Related papers: A 2-dimensional Geometry for Biological Time
This paper develops a framework for conceptualizing, visualizing, and measuring regularities in rhythmic data. I propose to think about rhythmic data in terms of interval segments: fixed-length groups of consecutive intervals, which can be…
Life has a special status, it even has its own science: biology. In many ways, the logic of life seems to differ from that of atoms, molecules, planets, or any other `inanimate object'. However, life is increasingly measured using…
A notion of biologic system or just a system implies a functional wholeness of comprising system components. Positive and negative feedback are the examples of how the idea to unite anatomical elements in the whole functional structure was…
In quantum mechanics, time is introduced as a non-measurable quantity, as there is no possibility to build a hermitian operator canonically conjugated to the Hamiltonian. We cannot have, therefore, the time operator, which means that the…
Geometries with horizons offer insights into relationships between general relativity and quantum physics. For static spherically symmetric space-times, the event horizon is coincident with a coordinate anomaly that introduces complications…
Increased attention has been paid over the last four years to dynamic network embedding. Existing dynamic embedding methods, however, consider the problem as limited to the evolution of a topology over a sequence of global, discrete states.…
The quantum mechanics description of a physical object stretched in space and stable in time from the relativistic space-time properties point of view, introduced in special theory of relativity, is considered and analysed. The mathematical…
In biology, predicting RNA secondary structures plays a vital role in determining its physical and chemical properties. Although we have powerful energy models to predict them as well as parametric analysis to understand the models…
Accurate geometric quantification of the human heart is a key step in the diagnosis of numerous cardiac diseases, and in the management of cardiac patients. Ultrasound imaging is the primary modality for cardiac imaging, however acquisition…
This paper proposes rigorous geometrical treatment of bioelectrodynamics, underpinning two fast-growing biomedical research fields: bioelectromagnetism, which deals with the ability of life to produce its own electromagnetism, and…
Frequently, transient changes in physiological signals, such as ECG morphology, precede or follow a rate change. Current methods for visualizing morphology allow only the tracking of preselected changes, severely limiting analytical…
The study of phases is useful for understanding novel states of matter. One such state of matter are time crystals which constitute periodically driven interacting many-body systems that spontaneously break time translation symmetry. Time…
Finite projective (lattice) geometries defined over rings instead of fields have recently been recognized to be of great importance for quantum information theory. We believe that there is much more potential hidden in these geometries to…
It is explained how the time evolution of the operadic variables may be introduced. As an example, a 2-dimensional binary operadic Lax representation of the harmonic oscillator is found.
Learning low-dimensional numerical representations from symbolic data, e.g., embedding the nodes of a graph into a geometric space, is an important concept in machine learning. While embedding into Euclidean space is common, recent…
We prove the existence and the uniqueness of a solution for a modified bidomain model, describing the electrical behaviour of the cardiac tissue in pathological situations. The leading idea is to reduce the problem to an abstract parabolic…
We develop a model of musical rhythm and meter based on optimizing the trade-off between human psychological preferences for perceiving repeated patterns in time with a desire for variety and complexity. By mapping these competing…
Time does not obviously appear amongst the coordinates on the constrained phase space of general relativity in the Hamiltonian formulation. Recent work in finite-dimensional models claims that topological obstructions generically make the…
We provide a rather simple proof of a homogenization result for the bidomain model of cardiac electrophysiology. Departing from a microscopic cellular model, we apply the theory of two-scale convergence to derive the bidomain model. To…
We present a comprehensive introduction to spacetime algebra that emphasizes its practicality and power as a tool for the study of electromagnetism. We carefully develop this natural (Clifford) algebra of the Minkowski spacetime geometry,…