On The Critical Points of some Iteration Methods for Solving Algebraic Equations. Global Convergence Properties

In this work we give su±cient conditions for k-th approximations of the polynomial roots of f(x) when the Maehly{Aberth{Ehrlich, Werner-Borsch-Supan, Tanabe, Improved Borsch-Supan iteration methods fail on the next step. For these methods all non-attractive sets are found. This is a subsequent improvement of previously developed techniques and known facts. The users of these methods can use the results presented here for software implementation in Distributed Applications and Simulation Environ- ments. Numerical examples with graphics are shown.

Damage propagation in reinforced concrete frames under external blast loading

Iconic and significant buildings are the common target of bombings by terrorists causing large numbers of casualties and extensive property damage. Recent incidents were external bomb attacks on multi-storey buildings with reinforced concrete frames. Under a blast load circumstance, crucial damage initiates at low level storeys in a building and may then lead to a progressive collapse of whole or part of the structure. It is therefore important to identify the critical initial influence regions along the height, width and depth of the building exposed to blast effects and the structure response in order to assess the vulnerability of the structure to disproportionate and progressive collapse. This paper discusses the blast response and the propagation of its effects on a two dimensional reinforced concrete (RC) frame, designed to withstand normal gravity loads. The explicit finite element code, LS DYNA is used for the analysis. A complete RC portal frame seven storeys by six bays is modelled with reinforcement details and appropriate materials to simulate strain rate effects. Explosion loads derived from standard manuals are applied as idealized triangular pressures on the column faces of the numerical models. The analysis reports the influence of blast propagation as displacements and material yielding of the structural elements in the RC frame. The effected regions are identified and classified according to the load cases. This information can be used to determine the vulnerability of multi-storey RC buildings to various external explosion scenarios and designing buildings to resist blast loads.

Scour of the seabed under a pipeline in oscillating flow

The scour of the seabed under a pipeline is studied experimentally in this paper. Tests are carried out in a U-shaped oscillatory water tunnel with a box imbedded in the bottom of the test section. By use of the standard sand, clay and plastic grain as the seabed material, the influence of the bed material on the scour is studied. The relationship between the critical initial gap-to-diameter ratio above which no scour occurs and the parameters of the oscillating flow is obtained. The self-burial phenomenon. which occurs for the pipeline not fixed to two sidewalls of the test section, is not observed for the Bred pipeline. The effect of the pipe on sand wave formation is discussed. The maximum equilibrium scour depths For different initial gap-to-diameter ratios, different Kc numbers and different bed sands are also given in this paper.

Insertion dans les soins après une première hospitalisation dans un secteur pour psychose [Linkage to care after first hospitalisation for psychosis]

BACKGROUND: First hospitalisation for a psychotic episode causes intense distress to patients and families, but offers an opportunity to make a diagnosis and start treatment. However, linkage to outpatient psychiatric care remains a notoriously difficult step for young psychotic patients, who frequently interrupt treatment after hospitalisation. Persistence of symptoms, and untreated psychosis may therefore remain a problem despite hospitalisation and proper diagnosis. With persisting psychotic symptoms, numerous complications may arise: breakdown in relationships, loss of family and social support, loss of employment or study interruption, denial of disease, depression, suicide, substance abuse and violence. Understanding mechanisms that might promote linkage to outpatient psychiatric care is therefore a critical issue, especially in early intervention in psychotic disorders. OBJECTIVE: To study which factors hinder or promote linkage of young psychotic patients to outpatient psychiatric care after a first hospitalisation, in the absence of a vertically integrated program for early psychosis. Method. File audit study of all patients aged 18 to 30 who were admitted for the first time to the psychiatric University Hospital of Lausanne in the year 2000. For statistical analysis, chi2 tests were used for categorical variables and t-test for dimensional variables; p<0.05 was considered as statistically significant. RESULTS: 230 patients aged 18 to 30 were admitted to the Lausanne University psychiatric hospital for the first time during the year 2000, 52 of them with a diagnosis of psychosis (23%). Patients with psychosis were mostly male (83%) when compared with non-psychosis patients (49%). Furthermore, they had (1) 10 days longer mean duration of stay (24 vs 14 days), (2) a higher rate of compulsory admissions (53% vs 22%) and (3) were more often hospitalised by a psychiatrist rather than by a general practitioner (83% vs 53%). Other socio-demographic and clinical features at admission were similar in the two groups. Among the 52 psychotic patients, 10 did not stay in the catchment area for subsequent treatment. Among the 42 psychotic patients who remained in the catchment area after discharge, 20 (48%) did not attend the scheduled or rescheduled outpatient appointment. None of the socio demographic characteristics were associated with attendance to outpatient appointments. On the other hand, voluntary admission and suicidal ideation before admission were significantly related to attending the initial appointment. Moreover, some elements of treatment seemed to be associated with higher likelihood to attend outpatient treatment: (1) provision of information to the patient regarding diagnosis, (2) discussion about the treatment plan between in- and outpatient staff, (3) involvement of outpatient team during hospitalisation, and (4) elaboration of concrete strategies to face basic needs, organise daily activities or education and reach for help in case of need. CONCLUSION: As in other studies, half of the patients admitted for a first psychotic episode failed to link to outpatient psychiatric care. Our study suggests that treatment rather than patient's characteristics play a critical role in this phenomenon. Development of a partnership and involvement of patients in the decision process, provision of good information regarding the illness, clear definition of the treatment plan, development of concrete strategies to cope with the illness and its potential complications, and involvement of the outpatient treating team already during hospitalisation, all came out as critical strategies to facilitate adherence to outpatient care. While the current rate of disengagement after admission is highly concerning, our finding are encouraging since they constitute strategies that can easily be implemented. An open approach to psychosis, the development of partnership with patients and a better coordination between inpatient and outpatient teams should therefore be among the targets of early intervention programs. These observations might help setting up priorities when conceptualising new programs and facilitate the implementation of services that facilitate engagement of patients in treatment during the critical initial phase of psychotic disorders.

Empilhamento sísmico por superfície de reflexão comum: um novo algoritmo usando otimização global e local

O método de empilhamento sísmico por Superfície de Reflexão Comum (ou empilhamento SRC) produz a simulação de seções com afastamento nulo (NA) a partir dos dados de cobertura múltipla. Para meios 2D, o operador de empilhamento SRC depende de três parâmetros que são: o ângulo de emergência do raio central com fonte-receptor nulo (β₀), o raio de curvatura da onda ponto de incidência normal (R_NIP) e o raio de curvatura da onda normal (R_N). O problema crucial para a implementação do método de empilhamento SRC consiste na determinação, a partir dos dados sísmicos, dos três parâmetros ótimos associados a cada ponto de amostragem da seção AN a ser simulada. No presente trabalho foi desenvolvido uma nova sequência de processamento para a simulação de seções AN por meio do método de empilhamento SRC. Neste novo algoritmo, a determinação dos três parâmetros ótimos que definem o operador de empilhamento SRC é realizada em três etapas: na primeira etapa são estimados dois parâmetros (β°₀ e R°_NIP) por meio de uma busca global bidimensional nos dados de cobertura múltipla. Na segunda etapa é usado o valor de β°₀ estimado para determinar-se o terceiro parâmetro (R°_N) através de uma busca global unidimensional na seção AN resultante da primeira etapa. Em ambas etapas as buscas globais são realizadas aplicando o método de otimização Simulated Annealing (SA). Na terceira etapa são determinados os três parâmetros finais (β₀, R_NIP e R_N) através uma busca local tridimensional aplicando o método de otimização Variable Metric (VM) nos dados de cobertura múltipla. Nesta última etapa é usado o trio de parâmetros (β°₀, R°_NIP, R°_N) estimado nas duas etapas anteriores como aproximação inicial. Com o propósito de simular corretamente os eventos com mergulhos conflitantes, este novo algoritmo prevê a determinação de dois trios de parâmetros associados a pontos de amostragem da seção AN onde há intersecção de eventos. Em outras palavras, nos pontos da seção AN onde dois eventos sísmicos se cruzam são determinados dois trios de parâmetros SRC, os quais serão usados conjuntamente na simulação dos eventos com mergulhos conflitantes. Para avaliar a precisão e eficiência do novo algoritmo, este foi aplicado em dados sintéticos de dois modelos: um com interfaces contínuas e outro com uma interface descontinua. As seções AN simuladas têm elevada razão sinal-ruído e mostram uma clara definição dos eventos refletidos e difratados. A comparação das seções AN simuladas com as suas similares obtidas por modelamento direto mostra uma correta simulação de reflexões e difrações. Além disso, a comparação dos valores dos três parâmetros otimizados com os seus correspondentes valores exatos calculados por modelamento direto revela também um alto grau de precisão. Usando a aproximação hiperbólica dos tempos de trânsito, porém sob a condição de R_NIP = R_N, foi desenvolvido um novo algoritmo para a simulação de seções AN contendo predominantemente campos de ondas difratados. De forma similar ao algoritmo de empilhamento SRC, este algoritmo denominado empilhamento por Superfícies de Difração Comum (SDC) também usa os métodos de otimização SA e VM para determinar a dupla de parâmetros ótimos (β₀, R_NIP) que definem o melhor operador de empilhamento SDC. Na primeira etapa utiliza-se o método de otimização SA para determinar os parâmetros iniciais β°₀ e R°_NIP usando o operador de empilhamento com grande abertura. Na segunda etapa, usando os valores estimados de β°₀ e R°_NIP, são melhorados as estimativas do parâmetro R_NIP por meio da aplicação do algoritmo VM na seção AN resultante da primeira etapa. Na terceira etapa são determinados os melhores valores de β°₀ e R°_NIP por meio da aplicação do algoritmo VM nos dados de cobertura múltipla. Vale salientar que a aparente repetição de processos tem como efeito a atenuação progressiva dos eventos refletidos. A aplicação do algoritmo de empilhamento SDC em dados sintéticos contendo campos de ondas refletidos e difratados, produz como resultado principal uma seção AN simulada contendo eventos difratados claramente definidos. Como uma aplicação direta deste resultado na interpretação de dados sísmicos, a migração pós-empilhamento em profundidade da seção AN simulada produz uma seção com a localização correta dos pontos difratores associados às descontinuidades do modelo.

Recent improvements in prediction of protein structure by global optimization of a potential energy function

Recent improvements of a hierarchical ab initio or de novo approach for predicting both α and β structures of proteins are described. The united-residue energy function used in this procedure includes multibody interactions from a cumulant expansion of the free energy of polypeptide chains, with their relative weights determined by Z-score optimization. The critical initial stage of the hierarchical procedure involves a search of conformational space by the conformational space annealing (CSA) method, followed by optimization of an all-atom model. The procedure was assessed in a recent blind test of protein structure prediction (CASP4). The resulting lowest-energy structures of the target proteins (ranging in size from 70 to 244 residues) agreed with the experimental structures in many respects. The entire experimental structure of a cyclic α-helical protein of 70 residues was predicted to within 4.3 Å α-carbon (Cα) rms deviation (rmsd) whereas, for other α-helical proteins, fragments of roughly 60 residues were predicted to within 6.0 Å Cα rmsd. Whereas β structures can now be predicted with the new procedure, the success rate for α/β- and β-proteins is lower than that for α-proteins at present. For the β portions of α/β structures, the Cα rmsd's are less than 6.0 Å for contiguous fragments of 30–40 residues; for one target, three fragments (of length 10, 23, and 28 residues, respectively) formed a compact part of the tertiary structure with a Cα rmsd less than 6.0 Å. Overall, these results constitute an important step toward the ab initio prediction of protein structure solely from the amino acid sequence.

Active barnase variants with completely random hydrophobic cores.

The central structural feature of natural proteins is a tightly packed and highly ordered hydrophobic core. If some measure of exquisite, native-like core packing is necessary for enzymatic function, this would constitute a significant obstacle to the development of novel enzymes, either by design or by natural or experimental evolution. To test the minimum requirements for a core to provide sufficient structural integrity for enzymatic activity, we have produced mutants of the ribonuclease barnase in which 12 of the 13 core residues have together been randomly replaced by hydrophobic alternatives. Using a sensitive biological screen, we find that a strikingly high proportion of these mutants (23%) retain enzymatic activity in vivo. Further substitution at the 13th core position shows that a similar proportion of completely random hydrophobic cores supports enzyme function. Of the active mutants produced, several have no wild-type core residues. These results imply that hydrophobicity is nearly a sufficient criterion for the construction of a functional core and, in conjunction with previous studies, that refinement of a crudely functional core entails more stringent sequence constraints than does the initial attainment of crude core function. Since attainment of crude function is the critical initial step in evolutionary innovation, the relatively scant requirements contributed by the hydrophobic core would greatly reduce the initial hurdle on the evolutionary pathway to novel enzymes. Similarly, experimental development of novel functional proteins might be simplified by limiting core design to mere specification of hydrophobicity and using iterative mutation-selection to optimize core structure.

Critical time scales for advection–diffusion–reaction processes

The concept of local accumulation time (LAT) was introduced by Berezhkovskii and coworkers in 2010–2011 to give a finite measure of the time required for the transient solution of a reaction–diffusion equation to approach the steady–state solution (Biophys J. 99, L59 (2010); Phys Rev E. 83, 051906 (2011)). Such a measure is referred to as a critical time. Here, we show that LAT is, in fact, identical to the concept of mean action time (MAT) that was first introduced by McNabb in 1991 (IMA J Appl Math. 47, 193 (1991)). Although McNabb’s initial argument was motivated by considering the mean particle lifetime (MPLT) for a linear death process, he applied the ideas to study diffusion. We extend the work of these authors by deriving expressions for the MAT for a general one–dimensional linear advection–diffusion–reaction problem. Using a combination of continuum and discrete approaches, we show that MAT and MPLT are equivalent for certain uniform–to-uniform transitions; these results provide a practical interpretation for MAT, by directly linking the stochastic microscopic processes to a meaningful macroscopic timescale. We find that for more general transitions, the equivalence between MAT and MPLT does not hold. Unlike other critical time definitions, we show that it is possible to evaluate the MAT without solving the underlying partial differential equation (pde). This makes MAT a simple and attractive quantity for practical situations. Finally, our work explores the accuracy of certain approximations derived using the MAT, showing that useful approximations for nonlinear kinetic processes can be obtained, again without treating the governing pde directly.

Asymptotic Approximations in the Near-Integrated Model with a Non-Zero Initial Condition

This paper considers various asymptotic approximations in the near-integrated firstorder autoregressive model with a non-zero initial condition. We first extend the work of Knight and Satchell (1993), who considered the random walk case with a zero initial condition, to derive the expansion of the relevant joint moment generating function in this more general framework. We also consider, as alternative approximations, the stochastic expansion of Phillips (1987c) and the continuous time approximation of Perron (1991). We assess how these alternative methods provide or not an adequate approximation to the finite-sample distribution of the least-squares estimator in a first-order autoregressive model. The results show that, when the initial condition is non-zero, Perron's (1991) continuous time approximation performs very well while the others only offer improvements when the initial condition is zero.

Determination of the critical coupling of explosive synchronization transitions in scale-free networks by mean-field approximations

An explosive synchronization can be observed in scale-free networks when Kuramoto oscillators have natural frequencies equal to their number of connections. The present paper reports on mean-field approximations to determine the critical coupling of such explosive synchronization. It has been verified that the equation obtained for the critical coupling has an inverse dependence on the network average degree. This expression differs from those whose frequency distributions are unimodal and even. In this case, the critical coupling depends on the ratio between the first and second statistical moments of the degree distribution. Numerical simulations were also conducted to verify our analytical results.

Initial clinical experience with the 4-F self-expanding XPERT stent system for infrapopliteal treatment of patients with severe claudication and critical limb ischemia

PURPOSE: To evaluate the primary success and short-term patency associated with a new 4-F sheath-compatible self-expanding nitinol stent after failed conventional angioplasty of distal popliteal and infrapopliteal lesions in severe lifestyle-limiting claudication (LLC) and chronic critical limb ischemia (CLI). MATERIALS AND METHODS: Between May 2003 and July 2005, 35 patients with Rutherford category 3-5 disease (16 patients with CLI, 19 patients with LLC) underwent percutaneous transluminal angioplasty (PTA) and stent implantation. Indications for stent placement were residual stenosis, flow-limiting dissections, or elastic recoil after PTA. Before and after the intervention and during the 6-month follow-up, clinical investigation, color-flow and duplex Doppler ultrasonography, and digital subtraction angiography were performed. Technical success, primary patency at 6 months, clinical improvement as defined by Rutherford with clinical and hemodynamic measures, and complications were evaluated. RESULTS: A total of 22 patients underwent distal popliteal artery stent placement and 13 underwent tibioperoneal artery stent placement. Stent implantation was successfully performed in all patients. After stent placement, the primary cumulative patency rate for the study group at 6 months was 82%. The mean resting ankle-brachial index at baseline was 0.50 +/- 0.16 and significantly increased to 0.90 +/- 0.17 at 12-24 hours after intervention and 0.82 +/- 0.24 at latest follow-up (P < .001 for both). The sustained clinical improvement rate was 80% at the 6-month follow-up. The 6-month limb salvage rate regarding major amputation was 100%. The rate of major complications was 17%. CONCLUSIONS: Infrapopliteal application of the new nitinol stent is a safe, feasible, and effective method with good short-term patency rate in the treatment of severe LLC and chronic CLI.

The way forward : report on the preparatory phase of prefabricated building design and construction methodology: identifying critical issues and recommending the way forward

This is an initial report of the PolyU SD part of the team to study Pre-fabricated Building Design and Construction Methodology and marks the completion of Phase 1. It follows our first notes prepared for the meeting on 2 February that identified some critical issues including future lifestyles, life expectancy of buildings, sustainability, size, flexibility and planning considerations. It is also an expansion of our presentation in Dongguan on 23 February. It is not a comprehensive survey of existing approaches or possible ways forward, but it has homed in on certain specific issues and does give specific examples to make the suggestions concrete. It is recommended that more comprehensive research be done to establish previous work and experience internationally. It is also recommended that more research be done on lifestyles as a preliminary to developing at least three concepts for evaluation before proceeding to the detailed design of one concept for full prototyping and market testing. The goal at this point is not to define a single direction but to suggest several future trajectories for further consideration. By the same token, this report is not intended as an exhaustive description of the considerable base of knowledge and ideas brought by the PolyU team to this exciting task. Before taking on an issue of this magnitude and importance in the definition of Hong Kong's future, one must carry out a thoughtful analysis of the issues at hand and an informed definition of paradigms, directions, goals and methods whereby our energies can be best used in the next steps. This report is the result of this analysis

Identification of critical input variables for risk-based cost estimates for road maintenance and rehabilitation

An estimation of costs for maintenance and rehabilitation is subject to variation due to the uncertainties of input parameters. This paper presents the results of an analysis to identify input parameters that affect the prediction of variation in road deterioration. Road data obtained from 1688 km of a national highway located in the tropical northeast of Queensland in Australia were used in the analysis. Data were analysed using a probability-based method, the Monte Carlo simulation technique and HDM-4’s roughness prediction model. The results of the analysis indicated that among the input parameters the variability of pavement strength, rut depth, annual equivalent axle load and initial roughness affected the variability of the predicted roughness. The second part of the paper presents an analysis to assess the variation in cost estimates due to the variability of the overall identified critical input parameters.

Critical thinking and organisation theory : embedding a process to encourage graduate capabilities

The need for the development of effective business curricula that meets the needs of the marketplace has created an increase in the adoption of core competencies lists identifying appropriate graduate skills. Many organisations and tertiary institutions have individual graduate capabilities lists including skills deemed essential for success. Skills recognised as ‘critical thinking’ are popular inclusions on core competencies and graduate capability lists. While there is literature outlining ‘critical thinking’ frameworks, methods of teaching it and calls for its integration into business curricula, few studies actually identify quantifiable improvements achieved in this area. This project sought to address the development of ‘critical thinking’ skills in a management degree program by embedding a process for critical thinking within a theory unit undertaken by students early in the program. Focus groups and a student survey were used to identify issues of both content and implementation and to develop a student perspective on their needs in thinking critically. A process utilising a framework of critical thinking was integrated through a workbook of weekly case studies for group analysis, discussions and experiential exercises. The experience included formative and summative assessment. Initial results indicate a greater valuation by students of their experience in the organisation theory unit; better marks for mid semester essay assignments and higher evaluations on the university administered survey of students’ satisfaction.

Correcting mean-field approximations for birth-death-movement processes

On the microscale, migration, proliferation and death are crucial in the development, homeostasis and repair of an organism; on the macroscale, such effects are important in the sustainability of a population in its environment. Dependent on the relative rates of migration, proliferation and death, spatial heterogeneity may arise within an initially uniform field; this leads to the formation of spatial correlations and can have a negative impact upon population growth. Usually, such effects are neglected in modeling studies and simple phenomenological descriptions, such as the logistic model, are used to model population growth. In this work we outline some methods for analyzing exclusion processes which include agent proliferation, death and motility in two and three spatial dimensions with spatially homogeneous initial conditions. The mean-field description for these types of processes is of logistic form; we show that, under certain parameter conditions, such systems may display large deviations from the mean field, and suggest computationally tractable methods to correct the logistic-type description.