Dark matter halo's and self similarity

This papers explores the self similar solutions of the Vlasov-Poisson system and their relation to the gravitational collapse of dynamically cold systems. Analytic solutions are derived for power law potential in one dimension, and extensions of these solutions in three dimensions are proposed. Next the self similarity of the collapse of cold dynamical systems is investigated numerically. The fold system in phase space is consistent with analytic self similar solutions, the solutions present all the proper self-similar scalings. An additional point is the appearance of an $x^{-(1/2)}$ law at the center of the system for initial conditions with power law index larger than $-(1/2)$. It is found that the first appearance of the $x^{-(1/2)}$ law corresponds to the formation of a singularity very close to the center. Finally the general properties of self similar multi dimensional solutions near equilibrium are investigated. Smooth and continuous self similar solutions have power law behavior at equilibrium. However cold initial conditions result in discontinuous phase space solutions, and the smoothed phase space density looses its auto similar properties. This problem is easily solved by observing that the probability distribution of the phase space density $P$ is identical except for scaling parameters to the probability distribution of the smoothed phase space density $P_S$. As a consequence $P_S$ inherit the self similar properties of $P$. This particular property is at the origin of the universal power law observed in numerical simulation for ${\rho}/{\sigma^3}$. The self similar properties of $P_S$ implies that other quantities should have also an universal power law behavior with predictable exponents. This hypothesis is tested using a numerical model of the phase space density of cold dark matter halo's, an excellent agreement is obtained.Comment: Final versio

General performance factors and group differences in assessment center ratings

PURPOSE – The purpose of this paper is to establish the extent of general performance factors (GPF) in assessment center (AC) exercises and dimensions. The study further aims to determine if larger GPF contributes to larger ethnic group differences across exercises and dimensions that are more cognitively loaded in an emerging market context. DESIGN/METHODOLOGY/APPROACH – The authors analyzed data across three independent AC samples (Sample 1: N = 172; Sample 2: N = 281; Sample 3: N = 428). The Schmid-Leiman solution was used to determine the extent of GPF in AC exercises and dimensions. An independent samples t-test and Cohen’s d was used to determine the size of ethnic group differences across exercises and dimensions. FINDINGS – The results indicate that GPF is consistently large for the in-basket exercise. Furthermore, dimensions that are more cognitively loaded, such as problem solving, strategic thinking, and business acumen, seem to produce the largest ethnic group differences. Overall, the research indicates that larger GPF is associated with larger ethnic group differences in relation to specific AC dimensions and exercises. ORIGINALITY/VALUE – The authors add to the literature by investigating the prevalence of a GPF in AC ratings across AC exercises and dimensions. A novel contribution of the research attempts to link the prevalence of a GPF in AC ratings to group membership in South Africa. The study offers an alternative statistical analysis procedure to examine GPF in AC ratings.IS

The Bane of Low-Dimensionality Clustering

In this paper, we give a conditional lower bound of $n^{\Omega(k)}$ on running time for the classic k-median and k-means clustering objectives (where n is the size of the input), even in low-dimensional Euclidean space of dimension four, assuming the Exponential Time Hypothesis (ETH). We also consider k-median (and k-means) with penalties where each point need not be assigned to a center, in which case it must pay a penalty, and extend our lower bound to at least three-dimensional Euclidean space. This stands in stark contrast to many other geometric problems such as the traveling salesman problem, or computing an independent set of unit spheres. While these problems benefit from the so-called (limited) blessing of dimensionality, as they can be solved in time $n^{O(k^{1-1/d})}$ or $2^{n^{1-1/d}}$ in d dimensions, our work shows that widely-used clustering objectives have a lower bound of $n^{\Omega(k)}$, even in dimension four. We complete the picture by considering the two-dimensional case: we show that there is no algorithm that solves the penalized version in time less than $n^{o(\sqrt{k})}$, and provide a matching upper bound of $n^{O(\sqrt{k})}$. The main tool we use to establish these lower bounds is the placement of points on the moment curve, which takes its inspiration from constructions of point sets yielding Delaunay complexes of high complexity

Random Triangle Theory with Geometry and Applications

What is the probability that a random triangle is acute? We explore this old question from a modern viewpoint, taking into account linear algebra, shape theory, numerical analysis, random matrix theory, the Hopf fibration, and much much more. One of the best distributions of random triangles takes all six vertex coordinates as independent standard Gaussians. Six can be reduced to four by translation of the center to $(0,0)$ or reformulation as a 2x2 matrix problem. In this note, we develop shape theory in its historical context for a wide audience. We hope to encourage other to look again (and differently) at triangles. We provide a new constructive proof, using the geometry of parallelians, of a central result of shape theory: Triangle shapes naturally fall on a hemisphere. We give several proofs of the key random result: that triangles are uniformly distributed when the normal distribution is transferred to the hemisphere. A new proof connects to the distribution of random condition numbers. Generalizing to higher dimensions, we obtain the "square root ellipticity statistic" of random matrix theory. Another proof connects the Hopf map to the SVD of 2 by 2 matrices. A new theorem describes three similar triangles hidden in the hemisphere. Many triangle properties are reformulated as matrix theorems, providing insight to both. This paper argues for a shift of viewpoint to the modern approaches of random matrix theory. As one example, we propose that the smallest singular value is an effective test for uniformity. New software is developed and applications are proposed

Assessment Report of Surveillance System and Outbreak Investigation in Yello Health Center, Loma District: Case Study

Surveillance is used for the application of health information for action under the following general set of conditions: in case of emergency situation, when timely response is demanded, needs public health epidemiologist must travel to & work in the field to solve the problem and when the extent of investigation is likely to be limited because of the imperative for timely intervention.The WHO-AFRO IDSR strategy focuses on the district level, but the goal of the IDSR strategy is to develop sufficient surveillance and response capacities at each level of the national system so that a flexible national infectious disease surveillance system will result. In a national adaptation of the strategy, a country might choose to focus initially on a few diseases depending on national resources and capacities.This study was done to assess the public health surveillance system and outbreak investigation in selected Yello Health Center, Loma District, South Ethiopia by using a cross sectional study was conducted from January 14-25 2/ 2012 in Yello Health Center.The data from different case team units in the health center is compiled but not analyzed by person, place and time dimensions. They perform trend analysis for malaria case only. They are using the information from statistics office to get denominator populationsSupervisors from woreda health office came to the health center three times in the past six months. The health center had made once supervision per month on the facilities under the health office i.e. health posts but no document was found about the supervision at all health posts.The health center has received written feedback from woreda health office but not from regional and supervisors. There is no standard case management protocol and contingency plan for epidemic prone diseases and possible outbreak in the health center. Activities conducted by health center on communicable disease prevention and control during the past 3 month includes Vitamin A supplementation, health education, malaria case management, ITN distribution and mass campaign like DDT spray. There is epidemic committee at the health center level. They are contributing to epidemic response activities by conducting case management, providing health education and immunization activities.Based on the assessment made, there is slightly alive surveillance system in the health center.The activities of IDSR system in health center are poor as it is evidenced by poor recording, analyzing, reporting, supervision and feedback. Therefore, a health center should create a link between laboratory and epidemiologic surveillance and need to increase the capacity to confirm cases and report to next higher level and reporting pattern of priority diseases need to be frequent and in line with the guideline. This works similarly for reporting to higher level and feedback to health posts. Keywords: IDSR, outbreak, Yello, catchment area, Loma Distric

THE IDENTIFICATION OF SOCIAL VALUE PROPOSITION IN SOCIAL ENTREPRENEURSHIP ORGANIZATION (A STUDY CASE RUMAH CEMARA)

Economic stability has an important role in nation’s development. The stronger the economy, the more a nation could improve its development, and vice versa. The economic growth could be supported by the number of entrepreneurs in a country. To increase the economic growth, there should be at least 2% entrepreneurs of the total population. In fact, the number of young entrepreneurs in Indonesia is still lagging with only 1,56%. As a part of entrepreneurship, social entrepreneurship is one of the factors that could bring positive impact to the nation’s development since it helps the country to solve social problems that occurs. One of the social problem that occurred in Indonesia is drugs abuse, driven by the data of Badan Narkotika Nasional (BNN) stated that the estimated number of the drugs users in Indonesia around 5 million people in 2015 and it’s increasing each year. Rumah Cemara is one of the social entrepreneur organization that put its concern on the social problem in Indonesia, focusing on the drug abuse and HIV/AIDS. This study explores the social value proposition within the social entrepreneurship organization. In particular, the authors evaluate the utilization of all the three dimensions which interpreted by Timmons for social entrepreneurship that consist of social need as the opportunity, social venture capital as the resource, also external stakeholder and internal stakeholder as the team and additional from Daryl Poon which consist political environment, legal environment, social environment, cultural environment and institutional environment. Study conducted by asking four higher up people of Rumah Cemara as the respondents. The purpose of this study to identified the social value proposition within the organization. Result revealed that there is no donor for the sport development program especially boxing, the organization need to develop their entrepreneurship program which is only contribute 3% to the allocation budget, also the treatment center only able to accommodate no more than 30 people, and the. It is recommended that for the future improving its own business unit, and the capacity of the treatment center in order to increase its performance and become sustainable