Efficient Computation of Maximal Anti-Exponent in Palindrome-Free Strings

A palindrome is a string x = a1 · · · an which is equal to its reversal x = an · · · a1. We consider gapped palindromes which are strings of the form uvu , where u, v are strings, |v| ≥ 2, and u is the reversal of u. Replicating the standard notion of string exponent, we define the anti- exponent of a gapped palindrome uvu as the quotient of |uvu | by |uv|. To get an efficient computation of maximal anti-exponent of factors in a palindrome-free string, we apply techniques based on the suffix au- tomaton and the reversed Lempel-Ziv factorisation. Our algorithm runs in O(n) time on a fixed-size alphabet or O(n log σ) on a large alphabet, which dramatically outperforms the naive cubic-time solution

Formalization of block pruning: reducing the number of cells computed in exact biological sequence comparison algorithms

This is a pre-copyedited, author-produced version of an article accepted for publication in The Computer Journal following peer review. The version of record Edans F O Sandes, George L M Teodoro, Maria Emilia M T Walter, Xavier Martorell, Eduard Ayguade, Alba C M A Melo; Formalization of Block Pruning: Reducing the Number of Cells Computed in Exact Biological Sequence Comparison Algorithms, The Computer Journal, Volume 61, Issue 5, 1 May 2018, Pages 687–713 is available online at: The Computer Journal https://academic.oup.com/comjnl/article-abstract/61/5/687/4539903 and https://doi.org/10.1093/comjnl/bxx090.Biological sequence comparison algorithms that compute the optimal local and global alignments calculate a dynamic programming (DP) matrix with quadratic time complexity. The DP matrix H is calculated with a recurrence relation in which the value of each cell Hi,j is the result of a maximum operation on the cells’ values Hi-1,j-1, Hi-1,j and Hi,j-1 added or subtracted by a constant value. Therefore, it can be noticed that the difference between the value of cell Hi,j being calculated and the values of direct neighbor cells previously computed respect well-defined upper and lower bounds. Using these bounds, we can show that it is possible to determine the maximum and the minimum value of every cell in H, for a given reference cell. We use this result to define a generic pruning method which determines the cells that can pruned (i.e. no need to be computed since they will not contribute to the final solution), accelerating the computation but keeping the guarantee that the optimal result will be produced. The goal of this paper is thus to investigate and formalize properties of the DP matrix in order to estimate and increase the pruning method efficiency. We also show that the pruning efficiency depends mainly on three characteristics: (a) the order in which the cells of H are calculated, (b) the values of the parameters used in the recurrence relation and (c) the contents of the sequences compared.Peer ReviewedPostprint (author's final draft

An investigation into the role of lamin A in the progression of colorectal cancer

Nuclear lamins are type V intermediate filaments which form a proteinaceous meshwork, termed the nuclear lamina, which underlines the inner nuclear membrane and provides mechanical strength to the nucleus and maintains nuclear shape. A-type lamins in particular have been implicated in DNA replication, the regulation of gene transcription, apoptosis and nuclear migration. Expression of lamin A/C is closely associated with the differentiated phenotype and loss of lamin A/C xpression has been correlated with increased proliferation, especially in tumours. I sought to investigate the expression and regulation of A- and B-type lamins during colorectal cancer (CRC) progression.Preferential down-regulation of lamin A expression over lamin C was observed in the most dedifferentiated CRC cell lines. Semi-quantitative RT-PCR suggested that this was achieved by both transcriptional and post-transcriptional mechanisms. A connection between loss of lamin A/C and proliferation was ruled out. Instead immunohistochemical analysis of CRC tissue sections indicated loss of lamin A may correlate with the differentiation status of cells. In normal colonic crypts lamin A/C expression was greatest in the differentiated compartment, whereas lamin A was absent and lamin A/C was present at barely detectable levels in Dukes' A malignant polyps with high grade dysplasia. Stable re- expression of lamin A constructs in SW480 colon cancer cells whichexpressed almost no endogenous lamin A rescued two-dimensional growth. Subsequent RNA profiling of 325 genes with reported relevance to colorectal carcinogenesis and general tumourigenesis confirmed that proliferation indices were unaffected by changes in the level of lamin A. Synemin, a cytoskeletal linker protein, was found to be significantly down-regulated in SW480 GFP-lamin A transfected cells versus SW480 GFP transfected cells. This suggests that lamin A functions to maintain nuclear and cellular integrity by indirect modulation of components of cytoskeletal architecture

Computação quântica : autômatos, jogos e complexidade

Orientador: Arnaldo Vieira MouraDissertação (mestrado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Desde seu surgimento, Teoria da Computação tem lidado com modelos computacionais de maneira matemática e abstrata. A noção de computação eficiente foi investigada usando esses modelos sem procurar entender as capacidades e limitações inerentes ao mundo físico. A Computação Quântica representa uma ruptura com esse paradigma. Enraizada nos postulados da Mecânica Quântica, ela é capaz de atribuir um sentido físico preciso à computação segundo nosso melhor entendimento da natureza. Esses postulados dão origem a propriedades fundamentalmente diferentes, uma em especial, chamada emaranhamento, é de importância central para computação e processamento de informação. O emaranhamento captura uma noção de correlação que é única a modelos quânticos. Essas correlações quânticas podem ser mais fortes do que qualquer correlação clássica estando dessa forma no coração de algumas capacidades quânticas que vão além do clássico. Nessa dissertação, nós investigamos o emaranhamento da perspectiva da complexidade computacional quântica. Mais precisamente, nós estudamos uma classe bem conhecida, definida em termos de verificação de provas, em que um verificador tem acesso à múltiplas provas não emaranhadas (QMA(k)). Assumir que as provas não contêm correlações quânticas parece ser uma hipótese não trivial, potencialmente fazendo com que essa classe seja maior do que aquela em que há apenas uma prova. Contudo, encontrar cotas de complexidade justas para QMA(k) permanece uma questão central sem resposta por mais de uma década. Nesse contexto, nossa contribuição é tripla. Primeiramente, estudamos classes relacionadas mostrando como alguns recursos computacionais podem afetar seu poder de forma a melhorar a compreensão a respeito da própria classe QMA(k). Em seguida, estabelecemos uma relação entre Probabilistically Checkable Proofs (PCP) clássicos e QMA(k). Isso nos permite recuperar resultados conhecidos de maneira unificada e simplificada. Para finalizar essa parte, mostramos que alguns caminhos para responder essa questão em aberto estão obstruídos por dificuldades computacionais. Em um segundo momento, voltamos nossa atenção para modelos restritos de computação quântica, mais especificamente, autômatos quânticos finitos. Um modelo conhecido como Two-way Quantum Classical Finite Automaton (2QCFA) é o objeto principal de nossa pesquisa. Seu estudo tem o intuito de revelar o poder computacional provido por memória quântica de dimensão finita. Nos estendemos esse autômato com a capacidade de colocar um número finito de marcadores na fita de entrada. Para qualquer número de marcadores, mostramos que essa extensão é mais poderosa do que seus análogos clássicos determinístico e probabilístico. Além de trazer avanços em duas linhas complementares de pesquisa, essa dissertação provê uma vasta exposição a ambos os campos: complexidade computacional e autômatosAbstract: Since its inception, Theoretical Computer Science has dealt with models of computation primarily in a very abstract and mathematical way. The notion of efficient computation was investigated using these models mainly without seeking to understand the inherent capabilities and limitations of the actual physical world. In this regard, Quantum Computing represents a rupture with respect to this paradigm. Rooted on the postulates of Quantum Mechanics, it is able to attribute a precise physical notion to computation as far as our understanding of nature goes. These postulates give rise to fundamentally different properties one of which, namely entanglement, is of central importance to computation and information processing tasks. Entanglement captures a notion of correlation unique to quantum models. This quantum correlation can be stronger than any classical one, thus being at the heart of some quantum super-classical capabilities. In this thesis, we investigate entanglement from the perspective of quantum computational complexity. More precisely, we study a well known complexity class, defined in terms of proof verification, in which a verifier has access to multiple unentangled quantum proofs (QMA(k)). Assuming the proofs do not exhibit quantum correlations seems to be a non-trivial hypothesis, potentially making this class larger than the one in which only a single proof is given. Notwithstanding, finding tight complexity bounds for QMA(k) has been a central open question in quantum complexity for over a decade. In this context, our contributions are threefold. Firstly, we study closely related classes showing how computational resources may affect its power in order to shed some light on \QMA(k) itself. Secondly, we establish a relationship between classical Probabilistically Checkable Proofs and QMA(k) allowing us to recover known results in unified and simplified way, besides exposing the interplay between them. Thirdly, we show that some paths to settle this open question are obstructed by computational hardness. In a second moment, we turn our attention to restricted models of quantum computation, more specifically, quantum finite automata. A model known as Two-way Quantum Classical Finite Automaton (2QCFA) is the main object of our inquiry. Its study is intended to reveal the computational power provided by finite dimensional quantum memory. We extend this automaton with the capability of placing a finite number of markers in the input tape. For any number of markers, we show that this extension is more powerful than its classical deterministic and probabilistic analogues. Besides bringing advances to these two complementary lines of inquiry, this thesis also provides a vast exposition to both subjects: computational complexity and automata theoryMestradoCiência da ComputaçãoMestre em Ciência da Computaçã

Quanten-Gittersysteme mit diskreten Zeitschritten

Discrete time quantum lattice systems recently have come into the focus of quantum computation because they provide a versatile tool for many different applications and they are potentially implementable in current experimental realizations. In this thesis we study the fundamental structures of such quantum lattice systems as well as consequences of experimental imperfections. Essentially, there are two models of discrete time quantum lattice systems, namely quantum cellular automata and quantum walks, which are quantum versions of their classical counterparts, i.e., cellular automata and random walks. In both cases, the dynamics acts locally on the lattice and is usually also translationally invariant. The main difference between these structures is that quantum cellular automata can describe the dynamics of many interacting particles, where quantum walks describe the evolution of a single particle. The first part of this thesis is devoted to quantum cellular automata. We characterize one-dimensional quantum cellular automata in terms of an index theory up to local deformations. Further, we characterize in detail a subclass of quantum cellular automata by requiring that Pauli operators are mapped to Pauli operators. This structure can be understood in terms of certain classical cellular automata. The second part of this thesis is concerned with quantum walks. We identify a quantum walk with the one-particle sector of a quantum cellular automaton. We also establish an index theory for quantum walks and we discuss decoherent quantum walks, i.e., the behavior of quantum walks with experimental imperfections.Quanten-Gittersysteme haben in den letzten Jahren zunehmend an Bedeutung im Bereich des Quantenrechnens gewonnen, weil sie ein vielseitiges Instrument für unterschiedliche Anwendungen darstellen und in derzeitigen experimentellen Realisierungen potentiell implementierbar sind. Wir untersuchen in dieser Arbeit sowohl grundlegende Strukturen solcher Quanten-Gittersysteme als auch experimentelle Imperfektionen. Im wesentlichen gibt es zwei Modelle von Quanten-Gittersystemen in diskreter Zeit: Quanten-Zellularautomaten und Quanten Walks. In beiden Fällen ist die Dynamik lokal und translationsinvariant. Der Hauptunterschied besteht darin, dass Quanten-Zellularautomaten viele miteinander wechselwirkende Teilchen beschreiben können, wohingegen Quanten Walks die Zeitentwicklung eines einzelnes Teilchen darstellen. Zu beiden Modellen gibt es entsprechende klassischen Strukturen, nämlich Zellularautomaten, bzw. Random Walks. Im ersten Teil dieser Arbeit werden Quanten-Zellularautomaten behandelt. Wir charakterisieren eindimensionale Automaten mithilfe einer Index Theorie bis auf lokale Deformation. Außerdem untersuchen wir im Detail die Struktur einer Unterklasse von Quanten-Zellularautomaten, die dadurch festgelegt ist, dass Pauli Operatoren auf Pauli Operatoren abgebildet werden. Wir zeigen, dass sich solche Automaten durch spezielle klassische Zellularautomaten verstehen lassen. Im zweiten Teil dieser Arbeit behandeln wir Quanten Walks, welche wir mit Ein-Teilchen-Sektoren von Quanten-Zellularautomaten identifizieren. Wir führen ebenso eine Index Theorie für Quanten Walks ein und wir diskutieren dekohärente Quanten Walks, d.h., das Verhalten von Quanten Walks mit experimentellen Imperfektionen

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum