Academic literature on the topic 'De Bruijn Identity'

De Bruijn's identity shows a link between two fundamental concepts in information theory: entropy and Fisher information. In the literature, De Bruijn's identity has been stated under the assumption of independence between input signal and an additive noise. However, in the real world, the noise could be highly dependent on the main signal. The main aim of this paper is, firstly, to extend De bruijn's identity for signal-dependent noise channels and, secondly, to study how Stein and heat identities are related to De bruijn's identity. Thus, new versions of De Bruijn's identity are introduced in the case when input signal and additive noise are dependent and are jointly distributed according to Archimedean and Gaussian copulas. It is shown that in this generalized model, the derivatives of the differential entropy can be expressed in terms of a function of Fisher information. Our finding enfolds the conventional De Bruijn's identity as some remarks. Then, the equivalence among the new De Bruijn-type identity, Stein's identity and heat equation identity is established. The paper concludes with an application of the developed results in information theory.

Several authors have considered relationships between individuals specified by the genes which they have in common, where two genes are regarded as the same if and only if they are identical by descent from some common ancestor. In particular Thompson [6] considered n pairs of genes, one pair from each of n individuals, and studied the number Nn of gene identity states, the number Mn, k of such states in which there are exactly k distinct genes and the number Dn of genetically distinct states (see Definitions 2 and 4 below). In this type of work the nature of the genes themselves is of no interest, but only which genes are identical to which, and precise definitions are best given in terms of orbits under group actions. Thompson did use some group theory in her work, but not the full machinery of Redfield-Pólya-de Bruijn enumeration.

In this paper, we focus on extended informational measures based on a convex function ϕ: entropies, extended Fisher information, and generalized moments. Both the generalization of the Fisher information and the moments rely on the definition of an escort distribution linked to the (entropic) functional ϕ. We revisit the usual maximum entropy principle—more precisely its inverse problem, starting from the distribution and constraints, which leads to the introduction of state-dependent ϕ-entropies. Then, we examine interrelations between the extended informational measures and generalize relationships such the Cramér–Rao inequality and the de Bruijn identity in this broader context. In this particular framework, the maximum entropy distributions play a central role. Of course, all the results derived in the paper include the usual ones as special cases.

In this paper, we generalize the notion of Shannon’s entropy power to the Rényi-entropy setting. With this, we propose generalizations of the de Bruijn identity, isoperimetric inequality, or Stam inequality. This framework not only allows for finding new estimation inequalities, but it also provides a convenient technical framework for the derivation of a one-parameter family of Rényi-entropy-power-based quantum-mechanical uncertainty relations. To illustrate the usefulness of the Rényi entropy power obtained, we show how the information probability distribution associated with a quantum state can be reconstructed in a process that is akin to quantum-state tomography. We illustrate the inner workings of this with the so-called “cat states”, which are of fundamental interest and practical use in schemes such as quantum metrology. Salient issues, including the extension of the notion of entropy power to Tsallis entropy and ensuing implications in estimation theory, are also briefly discussed.

We establish a few properties of eigenvalues and eigenvectors of the quaternionic Ginibre ensemble (QGE), analogous to what is known in the complex Ginibre case (see [7, 11, 14]). We first recover a version of Kostlan’s theorem that was already at the heart of an argument by Rider [1], namely, that the set of the squared radii of the eigenvalues is distributed as a set of independent gamma variables. Our proof technique uses the De Bruijn identity and properties of Pfaffians; it also allows to prove that the high powers of these eigenvalues are independent. These results extend to any potential beyond the Gaussian case, as long as radial symmetry holds; this includes for instance truncations of quaternionic unitary matrices, products of quaternionic Ginibre matrices, and the quaternionic spherical ensemble. We then study the eigenvectors of quaternionic Ginibre matrices. Angles between eigenvectors and the matrix of overlaps both exhibit some specific features that can be compared to the complex case. In particular, we compute the distribution and the limit of the diagonal overlap associated to an eigenvalue that is conditioned to be at the origin. This complements a recent study of overlaps in quaternionic ensembles by Akemann, Förster and Kieburg [1, 2].

Sequence assembly from short reads is an important problem in biology. It is known that solving the sequence assembly problem exactly on a bi-directed de Bruijn graph or a string graph is intractable. However, finding a shortest double stranded DNA string (SDDNA) containing all the k-long words in the reads seems to be a good heuristic to get close to the original genome. This problem is equivalent to finding a cyclic Chinese Postman (CP) walk on the underlying unweighted bi-directed de Bruijn graph built from the reads. The Chinese Postman walk Problem (CPP) is solved by reducing it to a general bi-directed flow on this graph which runs in O(|E|2 log 2(|V|)) time. In this paper we show that the cyclic CPP on bi-directed graphs can be solved without reducing it to bi-directed flow. We present a Θ(p(|V| + |E|) log (|V|) + (d max p)3) time algorithm to solve the cyclic CPP on a weighted bi-directed de Bruijn graph, where p = max {|{v|d in (v) - d out (v) > 0}|, |{v|d in (v) - d out (v) < 0}|} and d max = max {|d in (v) - d out (v)}. Our algorithm performs asymptotically better than the bi-directed flow algorithm when the number of imbalanced nodes p is much less than the nodes in the bi-directed graph. From our experimental results on various datasets, we have noticed that the value of p/|V| lies between 0.08% and 0.13% with 95% probability. Many practical bi-directed de Bruijn graphs do not have cyclic CP walks. In such cases it is not clear how the bi-directed flow can be useful in identifying contigs. Our algorithm can handle such situations and identify maximal bi-directed sub-graphs that have CP walks. A Θ(p(|V| + |E|)) time heuristic algorithm based on these ideas has been implemented for the SDDNA problem. This algorithm was tested on short reads from a plant genome and achieves an approximation ratio of at most 1.0134. We also present a Θ((|V| + |E|) log (V)) time algorithm for the single source shortest path problem on bi-directed de Bruijn graphs, which may be of independent interest.

Abstract De Bruijn's identity relates two important concepts in information theory: Fisher information and differential entropy. Unlike the common practice in the literature, in this paper we consider general additive non-Gaussian noise channels where more realistically, the input signal and additive noise are not independently distributed. It is shown that, for general dependent signal and noise, the first derivative of the differential entropy is directly related to the conditional mean estimate of the input. Then, by using Gaussian and Farlie–Gumbel–Morgenstern copulas, special versions of the result are given in the respective case of additive normally distributed noise. The previous result on independent Gaussian noise channels is included as a special case. Illustrative examples are also provided.

ABSTRACT The TspO outer membrane protein of Rhodobacter sphaeroides has been shown to be involved in controlling the transcription of a number of genes which encode enzymes involved in photopigment biosynthesis and the puc operon. The display of regulated genes appears identical to those genes encompassing the PpsR/AppA repressor/antirepressor regulon, although the effect of TspO is modest relative to that of PpsR/AppA. To directly address the hypothesis that TspO is effective through the PpsR/AppA system, we constructed mutant strains with mutations in bothtspO and appA. In all cases, the phenotypes examined resembled those of the appA lesion by itself, leading us to conclude that TspO works through or modulates the PpsR/AppA system and acts upstream of the site of action of these regulatory proteins. In earlier publications, we had suggested that TspO is involved in the efflux of a certain intermediate(s) of the porphyrin biosynthesis pathway and that transcriptional regulation of target gene expression could be explained by the accumulation of a coactivator of AppA function. Although the data reported here do not precisely identify this coactivator, they lend support to this hypothesis. We discuss the importance of this form of gene control as the result of the recent extension of the TspO system toSinorhizobium meliloti, as described by Davey and de Bruijn (M. E. Davey and F. J. de Bruijn, Appl. Environ. Microbiol. 66:5353–5359, 2000). It is therefore possible that this system constitutes a more widely, although not universally, demonstrated form of gene regulation.

L'objectif principal de cette thèse est le développement, l'amélioration et l'évaluation de méthodes de traitement de données massives de séquençage, principalement des lectures de séquençage d'ARN courtes et longues, pour éventuellement aider la communauté à répondre à certaines questions biologiques, en particulier dans les contextes de transcriptomique et d'épissage alternatif. Notre objectif initial était de développer des méthodes pour traiter les données d'ARN-seq de deuxième génération à l'aide de graphes de De Bruijn afin de contribuer à la littérature sur l'épissage alternatif, qui a été exploré dans les trois premiers travaux. Le premier article (Chapitre 3, article [77]) a exploré le problème que les répétitions apportent aux assembleurs de transcriptome si elles ne sont pas correctement traitées. Nous avons montré que la sensibilité et la précision de notre assembleur local d'épissage alternatif augmentaient considérablement lorsque les répétitions étaient formellement modélisées. Le second (Chapitre 4, article [11]) montre que l'annotation d'événements d'épissage alternatifs avec une seule approche conduit à rater un grand nombre de candidats, dont beaucoup sont importants. Ainsi, afin d'explorer de manière exhaustive les événements d'épissage alternatifs dans un échantillon, nous préconisons l'utilisation combinée des approches mapping-first et assembly-first. Étant donné que nous avons une énorme quantité de bulles dans les graphes de De Bruijn construits à partir de données réelles d'ARN-seq, qui est impossible à analyser dans la pratique, dans le troisième travail (Chapitre 5, articles [1, 2]), nous avons exploré théoriquement la manière de représenter efficacement et de manière compacte l'espace des bulles via un générateur des bulles. L'exploration et l'analyse des bulles dans le générateur sont réalisables dans la pratique et peuvent être complémentaires aux algorithmes de l'état de l'art qui analysent un sous-ensemble de l'espace des bulles. Les collaborations et les avancées sur la technologie de séquençage nous ont incités à travailler dans d'autres sous-domaines de la bioinformatique, tels que: études d'association à l'échelle des génomes, correction d'erreur et assemblage hybride. Notre quatrième travail (Chapitre 6, article [48]) décrit une méthode efficace pour trouver et interpréter des unitigs fortement associées à un phénotype, en particulier la résistance aux antibiotiques, ce qui rend les études d'association à l'échelle des génomes plus accessibles aux panels bactériens, surtout ceux qui contiennent des bactéries plastiques. Dans notre cinquième travail (Chapitre 7, article [76]), nous évaluons dans quelle mesure les méthodes existantes de correction d'erreur ADN à lecture longue sont capables de corriger les lectures longues d'ARN-seq à taux d'erreur élevé. Nous concluons qu'aucun outil ne surpasse tous les autres pour tous les indicateurs et est le mieux adapté à toutes les situations, et que le choix devrait être guidé par l'analyse en aval. Les lectures longues d'ARN-seq fournissent une nouvelle perspective sur la manière d'analyser les données transcriptomiques, puisqu'elles sont capables de décrire les séquences complètes des ARN messagers, ce qui n'était pas possible avec des lectures courtes dans plusieurs cas, même en utilisant des assembleurs de transcriptome de l'état de l'art. En tant que tel, dans notre dernier travail (Chapitre 8, article [75]), nous explorons une méthode hybride d'assemblage d'épissages alternatifs qui utilise des lectures à la fois courtes et longues afin de répertorier les événements d'épissage alternatifs de manière complète, grâce aux lectures courtes, guidé par le contexte intégral fourni par les lectures longues
The main goal of this thesis is the development, improvement and evaluation of methods to process massively sequenced data, mainly short and long RNA-sequencing reads, to eventually help the community to answer some biological questions, especially in the transcriptomic and alternative splicing contexts. Our initial objective was to develop methods to process second-generation RNA-seq data through de Bruijn graphs to contribute to the literature of alternative splicing, which was explored in the first three works. The first paper (Chapter 3, paper [77]) explored the issue that repeats bring to transcriptome assemblers if not addressed properly. We showed that the sensitivity and the precision of our local alternative splicing assembler increased significantly when repeats were formally modeled. The second (Chapter 4, paper [11]), shows that annotating alternative splicing events with a single approach leads to missing out a large number of candidates, many of which are significant. Thus, to comprehensively explore the alternative splicing events in a sample, we advocate for the combined use of both mapping-first and assembly-first approaches. Given that we have a huge amount of bubbles in de Bruijn graphs built from real RNA-seq data, which are unfeasible to be analysed in practice, in the third work (Chapter 5, papers [1, 2]), we explored theoretically how to efficiently and compactly represent the bubble space through a bubble generator. Exploring and analysing the bubbles in the generator is feasible in practice and can be complementary to state-of-the-art algorithms that analyse a subset of the bubble space. Collaborations and advances on the sequencing technology encouraged us to work in other subareas of bioinformatics, such as: genome-wide association studies, error correction, and hybrid assembly. Our fourth work (Chapter 6, paper [48]) describes an efficient method to find and interpret unitigs highly associated to a phenotype, especially antibiotic resistance, making genome-wide association studies more amenable to bacterial panels, especially plastic ones. In our fifth work (Chapter 7, paper [76]), we evaluate the extent to which existing long-read DNA error correction methods are capable of correcting high-error-rate RNA-seq long reads. We conclude that no tool outperforms all the others across all metrics and is the most suited in all situations, and that the choice should be guided by the downstream analysis. RNA-seq long reads provide a new perspective on how to analyse transcriptomic data, since they are able to describe the full-length sequences of mRNAs, which was not possible with short reads in several cases, even by using state-of-the-art transcriptome assemblers. As such, in our last work (Chapter 8, paper [75]) we explore a hybrid alternative splicing assembly method, which makes use of both short and long reads, in order to list alternative splicing events in a comprehensive manner, thanks to short reads, guided by the full-length context provided by the long reads

The title of this paper is "Two generations of African writers: Women who conform to norms, and women who make noise. Mariama Bâ and Calixthe Beyala”. In this study we analyze two novels, Une si longue lettre by Mariama Bâ (1979) and Assèze l’Africaine by Calixthe Beyala (1994). We examine the similarities and differences in expression, style and themes. Our objective is to determine whether Bâ and Beyala are representing two different groups of African female writers. We have combined a postcolonial approach with a comparative method. Our hypothesis is that the two novels stand in contrast to each other through differences in themes and styles. In order to test this hypothesis we use previous research. Our analysis shows that the work of Bâ has a sober and refined style of writing. Bâ is raising awareness of the situation of women, without deviating from social norms, choosing themes such as polygamy, sisterhood and the value of education. In the work of Beyala we see a more pronounced political criticism, in a bolder and more agitating style of writing. Our conclusion is that the two novels are strongly differentiated through themes and styles. Bâ and Beyala belong to two different generations of female French-speaking African authors.

This study aims to investigate how history teachers relate to whiteness and the whiteness norms in their teaching. The material mainly consists of qualitative interviews with history teachers who are active in lower secondary schools in Jönköping County. The questions are based on how the teachers reason regarding the whiteness norms, how they work with these in their teaching and how the teachers appraise that these norms affect their pupils' identity creation and history consciousness. The results show that a large part of the respondents show an uncertainty when they talk about the whiteness norm, this stems from a lack of understanding for the meaning of the concepts. It also appears that some respondents have reflected on the whiteness norms in their teaching before, however, a difference can be seen in the respondents’ answers depending on how or if they have reflected on the subject of whiteness norms or not. The respondents handle the uncertainty in different ways, among other things by being or not being a killjoy (a person who decides whether they should bring down the mood in the room through confrontation or not). In the conversation with the respondents, they describe how their view of the students' identity and that it can vary depending on whether the pupil belong or does not belong to the whiteness norm.

This dissertation studies several aspects of the interface between information theory and signal processing. Several new and existing results in information theory are researched from the perspective of signal processing. Similarly, some fundamental results in signal processing and statistics are studied from the information theoretic viewpoint. The first part of this dissertation focuses on illustrating the equivalence between Stein's identity and De Bruijn's identity, and providing two extensions of De Bruijn's identity. First, it is shown that Stein's identity is equivalent to De Bruijn's identity in additive noise channels with specific conditions. Second, for arbitrary but fixed input and noise distributions, and an additive noise channel model, the first derivative of the differential entropy is expressed as a function of the posterior mean, and the second derivative of the differential entropy is expressed in terms of a function of Fisher information. Several applications over a number of fields, such as statistical estimation theory, signal processing and information theory, are presented to support the usefulness of the results developed in Section 2. The second part of this dissertation focuses on three contributions. First, a connection between the result, proposed by Stoica and Babu, and the recent information theoretic results, the worst additive noise lemma and the isoperimetric inequality for entropies, is illustrated. Second, information theoretic and estimation theoretic justifications for the fact that the Gaussian assumption leads to the largest Cramer-Rao lower bound (CRLB) is presented. Third, a slight extension of this result to the more general framework of correlated observations is shown. The third part of this dissertation concentrates on deriving an alternative proof for an extremal entropy inequality (EEI), originally proposed by Liu and Viswanath. Compared with the proofs, presented by Liu and Viswanath, the proposed alternative proof is simpler, more direct, and more information-theoretic. An additional application for the extremal inequality is also provided. Moreover, this section illustrates not only the usefulness of the EEI but also a novel method to approach applications such as the capacity of the vector Gaussian broadcast channel, the lower bound of the achievable rate for distributed source coding with a single quadratic distortion constraint, and the secrecy capacity of the Gaussian wire-tap channel. Finally, a unifying variational and novel approach for proving fundamental information theoretic inequalities is proposed. Fundamental information theory results such as the maximization of differential entropy, minimization of Fisher information (Cramer-Rao inequality), worst additive noise lemma, entropy power inequality (EPI), and EEI are interpreted as functional problems and proved within the framework of calculus of variations. Several extensions and applications of the proposed results are briefly mentioned.

Biological interaction mainly depends on the interactions of various genes and genomes. To identify actual meaning of interactions we have to find out the facts and reasons for these interactions. Gene analysis allows to verify such environment. Gene annotation means to identify the exon regions in metagenomic samples. The de Bruijn graph plays significant role in gene prediction and next generation sequencing (NGS). Apart from that, Eular Path of de Bruijn graph introduced generalized gene annotation for translational and splicing signals, exon introns separation and coding regions. set of graph reduction rules have used to build a de Bruijn graph. Accurate solution for large scale sequencing, trims space complexity and generates optimal gene annotation have tested.

When confronted with a case of an infant with a bruise, it is cardinal to remember “if the infant is not cruising, they should not be bruising.” In patients who are nonmobile, a bruise could be a sign of child maltreatment, in particular physical abuse. In these cases, it is imperative that the history take into account the age and developmental stage of the patient. Complete exposure of the patient and a thorough physical exam is critical to identify any other injuries. Patterned bruising may resemble the object that struck the child or what the child was struck with. Laboratory evaluation and imaging are dependent on the age. Consideration of a medical explanation such as a bleeding disorder should also be excluded.

This chapter reflects on Batya Brutin's Holocaust Icons in Art: The Warsaw Ghetto Boy and Anne Frank (2020). This volume documents the engagement of artistic creativity with the photographs of the boy with raised hands in the Warsaw ghetto (1943) and those of Anne Frank. In the six chapters detailing the various ways in which artists from different cultures and countries integrated these iconic figures into their oeuvre, Brutin acquaints the reader with dozens of artists who, at some point in their artistic development, opted to “express their thoughts, emotions and perceptions of the Holocaust.” These artists' works touch on various themes elaborated upon by Brutin: the fate of Jewish children in the Holocaust; personal identification with the iconic figures; their use to represent Jewish identity and universal human situations; their uniqueness; their imaginative connection with the state of Israel; and their “facelessness,” “disappearance,” and “disintegration.” Thus, the photographs have been used for decades by artists to perform a function in their art.

Marital unhappiness is a persistent theme of the Holmes stories, from the first (A Study in Scarlet) to several of the last (‘The Adventure of the Retired Colourman’ and ‘The Adventure of the Veiled Lodger’, both published in 1927). A Study in Scarlet begins as a detective story but its backstory is, as we have seen, a melodrama of forced marriage and domestic tyranny. ‘A Case of Identity’ concerns a courtship that is an elaborate deception, and the story opens with a digression on the ‘Dundas separation case’. This is reported in a newspaper as a ‘husband’s cruelty to his wife’, prompting Watson to claim that he knows the details without even reading the article: ‘There is, of course, the other woman, the drink, the push, the blow, the bruise, the sympathetic sister or landlady. The crudest of writers could invent nothing more crude.’ However, Holmes has investigated the case and reveals that it is actually more unusual: ‘The husband was a teetotaller, there was no other woman, and the conduct complained of was that he had drifted into the habit of winding up every meal by taking out his false teeth and hurling them at his wife’ (Adventures, 31).