Faster algorithm to find anti-risk path between two nodes of an undirected graph

For a weighted 2-edge connected graph G=(V,E), we are to find a “minimum risk path” from source s to destination t. This is a shortest s?t path under the assumption that at most one edge on the path may be blocked. The fact that the edge is blocked is known only when we reach a site adjacent to the blocked edge. If n and m are the number of nodes and edges of G, then we show that this problem can be solved in O(n ²) time using only simple data structures. This is an improvement over the previous O(mn+n ²logn) time algorithm. Moreover, with use of more complicated data structures like Fibonacci Heaps and transmuters the time can be further reduced to O(m+nlogn).     

Maximum cardinality neighbourly sets in quadrilateral free graphs

Neighbourly set of a graph is a subset of edges which either share an end point or are joined by an edge of that graph. The maximum cardinality neighbourly set problem is known to be NP-complete for general graphs. Mahdian (Discret Appl Math 118:239–248, 2002) proved that it is in polynomial time for quadrilateral-free graphs and proposed an \(O(n^{11})\) algorithm for the same, here n is the number of vertices in the graph, (along with a note that by a straightforward but lengthy argument it can be proved to be solvable in \(O(n^5)\) running time). In this paper we propose an \(O(n^2)\) time algorithm for finding a maximum cardinality neighbourly set in a quadrilateral-free graph.     

Exploring Home Sharing for Elders

Research suggests that third party-arranged home sharing (“TPAHS”) enables elders to remain at home in advanced age by connecting elder home owners with suitable live-in “matches.” TPAHS potentially saves elders, their families, and Medicaid budgets millions of a dollars per year in avoided and postponed nursing home costs. In interviews with elder TPAHS participants of one TPAHS program, we found that similarity in values, ability to utilize the TPAHS organization's guidance, and, when relevant, familiarity with their matches' mental health challenges, correlated with said participants' satisfaction with their matches while a lack of these qualities correlated with match dissatisfaction. With these findings in mind, we suggest strategies TPAHS organizations can use to best serve the elderly TPAHS participants who may benefit from intensified match support but may not seek it.     

Inference from the Exponentiated Weibull Model with Applications to Real Data

In this paper, a novel Bayesian framework is used to derive the posterior density function, predictive density for a single future response, a bivariate future response, and several future responses from the exponentiated Weibull model (EWM). We study three related types of models, the exponentiated exponential, exponentiated Weibull, and beta generalized exponential, which are all utilized to determine the goodness of fit of two real data sets. The statistical analysis indicates that the EWM best fits both data sets. We determine the predictive means, standard deviations, highest predictive density intervals, and the shape characteristics for a single future response. We also consider a new parameterization method to determine the posterior kernel densities for the parameters. The summary results of the parameters are calculated by using the Markov chain Monte Carlo method.     

From Ordinary to Shrinkage Square-Root Estimators

Consider a skewed population. Suppose an intelligent guess could be made about an interval that contains the population mean. There may exist biased estimators with smaller mean squared error than the arithmetic mean within such an interval. This article indicates when it is advisable to shrink the arithmetic mean towards a guessed interval using root estimators. The goal is to obtain an estimator that is better near the average of natural origins. An estimator proposed. This estimator contains the Thompson (1968 Thompson , J. R. ( 1968 ). Accuracy borrowing in the estimation of the mean by shrinkage towards an interval . J. Amer. Statist. Assoc. 63 : 953 – 963 . [CSA] [CROSSREF] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) ordinary shrinkage estimator, the Jenkins et al. (1973 Jenkins , O. C. , Ringer , L. J. , Hartley , H. O. ( 1973 ). Root estimators . J Amer. Statist. Assoc. 68 : 414 – 419 . [CSA] [CROSSREF] [Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) square-root estimator, and the arithmetic sample mean as special cases. The bias and the mean squared error of the proposed more general estimator is compared with the three special cases. Shrinkage coefficients that yield minimum mean squared error estimators are obtained. The proposed estimator is considerably more efficient than the three special cases. This remains true for highly skewed populations. The merits of the proposed shrinkage square-root estimator are supported by the results of numerical and simulation studies.     

On the inadmssibelity of ridge estimator in a linear model

The necessary and sufficient conditions for the inadmissibility of the ridge regression is discussed under two different criteria, namely, average loss and Pitman nearness. Although the two criteria are very different, same conclusions are obtained. The loss functions considered in this article are th likelihood loss function and the Mahalanobis loss function. The two loss functions are motivated from the point of view of classification of two normal populations. Under the Mahalanobis loss it is demonstrated that the ridge regression is always inadmissible as long as the errors are assumed to be symmetrically distributed about the origin.     

Algorithms for testing occurrences of length 4 patterns in permutations

In this paper linear time sequential and optimal parallel algorithms for testing pattern involvement for all length 4 permutations are described. This is an improvement as the previous best sequential algorithms, for most of these pattern require \(O(n\log n)\) time. Our parallel algorithms can be implemented in \(O(\log n)\) time with \(n/\log n\) processors on the CREW PRAM model, or alternatively in \(O(\log \log \log n)\) time with \(n/\log \log \log n\) processors on a CRCW PRAM PRAM model. Parallel algorithm can also be implemented in constant time with \(n\log ^3 n\) processors on a CRCW PRAM model. The previous best parallel algorithms were available for only some of these patterns and took \(O(\log n)\) time with n processors on the CREW PRAM model.     

“Breaking Even” under Intensification? Gendered Trade‐Offs for Women Milk Marketers in Kenya*

Despite the commonly vaunted “win‐win” prospect of combining intensified livestock production with greater gender equality, the benefits of formal marketization of livestock products are generally skewed toward men. In response to this global trend, there is a growing impetus to better understand the gender dynamics underlying women's market participation to curtail the risk of worsening gender inequalities in agricultural systems transitioning to intensified production. This study analyzes the spectrum of women's informal milk market practices in two Kenyan Counties undergoing dairy system intensification. Qualitative data were gathered from dairy stakeholders and market traders to explore the localized system of gender relations mediating women's engagement with milk markets and current practices. Results indicate that increased dairy intensification and informal market use is challenging existing gender norms and disrupting the boundaries between hegemonic (socially acceptable) and pariah (socially disruptive) gender relations. While women are generally better able to control the proceeds from their dairy labor in informal markets, they also face high social culpability and danger from engaging in illicit activities that transgress local norms. These contradictory “win‐lose” dynamics and trade‐offs highlight the contested nature of gender market relations under agricultural intensification and commercialization currently being pursued under low emissions dairy development (LEDD) in Kenya. The risk of exacerbating existing gender inequalities has profound implications for LEDD and agricultural intensification more broadly.     

A family of shrinkage estimators for Weibull shape parameter in censored sampling

In this paper a new class of shrinkage estimators has been introduced for the shape parameter in an independently identically distributed two-parameterWeibull model under censored sampling. The main idea is to incorporate the prior guessed value by correcting the standard estimator, which is essentially an unbiased estimator, with optimally weighted ratios of the guessed value and the standard estimator, instead of considering a convex combination of the standard estimator and the difference of the guessed value and the standard estimator. The resulting estimator dominates the standard estimator in a surprisingly large neighborhood of the guessed value. The suggested estimator has also been compared with the minimum mean squared error estimator and a class of estimators suggested by Singh and Shukla in IAPQR Trans 25(2), 107–118, 2000. It is found that the suggested class of estimators has lesser bias as well as lesser mean squared error than its competitors subject to certain conditions.