Nuclear elements of degree 6 in the free alternative algebra

We construct five new elements of degree 6 in the nucleus of the free alternative algebra. We use the representation theory of the symmetric group to locate the elements. We use the computer algebra system ALBERT and an extension of ALBERT to express the elements in compact form and to show that these new elements are not a consequence of the known clegree-5 elements in the nucleus. We prove that these five new elements and four known elements form a basis for the subspace of nuclear elements of degree 6. Our calculations are done using modular arithmetic to save memory and time. The calculations can be done in characteristic zero or any prime greater than 6, and similar results are expected. We generated the nuclear elements using prime 103. We check our answer using five other primes.

Nonhomogeneous subalgebras of Lie and special Jordan superalgebras

We consider polynomial identities satisfied by nonhomogeneous subalgebras of Lie and special Jordan superalgebras: we ignore the grading and regard the superalgebra as an ordinary algebra. The Lie case has been studied by Volichenko and Baranov: they found identities in degrees 3, 4 and 5 which imply all the identities in degrees <= 6. We simplify their identities in degree 5, and show that there are no new identities in degree 7. The Jordan case has not previously been studied: we find identities in degrees 3, 4, 5 and 6 which imply all the identities in degrees <= 6, and demonstrate the existence of further new identities in degree 7. our proofs depend on computer algebra: we use the representation theory of the symmetric group, the Hermite normal form of an integer matrix, the LLL algorithm for lattice basis reduction, and the Chinese remainder theorem. (C) 2009 Elsevier Inc. All rights reserved.

Optimal clone identifier based on dynamic rules and process algebra

The rule creation to clone selection in different projects is a hard task to perform by using traditional implementations to control all the processes of the system. The use of an algebraic language is an alternative approach to manage all of system flow in a flexible way. In order to increase the power of versatility and consistency in defining the rules for optimal clone selection, this paper presents the software OCI 2 in which uses process algebra in the flow behavior of the system. OCI 2, controlled by an algebraic approach was applied in the rules elaboration for clone selection containing unique genes in the partial genome of the bacterium Bradyrhizobium elkanii Semia 587 and in the whole genome of the bacterium Xanthomonas axonopodis pv. citri. Copyright© (2009) by the International Society for Research in Science and Technology.

Probabilistic Recursion Theory and Implicit Computational Complexity

In this thesis we provide a characterization of probabilistic computation in itself, from a recursion-theoretical perspective, without reducing it to deterministic computation. More specifically, we show that probabilistic computable functions, i.e., those functions which are computed by Probabilistic Turing Machines (PTM), can be characterized by a natural generalization of Kleene's partial recursive functions which includes, among initial functions, one that returns identity or successor with probability 1/2. We then prove the equi-expressivity of the obtained algebra and the class of functions computed by PTMs. In the the second part of the thesis we investigate the relations existing between our recursion-theoretical framework and sub-recursive classes, in the spirit of Implicit Computational Complexity. More precisely, endowing predicative recurrence with a random base function is proved to lead to a characterization of polynomial-time computable probabilistic functions.

SimuMap: a computational system for spatial modelling

The paper presents a computational system based upon formal principles to run spatial models for environmental processes. The simulator is named SimuMap because it is typically used to simulate spatial processes over a mapped representation of terrain. A model is formally represented in SimuMap as a set of coupled sub-models. The paper considers the situation where spatial processes operate at different time levels, but are still integrated. An example of such a situation commonly occurs in watershed hydrology where overland flow and stream channel flow have very different flow rates but are highly related as they are subject to the same terrain runoff processes. SimuMap is able to run a network of sub-models that express different time-space derivatives for water flow processes. Sub-models may be coded generically with a map algebra programming language that uses a surface data model. To address the problem of differing time levels in simulation, the paper: (i) reviews general approaches for numerical solvers, (ii) considers the constraints that need to be enforced to use more adaptive time steps in discrete time specified simulations, and (iii) scaling transfer rates in equations that use different time bases for time-space derivatives. A multistep scheme is proposed for SimuMap. This is presented along with a description of its visual programming interface, its modelling formalisms and future plans. (C) 2003 Elsevier Ltd. All rights reserved.

A retrospective-longitudinal examination of the relationship between apportionment of seat time in community-college algebra courses and student academic performance

During the past decade, there has been a dramatic increase by postsecondary institutions in providing academic programs and course offerings in a multitude of formats and venues (Biemiller, 2009; Kucsera & Zimmaro, 2010; Lang, 2009; Mangan, 2008). Strategies pertaining to reapportionment of course-delivery seat time have been a major facet of these institutional initiatives; most notably, within many open-door 2-year colleges. Often, these enrollment-management decisions are driven by the desire to increase market-share, optimize the usage of finite facility capacity, and contain costs, especially during these economically turbulent times. So, while enrollments have surged to the point where nearly one in three 18-to-24 year-old U.S. undergraduates are community college students (Pew Research Center, 2009), graduation rates, on average, still remain distressingly low (Complete College America, 2011). Among the learning-theory constructs related to seat-time reapportionment efforts is the cognitive phenomenon commonly referred to as the spacing effect, the degree to which learning is enhanced by a series of shorter, separated sessions as opposed to fewer, more massed episodes. This ex post facto study explored whether seat time in a postsecondary developmental-level algebra course is significantly related to: course success; course-enrollment persistence; and, longitudinally, the time to successfully complete a general-education-level mathematics course. Hierarchical logistic regression and discrete-time survival analysis were used to perform a multi-level, multivariable analysis of a student cohort (N = 3,284) enrolled at a large, multi-campus, urban community college. The subjects were retrospectively tracked over a 2-year longitudinal period. The study found that students in long seat-time classes tended to withdraw earlier and more often than did their peers in short seat-time classes (p < .05). Additionally, a model comprised of nine statistically significant covariates (all with p-values less than .01) was constructed. However, no longitudinal seat-time group differences were detected nor was there sufficient statistical evidence to conclude that seat time was predictive of developmental-level course success. A principal aim of this study was to demonstrate—to educational leaders, researchers, and institutional-research/business-intelligence professionals—the advantages and computational practicability of survival analysis, an underused but more powerful way to investigate changes in students over time.

Inductive Theorem Proving and Computer Algebra in the Mathweb Software Bus

Reasoning systems have reached a high degree of maturity in the last decade. However, even the most successful systems are usually not general purpose problem solvers but are typically specialised on problems in a certain domain. The MathWeb SOftware Bus (Mathweb-SB) is a system for combining reasoning specialists via a common osftware bus. We described the integration of the lambda-clam systems, a reasoning specialist for proofs by induction, into the MathWeb-SB. Due to this integration, lambda-clam now offers its theorem proving expertise to other systems in the MathWeb-SB. On the other hand, lambda-clam can use the services of any reasoning specialist already integrated. We focus on the latter and describe first experimnents on proving theorems by induction using the computational power of the MAPLE system within lambda-clam.

A Retrospective-Longitudinal Examination of the Relationship between Apportionment of Seat Time in Community-College Algebra Courses and Student Academic Performance

During the past decade, there has been a dramatic increase by postsecondary institutions in providing academic programs and course offerings in a multitude of formats and venues (Biemiller, 2009; Kucsera & Zimmaro, 2010; Lang, 2009; Mangan, 2008). Strategies pertaining to reapportionment of course-delivery seat time have been a major facet of these institutional initiatives; most notably, within many open-door 2-year colleges. Often, these enrollment-management decisions are driven by the desire to increase market-share, optimize the usage of finite facility capacity, and contain costs, especially during these economically turbulent times. So, while enrollments have surged to the point where nearly one in three 18-to-24 year-old U.S. undergraduates are community college students (Pew Research Center, 2009), graduation rates, on average, still remain distressingly low (Complete College America, 2011). Among the learning-theory constructs related to seat-time reapportionment efforts is the cognitive phenomenon commonly referred to as the spacing effect, the degree to which learning is enhanced by a series of shorter, separated sessions as opposed to fewer, more massed episodes. This ex post facto study explored whether seat time in a postsecondary developmental-level algebra course is significantly related to: course success; course-enrollment persistence; and, longitudinally, the time to successfully complete a general-education-level mathematics course. Hierarchical logistic regression and discrete-time survival analysis were used to perform a multi-level, multivariable analysis of a student cohort (N = 3,284) enrolled at a large, multi-campus, urban community college. The subjects were retrospectively tracked over a 2-year longitudinal period. The study found that students in long seat-time classes tended to withdraw earlier and more often than did their peers in short seat-time classes (p < .05). Additionally, a model comprised of nine statistically significant covariates (all with p-values less than .01) was constructed. However, no longitudinal seat-time group differences were detected nor was there sufficient statistical evidence to conclude that seat time was predictive of developmental-level course success. A principal aim of this study was to demonstrate—to educational leaders, researchers, and institutional-research/business-intelligence professionals—the advantages and computational practicability of survival analysis, an underused but more powerful way to investigate changes in students over time.

A novel polar-based human face recognition computational model

Motivated by a recently proposed biologically inspired face recognition approach, we investigated the relation between human behavior and a computational model based on Fourier-Bessel (FB) spatial patterns. We measured human recognition performance of FB filtered face images using an 8-alternative forced-choice method. Test stimuli were generated by converting the images from the spatial to the FB domain, filtering the resulting coefficients with a band-pass filter, and finally taking the inverse FB transformation of the filtered coefficients. The performance of the computational models was tested using a simulation of the psychophysical experiment. In the FB model, face images were first filtered by simulated V1- type neurons and later analyzed globally for their content of FB components. In general, there was a higher human contrast sensitivity to radially than to angularly filtered images, but both functions peaked at the 11.3-16 frequency interval. The FB-based model presented similar behavior with regard to peak position and relative sensitivity, but had a wider frequency band width and a narrower response range. The response pattern of two alternative models, based on local FB analysis and on raw luminance, strongly diverged from the human behavior patterns. These results suggest that human performance can be constrained by the type of information conveyed by polar patterns, and consequently that humans might use FB-like spatial patterns in face processing.

Computational adjustment technique for digital mammographic images based on the digitizer characteristic curve

We evaluated the performance of a novel procedure for segmenting mammograms and detecting clustered microcalcifications in two types of image sets obtained from digitization of mammograms using either a laser scanner, or a conventional ""optical"" scanner. Specific regions forming the digital mammograms were identified and selected, in which clustered microcalcifications appeared or not. A remarkable increase in image intensity was noticed in the images from the optical scanner compared with the original mammograms. A procedure based on a polynomial correction was developed to compensate the changes in the characteristic curves from the scanners, relative to the curves from the films. The processing scheme was applied to both sets, before and after the polynomial correction. The results indicated clearly the influence of the mammogram digitization on the performance of processing schemes intended to detect microcalcifications. The image processing techniques applied to mammograms digitized by both scanners, without the polynomial intensity correction, resulted in a better sensibility in detecting microcalcifications in the images from the laser scanner. However, when the polynomial correction was applied to the images from the optical scanner, no differences in performance were observed for both types of images. (C) 2008 SPIE and IS&T [DOI: 10.1117/1.3013544]

Reactivity, photolability, and computational studies of the ruthenium nitrosyl complex with a substituted cyclam fac-[Ru(NO)Cl(2)(kappa(3)N(4),N(8),N(11)(1-carboxypropyl)cyclam)]Cl center dot H(2)O

Chemical reactivity, photolability, and computational studies of the ruthenium nitrosyl complex with a substituted cyclam, fac-[Ru(NO)Cl(2)(kappa(3)N(4),N(8),N(11)(1-carboxypropyl)cyclam)]Cl center dot H(2)O ((1-carboxypropyl) cyclam = 3-(1,4,8,11-tetraazacyclotetradecan-1-yl) propionic acid)), (I) are described. Chloride ligands do not undergo aquation reactions (at 25 degrees C, pH 3). The rate of nitric oxide (NO) dissociation (k(obs-NO)) upon reduction of I is 2.8 s(-1) at 25 +/- 1 degrees C (in 0.5 mol L(-1) HCl), which is close to the highest value found for related complexes. The uncoordinated carboxyl of I has a pK(a) of similar to 3.3, which is close to that of the carboxyl of the non coordinated (1-carboxypropyl) cyclam (pK(a) = 3.4). Two additional pK(a) values were found for I at similar to 8.0 and similar to 11.5. Upon electrochemical reduction or under irradiation with light (lambda(irr) = 350 or 520 nm; pH 7.4), I releases NO in aqueous solution. The cyclam ring N bound to the carboxypropyl group is not coordinated, resulting in a fac configuration that affects the properties and chemical reactivities of I, especially as NO donor, compared with analogous trans complexes. Among the computational models tested, the B3LYP/ECP28MDF, cc-pVDZ resulted in smaller errors for the geometry of I. The computational data helped clarify the experimental acid-base equilibria and indicated the most favourable site for the second deprotonation, which follows that of the carboxyl group. Furthermore, it showed that by changing the pH it is possible to modulate the electron density of I with deprotonation. The calculated NO bond length and the Ru/NO charge ratio indicated that the predominant canonical structure is [Ru(III)NO], but the Ru-NO bond angles and bond index (b.i.) values were less clear; the angles suggested that [Ru(II)NO(+)] could contribute to the electronic structure of I and b.i. values indicated a contribution from [Ru(IV)NO(-)]. Considering that some experimental data are consistent with a [Ru(II)NO(+)] description, while others are in agreement with [Ru(III)NO], the best description for I would be a linear combination of the three canonical forms, with a higher weight for [Ru(II)NO(+)] and [Ru(III)NO].

Pseudodifferential operators with C*-algebra-valued symbols: Abstract characterizations

Given a separable unital C*-algebra C with norm parallel to center dot parallel to, let E-n denote the Banach-space completion of the C-valued Schwartz space on R-n with norm parallel to f parallel to(2)=parallel to < f, f >parallel to(1/2), < f, g >=integral f(x)* g(x)dx. The assignment of the pseudodifferential operator A=a(x,D) with C-valued symbol a(x,xi) to each smooth function with bounded derivatives a is an element of B-C(R-2n) defines an injective mapping O, from B-C(R-2n) to the set H of all operators with smooth orbit under the canonical action of the Heisenberg group on the algebra of all adjointable operators on the Hilbert module E-n. In this paper, we construct a left-inverse S for O and prove that S is injective if C is commutative. This generalizes Cordes' description of H in the scalar case. Combined with previous results of the second author, our main theorem implies that, given a skew-symmetric n x n matrix J and if C is commutative, then any A is an element of H which commutes with every pseudodifferential operator with symbol F(x+J xi), F is an element of B-C(R-n), is a pseudodifferential operator with symbol G(x - J xi), for some G is an element of B-C(R-n). That was conjectured by Rieffel.

Fault Detection in Power Distribution Systems Using Automated Integration of Computational Intelligence Tools

The main purpose of this paper is to present architecture of automated system that allows monitoring and tracking in real time (online) the possible occurrence of faults and electromagnetic transients observed in primary power distribution networks. Through the interconnection of this automated system to the utility operation center, it will be possible to provide an efficient tool that will assist in decisionmaking by the Operation Center. In short, the desired purpose aims to have all tools necessary to identify, almost instantaneously, the occurrence of faults and transient disturbances in the primary power distribution system, as well as to determine its respective origin and probable location. The compilations of results from the application of this automated system show that the developed techniques provide accurate results, identifying and locating several occurrences of faults observed in the distribution system.

Wavelet-Galerkin method for one-dimensional elastoplasticity and damage problems: Constitutive modeling and computational aspects

This work presents an analysis of the wavelet-Galerkin method for one-dimensional elastoplastic-damage problems. Time-stepping algorithm for non-linear dynamics is presented. Numerical treatment of the constitutive models is developed by the use of return-mapping algorithm. For spacial discretization we can use wavelet-Galerkin method instead of standard finite element method. This approach allows to locate singularities. The discrete formulation developed can be applied to the simulation of one-dimensional problems for elastic-plastic-damage models. (C) 2007 Elsevier Inc. All rights reserved.