Ran Levi
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View article: Correction to the article An algebraic model for finite loop spaces
Correction to the article An algebraic model for finite loop spaces Open
We correct here two errors in our earlier paper "An algebraic model for finite loop spaces" [arXiv:1212.2033]
View article: Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding
Directed Semi-Simplicial Learning with Applications to Brain Activity Decoding Open
Graph Neural Networks (GNNs) excel at learning from pairwise interactions but often overlook multi-way and hierarchical relationships. Topological Deep Learning (TDL) addresses this limitation by leveraging combinatorial topological spaces…
View article: Heterogeneous and higher-order cortical connectivity undergirds efficient, robust, and reliable neural codes
Heterogeneous and higher-order cortical connectivity undergirds efficient, robust, and reliable neural codes Open
We hypothesized that the heterogeneous architecture of biological neural networks provides a substrate to regulate the well-known tradeoff between robustness and efficiency, thereby allowing different subpopulations of the same network to …
View article: Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy
Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy Open
The function of the neocortex is fundamentally determined by its repeating microcircuit motif, but also by its rich, interregional connectivity. We present a data-driven computational model of the anatomy of non-barrel primary somatosensor…
View article: Realizability of fusion systems by discrete groups
Realizability of fusion systems by discrete groups Open
For a prime $p$, fusion systems over discrete $p$-toral groups are categories that model and generalize the $p$-local structure of Lie groups and certain other infinite groups in the same way that fusion systems over finite $p$-groups mode…
View article: Author response: Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy
Author response: Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy Open
The function of the neocortex is fundamentally determined by its repeating microcircuit motif, but also by its rich, interregional connectivity. We present a data-driven computational model of the anatomy of non-barrel primary somatosensor…
View article: Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy
Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy Open
The function of the neocortex is fundamentally determined by its repeating microcircuit motif, but also by its rich, interregional connectivity. We present a data-driven computational model of the anatomy of non-barrel primary somatosensor…
View article: Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy
Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy Open
The function of the neocortex is fundamentally determined by its repeating microcircuit motif, but also by its rich, interregional connectivity. We present a data-driven computational model of the anatomy of non-barrel primary somatosensor…
View article: Heterogeneous and higher-order cortical connectivity undergirds efficient, robust and reliable neural codes
Heterogeneous and higher-order cortical connectivity undergirds efficient, robust and reliable neural codes Open
Simplified models of neural networks have demonstrated the importance of establishing a reasonable tradeoff between memory capacity and fault-tolerance in cortical coding schemes. The intensity of the tradeoff is mediated by the level of n…
View article: Foundations of Differential Calculus for modules over posets
Foundations of Differential Calculus for modules over posets Open
Let $k$ be a field and let $C$ be a small category. A $k$-linear representation of $C$, or a $kC$-module, is a functor from $C$ to the category of finite dimensional vector spaces over $k$. Unsurprisingly, it turns out that when the catego…
View article: Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy
Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy Open
The function of the neocortex is fundamentally determined by its repeating microcircuit motif, but also by its rich, interregional connectivity. We present a data-driven computational model of the anatomy of non-barrel primary somatosensor…
View article: A Model of Rat Non-barrel Somatosensory Cortex Anatomy
A Model of Rat Non-barrel Somatosensory Cortex Anatomy Open
We present a data-driven computational model of the anatomy of non-barrel primary somatosensory cortex of juvenile rat. The modeling process is based on a previously established workflow for a single cortical column, but is extended here t…
View article: A Model of Rat Non-barrel Somatosensory Cortex Anatomy
A Model of Rat Non-barrel Somatosensory Cortex Anatomy Open
A full description of the model is available in the two companion manuscripts: Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part II: Physi…
View article: A Model of Rat Non-barrel Somatosensory Cortex Anatomy
A Model of Rat Non-barrel Somatosensory Cortex Anatomy Open
A full description of the model is available in the two companion manuscripts: Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part I: Anatomy Modeling and Simulation of Neocortical Micro- and Mesocircuitry. Part II: Physi…
View article: Polyhedral products over finite posets
Polyhedral products over finite posets Open
Polyhedral products were defined by Bahri, Bendersky, Cohen and Gitler, to be spaces obtained as unions of certain product spaces indexed by the simplices of an abstract simplicial complex. In this paper we give a very general homotopy the…
View article: Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies
Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies Open
In motor-related brain regions, movement intention has been successfully decoded from in-vivo spike train by isolating a lower-dimension manifold that the high-dimensional spiking activity is constrained to. The mechanism enforcing this co…
View article: An application of neighbourhoods in digraphs to the classification of binary dynamics
An application of neighbourhoods in digraphs to the classification of binary dynamics Open
A binary state on a graph means an assignment of binary values to its vertices. A time-dependent sequence of binary states is referred to as binary dynamics. We describe a method for the classification of binary dynamics of digraphs, using…
View article: An application of neighbourhoods in digraphs to the classification of binary dynamics
An application of neighbourhoods in digraphs to the classification of binary dynamics Open
A binary state on a graph means an assignment of binary values to its vertices. For example, if one encodes a network of spiking neurons as a directed graph, then the spikes produced by the neurons at an instant of time is a binary state o…
View article: Input data and analyzed data of "Topology of synaptic connectivity constrains neuronal stimulus representation (...)"
Input data and analyzed data of "Topology of synaptic connectivity constrains neuronal stimulus representation (...)" Open
This dataset contains the input data, as well as the analyzed data that our preprint Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies to be found on bioRxiv is ba…
View article: Input data and analyzed data of "Topology of synaptic connectivity constrains neuronal stimulus representation (...)"
Input data and analyzed data of "Topology of synaptic connectivity constrains neuronal stimulus representation (...)" Open
This dataset contains the input data, as well as the analyzed data that our preprint Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies to be found on bioRxiv is ba…
View article: Input data and analyzed data of "Topology of synaptic connectivity constrains neuronal stimulus representation (...)"
Input data and analyzed data of "Topology of synaptic connectivity constrains neuronal stimulus representation (...)" Open
This dataset contains the input data, as well as the analyzed data that our preprint Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies to be found on bioRxiv is ba…
View article: Input data and analyzed data of "Topology of synaptic connectivity constrains neuronal stimulus representation (...)"
Input data and analyzed data of "Topology of synaptic connectivity constrains neuronal stimulus representation (...)" Open
This dataset contains the input data, as well as the analyzed data that our preprint Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies to be found on bioRxiv is ba…
View article: Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies
Topology of synaptic connectivity constrains neuronal stimulus representation, predicting two complementary coding strategies Open
1 Abstract In motor-related brain regions, movement intention has been successfully decoded from in-vivo spike train by isolating a lower-dimension manifold that the high-dimensional spiking activity is constrained to. The mechanism enforc…
View article: Characterisation of polyhedral products with finite generalised Postnikov decomposition
Characterisation of polyhedral products with finite generalised Postnikov decomposition Open
A generalised Postnikov tower for a space $X$ is a tower of principal fibrations with fibres generalised Eilenberg-MacLane spaces, whose inverse limit is weakly homotopy equivalent to $X$. In this paper we give a characterisation of a poly…
View article: Complexes of Tournaments, Directionality Filtrations and Persistent Homology
Complexes of Tournaments, Directionality Filtrations and Persistent Homology Open
Complete digraphs are referred to in the combinatorics literature as tournaments. We consider a family of semi-simplicial complexes, that we refer to as ``tournaplexes'', whose simplices are tournaments. In particular, given a digraph G, w…
View article: Computing Persistent Homology of Directed Flag Complexes
Computing Persistent Homology of Directed Flag Complexes Open
We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex. The persistent…
View article: Computing Persistent Homology of Directed Flag Complexes
Computing Persistent Homology of Directed Flag Complexes Open
We present a new computing package Flagser, designed to construct the directed flag complex of a finite directed graph, and compute persistent homology for flexibly defined filtrations on the graph and the resulting complex. The persistent…