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O objetivo do estudo foi analisar a influência do ceticismo profissional sobre o gerenciamento de impressão na divulgação da informação contábil. O ceticismo profissional foi analisado por meio das variáveis mente questionadora, suspensão de julgamento, busca de conhecimento, compreensão interpessoal, autonomia e autoestima, conforme constructo de Hurtt (2010). O gerenciamento de impressão foi analisado por meio das variáveis seletividade, distorção de medição e aprimoramento de divulgação, conforme Cardoso, Leite e Aquino (2018). A pesquisa caracteriza-se como descritiva, survey e quantitativa. A amostra do estudo foi composta por 201 acadêmicos do curso de Ciências Contábeis de duas Universidades Públicas do Estado de Santa Catarina. A análise dos dados se deu por meio de estatística descritiva e regressão OLS por meio do software SPSS®. Os resultados da pesquisa demonstraram que a característica mente questionadora influencia negativamente as variáveis aprimoramento de divulgação e distorção de medição, demonstrando que quanto maior o nível da característica mente questionadora num indivíduo, menor a possibilidade de este ser influenciado por duas das técnicas de gerenciamento de impressão.

Cutting-edge hyperscanning methods led to a paradigm shift in social neuroscience. It allowed researchers to measure dynamic mutual alignment of neural processes between two or more individuals in naturalistic contexts. The ever-growing interest in hyperscanning research calls for the development of transparent and validated data analysis methods to further advance the field. We have developed and tested a dual electroencephalography (EEG) analysis pipeline, namely DEEP. Following the preprocessing of the data, DEEP allows users to calculate Phase Locking Values (PLVs) and cross-frequency PLVs as indices of inter-brain phase alignment of dyads as well as time-frequency responses and EEG power for each participant. The pipeline also includes scripts to control for spurious correlations. Our goal is to contribute to open and reproducible science practices by making DEEP publicly available together with an example mother-infant EEG hyperscanning dataset.

We prove the existence of weak solutions to a system of two diffusion equations that are coupled by a pointwise volume constraint. The time evolution is given by gradient dynamics for a free energy functional. Our primary example is a model for the demixing of polymers, the corresponding energy is the one of Flory, Huggins and deGennes. Due to the non-locality in the equations, the dynamics considered here is qualitatively different from the one found in the formally related Cahn-Hilliard equations. Our angle of attack is from the theory of optimal mass transport, that is, we consider the evolution equations for the two components as two gradient flows in the Wasserstein distance with one joint energy functional that has the volume constraint built in. The main difference to our previous work arXiv:1712.06446 is the nonlinearity of the energy density in the gradient part, which becomes singular at the interface between pure and mixed phases., Comment: 25 pages, no figures

Conversations are an essential form of communication in daily family life. Specific patterns of caregiver–child conversations have been linked to children’s socio-cognitive development and child-relationship quality beyond the immediate family environment. Recently, interpersonal neural synchronization has been proposed as a neural mechanism supporting conversation. Here, we present a functional near-infrared spectroscopy (fNIRS) hyperscanning study looking at the temporal dynamics of neural synchrony during mother–child conversation. Preschoolers (20 boys and 20 girls, M age 5;07 years) and their mothers (M age 36.37 years) were tested simultaneously with fNIRS hyperscanning while engaging in a free verbal conversation lasting for 4 min. Neural synchrony (using wavelet transform coherence analysis) was assessed over time. Furthermore, each conversational turn was coded for conversation patterns comprising turn-taking, relevance, contingency and intrusiveness. Results from linear mixed-effects modeling revealed that turn-taking, but not relevance, contingency or intrusiveness predicted neural synchronization during the conversation over time. Results are discussed to point out possible variables affecting parent–child conversation quality and the potential functional role of interpersonal neural synchronization for parent–child conversation.

This article is concerned with the existence and the long time behavior of weak solutions to certain coupled systems of fourth-order degenerate parabolic equations of gradient flow type. The underlying metric is a Wasserstein-like transportation distance for vector-valued functions, with nonlinear mobilities in each component. Under the hypothesis of (flat) convexity of the driving free energy functional, weak solutions are constructed by means of the variational minimizing movement scheme for metric gradient flows. The essential regularity estimates are derived by variational methods., Comment: 28 pages, no figures. This research has been supported by the DFG Collaborative Research Center TRR 109 "Discretization in Geometry and Dynamics"

We introduce a novel spatio-temporal discretization for nonlinear Fokker--Planck equations on the multidimensional unit cube. This discretization is based on two structural properties of these equations: the first is the representation as a gradient flow of an entropy functional in the $L^2$-Wasserstein metric; the second is the Lagrangian nature, meaning that solutions can be written as the push-forward transformation of the initial density under suitable flow maps. The resulting numerical scheme is entropy diminishing and mass conserving. Further, we are able to prove consistency in the sense that if the discrete solutions are regular independently of the mesh size, then they converge to a classical solution. Finally, we present results from numerical experiments in space dimension d=2.

We perform a numerical approximation of coherent sets in finite-dimensional smooth dynamical systems by computing singular vectors of the transfer operator for a stochastically perturbed flow. This operator is obtained by solution of a discretized Fokker-Planck equation. For numerical implementation, we employ spectral collocation methods and an exponential time differentiation scheme. We experimentally compare our approach with the more classical method by Ulam that is based on discretization of the transfer operator of the unperturbed flow.

We study the barycenter of the Hellinger--Kantorovich metric over non-negative measures on compact, convex subsets of $\mathbb{R}^d$. The article establishes existence, uniqueness (under suitable assumptions) and equivalence between a coupled-two-marginal and a multi-marginal formulation. We analyze the HK barycenter between Dirac measures in detail, and find that it differs substantially from the Wasserstein barycenter by exhibiting a local `clustering' behaviour, depending on the length scale of the input measures. In applications it makes sense to simultaneously consider all choices of this scale, leading to a 1-parameter family of barycenters. We demonstrate the usefulness of this family by analyzing point clouds sampled from a mixture of Gaussians and inferring the number and location of the underlying Gaussians., Minor changes to keep consistent with journal version

Understanding others is fundamental to interpersonal coordination and successful cooperation. One mechanism posited to underlie both effective communication and behavioral coordination is interpersonal neural synchrony. Although presumably foundational for children's social development, research on neural synchrony in naturalistic caregiver-child interactions is lacking. Using dual-functional near-infrared spectroscopy (fNIRS), we examined the effects of interaction quality on neural synchrony during a problem-solving task in 42 dyads of mothers and their preschool children. In a cooperation condition, mothers and children were instructed to solve a tangram puzzle together. In an individual condition, mothers and children performed the same task alone with an opaque screen between them. Wavelet transform coherence (WTC) was used to assess the cross-correlation between the two fNIRS time series. Results revealed increased neural synchrony in bilateral prefrontal cortex and temporo-parietal areas during cooperative as compared to individual problem solving. Higher neural synchrony during cooperation correlated with higher behavioral reciprocity and neural synchrony predicted the dyad's problem-solving success beyond reciprocal behavior between mothers and children. State-like factors, such as maternal stress and child agency during the task, played a bigger role for neural synchronization than trait-like factors, such as child temperament. Our results emphasize neural synchrony as a biomarker for mother-child interaction quality. These findings further highlight the role of state-like factors in interpersonal synchronization processes linked to successful coordination with others and in the long-term might improve the understanding of others.

During social interactions infants predict and evaluate other people’s actions. Previous behavioral research found that infants’ imitation of others’ actions depends on these evaluations and is context-dependent: 1-year-olds predominantly imitated an unusual action (turning on a lamp with one’s forehead) when the model’s hands were free compared to when the model’s hands were occupied or restrained. In the present study, we adapted this behavioral paradigm to a neurophysiological study measuring infants’ brain activity while observing usual and unusual actions via electroencephalography. In particular, we measured differences in mu power (6 – 8 Hz) associated with motor activation. In a between-subjects design, 12- to 14-month-old infants watched videos of adult models demonstrating that their hands were either free or restrained. Subsequent test frames showed the models turning on a lamp or a soundbox by using their head or their hand. Results in the hands-free condition revealed that 12- to 14-month-olds displayed a reduction of mu power in frontal regions in response to unusual and thus unexpected actions (head touch) compared to usual and expected actions (hand touch). This may be explained by increased motor activation required for updating prior action predictions in response to unusual actions though alternative explanations in terms of general attention or cognitive control processes may also be considered. In the hands-restrained condition, responses in mu frequency band did not differ between action outcomes. This implies that unusual head-touch actions compared to hand-touch actions do not necessarily evoke a reduction of mu power. Thus, we conclude that reduction of mu frequency power is context-dependent during infants’ action perception. Our results are interpreted in terms of motor system activity measured via changes in mu frequency band as being one important neural mechanism involved in action prediction and evaluation from early on.

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Various degenerate diffusion equations exhibit a waiting time phenomenon: Dependening on the "flatness" of the compactly supported initial datum at the boundary of the support, the support of the solution may not expand for a certain amount of time. We show that this phenomenon is captured by particular Lagrangian discretizations of the porous medium and the thin-film equations, and we obtain suffcient criteria for the occurrence of waiting times that are consistent with the known ones for the original PDEs. Our proof is based on estimates on the fluid velocity in Lagrangian coordinates. Combining weighted entropy estimates with an iteration technique \`a la Stampacchia leads to upper bounds on free boundary propagation. Numerical simulations show that the phenomenon is already clearly visible for relatively coarse discretizations., Comment: 22 pages, 3 figures

We consider a non-standard finite-volume discretization of a strongly non-linear fourth order diffusion equation on the $d$-dimensional cube, for arbitrary $d \geq 1$. The scheme preserves two important structural properties of the equation: the first is the interpretation as a gradient flow in a mass transportation metric, and the second is an intimate relation to a linear Fokker-Planck equation. Thanks to these structural properties, the scheme possesses two discrete Lyapunov functionals. These functionals approximate the entropy and the Fisher information, respectively, and their dissipation rates converge to the optimal ones in the discrete-to-continuous limit. Using the dissipation, we derive estimates on the long-time asymptotics of the discrete solutions. Finally, we present results from numerical experiments which indicate that our discretization is able to capture significant features of the complex original dynamics, even with a rather coarse spatial resolution., 27 pages, minor changes

We prove the global-in-time existence of nonnegative weak solutions to a class of fourth order partial differential equations on a convex bounded domain in arbitrary spatial dimensions. Our proof relies on the formal gradient flow structure of the equation with respect to the $L^2$-Wasserstein distance on the space of probability measures. We construct a weak solution by approximation via the time-discrete minimizing movement scheme; necessary compactness estimates are derived by entropy-dissipation methods. Our theory essentially comprises the thin film and Derrida-Lebowitz-Speer-Spohn equations., Comment: 17 pages, no figures

During social interactions infants predict and evaluate other people's actions. Previous behavioral research found that infants' imitation of others' actions depends on these evaluations and is context-dependent: 1-year-olds predominantly imitated an unusual action (turning on a lamp with one's forehead) when the model's hands were free compared to when the model's hands were occupied or restrained. In the present study, we adapted this behavioral paradigm to a neurophysiological study measuring infants' brain activity while observing usual and unusual actions via electroencephalography. In particular, we measured differences in mu power (6 - 8 Hz) associated with motor activation. In a between-subjects design, 12- to 14-month-old infants watched videos of adult models demonstrating that their hands were either free or restrained. Subsequent test frames showed the models turning on a lamp or a soundbox by using their head or their hand. Results in the hands-free condition revealed that 12- to 14-month-olds displayed a reduction of mu power in frontal regions in response to unusual and thus unexpected actions (head touch) compared to usual and expected actions (hand touch). This may be explained by increased motor activation required for updating prior action predictions in response to unusual actions though alternative explanations in terms of general attention or cognitive control processes may also be considered. In the hands-restrained condition, responses in mu frequency band did not differ between action outcomes. This implies that unusual head-touch actions compared to hand-touch actions do not necessarily evoke a reduction of mu power. Thus, we conclude that reduction of mu frequency power is context-dependent during infants' action perception. Our results are interpreted in terms of motor system activity measured via changes in mu frequency band as being one important neural mechanism involved in action prediction and evaluation from early on.

A fully discrete Lagrangian scheme for numerical solution of the nonlinear fourth-order DLSS equation in one space dimension is analyzed. The discretization is based on the equation’s gradient flow structure in the $$L^2$$ -Wasserstein metric. By construction, the discrete solutions are strictly positive and mass conserving. A further key property is that they dissipate both the Fisher information and the logarithmic entropy. Our main result is a proof of convergence of fully discrete to weak solutions in the limit of vanishing mesh size. Convergence is obtained for arbitrary nonnegative, possibly discontinuous initial data with finite entropy, without any CFL-type condition. The key estimates in the proof are derived from the dissipations of the two Lyapunov functionals. Numerical experiments illustrate the practicability of the scheme.

We propose a variational form of the BDF2 method as an alternative to the commonly used minimizing movement scheme for the time-discrete approximation of gradient flows in abstract metric spaces. Assuming uniform semi-convexity --- but no smoothness --- of the augmented energy functional, we prove well-posedness of the method and convergence of the discrete approximations to a curve of steepest descent. In a smooth Hilbertian setting, classical theory would predict a convergence order of two in time, we prove convergence order of one-half in the general metric setting and under our weak hypotheses. Further, we illustrate these results with numerical experiments for gradient flows on a compact Riemannian manifold, in a Hilbert space, and in the $L^2$-Wasserstein metric., 30 pages, 6 figures

A Lagrangian discretization for nonlinear aggregation-diffusion equations in one space dimension is presented, and its convergence is rigorously analyzed. In comparison to related works by the first author and Osberger (ESAIM Math Model Numer Anal 48:697–726, 2014; Found Comput Math 1–54, 2015) on Lagrangian schemes for drift-diffusion equations, convergence is proven directly on the level on the Lagrangian maps, without passage through the density formulation.

A Lagrangian numerical scheme for solving nonlinear degenerate Fokker-Planck equations in space dimensions $d\ge2$ is presented. It applies to a large class of nonlinear diffusion equations, whose dynamics are driven by internal energies and given external potentials, e.g. the porous medium equation and the fast diffusion equation. The key ingredient in our approach is the gradient flow structure of the dynamics. For discretization of the Lagrangian map, we use a finite subspace of linear maps in space and a variational form of the implicit Euler method in time. Thanks to that time discretisation, the fully discrete solution inherits energy estimates from the original gradient flow, and these lead to weak compactness of the trajectories in the continuous limit. Consistency is analyzed in the planar situation, $d=2$. A variety of numerical experiments for the porous medium equation indicates that the scheme is well-adapted to track the growth of the solution's support., Comment: 32 pages, 7 figures

We study a Lagrangian numerical scheme for solution of a nonlinear drift diffusion equation on an interval. The discretization is based on the equation's gradient flow structure with respect to the Wasserstein distance. The scheme inherits various properties of the continuous flow, like entropy monotonicity, mass preservation, metric contraction and minimum/maximum principles. As the main result, we give a proof of convergence in the limit of vanishing mesh size under a CFL-type condition. We also present results from numerical experiments., 28 pages, 6 figures

This paper is concerned with the analysis of a sixth-order nonlinear parabolic equation whose solutions describe the evolution of the particle density in a quantum fluid. We prove the global-in-time existence of weak nonnegative solutions in two and three space dimensions under periodic boundary conditions. Moreover, we show that these solutions are smooth and classical whenever the particle density is strictly positive, and we prove the long-time convergence to the spatial homogeneous equilibrium at a universal exponential rate. Our analysis strongly uses the Lyapunov property of the entropy functional.

In this article, we study an analog of the Bjorling problem for isothermic surfaces (that are a generalization of minimal surfaces): given a regular curve \(\gamma \) in \(\mathbb {R}^3\) and a unit normal vector field n along \(\gamma \), find an isothermic surface that contains \(\gamma \), is normal to n there, and is such that the tangent vector \(\gamma '\) bisects the principal directions of curvature. First, we prove that this problem is uniquely solvable locally around each point of \(\gamma \), provided that \(\gamma \) and n are real analytic. The main result is that the solution can be obtained by constructing a family of discrete isothermic surfaces (in the sense of Bobenko and Pinkall) from data that is read off from \(\gamma \), and then passing to the limit of vanishing mesh size. The proof relies on a rephrasing of the Gauss-Codazzi-system as analytic Cauchy problem and an in-depth-analysis of its discretization which is induced from the geometry of discrete isothermic surfaces. The discrete-to-continuous limit is carried out for the Christoffel and the Darboux transformations as well.

In this paper, we establish a novel approach to proving existence of non-negative weak solutions for degenerate parabolic equations of fourth order, like the Cahn–Hilliard and certain thin film equations. The considered evolution equations are in the form of a gradient flow for a perturbed Dirichlet energy with respect to a Wasserstein-like transport metric, and weak solutions are obtained as curves of maximal slope. Our main assumption is that the mobility of the particles is a concave function of their spatial density. A qualitative difference of our approach to previous ones is that essential properties of the solution – non-negativity, conservation of the total mass and dissipation of the energy – are automatically guaranteed by the construction from minimizing movements in the energy landscape.

It is shown that the collisional gain operator for a Maxwell gas does not increase the Fisher information. Our proof is a variant of the one given by Villani in 1998 [2] , but it is shorter and based on Fourier techniques rather than direct estimates. The method we use also applies to general (non-symmetric) Wild convolutions.

A previously developed algebraic approach to proving entropy production inequalities is extended to deal with radially symmetric solutions for a class of higher-order diffusion equations in multiple space dimensions. In application of the method, novel a priori estimates are derived for the thin-film equation, the fourth-order Derrida- Lebowitz-Speer-Spohn equation, and a sixth-order quantum diffusion equation.

A class of Kac-like kinetic equations on the real line is considered, with general smoothing transforms as collisional kernels. These equations have been introduced recently e.g. in the context of econophysics (Cordier et al 2005 J. Stat. Phys. 120 253–77) or as models for granular gases with a background heat bath (Carrillo et al 2009 Discrete Contin. Dyn. Syst. 24 59–81). We show that the stationary solutions to these equations are not smooth in general, and we characterize their (finite) Sobolev regularity in dependence of the properties of the collisional kernel. Moreover, we prove that any initial Sobolev regularity below a well-defined threshold is uniformly propagated in time by the transient weak solutions, implying their strong convergence to the steady state. The applied techniques differ from the classical ones developed for the Kac equation as the models at hand neither dissipate the entropy nor the Fisher information. Instead, the proof relies on direct estimates on the collisional operator.

We study families of convex Sobolev inequalities, which arise as entropy–dissipation relations for certain linear Fokker–Planck equations. Extending the ideas recently developed by the first two authors, a refinement of the Bakry–Emery method is established, which allows us to prove non-trivial inequalities even in situations where the classical Bakry–Emery criterion fails. The main application of our theory concerns the linearized fast diffusion equation in dimensions d ≧ 1, which admits a Poincare, but no logarithmic Sobolev inequality. We calculate bounds on the constants in the interpolating convex Sobolev inequalities, and prove that these bounds are sharp on a specified range. In dimension d = 1, our estimates improve the corresponding results that can be obtained by the measure-theoretic techniques of Barthe and Roberto. As a by-product, we give a short and elementary alternative proof of the sharp spectral gap inequality first obtained by Denzler and McCann. In further applications of our method, we prove convex Sobolev inequalities for a mean field model for the redistribution of wealth in a simple market economy, and the Lasota model for blood cell production.

We propose a method for numerical integration of Wasserstein gradient flows based on the classical minimizing movement scheme. In each time step, the discrete approximation is obtained as the solution of a constrained quadratic minimization problem on a finite-dimensional function space. Our method is applied to the nonlinear fourth-order Derrida-Lebowitz-Speer-Spohn equation, which arises in quantum semiconductor theory. We prove well-posedness of the scheme and derive a priori estimates on the discrete solution. Furthermore, we present numerical results which indicate second-order convergence and unconditional stability of our scheme. Finally, we compare these results to those obtained from different semi- and fully implicit finite difference discretizations.

Global existence and long-time behavior of solutions to a family of nonlinear fourth order evolution equations on $R^d$ are studied. These equations constitute gradient flows for the perturbed information functionals $F[u] = 1/(2\alpha) \int | D (u^\alpha) |^2 dx + \lambda/2 \int |x|^2 u dx$ with respect to the $L^2$-Wasserstein metric. The value of $\alpha$ ranges from $\alpha=1/2$, corresponding to a simplified quantum drift diffusion model, to $\alpha=1$, corresponding to a thin film type equation., Comment: 33 pages, no figures

The existence of classical solutions to a one-dimensional non-linear fourth-order elliptic equation arising in quantum semiconductor modeling is proved for a class of non-homogeneous boundary conditions using degree theory. Furthermore, some non-existence results for other classes of boundary conditions are presented. To cite this article: P. Amster et al., C. R. Acad. Sci. Paris, Ser. I 346 (2008).

The logarithmic fourth-order equation $\partial_t u + \frac12\sum_{i,j=1}^d\partial_{ij}^2(u\partial_{ij}^2\log u) = 0,$ called the Derrida–Lebowitz–Speer–Spohn equation, with periodic boundary conditions is analyzed. The global-in-time existence of weak nonnegative solutions in space dimensions $d\leq 3$ is shown. Furthermore, a family of entropy-entropy dissipation inequalities is derived in arbitrary space dimensions, and rates of the exponential decay of the weak solutions to the homogeneous steady state are estimated. The proofs are based on the algorithmic entropy construction method developed by the authors and on an exponential variable transformation. Finally, an example for nonuniqueness of the solution is provided.

A recent application of the kinetic theory for many particle systems is the description of the redistribution of wealth among trading agents in a simple market economy. This paper provides an analytical investigation of the particular model with quenched saving propensities, which has been introduced by Chakrabarti, Chatterjee and Manna [11]. We prove uniqueness and dynamical stability of the stationary solution to the underlying Boltzmann equation, and provide estimates on the rate of equilibration. As one main result, we obtain that realistic steady wealth distributions with Pareto tail are only algebraically stable in this framework.

We analyze the large-time behavior of various kinetic models for the redistribution of wealth in simple market economies introduced in the pertinent literature in recent years. As specific examples, we study models with fixed saving propensity introduced by Chakraborti and Chakrabarti (Eur. Phys. J. B 17:167–170, 2000), as well as models involving both exchange between agents and speculative trading as considered by Cordier et al. (J. Stat. Phys. 120:253–277, 2005) We derive a sufficient criterion under which a unique non-trivial stationary state exists, and provide criteria under which these steady states do or do not possess a Pareto tail. In particular, we prove the absence of Pareto tails in pointwise conservative models, like the one in (Eur. Phys. J. B 17:167–170, 2000), while models with speculative trades introduced in (J. Stat. Phys. 120:253–277, 2005) develop fat tails if the market is “risky enough”. The results are derived by a Fourier-based technique first developed for the Maxwell-Boltzmann equation (Gabetta et al. in J. Stat. Phys. 81:901–934, 1995; Bisi et al. in J. Stat. Phys. 118(1–2):301–331, 2005; Pareschi and Toscani in J. Stat. Phys. 124(2–4):747–779, 2006) and from a recursive relation which allows to calculate arbitrary moments of the stationary state.

This paper is concerned with the existence, shape and dynamical stability of infinite-energy equilibria for a class of spatially homogeneous kinetic equations in space dimensions $d\ge2$. Our results cover in particular Bobylev's model for inelastic Maxwell molecules. First, we show under certain conditions on the collision kernel, that there exists an index $\alpha\in(0,2)$ such that the equation possesses a nontrivial stationary solution, which is a scale mixture of radially symmetric $\alpha$-stable laws. We also characterize the mixing distribution as the fixed point of a smoothing transformation. Second, we prove that any transient solution that emerges from the NDA of some (not necessarily radial symmetric) $\alpha$-stable distribution converges to an equilibrium. The key element of the convergence proof is an application of the central limit theorem to a representation of the transient solution as a weighted sum of projections of randomly rotated i.i.d. random vectors.

A new approach to the construction of entropies and entropy productions for a large class of nonlinear evolutionary PDEs of even order in one space dimension is presented. The task of proving entropy dissipation is reformulated as a decision problem for polynomial systems. The method is successfully applied to the porous medium equation, the thin film equation and the quantum drift–diffusion model. In all cases, an infinite number of entropy functionals together with the associated entropy productions is derived. Our technique can be extended to higher-order entropies, containing derivatives of the solution, and to several space dimensions. Furthermore, logarithmic Sobolev inequalities can be obtained.

New quantum hydrodynamic equations are derived from a Wigner-Boltzmann model, using the quantum entropy minimization method recently developed by Degond and Ringhofer. The model consists of conservation equations for the carrier, momentum, and energy densities. The derivation is based on a careful expansion of the quantum Maxwellian in powers of the Planck constant. In difference to the standard quantum hydrodynamic equations derived by Gardner, the new model includes vorticity terms and a dispersive term for the velocity. Numerical current-voltage characteristics of a one-dimensional resonant tunneling diode for both the new quantum hydrodynamic equations and Gardner's model are presented. The numerical results indicate that the dispersive velocity term regularizes the solution of the system.

Isothermal quantum hydrodynamic equations of order O(h 2 ) using the quantum entropy minimization method recently developed by Degond and Ringhofer are derived. The equations have the form of the usual quantum hydrodynamic model including a correction term of order O(h 2 ) which involves the vorticity. If the initial vorticity is of order 0(h), the standard model is obtained up to order O(h 4 ). The derivation is based on a careful expansion of the quantum equilibrium obtained from the entropy minimization in powers of h 2 .

A lattice-discretization of analytic Cauchy problems in two dimensions is presented. It is proven that the discrete solutions converge to a smooth solution of the original problem as the mesh size ε \varepsilon tends to zero. The convergence is in C ∞ C^\infty and the approximation error for arbitrary derivatives is quadratic in ε \varepsilon . In application, C ∞ C^\infty -approximation of conformal maps by Schramm’s orthogonal circle patterns and lattices of cross-ratio minus one is shown.

We introduce Wasserstein-like dynamical transport distances between vector-valued densities on the real line. The mobility function from the scalar theory is replaced by a mobility matrix, that is subject to positivity and concavity conditions. Our primary motivation is to cast certain systems of nonlinear parabolic evolution equations into the variational framework of gradient flows. In the first part of the paper, we investigate the structural properties of the new class of distances like geodesic completeness. The second part is devoted to the identification of $\lambda$-geodesically convex functionals and their $\lambda$-contractive gradient flows. One of our results is a generalized McCann condition for geodesic convexity of the internal energy. In the third part, the existence of weak solutions to a certain class of degenerate diffusion systems with drift is shown. Even if the underlying energy function is not geodesically convex w.r.t. our new distance, the construction of a weak solution is still possible using de Giorgi's minimizing movement scheme., Comment: 32 pages, no figures. v2: Results unchanged, some remarks added in introduction

We analyze a class of smoothing transformations on probability measures in multiple space dimensions. Applying a synthesis of probabilistic methods and Fourier analysis, we prove existence and uniqueness of a fixed point inside the class of probability measures of finite second moment, characterize it as a scale mixture of Gaussians, and discuss its regularity. We also classify its tail, which might be of Pareto type. As an application, we study the stability of stationary solutions in a Kac-type kinetic model. In particular, we prove that the domain of attraction is precisely the probability measures of finite second moment.

Introduction Morphological and metabolic complications in HIV patients on antiretroviral therapy remain a challenge. While new cases of lipoatrophy (LA) disappear, irreducible central lipohypertrophy (LH) and metabolic complications require highly specialized management. We described a day hospital dedicated to lipodystrophy (LD) and metabolic disorders in HIV patients on treatment in Geneva, Switzerland, with a focus on LH. Materials and Methods The “Groupe Lipo & Metabolism” is a multidisciplinary consultation where patients undergo a standard evaluation including questionnaire, physical examination, dual-energy x-ray absorptiometry (DEXA) and L5-level CT scans, blood tests and consultations with various specialists. Based on prospectively maintained data, we describe clinical, biological and radiological characteristics of patients ≥18 years who attended the consultation between 2008 and 2013. We defined LH by CT scan, the gold standard method, as abdominal visceral adipose tissue (VAT) ≥130 cm2, value associated with increased risk of cardiovascular event. Results A total of 195 patients attended the consultation during study period. Reasons for referral included LH in 28.3%, LA in 25% and mixed syndrome in 15.5% of cases. Metabolic disorders accounted for 19% of referrals with or without LD features. Among patients with a CT scan performed (n=183), 46 (25%) had LH with a VAT ≥130 cm2. In this population, mean age was 49.1 years and 53.6% were male. HIV viral load was 6% in 10.5% of patients. Vitamin-D level was

We study a system of two coupled nonlinear parabolic equations. It constitutes a variant of the Keller-Segel model for chemotaxis, i.e. it models the behaviour of a population of bacteria that interact by means of a signalling substance. We assume an external confinement for the bacteria and a nonlinear dependency of the chemotactic drift on the signalling substance concentration. We perform an analysis of existence and long-time behaviour of solutions based on the underlying gradient flow structure of the system. The result is that, for a wide class of initial conditions, weak solutions exist globally in time and converge exponentially fast to the unique stationary state under suitable assumptions on the convexity of the confinement and the strength of the coupling., Comment: Improved results: nonlinearity also comprises classical Keller-Segel model; moreover: references added, typos corrected