Hybrid mathematical and informational modeling of beam-to-column connections

The analysis of steel and composite frames has traditionally been carried out by idealizing beam-to-column connections as either rigid or pinned. Although some advanced analysis methods have been proposed to account for semi-rigid connections, the performance of these methods strongly depends on the proper modeling of connection behavior. The primary challenge of modeling beam-to-column connections is their inelastic response and continuously varying stiffness, strength, and ductility. In this dissertation, two distinct approaches—mathematical models and informational models—are proposed to account for the complex hysteretic behavior of beam-to-column connections. The performance of the two approaches is examined and is then followed by a discussion of their merits and deficiencies. To capitalize on the merits of both mathematical and informational representations, a new approach, a hybrid modeling framework, is developed and demonstrated through modeling beam-to-column connections. Component-based modeling is a compromise spanning two extremes in the field of mathematical modeling: simplified global models and finite element models. In the component-based modeling of angle connections, the five critical components of excessive deformation are identified. Constitutive relationships of angles, column panel zones, and contact between angles and column flanges, are derived by using only material and geometric properties and theoretical mechanics considerations. Those of slip and bolt hole ovalization are simplified by empirically-suggested mathematical representation and expert opinions. A mathematical model is then assembled as a macro-element by combining rigid bars and springs that represent the constitutive relationship of components. Lastly, the moment-rotation curves of the mathematical models are compared with those of experimental tests. In the case of a top-and-seat angle connection with double web angles, a pinched hysteretic response is predicted quite well by complete mechanical models, which take advantage of only material and geometric properties. On the other hand, to exhibit the highly pinched behavior of a top-and-seat angle connection without web angles, a mathematical model requires components of slip and bolt hole ovalization, which are more amenable to informational modeling. An alternative method is informational modeling, which constitutes a fundamental shift from mathematical equations to data that contain the required information about underlying mechanics. The information is extracted from observed data and stored in neural networks. Two different training data sets, analytically-generated and experimental data, are tested to examine the performance of informational models. Both informational models show acceptable agreement with the moment-rotation curves of the experiments. Adding a degradation parameter improves the informational models when modeling highly pinched hysteretic behavior. However, informational models cannot represent the contribution of individual components and therefore do not provide an insight into the underlying mechanics of components. In this study, a new hybrid modeling framework is proposed. In the hybrid framework, a conventional mathematical model is complemented by the informational methods. The basic premise of the proposed hybrid methodology is that not all features of system response are amenable to mathematical modeling, hence considering informational alternatives. This may be because (i) the underlying theory is not available or not sufficiently developed, or (ii) the existing theory is too complex and therefore not suitable for modeling within building frame analysis. The role of informational methods is to model aspects that the mathematical model leaves out. Autoprogressive algorithm and self-learning simulation extract the missing aspects from a system response. In a hybrid framework, experimental data is an integral part of modeling, rather than being used strictly for validation processes. The potential of the hybrid methodology is illustrated through modeling complex hysteretic behavior of beam-to-column connections. Mechanics-based components of deformation such as angles, flange-plates, and column panel zone, are idealized to a mathematical model by using a complete mechanical approach. Although the mathematical model represents envelope curves in terms of initial stiffness and yielding strength, it is not capable of capturing the pinching effects. Pinching is caused mainly by separation between angles and column flanges as well as slip between angles/flange-plates and beam flanges. These components of deformation are suitable for informational modeling. Finally, the moment-rotation curves of the hybrid models are validated with those of the experimental tests. The comparison shows that the hybrid models are capable of representing the highly pinched hysteretic behavior of beam-to-column connections. In addition, the developed hybrid model is successfully used to predict the behavior of a newly-designed connection.

Anemia screening in potential female blood donors: comparison of two different quantitative methods

Anemia screening before blood donation requires an accurate, quick, practical, and easy method with minimal discomfort for the donors. The aim of this study was to compare the accuracy of two quantitative methods of anemia screening: the HemoCue 201(+) (Aktiebolaget Leo Diagnostics) hemoglobin (Hb) and microhematocrit (micro-Hct) tests. Two blood samples of a single fingerstick were obtained from 969 unselected potential female donors to determine the Hb by HemoCue 201(+) and micro-Hct using HemataSTAT II (Separation Technology, Inc.), in alternating order. From each participant, a venous blood sample was drawn and run in an automatic hematology analyzer (ABX Pentra 60, ABX Diagnostics). Considering results of ABX Pentra 60 as true values, the sensitivity and specificity of HemoCue 201(+) and micro-Hct as screening methods were compared, using a venous Hb level of 12.0 g per dL as cutoff for anemia. The sensitivities of the HemoCue 201(+) and HemataSTAT II in detecting anemia were 56 percent (95% confidence interval [CI], 46.1%-65.5%) and 39.5 percent (95% CI, 30.2%-49.3%), respectively (p < 0.001). Analyzing only candidates with a venous Hb level lower than 11.0 g per dL, the deferral rate was 100 percent by HemoCue 201(+) and 77 percent by HemataSTAT II. The specificities of the methods were 93.5 and 93.2 percent, respectively. The HemoCue 201(+) showed greater discriminating power for detecting anemia in prospective blood donors than the micro-Hct method. Both presented equivalent deferral error rates of nonanemic potential donors. Compared to the micro-Hct, HemoCue 201(+) reduces the risk of anemic female donors giving blood, specially for those with lower Hb levels, without increasing the deferral of nonanemic potential donors.

Attitudes and practices of general practitioners in the diagnosis and management of attention-deficit/hyperactivity disorder

Objective: To assess understanding of, and actual and potential roles in management of attention-deficit/hyperactivity disorder (ADHD) among GPs. Methods: A cross-sectional questionnaire survey of Queensland GPs selected randomly from the Royal Australian College of General Practitioners directory of members was carried out. Main outcome measures were knowledge levels of ADHD, current management practices, referral patterns and self-perceived information and training needs. Results: Three hundred and ninety-nine GPs returned a completed questionnaire (response rate 76%). Roles identified by GPs were: the provisional diagnosis of ADHD and referral to specialist services for confirmation of the diagnosis and initiation of management; assistance with monitoring progress once a management plan was in place; education of the child and their family regarding the disorder; and liaison with the school where necessary. Perceived barriers to increased involvement of GPs were: time and resource constraints of general practice; concerns regarding abuse and addiction liability of prescription stimulants; complex diagnostic issues associated with childhood behavioural problems; and lack of training and education regarding ADHD. Conclusions: General practitioners identify a role for themselves in ADHD care that is largely supportive in nature and involves close liaison with specialist services.

Mathematical and numerical analysis for coagulation-fragmentation equations

Magdeburg, Univ., Fak. für Mathematik, Diss., 2010

A comparison of results from MRIO and interregional computable general equilibrium (CGE) analyses of the impacts of a positive demand shock on the ‘CO2 trade balance’ between Scotland and the rest of the UK

In previous work we have applied the environmental multi-region input-output (MRIO) method proposed by Turner et al (2007) to examine the ‘CO2 trade balance’ between Scotland and the Rest of the UK. In McGregor et al (2008) we construct an interregional economy-environment input-output (IO) and social accounting matrix (SAM) framework that allows us to investigate methods of attributing responsibility for pollution generation in the UK at the regional level. This facilitates analysis of the nature and significance of environmental spillovers and the existence of an environmental ‘trade balance’ between regions. While the existence of significant data problems mean that the quantitative results of this study should be regarded as provisional, we argue that the use of such a framework allows us to begin to consider questions such as the extent to which a devolved authority like the Scottish Parliament can and should be responsible for contributing to national targets for reductions in emissions levels (e.g. the UK commitment to the Kyoto Protocol) when it is limited in the way it can control emissions, particularly with respect to changes in demand elsewhere in the UK. However, while such analysis is useful in terms of accounting for pollution flows in the single time period that the accounts relate to, it is limited when the focus is on modelling the impacts of any marginal change in activity. This is because a conventional demand-driven IO model assumes an entirely passive supply-side in the economy (i.e. all supply is infinitely elastic) and is further restricted by the assumption of universal Leontief (fixed proportions) technology implied by the use of the A and multiplier matrices. In this paper we argue that where analysis of marginal changes in activity is required, a more flexible interregional computable general equilibrium approach that models behavioural relationships in a more realistic and theory-consistent manner, is more appropriate and informative. To illustrate our analysis, we compare the results of introducing a positive demand stimulus in the UK economy using both IO and CGE interregional models of Scotland and the rest of the UK. In the case of the latter, we demonstrate how more theory consistent modelling of both demand and supply side behaviour at the regional and national levels affect model results, including the impact on the interregional CO2 ‘trade balance’.

Complementarities between mathematical and computational modeling: the case of the repeated Prisoners' Dilemma

We study the properties of the well known Replicator Dynamics when applied to a finitely repeated version of the Prisoners' Dilemma game. We characterize the behavior of such dynamics under strongly simplifying assumptions (i.e. only 3 strategies are available) and show that the basin of attraction of defection shrinks as the number of repetitions increases. After discussing the difficulties involved in trying to relax the 'strongly simplifying assumptions' above, we approach the same model by means of simulations based on genetic algorithms. The resulting simulations describe a behavior of the system very close to the one predicted by the replicator dynamics without imposing any of the assumptions of the mathematical model. Our main conclusion is that mathematical and computational models are good complements for research in social sciences. Indeed, while computational models are extremely useful to extend the scope of the analysis to complex scenarios hard to analyze mathematically, formal models can be useful to verify and to explain the outcomes of computational models.

The three phases of the ensemble forecasting of niche models: geographic range and shifts in climatically suitable areas of Utetheisa ornatrix (Lepidoptera, Arctiidae)

Species' geographic ranges are usually considered as basic units in macroecology and biogeography, yet it is still difficult to measure them accurately for many reasons. About 20 years ago, researchers started using local data on species' occurrences to estimate broad scale ranges, thereby establishing the niche modeling approach. However, there are still many problems in model evaluation and application, and one of the solutions is to find a consensus solution among models derived from different mathematical and statistical models for niche modeling, climatic projections and variable combination, all of which are sources of uncertainty during niche modeling. In this paper, we discuss this approach of ensemble forecasting and propose that it can be divided into three phases with increasing levels of complexity. Phase I is the simple combination of maps to achieve a consensual and hopefully conservative solution. In Phase II, differences among the maps used are described by multivariate analyses, and Phase III consists of the quantitative evaluation of the relative magnitude of uncertainties from different sources and their mapping. To illustrate these developments, we analyzed the occurrence data of the tiger moth, Utetheisa ornatrix (Lepidoptera, Arctiidae), a Neotropical moth species, and modeled its geographic range in current and future climates.

A conceptual and practical overview of cDNA microarray technology: implications for basic and clinical sciences

cDNA microarray is an innovative technology that facilitates the analysis of the expression of thousands of genes simultaneously. The utilization of this methodology, which is rapidly evolving, requires a combination of expertise from the biological, mathematical and statistical sciences. In this review, we attempt to provide an overview of the principles of cDNA microarray technology, the practical concerns of the analytical processing of the data obtained, the correlation of this methodology with other data analysis methods such as immunohistochemistry in tissue microarrays, and the cDNA microarray application in distinct areas of the basic and clinical sciences.

Cooperative VS. Non-cooperative Truels: Little Agreement, but Does that Matter?

It is well-known that non-cooperative and cooperative game theory may yield different solutions to games. These differences are particularly dramatic in the case of truels, or three-person duels, in which the players may fire sequentially or simultaneously, and the games may be one-round or n-round. Thus, it is never a Nash equilibrium for all players to hold their fire in any of these games, whereas in simultaneous one-round and n-round truels such cooperation, wherein everybody survives, is in both the a -core and ß -core. On the other hand, both cores may be empty, indicating a lack of stability, when the unique Nash equilibrium is one survivor. Conditions under which each approach seems most applicable are discussed. Although it might be desirable to subsume the two approaches within a unified framework, such unification seems unlikely since the two approaches are grounded in fundamentally different notions of stability.

Rationalizability of Choice Functions on General Domains without Full Transitivity

The rationalizability of a choice function by means of a transitive relation has been analyzed thoroughly in the literature. However, not much seems to be known when transitivity is weakened to quasi-transitivity or acyclicity. We describe the logical relationships between the different notions of rationalizability involving, for example, the transitivity, quasi-transitivity, or acyclicity of the rationalizing relation. Furthermore, we discuss sufficient conditions and necessary conditions for rational choice on arbitrary domains. Transitive, quasi-transitive, and acyclical rationalizability are fully characterized for domains that contain all singletons and all two-element subsets of the universal set.

Efficiency in Uncertain Cooperative Games

A contingent contract in a transferable utility game under uncertainty specifies an outcome for each possible state. It is assumed that coalitions evaluate these contracts by considering the minimal possible excesses. A main question of the paper concerns the existence and characterization of efficient contracts. It is shown that they exist if and only if the set of possible coalitions contains a balanced subset. Moreover, a characterization of values that result in efficient contracts in the case of minimally balanced collections is provided.

In Search of Advice for Physicians in Entry-Level Medical Markets

We consider entry-level medical markets for physicians in the United Kingdom. These markets experienced failures which led to the adoption of centralized market mechanisms in the 1960's. However, different regions introduced different centralized mechanisms. We advise physicians who do not have detailed information about the rank-order lists submitted by the other participants. We demonstrate that in each of these markets in a low information environment it is not beneficial to reverse the true ranking of any two acceptable hospital positions. We further show that (i) in the Edinburgh 1967 market, ranking unacceptable matches as acceptable is not profitable for any participant and (ii) in any other British entry-level medical market, it is possible that only strategies which rank unacceptable positions as acceptable are optimal for a physician.

Aumann-Shapley Pricing : A Reconsideration of the Discrete Case

We reconsider the following cost-sharing problem: agent i = 1,...,n demands a quantity xi of good i; the corresponding total cost C(x1,...,xn) must be shared among the n agents. The Aumann-Shapley prices (p1,...,pn) are given by the Shapley value of the game where each unit of each good is regarded as a distinct player. The Aumann-Shapley cost-sharing method assigns the cost share pixi to agent i. When goods come in indivisible units, we show that this method is characterized by the two standard axioms of Additivity and Dummy, and the property of No Merging or Splitting: agents never find it profitable to split or merge their demands.