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.

Contractive metrics for a Boltzmann equation for granular gases: diffusive equilibriaThe Patterson-Sullivan embedding and minimal volume entropy for outer space

We quantify the long-time behavior of a system of (partially) inelastic particles in a stochastic thermostat by means of the contractivity of a suitable metric in the set of probability measures. Existence, uniqueness, boundedness of moments and regularity of a steady state are derived from this basic property. The solutions of the kinetic model are proved to converge exponentially as t→ ∞ to this diffusive equilibrium in this distance metrizing the weak convergence of measures. Then, we prove a uniform bound in time on Sobolev norms of the solution, provided the initial data has a finite norm in the corresponding Sobolev space. These results are then combined, using interpolation inequalities, to obtain exponential convergence to the diffusive equilibrium in the strong L¹-norm, as well as various Sobolev norms.

Infinite time aggregation for the critical Patlak-Keller-Segel model in R2

We analyze the two-dimensional parabolic-elliptic Patlak-Keller-Segel model in the whole Euclidean space R2. Under the hypotheses of integrable initial data with finite second moment and entropy, we first show local in time existence for any mass of "free-energy solutions", namely weak solutions with some free energy estimates. We also prove that the solution exists as long as the entropy is controlled from above. The main result of the paper is to show the global existence of free-energy solutions with initial data as before for the critical mass 8 Π/Χ. Actually, we prove that solutions blow-up as a delta dirac at the center of mass when t→∞ keeping constant their second moment at any time. Furthermore, all moments larger than 2 blow-up as t→∞ if initially bounded.

Bayesian Inference in the Time Varying Cointegration Model

There are both theoretical and empirical reasons for believing that the parameters of macroeconomic models may vary over time. However, work with time-varying parameter models has largely involved Vector autoregressions (VARs), ignoring cointegration. This is despite the fact that cointegration plays an important role in informing macroeconomists on a range of issues. In this paper we develop time varying parameter models which permit cointegration. Time-varying parameter VARs (TVP-VARs) typically use state space representations to model the evolution of parameters. In this paper, we show that it is not sensible to use straightforward extensions of TVP-VARs when allowing for cointegration. Instead we develop a specification which allows for the cointegrating space to evolve over time in a manner comparable to the random walk variation used with TVP-VARs. The properties of our approach are investigated before developing a method of posterior simulation. We use our methods in an empirical investigation involving a permanent/transitory variance decomposition for inflation.

Stochastic Search Variable Selection in Vector Error Correction Models with an Application to a Model of the UK Macroeconomy

This paper develops methods for Stochastic Search Variable Selection (currently popular with regression and Vector Autoregressive models) for Vector Error Correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK macroeconomic model.

On a size-structured two-phase population model with infinite states-at-birth

In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an “active” phase when individuals grow, reproduce and die and a second “resting” phase when individuals only grow. Transition between these two phases depends on individuals’ size. First we show that the problem is governed by a positive quasicontractive semigroup on the biologically relevant state space. Then we investigate, in the framework of the spectral theory of linear operators, the asymptotic behavior of solutions of the model. We prove that the associated semigroup has, under biologically plausible assumptions, the property of asynchronous exponential growth.

Learning-induced plasticity in human audition: Objects, time, and space.

The human auditory system is comprised of specialized but interacting anatomic and functional pathways encoding object, spatial, and temporal information. We review how learning-induced plasticity manifests along these pathways and to what extent there are common mechanisms subserving such plasticity. A first series of experiments establishes a temporal hierarchy along which sounds of objects are discriminated along basic to fine-grained categorical boundaries and learned representations. A widespread network of temporal and (pre)frontal brain regions contributes to object discrimination via recursive processing. Learning-induced plasticity typically manifested as repetition suppression within a common set of brain regions. A second series considered how the temporal sequence of sound sources is represented. We show that lateralized responsiveness during the initial encoding phase of pairs of auditory spatial stimuli is critical for their accurate ordered perception. Finally, we consider how spatial representations are formed and modified through training-induced learning. A population-based model of spatial processing is supported wherein temporal and parietal structures interact in the encoding of relative and absolute spatial information over the initial ∼300ms post-stimulus onset. Collectively, these data provide insights into the functional organization of human audition and open directions for new developments in targeted diagnostic and neurorehabilitation strategies.

Binding under Conflict Conditions: State-Space Analysis of Multivariate EEG Synchronization.

Real-world objects are often endowed with features that violate Gestalt principles. In our experiment, we examined the neural correlates of binding under conflict conditions in terms of the binding-by-synchronization hypothesis. We presented an ambiguous stimulus ("diamond illusion") to 12 observers. The display consisted of four oblique gratings drifting within circular apertures. Its interpretation fluctuates between bound ("diamond") and unbound (component gratings) percepts. To model a situation in which Gestalt-driven analysis contradicts the perceptually explicit bound interpretation, we modified the original diamond (OD) stimulus by speeding up one grating. Using OD and modified diamond (MD) stimuli, we managed to dissociate the neural correlates of Gestalt-related (OD vs. MD) and perception-related (bound vs. unbound) factors. Their interaction was expected to reveal the neural networks synchronized specifically in the conflict situation. The synchronization topography of EEG was analyzed with the multivariate S-estimator technique. We found that good Gestalt (OD vs. MD) was associated with a higher posterior synchronization in the beta-gamma band. The effect of perception manifested itself as reciprocal modulations over the posterior and anterior regions (theta/beta-gamma bands). Specifically, higher posterior and lower anterior synchronization supported the bound percept, and the opposite was true for the unbound percept. The interaction showed that binding under challenging perceptual conditions is sustained by enhanced parietal synchronization. We argue that this distributed pattern of synchronization relates to the processes of multistage integration ranging from early grouping operations in the visual areas to maintaining representations in the frontal networks of sensory memory.

Asymptotic flocking dynamics for the kinetic Cucker-Smale model

In this paper, we analyse the asymptotic behavior of solutions of the continuous kinetic version of flocking by Cucker and Smale [16], which describes the collective behavior of an ensemble of organisms, animals or devices. This kinetic version introduced in [24] is here obtained starting from a Boltzmann-type equation. The large-time behavior of the distribution in phase space is subsequently studied by means of particle approximations and a stability property in distances between measures. A continuous analogue of the theorems of [16] is shown to hold for the solutions on the kinetic model. More precisely, the solutions will concentrate exponentially fast their velocity to their mean while in space they will converge towards a translational flocking solution.

Segmentation of brain structures in presence of a space-occupying lesion.

Brain deformations induced by space-occupying lesions may result in unpredictable position and shape of functionally important brain structures. The aim of this study is to propose a method for segmentation of brain structures by deformation of a segmented brain atlas in presence of a space-occupying lesion. Our approach is based on an a priori model of lesion growth (MLG) that assumes radial expansion from a seeding point and involves three steps: first, an affine registration bringing the atlas and the patient into global correspondence; then, the seeding of a synthetic tumor into the brain atlas providing a template for the lesion; finally, the deformation of the seeded atlas, combining a method derived from optical flow principles and a model of lesion growth. The method was applied on two meningiomas inducing a pure displacement of the underlying brain structures, and segmentation accuracy of ventricles and basal ganglia was assessed. Results show that the segmented structures were consistent with the patient's anatomy and that the deformation accuracy of surrounding brain structures was highly dependent on the accurate placement of the tumor seeding point. Further improvements of the method will optimize the segmentation accuracy. Visualization of brain structures provides useful information for therapeutic consideration of space-occupying lesions, including surgical, radiosurgical, and radiotherapeutic planning, in order to increase treatment efficiency and prevent neurological damage.

Calomys callosus: an alternative model to study fibrosis in Schistosomiasis mansoni: the pathology of the acute phase

Twenty Calomys callosus, Rengger, 1830 (Rodentia-Cricetidae) were studied in the early stage of the acute schistosomal mansoni infection (42nd day). The same number of Swiss Webster mice were used as a comparative standard. Liver and intestinal sections, fixed in formalin-Millonig and embedded in paraffin, were stained with hematoxilin and eosin, PAS-Alcian Blue, pH = 1.0 and 2.5, Lennert's Giemsa, Picrosirius plus polarization microscopy, Periodic acid methanamine silver, Gomori's silver reticulin and resorcin-fuchsin. Immunohistological study (indirect immunofluorescence and peroxidase labeled extravidin-biotin methods) was done with antibodies specific to pro-collagen III, fibronectin, elastin, condroitin-sulfate, tenascin, alpha smooth muscle actin, vimentin and desmin. The hepatic granulomas were small, reaching only 27 of the volume of the hepatic Swiss Webster granuloma. They were composed mainly by large immature macrophages, often filled by schistosomal pigment, characterizing an exsudative-macrophage granuloma type. The granulomas were situated in the parenchyma and in the portal space. They were often intravascular, poor of extracellular matrix components, except fibronectin and presented, sometimes alpha smooth muscle actin and vimentin positive cells. The C. callosus intestinal granulomas were similar to Swiss Webster, showing predominance of macrophages. Therefore, the C. callosus acquire very well the Schistosoma mansoni infection, without developing strong hepatic acute granulomatous reaction, suggesting lack of histopathological signs of hypersensitivity.

Extended truncated Tweedie-Poisson model

It has been argued that by truncating the sample space of the negative binomial and of the inverse Gaussian-Poisson mixture models at zero, one is allowed to extend the parameter space of the model. Here that is proved to be the case for the more general three parameter Tweedie-Poisson mixture model. It is also proved that the distributions in the extended part of the parameter space are not the zero truncation of mixed poisson distributions and that, other than for the negative binomial, they are not mixtures of zero truncated Poisson distributions either. By extending the parameter space one can improve the fit when the frequency of one is larger and the right tail is heavier than is allowed by the unextended model. Considering the extended model also allows one to use the basic maximum likelihood based inference tools when parameter estimates fall in the extended part of the parameter space, and hence when the m.l.e. does not exist under the unextended model. This extended truncated Tweedie-Poisson model is proved to be useful in the analysis of words and species frequency count data.

Industrial Location and Space: New Insights

This paper tries to resolve some of the main shortcomings in the empirical literature of location decisions for new plants, i.e. spatial effects and overdispersion. Spatial effects are omnipresent, being a source of overdispersion in the data as well as a factor shaping the functional relationship between the variables that explain a firm’s location decisions. Using Count Data models, empirical researchers have dealt with overdispersion and excess zeros by developments of the Poisson regression model. This study aims to take this a step further, by adopting Bayesian methods and models in order to tackle the excess of zeros, spatial and non-spatial overdispersion and spatial dependence simultaneously. Data for Catalonia is used and location determinants are analysed to that end. The results show that spatial effects are determinant. Additionally, overdispersion is descomposed into an unstructured iid effect and a spatially structured effect. Keywords: Bayesian Analysis, Spatial Models, Firm Location. JEL Classification: C11, C21, R30.

An introduction to model-independent diffusion magnetic resonance imaging.

ABSTRACT: q-Space-based techniques such as diffusion spectrum imaging, q-ball imaging, and their variations have been used extensively in research for their desired capability to delineate complex neuronal architectures such as multiple fiber crossings in each of the image voxels. The purpose of this article was to provide an introduction to the q-space formalism and the principles of basic q-space techniques together with the discussion on the advantages as well as challenges in translating these techniques into the clinical environment. A review of the currently used q-space-based protocols in clinical research is also provided.

Hard-wired heterogeneity in blood stem cells revealed using a dynamic regulatory network model.

MOTIVATION: Combinatorial interactions of transcription factors with cis-regulatory elements control the dynamic progression through successive cellular states and thus underpin all metazoan development. The construction of network models of cis-regulatory elements, therefore, has the potential to generate fundamental insights into cellular fate and differentiation. Haematopoiesis has long served as a model system to study mammalian differentiation, yet modelling based on experimentally informed cis-regulatory interactions has so far been restricted to pairs of interacting factors. Here, we have generated a Boolean network model based on detailed cis-regulatory functional data connecting 11 haematopoietic stem/progenitor cell (HSPC) regulator genes. RESULTS: Despite its apparent simplicity, the model exhibits surprisingly complex behaviour that we charted using strongly connected components and shortest-path analysis in its Boolean state space. This analysis of our model predicts that HSPCs display heterogeneous expression patterns and possess many intermediate states that can act as 'stepping stones' for the HSPC to achieve a final differentiated state. Importantly, an external perturbation or 'trigger' is required to exit the stem cell state, with distinct triggers characterizing maturation into the various different lineages. By focusing on intermediate states occurring during erythrocyte differentiation, from our model we predicted a novel negative regulation of Fli1 by Gata1, which we confirmed experimentally thus validating our model. In conclusion, we demonstrate that an advanced mammalian regulatory network model based on experimentally validated cis-regulatory interactions has allowed us to make novel, experimentally testable hypotheses about transcriptional mechanisms that control differentiation of mammalian stem cells. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.