NP-hardness of Deciding Convexity of Quartic Polynomials and Related Problems

We show that unless P=NP, there exists no polynomial time (or even pseudo-polynomial time) algorithm that can decide whether a multivariate polynomial of degree four (or higher even degree) is globally convex. This solves a problem that has been open since 1992 when N. Z. Shor asked for the complexity of deciding convexity for quartic polynomials. We also prove that deciding strict convexity, strong convexity, quasiconvexity, and pseudoconvexity of polynomials of even degree four or higher is strongly NP-hard. By contrast, we show that quasiconvexity and pseudoconvexity of odd degree polynomials can be decided in polynomial time.Comment: 20 page

Procedural and declarative knowledge: an evolutionary perspective

It appears that there are resemblances in the organization of memory and the visual system, although the functions of these faculties differ considerably. In this article, the principles behind this organization are discussed. One important principle regards the distinction between declarative and procedural knowledge, between knowing that and knowing how. Declarative knowledge is considered here not as an alternative kind of knowledge, as is usually the case in theories of memory, but as part of procedural knowledge. In our view this leads to another approach with respect to the distinction. Declarative knowledge has occupied more attention in (cognitive) psychological research than can be justified on the basis of the importance of procedural knowledge for behavior. We also discuss the question whether there are other brain faculties that reflect the same organizational characteristics. We conclude with some speculations about the consequent role of consciousness in such a tentative model

Association of C-reactive protein with bacterial and respiratory syncytial virus-associated pneumonia among children aged <5 years in the PERCH study

Background. Lack of a gold standard for identifying bacterial and viral etiologies of pneumonia has limited evaluation of C-reactive protein (CRP) for identifying bacterial pneumonia. We evaluated the sensitivity and specificity of CRP for identifying bacterial vs respiratory syncytial virus (RSV) pneumonia in the Pneumonia Etiology Research for Child Health (PERCH) multicenter case-control study. Methods. We measured serum CRP levels in cases with World Health Organization-defined severe or very severe pneumonia and a subset of community controls. We evaluated the sensitivity and specificity of elevated CRP for "confirmed" bacterial pneumonia (positive blood culture or positive lung aspirate or pleural fluid culture or polymerase chain reaction [PCR]) compared to "RSV pneumonia" (nasopharyngeal/oropharyngeal or induced sputum PCR-positive without confirmed/suspected bacterial pneumonia). Receiver operating characteristic (ROC) curves were constructed to assess the performance of elevated CRP in distinguishing these cases. Results. Among 601 human immunodeficiency virus (HIV)-negative tested controls, 3% had CRP ≥40 mg/L. Among 119 HIVnegative cases with confirmed bacterial pneumonia, 77% had CRP ≥40 mg/L compared with 17% of 556 RSV pneumonia cases. The ROC analysis produced an area under the curve of 0.87, indicating very good discrimination; a cut-point of 37.1 mg/L best discriminated confirmed bacterial pneumonia (sensitivity 77%) from RSV pneumonia (specificity 82%). CRP ≥100 mg/L substantially improved specificity over CRP ≥40 mg/L, though at a loss to sensitivity. Conclusions. Elevated CRP was positively associated with confirmed bacterial pneumonia and negatively associated with RSV pneumonia in PERCH. CRP may be useful for distinguishing bacterial from RSV-associated pneumonia, although its role in discriminating against other respiratory viral-associated pneumonia needs further study

Cognitive development: Gaming your way out of dyslexia?

A recent study found that dyslexic children trained on action video games show significant improvements on basic measures of both attention and reading ability, suggesting future directions for the study of dyslexia intervention paradigms

Cognitive Development: Gaming Your Way Out of Dyslexia?

SummaryA recent study found that dyslexic children trained on action video games show significant improvements on basic measures of both attention and reading ability, suggesting future directions for the study of dyslexia intervention paradigms

Individual differences in RAN and reading: A response timing analysis

Thirty 8–11-year-old children were administered tests of rapid naming (RAN letters and digits) and reading-related skills. Consistent with the hypothesis that RAN predicts reading because it assesses the ability to establish arbitrary mappings between visual symbols and verbal labels, RAN accounted for independent variance in exception word reading when phonological skills were controlled. Response timing analysis of different components of RAN digits and letters revealed that neither average item duration nor average pause duration were unique predictors of reading skill. However, the number of pauses on digit naming predicted unique variance in exception word reading. Moreover, better readers paused more strategically than poorer readers (e.g. more often at the ends of lines). We suggest that rapid automatised naming may in part reflect differences in strategic control that are a result of differences in reading practice and experience