Discovering the roots: Uniform closure results for algebraic classes under factoring

Newton iteration (NI) is an almost 350 years old recursive formula that approximates a simple root of a polynomial quite rapidly. We generalize it to a matrix recurrence (allRootsNI) that approximates all the roots simultaneously. In this form, the process yields a better circuit complexity in the case when the number of roots $r$ is small but the multiplicities are exponentially large. Our method sets up a linear system in $r$ unknowns and iteratively builds the roots as formal power series. For an algebraic circuit $f(x_1,\ldots,x_n)$ of size $s$ we prove that each factor has size at most a polynomial in: $s$ and the degree of the squarefree part of $f$. Consequently, if $f_1$ is a $2^{\Omega(n)}$-hard polynomial then any nonzero multiple $\prod_{i} f_i^{e_i}$ is equally hard for arbitrary positive $e_i$'s, assuming that $\sum_i \text{deg}(f_i)$ is at most $2^{O(n)}$. It is an old open question whether the class of poly($n$)-sized formulas (resp. algebraic branching programs) is closed under factoring. We show that given a polynomial $f$ of degree $n^{O(1)}$ and formula (resp. ABP) size $n^{O(\log n)}$ we can find a similar size formula (resp. ABP) factor in randomized poly($n^{\log n}$)-time. Consequently, if determinant requires $n^{\Omega(\log n)}$ size formula, then the same can be said about any of its nonzero multiples. As part of our proofs, we identify a new property of multivariate polynomial factorization. We show that under a random linear transformation $\tau$, $f(\tau\overline{x})$ completely factors via power series roots. Moreover, the factorization adapts well to circuit complexity analysis. This with allRootsNI are the techniques that help us make progress towards the old open problems, supplementing the large body of classical results and concepts in algebraic circuit factorization (eg. Zassenhaus, J.NT 1969, Kaltofen, STOC 1985-7 \& Burgisser, FOCS 2001).Comment: 33 Pages, No figure

Active Physical Practice Followed by Mental Practice Using BCI-Driven Hand Exoskeleton: A Pilot Trial for Clinical Effectiveness and Usability

Appropriately combining mental practice (MP) and physical practice (PP) in a post-stroke rehabilitation is critical for ensuring a substantially positive rehabilitation outcome. Here we present a rehabilitation protocol incorporating a separate active PP stage followed by MP stage, using a hand exoskeleton and brain-computer interface (BCI). The PP stage was mediated by a force sensor feedback based assist-as-needed control strategy, whereas the MP stage provided BCI based multimodal neurofeedback combining anthropomorphic visual feedback and proprioceptive feedback of the impaired hand extension attempt. A 6 week long clinical trial was conducted on 4 hemiparetic stroke patients (screened out of 16) with left hand disability. The primary outcome, motor functional recovery, was measured in terms of changes in Grip-Strength (GS) and Action Research Arm Test (ARAT) scores; whereas the secondary outcome, usability of the system, was measured in terms of changes in mood, fatigue and motivation on a visual-analog-scale (VAS). A positive rehabilitative outcome was found as the group mean changes from the baseline in the GS and ARAT were +6.38 kg and +5.66 accordingly. The VAS scale measurements also showed betterment in mood (-1.38), increased motivation (+2.10) and reduced fatigue (-0.98) as compared to the baseline. Thus the proposed neurorehabilitation protocol is found to be promising both in terms of clinical effectiveness and usability

Understanding the genetic, molecular, and cellular basis of ageing as the biggest risk factor of Alzheimer's disease

Alzheimer’s disease (AD) is one of the leading causes of dementia. The disease is characterized by atrophy of brain tissue, with major physiological, molecular, and anatomical changes being observed in the hippocampus and entorhinal region of the temporal lobe. The risk of developing this disease increases with advancing age. Ageing is a chronological phenomenon wherein a considerable decline is observed in physiological functions due to the complex interplay of various exogenous and endogenous factors such as genetic construction, elevated levels of ROS, decrease in the telomerase activity, and epigenetic factors such as methylation of DNA, histone modification etc. The physiological and molecular changes in an ageing person especially in neurons overlap considerably with those observed during the progression of AD. This article highlights various factors responsible for ageing as well as AD with the latest review of literature. Understanding the factors that bring about the fated changes and how they are associated with the progression of disease can open new doors to bring about better treatment options and help cure an otherwise incurable disease. DOI: http://dx.doi.org/10.5281/zenodo.632379

A Survey on Community Detection Algorithm and Its Applications

Modern network science has made great improvements in the analysis of a large dynamic world. The existence of a community structure is one of the most prominent factors in these networks. Many algorithms have been proposed to detect structural characteristics and dynamic behaviour of networks over recent years. In this paper, present such a detailed study of recent community detection algorithm techniques such as clustering, modularity, dynamic, overlapped, etc based on various factors and their task in the analysis of the social network. Community detection enables us to evaluate participants with mutual interests or to discover a set of similar people on the basis of an area of interest, proposed a node influence k-nearest neighbours (NI-KNN) algorithm for detecting the community. Community detection is useful in many applications such as Recommendation Systems, Health care, politics, economics, e-commerce, social media, communication network, etc. A comparative analysis of different methods of community detection is also reported

Maternal morbidity due to unsafe medical abortion in rural practice is just the tip of the iceberg: is it really preventable?

Background: In India around 6.4 million abortions are performed annually, of which 3.6 million (56%) were unsafe abortions, account for 8-20% of all maternal deaths. Medical methods of abortion have been proven to be effective and safe option to save women’s lives when practiced under medical supervision. This study was carried out to determine the frequency of unsafe medical abortion, demographic profile of patients, reasons for seeking abortion, abortion providers, evaluation of significant adverse outcome and management.Methods: A 5 year retrospective observational study included 400 patients with history of unsafe medical abortion who were admitted with complications between June 2009 and May 2014, in the department of obstetrics and gynecology, government medical college (Chhattisgarh institute of medical sciences) and tertiary care hospital Bilaspur Chhattisgarh.Results: Unintended pregnancy was the main reason for the unsafe medical abortion in 378 (94.5%) women. Most frequent complains observed for admission were heavy bleeding and retained products (incomplete abortion). Major complications seen in 177 (44.25%) cases only, of which moderate to severe anaemia in 141 (35.25%), shock in 23 (5.75%), septicaemia in 11 (2.75%) and acute renal failure in 2 (0.5%) cases. Majority 206 (51.50%) required surgical intervention. However 5 (1.25%) patients could not survive despite of all resuscitative measures. Post-abortion family planning adopted by 27 (6.75%) cases only.Conclusions: Mostly unsafe abortions take place behind the scene, always remain unnoticed and never listed in government data. In Chhattisgarh state where majority of rural population are tribal, illiterate, living in difficult to reach areas, unaware of safe abortion and abortion rights and dependent on herbs, quacks or paramedics, due to unavailability of clinicians or lady medical officers in government facilities. Thus the best way remain to prevent unsafe abortion is the prevention of unwanted pregnancy