Coexisting Sickle Cell Anemia and Sarcoidosis: A Management Conundrum!

Sickle cell disease and Sarcoidosis are conditions that are more common in the African American population. In this report we share an unfortunate patient who had hepatic sarcoidosis but could not receive steroids since that precipitated acute liver failure. We have discussed potential therapy options but we need more options that improve mortality

Optimal Embedding of Functions for In-Network Computation: Complexity Analysis and Algorithms

We consider optimal distributed computation of a given function of distributed data. The input (data) nodes and the sink node that receives the function form a connected network that is described by an undirected weighted network graph. The algorithm to compute the given function is described by a weighted directed acyclic graph and is called the computation graph. An embedding defines the computation communication sequence that obtains the function at the sink. Two kinds of optimal embeddings are sought, the embedding that---(1)~minimizes delay in obtaining function at sink, and (2)~minimizes cost of one instance of computation of function. This abstraction is motivated by three applications---in-network computation over sensor networks, operator placement in distributed databases, and module placement in distributed computing. We first show that obtaining minimum-delay and minimum-cost embeddings are both NP-complete problems and that cost minimization is actually MAX SNP-hard. Next, we consider specific forms of the computation graph for which polynomial time solutions are possible. When the computation graph is a tree, a polynomial time algorithm to obtain the minimum delay embedding is described. Next, for the case when the function is described by a layered graph we describe an algorithm that obtains the minimum cost embedding in polynomial time. This algorithm can also be used to obtain an approximation for delay minimization. We then consider bounded treewidth computation graphs and give an algorithm to obtain the minimum cost embedding in polynomial time

Naturopathy: A Collective Lifestyle Modification Approach to Combat Hypertension

Hypertension is considered a highly prevalent disorder these days as Hypertension is the result of our hurried life and naturopathy stresses on normal pace of life hence suitable for hypertensive masses. A physiological understanding has been developed about hypertension as well as the Diagnostic and screening criteria of hypertension and relationship of hypertension with obesity revealed. Moreover, naturopathy covers all aspects of our life style modification it includes various kinds of modern exercise as well as yogasanas and stress relieving techniques. Hence, this review covers all the aspects of lifestyle modification in detail to combat hypertension through the weapons of Exercise, yogasanas and alternative medical practices to manage diabetes. Naturopathy believes that our body is made up of five basic elements and all the ailments can be treated with various kinds of therapies related to these basic elements of human body. These therapies include music therapy, meditation, hydrotherapy, mud therapy and colour therapy etc. Along with these therapies various kinds of alternative practices also mentioned that are utilised at Naturopathy centres to overcome high blood pressure like exercise, pranayam, unwise indulgence, food therapy and massage etc

A Near-Optimal Depth-Hierarchy Theorem for Small-Depth Multilinear Circuits

We study the size blow-up that is necessary to convert an algebraic circuit of product-depth $\Delta+1$ to one of product-depth $\Delta$ in the multilinear setting. We show that for every positive $\Delta = \Delta(n) = o(\log n/\log \log n),$ there is an explicit multilinear polynomial $P^{(\Delta)}$ on $n$ variables that can be computed by a multilinear formula of product-depth $\Delta+1$ and size $O(n)$, but not by any multilinear circuit of product-depth $\Delta$ and size less than $\exp(n^{\Omega(1/\Delta)})$. This result is tight up to the constant implicit in the double exponent for all $\Delta = o(\log n/\log \log n).$ This strengthens a result of Raz and Yehudayoff (Computational Complexity 2009) who prove a quasipolynomial separation for constant-depth multilinear circuits, and a result of Kayal, Nair and Saha (STACS 2016) who give an exponential separation in the case $\Delta = 1.$ Our separating examples may be viewed as algebraic analogues of variants of the Graph Reachability problem studied by Chen, Oliveira, Servedio and Tan (STOC 2016), who used them to prove lower bounds for constant-depth Boolean circuits

How does Recent Understanding of Molecular Mechanisms in Botulinum Toxin Impact Therapy?

Botulinum toxin, one of the most lethal toxins identified, is also used as a therapeutic agent for a variety of human conditions. The history of the discovery of botulinum toxin, an understanding of its function at the molecular level and its development into a therapeutic reagent are instructive and allow the reader to build a conceptual framework around which to understand its current therapeutic uses and consider potential further uses of botulinum toxin

Streaming algorithms for language recognition problems

We study the complexity of the following problems in the streaming model. Membership testing for \DLIN We show that every language in \DLIN\ can be recognised by a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error, and by a deterministic p-pass $O(n/p)$ space algorithm. We show that these algorithms are optimal. Membership testing for \LL$(k)$ For languages generated by \LL$(k)$ grammars with a bound of $r$ on the number of nonterminals at any stage in the left-most derivation, we show that membership can be tested by a randomized one-pass $O(r\log n)$ space algorithm with inverse polynomial (in $n$) one-sided error. Membership testing for \DCFL We show that randomized algorithms as efficient as the ones described above for \DLIN\ and \LL(k) (which are subclasses of \DCFL) cannot exist for all of \DCFL: there is a language in \VPL\ (a subclass of \DCFL) for which any randomized p-pass algorithm with error bounded by $\epsilon < 1/2$ must use $\Omega(n/p)$ space. Degree sequence problem We study the problem of determining, given a sequence $d_1, d_2,..., d_n$ and a graph $G$, whether the degree sequence of $G$ is precisely $d_1, d_2,..., d_n$. We give a randomized one-pass $O(\log n)$ space algorithm with inverse polynomial one-sided error probability. We show that our algorithms are optimal. Our randomized algorithms are based on the recent work of Magniez et al. \cite{MMN09}; our lower bounds are obtained by considering related communication complexity problems