Discrete approximations for strict convex continuous time problems and duality

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Homothetic preferences

This paper describes properties of upper semi-continuous homothetic preferences. First we give conditions for the existence of an upper semi-continuous representation which is homogeneous of degree one. Then we show that with the additional assumptions of monotonicity or strict convexity, the preference is continuous. Several counterexamples illustrate the tightness of the results.

Boolean Rings that are Baire Spaces

∗ The present article was originally submitted for the second volume of Murcia Seminar on Functional Analysis (1989). Unfortunately it has been not possible to continue with Murcia Seminar publication anymore. For historical reasons the present vesion correspond with the original one.

Convexity, Classification, and Risk Bounds

Many of the classification algorithms developed in the machine learning literature, including the support vector machine and boosting, can be viewed as minimum contrast methods that minimize a convex surrogate of the 0–1 loss function. The convexity makes these algorithms computationally efficient. The use of a surrogate, however, has statistical consequences that must be balanced against the computational virtues of convexity. To study these issues, we provide a general quantitative relationship between the risk as assessed using the 0–1 loss and the risk as assessed using any nonnegative surrogate loss function. We show that this relationship gives nontrivial upper bounds on excess risk under the weakest possible condition on the loss function—that it satisfies a pointwise form of Fisher consistency for classification. The relationship is based on a simple variational transformation of the loss function that is easy to compute in many applications. We also present a refined version of this result in the case of low noise, and show that in this case, strictly convex loss functions lead to faster rates of convergence of the risk than would be implied by standard uniform convergence arguments. Finally, we present applications of our results to the estimation of convergence rates in function classes that are scaled convex hulls of a finite-dimensional base class, with a variety of commonly used loss functions.

Correction to “The Importance of Convexity in Learning With Squared Loss” [Sep 98 1974-1980]

The paper "the importance of convexity in learning with squared loss" gave a lower bound on the sample complexity of learning with quadratic loss using a nonconvex function class. The proof contains an error. We show that the lower bound is true under a stronger condition that holds for many cases of interest.

Does section 420A impose ‘strict liability’ upon controllers for acts or omissions of agents and experts?

This article addresses in depth the question of whether section 420A of the Corporations Act 2001 (Cth) imposes ‘strict liability’ upon a controller for the failure of an agent or expert to take reasonable care. The weight of existing authority appears to suggest that controllers are liable under s 420A for the carelessness of their agents or expert advisers. However, a closer analysis of the text of the provision and relevant Australian and UK case law demonstrates that this aspect of the statutory construction of s 420A remains very much an open question. This article ultimately contends for a construction of s 420A which requires a controller to adequately supervise and scrutinise, but which does not render a blameless controller strictly liable for all careless acts and omissions of agents and expert advisers.

Proportionality of sanctions under the WADA Code : CAS jurisprudence and the need for a strict approach

This article suggests that the issue of proportionality in anti-doping sanctions has been inconsistently dealt with by the Court of Arbitration for Sport (CAS). Given CAS’s pre-eminent role in interpreting and applying the World Anti-Doping Code under the anti-doping policies of its signatories, an inconsistent approach to the application of the proportionality principle will cause difficulties for domestic anti-doping tribunals seeking guidance as to the appropriateness of their doping sanctions.

Total factor productivity growth and convergence in the petroleum industry : empirical analysis testing for convexity

While economic theory acknowledges that some features of technology (e.g., indivisibilities, economies of scale and specialization) can fundamentally violate the traditional convexity assumption, almost all empirical studies accept the convexity property on faith. In this contribution, we apply two alternative flexible production technologies to measure total factor productivity growth and test the significance of the convexity axiom using a nonparametric test of closeness between unknown distributions. Based on unique field level data on the petroleum industry, the empirical results reveal significant differences, indicating that this production technology is most likely non-convex. Furthermore, we also show the impact of convexity on answers to traditional convergence questions in the productivity growth literature.

Local polynomial convexity of the union of two totally-real surfaces at their intersection

We consider the following question: Let S (1) and S (2) be two smooth, totally-real surfaces in C-2 that contain the origin. If the union of their tangent planes is locally polynomially convex at the origin, then is S-1 boolean OR S-2 locally polynomially convex at the origin? If T (0) S (1) a (c) T (0) S (2) = {0}, then it is a folk result that the answer is yes. We discuss an obstruction to the presumed proof, and provide a different approach. When dim(R)(T0S1 boolean AND T0S2) = 1, we present a geometric condition under which no consistent answer to the above question exists. We then discuss conditions under which we can expect local polynomial convexity.

Polynomial Approximation, Local Polynomial convexity, and Degenerate CR Singularities- II

We provide some conditions for the graph of a Holder-continuous function on (D) over bar, where (D) over bar is a closed disk in C, to be polynomially convex. Almost all sufficient conditions known to date - provided the function (say F) is smooth - arise from versions of the Weierstrass Approximation Theorem on (D) over bar. These conditions often fail to yield any conclusion if rank(R)DF is not maximal on a sufficiently large subset of (D) over bar. We bypass this difficulty by introducing a technique that relies on the interplay of certain plurisubharmonic functions. This technique also allows us to make some observations on the polynomial hull of a graph in C(2) at an isolated complex tangency.

Loop transformations: convexity, pruning, and optimization

High-level loop transformations are a key instrument in mapping computational kernels to effectively exploit the resources in modern processor architectures. Nevertheless, selecting required compositions of loop transformations to achieve this remains a significantly challenging task; current compilers may be off by orders of magnitude in performance compared to hand-optimized programs. To address this fundamental challenge, we first present a convex characterization of all distinct, semantics-preserving, multidimensional affine transformations. We then bring together algebraic, algorithmic, and performance analysis results to design a tractable optimization algorithm over this highly expressive space. Our framework has been implemented and validated experimentally on a representative set of benchmarks running on state-of-the-art multi-core platforms.

Novel Papillomaviruses in Free-Ranging Iberian Bats: No Virus-Host Co-evolution, No Strict Host Specificity, and Hints for Recombination

Papillomaviruses (PVs) are widespread pathogens. However, the extent of PV infections in bats remains largely unknown. This work represents the first comprehensive study of PVs in Iberian bats. We identified four novel PVs in the mucosa of free-ranging Eptesicus serotinus (EserPV1, EserPV2, and EserPV3) and Rhinolophus ferrumequinum (RferPV1) individuals and analyzed their phylogenetic relationships within the viral family. We further assessed their prevalence in different populations of E. serotinus and its close relative E. isabellinus. Although it is frequent to read that PVs co-evolve with their host, that PVs are highly species-specific, and that PVs do not usually recombine, our results suggest otherwise. First, strict virus-host co-evolution is rejected by the existence of five, distantly related bat PV lineages and by the lack of congruence between bats and bat PVs phylogenies. Second, the ability of EserPV2 and EserPV3 to infect two different bat species (E. serotinus and E. isabellinus) argues against strict host specificity. Finally, the description of a second noncoding region in the RferPV1 genome reinforces the view of an increased susceptibility to recombination in the E2-L2 genomic region. These findings prompt the question of whether the prevailing paradigms regarding PVs evolution should be reconsidered.

Novel Papillomaviruses in Free-Ranging Iberian Bats: No Virus-Host Co-evolution, No Strict Host Specificity, and Hints for Recombination

Papillomaviruses (PVs) are widespread pathogens. However, the extent of PV infections in bats remains largely unknown. This work represents the first comprehensive study of PVs in Iberian bats. We identified four novel PVs in the mucosa of free-ranging Eptesicus serotinus (EserPV1, EserPV2, and EserPV3) and Rhinolophus ferrumequinum (RferPV1) individuals and analyzed their phylogenetic relationships within the viral family. We further assessed their prevalence in different populations of E. serotinus and its close relative E. isabellinus. Although it is frequent to read that PVs co-evolve with their host, that PVs are highly species-specific, and that PVs do not usually recombine, our results suggest otherwise. First, strict virus-host co-evolution is rejected by the existence of five, distantly related bat PV lineages and by the lack of congruence between bats and bat PVs phylogenies. Second, the ability of EserPV2 and EserPV3 to infect two different bat species (E. serotinus and E. isabellinus) argues against strict host specificity. Finally, the description of a second noncoding region in the RferPV1 genome reinforces the view of an increased susceptibility to recombination in the E2-L2 genomic region. These findings prompt the question of whether the prevailing paradigms regarding PVs evolution should be reconsidered.