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In this article, we study the Lagrangian controllablity of the Korteweg-de Vries (KdV) equation with the higher order velocity field for the N-solitons solution given in [4]. We prove that, for a given depth of the fluid h0, there exists LN > 0 such that if L < LN, then there exists a time T for which one can transport the fluid located in [0, L] to x > L. Physical applications of this result...
An algorithm for the estimation of the moments of linear systems and linear time-delay systems from input/output data is proposed. The estimate, which converges to the moments of the system, is exploited to construct a family of reduced order models. These models asymptotically match the moments of the unknown system to be reduced. The computational complexity of the algorithm is analyzed and the...
We consider the problem of imputing the function that describes an optimization or equilibrium process from noisy partial observations of nearly optimal (possibly non-cooperative) decisions. We generalize existing inverse optimization and variational inequality problems to construct a novel class of multi-objective optimization problems: approximate bilevel programs. In this class, the “ill” nature...
The fill rate is defined as the fraction of demand that is directly satisfied with the on-hand stock. Despite its definition is apparently simple, in the literature we find different interpretations and consequently different methods to compute it. In the majority of related works, the fill rate is computed by using the traditional approximation, which calculates the fill rate in terms of units short...
Recent technical advances in Unmanned Aerial Vehicles (UAV) made a realm of applications possible. In this paper we focus on the application of following a walking pedestrian in real-time, using optimised pedestrian detection and object tracking. For this we use an on-board embedded system, offering an optimal ratio of computational power and weight. We extend the commonly used ground plane estimation...
We consider a decentralized multisensor estimation problem where L sensor nodes observe noisy versions of a possibly correlated random source. The sensors amplify and forward their observations over a fading coherent multiple access channel (MAC) to a fusion center (FC). The FC is equipped with a large array of N antennas, and adopts a minimum mean square error (MMSE) approach for estimating the source...
The results of experimental research of both homogeneous and heterogeneous image superimposition quality by means of multiple view geometry. One of the most important tasks in the problem of image superimposition which has not been solved till now is the task to make the right selection of a set of key (corresponding) point pairs on superimposed images. The research shows image superimposition by...
This paper revisits the model order selection problem in the context of second-order spectrum sensing in cognitive radio. Taking advantage of the recent interest on the generalized likelihood ratio (GLR), the asymptotic performance of the minimum description length (MDL) rule under unknown noise variance is addressed. In particular, by exploiting the asymptotically Chi-squared distribution of the...
Consider the problem of estimating the Shannon entropy of a distribution on k elements from n independent samples. We show that the minimax mean-square error is within universal multiplicative constant factors of k over n log k + log2k over n. This implies the recent result of Valiant-Valiant [1] that the minimal sample size for consistent entropy estimation scales according to Θ(k over log k). The...
We study the excess mean square error (EMSE) above the minimum mean square error (MMSE) in large linear systems where the posterior mean estimator (PME) is evaluated with a postulated prior that differs from the true prior of the input signal. We focus on large linear systems where the measurements are acquired via an independent and identically distributed random matrix, and are corrupted by additive...
We consider a generalization of the problem of estimating the support size of a hidden subset S of a universe U from samples. This framework falls under the group testing [1] and the conditional sampling models [2, 3]. In group testing, for a query set, we are told if it intersects with the set S. We propose a generalization of this problem, where each element has a non-negative weight, and the objective...
Generalized Linear Models (GLMs), where a random vector x is observed through a noisy, possibly nonlinear, function of a linear transform z = Ax arise in a range of applications in nonlinear filtering and regression. Approximate Message Passing (AMP) methods, based on loopy belief propagation, are a promising class of approaches for approximate inference in these models. AMP methods are computationally...
Optimization on Riemannian manifolds is an intuitive generalization of the traditional optimization algorithms in Euclidean spaces. In these algorithms, minimizing along a search direction becomes minimizing along a search curve lying on a manifold. Computing such a curve to be subsequently searched upon is itself computational intensive. We propose a new minimization scheme aiming to find a better...
In the light of the recent interest in approximating the partition function of the Ising model using the dual normal factor graph, we revisit the classical duality result of Kramers and Wannier, where the dual normal factor graph may be viewed as an intermediate step in establishing such a result.
We investigate the problem of estimating on the fly the frequency at which items recur in large scale distributed data streams, which has become the norm in cloud-based application. This paper presents CASE, a combination of tools and probabilistic algorithms from the data streaming model. In this model, functions are estimated on a huge sequence of data items, in an online fashion, and with a very...
Many everyday human skills can be considered in terms of performing some task subject to a set of self-imposed or environmental constraints. In recent years, a number of new tools have become available in the learning and robotics community that allow data from constrained and/or redundant systems to be used to uncover underlying consistent behaviours that may be otherwise masked by the constraints...
In this contribution we present selected mathematical — statistical methods which are used to analyse oil field data from heavy off-road military vehicles. We apply selected regression functions for description of the oil additives degradation in time. This helps for creating the picture about the system — vehicle engine in our case — in service operation behaviour. We investigate the oil field data...
The use of normal approximation to estimate expanded uncertainty has been very widespread; yet this is one of the practices that is being criticized by various quarters for lack of rigor and potentially misleading. Monte Carlo method is probably the only method trusted to generate reliable expanded uncertainty. Unfortunately, Monte Carlo method is not applicable for type-A evaluations. This is one...
Formal verification can provide the highest degree of software assurance. Demand for it is growing, but there are still few projects that have successfully applied it to sizeable, real-world systems. This lack of experience makes it hard to predict the size, effort and duration of verification projects. In this paper, we aim to better understand possible leading indicators of proof size. We present...
The problem of source separation in two dimensions is studied in this paper. The problem is formulated in the Bayesian framework. The sources are modelled as MRFs to accommodate for the spatially correlated structure of the sources, which we exploit for separation in 2D. The difficulty of working analytically with general Gibbs distributions is overcome by using an approximate density. In this work,...
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