Lavinia Egidi

A lattice of classes of user-defined symbolic periodicities

User-defined calendars and periodicities are gaining an increasing relevance in AI and DB theory and applications. Thus several representation languages have been introduced to model them. Even focusing the attention on symbolic languages only, several different proposals can be chosen, and the comparisons between them are not trivial at all. In this paper, we propose a lattice of properties about periodicity and use it in order to classify different symbolic approaches in the literature. We then propose a language which covers all the properties in the lattice.

Bringing multimedia contents into MP3 files

The digital music revolution has improved the availability of music and made it easier to enjoy. The shift from hard support, such as audio CDs, to software leaves some unsatisfied by the loss of additional media contents, such as images, lyrics, and CD cover. We propose to fill the gap by enriching e-music with multimedia contents. Our proposal focuses specifically on MP3 as a widely distributed open format. The challenge we meet in enriching MP3 lies in maintaining audio compatibility and avoiding file size explosion. To this end, we define a description language to express multimedia contents in a textual way, with higher representation efficiency than existing languages. We also address security issues that arise from the use of an open format. Effectiveness is shown with an MP3 player capable of rendering multimedia contents.

Better spaced seeds using Quadratic Residues

Abstract Spaced seeds are used in approximate pattern matching algorithms to quickly discard regions where a match is not likely to occur. We propose a family of lossless spaced seeds based on Quadratic Residues modulo a prime number. Our seeds work with a threshold t > 1 in the sense that two regions are considered similar only if the seed hits t times within the regions. We prove that, for any number of errors, our seeds have an exponentially smaller probability of producing false positive matches than any traditional seed using a threshold t = 1 . To establish our result we introduce a formal notion of selectivity that generalizes the concept of seed weight, and we relate it to the minimum coverage and to a new structural property defined in terms on seed rotations. This groundwork will be useful for further analysis on seeds with threshold and we use it to provide improved bounds for approximate matching with 2 or 3 errors. Our results show that the use of a single seed with a threshold t > 1 should be considered as a possible alternative to single or multiple seeds with t = 1 .

Modelling a Secure Agent with Team Automata

We use Team Automata in order to model a protocol by Cachin et al. for securing agents in a hostile environment. Our study focuses on privacy properties of the agents. We use the framework to prove a result from the work by Cachin et al. As a by-product, our analysis gives some initial insight on the limits of the protocol. From a different perspective, this study continues a line of research on the expressive power and modelling capabilities of Team Automata. To the best of our knowledge, this is the first attempt to use Team Automata for the analysis of privacy properties.

Orthogonal Operators for User-Defined Symbolic Periodicities

We identify a set of orthogonal properties characterizing periodicities; based on these we define a lattice of classes (of periodicities). For each property, we introduce a language operator and, this way, we propose a family of symbolic languages, one for each subset of operators, one for each point in the lattice. So, the expressiveness and meaning of each operator, and thus of each language in the family, are clearly defined, and a user can select the language that exactly covers the properties of her domain. To the best of our knowledge, our language covering the top of the lattice (i.e., all of the properties) is more expressive than any other symbolic language in the AI and DB literature.

Hilbert function and complexity lower bounds for symmetric Boolean functions

This paper explores the application of certain algebraic geometry techniques involving Hilbert functions and Grobner bases to the analysis of properties of Boolean functions. It gives some results and applications for symmetric functions.

Spaced seeds design using perfect rulers

We consider the problem of lossless spaced seed design for approximate pattern matching. We show that, using mathematical objects known as perfect rulers, we can derive a family of spaced seeds for matching with up to two errors. We analyze these seeds with respect to the trade-off they offer between seed weight and the minimum length of the pattern to be matched. We prove that for patterns of length up to a few hundreds our seeds have a larger weight, hence a better filtration efficiency, than the ones known in the literature. In this context, we study in depth the specific case of Wichmann rulers and prove some preliminary results on the generalization of our approach to the larger class of unrestricted rulers.

From digital audiobook to secure digital multimedia-book

Portable devices and wireless connections are creating a new scenario in which digital information is entering our lives in a massive way. In this article we consider MP3 audiobook applications and propose an approach to completely restyle the applications to the current mobile and multimedia scenario. Our mechanism introduces multimedia contents (images and text) into the audiobook application and synchronizes them with the MP3 audio stream. Multimedia contents are protected by a security system that ensures perfect audio quality and full access to multimedia contents only to a legal user. A distribution architecture and a player that use the proposed mechanism are also presented.

A mathematical framework for the semantics of symbolic languages representing periodic time

In several areas, including Temporal DataBases (TDB), Presburger arithmetic has been chosen as a standard reference for the semantics of languages representing periodic time, and to study their expressiveness. On the other hand, the proposal of most symbolic languages in the AI literature has not been paired with an adequate semantic counterpart, making the task of studying the expressiveness of such languages and of comparing them a very complex one. In this paper, we first define a representation language which enables us to handle each temporal point as a complex object enriched with all the structure it is immersed in, and then we use it in order to provide a Presburger semantics for classes of symbolic languages coping with periodicity. Finally, we use the semantics to compare a few AI and TDB symbolic approaches.

A flexible approach to user-defined symbolic granularities in temporal databases

User-defined granularities, calendars and periodicities are gaining an increasing relevance in the area of temporal databases (TDB). In this paper, we discuss the advantages of adopting for TDBs a modular framework, based on a family of symbolic languages, defined starting from a set of mutually orthogonal properties that characterize periodicity. First, we show that one of the languages covers the notion of granularity (as defined in the TDB glossary), so that it can be used in order to define validity times of facts in a TDB. Second, we discuss the usefulness of using more expressive languages in the family to achieve such a goal. Third, we explore how such languages can be used in order to deal in an intensional way with infinite periodic data in temporal (relational) databases.