An Application of an Initialization Protocol to Permutation Routing in a Single-Hop Mobile Ad Hoc Networks

In 1999 Nakano, Olariu, and Schwing in [20], they showed that the permutation routing of n items pretitled on a mobile ad hoc network (MANET for short) of p stations (p known) and k channels (MANET{(n, p, k)) with k < p, can be carried out in broadcast rounds if k p and if each station has a -memory locations. And if k and if each station has a -memory locations, the permutations of these n pretitled items can be done also in broadcast rounds. They used two assumptions: first they suppose that each station of the mobile ad hoc network has an identifier beforehand. Secondly, the stations are partitioned into k groups such that each group has stations, but it was not shown how this partition can be obtained. In this paper, the stations have not identifiers beforehand and p is unknown. We develop a protocol which first names the stations, secondly gives the value of p, and partitions stations in groups of stations. Finally we show that the permutation routing problem can be solved on it in broadcast rounds in the worst case. It can be solved in broadcast rounds in the better case. Note that our approach does not impose any restriction on k.     

Computation of Battle–Lemarie Wavelets Using an FFT-Based Algorithm

Battle and Lemarie derived independently wavelets by orthonormalizing B-splines. The scaling function _m (t) corresponding to Battle–Lemarie's wavelet _m (t) is given by , where B _m(t) is the mth-order central B-spline and the coefficients _{m, k} satisfy . In this paper, we propose an FFT-based algorithm for computing the expansion coefficients _{m, k} and the two-scale relations of the scaling functions and wavelets. The algorithm is very simple and it can be easily implemented. Moreover, the expansion coefficients can be efficiently and accurately obtained via multiple sets of FFT computations. The computational approach presented in this paper here is noniterative and is more efficient than the matrix approach recently proposed in the literature.     

Stability of the Logistic Population Model with Delayed Environmental Response

The population dynamics model , was considered. For this model with uniform distribution of delays and a _n = 0, nonnegativeness and convexity of the sequence a _k (0 k n) was shown to be the sufficient stability condition. Therefore, there is no need to constrain the reproduction rate and the mean delay .     

On Projection Matrices $$\mathcal{P}^k \to \mathcal{P}^2 ,k = 3,...,6, $$ and their Applications in Computer Vision

Projection matrices from projective spaces have long been used in multiple-view geometry to model the perspective projection created by the pin-hole camera. In this work we introduce higher-dimensional mappings for the representation of various applications in which the world we view is no longer rigid. We also describe the multi-view constraints from these new projection matrices (where k > 3) and methods for extracting the (non-rigid) structure and motion for each application.     

A result on k-valent graphs and its application to a graph embedding problem

Summary It is proved that any n-vertex, k-valent undirected simple graph, G, contains a spanning tree with at least leaves. As a result of this it is shown that any such graph contains an independent set, of size at least n/5k, with the property that deleting the vertices in this set and their incident edges does not disconnect G. This latter result is applied by giving an improved upper bound on the area required to embed arbitrary graphs into grid graphs.     

Onn-column 0, 1-matrices with allk-projections surjective

This paper presents a new approach to construct a smalln-column 0, 1-matrix for two given integersn andk(k, such that everyk-column projection contains all 2 ^k possible row vectors, namely surjective on {0, 1} ^k . The number of the matrix's rows does not exceed . This approach has considerable advantage for smallk and practical sizes ofn. It can be applied to the test generation of VLSI circuits, the design of fault tolerant systems and other fields.     

Combining the Perceptron Algorithm with Logarithmic Simulated Annealing

We present results of computational experiments with an extension of the Perceptron algorithm by a special type of simulated annealing. The simulated annealing procedure employs a logarithmic cooling schedule , where is a parameter that depends on the underlying configuration space. For sample sets S of n-dimensional vectors generated by randomly chosen polynomials , we try to approximate the positive and negative examples by linear threshold functions. The approximations are computed by both the classical Perceptron algorithm and our extension with logarithmic cooling schedules. For and , the extension outperforms the classical Perceptron algorithm by about 15% when the sample size is sufficiently large. The parameter was chosen according to estimations of the maximum escape depth from local minima of the associated energy landscape.      

Two-Parameter Discrete Systems over a Residue Ring and Their Properties

A class of two-parameter discrete systems defined on the ring of class of residues of integers modulo m is studied. All solutions are shown to be periodic, stability conditions (equality of solutions to zero, beginning from a certain instant) and a controllability condition are formulated. Controllability is shown to guarantee stabilizability.     

The choice coordination problem

Summary In the course of a concurrent computation, processes P1,..., Pn must reach a common choice of one out of k alternatives A ₁,..., A _k. They do this by protocols using k shared variables, one for each alternative. If the range of the variables has m values then is necessary, and n + 2m is sufficient, for deterministic protocols solving the choice coordination problem (C.C.P.). We introduce very simple randomizing protocols which, independently of n, solve the C.C.P. by use of a fixed alphabet. A single-byte (256-valued) alphabet permits a solution with non-termination probability smaller than 2^–127. Many software and hardware tasks involving concurrency can be interpreted as choice coordination problems. Choice coordination problems occur also in nature.This research was supported in part by NSF grants: MCS77-02474 at Washington University, Seattle, MCS80-12716 at University of California at Berkeley. Presented at the Specker Symposium in Zürich, January 1980     

Conditions for Instability of One Class of Nonlinear Nonautomomous Dynamic Systems

Consideration was given to the conditions for instability of the equilibrium states of a nonlinear nonautonomous dynamic systems obeying an ordinary vector differential equation of arbitrary order whose right-hand side satisfies the following conditions: (i) for any t 0, div 0$$ " align="middle" border="0"> almost everywhere on the set H that is a neighborhood of the equilibrium point of the system and (ii) at any point . The equilibrium states of such systems can be both stable and unstable. For one class of these systems, sufficient instability conditions were given, which enables one to carry out studies using only the information about the right-hand side of the system.     

On the Number of Digital Discs

A digital disc is defined as the set of all integer points inside of a given real disc. In this paper we show that there are no more than

A Novel Class of Symmetric and Nonsymmetric Periodizing Variable Transformations for Numerical Integration

Variable transformations for numerical integration have been used for improving the accuracy of the trapezoidal rule. Specifically, one first transforms the integral via a variable transformation that maps [0,1] to itself, and then approximates the resulting transformed integral by the trapezoidal rule. In this work, we propose a new class of symmetric and nonsymmetric variable transformations which we denote , where r and s are positive scalars assigned by the user. A simple representative of this class is . We show that, in case , or but has algebraic (endpoint) singularities at x = 0 and/or x = 1, the trapezoidal rule on the transformed integral produces exceptionally high accuracies for special values of r and s. In particular, when and we employ , the error in the approximation is (i) O(h ^r ) for arbitrary r and (ii) O(h ^2r ) if r is a positive odd integer at least 3, h being the integration step. We illustrate the use of these transformations and the accompanying theory with numerical examples.      

A hierarchy theorem for multihead stack-counter automata

Summary Let L _b = {w ₁ ^*...* w _2b ¦w _i is in {0,1}^* and w _i = w _2b+1–i for 1i2b for b1. We show that the language L _b is not recognizable by any nondeterministic one-way k-head stack-counter automata if \left( {\begin{array}{*{20}c} k \\ 2 \\ \end{array} } \right)$$ " align="middle" border="0"> . As a corollary, we show that k+1 heads are better than k for one-way multihead stack-counter automata.     

Determination of the roots and of the global extremum of a lipschitz function

Conclusion The obvious deficiency of the method (1.3), (1.9) is the possible difficulty of the operation . In connection with this one can note that all the above given statements remain valid if the number is replaced by some positive lower bound of |f(t _k ,x)| on .In computational methods, the presence of the Lipschitz constant is considered as a deficiency. In connection with this we can note that the Lipschitz constant L can be replaced by any of its upper estimates. For example, for a differentiable function f(z) one can take .Translated from Kibernetika, No. 2, pp. 71–74, March–April, 1987.     

The Complexity of Learning According to Two Models of a Drifting Environment

We show that a bound on the rate of drift of the distribution generating the examples is sufficient for agnostic learning to relative accuracy , where c > 0 is a constant; this matches a known necessary condition to within a constant factor. We establish a sufficient condition for the realizable case, also matching a known necessary condition to within a constant factor. We provide a relatively simple proof of a bound of + on the sample complexity of agnostic learning in a fixed environment.     

On the complexity of approximating k-set packing

Given a k-uniform hypergraph, the Maximum k -Set Packing problem is to find the maximum disjoint set of edges. We prove that this problem cannot be efficiently approximated to within a factor of unless P = NP. This improves the previous hardness of approximation factor of by Trevisan. This result extends to the problem of k-Dimensional-Matching.     

Point Asymptotics for Probabilities of Large Deviations of the ω2 Statistics in Verification of the Symmetry Hypothesis

We consider the ² statistic, destined for testing the symmetry hypothesis, which has the form