We propose a stochastic epidemiological model for simplicial complex networks by means of differential equation (SDE) that extends the mean field approach social contagion model. show that, under appropriate conditions, if basic reproductive number is smaller than one, then disease dies out with probability one; otherwise solution SDE oscillates infinitely often around point which can be explicitly computed. perform numerical experiments illustrate theoretical results. In addition, we carry...

We study mirror symmetry for orbifold Hurwitz numbers. show that the Laplace transform of numbers satisfy a differential recursion, which is then proved to be equivalent integral recursion Eynard and Orantin with spectral curve given by $r$-Lambert curve. argue also arises in infinite framing limit Gromov-Witten theory $[\mathbb{C}^3 / (\mathbb{Z} r\mathbb{Z})]$. Finally, we prove model admits quantum

The aim of this work is to completely solve the reversibility problem for symmetric linear cellular automata with radius r = 3 and null boundary conditions. main result obtained explicit computation local transition functions inverse automata. This allows introduction possible interesting applications in digital image encryption.

In this paper the moduli space of Higgs pairs over a fixed smooth projective curve with extra formal data is defined and endowed scheme structure. We introduce relative version Krichever map using fibration Sato Grassmannians show that injective. This, together characterization points image map, allows us to prove closed subscheme product vector bundles (with data) anologue Hitchin base. This also provides method for explicitly computing KP-type equations describe pairs. Finally, case where...

The aim of these notes is three fold. First we introduce virtual cyclic cellular automata and show that the inverse a reversible (2R+1)-cyclic automaton with periodic boundary conditions automaton. These have two special characteristics: they active non cells at specific steps times reflect certain periodicity. We will relate particularities finite group action on automaton, prove transition dipolynomial an invariant under this action. Secondly, use recursive estimation neighbours (REN)...

The purpose of this paper is to give a twisted version the Eynard-Orantin topological recursion by 2D Topological Quantum Field Theory. We define kernel for TQFT and use an algebraic definition how twist standard TQFT. A-model side enumerative problem consists counting cell graphs where in addition vertices are decorated elements Frobenius algebra, which generalized Catalan numbers Dumitrescu-Mulase-Safnuk-Sorkin. show that function counts these satisfies same type with respect...

We study mirror symmetry for orbifold Hurwitz numbers. show that the Laplace transform of numbers satisfy a differential recursion, which is then proved to be equivalent integral recursion Eynard and Orantin with spectral curve given by r-Lambert curve. argue also arises in infinite framing limit Gromov-Witten theory [C3/(Z/rZ)]. Finally, we prove model admits quantum

This paper is devoted to the study of uniformization moduli space pairs (X, E) consisting an algebraic curve and a vector bundle on it. For this goal, we 5-tuples x, z, E, ϕ), genus g curve, point it, local coordinate, rank n degree d formal trivialization at point. A group acting it found shown that acts (infinitesimally) transitively identity between central extensions its Lie algebra proved. Furthermore, geometric explanation for offered.

The aim of this paper is to offer an algebraic definition infinite determinants finite potent endomorphisms using linear algebra techniques. It generalizes Grothendieck's determinant for rank and equivalent the classic analytic definitions. theory can be interpreted as a multiplicative analogue Tate's formalism abstract residues in terms traces operators on infinite-dimensional vector spaces, allows us relate Segal-Wilson pairing context loop groups.

Using the technique of Fourier-Mukai transform we give an explicit set generators ideal defining algebraic curve as a subscheme its Jacobian. Essentially, these ideals are generated by Fay's trisecant identities.