arXiv subjects

David Meyer

Publications and source records attributed to David Meyer.

28 records · Page 2Linked to original sources

arXiv2021

Copula-based synthetic data augmentation for machine-learning emulators

Can we improve machine-learning (ML) emulators with synthetic data? If data are scarce or expensive to source and a physical model is available, statistically generated data may be useful for augmenting training sets cheaply. Here we explore the use of copula-based models for generating synthetically augmented datasets in weather and climate by testing the method on a toy physical model of downwelling longwave radiation and corresponding neural network emulator. Results show that for copula-augmented datasets, predictions are improved by up to 62 % for the mean absolute error (from 1.17 to 0.44 W m$^{-2}$).

cs.LG↗

arXiv2020

Tracking the variety of interleavings

In topological data analysis persistence modules are used to distinguish the legitimate topological features of a finite data set from noise. Interleavings between persistence modules feature prominantly in the analysis. One can show that for $ε$ positive, the collection of $ε$-interleavings between two persistence modules $M$ and $N$ has the structure of an affine variety, Thus, the smallest value of $ε$ corresponding to a nonempty variety is the interleaving distance. With this in mind, it is natural to wonder how this variety changes with the value of $ε$, and what information about $M$ and $N$ can be seen from just the knowledge of their varieties. In this paper, we focus on the special case where $M$ and $N$ are interval modules. In this situation we classify all possible progressions of varieties, and determine what information about $M$ and $N$ is present in the progression.

math.AT↗

arXiv2019

Mapper Based Classifier

Topological data analysis aims to extract topological quantities from data, which tend to focus on the broader global structure of the data rather than local information. The Mapper method, specifically, generalizes clustering methods to identify significant global mathematical structures, which are out of reach of many other approaches. We propose a classifier based on applying the Mapper algorithm to data projected onto a latent space. We obtain the latent space by using PCA or autoencoders. Notably, a classifier based on the Mapper method is immune to any gradient based attack, and improves robustness over traditional CNNs (convolutional neural networks). We report theoretical justification and some numerical experiments that confirm our claims.

cs.LG↗

arXiv2019

Spatio-Temporal Deep Learning Models for Tip Force Estimation During Needle Insertion

Purpose. Precise placement of needles is a challenge in a number of clinical applications such as brachytherapy or biopsy. Forces acting at the needle cause tissue deformation and needle deflection which in turn may lead to misplacement or injury. Hence, a number of approaches to estimate the forces at the needle have been proposed. Yet, integrating sensors into the needle tip is challenging and a careful calibration is required to obtain good force estimates. Methods. We describe a fiber-optical needle tip force sensor design using a single OCT fiber for measurement. The fiber images the deformation of an epoxy layer placed below the needle tip which results in a stream of 1D depth profiles. We study different deep learning approaches to facilitate calibration between this spatio-temporal image data and the related forces. In particular, we propose a novel convGRU-CNN architecture for simultaneous spatial and temporal data processing. Results. The needle can be adapted to different operating ranges by changing the stiffness of the epoxy layer. Likewise, calibration can be adapted by training the deep learning models. Our novel convGRU-CNN architecture results in the lowest mean absolute error of 1.59 +- 1.3 mN and a cross-correlation coefficient of 0.9997, and clearly outperforms the other methods. Ex vivo experiments in human prostate tissue demonstrate the needle's application. Conclusions. Our OCT-based fiber-optical sensor presents a viable alternative for needle tip force estimation. The results indicate that the rich spatio-temporal information included in the stream of images showing the deformation throughout the epoxy layer can be effectively used by deep learning models. Particularly, we demonstrate that the convGRU-CNN architecture performs favorably, making it a promising approach for other spatio-temporal learning problems.

eess.IV↗

arXiv2018

Needle Tip Force Estimation using an OCT Fiber and a Fused convGRU-CNN Architecture

Needle insertion is common during minimally invasive interventions such as biopsy or brachytherapy. During soft tissue needle insertion, forces acting at the needle tip cause tissue deformation and needle deflection. Accurate needle tip force measurement provides information on needle-tissue interaction and helps detecting and compensating potential misplacement. For this purpose we introduce an image-based needle tip force estimation method using an optical fiber imaging the deformation of an epoxy layer below the needle tip over time. For calibration and force estimation, we introduce a novel deep learning-based fused convolutional GRU-CNN model which effectively exploits the spatio-temporal data structure. The needle is easy to manufacture and our model achieves a mean absolute error of 1.76 +- 1.5 mN with a cross-correlation coefficient of 0.9996, clearly outperforming other methods. We test needles with different materials to demonstrate that the approach can be adapted for different sensitivities and force ranges. Furthermore, we validate our approach in an ex-vivo prostate needle insertion scenario.

cs.CV↗

arXiv2017

Interleaving Distance as a Limit

Persistent homology is a way of determining the topological properties of a data set. It is well known that each persistence module admits the structure of a representation of a finite totally ordered set. In previous work, the authors proved an analogue of the isometry theorem of Bauer and Lesnick for representations of a certain class of finite posets. The isometry was between the interleaving metric of Bubenik, de Silva and Scott and a bottleneck metric which incorporated algebraic information. The key step in both isometry theorems was proving a matching theorem, that an interleaving gives rise to a matching of the same height. In this paper we continue this work, restricting to those posets which arise from data while making more general the choice of metrics. We first show that while an interleaving always produces a matching, for an arbitrary choice of weights it will not produce one of the same height. We then show that although the matching theorem fails in this sense, one obtains a "shifted" matching (of the correct height) from an interleaving by enlarging the category. We then prove an isometry theorem on this extended category. As an application, we make precise the way in which representations of finite partially ordered sets approximate persistence modules. Specifically, given two finite point clouds of data, we associate a generalized sequence (net) of algebras over which the persistence modules for both data sets can be compared. We recover the classical interleaving distance uniformly by taking limits.

math.AT↗

arXiv2017

An Isometry Theorem for Generalized Persistence Modules

In recent work, generalized persistence modules have proved useful in distinguishing noise from the legitimate topological features of a data set. Algebraically, generalized persistence modules can be viewed as representations for the poset algebra. The interplay between various metrics on persistence modules has been of wide interest, most notably, the isometry theorem of Bauer and Lesnick for (one-dimensional) persistence modules. The interleaving metric of Bubenik, de Silva and Scott endows the collection of representations of a poset with values in any category with the structure of a metric space. This metric makes sense for any poset, and has the advantage that post-composition by any functor is a contraction. In this paper, we prove an isometry theorem using this interleaving metric on a full subcategory of generalized persistence modules for a large class of posets.

math.AT↗

arXiv2016

Knowledge-Defined Networking

The research community has considered in the past the application of Artificial Intelligence (AI) techniques to control and operate networks. A notable example is the Knowledge Plane proposed by D.Clark et al. However, such techniques have not been extensively prototyped or deployed in the field yet. In this paper, we explore the reasons for the lack of adoption and posit that the rise of two recent paradigms: Software-Defined Networking (SDN) and Network Analytics (NA), will facilitate the adoption of AI techniques in the context of network operation and control. We describe a new paradigm that accommodates and exploits SDN, NA and AI, and provide use cases that illustrate its applicability and benefits. We also present simple experimental results that support its feasibility. We refer to this new paradigm as Knowledge-Defined Networking (KDN).

cs.NI↗

arXiv2012

Network Cosmology

Prediction and control of the dynamics of complex networks is a central problem in network science. Structural and dynamical similarities of different real networks suggest that some universal laws might accurately describe the dynamics of these networks, albeit the nature and common origin of such laws remain elusive. Here we show that the causal network representing the large-scale structure of spacetime in our accelerating universe is a power-law graph with strong clustering, similar to many complex networks such as the Internet, social, or biological networks. We prove that this structural similarity is a consequence of the asymptotic equivalence between the large-scale growth dynamics of complex networks and causal networks. This equivalence suggests that unexpectedly similar laws govern the dynamics of complex networks and spacetime in the universe, with implications to network science and cosmology.

gr-qc↗

arXiv1997

Damped Lyman-alpha Absorption Associated with an Early-Type Galaxy at Redshift z = 0.16377

We report new HST and ground-based observations of a damped Lyman-alpha absorption system toward the QSO 0850+4400. The redshift of the absorption system is z = 0.163770 and the neutral hydrogen column density of the absorption system is log N = 19.81 cm**-2. The absorption system is by far the lowest redshift confirmed damped Lyman-alpha absorption system yet identified, which provides an unprecedented opportunity to examine the nature, impact geometry, and kinematics of the absorbing galaxy in great detail. The observations indicate that the absorption system is remarkable in three respects: First, the absorption system is characterized by weak metal absorption lines and a low metal abundance, possibly less than 4% of the solar metal abundance. This cannot be explained as a consequence of dust, because the neutral hydrogen column density of the absorption system is far too low for obscuration by dust to introduce any significant selection effects. Second, the absorption system is associated with a moderate-luminosity early-type S0 galaxy, although the absorption may actually arise in one of several very faint galaxies detected very close to the QSO line of sight. Third, the absorbing material moves counter to the rotating galaxy disk, which rules out the possibility that the absorption arises in a thin or thick co-rotating gaseous disk. These results run contrary to the expectation that low-redshift damped Lyman-alpha absorption systems generally arise in the gas- and metal-rich inner parts of late-type spiral galaxies. We suggest instead that mounting evidence indicates that low-redshift galaxies of a variety of morphological types may contain significant quantities of low metal abundance gas at large galactocentric distances.

astro-ph↗