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}

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

Finding the Minimum-Weight k-Path

Given a weighted $n$-vertex graph $G$ with integer edge-weights taken from a range $[-M,M]$, we show that the minimum-weight simple path visiting $k$ vertices can be found in time \tilde{O}(2^k \poly(k) M n^\omega) = O^*(2^k M). If the weights are reals in $[1,M]$, we provide a $(1+\varepsilon)$-approximation which has a running time of \tilde{O}(2^k \poly(k) n^\omega(\log\log M + 1/\varepsilon)). For the more general problem of $k$-tree, in which we wish to find a minimum-weight copy of a $k$-node tree $T$ in a given weighted graph $G$, under the same restrictions on edge weights respectively, we give an exact solution of running time \tilde{O}(2^k \poly(k) M n^3) and a $(1+\varepsilon)$-approximate solution of running time \tilde{O}(2^k \poly(k) n^3(\log\log M + 1/\varepsilon)). All of the above algorithms are randomized with a polynomially-small error probability.Comment: To appear at WADS 201

Earlier stage for straggler detection and handling using combined CPU test and LATE methodology

Using MapReduce in Hadoop helps in lowering the execution time and power consumption for large scale data. However, there can be a delay in job processing in circumstances where tasks are assigned to bad or congested machines called "straggler tasks"; which increases the time, power consumptions and therefore increasing the costs and leading to a poor performance of computing systems. This research proposes a hybrid MapReduce framework referred to as the combinatory late-machine (CLM) framework. Implementation of this framework will facilitate early and timely detection and identification of stragglers thereby facilitating prompt appropriate and effective actions

Straggler handling approaches in mapreduce framework: a comparative study

The proliferation of information technology produces a huge amount of data called big data that cannot be processed by traditional database systems. These Various types of data come from different sources. However, stragglers are a major bottleneck in big data processing, and hence the early detection and accurate identification of stragglers can have important impacts on the performance of big data processing. This work aims to assess five stragglers identification methods: Hadoop native scheduler, LATE Scheduler, Mantri, MonTool, and Dolly. The performance of these techniques was evaluated based on three benchmarked methods: Sort, Grep and WordCount. The results show that the LATE Scheduler performs the best and it would be efficient to obtain better results for stragglers identification

On rr-Simple kk-Path

An $r$-simple $k$-path is a {path} in the graph of length $k$ that passes through each vertex at most $r$ times. The $r$-SIMPLE $k$-PATH problem, given a graph $G$ as input, asks whether there exists an $r$-simple $k$-path in $G$. We first show that this problem is NP-Complete. We then show that there is a graph $G$ that contains an $r$-simple $k$-path and no simple path of length greater than $4\log k/\log r$. So this, in a sense, motivates this problem especially when one's goal is to find a short path that visits many vertices in the graph while bounding the number of visits at each vertex. We then give a randomized algorithm that runs in time $$\mathrm{poly}(n)\cdot 2^{O( k\cdot \log r/r)}$$ that solves the $r$-SIMPLE $k$-PATH on a graph with $n$ vertices with one-sided error. We also show that a randomized algorithm with running time $\mathrm{poly}(n)\cdot 2^{(c/2)k/ r}$ with $c<1$ gives a randomized algorithm with running time \poly(n)\cdot 2^{cn} for the Hamiltonian path problem in a directed graph - an outstanding open problem. So in a sense our algorithm is optimal up to an $O(\log r)$ factor

Predicting the stress-strain behaviour of zeolite-cemented sand based on the unconfined compression test using GMDH type neural network

Stabilizing sand with cement is considered to be one of the most cost-effective and useful methods of in-situ soil improvement, and the effectiveness is often assessed using unconfined compressive tests. In certain cases, zeolite and cement blends have been used; however, even though this is a fundamental issue that affects the settlement response of a soil, very few attempts have been made to assess the stress-strain behaviour of the improved soil. Also, the majority of previous studies that predicted the unconfined compressive strength (UCS) of zeolite cemented sand did not examine the effect of the soil improvement variables and strain concurrently. Therefore, in this paper, an initiative is taken to predict the relationships for the stress-strain behaviour of cemented and zeolite-cemented sand. The analysis is based on using the unconfined compression test results and Group Method of Data Handling (GMDH) type Neural Network (NN). To achieve this end, 216 stress-strain diagrams resulting from unconfined compression tests for different cement and zeolite contents, relative densities, and curing times are collected and modelled via GMDH type NN. In order to increase the accuracy of the predictions, the parameters associated with successive stress and strain increments are considered. The results show that the suggested two and three hidden layer models appropriately characterise the stress-strain variations to produce accurate results. Moreover, the UCS values derived from this method are much more accurate than those provided in previous approaches. Moreover, the UCS values derived from this method are much more accurate than those provided in previous approaches which simply proposed the UCS values based on the content of the chemical binders, compaction, and/or curing time, not considering the relationship between stress and strain. Finally, GMDH models can be considered to be a powerful method to determine the mechanical properties of a soil including the stre

Analysis of Ethyl succinate and Ethyl β-riboside from Acalypha wilkesiana var. golden-yellow (Muell & Arg.)

Background: The genus, Acalypha is one of the many genera in the Euphorbiaceae family. A. wilkesiana var. golden-yellow (Muell &amp; Arg.) syn. A. wilkesiana var. tropical tempest is a species and variety employed in traditional medicine for the treatment of gastrointestinal disorders, inflammations, bacterial and skin fungal infections amongst many others. Before now, some biological investigations had been done but very limited chemical studies have been carried out on the plant. Objectives: This study was principally done to isolate chemical compound(s) inherent in the plant and also evaluate their antimicrobial potential. Methodology: The leaves were to extracted cold with 50% ethanol and the resultant aqueous crude extract partitioned with butanol. Isolates obtained from the silica-gel column chromatography of the butanol fraction were analysed for antimicrobial activities using the hole-in agar diffusion technique. The compounds were screened for both antibacterial and antifungal activities using the microbes namely, B. subtilis, S. aureus, E. coli, P. aeruginosa, S. typhi, V. cholerae and C. albicans. Results: Two compounds, designated as compounds W-1 [Rf (0.76); [n]20D (1.4333 )] and W-2 [Rf (0.58)] were isolated. The structures of W-1 and W-2 have been established to be 4-ethoxy-4-oxobutanoic acid (ethyl succinate) and 2-ethoxy-5(hydroxymethyl)-oxalane-3,4-diol (ethyl β-riboside) respectively using the 1H NMR, 13C NMR, MS and IR spectral techniques. Both compounds were inactive against B. subtilis, S. aureus and E. coli. Interestingly, W-1 and W-2 demonstrated very minimal activity against P. aeruginosa, S. typhi and V. cholerae. However, neither gave any anticandidal activity. Conclusion: The two isolates (though generally weakly active) would serve as chemotaxonomic markers for this species and variety in particular and the genus, Acalypha in general. Keywords: Ethyl succinate; ethyl β-riboside; A. wilkesiana var. golden-yellow (Muell &amp; Arg.

Dark Matter Spin-Dependent Limits for WIMP Interactions on 19-F by PICASSO

The PICASSO experiment at SNOLAB reports new results for spin-dependent WIMP interactions on $^{19}$F using the superheated droplet technique. A new generation of detectors and new features which enable background discrimination via the rejection of non-particle induced events are described. First results are presented for a subset of two detectors with target masses of $^{19}$F of 65 g and 69 g respectively and a total exposure of 13.75 $\pm$ 0.48 kgd. No dark matter signal was found and for WIMP masses around 24 GeV/c$^2$ new limits have been obtained on the spin-dependent cross section on $^{19}$F of $\sigma_F$ = 13.9 pb (90% C.L.) which can be converted into cross section limits on protons and neutrons of $\sigma_p$ = 0.16 pb and $\sigma_n$ = 2.60 pb respectively (90% C.L). The obtained limits on protons restrict recent interpretations of the DAMA/LIBRA annual modulations in terms of spin-dependent interactions.Comment: Revised version, accepted for publication in Phys. Lett. B, 20 pages, 7 figure

Addressing and Inspiring Vaccine Confidence in Black, Indigenous, and People of Color During the Coronavirus Disease 2019 Pandemic

During the coronavirus disease 2019 (COVID-19) pandemic, we have witnessed profound health inequities suffered by Black, Indigenous, and People of Color (BIPOC). These manifested as differential access to testing early in the pandemic, rates of severe disease and death 2-3 times higher than white Americans, and, now, significantly lower vaccine uptake compared with their share of the population affected by COVID-19. This article explores the impact of these COVID-19 inequities (and the underlying cause, structural racism) on vaccine acceptance in BIPOC populations, ways to establish trustworthiness of healthcare institutions, increase vaccine access for BIPOC communities, and inspire confidence in COVID-19 vaccines