Related papers: Dynamic Programming in Topological Spaces
Topological data analysis refers to approaches for systematically and reliably computing abstract ``shapes'' of complex data sets. There are various applications of topological data analysis in life and data sciences, with growing interest…
Living systems exhibit complex yet organized behavior on multiple spatiotemporal scales. To investigate the nature of multiscale coordination in living systems, one needs a meaningful and systematic way to quantify the complex dynamics, a…
While the algorithmic drawing of static trees is well-understood and well-supported by software tools, creating animations depicting how a tree changes over time is currently difficult: software support, if available at all, is not…
Real-time navigation in dense human environments is a challenging problem in robotics. Most existing path planners fail to account for the dynamics of pedestrians because introducing time as an additional dimension in search space is…
In this paper we present an algorithmic framework for solving a class of combinatorial optimization problems on graphs with bounded pathwidth. The problems are NP-hard in general, but solvable in linear time on this type of graphs. The…
Computational mechanics is a method for discovering, describing and quantifying patterns, using tools from statistical physics. It constructs optimal, minimal models of stochastic processes and their underlying causal structures. These…
We consider two classes of stream-based computations which admit taking linear combinations of execution runs: probabilistic sampling and generalized animation. The dataflow architecture is a natural platform for programming with streams.…
This paper studies the dynamic programming principle for general convex stochastic optimization problems introduced by Rockafellar and Wets in [30]. We extend the applicability of the theory by relaxing compactness and boundedness…
Dynamic programming (DP) is one of the fundamental paradigms in algorithm design. However, many DP algorithms have to fill in large DP tables, represented by two-dimensional arrays, which causes at least quadratic running times and space…
Digital memcomputing machines (DMMs) are a class of computational machines designed to solve combinatorial optimization problems. A practical realization of DMMs can be accomplished via electrical circuits of highly non-linear,…
A method is presented to exploit adaptive integration algorithms using importance sampling, like VEGAS, for the task of scanning theoretical predictions depending on a multi-dimensional parameter space. Usually, a parameter scan is…
There has been widespread interest in the use of grid-level storage to handle the variability from increasing penetrations of wind and solar energy. This problem setting requires optimizing energy storage and release decisions for anywhere…
Chaotic dynamics have emerged as a versatile resource for neuromorphic and probabilistic computing, enabling high-dimensional nonlinear processing and classical analogues of quantum randomness. Exploiting chaos for computation requires…
In this paper we introduce a dynamic programming algorithm to perform linear text segmentation by global minimization of a segmentation cost function which consists of: (a) within-segment word similarity and (b) prior information about…
In this paper we consider several constrained activity scheduling problems in the time and space domains, like finding activity orderings which optimize the values of several objective functions (time scheduling) or finding optimal…
Topological deep learning is a formalism that is aimed at introducing topological language to deep learning for the purpose of utilizing the minimal mathematical structures to formalize problems that arise in a generic deep learning…
An informative measurement is the most efficient way to gain information about an unknown state. We present a first-principles derivation of a general-purpose dynamic programming algorithm that returns an optimal sequence of informative…
We apply to logic programming some recently emerging ideas from the field of reduction-based communicating systems, with the aim of giving evidence of the hidden interactions and the coordination mechanisms that rule the operational…
Choreographic Programming is a development methodology for concurrent software that guarantees correctness by construction. The key to this paradigm is to disallow mismatched I/O operations in programs, called choreographies, and then…
We present an improved method for topology optimization with both adaptive mesh refinement and derefinement. Since the total volume fraction in topology optimization is usually modest, after a few initial iterations the domain of…