Phase-Locked Loop design applied to frequency-modulated atomic force microscope

The atomic force microscope (AFM) introduced the surface investigation with true atomic resolution. In the frequency modulation technique (FM-AFM) both the amplitude and the frequency of oscillation of the micro-cantilever must be kept constant even in the presence of tip-surface interaction forces. For that reason, the proper design of the Phase-Locked Loop (PLL) used in FM-AFM is vital to system performance. Here, the mathematical model of the FM-AFM control system is derived considering high order PLL In addition a method to design stable third-order Phase-Locked Loops is presented. (C) 2010 Elsevier B.V. All rights reserved.

Relative entropy measures applied to healthy and pathological voice characterization

Nowadays, noninvasive methods of diagnosis have increased due to demands of the population that requires fast, simple and painless exams. These methods have become possible because of the growth of technology that provides the necessary means of collecting and processing signals. New methods of analysis have been developed to understand the complexity of voice signals, such as nonlinear dynamics aiming at the exploration of voice signals dynamic nature. The purpose of this paper is to characterize healthy and pathological voice signals with the aid of relative entropy measures. Phase space reconstruction technique is also used as a way to select interesting regions of the signals. Three groups of samples were used, one from healthy individuals and the other two from people with nodule in the vocal fold and Reinke`s edema. All of them are recordings of sustained vowel /a/ from Brazilian Portuguese. The paper shows that nonlinear dynamical methods seem to be a suitable technique for voice signal analysis, due to the chaotic component of the human voice. Relative entropy is well suited due to its sensibility to uncertainties, since the pathologies are characterized by an increase in the signal complexity and unpredictability. The results showed that the pathological groups had higher entropy values in accordance with other vocal acoustic parameters presented. This suggests that these techniques may improve and complement the recent voice analysis methods available for clinicians. (C) 2008 Elsevier Inc. All rights reserved.

Using sentinels to detect intersections of convex and nonconvex polygons

We describe finite sets of points, called sentinels, which allow us to decide if isometric copies of polygons, convex or not, intersect. As an example of the applicability of the concept of sentinel, we explain how they can be used to formulate an algorithm based on the optimization of differentiable models to pack polygons in convex sets. Mathematical subject classification: 90C53, 65K05.

An Extension of the Invariance Principle for a Class of Differential Equations with Finite Delay

An extension of the uniform invariance principle for ordinary differential equations with finite delay is developed. The uniform invariance principle allows the derivative of the auxiliary scalar function V to be positive in some bounded sets of the state space while the classical invariance principle assumes that. V <= 0. As a consequence, the uniform invariance principle can deal with a larger class of problems. The main difficulty to prove an invariance principle for functional differential equations is the fact that flows are defined on an infinite dimensional space and, in such spaces, bounded solutions may not be precompact. This difficulty is overcome by imposing the vector field taking bounded sets into bounded sets.

EXISTENCE RESULTS FOR NEUTRAL INTEGRO-DIFFERENTIAL EQUATIONS WITH UNBOUNDED DELAY

In this paper we discuss the existence of mild, strict and classical solutions for a class of abstract integro-differential equations in Banach spaces. Some applications to ordinary and partial integro-differential equations are considered.

Existence Results for Abstract Partial Neutral Integro-differential Equation with Unbounded Delay

In this paper we study the existence and regularity of mild solutions for a class of abstract partial neutral integro-differential equations with unbounded delay.

GLOBAL SOLUTIONS FOR ABSTRACT FUNCTIONAL DIFFERENTIAL EQUATIONS WITH NONLOCAL CONDITIONS

In this paper we study the existence of global solutions for a class of abstract functional differential equation with nonlocal conditions. An application is considered.

Weighted S-Asymptotically omega-Periodic Solutions of a Class of Fractional Differential Equations

We study the existence of weighted S-asymptotically omega-periodic mild solutions for a class of abstract fractional differential equations of the form u' = partial derivative (alpha vertical bar 1)Au + f(t, u), 1 < alpha < 2, where A is a linear sectorial operator of negative type.

EXISTENCE RESULTS FOR ABSTRACT NEUTRAL FUNCTIONAL DIFFERENTIAL EQUATIONS

In this paper we discuss the existence of solutions for a class of abstract partial neutral functional differential equations.

AFFINE INTERVAL EXCHANGE TRANSFORMATIONS WITH FLIPS AND WANDERING INTERVALS

There exist uniquely ergodic affine interval exchange transformations of [0,1] with flips which have wandering intervals and are such that the support of the invariant measure is a Cantor set.

Minimal Nielsen Root Classes and Roots of Liftings

Given a continuous map f : K -> M from a 2-dimensional CW complex into a closed surface, the Nielsen root number N(f) and the minimal number of roots mu(f) of f satisfy N(f) <= mu(f). But, there is a number mu(C)(f) associated to each Nielsen root class of f, and an important problem is to know when mu(f) = mu(C)(f)N(f). In addition to investigate this problem, we determine a relationship between mu(f) and mu((f) over tilde), when (f) over tilde f is a lifting of f through a covering space, and we find a connection between this problems, with which we answer several questions related to them when the range of the maps is the projective plane.

On the k-restricted structure ratio in planar and outerplanar graphs

A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-restricted ratio is the infimum, over simple planar graphs H, of the ratio of the number of edges in a maximum k-restricted structure subgraph of H to the number edges of H. We prove that, as k tends to infinity, the planar k-restricted ratio tends to 1/2. The same result holds for the weighted version. Our results are based on analyzing the analogous ratios for outerplanar and weighted outerplanar graphs. Here both ratios tend to 1 as k goes to infinity, and we provide good estimates of the rates of convergence, showing that they differ in the weighted from the unweighted case.

An algorithmic Friedman-Pippenger theorem on tree embeddings and applications

An (n, d)-expander is a graph G = (V, E) such that for every X subset of V with vertical bar X vertical bar <= 2n - 2 we have vertical bar Gamma(G)(X) vertical bar >= (d + 1) vertical bar X vertical bar. A tree T is small if it has at most n vertices and has maximum degree at most d. Friedman and Pippenger (1987) proved that any ( n; d)- expander contains every small tree. However, their elegant proof does not seem to yield an efficient algorithm for obtaining the tree. In this paper, we give an alternative result that does admit a polynomial time algorithm for finding the immersion of any small tree in subgraphs G of (N, D, lambda)-graphs Lambda, as long as G contains a positive fraction of the edges of Lambda and lambda/D is small enough. In several applications of the Friedman-Pippenger theorem, including the ones in the original paper of those authors, the (n, d)-expander G is a subgraph of an (N, D, lambda)-graph as above. Therefore, our result suffices to provide efficient algorithms for such previously non-constructive applications. As an example, we discuss a recent result of Alon, Krivelevich, and Sudakov (2007) concerning embedding nearly spanning bounded degree trees, the proof of which makes use of the Friedman-Pippenger theorem. We shall also show a construction inspired on Wigderson-Zuckerman expander graphs for which any sufficiently dense subgraph contains all trees of sizes and maximum degrees achieving essentially optimal parameters. Our algorithmic approach is based on a reduction of the tree embedding problem to a certain on-line matching problem for bipartite graphs, solved by Aggarwal et al. (1996).

On the resilience of long cycles in random graphs

In this paper we determine the local and global resilience of random graphs G(n,p) (p >> n(-1)) with respect to the property of containing a cycle of length at least (1 - alpha)n. Roughly speaking, given alpha > 0, we determine the smallest r(g) (G, alpha) with the property that almost surely every subgraph of G = G(n,p) having more than r(g) (G, alpha)vertical bar E(G)vertical bar edges contains a cycle of length at least (1 - alpha)n (global resilience). We also obtain, for alpha < 1/2, the smallest r(l) (G, alpha) such that any H subset of G having deg(H) (v) larger than r(l) (G, alpha) deg(G) (v) for all v is an element of V(G) contains a cycle of length at least (1 - alpha)n (local resilience). The results above are in fact proved in the more general setting of pseudorandom graphs.