Paulo J. S. Silva

Gene Expression Profile Associated with Response to Doxorubicin-Based Therapy in Breast Cancer

Purpose: This study was designed to identify genes that could predict response to doxorubicin-based primary chemotherapy in breast cancer patients. Experimental Design: Biopsy samples were obtained before primary treatment with doxorubicin and cyclophosphamide. RNA was extracted and amplified and gene expression was analyzed using cDNA microarrays. Results: Response to chemotherapy was evaluated in 51 patients, and based on Response Evaluation Criteria in Solid Tumors guidelines, 42 patients, who presented at least a partial response (≥30% reduction in tumor dimension), were classified as responsive. Gene profile of samples, divided into training set (n = 38) and independent validation set (n = 13), were at first analyzed against a cDNA microarray platform containing 692 genes. Unsupervised clustering could not separate responders from nonresponders. A classifier was identified comprising EMILIN1, FAM14B, and PBEF, which however could not correctly classify samples included in the validation set. Our next step was to analyze gene profile in a more comprehensive cDNA microarray platform, containing 4,608 open reading frame expressed sequence tags. Seven samples of the initial training set (all responder patients) could not be analyzed. Unsupervised clustering could correctly group all the resistant samples as well as at least 85% of the sensitive samples. Additionally, a classifier, including PRSS11, MTSS1, and CLPTM1, could correctly distinguish 95.4% of the 44 samples analyzed, with only two misclassifications, one sensitive sample and one resistant tumor. The robustness of this classifier is 2.5 greater than the first one. Conclusion: A trio of genes might potentially distinguish doxorubicin-responsive from nonresponsive tumors, but further validation by a larger number of samples is still needed.

A relaxed constant positive linear dependence constraint qualification and applications

In this work we introduce a relaxed version of the constant positive linear dependence constraint qualification (CPLD) that we call RCPLD. This development is inspired by a recent generalization of the constant rank constraint qualification by Minchenko and Stakhovski that was called RCRCQ. We show that RCPLD is enough to ensure the convergence of an augmented Lagrangian algorithm and that it asserts the validity of an error bound. We also provide proofs and counter-examples that show the relations of RCRCQ and RCPLD with other known constraint qualifications. In particular, RCPLD is strictly weaker than CPLD and RCRCQ, while still stronger than Abadie’s constraint qualification. We also verify that the second order necessary optimality condition holds under RCRCQ.

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, ...

A practical relative error criterion for augmented Lagrangians

This paper develops a new error criterion for the approximate minimization of augmented Lagrangian subproblems. This criterion is practical since it is readily testable given only a gradient (or subgradient) of the augmented Lagrangian. It is also “relative” in the sense of relative error criteria for proximal point algorithms: in particular, it uses a single relative tolerance parameter, rather than a summable parameter sequence. Our analysis first describes an abstract version of the criterion within Rockafellar’s general parametric convex duality framework, and proves a global convergence result for the resulting algorithm. Specializing this algorithm to a standard formulation of convex programming produces a version of the classical augmented Lagrangian method with a novel inexact solution condition for the subproblems. Finally, we present computational results drawn from the CUTE test set—including many nonconvex problems—indicating that the approach works well in practice.

Feature selection algorithms to find strong genes

The cDNA microarray technology allows us to estimate the expression of thousands of genes of a given tissue. It is natural then to use such information to classify different cell states, like healthy or diseased, or one particular type of cancer or another. However, usually the number of microarray samples is very small and leads to a classification problem with only tens of samples and thousands of features. Recently, Kim et al. proposed to use a parameterized distribution based on the original sample set as a way to attenuate such difficulty. Genes that contribute to good classifiers in such setting are called strong. In this paper, we investigate how to use feature selection techniques to speed up the quest for strong genes. The idea is to use a feature selection algorithm to filter the gene set considered before the original strong feature technique, that is based on a combinatorial search. The filtering helps us to find very good strong gene sets, without resorting to super computers. We have tested several filter options and compared the strong genes obtained with the ones got by the original full combinatorial search.

Rescaling and Stepsize Selection in Proximal Methods Using Separable Generalized Distances

This paper presents a convergence proof technique for a broad class of proximal algorithms in which the perturbation term is separable and may contain barriers enforcing interval constraints. There are two key ingredients in the analysis: a mild regularity condition on the differential behavior of the barrier as one approaches an interval boundary and a lower stepsize limit that takes into account the curvature of the proximal term. We give two applications of our approach. First, we prove subsequential convergence of a very broad class of proximal minimization algorithms for convex optimization, where different stepsizes can be used for each coordinate. Applying these methods to the dual of a convex program, we obtain a wide class of multiplier methods with subsequential convergence of both primal and dual iterates and independent adjustment of the penalty parameter for each constraint. The adjustment rules for the penalty parameters generalize a well-established scheme for the exponential method of multipliers. The results may also be viewed as a generalization of recent work by Ben-Tal and Zibulevsky [SIAM J. Optim, 7 (1997), pp. 347--366] and Auslender, Teboulle, and Ben-Tiba [ Comput. Optim. Appl., 12 (1999), pp. 31--40; Math. Oper. Res., 24 (1999), pp. 645--668] on methods derived from

Being Extreme in the Classroom: experiences Teaching XP

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Transcriptional Alterations Related to Neuropathology and Clinical Manifestation of Alzheimer's Disease

-divergences. The second application established full convergence, under a novel stepsize condition, of Bregman-function-based proximal methods for general monotone operator problems over a box. Prior results in this area required strong restrictive assumptions on the monotone operator.

A CONE-CONTINUITY CONSTRAINT QUALIFICATION AND ALGORITHMIC CONSEQUENCES

Agile Methods propose a new way of looking at software development that questions many of the beliefs of conventional Software Engineering. Agile methods such as Extreme Programming (XP) have been very effective in producing high-quality software in real-world projects with strict time constraints.Nevertheless, most university courses and industrial training programs are still based on old-style heavyweight methods. This article, based on our experiences teaching XP in academic and industrial environments, presents effective ways of teaching students and professionals on how to develop high-quality software following the principles of agile software development. We also discuss related work in the area, describe real-world cases, and discuss open problems not yet resolved.

An Exact Algorithm for Optimal MAE Stack Filter Design

Alzheimer’s disease (AD) is the most common cause of dementia in the human population, characterized by a spectrum of neuropathological abnormalities that results in memory impairment and loss of other cognitive processes as well as the presence of non-cognitive symptoms. Transcriptomic analyses provide an important approach to elucidating the pathogenesis of complex diseases like AD, helping to figure out both pre-clinical markers to identify susceptible patients and the early pathogenic mechanisms to serve as therapeutic targets. This study provides the gene expression profile of postmortem brain tissue from subjects with clinic-pathological AD (Braak IV, V, or V and CERAD B or C; and CDR ≥1), preclinical AD (Braak IV, V, or VI and CERAD B or C; and CDR = 0), and healthy older individuals (Braak ≤ II and CERAD 0 or A; and CDR = 0) in order to establish genes related to both AD neuropathology and clinical emergence of dementia. Based on differential gene expression, hierarchical clustering and network analysis, genes involved in energy metabolism, oxidative stress, DNA damage/repair, senescence, and transcriptional regulation were implicated with the neuropathology of AD; a transcriptional profile related to clinical manifestation of AD could not be detected with reliability using differential gene expression analysis, although genes involved in synaptic plasticity, and cell cycle seems to have a role revealed by gene classifier. In conclusion, the present data suggest gene expression profile changes secondary to the development of AD-related pathology and some genes that appear to be related to the clinical manifestation of dementia in subjects with significant AD pathology, making necessary further investigations to better understand these transcriptional findings on the pathogenesis and clinical emergence of AD.