Approximating a class of combinatorial problems with rational objective function

In the late seventies, Megiddo proposed a way to use an algorithm for the problem of minimizing a linear function a(0) + a(1)x(1) + ... + a(n)x(n) subject to certain constraints to solve the problem of minimizing a rational function of the form (a(0) + a(1)x(1) + ... + a(n)x(n))/(b(0) + b(1)x(1) + ... + b(n)x(n)) subject to the same set of constraints, assuming that the denominator is always positive. Using a rather strong assumption, Hashizume et al. extended Megiddo`s result to include approximation algorithms. Their assumption essentially asks for the existence of good approximation algorithms for optimization problems with possibly negative coefficients in the (linear) objective function, which is rather unusual for most combinatorial problems. In this paper, we present an alternative extension of Megiddo`s result for approximations that avoids this issue and applies to a large class of optimization problems. Specifically, we show that, if there is an alpha-approximation for the problem of minimizing a nonnegative linear function subject to constraints satisfying a certain increasing property then there is an alpha-approximation (1 1/alpha-approximation) for the problem of minimizing (maximizing) a nonnegative rational function subject to the same constraints. Our framework applies to covering problems and network design problems, among others.

The first group (co)homology of a group G with coefficients in some G-modules

Let G be a group. We give some formulas for the first group homology and cohomology of a group G with coefficients in an arbitrary G-module (Z) over tilde. More explicit calculations are done in the special cases of free groups, abelian groups and nilpotent groups. We also perform calculations for certain G-module M, by reducing it to the case where the coefficient is a G-module (Z) over tilde. As a result of the well known equalities H-1(X, M) = H-1(pi(1)(X), M) and H-1(X, M) = H-1(pi(1) (X), M), for any G-module M, we are able to calculate the first homology and cohomology groups of topological spaces with certain local system of coefficients.

Variance component estimates applying random regression models for test-day milk yield in Caracu heifers (Bos taurus Artiodactyla, Bovidae)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On Complementary Root Locus of Biproper Transfer Functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

One-sided and two-sided Green's functions

We discuss the one-sided Green's function, associated with an initial value problem and the two-sided Green's function related to a boundary value problem. We present a specific calculation associated with a differential equation with constant coefficients. For both problems, we also present the Laplace integral transform as another methodology to calculate these Green's functions and conclude which is the most convenient one. An incursion in the so-called fractional Green's function is also presented. As an example, we discuss the isotropic harmonic oscillator.

A generalized finite element method with global-local enrichment functions for confined plasticity problems

The main feature of partition of unity methods such as the generalized or extended finite element method is their ability of utilizing a priori knowledge about the solution of a problem in the form of enrichment functions. However, analytical derivation of enrichment functions with good approximation properties is mostly limited to two-dimensional linear problems. This paper presents a procedure to numerically generate proper enrichment functions for three-dimensional problems with confined plasticity where plastic evolution is gradual. This procedure involves the solution of boundary value problems around local regions exhibiting nonlinear behavior and the enrichment of the global solution space with the local solutions through the partition of unity method framework. This approach can produce accurate nonlinear solutions with a reduced computational cost compared to standard finite element methods since computationally intensive nonlinear iterations can be performed on coarse global meshes after the creation of enrichment functions properly describing localized nonlinear behavior. Several three-dimensional nonlinear problems based on the rate-independent J (2) plasticity theory with isotropic hardening are solved using the proposed procedure to demonstrate its robustness, accuracy and computational efficiency.

Police Interviews with Victims and Suspects of Violent and Sexual Crimes : Interviewee's experiences and interview outcomes

The police interview is one of the most important investigative tools that law enforcement has close at hand, and police interview methods have changed during the twentieth century. A good police interview is conducted in the frame of the law, is governed by the interview goal, and is influenced by facilitating factors that may affect the elicited report. The present doctoral dissertation focuses on police interviews in cases of very serious crimes of violence and sexual offences. Results reveal crime victims’ and perpetrators’ experiences of being interviewed and police officers’ attitudes towards conducting interviews related to traumatizing crimes. Study 1 revealed that when police officers interviewed murderers and sexual offenders, the interviewees perceived attitudes characterized by either dominance or humanity. Police interviews marked by dominance and suspects’ responses of anxiety were mainly associated with a higher proportion of denials, whereas an approach marked by humanity, and responses of being respected were significantly associated with admissions. In line with Study 1, the victims of rape and aggravated assault in Study 2 also revealed the experience of two police interview styles, where an interviewing style marked by dominance and responses of anxiety was significantly associated with crime victims’ omissions of information. Moreover, a humanitarian interviewing style, and crime victims’ feelings of being respected and co-operative, was significantly related to crime victims providing all information from painful events. Special squad police officers’ attitudes towards interviewing crime victims, in Study 3, also showed a humanitarian approach and two dominant approaches, one affective and the other refusing. The attitude towards interviewing suspects of crimes in focus revealed humanitarian and dominant interviewing attitudes, and an approach marked by kindness. The present thesis shows that, during their entire career, an overwhelming majority of the special squad police officers have experienced stressful events during patrol as well as investigative duty. Results show that symptoms from stressful event exposures and coping mechanisms are associated with negative attitudes towards interviewing suspects and supportive attitudes towards crime victim interviews. Thus, experiences from stressful exposures may automatically activate ego-defensive functions that automatically generate dominant attitudes. Moreover, it is important to offer police officers who have been exposed to stressful events the opportunity to work through their experiences, for example, through debriefing procedures. After debriefings, police officers are better prepared to meet crime victims and suspects and, through conscious closed-loop processes, to conduct police interviews without awaking ego-defensive functions.

Video-based quantification of body movement during social interaction indicates the severity of negative symptoms in patients with schizophrenia

In schizophrenia, nonverbal behavior, including body movement, is of theoretical and clinical importance. Although reduced nonverbal expressiveness is a major component of the negative symptoms encountered in schizophrenia, few studies have objectively assessed body movement during social interaction. In the present study, 378 brief, videotaped role-play scenes involving 27 stabilized outpatients diagnosed with paranoid-type schizophrenia were analyzed using Motion Energy Analysis (MEA). This method enables the objective measuring of body movement in conjunction with ordinary video recordings. Correlations between movement parameters (percentage of time in movement, movement speed) and symptom ratings from independent PANSS interviews were calculated. Movement parameters proved to be highly reliable. In keeping with predictions, reduced movement and movement speed correlated with negative symptoms. Accordingly, in patients who exhibited noticeable movement for less than 20% of the observation time, prominent negative symptoms were highly probable. As a control measure, the percentage of movement exhibited by the patients during role-play scenes was compared to that of their normal interactants. Patients with negative symptoms differed from normal interactants by showing significantly reduced head and body movement. Two specific positive symptoms were possibly related to movement parameters: suspiciousness tended to correlate with reduced head movement, and the expression of unusual thought content tended to relate to increased movement. Overall, a close and theoretically meaningful association between the objective movement parameters and the symptom profiles was found. MEA appears to be an objective, reliable and valid method for quantifying nonverbal behavior, an aspect which may furnish new insights into the processes related to reduced expressiveness in schizophrenia.

Impaired verbal memory in Parkinson disease: relationship to prefrontal dysfunction and somatosensory discrimination

OBJECTIVE: To study the neurocognitive profile and its relationship to prefrontal dysfunction in non-demented Parkinson's disease (PD) with deficient haptic perception. METHODS: Twelve right-handed patients with PD and 12 healthy control subjects underwent thorough neuropsychological testing including Rey complex figure, Rey auditory verbal and figural learning test, figural and verbal fluency, and Stroop test. Test scores reflecting significant differences between patients and healthy subjects were correlated with the individual expression coefficients of one principal component, obtained in a principal component analysis of an oxygen-15-labeled water PET study exploring somatosensory discrimination that differentiated between the two groups and involved prefrontal cortices. RESULTS: We found significantly decreased total scores for the verbal learning trials and verbal delayed free recall in PD patients compared with normal volunteers. Further analysis of these parameters using Spearman's ranking correlation showed a significantly negative correlation of deficient verbal recall with expression coefficients of the principal component whose image showed a subcortical-cortical network, including right dorsolateral-prefrontal cortex, in PD patients. CONCLUSION: PD patients with disrupted right dorsolateral prefrontal cortex function and associated diminished somatosensory discrimination are impaired also in verbal memory functions. A negative correlation between delayed verbal free recall and PET activation in a network including the prefrontal cortices suggests that verbal cues and accordingly declarative memory processes may be operative in PD during activities that demand sustained attention such as somatosensory discrimination. Verbal cues may be compensatory in nature and help to non-specifically enhance focused attention in the presence of a functionally disrupted prefrontal cortex.

Continued fractions built from convex sets and convex functions

In a partially ordered semigroup with the duality (or polarity) transform, it is pos- sible to define a generalisation of continued fractions. General sufficient conditions for convergence of continued fractions are provided. Two particular applications concern the cases of convex sets with the Minkowski addition and the polarity transform and the family of non-negative convex functions with the Legendre–Fenchel and Artstein-Avidan–Milman transforms.

End4p/Sla2p Interacts with Actin-associated Proteins for Endocytosis in Saccharomyces cerevisiae

end4–1 was isolated as a temperature-sensitive endocytosis mutant. We cloned and sequenced END4 and found that it is identical to SLA2/MOP2. This gene is required for growth at high temperature, viability in the absence of Abp1p, polarization of the cortical actin cytoskeleton, and endocytosis. We used a mutational analysis of END4 to correlate in vivo functions with regions of End4p and we found that two regions of End4p participate in endocytosis but that the talin-like domain of End4p is dispensable. The N-terminal domain of End4p is required for growth at high temperature, endocytosis, and actin organization. A central coiled-coil domain of End4p is necessary for formation of a soluble sedimentable complex. Furthermore, this domain has an endocytic function that is redundant with the function(s) of ABP1 and SRV2. The endocytic function of Abp1p depends on its SH3 domain. In addition we have isolated a recessive negative allele of SRV2 that is defective for endocytosis. Combined biochemical, functional, and genetic analysis lead us to propose that End4p may mediate endocytosis through interaction with other actin-associated proteins, perhaps Rvs167p, a protein essential for endocytosis.

Mathematical approach for predicting non-negative tristimulus values using the CAT02 chromatic adaptation transform

It has been reported that for certain colour samples, the chromatic adaptation transform CAT02 imbedded in the CIECAM02 colour appearance model predicts corresponding colours with negative tristimulus values (TSVs), which can cause problems in certain applications. To overcome this problem, a mathematical approach is proposed for modifying CAT02. This approach combines a non-negativity constraint for the TSVs of corresponding colours with the minimization of the colour differences between those values for the corresponding colours obtained by visual observations and the TSVs of the corresponding colours predicted by the model, which is a constrained non-linear optimization problem. By solving the non-linear optimization problem, a new matrix is found. The performance of the CAT02 transform with various matrices including the original CAT02 matrix, and the new matrix are tested using visual datasets and the optimum colours. Test results show that the CAT02 with the new matrix predicted corresponding colours without negative TSVs for all optimum colours and the colour matching functions of the two CIE standard observers under the test illuminants considered. However, the accuracy with the new matrix for predicting the visual data is approximately 1 CIELAB colour difference unit worse compared with the original CAT02. This indicates that accuracy has to be sacrificed to achieve the non-negativity constraint for the TSVs of the corresponding colours.

The negative effects of failed service recoveries

Research has shown that more than half of attempted recovery efforts fail, producing a ‘double deviation’ effect. Surprisingly, these double deviation effects have received little attention in marketing literature. This paper examines what happens after these critical encounters, which behavior or set of behaviors the customers are prone to follow and how customers’ perceptions of the firm’s recovery efforts influence these behaviors. For the analysis of choice of the type of response (complaining, exit, complaining and exit, and no-switching), we estimate multinomial Logit models with random coefficients (RCL). The results of our study show that magnitude of service failure, explanations, apologies, perceived justice, angry and frustration felt by the customer, and satisfaction with service recovery have a significant effect on customers’ choice of the type of response. Implications from the findings are offered.

Stability in Linear Optimization Under Perturbations of the Left-Hand Side Coefficients

This paper studies stability properties of linear optimization problems with finitely many variables and an arbitrary number of constraints, when only left hand side coefficients can be perturbed. The coefficients of the constraints are assumed to be continuous functions with respect to an index which ranges on certain compact Hausdorff topological space, and these properties are preserved by the admissible perturbations. More in detail, the paper analyzes the continuity properties of the feasible set, the optimal set and the optimal value, as well as the preservation of desirable properties (boundedness, uniqueness) of the feasible and of the optimal sets, under sufficiently small perturbations.

Benefit finding in multiple sclerosis, and associations with positive and negative outcomes

This study examined the direct and stress-buffering effects of benefit finding on positive and negative outcomes. A total of 502 people with multiple sclerosis completed a questionnaire at Time 1 and, 3 months later, at Time 2 (n = 404). Measures of illness were collected at Time 1, and number of problems, stress appraisal, benefit finding, subjective health, and negative (global distress, negative affect) and positive (life satisfaction, positive affect, dyadic adjustment) outcomes were measured at Time 2. Factor analyses showed the Benefit Finding scale to have 2 dimensions: Personal Growth and Family Relations Growth. Hierarchical regressions showed that after controlling for the effects of demographics, illness, problems, and appraisal, benefit finding showed strong direct effects on the positive outcomes. Benefit finding did not have a direct effect on distress, or subjective health but had a weak association with negative affect. Family Relations Growth had a stress-buffering effect on distress.