On divisors of pseudovarieties generated by some classes of full transformation semigroups

Algebra Colloquium, 15 (2008), p. 581–588

Partial classification of Lorenz knots: Syllable permutations of torus knots words

We define families of aperiodic words associated to Lorenz knots that arise naturally as syllable permutations of symbolic words corresponding to torus knots. An algorithm to construct symbolic words of satellite Lorenz knots is defined. We prove, subject to the validity of a previous conjecture, that Lorenz knots coded by some of these families of words are hyperbolic, by showing that they are neither satellites nor torus knots and making use of Thurston's theorem. Infinite families of hyperbolic Lorenz knots are generated in this way, to our knowledge, for the first time. The techniques used can be generalized to study other families of Lorenz knots.

An existence result for discontinuous games

We introduce a notion of upper semicontinuity, weak upper semicontinuity, and show that it, together with a weak form of payoff security, is enough to guarantee the existence of Nash equilibria in compact, quasiconcave normal form games. We show that our result generalizes the pure strategy existence theorem of Dasgupta and Maskin (1986) and that it is neither implied nor does it imply the existence theorems of Baye, Tian, and Zhou (1993) and Reny (1999). Furthermore, we show that an equilibrium may fail to exist when, while maintaining weak payoff security, weak upper semicontinuity is weakened to reciprocal upper semicontinuity.

Microvascularização arterial da cóclea

RESUMO: Na descrição deste estudo foi utilizada a terminologia anatómica da Sociedade Brasileira de Anatomia adaptada ao português por J. A. Esperança-Pina de acordo com o tratado Anatomia Humana da Relação. Os actuais estudos sobre hipoacusia sensorioneural implicam um grupo crescente de situações, em que a lesão se situa ao nível da microvascularização coclear, daí que o conhecimento exacto da angiomorfologia normal se torne essencial na fase actual do conhecimento. A autora tem vindo a estudar, desde 1986, a angiomorfologia do ouvido Interno no modelo experimental, o Cobaio, utilizando várias técnicas microvasculares. sendo dado enfâse particular neste estudo à técnica de microscopia electrónica de varrimento em moldes vasculares. Os animais usados no presente estudo pertencem à espécie cavia porcellus, cobaio, por serem considerados na comunidade cientifica internacional como o melhor modelo experimental para estudo do ouvido interno, pelo facto de a morfologia coclear ser muito semelhante à do Homem e por isso ser um modelo fiável para cirurgia experimental e microdissecção. Este estudo foi realizado em 100 cobaios, cavia porcellus, de ambos os sexos com peso médio de 450g. A vascularização do ouvido interno, no cobaio como no homem, faz-se através dos ramos de divisão da artéria auditiva interna ou labiríntica. A artéria labiríntica origina-se como ramo colateral da artéria cerebelosa ântero-inferior a qual tem origem na artéria basilar ou na artéria vertebral. Embora no homem a artéria auditiva interna possa também destacar-se da artéria basilar e até da artéria vertebral, no cobaio em todos os casos estudados a sua origem verificou-se sempre na artéria cerebelosa ântero-inferior. A artéria labiríntica, ao passar abaixo do meato auditivo interno, divide-se na artéria vestibular anterior e na artéria coclear comum.A artéria vestibular anterior dirige-se para o nervo vestibular, emite vasa nervorum para este nervo e vasculariza o utrículo e os canais semicirculares. A artéria coclear comum origina dois ramos principais, a artéria vestíbulo‑coclear ou vestibular posterior no cobaio, a qual se destaca junto à espira basal da cóclea e a artéria coclear, como ramo terminal, que passa a denominar-se de artéria modiolar ou espiralada, após entrar no modíolo. A artéria modiolar ascende no modíolo promovendo através dos seus ramos colaterais e dos seus ramos terminais a microvascularização coclear, numa vascularização de órgão de tipo terminal. Ao longo do seu trajecto verificou‑se de modo constante uma redução gradual de calibre em cada uma das espiras, por emissão de ramos colaterais, sendo que o calibre da artéria na base da cóclea apresenta um valor que diminui gradualmente até ao ápice. A artéria modiolar origina em todo o seu trajecto ramos colaterais, cujo número diminui em valor absoluto da base para o ápice: Arteríolas radiárias internas, arteríolas de trajecto flexuoso que caminham junto às estruturas sensorioneurais da parede interna da cóclea, junto ao lábio timpânico da lâmina espiral óssea e na parede do próprio modíolo, que se relacionam intimamente com este. As arteríolas radiárias internas originam‑se no flanco da artéria modiolar espiralada. Contam‑se dez a doze em cada espira, extraordinariamente flexuosas desde a sua origem. As arteríolas radiárias internas originam como ramos colaterais, vários grupos de arteríolas de menor calibre, que vascularizam distintas regiões da parede interna da cóclea, as arteríolas do gânglio espiral, a rede espiral interna, as arteríolas de origem dos glomérulos de Schwalbe e a arteríola da lâmina basilar. As arteríolas radiárias externas importantes ramos colaterais da artéria modiolar espiralada promovem a vascularização de importantes estruturas da parede externa. Ao atingir o limite externo do ligamento espiral, as arteríolas radiárias externas dividem‑se em vários ramos arteriolares de menor calibre, ao longo da convexidade do limite externo do ligamento espiral, originando a rede capilar pós-estriada que ocupa a porção lateral do ligamento espiral e a rede capilar ad‑ -estriada, na sua porção mais medial em íntima relação com a estria vascular. A espira basal da cóclea apresenta grande riqueza de vascularização, com características particulares apenas a esta espira, a qual é metabolicamente a mais exigente. A arteríola da janela da cóclea aborda a janela da cóclea pela sua convexidade e divide-se numa rica rede vascular da qual emergem arteríolas pré-capilares que se ramificam em capilares, os quais se dirigem em profundidade penetrando a rampa timpânica da cóclea ao nível da espira basal. Importou neste estudo verificar quais as semelhanças em termos de calibre de estruturas análogas, na parede interna e na parede externa da cóclea, com particular incidência na rede capilar. Do estudo estatístico realizado com testes paramétricos de Tamahane e não paramétricos de Mann-Whitney, verifica-se que comparando todas as estruturas consideradas estas têm calibres diferentes, com excepção dos capilares da estria vascular e do ligamento espiral, pertencentes à parede externa da cóclea que têm calibres iguais aos capilares da rede espiral interna e aos capilares da parede interna da cóclea, dependentes das arteríolas da rede espiral interna. As redes capilares dependentes das arteríolas radiárias internas que vascularizam as estruturas sensorioneurais junto á parede interna do modiolo são em tudo semelhantes em termos de calibre às redes capilares da parede externa da cóclea, incluindo os capilares da estria vascular. Esta particularidade traduz num órgão com vascularização de tipo terminal,um mecanismo de controlo do fluxo sanguíneo coclear tão importante na parede interna como na parede externa da cóclea. ------------ ABSTRACT:Current studies on sensorineural hearing loss, imply a growing group of situations in which the lesion is located at the level of the cochlear microvasculature, hence the exact knowledge of normal angiomorfology becomes essential in current state of knowledge. The author has been studying since 1986, the angiomorfology of inner on the experimental model, the guinea pig, using various microvascular techniques being given particular emphasis in this study to the results of the technique of scanning electron microscopy on corrosion casts. The animals used in this study belong to the species cavia porcellus, guinea pig, to be considered in the international scientific community as the best experimental model for the study of the inner ear, the cochlear morphology is very similar to human and therefore a reliable model for experimental surgery and microdissection. This study was performed in 100 guinea pigs of both sexes with average weight of 450g. There shall be a brief description of embryology, anatomy and cochlear physiology in the light of developmental biology, regarding also the spatial location of the cochlea and the determinism of morphogenetic fields in their development and function. The cochlear transduction mechanism converts the sound wave in stimuli sound and so afferent auditory nerve fibres and deafness are closely related to the cochlear microvasculature. Cochlear ischemia is accompanied by immediate hearing loss. The different type of cochlear injury that leads to sensorineural deafness is well studied in presbycusis where an objective link with the audiometric pattern as been established. The sensory type of deafness, is closely related to the degeneracy of the organ of Corti and damage to the outer hair cells at the basal turn of the cochlea. Keeping in mind cochlear tonotopy with location of high frequency sounds at the level of the base of the cochlea, it explains the audiometric pattern with loss in high frequencies. The neural type of deafness, is characterized by neuronal loss with loss of descendant important neuronal afferents, with audiometric translation on a gradually curve with important loss of auditory discrimination. The metabolic type of deafness results in atrophy of the vascular stria, with consequent change in the potential of the endolymph by decreasing the vascular stria cells and changes in K + recycling mechanism. There is also a change in the morphology of the spiral ligament and the audiometric patern as a flattened curve with loss at all frequencies. Bearing in mind cochlear tonotopy and being characterized all types of sensorineural deafness, we may inquire to what extent the cochlear microvasculature, considering not only the cochlea as a whole but different regions of the inner wall and the outer wall of the cochlea, contributes to deafness. We analysed the entire cochlear morphology on scanning electron microscopy with particular emphasis on bone and membranous cochlea. The inner wall of the cochlea and intramodiolar structures such as the spiral ganglion, the morphology of its cell bodies and their axons are analyzed. The morphology of Corti’s organ is described in detail, with description and large detail of the inner and outer hair cells. Is then presented the study of the microvasculature itself. The spiral modiolar artery is observed with the diaphanization technique and the technique of scanning electron microscopy on corrosion vascular casts. After emergence of collateral branches of the greatest importance, the radiating internal and external arterioles, the modiolar artery gives rise to its terminal branches, the arterioles of the cochear apex. Arterial vasa vasorum and vasa nervorum are displayed with a great detail, which was not yet described in such detail in previous microvascular studies. The arterial radiating arterioles originate in the flank of the spiral modiolar artery in number of ten to twelve in each loop, and they vascularize through their branches the inner wall cochlear sensorineural structures located in the modiolus as the spiral ganglion and structures near the organ of Corti. Their caliber is above 20 μm on the basal turn and in the second loop it decreases to values between 12 and 20 μm, decreasing progressively to the apex of the cochlea.They arise near the modiolus or on their way in the spiral lamina forming vascular loops, and divide without presenting vascular constrictions in their divisions, originating new vascular loops of lower caliber. Internal ratiating arterioles originate as collateral branches several groups of smaller caliber arterioles, which vascularize distinct regions of the inner wall of the cochlea namely, the arterioles of the spiral ganglion, the internal spiral network, the arterioles of origin of the glomeruli of Schwalbe and the arterioles of the basilar membrane. The glomeruli of Schwalbe play an important functional role as relay-stations, in hemodynamic terms, to control the cochlear microvasculature. External radiating arterioles have their origin in the spiral modiolar artery, they are directed towards the outer wall of the cochlea and run through the roof of the scala vestibuli. Above the insertion of Reissner’s membrane on the external wall the external radiating arterioles originate the spiral ligament arterioles, which vascularize the spiral ligament, they divide into several arteriolar branches of smaller caliber, along the convexity of the outer edge of the spiral ligament. The connective tissue of the spiral ligament forms a mesh with supporting function of the highly specialized epithelium, where pericytes were identifiable. Next to its base there is the microvascular network of stria vascularis. The adstriated vascular network which is divided into a capillary network, the capillary network of stria vascularis. The stria vascularis, the only vascularized epithelium of the human body, plays an important role, forming an haemato-labyrintine barrier to assure labyrinthine endocochlear potential and transport of ions, essential for the mechanism of transduction of external hair cells. The cochlear basal turn has a special feature on its external wall, the region of the windows, the round windows giving access to scala tympani and the oval window thatleads into scala vestibuli, and so it is metabolic demanding. For their role in cochlear tonotopy the sensorineural structures and those of the external wall of the cochlea, are particularly vulnerable to hypoxia. Although the complementarity of all the techniques was important for three- -dimensional reconstruction of the microvasculature of the cochlea, the scanning electron microscopy technique, especially when we used the system Semafore was fundamental to perform precise morphometric mesures regarding all vascular structures.Regarding the capillaries of the inner and outer wall of the cochlea networks this technique allowed their characterization in morphometric terms. To conclude the capillaries of the inner wall and of the external wall of the cochlea have similar size. So although located at different cochlear regions, with a different functional role, in cochlear physiology these networks consist of capillaries of similar caliber. It seems to translate a cochlear blood flow control mechanism that is so important in the inner wall as in and the external wall of the cochlea to provide for in inner ear homeosthasia.

The flow-performance relationship around the world

We use a new dataset to study how mutual fund flows depend on past performance across 28 countries. We show that there are marked differences in the flow-performance relationship across countries, suggesting that US findings concerning its shape do not apply universally. We find that mutual fund investors sell losers more and buy winners less in more developed countries. This is because investors in more developed countries are more sophisticated and face lower costs of participating in the mutual fund industry. Higher country-level convexity is positively associated with higher levels of risk taking by fund managers.

On simple bounds for eigenvalues of symmetric tridiagonal matrices

How much can be said about the location of the eigenvalues of a symmetric tridiagonal matrix just by looking at its diagonal entries? We use classical results on the eigenvalues of symmetric matrices to show that the diagonal entries are bounds for some of the eigenvalues regardless of the size of the off-diagonal entries. Numerical examples are given to illustrate that our arithmetic-free technique delivers useful information on the location of the eigenvalues.

Refinement in hybridised institutions

Hybrid logics, which add to the modal description of transition structures the ability to refer to specific states, offer a generic framework to approach the specification and design of reconfigurable systems, i.e., systems with reconfiguration mechanisms governing the dynamic evolution of their execution configurations in response to both external stimuli or internal performance measures. A formal representation of such systems is through transition structures whose states correspond to the different configurations they may adopt. Therefore, each node is endowed with, for example, an algebra, or a first-order structure, to precisely characterise the semantics of the services provided in the corresponding configuration. This paper characterises equivalence and refinement for these sorts of models in a way which is independent of (or parametric on) whatever logic (propositional, equational, fuzzy, etc) is found appropriate to describe the local configurations. A Hennessy–Milner like theorem is proved for hybridised logics.

Sistemas de Tipos para Verificación de Programas Concurrentes. Type Systems for Concurrent Programs Verification.

La programación concurrente es una tarea difícil aún para los más experimentados programadores. Las investigaciones en concurrencia han dado como resultado una gran cantidad de mecanismos y herramientas para resolver problemas de condiciones de carrera de datos y deadlocks, problemas que surgen por el mal uso de los mecanismos de sincronización. La verificación de propiedades interesantes de programas concurrentes presenta dificultades extras a los programas secuenciales debido al no-determinismo de su ejecución, lo cual resulta en una explosión en el número de posibles estados de programa, haciendo casi imposible un tratamiento manual o aún con la ayuda de computadoras. Algunos enfoques se basan en la creación de lenguajes de programación con construcciones con un alto nivel de abstración para expresar concurrencia y sincronización. Otros enfoques tratan de desarrollar técnicas y métodos de razonamiento para demostrar propiedades, algunos usan demostradores de teoremas generales, model-checking o algortimos específicos sobre un determinado sistema de tipos. Los enfoques basados en análisis estático liviano utilizan técnicas como interpretación abstracta para detectar ciertos tipos de errores, de una manera conservativa. Estas técnicas generalmente escalan lo suficiente para aplicarse en grandes proyectos de software pero los tipos de errores que pueden detectar es limitada. Algunas propiedades interesantes están relacionadas a condiciones de carrera y deadlocks, mientras que otros están interesados en problemas relacionados con la seguridad de los sistemas, como confidencialidad e integridad de datos. Los principales objetivos de esta propuesta es identificar algunas propiedades de interés a verificar en sistemas concurrentes y desarrollar técnicas y herramientas para realizar la verificación en forma automática. Para lograr estos objetivos, se pondrá énfasis en el estudio y desarrollo de sistemas de tipos como tipos dependientes, sistema de tipos y efectos, y tipos de efectos sensibles al flujo de datos y control. Estos sistemas de tipos se aplicarán a algunos modelos de programación concurrente como por ejemplo, en Simple Concurrent Object-Oriented Programming (SCOOP) y Java. Además se abordarán propiedades de seguridad usando sistemas de tipos específicos. Concurrent programming has remained a dificult task even for very experienced programmers. Concurrency research has provided a rich set of tools and mechanisms for dealing with data races and deadlocks that arise of incorrect use of synchronization. Verification of most interesting properties of concurrent programs is a very dificult task due to intrinsic non-deterministic nature of concurrency, resulting in a state explosion which make it almost imposible to be manually treat and it is a serious challenge to do that even with help of computers. Some approaches attempts create programming languages with higher levels of abstraction for expressing concurrency and synchronization. Other approaches try to develop reasoning methods to prove properties, either using general theorem provers, model-checking or specific algorithms on some type systems. The light-weight static analysis approach apply techniques like abstract interpretation to find certain kind of bugs in a conservative way. This techniques scale well to be applied in large software projects but the kind of bugs they may find are limited. Some interesting properties are related to data races and deadlocks, while others are interested in some security problems like confidentiality and integrity of data. The main goals of this proposal is to identify some interesting properties to verify in concurrent systems and develop techniques and tools to do full automatic verification. The main approach will be the application of type systems, as dependent types, type and effect systems, and flow-efect types. Those type systems will be applied to some models for concurrent programming as Simple Concurrent Object-Oriented Programming (SCOOP) and Java. Other goals include the analysis of security properties also using specific type systems.

Dois teoremas sôbre a função gama

This paper proves the following theorems on the gamma function: Theorem I The integral ∫O∞ t u e-t dt = Γ ( u + 1 ) , where u, real or complex, is such that R (u) > -1, will not change its value if we substitute z = Q (cos φ + i sen φ) for the real variable t, being jconstant and such that - Π/2 < φ < Π/2 , Theorem II The integral ∫-∞∞ w2u + 1 e -w² dw = Γ ( u + 1 ) , where 2u + 1 is supposed to be a non negative even integer, will not change its value if we substitute z = w + fi, f being a real constant, for the real variable w. The proof of both theorems is obtained by means of the well known Cauchy theorem on contour integrals on the complex plane, as suggested by CRAMÉR (1, p. 126) and LEVY (3, p. 178).

Contractions in the 2-wasserstein lenght space and thermalization of granular media

An algebraic decay rate is derived which bounds the time required for velocities to equilibrate in a spatially homogeneous flow-through model representing the continuum limit of a gas of particles interacting through slightly inelastic collisions. This rate is obtained by reformulating the dynamical problem as the gradient flow of a convex energy on an infinite-dimensional manifold. An abstract theory is developed for gradient flows in length spaces, which shows how degenerate convexity (or even non-convexity) | if uniformly controlled | will quantify contractivity (limit expansivity) of the flow.

The Zariski-Lefschetz principle for higher homotopy groups of nongeneric pencils

We prove a general Zariski-van Kampen-Lefschetz type theorem for higher homotopy groups of generic and nongeneric pencils on singular open complex spaces.

Corrigendum stable matchings and preferences of couples

We correct an omission in the definition of our domain of weakly responsive preferences introduced in Klaus and Klijn (2005) or KK05 for short. The proof of the existence of stable matchings (KK05, Theorem 3.3) and a maximal domain result (KK05, Theorem 3.5) are adjusted accordingly.

Approval voting ion dichotomous preferences

The aim of this paper is to find normative foundations of Approval Voting. In order to show that Approval Voting is the only social choice function that satisfies anonymity, neutrality, strategy-proofness and strict monotonicity we rely on an intermediate result which relates strategy-proofness of a social choice function to the properties of Independence of Irrelevant Alternatives and monotonicity of the corresponding social welfare function. Afterwards we characterize Approval Voting by means of strict symmetry, neutrality and strict monotonicity and relate this result to May's Theorem. Finally, we show that it is possible to substitute the property of strict monotonicity by the one efficiency of in the second characterization.

Fair and efficient student placement with couples

We study situations of allocating positions or jobs to students or workers based on priorities. An example is the assignment of medical students to hospital residencies on the basis of one or several entrance exams. For markets without couples, e.g., for ``undergraduate student placement,'' acyclicity is a necessary and sufficient condition for the existence of a fair and efficient placement mechanism (Ergin, 2002). We show that in the presence of couples, which introduces complementarities into the students' preferences, acyclicity is still necessary, but not sufficient (Theorem 4.1). A second necessary condition (Theorem 4.2) is ``priority-togetherness'' of couples. A priority structure that satisfies both necessary conditions is called pt-acyclic. For student placement problems where all quotas are equal to one we characterize pt-acyclicity (Lemma 5.1) and show that it is a sufficient condition for the existence of a fair and efficient placement mechanism (Theorem 5.1). If in addition to pt-acyclicity we require ``reallocation-'' and ``vacancy-fairness'' for couples, the so-called dictator-bidictator placement mechanism is the unique fair and efficient placement mechanism (Theorem 5.2). Finally, for general student placement problems, we show that pt-acyclicity may not be sufficient for the existence of a fair and efficient placement mechanism (Examples 5.4, 5.5, and 5.6). We identify a sufficient condition such that the so-called sequential placement mechanism produces a fair and efficient allocation (Theorem 5.3).

Increasing quasiconcave production and utility functions with diminishing returns to scale

In microeconomic analysis functions with diminishing returns to scale (DRS) have frequently been employed. Various properties of increasing quasiconcave aggregator functions with DRS are derived. Furthermore duality in the classical sense as well as of a new type is studied for such aggregator functions in production and consumer theory. In particular representation theorems for direct and indirect aggregator functions are obtained. These involve only small sets of generator functions. The study is carried out in the contemporary framework of abstract convexity and abstract concavity.