A stochastic model on the mean time to recruitment for a two graded manpower system associated with a univariate policy of recruitment involving combined thresholds using same geometric process for inter-decesion times

In this paper, an organization with two grades subjected to loss of manpower due to the policy decisions taken by the organization is considered. A mathematical model is constructed and an appropriate univariate recruitment policy, based on shock model approach involving combined optional thresholds and combined mandatory thresholds for the loss of manpower in the organization is suggested. The expected time for recruitment is obtained for different cases on the distribution of the thresholds when (i) the loss of manpower forms a sequence of independent and identically distributed exponential random variables and (ii) the inter-decision times for the two grades form the same geometric process. The analytical results are substantiated by numerical illustrations and relevant conclusions are presented

Variance of the Time to Recruitment in an Organization with Two Grades

In this paper, a two grade organization subjected to random exit of personal due to policy decisions taken by the organization is considered. There is an associated loss of manpower if a person quits. As the exit of personnel is unpredictable, a new recruitment policy involving two thresholds for each grade-one is optional and the other mandatory is suggested to enable the organization to plan its decision on recruitment. Based on shock model approach two mathematical models are constructed using an appropriate univariate policy of recruitment. Performance measures namely mean and variance of the time to recruitment are obtained for both the models when (i) the loss of manhours process forms a sequence of independent and identically distributed exponential random variables (ii) the inter-decision times are independent and identically distributed exponential random variables and (iii) the optional and mandatory thresholds are exponential random variables. The analytical results are substantiated by numerical illustrations and the influence of nodal parameters on the performance measures is also analyzed

Expected Time to Recruitment in an Organization with Two Grades using a Univariate Recruitment Policy Involving Two Thresholds

An organization with two grades subjected to loss of man power due to the policy decisions taken by the organization is considered in this paper. Two mathematical models are constructed and an appropriate univariate recruitment policy, based on shock model approach involving optional and mandatory thresholds for the loss of manhours in each grade is suggested. Performance measures namely mean and variance of the time to recruitment are obtained for both the models when (i) the loss of manhours process forms a sequence of independent and identically distributed exponential random variables (ii) the inter-decision times are independent and identically distributed exponential random variables and (iii) the optional thresholds are exponential random variable and the distributions of the mandatory thresholds have SCBZ property. The analytical results are substantiated by numerical illustrations and the influence of nodal parameters on the performance measures is also analyzed

Some new mathematical features in cascade theory

AbstractThe fluctuation problem in cascade theory is viewed from the standpoint of the invariant imbedding method of Bellman et al. [1]. The correlation functions that are used in the description of the electromagnetic cascades are shown to obey a simple system of two component vector differential equations. The advantage of the present method over the conventional approach of writing down Kolmogorov forward equations for these functions lies in that we encounter 2 × 2 matrices of a particular type only. In view of the simplicity of the structure it is possible to generalize the equations to correlation functions of arbitrary order. The reduction in dimension from 2n × 2n matrices to only 2 × 2 matrices which may, at first sight, appear perplexing is due to the fact that each of the 2n elements that appear in the single system of differential equations, corresponding to the two different initial conditions, can be obtained by considering 2n disjoint systems of two component vector equations. The imbedding technique is also used to arrive at the independent differential equations satisfied by sequent product densities that are encountered in more comprehensive description of electromagnetic cascades

Computing fuzzy rough approximations in large scale information systems

Rough set theory is a popular and powerful machine learning tool. It is especially suitable for dealing with information systems that exhibit inconsistencies, i.e. objects that have the same values for the conditional attributes but a different value for the decision attribute. In line with the emerging granular computing paradigm, rough set theory groups objects together based on the indiscernibility of their attribute values. Fuzzy rough set theory extends rough set theory to data with continuous attributes, and detects degrees of inconsistency in the data. Key to this is turning the indiscernibility relation into a gradual relation, acknowledging that objects can be similar to a certain extent. In very large datasets with millions of objects, computing the gradual indiscernibility relation (or in other words, the soft granules) is very demanding, both in terms of runtime and in terms of memory. It is however required for the computation of the lower and upper approximations of concepts in the fuzzy rough set analysis pipeline. Current non-distributed implementations in R are limited by memory capacity. For example, we found that a state of the art non-distributed implementation in R could not handle 30,000 rows and 10 attributes on a node with 62GB of memory. This is clearly insufficient to scale fuzzy rough set analysis to massive datasets. In this paper we present a parallel and distributed solution based on Message Passing Interface (MPI) to compute fuzzy rough approximations in very large information systems. Our results show that our parallel approach scales with problem size to information systems with millions of objects. To the best of our knowledge, no other parallel and distributed solutions have been proposed so far in the literature for this problem

An outbreak investigation of typhoid fever in Pondicherry, South India, 2013

Background: Preliminary investigation at Pediatric ward of Indira Gandhi Medical College revealed admission of a cluster of typhoid cases who were residents of one particular street in a nearby locality. Objectives: This study was undertaken to estimate the magnitude of the outbreak, identify the source of infection, and, thereby, institute control measures. Materials and Methods: An investigation team including 10 MBBS students carried out a sanitary survey, house-to-house survey, data collection using epidemiological case sheets, and spot mapping. Typhoid diagnosis was confirmed as per the IDSP guidelines, i.e., either a blood culture growth positive for Salmonella typhi or a fourfold rise in antibody titer. An age- and gender-matched case–control study was conducted to find the association of occurrence of typhoid with various possible sources of infection. Water samples were collected from the affected households and public taps for investigation. Results: Rapid survey of all the 6 streets of Thilaspet covered 1106 people living in 283 households. All nine confirmed cases were residents of one particular street. The attack rate calculated was 3.4% in this street. A significant association of occurrence of typhoid was found only with consumption of raw drinking water (OR = 12.6, P = 0.01). Water samples only from the affected street tested positive for the presence of coliforms. The sanitary survey documented water pipeline breakage at the junction of this street. Further spread of disease was stopped by advocating drinking of boiled water and repair of pipeline. Conclusion: Strengthening of disease surveillance for early identification of localized outbreaks and instituting control measures can effectively control disease spread