Speeding up Deciphering by Hypergraph Ordering

The "Gluing Algorithm" of Semaev [Des.\ Codes Cryptogr.\ 49 (2008), 47--60] --- that finds all solutions of a sparse system of linear equations over the Galois field $GF(q)$ --- has average running time $O(mq^{\max \left\vert \cup_{1}^{k}X_{j}\right\vert -k}),$ where $m$ is the total number of equations, and $\cup_{1}^{k}X_{j}$ is the set of all unknowns actively occurring in the first $k$ equations. Our goal here is to minimize the exponent of $q$ in the case where every equation contains at most three unknowns. %Applying hypergraph-theoretic methods we prove The main result states that if the total number $\left\vert \cup_{1}^{m}X_{j}\right\vert$ of unknowns is equal to $m$, then the best achievable exponent is between $c_1m$ and $c_2m$ for some positive constants $c_1$ and $c_2.

Speeding up deciphering by hypergraph ordering

The " Gluing Algorithm" of Semaev (Des. Codes Cryptogr. 49:47-60, 2008)-that finds all solutions of a sparse system of linear equations over the Galois field {Mathematical expression}-has average running time {Mathematical expression} where {Mathematical expression} is the total number of equations, and {Mathematical expression} is the set of all unknowns actively occurring in the first {Mathematical expression} equations. In order to make the implementation of the algorithm faster, our goal here is to minimize the exponent of {Mathematical expression} in the case where every equation contains at most three unknowns. The main result states that if the total number {Mathematical expression} of unknowns is equal to {Mathematical expression}, then the best achievable exponent is between {Mathematical expression} and {Mathematical expression} for some positive constants {Mathematical expression} and {Mathematical expression} © 2013 Springer Science+Business Media New York

A Combinatorial Problem Related to Sparse Systems of Equations

Nowadays sparse systems of equations occur frequently in science and engineering. In this contribution we deal with sparse systems common in cryptanalysis. Given a cipher system, one converts it into a system of sparse equations, and then the system is solved to retrieve either a key or a plaintext. Raddum and Semaev proposed new methods for solving such sparse systems. It turns out that a combinatorial MaxMinMax problem provides bounds on the average computational complexity of sparse systems. In this paper we initiate a study of a linear algebra variation of this MaxMinMax problem

Human Perception-Inspired Grain Segmentation Refinement Using Conditional Random Fields

Accurate segmentation of interconnected line networks, such as grain boundaries in polycrystalline material microstructures, poses a significant challenge due to the fragmented masks produced by conventional computer vision algorithms, including convolutional neural networks. These algorithms struggle with thin masks, often necessitating intricate post-processing for effective contour closure and continuity. Addressing this issue, this paper introduces a fast, high-fidelity post-processing technique, leveraging domain knowledge about grain boundary connectivity and employing conditional random fields and perceptual grouping rules. This approach significantly enhances segmentation mask accuracy, achieving a 79% segment identification accuracy in validation with a U-Net model on electron microscopy images of a polycrystalline oxide. Additionally, a novel grain alignment metric is introduced, showing a 51% improvement in grain alignment, providing a more detailed assessment of segmentation performance for complex microstructures. This method not only enables rapid and accurate segmentation but also facilitates an unprecedented level of data analysis, significantly improving the statistical representation of grain boundary networks, making it suitable for a range of disciplines where precise segmentation of interconnected line networks is essential

Qualitative Spatial Configuration Queries Towards Next Generation Access Methods for GIS

For a long time survey, management, and provision of geographic information in Geographic Information Systems (GIS) have mainly had an authoritative nature. Today the trend is changing and such an authoritative geographic information source is now accompanied by a public and freely available one which is usually referred to as Volunteered Geographic Information (VGI). Actually, the term VGI does not refer only to the mere geographic information, but, more generally, to the whole process which assumes the engagement of volunteers to collect and maintain such information in freely accessible GIS. The quick spread of VGI gives new relevance to a well-known challenge: developing new methods and techniques to ease down the interaction between users and GIS. Indeed, in spite of continuous improvements, GIS mainly provide interfaces tailored for experts, denying the casual user usually a non-expert the possibility to access VGI information. One main obstacle resides in the different ways GIS and humans deal with spatial information: GIS mainly encode spatial information in a quantitative format, whereas human beings typically prefer a qualitative and relational approach. For example, we use expressions like the lake is to the right-hand side of the wood or is there a supermarket close to the university? which qualitatively locate a spatial entity with respect to another. Nowadays, such a gap in representation has to be plugged by the user, who has to learn about the system structure and to encode his requests in a form suitable to the system. Contrarily, enabling gis to explicitly deal with qualitative spatial information allows for shifting the translation effort to the system side. Thus, to facilitate the interaction with human beings, GIS have to be enhanced with tools for efficiently handling qualitative spatial information. The work presented in this thesis addresses the problem of enabling Qualitative Spatial Configuration Queries (QSCQs) in GIS. A QSCQ is a spatial database query which allows for an automatic mapping of spatial descriptions produced by humans: A user naturally expresses his request of spatial information by drawing a sketch map or producing a verbal description. The qualitative information conveyed by such descriptions is automatically extracted and encoded into a QSCQ. The focus of this work is on two main challenges: First, the development of a framework that allows for managing in a spatial database the variety of spatial aspects that might be enclosed in a spatial description produced by a human. Second, the conception of Qualitative Spatial Access Methods (QSAMs): algorithms and data structures tailored for efficiently solving QSCQs. The main objective of a QSAM is that of countering the exponential explosion in terms of storage space occurring when switching from a quantitative to a qualitative spatial representation while keeping query response time acceptable

MaxMinMax problem and sparse equations over finite fields

Asymptotical complexity of sparse equation systems over finite field $F_q$ is studied. Let the variable sets belong to a fixed family $\mathcal{X}=\{X_1,\ldots,X_m\}$ while the polynomials $f_i(X_i)$ are taken independently and uniformly at random from the set of all polynomials of degree $\leq q-1$ in each of the variables in $X_i$. In particular, for $|X_i|\le3$, $m=n$, we prove the average complexity of finding all solutions to $f_i(X_i)=0, i=1,\ldots,m$ by Gluing algorithm ( Semaev, Des. Codes Cryptogr., vol. 49 (2008), pp.47--60) is at most $q^{\frac{n}{5.7883}+O(\log n)}$ for arbitrary $\mathcal{X}$ and $q$. The proof results from a detailed analysis of 3-MaxMinMax problem, a novel problem for hyper-graphs

Unravelling the complexity of metabolic networks

Network science provides an invaluable set of tools and techniques for improving our understanding of many important biological processes at the systems level. A network description provides a simplied view of such a system, focusing upon the interactions between a usually large number of similar biological units. At the cellular level, these units are usually interacting genes, proteins or small molecules, resulting in various types of biological networks. Metabolic networks, in particular, play a fundamental role, since they provide the building blocks essential for cellular function, and thus, have recently received a lot of attention. In particular, recent studies have revealed a number of universal topological characteristics, such as a small average path-length, large clustering coecient and a hierarchical modular structure. Relations between structure, function and evolution, however, for even the simplest of organisms is far from understood. In this thesis, we employ network analysis in order to determine important links between an organism's metabolic network structure and the environment under which it evolved. We address this task from two dierent perspectives: (i) a network classication approach; and (ii) a more physiologically realistic modelling approach, namely hypernetwork models. One of the major contributions of this thesis is the development of a novel graph embedding approach, based on low-order network motifs, that compares the structural properties of large numbers of biological networks simultaneously. This method was prototyped on a cohort of 383 bacterial networks, and provides powerful evidence for the role that both environmental variability, and oxygen requirements, play in the forming of these important networked structures. In addition to this, we consider a hypernetwork formalism of metabolism, in an attempt to extend complex network reasoning to this more complicated, yet physiologically more realistic setting. In particular, we extend the concept of network reciprocity to hypernetworks, and again evidence a signicant relationship between bacterial hypernetwork structure and the environment in which these organisms evolved. Moreover, we extend the concept of network percolation to undirected hypernetworks, as a technique for quantifying robustness and fragility within metabolic hypernetworks, and in the process nd yet further evidence of increased topological complexity within organisms inhabiting more uncertain environments. Importantly, many of these relationships are not apparent when considering the standard approach, thus suggesting that a hypernetwork formalism has the potential to reveal biologically relevant information that is beyond the standard network approach

Privacy by Design in Data Mining

Privacy is ever-growing concern in our society: the lack of reliable privacy safeguards in many current services and devices is the basis of a diffusion that is often more limited than expected. Moreover, people feel reluctant to provide true personal data, unless it is absolutely necessary. Thus, privacy is becoming a fundamental aspect to take into account when one wants to use, publish and analyze data involving sensitive information. Many recent research works have focused on the study of privacy protection: some of these studies aim at individual privacy, i.e., the protection of sensitive individual data, while others aim at corporate privacy, i.e., the protection of strategic information at organization level. Unfortunately, it is in- creasingly hard to transform the data in a way that it protects sensitive information: we live in the era of big data characterized by unprecedented opportunities to sense, store and analyze complex data which describes human activities in great detail and resolution. As a result anonymization simply cannot be accomplished by de-identification. In the last few years, several techniques for creating anonymous or obfuscated versions of data sets have been proposed, which essentially aim to find an acceptable trade-off between data privacy on the one hand and data utility on the other. So far, the common result obtained is that no general method exists which is capable of both dealing with “generic personal data” and preserving “generic analytical results”. In this thesis we propose the design of technological frameworks to counter the threats of undesirable, unlawful effects of privacy violation, without obstructing the knowledge discovery opportunities of data mining technologies. Our main idea is to inscribe privacy protection into the knowledge discovery technol- ogy by design, so that the analysis incorporates the relevant privacy requirements from the start. Therefore, we propose the privacy-by-design paradigm that sheds a new light on the study of privacy protection: once specific assumptions are made about the sensitive data and the target mining queries that are to be answered with the data, it is conceivable to design a framework to: a) transform the source data into an anonymous version with a quantifiable privacy guarantee, and b) guarantee that the target mining queries can be answered correctly using the transformed data instead of the original ones. This thesis investigates on two new research issues which arise in modern Data Mining and Data Privacy: individual privacy protection in data publishing while preserving specific data mining analysis, and corporate privacy protection in data mining outsourcing

Predicting Linguistic Structure with Incomplete and Cross-Lingual Supervision

Contemporary approaches to natural language processing are predominantly based on statistical machine learning from large amounts of text, which has been manually annotated with the linguistic structure of interest. However, such complete supervision is currently only available for the world's major languages, in a limited number of domains and for a limited range of tasks. As an alternative, this dissertation considers methods for linguistic structure prediction that can make use of incomplete and cross-lingual supervision, with the prospect of making linguistic processing tools more widely available at a lower cost. An overarching theme of this work is the use of structured discriminative latent variable models for learning with indirect and ambiguous supervision; as instantiated, these models admit rich model features while retaining efficient learning and inference properties. The first contribution to this end is a latent-variable model for fine-grained sentiment analysis with coarse-grained indirect supervision. The second is a model for cross-lingual word-cluster induction and the application thereof to cross-lingual model transfer. The third is a method for adapting multi-source discriminative cross-lingual transfer models to target languages, by means of typologically informed selective parameter sharing. The fourth is an ambiguity-aware self- and ensemble-training algorithm, which is applied to target language adaptation and relexicalization of delexicalized cross-lingual transfer parsers. The fifth is a set of sequence-labeling models that combine constraints at the level of tokens and types, and an instantiation of these models for part-of-speech tagging with incomplete cross-lingual and crowdsourced supervision. In addition to these contributions, comprehensive overviews are provided of structured prediction with no or incomplete supervision, as well as of learning in the multilingual and cross-lingual settings. Through careful empirical evaluation, it is established that the proposed methods can be used to create substantially more accurate tools for linguistic processing, compared to both unsupervised methods and to recently proposed cross-lingual methods. The empirical support for this claim is particularly strong in the latter case; our models for syntactic dependency parsing and part-of-speech tagging achieve the hitherto best published results for a wide number of target languages, in the setting where no annotated training data is available in the target language

Topology Reconstruction of Dynamical Networks via Constrained Lyapunov Equations

The network structure (or topology) of a dynamical network is often unavailable or uncertain. Hence, we consider the problem of network reconstruction. Network reconstruction aims at inferring the topology of a dynamical network using measurements obtained from the network. In this technical note we define the notion of solvability of the network reconstruction problem. Subsequently, we provide necessary and sufficient conditions under which the network reconstruction problem is solvable. Finally, using constrained Lyapunov equations, we establish novel network reconstruction algorithms, applicable to general dynamical networks. We also provide specialized algorithms for specific network dynamics, such as the well-known consensus and adjacency dynamics.Comment: 8 page