Magnetoelastic modelling in soft nanocrystalline alloys

Magnetoelastic effects in ultra soft nanocrystalline alloys are investigated theoretically and experimentally. From Hc measurements, extraction of magnetoelastic contribution is carried out using a formalism obtained revisiting random anisotropy model (RAM) in the light of domain walls (DW) displacements, our approach based on theoretical investigations on the way of a reversal of a correlated volume (CV) located in the vicinity of a DW. Modelling of magnetoelastic effects shows that even in perfectly relaxed samples, a magnetoelastic contribution exists due to elastic frustration experienced by a CV during its magnetization reversal. Magnitude of this energy is large enough to drive coercivity of samples featuring grain diameter D around 10 nm, which are of major interest for applications

Data-Driven Analysis of Pareto Set Topology

When and why can evolutionary multi-objective optimization (EMO) algorithms cover the entire Pareto set? That is a major concern for EMO researchers and practitioners. A recent theoretical study revealed that (roughly speaking) if the Pareto set forms a topological simplex (a curved line, a curved triangle, a curved tetrahedron, etc.), then decomposition-based EMO algorithms can cover the entire Pareto set. Usually, we cannot know the true Pareto set and have to estimate its topology by using the population of EMO algorithms during or after the runtime. This paper presents a data-driven approach to analyze the topology of the Pareto set. We give a theory of how to recognize the topology of the Pareto set from data and implement an algorithm to judge whether the true Pareto set may form a topological simplex or not. Numerical experiments show that the proposed method correctly recognizes the topology of high-dimensional Pareto sets within reasonable population size.Comment: 8 pages, accepted at GECCO'18 as a full pape

Molecular Shape Analysis based uponthe Morse-Smale Complexand the Connolly Function

Docking is the process by which two or several molecules form a complex. Docking involves the geometry of the molecular surfaces, as well as chemical and energetical considerations. In the mid-eighties, Connolly proposed a docking algorithm matching surface {\em knobs} with surface {\em depressions}. Knobs and depressions refer to the extrema of the {\em Connolly} function, which is defined as follows. Given a surface \calM bounding a three-dimensional domain $X$, and a sphere $S$ centered at a point $p$ of \calM, the Connolly function is equal to the solid angle of the portion of $S$ containing within $X$. We recast the notions of knob and depression of the Connolly function in the framework of Morse theory for functions defined over two-dimensional manifolds. First, we study the critical points of the Connolly function for smooth surfaces. Second, we provide an efficient algorithm for computing the Connolly function over a triangulated surface. Third, we introduce a Morse-Smale decomposition based on Forman's discrete Morse theory, and provide an $O(n\log n)$ algorithm to construct it. This decomposition induces a partition of the surface into regions of homogeneous flow, and provides an elegant way to relate local quantities to global ones ---from critical points to Euler's characteristic of the surface. Fourth, we apply this Morse-Smale decomposition to the discrete gradient vector field induced by Connolly's function, and present experimental results for several mesh models

A comparison of statistical machine learning methods in heartbeat detection and classification

In health care, patients with heart problems require quick responsiveness in a clinical setting or in the operating theatre. Towards that end, automated classification of heartbeats is vital as some heartbeat irregularities are time consuming to detect. Therefore, analysis of electro-cardiogram (ECG) signals is an active area of research. The methods proposed in the literature depend on the structure of a heartbeat cycle. In this paper, we use interval and amplitude based features together with a few samples from the ECG signal as a feature vector. We studied a variety of classification algorithms focused especially on a type of arrhythmia known as the ventricular ectopic fibrillation (VEB). We compare the performance of the classifiers against algorithms proposed in the literature and make recommendations regarding features, sampling rate, and choice of the classifier to apply in a real-time clinical setting. The extensive study is based on the MIT-BIH arrhythmia database. Our main contribution is the evaluation of existing classifiers over a range sampling rates, recommendation of a detection methodology to employ in a practical setting, and extend the notion of a mixture of experts to a larger class of algorithms

Biomechanical experimental data curation: an example for main lumbar spine ligaments characterization for a MBS spine model

Series : Mechanisms and machine science, ISSN 2211-0984, vol. 24This work overviews an extensive analysis in the context of mechanical characterization of human biomaterials, carried out over a broad set of published experimental data. Focused on main lumbar spine ligaments, several test procedures are exhaustively analyzed, in order to identify possible causes for divergences that have been found in some results. Moreover, guidelines are proposed for da-ta filtering and selection. The main objective of the task was to retrieve trustworthy inputs to a hybrid Finite Element Analysis / Multibody System dynamic simulation model of the human intervertebral disc, which can be used on the prediction of nucleus prosthetics working performance

Analyzing Collective Motion with Machine Learning and Topology

We use topological data analysis and machine learning to study a seminal model of collective motion in biology [D'Orsogna et al., Phys. Rev. Lett. 96 (2006)]. This model describes agents interacting nonlinearly via attractive-repulsive social forces and gives rise to collective behaviors such as flocking and milling. To classify the emergent collective motion in a large library of numerical simulations and to recover model parameters from the simulation data, we apply machine learning techniques to two different types of input. First, we input time series of order parameters traditionally used in studies of collective motion. Second, we input measures based in topology that summarize the time-varying persistent homology of simulation data over multiple scales. This topological approach does not require prior knowledge of the expected patterns. For both unsupervised and supervised machine learning methods, the topological approach outperforms the one that is based on traditional order parameters.Comment: Published in Chaos 29, 123125 (2019), DOI: 10.1063/1.512549

Elastic deformation of a fluid membrane upon colloid binding

When a colloidal particle adheres to a fluid membrane, it induces elastic deformations in the membrane which oppose its own binding. The structural and energetic aspects of this balance are theoretically studied within the framework of a Helfrich Hamiltonian. Based on the full nonlinear shape equations for the membrane profile, a line of continuous binding transitions and a second line of discontinuous envelopment transitions are found, which meet at an unusual triple point. The regime of low tension is studied analytically using a small gradient expansion, while in the limit of large tension scaling arguments are derived which quantify the asymptotic behavior of phase boundary, degree of wrapping, and energy barrier. The maturation of animal viruses by budding is discussed as a biological example of such colloid-membrane interaction events.Comment: 14 pages, 9 figures, REVTeX style, follow-up on cond-mat/021242

Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version, to appear in Foundations of Computational Mathematics. Minor changes and addition

Algorithm for the classification of multi-modulating signals on the electrocardiogram

This article discusses the algorithm to measure electrocardiogram (ECG) and respiration simultaneously and to have the diagnostic potentiality for sleep apnoea from ECG recordings. The algorithm is composed by the combination with the three particular scale transform of a(j)(t), u(j)(t), o(j)(a(j)) and the statistical Fourier transform (SFT). Time and magnitude scale transforms of a(j)(t), u(j)(t) change the source into the periodic signal and τ(j) = o(j)(a(j)) confines its harmonics into a few instantaneous components at τ(j) being a common instant on two scales between t and τ(j). As a result, the multi-modulating source is decomposed by the SFT and is reconstructed into ECG, respiration and the other signals by inverse transform. The algorithm is expected to get the partial ventilation and the heart rate variability from scale transforms among a(j)(t), a(j+1)(t) and u(j+1)(t) joining with each modulation. The algorithm has a high potentiality of the clinical checkup for the diagnosis of sleep apnoea from ECG recordings