Conformal group with two observer independent scales

The Poincar\'e sector of a recently deformed conformal algebra is proposed to describe, after the identification of the deformation parameter with the Planck length, the symmetries of a new relativistic theory with two observer-independent scales (or DSR theory). Also a new non-commutative space-time is proposed. It is found that momentum space exhibits the same features of the DSR proposals preserving Lorentz invariance in a deformed way. The space-time sector is a generalization of the well known non-commutative $\kappa$-Minkowski space-time which however does not preserve Lorentz invariance, not even in the deformed sense. It is shown that this behavior could be expected in some attempts to construct DSR theories starting from the Poincar\'e sector of a deformed symmetry larger than Poincar\'e symmetry, unless one takes a variable Planck length. It is also shown that the formalism can be useful in analyzing the role of quantum deformations in the ``AdS-CFT correspondence".Comment: 3 pages, brief summary of a talk given at the Tenth Marcel Grossmann Meeting, Rio de Janeiro, 2003, based on results previously obtained in hep-th/0306089 and hep-th/030503

Valuing Coupon Bond Linked to Variable Interest Rate

The paper analyses coupon bonds linked to variable interest rate in a contingent claim approach such that it can be decomposed in elementary options on interest rate and options to default. It is considered the case of continuous arithmetic average of interest rate in a simple capitalization to value the variable coupon paid by the bonds at maturity. The paper determines the expected interest rate on the bonds and the risk spread due to the default risk.Contingent claim, Asian option, Stochastic continuous process

On Optimally Partitioning Variable-Byte Codes

The ubiquitous Variable-Byte encoding is one of the fastest compressed representation for integer sequences. However, its compression ratio is usually not competitive with other more sophisticated encoders, especially when the integers to be compressed are small that is the typical case for inverted indexes. This paper shows that the compression ratio of Variable-Byte can be improved by 2x by adopting a partitioned representation of the inverted lists. This makes Variable-Byte surprisingly competitive in space with the best bit-aligned encoders, hence disproving the folklore belief that Variable-Byte is space-inefficient for inverted index compression. Despite the significant space savings, we show that our optimization almost comes for free, given that: we introduce an optimal partitioning algorithm that does not affect indexing time because of its linear-time complexity; we show that the query processing speed of Variable-Byte is preserved, with an extensive experimental analysis and comparison with several other state-of-the-art encoders.Comment: Published in IEEE Transactions on Knowledge and Data Engineering (TKDE), 15 April 201

Questioning and responding in Italian

Questions are design problems for both the questioner and the addressee. They must be produced as recognizable objects and must be comprehended by taking into account the context in which they occur and the local situated interests of the participants. This paper investigates how people do ‘questioning’ and ‘responding’ in Italian ordinary conversations. I focus on the features of both questions and responses. I first discuss formal linguistic features that are peculiar to questions in terms of intonation contours (e.g. final rise), morphology (e.g. tags and question words) and syntax (e.g. inversion). I then show additional features that characterize their actual implementation in conversation such as their minimality (often the subject or the verb is only implied) and the usual occurrence of speaker gaze towards the recipient during questions. I then look at which social actions (e.g. requests for information, requests for confirmation) the different question types implement and which responses are regularly produced in return. The data shows that previous descriptions of “interrogative markings” are neither adequate nor sufficient to comprehend the actual use of questions in natural conversation

Handling Massive N-Gram Datasets Efficiently

This paper deals with the two fundamental problems concerning the handling of large n-gram language models: indexing, that is compressing the n-gram strings and associated satellite data without compromising their retrieval speed; and estimation, that is computing the probability distribution of the strings from a large textual source. Regarding the problem of indexing, we describe compressed, exact and lossless data structures that achieve, at the same time, high space reductions and no time degradation with respect to state-of-the-art solutions and related software packages. In particular, we present a compressed trie data structure in which each word following a context of fixed length k, i.e., its preceding k words, is encoded as an integer whose value is proportional to the number of words that follow such context. Since the number of words following a given context is typically very small in natural languages, we lower the space of representation to compression levels that were never achieved before. Despite the significant savings in space, our technique introduces a negligible penalty at query time. Regarding the problem of estimation, we present a novel algorithm for estimating modified Kneser-Ney language models, that have emerged as the de-facto choice for language modeling in both academia and industry, thanks to their relatively low perplexity performance. Estimating such models from large textual sources poses the challenge of devising algorithms that make a parsimonious use of the disk. The state-of-the-art algorithm uses three sorting steps in external memory: we show an improved construction that requires only one sorting step thanks to exploiting the properties of the extracted n-gram strings. With an extensive experimental analysis performed on billions of n-grams, we show an average improvement of 4.5X on the total running time of the state-of-the-art approach.Comment: Published in ACM Transactions on Information Systems (TOIS), February 2019, Article No: 2

On optimally partitioning a text to improve its compression

In this paper we investigate the problem of partitioning an input string T in such a way that compressing individually its parts via a base-compressor C gets a compressed output that is shorter than applying C over the entire T at once. This problem was introduced in the context of table compression, and then further elaborated and extended to strings and trees. Unfortunately, the literature offers poor solutions: namely, we know either a cubic-time algorithm for computing the optimal partition based on dynamic programming, or few heuristics that do not guarantee any bounds on the efficacy of their computed partition, or algorithms that are efficient but work in some specific scenarios (such as the Burrows-Wheeler Transform) and achieve compression performance that might be worse than the optimal-partitioning by a $\Omega(\sqrt{\log n})$ factor. Therefore, computing efficiently the optimal solution is still open. In this paper we provide the first algorithm which is guaranteed to compute in O(n \log_{1+\eps}n) time a partition of T whose compressed output is guaranteed to be no more than $(1+\epsilon)$-worse the optimal one, where $\epsilon$ may be any positive constant