Behavioral equivalence of hidden k-logics: an abstract algebraic approach

This work advances a research agenda which has as its main aim the application of Abstract Algebraic Logic (AAL) methods and tools to the specification and verification of software systems. It uses a generalization of the notion of an abstract deductive system to handle multi-sorted deductive systems which differentiate visible and hidden sorts. Two main results of the paper are obtained by generalizing properties of the Leibniz congruence — the central notion in AAL. In this paper we discuss a question we posed in [1] about the relationship between the behavioral equivalences of equivalent hidden logics. We also present a necessary and sufficient intrinsic condition for two hidden logics to be equivalent.

Strong shift equivalence, algebraic K-theory, and isolating zero-dimensional dynamics on manifolds

We study the relations of shift equivalence and strong shift equivalence for matrices over a ring $\mathcal{R}$, and establish a connection between these relations and algebraic K-theory. We utilize this connection to obtain results in two areas where the shift and strong shift equivalence relations play an important role: the study of finite group extensions of shifts of finite type, and the Generalized Spectral Conjectures of Boyle and Handelman for nonnegative matrices over subrings of the real numbers. We show the refinement of the shift equivalence class of a matrix $A$ over a ring $\mathcal{R}$ by strong shift equivalence classes over the ring is classified by a quotient $NK_{1}(\mathcal{R}) / E(A,\mathcal{R})$ of the algebraic K-group $NK_{1}(\calR)$. We use the K-theory of non-commutative localizations to show that in certain cases the subgroup $E(A,\mathcal{R})$ must vanish, including the case $A$ is invertible over $\mathcal{R}$. We use the K-theory connection to clarify the structure of algebraic invariants for finite group extensions of shifts of finite type. In particular, we give a strong negative answer to a question of Parry, who asked whether the dynamical zeta function determines up to finitely many topological conjugacy classes the extensions by $G$ of a fixed mixing shift of finite type. We apply the K-theory connection to prove the equivalence of a strong and weak form of the Generalized Spectral Conjecture of Boyle and Handelman for primitive matrices over subrings of $\mathbb{R}$. We construct explicit matrices whose class in the algebraic K-group $NK_{1}(\mathcal{R})$ is non-zero for certain rings $\mathcal{R}$ motivated by applications. We study the possible dynamics of the restriction of a homeomorphism of a compact manifold to an isolated zero-dimensional set. We prove that for $n \ge 3$ every compact zero-dimensional system can arise as an isolated invariant set for a homeomorphism of a compact $n$-manifold. In dimension two, we provide obstructions and examples.

The Real-Quaternionic Indicator of Irreducible Self-Conjugate Representations of Real Reductive Algebraic Groups and A Comment on the Local Langlands Correspondence of GL(2, F )

The real-quaternionic indicator, also called the $\delta$ indicator, indicates if a self-conjugate representation is of real or quaternionic type. It is closely related to the Frobenius-Schur indicator, which we call the $\varepsilon$ indicator. The Frobenius-Schur indicator $\varepsilon(\pi)$ is known to be given by a particular value of the central character. We would like a similar result for the $\delta$ indicator. When $G$ is compact, $\delta(\pi)$ and $\varepsilon(\pi)$ coincide. In general, they are not necessarily the same. In this thesis, we will give a relation between the two indicators when $G$ is a real reductive algebraic group. This relation also leads to a formula for $\delta(\pi)$ in terms of the central character. For the second part, we consider the construction of the local Langlands correspondence of $GL(2,F)$ when $F$ is a non-Archimedean local field with odd residual characteristics. By re-examining the construction, we provide new proofs to some important properties of the correspondence. Namely, the construction is independent of the choice of additive character in the theta correspondence.

Algebraic geometric codes over rings

The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980's. Recently, there has been an increased interest in the study of linear codes over finite rings. In this thesis, we combine these two approaches to coding theory by introducing and studying algebraic geometric codes over rings.

A divide-and-conquer bound for aggregate's quality and algebraic connectivity

info:eu-repo/semantics/submittedForPublication

Very special divisors on 4-gonal real algebraic curves

International audience

An algebraic pedotransfer function to calculate standardized in situ determined field capacity.

Despite the large applicability of the field capacity (FC) concept in hydrology and engineering, it presents various ambiguities and inconsistencies due to a lack of methodological procedure standardization. Experimental field and laboratory protocols taken from the literature were used in this study to determine the value of FC for different depths in 29 soil profiles, totaling 209 soil samples. The volumetric water content (θ) values were also determined at three suction values (6 kPa, 10 kPa, 33 kPa), along with bulk density (BD), texture (T) and organic matter content (OM). The protocols were devised based on the water processes involved in the FC concept aiming at minimizing hydraulic inconsistencies and procedural difficulty while maintaining the practical meaning of the concept. A high correlation between FC and θ(6 kPa) allowed the development of a pedotransfer function (Equation 3) quadratic for θ(6 kPa), resulting in an accurate and nearly bias-free calculation of FC for the four database geographic areas, with a global root mean squared residue (RMSR) of 0.026 m3·m-3. At the individual soil profile scale, the maximum RMSR was only 0.040 m3·m-3. The BD, T and OM data were generally of a low predicting quality regarding FC when not accompanied by the moisture variables. As all the FC values were obtained by the same experimental protocol and as the predicting quality of Equation 3 was clearly better than that of the classical method, which considers FC equal to θ(6), θ(10) or θ(33), we recommend using Equation 3 rather than the classical method, as well as the protocol presented here, to determine in-situ FC.

Interpretable Convolutional Neural Networks for Decoding and Analyzing Neural Time Series Data

Machine learning is widely adopted to decode multi-variate neural time series, including electroencephalographic (EEG) and single-cell recordings. Recent solutions based on deep learning (DL) outperformed traditional decoders by automatically extracting relevant discriminative features from raw or minimally pre-processed signals. Convolutional Neural Networks (CNNs) have been successfully applied to EEG and are the most common DL-based EEG decoders in the state-of-the-art (SOA). However, the current research is affected by some limitations. SOA CNNs for EEG decoding usually exploit deep and heavy structures with the risk of overfitting small datasets, and architectures are often defined empirically. Furthermore, CNNs are mainly validated by designing within-subject decoders. Crucially, the automatically learned features mainly remain unexplored; conversely, interpreting these features may be of great value to use decoders also as analysis tools, highlighting neural signatures underlying the different decoded brain or behavioral states in a data-driven way. Lastly, SOA DL-based algorithms used to decode single-cell recordings rely on more complex, slower to train and less interpretable networks than CNNs, and the use of CNNs with these signals has not been investigated. This PhD research addresses the previous limitations, with reference to P300 and motor decoding from EEG, and motor decoding from single-neuron activity. CNNs were designed light, compact, and interpretable. Moreover, multiple training strategies were adopted, including transfer learning, which could reduce training times promoting the application of CNNs in practice. Furthermore, CNN-based EEG analyses were proposed to study neural features in the spatial, temporal and frequency domains, and proved to better highlight and enhance relevant neural features related to P300 and motor states than canonical EEG analyses. Remarkably, these analyses could be used, in perspective, to design novel EEG biomarkers for neurological or neurodevelopmental disorders. Lastly, CNNs were developed to decode single-neuron activity, providing a better compromise between performance and model complexity.

Decoding Agc1 deficiency: bioinformatics approaches to unveil the functional implications of Slc25a12 on the transcriptome and epigenome

In the brain, mutations in SLC25A12 gene encoding AGC1 cause an ultra-rare genetic disease reported as a developmental and epileptic encephalopathy associated with global cerebral hypomyelination. Symptoms of the disease include diffused hypomyelination, arrested psychomotor development, severe hypotonia, seizures and are common to other neurological and developmental disorders. Amongst the biological components believed to be most affected by AGC1 deficiency are oligodendrocytes, glial cells responsible for myelination. Recent studies (Poeta et al, 2022) have also shown how altered levels of transcription factors and epigenetic modifications greatly affect proliferation and differentiation in oligodendrocyte precursor cells (OPCs). In this study we explore the transcriptomic landscape of Agc1 in two different system models: OPCs silenced for Agc1 and iPSCs from human patients differentiated to neural progenitors. Analyses range from differential expression analysis, alternative splicing, master regulator analysis. ATAC-seq results on OPCs were integrated with results from RNA-Seq to assess the activity of a TF based on the accessibility data from its putative targets, which allows to integrate RNA-Seq data to infer their role as either activators or repressors. All the findings for this model were also integrated with early data from iPSCs RNA-seq results, looking for possible commonalities between the two different system models, among which we find a downregulation in genes encoding for SREBP, a transcription factor regulating fatty acids biosynthesis, a key process for myelination which could explain the hypomyelinated state of patients. We also find that in both systems cells tend to form more neurites, likely losing their ability to differentiate, considering their progenitor state. We also report several alterations in the chromatin state of cells lacking Agc1, which confirms the hypothesis for which Agc1 is not a disease restricted only to metabolic alterations in the cells, but there is a profound shift of the regulatory state of these cells.

Decoding complex flow phenomena via Dynamic Mode Decomposition

In this thesis, the viability of the Dynamic Mode Decomposition (DMD) as a technique to analyze and model complex dynamic real-world systems is presented. This method derives, directly from data, computationally efficient reduced-order models (ROMs) which can replace too onerous or unavailable high-fidelity physics-based models. Optimizations and extensions to the standard implementation of the methodology are proposed, investigating diverse case studies related to the decoding of complex flow phenomena. The flexibility of this data-driven technique allows its application to high-fidelity fluid dynamics simulations, as well as time series of real systems observations. The resulting ROMs are tested against two tasks: (i) reduction of the storage requirements of high-fidelity simulations or observations; (ii) interpolation and extrapolation of missing data. The capabilities of DMD can also be exploited to alleviate the cost of onerous studies that require many simulations, such as uncertainty quantification analysis, especially when dealing with complex high-dimensional systems. In this context, a novel approach to address parameter variability issues when modeling systems with space and time-variant response is proposed. Specifically, DMD is merged with another model-reduction technique, namely the Polynomial Chaos Expansion, for uncertainty quantification purposes. Useful guidelines for DMD deployment result from the study, together with the demonstration of its potential to ease diagnosis and scenario analysis when complex flow processes are involved.

prism: rinfrangere distribuzioni di probabilità in riassunti astrattivi mediante strategie di decoding

Negli ultimi quattro anni la summarization astrattiva è stata protagonista di una evoluzione senza precedenti dettata da nuovi language model neurali, architetture transformer-based, elevati spazi dimensionali, ampi dataset e innovativi task di pre-training. In questo contesto, le strategie di decoding convertono le distribuzioni di probabilità predette da un modello in un testo artificiale, il quale viene composto in modo auto regressivo. Nonostante il loro cruciale impatto sulla qualità dei riassunti inferiti, il ruolo delle strategie di decoding è frequentemente trascurato e sottovalutato. Di fronte all'elevato numero di tecniche e iperparametri, i ricercatori necessitano di operare scelte consapevoli per ottenere risultati più affini agli obiettivi di generazione. Questa tesi propone il primo studio altamente comprensivo sull'efficacia ed efficienza delle strategie di decoding in task di short, long e multi-document abstractive summarization. Diversamente dalle pubblicazioni disponibili in letteratura, la valutazione quantitativa comprende 5 metriche automatiche, analisi temporali e carbon footprint. I risultati ottenuti dimostrano come non vi sia una strategia di decoding dominante, ma come ciascuna possieda delle caratteristiche adatte a task e dataset specifici. I contributi proposti hanno l'obiettivo di neutralizzare il gap di conoscenza attuale e stimolare lo sviluppo di nuove tecniche di decoding.

Transmission Of Intra-cellular Genetic Information: A System Proposal.

One of the great challenges of the scientific community on theories of genetic information, genetic communication and genetic coding is to determine a mathematical structure related to DNA sequences. In this paper we propose a model of an intra-cellular transmission system of genetic information similar to a model of a power and bandwidth efficient digital communication system in order to identify a mathematical structure in DNA sequences where such sequences are biologically relevant. The model of a transmission system of genetic information is concerned with the identification, reproduction and mathematical classification of the nucleotide sequence of single stranded DNA by the genetic encoder. Hence, a genetic encoder is devised where labelings and cyclic codes are established. The establishment of the algebraic structure of the corresponding codes alphabets, mappings, labelings, primitive polynomials (p(x)) and code generator polynomials (g(x)) are quite important in characterizing error-correcting codes subclasses of G-linear codes. These latter codes are useful for the identification, reproduction and mathematical classification of DNA sequences. The characterization of this model may contribute to the development of a methodology that can be applied in mutational analysis and polymorphisms, production of new drugs and genetic improvement, among other things, resulting in the reduction of time and laboratory costs.

Fundamentos geometricos e algebricos da calibração e reconstrução tridimensional : aplicação na analise cinematica de movimentos humanos

Universidade Estadual de Campinas . Faculdade de Educação Física

Anomalias dentárias associadas: o ortodontista decodificando a genética que rege os distúrbios de desenvolvimento dentário

O presente trabalho versa sobre o diagnóstico e a abordagem ortodôntica das anomalias dentárias, enfatizando os aspectos etiológicos que definem tais irregularidades de desenvolvimento. Parece existir uma inter-relação genética na determinação de algumas dessas anomalias, considerando-se a alta frequência de associações. Um mesmo defeito genético pode originar diferentes manifestações fenotípicas, incluindo agenesias, microdontias, ectopias e atraso no desenvolvimento dentário. As implicações clínicas das anomalias dentárias associadas são muito relevantes, uma vez que o diagnóstico precoce de uma determinada anomalia dentária pode alertar o clínico sobre a possibilidade de desenvolvimento de outras anomalias associadas no mesmo paciente ou em outros membros da família, permitindo a intervenção ortodôntica em época oportuna.