Simulation of simultaneous safe recursion over an arbitrary structure

In [O. Bournez, F. Cucker, P.J. de Naurois, J.Y. Marion, Computability over an arbitrary structure. Sequential and parallel polynomial time, in: Lecture Notes in Computer Science, vol. 2620, Springer, Berlin, 2003, pp. 185-199] the class of safe recursive functions over an arbitrary structure is defined. A question of simulation of the simultaneous safe recursion by single safe recursion was set. We prove that this simulation is feasible using bounded coding and decoding functions.     

The Monadic Quantifier Alternation Hierarchy over Grids and Graphs

The monadic second-order quantifier alternation hierarchy over the class of finite graphs is shown to be strict. The proof is based on automata theoretic ideas and starts from a restricted class of graph-like structures, namely finite two-dimensional grids. Considering grids where the width is a function of the height, we prove that the difference between the levels k+1 and k of the monadic hierarchy is witnessed by a set of grids where this function is (k+1)-fold exponential. We then transfer the hierarchy result to the class of directed (or undirected) graphs, using an encoding technique called strong reduction. It is notable that one can obtain sets of graphs which occur arbitrarily high in the monadic hierarchy but are already definable in the first-order closure of existential monadic second-order logic. We also verify that these graph properties even belong to the complexity class NLOG, which indicates a profound difference between the monadic hierarchy and the polynomial hierarchy.     

Distributed control design for systems interconnected over an arbitrary graph

We consider the problem of synthesizing a distributed dynamic output feedback controller achieving H/sub /spl infin// performance for a system composed of different interconnected sub-units, when the topology of the underlying graph is arbitrary. First, using tools inspired by dissipativity theory, we derive sufficient conditions in the form of finite-dimensional linear matrix inequalities when the interconnections are assumed to be ideal. These inequalities are coupled in a way that reflects the spatial structure of the problem and can be exploited to design distributed synthesis algorithms. We then investigate the case of lossy interconnection links and derive similar results for systems whose interconnection relations can be captured by a class of integral quadratic constraints that includes constant delays.     

Radiation and scattering from an arbitrary elastic structure using consistent fluid structure formulation

The harmonic vibralional response and the resulting acoustic radiation from an arbitrary elastic structure immersed in an infinite inviscid fluid are formulated. Basic functions given by a cubic polynomial of the local coordinates are often used for the inertial and elastic formulation of the surface finite elements. To use the same basis functions for pressure and velocity variations on the finite surface area, the surface Helmholtz integral and its directional derivative are employed. This consistent formulation result is compared with the case where the velocity distribution on the finite surface area is given by a cubic polynomial basis function, whereas the pressure distribution is defined by a first-order polynomial basis function. The set of computer programs developed here, given the acronym FIST, allows the use of the interior points to solve the set of over-determined system equations in the least-squares sense to obtain the solution at the resonance frequency of the interior problem. Many examples with known analytic or numerical solutions have been checked with the use of the least number of finite elements. Finally, an arbitrary, complex axisymmetric structure has been analyzed using this program.     

Optimal Implicit Dictionaries over Unbounded Universes

An array of n distinct keys can be sorted for logarithmic searching or can be organized as a heap for logarithmic updating, but it is unclear how to attain logarithmic time for both searching and updating. This natural question dates back to the heap of Williams and Floyd in the sixties and relates to the fundamental issue whether additional space besides those for the keys gives more computational power in dictionaries and how data ordering helps. Implicit data structures were introduced in the eighties with this goal, providing the best bound of O(log² n) time, until a recent result showing O(log² n/log log n) time. In this paper we describe the flat implicit tree, which is the first data structure obtaining O(log n) time for search and (amortized) update using an array of n cells.     

任意拓扑网的细分改进

在改进任意拓扑网构造光滑表面时,初始控制网格确定的情况下,生成的曲面形状惟一确定,最终的物体造型也随之确定,不具有可调性,因而在曲面细分过程中引入了控制参数和摄动。通过引入控制参数,调节一个参数值,使得所得的细分曲面的表达度可控,可以得到一系列的细分曲面。引入摄动是为了改进了空间位置,允许局部地调控约束曲面的形状。最后给出了曲面设计的实例,表明这种算法简单、有效。     

基于任意拓扑网的细分可控表达方法

在初始控制网格确定的情况下,生成的曲面形状惟一确定,最终的物体造型也随之确定,不具有可调性.通过在曲面细分过程中引入一个参数,给出一种新的细分曲面构造的算法,使得所得的细分曲面的表达度可控.调节一个参数值,可以得到一系列的细分曲面.最后给出了曲面设计的实例,表明这种算法简单、有效.     

基于块的任意曲面上的纹理合成

一种新的曲面纹理合成技术被提出,它采用求最小割集来解决块拼接时的礁缝走样问题。算法在预处理期对模型的三维网格进行了重建,使其规则并且建立网格点与参数化栅格采样后的图像点一一对应的关系,无论对合成的速度和质量都有很大的提高。提出了在曲面上进行纹理粘贴的算法,对于渲染存在不完整性的自然物体取得了较好的效果。     

Multicommodity flows over time: Efficient algorithms and complexity

Flow variation over time is an important feature in network flow problems arising in various applications such as road or air traffic control, production systems, communication networks (e.g. the Internet) and financial flows. The common characteristic are networks with capacities and transit times on the arcs which specify the amount of time it takes for flow to travel through a particular arc. Moreover, in contrast to static flow problems, flow values on arcs may change with time in these networks.     

Building spacetime meshes over arbitrary spatial domains

We present an algorithm to construct meshes suitable for spacetime discontinuous Galerkin finite-element methods. Our method generalizes and improves the Tent Pitcher algorithm of Üngör and Sheffer. Given an arbitrary simplicially meshed domain X of any dimension and a time interval [0, T], our algorithm builds a simplicial mesh of the spacetime domain X × [0, T], in constant time per element. Our algorithm avoids the limitations of previous methods by carefully adapting the durations of spacetime elements to the local quality and feature size of the underlying space mesh.This work was supported in part by The Center for Process Simulation and Design at the University of Illinois, Urbana-Champaign, under NSF ITR grant DMR-0121695. A preliminary version of this paper was presented at the 11th International Meshing Roundtable [9].     

Tight complexity analysis of the relocation problem with arbitrary release dates

The paper considers makespan minimization on a single machine subject to release dates in the relocation problem, originated from a resource-constrained redevelopment project in Boston. Any job consumes a certain amount of resource from a common pool at the start of its processing and returns to the pool another amount of resource at its completion. In this sense, the type of our resource constraints extends the well-known constraints on resumable resources, where the above two amounts of resource are equal for each job. In this paper, we undertake the first complexity analysis of this problem in the case of arbitrary release dates. We develop an algorithm, based on a multi-parametric dynamic programming technique (when the number of parameters that undergo enumeration of their values in the DP-procedure can be arbitrarily large). It is shown that the algorithm runs in pseudo-polynomial time when the number m of distinct release dates is bounded by a constant. This result is shown to be tight: (1) it cannot be extended to the case when m is part of the input, since in this case the problem becomes strongly NP-hard, and (2) it cannot be strengthened up to designing a polynomial time algorithm for any constant m>1, since the problem remains NP-hard for m=2. A polynomial-time algorithm is designed for the special case where the overall contribution of each job to the resource pool is nonnegative. As a counterpart of this result, the case where the contributions of all jobs are negative is shown to be strongly NP-hard.     

On non-linearity and affine equivalence of permutations over an arbitrary finite commutative ring with unity

Cryptographic properties of permutations viz non-linearity, affine equivalence, and mode transform have been studied in the literature, treating them as bijections on ?_n. In this article, the authors consider them as bijection on an arbitrary finite commutative ring with unity. Treating them this way, they achieve a generalization of the above mentioned properties. The authors also propose an algorithm for computing non-linearity in their generalized scenario, which is faster compared to the direct approach in many cases.     

Control design with arbitrary information structure constraints

In this paper, a new method is proposed for designing robust control laws that are subject to arbitrary information structure constraints. The computation of the gain matrix is formulated in terms of a static output feedback problem, which can be efficiently solved using linear matrix inequalities. The resulting control laws ensure stability with respect to a broad class of additive nonlinear uncertainties in the system.     

Quantifier Elimination over Algebraically Closed Fields in a Proof Assistant using a Computer Algebra System

We propose a decision procedure for algebraically closed fields based on a quantifier elimination method. The procedure is intended to build proofs for systems of polynomial equations and inequations. We describe how this procedure can be carried out in a proof assistant using a Computer Algebra system in a purely skeptical way. We present an implementation in the particular framework of Coq and Maple giving some details regarding the interface between the two tools. This allows us to show that a Computer Algebra system can be used not only to bring additional computational power to a proof assistant but also to enhance the automation of such tools.