A simple proof for generalized Fibonacci numbers with dying rabbits

We consider the generalized Fibonacci counting problem with rabbits that become fertile at age $f$ and die at age $d$, with $1<=f<=d$ and $d$ finite or infinite. We provide a simple proof, based exclusively on a counting argumentation, for a recursive formula that gives the $n$th generalized Fibonacci number as a function of at most 3 previous numbers. The formula generalizes both the original Fibonacci sequence, for $f=2$ and $d=\infty$ (or $f=1$ and $d=2$), and other Fibonacci-related sequences, such as the Padovan sequence, for $f=2$ and $d=3$, the Tribonacci, for $f=1$ and $d=3$, Tetranacci, for $f=1$ and $d=4$, and alike sequences, for $f=1$ and finite values of $d$

Catastrophic Faults in Reconfigurable Linear Arrays of Processors

In regular architectures of identical processing elements, a widely used technique to improve the reconfigurability of the system consists of providing redundant processing elements and mechanisms of reconfiguration. In this paper we consider linear arrays of processing elements, with unidirectional bypass links of length g. We count the number of particular sets of faulty processing elements. We show that the number of catastrophic faults of g elements is equal to the (g-1)-th Catalan number. We also provide algorithms to rank and unrank all catastrophic sets of g faults. Finally, we describe a linear time algorithm that generate all such sets of faults

Optimal Colored Threshold Visual Cryptography Schemes

Visual cryptography schemes allow the encoding of a secret image into n shares which are distributed to the participants. The shares are such that only qualified subsets of participants can visually recover the secret image. Usually the secret image consist of black and white pixels. In colored threshold visual cryptography schemes the secret image is composed of pixels taken from a given set of c colors. The pixels expansion and the contrast of a scheme are two measures of the goodness of the scheme. In this paper, we study c-color (k,n)-threshold visual cryptography schemes and provide a characterization of contrast-optimal schemes. More specifically we prove that there exists a contrast-optimal scheme that is a member of a special set of schemes, which we call canonical schemes, and that satisfy strong symmetry properties. Then we use canonical schemes to provide a constructive proof of optimality, with respect to the pixel expansion, of c-color (n,n)-threshold visual cryptography schemes. Finally, we provide constructions of c-color (2,n)-threshold schemes whose pixels expansion improves on previously proposed schemes

Minimal Path Length of Trees with Known Fringe

In this paper we continue the study of the path length of trees with known fringe as initiated by [1] and [2]. We compute the path length of the minimal tree with given number of leaves N and fringe ∆ for the case ∆ ≥ N/2. This complements the result of [2] that studied the case ∆ ≤ N/2. Our methods also yields a linear time algorithm for constructing the minimal tree when ∆ ≥ N/2

A Differential Evolution Algorithm Assisted by ANFIS for Music Fingering

Music fingering is a cognitive process whose goal is to map each note of a music score to a fingering on some instrument. A fingering specifies the fingers of the hands that the player should use to play the notes. This problem arises for many instruments and it can be quite different from instrument to instrument; guitar fingering, for example, is different from piano fingering. Previous work focuses on specific instruments, in particular the guitar, and evolutionary algorithms have been used. In this paper, we propose a differential evolution (DE) algorithm designed for general music fingering (any kind of music instruments). The algorithm uses an Adaptive Neuro-Fuzzy Inference System (ANFIS) engine that learns the fingering from music already fingered. The algorithm follows the basic DE strategy but exploits also some customizations specific to the fingering problem. We have implemented the DE algorithm in Java and we have used the ANFIS network in Matlab. The two systems communicate by using the MatlabControl library. Several tests have been performed to evaluate its efficacy

Revisiting the Paxos algorithm

Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 1997.Includes bibliographical references (p. 138-142).by Roberto de Prisco.M.S

The power of verification for one-parameter agents

We initiate the study of mechanisms with verification for one-parameter agents. We give an algorithmic characterization of such mechanisms and show that they are provably better than mechanisms without verification, i.e., those previously considered in the literature. These results are obtained for a number of optimization problems motivated by the Internet and recently studied in the algorithmic mechanism design literature. The characterization can be regarded as an alternative approach to existing techniques to design truthful mechanisms. The construction of such mechanisms reduces to the construction of an algorithm satisfying certain “monotonicity” conditions which, for the case of verification, are much less stringent. In other words, verification makes the construction easier and the algorithm more efficient (both computationally and in terms of approximability)

New Constructions for Mechanisms with Verification

A social choice function A is implementable with verification if there exists a payment scheme P such that (A,P) is a truthful mechanism for verifiable agents [Nisan and Ronen, STOC 99]. We give a simple sufficient condition for a social choice function to be implementable with verification for comparable types. Comparable types are a generalization of the well-studied one-parameter agents. Based on this characterization, we show that a large class of objective functions μ admit social choice functions that are implementable with verification and minimize (or maximize) μ.We then focus on the well-studied case of oneparameter agents.We give a general technique for constructing efficiently computable social choice functions that minimize or approximately minimize objective functions that are non-increasing and neutral (these are functions that do not depend on the valuations of agents that have no work assigned to them). As a corollary we obtain efficient online and offline mechanisms with verification for some hard scheduling problems on related machines

Secure two-party computation: a visual way

In this paper we propose a novel method for performing secure two-party computation. By merging together in a suitable way two beautiful ideas of the 80\u27s and the 90\u27s, Yao\u27s garbled circuit construction and Naor and Shamir\u27s visual cryptography, respectively, we enable Alice and Bob to securely evaluate a function $f(\cdot,\cdot)$ of their inputs, $x$ and $y$, through a {\em pure physical} process. Indeed, once Alice has prepared a set of properly constructed transparencies, Bob computes the function value $f(x,y)$ by applying a sequence of simple steps which require the use of a pair of scissors, superposing transparencies, and the human visual system. A crypto-device for the function evaluation process is not needed any more