arXiv subjects

Robert Martin

Publications and source records attributed to Robert Martin.

17 recordsLinked to original sources

arXiv2025

Constitutive properties for isotropic energies in ideal nonlinear elasticity for solid materials: numerical evidences for invertibility and monotonicity in different stress-strain pairs

As a service for the solid mechanics community we gather in this paper constitutive properties of a collective list of isotropic elastic energies for compressible materials. Of interest to us are the invertibility and monotonicity of certain stress-strain pairs. The calculations are done numerically by our own evaluation algorithm and presented in a yes/no-table. Such an overview has been missing up to now. It is intended to expand the table with further energies as time goes on and updates will be found on arxive.

physics.class-ph↗

arXiv2024

Invariant Measures in Time-Delay Coordinates for Unique Dynamical System Identification

While invariant measures are widely employed to analyze physical systems when a direct study of pointwise trajectories is intractable, e.g., due to chaos or noise, they cannot uniquely identify the underlying dynamics. Our first result shows that, in contrast to invariant measures in state coordinates, e.g., $[x(t), y(t), z(t)]$, the invariant measure expressed in time-delay coordinates, e.g., $[x(t), x(t-\tau),\ldots, x(t-(m-1)\tau)]$, can identify the dynamics up to a topological conjugacy. Our second result resolves the remaining ambiguity: by combining invariant measures constructed from multiple delay frames with distinct observables, the system is uniquely identifiable, provided that a suitable initial condition is satisfied. These guarantees require informative observables and appropriate delay parameters ($m,\tau$), which can be limiting in certain settings. We support our theoretical contributions through a series of physical examples demonstrating how invariant measures expressed in delay-coordinates can be used to perform robust system identification in practice.

math.DS↗

arXiv2023

BELB: a Biomedical Entity Linking Benchmark

Biomedical entity linking (BEL) is the task of grounding entity mentions to a knowledge base. It plays a vital role in information extraction pipelines for the life sciences literature. We review recent work in the field and find that, as the task is absent from existing benchmarks for biomedical text mining, different studies adopt different experimental setups making comparisons based on published numbers problematic. Furthermore, neural systems are tested primarily on instances linked to the broad coverage knowledge base UMLS, leaving their performance to more specialized ones, e.g. genes or variants, understudied. We therefore developed BELB, a Biomedical Entity Linking Benchmark, providing access in a unified format to 11 corpora linked to 7 knowledge bases and spanning six entity types: gene, disease, chemical, species, cell line and variant. BELB greatly reduces preprocessing overhead in testing BEL systems on multiple corpora offering a standardized testbed for reproducible experiments. Using BELB we perform an extensive evaluation of six rule-based entity-specific systems and three recent neural approaches leveraging pre-trained language models. Our results reveal a mixed picture showing that neural approaches fail to perform consistently across entity types, highlighting the need of further studies towards entity-agnostic models.

cs.CL↗

arXiv2023

Learning dynamics on invariant measures using PDE-constrained optimization

We extend the methodology in [Yang et al., 2023] to learn autonomous continuous-time dynamical systems from invariant measures. The highlight of our approach is to reformulate the inverse problem of learning ODEs or SDEs from data as a PDE-constrained optimization problem. This shift in perspective allows us to learn from slowly sampled inference trajectories and perform uncertainty quantification for the forecasted dynamics. Our approach also yields a forward model with better stability than direct trajectory simulation in certain situations. We present numerical results for the Van der Pol oscillator and the Lorenz-63 system, together with real-world applications to Hall-effect thruster dynamics and temperature prediction, to demonstrate the effectiveness of the proposed approach.

math.DS↗

arXiv2022

BigBIO: A Framework for Data-Centric Biomedical Natural Language Processing

Training and evaluating language models increasingly requires the construction of meta-datasets --diverse collections of curated data with clear provenance. Natural language prompting has recently lead to improved zero-shot generalization by transforming existing, supervised datasets into a diversity of novel pretraining tasks, highlighting the benefits of meta-dataset curation. While successful in general-domain text, translating these data-centric approaches to biomedical language modeling remains challenging, as labeled biomedical datasets are significantly underrepresented in popular data hubs. To address this challenge, we introduce BigBIO a community library of 126+ biomedical NLP datasets, currently covering 12 task categories and 10+ languages. BigBIO facilitates reproducible meta-dataset curation via programmatic access to datasets and their metadata, and is compatible with current platforms for prompt engineering and end-to-end few/zero shot language model evaluation. We discuss our process for task schema harmonization, data auditing, contribution guidelines, and outline two illustrative use cases: zero-shot evaluation of biomedical prompts and large-scale, multi-task learning. BigBIO is an ongoing community effort and is available at https://github.com/bigscience-workshop/biomedical

cs.CL↗

arXiv2022

Parameter Inference of Time Series by Delay Embeddings and Learning Differentiable Operators

We provide a method to identify system parameters of dynamical systems, called ID-ODE -- Inference by Differentiation and Observing Delay Embeddings. In this setting, we are given a dataset of trajectories from a dynamical system with system parameter labels. Our goal is to identify system parameters of new trajectories. The given trajectories may or may not encompass the full state of the system, and we may only observe a one-dimensional time series. In the latter case, we reconstruct the full state by using delay embeddings, and under sufficient conditions, Taken's Embedding Theorem assures us the reconstruction is diffeomorphic to the original. This allows our method to work on time series. Our method works by first learning the velocity operator (as given or reconstructed) with a neural network having both state and system parameters as variable inputs. Then on new trajectories we backpropagate prediction errors to the system parameter inputs giving us a gradient. We then use gradient descent to infer the correct system parameter. We demonstrate the efficacy of our approach on many numerical examples: the Lorenz system, Lorenz96, Lotka-Volterra Predator-Prey, and the Compound Double Pendulum. We also apply our algorithm on a real-world dataset: propulsion of the Hall-effect Thruster (HET).

cs.LG↗

arXiv2021

Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures

We study an optimal transportation approach for recovering parameters in dynamical systems with a single smoothly varying attractor. We assume that the data is not sufficient for estimating time derivatives of state variables but enough to approximate the long-time behavior of the system through an approximation of its physical measure. Thus, we fit physical measures by taking the Wasserstein distance from optimal transportation as a misfit function between two probability distributions. In particular, we analyze the regularity of the resulting loss function for general transportation costs and derive gradient formulas. Physical measures are approximated as fixed points of suitable PDE-based Perron--Frobenius operators. Test cases discussed in the paper include common low-dimensional dynamical systems.

math.DS↗

arXiv2019

Impact of Embedding View on Cross Mapping Convergence

Convergent cross mapping (CCM) provides a powerful technique for exploring causal relationships in nonlinear coupled systems. The method relies on Takens' theorem exploiting that time delay embeddings of infinite length general observations of smooth nonlinear coupled systems are diffeomorphic to the original coupled state space attractor. However, for finite length data that is corrupted by quantization and noise, not every view of the embedding is equally useful at identifying the system dynamics. Classically, the heuristic of the first minimum of mutual information (MI) has been proposed as a means to select appropriate lags for time delay embedding methods. This criteria is sensitive to additive noise and known to fail for systems with monotonically decreasing MI. In this work, alternative heuristics on MI for identifying useful embedding views are explored. The impact of coordinate system and noise level on the identification of a useful time lag representative of the structure in chaotic data is studied. The impact of selecting the first minimum of MI relative to several alternate heuristics for the appropriate time lag in the context of of CCM method is then presented. Both simple dynamical systems as well as experimental data derived from observations of a Hall Effect Thruster plasma propulsion device are used. It is found that the shorter of the two global maxima of MI from signal pairs in a stretched discrete Legendre orthonormal coordinate system is a more robust option relative to the alternatives studied for selecting embedding lag for use with the CCM method. The choice identifies time lags commensurate with the brute force maximum bidirectional CCM correlation results generated. This enhanced performance results from a decreased sensitivity to noise and fluctuations in the estimates of MI when compared to lags derived from local criteria on MI.

nlin.CD↗

arXiv2017

Reuters Tracer: Toward Automated News Production Using Large Scale Social Media Data

To deal with the sheer volume of information and gain competitive advantage, the news industry has started to explore and invest in news automation. In this paper, we present Reuters Tracer, a system that automates end-to-end news production using Twitter data. It is capable of detecting, classifying, annotating, and disseminating news in real time for Reuters journalists without manual intervention. In contrast to other similar systems, Tracer is topic and domain agnostic. It has a bottom-up approach to news detection, and does not rely on a predefined set of sources or subjects. Instead, it identifies emerging conversations from 12+ million tweets per day and selects those that are news-like. Then, it contextualizes each story by adding a summary and a topic to it, estimating its newsworthiness, veracity, novelty, and scope, and geotags it. Designing algorithms to generate news that meets the standards of Reuters journalists in accuracy and timeliness is quite challenging. But Tracer is able to achieve competitive precision, recall, timeliness, and veracity on news detection and delivery. In this paper, we reveal our key algorithm designs and evaluations that helped us achieve this goal, and lessons learned along the way.

cs.SI↗

arXiv2016

Minimal geodesics on GL(n) for left-invariant, right-O(n)-invariant Riemannian metrics

We provide an easy approach to the geodesic distance on the general linear group GL(n) for left-invariant Riemannian metrics which are also right-O(n)-invariant. The parametrization of geodesic curves and the global existence of length minimizing geodesics are deduced using simple methods based on the calculus of variations and classical analysis only. The geodesic distance is discussed for some special cases and applications towards the theory of nonlinear elasticity are indicated.

math.DG↗

arXiv2014

Some remarks on the monotonicity of primary matrix functions on the set of symmetric matrices

This note contains some observations on primary matrix functions and different notions of monotonicity with relevance towards constitutive relations in nonlinear elasticity. Focussing on primary matrix functions on the set of symmetric matrices, we discuss and compare different criteria for monotonicity. The demonstrated results are particularly applicable to computations involving the true-stress-true-strain monotonicity condition, a constitutive inequality recently introduced in an Arch. Appl. Mech. article by C.S. Jog and K.D. Patil. We also clarify a statement by Jog and Patil from the same article which could be misinterpreted.

math.CA↗

arXiv2014

The exponentiated Hencky-logarithmic strain energy. Part II: Coercivity, planar polyconvexity and existence of minimizers

We consider a family of isotropic volumetric-isochoric decoupled strain energies $$ F\mapsto W_{\rm eH}(F):=\widehat{W}_{\rm eH}(U):=\left\{\begin{array}{lll} \fracμ{k}\,e^{k\,\|{\rm dev}_n\log {U}\|^2}+\fracκ{2\hat{k}}\,e^{\hat{k}\,[{\rm tr}(\log U)]^2}&\text{if}& {\rm det}\, F>0,\\ +\infty &\text{if} &{\rm det} F\leq 0, \end{array}\right.\quad $$ based on the Hencky-logarithmic (true, natural) strain tensor $\log U$, where $μ>0$ is the infinitesimal shear modulus, $κ=\frac{2μ+3λ}{3}>0$ is the infinitesimal bulk modulus with $λ$ the first Lamé constant, $k,\hat{k}$ are dimensionless parameters, $F=\nabla φ$ is the gradient of deformation, $U=\sqrt{F^T F}$ is the right stretch tensor and ${\rm dev}_n\log {U} =\log {U}-\frac{1}{n} {\rm tr}(\log {U})\cdot 1\!\!1$ is the deviatoric part (the projection onto the traceless tensors) of the strain tensor $\log U$. For small elastic strains the energies reduce to first order to the classical quadratic Hencky energy $$ F\mapsto W{_{\rm H}}(F):=\widehat{W}_{_{\rm H}}(U):=μ\,\|{\rm dev}_n\log U\|^2+\fracκ{2}\,[{\rm tr}(\log U)]^2, $$ which is known to be not rank-one convex. The main result in this paper is that in plane elastostatics the energies of the family $W_{_{\rm eH}}$ are polyconvex for $k\geq \frac{1}{3}$, $\widehat{k}\geq \frac{1}{8}$, extending a previous finding on its rank-one convexity. Our method uses a judicious application of Steigmann's polyconvexity criteria based on the representation of the energy in terms of the principal invariants of the stretch tensor $U$. These energies also satisfy suitable growth and coercivity conditions. We formulate the equilibrium equations and we prove the existence of minimizers by the direct methods of the calculus of variations.

math.CA↗

arXiv2014

Rediscovering G.F. Becker's early axiomatic deduction of a multiaxial nonlinear stress-strain relation based on logarithmic strain

We discuss a completely forgotten work of the geologist G.F. Becker on the ideal isotropic nonlinear stress-strain function. In doing this we provide the original paper from 1893 newly typeset in LaTeX and with corrections of typographical errors as well as an updated notation. Due to the fact that the mathematical modelling of elastic deformations has evolved greatly since the original publication we give a modern reinterpretation of Becker's work, combining his approach with the current framework of the theory of nonlinear elasticity. Interestingly, Becker introduces a multiaxial constitutive law incorporating the logarithmic strain tensor, more than 35 years before the quadratic Hencky strain energy was introduced by Heinrich Hencky in 1929. Becker's deduction is purely axiomatic in nature. He considers the finite strain response to applied shear stresses and spherical stresses, formulated in terms of the principal strains and stresses, and postulates a principle of superposition for principal forces which leads, in a straightforward way, to a unique invertible constitutive relation. In the special case where Poisson's number is zero, the formulation is hyperelastic and the corresponding strain energy has the form of the maximum entropy function.

math.HO↗

arXiv2014

The axiomatic deduction of the quadratic Hencky strain energy by Heinrich Hencky

The introduction of the quadratic Hencky strain energy based on the logarithmic strain tensor log V is a milestone in the development of nonlinear elasticity theory in the first half of the 20th century. Since the original manuscripts are written in German, they are not easily accessible today. However, we believe that the deductive approach taken by Hencky deserves to be rediscovered today. In this work we have gathered parts of the original contributions "Über die Form des Elastizitätsgesetzes bei ideal elastischen Stoffen", "Welche Umstände bedingen die Verfestigung bei der bildsamen Verformung von festen isotropen Körpern?" and "Das Superpositionsgesetz eines endlich deformierten relaxationsfähigen elastischen Kontinuums und seine Bedeutung für eine exakte Ableitung der Gleichungen für die zähe Flüssigkeit in der Eulerschen Form" which center around this deductive approach. We tried to provide, for the first time, a faithful translation into English. All footnotes are our addition.

math.HO↗

arXiv2013

A Riemannian approach to strain measures in nonlinear elasticity

The isotropic Hencky strain energy appears naturally as a distance measure of the deformation gradient to the set SO(n) of rigid rotations in the canonical left-invariant Riemannian metric on the general linear group GL(n). Objectivity requires the Riemannian metric to be left-GL(n)-invariant, isotropy requires the Riemannian metric to be right-O(n)-invariant. The latter two conditions are satisfied for a three-parameter family of Riemannian metrics on the tangent space of GL(n). Surprisingly, the final result is basically independent of the chosen parameters. In deriving the result, geodesics on GL(n) have to be parametrized and a novel minimization problem, involving the matrix logarithm for non-symmetric arguments, has to be solved.

math.CA↗

arXiv2007

On Information Theory, Spectral Geometry and Quantum Gravity

We show that there exists a deep link between the two disciplines of information theory and spectral geometry. This allows us to obtain new results on a well known quantum gravity motivated natural ultraviolet cutoff which describes an upper bound on the spatial density of information. Concretely, we show that, together with an infrared cutoff, this natural ultraviolet cutoff beautifully reduces the path integral of quantum field theory on curved space to a finite number of ordinary integrations. We then show, in particular, that the subsequent removal of the infrared cutoff is safe.

gr-qc↗

arXiv2007

Simulation of Robustness against Lesions of Cortical Networks

Structure entails function and thus a structural description of the brain will help to understand its function and may provide insights into many properties of brain systems, from their robustness and recovery from damage, to their dynamics and even their evolution. Advances in the analysis of complex networks provide useful new approaches to understanding structural and functional properties of brain networks. Structural properties of networks recently described allow their characterization as small-world, random (exponential) and scale-free. They complement the set of other properties that have been explored in the context of brain connectivity, such as topology, hodology, clustering, and hierarchical organization. Here we apply new network analysis methods to cortical inter-areal connectivity networks for the cat and macaque brains. We compare these corticocortical fibre networks to benchmark rewired, small-world, scale-free and random networks, using two analysis strategies, in which we measure the effects of the removal of nodes and connections on the structural properties of the cortical networks. The brain networks' structural decay is in most respects similar to that of scale-free networks. The results implicate highly connected hub-nodes and bottleneck connections as structural basis for some of the conditional robustness of brain systems. This informs the understanding of the development of brain networks' connectivity.

q-bio.NC↗