Related papers: On the recursive structure of multigrid cycles
The purpose of this paper is to study the number of limit cycles of canard type in linear regularizations of piecewise linear systems with non-monotonic transition functions. Using the notion of slow divergence integral and elementary…
A ($\kappa$,$\tau$)-regular set is a vertex subset S inducing a $\kappa$-regular subgraph such that every vertex out of S has $\tau$ neighbors in S. This article is an expository overview of the main results obtained for graphs with…
An open-source C++ framework for discovering fast matrix multiplication schemes using the flip graph approach is presented. The framework supports multiple coefficient rings -- binary ($\mathbb{Z}_2$), modular ternary ($\mathbb{Z}_3$) and…
We provide a fast distributed algorithm for detecting $h$-cycles in the \textsf{Congested Clique} model, whose running time decreases as the number of $h$-cycles in the graph increases. In undirected graphs, constant-round algorithms are…
The continuous development of new adaptive filters (AFs) based on novel cost functions (CFs) is driven by the demands of various application scenarios and noise environments. However, these algorithms typically demonstrate optimal…
Parallel dataflow systems are a central part of most analytic pipelines for big data. The iterative nature of many analysis and machine learning algorithms, however, is still a challenge for current systems. While certain types of bulk…
We propose a reference-free learning model predictive controller for periodic repetitive tasks. We consider a problem in which dynamics, constraints and stage cost are periodically time-varying. The controller uses the closed-loop data to…
We present the outline of a research project aimed at designing and constructing a hybrid computing system that can be easily scaled up to petaflops speeds. As a first step, we envision building a prototype which will consist of three main…
In [5], Holroyd, Levine, M\'esz\'aros, Peres, Propp and Wilson characterize recurrent chip-and-rotor configurations for strongly connected digraphs. However, the number of steps needed to recur, and the number of orbits is left open for…
This paper provides a unified framework connecting dynamical systems with tools from topological data analysis and geometric topology and inspires new interactions among dynamical systems, topology, and nonlinear analysis. To this end, we…
In this paper, we discuss the U-MUSCL reconstruction scheme -- an unstructured-grid extension of Van Leer's kappa-scheme -- proposed by Burg for the edge-based discretization [AIAA Paper 2005-4999]. This technique has been widely used in…
Constrained coding is a fundamental field in coding theory that tackles efficient communication through constrained channels. While channels with fixed constraints have a general optimal solution, there is increasing demand for parametric…
Many scientific workflows can be represented by a Directed Acyclic Graph (DAG) where each node represents a task, and there will be a directed edge between two tasks if and only if there is a dependency relationship between the two i.e. the…
A new approach to designing processor accelerators is presented. A new computing model and a special kind of accelerator with dynamic (end-user programmable) architecture is suggested. The new model considers a processor, in which a newly…
With an increasing share of renewable energy sources, accurate and efficient modeling of grid-forming inverters is becoming crucial for system stability. Linear methods are a powerful tool for understanding dynamics close to an operating…
Graph pattern matching algorithms to handle million-scale dynamic graphs are widely used in many applications such as social network analytics and suspicious transaction detections from financial networks. On the other hand, the computation…
Structured recursion schemes have been widely used in constructing, optimising, and reasoning about programs over inductive and coinductive datatypes. Their plain forms, catamorphisms and anamorphisms, are restricted in expressiveness. Thus…
We present Cyclotron, a framework and compiler for using recurrence equations to express streaming dataflow algorithms, which then get portably compiled to distributed topologies of interlinked processors. Our framework provides an input…
We call matrix algorithms superfast if they use much fewer flops and memory cells than the input matrix has entries. Using such algorithms is indispensable for Big Data Mining and Analysis, where the input matrices are so immense that one…
Multi-Agent Path Finding (MAPF) is NP-hard to solve optimally, even on graphs, suggesting no polynomial-time algorithms can compute exact optimal solutions for them. This raises a natural question: How optimal can polynomial-time algorithms…