A set of elements with a binary operation is called a system, or, more explicitly, a mathematical system. The following discussion will involve systems with only one operation. This operation will be denoted by "⋅" and will sometimes be referred to as a product. A system, S, of n elements (x1, x2, ..., xn) is associative if xi ⋅ (xj ⋅ xk) = (xi ⋅ xj) ⋅ xk for all i, j, k ≤ n. In a modern algebra class the following problem was proposed. What is the least number of elements a system can have and be non-associative? A system, S, of n elements (x1, x2, ..., xn) is associative if xi ⋅ (xj ⋅ xk) /= (xi ⋅ xj) ⋅ xk for some i, j, k ≤ n. It is obvious that a system of one element must be associative. Any binary operation could have but one result. A nonassociative system of two elements (a, b) can be constructed by letting a ⋅ a = b⋅a = b. , a⋅(a⋅a) = a⋅b and (a⋅a)⋅a = b⋅a = b. If a⋅b = a, then a⋅(a⋅a) /= (a⋅a)⋅a Thus the system is nonassociative. As is often the case this question leads to others. Are there systems of n elements such that xi ⋅ (xj ⋅ xk) /= (xi ⋅ xj) ⋅ xk for all i, j, k ≤ n? If such systems exist, what are their charcateristics? Such questions as these led to the development of this paper. A system, S, of n elements such that xi ⋅ (xj ⋅ xk) /= (xi ⋅ xj) ⋅ xk for all i, j, k ≤ n is called an anti-associative system. The purpose of this paper is to establish the existence of antiassociative systems of n elements and to find characteristics of these systems in as much detail as possible. Propositions will first be considered that apply to anti-associative systems in general. Then anti-associative systems of two, three, and four elements will be obtained. The general results that each of these special cases lead to will be developed. A special type of anti-associative system will be considered. These special anti-associative systems suggest a broader field. For a set of elements a group of classes of systems is defined. The operation may associative, anti-associative, or neither. Many questions are let unanswered as to the characteristics of anti-associative systems, but this paper opens new avenues to attack a broader problem.

In this thesis we look at hom-associative algebras (which turn out to be exactly the G1-hom-associative algebras), by, in two and three dimensions, trying to find the structure constants for which an algebra becomes hom-associative when the homomorphism 𝛼 is defined as different matrix units. These algebras are also hom-Lie admissible (or G6-hom-associative, which turn out to be the same thing) with a commutator, so we also find the commutator for each of these hom-Lie admissible algebras. We end up finding every hom-associative and hom-Lie algebra for 𝛼 defined as each 2×2 matrix unit in two dimensions, each 3×3 matrix unit in three dimensions when the problem is mapped to one dimension, for three 3×3 matrix units in three dimensions when the problem is mapped to two dimensions (but with the commutators not having been calculated), and only a few hom-associative algebras and hom-Lie algebras for one 3×3 matrix unit in the full three dimensions. We also compare the results for the different values of 𝛼, and find that in 𝑛 dimensions it is possible to find the values of the structure constants for all 𝑛2 different 𝛼:s simply by finding all of the solutions for 𝑛 different 𝛼:s (chosen in a specific way) and then permutating all of the indices.

No description available.

Depuis plusieurs années, la robotique mobile tente de s'extraire de l'espace amniotique des laboratoires de recherche afin d'explorer l'univers imprévisible, voire hostile, de nos lieux de vie, de travail, pour nous servir ou nous divertir. Or, les méthodes classiques de l'intelligence artificielle nécessitent des modèles du robot, de ses actions et de ses perceptions, conçus a priori. Elles sont donc peu adaptées à l'inattendu et à la nouveauté. D'autre part, les systèmes d'apprentissage artificiel, souvent d'inspiration biologique, semblent à présent en voie de fournir les capacités d'adaptation manquantes à ces premières. Nous envisageons dans cette thèse l'apprentissage comme un mécanisme central de l'architecture robotique. Celle-ci peut être représentée sous les traits d'une boucle sensori-motrice où actions et perceptions se rejoignent au sein d'une structure associative. L'apprentissage permet l'acquisition de connaissances nouvelles sur l'environnement mais il intervient également dans la modélisation des actions du robot : en associant des combinaisons de consignes simples sur les moteurs, et en mémorisant les effets de ces actions sur l'environnement ou sur le robot lui-même. Cette forme d'apprentissage a pour support un réseau de neurones permettant un apprentissage en ligne non supervisé. Cette architecture permet également d'exprimer les motivations et les objectifs du robot par le biais d'un second système d'apprentissage en associant une valeur de récompense aux représentations des actions ou des perceptions, par un apprentissage par renforcement. C'est donc l'utilité de chaque action, qui permettra finalement à un processus décisionnel d'avoir lieu.

The medial prefrontal cortex (mPFC) plays a critical role in the organization of goal directed behavior. This role is suggested by the anatomy of mPFC as the region rests at the top of a complex cortical and sub-cortical hierarchy, receives convergent sensory and motor information from multiple modalities, and is the target of modulatory brainstem nuclei that respond to prediction and reward. Given these observations, it was hypothesized that mPFC neurons store associations between stimuli when the stimuli contribute to the prediction of reward. To test this hypothesis, neural ensemble spiking activity was recorded in the mPFC as rats performed a paired-associate discrimination task. In one condition, both elements of the paired-associate stimulus-sequence provided information about reward delivery. In another condition, only the first stimulus contributed to the prediction. As hypothesized, stimulus-selective, prospective delay activity was observed during sequences in which both elements contributed to reward-prediction. Unexpectedly, however, selective delay responses were associated with slight variations in head position and thus were not necessarily generated by intrinsic mnemonic processes. Interestingly, the sensitivity of neurons to head position was greatest during intervals when reward delivery was certain. These result suggest that a major portion of delay activity in the rat mPFC reflects task-relevant sensory-motor activity, possibly related to behavioral strategies rather than to the local storage of stimulus-stimulus associations. These observations agree with evidence suggesting that mPFC neurons are particularly responsive during the performance of actions related to the acquisition of reward. These results also indicate that considerable attention must be given to the monitoring of sensory-motor variables during delay tasks as slight changes in position can produce activity that appears to be driven by intrinsic mechanisms. It is further suggested that such activity may perform an important role in memory guided behavior, although this role may contrast sharply with standard theories of delay activity and short term memory storage. In particular, it is suggested that delay activity observed in the prefrontal cortex may correspond to the maintenance of memories that are 'stored' in the body or in the environment in the forms of embodied or situated behaviors.

This thesis is concerned with one important question in artificial neural networks, that is, how biologically inspired connectivity of a network affects its associative memory performance. In recent years, research on the mammalian cerebral cortex, which has the main responsibility for the associative memory function in the brains, suggests that the connectivity of this cortical network is far from fully connected, which is commonly assumed in traditional associative memory models. It is found to be a sparse network with interesting connectivity characteristics such as the “small world network” characteristics, represented by short Mean Path Length, high Clustering Coefficient, and high Global and Local Efficiency. Most of the networks in this thesis are therefore sparsely connected. There is, however, no conclusive evidence of how these different connectivity characteristics affect the associative memory performance of a network. This thesis addresses this question using networks with different types of connectivity, which are inspired from biological evidences. The findings of this programme are unexpected and important. Results show that the performance of a non-spiking associative memory model is found to be predicted by its linear correlation with the Clustering Coefficient of the network, regardless of the detailed connectivity patterns. This is particularly important because the Clustering Coefficient is a static measure of one aspect of connectivity, whilst the associative memory performance reflects the result of a complex dynamic process. On the other hand, this research reveals that improvements in the performance of a network do not necessarily directly rely on an increase in the network’s wiring cost. Therefore it is possible to construct networks with high associative memory performance but relatively low wiring cost. Particularly, Gaussian distributed connectivity in a network is found to achieve the best performance with the lowest wiring cost, in all examined connectivity models. Our results from this programme also suggest that a modular network with an appropriate configuration of Gaussian distributed connectivity, both internal to each module and across modules, can perform nearly as well as the Gaussian distributed non-modular network. Finally, a comparison between non-spiking and spiking associative memory models suggests that in terms of associative memory performance, the implication of connectivity seems to transcend the details of the actual neural models, that is, whether they are spiking or non-spiking neurons.

The dissertation focuses on the structure of π-regular (regular) rings.

Pavlov (1927) first reported that following appetitive conditioning of multiple stimuli, extinction of one CS attenuated responding to others which had not undergone direct extinction. Four experiments with rat subjects investigated potential mechanisms of this secondary extinction effect. Experiment 1 assessed whether secondary extinction would be more likely to occur with target CSs that have themselves undergone some prior extinction. Two CSs were initially paired with shock. One CS was subsequently extinguished before the second CS was tested. The target CS was partially extinguished for half the rats and not extinguished CS for the other half. A robust secondary extinction effect was obtained with the non-extinguished target CS. Experiment 2 investigated whether secondary extinction occurs if the target CS is tested outside the context where the first CS is extinguished. Despite the context switch secondary extinction was observed. Extinction of one CS was also found to thwart renewal of suppression to a second CS when it was tested in a neutral context. Experiment 3 examined whether secondary extinction can be attributed to mediated generalization caused by association of the CSs with a common US during conditioning. Rats received conditioning with three CSs and then extinction with one of them. Secondary extinction was observed with a shock-associated CS when the extinguished CS had been associated with either food pellets or shock, suggesting that secondary extinction is not US-specific and is thus not explained by this mediated generalization mechanism. Experiment 4 examined whether intermixing trials with the two stimuli during conditioning is necessary for secondary extinction to occur. Rats were either conditioned with intermixed trials as in Experiments 1-3, or with blocked trials of each CS presented in conditioning sessions separated by a day. Secondary extinction was observed only in the former condition. The results are consistent with the hypothesis that CSs must be associated with a common temporal context for secondary extinction to occur.

La thèse comporte six chapitres. Dans le premier chapitre, on rappelle les bases de la théorie et on étudie la structure des algèbres Hom-associatives ainsi que les différentes constructions comme la composition avec des endomorphismes qui nous permet de construire de nouveaux objets et d’établir certaines nouvelles propriétés. Parmi les résultats originaux, on peut signaler l’étude des algèbres Hom-associatives simples ainsi que leurs constructions. On a montré que toutes les algèbres Hom-associatives multiplicatives simples s’obtiennent par composition d’algèbres simples et d’automorphismes. Dans le deuxième chapitre, on commence par étudier les propriétés des changements de base dans ces structures algébriques. On a calculé la base de Gröbner de l’idéal engendrant la variété algébrique des algèbres Hom-associatives de dimension 2 où la multiplication µ et l’application linéaire α sont identifiées à leurs constantes de structure relativement à une base donnée. La classification, à isomorphisme près, des algèbres Hom-associatives unitaires et non unitaires est établie en dimension 2 et 3. On a aussi décrit les algèbres de type associatif en se basant sur le théorème de twist de Yau. Dans le troisième chapitre, on étudie certaines propriétés et invariants comme les dérivations, αk-dérivations où k est un entier positif. Dans le quatrième chapitre, on établit la cohomologie de ces algèbres. On a pu lister les algèbres rigides grâce à leur classe de cohomologie puis on s'est 'intéressé aux déformations infinitésimales et dégénérations. D’une part, la cohomologie et déformation de ces algèbres nous a permis d’identifier les algèbres rigides dont le deuxième groupe de cohomologie est nulle, et d’autre part de caractérisation de composante irréductible. Dans le cinquième chapitre, on s’intéresse aux structures Rota-Baxter de poids λ ϵK de ces algèbres. Enfin, dans le dernier chapitre, on a travaillé sur les structures Hom-bialgèbres et leurs invariants. / The purpose of this thesis is to study the structure of Hom-associative algebras and provide classifications. Among the results obtained in this thesis, we provide 2-dimensional and 3-dimensional Hom-associative algebras and give a characterization of multiplicative simple Hom-associative algebras. Moreover we compute some invariants and discuss irreducible components of the corresponding algebraic varieties. The thesis is organized as follows. In the first chapter we give the basics about Hom-associative algebras and provide some new properties. Moreover, we discuss unital Hom-associative algebras. Chapter 2 deals with simple multiplicative Hom-associative algebras. We present one of the main results of this paper, that is a characterization of simple multiplicative Hom-associative algebras. Indeed, we show that they are all obtained by twistings of simple associative algebras. Chapter 3 is dedicated to describe algebraic varieties of Hom-associative algebras and provide classifications, up to isomorphism, of 2-dimensional and 3-dimensional Hom-associative algebras. In chapter 4, we compute their derivations and twisted derivations, whereas in chapter 5, we compute their Hom-Type Hochschild cohomology. In the last section of this chapter, we consider the geometric classification problem using one-parameter formel deformations, and describe the irreducible components. In chapter 6, we compute Rota-Baxter structures of weight k of Hom-associative algebras appearing in our classification. In chapter 7, We work out Hom-bialgebras structures as well as their invariants. Properties and classifications, as well as the calculation of certain invariants such as the first and second cohomology groups, were studied.

Pretendeu-se com o desenvolvimento desta pesquisa levantar e aprofundar a análise da documentação existente em torno do Primeiro Congresso Brasileiro de Enfermagem, realizado no ano de 1947, na Escola de Enfermagem da Faculdade de Medicina da Universidade de São Paulo. O objetivo geral da presente investigação foi identificar reformulação do ensino e do exercício profissional da enfermagem brasileira, na década de 1940, consubstanciadas no primeiro evento de natureza científica do Brasil. Teve como objetivos específicos: identificar questões relativas ao ensino de enfermagem por intermédio do reconhecimento de temas abordados no Primeiro Congresso Nacional de Enfermagem, bem como nas legislações do ensino do período delimitado neste estudo; reconhecer o contexto sócio-político da década de 1940 (mais especificamente no Estado de SP) e sua influência sobre a enfermagem e descrever a atuação e liderança de Edith de Magalhães Fraenkel no contexto da Escola de Enfermagem da USP e dos movimentos da enfermagem paulista na década de 1940, por intermédio da documentação e bibliografia existentes. Trata-se de um estudo qualitativo, de abordagem histórico-social com utilização do método da pesquisa documental e da micro-história. O material disponível nos acervos do Centro Histórico Cultural da Enfermagem Ibero-Americana, Arquivo Histórico da Associação Brasileira de Enfermagem Seção São Paulo, Centro de Documentação da Escola de Enfermagem Anna Nery CEDOC/EEAN/UFRJ, Biblioteca Wanda de Aguiar Horta da Escola de Enfermagem da USP, Biblioteca da Faculdade de Saúde Pública da USP e Fundação Casa de Oswaldo Cruz COC/FIOCRUZ serviram a pesquisa realizada. Os desdobramentos do movimento associativo paulista resultaram na importância da criação de cursos para formação de Enfermeira-Chefe e Enfermagem Psiquiátrica, levantamento de questões relativas ao problema em Enfermagem em Saúde Pública na década de 1940, bem como a criação do curso de auxiliar de enfermagem. A EEUSP rompeu o padrão estabelecido para a formação profissional, sugerido pelo Decreto 20.109/31, que elegia normas específicas que deveriam ser assumidas pelas escolas existentes no país. A fundação da EEUSP foi um marco para a renovação dos processos educacionais da Enfermagem brasileira, que corroborou para a promulgação da Lei 775/49, impactando, inclusive, na formação da identidade profissional. As ações e intencionalidades do movimento associativo paulista em enfermagem foi, desde o seu início, congregar enfermeiras em torno de seus interesses, sejam voltadas para as questões do ensino, da formação, seja na atenção às demandas assistenciais, gerencias, dentre outras, como a capacitação da própria enfermeira para liderar sua equipe de trabalho / It was intended with the development of this research to raise and to deepen the analysis of the existing documentation around the First Brazilian Congress of Nursing, carried through in the year of 1947, the School of Nursing of the College of Medicine of the University of São Paulo. The general objective of the present inquiry was to identify reformularization of the education and the professional exercise of the Brazilian nursing, in the decade of 1940, embodied in the first event of scientific nature of Brazil. It had as objective specific: to identify issues related to nursing education through the recognition of issues addressed in the First National Congress of Nursing, as well as teaching the laws of the period defined in this study, recognizing the socio-political context of the 1940s (more specifically in the State of São Paulo) and its influence on nursing practice and describe the action and leadership of Edith Magalhães Fraenkel in the context of the USP School of Nursing and nursing movements Sao Paulo nursing in the decade of 1940, for intermediary of the existing documentation and bibliography. One is to a qualitative study, description-social boarding with use of the method of the documentary research and micro-history. The available material in the collections of the Centro Cultural History of Nursing Ibero-American Historical Archives of the Brazilian Nursing Association - São Paulo Section, Center for Documentation of Anna Nery School of Nursing - CEDOC / EEAN / UFRJ, Wanda de Aguiar Horta Library School Nursing USP, Library of the Faculty of Public Health of USP and Casa de Oswaldo Cruz Foundation - COC / Fiocruz served research.The unfoldings of the São Paulo associative movement had resulted in the importance of the creation of courses for formation of Nurse-Head and Psychiatric Nursing, survey of relative questions to the problem in Nursing in Public Health in the decade of 1940, as well as the creation of the course of nurse aid. The EEUSP breached the standard established for the professional formation, suggested for Decree 20.109/31, that it chose specific norms that would have to be assumed by the existing schools in the country. The foundation of the EEUSP was a landmark for the renewal of the educational processes of the Brazilian Nursing, that it corroborated for the promulgation of Law 775/49, impacting, also, in the formation of the professional identity. The actions and intentions of the associative movement in São Paulo was nursing, since its inception, nurses gather around their interests are focused on the issues of education, training, whether in health care demands attention to, manage, among others, such as enabling the nurse to lead his own team