The next-to-leading order three-jet cross section in hadron collisions is calculated in the simplified case when the matrix elements of all QCD subprocesses are approximated by the pure gluon matrix element. The longitudinallyinvariant k⊥ jet-clustering algorithm is used. The important property of reduced renormalization and factorization scale dependence of the next-toleading order physical cr...

We consider the non-square matrix sensing problem, under restricted isometry property (RIP) assumptions. We focus on the non-convex formulation, where any rank-r matrix X ∈ R is represented as UV , where U ∈ R and V ∈ R. In this paper, we complement recent findings on the nonconvex geometry of the analogous PSD setting [5], and show that matrix factorization does not introduce any spurious loca...

Let C : y = f(x) be a hyperelliptic curve defined over Q. Let K be a number field and suppose f factors over K as a product of irreducible polynomials f = f1f2 . . . fr. We shall define a “Selmer set” corresponding to this factorization with the property that if it is empty then C(Q) = ∅. We shall demonstrate the effectiveness of our new method by solving the generalized Fermat equation with si...

A brief and incomplete review of known integrable and (quasi)-exactly-solvable quantum models with rational (meromorphic in Cartesian coordinates) potentials is given. All of them are characterized by (i) a discrete symmetry of the Hamiltonian, (ii) a number of polynomial eigenfunctions, (iii) a factorization property for eigenfunctions, and admit (iv) the separation of the radial coordinate an...

We propose a new method for simulating QCD at finite density. The method is based on a general factorization property of distribution functions of observables, and it is therefore applicable to any system with a complex action. The so-called overlap problem is completely eliminated by the use of constrained simulations. We test this method in a Random Matrix Theory for finite density QCD, where...

We introduce a new class of graphical models that generalizes Lauritzen-Wermuth-Frydenberg chain graphs by relaxing the semi-directed acyclity constraint so that only directed cycles are forbidden. Moreover, up to two edges are allowed between any pair of nodes. Specifically, we present local, pairwise and global Markov properties for the new graphical models and prove their equivalence. We als...

We propose two computationally efficient key agreement algorithms. The schemes are ideally suited for computationally constrained environments such as sensor networks. The first proposed technique is general and uses matrix factorization. We provide constructive algorithms to implement the scheme. The second algorithm uses commutative property of matrices to distribute keys and provides two dif...

Graph bundles generalize the notion of covering graphs and graph products. In [8], authors constructed an algorithm that ÿnds a presentation as a nontrivial Cartesian graph bundle for all graphs that are Cartesian graph bundles over triangle-free simple base. In [21], the unique square property is deÿned and it is shown that any equivalence relation possessing the unique square property determi...

Directed acyclic graph (DAG) models may be characterized in four different ways: via a factorization, the dseparation criterion, the moralization criterion, and the local Markov property. As pointed out by Robins [2, 1], Verma and Pearl [6], and Tian and Pearl [5], marginals of DAG models also imply equality constraints that are not conditional independences. The well-known ‘Verma constraint’ i...

Let F be a field. We show that certain subrings contained between the polynomial ring F [X] = F [X1, · · · , Xn] and the power series ring F [X][[Y ]] = F [X1, · · · , Xn][[Y ]] have Weierstrass Factorization, which allows us to deduce both unique factorization and the Noetherian property. These intermediate subrings are obtained from elements of F [X][[Y ]] by bounding their total X-degree abo...