Sublinear DTD Validity

International audienceWe present an efficient algorithm for testing approximate DTD validity modulo the strong tree edit distance. Our algorithm inspects XML documents in a probabilistic manner. It detects with high probability the nonvalidity of XML documents with a large fraction of errors, measured in terms of the strong tree edit distance from the DTD. The run time depends polynomially on the depth of the XML document tree but not on its size, so that it is sublinear in most cases. Therefore, our algorithm can be used to speed up exact DTD validators that run in linear time. We also prove a negative result showing that the run time of any approximate DTD validity tester must depend on the depth of the input tree. A long version is available here.</p

Streaming Property Testing of Visibly Pushdown Languages

In the context of language recognition, we demonstrate the superiority of streaming property testers against streaming algorithms and property testers, when they are not combined. Initiated by Feigenbaum et al., a streaming property tester is a streaming algorithm recognizing a language under the property testing approximation: it must distinguish inputs of the language from those that are $\varepsilon$-far from it, while using the smallest possible memory (rather than limiting its number of input queries). Our main result is a streaming $\varepsilon$-property tester for visibly pushdown languages (VPL) with one-sided error using memory space $\mathrm{poly}((\log n) / \varepsilon)$. This constructions relies on a (non-streaming) property tester for weighted regular languages based on a previous tester by Alon et al. We provide a simple application of this tester for streaming testing special cases of instances of VPL that are already hard for both streaming algorithms and property testers. Our main algorithm is a combination of an original simulation of visibly pushdown automata using a stack with small height but possible items of linear size. In a second step, those items are replaced by small sketches. Those sketches relies on a notion of suffix-sampling we introduce. This sampling is the key idea connecting our streaming tester algorithm to property testers.Comment: 23 pages. Major modifications in the presentatio

Optimizing ADMM and Over-Relaxed ADMM Parameters for Linear Quadratic Problems

The Alternating Direction Method of Multipliers (ADMM) has gained significant attention across a broad spectrum of machine learning applications. Incorporating the over-relaxation technique shows potential for enhancing the convergence rate of ADMM. However, determining optimal algorithmic parameters, including both the associated penalty and relaxation parameters, often relies on empirical approaches tailored to specific problem domains and contextual scenarios. Incorrect parameter selection can significantly hinder ADMM's convergence rate. To address this challenge, in this paper we first propose a general approach to optimize the value of penalty parameter, followed by a novel closed-form formula to compute the optimal relaxation parameter in the context of linear quadratic problems (LQPs). We then experimentally validate our parameter selection methods through random instantiations and diverse imaging applications, encompassing diffeomorphic image registration, image deblurring, and MRI reconstruction.Comment: Accepted to AAAI 202

Streaming Property Testing of Visibly Pushdown Languages

In the context of formal language recognition, we demonstrate the superiority of streaming property testers against streaming algorithms and property testers, when they are not combined. Initiated by Feigenbaum et al., a streaming property tester is a streaming algorithm recognizing a language under the property testing approximation: it must distinguish inputs of the language from those that are eps-far from it, while using the smallest possible memory (rather than limiting its number of input queries). Our main result is a streaming eps-property tester for visibly pushdown languages (V_{PL}) with memory space poly(log n /epsilon). Our construction is done in three steps. First, we simulate a visibly pushdown automaton in one pass using a stack of small height but whose items can be of linear size. In a second step, those items are replaced by small sketches. Those sketches rely on a notion of suffix-sampling we introduce. This sampling is the key idea for taking benefit of both streaming algorithms and property testers in the third step. Indeed, the last step relies on a (non-streaming) property tester for weighted regular languages based on a previous tester by Alon et al. This tester can directly be used for streaming testing special cases of instances of V_{PL} that are already hard for both streaming algorithms and property testers. We then use it to decide the correctness of completed items, given their sketches, before removing them from the stack

Language and Automata Theory and Applications

International audienc

Optimizing ADMM and Over-Relaxed ADMM Parameters for Linear Quadratic Problems

The Alternating Direction Method of Multipliers (ADMM) has gained significant attention across a broad spectrum of machine learning applications. Incorporating the over-relaxation technique shows potential for enhancing the convergence rate of ADMM. However, determining optimal algorithmic parameters, including both the associated penalty and relaxation parameters, often relies on empirical approaches tailored to specific problem domains and contextual scenarios. Incorrect parameter selection can significantly hinder ADMM's convergence rate. To address this challenge, in this paper we first propose a general approach to optimize the value of penalty parameter, followed by a novel closed-form formula to compute the optimal relaxation parameter in the context of linear quadratic problems (LQPs). We then experimentally validate our parameter selection methods through random instantiations and diverse imaging applications, encompassing diffeomorphic image registration, image deblurring, and MRI reconstruction

Fluctuations effects in population genetics and in protein translation

This thesis is an investigation of the effects of fluctuations in some problems at the interface between statistical physics and biology. In the first chapter we introduce Langevin equations with multiplicative noise, by focusing, in particular, on a generic power-law amplitude of the noise. This equation, depending on the noise exponent (i.e., on the character of the fluctuations), encompasses many known stochastic systems, and we show that the absorbing properties of the boundaries strongly depend on this exponent. The second chapter investigates the role of fluctuations in population genetics, which describes how the biodiversity and the composition of a population evolve in time due to the action of evolutionary forces. In the absence of mutations, every population constituted by a finite number of individuals will eventually lose its biodiversity through a process called fixation. We show that, if the evolutionary force known as balancing selection acts on a subdivided population, the mean time to fixation as a function of the migration rate develops a nonmonotonicity. Furthermore our analysis predicts, in the limit of infinitely many subpopulations, a transition between a phase characterized by the presence of biodiversity in the total population and a phase characterized by its absence. The third chapter deals with the role of fluctuations in protein translation, a crucial and only partly understood step in gene expression and one of the most common biochemical reactions occurring in the cell: the individual triplets of nucleotides (the codons) composing a messenger RNA (mRNA) are translated into amino acids (the units composing the proteins) by the ribosomes. More in detail we address an intriguing question concerning the binding time distribution, i.e., the distribution of the time intervals needed by the ribosome to bind with a transport RNA (tRNA) charged with the correct amino acid. We provide an analytic estimate for this distribution, which deviates from the exponential distribution expected in the absence of fluctuations in the number of charged tRNAs around the ribosome

Property Testing of Regular Languages with Applications to Streaming Property Testing of Visibly Pushdown Languages

In this work, we revisit the problem of testing membership in regular languages, first studied by Alon et al. [Alon et al., 2001]. We develop a one-sided error property tester for regular languages under weighted edit distance that makes ?(?^{-1} log(1/?)) non-adaptive queries, assuming that the language is described by an automaton of constant size. Moreover, we show a matching lower bound, essentially closing the problem for the edit distance. As an application, we improve the space bound of the current best streaming property testing algorithm for visibly pushdown languages from ?(?^{-4} log? n) to ?(?^{-3} log? n log log n), where n is the size of the input. Finally, we provide a ?(max(?^{-1}, log n)) lower bound on the memory necessary to test visibly pushdown languages in the streaming model, significantly narrowing the gap between the known bounds

ANALISI NUMERICA DELLA FISICA DELLA PROPULSIONE A RAZZO IBRIDA

L’obiettivo di questo studio è quello di investigare la fisica della combustione dei razzi ibridi tramite simulationi RANS compiute da un software CFD commerciale (Ansys Fluent), in particolare il ruolo della densità nella determinazione della velocità di regressione dei combustibili solidi. Nonostante questa tecnologia abbia compiuto passi importanti nelle ultime decadi, molti aspetti sono ancora poco compresi. Da qui la necessità di condurre una serie di esperimenti virtuali, prima per assicurarsi della validità dei modelli matematici impiegati, poi per estrapolare dai dati interessanti spunti riguardo la fisica sottostante il fenomeno in questione. L’abilità di determinare, anche solo qualitativamente, quale caratteristica del carburante influisca sul funzionamento dell’intero sistema potrebbe indirizzare gli sforzi dei ricercatori in comprendere meglio la fisica o l’industria a cercare nuovi ed efficienti carburanti. Tre tipi di esperimenti sono stati portati a termine: simulazioni a freddo isoterme, non-isoterme e con combustione. Nelle prime due l’idea che la densità della specie chimica iniettata possa avere un’influenza sul comportamento dello strato limite è stata investigata in un caso semplificato. Dopo aver ottenuto una buona comprensione dell’effetto, si è proceduto ad impostare delle simulazioni di veri razzi ibridi per comparare i risultati dei casi con combustione con le predizioni di quelli semplificati. La validazione delle prime due simulazioni è stata condotta su dati sperimentali e numerici forniti da Prokein e Wolfersdorf [23], Landis e Mills [15], Romanenko e Kharchenko [24] and Meinert et al. [18]. Un buon accordo con questi dati è stato trovato. Il terzo caso, invece, è stato verificato con test portati a termine all’Università Federico II di Napoli da Carmicino e Di Martino ([3], [5], [7]) su due propulsori ibridi, uno da 200 N e l’altro da 1kN, entrambi basati su HDPE/HTPB e ossigeno gassoso. Per la generazione della mesh è stato usato ICEM CFD (Ansys) per creare griglie computazionali 2D di alta qualità e una UDF (User Defined Function) è stata accoppiata a Fluent per generare le condizioni al contorno corrette a simulare la traspirazione.The objective of this work is to investigate the physics of combustion in hybrid rockets by using RANS simulations run on commercial CFD software (Ansys Fluent) and in particular the role of density in the determination of regression rate in the solid fuel. Although this technology did important steps in the last decades, many aspects are still not well understood. Here the necessity to conduct a series of virtual experiments, firstly to asses the validity of the employed models, then to extrapolate from the data interesting insights regarding the physics beneath the phenomena in question. The ability to determine, even only qualitatively, which characteristics of the fuel affect the behavior of the entire system could direct the efforts of the research to a better understanding of the physics or the industry to search for new, highly efficient propellants. Three types of experiments have been set up: cold-flow isothermal, cold-flow non-isothermal and hot combusting-flow simulations. In the former two the idea that the density of the injected species modify the behavior of the boundary layer has been investigated in a simplified environment. After a good qualitative understanding of the effect has been built, the work proceed with setting up other simulations of real hybrid rockets to compare the results and prediction of the simplified cases with the ones involving combustion phenomena. The validation of the former two cases has been conducted on the experimental and numerical data provided by Prokein and Wolfersdorf [23], Landis and Mills [15], Romanenko and Kharchenko [24] and Meinert et al. [18]. A good agreement with these data has been found. The third case, instead, has been verified on the experiments performed at Università Federico II di Napoli by Carmicino and Di Martino ([3], [5], [7]) on two hydrid propulsion systems, one rated 200 N and the other 1 kN, both based on HDPE/HTPB + gaseous oxygen. For the mesh generation ICEM CFD (Ansys) has been used to create a high quality 2D grid and an UDF (User Defined Function) has been coupled with Fluent to impose the correct boundary conditions to simulate transpiration or blowing