Related papers: Duality in mass-action networks
We establish a duality between monads and monadic morphisms in any $(\infty,2)$-category and characterize monadic morphisms in a wide class of examples. This duality unifies several dualities between algebraic structures and their…
In most natural sciences there is currently the insight that it is necessary to bridge gaps between different processes which can be observed on different scales. This is especially true in the field of chemical reactions where the…
We define a duality operation connecting closure operations, interior operations, and test ideals, and describe how the duality acts on common constructions such as trace, torsion, tight and integral closures, and divisible submodules. This…
Supermembrane compactified on a $M_9\times T^2$ target space is globally described by the inequivalent classes of torus bundles over torus. These torus bundles have monodromy in $SL(2,Z)$ when they correspond to the nontrivial central…
The induced kinetic differential equation of a reaction network endowed with mass action type kinetics is a system of polynomial differential equations. The problem studied here is: Given a polynomial differential equation, is it possible…
Many biochemical processes can successfully be described by dynamical systems allowing some form of switching when, depending on their initial conditions, solutions of the dynamical system end up in different regions of state space…
We dualize previous work on generalized persistence diagrams for filtrations to cofiltrations. When the underlying space is a manifold, we express this duality as a Poincar\'e duality between their generalized persistence diagrams. A heavy…
Micro-Electro-Mechanical-Systems are complex structures, often involving nonlinearites of geometric and multiphysics nature, that are used as sensors and actuators in countless applications. Starting from full-order representations, we…
The controllability of networks comprising homogeneous multi-input multi-output linear subsystems with linear couplings among them is examined, from a modal perspective. The eigenvalues of the network model are classified into two groups:…
Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and when a network exhibits bistability is a hard and open…
Hidden symmetries are the backbone of Integrable two-dimensional theories. They provide classical solutions of higher dimensional models as well, they seem to survive partially quantisation and their discrete remnants in M-theory called…
Strongly interacting binary mixtures of superparamagnetic colloidal particles confined to a two-dimensional water-air interface are examined by theory, computer simulation and experiment. The mixture exhibits a partial clustering in…
We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the…
Elements of networks interact in many ways, so modeling them with graphs requires multiple types of edges (or network layers). Here we show that such multiplex networks are generically more vulnerable to global cascades than simplex…
Multilayer networks allow for modeling complex relationships, where individuals are embedded in multiple social networks at the same time. Given the ubiquity of such relationships, these networks have been increasingly gaining attention in…
We study the set of all pseudoline arrangements with contact points which cover a given support. We define a natural notion of flip between these arrangements and study the graph of these flips. In particular, we provide an enumeration…
We construct a general Lagrangian, quadratic in the field strengths of $n$ abelian gauge fields, which interpolates between BI actions of n abelian vectors and actions, quadratic in the vector field-strengths, describing Maxwell fields…
A duality invariant first order action is constructed on the loop group of a Drinfeld double. It gives at the same time the description of both of the pair of $\sigma$-models related by Poisson-Lie T-duality. Remarkably, the action contains…
Macaulay Duality, between quotients of a polynomial ring over a field, annihilated by powers of the variables, and finitely generated submodules of the ring's graded dual, is generalized over any Noetherian ring, and used to provide…
Experimental results often do not assess network structure; rather, the network structure is inferred by the dynamics of the nodes. From the dynamics of the nodes one then constructs a network of functional relations, termed the functional…