on 19 data sets for
regression. Furthermore, the new method is also applied to solving practical
problems of forecasting short-term traffic flows. In the end, we compare the
proposed method with other three related kernel regression methods on all test
data sets under two criterions. Experimental results show that the proposed
method is much more competitive.
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Learning MSO-definable hypotheses on string | We study the classification problems over string data for hypotheses
specified by formulas of monadic second-order logic MSO. The goal is to design
learning algorithms that run in time polynomial in the size of the training
set, independently of or at least sublinear in the size of the whole data set.
We prove negative as well as positive results. If the data set is an
unprocessed string to which our algorithms have local access, then learning in
sublinear time is impossible even for hypotheses definable in a small fragment
of first-order logic. If we allow for a linear time pre-processing of the
string data to build an index data structure, then learning of MSO-definable
hypotheses is possible in time polynomial in the size of the training set,
independently of the size of the whole data set.
| 1 | 0 | 0 | 0 | 0 | 0 |
From semimetal to chiral Fulde-Ferrell superfluids | The recent realization of two-dimensional (2D) synthetic spin-orbit (SO)
coupling opens a broad avenue to study novel topological states for ultracold
atoms. Here, we propose a new scheme to realize exotic chiral Fulde-Ferrell
superfluid for ultracold fermions, with a generic theory being shown that the
topology of superfluid pairing phases can be determined from the normal states.
The main findings are two fold. First, a semimetal is driven by a new type of
2D SO coupling whose realization is even simpler than the recent experiment,
and can be tuned into massive Dirac fermion phases with or without inversion
symmetry. Without inversion symmetry the superfluid phase with nonzero pairing
momentum is favored under an attractive interaction. Furthermore, we show a
fundamental theorem that the topology of a 2D chiral superfluid can be uniquely
determined from the unpaired normal states, with which the topological chiral
Fulde-Ferrell superfluid with a broad topological region is predicted for the
present system. This generic theorem is also useful for condensed matter
physics and material science in search for new topological superconductors.
| 0 | 1 | 0 | 0 | 0 | 0 |
TumorNet: Lung Nodule Characterization Using Multi-View Convolutional Neural Network with Gaussian Process | Characterization of lung nodules as benign or malignant is one of the most
important tasks in lung cancer diagnosis, staging and treatment planning. While
the variation in the appearance of the nodules remains large, there is a need
for a fast and robust computer aided system. In this work, we propose an
end-to-end trainable multi-view deep Convolutional Neural Network (CNN) for
nodule characterization. First, we use median intensity projection to obtain a
2D patch corresponding to each dimension. The three images are then
concatenated to form a tensor, where the images serve as different channels of
the input image. In order to increase the number of training samples, we
perform data augmentation by scaling, rotating and adding noise to the input
image. The trained network is used to extract features from the input image
followed by a Gaussian Process (GP) regression to obtain the malignancy score.
We also empirically establish the significance of different high level nodule
attributes such as calcification, sphericity and others for malignancy
determination. These attributes are found to be complementary to the deep
multi-view CNN features and a significant improvement over other methods is
obtained.
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An apparatus architecture for femtosecond transmission electron microscopy | The motion of electrons in or near solids, liquids and gases can be tracked
by forcing their ejection with attosecond x-ray pulses, derived from
femtosecond lasers. The momentum of these emitted electrons carries the imprint
of the electronic state. Aberration corrected transmission electron microscopes
have observed individual atoms, and have sufficient energy sensitivity to
quantify atom bonding and electronic configurations. Recent developments in
ultrafast electron microscopy and diffraction indicate that spatial and
temporal information can be collected simultaneously. In the present work, we
push the capability of femtosecond transmission electron microscopy (fs-TEM)
towards that of the state of the art in ultrafast lasers and electron
microscopes. This is anticipated to facilitate unprecedented elucidation of
physical, chemical and biological structural dynamics on electronic time and
length scales. The fs-TEM numerically studied employs a nanotip source,
electrostatic acceleration to 70 keV, magnetic lens beam transport and
focusing, a condenser-objective around the sample and a terahertz temporal
compressor, including space charge effects during propagation. With electron
emission equivalent to a 20 fs laser pulse, we find a spatial resolution below
10 nm and a temporal resolution of below 10 fs will be feasible for pulses
comprised of on average 20 electrons. The influence of a transverse electric
field at the sample is modelled, indicating that a field of 1 V/$\mu$m can be
resolved.
| 0 | 1 | 0 | 0 | 0 | 0 |
HourGlass: Predictable Time-based Cache Coherence Protocol for Dual-Critical Multi-Core Systems | We present a hardware mechanism called HourGlass to predictably share data in
a multi-core system where cores are explicitly designated as critical or
non-critical. HourGlass is a time-based cache coherence protocol for
dual-critical multi-core systems that ensures worst-case latency (WCL) bounds
for memory requests originating from critical cores. Although HourGlass does
not provide either WCL or bandwidth guarantees for memory requests from
non-critical cores, it promotes the use of timers to improve its bandwidth
utilization while still maintaining WCL bounds for critical cores. This
encourages a trade-off between the WCL bounds for critical cores, and the
improved memory bandwidth for non-critical cores via timer configurations. We
evaluate HourGlass using gem5, and with multithreaded benchmark suites
including SPLASH-2, and synthetic workloads. Our results show that the WCL for
critical cores with HourGlass is always within the analytical WCL bounds, and
provides a tighter WCL bound on critical cores compared to the state-of-the-art
real-time cache coherence protocol. Further, we show that HourGlass enables a
trade-off between provable WCL bounds for critical cores, and improved
bandwidth utilization for non-critical cores. The average-case performance of
HourGlass is comparable to the state-of-the-art real-time cache coherence
protocol, and suffers a slowdown of 1.43x and 1.46x compared to the
conventional MSI and MESI protocols.
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Frictional Effects on RNA Folding: Speed Limit and Kramers Turnover | We investigated frictional effects on the folding rates of a human telomerase
hairpin (hTR HP) and H-type pseudoknot from the Beet Western Yellow Virus (BWYV
PK) using simulations of the Three Interaction Site (TIS) model for RNA. The
heat capacity from TIS model simulations, calculated using temperature replica
exchange simulations, reproduces nearly quantitatively the available
experimental data for the hTR HP. The corresponding results for BWYV PK serve
as predictions. We calculated the folding rates ($k_\mathrm{F}$) from more than
100 folding trajectories for each value of the solvent viscosity ($\eta$) at a
fixed salt concentration of 200 mM. By using the theoretical estimate
($\propto$$\sqrt{N}$ where $N$ is the number of nucleotides) for folding free
energy barrier, $k_\mathrm{F}$ data for both the RNAs are quantitatively fit
using one-dimensional Kramers' theory with two parameters specifying the
curvatures in the unfolded basin and the barrier top. In the high-friction
regime ($\eta\gtrsim10^{-5}\,\textrm{Pa\ensuremath{\cdot}s}$), for both HP and
PK, $k_\mathrm{F}$s decrease as $1/\eta$ whereas in the low friction regime,
$k_\mathrm{F}$ values increase as $\eta$ increases, leading to a maximum
folding rate at a moderate viscosity
($\sim10^{-6}\,\textrm{Pa\ensuremath{\cdot}s}$), which is the Kramers turnover.
From the fits, we find that the speed limit to RNA folding at water viscosity
is between 1 and 4 $\mathrm{\mu s}$, which is in accord with our previous
theoretical prediction as well as results from several single molecule
experiments. Both the RNA constructs fold by parallel pathways. Surprisingly,
we find that the flux through the pathways could be altered by changing solvent
viscosity, a prediction that is more easily testable in RNA than in proteins.
| 0 | 0 | 0 | 0 | 1 | 0 |
Learning to Rank based on Analogical Reasoning | Object ranking or "learning to rank" is an important problem in the realm of
preference learning. On the basis of training data in the form of a set of
rankings of objects represented as feature vectors, the goal is to learn a
ranking function that predicts a linear order of any new set of objects. In
this paper, we propose a new approach to object ranking based on principles of
analogical reasoning. More specifically, our inference pattern is formalized in
terms of so-called analogical proportions and can be summarized as follows:
Given objects $A,B,C,D$, if object $A$ is known to be preferred to $B$, and $C$
relates to $D$ as $A$ relates to $B$, then $C$ is (supposedly) preferred to
$D$. Our method applies this pattern as a main building block and combines it
with ideas and techniques from instance-based learning and rank aggregation.
Based on first experimental results for data sets from various domains (sports,
education, tourism, etc.), we conclude that our approach is highly competitive.
It appears to be specifically interesting in situations in which the objects
are coming from different subdomains, and which hence require a kind of
knowledge transfer.
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Modeling Spatial Overdispersion with the Generalized Waring Process | Modeling spatial overdispersion requires point processes models with finite
dimensional distributions that are overdisperse relative to the Poisson.
Fitting such models usually heavily relies on the properties of stationarity,
ergodicity, and orderliness. And, though processes based on negative binomial
finite dimensional distributions have been widely considered, they typically
fail to simultaneously satisfy the three required properties for fitting.
Indeed, it has been conjectured by Diggle and Milne that no negative binomial
model can satisfy all three properties. In light of this, we change
perspective, and construct a new process based on a different overdisperse
count model, the Generalized Waring Distribution. While comparably tractable
and flexible to negative binomial processes, the Generalized Waring process is
shown to possess all required properties, and additionally span the negative
binomial and Poisson processes as limiting cases. In this sense, the GW process
provides an approximate resolution to the conundrum highlighted by Diggle and
Milne.
| 0 | 0 | 1 | 1 | 0 | 0 |
Adversarial examples for generative models | We explore methods of producing adversarial examples on deep generative
models such as the variational autoencoder (VAE) and the VAE-GAN. Deep learning
architectures are known to be vulnerable to adversarial examples, but previous
work has focused on the application of adversarial examples to classification
tasks. Deep generative models have recently become popular due to their ability
to model input data distributions and generate realistic examples from those
distributions. We present three classes of attacks on the VAE and VAE-GAN
architectures and demonstrate them against networks trained on MNIST, SVHN and
CelebA. Our first attack leverages classification-based adversaries by
attaching a classifier to the trained encoder of the target generative model,
which can then be used to indirectly manipulate the latent representation. Our
second attack directly uses the VAE loss function to generate a target
reconstruction image from the adversarial example. Our third attack moves
beyond relying on classification or the standard loss for the gradient and
directly optimizes against differences in source and target latent
representations. We also motivate why an attacker might be interested in
deploying such techniques against a target generative network.
| 0 | 0 | 0 | 1 | 0 | 0 |
Sparse covariance matrix estimation in high-dimensional deconvolution | We study the estimation of the covariance matrix $\Sigma$ of a
$p$-dimensional normal random vector based on $n$ independent observations
corrupted by additive noise. Only a general nonparametric assumption is imposed
on the distribution of the noise without any sparsity constraint on its
covariance matrix. In this high-dimensional semiparametric deconvolution
problem, we propose spectral thresholding estimators that are adaptive to the
sparsity of $\Sigma$. We establish an oracle inequality for these estimators
under model miss-specification and derive non-asymptotic minimax convergence
rates that are shown to be logarithmic in $n/\log p$. We also discuss the
estimation of low-rank matrices based on indirect observations as well as the
generalization to elliptical distributions. The finite sample performance of
the threshold estimators is illustrated in a numerical example.
| 0 | 0 | 1 | 0 | 0 | 0 |
Dynamic controllers for column synchronization of rotation matrices: a QR-factorization approach | In the multi-agent systems setting, this paper addresses continuous-time
distributed synchronization of columns of rotation matrices. More precisely, k
specific columns shall be synchronized and only the corresponding k columns of
the relative rotations between the agents are assumed to be available for the
control design. When one specific column is considered, the problem is
equivalent to synchronization on the (d-1)-dimensional unit sphere and when all
the columns are considered, the problem is equivalent to synchronization on
SO(d). We design dynamic control laws for these synchronization problems. The
control laws are based on the introduction of auxiliary variables in
combination with a QR-factorization approach. The benefit of this
QR-factorization approach is that we can decouple the dynamics for the k
columns from the remaining d-k ones. Under the control scheme, the closed loop
system achieves almost global convergence to synchronization for quasi-strong
interaction graph topologies.
| 1 | 0 | 1 | 0 | 0 | 0 |
The ELEGANT NMR Spectrometer | Compact and portable in-situ NMR spectrometers which can be dipped in the
liquid to be measured, and are easily maintained, with affordable coil
constructions and electronics, together with an apparatus to recover depleted
magnets are presented, that provide a new real-time processing method for NMR
spectrum acquisition, that remains stable despite magnetic field fluctuations.
| 0 | 1 | 0 | 0 | 0 | 0 |
What Would a Graph Look Like in This Layout? A Machine Learning Approach to Large Graph Visualization | Using different methods for laying out a graph can lead to very different
visual appearances, with which the viewer perceives different information.
Selecting a "good" layout method is thus important for visualizing a graph. The
selection can be highly subjective and dependent on the given task. A common
approach to selecting a good layout is to use aesthetic criteria and visual
inspection. However, fully calculating various layouts and their associated
aesthetic metrics is computationally expensive. In this paper, we present a
machine learning approach to large graph visualization based on computing the
topological similarity of graphs using graph kernels. For a given graph, our
approach can show what the graph would look like in different layouts and
estimate their corresponding aesthetic metrics. An important contribution of
our work is the development of a new framework to design graph kernels. Our
experimental study shows that our estimation calculation is considerably faster
than computing the actual layouts and their aesthetic metrics. Also, our graph
kernels outperform the state-of-the-art ones in both time and accuracy. In
addition, we conducted a user study to demonstrate that the topological
similarity computed with our graph kernel matches perceptual similarity
assessed by human users.
| 1 | 0 | 0 | 1 | 0 | 0 |
A sure independence screening procedure for ultra-high dimensional partially linear additive models | We introduce a two-step procedure, in the context of ultra-high dimensional
additive models, which aims to reduce the size of covariates vector and
distinguish linear and nonlinear effects among nonzero components. Our proposed
screening procedure, in the first step, is constructed based on the concept of
cumulative distribution function and conditional expectation of response in the
framework of marginal correlation. B-splines and empirical distribution
functions are used to estimate the two above measures. The sure property of
this procedure is also established. In the second step, a double penalization
based procedure is applied to identify nonzero and linear components,
simultaneously. The performance of the designed method is examined by several
test functions to show its capabilities against competitor methods when errors
distribution are varied. Simulation studies imply that the proposed screening
procedure can be applied to the ultra-high dimensional data and well detect the
in uential covariates. It is also demonstrate the superiority in comparison
with the existing methods. This method is also applied to identify most in
uential genes for overexpression of a G protein-coupled receptor in mice.
| 0 | 0 | 1 | 1 | 0 | 0 |
Unbiased Multi-index Monte Carlo | We introduce a new class of Monte Carlo based approximations of expectations
of random variables such that their laws are only available via certain
discretizations. Sampling from the discretized versions of these laws can
typically introduce a bias. In this paper, we show how to remove that bias, by
introducing a new version of multi-index Monte Carlo (MIMC) that has the added
advantage of reducing the computational effort, relative to i.i.d. sampling
from the most precise discretization, for a given level of error. We cover
extensions of results regarding variance and optimality criteria for the new
approach. We apply the methodology to the problem of computing an unbiased
mollified version of the solution of a partial differential equation with
random coefficients. A second application concerns the Bayesian inference (the
smoothing problem) of an infinite dimensional signal modelled by the solution
of a stochastic partial differential equation that is observed on a discrete
space grid and at discrete times. Both applications are complemented by
numerical simulations.
| 0 | 0 | 0 | 1 | 0 | 0 |
Hilbert Transformation and $r\mathrm{Spin}(n)+\mathbb{R}^n$ Group | In this paper we study symmetry properties of the Hilbert transformation of
several real variables in the Clifford algebra setting. In order to describe
the symmetry properties we introduce the group $r\mathrm{Spin}(n)+\mathbb{R}^n,
r>0,$ which is essentially an extension of the ax+b group. The study concludes
that the Hilbert transformation has certain characteristic symmetry properties
in terms of $r\mathrm{Spin}(n)+\mathbb{R}^n.$ In the present paper, for $n=2$
and $3$ we obtain, explicitly, the induced spinor representations of the
$r\mathrm{Spin}(n)+\mathbb{R}^n$ group. Then we decompose the natural
representation of $r\mathrm{Spin}(n)+\mathbb{R}^n$ into the direct sum of some
two irreducible spinor representations, by which we characterize the Hilbert
transformation in $\mathbb{R}^3$ and $\mathbb{R}^2.$ Precisely, we show that a
nontrivial skew operator is the Hilbert transformation if and only if it is
invariant under the action of the $r\mathrm{Spin}(n)+\mathbb{R}^n, n=2,3,$
group.
| 0 | 0 | 1 | 0 | 0 | 0 |
Asymptotic limit and decay estimates for a class of dissipative linear hyperbolic systems in several dimensions | In this paper, we study the large-time behavior of solutions to a class of
partially dissipative linear hyperbolic systems with applications in
velocity-jump processes in several dimensions. Given integers $n,d\ge 1$, let
$\mathbf A:=(A^1,\dots,A^d)\in (\mathbb R^{n\times n})^d$ be a matrix-vector,
where $A^j\in\mathbb R^{n\times n}$, and let $B\in \mathbb R^{n\times n}$ be
not required to be symmetric but have one single eigenvalue zero, we consider
the Cauchy problem for linear $n\times n$ systems having the form
\begin{equation*}
\partial_{t}u+\mathbf A\cdot \nabla_{\mathbf x} u+Bu=0,\qquad (\mathbf
x,t)\in \mathbb R^d\times \mathbb R_+. \end{equation*} Under appropriate
assumptions, we show that the solution $u$ is decomposed into
$u=u^{(1)}+u^{(2)}$, where $u^{(1)}$ has the asymptotic profile which is the
solution, denoted by $U$, of a parabolic equation and $u^{(1)}-U$ decays at the
rate $t^{-\frac d2(\frac 1q-\frac 1p)-\frac 12}$ as $t\to +\infty$ in any
$L^p$-norm, and $u^{(2)}$ decays exponentially in $L^2$-norm, provided
$u(\cdot,0)\in L^q(\mathbb R^d)\cap L^2(\mathbb R^d)$ for $1\le q\le p\le
\infty$. Moreover, $u^{(1)}-U$ decays at the optimal rate $t^{-\frac d2(\frac
1q-\frac 1p)-1}$ as $t\to +\infty$ if the system satisfies a symmetry property.
The main proofs are based on asymptotic expansions of the solution $u$ in the
frequency space and the Fourier analysis.
| 0 | 0 | 1 | 0 | 0 | 0 |
(G, μ)-displays and Rapoport-Zink spaces | Let (G, \mu) be a pair of a reductive group G over the p-adic integers and a
minuscule cocharacter {\mu} of G defined over an unramified extension. We
introduce and study "(G, \mu)-displays" which generalize Zink's Witt vector
displays. We use these to define certain Rapoport-Zink formal schemes purely
group theoretically, i.e. without p-divisible groups.
| 0 | 0 | 1 | 0 | 0 | 0 |
Selecting Representative Examples for Program Synthesis | Program synthesis is a class of regression problems where one seeks a
solution, in the form of a source-code program, mapping the inputs to their
corresponding outputs exactly. Due to its precise and combinatorial nature,
program synthesis is commonly formulated as a constraint satisfaction problem,
where input-output examples are encoded as constraints and solved with a
constraint solver. A key challenge of this formulation is scalability: while
constraint solvers work well with a few well-chosen examples, a large set of
examples can incur significant overhead in both time and memory. We describe a
method to discover a subset of examples that is both small and representative:
the subset is constructed iteratively, using a neural network to predict the
probability of unchosen examples conditioned on the chosen examples in the
subset, and greedily adding the least probable example. We empirically evaluate
the representativeness of the subsets constructed by our method, and
demonstrate such subsets can significantly improve synthesis time and
stability.
| 1 | 0 | 0 | 0 | 0 | 0 |
Semistable rank 2 sheaves with singularities of mixed dimension on $\mathbb{P}^3$ | We describe new irreducible components of the Gieseker-Maruyama moduli scheme
$\mathcal{M}(3)$ of semistable rank 2 coherent sheaves with Chern classes
$c_1=0,\ c_2=3,\ c_3=0$ on $\mathbb{P}^3$, general points of which correspond
to sheaves whose singular loci contain components of dimensions both 0 and 1.
These sheaves are produced by elementary transformations of stable reflexive
rank 2 sheaves with $c_1=0,\ c_2=2,\ c_3=2$ or 4 along a disjoint union of a
projective line and a collection of points in $\mathbb{P}^3$. The constructed
families of sheaves provide first examples of irreducible components of the
Gieseker-Maruyama moduli scheme such that their general sheaves have
singularities of mixed dimension.
| 0 | 0 | 1 | 0 | 0 | 0 |
From jamming to collective cell migration through a boundary induced transition | Cell monolayers provide an interesting example of active matter, exhibiting a
phase transition from a flowing to jammed state as they age. Here we report
experiments and numerical simulations illustrating how a jammed cellular layer
rapidly reverts to a flowing state after a wound. Quantitative comparison
between experiments and simulations shows that cells change their
self-propulsion and alignement strength so that the system crosses a phase
transition line, which we characterize by finite-size scaling in an active
particle model. This wound-induced unjamming transition is found to occur
generically in epithelial, endothelial and cancer cells.
| 0 | 0 | 0 | 0 | 1 | 0 |
An Approximate Bayesian Long Short-Term Memory Algorithm for Outlier Detection | Long Short-Term Memory networks trained with gradient descent and
back-propagation have received great success in various applications. However,
point estimation of the weights of the networks is prone to over-fitting
problems and lacks important uncertainty information associated with the
estimation. However, exact Bayesian neural network methods are intractable and
non-applicable for real-world applications. In this study, we propose an
approximate estimation of the weights uncertainty using Ensemble Kalman Filter,
which is easily scalable to a large number of weights. Furthermore, we optimize
the covariance of the noise distribution in the ensemble update step using
maximum likelihood estimation. To assess the proposed algorithm, we apply it to
outlier detection in five real-world events retrieved from the Twitter
platform.
| 1 | 0 | 0 | 1 | 0 | 0 |
Estimates of covering type and the number of vertices of minimal triangulations | The covering type of a space $X$ is defined as the minimal cardinality of a
good cover of a space that is homotopy equivalent to $X$. We derive estimates
for the covering type of $X$ in terms of other invariants of $X$, namely the
ranks of the homology groups, the multiplicative structure of the cohomology
ring and the Lusternik-Schnirelmann category of $X$. By relating the covering
type to the number of vertices of minimal triangulations of complexes and
combinatorial manifolds, we obtain, within a unified framework, several
estimates which are either new or extensions of results that have been
previously obtained by ad hoc combinatorial arguments. Moreover, our methods
give results that are valid for entire homotopy classes of spaces.
| 0 | 0 | 1 | 0 | 0 | 0 |
Principal Floquet subspaces and exponential separations of type II with applications to random delay differential equations | This paper deals with the study of principal Lyapunov exponents, principal
Floquet subspaces, and exponential separation for positive random linear
dynamical systems in ordered Banach spaces. The main contribution lies in the
introduction of a new type of exponential separation, called of type II,
important for its application to nonautonomous random differential equations
with delay. Under weakened assumptions, the existence of an exponential
separation of type II in an abstract general setting is shown, and an
illustration of its application to dynamical systems generated by scalar linear
random delay differential equations with finite delay is given.
| 0 | 0 | 1 | 0 | 0 | 0 |
DNA insertion mutations can be predicted by a periodic probability function | It is generally difficult to predict the positions of mutations in genomic
DNA at the nucleotide level. Retroviral DNA insertion is one mode of mutation,
resulting in host infections that are difficult to treat. This mutation process
involves the integration of retroviral DNA into the host-infected cellular
genomic DNA following the interaction between host DNA and a pre-integration
complex consisting of retroviral DNA and integrase. Here, we report that
retroviral insertion sites around a hotspot within the Zfp521 and N-myc genes
can be predicted by a periodic function that is deduced using the diffraction
lattice model. In conclusion, the mutagenesis process is described by a
biophysical model for DNA-DNA interactions.
| 0 | 1 | 0 | 0 | 0 | 0 |
Machine Learning Molecular Dynamics for the Simulation of Infrared Spectra | Machine learning has emerged as an invaluable tool in many research areas. In
the present work, we harness this power to predict highly accurate molecular
infrared spectra with unprecedented computational efficiency. To account for
vibrational anharmonic and dynamical effects -- typically neglected by
conventional quantum chemistry approaches -- we base our machine learning
strategy on ab initio molecular dynamics simulations. While these simulations
are usually extremely time consuming even for small molecules, we overcome
these limitations by leveraging the power of a variety of machine learning
techniques, not only accelerating simulations by several orders of magnitude,
but also greatly extending the size of systems that can be treated. To this
end, we develop a molecular dipole moment model based on environment dependent
neural network charges and combine it with the neural network potentials of
Behler and Parrinello. Contrary to the prevalent big data philosophy, we are
able to obtain very accurate machine learning models for the prediction of
infrared spectra based on only a few hundreds of electronic structure reference
points. This is made possible through the introduction of a fully automated
sampling scheme and the use of molecular forces during neural network potential
training. We demonstrate the power of our machine learning approach by applying
it to model the infrared spectra of a methanol molecule, n-alkanes containing
up to 200 atoms and the protonated alanine tripeptide, which at the same time
represents the first application of machine learning techniques to simulate the
dynamics of a peptide. In all these case studies we find excellent agreement
between the infrared spectra predicted via machine learning models and the
respective theoretical and experimental spectra.
| 0 | 1 | 0 | 1 | 0 | 0 |
Statistically Optimal and Computationally Efficient Low Rank Tensor Completion from Noisy Entries | In this article, we develop methods for estimating a low rank tensor from
noisy observations on a subset of its entries to achieve both statistical and
computational efficiencies. There have been a lot of recent interests in this
problem of noisy tensor completion. Much of the attention has been focused on
the fundamental computational challenges often associated with problems
involving higher order tensors, yet very little is known about their
statistical performance. To fill in this void, in this article, we characterize
the fundamental statistical limits of noisy tensor completion by establishing
minimax optimal rates of convergence for estimating a $k$th order low rank
tensor under the general $\ell_p$ ($1\le p\le 2$) norm which suggest
significant room for improvement over the existing approaches. Furthermore, we
propose a polynomial-time computable estimating procedure based upon power
iteration and a second-order spectral initialization that achieves the optimal
rates of convergence. Our method is fairly easy to implement and numerical
experiments are presented to further demonstrate the practical merits of our
estimator.
| 0 | 0 | 1 | 1 | 0 | 0 |
The cohomology of the full directed graph complex | In his seminal paper "Formality conjecture", M. Kontsevich introduced a graph
complex $GC_{1ve}$ closely connected with the problem of constructing a
formality quasi-isomorphism for Hochschild cochains. In this paper, we express
the cohomology of the full directed graph complex explicitly in terms of the
cohomology of $GC_{1ve}$. Applications of our results include a recent work by
the first author which completely characterizes homotopy classes of formality
quasi-isomorphisms for Hochschild cochains in the stable setting.
| 0 | 0 | 1 | 0 | 0 | 0 |
Model equations and structures formation for the media with memory | We propose new types of models of the appearance of small- and large scale
structures in media with memory, including a hyperbolic modification of the
Navier-Stokes equations and a class of dynamical low-dimensional models with
memory effects. On the basis of computer modeling, the formation of the
small-scale structures and collapses and the appearance of new chaotic
solutions are demonstrated. Possibilities of the application of some proposed
models to the description of the burst-type processes and collapses o nthe Sun
are discussed.
| 0 | 1 | 0 | 0 | 0 | 0 |
On the Support Recovery of Jointly Sparse Gaussian Sources using Sparse Bayesian Learning | In this work, we provide non-asymptotic, probabilistic guarantees for
successful sparse support recovery by the multiple sparse Bayesian learning
(M-SBL) algorithm in the multiple measurement vector (MMV) framework. For joint
sparse Gaussian sources, we show that M-SBL perfectly recovers their common
nonzero support with arbitrarily high probability using only finitely many
MMVs. In fact, the support error probability decays exponentially fast with the
number of MMVs, with the decay rate depending on the restricted isometry
property of the self Khatri-Rao product of the measurement matrix. Our analysis
theoretically confirms that M-SBL is capable of recovering supports of size as
high as $\mathcal{O}(m^2)$, where $m$ is the number of measurements per sparse
vector. In contrast, popular MMV algorithms in compressed sensing such as
simultaneous orthogonal matching pursuit and row-LASSO can recover only
$\mathcal{O}(m)$ sized supports. In the special case of noiseless measurements,
we show that a single MMV suffices for perfect recovery of the $k$-sparse
support in M-SBL, provided any $k + 1$ columns of the measurement matrix are
linearly independent. Unlike existing support recovery guarantees for M-SBL,
our sufficient conditions are non-asymptotic in nature, and do not require the
orthogonality of the nonzero rows of the joint sparse signals.
| 1 | 0 | 0 | 0 | 0 | 0 |
A Critical-like Collective State Leads to Long-range Cell Communication in Dictyostelium discoideum Aggregation | The transition from single-cell to multicellular behavior is important in
early development but rarely studied. The starvation-induced aggregation of the
social amoeba Dictyostelium discoideum into a multicellular slug is known to
result from single-cell chemotaxis towards emitted pulses of cyclic adenosine
monophosphate (cAMP). However, how exactly do transient short-range chemical
gradients lead to coherent collective movement at a macroscopic scale? Here, we
use a multiscale model verified by quantitative microscopy to describe
wide-ranging behaviors from chemotaxis and excitability of individual cells to
aggregation of thousands of cells. To better understand the mechanism of
long-range cell-cell communication and hence aggregation, we analyze cell-cell
correlations, showing evidence for self-organization at the onset of
aggregation (as opposed to following a leader cell). Surprisingly, cell
collectives, despite their finite size, show features of criticality known from
phase transitions in physical systems. Application of external cAMP
perturbations in our simulations near the sensitive critical point allows
steering cells into early aggregation and towards certain locations but not
once an aggregation center has been chosen.
| 0 | 0 | 0 | 0 | 1 | 0 |
Twistor theory at fifty: from contour integrals to twistor strings | We review aspects of twistor theory, its aims and achievements spanning
thelast five decades. In the twistor approach, space--time is secondary with
events being derived objects that correspond to compact holomorphic curves in a
complex three--fold -- the twistor space. After giving an elementary
construction of this space we demonstrate how solutions to linear and nonlinear
equations of mathematical physics: anti-self-duality (ASD) equations on
Yang--Mills, or conformal curvature can be encoded into twistor cohomology.
These twistor correspondences yield explicit examples of Yang--Mills, and
gravitational instantons which we review. They also underlie the twistor
approach to integrability: the solitonic systems arise as symmetry reductions
of ASD Yang--Mills equations, and Einstein--Weyl dispersionless systems are
reductions of ASD conformal equations.
We then review the holomorphic string theories in twistor and ambitwistor
spaces, and explain how these theories give rise to remarkable new formulae for
the computation of quantum scattering amplitudes. Finally we discuss the
Newtonian limit of twistor theory, and its possible role in Penrose's proposal
for a role of gravity in quantum collapse of a wave function.
| 0 | 1 | 1 | 0 | 0 | 0 |
Strong convergence rates of probabilistic integrators for ordinary differential equations | Probabilistic integration of a continuous dynamical system is a way of
systematically introducing model error, at scales no larger than errors
introduced by standard numerical discretisation, in order to enable thorough
exploration of possible responses of the system to inputs. It is thus a
potentially useful approach in a number of applications such as forward
uncertainty quantification, inverse problems, and data assimilation. We extend
the convergence analysis of probabilistic integrators for deterministic
ordinary differential equations, as proposed by Conrad et al.\ (\textit{Stat.\
Comput.}, 2016), to establish mean-square convergence in the uniform norm on
discrete- or continuous-time solutions under relaxed regularity assumptions on
the driving vector fields and their induced flows. Specifically, we show that
randomised high-order integrators for globally Lipschitz flows and randomised
Euler integrators for dissipative vector fields with polynomially-bounded local
Lipschitz constants all have the same mean-square convergence rate as their
deterministic counterparts, provided that the variance of the integration noise
is not of higher order than the corresponding deterministic integrator. These
and similar results are proven for probabilistic integrators where the random
perturbations may be state-dependent, non-Gaussian, or non-centred random
variables.
| 0 | 0 | 1 | 1 | 0 | 0 |
The G-centre and gradable derived equivalences | We propose a generalisation for the notion of the centre of an algebra in the
setup of algebras graded by an arbitrary abelian group G.
Our generalisation, which we call the G-centre, is designed to control the
endomorphism category of the grading shift functors. We show that the G-centre
is preserved by gradable derived equivalences given by tilting modules. We also
discuss links with existing notions in superalgebra theory and apply our
results to derived equivalences of superalgebras.
| 0 | 0 | 1 | 0 | 0 | 0 |
RFCDE: Random Forests for Conditional Density Estimation | Random forests is a common non-parametric regression technique which performs
well for mixed-type data and irrelevant covariates, while being robust to
monotonic variable transformations. Existing random forest implementations
target regression or classification. We introduce the RFCDE package for fitting
random forest models optimized for nonparametric conditional density
estimation, including joint densities for multiple responses. This enables
analysis of conditional probability distributions which is useful for
propagating uncertainty and of joint distributions that describe relationships
between multiple responses and covariates. RFCDE is released under the MIT
open-source license and can be accessed at this https URL .
Both R and Python versions, which call a common C++ library, are available.
| 0 | 0 | 0 | 1 | 0 | 0 |
The symplectic approach of gauged linear $σ$-model | Witten's Gauged Linear $\sigma$-Model (GLSM) unifies the Gromov-Witten theory
and the Landau-Ginzburg theory, and provides a global perspective on mirror
symmetry. In this article, we summarize a mathematically rigorous construction
of the GLSM in the geometric phase using methods from symplectic geometry.
| 0 | 0 | 1 | 0 | 0 | 0 |
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