Predicting DAX trends from Dow Jones data by methods of the mathematical theory of democracy

The mathematical theory of democracy operates on the indices of popularity and universality which are used to find socially optimal representatives and representative bodies. Regarded mathematically, neither the ‘society’, nor its ‘representatives’ are necessarily human, so that some objects can represent the behavior of other objects. This idea is applied to predicting the DAX-trends (German stock index) from the actual Dow-Jones data; the current fluctuations of stock prices in New York are regarded as representative indicators of future stock price fluctuations in Frankfurt. In particular, it is found that American Express anticipates on the average the price ±fluctuations of 2/3 of the DAX stocks. The statistical significance of the null hypothesis that such a bias from the uncertainty 50% can occur by chance is only 3.5%.     

Extra Theory Morphisms for Institutions: Logical Semantics for Multi-Paradigm Languages

We extend the ordinary concept of theory morphism in institutions to extra theory morphisms. Extra theory morphisms map theories belonging to different institutions across institution morphisms. We investigate the basic mathematical properties of extra theory morphisms supporting the semantics of logical multi-paradigm languages, especially structuring specifications (module systems) á la OBJ-Clear. They include model reducts, free constructions (liberality), co-limits, model amalgamation (exactness), and inclusion systems.We outline a general logical semantics for languages whose semantics satisfy certain logical principles by extending the institutional semantics developed within the Clear-OBJ tradition. Finally, in the Appendix, we briefly illustrate this with the concrete example of CafeOBJ.     

On non-strong jumping numbers and density structures of hypergraphs

Estimating Turán densities of hypergraphs is believed to be one of the most challenging problems in extremal set theory. The concept of ‘jump’ concerns the distribution of Turán densities. A number α∈[0,1) is a jump for r-uniform graphs if there exists a constant c>0 such that for any family F of r-uniform graphs, if the Turán density of F is greater than α, then the Turán density of F is at least α+c. A fundamental result in extremal graph theory due to Erd?s and Stone implies that every number in [0,1) is a jump for graphs. Erd?s also showed that every number in [0,r!/r^r) is a jump for r-uniform hypergraphs. Furthermore, Frankl and Rödl showed the existence of non-jumps for hypergraphs. Recently, more non-jumps were found in [r!/r^r,1) for r-uniform hypergraphs. But there are still a lot of unknowns regarding jumps for hypergraphs. In this paper, we propose a new but related concept-strong-jump and describe several sequences of non-strong-jumps. It might help us to understand the distribution of Turán densities for hypergraphs better by finding more non-strong-jumps.     

Cárnico-ICSPEA2—A metaheuristic co-evolutionary navigator for a complex co-evolutionary farming system

This paper introduces Cárnico-ICSPEA2, a metaheuristic co-evolutionary navigator designed by its end-user as an aid for the analysis and multi-objective optimisation of a beef cattle enterprise running on temperate pastures and fodder crops in Chalco, Mexico State, in the central plateau of Mexico. By combining simulation routines and a multi-objective evolutionary algorithm with a deterministic and stochastic framework, the software imitates the evolutionary behaviour of the system of interest, helping the farm manager to ‘navigate’ through his system’s dynamic phase space. The ultimate goal was to enhance the manager’s decision-making process and co-evolutionary skills, through an increased understanding of his system and the discovery of new, improved heuristics. This paper describes the numerical simulation and optimisation resulting from the application of Cárnico-ICSPEA2 to solve a specific multi-objective optimisation problem, along with implications for the management of the system of interest.     

Diophantine approximation and badly approximable sets

Let (X,d) be a metric space and (Ω,d) a compact subspace of X which supports a non-atomic finite measure m. We consider ‘natural’ classes of badly approximable subsets of Ω. Loosely speaking, these consist of points in Ω which ‘stay clear’ of some given set of points in X. The classical set Bad of ‘badly approximable’ numbers in the theory of Diophantine approximation falls within our framework as do the sets Bad(i,j) of simultaneously badly approximable numbers. Under various natural conditions we prove that the badly approximable subsets of Ω have full Hausdorff dimension. Applications of our general framework include those from number theory (classical, complex, p-adic and formal power series) and dynamical systems (iterated function schemes, rational maps and Kleinian groups).     

An economic production lot size model in an imperfect production system

The paper investigates an EPL (Economic Production Lotsize) model in an imperfect production system in which the production facility may shift from an ‘in-control’ state to an ‘out-of-control’ state at any random time. The basic assumption of the classical EPL model is that 100% of produced items are perfect quality. This assumption may not be valid for most of the production environments. More specifically, the paper extends the article of Khouja and Mehrez [Khouja, M., Mehrez, A., 1994. An economic production lot size model with imperfect quality and variable production rate. Journal of the Operational Research Society 45, 1405–1417]. Generally, the manufacturing process is ‘in-control’ state at the starting of the production and produced items are of conforming quality. In long-run process, the process shifts from the ‘in-control’ state to the ‘out-of-control’ state after certain time due to higher production rate and production-run-time.The proposed model is formulated assuming that a certain percent of total product is defective (imperfect), in ‘out-of-control’ state. This percentage also varies with production rate and production-run time. The defective items are restored in original quality by reworked at some costs to maintain the quality of products in a competitive market. The production cost per unit item is convex function of production rate. The total costs in this investment model include manufacturing cost, setup cost, holding cost and reworking cost of imperfect quality products. The associated profit maximization problem is illustrated by numerical examples and also its sensitivity analysis is carried out.     

Diagnostic assessment of children’s proportional reasoning

A proportional reasoning item bank was created from the relevant literature and tested in various forms. Rasch analyses of 303 pupils’ test results were used to calibrate the bank, and data from 84 pupils’ interviews was used to confirm our diagnostic interpretations. A number of sub-tests were scaled, including parallel ‘without models’ and ‘with models’ forms. We provide details of the 13-item ‘without models’ test which was formed from the ‘richest’ diagnostic items and verified on a further test sample (N=212, ages 10-13). Two scales were constructed for this test, one that measures children’s ‘ratio attainment’ and one that measures their ‘tendency for additive strategy.’ Other significant errors — ‘incorrect build-up,’ ‘magical doubling/halving,’ ‘constant sum’ and ‘incomplete reasoning’ — were identified. Finally, an empirical hierarchy of pupils’ attainment of proportional reasoning was formed, incorporating the significant errors and the additive scale.     

The reality of Mathematics

The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic ‘computation’, is examined and commended upon.     

Average value problems in ordinary differential equations

Using Schauder's fixed point theorem, with the help of an integral representation in ‘Sharp conditions for weighted 1-dimensional Poincaré inequalities’, Indiana Univ. Math. J., 49 (2000) 143-175, by Chua and Wheeden, we obtain existence and uniqueness theorems and ‘continuous dependence of average condition’ for average value problem:

y^′=F(x,y),     

Norm statistics and the complexity of clustering problems

In this paper we introduce a new class of clustering problems. These are similar to certain classical problems but involve a novel combination of ?_p-statistics and ?_q norms. We discuss a real world application in which the case p=2 and q=1 arises in a natural way. We show that, even for one dimension, such problems are NP-hard, which is surprising because the same 1-dimensional problems for the ‘pure’ ?₂-statistic and ?₂ norm are known to satisfy a ‘string property’ and can be solved in polynomial time. We generalize the string property for the case p=q. The string property need not hold when q≤p−1 and we show that instances may be constructed, for which the best solution satisfying the string property does arbitrarily poorly. We state some open problems and conjectures.     

Second order nonlinear multivalued boundary problems in Hilbert spaces

In this paper we consider second order differential inclusions in real Hilbert space, namely p(t)⋅x^″(t)+r(t)⋅x^′(t)∈Ax(t)+F(t,x(t)), a.e. on [0,T], under the nonlinear boundary conditions. Using techniques from multivalued analysis and the theory of operators of monotone type, we prove the existence of solutions for both the ‘convex’ and ‘nonconvex’ problems. Finally, we present a special case of interest, which fit into our framework, illustrating the generality of our results.     

Automorphism groups of positive entropy on minimal projective varieties

We determine the geometric structure of a minimal projective threefold having two ‘independent and commutative’ automorphisms of positive topological entropy, and generalize this result to higher-dimensional smooth minimal pairs (X,G). As a consequence, we give an effective lower bound for the first dynamical degree of these automorphisms of X fitting the ‘boundary case’.     

Color-bounded hypergraphs, II: Interval hypergraphs and hypertrees

A color-bounded hypergraph is a hypergraph (set system) with vertex set X and edge set E={E₁,…,E_m}, together with integers s_i and t_i (1≤s_i≤t_i≤|E_i|) for i=1,…,m. A vertex coloring φ is feasible if the number of colors occurring in edge E_i satisfies s_i≤|φ(E_i)|≤t_i, for every i≤m.In this paper we point out that hypertrees-hypergraphs admitting a representation over a (graph) tree where each hyperedge E_i induces a subtree of the underlying tree-play a central role concerning the set of possible numbers of colors that can occur in feasible colorings. We also consider interval hypergraphs and circular hypergraphs, where the underlying graph is a path or a cycle, respectively. Sufficient conditions are given for a ‘gap-free’ chromatic spectrum; i.e., when each number of colors is feasible between minimum and maximum. The algorithmic complexity of colorability is studied, too.Compared with the ‘mixed hypergraphs’-where ‘D-edge’ means (s_i,t_i)=(2,|E_i|), while ‘C-edge’ assumes (s_i,t_i)=(1,|E_i|−1)-the differences are rather significant.     

Looking at the complexity of two young children's understanding of number

This paper presents a qualitative study that investigated two third-grade students’ understanding of number. The children were videotaped while they worked to record everything they knew about the number, 72. Their artifacts and conversations were then analyzed using the Pirie-Kieren dynamical theory for the growth of mathematical understanding as the theoretical framework. The results of the video analysis revealed the two students’ understanding of natural numbers as being conceptually complex and existing in several different realms of the Pirie-Kieren model. Significant instances of Primitive Knowing, Image Making, Image Having, Property Noticing, Formalizing, Observing, as well as how the children's understanding existed beyond “Don’t Need” Boundaries are identified and examined in detail. Other features of the model — Structuring, Inventising, Folding Back, and Connected Understanding - are also explained and possible examples illustrating these kinds of mathematical thinking in relation to the two children's understanding of number are offered.     

Operational research and ethics: A literature review

Any human activity raises ethical questions, questions about ‘good’ and ‘right’ ways to act and to live; or to put it differently, questions of values and responsibility. From its inception operational research (OR) has engaged with such questions in terms of professional behavior, the handling of preferences in OR, the societal role of OR, the process of OR intervention and the content of OR analysis. As a result, analytical methods and processes have been developed to help clients explore the ethical dimension of their decisions. The paper reviews the literature published in selected OR journals (Management Science; Operations Research; Interfaces; the European Journal of Operational Research; the Journal of the Operations Research Society; Omega; International Transactions in Operational Research; the Journal of Multi-Criteria Decision Analysis), organizing it along the lines of OR’s core competences. The review identifies a number of significant research programmes that are well established and are being energetically pursued; the research findings are being applied to a wide range of important issues. Ethical questions lie at the heart of the great governmental and commercial issues of the day: economic growth and instability; inequality and injustice; environmental degradation and sustainability. They also lie at the heart of the more mundane decisions of day-to-day OR. ‘Ethics’ therefore provides a useful focus for OR both in terms of raising the awareness of all concerned and in providing a theme for research. As a result of the review some research questions are suggested. There is much of interest, much to do.     

Fundamental groups and finite sheeted coverings

It is well known that for a connected locally path-connected semi-locally 1-connected space X, there exists a bi-unique correspondence between the pointed d-fold connected coverings and the transitive representations of the fundamental group of X in the symmetric group Σ_d of degree d.The classification problem becomes more difficult if X is a more general space, particularly if X is not locally connected. In attempt to solve the problem for general spaces, several notions of coverings have been introduced, for example, those given by Lubkin or by Fox. On the other hand, different notions of ‘fundamental group’ have appeared in the mathematical literature, for instance, the Brown-Grossman-Quigley fundamental group, the ?ech-Borsuk fundamental group, the Steenrod-Quigley fundamental group, the fundamental profinite group or the fundamental localic group.The main result of this paper determines different ‘fundamental groups’ that can be used to classify pointed finite sheeted connected coverings of a given space X depending on topological properties of X.     

A dominant subset of V-shaped sequences for a class of single machine sequencing problems

In this note we define a subset of V-shaped sequences, ‘V-shaped about T’, which generalize ‘V-shaped about d’ sequences. We derive a condition under which this subset contains an optimal sequence for a class of single machine sequencing problems. Cost functions from the literature are used to illustrate our results.     

On the topological lower bound for the multichromatic number

In 1976, Stahl [14] defined the m-tuple coloring of a graph G and formulated a conjecture on the multichromatic number of Kneser graphs. For m=1 this conjecture is Kneser’s conjecture, which was proved by Lovász in 1978 [10]. Here we show that Lovász’s topological lower bound given in this way cannot be used to prove Stahl’s conjecture. We obtain that the strongest index bound only gives the trivial m⋅ω(G) lower bound if m≥|V(G)|. On the other hand, the connectivity bound for Kneser graphs is constant if m is sufficiently large. These findings provide new examples of graphs showing that the gaps between the chromatic number, the index bound and the connectivity bound can be arbitrarily large.     

Ordinal machines and admissible recursion theory

We generalize standard Turing machines, which work in time ω on a tape of length ω, to α-machines with time α and tape length α, for α some limit ordinal. We show that this provides a simple machine model adequate for classical admissible recursion theory as developed by G. Sacks and his school. For α an admissible ordinal, the basic notions of α-recursive or α-recursively enumerable are equivalent to being computable or computably enumerable by an α-machine, respectively. We emphasize the algorithmic approach to admissible recursion theory by indicating how the proof of the Sacks–Simpson theorem, i.e., the solution of Post’s problem in α-recursion theory, could be based on α-machines, without involving constructibility theory.