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Many geometric optimization problems can be reduced to finding points in space (centers) minimizing an objective function which continuously depends on the distances from the centers to given input points. Examples are $k$-Means, Geometric…
Neural networks have proven practical for a synergistic combination of advanced control techniques. This work analyzes the implementation of rectified linear unit neural networks to achieve constrained control in differentially flat…
The fastest known algorithms for dealing with structured matrices, in the sense of the displacement rank measure, are randomized. For handling classical displacement structures, they achieve the complexity bounds…
The paper addresses the exact linearization of flat nonlinear discrete-time systems by generalized static or dynamic feedbacks which may also depend on forward-shifts of the new input. We first investigate the question which forward-shifts…
The aim of the paper is to introduce general techniques in order to optimize the parallel execution time of sorting on a distributed architectures with processors of various speeds. Such an application requires a partitioning step. For…
The N-body problem is a classic problem involving a system of N discrete bodies mutually interacting in a dynamical system. At any moment in time there are N*(N - 1)/2 such interactions occurring. This scaling as N^2 leads to computational…
While modern best practices advocate for scalable architectures that support long-range interactions, object-centric models are yet to fully embrace these architectures. In particular, existing object-centric models for handling sequential…
Consider the example of the relationship of the group O(3) of rotations in 3-space to the special unitary group SU(2). Given other unitary groups, what transformations can we find? In this paper we describe a method of constructing…
We introduce a general framework for leveraging graph stream data for temporal prediction-based applications. Our proposed framework includes novel methods for learning an appropriate graph time-series representation, modeling and weighting…
Convolutional neural networks have become the main tools for processing two-dimensional data. They work well for images, yet convolutions have a limited receptive field that prevents its applications to more complex 2D tasks. We propose a…
This paper presents a unifying theory of Linear second order systems that allows time-varying and time invariant systems to be treated in the same way for the first time. In the process, a transformation is given that diagonalizes an…
Many time series are generated by a set of entities that interact with one another over time. This paper introduces a broad, flexible framework to learn from multiple inter-dependent time series generated by such entities. Our framework…
Reasoning about graphs evolving over time is a challenging concept in many domains, such as bioinformatics, physics, and social networks. We consider a common case in which edges can be short term interactions (e.g., messaging) or long term…
Recurrent neural networks (RNNs) sequentially process data by updating their state with each new data point, and have long been the de facto choice for sequence modeling tasks. However, their inherently sequential computation makes them…
We analyze the evolution of the local simulation times (LST) in Parallel Discrete Event Simulations. The new ingredients introduced are i) we associate the LST with the nodes and not with the processing elements, and 2) we propose to…
In this paper we analyze, evaluate, and improve the performance of training generalized linear models on modern CPUs. We start with a state-of-the-art asynchronous parallel training algorithm, identify system-level performance bottlenecks,…
In this paper we first study the fixed-time stabilizability of discrete-time switched linear control systems. Using a geometric approach, we derive conditions under which such systems can be stabilized within a prescribed number of steps,…
This work introduces an innovative parallel, fully-distributed finite element framework for growing geometries and its application to metal additive manufacturing. It is well-known that virtual part design and qualification in additive…
Shape formation has been recently studied in distributed systems of programmable particles. In this paper we consider the shape recovery problem of restoring the shape when $f$ of the $n$ particles have crashed. We focus on the basic line…
Turing's model has been widely used to explain how simple, uniform structures can give rise to complex, patterned structures during the development of organisms. However, it is very hard to establish rigorous theoretical results for the…