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1
Adnan, Zifirdaus. "‘Ideal-Problem-Solution’ (IPS) Model." Australian Review of Applied Linguistics 34, no. 1 (January 1, 2011): 75–103. http://dx.doi.org/10.1075/aral.34.1.05adn.
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Research article introductions (RAIs) play a significant role in gaining publication, and therefore have been studied by many applied linguists. Research into RAIs published in Indonesia has begun to be developed (Adnan, 2009; Mirahayuni, 2001; Safnil, 2000), and generally conclude that Indonesian Humanities RAIs were structured differently from English RAIs. However, as these are early studies, their findings still awaits scrutiny, and little information on Indonesian RAIs especially in Education has been published. Several models describing discourse structure of research article introductions have been proposed, but they have been problematic when applied to analyse RAIs. This paper reports an examination of the applicability of two important models, the CARS (Swales, 1990) and the PJP model claimed to be an Indonesian model of Humanities RAIs (Safnil, 2000), using a selection of 21 Indonesian research article Introductions (RAIs) written by Indonesian academics in Education. It concentrates on the following questions: To what extent do these models fit the data and why? The examination found that none of the RAIs fit the CARS, and only less than half fit the PJP model for various reasons. Therefore a new model is proposed. This model fits most of the data. The paper claims that apart from national concerns, discourse patterns of RAIs are also affected by writing guides provided by the discipline.
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ZHU, K., X. H. MO, C. Z. YUAN, and P. WANG. "A MATHEMATICAL REVIEW ON THE MULTIPLE-SOLUTION PROBLEM." International Journal of Modern Physics A 26, no. 25 (October 10, 2011): 4511–20. http://dx.doi.org/10.1142/s0217751x11054589.
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The recent multiple-solution problem in extracting physics information from a fit to the experimental data in high energy physics is reviewed from a mathematical viewpoint. All these multiple solutions were previously found via a fit process, while in this paper we prove that if the sum of two coherent Breit–Wigner functions is used to fit the measured distribution, there should be two and only two nontrivial solutions, and they are related to each other by analytical formulae. For real experimental measurements in more complicated situations, we also provide a numerical method to derive the other solution from the already obtained one. The excellent consistency between the exact solution obtained this way and the fit process justifies the method. From our results it is clear that the physics interpretation should be very different depending on which solution is selected. So we suggest that all the experimental measurements with potential multiple solutions be re-analyzed to find the other solution because the result is not complete if only one solution is reported.
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Guo, Xin. "An explicit solution to an optimal stopping problem with regime switching." Journal of Applied Probability 38, no. 02 (June 2001): 464–81. http://dx.doi.org/10.1017/s0021900200019975.
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We investigate an optimal stopping time problem which arises from pricing Russian options (i.e. perpetual look-back options) on a stock whose price fluctuations are modelled by adjoining a hidden Markov process to the classical Black-Scholes geometric Brownian motion model. By extending the technique of smooth fit to allow jump discontinuities, we obtain an explicit closed-form solution. It gives a non-standard application of the well-known smooth fit principle where the optimal strategy involves jumping over the optimal boundary and by an arbitrary overshoot. Based on the optimal stopping analysis, an arbitrage-free price for Russian options under the hidden Markov model is derived.
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Guo, Xin. "An explicit solution to an optimal stopping problem with regime switching." Journal of Applied Probability 38, no. 2 (June 2001): 464–81. http://dx.doi.org/10.1239/jap/996986756.
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We investigate an optimal stopping time problem which arises from pricing Russian options (i.e. perpetual look-back options) on a stock whose price fluctuations are modelled by adjoining a hidden Markov process to the classical Black-Scholes geometric Brownian motion model. By extending the technique of smooth fit to allow jump discontinuities, we obtain an explicit closed-form solution. It gives a non-standard application of the well-known smooth fit principle where the optimal strategy involves jumping over the optimal boundary and by an arbitrary overshoot. Based on the optimal stopping analysis, an arbitrage-free price for Russian options under the hidden Markov model is derived.
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Reister, David B. "The least squares fit of a hyperplane to uncertain data." Robotica 15, no. 4 (July 1997): 461–64. http://dx.doi.org/10.1017/s0263574797000556.
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Sensor based robotic systems are an important emerging technology. When robots are working in unknown or partially known environments, they need range sensors that will measure the Cartesian coordinates of surfaces of objects in their environment. Like any sensor, range sensors must be calibrated. The range sensors can be calibrated by comparing a measured surface shape to a known surface shape. The most simple surface is a plane and many physical objects have planar surfaces. Thus, an important problem in the calibration of range sensors is to find the best (least squares) fit of a plane to a set of 3D points. We have formulated a constrained optimization problem to determine the least squares fit of a hyperplane to uncertain data. The first order necessary conditions require the solution of an eigenvalue problem. We have shown that the solution satisfies the second order conditions (the Hessian matrix is positive definite). Thus, our solution satisfies the sufficient conditions for a local minimum. We have performed numerical experiments that demonstrate that our solution is superior to alternative methods.
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Cao, Huantian, Rita Chang, Jo Kallal, Grace Manalo, Jennifer McCord, Jenna Shaw, and Heather Starner. "Adaptable apparel: a sustainable design solution for excess apparel consumption problem." Journal of Fashion Marketing and Management 18, no. 1 (March 4, 2014): 52–69. http://dx.doi.org/10.1108/jfmm-08-2012-0046.
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Purpose – Excess consumption of apparel is driven by the apparel industry to offer more styles at lower prices in shorter time and the consumers’ desire to change fashion. The purpose of this paper is to apply adaptable design in apparel as a sustainable design solution for excess consumption problem. Design/methodology/approach – Guided by sustainable apparel design model C2CAD, two adaptable apparel prototypes for female college students were designed and developed. Focus group discussion and wear test were conducted with female college students to evaluate users’ acceptance, fit, comfort, and adaptability of the two prototypes. Findings – Both prototypes were comfortable to wear by users with different sizes, indicating the users could wear the garment when she changed size. The adaptations and conversions were easily and enjoyably figured out by the users. The users would keep and use the adaptable apparel for a long time. The users would also buy fewer apparel if they were to own the adaptable apparel. Adaptable apparel would increase apparel utilization, eliminate the need to purchase unnecessary additional amount of clothing, and reduce excess consumption. Originality/value – This research provided a pilot study on adaptable apparel design as an innovative approach to help solve excessive consumption problem. The adaptable garment prototypes would allow the fashion-forward female college student to easily change the function, fit, and style of the environmentally friendly garments.
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Miller, Edward B., Robert B. Murphy, Daniel Sindhikara, Kenneth W. Borrelli, Matthew J. Grisewood, Fabio Ranalli, Steven L. Dixon, et al. "Reliable and Accurate Solution to the Induced Fit Docking Problem for Protein–Ligand Binding." Journal of Chemical Theory and Computation 17, no. 4 (March 29, 2021): 2630–39. http://dx.doi.org/10.1021/acs.jctc.1c00136.
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Buonaguidi, Bruno, and Pietro Muliere. "On the Disorder Problem for a Negative Binomial Process." Journal of Applied Probability 52, no. 01 (March 2015): 167–79. http://dx.doi.org/10.1017/s0021900200012262.
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We study the Bayesian disorder problem for a negative binomial process. The aim is to determine a stopping time which is as close as possible to the random and unknown moment at which a sequentially observed negative binomial process changes the value of its characterizing parameter p ∈ (0, 1). The solution to this problem is explicitly derived through the reduction of the original optimal stopping problem to an integro-differential free-boundary problem. A careful analysis of the free-boundary equation and of the probabilistic nature of the boundary point allows us to specify when the smooth fit principle holds and when it breaks down in favour of the continuous fit principle.
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Buonaguidi, Bruno, and Pietro Muliere. "On the Disorder Problem for a Negative Binomial Process." Journal of Applied Probability 52, no. 1 (March 2015): 167–79. http://dx.doi.org/10.1239/jap/1429282613.
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We study the Bayesian disorder problem for a negative binomial process. The aim is to determine a stopping time which is as close as possible to the random and unknown moment at which a sequentially observed negative binomial process changes the value of its characterizing parameter p ∈ (0, 1). The solution to this problem is explicitly derived through the reduction of the original optimal stopping problem to an integro-differential free-boundary problem. A careful analysis of the free-boundary equation and of the probabilistic nature of the boundary point allows us to specify when the smooth fit principle holds and when it breaks down in favour of the continuous fit principle.
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Hu, Shicheng, Zhaoze Zhang, Qingsong He, and Xuedong Sun. "An Iterated Local Search Algorithm for a Place Scheduling Problem." Mathematical Problems in Engineering 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/659297.
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We study the place scheduling problem which has many application backgrounds in realities. For the block manufacturing project with special manufacturing platform requirements, we propose a place resource schedule problem. First, the mathematical model for the place resource schedule problem is given. On the basis of resource-constrained project scheduling problem and packing problem, we develop a hybrid heuristic method which combines priority rules and three-dimensional best fit algorithm, in which the priority rules determine the scheduling order and the three-dimensional best fit algorithm solves the placement. After this method is used to get an initial solution, the iterated local search is employed to get an improvement. Finally, we use a set of simulation data to demonstrate the steps of the proposed method and verify its feasibility.
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Wehr, Richard, and Scott R. Saleska. "The long-solved problem of the best-fit straight line: application to isotopic mixing lines." Biogeosciences 14, no. 1 (January 3, 2017): 17–29. http://dx.doi.org/10.5194/bg-14-17-2017.
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Abstract. It has been almost 50 years since York published an exact and general solution for the best-fit straight line to independent points with normally distributed errors in both x and y. York's solution is highly cited in the geophysical literature but almost unknown outside of it, so that there has been no ebb in the tide of books and papers wrestling with the problem. Much of the post-1969 literature on straight-line fitting has sown confusion not merely by its content but by its very existence. The optimal least-squares fit is already known; the problem is already solved. Here we introduce the non-specialist reader to York's solution and demonstrate its application in the interesting case of the isotopic mixing line, an analytical tool widely used to determine the isotopic signature of trace gas sources for the study of biogeochemical cycles. The most commonly known linear regression methods – ordinary least-squares regression (OLS), geometric mean regression (GMR), and orthogonal distance regression (ODR) – have each been recommended as the best method for fitting isotopic mixing lines. In fact, OLS, GMR, and ODR are all special cases of York's solution that are valid only under particular measurement conditions, and those conditions do not hold in general for isotopic mixing lines. Using Monte Carlo simulations, we quantify the biases in OLS, GMR, and ODR under various conditions and show that York's general – and convenient – solution is always the least biased.
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Buhl, David A., Michael A. Morissette, and Jeffrey Wolff. "Maximizing the Fit of a Box Spring Mattress up a Stairwell." Mathematics Teacher 100, no. 4 (November 2006): 241–46. http://dx.doi.org/10.5951/mt.100.4.0241.
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A class investigation into the mathematics of determining the maximum size of a box spring mattress that could be carried up a stairwell. The Geometer's Sketchpad was used for the problem exploration in order to help avoid common mistakes when deriving the mathematical model. The numerical solution was described using graphical method.
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Buhl, David A., Michael A. Morissette, and Jeffrey Wolff. "Maximizing the Fit of a Box Spring Mattress up a Stairwell." Mathematics Teacher 100, no. 4 (November 2006): 241–46. http://dx.doi.org/10.5951/mt.100.4.0241.
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A class investigation into the mathematics of determining the maximum size of a box spring mattress that could be carried up a stairwell. The Geometer's Sketchpad was used for the problem exploration in order to help avoid common mistakes when deriving the mathematical model. The numerical solution was described using graphical method.
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Foysal, Kamrul H., Hyo Jung Chang, Francine Bruess, and Jo Woon Chong. "SmartFit: Smartphone Application for Garment Fit Detection." Electronics 10, no. 1 (January 5, 2021): 97. http://dx.doi.org/10.3390/electronics10010097.
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The apparel e-commerce industry is growing day by day. In recent times, consumers are particularly interested in an easy and time-saving way of online apparel shopping. In addition, the COVID-19 pandemic has generated more need for an effective and convenient online shopping solution for consumers. However, online shopping, particularly online apparel shopping, has several challenges for consumers. These issues include sizing, fit, return, and cost concerns. Especially, the fit issue is one of the cardinal factors causing hesitance and drawback in online apparel purchases. The conventional method of clothing fit detection based on body shapes relies upon manual body measurements. Since no convenient and easy-to-use method has been proposed for body shape detection, we propose an interactive smartphone application, “SmartFit”, that will provide the optimal fitting clothing recommendation to the consumer by detecting their body shape. This optimal recommendation is provided by using image processing and machine learning that are solely dependent on smartphone images. Our preliminary assessment of the developed model shows an accuracy of 87.50% for body shape detection, producing a promising solution to the fit detection problem persisting in the digital apparel market.
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Filep, Levente, and László Illyés. "Exact fit problem generator for cutting and packing, revisiting of the upper deck placement algorithm." Acta Universitatis Sapientiae, Informatica 10, no. 1 (August 1, 2018): 73–85. http://dx.doi.org/10.2478/ausi-2018-0005.
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Abstract Problem generators are practical solutions for generating a set of inputs to specific problems. These inputs are widely used for testing, comparing and optimizing placement algorithms. The problem generator presented in this paper fills the gap in the area of 2D Cutting & Packing as the sum of the area of the small objects is equal to the area of the Large Object and has at least one perfect solution. In this paper, the already proposed Upper Deck algorithm is revisited and used to test the proposed generator outputs. This algorithm bypasses the dead area problem that occurs in most of all well-known strategies of the 2D Single Knapsack Problem where we have a single large rectangle to cover with small, heterogeneous rectangle shapes, whom total area exceeds the large object’s area. The idea of placing the small shapes in a free corner simplifies and speeds the placement algorithm as only the available angles are checked for possible placements, and collision detection only requires the checking of corners and edges of the placed shape. Since the proposed generator output has at least one exact solution, a series of optimization performed on the algorithm is also presented.
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Maydeu-Olivares, Albert, and Thomas J. D'Zurilla. "The Factor Structure of the Problem Solving Inventory." European Journal of Psychological Assessment 13, no. 3 (September 1997): 206–15. http://dx.doi.org/10.1027/1015-5759.13.3.206.
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Heppner and Petersen (1982) derived a three-dimensional structure for the items of the Problem Solving Inventory using principal components analysis. D'Zurilla and Maydeu-Olivares (1995) pointed out the lack of any clear link of the scales of the Problem Solving Inventory (PSI) to social problem-solving theory, which impairs the interpretation of any empirical results obtained with the use of this inventory. To address this issue, we used maximum likelihood factor analysis to investigate the dimensional structure of this inventory. We found that an unrestricted three-dimensional model adequately fit this data but did not match Heppner and Petersen's structure, nor could it be interpreted substantively. Neither four- nor five-dimensional models could be interpreted regardless of the rotation procedure used. Although a two-factor model did not fit the data adequately either, a careful content analysis of the PSI items revealed only two interpretable clusters of items in this inventory, measuring problem-solving self-efficacy and problem solving skills, respectively. In addition, there is also a heterogeneous cluster of items responsible for the residual third dimension appearing in Heppner and Petersen's as well as in the current analyses. Using a theory-guided item-selection procedure we constructed two new PSI scales measuring the two interpretable constructs. The items composing these scales are shown to fit an independent clusters two-dimensional solution.
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Nowlin, Donald. "Practical Geometry Problems: The Case of the Ritzville Pyramids." Mathematics Teacher 86, no. 3 (March 1993): 198–200. http://dx.doi.org/10.5951/mt.86.3.0198.
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The wheat-producing country of eastern Washington state furnishes a practical example of an applied geometry problem requiring only a knowledge of the relationship between the parts of a circle and the parts of a right triangle. The solution of this problem is related to several topics in the Curriculum and Evaluation Standards (NCTM 1989) that do not appear in a traditional curriculum. One of the main features of this example is that it shows that memorized formulas from textbooks must sometimes be modified to fit real-world problems. The solution of the problem requires the students to make some desirable connections among mathematical concepts that may otherwise be perceived as unrelated.
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Lim, Eunji, and Mina Attallah. "Estimation of Smooth Functions via Convex Programs." International Journal of Statistics and Probability 5, no. 4 (June 27, 2016): 150. http://dx.doi.org/10.5539/ijsp.v5n4p150.
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One of the numerically preferred methods for fitting a function to noisy data when the underlying function is known to be smooth is to minimize the roughness of the fit while placing a limit on the sum of squared errors. We show that the fit can be formulated as a solution to a convex program. Since convex programs can be solved by various methods with guaranteed convergence, our formulation enables one to use these methods to compute the fit numerically. Numerical results show that our formulation is successfully applied to the problem of sensitivity estimation of option prices as functions of the underlying stock price.
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Alestas, George, and Leandros Perivolaropoulos. "Late-time approaches to the Hubble tension deforming H(z), worsen the growth tension." Monthly Notices of the Royal Astronomical Society 504, no. 3 (April 20, 2021): 3956–62. http://dx.doi.org/10.1093/mnras/stab1070.
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ABSTRACT Many late-time approaches for the solution of the Hubble tension use late time smooth deformations of the Hubble expansion rate H(z) of the Planck18/ΛCDM best fit to match the locally measured value of H0 while effectively keeping the comoving distance to the last scattering surface and Ω0mh2 fixed to maintain consistency with Planck CMB measurements. A well-known problem of these approaches is that they worsen the fit to low z distance probes. Here, we show that another problem of these approaches is that they worsen the level of the Ω0m − σ8 growth tension. We use the generic class of CPL parametrizations corresponding to evolving dark energy equation of state parameter $w(z)=w_0+w_1\frac{z}{1+z}$ with local measurements H0 prior and identify the pairs (w0, w1) that satisfy this condition. This is a generic class of smooth deformations of H(z) that are designed to address the Hubble tension. We show that for these models the growth tension between dynamical probe data and CMB constraints is worse than the corresponding tension of the standard Planck18/ΛCDM model. We justify this feature using a full numerical solution of the growth equation and fit to the data, as well as by using an approximate analytic approach. The problem does not affect recent proposed solutions of the Hubble crisis involving a SnIa intrinsic luminosity transition at zt ≃ 0.01.
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Alonso, Maria Teresa, Carlo Ferigato, Deimos Ibanez Segura, Domenico Perrotta, Adria Rovira-Garcia, and Emmanuele Sordini. "Analysis of ‘Pre-Fit’ Datasets of gLAB by Robust Statistical Techniques." Stats 4, no. 2 (May 24, 2021): 400–418. http://dx.doi.org/10.3390/stats4020026.
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The GNSS LABoratory tool (gLAB) is an interactive educational suite of applications for processing data from the Global Navigation Satellite System (GNSS). gLAB is composed of several data analysis modules that compute the solution of the problem of determining a position by means of GNSS measurements. The present work aimed to improve the pre-fit outlier detection function of gLAB since outliers, if undetected, deteriorate the obtained position coordinates. The methodology exploits robust statistical tools for regression provided by the Flexible Statistics and Data Analysis (FSDA) toolbox, an extension of MATLAB for the analysis of complex datasets. Our results show how the robust analysis FSDA technique improves the capability of detecting actual outliers in GNSS measurements, with respect to the present gLAB pre-fit outlier detection function. This study concludes that robust statistical analysis techniques, when applied to the pre-fit layer of gLAB, improve the overall reliability and accuracy of the positioning solution.
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Prime, Michael B., and Michael R. Hill. "Uncertainty, Model Error, and Order Selection for Series-Expanded, Residual-Stress Inverse Solutions." Journal of Engineering Materials and Technology 128, no. 2 (November 7, 2005): 175–85. http://dx.doi.org/10.1115/1.2172278.
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Measuring the spatial variation of residual stresses often requires the solution of an elastic inverse problem such as a Volterra equation. Using a maximum likelihood estimate (least squares fit), a series expansion for the spatial distribution of stress or underlying eigenstrain can be an effective solution. Measurement techniques that use a series expansion inverse include incremental slitting (crack compliance), incremental hole drilling, a modified Sach’s method, and others. This paper presents a comprehensive uncertainty analysis and order selection methodology, with detailed development for the slitting method. For the uncertainties in the calculated stresses caused by errors in the measured data, an analytical formulation is presented which includes the usually ignored but important contribution of covariances between the fit parameters. Using Monte Carlo numerical simulations, it is additionally demonstrated that accurate uncertainty estimates require the estimation of model error, the ability of the chosen series expansion to fit the actual stress variation. An original method for estimating model error for a series expansion inverse solution is presented. Finally, it is demonstrated that an optimal order for the series expansion can usually be chosen by minimizing the estimated uncertainty in the calculated stresses.
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Araújo, Olinto César Bassi de, and Vinícius Amaral Armentano. "A multi-start random constructive heuristic for the container loading problem." Pesquisa Operacional 27, no. 2 (August 2007): 311–31. http://dx.doi.org/10.1590/s0101-74382007000200007.
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This paper deals with the container loading problem which involves the selection of a subset of boxes, each box with a given volume, such that they fit in a single container and maximize its volume utilization subject to orientation and stability constraints. We propose a multi-start random constructive heuristic with a load arrangement that is based on maximal cuboids that fit in given empty spaces. Each instance is adaptively evaluated by a set of criteria, and at each step of the construction process one maximal cuboid is chosen probabilistically from a restricted list of candidates. In order to enhance the flexibility in the construction of a solution, a probabilistic reduction on such cuboids is allowed. Computational tests on several instances from the literature show that the proposed method performs better than other approaches.
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Matsuda, Shinya, Keiji Muramatsu, Tatsuhiko Kubo, and Yoshihisa Fujino. "Disease Burden of MSD for the Japanese Society Fit for Work Scheme as a Solution for This Problem." Asian Pacific Journal of Disease Management 6, no. 2 (2014): 37–44. http://dx.doi.org/10.7223/apjdm.6.37.
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Birch, Stephen, and Amiram Gafni. "Changing the problem to fit the solution: Johannesson and Weinstein's (mis) application of economics to real world problems." Journal of Health Economics 12, no. 4 (December 1993): 469–76. http://dx.doi.org/10.1016/0167-6296(93)90006-z.
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Roy, Dhrubojyoti, Sangeeta Srivastava, Aditya Kusupati, Pranshu Jain, Manik Varma, and Anish Arora. "One Size Does Not Fit All." ACM Transactions on Sensor Networks 17, no. 2 (June 2021): 1–27. http://dx.doi.org/10.1145/3439957.
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Edge sensing with micro-power pulse-Doppler radars is an emergent domain in monitoring and surveillance with several smart city applications. Existing solutions for the clutter versus multi-source radar classification task are limited in terms of either accuracy or efficiency, and in some cases, struggle with a tradeoff between false alarms and recall of sources. We find that this problem can be resolved by learning the classifier across multiple time-scales. We propose a multi-scale, cascaded recurrent neural network architecture, MSC-RNN, composed of an efficient multi-instance learning (MIL) Recurrent Neural Network (RNN) for clutter discrimination at a lower tier and a more complex RNN classifier for source classification at the upper tier. By controlling the invocation of the upper RNN with the help of the lower tier conditionally, MSC-RNN achieves an overall accuracy of 0.972. Our approach holistically improves the accuracy and per-class recalls over machine learning models suitable for radar inferencing. Notably, we outperform cross-domain handcrafted feature engineering with purely time-domain deep feature learning, while also being up to ∼3× more efficient than a competitive solution.
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Chennareddy, Rahulreddy, Susan Bogus Halter, and Mahmoud M. Reda Taha. "Fit-in GFRP Liner for Retrofitting Corroded Metal Culverts." MATEC Web of Conferences 271 (2019): 01013. http://dx.doi.org/10.1051/matecconf/201927101013.
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Corrugated metal pipes (CMPs) have been used as culverts in North America since the 1950s. Today, corrosion of CMPs is a major problem that requires an urgent and efficient solution to retrofit thousands of corroded CMPs across the country. One potential solution gaining wide acceptance is to use a fit-in Glass Fiber Reinforced Polymer (GFRP) liner inside the old CMPs and to connect them using polymer grout. In this paper, a methodology to retrofit corrugated metal culvert using a fit-in GFRP profile liner was developed and implemented. First, material characterization of the GFRP material and the epoxy grout were carried out for proper design of the retrofit system. Second, full-scale CMP-GFRP composite section was tested under three-point bending configuration to observe the retrofitted culvert behavior to failure. The new CMP-GFRP section develops full composite action and shows failure capacity of 75 kip with a deflection of 3.52 in at the end of the test. Post failure of the polymeric grout, GFRP pipe failure was observed at mid-span location starting on the tension side. A finite element model was developed to understand the behavior of the CMP-GFRP composite pipe and to allow for the efficient design of the proposed retrofitting system.
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Rice, jr., Martin A. "INTUITING MORALITY." Philosophia Reformata 71, no. 2 (December 2, 2006): 154–70. http://dx.doi.org/10.1163/22116117-90000386.
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1. Introduction: What is the Problem? There are long standing problems of how one can account for moral properties, problems that are driven by the background metaphysical milieu into which one is trying to fit the moral properties in question. David Hume faced this problem in the context of the Newtonian-mechanistic worldview. His solution was to compromise the mechanistic worldview by undermining the physicalistic notion of causal relations via his famous Critique of Induction and reduce moral properties to a sensory “sentiment.”
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Göküzüm, Felix Selim, Lu Trong Khiem Nguyen, and Marc-André Keip. "An Artificial Neural Network Based Solution Scheme for Periodic Computational Homogenization of Electrostatic Problems." Mathematical and Computational Applications 24, no. 2 (April 17, 2019): 40. http://dx.doi.org/10.3390/mca24020040.
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The present work addresses a solution algorithm for homogenization problems based on an artificial neural network (ANN) discretization. The core idea is the construction of trial functions through ANNs that fulfill a priori the periodic boundary conditions of the microscopic problem. A global potential serves as an objective function, which by construction of the trial function can be optimized without constraints. The aim of the new approach is to reduce the number of unknowns as ANNs are able to fit complicated functions with a relatively small number of internal parameters. We investigate the viability of the scheme on the basis of one-, two- and three-dimensional microstructure problems. Further, global and piecewise-defined approaches for constructing the trial function are discussed and compared to finite element (FE) and fast Fourier transform (FFT) based simulations.
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Schmidt, Sabrina, and Matthias Rätzer. "How does a future-fit economy take root? An analysis of diffusion and adoption of future-fit business practices in brewing and printing companies." GAIA - Ecological Perspectives for Science and Society 30, no. 2 (July 15, 2021): 114–21. http://dx.doi.org/10.14512/gaia.30.2.9.
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Only a few companies are seeking to contribute to a future-fit way of doing business. As such, they are considered major drivers of institutional change. However, conventional companies are not likely to follow these new paths based solely on good examples.In the face of the worsening ecological crisis, more and more people are looking to pioneering companies which have made it their task to be part of the solution to this problem by deploying sustainable production and business practices. But how do these future-fit approaches spread within the economy? We present results from brewing and printing companies which suggest that successful diffusion of these approaches may be more complex than commonly assumed. For example, conventional companies tend not to adopt sustainable business practices merely because they are being promoted by future-fit small and medium-sized enterprises. Rather, change agents in conventional companies must be educated on how specific sustainable business practices serve as concrete solutions. Additionally, these practices must align with the company’s predominant view of the problem. Our results stress that future-fit companies cannot be the exclusive drivers of profound change; rather, they can only make their contribution when supported in this effort by science, politics and society in general.
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Botić, Katarina. "Neolithisation of Sava-Drava-Danube interfluve at the end of the 6600–6000 BC period of Rapid Climate Chang: a new solution to an old problem." Documenta Praehistorica 43 (December 30, 2016): 183–208. http://dx.doi.org/10.4312/dp.43.9.
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The idea of the Neolithisation of the Sava-Drava-Danube interfluve has undergone very little change since S. Dimitrijević's time. Despite their many shortcomings, new archaeological excavations and radiocarbon dates of Early Neolithic sites have provided us with new insight into the process of Neolihisation of this region. Using the recently published work by B. Weninger and L. Clare (Clare, Weninger 2010; Weninger et al. 2009; Weninger et al. 2014) as a starting point, the available radiocarbon and archaeological data are used to build up a time frame comparable to the wider region of Southeast Europe and climate conditions for specific period. The results fit the model of Neolithisation well (Weninger et al. 2014.9, Fig. 4), filling in the geographical gaps.
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Rohan, Dewanto Harwin, and Nur Hayati. "Persamaan Lorenz untuk Keamanan Nomor Serial Sistem Operasi Window7." Jurnal Ilmiah FIFO 10, no. 2 (March 1, 2019): 1. http://dx.doi.org/10.22441/fifo.2018.v10i2.001.
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Serial number of operating system windows 7 needs to be safeguarded, so can’t be used by the others. Security of the data can use by modern cryptography such as Vernam Cipher methods and classic cryptography such as Caesar Cipher methods. The security level both of this method depends on the keywords used and it will difficult to crack if the random key is used more and more. To get a random key, we can take from chaos of Lorenz equations as key-generator for encryption and description. Before utilizing chaos in the Lorenz equations, we have to find the maximum t (time) for the inverse problem solution to fit with the forward problem solution. We can use Runge-Kutta method in the Lorenz equations for forward problem solution and inverse problem solution. The solution of integral that obtained by the Runge-Kutta method can be searched by Trapezoidal method. The result of Runge-Kutta solution and Trapezoidal will be used as key-generator for encryption and description. In the simulations performed, the best orde in Runge-Kutta method is 4 and t max is 2. The encryption key is used as the initial condition of Lorenz equation, then the result is integrable by the Trapezoidal method. The result of orde 4 from Runge-Kutta method and Trapezoidal method used as a key-generator. Application of Lorenz equation as key-generator for encryption and decryption, may change the cryptography algorithms of symmetric to be asymmetric.
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Shlyakhin, D. A., and Zh M. Dauletmuratova. "Non-stationary coupled axisymmetric thermoelasticity problem for a rigidly fixed round plate." PNRPU Mechanics Bulletin, no. 4 (December 15, 2019): 191–200. http://dx.doi.org/10.15593/perm.mech/2019.4.18.
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A new closed solution is constructed for the axisymmetric dynamic problem of the classical (CTE) theory of thermoelasticity for a rigidly fixed circular isotropic plate in the case of a temperature change on its face surfaces (boundary conditions of the first kind). The mathematical formulation of the problem under consideration includes linear equations of thermal conductivity and equilibrium in a spatial setting, assuming that their inertial elastic characteristics can be neglected in the structures under study. In constructing a general solution of related non-self-conjugate equations, we use the mathematical apparatus of separation of variables in the form of finite integral transformations i.e. Hankel along the radial coordinate and biorthogonal transformation (FIT) with respect to the axial variable. At each stage of the investigation, a procedure is performed to reduce the boundary conditions to a form that allows the corresponding transformation to be applied. A particular feature of this solution is the application of a FIT based on a multicomponent relation of the eigenvector functions of two homogeneous boundary value problems. An important point in the procedure of the structural algorithm is the separation of the adjoint operator, without which it is impossible to solve non-self-adjoint linear problems of mathematical physics. This transformation is the most effective method for studying similar boundary value problems. The calculated design relationships make it possible to determine the stress-strain state and the character of the distribution of the temperature field in a rigidly fixed circular isotropic plate for an arbitrary external temperature effect with respect to time. Numerical analysis of the strength characteristics of the concrete structure shows that during the period of the unsteady load the maximum values of mechanical stresses are observed. Later, at a constant temperature regime, as a result of heating the entire plate, the displacements increase and the stresses fall.
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Dumsday, Travis. "The Internal Unity of Natural Kinds." American Catholic Philosophical Quarterly 93, no. 4 (2019): 587–610. http://dx.doi.org/10.5840/acpq2019927188.
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It is often assumed that the essence of a natural kind is complex, being such as to include (or to wholly consist of) multiple fundamental properties. For instance, perhaps the essence of the kind “electron” includes both negative charge and a precise rest mass, where neither of these is derivable from the other, nor derivable from some other foundational property. This assumption raises the ‘unity problem’: how to explain what unifies or holds together these properties. One important answer is developed by David Oderberg. His model draws on insights from both analytic metaphysics and the Scholastic tradition. I provide a summary of his solution to the unity problem and point to a potential worry it faces. I conclude by adverting to an alternative solution that would still fit within Oderberg’s overall system.
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Bernard, J. E., S. K. Kwon, and J. A. Wilson. "Differentiation of Mass and Stiffness Matrices for High Order Sensitivity Calculations in Finite Element-Based Equilibrium Problems." Journal of Mechanical Design 115, no. 4 (December 1, 1993): 829–32. http://dx.doi.org/10.1115/1.2919275.
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Extension of sensitivity methods to include higher order terms depends on the ability to compute higher order derivatives of the mass and stiffness matrices. This paper presents a method based on the use of cubic polynomials to fit mass and stiffness matrices across a range of interest of the design variable. The method is illustrated through an example which uses Pade´ approximants to expand the solution to a statics problem. The design variable is the thickness of one part of a plate with fixed boundaries. The solution gives a very good approximation over fivefold change in the value of the design variable.
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Madhumala, R. B., Harshvardhan Tiwari, and Verma C. Devaraj. "Virtual Machine Placement Using Energy Efficient Particle Swarm Optimization in Cloud Datacenter." Cybernetics and Information Technologies 21, no. 1 (March 1, 2021): 62–72. http://dx.doi.org/10.2478/cait-2021-0005.
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Abstract Efficient resource allocation through Virtual machine placement in a cloud datacenter is an ever-growing demand. Different Virtual Machine optimization techniques are constructed for different optimization problems. Particle Swam Optimization (PSO) Algorithm is one of the optimization techniques to solve the multidimensional virtual machine placement problem. In the algorithm being proposed we use the combination of Modified First Fit Decreasing Algorithm (MFFD) with Particle Swarm Optimization Algorithm, used to solve the best Virtual Machine packing in active Physical Machines to reduce energy consumption; we first screen all Physical Machines for possible accommodation in each Physical Machine and then the Modified Particle Swam Optimization (MPSO) Algorithm is used to get the best fit solution.. In our paper, we discuss how to improve the efficiency of Particle Swarm Intelligence by adapting the efficient mechanism being proposed. The obtained result shows that the proposed algorithm provides an optimized solution compared to the existing algorithms.
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Xu, Yan-xin. "An Efficient Heuristic Approach for Irregular Cutting Stock Problem in Ship Building Industry." Mathematical Problems in Engineering 2016 (2016): 1–12. http://dx.doi.org/10.1155/2016/8703782.
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This paper presents an efficient approach for solving a real two-dimensional irregular cutting stock problem in ship building industry. Cutting stock problem is a common cutting and packing problem that arises in a variety of industrial applications. A modification of selection heuristic Exact Fit is applied in our research. In the case referring to irregular shapes, a placement heuristics is more important to construct a complete solution. A placement heuristic relating to bottom-left-fill is presented. We evaluate the proposed approach using generated instance only with convex shapes in literatures and some instances with nonconvex shapes based on real problem from ship building industry. The results demonstrate that the effectiveness and efficiency of the proposed approach are significantly better than some conventional heuristics.
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Kopytko, B. I., and A. F. Novosyadlo. "On a nonclassical problem for the heat equation and the Feller semigroup generated by it." Carpathian Mathematical Publications 12, no. 2 (November 3, 2020): 297–310. http://dx.doi.org/10.15330/cmp.12.2.297-310.
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The initial boundary value problem for the equation of heat conductivity with the Wenzel conjugation condition is studied. It does not fit into the general theory of parabolic initial boundary value problems and belongs to the class of conditionally correct ones. In space of bounded continuous functions by the method of boundary integral equations its classical solvability under some conditions is established. In addition, it is proved that the obtained solution is a Feller semigroup, which represents some homogeneous generalized diffusion process in the area considered here.
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Verde, Paula, Rubén Ferrero-Guillén, Rubén Álvarez, Javier Díez-González, and Hilde Perez. "Node Distribution Optimization in Positioning Sensor Networks through Memetic Algorithms in Urban Scenarios." Engineering Proceedings 2, no. 1 (November 14, 2020): 73. http://dx.doi.org/10.3390/ecsa-7-08220.
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Local Positioning Systems rely on ad-hoc node deployments which fit the environment characteristics in order to reduce system uncertainties. The obtainment of competitive results through these systems requires the solution of the Node Location Problem. This problem has been assigned as NP-Hard; therefore, a heuristic solution is recommended for addressing this complex problem. Genetic Algorithms (GA) have shown an excellent trade-off between diversification and intensification in the literature. However, in Non-Line-of-Sight environments in which there is not continuity in the fitness function evaluation among contiguous solutions, challenges arise for the GA. Consequently, in this paper, we introduce a Memetic Algorithm (MA) with a Local Search strategy for exploring the most different individuals of the population in search of improving the NLP results in urban scenarios for the first time. Results show that the MA proposed outperforms the GA optimization and attains an improvement of 6.51% in accuracy in the scenario proposed.
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Finney, MA. "The Missing Tail and Other Considerations for the Use of Fire History Models." International Journal of Wildland Fire 5, no. 4 (1995): 197. http://dx.doi.org/10.1071/wf9950197.
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This paper reviews methods used for testing the fit of the cumulative form of a negative exponential distribution to the cumulative distribution of forest age-classes. It is shown that existing methods can lead to a greater chance of falsely rejecting the fit of the negative exponential model and inferring that fire frequencies have changed through time. This results when the old-age tail of a negative exponential distribution is mathematically assumed to be present at the end of the age-class distribution. In reality, the tail is censored from sample distributions of forest age-classes. Censoring alters the shape of a cumulative age-class distribution from the straight line expected for a semi-log graph of the cumulative negative exponential model. A solution to this problem is proposed that restricts the tests-of-fit to the portion of the negative exponential distribution that overlaps with the data to be tested. The cumulative age-class distribution can then be compared directly with the cumulative of a truncated negative exponential distribution. Considerations for interpreting a poor fit are then discussed.
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Valerio, Wendy H., Alison M. Reynolds, Grant B. Morgan, and Anne A. McNair. "Construct Validity of the Children’s Music-Related Behavior Questionnaire." Journal of Research in Music Education 60, no. 2 (May 9, 2012): 186–200. http://dx.doi.org/10.1177/0022429412444450.
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The purpose of this research was to investigate the construct validity of the Children’s Music-Related Behavior Questionnaire (CMRBQ), an instrument designed for parents to document music-related behaviors about their children and themselves. The research problem was to examine the hypothesized factorial structure of the questionnaire. From a national sample, parents of children 5 years old or younger returned 616 usable questionnaires. Items were parceled, and the model was subjected to a confirmatory factor analysis to assess the goodness of model-data fit for a one-factor solution using the parcels as indicators. Internal consistency of subscale reliability estimates ranged from α = .77 to α = .97. Three multiple fit indices suggested that the one-factor model adequately fit the data: standardized root square residual (.028), comparative fit index (.968), and Tucker-Lewis index (.955). Greater knowledge regarding parents’ observations of music’s role in children’s development may help researchers, practitioners, parents, and policy makers collaboratively consider how best to meet musical needs of young children in childcare and school settings.
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Fleischmann, Christopher, Irina Leher, Reinhold Hartwich, Marc Hainke, and Stefan Sesselmann. "A new approach to quickly edit geometries and estimate stresses and displacements of implants in real-time." Current Directions in Biomedical Engineering 5, no. 1 (September 1, 2019): 553–56. http://dx.doi.org/10.1515/cdbme-2019-0139.
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AbstractAlthough osteosynthesis plates rarely break, such cases still occur. Since the construction of these plates is mainly focussing on the best fit for anatomical structures, they may not provide optimal mechanical stability. It should be considered whether they might be changed in terms of e.g. hole size and number. Finite element analysis can help to estimate whether the plates will withstand loads or break. However, these analyses can be very time-consuming. To counteract this problem, a new software solution (ANSYS Discovery Live) has been established for estimation of stresses in real time. In this study the accuracy of the new software was compared to a conventional finite element analysis software solution to investigate whether this software solution provides appropriate accuracy to be used for medical applications.
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DA SILVA, FABRICIO ALVES BARBOSA, and ISAAC D. SCHERSON. "EFFICIENT PARALLEL JOB SCHEDULING USING GANG SERVICE." International Journal of Foundations of Computer Science 12, no. 03 (June 2001): 265–84. http://dx.doi.org/10.1142/s0129054101000485.
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Gang scheduling has been widely used as a practical solution to the dynamic parallel job scheduling problem. To overcome some of the limitations of traditional Gang scheduling algorithms, Concurrent Gang is proposed as a class of scheduling policies which allows the flexible and simultaneous scheduling of multiple parallel jobs. It hence improves the space sharing characteristics of Gang scheduling while preserving all other advantages. To provide a sound analysis of Concurrent Gang performance, a novel methodology based on the traditional concept of competitive ratio is also introduced. Dubbed dynamic competitive ratio, the new method is used to compare dynamic bin packing algorithms used in this paper. These packing algorithms apply to the Concurrent Gang scheduling of a workload generated by a statistical model. Moreover, dynamic competitive ratio is the figure of merit used to evaluate and compare packing strategies for job scheduling under multiple constraints. It will be shown that for the unidimensional case there is a small difference between the performance of best fit and first fit; first fit can hence be used without significant system degradation. For the multidimensional case, when memory is also considered, we concluded that the packing algorithm must try to balance the resource utilization in all dimensions simulataneously, instead of given priority to only one dimension of the problem.
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Al‐Chalabi, M. "Parameter nonuniqueness in velocity versus depth functions." GEOPHYSICS 62, no. 3 (May 1997): 970–79. http://dx.doi.org/10.1190/1.1444203.
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Except for hypothetical cases that are never encountered in practice, the solution for the parameters of analytic velocity versus depth functions is inherently nonunique. This nonuniqueness means that there is no particular parameter combination that represents “the” solution. The average discrepancy between the observed velocity‐depth (or time‐depth) curve and the calculated function curve gives a measure of the degree of fit between the two curves. In the parameter space, within a given degree of fit that may be considered as the margin of tolerance for the particular problem in hand, every parameter combination provides a valid solution. The solution trough is defined as the region in the parameter space containing these solutions. The shape of the solution trough depends on the relationship between the parameters and, therefore, on the form of the function being used. If the parameters are related linearly or if the relation is linearized then the axis of the solution trough is a straight line. The slope of the axis corresponds to a point close to the average depth of the interval to which the observed data pertain. The intercept corresponds to a velocity value that is quite close to the average velocity over the interval. These properties are extremely useful for understanding the nature of the solution trough in parameter space. Hence, composite displays of solution troughs pertaining to a number of wells can be interpreted to provide information on whether the unit to which the function corresponds has undergone any lateral changes. Such displays also illustrate how current practices that assume the existence of a unique or “true” solution need to be critically revised.
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Paradis, Gregory, Mathieu Bouchard, Luc LeBel, and Sophie D’Amours. "A bi-level model formulation for the distributed wood supply planning problem." Canadian Journal of Forest Research 48, no. 2 (February 2018): 160–71. http://dx.doi.org/10.1139/cjfr-2017-0240.
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The classic wood supply optimisation model maximises even-flow harvest levels and implicitly assumes infinite fibre demand. In many jurisdictions, this modelling assumption is a poor fit for actual fibre consumption, which is typically a subset of total fibre allocation. Failure of the model to anticipate this bias in industrial wood fibre consumption has been linked to increased risk of wood supply failure. In particular, we examine the distributed wood supply planning problem where the roles of forest owner and fibre consumer are played by independent agents. We use game theory to frame interactions between public forest land managers and industrial fibre consumers. We show that the distributed wood supply planning problem can be modelled more accurately using a bi-level formulation and present an extension of the classic wood supply optimisation model that explicitly anticipates industrial fibre consumption behaviour. We present a solution methodology that can solve a convex special case of the problem to global optimality and compare output and solution times of classic and bi-level model formulations using a computational experiment on a realistic dataset. Experimental results show that the bi-level formulation can mitigate risk of wood supply failure.
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Tsung, Chen-Kun, Hann-Jang Ho, Chien-Yu Chen, Tien-Wei Chang, and Sing-Ling Lee. "Detecting Overlapping Communities in Modularity Optimization by Reweighting Vertices." Entropy 22, no. 8 (July 27, 2020): 819. http://dx.doi.org/10.3390/e22080819.
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On the purpose of detecting communities, many algorithms have been proposed for the disjointed community sets. The major challenge of detecting communities from the real-world problems is to determine the overlapped communities. The overlapped vertices belong to some communities, so it is difficult to be detected using the modularity maximization approach. The major problem is that the overlapping structure barely be found by maximizing the fuzzy modularity function. In this paper, we firstly introduce a node weight allocation problem to formulate the overlapping property in the community detection. We propose an extension of modularity, which is a better measure for overlapping communities based on reweighting nodes, to design the proposed algorithm. We use the genetic algorithm for solving the node weight allocation problem and detecting the overlapping communities. To fit the properties of various instances, we introduce three refinement strategies to increase the solution quality. In the experiments, the proposed method is applied on both synthetic and real networks, and the results show that the proposed solution can detect the nontrivial valuable overlapping nodes which might be ignored by other algorithms.
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Mishuris, Gennady S., and Zbigniew S. Olesiak. "On boundary value problems in fracture of elastic Composites." European Journal of Applied Mathematics 6, no. 6 (December 1995): 591–610. http://dx.doi.org/10.1017/s0956792500002084.
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We present a method of solution of a class of fracture problems in the theory of elasticity. The method can be applied to any problem reducible to Poisson's equation, e.g. heat conduction and mass diffusion in solids, theory of consolidation and the like. The novelty of the paper is that we address regions of layered composites with notches, or, in a particular case, with a crack. Within the framework of classical analysis, we apply Fourier and Mellin transforms, 'fit' them together, and reduce the problem to solving a singular integral equation with fixed singularities on a semi-axis. We show the existence and uniqueness of solutions of the equations under consideration, and justify the asymptotics necessary for applications. We show the practical usefulness of the method on the examples of an antiplane problem of fracture mechanics. From our solution, we are able to find the stress intensity factor in the case when a crack tip penetrates a layered composite consisting of 60 layers, and show the limits of applicability of the anisotropic model of such composites.
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Jin, Guo Dong, Li Bin Lu, and Xiao Fei Zhu. "A Method of Order Determination for ARX and ARMA Models Based on Nonnegative Garrote." Applied Mechanics and Materials 721 (December 2014): 496–99. http://dx.doi.org/10.4028/www.scientific.net/amm.721.496.
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Classical order determination methods of ARX and ARMA models suffer from the drawbacks of computationally infeasible and poor stability. To solve these problems, order determination using nonnegative garrote (NNG) method is proposed. By analyzing the properties of ARX and ARMA models, a modification of original NNG method is made to fit the dynamical system identification problem. Furthermore, the solution algorithm of proposed method is presented. Simulations show the validation of proposed method, which has better stability than classical information based criteria methods.
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Tan, Bing, Peng Lu, Zhijun Li, Enmin Feng, and Juan Wang. "Simulation and Domain Identification of Sea Ice Thermodynamic System." Journal of Applied Mathematics 2012 (2012): 1–16. http://dx.doi.org/10.1155/2012/532870.
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Based on the measured data and characteristics of sea ice temperature distribution in space and time, this study is intended to consider a parabolic partial differential equation of the thermodynamic field of sea ice (coupled by snow, ice, and sea water layers) with a time-dependent domain and its parameter identification problem. An optimal model with state constraints is presented with the thicknesses of snow and sea ice as parametric variables and the deviation between the calculated and measured sea ice temperatures as the performance criterion. The unique existence of the weak solution of the thermodynamic system is proved. The properties of the identification problem and the existence of the optimal parameter are discussed, and the one-order necessary condition is derived. Finally, based on the nonoverlapping domain decomposition method and semi-implicit difference scheme, an optimization algorithm is proposed for the numerical simulation. Results show that the simulated temperature of sea ice fit well with the measured data, and the better fit is corresponding to the deeper sea ice.
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Gradišar, Dejan, and Miha Glavan. "Material Requirements Planning Using Variable-Sized Bin-Packing Problem Formulation with Due Date and Grouping Constraints." Processes 8, no. 10 (October 2, 2020): 1246. http://dx.doi.org/10.3390/pr8101246.
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Correct planning is crucial for efficient production and best quality of products. The planning processes are commonly supported with computer solutions; however manual interactions are commonly needed, as sometimes the problems do not fit the general-purpose planning systems. The manual planning approach is time consuming and prone to errors. Solutions to automatize structured problems are needed. In this paper, we deal with material requirements planning for a specific problem, where a group of work orders for one product must be produced from the same batch of material. The presented problem is motivated by the steel-processing industry, where raw materials defined in a purchase order must be cut in order to satisfy the needs of the planned work order while also minimizing waste (leftover) and tardiness, if applicable. The specific requirements of the problem (i.e., restrictions of which work orders can be produced from a particular group of raw materials) does not fit the regular planning system used by the production company, therefore a case-specific solution was developed that can be generalized also to other similar cases. To solve this problem, we propose using the generalized bin-packing problem formulation which is described as an integer programming problem. An extension of the bin-packing problem formulation was developed based on: (i) variable bin sizes, (ii) consideration of time constraints and (iii) grouping of items/bins. The method presented in the article can be applied for small- to medium-sized problems as first verified by several examples of increasing complexity and later by an industrial case study.
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LI, S. P., and KA-LOK NG. "STUDY OF THE UNEQUAL SPHERES PACKING PROBLEM: AN APPLICATION TO RADIOSURGERY TREATMENT." International Journal of Modern Physics C 14, no. 06 (July 2003): 815–23. http://dx.doi.org/10.1142/s0129183103004966.
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We employ the Monte Carlo method to study a constrained optimization problem — packing hard spheres with unequal radii (r2 > r1) into a 3D bounded region and discuss its connection with the Gamma Knife radiosurgery treatment planning. Selection of the best fit solution is based on the Boltzmann factor, e-ΔE/T, which allows us to search for the global optimal solution. As an illustration we determined the least number (≤15) of packed spheres that will occupy the largest volume for three different hypothetical tumor sizes (4115, 10 000 and 36 000 voxels). For the bounded regions and the sizes of the packed spheres that we studied here, the optimal volume packing ratio ranges from 41.3 to 48.7%. From our study, using a lower r2/r1 ratio is more desirable due to the ≤15 radiation shots constraint. The optimal volume packing ratio can be obtained within a relative short CPU computing time and could provide a good starting point for the radiosurgery treatment planning.