Related papers: Torus Graphs for Multivariate Phase Coupling Analy…
Circular variables such as phase or orientation have received considerable attention throughout the scientific and engineering communities and have recently been quite prominent in the field of neuroscience. While many analytic techniques…
Neural manifolds summarize the intrinsic structure of the information encoded by a population of neurons. Advances in experimental techniques have made simultaneous recordings from multiple brain regions increasingly commonplace, raising…
For $d\ge 3$ we construct a new coupling of the trace left by a random walk on a large $d$-dimensional discrete torus with the random interlacements on $\mathbb Z^d$. This coupling has the advantage of working up to macroscopic subsets of…
Multivariate circular observations, i.e. points on a torus are nowadays very common. Multivariate wrapped models are often appropriate to describe data points scattered on p-dimensional torus. However, statistical inference based on this…
The entrainment between weakly-coupled nonlinear oscillators, as well as between complex signals such as those representing physiological activity, is frequently assessed in terms of whether a stable relationship is detectable between the…
Coherence and phase synchronization between time series corresponding to different spatial locations are usually interpreted as indicators of the connectivity between locations. In neurophysiology, time series of electric neuronal activity…
Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…
The motion of and interaction between phase singularities that anchor spiral waves captures many qualitative and, in some cases, quantitative features of complex dynamics in excitable systems. Being able to accurately reconstruct their…
Synchronized neural spiking is associated with many cognitive functions and thus, merits study for its own sake. The analysis of neural synchronization naturally leads to the study of repetitive spiking and consequently to the analysis of…
The Circle of Willis (CoW) vessels is critical to connecting major circulations of the brain. The topology of the vascular structure is clinical significance to evaluate the risk, severity of the neuro-vascular diseases. The CoW has two…
We study the quasi-periodicity phenomena occurring at the transition between tonic spiking and bursting activities in exemplary biologically plausible Hodgkin-Huxley type models of individual cells and reduced phenomenological models with…
We consider a random partition of the vertex set of an arbitrary graph that can be sampled using loop-erased random walks stopped at a random independent exponential time of parameter $q>0$, that we see as a tuning parameter.The related…
Consider a graph $G$ and an initial random configuration, where each node is black with probability $p$ and white otherwise, independently. In discrete-time rounds, each node becomes black if it has at least $r$ black neighbors and white…
Topological phases exhibit a plethora of striking phenomena including disorder-robust localization and propagation of waves of various nature. Of special interest are the transitions between the different topological phases which are…
The global functional brain network (graph) is more suitable for characterizing brain states than local analysis of the connectivity of brain regions. Therefore, graph-theoretic approaches are the natural methods to study the brain.…
The central nervous system is composed of many individual units -- from cells to areas -- that are connected with one another in a complex pattern of functional interactions that supports perception, action, and cognition. One natural and…
Brain surface analysis is essential to neuroscience, however, the complex geometry of the brain cortex hinders computational methods for this task. The difficulty arises from a discrepancy between 3D imaging data, which is represented in…
Memristive devices have revolutionized non-volatile memory and neuromorphic computing, yet the geometry of their hysteresis loops -- in particular, the occurrence and robustness of multiple self-crossings -- remains poorly understood. Here…
Interacting, self-propelled particles such as epithelial cells can dynamically self-organize into complex multicellular patterns, which are challenging to classify without a priori information. Classically, different phases and phase…
We present a braided circuit topology framework for investigating topology and structural phase transitions in aggregates of semiflexible polymers. In the conventional approach to circuit topology, which specifically applies to single…