Design Science,the design of systems and Operational Research: back to the future?

The relationship between the science of decision making and the design of systems that support or automate the decision-making process is vital to both academic and practical Operational Research (OR). There is a long-standing need to better understand how OR can be structured so as to contribute to the design of systems, rather than just the science of decisions. This paper articulates the notion of design-oriented OR, particularly within the context of IT-enabled systems, as one approach to addressing this issue. It proposes Design Science (DS) as one way of achieving design-oriented OR, and suggests a reference model for DS as a design-oriented approach to OR. The use and value of DS within the broader remit of management research, and differences with existing systems methodologies, are briefly considered. It concludes by noting that a DS approach would return OR, at least partially, to the values and approach of early OR practitioners, and hence back to the future.     

How hard is it to tell which is a Condorcet committee?

This paper establishes the computational complexity status for a problem of deciding on the quality of a committee. Starting with individual preferences over alternatives, we analyse when it can be determined efficiently if a given committee C$C$ satisfies a weak (resp. strong) Condorcet criterion–i.e., if C$C$ is at least as good as (resp. better than) every other committee in a pairwise majority comparison. Scoring functions used in classic voting rules are adapted for these comparisons. In particular, we draw the sharp separation line between computationally tractable and intractable instances with respect to different voting rules. Finally, we show that deciding if there exists a committee which satisfies the weak (resp. strong) Condorcet criterion is computationally hard.     

Operational Research in the U.K. in 1977: The Causes and Consequences of a Myth?

Instead of maintaining the original ideal of having a broad scientific basis for practical Operational Research, it is suggested that the O.R. community has uncritically accepted a myth which views O.R. as a "Hard" (Physical or even Mathematical) Science. It is argued that this has had profound consequences which explain the present difficulties O.R. workers have with problems involving major Social or Behavioural features. It is concluded that the "Hard" Science myth must be replaced, and a return made to the original conception of O.R., if we are to assist effectively in the complex social issues we face today.     

How strict is strictification?

The subject of this paper is the higher structure of the strictification adjunction, which relates the two fundamental bases of three-dimensional category theory: the Gray-category of 2-categories and the tricategory of bicategories. We show that – far from requiring the full weakness provided by the definitions of tricategory theory – this adjunction can be strictly enriched over the symmetric closed multicategory of bicategories defined by Verity. Moreover, we show that this adjunction underlies an adjunction of bicategory-enriched symmetric multicategories. An appendix introduces the symmetric closed multicategory of pseudo double categories, into which Verity's symmetric multicategory of bicategories embeds fully.     

How rich is the class of multifractional Brownian motions?

The multifractional Brownian motion (MBM) processes are locally self-similar Gaussian processes. They extend the classical fractional Brownian motion processes _BH={_BH(t)_}t∈R$B_H=\{B_H(t){\}}_{t\in \mathbb{R}}$ by allowing their self-similarity parameter H∈(0,1)$H\in (0,1)$ to depend on time.     

How to estimate the sum of a series?

<正>Now we’ll learn how to estimate the sum of a series?We have been able to use the integral test to show that a series ∞∑(n=1)a_n is convergent or divergent.But we also don’t know the best way to find the sum of the series.It is difficult to compute the sum of any series.Here is the best way to find an approximation to the sum of the series.You know     

How to use the Fundamental Theorem of Calculus?

Now we can put the two part of the Fundamental Theorem of Calculus together named the Fundamental Theorem of Calculus:Suppose f（x）is continuous on[a,b].1.If F（x）=∫₀^xf（t）dt,then F’（x）=f（x）.2.∫_α^bf（x）dx=F（b）-F（a）,where     

The Case of Gaël

The Theory of Didactical Situations has had a central position in French mathematics education research since the early 1970s. A major component of this theory is the didactical contract, a completely implicit but highly powerful aspect of the relationship between teacher and student. In this article we relate the series of tutorial sessions which provoked the original formulation of that theory, and in which the theory was validated by its first application.Gaël was an intelligent child who was failing exclusively in mathematics. He was one of nine cases studied between 1980 and 1985 (at the Bordeaux COREM³). After observing him in class and offering him various learning situations, both didactical and adidactical, we arrived at the hypothesis that Gaël was implementing a strategy of avoidance of the “conflict of knowing,” which we characterized as “hysteroid type avoidance,” whereas the others exhibited “obsessional type avoidance” (note that these behaviors should not be confused with the psychiatric categories of the same name, which are serious personality disorders). It was possible to offer psychological explanations for this behavior, but they did not provide the means for correcting the avoidance, and they focused the interest of the researchers on a characteristic of the child or on his competencies, rather than remaining at the level of his behavior and the conditions which provoked it or which might modify it. This behavior demonstrated the refusal, conscious or not, of the child to accept his share of the decision-making responsibilities in a didactical situation and hence to learn while working with an adult.Studying Gaël's behavior enabled the experimenters to explore and understand the constraints of the didactical situation, interpreted as a “didactical contract.” It is the simulacrum of a contract, an illusion, intangible and necessarily broken, but a fiction that is necessary in order for the two protagonists, the teacher and the learner, to engage in and carry out the didactical dialectic. The didactical means to get a student to enter into such a contract is devolution. It is not a pedagogical device, because it depends in an essential way on the content. It consists of putting the student into a relationship with a milieu from which the teacher is able to exclude herself, at least partially (adidactical situation). The mechanism implemented was devised to engage Gaël progressively but explicitly in a challenge in which the teacher could be “on the student's side.”The mathematical aspects of this situation subsequently proved to be one of the fundamental didactical situations of subtraction.     

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 Arrange it?

Problem: If you arrange 24 people in 6 rows and each one must have 5 people,how can you range them?Answer: If you range 24 people in 6 rows, you must have 5 people per row. Isit possible to range so? For there are 6 rows and each one should have 5 people,i.e. 5×6= 30 people !     

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     

How to discretize the Total Variation of an image?

Because they are based on finite differences, usual discretizations of the Total Variation lead to aliased images. We propose a new discretization called spectral total variation that agrees with Shannon sampling principles and produces images that can be exactly interpolated. The quality improvement is illustrated experimentally in the case of image deblurring. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

How likely is Buffon's ring toss to intersect a planar Cantor set?

In Bateman and Volberg (2008) [1], it was shown that the n-th partial 1/4 Cantor in the plane set decays in Favard length no faster than $C\frac{\log n}{n}$. In Bond and Volberg (2008) [2], the so-called circular Favard length of the same set is studied, and the same estimate is shown to persist when the circle has radius $r?Cn$. By considering characteristic functions, the result of Bond and Volberg (2008) [2] naturally leads to a conjecture which (if true) would imply the sharpness of the $L\log \log L$ boundedness of the circular maximal operator proved by Seeger, Tao and Wright (2005) [3].     

One hundred years of Operational Research in Health—UK 1948–2048

This paper presents a personal view, drawing on some 30 years of working in this area, of past, present and future contributions of operational research (OR) in health in the UK. It considers developments in health and care and in OR contributions to these at local and national level since the creation of the National Health Service 60 years ago; likely future developments in health and care; and associated priorities for preparing now for OR to make a major impact on health and care in the next 40 years. The aim is to stimulate reflective thinking and promote anticipatory action among health OR practitioners of the future.     

How hard is half-space range searching?

We investigate the complexity ofhalf-space range searching: givenn points ind-space, build a data structure that allows us to determine efficiently how many points lie in a query half-space. We establish a tradeoff between the storagem and the worst-case query timet in the Fredman/Yao arithmetic model of computation. We show thatt must be at least on the order of $$\frac{{(n/\log n)^{1 - (d - 1)/d(d + 1)} }}{{m^{1/d} }}$$ Although the bound is unlikely to be optimal, it falls reasonably close to the recent upper bound ofO(n/m ^1/d ) established by Matou?ek. We also show that it is possible to devise a sequence ofn inserts and half-space range queries that require a total time ofn ^2-O(1/d) . Our results imply the first nontrivial lower bounds for spherical range searching in any fixed dimension. For example, they show that, with linear storage, circular range queries in the plane require Ω(n ^1/3) time (modulo a logarithmic factor).     

How to Play M 13?

A puzzle called “M ₁₃” J. H. Conway has described recently is explained. We report an implementation of the puzzle in the programming language Java. The program allows the human user to “play M ₁₃” interactively (and to cheat by solving it automatically). The program is an example on how to bring to life a nice piece of discrete mathematics. In this sense it presents not only a didactical way of seeing “mathematics at work”, but also displays the stabilizer chain method developed by C. Sims to solve group theoretic puzzles, the most famous of which being Rubik's cube.