A Simple Algorithm for Hamiltonicity

We develop a new algebraic technique that solves the following problem: Given a black box that contains an arithmetic circuit $f$ over a field of characteristic $2$ of degree~$d$. Decide whether $f$, expressed as an equivalent multivariate polynomial, contains a multilinear monomial of degree $d$. This problem was solved by Williams \cite{W} and Bj\"orklund et. al. \cite{BHKK} for a white box (the circuit is given as an input) that contains arithmetic circuit. We show a simple black box algorithm that solves the problem with the same time complexity. This gives a simple randomized algorithm for the simple $k$-path problem for directed graphs of the same time complexity\footnote{$O^*(f(k))$ is $O(poly(n)\cdot f(k))$} $O^*(2^k)$ as in \cite{W} and with reusing the same ideas from \cite{BHKK} with the above gives another algorithm (probably not simpler) for undirected graphs of the same time complexity $O^*(1.657^k)$ as in \cite{B10,BHKK}

Error-Tolerant Non-Adaptive Learning of a Hidden Hypergraph

We consider the problem of learning the hypergraph using edge-detecting queries. In this model, the learner is allowed to query whether a set of vertices includes an edge from a hidden hypergraph. Except a few, all previous algorithms assume that a query\u27s result is always correct. In this paper we study the problem of learning a hypergraph where alpha -fraction of the queries are incorrect. The main contribution of this paper is generalizing the well-known structure CFF (Cover Free Family) to be Dense (we will call it DCFF - Dense Cover Free Family) while presenting three different constructions for DCFF. Later, we use these constructions wisely to give a polynomial time non-adaptive learning algorithm for a hypergraph problem with at most alpha-fracion incorrect queries. The hypergraph problem is also known as both monotone DNF learning problem, and complexes group testing problem

Learning Boolean Halfspaces with Small Weights from Membership Queries

We consider the problem of proper learning a Boolean Halfspace with integer weights $\{0,1,\ldots,t\}$ from membership queries only. The best known algorithm for this problem is an adaptive algorithm that asks $n^{O(t^5)}$ membership queries where the best lower bound for the number of membership queries is $n^t$ [Learning Threshold Functions with Small Weights Using Membership Queries. COLT 1999] In this paper we close this gap and give an adaptive proper learning algorithm with two rounds that asks $n^{O(t)}$ membership queries. We also give a non-adaptive proper learning algorithm that asks $n^{O(t^3)}$ membership queries

Comparison of Eight Weeks of Training in the Water and Land on Changes in Lumbar Lordosis of Girl Students of Yazd City

Introduction: Injuries related to lordosis 30 to 40 percent of spinal disorders have been allocated that the economic aspects of health care has also attracted attention. The aim of the present study was comparison of effect of eight weeks training in dry and water on change in lordosis of female students in Yazd. Materials and Methods: In this research 42 girls with lordosis in 9 to 12 years old were randomly selected from schools in Yazd and randomly divided into three groups of training in water (14 cases), land (n=14) and control group (14 people). Training program participants for eight weeks was carried out. Subject's lordosis was measured by flexible ruler as a noninvasive and reliable method of exercise before and after eight weeks. Repeated measures method was used for data analysis of pre-test and post-test. Results: The findings show that training on land and water had a positive effect on improving participant’s lordosis (P≤/05), but there was no significant difference in lordosis correction between two study groups (P≥/05). Conclusion: According to the results, both on land and water corrective exercise program for girls with lumbar lordosis is useful and there was no difference between the two programs in the reduction of lumbar lordosis. It is recommended that the land and water exercises for people with lumbar lordosis given, and each of these methods has its own specific characteristics which, according to experts identify the persons recommended.Keywords: Lordosis, Exercise on Land and Water, Corrective Exercise

Antibacterial, antioxidant and photocatalytic activity of novel Rubus ellipticus leaf mediated silver nanoparticles

Nanotechnology is an emerging field of science that has significant applications in applied sciences. In this study, silver nanoparticles (SNPs) were synthesized utilizing the leaf filtrate of Rubus ellipticus. SNPs were characterized using UV–visible spectroscopy, scanning electron microscopy, energy dispersive X-ray spectroscopy, and X-ray diffraction patterns to determine their morphology and chemical composition. The surface plasmon resonance of SNPs revealed a peak at 415 nm. The synthesized SNPs were mainly spherical crystals with an average size of 21.43 nm. When compared to plant extract and positive controls (AgNO3 and penicillin), SNPs demonstrated significant bactericidal activity against all the tested bacteria (gram-positive and gram-negative). The most effective bactericidal activity was found against Pseudomonas aeruginosa, with a minimum inhibitory concentration of 1.25 µg/mL. In addition, a dose-dependent antioxidant activity of SNPs was found against the 2,2-diphenyl-1-picrylhydrazyl (DPPH) free radical with an average IC50 value of 72.84 µg/mL. The photocatalytic activity of Methylene blue (MB) dye decomposition under sunlight was studied. The results showed that MB degraded by 98 % after 150 min in the sun. Overall, the findings of this study indicate that R. ellipticus biosynthesized SNPs may have bactericidal and photocatalytic effects