On the distribution of the signs of the conjugates of the cyclotomic units in the maximal real subfield of the qth cyclotomic field, q A prime

Let F = Ǫ(ζ + ζ ^–1) be the maximal real subfield of the cyclotomic field Ǫ(ζ) where ζ is a primitive qth root of unity and q is an odd rational prime. The numbers u₁=-1, u_k=(ζ^k-ζ^-k)/(ζ-ζ^-1), k=2,…,p, p=(q-1)/2, are units in F and are called the cyclotomic units. In this thesis the sign distribution of the conjugates in F of the cyclotomic units is studied.

Let G(F/Ǫ) denote the Galoi's group of F over Ǫ, and let V denote the units in F. For each σϵ G(F/Ǫ) and μϵV define a mapping sgn_σ: V→GF(2) by sgn_σ(μ) = 1 iff σ(μ) ˂ 0 and sgn_σ(μ) = 0 iff σ(μ) ˃ 0. Let {σ₁, ... , σ_p} be a fixed ordering of G(F/Ǫ). The matrix M_q=(sgn_σj(v_i) ) , i, j = 1, ... , p is called the matrix of cyclotomic signatures. The rank of this matrix determines the sign distribution of the conjugates of the cyclotomic units. The matrix of cyclotomic signatures is associated with an ideal in the ring GF(2) [x] / (x^p+ 1) in such a way that the rank of the matrix equals the GF(2)-dimension of the ideal. It is shown that if p = (q-1)/ 2 is a prime and if 2 is a primitive root mod p, then M_q is non-singular. Also let p be arbitrary, let ℓ be a primitive root mod q and let L = {i | 0 ≤ i ≤ p-1, the least positive residue of defined by ℓⁱ mod q is greater than p}. Let H_q(x) ϵ GF(2)[x] be defined by H_q(x) = g. c. d. ((Σ xⁱ/I ϵ L) (x+1) + 1, x^p + 1). It is shown that the rank of M_q equals the difference p - degree H_q(x).

Further results are obtained by using the reciprocity theorem of class field theory. The reciprocity maps for a certain abelian extension of F and for the infinite primes in F are associated with the signs of conjugates. The product formula for the reciprocity maps is used to associate the signs of conjugates with the reciprocity maps at the primes which lie above (2). The case when (2) is a prime in F is studied in detail. Let T denote the group of totally positive units in F. Let U be the group generated by the cyclotomic units. Assume that (2) is a prime in F and that p is odd. Let F₍₂₎ denote the completion of F at (2) and let V₍₂₎ denote the units in F₍₂₎. The following statements are shown to be equivalent. 1) The matrix of cyclotomic signatures is non-singular. 2) U∩T = U². 3) U∩F²₍₂₎ = U². 4) V₍₂₎/ V₍₂₎² = ˂v₁ V₍₂₎²˃ ʘ…ʘ˂v_p V₍₂₎²˃ ʘ ˂3V₍₂₎²˃.

The rank of M_q was computed for 5≤q≤929 and the results appear in tables. On the basis of these results and additional calculations the following conjecture is made: If q and p = (q -1)/ 2 are both primes, then M_q is non-singular.

LC-MS based methods for phytosterols determination in oenological matrices. Targeted metabolomic study of Rioja grape varieties

221 p.+ anexos

Toeplitz矩阵的循环延拓及其分析与应用

In this paper, we have presented the combined preconditioner which is derived from k =±-1~(1/2) circulant extensions of the real symmetric positive-definite Toeplitz matrices, proved it with great efficiency and stability and shown that it is easy to make error analysis and to remove the boundary effect with the combined preconditioner. This paper has also presented the methods for the direct and inverse computation of the real Toeplitz sets of equations and discussed many problems correspondingly, especially replaced the Toeplitz matrices with the combined preconditoners for analysis. The paper has also discussed the spectral analysis and boundary effect. Finally, as an application in geophysics, the paper makes some discussion about the squared root of a real matrix which comes from the Laplace algorithm.

Językowe środki wyrażania postawy mówiącego w łotewskich debatach sejmowych

Wydział Neofilologii: Instytut Językoznawstwa

An Independent-Connection Model for Traffic Matrices

A common assumption made in traffic matrix (TM) modeling and estimation is independence of a packet's network ingress and egress. We argue that in real IP networks, this assumption should not and does not hold. The fact that most traffic consists of two-way exchanges of packets means that traffic streams flowing in opposite directions at any point in the network are not independent. In this paper we propose a model for traffic matrices based on independence of connections rather than packets. We argue that the independent connection (IC) model is more intuitive, and has a more direct connection to underlying network phenomena than the gravity model. To validate the IC model, we show that it fits real data better than the gravity model and that it works well as a prior in the TM estimation problem. We study the model's parameters empirically and identify useful stability properties. This justifies the use of the simpler versions of the model for TM applications. To illustrate the utility of the model we focus on two such applications: synthetic TM generation and TM estimation. To the best of our knowledge this is the first traffic matrix model that incorporates properties of bidirectional traffic.

Component Neural Systems for the Creation of Emotional Memories during Free Viewing of a Complex, Real-World Event.

To investigate the neural systems that contribute to the formation of complex, self-relevant emotional memories, dedicated fans of rival college basketball teams watched a competitive game while undergoing functional magnetic resonance imaging (fMRI). During a subsequent recognition memory task, participants were shown video clips depicting plays of the game, stemming either from previously-viewed game segments (targets) or from non-viewed portions of the same game (foils). After an old-new judgment, participants provided emotional valence and intensity ratings of the clips. A data driven approach was first used to decompose the fMRI signal acquired during free viewing of the game into spatially independent components. Correlations were then calculated between the identified components and post-scanning emotion ratings for successfully encoded targets. Two components were correlated with intensity ratings, including temporal lobe regions implicated in memory and emotional functions, such as the hippocampus and amygdala, as well as a midline fronto-cingulo-parietal network implicated in social cognition and self-relevant processing. These data were supported by a general linear model analysis, which revealed additional valence effects in fronto-striatal-insular regions when plays were divided into positive and negative events according to the fan's perspective. Overall, these findings contribute to our understanding of how emotional factors impact distributed neural systems to successfully encode dynamic, personally-relevant event sequences.

A prospective clinical trial of a real-time polymerase chain reaction assay for the diagnosis of candidemia in nonneutropenic, critically ill adults

Background. Invasive Candida infection among nonneutropenic, critically ill adults is a clinical problem that has received increasing attention in recent years. Poor performance of extant diagnostic modalities has promoted risk-based, preemptive prescribing in view of the poor outcomes associated with inadequate or delayed antifungal therapy; this risks unnecessary overtreatment. A rapid, reliable diagnostic test could have a substantial impact on therapeutic practice in this patient population.

Methods. Three TaqMan-based real-time polymerase chain reaction assays were developed that are capable of detecting the main medically important Candida species, categorized according to the likelihood of fluconazole susceptibility. Assay 1 detected Candida albicans, Candida parapsilosis, Candida tropicalis, and Candida dubliniensis. Assays 2 and 3 detected Candida glabrata and Candida krusei, respectively. The clinical performance of these assays, applied to serum, was evaluated in a prospective trial of nonneutropenic adults in a single intensive care unit.

Results. In all, 527 specimens were obtained from 157 participants. All 3 assays were run in parallel for each specimen; they could be completed within 1 working day. Of these, 23 specimens were obtained from 23 participants categorized as having proven Candida infection at the time of sampling. If a single episode of Candida famata candidemia was excluded, the estimated clinical sensitivity, specificity, and positive and negative predictive values of the assays in this trial were 90.9%, 100%, 100% and 99.8%, respectively.

Conclusions. These data suggest that the described assays perform well in this population for enhancing the diagnosis of candidemia. The extent to which they may affect clinical outcomes, prescribing practice, and cost-effectiveness of care remains to be ascertained.

Positive dilations of piecewise monotonic Markov maps

We provide an explicit formula which gives natural extensions of piecewise monotonic Markov maps defined on an interval of the real line. These maps are exact endomorphisms and define chaotic discrete dynamical systems.

Comparison of porcine urine and bile as matrices to screen for the residues of two sulfonamides using a semi-automated enzyme immunoassay.

Porcine urine enzyme immunoassays for sulfamethazine and sulfadiazine have previously been employed as screening tests to predict the concentrations of the drugs in the corresponding tissues (kidneys), If a urine was found positive (> 800 ng ml(-1)) the corresponding kidney was then analysed by an enzyme immunoassay and, if found positive, a confirmatory analysis by HPLC was performed. Urine was chosen as the screening matrix since sulfonamides are mainly eliminated through this body fluid, However, after obtaining a number of false positive predictions, an investigation was carried out to assess the possibility of using an alternative body fluid which would act as a superior indicator of the presence of sulfonamides in porcine kidney, An initial study indicated that serum, plasma and bile could all be used as screening matrices. From these, bile was chosen as the preferred sample matrix and an extensive study followed to compare the efficiencies of sulfonamide positive bile and urine at predicting sulphonamide positive kidneys, Bile was found to be 17 times more efficient than urine at predicting a sulfamethazine positive kidney and 11 times more efficient at predicting a sulfadiazine positive kidney, With this enhanced performance of the initial screening test, the need for the costly and time consuming kidney enzyme immunoassay, prior to HPLC analysis, was eliminated

Distribution of the Demmel Condition Number of Wishart Matrices

This paper studies the Demmel condition number of Wishart matrices, a quantity which has numerous applications to wireless communications, such as adaptive switching between beamforming and diversity coding, link adaptation, and spectrum sensing. For complex Wishart matrices, we give an exact analytical expression for the probability density function (p.d.f.) of the Demmel condition number, and also derive simplified expressions for the high tail regime. These results indicate that the condition of complex Wishart matrices is dominantly decided by the difference between the matrix dimension and degree of freedom (DoF), i.e., the probability of drawing a highly ill conditioned matrix decreases considerably when the difference between the matrix dimension and DoF increases. We further investigate real Wishart matrices, and derive new expressions for the p.d.f. of the smallest eigenvalue, when the difference between the matrix dimension and DoF is odd. Based on these results, we succeed to obtain an exact p.d.f. expression for the Demmel condition number, and simplified expressions for the high tail regime.

Cross-Cultural Patterns in Dynamic Ratings of Positive and Negative Natural Emotional Behaviour

Background: Studies of cross-cultural variations in the perception of emotion have typically compared rates of recognition of static posed stimulus photographs. That research has provided evidence for universality in the recognition of a range of emotions but also for some systematic cross-cultural variation in the interpretation of emotional expression. However, questions remain about how widely such findings can be generalised to real life emotional situations. The present study provides the first evidence that the previously reported interplay between universal and cultural influences extends to ratings of natural, dynamic emotional stimuli.

Methodology/Principal Findings: Participants from Northern Ireland, Serbia, Guatemala and Peru used a computer based tool to continuously rate the strength of positive and negative emotion being displayed in twelve short video sequences by people from the United Kingdom engaged in emotional conversations. Generalized additive mixed models were developed to assess the differences in perception of emotion between countries and sexes. Our results indicate that the temporal pattern of ratings is similar across cultures for a range of emotions and social contexts. However, there are systematic differences in intensity ratings between the countries, with participants from Northern Ireland making the most extreme ratings in the majority of the clips.

Conclusions/Significance: The results indicate that there is strong agreement across cultures in the valence and patterns of ratings of natural emotional situations but that participants from different cultures show systematic variation in the intensity with which they rate emotion. Results are discussed in terms of both ‘in-group advantage’ and ‘display rules’ approaches. This study indicates that examples of natural spontaneous emotional behaviour can be used to study cross-cultural variations in the perception of emotion.

Press perturbations and indirect effects in real food webs

The prediction of the effects of disturbances in natural systems is limited by the general lack of knowledge on the strength of species interactions, i.e., the effect of one species on the population growth rate of another, and by the uncertainty of the effects that may be manifested via indirect pathways within the food web. Here we explored the consequences of changes in species populations for the remaining species within nine exceptionally well-characterized empirical food webs, for which, unlike the vast majority of other published webs, feeding links have been fully quantied. Using the inverse of the Jacobian matrix, we found that perturbations to species with few connections have larger net effects (considering both direct and indirect pathways between two species) on the rest of the food web than do disturbances to species that are highly connected. For 40% of predator-prey links, predators had positive net effects on prey populations, due to the predominance of indirect interactions. Our results highlight the fundamental, but often counterintuitive, role of indirect effects for the maintenance of food web complexity and biodiversity.

Identification of Pseudomonas aeruginosa by a duplex real-time polymerase chain reaction assay targeting the ecfX and the gyrB genes

Phenotypic identification of Gram-negative bacteria from respiratory specimens of patients with cystic fibrosis carries a high risk of misidentification. Molecular identification techniques that use single-gene targets are also susceptible to error, including cross-reaction issues with other Gram-negative organisms. In this study, we have designed a Pseudomonas aeruginosa duplex real-time polymerase chain reaction (PCR) (PAduplex) assay targeting the ecfX and the gyrB genes. The PAduplex was evaluated against a panel of 91 clinical and environmental isolates that were presumptively identified as P. aeruginosa. The results were compared with those obtained using a commercial biochemical identification kit and several other P. aeruginosa PCR assays. The results showed that the PAduplex assay is highly suitable for routine identification of P. aeruginosa isolates from clinical or environmental samples. The 2-target format provides simultaneous confirmation of P. aeruginosa identity where both the ecfX and gyrB PCR reactions are positive and may also reduce the potential for false negatives caused by sequence variation in primer or probe targets.

Discovering subgroups of patients from DNA copy number data using NMF on compacted matrices

In the study of complex genetic diseases, the identification of subgroups of patients sharing similar genetic characteristics represents a challenging task, for example, to improve treatment decision. One type of genetic lesion, frequently investigated in such disorders, is the change of the DNA copy number (CN) at specific genomic traits. Non-negative Matrix Factorization (NMF) is a standard technique to reduce the dimensionality of a data set and to cluster data samples, while keeping its most relevant information in meaningful components. Thus, it can be used to discover subgroups of patients from CN profiles. It is however computationally impractical for very high dimensional data, such as CN microarray data. Deciding the most suitable number of subgroups is also a challenging problem. The aim of this work is to derive a procedure to compact high dimensional data, in order to improve NMF applicability without compromising the quality of the clustering. This is particularly important for analyzing high-resolution microarray data. Many commonly used quality measures, as well as our own measures, are employed to decide the number of subgroups and to assess the quality of the results. Our measures are based on the idea of identifying robust subgroups, inspired by biologically/clinically relevance instead of simply aiming at well-separated clusters. We evaluate our procedure using four real independent data sets. In these data sets, our method was able to find accurate subgroups with individual molecular and clinical features and outperformed the standard NMF in terms of accuracy in the factorization fitness function. Hence, it can be useful for the discovery of subgroups of patients with similar CN profiles in the study of heterogeneous diseases.

Rapid detection of health-care-associated bloodstream infection in critical care using multipathogen real-time polymerase chain reaction technology: a diagnostic accuracy study and systematic review

Background: There is growing interest in the potential utility of real-time polymerase chain reaction (PCR) in diagnosing bloodstream infection by detecting pathogen deoxyribonucleic acid (DNA) in blood samples within a few hours. SeptiFast (Roche Diagnostics GmBH, Mannheim, Germany) is a multipathogen probe-based system targeting ribosomal DNA sequences of bacteria and fungi. It detects and identifies the commonest pathogens causing bloodstream infection. As background to this study, we report a systematic review of Phase III diagnostic accuracy studies of SeptiFast, which reveals uncertainty about its likely clinical utility based on widespread evidence of deficiencies in study design and reporting with a high risk of bias. 

Objective: Determine the accuracy of SeptiFast real-time PCR for the detection of health-care-associated bloodstream infection, against standard microbiological culture. 

Design: Prospective multicentre Phase III clinical diagnostic accuracy study using the standards for the reporting of diagnostic accuracy studies criteria. 

Setting: Critical care departments within NHS hospitals in the north-west of England. 

Participants: Adult patients requiring blood culture (BC) when developing new signs of systemic inflammation. 

Main outcome measures: SeptiFast real-time PCR results at species/genus level compared with microbiological culture in association with independent adjudication of infection. Metrics of diagnostic accuracy were derived including sensitivity, specificity, likelihood ratios and predictive values, with their 95% confidence intervals (CIs). Latent class analysis was used to explore the diagnostic performance of culture as a reference standard. 

Results: Of 1006 new patient episodes of systemic inflammation in 853 patients, 922 (92%) met the inclusion criteria and provided sufficient information for analysis. Index test assay failure occurred on 69 (7%) occasions. Adult patients had been exposed to a median of 8 days (interquartile range 4–16 days) of hospital care, had high levels of organ support activities and recent antibiotic exposure. SeptiFast real-time PCR, when compared with culture-proven bloodstream infection at species/genus level, had better specificity (85.8%, 95% CI 83.3% to 88.1%) than sensitivity (50%, 95% CI 39.1% to 60.8%). When compared with pooled diagnostic metrics derived from our systematic review, our clinical study revealed lower test accuracy of SeptiFast real-time PCR, mainly as a result of low diagnostic sensitivity. There was a low prevalence of BC-proven pathogens in these patients (9.2%, 95% CI 7.4% to 11.2%) such that the post-test probabilities of both a positive (26.3%, 95% CI 19.8% to 33.7%) and a negative SeptiFast test (5.6%, 95% CI 4.1% to 7.4%) indicate the potential limitations of this technology in the diagnosis of bloodstream infection. However, latent class analysis indicates that BC has a low sensitivity, questioning its relevance as a reference test in this setting. Using this analysis approach, the sensitivity of the SeptiFast test was low but also appeared significantly better than BC. Blood samples identified as positive by either culture or SeptiFast real-time PCR were associated with a high probability (> 95%) of infection, indicating higher diagnostic rule-in utility than was apparent using conventional analyses of diagnostic accuracy. 

Conclusion: SeptiFast real-time PCR on blood samples may have rapid rule-in utility for the diagnosis of health-care-associated bloodstream infection but the lack of sensitivity is a significant limiting factor. Innovations aimed at improved diagnostic sensitivity of real-time PCR in this setting are urgently required. Future work recommendations include technology developments to improve the efficiency of pathogen DNA extraction and the capacity to detect a much broader range of pathogens and drug resistance genes and the application of new statistical approaches able to more reliably assess test performance in situation where the reference standard (e.g. blood culture in the setting of high antimicrobial use) is prone to error.