Equidistribution estimates for Fekete points on complex manifolds

We study the equidistribution of Fekete points in a compact complex manifold. These are extremal point configurations defined through sections of powers of a positive line bundle. Their equidistribution is a known result. The novelty of our approach is that we relate them to the problem of sampling and interpolation on line bundles, which allows us to estimate the equidistribution of the Fekete points quantitatively. In particular we estimate the Kantorovich-Wasserstein distance of the Fekete points to its limiting measure. The sampling and interpolation arrays on line bundles are a subject of independent interest, and we provide necessary density conditions through the classical approach of Landau, that in this context measures the local dimension of the space of sections of the line bundle. We obtain a complete geometric characterization of sampling and interpolation arrays in the case of compact manifolds of dimension one, and we prove that there are no arrays of both sampling and interpolation in the more general setting of semipositive line bundles.

A new compact linear programming formulation for choice network revenue management

The choice network revenue management model incorporates customer purchase behavioras a function of the offered products, and is the appropriate model for airline and hotel networkrevenue management, dynamic sales of bundles, and dynamic assortment optimization.The optimization problem is a stochastic dynamic program and is intractable. A certainty-equivalencerelaxation of the dynamic program, called the choice deterministic linear program(CDLP) is usually used to generate dyamic controls. Recently, a compact linear programmingformulation of this linear program was given for the multi-segment multinomial-logit (MNL)model of customer choice with non-overlapping consideration sets. Our objective is to obtaina tighter bound than this formulation while retaining the appealing properties of a compactlinear programming representation. To this end, it is natural to consider the affine relaxationof the dynamic program. We first show that the affine relaxation is NP-complete even for asingle-segment MNL model. Nevertheless, by analyzing the affine relaxation we derive a newcompact linear program that approximates the dynamic programming value function betterthan CDLP, provably between the CDLP value and the affine relaxation, and often comingclose to the latter in our numerical experiments. When the segment consideration sets overlap,we show that some strong equalities called product cuts developed for the CDLP remain validfor our new formulation. Finally we perform extensive numerical comparisons on the variousbounds to evaluate their performance.

Recontracting and competition

We characterize the set of Walrasian allocations of an economy as theset of allocations which can be supported by abstract equilibria that satisfy a recontracting condition which reflects the idea that agents can freely trade with each other. An alternative (and weaker) recontracting condition characterizesthe core. The results are extended to production economies by extending thedefinition of the recontracting condition to include the possibility of agentsto recontract with firms. However, no optimization requirement is imposed onfirms. In pure exchange economies, an abstract equilibrium is a feasible allocation and a list of choice sets, one for each agent, that satisfy thefollowing conditions: an agent's choice set is a subset of the commodity space that includes his endowment; and each agent's equilibrium bundle isa maximal element in his choice set, with respect to his preferences. Therecontracting condition requires that any agent can buy bundles from any other agent's choice set by offering the other agent a bundle he prefers tohis equilibrium bundle.

Unified formalism for non-autonomous mechanical systems

We present a unified geometric framework for describing both the Lagrangian and Hamiltonian formalisms of regular and non-regular time-dependent mechanical systems, which is based on the approach of Skinner and Rusk (1983). The dynamical equations of motion and their compatibility and consistency are carefully studied, making clear that all the characteristics of the Lagrangian and the Hamiltonian formalisms are recovered in this formulation. As an example, it is studied a semidiscretization of the nonlinear wave equation proving the applicability of the proposed formalism.

Spermiogenesis and spermatozoon ultrastructure of the bothriocephalidean cestode Clestobothrium crassiceps (Rudolphi, 1819), a parasite of the teleost fish Merluccius merluccius (Gadiformes: Merlucciidae)

Spermiogenesis and the ultrastructure of the spermatozoon of the bothriocephalidean cestode Clestobothrium crassiceps (Rudolphi, 1819), a parasite of the teleost fish Merluccius merluccius (Linnaeus, 1758), have been studied by means of transmission electron microscopy. Spermiogenesis involves firstly the formation of a differentiation zone. It is characterized by the presence of two centrioles associated with striated rootlets, an intercentriolar body and an electron-dense material in the apical region of this zone. Later, two flagella develop from the centrioles, growing orthogonally in relation to the median cytoplasmic process. Flagella then undergo a rotation of 90° until they become parallel to the median cytoplasmic process, followed by the proximodistal fusion of the flagella with the median cytoplasmic process. The nucleus elongates and afterwards it migrates along the spermatid body. Spermiogenesis finishes with the appearance of the apical cone surrounded by the single helical crested body at the base of the spermatid. Finally, the narrowing of the ring of arched membranes detaches the fully formed spermatozoon. The mature spermatozoon of C. crassiceps is filiform and contains two axonemes of the 9 + '1' trepaxonematan pattern, a parallel nucleus, parallel cortical microtubules, and electron-dense granules of glycogen. The anterior extremity of the gamete exhibits a short electron-dense apical cone and one crested body, which turns once around the sperm cell. The first axoneme is surrounded by a ring of thick cortical microtubules that persist until the appearance of the second axoneme. Later, these thick cortical microtubules disappear and thus, the mature spermatozoon exhibits two bundles of thin cortical microtubules. The posterior extremity of the male gamete presents only the nucleus. Results are discussed and compared particularly with the available ultrastructural data on the former 'pseudophyllideans'. Two differences can be established between spermatozoa of Bothriocephalidea and Diphyllobothriidea, the type of spermatozoon (II vs I) and the presence/absence of the ring of cortical microtubules.

Reelin regulates the development and synaptogenesis of the layer-specific entorhino-hippocampal connections

Here we examine the role of Reelin, an extracellular protein involved in neuronal migration, in the formation of hippocampal connections. Both at prenatal and postnatal stages, the general laminar and topographic distribution of entorhinal projections is preserved in the hippocampus of reeler mutant mice, in the absence of Reelin. However, developing and adult entorhinal afferents show severe alterations, including increased numbers of misrouted fibers and the formation of abnormal patches of termination from the medial and lateral entorhinal cortices. At perinatal stages, single entorhinal axons in reeler mice are grouped into thick bundles, and they have decreased axonal branching and decreased extension of axon collaterals. We also show that the number of entorhino-hippocampal synapses is lower in reeler mice than in control animals during development. Studies performed in mixed entorhino-hippocampal co-cultures combining slices from reeler and wild-type mice indicate that these abnormalities are caused by the lack of Reelin in the target hippocampus. These findings imply that Reelin fulfills a modulatory role during the formation of layer-specific and topographic connections in the hippocampus. They also suggest that Reelin promotes maturation of single fibers and synaptogenesis by entorhinal afferents.

Spermiogenesis and spermatozoon ultrastructure of the bothriocephalidean cestode Clestobothrium crassiceps (Rudolphi, 1819), a parasite of the teleost fish Merluccius merluccius (Gadiformes: Merlucciidae)

Spermiogenesis and the ultrastructure of the spermatozoon of the bothriocephalidean cestode Clestobothrium crassiceps (Rudolphi, 1819), a parasite of the teleost fish Merluccius merluccius (Linnaeus, 1758), have been studied by means of transmission electron microscopy. Spermiogenesis involves firstly the formation of a differentiation zone. It is characterized by the presence of two centrioles associated with striated rootlets, an intercentriolar body and an electron-dense material in the apical region of this zone. Later, two flagella develop from the centrioles, growing orthogonally in relation to the median cytoplasmic process. Flagella then undergo a rotation of 90° until they become parallel to the median cytoplasmic process, followed by the proximodistal fusion of the flagella with the median cytoplasmic process. The nucleus elongates and afterwards it migrates along the spermatid body. Spermiogenesis finishes with the appearance of the apical cone surrounded by the single helical crested body at the base of the spermatid. Finally, the narrowing of the ring of arched membranes detaches the fully formed spermatozoon. The mature spermatozoon of C. crassiceps is filiform and contains two axonemes of the 9 + '1' trepaxonematan pattern, a parallel nucleus, parallel cortical microtubules, and electron-dense granules of glycogen. The anterior extremity of the gamete exhibits a short electron-dense apical cone and one crested body, which turns once around the sperm cell. The first axoneme is surrounded by a ring of thick cortical microtubules that persist until the appearance of the second axoneme. Later, these thick cortical microtubules disappear and thus, the mature spermatozoon exhibits two bundles of thin cortical microtubules. The posterior extremity of the male gamete presents only the nucleus. Results are discussed and compared particularly with the available ultrastructural data on the former 'pseudophyllideans'. Two differences can be established between spermatozoa of Bothriocephalidea and Diphyllobothriidea, the type of spermatozoon (II vs I) and the presence/absence of the ring of cortical microtubules.

On the tractability of the piecewise-linear approximation for general discrete-choice network revenue management

The choice network revenue management (RM) model incorporates customer purchase behavioras customers purchasing products with certain probabilities that are a function of the offeredassortment of products, and is the appropriate model for airline and hotel network revenuemanagement, dynamic sales of bundles, and dynamic assortment optimization. The underlyingstochastic dynamic program is intractable and even its certainty-equivalence approximation, inthe form of a linear program called Choice Deterministic Linear Program (CDLP) is difficultto solve in most cases. The separation problem for CDLP is NP-complete for MNL with justtwo segments when their consideration sets overlap; the affine approximation of the dynamicprogram is NP-complete for even a single-segment MNL. This is in contrast to the independentclass(perfect-segmentation) case where even the piecewise-linear approximation has been shownto be tractable. In this paper we investigate the piecewise-linear approximation for network RMunder a general discrete-choice model of demand. We show that the gap between the CDLP andthe piecewise-linear bounds is within a factor of at most 2. We then show that the piecewiselinearapproximation is polynomially-time solvable for a fixed consideration set size, bringing itinto the realm of tractability for small consideration sets; small consideration sets are a reasonablemodeling tradeoff in many practical applications. Our solution relies on showing that forany discrete-choice model the separation problem for the linear program of the piecewise-linearapproximation can be solved exactly by a Lagrangian relaxation. We give modeling extensionsand show by numerical experiments the improvements from using piecewise-linear approximationfunctions.

Spermatological characteristics of Pleurogenidae (Digenea) inferred from the ultrastructural study of Pleurogenes claviger, Pleurogenoides medians and Prosotocus confusus

The present work constitutes the first ultrastructural analysis of the spermatozoon in the Pleurogenidae, with the study of three species belonging to three of the 16 genera included in this family, namely Pleurogenes claviger, Pleurogenoides medians and Prosotocus confusus. The mature spermatozoa of these pleurogenids present two axonemes of the 9+'1' trepaxonematan pattern, a nucleus, two mitochondria, two bundles of parallel cortical microtubules, external ornamentation, spine-like bodies and granules of glycogen. The organization of these characters in the sperm cell is similar in the three species. Thus, the anterior spermatozoon extremity is filiform and a continuous and submembranous layer of parallel cortical microtubules surrounds the axonemes at their anterior end. The posterior spermatozoon extremity exhibits the second axoneme and corresponds to the Cryptogonimidean type of Quilichini et al. (2010). Slight differences were noted between the spermatozoon of P. confusus and those of the two remaining species in the location of mitochondria.

Brittle to ductile transition in a fiber bundle with strong heterogeneity

We analyze the failure process of a two-component system with widely different fracture strength in the framework of a fiber bundle model with localized load sharing. A fraction 0≤α≤1 of the bundle is strong and it is represented by unbreakable fibers, while fibers of the weak component have randomly distributed failure strength. Computer simulations revealed that there exists a critical composition αc which separates two qualitatively different behaviors: Below the critical point, the failure of the bundle is brittle, characterized by an abrupt damage growth within the breakable part of the system. Above αc, however, the macroscopic response becomes ductile, providing stability during the entire breaking process. The transition occurs at an astonishingly low fraction of strong fibers which can have importance for applications. We show that in the ductile phase, the size distribution of breaking bursts has a power law functional form with an exponent μ=2 followed by an exponential cutoff. In the brittle phase, the power law also prevails but with a higher exponent μ=92. The transition between the two phases shows analogies to continuous phase transitions. Analyzing the microstructure of the damage, it was found that at the beginning of the fracture process cracks nucleate randomly, while later on growth and coalescence of cracks dominate, which give rise to power law distributed crack sizes.

Marià Vallès i Vallès, arxiver de la Diputació de Barcelona (1893-1919)

Des de la creació de l’Arxiu (1820) ha evolucionat el tractament dels seus fons. Segons els Reglaments (1822, 1879) els oficials descrivien els expedients, el registrador resseguia el tràmit, i l’arxiver controlava amb un registre la ubicació dels lligalls. Esteve (1836) inventarià la documentació antiga, estructurada en seccions per Quintana. Solà (1854), seguit per Rancés, classificà per negociats i matèries i millorà la descripció dels lligalls. Vallès confeccionà un Registre-inventari que descriu cronològicament per negociats i matèries tots els fons. També inventarià col•leccions i fons afegits, que la Mancomunitat destinà a l’IEC, la Biblioteca de Catalunya i els Museus d’Art. Paraules clau: Història d’arxius, arxivística catalana, arxivers catalans, Marià Vallès, Vallès i Vallès, arxiu, Diputació, Mancomunitat, Jacint Verdaguer, Prat de la Riba

Concurs per a una Llar d'Infants

El projecte defineix un carrer interior tangent a l’edifici del pavelló per on es produeix l’entrada i per on s’atravessa visualment l’edifici, de manera que la façana del pavelló te continuïtat cap a l’interior de la llar d’infants. Perpendicularment es disposa l’espai del vestíbul que articula els espais de circulació i dona sortida i visuals al pati de jocs. Les zones de pas tenen una alçada inferior a la de les altres àrees per lògica d’us i per donar claredat volumètrica a l’edifici. L’entrada es produeix per una rampa, sota un voladís que a l’hora recull l’escletxa oberta a la façana del pavelló per il•luminar l’àrea administrativa. L’altre extrem del carrer és una sortida d’emergència. En una visió general s’observa que el pla de façana del pavelló fa de suport a dos volums que entren en relació: la rampa d’accés al pavelló i la coberta del carrer interior de la llar d’infants. Pel que fa a les alçades, el conjunt manté el criteri de donar major alçada als espais principals (pista i aules) respecte els d’accés. Pel que fa a la forma, el cos d’aules adopta la coberta plana per entrar en relació amb l’horitzontalitat de la visera de la façana principal del pavelló i no la forma corba perquè l’escala del cos d’aules no admet aquesta solució. S’enfatitzaria al màxim la percepció de conjunt si les cobertes de les aules i del pavelló fossin igualment inclinades. Les dependències s’organitzen en dues àrees: L’àrea administrativa es col•loca sota el forjat que defineix el projecte del pavelló. Atès que l’alçada lliure interior és de 3.00 m., i per tal de poder garantir il•luminació i ventil•lació natural a aquestes peces, es proposa baixar la cota de tota la llar d’infants 80 cm. respecte la cota del carrer. Consta d'una sala de reunions propera al vestíbul, un despatx per la direcció del centre uns vestidors amb bany per al personal i una sala d'usos múltiples. L’àrea d’activitats es col•loca separada del pavelló, definint un volum independent, tant en planta com en secció. Consta de 3 aules de 20 alumnes que donen resposta a les necessitats plantejades pel programa. Aquestes s’obren generosament al pati de jocs buscant la llum de nord i per la part superior amb una obertura molt més controlada tenen la llum del sud. Això permet il•luminar i ventil•lar de forma creuada. El tram de carrer interior davant de les aules es converteix en una zona de jocs comuna.

Spermiogenesis and spermatozoon of the liver fluke Mediogonimus jourdanei (Microphalloidea: Prosthogonimidae), a parasite of Myodes glareolus (Rodentia: Cricetidae)

Spermatological characters of the liver fluke Mediogonimus jourdanei Mas-Coma et Rocamora, 1978 were studied by means of transmission and scanning electron microscopy. Spermiogenesis begins with the formation of the differentiation zone containing two centrioles associated with striated rootlets and an intercentriolar body. These two centrioles originate two free flagella that undergo a 90 degrees rotation before fusing with the median cytoplasmic process. Both nuclear and mitochondrial migrations toward the median cytoplasmic process occur before the proximodistal fusion of flagella. Finally, the constriction of the ring of arched membranes gives rise to the young spermatozoon. The mature sperm of M. jourdanei measures about 260 microm and presents two axonemes of different lengths with the typical pattern of the Trepaxonemata, two bundles of parallel cortical microtubules, one mitochondrion, a nucleus and granules of glycogen. An analysis of all the microphalloidean species studied to date emphasised some differences in certain characters found in Maritrema linguilla Jägerskiöld, 1908 and Ganeo tigrinum Mehra et Negi, 1928 in comparison to those in the remaining microphalloideans. The presence and variability of such ultrastructural characters according to family, superfamily or order have led several authors to propose their use in the analysis of trematode relationships and phylogeny. Therefore, apart from producing new data on the family Prosthogonimidae, the present study also compares the spermatological organization of M jourdanei with other available ultrastructural studies focusing on the Microphalloidea.

Spermiogenesis and spermatozoon of the liver fluke Mediogonimus jourdanei (Microphalloidea: Prosthogonimidae), a parasite of Myodes glareolus (Rodentia: Cricetidae)

Spermatological characters of the liver fluke Mediogonimus jourdanei Mas-Coma et Rocamora, 1978 were studied by means of transmission and scanning electron microscopy. Spermiogenesis begins with the formation of the differentiation zone containing two centrioles associated with striated rootlets and an intercentriolar body. These two centrioles originate two free flagella that undergo a 90 degrees rotation before fusing with the median cytoplasmic process. Both nuclear and mitochondrial migrations toward the median cytoplasmic process occur before the proximodistal fusion of flagella. Finally, the constriction of the ring of arched membranes gives rise to the young spermatozoon. The mature sperm of M. jourdanei measures about 260 microm and presents two axonemes of different lengths with the typical pattern of the Trepaxonemata, two bundles of parallel cortical microtubules, one mitochondrion, a nucleus and granules of glycogen. An analysis of all the microphalloidean species studied to date emphasised some differences in certain characters found in Maritrema linguilla Jägerskiöld, 1908 and Ganeo tigrinum Mehra et Negi, 1928 in comparison to those in the remaining microphalloideans. The presence and variability of such ultrastructural characters according to family, superfamily or order have led several authors to propose their use in the analysis of trematode relationships and phylogeny. Therefore, apart from producing new data on the family Prosthogonimidae, the present study also compares the spermatological organization of M jourdanei with other available ultrastructural studies focusing on the Microphalloidea.

Spermiogenesis and the spermatozoon ultrastructure of Robphildollfusium fractum (Digenea: Gyliauchenidae), an intestinal parasite of Sarpa salpa (Pisces: Teleostei)

Spermiogenesis in Robphildollfusium fractum begins with the formation of a differentiation zone containing: two centrioles, each bearing striated rootlets, nucleus, several mitochondria and an intercentriolar body constituted by seven electron-dense layers. The two centrioles originate two free flagella growing orthogonally to the median cytoplasmic process. Later, the free flagella rotate and undergo proximodistal fusion with the median cytoplasmic process. Nuclear and mitochondrial migrations occur before this proximodistal fusion. Finally, the young spermatozoon detaches from the residual cytoplasm after the constriction of the ring of arched membranes. The spermatozoon of R. fractum exhibits two axonemes of different length of the 9 +"1" trepaxonematan pattern, nucleus, two mitochondria, two bundles of parallel cortical microtubules, external ornamentation of the plasma membrane, spine-like bodies and granules of glycogen. Additionally, a shorter axoneme, which does not reach the nuclear region, the presence of an electron-dense material in the anterior spermatozoon extremity and the morphologies of both spermatozoon extremities characterize the mature sperm of R. fractum.