3D printers based on the additive manufacturing technology create objects layer-by-layer dropping fused material. As a consequence, strong overhangs cannot be printed because the new-come material does not find a suitable support over the last deposed layer. In these cases, one can add support structures (scaffolds) which make the object printable, to be removed at the end. In this paper, we propose a level set based method to create object-dependent support structures, specifically conceived to reduce both the amount of additional material and the printing time. We also review some open problems about 3D printing which can be of interests for the mathematical community.

This paper investigates the problem of quantifying the impact of unex- pected deviations of mortality trend on a longevity indexed life annuity in a Solvency II perspective. Solvency II quantitative requirements regulate the margins required to offset the insurance risk in a one year risk horizon. Indeed, the idea of deepening the expected changes of future mortality rates over a single year is gaining. In the following the authors propose a com- putational tractable approach to assess the technical provisions by means of an internal model, in line with Solvency II directives. The impact of adverse effects of the mortality dynamics is investigated. Mortality is modelled by means of a stochastic CIR type model; an ex post analysis is proposed relying on Italian mortality data.

A Leaky Integrate-and-Fire (LIF) model with stochastic current-based linkages is considered to describe the firing activity of neurons interacting in a (2. ×. 2)-size feed-forward network. In the subthreshold regime and under the assumption that no more than one spike is exchanged between coupled neurons, the stochastic evolution of the neuronal membrane voltage is subject to random jumps due to interactions in the network. Linked Gauss-Diffusion processes are proposed to describe this dynamics and to provide estimates of the firing probability density of each neuron. To this end, an iterated integral equation-based approach is applied to evaluate numerically the first passage time density of such processes through the firing threshold. Asymptotic approximations of the firing densities of surrounding neurons are used to obtain closed-form expressions for the mean of the involved processes and to simplify the numerical procedure. An extension of the model to an (N ×. N)-size network is also given. Histograms of firing times obtained by simulations of the LIF dynamics and numerical firings estimates are compared.

We discuss the problem of partitioning a macroscopic system into a collection of independent subsystems. The partitioning of a system into replica-like subsystems is nowadays a subject of major interest in several fields of theoretical and applied physics. The thermodynamic approach currently favoured by practitioners is based on a phenomenological definition of an interface energy associated with the partition, due to a lack of easily computable expressions for a microscopic (i.e. particle-based) interface energy. In this article, we outline a general approach to derive sharp and computable bounds for the interface free energy in terms of microscopic statistical quantities. We discuss potential applications in nanothermodynamics and outline possible future directions.

The time-reversal properties of charged systems in a constant external magnetic field are reconsidered in this paper. We show that the evolution equations of the system are invariant under a new symmetry operation that implies a new signature property for time-correlation functions under time reversal. We then show how these findings can be combined with a previously identified symmetry to determine, for example, null components of the correlation functions of velocities and currents and of the associated transport coefficients. These theoretical predictions are illustrated by molecular dynamics simulations of superionic AgI.

In the first part of this paper we review a mathematical model for the onset and progression of Alzheimer's disease (AD) that was developed in subsequent steps over several years. The model is meant to describe the evolution of AD in vivo. In Achdou et al (2013 J. Math. Biol. 67 1369-92) we treated the problem at a microscopic scale, where the typical length scale is a multiple of the size of the soma of a single neuron. Subsequently, in Bertsch et al (2017 Math. Med. Biol. 34 193-214) we concentrated on the macroscopic scale, where brain neurons are regarded as a continuous medium, structured by their degree of malfunctioning. In the second part of the paper we consider the relation between the microscopic and the macroscopic models. In particular we show under which assumptions the kinetic transport equation, which in the macroscopic model governs the evolution of the probability measure for the degree of malfunctioning of neurons, can be derived from a particle-based setting. The models are based on aggregation and diffusion equations for ?-Amyloid (A? from now on), a protein fragment that healthy brains regularly produce and eliminate. In case of dementia A? monomers are no longer properly washed out and begin to coalesce forming eventually plaques. Two different mechanisms are assumed to be relevant for the temporal evolution of the disease: (i) diffusion and agglomeration of soluble polymers of amyloid, produced by damaged neurons; (ii) neuron-to-neuron prion-like transmission. In the microscopic model we consider mechanism (i), modelling it by a system of Smoluchowski equations for the amyloid concentration (describing the agglomeration phenomenon), with the addition of a diffusion term as well as of a source term on the neuronal membrane. At the macroscopic level instead we model processes (i) and (ii) by a system of Smoluchowski equations for the amyloid concentration, coupled to a kinetic-type transport equation for the distribution function of the degree of malfunctioning of the neurons. The transport equation contains an integral term describing the random onset of the disease as a jump process localized in particularly sensitive areas of the brain

In this article we propose a mathematical model for the onset and progression of Alzheimer's disease based on transport and diffusion equations. We regard brain neurons as a continuous medium and structure them by their degree of malfunctioning. Two different mechanisms are assumed to be relevant for the temporal evolution of the disease: i) diffusion and agglomeration of soluble polymers of amyloid, produced by damaged neurons and ii) neuron-to-neuron prion-like transmission. We model these two processes by a system of Smoluchowski equations for the amyloid concentration, coupled to a kinetic-type transport equation for the distribution function of the degree of malfunctioning of neurons. The second equation contains an integral term describing the random onset of the disease as a jump process localized in particularly sensitive areas of the brain. Our numerical simulations are in good qualitative agreement with clinical images of the disease distribution in the brain which vary from early to advanced stages.

We present a comprehensive study of concentrated emulsions flowing in microfluidic channels, one wall of which is patterned with micron-size equally spaced grooves oriented perpendicularly to the flow direction. We find a scaling law describing the roughness-induced fluidization as a function of the density of the grooves, thus fluidization can be predicted and quantitatively regulated. This suggests common scenarios for droplet trapping and release, potentially applicable for other jammed systems as well. Numerical simulations confirm these views and provide a direct link between fluidization and the spatial distribution of plastic rearrangements.

The Voronoi diagrams are an important tool having theoretical and practical applications in a large number of fields. We present a new procedure, implemented as a set of CUDA kernels, which detects, in a general and efficient way, topological changes in case of dynamic Voronoi diagrams whose generating points move in time. The solution that we provide has been originally developed to identify plastic events during simulations of soft-glassy materials based on a lattice Boltzmann model with frustrated-short range attractive and mid/long-range repulsive-interactions. Along with the description of our approach, we present also some preliminary physics results.

The existence of solutions to a one-dimensional problem arising in magneto-viscoelasticity is here considered. Specifically, a non-linear system of integro-differential equations is analysed; it is obtained coupling an integro-differential equation modelling the viscoelastic behaviour, in which the kernel represents the relaxation function, with the non-linear partial differential equations modelling the presence of a magnetic field. The case under investigation generalizes a previous study since the relaxation function is allowed to be unbounded at the origin, provided it belongs to L-1; the magnetic model equation adopted, as in the previous results (Garillo et al., 2011, 2012; Chipot et al. 2008, 2009) is the penalized Ginzburg-Landau magnetic evolution equation. (C) 2016 Elsevier Ltd. All rights reserved.

The boundedness of the Hardy-Littlewood maximal operator is proved in weighted grand variable exponent Lebesgue space with power weights.

For kernels zi which are positive and integrable we show that the operator g bar right arrow J(v)g = integral(x)(0) v(x-s)g(s)ds on a finite time interval enjoys a regularizing effect when applied to Holder continuous and Lebesgue functions and a "contractive" effect when applied to Sobolev functions. For Holder continuous functions, we establish that the improvement of the regularity of the modulus of continuity is given by the integral of the kernel, namely by the factor N(x) = integral(x)(0) v(s)ds. For functions in Lebesgue spaces, we prove that an improvement always exists, and it can be expressed in terms of Orlicz integrability. Finally, for functions in Sobolev spaces, we show that the operator J. "shrinks" the norm of the argument by a factor that, as in the Holder case, depends on the function N (whereas no regularization result can be obtained). These results can be applied, for instance, to Abel kernels and to the Volterra function Z(x) = mu(x,0, -1) = integral(infinity)(0)x(s-1)/Gamma(s)ds, the latter being relevant for instance in the analysis of the Schrodinger equation with concentrated nonlinearities in R-2.

The dynamics of thermally fluctuating conserved order parameters are described by stochastic conservation laws. Thermal equilibrium in such systems requires the dissipative and stochastic components of the flux to be related by detailed balance. Preserving this relation in spatial and temporal discretization is necessary to obtain solutions that have fidelity to the continuum. Here, we propose a finite-difference discretization that preserves the detailed balance on the lattice, has a spatial error that is isotropic to leading order in lattice spacing, and can be integrated accurately in time using a delayed difference method. We benchmark the method for model B dynamics with a phi(4) Landau free energy and obtain excellent agreement with the analytical results.

We present a novel application of the Lattice Boltzmann Method to the study of pulsed reactive flows in transitional Knudsen number regimes, namely 0.1 < Kn < 1. We characterize the conversion efficiency of catalytic particles for different geometries and configurations, including single catalytic particle and nanoporous gold (npAu) spheres, within pulsed-flow reactors. For all the explored configurations, the reactivity is found to increase with the Knudsen number of the flow, consistently with previous theoretical models and in reasonable agreement with experimental results in the literature.

The surface structure and composition of a multi-component catalyst are critical factors in determining its catalytic performance. The surface composition can depend on the local pressure of the reacting species, leading to the possibility that the flow through a nanoporous catalyst can affect its structure and reactivity. Here, we explore this possibility for oxidation reactions on nanoporous gold, an AgAu bimetallic catalyst. We use microscopy and digital reconstruction to obtain the morphology of a two-dimensional slice of a nanoporous gold sample. Using lattice Boltzmann fluid dynamics simulations along with thermodynamic models based on first-principles total-energy calculations, we show that some sections of this sample have low local O-2 partial pressures when exposed to reaction conditions, which leads to a pure Au surface in these regions, instead of the active bimetallic AgAu phase. We also explore the effect of temperature on the surface structure and find that moderate temperatures (approximate to 300-450 K) should result in the highest intrinsic catalytic performance, in apparent agreement with experimental results. Published by AIP Publishing.

This paper presents a methodology to generate maps of atmosphere's precipitable water vapor (PWV) over large areas with a length of hundreds of kilometers and a width of about 250 km, based on the use of interferometric Sentinel-1A/BC-band synthetic aperture radar (SAR) data with a high spatial resolution of 5 x 20 m(2) and the revisiting time of six days. An algorithm to calibrate and merge PWV maps from different swaths of Sentinel-1 acquired along the same track, using global navigation satellite system (GNSS) measurements, is described. The proposed methodology is tested on Sentinel-1A SAR images acquired over the Iberian Peninsula, along both descending and ascending tracks. The assessment with an independent set of GNSS measurements shows a mean difference of a fraction of millimeter and a dispersion lower than 2 mm. Both the use of Sentinel-1A/B SAR images and the proposed methodology open new perspectives on the application of SAR meteorology for the high-resolution mapping of PWV over large region-spanning areas and the assimilation of interferometric SAR data into numerical weather models.

Talk

Objective: Neuroimaging studies provide evidence of disturbed resting-state brain networks in Schizophrenia (SZ). However, untangling the neuronal mechanisms that subserve these baseline alterations requires measurement of their electrophysiological underpinnings. This systematic review specifically investigates the contributions of resting-state Magnetoencephalography (MEG) in elucidating abnormal neural organization in SZ patients.& para;& para;Method: A systematic literature review of resting-state MEG studies in SZ was conducted. This literature is discussed in relation to findings from resting-state fMRI and EEG, as well as to task-based MEG research in SZ population. Importantly, methodological limitations are considered and recommendations to overcome current limitations are proposed.& para;& para;Results: Resting-state MEG literature in SZ points towards altered local and long-range oscillatory network dynamics in various frequency bands. Critical methodological challenges with respect to experiment design, and data collection and analysis need to be taken into consideration.& para;& para;Conclusion: Spontaneous MEG data show that local and global neural organization is altered in SZ patients. MEG is a highly promising tool to fill in knowledge gaps about the neurophysiology of SZ. However, to reach its fullest potential, basic methodological challenges need to be overcome.& para;& para;Significance: MEG-based resting-state power and connectivity findings could be great assets to clinical and translational research in psychiatry, and SZ in particular. (C) 2017 International Federation of Clinical Neurophysiology. Published by Elsevier Ireland Ltd. All rights reserved.

NeuroPycon is an open-source multi-modal brain data analysis kit which provides Python-based pipelines for advanced multi-thread processing of fMRI, MEG and EEG data, with a focus on connectivity and graph analyses [1]. NeuroPycon is based on NiPype framework [2] which facilitates data analyses by wrapping many commonly-used neuroimaging software into a common python framework. Therefore, a major strength of NeuroPycon is that it relies on (and interfaces with) several freely available Python packages developed for efficient and fast parallel processing and that it seamlessly connects with existing open-science neuroimaging and signal processing toolboxes. The flexible design allows users to configure analysis pipelines defined by connecting different nodes, where each node may be a user-defined function or a well-established tool or python-wrapped module (e.g. MNE-python for MEG analysis [3], etc.). The current implementation of NeuroPycon contains three different packages: - ephypype includes pipelines for electrophysiology analysis; current implementations allow for MEG/EEG data import, data pre-processing and cleaning by an automatic removal of eyes and heart related artefacts, sensor or source-level connectivity analyses - graphpype allows to study functional connectivity exploiting graph-theoretical metrics including also modular partitions - clipype is a command line interface for ephypype package. NeuroPycon will shortly be available for download via github (installation via Docker) and is currently being documented. Future developments include fusion of multi-modal data (ex. MEG and fMRI or iEEG and fMRI). References 1. Bullmore, Sporns (2009), Nat Rev Neurosci 2. Gorgolewski et al. (2011) Front. Neuroinform 3. Gramfort et al. (2013), Front. Neurosci

The effect of the choice of the inverse method on the cortico-cortical coupling analysis has been largely overlooked in the literature. Here, we set out to investigate the impact of three inverse methods on source coherence detection using simulated MEG data. To this end, we created thousands of randomly located pairs of sources and varied their inter- and intra-source correlation strength, source size and spatial configuration. Then, we used the simulated pairs of sources to generate sensor-level MEG measurements at varying signal-to-noise ratios (SNR). Next, we reconstructed the sources using L2-Minimum-Norm Estimate (MNE), Linearly Constrained Minimum Variance (LCMV) beamforming, and Dynamic Imaging of Coherent Sources (DICS) beamforming; and calculated source level power and coherence maps. We evaluated the performance of the methods using the Receiver Operating Characteristic (ROC) curves. The results indicate that beamformers perform better than MNE for coherence reconstructions of interacting point-like sources; but MNE provides better connectivity estimation than beamformers of interacting extended cortical patches, if each patch consists of dipoles with identical time series (high intra-patch coherence). However, the performance of the beamformers for interacting patches improves substantially if each cortical patch is simulated with partly coherent time series (partial intra-patch coherence). These results demonstrate that the choice of the inverse method impacts the results of MEG source-space coherence analysis, and that the optimal choice of the inverse solution depends on the spatial and synchronization profile of the interacting cortical sources. Our conclusions can guide method selection and help improve data interpretation regarding MEG connectivity estimation.