Related papers: Torus Graphs for Multivariate Phase Coupling Analy…

We investigate regions formed by cylinders of circles of fixed radii. We investigate graphs obtained by collapsing each level set of the functions represented by the natural projections of them to the $1$-dimensional line. Some specific…

For every $n$, we construct two curves in the plane that intersect at least $n$ times and do not form spirals. The construction is in three stages: we first exhibit closed curves on the torus that do not form double spirals, then arcs on…

There are two approaches for simulating memory as well as learning in artificial intelligence; the functionalistic approach and the cognitive approach. The necessary condition to put the second approach into account is to provide a model of…

Adaptive behavior, cognition and emotion are the result of a bewildering variety of brain spatiotemporal activity patterns. An important problem in neuroscience is to understand the mechanism by which the human brain's 100 billion neurons…

Many applications collect a large number of time series, for example, the financial data of companies quoted in a stock exchange, the health care data of all patients that visit the emergency room of a hospital, or the temperature sequences…

We estimate from below the number of lines meeting each of given 4 disjoint smooth closed curves in a given cyclic order in the real projective 3-space and in a given linear order in the Euclidean 3-space. Similarly, we estimate the number…

Multi-channel ECG-based cardiac disorders detection has an impact on cardiac care and treatment. Limitations of existing methods included variation in ECG waveforms due to the location of electrodes, high non-linearity in the signal, and…

Electroencephalography (EEG), a technique that records electrical activity from the scalp using electrodes, plays a vital role in affective computing. However, fully utilizing the multi-domain characteristics of EEG signals remains a…

In this study, we present a general framework for comparing two dynamical processes that describe the synchronization of oscillators coupled through networks of the same size. We introduce a measure of dissimilarity defined in terms of a…

We propose a generalization of the Kuramoto model of interacting oscillators in which the particles move on the surface of a $D$-dimensional torus. In contrast with the traditional one-dimensional version, this model has a first order phase…

As a person learns a new skill, distinct synapses, brain regions, and circuits are engaged and change over time. In this paper, we develop methods to examine patterns of correlated activity across a large set of brain regions. Our goal is…

Traditional visualisations are designed to be shown on a flat surface (screen or page) but most data is not "flat". For example, the surface of the earth exists on a sphere, however, when that surface is presented on a flat map, key…

Dissipative mechanical systems on the torus with a friction that is proportional to the velocity are modeled by conformally symplectic maps on the annulus, which are maps that transport the symplectic form into a multiple of itself (with a…

We generalize our recent approach to reconstruction of phase dynamics of coupled oscillators from data [B. Kralemann et al., Phys. Rev. E, 77, 066205 (2008)] to cover the case of small networks of coupled periodic units. Starting from the…

The discovery of topological phases in condensed matter systems has changed the modern conception of phases of matter. The global nature of topological ordering makes these phases robust and hence promising for applications. However, the…

The dynamically triangulated random surface (DTRS) approach to Euclidean quantum gravity in two dimensions is considered for the case of the elemental building blocks being quadrangles instead of the usually used triangles. The well-known…

Time-fluctuating signals are ubiquitous and diverse in many physical, chemical, and biological systems, among which random telegraph signals (RTSs) refer to a series of instantaneous switching events between two discrete levels from…

Topological phase transitions track changes in topological properties of a system and occur in real materials as well as quantum engineered systems, all of which differ greatly in terms of dimensionality, symmetries, interactions, and…

At the level of individual neurons, various coding properties can be inferred from the input-output relationship of a cell. For small inputs, this relation is captured by the phase-response curve (PRC), which measures the effect of a small…

We use methods from computational algebraic topology to study functional brain networks, in which nodes represent brain regions and weighted edges encode the similarity of fMRI time series from each region. With these tools, which allow one…