Typical delay determines waiting time on periodic-food schedules: Static and dynamic tests.

Pigeons and other animals soon learn to wait (pause) after food delivery on periodic-food schedules before resuming the food-rewarded response. Under most conditions the steady-state duration of the average waiting time, t, is a linear function of the typical interfood interval. We describe three experiments designed to explore the limits of this process. In all experiments, t was associated with one key color and the subsequent food delay, T, with another. In the first experiment, we compared the relation between t (waiting time) and T (food delay) under two conditions: when T was held constant, and when T was an inverse function of t. The pigeons could maximize the rate of food delivery under the first condition by setting t to a consistently short value; optimal behavior under the second condition required a linear relation with unit slope between t and T. Despite this difference in optimal policy, the pigeons in both cases showed the same linear relation, with slope less than one, between t and T. This result was confirmed in a second parametric experiment that added a third condition, in which T + t was held constant. Linear waiting appears to be an obligatory rule for pigeons. In a third experiment we arranged for a multiplicative relation between t and T (positive feedback), and produced either very short or very long waiting times as predicted by a quasi-dynamic model in which waiting time is strongly determined by the just-preceding food delay.

Assessment of LD matrix measures for the analysis of biological pathway association.

Complex diseases will have multiple functional sites, and it will be invaluable to understand the cross-locus interaction in terms of linkage disequilibrium (LD) between those sites (epistasis) in addition to the haplotype-LD effects. We investigated the statistical properties of a class of matrix-based statistics to assess this epistasis. These statistical methods include two LD contrast tests (Zaykin et al., 2006) and partial least squares regression (Wang et al., 2008). To estimate Type 1 error rates and power, we simulated multiple two-variant disease models using the SIMLA software package. SIMLA allows for the joint action of up to two disease genes in the simulated data with all possible multiplicative interaction effects between them. Our goal was to detect an interaction between multiple disease-causing variants by means of their linkage disequilibrium (LD) patterns with other markers. We measured the effects of marginal disease effect size, haplotype LD, disease prevalence and minor allele frequency have on cross-locus interaction (epistasis). In the setting of strong allele effects and strong interaction, the correlation between the two disease genes was weak (r=0.2). In a complex system with multiple correlations (both marginal and interaction), it was difficult to determine the source of a significant result. Despite these complications, the partial least squares and modified LD contrast methods maintained adequate power to detect the epistatic effects; however, for many of the analyses we often could not separate interaction from a strong marginal effect. While we did not exhaust the entire parameter space of possible models, we do provide guidance on the effects that population parameters have on cross-locus interaction.

Local kinetic interpretation of entropy production through reversed diffusion.

The time reversal of stochastic diffusion processes is revisited with emphasis on the physical meaning of the time-reversed drift and the noise prescription in the case of multiplicative noise. The local kinematics and mechanics of free diffusion are linked to the hydrodynamic description. These properties also provide an interpretation of the Pope-Ching formula for the steady-state probability density function along with a geometric interpretation of the fluctuation-dissipation relation. Finally, the statistics of the local entropy production rate of diffusion are discussed in the light of local diffusion properties, and a stochastic differential equation for entropy production is obtained using the Girsanov theorem for reversed diffusion. The results are illustrated for the Ornstein-Uhlenbeck process.

Game-Theoretically Allocating Resources to Catch Evaders and Payments to Stabilize Teams

Allocating resources optimally is a nontrivial task, especially when multiple

self-interested agents with conflicting goals are involved. This dissertation

uses techniques from game theory to study two classes of such problems:

allocating resources to catch agents that attempt to evade them, and allocating

payments to agents in a team in order to stabilize it. Besides discussing what

allocations are optimal from various game-theoretic perspectives, we also study

how to efficiently compute them, and if no such algorithms are found, what

computational hardness results can be proved.

The first class of problems is inspired by real-world applications such as the

TOEFL iBT test, course final exams, driver's license tests, and airport security

patrols. We call them test games and security games. This dissertation first

studies test games separately, and then proposes a framework of Catcher-Evader

games (CE games) that generalizes both test games and security games. We show

that the optimal test strategy can be efficiently computed for scored test

games, but it is hard to compute for many binary test games. Optimal Stackelberg

strategies are hard to compute for CE games, but we give an empirically

efficient algorithm for computing their Nash equilibria. We also prove that the

Nash equilibria of a CE game are interchangeable.

The second class of problems involves how to split a reward that is collectively

obtained by a team. For example, how should a startup distribute its shares, and

what salary should an enterprise pay to its employees. Several stability-based

solution concepts in cooperative game theory, such as the core, the least core,

and the nucleolus, are well suited to this purpose when the goal is to avoid

coalitions of agents breaking off. We show that some of these solution concepts

can be justified as the most stable payments under noise. Moreover, by adjusting

the noise models (to be arguably more realistic), we obtain new solution

concepts including the partial nucleolus, the multiplicative least core, and the

multiplicative nucleolus. We then study the computational complexity of those

solution concepts under the constraint of superadditivity. Our result is based

on what we call Small-Issues-Large-Team games and it applies to popular

representation schemes such as MC-nets.

Multi-View Weighted Network

Extensive investigation has been conducted on network data, especially weighted network in the form of symmetric matrices with discrete count entries. Motivated by statistical inference on multi-view weighted network structure, this paper proposes a Poisson-Gamma latent factor model, not only separating view-shared and view-specific spaces but also achieving reduced dimensionality. A multiplicative gamma process shrinkage prior is implemented to avoid over parameterization and efficient full conditional conjugate posterior for Gibbs sampling is accomplished. By the accommodating of view-shared and view-specific parameters, flexible adaptability is provided according to the extents of similarity across view-specific space. Accuracy and efficiency are tested by simulated experiment. An application on real soccer network data is also proposed to illustrate the model.