16 papers · ranked by Valyu relevance
Justin Allman, Anran Huang
Persistent homology has become a ubiquitous tool in topological data analysis. Throughout this paper, we consider persistent homology of a fixed dataset which is assumed to be a point cloud in a Euclidean space RN . Further, we use the Rips construction for computation of persistent homology which, in our setup, takes…
Marisa Saggio
High-codimension bifurcations play a key role in shaping the dynamics of nonlinear models, as their unfoldings establish structured relationships between lower-codimension bifurcations and, ultimately, the attractors they generate. Owing to this unifying and predictive capacity, such bifurcations are attracting growing…
Maria Luisa Saggio, Andreas Spiegler, Christophe Bernard, Viktor K. Jirsa
'Viktor K. Jirsa'] Bursting is a phenomenon found in a variety of physical and biological systems. For example, in neuroscience, bursting is believed to play a key role in the way information is transferred in the nervous system. In this work, we propose a model that, appropriately tuned, can display several types of…
Nicola Guglielmi, Ernst Hairer
This article considers the numerical treatment of piecewise-smooth dynamical systems. Classical solutions as well as sliding modes up to codimension-2 are treated. An algorithm is presented that, in the case of non-uniqueness, selects a solution that is the formal limit solution of a regularized problem. The numerical…
Brandon Jungwoo Han, Arij Daou
Temperature fluctuations can have detrimental effects on the firing pattern and electrical activity of biological neurons, eliciting diverse responses depending on the neuronal cell types and the underlying ion channels exhibited. Using the classical Hodgkin-Huxley (HH) model, we performed a comprehensive dynamical…
Zhiguo Zhao, Li Li, Huaguang Gu
Hyperpolarization-activated cyclic nucleotide-gated cation current (I*h) plays important roles in the achievement of many physiological/pathological functions in the nervous system by modulating the electrophysiological activities, such as the rebound (spike) to hyperpolarization stimulations, subthreshold membrane…
Colin M. Lynch, Bryan C. Daniels
Characterizing how behavior must be tuned to produce useful coordination is key to understanding the evolution and regulation of collective behavior. While computational models can answer this question for specific instances, recurring patterns in model dynamics hint at a more general means of classifying collective…
Zhiguo Zhao, Huaguang Gu
Neuronal excitabilities behave as the basic and important dynamics related to the transitions between firing and resting states, and are characterized by distinct bifurcation types and spiking frequency responses. Switches between class I and II excitabilities induced by modulations outside the neuron (for example…
PierGianLuca Porta Mana
This note provides a short guide to dimensional analysis in Lorentzian and general relativity and in differential geometry. It tries to revive Dorgelo and Schouten's notion of 'intrinsic' or 'absolute' dimension of a tensorial quantity. The intrinsic dimension is independent of the dimensions of the coordinates and…
Jaehoon Cha, Jinhae Park, Samuel Pinilla, Kyle L. Morris + 3 more
'Christopher S. Allen' 'Mark I. Wilkinson' 'Jeyan Thiyagalingam'] Learning meaningful representations of images in scientific domains that are robust to variations in centroids and orientations remains an important challenge. Here we introduce centroid- and orientation-aware disentangling autoencoder (CODAE), an…
Maxwell P. Bobbin, Colin Jones, John Velkey, Tyler R. Josephson
Dimensional analysis is fundamental to the formulation and validation of physical laws, ensuring that equations are dimensionally homogeneous and scientifically meaningful. In this work, we use Lean 4 to formalize the mathematics of dimensional analysis. We define physical dimensions as mappings from base dimensions to…
S. Carlip
If gravity is asymptotically safe, operators will exhibit anomalous scaling at the ultraviolet fixed point in a way that makes the theory effectively twodimensional. A number of independent lines of evidence, based on different approaches to quantization, indicate a similar short-distance dimensional reduction. I will…
Subhash Kak
We present an information-theoretic approach to the optimal representation of the intrinsic dimensionality of data and show it is a noninteger. Since optimality is accepted as a physical principle, this provides a theoretical explanation for why noninteger dimensions are useful in many branches of physics, where they…
Jacopo Fadanni, Rosalba Pacelli, Alberto Zucchetta, Pietro Rotondo + 1 more
Recent technical breakthroughs have enabled a rapid surge in the number of neurons that can be simultaneously recorded, calling for the development of robust methods to investigate neural activity at a population level. In this context, it is becoming increasingly important to characterize the neural activity manifold…
Christiane Ahlheim, Bradley C. Love
Recent advances in multivariate fMRI analysis stress the importance of information inherent to voxel patterns. Key to interpreting these patterns is estimating the underlying dimensionality of neural representations. Dimensions may correspond to psychological dimensions, such as length and orientation, or involve other…
Authors not listed
This work investigates different formulations of internal Coordinates for molecular dynamics (MD) simulations. The goal is to assess their advantages and limitations. Furthermore, a method is presented that evaluates the quality of the partitioning of molecular structural data into clusters based on statistical…