Owner-Intruder Contests with Information Asymmetry

Owner-Intruder Contests with Information Asymmetry Faheem Farooq, Depts. of Biology and Chemistry, Jay Bisen, Manaeil Hasan, and Akhil Patel, with Dr. Jan Rychtar, Dept. of Mathematics and Discrete Mathematics, and Dr. Dewey T. Taylor, Dept. of Mathematics and Discrete Mathematics We consider kleptoparasitic interactions between two individuals - Owner and Intruder - and model the situation as a sequential game in an extensive form. Owner is in a possession of a valuable resource when it spots Intruder. Owner has to decide whether to defend the resource; if the Owner defends, the Intruder has to decide whether to fight with the Owner. The individuals may value the resource differently and we distinguish three information cases: (a) both individuals know resource values to both of them, (b) individuals know only their own valuation, (c) individuals do not know the value at all. We solve the game in all three cases. We find that it is typically beneficial for the individuals to know as much information as possible. However, we identify several scenarios where knowing less seems better. We also show that an individual may or may not benefit from their opponent knowing less. Finally, we consider the same kind of interactions but with the reversed order of decisions. We find that typically the individual initiating the interaction has an advantage. However, when individuals know only their own valuation and not the valuations to their opponents, it is sometimes better when the opponent initiates.https://scholarscompass.vcu.edu/uresposters/1298/thumbnail.jp

On the deterministic solution of multidimensional parametric models using the Proper Generalized Decomposition

This paper focuses on the efficient solution of models defined in high dimensional spaces. Those models involve numerous numerical challenges because of their associated curse of dimensionality. It is well known that in mesh-based discrete models the complexity (degrees of freedom) scales exponentially with the dimension of the space. Many models encountered in computational science and engineering involve numerous dimensions called configurational coordinates. Some examples are the models encoun- tered in biology making use of the chemical master equation, quantum chemistry involving the solution of the Schrödinger or Dirac equations, kinetic theory descriptions of complex systems based on the solution of the so-called Fokker–Planck equation, stochastic models in which the random variables are included as new coordinates, financial mathematics, etc. This paper revisits the curse of dimensionality and proposes an efficient strategy for circumventing such challenging issue. This strategy, based on the use of a Proper Generalized Decomposition, is specially well suited to treat the multidimensional parametric equations

Spectral graph theory : from practice to theory

Graph theory is the area of mathematics that studies networks, or graphs. It arose from the need to analyse many diverse network-like structures like road networks, molecules, the Internet, social networks and electrical networks. In spectral graph theory, which is a branch of graph theory, matrices are constructed from such graphs and analysed from the point of view of their so-called eigenvalues and eigenvectors. The first practical need for studying graph eigenvalues was in quantum chemistry in the thirties, forties and fifties, specifically to describe the Hückel molecular orbital theory for unsaturated conjugated hydrocarbons. This study led to the field which nowadays is called chemical graph theory. A few years later, during the late fifties and sixties, graph eigenvalues also proved to be important in physics, particularly in the solution of the membrane vibration problem via the discrete approximation of the membrane as a graph. This paper delves into the journey of how the practical needs of quantum chemistry and vibrating membranes compelled the creation of the more abstract spectral graph theory. Important, yet basic, mathematical results stemming from spectral graph theory shall be mentioned in this paper. Later, areas of study that make full use of these mathematical results, thus benefitting greatly from spectral graph theory, shall be described. These fields of study include the P versus NP problem in the field of computational complexity, Internet search, network centrality measures and control theory.peer-reviewe

An Analysis of Publication Venues for Automatic Differentiation Research

We present the results of our analysis of publication venues for papers on automatic differentiation (AD), covering academic journals and conference proceedings. Our data are collected from the AD publications database maintained by the autodiff.org community website. The database is purpose-built for the AD field and is expanding via submissions by AD researchers. Therefore, it provides a relatively noise-free list of publications relating to the field. However, it does include noise in the form of variant spellings of journal and conference names. We handle this by manually correcting and merging these variants under the official names of corresponding venues. We also share the raw data we get after these corrections.Comment: 6 pages, 3 figure