Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

Economic Impact of Identity Theft in India: Lessons from Western Countries

In this computerized, globalised and internet world our computer collects various types of information’s about every human being and stores them in files secreted deep on its hard drive. Files like cache, browser history and other temporary Internet files can be used to store sensitive information like logins and passwords, names addresses, and even credit card numbers. Now, a hacker can get at this information by wrong means and share with someone else or can install some nasty software on your computer that will extract your sensitive and secret information. Identity Theft posses a very serious problem to everyone today. If you have a driver’s license, a bank account, a computer, ration card number, PAN card number, ATM card or simply a social security number you are more than at risk, you are a target. Whether you are new to the idea of ID Theft, or you have some unanswered questions, we’ve compiled a quick refresher list below that should bring you up to speed. Identity theft is a term used to refer to fraud that involves pretending to be someone else in order to steal money or get other benefits. Identity theft is a serious crime, which is increasing at tremendous rate all over the world after the Internet evolution. There is widespread agreement that identity theft causes financial damage to consumers, lending institutions, retail establishments, and the economy as a whole. Surprisingly, there is little good public information available about the scope of the crime and the actual damages it inflicts. Accounts of identity theft in recent mass media and in film or literature have centered on the exploits of 'hackers' - variously lauded or reviled - who are depicted as cleverly subverting corporate firewalls or other data protection defenses to gain unauthorized access to credit card details, personnel records and other information. Reality is more complicated, with electronic identity fraud taking a range of forms. The impact of those forms is not necessarily quantifiable as a financial loss; it can involve intangible damage to reputation, time spent dealing with disinformation and exclusion from particular services because a stolen name has been used improperly. Overall we can consider electronic networks as an enabler for identity theft, with the thief for example gaining information online for action offline and the basis for theft or other injury online. As Fisher pointed out "These new forms of hightech identity and securities fraud pose serious risks to investors and brokerage firms across the globe," I am a victim of identity theft. Being a victim of identity theft I felt the need for creating an awareness among the computer and internet users particularly youngsters in India. Nearly 70 per cent of Indian‘s population are living in villages. Government of India already started providing computer and internet facilities even to the remote villages through various rural development and rural upliftment programmes. Highly educated people, established companies, world famous financial institutions are becoming victim of identity theft. The question here is how vulnerable the illiterate and innocent rural people are if they suddenly exposed to a new device through which some one can extract and exploit their personal data without their knowledge? In this research work an attempt has been made to bring out the real problems associated with Identity theft in developed countries from an economist point of view.

Stability of preconditioned finite volume schemes at low Mach numbers

In [4], Guillard and Viozat propose a finite volume method for the simulation of inviscid steady as well as unsteady flows at low Mach numbers, based on a preconditioning technique. The scheme satisfies the results of a single scale asymptotic analysis in a discrete sense and comprises the advantage that this can be derived by a slight modification of the dissipation term within the numerical flux function. Unfortunately, it can be observed by numerical experiments that the preconditioned approach combined with an explicit time integration scheme turns out to be unstable if the time step Dt does not satisfy the requirement to be O(M2) as the Mach number M tends to zero, whereas the corresponding standard method remains stable up to Dt=O(M), M to 0, which results from the well-known CFL-condition. We present a comprehensive mathematical substantiation of this numerical phenomenon by means of a von Neumann stability analysis, which reveals that in contrast to the standard approach, the dissipation matrix of the preconditioned numerical flux function possesses an eigenvalue growing like M-2 as M tends to zero, thus causing the diminishment of the stability region of the explicit scheme. Thereby, we present statements for both the standard preconditioner used by Guillard and Viozat [4] and the more general one due to Turkel [21]. The theoretical results are after wards confirmed by numerical experiments.

Numerical Simulation of Flows at Low Mach Numbers with Heat Sources

This work is concerned with finite volume methods for flows at low mach numbers which are under buoyancy and heat sources. As a particular application, fires in car tunnels will be considered. To extend the scheme for compressible flow into the low Mach number regime, a preconditioning technique is used and a stability result on this is proven. The source terms for gravity and heat are incorporated using operator splitting and the resulting method is analyzed.

Estimators and Tests based on Likelihood-Depth with Application to Weibull Distribution, Gaussian and Gumbel Copula

In dieser Arbeit werden mithilfe der Likelihood-Tiefen, eingeführt von Mizera und Müller (2004), (ausreißer-)robuste Schätzfunktionen und Tests für den unbekannten Parameter einer stetigen Dichtefunktion entwickelt. Die entwickelten Verfahren werden dann auf drei verschiedene Verteilungen angewandt. Für eindimensionale Parameter wird die Likelihood-Tiefe eines Parameters im Datensatz als das Minimum aus dem Anteil der Daten, für die die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, und dem Anteil der Daten, für die diese Ableitung nicht positiv ist, berechnet. Damit hat der Parameter die größte Tiefe, für den beide Anzahlen gleich groß sind. Dieser wird zunächst als Schätzer gewählt, da die Likelihood-Tiefe ein Maß dafür sein soll, wie gut ein Parameter zum Datensatz passt. Asymptotisch hat der Parameter die größte Tiefe, für den die Wahrscheinlichkeit, dass für eine Beobachtung die Ableitung der Loglikelihood-Funktion nach dem Parameter nicht negativ ist, gleich einhalb ist. Wenn dies für den zu Grunde liegenden Parameter nicht der Fall ist, ist der Schätzer basierend auf der Likelihood-Tiefe verfälscht. In dieser Arbeit wird gezeigt, wie diese Verfälschung korrigiert werden kann sodass die korrigierten Schätzer konsistente Schätzungen bilden. Zur Entwicklung von Tests für den Parameter, wird die von Müller (2005) entwickelte Simplex Likelihood-Tiefe, die eine U-Statistik ist, benutzt. Es zeigt sich, dass für dieselben Verteilungen, für die die Likelihood-Tiefe verfälschte Schätzer liefert, die Simplex Likelihood-Tiefe eine unverfälschte U-Statistik ist. Damit ist insbesondere die asymptotische Verteilung bekannt und es lassen sich Tests für verschiedene Hypothesen formulieren. Die Verschiebung in der Tiefe führt aber für einige Hypothesen zu einer schlechten Güte des zugehörigen Tests. Es werden daher korrigierte Tests eingeführt und Voraussetzungen angegeben, unter denen diese dann konsistent sind. Die Arbeit besteht aus zwei Teilen. Im ersten Teil der Arbeit wird die allgemeine Theorie über die Schätzfunktionen und Tests dargestellt und zudem deren jeweiligen Konsistenz gezeigt. Im zweiten Teil wird die Theorie auf drei verschiedene Verteilungen angewandt: Die Weibull-Verteilung, die Gauß- und die Gumbel-Copula. Damit wird gezeigt, wie die Verfahren des ersten Teils genutzt werden können, um (robuste) konsistente Schätzfunktionen und Tests für den unbekannten Parameter der Verteilung herzuleiten. Insgesamt zeigt sich, dass für die drei Verteilungen mithilfe der Likelihood-Tiefen robuste Schätzfunktionen und Tests gefunden werden können. In unverfälschten Daten sind vorhandene Standardmethoden zum Teil überlegen, jedoch zeigt sich der Vorteil der neuen Methoden in kontaminierten Daten und Daten mit Ausreißern.

Contradictions within the Modern Food System: Nutritional Disbalance across the Globe, Its Main Drivers and Possible Ways Out

Contemporary food production, given the degree of technology being applied in it and the present state of scientific knowledge, should be able to feed the world. Corresponding statistics show that in fact the volumes of modern food production confirm this statement. Yet, the present nutritional situation across the globe leaves much to be desired: on the one hand the numbers of undernourished and malnourished people are still high and even growing in some regions, and on the other hand there is an increasing number of overweight and obese people who are experiencing (or are at risk of) adverse health impacts as consequences. The question arises how this situation is possible given the present state of food production and knowledge, and also in terms of nutrition basics when talking about the latter. When arguing about the main causes of the present situation with nutrition across the globe, it is the modern food system with its distortions that is often criticised with emphasis placed on inappropriate food distribution as one of the key problems. However it is not only food distribution that shapes inequalities in terms of food availability and accessibility – there is a number of other factors contributing to this situation including political influences. Each of the drivers of the present situation might affect more than one part and have outcomes in different dimensions. Therefore it makes sense to apply a holistic approach when viewing the modern food system, embracing all the elements and existing relationships between them for this will facilitate taking appropriate actions in order to target the desired outcome in the best possible way. Applying a systematic approach and linking various elements with corresponding interactions among them allows for picturing all the possible outcomes and hence finding the way for a better solution on global level – a solution to the present problem with nutritional disbalance across the globe.

Fast Learning by Bounding Likelihoods in Sigmoid Type Belief Networks

Sigmoid type belief networks, a class of probabilistic neural networks, provide a natural framework for compactly representing probabilistic information in a variety of unsupervised and supervised learning problems. Often the parameters used in these networks need to be learned from examples. Unfortunately, estimating the parameters via exact probabilistic calculations (i.e, the EM-algorithm) is intractable even for networks with fairly small numbers of hidden units. We propose to avoid the infeasibility of the E step by bounding likelihoods instead of computing them exactly. We introduce extended and complementary representations for these networks and show that the estimation of the network parameters can be made fast (reduced to quadratic optimization) by performing the estimation in either of the alternative domains. The complementary networks can be used for continuous density estimation as well.

Bit-Width Analysis for General Applications

It has been widely known that a significant part of the bits are useless or even unused during the program execution. Bit-width analysis targets at finding the minimum bits needed for each variable in the program, which ensures the execution correctness and resources saving. In this paper, we proposed a static analysis method for bit-widths in general applications, which approximates conservatively at compile time and is independent of runtime conditions. While most related work focus on integer applications, our method is also tailored and applicable to floating point variables, which could be extended to transform floating point number into fixed point numbers together with precision analysis. We used more precise representations for data value ranges of both scalar and array variables. Element level analysis is carried out for arrays. We also suggested an alternative for the standard fixed-point iterations in bi-directional range analysis. These techniques are implemented on the Trimaran compiler structure and tested on a set of benchmarks to show the results.

The Inertio-Elastic Planar Entry Flow of Low-Viscosity Elastic Fluids in Micro-fabricated Geometries

The non-Newtonian flow of dilute aqueous polyethylene oxide (PEO) solutions through microfabricated planar abrupt contraction-expansions is investigated. The contraction geometries are fabricated from a high-resolution chrome mask and cross-linked PDMS gels using the tools of soft-lithography. The small length scales and high deformation rates in the contraction throat lead to significant extensional flow effects even with dilute polymer solutions having time constants on the order of milliseconds. The dimensionless extra pressure drop across the contraction increases by more than 200% and is accompanied by significant upstream vortex growth. Streak photography and videomicroscopy using epifluorescent particles shows that the flow ultimately becomes unstable and three-dimensional. The moderate Reynolds numbers (0.03 ≤ Re ≤ 44) associated with these high Deborah number (0 ≤ De ≤ 600) microfluidic flows results in the exploration of new regions of the Re-De parameter space in which the effects of both elasticity and inertia can be observed. Understanding such interactions will be increasingly important in microfluidic applications involving complex fluids and can best be interpreted in terms of the elasticity number, El = De/Re, which is independent of the flow kinematics and depends only on the fluid rheology and the characteristic size of the device.

Enseñar a aprender a pensar en los centros educativos, incluso en las actividades de evaluación.= Teaching to learn how to think at schools, even within assessment activities

El auténtico protagonismo de los centros educativos tiene que dirigirse a ayudar a pensar a sus alumnos y a enseñarlos a aprender, es decir, el docente tiene que enseñar estrategias de aprendizaje y debe promover el esfuerzo del estudiante para facilitar la construcción de esquemas y el aprendizaje permanente. El profesor debe utilizar cualquier situación de aprendizaje para enseñar dichas estrategias de aprendizaje, incluso en las situaciones de evaluación; por lo tanto, en este trabajo se sugiere que en las evaluaciones de los alumnos y alumnas se tenga en cuenta la metacognición como factor fundamental en el aprendizaje y la enseñanza

Kinship foster care: a study from the perspective of the of the caregivers, the children and the child welfare workers

In the last twenty years, in most Western countries, kinship foster care has become an integral part of childcare systems, growing progressively with regard to the numbers of children involved and relative weight as a care resource within the system; indeed, in some countries it is even more common than other placement options, such as non-kinship foster care and residential care. Research on this phenomenon is still recent and scarce, and there are few programmes targeting this population. In this article we present the results of a descriptive study on kinship foster care in the city of Barcelona, including information and data from the different stakeholders involved. From a quality of life research perspective we analyze the perceptions, evaluation and expressed satisfaction of caregivers, children and practitioners from the specialist Child and Adolescent Teams (EAIAs) responsible for the study and follow-up of kinship foster care cases. The research presented results are in line with those of current research in this field, and lays the basis for the future development of kinship foster care programmes

Numbers game

This is an exercise to use with groups. It was sent to Debra Morris in 2007, by David Jaques, an educationalist with many years' experience in groupwork.

MA17xexam01

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files

MA17xexam00pdf

Exam questions and solutions in PDF

MA17xexam00

Exam questions and solutions in LaTex. Diagrams for the questions are all together in the support.zip file, as .eps files