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Building upon the pertinence of the factor decomposition to break the curse of dimensionality inherent to multivariate volatility processes, we develop a factor model-based multivariate stochastic volatility (fMSV) framework that relies on two viewpoints: sparse approximate factor model and sparse factor loading matrix. We propose a two-stage estimation procedure for the fMSV model: the first stage obtains the estimators of the factor model, and the second stage estimates the MSV part using the estimated common factor variables. We derive the asymptotic properties of the estimators. Simulated experiments are performed to assess the forecasting performances of the covariance matrices. The empirical analysis based on vectors of asset returns illustrates that the forecasting performances of the fMSV models outperforms competing conditional covariance models.

Objective: In medical imaging, it is often crucial to accurately assess and correct movement during image-guided therapy. Deformable image registration (DIR) consists in estimating the required spatial transformation to align a moving image with a fixed one. However, it is acknowledged that, boundary conditions applied to the solution are critical in preventing mis-registration. Despite the extensive research on registration techniques, relatively few have addressed the issue of boundary conditions in the context of medical DIR. Our aim is a step towards customizing boundary conditions to suit the diverse registration tasks at hand. Approach: We propose a generic, locally adaptive, Robin-type condition enabling to balance between Dirichlet and Neumann boundary conditions, depending on incoming/outgoing flow fields on the image boundaries. The proposed framework is entirely automatized through the determination of a reduced set of hyperparameters optimized via energy minimization. Main results: The proposed approach was tested on a mono-modal CT thorax registration task and an abdominal CT to MRI registration task. For the first task, we observed a relative improvement in terms of target registration error of up to 12% (mean 4%), compared to homogeneous Dirichlet and homogeneous Neumann. For the second task, the automatic framework provides results closed to the best achievable. Significance: This study underscores the importance of tailoring the registration problem at the image boundaries. In this research, we introduce a novel method to adapt the boundary conditions on a voxel-by-voxel basis, yielding optimized results in two distinct tasks: mono-modal CT thorax registration and abdominal CT to MRI registration. The proposed framework enables optimized boundary conditions in image registration without any a priori assumptions regarding the images or the motion., Comment: 20 pages, 5 figures, 2 tables

We consider the estimation of factor model-based variance-covariance matrix when the factor loading matrix is assumed sparse. To do so, we rely on a system of penalized estimating functions to account for the identification issue of the factor loading matrix while fostering sparsity in potentially all its entries. We prove the oracle property of the penalized estimator for the factor model when the dimension is fixed. That is, the penalization procedure can recover the true sparse support, and the estimator is asymptotically normally distributed. Consistency and recovery of the true zero entries are established when the number of parameters is diverging. These theoretical results are supported by simulation experiments, and the relevance of the proposed method is illustrated by an application to portfolio allocation.

In this paper, we describe the magnetic potential in the vicinity of a corner of a conducting body embedded in a dielectric medium in a bidimensional setting. We make explicit the corner asymptotic expansion for this potential as the distance to the corner goes to zero. This expansion involves singular functions and singular coefficients. We introduce a method for the calculation of the singular functions near the corner and we provide two methods to compute the singular coefficients: the method of moments and the method of quasi-dual singular functions. Estimates for the convergence of both approximate methods are proven. We eventually illustrate the theoretical results with finite element computations. The specific non-standard feature of this problem lies in the structure of its singular functions: They have the form of series whose first terms are harmonic polynomials and further terms are genuine non-smooth functions generated by the piecewise constant zeroth order term of the operator.

Although multivariate stochastic volatility models usually produce more accurate forecasts compared to the MGARCH models, their estimation techniques such as Bayesian MCMC typically suffer from the curse of dimensionality. We propose a fast and efficient estimation approach for MSV based on a penalized OLS framework. Specifying the MSV model as a multivariate state space model, we carry out a two-step penalized procedure. We provide the asymptotic properties of the two-step estimator and the oracle property of the first-step estimator when the number of parameters diverges. The performances of our method are illustrated through simulations and financial data.

We study the large sample properties of sparse M-estimators in the presence of pseudo-observations. Our framework covers a broad class of semi-parametric copula models, for which the marginal distributions are unknown and replaced by their empirical counterparts. It is well known that the latter modification significantly alters the limiting laws compared to usual M-estimation. We establish the consistency and the asymptotic normality of our sparse penalized M-estimator and we prove the asymptotic oracle property with pseudo-observations, possibly in the case when the number of parameters is diverging. Our framework allows to manage copula-based loss functions that are potentially unbounded. Additionally, we state the weak limit of multivariate rank statistics for an arbitrary dimension and the weak convergence of empirical copula processes indexed by maps. We apply our inference method to Canonical Maximum Likelihood losses with Gaussian copulas, mixtures of copulas or conditional copulas. The theoretical results are illustrated by two numerical experiments.

A dead zone in the interaction between two dynamical systems is a region of their joint phase space where one system is insensitive to the changes in the other. These can arise in a number of contexts, and their presence in phase interaction functions has interesting dynamical consequences for the emergent dynamics. In this paper, we consider dead zones in the interaction of general coupled dynamical systems. For weakly coupled limit cycle oscillators, we investigate criteria that give rise to dead zones in the phase interaction functions. We give applications to coupled multiscale oscillators where coupling on only one branch of a relaxation oscillation can lead to the appearance of dead zones in a phase description of their interaction.

The aim of this paper is to investigate the asymptotic behavior of a biphase tumor fluid flow derived by 2-scale homogenisation techniques in recent works. This biphase fluid flow model accounts for the capillary wall permeability, and the interstitial avascular phase, both being mixed in the limit homogenised problem. When the vessel walls become more permeable, we show that the biphase fluid flow exhibits a boundary layer that makes the computation of the full problem costly and unstable. In the limit, both capillary and interstitial pressures coincide except in the vicinity of the boundary where different boundary conditions are applied. Thanks to a rigorous asymptotic analysis, we prove that the solution to the full problem can be approached at any order of approximation by a monophasic model with appropriate boundary conditions on the tumor boundary and appropriate correcting terms near the boundary are given. Numerical simulations in spherical geometry illustrate the theoretical results.

Various multi-modal imaging sensors are currently involved at different steps of an interventional therapeutic work-flow. Cone beam computed tomography (CBCT), computed tomography (CT) or Magnetic Resonance (MR) images thereby provides complementary functional and/or structural information of the targeted region and organs at risk. Merging this information relies on a correct spatial alignment of the observed anatomy between the acquired images. This can be achieved by the means of multi-modal deformable image registration (DIR), demonstrated to be capable of estimating dense and elastic deformations between images acquired by multiple imaging devices. However, due to the typically different field-of-view (FOV) sampled across the various imaging modalities, such algorithms may severely fail in finding a satisfactory solution. In the current study we propose a new fast method to align the FOV in multi-modal 3D medical images. To this end, a patch-based approach is introduced and combined with a state-of-the-art multi-modal image similarity metric in order to cope with multi-modal medical images. The occurrence of estimated patch shifts is computed for each spatial direction and the shift value with maximum occurrence is selected and used to adjust the image field-of-view. We show that a regional registration approach using voxel patches provides a good structural compromise between the voxel-wise and "global shifts" approaches. The method was thereby beneficial for CT to CBCT and MRI to CBCT registration tasks, especially when highly different image FOVs are involved. Besides, the benefit of the method for CT to CBCT and MRI to CBCT image registration is analyzed, including the impact of artifacts generated by percutaneous needle insertions. Additionally, the computational needs are demonstrated to be compatible with clinical constraints in the practical case of on-line procedures., Comment: 22 pages, 9 figures

Detecting influential features in non-linear and/or high-dimensional data is a challenging and increasingly important task in machine learning. Variable selection methods have thus been gaining much attention as well as post-selection inference. Indeed, the selected features can be significantly flawed when the selection procedure is not accounted for. We propose a selective inference procedure using the so-called model-free "HSIC-Lasso" based on the framework of truncated Gaussians combined with the polyhedral lemma. We then develop an algorithm, which allows for low computational costs and provides a selection of the regularisation parameter. The performance of our method is illustrated by both artificial and real-world data based experiments, which emphasise a tight control of the type-I error, even for small sample sizes., Comment: Changes to previous version: * Incorporating comments and remarks from reviewers * Evaluation of power of the proposed method * Summarising behaviour for different hyper-parameters in one paragraph, instead of several figures * Pseudocode of the algorithm * Additional, in-depth experiment on real-world data

The definition of an innovative therapeutic protocol requires the fine tuning of all the involved operations in order to maximize the efficiency. In some cases, the price of the experiments, or their duration, represents a great obstacle and the full potential of the protocol risks to be reduced or even hidden by a non-optimal application. The implementation of a numerical model of the protocol may represent the solution, allowing a systematic exploration of all the different alternatives, shedding the light on the most promising combination and also identifying the key elements/parameters. In this paper, the injection of a plasmid, preceded by a hyaluronidase injection, is simulated through a mathematical model. Some key elements of the administration protocol are identified by means of a mathematical optimization procedure, maximizing the efficacy of the therapy. As a side effect of the extensive investigation, robust solutions able to reduce the effects of human errors in the administration are also obtained.

The dynamics of networks of interacting dynamical systems depend on the nature of the coupling between individual units. We explore networks of oscillatory units with coupling functions that have "dead zones", that is, the coupling functions are zero on sets with interior. For such networks, it is convenient to look at the effective interactions between units rather than the (fixed) structural connectivity to understand the network dynamics. For example, oscillators may effectively decouple in particular phase configurations. Along trajectories the effective interactions are not necessarily static, but the effective coupling may evolve in time. Here, we formalize the concepts of dead zones and effective interactions. We elucidate how the coupling function shapes the possible effective interaction schemes and how they evolve in time.

We provide finite sample properties of sparse multivariate ARCH processes, where the linear representation of ARCH models allows for an ordinary least squares estimation. Under the restricted strong convexity of the unpenalized loss function, regularity conditions on the penalty function, strict stationary and beta-mixing process, we prove non-asymptotic error bounds on the regularized ARCH estimator. Based on the primal-dual witness method of Loh and Wainwright (2017), we establish variable selection consistency, including the case when the penalty function is non-convex. These theoretical results are supported by empirical studies., Comment: The concentration inequality contains a mistake

We introduce a numerical framework that enables unprecedented direct numerical studies of the electropermeabilization effects of a cell aggregate at the meso-scale. Our simulations qualitatively replicate the shadowing effect observed in experiments and reproduce the time evolution of the impedance of the cell sample in agreement with the trends observed in experiments. This approach sets the scene for performing homogenization studies for understanding the effect of tissue environment on the efficiency of electropermeabilization. We employ a forest of Octree grids along with a Voronoi mesh in a parallel environment that exhibits excellent scalability. We exploit the electric interactions between the cells through a nonlinear phenomenological model that is generalized to account for the permeability of the cell membranes. We use the Voronoi Interface Method (VIM) to accurately capture the sharp jump in the electric potential on the cell boundaries. The case study simulation covers a volume of $(1\ mm)^3$ with more than $27,000$ well-resolved cells with a heterogeneous mix of morphologies that are randomly distributed throughout a spheroid region., Comment: 23 pages, 19 figures, submitted to Journal of Computational Physics

We investigate the effects of structural perturbations of both, undirected and directed diffusive networks on their ability to synchronize. We establish a classification of directed links according to their impact on synchronizability. We focus on adding directed links in weakly connected networks having a strongly connected component acting as driver. When the connectivity of the driver is not stronger than the connectivity of the slave component, we can always make the network strongly connected while hindering synchronization. On the other hand, we prove the existence of a perturbation which makes the network strongly connected while increasing the synchronizability. Under additional conditions, there is a node in the driving component such that adding a single link starting at an arbitrary node of the driven component and ending at this node increases the synchronizability.

This article deals with the spectra of Laplacians of weighted graphs. In this context, two objects are of fundamental importance for the dynamics of complex networks: the second eigenvalue of such a spectrum (called algebraic connectivity) and its associated eigenvector, the so-called Fiedler vector. Here we prove that, given a Laplacian matrix, it is possible to perturb the weights of the existing edges in the underlying graph in order to obtain simple eigenvalues and a Fiedler vector composed of only non-zero entries. These structural genericity properties with the constraint of not adding edges in the underlying graph are stronger than the classical ones, for which arbitrary structural perturbations are allowed. These results open the opportunity to understand the impact of structural changes on the dynamics of complex systems.

This paper proposes a general framework for penalized convex empirical criteria and a new version of the Sparse-Group LASSO (SGL, Simon and al., 2013), called the adaptive SGL, where both penalties of the SGL are weighted by preliminary random coefficients. We explore extensively its asymptotic properties and prove that this estimator satisfies the so-called oracle property (Fan and Li, 2001), that is the sparsity based estimator recovers the true underlying sparse model and is asymptotically normally distributed. Then we study its asymptotic properties in a double-asymptotic framework, where the number of parameters diverges with the sample size. We show by simulations that the adaptive SGL outperforms other oracle-like methods in terms of estimation precision and variable selection.

Consider an ambient medium and a heterogeneous entity composed of a bidimensional material surrounded by a thin membrane. The electromagnetic constants of these materials are different. By analogy with biological cells, we call this entity a cell. We study the asymptotic behavior of the electric field in the transverse magnetic (TM) mode, when the thickness of the membrane tends to zero. The membrane is of thickness of hf(s), with s a curvilinear coordinate. We provide a rigorous derivation of the first two terms of the asymptotic expansion for h tending to zero. In the membrane, these terms are given explicitly in local coordinates in terms of the boundary data and of the function f, while outside the membrane they are the solutions of a scalar Helmholtz equation with appropriate boundary and transmissions conditions given explicitly in terms of the boundary data and of the above function f. We prove that the remainder terms are of order O(h3/2). In addition, if the complex dielectric permittivity in the membrane, denoted by z_m, tends to zero faster than h, we give the difference between the exact solution and the above asymptotic with z_m = 0; it is of order O(h^{3/2}+|z_m|)., Comment: 26 pages. Submitted

We study the behavior of steady state voltage potentials in two kinds of bidimensional media composed of material of complex permittivity equal to 1 (respectively $\alpha$) surrounded by a thin membrane of thickness $h$ and of complex permittivity $\alpha$ (respectively 1). We provide in both cases a rigorous derivation of the asymptotic expansion of steady state voltage potentials at any order as $h$ tends to zero, when Neumann boundary condition is imposed on the exterior boundary of the thin layer. Our complex parameter $\alpha$ is bounded but may be very small compared to 1, hence our results describe the asymptotics of steady state voltage potentials in all heterogeneous and highly heterogeneous media with thin layer. The terms of the potential in the membrane are given explicitly in local coordinates in terms of the boundary data and of the curvature of the domain, while these of the inner potential are the solutions to the so-called dielectric formulation with appropriate boundary conditions. The error estimates are given explicitly in terms of $h$ and $\alpha$ with appropriate Sobolev norm of the boundary data. We show that the two situations described above lead to completely different asymptotic behaviors of the potentials., Comment: submitted. 28 pages