Conditioning and preconditioning of the optimal state estimation problem

Optimal state estimation is a method that requires minimising a weighted, nonlinear, least-squares objective function in order to obtain the best estimate of the current state of a dynamical system. Often the minimisation is non-trivial due to the large scale of the problem, the relative sparsity of the observations and the nonlinearity of the objective function. To simplify the problem the solution is often found via a sequence of linearised objective functions. The condition number of the Hessian of the linearised problem is an important indicator of the convergence rate of the minimisation and the expected accuracy of the solution. In the standard formulation the convergence is slow, indicating an ill-conditioned objective function. A transformation to different variables is often used to ameliorate the conditioning of the Hessian by changing, or preconditioning, the Hessian. There is only sparse information in the literature for describing the causes of ill-conditioning of the optimal state estimation problem and explaining the effect of preconditioning on the condition number. This paper derives descriptive theoretical bounds on the condition number of both the unpreconditioned and preconditioned system in order to better understand the conditioning of the problem. We use these bounds to explain why the standard objective function is often ill-conditioned and why a standard preconditioning reduces the condition number. We also use the bounds on the preconditioned Hessian to understand the main factors that affect the conditioning of the system. We illustrate the results with simple numerical experiments.

Corruption, governance and collective sanctions: : can a wicked problem be tamed?

Tackling a problem requires mostly, an ability to read it, conceptualize it, represent it, define it, and then applying the necessary mechanisms to solve it. This may sound self-evident except when the problem to be tackled happens to be “complex, “ “ill-structured,” and/or “wicked.” Corruption is one of those kinds of problems. Both in its global and national manifestations it is ill-structured. Where it is structural in nature, endemic and pervasive, it is perhaps even wicked. Qualities of the kind impose modest expectations regarding possibilities of any definitive solution to this insidious phenomenon. If so, it may not suffice to address the problem of corruption using existing categories of law and/or good governance, which overlook the “long-term memory” of the collective and cultural specific dimensions of the subject. Such socio-historical conditions require focusing on the interactive and self-reproducing networks of corruption and attempting to ‘subvert’ that phenomenon’s entire matrix. Concepts such as collective responsibility, collective punishment and sanctions are introduced as relevant categories in the structural, as well as behavioral, subversion of some of the most prevalent aspects of corruption. These concepts may help in the evolving of a new perspective on corruption fighting strategies.

Integrability and the demand for monetary assets: an alternative approach to an old problem

This note provides necessary and su¢cient conditions for some speci…c multidimensional consumer’s surplus welfare measures to be well posed (path independent). We motivate the problem by investigating partial-equilibrium measures of the welfare costs of in‡ation. The results can also be used for checking path independence of alternative de…nitions of Divisia indexes of monetary services. Consumer theory classically approaches the integrability problem by considering compensated demands, homothetic preferences or quasi-linear utility functions. Here, instead, we consider demands of monetary assets generated from a shopping-time perspective. Paralleling the above mentioned procedure, of …nding special classes of utility functions that satisfy the integrability conditions, we try to infer what particular properties of the transacting technology could assure path independence of multidimensional welfare measures. We show that the integrability conditions are satis…ed if and only if the transacting technology is blockwise weakly separable. We use two examples to clarify the point.

Prevention of mental ill-health and suicide: Public health perspectives

According to the World Health Organization (WHO) estimates for the year 2020, approximately 1.5 million people will commit suicide, and at least 10 times that many will make an attempt. This paper offers a brief overview of the current state of the epidemiology of suicide, a burgeoning public health problem. The information provided is based in large measure on reports of suicide mortality from 130/193 countries. In order to contextualize these data, this paper explores the contribution of both individual and sociocultural factors that influence suicidal behavior, from which much has been learned. Outlining the history of attempts by international and national organizations like WHO, United Nations, member states in the European community and other countries to regularize identification and suicide reporting procedures, this paper also demonstrates that serious knowledge gaps remain. Minimal requirements for successful evidence-based interventions are presented. (C) 2010 Published by Elsevier Masson SAS.

Electroconvulsive Therapy in Brazil After the "Psychiatric Reform" A Public Health Problem-Example From a University Service

Objectives: The Brazilian public health system does not provide electroconvulsive therapy (ECT), which is limited to a few academic services. National mental health policies are against ECT. Our objectives were to analyze critically the public policies toward ECT and present the current situation using statistics from the Institute of Psychiatry of the University of Sao Paulo (IPq-HCFMUSP) and summary data from the other 13 ECT services identified in the country. Methods: Data regarding ECT treatment at the IPq-HCFMUSP were collected from January 2009 to June 2010 (demographical, number of sessions, and diagnoses). All the data were analyzed using SPSS 19, Epic Info 2000, and Excel. Results: During this period, 331 patients were treated at IPq-HCFMUSP: 221 (67%) were from Sao Paulo city, 50 (15.2%) from Sao Paulo's metropolitan area, 39 (11.8%) from Sao Paulo's countryside, and 20 (6.1%) from other states; 7352 ECT treatments were delivered-63.0% (4629) devoted entirely via the public health system (although not funded by the federal government); the main diagnoses were a mood disorder in 86.4% and schizophrenia in 7.3% of the cases. Conclusions: There is an important lack of public assistance for ECT, affecting mainly the poor and severely ill patients. The university services are overcrowded and cannot handle all the referrals. The authors press for changes in the mental health policies.

On a Problem of Burnside

Burnside posed the question as to whether or not there exist groups having an external automorphism that behaves in a certain, specific way like an inner automorphism: we shall define such automorphisms to be nearly-inner. NI-groups are fairly rare. With the aid of the computer algebra system Magma - in particular with the aid of its small group database - we set out to test this hypothesis.

A study of nurses' perceptions of and participation in the resolution of treatment dilemmas for critically ill newborns

This study was an exploratory investigation of variables which are associated with neonatal intensive care nurses' perceptions of and participation in life-sustaining treatment decisions for critically ill newborns. The primary purpose of the research was to examine the extent to which assessment of infants' physical and mental prognoses, parents' preferences regarding treatment, and legal consequences of non-treatment influence nurses' recommendations about life-saving treatment decisions for handicapped newborns. Secondly, the research explored the extent and nature of nurses' reported participation in the resolution of treatment dilemmas for these critically ill newborns. The framework of the study draws upon the work of Crane (1977), Blum (1980), and Pearlman (1982) who have explored the sociological context of decision-making with critical care patients.^ Participants in the study were a volunteer sample of eighty-three registered nurses who were currently working in neonatal intensive care units in five large urban hospitals in Texas. Data were collected through the use of intensive interviews and case study questionnaires. Results from the study indicate that physical and mental prognoses as well as parent preferences and concerns about legal liability are related to nurses' treatment recommendations, but their levels of significance vary according to the type of handicapping condition and whether the treatment questions are posed in terms of initiating aggressive therapy or withdrawing aggressive therapy.^ The majority of nurses reported that the extent of their participation in formal decision-making regarding handicapped newborns was fairly minimal although they provide much of the definitive data used to make decisions by physicians and parents. There was substantial evidence that nurse respondents perceive their primary role as advocates for critically ill newborns, and believe that their involvement in the resolution of treatment dilemmas should be increased. ^

Factors related to employment among chronically mentally ill patients

A descriptive study of demographic and psychosocial factors believed to be associated with employment was carried out through face-to-face interviews with 417 chronically mentally-ill patients. Subjects had been hospitalized a minimum of two times for psychiatric treatment, had been discharged from at least one of these hospitalizations in the two years prior to the study, and were currently residing within a specific community mental health center catchment area in Texas. The study group ranged in age from 16 to 68 years and over one-half had chart diagnoses of schizophrenia.^ A structured interview was developed which addressed current employment status, length of current employment, job title of current or last job, and detailed work history for the prior five years. Four measures of social support were included in the interview. Each subject was asked to identify one recent work and one recent non-work situation which had been stressful or very demanding. A coping questionnaire was verbally administered to measure the ways in which subjects had coped with these specific stressful situations.^ Analysis of results revealed that 27 percent of the sample was gainfully employed at time of interview. Differences between the employed and unemployed groups were analyzed by t-test an chi square. The employed demonstrated significantly more weeks of employment in the prior five years than the unemployed. The current jobs of the employed required a significantly higher relationship to "things" or inanimate objects than the last jobs of the unemployed. Subjects diagnosed as schizophrenic were significantly less likely to be employed than subjects with other diagnoses.^ Employed subjects scored significantly higher on three of four measures of social support than unemployed subjects, including reported frequency of social group attendance and/or meetings with mental health professionals. Problem-focused coping was used significantly more by the employed than by the unemployed to deal with stressful situations in the work, but not the non-work, context. ^

Problem-based learning supported by semantic techniques

Problem-based learning has been applied over the last three decades to a diverse range of learning environments. In this educational approach, different problems are posed to the learners so that they can develop different solutions while learning about the problem domain. When applied to conceptual modelling, and particularly to Qualitative Reasoning, the solutions to problems are models that represent the behaviour of a dynamic system. The learner?s task then is to bridge the gap between their initial model, as their first attempt to represent the system, and the target models that provide solutions to that problem. We propose the use of semantic technologies and resources to help in bridging that gap by providing links to terminology and formal definitions, and matching techniques to allow learners to benefit from existing models.

Structural efficiency variation with the problem size in some bending problems = Variación del rendimiento estructural con el tamaño del problema en algunos casos de flexión simple

Existe normalmente el propósito de obtener la mejor solución posible cuando se plantea un problema estructural, entendiendo como mejor la solución que cumpliendo los requisitos estructurales, de uso, etc., tiene un coste físico menor. En una primera aproximación se puede representar el coste físico por medio del peso propio de la estructura, lo que permite plantear la búsqueda de la mejor solución como la de menor peso. Desde un punto de vista práctico, la obtención de buenas soluciones—es decir, soluciones cuyo coste sea solo ligeramente mayor que el de la mejor solución— es una tarea tan importante como la obtención de óptimos absolutos, algo en general difícilmente abordable. Para disponer de una medida de la eficiencia que haga posible la comparación entre soluciones se propone la siguiente definición de rendimiento estructural: la razón entre la carga útil que hay que soportar y la carga total que hay que contabilizar (la suma de la carga útil y el peso propio). La forma estructural puede considerarse compuesta por cuatro conceptos, que junto con el material, definen una estructura: tamaño, esquema, proporción, y grueso.Galileo (1638) propuso la existencia de un tamaño insuperable para cada problema estructural— el tamaño para el que el peso propio agota una estructura para un esquema y proporción dados—. Dicho tamaño, o alcance estructural, será distinto para cada material utilizado; la única información necesaria del material para su determinación es la razón entre su resistencia y su peso especifico, una magnitud a la que denominamos alcance del material. En estructuras de tamaño muy pequeño en relación con su alcance estructural la anterior definición de rendimiento es inútil. En este caso —estructuras de “talla nula” en las que el peso propio es despreciable frente a la carga útil— se propone como medida del coste la magnitud adimensional que denominamos número de Michell, que se deriva de la “cantidad” introducida por A. G. M. Michell en su artículo seminal de 1904, desarrollado a partir de un lema de J. C. Maxwell de 1870. A finales del siglo pasado, R. Aroca combino las teorías de Galileo y de Maxwell y Michell, proponiendo una regla de diseño de fácil aplicación (regla GA), que permite la estimación del alcance y del rendimiento de una forma estructural. En el presente trabajo se estudia la eficiencia de estructuras trianguladas en problemas estructurales de flexión, teniendo en cuenta la influencia del tamaño. Por un lado, en el caso de estructuras de tamaño nulo se exploran esquemas cercanos al optimo mediante diversos métodos de minoración, con el objetivo de obtener formas cuyo coste (medido con su numero deMichell) sea muy próximo al del optimo absoluto pero obteniendo una reducción importante de su complejidad. Por otro lado, se presenta un método para determinar el alcance estructural de estructuras trianguladas (teniendo en cuenta el efecto local de las flexiones en los elementos de dichas estructuras), comparando su resultado con el obtenido al aplicar la regla GA, mostrando las condiciones en las que es de aplicación. Por último se identifican las líneas de investigación futura: la medida de la complejidad; la contabilidad del coste de las cimentaciones y la extensión de los métodos de minoración cuando se tiene en cuenta el peso propio. ABSTRACT When a structural problem is posed, the intention is usually to obtain the best solution, understanding this as the solution that fulfilling the different requirements: structural, use, etc., has the lowest physical cost. In a first approximation, the physical cost can be represented by the self-weight of the structure; this allows to consider the search of the best solution as the one with the lowest self-weight. But, from a practical point of view, obtaining good solutions—i.e. solutions with higher although comparable physical cost than the optimum— can be as important as finding the optimal ones, because this is, generally, a not affordable task. In order to have a measure of the efficiency that allows the comparison between different solutions, a definition of structural efficiency is proposed: the ratio between the useful load and the total load —i.e. the useful load plus the self-weight resulting of the structural sizing—. The structural form can be considered to be formed by four concepts, which together with its material, completely define a particular structure. These are: Size, Schema, Slenderness or Proportion, and Thickness. Galileo (1638) postulated the existence of an insurmountable size for structural problems—the size for which a structure with a given schema and a given slenderness, is only able to resist its self-weight—. Such size, or structural scope will be different for every different used material; the only needed information about the material to determine such size is the ratio between its allowable stress and its specific weight: a characteristic length that we name material structural scope. The definition of efficiency given above is not useful for structures that have a small size in comparison with the insurmountable size. In this case—structures with null size, inwhich the self-weight is negligible in comparisonwith the useful load—we use as measure of the cost the dimensionless magnitude that we call Michell’s number, an amount derived from the “quantity” introduced by A. G. M. Michell in his seminal article published in 1904, developed out of a result from J. C.Maxwell of 1870. R. Aroca joined the theories of Galileo and the theories of Maxwell and Michell, obtaining some design rules of direct application (that we denominate “GA rule”), that allow the estimation of the structural scope and the efficiency of a structural schema. In this work the efficiency of truss-like structures resolving bending problems is studied, taking into consideration the influence of the size. On the one hand, in the case of structures with null size, near-optimal layouts are explored using several minimization methods, in order to obtain forms with cost near to the absolute optimum but with a significant reduction of the complexity. On the other hand, a method for the determination of the insurmountable size for truss-like structures is shown, having into account local bending effects. The results are checked with the GA rule, showing the conditions in which it is applicable. Finally, some directions for future research are proposed: the measure of the complexity, the cost of foundations and the extension of optimization methods having into account the self-weight.

Desensitization of N-methyl-D-aspartate receptors: a problem of interpretation.

The phenomenon of desensitization is universal, but its mechanism is still ill-understood and controversial. A recently published study [Lin, F. & Stevens, C. F. (1994) J. Neurosci, 14, 2153-2160] attempted to cast light on the mechanism of desensitization of N-methyl-D-aspartate (NMDA) receptors, in particular the vexed question of whether the channel must open before it can desensitize. During the desensitizing preexposure to agonist in those experiments, more desensitization was produced when channel openings were observed than when no openings were observed. The conclusion that "desensitization occurs more rapidly from the open state" unfortunately was based on a stochastic fallacy, and we present here a theoretical treatment and illustration showing that the observed behavior is predicted by a simple mechanism in which desensitization can occur only from a shut state.

A study of the non-uniform convergence of the inverse of a doubly-infinite matrix associated with a boundary value problem in a waveguide /

"Contract AF33(616)-6079 Project No. 9-(13-6278), Task No. 40572. Sponsored by: Aeronautical Systems Division"

Solving the problem : a series of lectures by the late Rev. M.C.B. Mason /

Mode of access: Internet.

What's going on here? : the Collinwoods subdivision lead contamination problem.

Caption title.

Our currency problem,

Mode of access: Internet.