Search results for "Graph theory"
showing 10 items of 784 documents
Serial subalgebras of finitary Lie algebras
2000
A Lie subalgebra L of glK(V ) is said to be finitary if it consists of elements of finite rank. We show that, if L acts irreducibly on V , and if V is infinite-dimensional, then every non-trivial ascendant Lie subalgebra of L acts irreducibly on V too. When CharK 6= 2, it follows that the locally solvable radical of such L is trivial. In general, locally solvable finitary Lie algebras over fields of characteristic 6= 2 are hyperabelian.
The Herzog-Vasconcelos conjecture for affine semigroup rings
1999
Let S be a simplicial affine semigroup such that its semigroup ring A = k[S] is Buchsbaum. We prove for such A the Herzog-Vasconcelos conjecture: If the A-module Der(k)A of k-linear derivations of A has finite projective dimension then it is free and hence A is a polynomial ring by the well known graded case of the Zariski-Lipman conjecture.
Nonmalleable encryption of quantum information
2008
We introduce the notion of "non-malleability" of a quantum state encryption scheme (in dimension d): in addition to the requirement that an adversary cannot learn information about the state, here we demand that no controlled modification of the encrypted state can be effected. We show that such a scheme is equivalent to a "unitary 2-design" [Dankert et al.], as opposed to normal encryption which is a unitary 1-design. Our other main results include a new proof of the lower bound of (d^2-1)^2+1 on the number of unitaries in a 2-design [Gross et al.], which lends itself to a generalization to approximate 2-design. Furthermore, while in prime power dimension there is a unitary 2-design with =…
Any AND-OR Formula of Size N Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer
2007
Consider the problem of evaluating an AND-OR formula on an $N$-bit black-box input. We present a bounded-error quantum algorithm that solves this problem in time $N^{1/2+o(1)}$. In particular, approximately balanced formulas can be evaluated in $O(\sqrt{N})$ queries, which is optimal. The idea of the algorithm is to apply phase estimation to a discrete-time quantum walk on a weighted tree whose spectrum encodes the value of the formula.
Enumeration of L-convex polyominoes by rows and columns
2005
In this paper, we consider the class of L-convex polyominoes, i.e. the convex polyominoes in which any two cells can be connected by a path of cells in the polyomino that switches direction between the vertical and the horizontal at most once.Using the ECO method, we prove that the number fn of L-convex polyominoes with perimeter 2(n + 2) satisfies the rational recurrence relation fn = 4fn-1 - 2fn-2, with f0 = 1, f1 = 2, f2 = 7. Moreover, we give a combinatorial interpretation of this statement. In the last section, we present some open problems.
Elementary (-1)-curves of P-3
2006
In this note we deal with rational curves in P^3 which are images of a line by means of a finite sequence of cubo-cubic Cremona transformations. We prove that these curves can always be obtained applying to the line a sequence of such transformations increasing at each step the degree of the curve. As a corollary we get a result about curves that can give speciality for linear systems of P^3.
Probabilistic entailment and iterated conditionals
2020
In this paper we exploit the notions of conjoined and iterated conditionals, which are defined in the setting of coherence by means of suitable conditional random quantities with values in the interval $[0,1]$. We examine the iterated conditional $(B|K)|(A|H)$, by showing that $A|H$ p-entails $B|K$ if and only if $(B|K)|(A|H) = 1$. Then, we show that a p-consistent family $\mathcal{F}=\{E_1|H_1,E_2|H_2\}$ p-entails a conditional event $E_3|H_3$ if and only if $E_3|H_3=1$, or $(E_3|H_3)|QC(\mathcal{S})=1$ for some nonempty subset $\mathcal{S}$ of $\mathcal{F}$, where $QC(\mathcal{S})$ is the quasi conjunction of the conditional events in $\mathcal{S}$. Then, we examine the inference rules $A…
Minimum node weight spanning trees searching algorithm for broadcast transmission in sensor networks
2017
A minimum node weight spanning tree in a weighted, directed graph is a tree whose node with maximum out-weight is minimal among all spanning trees. This type of trees are important because they appear in the solutions of the maximum lifetime broadcasting problem in wireless sensor networks. In a complete graph build of N nodes there are NN-2 spanning trees and to find such trees it is necessary to perform more than O(NN-2) operations. In this paper we propose an algorithm for searching the minimum node weight spanning trees in the graph. In the proposed algorithm, instead of calculating the symbolic determinant of the generalized Laplacian matrix, numerical operations on its exponents are p…
INTERVAL-BASED TRACING OF STRANGE ATTRACTORS
2006
The method described here relies on interval arithmetic and graph theory to compute guaranteed coverings of strange attractors like Hénon attractor. It copes with infinite intervals, using either a geometric method or a new directed projective interval arithmetic.
Real Line Arrangements and Surfaces with Many Real Nodes
2008
A long standing question is if the maximum number μ(d) of nodes on a surface of degree d in P( ) can be achieved by a surface defined over the reals which has only real singularities. The currently best known asymptotic lower bound, μ(d) 5 12 d, is provided by Chmutov’s construction from 1992 which gives surfaces whose nodes have non-real coordinates. Using explicit constructions of certain real line arrangements we show that Chmutov’s construction can be adapted to give only real singularities. All currently best known constructions which exceed Chmutov’s lower bound (i.e., for d = 3, 4, . . . , 8, 10, 12) can also be realized with only real singularities. Thus, our result shows that, up t…