Related papers: Computing modular coincidences

The notion of singular reduction modules, i.e., of singular modules of nonclassical (conditional) symmetry, of differential equations is introduced. It is shown that the derivation of nonclassical symmetries for differential equations can…

We consider the demixing problem of two (or more) high-dimensional vectors from nonlinear observations when the number of such observations is far less than the ambient dimension of the underlying vectors. Specifically, we demonstrate an…

The paper introduces a generalization for known probabilistic models such as log-linear and graphical models, called here multiplicative models. These models, that express probabilities via product of parameters are shown to capture…

Let M be a meromorphic connection with poles along a smooth divisor D in a smooth algebraic variety. Let Sol M be the solution complex of M. We prove that the good formal decomposition locus of M coincides with the locus where the…

The problem of counting polymer coverings on the rectangular lattices is investigated. In this model, a linear rigid polymer covers $k$ adjacent lattice sites such that no two polymers occupy a common site. Those unoccupied lattice sites…

We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.

The study of the sub-structure of complex networks is of major importance to relate topology and functionality. Many efforts have been devoted to the analysis of the modular structure of networks using the quality function known as…

Using an alternate description of support varieties of pairs of modules over a complete intersection, we give several new applications of such varieties, including results for support varieties of intermediate complete intersections.…

This paper studies the proof of Collatz conjecture for some set of sequence of odd numbers with infinite number of elements. These set generalized to the set which contains all positive odd integers. This extension assumed to be the proof…

Let $(G_n(x))_{n=0}^\infty$ be a $d$-th order linear recurrence sequence having polynomial characteristic roots, one of which has degree strictly greater than the others. Moreover, let $m\geq 2$ be a given integer. We ask for…

Operations research practitioners frequently want to model complicated functions that are are difficult to encode in their underlying optimisation framework. A common approach is to solve an approximate model, and to use a simulation to…

We present a new asynchronous model of computation named Stellar Resolution based on first-order unification. This model of computation is obtained as a formalisation of Girard's transcendental syntax programme, sketched in a series of…

A new model for mechanical computing is demonstrated that requires only two basic parts: links and rotary joints. These basic parts are combined into two main higher level structures: locks and balances, which suffice to create all…

In this paper we introduce a non-fuzzy measure which has been designed to rank the partitions of a network's nodes into overlapping communities. Such a measure can be useful for both quantifying clusters detected by various methods and…

We calculate the decomposition series of the D-module defined as the push-forward of a rank one linear system on the complement of a normal crossings hyperplane configuration and use data of a resolution of singularities to give a…

Let P be a d-dimensional lattice polytope. We show that there exists a natural number c_d, only depending on d, such that the multiples cP have a unimodular cover for every natural number c >= c_d. Actually, a subexponential upper bound for…

The component-by-component construction is the standard method of finding good lattice rules or polynomial lattice rules for numerical integration. Several authors have reported that in numerical experiments the generating vector sometimes…

Crossing probabilities for critical 2-D percolation on large but finite lattices have been derived via boundary conformal field theory. These predictions agree very well with numerical results. However, their derivation is heuristic and…

There are several forms of irreducibility in computing systems, ranging from undecidability to intractability to nonlinearity. This paper is an exploration of the conceptual issues that have arisen in the course of investigating speed-up…

In deduction modulo, a theory is not represented by a set of axioms but by a congruence on propositions modulo which the inference rules of standard deductive systems---such as for instance natural deduction---are applied. Therefore, the…