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.     

Optimization of biochemical systems through mathematical programming: Methods and applications

In this work we present a general (mono and multiobjective) optimization framework for the technological improvement of biochemical systems. The starting point of the method is a mathematical model in ordinary differential equations (ODEs) of the investigated system, based on qualitative biological knowledge and quantitative experimental data. In the method we take advantage of the special structural features of a family of ODEs called power-law models to reduce the computational complexity of the optimization program. In this way, the genetic manipulation of a biochemical system to meet a certain biotechnological goal can be expressed as an optimization program with some desired properties such as linearity or convexity.The general method of optimization is presented and discussed in its linear and geometric programming versions. We furthermore illustrate the use of the method by several real case studies. We conclude that the technological improvement of microorganisms can be afforded using the combination of mathematical modelling and optimization. The systematic nature of this approach facilitates the redesign of biochemical systems and makes this a predictive exercise rather than a trial-and-error procedure.     

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.     

Sensor data integration for indoor human tracking

A human tracking system based on the integration of the measurements from an inertial motion capture system and a UWB (Ultra-Wide Band) location system has been developed. On the one hand, the rotational measurements from the inertial system are used to track precisely all limbs of the body of the human. On the other hand, the translational measurements from both systems are combined by three different fusion algorithms (a Kalman filter, a particle filter and a combination of both) in order to obtain a precise global localization of the human in the environment. Several experiments have been performed to compare their accuracy and computational efficiency.     

Line planning on tree networks with applications to the Quito Trolebús system

We discuss an optimization model for the line planning problem in public transport in order to minimize operation costs while guaranteeing a certain level of quality of service, in terms of available transport capacity. We analyze the computational complexity of this problem for tree network topologies as well as several categories of line operations that are important for the Quito Trolebús system. In practice, these instances can be solved quite well, and significant optimization potentials can be demonstrated.     

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.