Graph Spectral Properties of Deterministic Finite Automata

We prove that a minimal automaton has a minimal adjacency matrix rank and a minimal adjacency matrix nullity using equitable partition (from graph spectra theory) and Nerode partition (from automata theory). This result naturally introduces the notion of matrix rank into a regular language L, the minimal adjacency matrix rank of a deterministic automaton that recognises L. We then define and focus on rank-one languages: the class of languages for which the rank of minimal automaton is one. We also define the expanded canonical automaton of a rank-one language.Comment: This paper has been accepted at the following conference: 18th International Conference on Developments in Language Theory (DLT 2014), August 26 - 29, 2014, Ekaterinburg, Russi

Quantum finite automata and linear context-free languages: a decidable problem

We consider the so-called measure once finite quantum automata model introduced by Moore and Crutchfield in 2000. We show that given a language recognized by such a device and a linear context-free language, it is recursively decidable whether or not they have a nonempty intersection. This extends a result of Blondel et al. which can be interpreted as solving the problem with the free monoid in place of the family of linear context-free languages. © 2013 Springer-Verlag

Simulation study of magnetic holes at the Earth's collisionless bow shock

Recent observations by the Cluster and Double Star spacecraft at the Earth's bow shock have revealed localized magnetic field and density holes in the solar wind plasma. These structures are characterized by a local depletion of the magnetic field and the plasma density, and by a strong increase of the plasma temperature inside the magnetic and density cavities. Our objective here is to report results of a hybrid-Vlasov simulations of ion-Larmor-radius sized plasma density cavities with parameters that are representative of the high-beta solar wind plasma at the Earth's bow shock. We observe the asymmetric self-steepening and shock-formation of the cavity, and a strong localized temperature increase (by a factor of 5–7) of the plasma due to reflections and shock surfing of the ions against the collisionless shock. Temperature maxima are correlated with density minima, in agreement with Cluster observations. For oblique incidence of the solar wind, we observe efficient acceleration of ions along the magnetic field lines by the shock drift acceleration process

Long‐term surveillance biopsy: Is it necessary after pediatric heart transplant?

Due to limited and conflicting data in pediatric patients, long‐term routine surveillance endomyocardial biopsy (RSB) in pediatric heart transplant (HT) remains controversial. We sought to characterize the rate of positive RSB and determine factors associated with RSB‐detected rejection. Records of patients transplanted at a single institution from 1995 to 2015 with >2 year of post‐HT biopsy data were reviewed for RSB‐detected rejections occurring >2 year post‐HT. We illustrated the trajectory of significant rejections (ISHLT Grade ≥3A/2R) among total RSB performed over time and used multivariable logistic regression to model the association between time and risk of rejection. We estimated Kaplan‐Meier freedom from rejection rates by patient characteristics and used the log‐rank test to assess differences in rejection probabilities. We identified the best‐fitting Cox proportional hazards regression model. In 140 patients, 86% did not have any episodes of significant RSB‐detected rejection >2 year post‐HT. The overall empirical rate of RSB‐detected rejection >2 year post‐HT was 2.9/100 patient‐years. The percentage of rejection among 815 RSB was 2.6% and remained stable over time. Years since transplant remained unassociated with rejection risk after adjusting for patient characteristics (OR = 0.98; 95% CI 0.78‐1.23; P = 0.86). Older age at HT was the only factor that remained significantly associated with risk of RSB‐detected rejection under multivariable Cox analysis (P = 0.008). Most pediatric patients did not have RSB‐detected rejection beyond 2 years post‐HT, and the majority of those who did were older at time of HT. Indiscriminate long‐term RSB in pediatric heart transplant should be reconsidered given the low rate of detected rejection.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/147767/1/petr13330_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/147767/2/petr13330.pd

Regular Expressions and Transducers over Alphabet-invariant and User-defined Labels

We are interested in regular expressions and transducers that represent word relations in an alphabet-invariant way---for example, the set of all word pairs u,v where v is a prefix of u independently of what the alphabet is. Current software systems of formal language objects do not have a mechanism to define such objects. We define transducers in which transition labels involve what we call set specifications, some of which are alphabet invariant. In fact, we give a more broad definition of automata-type objects, called labelled graphs, where each transition label can be any string, as long as that string represents a subset of a certain monoid. Then, the behaviour of the labelled graph is a subset of that monoid. We do the same for regular expressions. We obtain extensions of a few classic algorithmic constructions on ordinary regular expressions and transducers at the broad level of labelled graphs and in such a way that the computational efficiency of the extended constructions is not sacrificed. For regular expressions with set specs we obtain the corresponding partial derivative automata. For transducers with set specs we obtain further algorithms that can be applied to questions about independent regular languages, in particular the witness version of the independent property satisfaction question

Pepsinogen A, pepsinogen C, and gastrin as markers of atrophic chronic gastritis in European dyspeptics

Serum levels of pepsinogen and gastrin are parameters that can be used as biomarkers for gastric mucosa. The aim of this study was to validate these serum biomarkers, that is pepsinogen A (PGA), pepsinogen C (PGC), PGA/PGC ratio, and gastrin, as screening tests for precancerous lesions: atrophic chronic gastritis (ACG) or Helicobacter pylori-related corpus-predominant or multifocal atrophy. The study population was comprised of a subsample of 284 patients from the 451 included in the Eurohepygast cohort, between 1995 and 1997. The concentrations of PGA, PGC, and gastrin were measured by radioimmunoassays. Histological diagnosis was the gold standard. Cut-off points were calculated using receiving operator characteristics (ROC) curves. Factors linked to variation of biomarkers were identified using multivariate linear regression. The mean of each biomarker in the sample was: PGA, 77.4 μg l−1; PGC, 13.2 μg l−1; PGA/PGC, 6.7; and gastrin, 62.4 ng l−1. For ACG patients, the areas under the PGA, PGC, PGA/PGC, and gastrin ROC curves were 0.55, 0.62, 0.73, and 0.58, respectively. The best cut-off point for PGA/PGC was 5.6, with sensitivity 65% and specificity 77.9%. For H. pylori-related corpus-predominant or multifocal atrophy, the areas under the respective ROC curves were 0.57, 0.67, 0.84, and 0.69. The best cut-off point for PGA/PGC was 4.7, with sensitivity 77.1% and specificity 87.4%. The results suggested that only the PGA/PGC ratio can be considered as a biomarker for precancerous lesions of the stomach, and may be useful as a screening test

HIV Incidence in Rural South Africa: Comparison of Estimates from Longitudinal Surveillance and Cross-Sectional cBED Assay Testing

The original publication is available at http:/www.plosone.orgBackground: The BED IgG-Capture Enzyme Immunoassay (cBED assay), a test of recent HIV infection, has been used to estimate HIV incidence in cross-sectional HIV surveys. However, there has been concern that the assay overestimates HIV incidence to an unknown extent because it falsely classifies some individuals with non-recent HIV infections as recently infected. We used data from a longitudinal HIV surveillance in rural South Africa to measure the fraction of people with nonrecent HIV infection who are falsely classified as recently HIV-infected by the cBED assay (the long-term false-positive ratio (FPR)) and compared cBED assay-based HIV incidence estimates to longitudinally measured HIV incidence. Methodology/Principal Findings: We measured the long-term FPR in individuals with two positive HIV tests (in the HIV surveillance, 2003-2006) more than 306 days apart (sample size n = 1,065). We implemented four different formulae to calculate HIV incidence using cBED assay testing (n = 11,755) and obtained confidence intervals (CIs) by directly calculating the central 95th percentile of incidence values. We observed 4,869 individuals over 7,685 person-years for longitudinal HIV incidence estimation. The long-term FPR was 0.0169 (95% CI 0.0100-0.0266). Using this FPR, the cross-sectional cBED-based HIV incidence estimates (per 100 people per year) varied between 3.03 (95% CI 2.44-3.63) and 3.19 (95% CI 2.57-3.82), depending on the incidence formula. Using a long-term FPR of 0.0560 based on previous studies, HIV incidence estimates varied between 0.65 (95% CI 0.00-1.32) and 0.71 (95% CI 0.00-1.43). The longitudinally measured HIV incidence was 3.09 per 100 people per year (95% CI 2.69-3.52), after adjustment to the sex-age distribution of the sample used in cBED assay-based estimation. Conclusions/Significance: In a rural community in South Africa with high HIV prevalence, the long-term FPR of the cBED assay is substantially lower than previous estimates. The cBED assay performs well in HIV incidence estimation if the locally measured long-term FPR is used, but significantly underestimates incidence when a FPR estimate based on previous studies in other settings is used. © 2008 Bärnighausen et al.Publishers' Versio

Dual Testing Algorithm of BED-CEIA and AxSYM Avidity Index Assays Performs Best in Identifying Recent HIV Infection in a Sample of Rwandan Sex Workers

To assess the performance of BED-CEIA (BED) and AxSYM Avidity Index (Ax-AI) assays in estimating HIV incidence among female sex workers (FSW) in Kigali, Rwanda. Eight hundred FSW of unknown HIV status were HIV tested; HIV-positive women had BED and Ax-AI testing at baseline and ≥12 months later to estimate assay false-recent rates (FRR). STARHS-based HIV incidence was estimated using the McWalter/Welte formula, and adjusted with locally derived FRR and CD4 results. HIV incidence and local assay window periods were estimated from a prospective cohort of FSW. At baseline, 190 HIV-positive women were BED and Ax-AI tested; 23 were classified as recent infection (RI). Assay FRR with 95% confidence intervals were: 3.6% (1.2-8.1) (BED); 10.6% (6.1-17.0) (Ax-AI); and 2.1% (0.4-6.1) (BED/Ax-AI combined). After FRR-adjustment, incidence estimates by BED, Ax-AI, and BED/Ax-AI were: 5.5/100 person-years (95% CI 2.2-8.7); 7.7 (3.2-12.3); and 4.4 (1.4-7.3). After CD4-adjustment, BED, Ax-AI, and BED/Ax-AI incidence estimates were: 5.6 (2.6-8.6); 9.7 (5.0-14.4); and 4.7 (2.0-7.5). HIV incidence rates in the first and second 6 months of the cohort were 4.6 (1.6-7.7) and 2.2 (0.1-4.4). Adjusted incidence estimates by BED/Ax-AI combined were similar to incidence in the first 6 months of the cohort. Furthermore, false-recent rate on the combined BED/Ax-AI algorithm was low and substantially lower than for either assay alone. Improved assay specificity with time since seroconversion suggests that specificity would be higher in population-based testing where more individuals have long-term infectio

Estimation of HIV-1 incidence among five focal populations in Dehong, Yunnan: a hard hit area along a major drug trafficking route

<p>Abstract</p> <p>Background</p> <p>Since 1989 when the first 146 HIV positives in China were identified, Dehong Prefecture had been one of the areas hardest-hit by HIV in China. The local and national governments have put substantial financial resources into tackling the HIV epidemic in Dehong from 2004. The objective of this study was to track dynamic changes in HIV-1 prevalence and incidence among five focal populations in Dehong and to assess the impact of HIV prevention and control efforts.</p> <p>Methods</p> <p>Consecutive cross-sectional surveys conducted in five focal populations between 2004 and 2008. Specimens seropositive for HIV were tested with the BED IgG capture enzyme immunoassay to identify recent seroconversions (median, 155 days) using normalized optical density of 0.8 and adjustments.</p> <p>Results</p> <p>From 2004 to 2008, estimated annual HIV incidence among injecting drug users (IDUs) decreased significantly [from 15.0% (95% CI = 11.4%-18.5%) in 2004 to 4.3% (95% CI = 2.4%-6.2%) in 2008; trend test P < 0.0001]. The incidence among other focal populations, such as HIV discordant couples (varying from 5.5% to 4.7%), female sex workers (varying from 1.4% to 1.3%), pregnant women (0.1%), and pre-marital couples (0.2 to 0.1%) remained stable. Overall, the proportion of recent HIV-1 infections was higher among females than males (P < 0.0001).</p> <p>Conclusions</p> <p>The HIV epidemic in Dehong continued to expand during a five-year period but at a slowing rate among IDUs, and HIV incidence remains high among IDUs and discordant couples. Intensive prevention measures should target sub-groups at highest risk to further slow the epidemic and control the migration of HIV to other areas of China, and multivariate analysis is needed to explore which measures are more effective for different populations.</p

Two Groups Associated With Quadratic Pisot Units

In a previous work, we have investigated an automata-theoretic property of numeration systems associated with quadratic Pisot units that yields, for every such number `, a certain group G `