6,385 research outputs found
Equilibria of biological aggregations with nonlocal repulsive-attractive interactions
We consider the aggregation equation in , where the interaction potential
incorporates short-range Newtonian repulsion and long-range power-law
attraction. We study the global well-posedness of solutions and investigate
analytically and numerically the equilibrium solutions. We show that there
exist unique equilibria supported on a ball of . By using the
method of moving planes we prove that such equilibria are radially symmetric
and monotone in the radial coordinate. We perform asymptotic studies for the
limiting cases when the exponent of the power-law attraction approaches
infinity and a Newtonian singularity, respectively. Numerical simulations
suggest that equilibria studied here are global attractors for the dynamics of
the aggregation model
Environmental boundary tracking and estimation using multiple autonomous vehicles
In this paper, we develop a framework for environmental
boundary tracking and estimation by considering the
boundary as a hidden Markov model (HMM) with separated
observations collected from multiple sensing vehicles. For each
vehicle, a tracking algorithm is developed based on Page’s
cumulative sum algorithm (CUSUM), a method for change-point
detection, so that individual vehicles can autonomously
track the boundary in a density field with measurement noise.
Based on the data collected from sensing vehicles and prior
knowledge of the dynamic model of boundary evolvement, we
estimate the boundary by solving an optimization problem, in
which prediction and current observation are considered in the
cost function. Examples and simulation results are presented
to verify the efficiency of this approach
Consistent Dynamic Mode Decomposition
We propose a new method for computing Dynamic Mode Decomposition (DMD)
evolution matrices, which we use to analyze dynamical systems. Unlike the
majority of existing methods, our approach is based on a variational
formulation consisting of data alignment penalty terms and constitutive
orthogonality constraints. Our method does not make any assumptions on the
structure of the data or their size, and thus it is applicable to a wide range
of problems including non-linear scenarios or extremely small observation sets.
In addition, our technique is robust to noise that is independent of the
dynamics and it does not require input data to be sequential. Our key idea is
to introduce a regularization term for the forward and backward dynamics. The
obtained minimization problem is solved efficiently using the Alternating
Method of Multipliers (ADMM) which requires two Sylvester equation solves per
iteration. Our numerical scheme converges empirically and is similar to a
provably convergent ADMM scheme. We compare our approach to various
state-of-the-art methods on several benchmark dynamical systems
Zero Shot Learning with the Isoperimetric Loss
We introduce the isoperimetric loss as a regularization criterion for
learning the map from a visual representation to a semantic embedding, to be
used to transfer knowledge to unknown classes in a zero-shot learning setting.
We use a pre-trained deep neural network model as a visual representation of
image data, a Word2Vec embedding of class labels, and linear maps between the
visual and semantic embedding spaces. However, the spaces themselves are not
linear, and we postulate the sample embedding to be populated by noisy samples
near otherwise smooth manifolds. We exploit the graph structure defined by the
sample points to regularize the estimates of the manifolds by inferring the
graph connectivity using a generalization of the isoperimetric inequalities
from Riemannian geometry to graphs. Surprisingly, this regularization alone,
paired with the simplest baseline model, outperforms the state-of-the-art among
fully automated methods in zero-shot learning benchmarks such as AwA and CUB.
This improvement is achieved solely by learning the structure of the underlying
spaces by imposing regularity.Comment: Accepted to AAAI-2
Reverse undercompressive shock structures in driven thin film flow
We show experimental evidence of a new structure involving an
undercompressive and reverse undercompressive shock for draining films driven
by a surface tension gradient against gravity. The reverse undercompressive
shock is unstable to transverse perturbations while the leading
undercompressive shock is stable. Depending on the pinch-off film thickness, as
controlled by the meniscus, either a trailing rarefaction wave or a compressive
shock separates from the reverse undercompressive shock
Logic Programming approaches for routing fault-free and maximally-parallel Wavelength Routed Optical Networks on Chip (Application paper)
One promising trend in digital system integration consists of boosting
on-chip communication performance by means of silicon photonics, thus
materializing the so-called Optical Networks-on-Chip (ONoCs). Among them,
wavelength routing can be used to route a signal to destination by univocally
associating a routing path to the wavelength of the optical carrier. Such
wavelengths should be chosen so to minimize interferences among optical
channels and to avoid routing faults. As a result, physical parameter selection
of such networks requires the solution of complex constrained optimization
problems. In previous work, published in the proceedings of the International
Conference on Computer-Aided Design, we proposed and solved the problem of
computing the maximum parallelism obtainable in the communication between any
two endpoints while avoiding misrouting of optical signals. The underlying
technology, only quickly mentioned in that paper, is Answer Set Programming
(ASP). In this work, we detail the ASP approach we used to solve such problem.
Another important design issue is to select the wavelengths of optical
carriers such that they are spread across the available spectrum, in order to
reduce the likelihood that, due to imperfections in the manufacturing process,
unintended routing faults arise. We show how to address such problem in
Constraint Logic Programming on Finite Domains (CLP(FD)).
This paper is under consideration for possible publication on Theory and
Practice of Logic Programming.Comment: Paper presented at the 33nd International Conference on Logic
Programming (ICLP 2017), Melbourne, Australia, August 28 to September 1,
2017. 16 pages, LaTeX, 5 figure
Characterization of radially symmetric finite time blowup in multidimensional aggregation equations,
This paper studies the transport of a mass in by a
flow field . We focus on kernels for
for which the smooth densities are known to develop
singularities in finite time. For this range This paper studies the transport
of a mass in by a flow field . We
focus on kernels for for which the
smooth densities are known to develop singularities in finite time. For this
range we prove the existence for all time of radially symmetric measure
solutions that are monotone decreasing as a function of the radius, thus
allowing for continuation of the solution past the blowup time. The monotone
constraint on the data is consistent with the typical blowup profiles observed
in recent numerical studies of these singularities. We prove monotonicity is
preserved for all time, even after blowup, in contrast to the case
where radially symmetric solutions are known to lose monotonicity. In the case
of the Newtonian potential (), under the assumption of radial
symmetry the equation can be transformed into the inviscid Burgers equation on
a half line. This enables us to prove preservation of monotonicity using the
classical theory of conservation laws. In the case and at
the critical exponent we exhibit initial data in for which the
solution immediately develops a Dirac mass singularity. This extends recent
work on the local ill-posedness of solutions at the critical exponent.Comment: 30 page
The regularity of the boundary of a multidimensional aggregation patch
Let and let be the fundamental solution of the Laplace
equation in We consider the aggregation equation with
initial data , where is the indicator
function of a bounded domain We now fix and
take to be a bounded domain (a domain with smooth boundary
of class ). Then we have Theorem: If is a
domain, then the initial value problem above has a solution given by
where is a domain for all
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