Avalanche dynamics of fiber bundle models

We present a detailed analytical and numerical study of the avalanche distributions of the continuous damage fiber bundle model CDFBM . Linearly elastic fibers undergo a series of partial failure events which give rise to a gradual degradation of their stiffness. We show that the model reproduces a wide range of mechanical behaviors. We find that macroscopic hardening and plastic responses are characterized by avalanche distributions, which exhibit an algebraic decay with exponents between 5/2 and 2 different from those observed in mean-field fiber bundle models. We also derive analytically the phase diagram of a family of CDFBM which covers a large variety of potential avalanche size distributions. Our results provide a unified view of the statistics of breaking avalanches in fiber bundle models

Critical ruptures in a bundle of slowly relaxing fibers

We study the damage enhanced creep rupture of disordered materials by means of a fiber bundle model. Broken fibers undergo a slow stress relaxation modeled by a Maxwell element whose stress exponent m can vary in a broad range. Under global load sharing we show that due to the strength disorder of fibers, the lifetime ʧ of the bundle has sample-to-sample fluctuations characterized by a log-normal distribution independent of the type of disorder. We determine the Monkman-Grant relation of the model and establish a relation between the rupture life tʄ and the characteristic time tm of the intermediate creep regime of the bundle where the minimum strain rate is reached, making possible reliable estimates of ʧ from short term measurements. Approaching macroscopic failure, the deformation rate has a finite time power law singularity whose exponent is a decreasing function of m. On the microlevel the distribution of waiting times is found to have a power law behavior with m-dependent exponents different below and above the critical load of the bundle. Approaching the critical load from above, the cutoff value of the distributions has a power law divergence whose exponent coincides with the stress exponent of Maxwell elements

Regional and cellular patterns of reelin mRNA expression in the forebrain of the developing and adult mouse

The reelin gene encodes an extracellular protein that is crucial for neuronal migration in laminated brain regions. To gain insights into the functions of Reelin, we performed high-resolution in situ hybridization analyses to determine the pattern of reelin expression in the developing forebrain of the mouse. We also performed double-labeling studies with several markers, including calcium-binding proteins, GAD65/67, and neuropeptides, to characterize the neuronal subsets that express reelin transcripts. reelinexpression was detected at embryonic day 10 and later in the forebrain, with a distribution that is consistent with the prosomeric model of forebrain regionalization. In the diencephalon, expression was restricted to transverse and longitudinal domains that delineated boundaries between neuromeres. During embryogenesis,reelin was detected in the cerebral cortex in Cajal-Retzius cells but not in the GABAergic neurons of layer I. At prenatal stages, reelin was also expressed in the olfactory bulb, and striatum and in restricted nuclei in the ventral telencephalon, hypothalamus, thalamus, and pretectum. At postnatal stages, reelin transcripts gradually disappeared from Cajal-Retzius cells, at the same time as they appeared in subsets of GABAergic neurons distributed throughout neocortical and hippocampal layers. In other telencephalic and diencephalic regions,reelin expression decreased steadily during the postnatal period. In the adult, there was prominent expression in the olfactory bulb and cerebral cortex, where it was restricted to subsets of GABAergic interneurons that co-expressed calbindin, calretinin, neuropeptide Y, and somatostatin. This complex pattern of cellular and regional expression is consistent with Reelin having multiple roles in brain development and adult brain function.

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.

Pattern of injury with a graded excitotoxic insult and ensuing chronic medial septal damage in the rat brain

Brain damage caused by an acute injury depends on the initial severity of the injury and the time elapsed after the injury. To determine whether these two variables activate common mechanisms, we compared the response of the rat medial septum to insult with a graded series of concentrations of a-amino-3-hydroxy-5-methyl-4-isoxazole propionic acid (AMPA) with the time-course effects of a low dose of AMPA. For this purpose we conducted a dose-response study at concentrations of AMPA between 0.27 and 10.8 nmol to measure atrophy of the septal area, losses of cholinergic and GABAergic neurons, astroglial and microglial reactions, and calcification. Cholinergic neurons, whose loss paralleled the degree of septal atrophy produced by AMPA, are more sensitive than GABAergic neurons to the injury produced by AMPA. At doses of AMPA above 2.7 nmol, calcification and the degree of microglial reaction increased only in the GABAergic region of the septal area, whereas atrophy and neuronal loss reached a plateau. We chose the 2.7-nmol dose of AMPA to determine how these parameters were modified between 4 days and 6 months after injection. We found that atrophy and neuronal loss increased progressively through the 6-month study period, whereas astrogliosis ceased to be observed after 1 month, and calcium precipitates were never detected. We conclude that septal damage does not increase with the intensity of an excitotoxic insult. Rather, it progresses continuously after the insult. Because these two situations involve different mechanisms, short-term paradigms are inappropriate for interpreting the pathogenic mechanisms responsible for long-term neurodegenerative processes.

Estudio del desarrollo y conectividad de las neuronas vasotocinérgicas en el prosencéfalo de pollo

En este Trabajo de Fin de Grado se estudia el origen embrionario de las distintas poblaciones neuronales que forman la amígdala medial extendida. La amígdala es una estructura del cerebro anterior involucrada en otorgar un significado emocional a los estímulos ambientales y en el control de distintos aspectos del comportamiento social (p.ej. comportamientos sexual, maternal, agresivo y afiliativo). Ante dichos estímulos, la amígdala pone en marcha una serie de reacciones de carácter motor, autonómico y endocrino que constituyen la respuesta emocional. Algunos desórdenes de carácter neuropsiquiátrico en humanos están relacionados con una disfunción en el control de las emociones y del comportamiento social, y varios de ellos se asocian a alteraciones en el desarrollo de la amígdala. El objetivo del presente trabajo ha sido investigar el origen de las neuronas de la amígdala medial extendida en embriones de pollo (E15 y E18) mediante ensayos de inmunocitoquímica, técnica utilizada para localizar las células que contienen el neuropéptido vasotocina (AVT) y proteínas reguladoras del desarrollo (la producida a partir del gen Otp) para ayudar en la delimitación de los distintos dominios embrionarios del prosencéfalo y distintas subdivisiones de la amígdala extendida. Los resultados de estos ensayos se combinaron con ensayos de trazado de conexiones para analizar la conectividad de las neuronas vasotocinérgicas de esta estructura. Los resultados obtenidos sugieren que las neuronas AVT-positivas podrían derivar del dominio Supra-Opto-Paraventricular (SPV), y algunas poblaciones alcanzarían su posición definitiva dentro del propio dominio por migración radial, mientras que otras invadirían otros dominios cerebrales por migración tangencial. En conclusión, la investigación proporciona importantes datos que clarifican aspectos relevantes del desarrollo y organización adulta de la amígdala extendida, y ayuda a establecer las bases para una mejor comprensión del control neural de las emociones y el comportamiento social en condiciones normales y patológicas.

Studying Memory Encoding to Promote Reliable Engagement of the Medial Temporal Lobe at the Single-subject Level

The medial temporal lobe (MTL)-comprising hippocampus and the surrounding neocortical regions-is a targeted brain area sensitive to several neurological diseases. Although functional magnetic resonance imaging (fMRI) has been widely used to assess brain functional abnormalities, detecting MTL activation has been technically challenging. The aim of our study was to provide an fMRI paradigm that reliably activates MTL regions at the individual level, thus providing a useful tool for future research in clinical memory-related studies. Twenty young healthy adults underwent an event-related fMRI study consisting of three encoding conditions: word-pairs, face-name associations and complex visual scenes. A region-of-interest analysis at the individual level comparing novel and repeated stimuli independently for each task was performed. The results of this analysis yielded activations in the hippocampal and parahippocampal regions in most of the participants. Specifically, 95% and 100% of participants showed significant activations in the left hippocampus during the face-name encoding and in the right parahippocampus, respectively, during scene encoding. Additionally, a whole brain analysis, also comparing novel versus repeated stimuli at the group level, showed mainly left frontal activation during the word task. In this group analysis, the face-name association engaged the HP and fusiform gyri bilaterally, along with the left inferior frontal gyrus, and the complex visual scenes activated mainly the parahippocampus and hippocampus bilaterally. In sum, our task design represents a rapid and reliable manner to study and explore MTL activity at the individual level, thus providing a useful tool for future research in clinical memory-related fMRI studies.

Is bundling anticompetitive?

I analyze the implications of bundling on price competition in a market for complementary products. Using a model of imperfect competition with product differentiation, I identify the incentives to bundle for two types of demand functions and study how they change with the size of the bundle. With an inelastic demand, bundling creates an advantage over uncoordinated rivals who cannot improve by bundling. I show that this no longer holds with an elastic demand. The incentives to bundle are stronger and the market outcome is symmetric bundling, the most competitive one. Profits are lowest and consumer surplus is maximized.

The entropy conjecture for partially hyperbolic diffeomorphisms with 1-D center

We prove that if f is a partially hyperbolic diffeomorphism on the compact manifold M with one dimensional center bundle, then the logarithm of the spectral radius of the map induced by f on the real homology groups of M is smaller or equal to the topological entropy of f. This is a particular case of the Shub's entropy conjecture, which claims that the same conclusion should be true for any C1 map on any compact manifold.

Influence of the in vivo deregulation of the expression of ntrk3 (trkc) on cortical development of a murine model of panic/anxiety disorder

Alteracions durant el desenvolupament cerebral produirien canvis en la connectivitat neuronal i la bioquímica cel•lular que podrien resultar en una disfunció cognitiva i/o emocional, desembocant a trastorns psiquiàtrics. Les neurotrofines intervenen en els processos del neurodesenvolupament i en la funcionalitat del cervell adult i, conseqüentment, serien bons candidats com a factors de predisposició en diverses malalties mentals. S’ha suggerit la implicació del receptor de la neurotrofina 3, TrkC, en el trastorn de pànic. Nosaltres proposem que la sobreexpressió del gen NTRK3 (TrkC) és un mediador comú dels desencadenants genètics i ambientals d’aquest trastorn. Concretament, la seva desregulació podria produir canvis estructurals i funcionals a l’escorça cerebral dels pacients pel seu paper durant l’establiment dels circuïts corticals i la neuroplasticitat a l’adult, probablement esdevenint elements de predisposició a patir atacs de pànic. Els objectius principals d’aquest treball han estat: 1/determinar la contribució específica del gen NTRK3 a les alteracions de l’escorça cerebral observades en pacients, utilitzant un model murí modificat genèticament (TgNTRK3), i 2/analitzar l’impacte específic de la sobreexpressió de NTRK3 sobre la corticogènesi durant estadis embrionaris o postnatals estudiant la neurogènesi i la neuritogènesi. Els resultats indiquen que la sobreexpressió de NTRK3 als ratolins produeix una reducció del gruix de l’escorça frontal, recapitulant la hipofrontalitat dels pacients, que comportaria una menor inhibició dels nuclis subcorticals del sistema límbic com l’amígdala, i alteracions citoarquitectòniques a l’escorça prefrontal medial que recolzen la hipòtesi del seu mal funcionament. Tanmateix, els ratolins TgNTRK3 presenten canvis estructurals a l’escorça somatosensorial, suggerint que el processament de la informació sensorial podria estar alterat, el que encara no s’ha explorat en pacients. La sobreexpressió de NTRK3 també afecta la neuritogènesi en cultius primaris corticals i modifica la resposta de les neurones a l’estimulació amb neurotrofines. Per tant, el fenotip cortical adult dels TgNTRK3 podria dependre d’alteracions durant la corticogènesi.

Recovering Euclidean deformable models from stereo-motion

In this paper we present a novel structure from motion (SfM) approach able to infer 3D deformable models from uncalibrated stereo images. Using a stereo setup dramatically improves the 3D model estimation when the observed 3D shape is mostly deforming without undergoing strong rigid motion. Our approach first calibrates the stereo system automatically and then computes a single metric rigid structure for each frame. Afterwards, these 3D shapes are aligned to a reference view using a RANSAC method in order to compute the mean shape of the object and to select the subset of points on the object which have remained rigid throughout the sequence without deforming. The selected rigid points are then used to compute frame-wise shape registration and to extract the motion parameters robustly from frame to frame. Finally, all this information is used in a global optimization stage with bundle adjustment which allows to refine the frame-wise initial solution and also to recover the non-rigid 3D model. We show results on synthetic and real data that prove the performance of the proposed method even when there is no rigid motion in the original sequence

Monocular-based 3-D seafloor reconstruction and ortho-mosaicing by piecewise planar representation

Photo-mosaicing techniques have become popular for seafloor mapping in various marine science applications. However, the common methods cannot accurately map regions with high relief and topographical variations. Ortho-mosaicing borrowed from photogrammetry is an alternative technique that enables taking into account the 3-D shape of the terrain. A serious bottleneck is the volume of elevation information that needs to be estimated from the video data, fused, and processed for the generation of a composite ortho-photo that covers a relatively large seafloor area. We present a framework that combines the advantages of dense depth-map and 3-D feature estimation techniques based on visual motion cues. The main goal is to identify and reconstruct certain key terrain feature points that adequately represent the surface with minimal complexity in the form of piecewise planar patches. The proposed implementation utilizes local depth maps for feature selection, while tracking over several views enables 3-D reconstruction by bundle adjustment. Experimental results with synthetic and real data validate the effectiveness of the proposed approach

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.

Universality class of fiber bundles with strong heterogeneities

We study the effect of strong heterogeneities on the fracture of disordered materials using a fiber bundle model. The bundle is composed of two subsets of fibers, i.e. a fraction 0 ≤ α ≤ 1 of fibers is unbreakable, while the remaining 1 - α fraction is characterized by a distribution of breaking thresholds. Assuming global load sharing, we show analytically that there exists a critical fraction of the components αc which separates two qualitatively diferent regimes of the system: below αc the burst size distribution is a power law with the usual exponent Ƭ= 5/2, while above αc the exponent switches to a lower value Ƭ = 9/4 and a cutoff function occurs with a diverging characteristic size. Analyzing the macroscopic response of the system we demonstrate that the transition is conditioned to disorder distributions where the constitutive curve has a single maximum and an inflexion point defining a novel universality class of breakdown phenomena