546 research outputs found
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
Canale di Reno e Paladozza; ricerca storica e progetto di riqualificazione
Progettazione di riqualificazione a scala urbana della via Riva di Reno, del Piazzale Azzarita, del Giardino Decorato Onore Civile e di piazza Resistenza, con ricerca storica sul sistema canali Bolognese, area Porto e Palazzetto dello Sport
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
A Harmonic Extension Approach for Collaborative Ranking
We present a new perspective on graph-based methods for collaborative ranking
for recommender systems. Unlike user-based or item-based methods that compute a
weighted average of ratings given by the nearest neighbors, or low-rank
approximation methods using convex optimization and the nuclear norm, we
formulate matrix completion as a series of semi-supervised learning problems,
and propagate the known ratings to the missing ones on the user-user or
item-item graph globally. The semi-supervised learning problems are expressed
as Laplace-Beltrami equations on a manifold, or namely, harmonic extension, and
can be discretized by a point integral method. We show that our approach does
not impose a low-rank Euclidean subspace on the data points, but instead
minimizes the dimension of the underlying manifold. Our method, named LDM (low
dimensional manifold), turns out to be particularly effective in generating
rankings of items, showing decent computational efficiency and robust ranking
quality compared to state-of-the-art methods
A Model for Optimal Human Navigation with Stochastic Effects
We present a method for optimal path planning of human walking paths in
mountainous terrain, using a control theoretic formulation and a
Hamilton-Jacobi-Bellman equation. Previous models for human navigation were
entirely deterministic, assuming perfect knowledge of the ambient elevation
data and human walking velocity as a function of local slope of the terrain.
Our model includes a stochastic component which can account for uncertainty in
the problem, and thus includes a Hamilton-Jacobi-Bellman equation with
viscosity. We discuss the model in the presence and absence of stochastic
effects, and suggest numerical methods for simulating the model. We discuss two
different notions of an optimal path when there is uncertainty in the problem.
Finally, we compare the optimal paths suggested by the model at different
levels of uncertainty, and observe that as the size of the uncertainty tends to
zero (and thus the viscosity in the equation tends to zero), the optimal path
tends toward the deterministic optimal path
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