Robust solutions to Stackelberg games: Addressing bounded rationality and limited observations in human cognition

How do we build algorithms for agent interactions with human adversaries? Stackelberg games are natural models for many important applications that involve human interaction, such as oligopolistic markets and security domains. In Stackelberg games, one player, the leader, commits to a strategy and the follower makes her decision with knowledge of the leader's commitment. Existing algorithms for Stackelberg games efficiently find optimal solutions (leader strategy), but they critically assume that the follower plays optimally. Unfortunately, in many applications, agents face human followers (adversaries) who — because of their bounded rationality and limited observation of the leader strategy — may deviate from their expected optimal response. In other words, human adversaries' decisions are biased due to their bounded rationality and limited observations. Not taking into account these likely deviations when dealing with human adversaries may cause an unacceptable degradation in the leader's reward, particularly in security applications where these algorithms have seen deployment. The objective of this paper therefore is to investigate how to build algorithms for agent interactions with human adversaries.To address this crucial problem, this paper introduces a new mixed-integer linear program (MILP) for Stackelberg games to consider human adversaries, incorporating: (i) novel anchoring theories on human perception of probability distributions and (ii) robustness approaches for MILPs to address human imprecision. Since this new approach considers human adversaries, traditional proofs of correctness or optimality are insufficient; instead, it is necessary to rely on empirical validation. To that end, this paper considers four settings based on real deployed security systems at Los Angeles International Airport (Pita et al., 2008 [35]), and compares 6 different approaches (three based on our new approach and three previous approaches), in 4 different observability conditions, involving 218 human subjects playing 2960 games in total. The final conclusion is that a model which incorporates both the ideas of robustness and anchoring achieves statistically significant higher rewards and also maintains equivalent or faster solution speeds compared to existing approaches.     

Learning a generic 3D face model from 2D image databases using incremental Structure-from-Motion

Over the last decade 3D face models have been extensively used in many applications such as face recognition, facial animation and facial expression analysis. 3D Morphable Models (MMs) have become a popular tool to build and fit 3D face models to images. Critical to the success of MMs is the ability to build a generic 3D face model. Major limitations in the MMs building process are: (1) collecting 3D data usually involves the use of expensive laser scans and complex capture setups, (2) the number of available 3D databases is limited, and typically there is a lack of expression variability and (3) finding correspondences and registering the 3D model is a labor intensive and error prone process.     

Boundary-Conforming Discontinuous Galerkin Methods via Extensions from Subdomains

A new way of devising numerical methods is introduced whose distinctive feature is the computation of a finite element approximation only in a polyhedral subdomain D{\mathsf{D}} of the original, possibly curved-boundary domain. The technique is applied to a discontinuous Galerkin method for the one-dimensional diffusion-reaction problem. Sharp a priori error estimates are obtained which identify conditions, on the subdomain D{\mathsf{D}} and the discretization parameters of the discontinuous Galerkin method, under which the method maintains its original optimal convergence properties. The error analysis is new even in the case in which D=W{\mathsf{D}}=\Omega . It allows to see that the uniform error at any given interval is bounded by an interpolation error associated to the interval plus a significantly smaller error of a global nature. Numerical results confirming the sharpness of the theoretical results are displayed. Also, preliminary numerical results illustrating the application of the method to two-dimensional second-order elliptic problems are shown.     

Reasoning with graph constraints

Graph constraints were introduced in the area of graph transformation, in connection with the notion of (negative) application conditions, as a form to limit the applicability of transformation rules. However, we believe that graph constraints may also play a significant role in the area of visual software modelling or in the specification and verification of semi-structured documents or websites (i.e. HTML or XML sets of documents). In this sense, after some discussion on these application areas, we concentrate on the problem of how to prove the consistency of specifications based on this kind of constraints. In particular, we present proof rules for two classes of graph constraints and show that our proof rules are sound and (refutationally) complete for each class. In addition, we study clause subsumption in this context as a form to speed up refutation.     

Providing EAP-based Kerberos pre-authentication and advanced authorization for network federations

Kerberos is a well-known standard protocol which is becoming one of the most widely deployed for authentication and key distribution in application services. However, whereas service providers use the protocol to control their own subscribers, they do not widely deploy Kerberos infrastructures to handle subscribers coming from foreign domains, as happens in network federations. Instead, the deployment of Authentication, Authorization and Accounting (AAA) infrastructures has been preferred for that operation. Thus, the lack of a correct integration between these infrastructures and Kerberos limits the service access only to service provider's subscribers. To avoid this limitation, we design an architecture which integrates a Kerberos pre-authentication mechanism, based on the use of the Extensible Authentication Protocol (EAP), and advanced authorization, based on the standards SAML and XACML, to link the end user authentication and authorization performed through an AAA infrastructure with the delivery of Kerberos tickets in the service provider's domain. We detail the interfaces, protocols, operation and extensions required for our solution. Moreover, we discuss important aspects such as the implications on existing standards.     

Realistic real-time sound re-synthesis and processing for interactive virtual worlds

We present new GPU-based techniques for implementing linear digital filters for real-time audio processing. Our solution for recursive filters is the first presented in the literature. We demonstrate the relevance of these algorithms to computer graphics by synthesizing realistic sounds of colliding objects made of different materials, such as glass, plastic, and wood, in real time. The synthesized sounds can be parameterized by the object materials, velocities, and collision angles. Despite its flexibility, our approach uses very little memory, since it essentially requires a set of coefficients representing the impulse response of each material sound. Such features make our approach an attractive alternative to traditional CPU-based techniques that use playback of pre-recorded sounds.     

Real-time collaboration of virtual laboratories through the Internet

Web-based learning environments are becoming increasingly popular in higher education. One of the most important web-learning resources is the virtual laboratory (VL), which gives students an easy way for training and learning through the Internet. Moreover, on-line collaborative communication represents a practical method to transmit the knowledge and experience from the teacher to students overcoming physical distance and isolation. Considering these facts, the authors of this document have developed a new dynamic collaborative e-learning system which combines the main advantages of virtual laboratories and collaborative learning practices. In this system, the virtual laboratories are based on Java applets which have embedded simulations developed in Easy Java Simulations (EJS), an open-source tool for teachers who do not need complex programming skills. The collaborative e-learning is based on a real-time synchronized communication among these Java applets. Therefore, this original approach provides a new tool which integrates virtual laboratories inside a synchronous collaborative e-learning framework. This paper describes the main features of this system and its successful application in a distance education environment among different universities from Spain.     

Stability independent of delay using rational functions

This paper is concerned with the problem of assessing the stability of linear systems with a single time-delay. Stability analysis of linear systems with time-delays is complicated by the need to locate the roots of a transcendental characteristic equation. In this paper we show that a linear system with a single time-delay is stable independent of delay if and only if a certain rational function parameterized by an integer k and a positive real number T has only stable roots for any finite T≥0 and any k≥2. We then show how this stability result can be further simplified by analyzing the roots of an associated polynomial parameterized by a real number δ in the open interval (0,1). The paper is closed by showing counterexamples where stability of the roots of the rational function when k=1 is not sufficient for stability of the associated linear system with time-delay. We also introduce a variation of an existing frequency-sweeping necessary and sufficient condition for stability independent of delay which resembles the form of a generalized Nyquist criterion. The results are illustrated by numerical examples.