Derived equivalences and sl_2-categorifications for U_q(gl_n)

We give a construction of sl_2-categorifications (in the sense of Chuang-Rouquier) for representations of U_q(gl_n), for generic q and for q a root of unity.Comment: 15 pages, references added, exposition streamlined, all comments welcom

Anonymity and Information Hiding in Multiagent Systems

We provide a framework for reasoning about information-hiding requirements in multiagent systems and for reasoning about anonymity in particular. Our framework employs the modal logic of knowledge within the context of the runs and systems framework, much in the spirit of our earlier work on secrecy [Halpern and O'Neill 2002]. We give several definitions of anonymity with respect to agents, actions, and observers in multiagent systems, and we relate our definitions of anonymity to other definitions of information hiding, such as secrecy. We also give probabilistic definitions of anonymity that are able to quantify an observer s uncertainty about the state of the system. Finally, we relate our definitions of anonymity to other formalizations of anonymity and information hiding, including definitions of anonymity in the process algebra CSP and definitions of information hiding using function views.Comment: Replacement. 36 pages. Full version of CSFW '03 paper, submitted to JCS. Made substantial changes to Section 6; added references throughou

CENTURION: Incentivizing Multi-Requester Mobile Crowd Sensing

The recent proliferation of increasingly capable mobile devices has given rise to mobile crowd sensing (MCS) systems that outsource the collection of sensory data to a crowd of participating workers that carry various mobile devices. Aware of the paramount importance of effectively incentivizing participation in such systems, the research community has proposed a wide variety of incentive mechanisms. However, different from most of these existing mechanisms which assume the existence of only one data requester, we consider MCS systems with multiple data requesters, which are actually more common in practice. Specifically, our incentive mechanism is based on double auction, and is able to stimulate the participation of both data requesters and workers. In real practice, the incentive mechanism is typically not an isolated module, but interacts with the data aggregation mechanism that aggregates workers' data. For this reason, we propose CENTURION, a novel integrated framework for multi-requester MCS systems, consisting of the aforementioned incentive and data aggregation mechanism. CENTURION's incentive mechanism satisfies truthfulness, individual rationality, computational efficiency, as well as guaranteeing non-negative social welfare, and its data aggregation mechanism generates highly accurate aggregated results. The desirable properties of CENTURION are validated through both theoretical analysis and extensive simulations

Learning to Optimize Computational Resources: Frugal Training with Generalization Guarantees

Algorithms typically come with tunable parameters that have a considerable impact on the computational resources they consume. Too often, practitioners must hand-tune the parameters, a tedious and error-prone task. A recent line of research provides algorithms that return nearly-optimal parameters from within a finite set. These algorithms can be used when the parameter space is infinite by providing as input a random sample of parameters. This data-independent discretization, however, might miss pockets of nearly-optimal parameters: prior research has presented scenarios where the only viable parameters lie within an arbitrarily small region. We provide an algorithm that learns a finite set of promising parameters from within an infinite set. Our algorithm can help compile a configuration portfolio, or it can be used to select the input to a configuration algorithm for finite parameter spaces. Our approach applies to any configuration problem that satisfies a simple yet ubiquitous structure: the algorithm's performance is a piecewise constant function of its parameters. Prior research has exhibited this structure in domains from integer programming to clustering

Extension of Bernstein Polynomials to Infinite Dimensional Case

The purpose of this paper is to study some new concrete approximation processes for continuous vector-valued mappings defined on the infinite dimensional cube or on a subset of a real Hilbert space. In both cases these operators are modelled on classical Bernstein polynomials and represent a possible extension to an infinite dimensional setting. The same idea is generalized to obtain from a given approximation process for function defined on a real interval a new approximation process for vector-valued mappings defined on subsets of a real Hilbert space.Comment: 14 pages. to appear on Journal of Approximation Theor

Holomorphic automorphic forms and cohomology

We investigate the correspondence between holomorphic automorphic forms on the upper half-plane with complex weight and parabolic cocycles. For integral weights at least 2 this correspondence is given by the Eichler integral. Knopp generalized this to real weights. We show that for weights that are not an integer at least 2 the generalized Eichler integral gives an injection into the first cohomology group with values in a module of holomorphic functions, and characterize the image. We impose no condition on the growth of the automorphic forms at the cusps. For real weights that are not an integer at least 2 we similarly characterize the space of cusp forms and the space of entire automorphic forms. We give a relation between the cohomology classes attached to holomorphic automorphic forms of real weight and the existence of harmonic lifts. A tool in establishing these results is the relation to cohomology groups with values in modules of "analytic boundary germs", which are represented by harmonic functions on subsets of the upper half-plane. Even for positive integral weights cohomology with these coefficients can distinguish all holomorphic automorphic forms, unlike the classical Eichler theory.Comment: 150 pages. An earlier version appeared as an Oberwolfach Preprint (OWP 2014-07