Finite objects and automorphisms

We show that every K-finite decidable object X of an elementary topos E is Dedekind-finite, i.e., that every monic endomorphism of X is an automorphism. As an easy corollary, every epic endomorphism of X is likewise an automorphism. The proof depends in part on an analysis of the finite cardinals of E and in part on the equivalence, in any Boolean tbpos, of Kfiniteness and Tarski-finiteness (Theorem 6). Here X is Tarski-finite iff every inhabited collection of arbitrary elements of ω ^X (subobjects of X ) contains a ¨—minimal element.     

Finite difference approach to trigonometry

Two interrelated, finite difference and graph theoretic, approaches to trigonometry are developed by combining a generalization of the finite difference method first employed by Viète, with solution techniques, based on signal flow graphs, for finite difference equations with variable coefficients, and a scaling approach to trigonometry, based on the polygonometric identities.     

Hierarchical modeling of heterogeneous plates

The use of asymptotic limits to model heterogeneous plates can be troublesome, because it requires a priori knowledge on the ratio between characteristic lengths of heterogeneities and thickness. Moreover, it also relies on some assumption on the inclusions, like periodicity. We propose and analyze here hierarchical modeling techniques and show that such approach not only avoids such pitfalls, but it is actually simpler to obtain, and it provably converges to the correct asymptotic limits. Its derivation does not requires any restrictive assumptions on the heterogeneities. Copyright © 2014 John Wiley & Sons, Ltd.     

Agent-based approach to complex systems modeling

In this paper, we propose a method for detection of local system structures in a complex database. The complex database is viewed as consisting of mixed numeric and nominal attributes, and the local system structure as expressed by “if–then” rules. The detection of local system structures is an important task, and is concerned with inter-dependent issues. The issues involved in the detection of “if–then” rules include finding the objects that share common interests and then finding if–then rules that characterize those objects. To deal with these issues, an agent-based approach is proposed. Each agent has the role of collecting data points (objects) based on their similarity, for mixed data and detecting a rule. The similarity is introduced so that the agent can handle a mixed database. Each agent will occupy a part of the database as its territory according to the predefined algorithm with which agents try to expand or reduce their territories.     

A relaxation-based approach to damage modeling

Common material models that take into account softening effects due to damage have the problem of ill-posed boundary value problems if no regularization is applied. This condition leads to a non-unique solution for the resulting algebraic system and a strong mesh dependence of the numerical results. A possible solution approach to prevent this problem is to apply regularization techniques that take into account the non-local behavior of the damage [1]. For this purpose a field function is often used to couple the local damage parameter to a non-local level, in which differences between the local and non-local parameter as well as the gradient of the non-local parameter can be penalized. In contrast, we present a novel approach [2] to regularization that no longer needs a non-local level but directly provides mesh-independent results. Due to the new variational approach we are also able to improve the calculation times and convergence behavior. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Meta-synthesis approach to complex system modeling

Meta-synthesis method is proposed to tackle with open complex giant system problems which cannot be effectively solved by traditional reductionism methods by a Chinese system scientist Qian, Xuesen (Tsien HsueShen) around the early 1990s. The method emphasizes the synthesis of collected information and knowledge of various kinds of experts, and combining quantitative methods with qualitative knowledge. Since then, continuous endeavors have been taken to put those ideas into practice. In this paper, firstly we review meta-synthesis approach and other research relevant to complex system modeling briefly. Then we discuss two main issues, model integration and opinion synthesis, which are often confronted when applying meta-synthesis approach, together with an exhibit of the development of an embryonic meta-synthetic support prototype. Such a demonstration shows how to model complex problems, such as macro-economic problems in Hall for Workshop on Meta-Synthetic Engineering with versatile resources in information collection, model integration and opinion synthesis. Finally, some future work is indicated.     

Finite element approach to the Stokes problem

We approximate the Stokes problem by using a finite element method. This method utilizes the approach of Kleiser–Schumann, in which a boundary condition for the pressure is implicitly defined by a condition on the velocity. We consider a suitable splitting of the unknowns that allows one to reduce the Stokes problem to a cascade of classical Dirichlet problems and to a boundary integral equation.     

Performance modeling of heterogeneous data networks

A heterogeneous data network consists of Local Area Networks (LANs) interconnected with either leased lines, packet-switched networks, Metropolitan Area Networks (MANs), or combinations thereof. Heterogeneous networks are characterized by bursty traffic, nested segmentation and reassembly of packets, window flow control and round-robin channel access. We develop a performance methodology for estimating user perceived delay and buffer overflow in heterogeneous data networks. The methodology is based on well-known two-moment approximation schemes. Modifications of these schemes are proposed in order to model the bandwidth allocation policies of the MANs and to capture the burstiness of the traffic. The methodology is applied to several LAN-MAN and LAN-MAN-WAN network examples.Supported partially through AT&T Grant No. 5-20491 and partially through NSF Grant No. NCR-8914447.     

An agent-based approach to modeling insider threat

This paper describes the modeling of the potential of an organization to develop an insider threat given certain attributes of its culture. The model represents all employees of the organization and their likelihood of becoming an insider threat. Each employee is instantiated in an agent-zero construct, which accounts for affective, rational, and social behavioral influences. The main driver of behavior is the employee’s level of disgruntlement against the organization. The simulation is run over a period of 10 years and the total number of employees that exceed a certain threshold of becoming an insider threat are computed. This number is compared with survey data on work force ethics as a measure of validity of the simulation results.     

A defect correction approach to turbulence modeling

A method for resolving turbulent flow problems is presented, aiming at competing with the existing mathematical tractable Approximate Deconvolution Models in terms of accuracy, and outperforming these models in terms of the computational time needed. Full numerical analysis is performed, and the method is shown to be stable, easy to implement and parallelize, and computationally fast. The proposed method employs the defect correction approach to solve spatially filtered Navier–Stokes equations. A simple numerical test is provided that compares the method against the approximate deconvolution turbulence model (ADM). When resolving a fluid flow at high Reynolds number, the numerical example verifies the key feature of the method: while having the accuracy comparable to that of the ADM, the method computes in less than 80% of the time needed for the turbulence model—even before the parallelization.© 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 268–288, 2015     

A semiparametric panel approach to mortality modeling

During the past twenty years, there has been a rapid growth in life expectancy and an increased attention on funding for old age. Attempts to forecast improving life expectancy have been boosted by the development of stochastic mortality modeling, for example the Cairns–Blake–Dowd (CBD) 2006 model. The most common optimization method for these models is maximum likelihood estimation (MLE) which relies on the assumption that the number of deaths follows a Poisson distribution. However, several recent studies have found that the true underlying distribution of death data is overdispersed in nature (see Cairns et al. 2009 and Dowd et al. 2010). Semiparametric models have been applied to many areas in economics but there are very few applications of such models in mortality modeling. In this paper we propose a local linear panel fitting methodology to the CBD model which would free the Poisson assumption on number of deaths. The parameters in the CBD model will be considered as smooth functions of time instead of being treated as a bivariate random walk with drift process in the current literature. Using the mortality data of several developed countries, we find that the proposed estimation methods provide comparable fitting results with the MLE method but without the need of additional assumptions on number of deaths. Further, the 5-year-ahead forecasting results show that our method significantly improves the accuracy of the forecast.     

The Laurent series approach to structural modeling

Caves and Christensen (1980) have provided a procedure for displaying the regular regions of a flexible functional form in the 2-good homothetic and nonhomothetic cases and in the 3-good homothetic case. We extend the procedure to the nonhomothetic 3-good case, and we apply the extended procedure to the translog, generalized Leontief, and minflex Laurent flexible functional forms. In addition, we acquire the regular regions for the minflex Laurent model in the 2-good nonhomothetic case and superimpose the resulting regions on those already found by Caves and Christensen for the translog and generalized Leontief models.We find that the new minflex Laurent model generally has the largest regular regions of the three flexible functional forms. In addition, the regular region of the minflex Laurent model is found to expand as real income increases. As a result, that model is particularly well suited for use with time series data, which typically is characterized by positive long term growth trends in real income. In such applications, all recent data and future forecasts can be expected to lie within the regular region of the minflex Laurent model. Although it is possible for some of the earliest data to fall outside that regular region, the model's regular region nevertheless is sufficiently large to hold even all of those earliest data points in many data sets.The regular region of each of the three models moves when the model's parameters are changed. With the generalized Leontief or translog model, the regular region's shape, location, and size are unpredictable without prior knowledge of the model's parameters. With either of those models, the intersection of the model's regular regions, as the parameters are changed, is contained within a very small neighborhood of the one point at which we require the model to be regular. With the minflex Laurent model, the primary properties of the regular regions are invariant to the values of the parameters, and the intersection of the displayed regular regions is a very large unbounded set. The width of that intersection increases without limit as real income increases.     

A new approach to fuzzy wavelet system modeling

In this paper, we propose simple but effective two different fuzzy wavelet networks (FWNs) for system identification. The FWNs combine the traditional Takagi–Sugeno–Kang (TSK) fuzzy model and discrete wavelet transforms (DWT). The proposed FWNs consist of a set of if–then rules and, then parts are series expansion in terms of wavelets functions. In the first system, while the only one scale parameter is changing with it corresponding rule number, translation parameter sets are fixed in each rule. As for the second system, DWT is used completely by using wavelet frames. The performance of proposed fuzzy models is illustrated by examples and compared with previously published examples. Simulation results indicate the remarkable capabilities of the proposed methods. It is worth noting that the second FWN achieves high function approximation accuracy and fast convergence.     

A modeling approach to logistics in concurrent engineering

This paper advocates logistics involvement in the early phases of product design and development in a concurrent engineering environment. A concurrent engineering environment and the benefits of such involvement are explained in detail. The paper focuses on facilitating an interface and a collaboration between the designer and the logistician. A conceptual interface for design for logistics is presented. Four areas of interface are considered: (a) logistics engineering, (b) manufacturing logistics, (c) design for packaging, and (d) design for transportability. A set of detailed design factors pertaining to each area are presented. A modeling approach, Bond Energy Algorithm, is used to accomplish the design for logistics concerns developed throughout the paper. An example is provided to test and validate the algorithm. The results are analyzed and appropriate perspectives for managerial implication of the methodology are provided. Finally, some conclusions and assessments are presented.     

A parameterized approach to modeling and forecasting mortality

A new method is proposed of constructing mortality forecasts. This parameterized approach utilizes Generalized Linear Models (GLMs), based on heteroscedastic Poisson (non-additive) error structures, and using an orthonormal polynomial design matrix. Principal Component (PC) analysis is then applied to the cross-sectional fitted parameters. The produced model can be viewed either as a one-factor parameterized model where the time series are the fitted parameters, or as a principal component model, namely a log-bilinear hierarchical statistical association model of Goodman [Goodman, L.A., 1991. Measures, models, and graphical displays in the analysis of cross-classified data. J. Amer. Statist. Assoc. 86(416), 1085-1111] or equivalently as a generalized Lee-Carter model with p interaction terms. Mortality forecasts are obtained by applying dynamic linear regression models to the PCs. Two applications are presented: Sweden (1751-2006) and Greece (1957-2006).     

A forecast reconciliation approach to cause-of-death mortality modeling

Life expectancy has been increasing sharply around the globe since the second half of the 20th century. Mortality modeling and forecasting have therefore attracted increasing attention from various areas, such as the public pension systems, commercial insurance sectors, as well as actuarial, demographic and epidemiological research. Compared to the aggregate mortality experience, cause-specific mortality rates contain more detailed information, and can help us better understand the ongoing mortality improvements. However, when conducting cause-of-death mortality modeling, it is important to ensure coherence in the forecasts. That is, the forecasts of cause-specific mortality rates should add up to the forecasts of the aggregate mortality rates. In this paper, we propose a novel forecast reconciliation approach to achieve this goal. We use the age-specific mortality experience in the U.S. during 1970–2015 as a case study. Seven major causes of death are considered in this paper. By incorporating both the disaggregate cause-specific data and the aggregate total-level data, we achieve better forecasting results at both levels and coherence across forecasts. Moreover, we perform a cluster analysis on the cause-specific mortality data. It is shown that combining mortality experience from causes with similar mortality patterns can provide additional useful information, and thus further improve forecast accuracy. Finally, based on the proposed reconciliation approach, we conduct a scenario-based analysis to project future mortality rates under the assumption of certain causes being eliminated.     

A new approach to fuzzy wavelet system modeling

In this paper, we propose simple but effective two different fuzzy wavelet networks (FWNs) for system identification. The FWNs combine the traditional Takagi–Sugeno–Kang (TSK) fuzzy model and discrete wavelet transforms (DWT). The proposed FWNs consist of a set of if–then rules and, then parts are series expansion in terms of wavelets functions. In the first system, while the only one scale parameter is changing with it corresponding rule number, translation parameter sets are fixed in each rule. As for the second system, DWT is used completely by using wavelet frames. The performance of proposed fuzzy models is illustrated by examples and compared with previously published examples. Simulation results indicate the remarkable capabilities of the proposed methods. It is worth noting that the second FWN achieves high function approximation accuracy and fast convergence.     

A mixed-integer mathematical modeling approach to exam timetabling

This paper explores mathematical programming models for an exam timetabling problem related to Kuwait University (KU). In particular, we consider two subproblems: (a) the ExamTimetabling Problem (ETP), which is concerned with assigning exams to designated exam-periods and classrooms, and (b) the Proctor Assignment Problem (PAP), which deals with the assignment of proctors to exams. While this exam timetabling problem is ubiquitous in many academic institutions worldwide, idiosyncrasies of the problem related to gender-based policies and having multiple exam centers at KU require novel models. A mixed-integer exam timetabling programming model (ETM) is developed for ETP, which takes into account restrictions related to exam-period conflicts, facility and human resources, and commuting and traffic considerations. Assuming that exam-periods are specified for all exams as determined by ETM, another mixed-integer programming model is formulated for PAP, denoted by PAM, which incorporates the proctors’ preferences for specific days and exam-periods. Computational results are reported and analyzed for solving ETM and PAM directly using the CPLEX Optimization Software (version 9.0), and for implementing a specialized sequential LP-based heuristic for solving PAM. The results obtained significantly improve upon those derived via the existing manual approach implemented at KU, in terms of eliminating conflicts as well as from the overall efficiency and equity points of view.     

Finite element modeling of welding processes

This work deals with the simulation of fusion welding by the Finite Element Method. The implemented models include a moving heat source, temperature dependence of thermo-physical properties, elasto-plasticity, non-steady state heat transfer, and mechanical analysis. The thermal problem is assumed to be uncoupled from the mechanical one, so the thermal analysis is performed separately and previously to the mechanical analysis at each time step. The mechanical problem is based on the thermal history. A special treatment is performed on mechanical elements during the liquid/solid and solid/liquid phase changes to account for stress states. The three-dimensional stress state of a butt-welded joint is obtained as an example of an application.     

Finite approach to the problem of optimizing theorem-proving algorithms

Theorem-proving algorithms in a finite set S of predicate logic formulas are examined. Let F be a consistent and sufficiently strong formal system and let proof of correctness mean a proof in F. If set S is sufficiently rich, then neither a decision algorithm, whose correctness is provable in F (when card(S)C·length of (F)), nor a practically simple to operate search algorithm in S, in which the proof of correctness would be sufficiently short, is possible.Results announced on Oct. 11, 1973.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 49, pp. 123–130, 1975.