What’s decidable about linear loops?

We consider the MSO model-checking problem for simple linear loops, or equivalently discrete-time linear dynamical systems, with semialgebraic predicates (i.e., Boolean combinations of polynomial inequalities on the variables). We place no restrictions on the number of program variables, or equivalently the ambient dimension. We establish decidability of the model-checking problem provided that each semialgebraic predicate either has intrinsic dimension at most 1, or is contained within some three-dimensional subspace. We also note that lifting either of these restrictions and retaining decidability would necessarily require major breakthroughs in number theory.

A topological approach to inferring the intrinsic dimension of convex sensing data

We consider a common measurement paradigm, where an unknown subset of an affine space is measured by unknown continuous quasi-convex functions. Given the measurement data, can one determine the dimension of this space? In this paper, we develop a method for inferring the intrinsic dimension of the data from measurements by quasi-convex functions, under natural assumptions. The dimension inference problem depends only on discrete data of the ordering of the measured points of space, induced by the sensor functions. We construct a filtration of Dowker complexes, associated to measurements by quasi-convex functions. Topological features of these complexes are then used to infer the intrinsic dimension. We prove convergence theorems that guarantee obtaining the correct intrinsic dimension in the limit of large data, under natural assumptions. We also illustrate the usability of this method in simulations.

Scikit-Dimension: A Python Package for Intrinsic Dimension Estimation

Dealing with uncertainty in applications of machine learning to real-life data critically depends on the knowledge of intrinsic dimensionality (ID). A number of methods have been suggested for the purpose of estimating ID, but no standard package to easily apply them one by one or all at once has been implemented in Python. This technical note introduces scikit-dimension, an open-source Python package for intrinsic dimension estimation. The scikit-dimension package provides a uniform implementation of most of the known ID estimators based on the scikit-learn application programming interface to evaluate the global and local intrinsic dimension, as well as generators of synthetic toy and benchmark datasets widespread in the literature. The package is developed with tools assessing the code quality, coverage, unit testing and continuous integration. We briefly describe the package and demonstrate its use in a large-scale (more than 500 datasets) benchmarking of methods for ID estimation for real-life and synthetic data.

Evaluating the Voice Type Component Distributions of Excised Larynx Phonations at Three Subglottal Pressures

Purpose The excised canine larynx provides an advantageous experimental framework in the study of voice physiology. In recent years, signal processing methods have been applied to analyze phonations in excised canine larynx experiments. However, phonations have a highly complex and nonstationary nature corresponding to different proportions of regular and chaotic signal elements. Current nonlinear dynamic methods that are used to assess the degree of irregularity in the voice fail to recognize the distribution of voice type components (VTCs). Method Based on measures of intrinsic dimension, this article presents a method to analyze the VTC distribution of phonations in excised canine larynx experiments. Thirty-nine phonation samples from 13 excised canine larynges at three different subglottal pressures were analyzed. Results Phonation produced with subglottal pressures above phonation instability pressure (PIP) and below phonation threshold pressure (PTP) resulted in high proportions of Voice Types 3 and 4, characterized by chaotic and noisy signals. Phonation produced with pressure between PTP and PIP contained mostly Type 1 voice, characterized by a regular and nearly periodic signal. Mean proportions of all VTCs varied significantly in comparisons of phonations produced with Sub-PTP and PTP as well as in comparisons of phonations produced with PTP and PIP. Conclusions Across all VTCs, the VTC profiles of normal and abnormal phonation differ significantly. Normal phonation is strongly associated with VTC 1 (Voice Type Component 1), whereas abnormal phonation exhibits increased VTC 4 (Voice Type Component 4). The study further demonstrates the ability of intrinsic dimension to successfully detect multiple voice types in an acoustic signal and highlights the need for expanded use of intrinsic dimension in human voice. Supplemental Material https://doi.org/10.23641/asha.14417585

On Recovery Guarantees for One-Bit Compressed Sensing on Manifolds

This paper studies the problem of recovering a signal from one-bit compressed sensing measurements under a manifold model; that is, assuming that the signal lies on or near a manifold of low intrinsic dimension. We provide a convex recovery method based on the Geometric Multi-Resolution Analysis and prove recovery guarantees with a near-optimal scaling in the intrinsic manifold dimension. Our method is the first tractable algorithm with such guarantees for this setting. The results are complemented by numerical experiments confirming the validity of our approach.