Related papers: Dynamic Products of Ranks
Preferences, fundamental in all forms of strategic behavior and collective decision-making, in their raw form, are an abstract ordering on a set of alternatives. Agents, we assume, revise their preferences as they gain more information…
Dynamic programming is a class of algorithms used to compute optimal control policies for Markov decision processes. Dynamic programming is ubiquitous in control theory, and is also the foundation of reinforcement learning. In this paper,…
Optimization algorithms can be interpreted through the lens of dynamical systems as the interconnection of linear systems and a set of subgradient nonlinearities. This dynamical systems formulation allows for the analysis and synthesis of…
In this paper we present new data structures for two extensively studied variants of the orthogonal range searching problem. First, we describe a data structure that supports two-dimensional orthogonal range minima queries in $O(n)$ space…
We develop a novel hierarchy for zero-dimensional persistence pairs, i.e., connected components, which is capable of capturing more fine-grained spatial relations between persistence pairs. Our work is motivated by a lack of spatial…
Dynamic pricing of goods in a competitive environment to maximize revenue is a natural objective and has been a subject of research over the years. In this paper, we focus on a class of markets exhibiting the substitutes property with…
The notions of real and user cardinality of a sign are introduced. Rank distributions can be extended to arbitrary sign objects, i.e., semiotic systems. The dynamics of the distribution of consumer durables, such as automobiles, is studied.
In the theory of dynamic programming, an optimal policy is a policy whose lifetime value dominates that of all other policies from every possible initial condition in the state space. This raises a natural question: when does optimality…
The links between optimal control of dynamical systems and neural networks have proved beneficial both from a theoretical and from a practical point of view. Several researchers have exploited these links to investigate the stability of…
In this paper we describe a fully-dynamic data structure for the planar point location problem in the external memory model. Our data structure supports queries in $O(\log_B n(\log\log_B n)^3))$ I/Os and updates in $O(\log_B n(\log\log_B…
We consider the linear and quadratic higher order terms associated to the response of the statistical properties of a dynamical system to suitable small perturbations. These terms are related to the first and second derivative of the…
Dynamical processes can be classified in various ways as deterministic or stochastic, and continuous or discrete time. All these types can be studied by the path-spaces they generate, and stationary measures on that path-space. Such…
Central to all machine learning algorithms is data representation. For multi-agent systems, selecting a representation which adequately captures the interactions among agents is challenging due to the latent group structure which tends to…
Preference-based data often appear complex and noisy but may conceal underlying homogeneous structures. This paper introduces a novel framework of ranking structure recognition for preference-based data. We first develop an approach to…
We consider the problem of matching applicants to posts where applicants have preferences over posts. Thus the input to our problem is a bipartite graph G = (A U P,E), where A denotes a set of applicants, P is a set of posts, and there are…
The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a…
A combinatorial trade is a pair of sets of blocks of elements that can be exchanged while preserving relevant subset intersection constraints. The class of balanced and swap-robust minimal trades was proposed in [1] for exchanging blocks of…
In this article we will look at the PageRank algorithm used as part of the ranking process of different Internet pages in search engines by for example Google. This article has its main focus in the understanding of the behavior of PageRank…
This chapter discusses the interplay between structure and dynamics in complex networks. Given a particular network with an endowed dynamics, our goal is to find partitions aligned with the dynamical process acting on top of the network. We…
We investigate the behavior of data structures when the input and operations are generated by an event graph. This model is inspired by Markov chains. We are given a fixed graph G, whose nodes are annotated with operations of the type…