21 citations · 43 across the 16 of their papers we have counts for
18 papers
Ramification Subgroups of Knot Groups and their Profinite and Cohomological Structure
Marina Palaisti, Federico W. Pasini
We formalize a ramification theory for finite covers of knot exteriors. Given a knot group and a finite-index subgroup , we define meridional inertia subgroups $U\c…
A mathematical language for linking fine-scale structure in spikes from hundreds to thousands of neurons with behaviour
Alexandra N. Busch, Roberto C. Budzinski, Federico W. Pasini +8
Recent advances in neural recording technology allow simultaneously recording action potentials from hundreds to thousands of neurons in awake, behaving animals. However, character…
An exact mathematical description of computation with transient spatiotemporal dynamics in a complex-valued neural network
Roberto C. Budzinski, Alexandra N. Busch, Samuel Mestern +7
We study a complex-valued neural network (cv-NN) with linear, time-delayed interactions. We report the cv-NN displays sophisticated spatiotemporal dynamics, including partially syn…
On the arithmetic of the join rings over finite fields
Sunil K. Chebolu, Jonathan Merzel, Ján Mináč +3
Given a collection of finite groups and a ring , we have previously introduced and studied certain foundational properties of the join ring $\mathcal{J}_{G_1,…
Spectral perturbation by rank- matrices
Jonathan L. Merzel, Ján Mináč, Tung T. Nguyen +1
Let and designate matrices with coefficients in a field . In this paper, we completely answer the following question: For fixed, what are the possible ch…
An algebraic approach to spike-time neural codes in the hippocampus
Federico W. Pasini, Alexandra N. Busch, Ján Mináč +2
Although temporal coding through spike-time patterns has long been of interest in neuroscience, the specific structures that could be useful for spike-time codes remain highly uncl…