Related papers: A tropical geometry for bounded biochemical state …
A geometrical characterization of robustly separable (that is, remaining separable under sufficiently small variiations) mixed states of a bipartite quantum system is given. It is shown that the density matrix of any such state can be…
One considers geometry with the intransitive equaivalence relation. Such a geometry is a physical geometry, i.e. it is described completely by the world function, which is a half of the squared distance function. The physical geometry…
Limitation of computational resources is considered as a universal principle that for simulation is as fundamental as physical laws are. It claims that all experimentally verifiable implications of physical laws can be simulated by the…
Systems biology uses large networks of biochemical reactions to model the functioning of biological cells from the molecular to the cellular scale. The dynamics of dissipative reaction networks with many well separated time scales can be…
We illustrate through numerical results a number of features of environment-induced decoherence under a broad class of apparatus-environment interactions in quantum measurements wherein the reduced system-apparatus density matrix evolves…
We develop a continuum theory for thermoelectric bodies following the framework of continuum mechanics and conforming to general principles of thermodynamics. For steady states, the governing equations for local fields are intrinsically…
In this paper, we propose a new type of bulk-boundary correspondence as a generic approach to theoretically and experimentally detect fragile topological states. When the fragile phase can be written as a difference of a trivial atomic…
Potential energy landscape (PEL) is essential to determine phase stability, reaction path, and other important physical as well as chemical properties. Whereas given PEL can reasonably determine the properties in thermodynamically…
The paper studies intrinsic geometry in the tropical plane. Tropical structure in the real affine $n$-space is determined by the integer tangent vectors. Tropical isomorphisms are affine transformations preserving the integer lattice of the…
The field of numerical algebraic geometry consists of algorithms for numerically solving systems of polynomial equations. When the system is exact, such as having rational coefficients, the solution set is well-defined. However, for a…
Waveguiding structures made of anisotropic media support bound states in the continuum (BICs) that arise when the radiation channel of otherwise semi-leaky modes is suppressed. Hitherto, only structures with optical axes aligned in…
Resonances, also known as quasinormal modes (QNM) in the non-Hermitian case, play a ubiquitous role in all domains of physics ruled by wave phenomena, notably in continuum mechanics, acoustics, electrodynamics, and quantum theory. The…
We define the tropical moduli space of covers of a tropical line in the plane as weighted abstract polyhedral complex, and the tropical branch map recording the images of the simple ramifications. Our main result is the invariance of the…
There is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and artificial…
Biochemical molecules interact through modification and binding reactions, giving raise to a combinatorial number of possible biochemical species. The time-dependent evolution of concentrations of the species is commonly described by a…
This is a survey article written for the Jahresberichte der DMV. Tropical geometry can be viewed as an efficient combinatorial tool to study degenerations in algebraic geometry. Abstract tropical curves are essentially metric graphs, and…
Turing patterns play a fundamental role in morphogenesis and population dynamics, encoding key information about the underlying biological mechanisms. Yet, traditional inverse problems have largely relied on non-biological data such as…
Mathematical modelling is a cornerstone of computational biology. While mechanistic models might describe the interactions of interest of a system, they are often difficult to study. On the other hand, abstract models might capture key…
We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…
We derive the universal real time $U(1)$ topological gauge field action for mixed quantum states of weakly correlated fermions in all dimensions, and demonstrate its independence of the underlying equilibrium or non-equilibrium nature of…