Related papers: The augmented external activity complex of a matro…
We study the swelling of a flexible linear chain composed of active particles by analytical theory and computer simulation. Three different situations are considered: a free chain, a chain confined to an external harmonic trap, and a chain…
The Lagrangian geometry of matroids was introduced in [ADH20] through the construction of the conormal fan of a matroid M. We used the conormal fan to give a Lagrangian-geometric interpretation of the h-vector of the broken circuit complex…
The $es$-splitting operation on binary bridge-less matroids never produces an Eulerian matroid. But for matroids representable over $GF(p),(p>2),$ called $p$-matroids, the $es$-splitting operation may yield Eulerian matroids. In this work,…
Given an arbitrary hypergraph $\mathcal{H}$, we may glue to $\mathcal{H}$ a family of hypergraphs to get a new hypergraph $\mathcal{H}'$ having $\mathcal{H}$ as an induced subhypergraph. In this paper, we introduce three gluing techniques…
The rheological properties of tangentially propelled flexible polymers under linear shear flow are studied by computer simulations and are compared with analytical calculations. We find a significant impact of the coupled nonequilibrium…
A matroid complex is a pure complex such that every restriction is again pure. It is a long-standing open problem to classify all possible $h$-vectors of such complexes. In the case when the complex has dimension 1 we completely resolve…
Spontaneous self-replication in cellular automata has long been considered rare, with most known examples requiring careful design or artificial initialization. In this paper, we present formal, causal evidence that such replication can…
We show that the equations of motion associated with a complexified sigma-model action do not admit manifest dual SO(n,n) symmetry. In the process we discover new type of numbers which we called `complexoids' in order to emphasize their…
Consider a polynomial F such that each variable appears in exactly one monomial. The hypersurface defined by the polynomial F is called a hypersurface with separable variables. A variety is called rigid if there are no nontrivial actions of…
We show that an 'almost strong Lefschetz' property holds for the barycentric subdivision of a shellable complex. From this we conclude that for the barycentric subdivision of a Cohen-Macaulay complex, the $h$-vector is unimodal, peaks in…
Following our recent letter, we study in detail an entry-wise diffusion of non-hermitian complex matrices. We obtain an exact partial differential equation (valid for any matrix size $N$ and arbitrary initial conditions) for evolution of…
In this paper, we define generalized splitting and element splitting operations on $p$-matroids. $p$-matroids are the matroids representable over $GF(p).$ The circuits and the bases of the new matroid are characterized in terms of circuits…
Adding a non-adsorbing polymer to passive colloids induces an attraction between the particles via the `depletion' mechanism. High enough polymer concentrations lead to phase separation. We combine experiments, theory and simulations to…
A phased matroid is a matroid with additional structure which plays the same role for complex vector arrangements that oriented matroids play for real vector arrangements. The realization space of an oriented (resp., phased) matroid is the…
Matroid theory provides a unifying framework for studying dependence across combinatorics, geometry, and applications ranging from rigidity to statistics. In this work, we study circuit varieties of matroids, defined by their minimal…
In this paper we show that the basic external (i.e. not determined by the equations) object in Classical electrodynamics equations is a complex structure. In the 3-dimensional standard form of Maxwell equations this complex structure…
The aim of this work is to investigate and characterise particle behaviour in an (observationally-driven) 3D MHD model of the solar atmosphere above a slowly evolving, non-flaring active region. We use a relativistic guiding-centre particle…
We define a cellular automaton where a resting cell excites if number of its excited neighbours belong to some specified interval and boundaries of the interval change depending on ratio of excited and refractory neighbours in the cell's…
We study a mixture of extensile and contractile cells using a vertex model extended to include active nematic stresses. The two cell populations phase separate over time. While phase separation strengthens monotonically with an increasing…
We initiate the study of group actions on (possibly infinite) semimatroids and geometric semilattices. To every such action is naturally associated an orbit-counting function, a two-variable "Tutte" polynomial and a poset which, in the…