We present in this paper a detailed note on the computation of Puiseux series solutions of the Riccatti equation associated with a homogeneous linear ordinary differential equation. This paper is a continuation of [1] which was on the complexity of solving arbitrary ordinary polynomial differential equations in terms of Puiseux series. Introduction LetK = Q(T1, . . . , Tl)[η] be a finite extens...

Abstract. We show that the independence polytope of every regular matroid has an extended formulation of size quadratic in the size of its ground set. This generalizes a similar statement for (co-)graphic matroids, which is a simple consequence of Martin’s [9] extended formulation for the spanning-tree polytope. In our construction, we make use of Seymour’s decomposition theorem for regular mat...

Recent advances in Monte Carlo methods allow us to revisit work by de Finetti who suggested the use of approximate exchangeability in the analyses of contingency tables. This paper gives examples of computational implementations using Metropolis Hastings, Langevin and Hamiltonian Monte Carlo to compute posterior distributions for test statistics relevant for testing independence, reversible or ...

We consider optimization of nonlinear objective functions that balance d linear criteria over n-element independence systems presented by linear-optimization oracles. For d = 1, we have previously shown that an r-best approximate solution can be found in polynomial time. Here, using an extended Erdős–Ko–Rado theorem of Frankl, we show that for d = 2, finding a ρn-best solution requires exponent...

The well-known greedy algorithm MIN for 6nding a maximal independent set in a graph G is based on recursively removing the closed neighborhood of a vertex which has (in the currently existing graph) minimum degree. We give a forbidden induced subgraph condition under which algorithm MIN always results in 6nding a maximum independent set of G, and hence yields the exact value of the independence...

This paper provides algorithms that use an information-theoretic analysis to learn Bayesian network structures from data. Based on our three-phase learning framework, we develop efficient algorithms that can effectively learn Bayesian networks, requiring only polynomial numbers of conditional independence (CI) tests in typical cases. We provide precise conditions that specify when these algorit...

We consider quantum holonomy of some three-dimensional general covariant non-Abelian field theory in the Landau gauge and confirm a previous result partially proven. We show that quantum holonomy retains metric independence after explicit gauge fixing and hence possesses the topological property of a link invariant. We examine the generalized quantum holonomy defined on a multicomponent link an...

We consider a simple sequential allocation procedure for sharing indivisible items between agents in which agents take turns to pick items. Supposing additive utilities and independence between the agents, we show that the expected utility of each agent is computable in polynomial time. Using this result, we prove that the expected utilitarian social welfare is maximized when agents take altern...

The Phase Vocoder [1] was originally introduced as an alternative approach to speech coding but has won much greater acceptance among the music community as a tool both for sound analysis and composition [2]. Although dormant for some time, there has been a resurgence of interest in AM-FM speech signal descriptions in the last ten years [3], [4]. With the intention of building on some of the ne...

In a recent paper, we constructed a basis for the contact-order filtration of the module of derivations on the orbit space of a finite real reflection group acting on an -dimensional Euclidean space. Recently M. Yoshinaga constructed another basis for the contact-order filtration. In this note we give an explicit formula relating Yoshinaga’s basis to the basis we constructed earlier. The two ba...