Topology Verification for Isosurface Extraction

The broad goals of verifiable visualization rely on correct algorithmic implementations. We extend a framework for verification of isosurfacing implementations to check topological properties. Specifically, we use stratified Morse theory and digital topology to design algorithms which verify topological invariants. Our extended framework reveals unexpected behavior and coding mistakes in popular publicly available isosurface codes.

A note on permutation regularity

The existence of a small partition of a combinatorial structure into random-like subparts, a so-called regular partition, has proven to be very useful in the study of extremal problems, and has deep algorithmic consequences. The main result in this direction is the Szemeredi Regularity Lemma in graph theory. In this note, we are concerned with regularity in permutations: we show that every permutation of a sufficiently large set has a regular partition into a small number of intervals. This refines the partition given by Cooper (2006) [10], which required an additional non-interval exceptional class. We also introduce a distance between permutations that plays an important role in the study of convergence of a permutation sequence. (C) 2011 Elsevier B.V. All rights reserved.

Combinatorial-topological framework for the analysis of global dynamics

We discuss an algorithmic framework based on efficient graph algorithms and algebraic-topological computational tools. The framework is aimed at automatic computation of a database of global dynamics of a given m-parameter semidynamical system with discrete time on a bounded subset of the n-dimensional phase space. We introduce the mathematical background, which is based upon Conley's topological approach to dynamics, describe the algorithms for the analysis of the dynamics using rectangular grids both in phase space and parameter space, and show two sample applications. (C) 2012 American Institute of Physics. [http://dx.doi.org/10.1063/1.4767672]

COMPLEXITY MEASURE: A QUANTUM INFORMATION APPROACH

In the past decades, all of the efforts at quantifying systems complexity with a general tool has usually relied on using Shannon's classical information framework to address the disorder of the system through the Boltzmann-Gibbs-Shannon entropy, or one of its extensions. However, in recent years, there were some attempts to tackle the quantification of algorithmic complexities in quantum systems based on the Kolmogorov algorithmic complexity, obtaining some discrepant results against the classical approach. Therefore, an approach to the complexity measure is proposed here, using the quantum information formalism, taking advantage of the generality of the classical-based complexities, and being capable of expressing these systems' complexity on other framework than its algorithmic counterparts. To do so, the Shiner-Davison-Landsberg (SDL) complexity framework is considered jointly with linear entropy for the density operators representing the analyzed systems formalism along with the tangle for the entanglement measure. The proposed measure is then applied in a family of maximally entangled mixed state.

Acute Cardiorespiratory and Metabolic Responses During Resistance Exercise in the Lactate Threshold Intensity

The aims were both to determine lactate and ventilatory threshold during incremental resistance training and to analyze the acute cardiorespiratory and metabolic responses during constant-load resistance exercise at lactate threshold (LT) intensity. Ten healthy men performed 2 protocols on leg press machine. The incremental test was performed to determine the lactate and ventilatory thresholds through an algorithmic adjustment method. After 48 h, a constant-load exercise at LT intensity was executed. The intensity of LT and ventilatory threshold was 27.1 +/- 3.7 and 30.3 +/- 7.9% of 1RM, respectively (P=0.142). During the constant-load resistance exercise, no significant variation was observed between set 9 and set 15 for blood lactate concentration (3.3 +/- 0.9 and 4.1 +/- 1.4 mmol.L-1, respectively. P=0.166) and BORG scale (11.5 +/- 2.9 and 13.0 +/- 3.5, respectively. P=0.783). No significant variation was observed between set 6 and set 15 for minute ventilation (19.4 +/- 4.9 and 22.4 +/- 5.5L. min(-1), respectively. P=0.091) and between S3 and S15 for VO2 (0.77 +/- 0.18 and 0.83 +/- 0.16L. min(-1), respectively. P=1.0). Constant-load resistance exercise at LT intensity corresponds to a steady state of ventilatory, cardio-metabolic parameters and ratings of perceived exertion.

TWO NEW WEAK CONSTRAINT QUALIFICATIONS AND APPLICATIONS

We present two new constraint qualifications (CQs) that are weaker than the recently introduced relaxed constant positive linear dependence (RCPLD) CQ. RCPLD is based on the assumption that many subsets of the gradients of the active constraints preserve positive linear dependence locally. A major open question was to identify the exact set of gradients whose properties had to be preserved locally and that would still work as a CQ. This is done in the first new CQ, which we call the constant rank of the subspace component (CRSC) CQ. This new CQ also preserves many of the good properties of RCPLD, such as local stability and the validity of an error bound. We also introduce an even weaker CQ, called the constant positive generator (CPG), which can replace RCPLD in the analysis of the global convergence of algorithms. We close this work by extending convergence results of algorithms belonging to all the main classes of nonlinear optimization methods: sequential quadratic programming, augmented Lagrangians, interior point algorithms, and inexact restoration.

LAGOA SANTA REVISITED: AN OVERVIEW OF THE CHRONOLOGY, SUBSISTENCE, AND MATERIAL CULTURE OF PALEOINDIAN SITES IN EASTERN CENTRAL BRAZIL

Lagoa Santa, a karstic area in eastern Central Brazil, has been subject to research on human paleontology and archaeology for 175 years. Almost 300 Paleoindian human skeletons have been found since Danish naturalist Peter Lund's pioneering work. Even so, some critical issues such as the role of rockshelters in settlement systems, and the possible paleoclimatic implications of the peopling of the region have yet to be addressed. We present some results obtained from recent excavations at four rockshelters and two open-air sites, new dates for human Paleoindian skeletons, and a model to explain the cultural patterns observed so far. It is also argued that the Paleoindian subsistence system at Lagoa Santa was similar to other locations in South America: generalized small-game hunting complemented by fruits, seed, and root gathering.