arXiv subjects

Filippo Mignosi

Publications and source records attributed to Filippo Mignosi.

11 recordsLinked to original sources

arXiv2026

Explaining Neural Networks in Preference Learning: a Post-hoc Inductive Logic Programming Approach

In this paper, we propose using Learning from Answer Sets to approximate black-box models, such as Neural Networks (NN), in the specific case of learning user preferences. We specifically explore the use of ILASP (Inductive Learning of Answer Set Programs) to approximate preference learning systems through weak constraints. We have created a dataset on user preferences over a set of recipes, which is used to train the NNs that we aim to approximate with ILASP. Our experiments investigate ILASP both as a global and a local approximator of the NNs. These experiments address the challenge of approximating NNs working on increasingly high-dimensional feature spaces while achieving appropriate fidelity on the target model and limiting the increase in computational time. To handle this challenge, we propose a preprocessing step that exploits Principal Component Analysis to reduce the dataset's dimensionality while keeping our explanations transparent. Under consideration for publication in Theory and Practice of Logic Programming (TPLP).

cs.AI↗

arXiv2023

On the $k$-Hamming and $k$-Edit Distances

In this paper we consider the weighted $k$-Hamming and $k$-Edit distances, that are natural generalizations of the classical Hamming and Edit distances. As main results of this paper we prove that for any $k\geq 2$ the DECIS-$k$-Hamming problem is $\mathbb{P}$-SPACE-complete and the DECIS-$k$-Edit problem is NEXPTIME-complete.

cs.CC↗

arXiv2022

Ensemble CNN and Uncertainty Modeling to Improve Automatic Identification/Segmentation of Multiple Sclerosis Lesions in Magnetic Resonance Imaging

To date, several automated strategies for identification/segmentation of Multiple Sclerosis (MS) lesions with the use of Magnetic Resonance Imaging (MRI) have been presented, but they are outperformed by human experts, from whom they act very differently. This is mainly due to: the ambiguity originated by MRI instabilities; peculiar variability of MS; non specificity of MRI regarding MS. Physicians partially manage the uncertainty generated by ambiguity relying on radiological/clinical/anatomical background and experience. To emulate human diagnosis, we present an automated framework for identification/segmentation of MS lesions from MRI based on three pivotal concepts: 1. the modelling of uncertainty; 2. the proposal of two, separately trained, CNN, one optimized for lesions and the other for lesions with respect to the environment surrounding them, respectively repeated for axial, coronal and sagittal directions; 3. the definition of an ensemble classifier to merge the information collected by different CNN. The proposed framework is trained, validated and tested on the 2016 MSSEG benchmark public data set from a single imaging modality, the FLuid-Attenuated Inversion Recovery (FLAIR). The comparison with the ground-truth and with each of 7 human raters, proves that there is no significant difference between the automated and the human raters.

eess.IV↗

arXiv2021

A Service for Supporting Digital and Immersive Cultural Experiences

Cultural heritage sites in Italy typically attract a large number of tourists every year. However, the lack of support for i) locating contents of interest; ii) discovering information on specific contents; and iii) ease of navigation within the heritage site; hinders the overall experience of the visitor. To this end, in this work, we present a Digital Object Space Management service developed as a part of the VASARI project. The service generates a digital twin (with 3D visualization) of a given cultural heritage site and further provides support for navigation and localization, thereby providing an immersive cultural experience to the visitor.

cs.CY↗

arXiv2020

Entropy and Compression: A simple proof of an inequality of Khinchin-Ornstein-Shields

This paper concerns the folklore statement that ``entropy is a lower bound for compression''. More precisely we derive from the entropy theorem a simple proof of a pointwise inequality firstly stated by Ornstein and Shields and which is the almost-sure version of an average inequality firstly stated by Khinchin in 1953. We further give an elementary proof of original Khinchin inequality that can be used as an exercise for Information Theory students and we conclude by giving historical and technical notes of such inequality.

cs.IT↗

arXiv2017

Abelian-Square-Rich Words

An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain at most $Θ(n^2)$ distinct factors, and there exist words of length $n$ containing $Θ(n^2)$ distinct abelian-square factors, that is, distinct factors that are abelian squares. This motivates us to study infinite words such that the number of distinct abelian-square factors of length $n$ grows quadratically with $n$. More precisely, we say that an infinite word $w$ is {\it abelian-square-rich} if, for every $n$, every factor of $w$ of length $n$ contains, on average, a number of distinct abelian-square factors that is quadratic in $n$; and {\it uniformly abelian-square-rich} if every factor of $w$ contains a number of distinct abelian-square factors that is proportional to the square of its length. Of course, if a word is uniformly abelian-square-rich, then it is abelian-square-rich, but we show that the converse is not true in general. We prove that the Thue-Morse word is uniformly abelian-square-rich and that the function counting the number of distinct abelian-square factors of length $2n$ of the Thue-Morse word is $2$-regular. As for Sturmian words, we prove that a Sturmian word $s_α$ of angle $α$ is uniformly abelian-square-rich if and only if the irrational $α$ has bounded partial quotients, that is, if and only if $s_α$ has bounded exponent.

cs.DM↗

arXiv2016

Abelian Powers and Repetitions in Sturmian Words

Richomme, Saari and Zamboni (J. Lond. Math. Soc. 83: 79-95, 2011) proved that at every position of a Sturmian word starts an abelian power of exponent $k$ for every $k > 0$. We improve on this result by studying the maximum exponents of abelian powers and abelian repetitions (an abelian repetition is an analogue of a fractional power) in Sturmian words. We give a formula for computing the maximum exponent of an abelian power of abelian period $m$ starting at a given position in any Sturmian word of rotation angle $α$. vAs an analogue of the critical exponent, we introduce the abelian critical exponent $A(s_α)$ of a Sturmian word $s_α$ of angle $α$ as the quantity $A(s_α) = limsup\ k_{m}/m=limsup\ k'_{m}/m$, where $k_{m}$ (resp. $k'_{m}$) denotes the maximum exponent of an abelian power (resp.~of an abelian repetition) of abelian period $m$ (the superior limits coincide for Sturmian words). We show that $A(s_α)$ equals the Lagrange constant of the number $α$. This yields a formula for computing $A(s_α)$ in terms of the partial quotients of the continued fraction expansion of $α$. Using this formula, we prove that $A(s_α) \geq \sqrt{5}$ and that the equality holds for the Fibonacci word. We further prove that $A(s_α)$ is finite if and only if $α$ has bounded partial quotients, that is, if and only if $s_α$ is $β$-power-free for some real number $β$. Concerning the infinite Fibonacci word, we prove that: i) The longest prefix that is an abelian repetition of period $F_j$, $j>1$, has length $F_j( F_{j+1}+F_{j-1} +1)-2$ if $j$ is even or $F_j( F_{j+1}+F_{j-1} )-2$ if $j$ is odd, where $F_{j}$ is the $j$th Fibonacci number; ii) The minimum abelian period of any factor is a Fibonacci number. Further, we derive a formula for the minimum abelian periods of the finite Fibonacci words

math.CO↗

arXiv2015

Words with the Maximum Number of Abelian Squares

An abelian square is the concatenation of two words that are anagrams of one another. A word of length $n$ can contain $Θ(n^2)$ distinct factors that are abelian squares. We study infinite words such that the number of abelian square factors of length $n$ grows quadratically with $n$.

cs.DM↗

arXiv2013

Abelian Repetitions in Sturmian Words

We investigate abelian repetitions in Sturmian words. We exploit a bijection between factors of Sturmian words and subintervals of the unitary segment that allows us to study the periods of abelian repetitions by using classical results of elementary Number Theory. We prove that in any Sturmian word the superior limit of the ratio between the maximal exponent of an abelian repetition of period $m$ and $m$ is a number $\geq\sqrt{5}$, and the equality holds for the Fibonacci infinite word. We further prove that the longest prefix of the Fibonacci infinite word that is an abelian repetition of period $F_j$, $j>1$, has length $F_j(F_{j+1}+F_{j-1} +1)-2$ if $j$ is even or $F_j(F_{j+1}+F_{j-1})-2$ if $j$ is odd. This allows us to give an exact formula for the smallest abelian periods of the Fibonacci finite words. More precisely, we prove that for $j\geq 3$, the Fibonacci word $f_j$ has abelian period equal to $F_n$, where $n = \lfloor{j/2}\rfloor$ if $j = 0, 1, 2\mod{4}$, or $n = 1 + \lfloor{j/2}\rfloor$ if $ j = 3\mod{4}$.

cs.FL↗

arXiv2012

Note on the Greedy Parsing Optimality for Dictionary-Based Text Compression

Dynamic dictionary-based compression schemes are the most daily used data compression schemes since they appeared in the foundational papers of Ziv and Lempel in 1977, commonly referred to as LZ77. Their work is the base of Deflate, gZip, WinZip, 7Zip and many others compression software. All of those compression schemes use variants of the greedy approach to parse the text into dictionary phrases. Greedy parsing optimality was proved by Cohn et al. (1996) for fixed length code and unbounded dictionaries. The optimality of the greedy parsing was never proved for bounded size dictionary which actually all of those schemes require. We define the suffix-closed property for dynamic dictionaries and we show that any LZ77-based dictionary, including the bounded variants, satisfy this property. Under this condition we prove the optimality of the greedy parsing as a variant of the proof by Cohn et al.

cs.DS↗

arXiv2012

The Rightmost Equal-Cost Position Problem

LZ77-based compression schemes compress the input text by replacing factors in the text with an encoded reference to a previous occurrence formed by the couple (length, offset). For a given factor, the smallest is the offset, the smallest is the resulting compression ratio. This is optimally achieved by using the rightmost occurrence of a factor in the previous text. Given a cost function, for instance the minimum number of bits used to represent an integer, we define the Rightmost Equal-Cost Position (REP) problem as the problem of finding one of the occurrences of a factor which cost is equal to the cost of the rightmost one. We present the Multi-Layer Suffix Tree data structure that, for a text of length n, at any time i, it provides REP(LPF) in constant time, where LPF is the longest previous factor, i.e. the greedy phrase, a reference to the list of REP({set of prefixes of LPF}) in constant time and REP(p) in time O(|p| log log n) for any given pattern p.

cs.DS↗