Related papers: Sheaf-theoretic representation of the proteolipid …
Theory of multi-dimensional representation of free energy surface of protein folding is developed by adopting structural order parameters of multiple regions in protein as multiple coordinates. Various scenarios of folding are classified in…
An approach that combines Self-Organizing maps, hierarchical clustering and network components is presented, aimed at comparing protein conformational ensembles obtained from multiple Molecular Dynamic simulations. As a first result the…
Spatial navigation in mammals is based on building a mental representation of their environment---a cognitive map. However, both the nature of this cognitive map and its underpinning in neural structures and activity remains vague. A key…
We consider some generalization of the theory of quantum states and demonstrate that the consideration of quantum states as sheaves can provide, in principle, more deep understanding of some well-known phenomena. The key ingredients of the…
We compute the sheaf homology of the intersection lattice of a hyperplane arrangement with coefficients in the graded exterior sheaf of the natural sheaf. This builds on the results of our previous paper, where this homology was computed…
Soft particles such as microgels and core-shell particles can undergo significant and anisotropic deformations when adsorbed to a liquid interface. This, in turn, leads to a complex phase behavior upon compression. Here we develop a…
In a Systems Engineering setting, various models are produced using a variety of methods and tools. Focusing on a type of models -- called descriptive models -- which we shall describe, we argue that, while the clarity and precision of…
The structure of real-world networks is usually difficult to characterize owing to the variation of topological scales, the nondyadic complex interactions, and the fluctuations in the network. We aim to address these problems by introducing…
We propose a novel framework for analyzing the geometric structure of horseshoes arising in three- and four-dimensional H\'enon-type maps by introducing paperfolding structures as geometric templates. These structures capture the folding…
Understanding, reasoning, and manipulating semantic concepts of images have been a fundamental research problem for decades. Previous work mainly focused on direct manipulation on natural image manifold through color strokes, key-points,…
This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase…
Multiscale phenomena exhibit complex structure-function relationships, and predicting their macroscopic behavior requires deducing differential equations at different scales. The complexity of these equations and the number of essential…
We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of…
We introduce the BioBeta Framework, a meta-model for both protein-level and membrane-level interactions of living cells. This formalism aims to provide a formal setting where to encode, compare and merge models at different abstraction…
We introduce semiframes (an algebraic structure) and investigate their duality with semitopologies (a topological one). Both semitopologies and semiframes are relatively recent developments, arising from a novel application of topological…
This paper develops a conceptual extension of the Kinetic Theory of Active Particles, building upon the framework introduced in [2]. Living systems cannot be adequately described within classical single-scale paradigms, even when refined.…
In this paper higher order mimetic discretizations are introduced which are firmly rooted in the geometry in which the variables are defined. The paper shows how basic constructs in differential geometry have a discrete counterpart in…
Predicting the structure of a protein from its sequence is a cornerstone task of molecular biology. Established methods in the field, such as homology modeling and fragment assembly, appeared to have reached their limit. However, this year…
We propose that protein loops can be interpreted as topological domain-wall solitons. They interpolate between ground states that are the secondary structures like alpha-helices and beta-strands. Entire proteins can then be folded simply by…
Since the time when the first optical instruments have been invented, an idea that the visible image of an object under observation depends on tools of observation became commonly assumed in physics. A way to formalize it in mathematics is…