BEC-BCS Crossover in Neutron Matter with Renormalization Group based Effective Interactions

We study pure neutron matter in the BEC-BCS crossover regime using renormalization group based low-momentum interactions within the Nozi\`eres-Schmitt-Rink framework. This is an attempt to go beyond the mean field description for low-density matter. We work in the basis of so-called Weinberg eigenvectors where the operator $G_0V$ is diagonal, which proves to be an excellent choice that allows one to use non-local interactions in a very convenient way. We study the importance of correlations as a function of density. We notice that there is a significant reduction of the BCS critical temperature at low-densities as the neutron matter approaches the unitary limit.Comment: 10 pages and 8 figures, Figs 6 and 7 now includes higher cut-offs, discussion of the cut-off dependence improved, new Summary and Outlook section and new references adde

Magnetic resonance imaging (MRI) of heavy-metal transport and fate in an artificial biofilm

Unlike planktonic systems, reaction rates in biofilms are often limited by mass transport, which controls the rate of supply of contaminants into the biofilm matrix. To help understand this phenomenon, we investigated the potential of magnetic resonance imaging (MRI) to spatially quantify copper transport and fate in biofilms. For this initial study we utilized an artificial biofilm composed of a 50:50 mix of bacteria and agar. MRI successfully mapped Cu2+ uptake into the artificial biofilm by mapping T2 relaxation rates. A calibration protocol was used to convert T2 values into actual copper concentrations. Immobilization rates in the artificial biofilm were slow compared to the rapid equilibration of planktonic systems. Even after 36 h, the copper front had migrated only 3 mm into the artificial biofilm and at this distance from the copper source, concentrations were very low. This slow equilibration is a result of (1) the time it takes copper to diffuse over such distances and (2) the adsorption of copper onto cell surfaces, which further impedes copper diffusion. The success of this trial run indicates MRI could be used to quantitatively map heavy metal transport and immobilization in natural biofilms

Existence of Universal Connections

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Existence of Universal Connections II

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On Nori's Fundamental Group Scheme

We determine the quotient category which is the representation category of the kernel of the homomorphism from Nori's fundamental group scheme to its \'etale and local parts. Pierre Deligne pointed out an error in the first version of this article. We profoundly thank him, in particular for sending us his enlightning example reproduced in Remark 2.4 2).Comment: 29 page

A Study of Serum Electrolytes and Red Cell Distribution Width in Acute Exacerbation of Chronic Obstructive Pulmonary Disease Patients

BACKGROUND: The aim of this study is to analyse the relationship between Red cell distribution width and serum electrolytes (serum sodium and potassium) with the severity of acute exacerbation in COPD patients. MATERIALS AND METHODS: This is a comparative cross-sectional study of 100 cases managed for COPD with acute exacerbations in the medical ward of Coimbatore Medical College and Hospital and 30 age and sex matched healthy community controls. All the test done with due permission from the Institutional Ethical Committee and informed consent from the subjects. RESULTS: In this study, we found that low levels of serum electrolytes (serum sodium and potassium) and higher levels of RDW were associated with increased severity of acute exacerbation of COPD as indicated by various indices like MMRC grading, 6 minute walk tests, GOLD criteria and BODE index. CONCLUSION: Variability in size of circulating RBCs increases as the severity of COPD increases and correlation was found between RDW and severity of COPD. Thus RDW can be used as a biomarker to assess the severity of COPD. Similarly serum sodium and serum potassium showed negative correlation with severity of acute exacerbation of COPD. Thus these values should also be closely monitored and correction should be made at the earliest to improve outcomes

Distributed Parameter Estimation in Sensor Networks: Nonlinear Observation Models and Imperfect Communication

The paper studies distributed static parameter (vector) estimation in sensor networks with nonlinear observation models and noisy inter-sensor communication. It introduces \emph{separably estimable} observation models that generalize the observability condition in linear centralized estimation to nonlinear distributed estimation. It studies two distributed estimation algorithms in separably estimable models, the $\mathcal{NU}$ (with its linear counterpart $\mathcal{LU}$) and the $\mathcal{NLU}$. Their update rule combines a \emph{consensus} step (where each sensor updates the state by weight averaging it with its neighbors' states) and an \emph{innovation} step (where each sensor processes its local current observation.) This makes the three algorithms of the \textit{consensus + innovations} type, very different from traditional consensus. The paper proves consistency (all sensors reach consensus almost surely and converge to the true parameter value,) efficiency, and asymptotic unbiasedness. For $\mathcal{LU}$ and $\mathcal{NU}$, it proves asymptotic normality and provides convergence rate guarantees. The three algorithms are characterized by appropriately chosen decaying weight sequences. Algorithms $\mathcal{LU}$ and $\mathcal{NU}$ are analyzed in the framework of stochastic approximation theory; algorithm $\mathcal{NLU}$ exhibits mixed time-scale behavior and biased perturbations, and its analysis requires a different approach that is developed in the paper.Comment: IEEE Transactions On Information Theory, Vol. 58, No. 6, June 201