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Elementary flux modes (EFMs) are vectors defined from a metabolic reaction network, giving the connections between substrates and products. EFMs-based metabolic flux analysis (MFA) estimates the flux over each EFM from external flux…
We compare two methods of proving separable reduction theorems in functional analysis -- the method of rich families and the method of elementary submodels. We show that any result proved using rich families holds also when formulated with…
Elementary flux modes (EFMs) are pathways through a metabolic reaction network that connect external substrates to products. Using EFMs, a metabolic network can be transformed into its macroscopic counterpart, in which the internal…
This paper addresses the semantics of weighted argumentation graphs that are bipolar, i.e. contain both attacks and supports for arguments. It builds on previous work by Amgoud, Ben-Naim et. al. We study the various characteristics of…
Complex biological systems are very robust to genetic and environmental changes at all levels of organization. Many biological functions of Escherichia coli metabolism can be sustained against single-gene or even multiple-gene mutations by…
The theory of modular deformations is generalized for the category of complex analytic polyhedra which includes germs of complex space as well as any compact complex analytic space. The objective of the theory is a construction of fine…
The heterogeneity of reaction fluxes present in a metabolic network within a single flux state can be exploited to construct the so-called backbone as a reduced version of metabolism. The backbone maintains all significant fluxes producing…
A recent body of work has demonstrated that Transformer embeddings can be linearly decomposed into well-defined sums of factors, that can in turn be related to specific network inputs or components. There is however still a dearth of work…
Metabolism displays striking and robust regularities in the forms of modularity and hierarchy, whose composition may be compactly described. This renders metabolic architecture comprehensible as a system, and suggests the order in which…
We give a necessary and sufficient condition for extremality of a supermodular function based on its min-representation by means of (vertices of) the corresponding core polytope. The condition leads to solving a certain simple linear…
We extend the classical Feferman-Vaught theorem to logic for metric structures. This implies that the reduced powers of elementarily equivalent structures are elementarily equivalent, and therefore they are isomorphic under the Continuum…
Modular Decomposition focuses on repeatedly identifying a module M (a collection of vertices that shares exactly the same neighbourhood outside of M) and collapsing it into a single vertex. This notion of exactitude of neighbourhood is very…
An important problem is to determine under which circumstances a metric on a conformally compact manifold is conformal to a Poincar\'e--Einstein metric. Such conformal rescalings are in general obstructed by conformal invariants of the…
The mechanics of a foam typically depends on the bubble geometry, topology, and the material at hand, be it metallic or polymeric, for example. While the foam energy functional for each bubble is typically minimization of surface area for a…
It is well-known that every regular language admits a unique minimal deterministic acceptor. Establishing an analogous result for non-deterministic acceptors is significantly more difficult, but nonetheless of great practical importance. To…
By "parallelogram geometry" we mean the elementary, "commutative", geometry corresponding to vector addition, and by "trapezoid geometry" a certain "non-commutative deformation" of the former. This text presents an elementary approach via…
In this note, we use elementary submodels to prove that a separable monotonically normal compactum can be mapped on a separable metric space via a continuous function whose fibers have cardinality at most 2.
Conventional particle theories such as the Standard Model have a number of freely adjustable coupling constants and mass parameters, depending on the symmetry algebra of the local gauge group and the representations chosen for the spinor…
The geometric and algebraic theory of monomial ideals and multigraded modules is initiated over real-exponent polynomial rings and, more generally, monoid algebras for real polyhedral cones. The main results include the generalization of…
It is known that no length or time measurements are possible in sub-Planckian regions of spacetime. The Volovich hypothesis postulates that the micro-geometry of spacetime may therefore be assumed to be non-archimedean. In this letter, the…