Integrating the collection,fusion, and dissemination of traveler information in Edinburgh,Scotland

The Edinburgh traveler information system, currently being designed for the Edinburgh City Council (ECC), is notable both for its multifaceted approach to the challenges of traffic management in an urban setting and its ability to integrate past, present, and future elements. Integration plays a part in the system design in the following ways:

• •• integration of new and existing systems;
• •• linking together of several disparate systems and procedures;
• •• tight integration of response capabilities with the National Driver Information and Control System (NADICS) operated by the Scottish Office, covering interurban motorways;
• •• incorporation of modularity and flexibility to accommodate future integration.

In describing how the Edinburgh traveler information system is intended to operate, the paper refers to the different types of integration and shows how they are used to benefit the system.The paper begins with a Background outlining the physical, geographical, and institutional context for the system. The Council's environmentally aware policies are referred to, and existing and planned systems, both within and outside Edinburgh, which are relevant to Edinburgh traveler information are briefly described.Following the Background is an overview of the System Design, describing the value added by new elements of the Edinburgh traveler information system and the basic functions to be performed by the system. The Data Collection, Data Fusion, and Data Dissemination aspects of the system are then investigated individually. From the sections describing system structure and operations, it is apparent that the design aims to maximize the collection sources and dissemination mechanisms, but to consolidate the processing of all inputs and outputs in one central location. The system design can accommodate a number of diverse dissemination technologies to ensure that as many target audiences as possible will be exposed to the Information, e.g., variable message signs, remote display terminals, interactive telephone, electronic data exchange, etc.The System Benefits are then outlined and related to the Council policy objectives. The paper ends with a Conclusion and Outlook section which recaps the main points and looks ahead by identifying system enhancements which are anticipated to be integrated in the future.     

A Note on Old Babylonian Computational Techniques

Analysis of the errors in two Old Babylonian “algebraic” problems shows

• •that the computations were performed on a device where additive contributions were no longer identifiable once they had entered the computation;
• •that this device must have been some kind of counting board or abacus where numbers were represented as collections of calculi;
• •that units and tens were represented in distinct ways, perhaps by means of different calculi.

© 2002 Elsevier Science (USA).Eine Analyse der Rechenfehler in zwei altbabylonischen “algebraischen” Aufgaben läßt mehrere Rückschlüsse auf ein Hilfsmittel zu, das zur Durchführung von Rechnungen benutzt worden sein kann:

• •Additive Beiträge waren nach ihrer Eintragung in die Rechnung nicht länger identifizierbar.
• •Das Gerät war eine Art Rechenbrett, auf welchem Zahlen als Haufen von Rechensteinen erschienen.
• •Einer und Zehner wurden in verschiedener Weise, evtl. mittels verschiedener Rechensteine repräsentiert.

© 2002 Elsevier Science (USA).MSC subject classification: 01A17.     

Analysis of performance of an iron-bath reactor using computational fluid dynamics

The performance of an iron-bath reactor has been studied using a comprehensive numerical model that combines a computational fluid dynamics approach for the gas phase and a heat and mass balance model for the bath. The model calculates:

• •coal, ore, flux and oxygen consumption;
• •post-combustion ratio (PCR);
• •heat-transfer efficiency (HTE);
• •off-gas temperature and composition;
• •heat transfer and chemical reactions between gas and iron and slag droplets; and
• •heat transfer between gas and bath, refractories and lance.

The model was validated with data reported by the Nippon Steel Corporation for a 100 t pilot plant, and the calculated and measured data are in good agreement. Modelling results showed that the dominant mechanisms of heat transfer from the gas to the bath are radiation to the slag surface and convection heat transfer to droplets.     

Formal aspects of egress complexity

Egress complexity is concerned with the summative uncertainty experienced by a naive occupant of a building when faced with a challenge to evacuate without the assistance of signage. This paper takes the present model of egress complexity and recasts its basic initiative in terms of elementary order theory. Arguments are presented to demonstrate

• •the existence of distinct maximum and minimum exit complexities for a given number of compartments,
• •the monotonic nature of complexity and
• •the relationship of a given floorplan complexity to the corresponding measures of its homomorphic images

The uniqueness of the theory on which the model is developed stems from a scenario-independent nonmetric approach to egress measurement.     

Symplectic geometry,minors and graph Laplacians

In my talk, I will present some works done in the nineties on Laplacians on graphs: from eigenvalue problems to inverse problem for resistor networks. I will focus on the motivations and the main results as well as on the main ideas:

• •A differential topology point of view on the minor relation: a nice stratification associated to a finite graph Γ whose strata are associated to the minors of Γ
• •“Discrete” (graphs) versus “continuous” (Riemannian manifolds)
• •Stability of spectra with respect to singular limits: a finite dimensional theory of operators with domains (Von Neumann theory).

The link with topology will appear in some results about my graph parameter μ, in particular the planarity and the linkless embedding properties.     

Maximizing profit of a food retailing chain by targeting and promoting valuable customers using Loyalty Card and Scanner Data

In this paper, we set up a House of Profit Model, an approach of maximizing profit of a food retailing chain by targeting and promoting valuable customers. Our model combines

• •segmentation analysis of households using Loyalty Card and Scanner Data,
• •price and promotion elasticity analysis,
• •simulation of effects of pricing and promotion,
• •price and promotion optimization to maximize profit.

These components are well-known in the literature and each of them has received considerable independent study. However, in this study we combine each of these components into one consistent, application-orientated model. We then demonstrate using panel data that the combination has a synergic effect on the efficiency of estimation and the maximization of profit (e.g., price and promotion elasticity estimation is improved by conducting it within market segments rather than across an entire hetereogeneous population). These estimates are further improved by incorporating “pass through”—a functional relationship between a retailer’s unit prices and unit costs.     

Error Bounds for Approximation with Neural Networks

In this paper we prove convergence rates for the problem of approximating functions f by neural networks and similar constructions. We show that the rates are the better the smoother the activation functions are, provided that f satisfies an integral representation. We give error bounds not only in Hilbert spaces but also in general Sobolev spaces W^m, r(Ω). Finally, we apply our results to a class of perceptrons and present a sufficient smoothness condition on f guaranteeing the integral representation.     

Positive Lyapunov exponent for generic one-parameter families of unimodal maps

Letf _{a a∈A} be a C² one-parameter family of non-flat unimodal maps of an interval into itself anda* a parameter value such that

1. f_a* satisfies the Misiurewicz Condition,
2. f_a* satisfies a backward Collet-Eckmann-like condition,
3. the partial derivatives with respect tox anda of f _a ⁿ (x), respectively at the critical value and ata*, are comparable for largen.

Thena* is a Lebesgue density point of the set of parameter valuesa such that the Lyapunov exponent of f_a at the critical value is positive, and f_a admits an invariant probability measure absolutely continuous with respect to the Lebesgue measure. We also show that given f_a* satisfying (a) and (b), condition (c) is satisfied for an open dense set of one-parameter families passing through f_a*.     

A note on the three versions of distributional chaos

The concept of distributional chaos was introduced by Schweizer et al. [Schweizer B, Sklar A, Smítal J. Measures of chaos and a spectral decomposition of dynamical systems on the interval. Tran Amer Math Soc 1994;344:737–854.] for a continuous selfmap on an interval. However, it turns out that, for a continuous selfmap on a compact metric space, three mutually nonequivalent versions of distributional chaos, DC1–DC3, can be discussed. In this paper, we consider a continuous map f : X → X, where X is a compact metric space, and show that DC1 (resp. DC2) is an iteration invariant, that is, for any integer N > 0, f is DC1 (resp. DC2) if and only if f^N is also DC1(resp. DC2). As applications, we show that the following statements hold:

• (1)Let G be a graph and f : G → G a continuous map. Then f is DC1 if and only if f is DC2.
• (2)For a continuous selfmap f on a tree T, these three versions of distributional chaos, DC1 − DC3 are mutually equivalent.

Furthermore, we present two examples which show that DC3 may be an iteration invariant. We will also discuss and partly solve the problem.     

Improved OR education through the use of spreadsheet models

The first and major part of this presentation shows how OR education may be improved through the use of spreadsheets, with several examples:

• •in decision theory, where the drawing capabilities of Excel are used to represent decision trees and where window switching and macros allow the educator to animate his presentation;
• •in linear programming, where the solver is used (remarks are made relating to the adequacy of the solver's solutions), and where the spreadsheet's graphing capabilities are used both to represent the feasible set and the objective function, and to interactively animate the objective function or constraint movements;
• •in dynamic programming, deterministic or stochastic, where it is shown that several standard spreadsheet functions facilitate the development of specialized models;
• •in simulation, where it will be seen how stochastic simulation may be facilitated through the use of an add-in, and how a decision support system may thus be built from scratch in less than 10 minutes.

A creative use of the spreadsheet in business OR models is presented in the second part of this presentation, with an example in process simulation: airport luggage traffic simulation. A short third part presents the possibilities offered by spreadsheet add-ins.     

Free energy and solutions of the Vlasov-Poisson-Fokker-Planck system: external potential and confinement (Large time behavior and steady states)

This paper is devoted to the characterization of external electrostatic potentials for which the Vlasov-Poisson-Fokker-Planck system satisfies one of the following properties:

• (i) the system admits stationary solutions,
• (ii) any solution to the evolution problem converges to a stationary solution, or, equivalently, no mass vanishes for large times,
• (iii) the free energy is bounded from below, We give conditions under which these different notions of confinement are equivalent.

     

Order stars and stability theorems

This paper clears up to the following three conjectures:

1. The conjecture of Ehle [1] on theA-acceptability of Padé approximations toe ^z , which is true;
2. The conjecture of Nørsett [5] on the zeros of the “E-polynomial”, which is false;
3. The conjecture of Daniel and Moore [2] on the highest attainable order of certainA-stable multistep methods, which is true, generalizing the well-known Theorem of Dahlquist.

We further give necessary as well as sufficient conditions forA-stable (acceptable) rational approximations, bounds for the highest order of “restricted” Padé approximations and prove the non-existence ofA-acceptable restricted Padé approximations of order greater than 6. The method of proof, just looking at “order stars” and counting their “fingers”, is very natural and geometric and never uses very complicated formulas.     

Heat flow and Hardy inequality in complete Riemannian manifolds with singular initial conditions

Upper bounds are obtained for the heat content of an open set D with singular initial condition f on a complete Riemannian manifold, provided (i) the Dirichlet-Laplace-Beltrami operator satisfies a strong Hardy inequality, and (ii) f satisfies an integrability condition. Precise asymptotic results for the heat content are obtained for an open bounded and connected set D in Euclidean space with C² boundary, and with initial condition f(x)=δ(x)^−α,0<α<2, where δ(x) is the distance from x to the boundary of D.     

An optimal time to sleep for an auto-sleep system considering multi-usage states

An auto-sleep system is defined by the following two properties:

• 1.(i) a call for the system occurs randomly and intermittently
• 2.(ii) the system automatically goes to sleep if there occurs no call during a prespecified time T.

It considers four states:

• 1.(a) sleep
• 2.(b) warm-up
• 3.(c) nonusage
• 4.(d) usage.

For such a system, the time to sleep has been discussed based on suitable criteria. This study extends the model for an auto-sleep system so that the model can deal with multi-usage states. With a view to determining an optimal time to sleep under the extended model, the expected energy consumed per unit time is formulated as a criterion to be minimized. The existence of an optimal time to sleep is examined under a general call distribution. Numerical examples are also provided for a Weibull as well as a log-normal call distribution.     

Computing over the Reals with Addition and Order: Higher Complexity Classes

This paper deals with issues of structural complexity in a linear version of the Blum-Shub-Smale model of computation over the real numbers. Real versions of PSPACE and of the polynomial time hierarchy are defined, and their properties are investigated. Mainly two types of results are presented:

• •Equivalence between quantification over the real numbers and over {0, 1};
• •Characterizations of recognizable subsets of {0, 1}* in terms of familiar discrete complexity classes.

The complexity of the decision and quantifier elimination problems in the theory of the reals with addition and order is also studied.     

Ultrafilters,independent collections,and applications to topology

The following are consequences of the main results in this paper:

• 1.(1) The number of countably compact, completely regular spaces of density κ is 2^22κ.
• 2.(2) There are 2^2κ points in U(κ) (= space of uniform ultrafilters on κ), each of which has tightness 2^κ in U(κ) and is a limit point of a countable subset of U(κ).
• 3.(3) There are 2^2κ points in U(κ), each of which has tightness 2^κ and is a weak P-point of κ¹.
• 4.(4) For each λ ⩽ κ there are at least 2^2λ · κ points in βκ, each of which has tightness 2^λ in β κ and is a weak P-point of κ¹. Moreover, under GCH there are at least 2^2λ · κ^λ such points.

     

Softness of hypercoherences and MALL full completeness

We prove a full completeness theorem for multiplicative–additive linear logic (i.e. MALL) using a double gluing construction applied to Ehrhard’s *-autonomous category of hypercoherences. This is the first non-game-theoretic full completeness theorem for this fragment. Our main result is that every dinatural transformation between definable functors arises from the denotation of a cut-free MALL proof.Our proof consists of three steps. We show:

• •Dinatural transformations on this category satisfy Joyal’s softness property for products and coproducts.
• •Softness, together with multiplicative full completeness, guarantees that every dinatural transformation corresponds to a Girard MALL proof-structure.
• •The proof-structure associated with any dinatural transformation is a MALL proof-net, hence a denotation of a proof. This last step involves a detailed study of cycles in additive proof-structures.

The second step is a completely general result, while the third step relies on the concrete structure of a double gluing construction over hypercoherences.