A Compilation Strategy for Numerical Programs Based on Partial Evaluation

This work demonstrates how partial evaluation can be put to practical use in the domain of high-performance numerical computation. I have developed a technique for performing partial evaluation by using placeholders to propagate intermediate results. For an important class of numerical programs, a compiler based on this technique improves performance by an order of magnitude over conventional compilation techniques. I show that by eliminating inherently sequential data-structure references, partial evaluation exposes the low-level parallelism inherent in a computation. I have implemented several parallel scheduling and analysis programs that study the tradeoffs involved in the design of an architecture that can effectively utilize this parallelism. I present these results using the 9- body gravitational attraction problem as an example.

Memory Usage Inference for Object-Oriented Programs

We present a type-based approach to statically derive symbolic closed-form formulae that characterize the bounds of heap memory usages of programs written in object-oriented languages. Given a program with size and alias annotations, our inference system will compute the amount of memory required by the methods to execute successfully as well as the amount of memory released when methods return. The obtained analysis results are useful for networked devices with limited computational resources as well as embedded software.

On-the-Fly Maintenance of Series-Parallel Relationships in Fork-Join Multithreaded Programs

A key capability of data-race detectors is to determine whether one thread executes logically in parallel with another or whether the threads must operate in series. This paper provides two algorithms, one serial and one parallel, to maintain series-parallel (SP) relationships "on the fly" for fork-join multithreaded programs. The serial SP-order algorithm runs in O(1) amortized time per operation. In contrast, the previously best algorithm requires a time per operation that is proportional to Tarjan’s functional inverse of Ackermann’s function. SP-order employs an order-maintenance data structure that allows us to implement a more efficient "English-Hebrew" labeling scheme than was used in earlier race detectors, which immediately yields an improved determinacy-race detector. In particular, any fork-join program running in T₁ time on a single processor can be checked on the fly for determinacy races in O(T₁) time. Corresponding improved bounds can also be obtained for more sophisticated data-race detectors, for example, those that use locks. By combining SP-order with Feng and Leiserson’s serial SP-bags algorithm, we obtain a parallel SP-maintenance algorithm, called SP-hybrid. Suppose that a fork-join program has n threads, T₁ work, and a critical-path length of T[subscript ∞]. When executed on P processors, we prove that SP-hybrid runs in O((T₁/P + PT[subscript ∞]) lg n) expected time. To understand this bound, consider that the original program obtains linear speed-up over a 1-processor execution when P = O(T₁/T[subscript ∞]). In contrast, SP-hybrid obtains linear speed-up when P = O(√T₁/T[subscript ∞]), but the work is increased by a factor of O(lg n).

Aitchison Geometry for Probability and Likelihood as a new approach to mathematical statistics

The Aitchison vector space structure for the simplex is generalized to a Hilbert space structure A2(P) for distributions and likelihoods on arbitrary spaces. Central notations of statistics, such as Information or Likelihood, can be identified in the algebraical structure of A2(P) and their corresponding notions in compositional data analysis, such as Aitchison distance or centered log ratio transform. In this way very elaborated aspects of mathematical statistics can be understood easily in the light of a simple vector space structure and of compositional data analysis. E.g. combination of statistical information such as Bayesian updating, combination of likelihood and robust M-estimation functions are simple additions/ perturbations in A2(Pprior). Weighting observations corresponds to a weighted addition of the corresponding evidence. Likelihood based statistics for general exponential families turns out to have a particularly easy interpretation in terms of A2(P). Regular exponential families form finite dimensional linear subspaces of A2(P) and they correspond to finite dimensional subspaces formed by their posterior in the dual information space A2(Pprior). The Aitchison norm can identified with mean Fisher information. The closing constant itself is identified with a generalization of the cummulant function and shown to be Kullback Leiblers directed information. Fisher information is the local geometry of the manifold induced by the A2(P) derivative of the Kullback Leibler information and the space A2(P) can therefore be seen as the tangential geometry of statistical inference at the distribution P. The discussion of A2(P) valued random variables, such as estimation functions or likelihoods, give a further interpretation of Fisher information as the expected squared norm of evidence and a scale free understanding of unbiased reasoning

Statistical evidences of cyclic changes in volcanic gas chemistry composition by inverse modelling

The identification of compositional changes in fumarolic gases of active and quiescent volcanoes is one of the most important targets in monitoring programs. From a general point of view, many systematic (often cyclic) and random processes control the chemistry of gas discharges, making difficult to produce a convincing mathematical-statistical modelling. Changes in the chemical composition of volcanic gases sampled at Vulcano Island (Aeolian Arc, Sicily, Italy) from eight different fumaroles located in the northern sector of the summit crater (La Fossa) have been analysed by considering their dependence from time in the period 2000-2007. Each intermediate chemical composition has been considered as potentially derived from the contribution of the two temporal extremes represented by the 2000 and 2007 samples, respectively, by using inverse modelling methodologies for compositional data. Data pertaining to fumaroles F5 and F27, located on the rim and in the inner part of La Fossa crater, respectively, have been used to achieve the proposed aim. The statistical approach has allowed us to highlight the presence of random and not random fluctuations, features useful to understand how the volcanic system works, opening new perspectives in sampling strategies and in the evaluation of the natural risk related to a quiescent volcano

Implementation of training programs in self-regulated learning strategies in Moodle format : Results of a experience in higher education

Resumen tomado de la publicaci??n

The ISSA Pedagogical Standards: a tool to influence quality in early childhood programs

The ISSA Pedagogical Standards were first published in 2001 as a network-developed tool that defined quality in teaching practices and the classroom environment and captured the changes that had occurred in the region since 1994 when the Step by Step Program, an initiative to promote democratic principles in early childhood development and education, was launched. The Program was built on belief that each child has the right to receive maximum support for the development of his or her full potential, and this work should be done in partnership and close cooperation with families, communities and professionals

Mathematical Methods 4

Exercises, exams and solutions for a third year maths course.

Mathematical Methods 2

Exercises, exams and solutions for a first year maths course.

Mathematical Programming

Exam questions and solutions for a third year mathematical programming course.

Mathematical Population Biology

math3052 lecture notes (2008-9)

Abstraction: From Transistors to Computers and from Bits to Programs

Takes the Tanenbaum (Structured Computer Organisation) approach to show how application of successive levels of abstraction allow us to understand how computers are made from transitors and how they are programmed.

Intervention strategies on teachers focused on creating meaningful educational environments for mathematical abilities development

This article describes an intervention process undertaken in a training program for preschool and first grade teachers from public schools in Cali, Colombia. The objective of this process is to provide a space for teachers to reflect on pedagogical practices which allow them to generate educational processes that foster children’s understanding of mathematical knowledge in the classroom. A set of support strategies was presented for helping teachers in the design, analysis and implementation of learning environments as meaningful educational spaces. Furthermore, participants engaged in an analysis of their own intervention modalities to identify which modalities facilitate the development of mathematical abilities in children. In order to ascertain the transformations in the teachers’ learning environments, the mathematical competences and cognitive processes underlying the activities proposed in the classroom, as well as teacher intervention modalities and the types of student participation in classroom activities were examined both before and after the intervention process. Transformations in the teachers’ conceptions about the children’s abilities and their own practices in teaching mathematics in the classroom were evidenced.

SIDUR: development of an information system, using controlled vocabulary designed to the characterization and sample of population with and without disability, attended by Rehabilitation programs, University of Rosario

Introduction: the statistical record used in the Field Academic Programs (PAC for it’s initials in Spanish) of Rehabilitation denotes generalities in the data conceptualization, which complicates the reliable guidance in making decisions and provides a low support for research in rehabilitation and disability. In response, the Research Group in Rehabilitation and Social Integration of Persons with Disabilities has worked on the creation of a registry to characterize the population seen by Rehabilitation PAC. This registry includes the use of the International Classification of Functioning, Disability and Health (ICF) of the WHO. Methodology: the proposed methodology includes two phases: the first one is a descriptive study and the second one involves performing methodology Methontology, which integrates the identification and development of ontology knowledge. This article contextualizes the progress made in the second phase. Results: the development of the registry in 2008, as an information system, included documentary review and the analysis of possible use scenarios to help guide the design and development of the SIDUR system. The system uses the ICF given that it is a terminology standardization that allows the reduction of ambiguity and that makes easier the transformation of health facts into data translatable to information systems. The record raises three categories and a total of 129 variables Conclusions: SIDUR facilitates accessibility to accurate and updated information, useful for decision making and research.

Description and analysis of pulmonary rehabilitation care programs current state in four cities of Colombia

Purpose: there are many studies reporting the benefits of pulmonary rehabilitation, but few of them exhibit the behavior and activities of these services. This article presents the characteristics of services, parts management and training level of team members, in addition to the variables or instruments used to measure the effectiveness and impact in these programs. Method: it was made a cross sectional convenience sample which included seven pulmonary rehabilitation services in four Colombian cities (Bogotá, Medellín, Manizales and Cali), selected by the coverage, for having at least one year of experience and for being formally established and recognized nationwide. The interdisciplinary team of each service answered a survey that was validated through a pilot test and expert consensus. Participation was voluntary. Results: labor onset pulmonary rehabilitation services correspond to an average of a decade, with COPD and asthma pathologies of attention. The programs are characterized by an outpatient treatment with an average duration of eight to twelve weeks, with a frequency of an hour three times a week. Also, the director of the service is regularly a pulmonologist and the coordinator a physiotherapist (57.14%). The posgradual training of these professionals is notable, and they report to have procedural, administrative and communicative skills, but qualify regular there research skills. The physical and technological resources are well tested. 71.42% have done impact studies, but only 28.57% have been published. All have in common training in upper limbs, lower limbs, respiratory muscles, counseling, functional assessment and quality of life. The effectiveness and impact of programs is measured by the walking test, quality of life questionnaires and activities of daily living.