In this paper we describe how to swap two 2 × 2 blocks in a real Schur form and a generalized real Schur form. We pay special attention to the numerical stability of the method. We also illustrate the stability of our approach by a series of numerical tests.

Let X={X1,X2,...,Xm} be a system of smooth vector fields in R^n satisfying the Hörmander's finite rank condition. We prove the following Sobolev inequality with reciprocal weights in Carnot-Carathéodory space G associated to system X (1?BRK(x)dx?BR|u|tK(x)dx)1/t<=CR??1?BR1K(x)dx?BR|Xu|2K(x)dx??1/2, where Xu denotes the horizontal gradient of u with respect to X. We assume that the weight K belongs to Muckenhoupt's class A_2 and Gehring's class G_?, where ? is a suitable exponent related to the homogeneous dimension.

We study an eigenvalue problem involving a fully anisotropic elliptic differential operator in arbitrary Orlicz-Sobolev spaces. The relevant equations are associated with constrained minimization problems for integral functionals depending on the gradient of competing functions through general anisotropic N-functions. In particular, the latter need neither be radial, nor have a polynomial growth, and are not even assumed to satisfy the so called \Delta_2-condition. The resulting analysis requires the development of some new aspects of the theory of anisotropic Orlicz-Sobolev spaces.

We introduce non-local dynamics on directed networks through the construction of a fractional version of a non-symmetric Laplacian for weighted directed graphs. Furthermore, we provide an analytic treatment of fractional dynamics for both directed and undirected graphs, showing the possibility of exploring the network employing random walks with jumps of arbitrary length. We also provide some examples of the applicability of the proposed dynamics, including consensus over multi-agent systems described by directed networks.

Visibility has an encompassing importance in humans' perception of the landscape, since the first encounter with a new environment normally occurs through sight. In historical and archaeological studies, two main methods (i.e., the geometric method and the Geographical Information System [GIS] computation) have been employed to determine the distance from which an object can be recognized. However, neither is exhaustive when applied to a maritime context, where the main factor affecting the visibility radius is weather. To establish how far at sea an object can be seen, and how its visibility would have changed in different weather conditions, we adopted a method from Aerosol Optics based on a well-established mathematical model of the light scattering phenomena. We applied this method to compute the visibility radius in historical studies. To demonstrate its application, we choose to examine the visibility of a key point in both historical and current seafaring, namely Mount Etna (Sicily, Italy), from the Ionian coast of Calabria (Italy). The results obtained by the application of this method have been validated by comparing them with mentions of Mount Etna in both written sources and on-the-ground records.

The computation of matrix functions using quadrature formulas and rational approximations of very large structured matrices using tensor trains (TT), and quantized tensor trains (QTT) is considered here. The focus is on matrices with a small TT/QTT rank. Some analysis of the error produced by the use of the TT/QTT representation and the underlying approximation formula used is also provided. Promising experiments on exponential, power, Mittag-Leffler and logarithm function of multilevel Toeplitz matrices, that are among those which generate a low TT/QTT rank representation, are also provided, confirming that the proposed approach is feasible. (C) 2019 Elsevier B.V. All rights reserved.

In this work we introduce and study a nonlocal version of the PageRank. In our approach, the random walker explores the graph using longer excursions than just moving between neighboring nodes. As a result, the corresponding ranking of the nodes, which takes into account a long-range interaction between them, does not exhibit concentration phenomena typical of spectral rankings which take into account just local interactions. We show that the predictive value of the rankings obtained using our proposals is considerably improved on different real world problems.

We use computer simulations to study the morphology and rheological properties of a bidimensional emulsion resulting from a mixture of a passive isotropic fluid and an active contractile polar gel, in the presence of a surfactant that favours the emulsification of the two phases. By varying the intensity of the contractile activity and of an externally imposed shear flow, we find three possible morphologies. For low shear rates, a simple lamellar state is obtained. For intermediate activity and shear rate, an asymmetric state emerges, which is characterized by shear and concentration banding at the polar/isotropic interface. A further increment in the active forcing leads to the self-assembly of a soft channel where an isotropic fluid flows between two layers of active material. We characterize the stability of this state by performing a dynamical test varying the intensity of the active forcing and shear rate. Finally, we address the rheological properties of the system by measuring the effective shear viscosity, finding that this increases as active forcing is increased-so that the fluid thickens with activity.

The main focus of this paper is the characterization and exploitation of the asymptotic spectrum of the saddle--point matrix sequences arising from the discretization of optimization problems constrained by elliptic partial differential equations. They uncover the existence of an hidden structure in these matrix sequences, namely, they show that these are indeed an example of Generalized Locally Toeplitz (GLT) sequences. They show that this enables a sharper characterization of the spectral properties of such sequences than the one that is available by using only the fact that they deal with saddle--point matrices. Finally, they exploit it to propose an optimal preconditioner strategy for the GMRES, and Flexible--GMRES methods.

Rational Krylov methods are a powerful alternative for computing the product of a function of a large matrix times a given vector. However, the creation of the underlying rational subspaces requires solving sequences of large linear systems, a delicate task that can require intensive computational resources and should be monitored to avoid the creation of subspace different to those required. We propose the use of robust preconditioned iterative techniques to speedup the underlying process. We also discuss briefly how the inexact solution of these linear systems can affect the computed subspace. A preliminary test approximating a fractional power of the Laplacian matrix is included.

Recent years have witnessed a massive push towards reproducible research in neuroscience. Unfortunately, this endeavor is often challenged by the large diversity of tools used, project-specific custom code and the difficulty to track all user-defined parameters. NeuroPycon is an open-source multi-modal brain data analysis toolkit which provides Python-based template pipelines for advanced multi-processing of MEG, EEG, functional and anatomical MRI data, with a focus on connectivity and graph theoretical analyses. Importantly, it provides shareable parameter files to facilitate replication of all analysis steps. NeuroPycon is based on the NiPype framework which facilitates data analyses by wrapping many commonly-used neuroimaging software tools into a common Python environment. In other words, rather than being a brain imaging software with is own implementation of standard algorithms for brain signal processing, NeuroPycon seamlessly integrates existing packages (coded in python, Matlab or other languages) into a unified python framework. Importantly, thanks to the multi-threaded processing and computational efficiency afforded by NiPype, NeuroPycon provides an easy option for fast parallel processing, which critical when handling large sets of multi-dimensional brain data. Moreover, its fiexible design allows users to easily configure analysis pipelines by connecting distinct nodes to each other. Each node can be a Python-wrapped module, a user-defined function or a well-established tool (e.g. MNE-Python for MEG analysis, Radatools for graph theoretical metrics, etc.). Last but not least, the ability to use NeuroPycon parameter files to fully describe any pipeline is an important feature for reproducibility, as they can be shared and used for easy replication by others. The current implementation of NeuroPycon contains two complementary packages: The first, called ephypype, includes pipelines for electrophysiology analysis and a command-line interface for on the fiy pipeline creation. Current implementations allow for MEG/EEG data import, pre-processing and cleaning by automatic removal of ocular and cardiac artefacts, in addition to sensor or source-level connectivity analyses. The second package, called graphpype, is designed to investigate functional connectivity via a wide range of graph-theoretical metrics, including modular partitions. The present article describes the philosophy, architecture, and functionalities of the toolkit and provides illustrative examples through interactive notebooks. NeuroPycon is available for download via github (https://github.com/neuropycon) and the two principal packages are documented online (https://neuropycon.github.io/ephypype/index.html, and https://neuropycon.github.io/graph pype/index.html). Future developments include fusion of multi-modal data (eg. MEG and fMRI or intracranial EEG and fMRI). We hope that the release of NeuroPycon will attract many users and new contributors, and facilitate the efforts of our community towards open source tool sharing and development, as well as scientific reproducibility.

Current theories of schizophrenia emphasize the role of altered information integration as the core dysfunction of this illness. While ample neuroimaging evidence for such accounts comes from investigations of spatial connectivity, understanding temporal disruptions is important to fully capture the essence of dysconnectivity in schizophrenia. Recent electrophysiology studies suggest that long-range temporal correlation (LRTC) in the amplitude dynamics of neural oscillations captures the integrity of transferred information in the healthy brain.Thus, in this study, 25 schizophrenia patients and 25 controls (8 females/group) were recorded during two five-minutes of resting-state magnetoencephalography (once with eyes-open and once with eyes-closed). We used source-level analyses to investigate temporal dysconnectivity in patients by characterizing LRTCs across cortical and sub-cortical brain regions. In addition to standard statistical assessments, we applied a machine learning framework using support vector machine to evaluate the discriminative power of LRTCs in identifying patients from healthy controls.We found that neural oscillations in schizophrenia patients were characterized by reduced signal memory and higher variability across time, as evidenced by cortical and subcortical attenuations of LRTCs in the alpha and beta frequency bands. Support vector machine significantly classified participants using LRTCs in key limbic and paralimbic brain areas, with decoding accuracy reaching 82%. Importantly, these brain regions belong to networks that are highly relevant to the symptomology of schizophrenia. These findings thus posit temporal dysconnectivity as a hallmark of altered information processing in schizophrenia, and help advance our understanding of this pathology.

The T-box transcription factor TBX1 has critical roles in the cardiopharyngeal lineage and the gene is haploinsufficient in DiGeorge syndrome, a typical developmental anomaly of the pharyngeal apparatus. Despite almost two decades of research, if and how TBX1 function triggers chromatin remodeling is not known. Here, we explored genome-wide gene expression and chromatin remodeling in two independent cellular models of Tbx1 loss of function, mouse embryonic carcinoma cells P19Cl6, and mouse embryonic stem cells (mESCs). The results of our study revealed that the loss or knockdown of TBX1 caused extensive transcriptional changes, some of which were cell type-specific, some were in common between the two models. However, unexpectedly we observed only limited chromatin changes in both systems. In P19Cl6 cells, differentially accessible regions (DARs) were not enriched in T-BOX binding motifs; in contrast, in mESCs, 34% (n = 47) of all DARs included a T-BOX binding motif and almost all of them gained accessibility in Tbx1 -/- cells. In conclusion, despite a clear transcriptional response of our cell models to loss of TBX1 in early cell differentiation, chromatin changes were relatively modest.

In this paper we propose and study a hybrid discrete-continuous mathematical model of collective motion under alignment and chemotaxis effect. Starting from paper [23], in which the Cucker-Smale model [22] was coupled with other cell mechanisms, to describe the cell migration and self-organization in the zebrafish lateral line primordium, we introduce a simplified model in which the coupling between an alignment and chemotaxis mechanism acts on a system of interacting particles. In particular we rely on a hybrid description in which the agents are discrete entities, while the chemoattractant is considered as a continuous signal. The proposed model is then studied both from an analytical and a numerical point of view. From the analytic point of view we prove, globally in time, existence and uniqueness of the solution. Then, the asymptotic behaviour of a linearised version of the system is investigated. Through a suitable Lyapunov functional we show that for t -&gt; +infinity, the migrating aggregate exponentially converges to a state in which all the particles have a same position with zero velocity. Finally, we present a comparison between the analytical findings and some numerical results, concerning the behaviour of the full nonlinear system.

The dynamic behaviour of rigid blocks subjected to support excitation is represented by discontinuous differential equations with state jumps. In the numerical simulation of these systems, the jump times corresponding to the numerical trajectory do not coincide with the ones of the given problem. When multiple state jumps occur, this approximation may affect the accuracy of the solution and even cause an order reduction in the method. Focus here is on the error behaviour in the numerical dynamic. The basic idea is to investigate how the error propagates in successive impacts by decomposing the numerical integration process of the overall system into a sequence of discretized perturbed problems.

The integral representation of some biological phenomena consists in Volterra equations whose kernels involve a convolution term plus a non convolution one. Some significative applications arise in linearised models of cell migration and collective motion, as described in Di Costanzo et al. (Discrete Contin. Dyn. Syst. Ser. B 25 (2020) 443-472), Etchegaray et al. (Integral Methods in Science and Engineering (2015)), Grec et al. (J. Theor. Biol. 452 (2018) 35-46) where the asymptotic behaviour of the analytical solution has been extensively investigated. Here we consider this type of problems from a numerical point of view and we study the asymptotic dynamics of numerical approximations by linear multistep methods. Through a suitable reformulation of the equation, we collect all the non convolution parts of the kernel into a generalized forcing function, and we transform the problem into a convolution one. This allows us to exploit the theory developed in Lubich (IMA J. Numer. Anal. 3 (1983) 439-465) and based on discrete variants of Paley-Wiener theorem. The main effort consists in the numerical treatment of the generalized forcing term, which will be analysed under suitable assumptions. Furthermore, in cases of interest, we connect the results to the behaviour of the analytical solution.

The optimal Orlicz target space and the optimal rearrangement- invariant target space are exhibited for embeddings of fractional-order Orlicz- Sobolev spaces W^{s,A}(R^n). Related Hardy type inequalities are proposed as well. Versions for fractional Orlicz-Sobolev seminorms of the Bourgain-Brezis-Mironescu theorem on the limit as s->1^- and of the Maz'ya-Shaposhnikova theorem on the limit as s ->0^+ are established. This is a joint work with Andrea Cianchi, Lubos Pick and Lenka Slavikova.

We provide a brief survey of our current developments in the simulation-based design of novel families of mesoscale porous materials using computational kinetic theory. Prospective applications on exascale computers are also briefly discussed and commented on, with reference to two specific examples of soft mesoscale materials: microfluid crystals and bi-continuous jels.

We numerically study the dynamic behavior under a symmetric shear flow of selected examples of concentrated phase emulsions with multicore morphology confined within a microfluidic channel. A variety of nonequilibrium steady states is reported. Under low shear rates, the emulsion is found to exhibit a solidlike behavior, in which cores display a periodic planetarylike motion with approximately equal angular velocity. At higher shear rates, two steady states emerge, one in which all inner cores align along the flow and become essentially motionless and a further one in which some cores accumulate near the outer interface and produce a dynamical elliptical-shaped ring chain, reminiscent of a treadmillinglike structure, while others occupy the center of the emulsion. A quantitative description in terms of the (i) motion of the cores, (ii) rate of deformation of the emulsion, and (iii) structure of the fluid flow within the channel is also provided.

We consider a natural generalization of the eigenvalue problem for the Laplacian with homogeneous Dirichlet boundary conditions. This corresponds to look for the critical values of the Dirichlet integral, constrained to the unit Lq sphere. We collect some results, present some counter-examples and compile a list of open problems.