Related papers: Singularity confinement and full-deautonomisation:…
In this paper, we will discuss new developments regarding the Geometric Nonholonomic Integrator (GNI) [23, 24]. GNI is a discretization scheme adapted to nonholonomic mechanical systems through a discrete geometric approach. This method was…
A recent proposal of data dependent similarity called Isolation Kernel/Similarity has enabled SVM to produce better classification accuracy. We identify shortcomings of using a tree method to implement Isolation Similarity; and propose a…
We provide algorithmically verifiable necessary and sufficient conditions for fundamental system theoretic properties of discrete time linear systems subject to data losses. More precisely, the systems in our modeling framework are subject…
We discuss in detail the uniform discretization approach to the quantization of totally constrained theories. This approach allows to construct the continuum theory of interest as a well defined, controlled, limit of well behaved discrete…
Accurate evaluation of nearly singular integrals plays an important role in many boundary integral equation based numerical methods. In this paper, we propose a variant of singularity swapping method to accurately evaluate the layer…
A canonical formalism and constraint analysis for discrete systems subject to a variational action principle are devised. The formalism is equivalent to the covariant formulation, encompasses global and local discrete time evolution moves…
We introduce distance entropy as a measure of homogeneity in the distribution of path lengths between a given node and its neighbours in a complex network. Distance entropy defines a new centrality measure whose properties are investigated…
It is widely believed, and axiomatically postulated in mathematical quantum field theory, that the vacuum is a unique vector state. The recent solution of the quantum Yang-Mills theory of the strong interaction revealed the presence of two…
Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof.…
This paper deals with the controllability for a class of non-autonomous neutral differential equations of fractional order with infinite delay in an abstract space. The semi-group theory of bounded linear operators, fractional calculus, and…
Trustworthiness assessment is an essential step to assure that interdependent systems perform critical functions as anticipated, even under adverse conditions. In this paper, a holistic trustworthiness assessment framework for…
Modern autonomous systems with machine learning components often use uncertainty quantification to help produce assurances about system operation. However, there is a lack of consensus in the community on what uncertainty is and how to…
The main theme of the article is the study of discrete systems of material points subjected to constraints not only of a geometric type (holonomic constraints) but also of a kinematic type (nonholonomic constraints). The setting up of the…
We study the convergence of a discrete Luenberger observer for the barotropic Euler equations in one dimension, for measurements of the velocity only. We use a mixed finite element method in space and implicit Euler integration in time. We…
In this paper, we present an approach to quantize singular systems. This is an extension of the constant integration method (Belhadi et al. (2014)) which is applicable only for the case of exactly solvable systems. In our approach, we…
We propose a novel two-stage framework for sensor depth enhancement, called Perfecting Depth. This framework leverages the stochastic nature of diffusion models to automatically detect unreliable depth regions while preserving geometric…
Nonlinear systems of affine control inputs overarch many sensor fusion instances. Analyzing whether a state variable in such a nonlinear system can be estimated (i.e., observability) informs better estimator design. Among the research on…
As autonomy becomes prevalent in many applications, ranging from recommendation systems to fully autonomous vehicles, there is an increased need to provide safety guarantees for such systems. The problem is difficult, as these are large,…
We study the dynamics of the metrics generated by measure preserving transformations. We consider a sequence of average metrics and define the corresponding sequence of $\epsilon$-entropies ({\it scaling sequence}) of the measure with…
Depth completion aims at inferring a dense depth image from sparse depth measurement since glossy, transparent or distant surface cannot be scanned properly by the sensor. Most of existing methods directly interpolate the missing depth…