Discrete series representations and K multiplicities for U(p,q). User's guide

This document is a companion for the Maple program : Discrete series and K-types for U(p,q) available on:http://www.math.jussieu.fr/~vergne We explain an algorithm to compute the multiplicities of an irreducible representation of U(p)x U(q) in a discrete series of U(p,q). It is based on Blattner's formula. We recall the general mathematical background to compute Kostant partition functions via multidimensional residues, and we outline our algorithm. We also point out some properties of the piecewise polynomial functions describing multiplicities based on Paradan's results.Comment: 51 page

Flow polytopes of signed graphs and the Kostant partition function

We establish the relationship between volumes of flow polytopes associated to signed graphs and the Kostant partition function. A special case of this relationship, namely, when the graphs are signless, has been studied in detail by Baldoni and Vergne using techniques of residues. In contrast with their approach, we provide entirely combinatorial proofs inspired by the work of Postnikov and Stanley on flow polytopes. As a fascinating special family of flow polytopes, we study the Chan-Robbins-Yuen polytopes. Motivated by the beautiful volume formula $\prod_{k=1}^{n-2} Cat(k)$ for the type $A_n$ version, where $Cat(k)$ is the $k$th Catalan number, we introduce type $C_{n+1}$ and $D_{n+1}$ Chan-Robbins-Yuen polytopes along with intriguing conjectures pertaining to their properties.Comment: 29 pages, 13 figure

Multiple Bernoulli series and volumes of moduli spaces of flat bundles over surfaces

Using Szenes formula for multiple Bernoulli series we explain how to compute Witten series associated to classical Lie algebras. Particular instances of these series compute volumes of moduli spaces of flat bundles over surfaces, and also certain multiple zeta values.Comment: 51 pages, 3 figures; formula in Proposition 3.1 for the Lie group of type G_2 is corrected; new references adde

Extend Commitment Protocols with Temporal Regulations: Why and How

The proposal of Elisa Marengo's thesis is to extend commitment protocols to explicitly account for temporal regulations. This extension will satisfy two needs: (1) it will allow representing, in a flexible and modular way, temporal regulations with a normative force, posed on the interaction, so as to represent conventions, laws and suchlike; (2) it will allow committing to complex conditions, which describe not only what will be achieved but to some extent also how. These two aspects will be deeply investigated in the proposal of a unified framework, which is part of the ongoing work and will be included in the thesis.Comment: Proceedings of the Doctoral Consortium and Poster Session of the 5th International Symposium on Rules (RuleML 2011@IJCAI), pages 1-8 (arXiv:1107.1686

Investigating the Cost of Anonymity on Dynamic Networks

In this paper we study the difficulty of counting nodes in a synchronous dynamic network where nodes share the same identifier, they communicate by using a broadcast with unlimited bandwidth and, at each synchronous round, network topology may change. To count in such setting, it has been shown that the presence of a leader is necessary. We focus on a particularly interesting subset of dynamic networks, namely \textit{Persistent Distance} - ${\cal G}($PD$)_{h}$, in which each node has a fixed distance from the leader across rounds and such distance is at most $h$. In these networks the dynamic diameter $D$ is at most $2h$. We prove the number of rounds for counting in ${\cal G}($PD$)_{2}$ is at least logarithmic with respect to the network size $|V|$. Thanks to this result, we show that counting on any dynamic anonymous network with $D$ constant w.r.t. $|V|$ takes at least $D+ \Omega(\text{log}\, |V| )$ rounds where $\Omega(\text{log}\, |V|)$ represents the additional cost to be payed for handling anonymity. At the best of our knowledge this is the fist non trivial, i.e. different from $\Omega(D)$, lower bounds on counting in anonymous interval connected networks with broadcast and unlimited bandwith

A Blockchain-Based Solution for Enabling Log-Based Resolution of Disputes in Multi-party Transactions

We are witnessing an ongoing global trend towards the automation of almost any transaction through the employment of some Internet-based mean. Furthermore, the large spread of cloud computing and the massive emergence of the software as a service (Saas) paradigm have unveiled many opportunities to combine distinct services, provided by different parties, to establish higher level and more advanced services, that can be offered to end users and enterprises. Business-to-business (B2B) integration and third-party authorization (i.e. using standards like OAuth) are examples of processes requiring more parties to interact with each other to deliver some desired functionality. These kinds of interactions mostly consist of transactions and are usually regulated by some agreement which defines the obligations that involved parties have to comply with. In case one of the parties claims a violation of some clause of such agreement, disputes can occur if the party accused of the infraction refuses to recognize its fault. Moreover, in case of auditing, for convenience reasons a party may deny to have taken part in a given transaction, or may forge historical records related to that transaction. Solutions based on a trusted third party (TTP) have drawbacks: high overhead due to the involvement of an additional party, possible fees to pay for each transaction, and the risks stemming from having to blindly trust another party. If it were possible to only base on transaction logs to sort disputes out, then it would be feasible to get rid of any TTP and related shortcomings. In this paper we propose SLAVE, a blockchain-based solution which does not require any TTP. Storing transactions in a public blockchain like Bitcoin’s or Ethereum’s provides strong guarantees on transactions’ integrity, hence they can be actually used as proofs when controversies arise. The solution we propose defines how to embed transaction logs in a public blockchain, so that each involved party can verify the identity of the others while keeping confident the content of transactions

Survey of Machine Learning Techniques for Malware Analysis

Coping with malware is getting more and more challenging, given their relentless growth in complexity and volume. One of the most common approaches in literature is using machine learning techniques, to automatically learn models and patterns behind such complexity, and to develop technologies for keeping pace with the speed of development of novel malware. This survey aims at providing an overview on the way machine learning has been used so far in the context of malware analysis. We systematize surveyed papers according to their objectives (i.e., the expected output, what the analysis aims to), what information about malware they specifically use (i.e., the features), and what machine learning techniques they employ (i.e., what algorithm is used to process the input and produce the output). We also outline a number of problems concerning the datasets used in considered works, and finally introduce the novel concept of malware analysis economics, regarding the study of existing tradeoffs among key metrics, such as analysis accuracy and economical costs