Evolving to the edge of chaos: Chance or necessity?

We show that ecological systems evolve to edges of chaos (EOC). This has been demonstrated by analyzing three diverse model ecosystems using numerical simulations in combination with analytical procedures. It has been found that all these systems reside on EOC and display short-term recurrent chaos (strc). The first two are non-linear food chains and the third one is a linear food chain. The dynamics of first two is dictated by deterministic changes in system parameters. In contrast to this, dynamics of the third model system (the linear food chain) is governed by both deterministic changes in system parameters as well as exogenous stochastic perturbations (unforeseen changes in initial conditions) of these dynamical systems.     

To charge or not to charge?

Discussions on the success or failure of OR practice tend to focus on specific case studies which often highlight major dilemmas that face OR professionals: Model robustness, simplicity vs complexity, optimising vs satisficing, conflict between criteria, who is the ‘client’?, and so on. But above all, the following issues predominate: Should OR be concerned with tactical or strategic problems? Where should it be placed in the organisational structure and who should it report to? These issues inevitably raise the questions of accountability, coupled with that of charging for OR services. It is this issue in particular, whether to charge or not to charge for OR services, that the paper seeks to explore.     

Should European gamblers play lotto in the USA?

Any jackpot building game is designed to have a negative expected return for the gambler, but it can be profitable under certain circumstances. Previous studies have shown that the purchase of a single ticket of US-American state lotteries is sometimes a gamble with a positive expected value. Lottery winnings are not taxed in Europe, which suggests that the profitability of European games may be even higher. We present an exact formula for the calculation of the expected value of a single lotto ticket and find European lottery drawings to be far less profitable for the gambler compared to the US-American lotto market. Those US lotteries that generate profitable drawings are not characterized by higher redistribution rates or by their specific rules, but by the purchasing behavior of the gamblers. These gamblers buy far fewer tickets (per capita) and they barely react to increasing jackpots, even though the jackpots are large enough to cause positive expected winnings.     

Results of a beer game experiment: Should a manager always behave according to the book?

We investigate the effect of the literature suggested optimal values of the parameters of a dynamic decision‐making heuristic in the presence of semirationally managed supply chain echelons using a soft coded one‐to‐one version of The Beer Game as an experimental platform. According to the counterintuitive results obtained in this study, it is possible for a “rational manager” to obtain higher costs than the costs generated by a “semirational manager.” Thus, the results do not support the use of the well‐established decision parameter values for the echelon of concern if the other echelons' inventories are managed suboptimally. © 2015 Wiley Periodicals, Inc. Complexity 21: 190–199, 2016     

To lay out or not to lay out?

The Quadratic Assignment Problem (QAP) is known as one of the most difficult problems within combinatorial optimization. It is used to model many practical problems including different layout problems. The main topic of this paper is to provide methods to check whether a particular instance of the QAP is a layout problem. An instance is a layout problem if the distances of the objects can be reconstructed on the plane and/or in the 3-dimensional space. A new mixed integer programming model is suggested for the case if the distances of the objects are supposed to be rectilinear distances. If the distances are Euclidean distances then the use of the well-known Multi-Dimensional Scaling (MDS) method of statistics is suggested for reconstruction purposes. The well-known difficulty of QAP makes it a popular and suitable experimental field for many algorithmic ideas including artificial intelligence methods. These types of results are published sometimes as layout problems. The methods of reconstruction can be used to decide whether the topic of a paper is layout or only general QAP. The issue what the OR community should expect from AI based algorithms, is also addressed.     

What part of the concept of acceleration is difficult to understand: the mathematics, the physics, or both?

In this paper, details of student difficulties in understanding the concept of acceleration and the mathematical and physical/intuitive sources of these are delineated by utilizing the teaching experiment methodology. As a result of the study, two anchoring analogies are proposed that can be used as a diagnostic tool for students’ alternative conceptions. These can be used in teaching to highlight the peculiarity of acceleration concept. This study portrays how seeing acceleration as ‘rate of change’ of a quantity (velocity) and recognizing the consequences of such a definition are hindered in certain ways which in turn negatively affect learning the concept of force. This is also an example that illustrates that a rather “simple” mathematical concept (i.e., rate of change) for the expert can become a complex phenomenon when embedded in a physical concept (i.e., acceleration) which is consistently found to be as a misconception among learners at various levels that is widely occurring and very resistant to change.     

Should civil society organizations cooperate or compete in fighting a corrupt government?

We consider a dynamic game with a corrupt government and multiple civil society organizations as the players. We characterize feedback Stackelberg equilibria with the government as leader and two civil society organizations as the followers who can compete or cooperate when deciding their monitoring efforts. Overall, the numerical results show that a cooperation yields a higher institutional quality and output than does the competitive regime as it does for both individuals and government payoff while the players invest less efforts. In a nutshell, we found that it is in the best interest of both the government and civil society organizations that the latter coordinate their actions and efforts and cooperate in fight against corruption.     

How to use the Limit Laws?

We used tables and graphs by using graphing-calculator to guess values of limits,however,we found methods we used don’t always lead to the correct answer.Theproperties of limits have been found.It iseasy to believe they are true.For example,iff(x)is close to Land g(x)is close to M,itis reasonable to get the result that f(x)+g     

How to prove the integral test?

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How Close is the Sample Covariance Matrix to?the?Actual Covariance Matrix?

Given a probability distribution in ? ⁿ with general (nonwhite) covariance, a classical estimator of the covariance matrix is the sample covariance matrix obtained from a sample of N independent points. What is the optimal sample size N=N(n) that guarantees estimation with a fixed accuracy in the operator norm? Suppose that the distribution is supported in a centered Euclidean ball of radius $O(\sqrt{n})$ . We conjecture that the optimal sample size is N=O(n) for all distributions with finite fourth moment, and we prove this up to an iterated logarithmic factor. This problem is motivated by the optimal theorem of Rudelson (J. Funct. Anal. 164:60?C72, 1999), which states that N=O(nlog?n) for distributions with finite second moment, and a recent result of Adamczak et al. (J. Am. Math. Soc. 234:535?C561, 2010), which guarantees that N=O(n) for subexponential distributions.     

How to use the method of the improvising differentiation?

<正>We know the Substitution Rule,which is based on the following identity in differentiation.∫f(g(x))g′(x)dx=∫f(u)du(where u=g(x)).Now,we'll talk about how to use the method of the improvising differentiation,and give some examples by using basic     

Semi-Lagrangian relaxation applied to?the?uncapacitated facility location problem

We show how the performance of general purpose Mixed Integer Programming (MIP) solvers, can be enhanced by using the Semi-Lagrangian Relaxation (SLR) method. To illustrate this procedure we perform computational experiments on large-scale instances of the Uncapacitated Facility Location (UFL) problems with unknown optimal values. CPLEX solves 3 out of the 36 instances. By combining CPLEX with SLR, we manage to solve 18 out of the 36 instances and improve the best known lower bound for the other instances. The key point has been that, on average, the SLR approach, has reduced by more than 90% the total number of relevant UFL variables.