Emergence of chaotic attractor and anti-synchronization for two coupled monostable neurons

The dynamics of two coupled piece-wise linear one-dimensional monostable maps is investigated. The single map is associated with Poincare section of the FitzHugh-Nagumo neuron model. It is found that a diffusive coupling leads to the appearance of chaotic attractor. The attractor exists in an invariant region of phase space bounded by the manifolds of the saddle fixed point and the saddle periodic point. The oscillations from the chaotic attractor have a spike-burst shape with anti-phase synchronized spiking.Comment: To be published in CHAO

Limitations to Frechet's Metric Embedding Method

Frechet's classical isometric embedding argument has evolved to become a major tool in the study of metric spaces. An important example of a Frechet embedding is Bourgain's embedding. The authors have recently shown that for every e>0 any n-point metric space contains a subset of size at least n^(1-e) which embeds into l_2 with distortion O(\log(2/e) /e). The embedding we used is non-Frechet, and the purpose of this note is to show that this is not coincidental. Specifically, for every e>0, we construct arbitrarily large n-point metric spaces, such that the distortion of any Frechet embedding into l_p on subsets of size at least n^{1/2 + e} is \Omega((\log n)^{1/p}).Comment: 10 pages, 1 figur

Interleukin-6 and interleukin-6 receptor secretion by chronic lymphatic leukaemia and normal B lymphocytes: effect of PMA and PWM

Interleukin-6 (IL-6) and soluble interleukin-6 receptor (sIL-6R) were detected in supernatants of cultures of B chronic lymphatic leukaemia (CLL) lymphocytes. Phorbol-12-myristate 13 acetate (PMA) caused a decrease in the levels of IL-6 in 14 out of 16 cultures and an increase in levels of sIL6R in all 15 cases. The effect of pokeweed mitogen (PWM) was variable and not significant. The levels of IL-6 were below the detection limit (60 pg/ml) in sera of 13 CLL patients whereas sIL-6R was detected (13 ng/ml to 97 ng/ml) in the 13 sera. IL6 was not detected in cultures of unstimulated or stimulated with PMA or PWM normal human B cells. Levels of sIL-6R were minimal in cultures of normal B lymphocytes and were increased in PMA stimulated cultures. The results are consistent with the view that B-CLL cells produce spontaneously IL-6 which could act in an autocrine fashion to cause shedding of surface IL-6R and account for the correlation found between serum levels of sIL-6R and B-CLL lymphocyte numbers. The fall in levels of IL-6 in PMA stimulated CLL cultures might express masking or degradation of IL-6 after combination with the receptor

Multiclass Semi-Supervised Learning on Graphs using Ginzburg-Landau Functional Minimization

We present a graph-based variational algorithm for classification of high-dimensional data, generalizing the binary diffuse interface model to the case of multiple classes. Motivated by total variation techniques, the method involves minimizing an energy functional made up of three terms. The first two terms promote a stepwise continuous classification function with sharp transitions between classes, while preserving symmetry among the class labels. The third term is a data fidelity term, allowing us to incorporate prior information into the model in a semi-supervised framework. The performance of the algorithm on synthetic data, as well as on the COIL and MNIST benchmark datasets, is competitive with state-of-the-art graph-based multiclass segmentation methods.Comment: 16 pages, to appear in Springer's Lecture Notes in Computer Science volume "Pattern Recognition Applications and Methods 2013", part of series on Advances in Intelligent and Soft Computin

Internal versus external determinants of Schistosoma japonicum transmission in irrigated agricultural villages

Currently schistosomiasis transmission has been suppressed to low levels in many historically endemic areas of China by widespread use of praziquantel in human and bovine populations and application of niclosamide for snail control. However, re-emergent transmission has signalled the need for sustainable interventions beyond these repeated chemical interventions. To take advantage of ongoing investment in rural infrastructure, an index of schistosomiasis transmission potential is needed to identify villages where environmental modifications would be particularly effective. Based on a retrospective analysis of data from 10 villages in Sichuan Province, an index linked to the basic reproductive number is shown to have promise in meeting this need. However, a lack of methods for estimating the spatial components of the proposed metric and for estimating the import of cercariae and miracidia from neighbouring villages leads to significant uncertainty in its estimation. These findings suggest a priority effort to develop methods for measuring the free-swimming forms of the parasite in surface waters. This need is underscored by the high cost and limited sensitivity of current methods for diagnosing human infection and mounting evidence of the inadequacy of snail surveys to identify environments supporting low levels of transmission

Maximum gradient embeddings and monotone clustering

Let (X,d_X) be an n-point metric space. We show that there exists a distribution D over non-contractive embeddings into trees f:X-->T such that for every x in X, the expectation with respect to D of the maximum over y in X of the ratio d_T(f(x),f(y)) / d_X(x,y) is at most C (log n)^2, where C is a universal constant. Conversely we show that the above quadratic dependence on log n cannot be improved in general. Such embeddings, which we call maximum gradient embeddings, yield a framework for the design of approximation algorithms for a wide range of clustering problems with monotone costs, including fault-tolerant versions of k-median and facility location.Comment: 25 pages, 2 figures. Final version, minor revision of the previous one. To appear in "Combinatorica

Hmong Adults Self-Rated Oral Health: A Pilot Study

Since 1975, the Hmong refugee population in the U.S. has increased over 200%. However, little is known about their dental needs or self-rated oral health (SROH). The study aims were to: (1) describe the SROH, self-rated general health (SRGH), and use of dental/physician services; and (2) identify the factors associated with SROH among Hmong adults. A cross-sectional study design with locating sampling methodology was used. Oral health questionnaire was administered to assess SROH and SRGH, past dental and physician visits, and language preference. One hundred twenty adults aged 18–50+ were recruited and 118 had useable information. Of these, 49% rated their oral health as poor/fair and 30% rated their general health as poor/fair. Thirty-nine percent reported that they did not have a regular source of dental care, 46% rated their access to dental care as poor/fair, 43% visited a dentist and 66% visited a physician within the past 12 months. Bivariate analyses demonstrated that access to dental care, past dental visits, age and SRGH were significantly associated with SROH (P \u3c 0.05). Multivariate analyses demonstrated a strong association between access to dental care and good/excellent SROH. About half of Hmong adults rated their oral health and access to dental care as poor. Dental insurance, access to dental care, past preventive dental/physician visits and SRGH were associated with SROH

The unfolded protein response affects readthrough of premature termination codons

One-third of monogenic inherited diseases result from premature termination codons (PTCs). Readthrough of in-frame PTCs enables synthesis of full-length functional proteins. However, extended variability in the response to readthrough treatment is found among patients, which correlates with the level of nonsense transcripts. Here, we aimed to reveal cellular pathways affecting this inter-patient variability. We show that activation of the unfolded protein response (UPR) governs the response to readthrough treatment by regulating the levels of transcripts carrying PTCs. Quantitative proteomic analyses showed substantial differences in UPR activation between patients carrying PTCs, correlating with their response. We further found a significant inverse correlation between the UPR and nonsense-mediated mRNA decay (NMD), suggesting a feedback loop between these homeostatic pathways. We uncovered and characterized the mechanism underlying this NMD-UPR feedback loop, which augments both UPR activation and NMD attenuation. Importantly, this feedback loop enhances the response to readthrough treatment, highlighting its clinical importance. Altogether, our study demonstrates the importance of the UPR and its regulatory network for genetic diseases caused by PTCs and for cell homeostasis under normal conditions

Uncertainty quantification in graph-based classification of high dimensional data

Classification of high dimensional data finds wide-ranging applications. In many of these applications equipping the resulting classification with a measure of uncertainty may be as important as the classification itself. In this paper we introduce, develop algorithms for, and investigate the properties of, a variety of Bayesian models for the task of binary classification; via the posterior distribution on the classification labels, these methods automatically give measures of uncertainty. The methods are all based around the graph formulation of semi-supervised learning. We provide a unified framework which brings together a variety of methods which have been introduced in different communities within the mathematical sciences. We study probit classification in the graph-based setting, generalize the level-set method for Bayesian inverse problems to the classification setting, and generalize the Ginzburg-Landau optimization-based classifier to a Bayesian setting; we also show that the probit and level set approaches are natural relaxations of the harmonic function approach introduced in [Zhu et al 2003]. We introduce efficient numerical methods, suited to large data-sets, for both MCMC-based sampling as well as gradient-based MAP estimation. Through numerical experiments we study classification accuracy and uncertainty quantification for our models; these experiments showcase a suite of datasets commonly used to evaluate graph-based semi-supervised learning algorithms.Comment: 33 pages, 14 figure

Microscope and microâ camera assessment of Schneiderian membrane perforation via transcrestal sinus floor elevation: A randomized ex vivo study

ObjectiveWe sought to assess the effectiveness of using a microscope and nonâ invasive camera for assessing sinus membrane perforations during transcrestal sinus floor elevation (TSFE).Materials and methodsFive fresh human cadaver heads corresponding to eight maxillary sinuses (six bilateral and two unilateral) underwent 4 TSFEs per sinus (a total of 32 single site elevations). Each elevation was randomly assigned to receive a three or six mm membrane elevation height (MEH). A microscope and microâ camera were used to assess the sinus membrane perforation. Afterwards, radiological and clinical membrane perforation assessments were performed. The statistical analysis results are expressed using the means, standard deviations, range values of the residual ridge height (RRH), residual ridge width (RRW), sinus membrane thickness (SMT) and incidence of perforation (IoP). Generalized linear methods were used to test for the correlation of RRH and MEH to the microscope and microâ camera perforation assessments and the correlation of microscope and microâ camera assessments with the postâ operative CBCT and crestal liquid evaluation.ResultsThe cumulative percentage of IoP was 40.62%, (23.07% with 3 mm MEH, and 76.92% with 6 mm MEH, p < 0.05). The perforation assessed using either the microscope or microâ camera coincided with the postâ operative CBCT and crestal liquid assessment in 87.55% sites. No significant correlation was found between the microscope or microâ camera assessments with RRH or MEH.ConclusionApplication of a microscope and microâ camera during transcrestal sinus floor elevation may allow the detection of the integrity of the Schneiderian membrane with greater than 85% accuracy in this ex vivo model.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/149727/1/clr13453.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/149727/2/clr13453_am.pd