A visual workspace for constructing hybrid MDS algorithms and coordinating multiple views

Data can be distinguished according to volume, variable types and distribution, and each of these characteristics imposes constraints upon the choice of applicable algorithms for their visualisation. This has led to an abundance of often disparate algorithmic techniques. Previous work has shown that a hybrid algorithmic approach can be successful in addressing the impact of data volume on the feasibility of multidimensional scaling (MDS). This paper presents a system and framework in which a user can easily explore algorithms as well as their hybrid conjunctions and the data flowing through them. Visual programming and a novel algorithmic architecture let the user semi-automatically define data flows and the co-ordination of multiple views of algorithmic and visualisation components. We propose that our approach has two main benefits: significant improvements in run times of MDS algorithms can be achieved, and intermediate views of the data and the visualisation program structure can provide greater insight and control over the visualisation process

Can Markets Learn to Avoid Bubbles?

One of the most striking results in experimental economics is the ease with which market bubbles form in a laboratory setting and the difficulty of preventing them. This article re-examines bubble experiments in light of the results of an earlier series of market experiments that examine how learning occurs in markets characterized by an asymmetry of information between buyers and sellers, such as found in Akerlof’s lemons model and Spence’s signaling model and extends the arguments put forth in the author’s book, Paving Wall Street: Experimental Economics and the Quest for the Perfect Market. Markets with asymmetric information are incomplete because they lack markets for specific levels of product quality. Such markets either lump all qualities together (lemons) or using external indications of quality to separate them (signaling). Similarly, the markets used in bubble experiments are incomplete in that they are lacking a complete set of forward or futures markets, depriving traders of the information supplied by the prices in those markets. Preliminary experimental results suggest that the addition of a single forward market can sometimes mitigate bubble formation and this article suggests more extensive research in this direction is warranted. Market bubbles outside of the laboratory usually are found in markets in with forward and futures markets that are either legally restricted or otherwise limited. Experimentation in markets with asymmetric information also indicates that the ability of subjects to learn how to send and receive signals can be enhanced by changing the way that market information is presented to them. We explore how this result might be used to help asset markets learn to avoid bubbles.Market bubbles, learning and adaptation, behavioral finance, signaling, asymmetric information

A problem in optimal search and stop

Problem in optimal search and sto

An approach to intersection theory on singular varieties using motivic complexes

We introduce techniques of Suslin, Voevodsky, and others into the study of singular varieties. Our approach is modeled after Goresky-MacPherson intersection homology. We provide a formulation of perversity cycle spaces leading to perversity homology theory and a companion perversity cohomology theory based upon generalized cocycle spaces. These theories lead to conditions on pairs of cycles which can be intersected and a suitable equivalence relation on cocycles/cycles enabling pairings on equivalence classes. We establish suspension and splitting theorems, as well as a localization property. Some examples of intersections on singular varieties are computed.Comment: revised version, to appear in Compositio Mathematic

A hybrid layout algorithm for sub-quadratic multidimensional scaling

Many clustering and layout techniques have been used for structuring and visualising complex data. This paper is inspired by a number of such contemporary techniques and presents a novel hybrid approach based upon stochastic sampling, interpolation and spring models. We use Chalmers' 1996 O(N/sup 2/) spring model as a benchmark when evaluating our technique, comparing layout quality and run times using data sets of synthetic and real data. Our algorithm runs in O(N/spl radic/N) and executes significantly faster than Chalmers' 1996 algorithm, whilst producing superior layouts. In reducing complexity and run time, we allow the visualisation of data sets of previously infeasible size. Our results indicate that our method is a solid foundation for interactive and visual exploration of data

An Optimal Control Theory for the Traveling Salesman Problem and Its Variants

We show that the traveling salesman problem (TSP) and its many variants may be modeled as functional optimization problems over a graph. In this formulation, all vertices and arcs of the graph are functionals; i.e., a mapping from a space of measurable functions to the field of real numbers. Many variants of the TSP, such as those with neighborhoods, with forbidden neighborhoods, with time-windows and with profits, can all be framed under this construct. In sharp contrast to their discrete-optimization counterparts, the modeling constructs presented in this paper represent a fundamentally new domain of analysis and computation for TSPs and their variants. Beyond its apparent mathematical unification of a class of problems in graph theory, the main advantage of the new approach is that it facilitates the modeling of certain application-specific problems in their home space of measurable functions. Consequently, certain elements of economic system theory such as dynamical models and continuous-time cost/profit functionals can be directly incorporated in the new optimization problem formulation. Furthermore, subtour elimination constraints, prevalent in discrete optimization formulations, are naturally enforced through continuity requirements. The price for the new modeling framework is nonsmooth functionals. Although a number of theoretical issues remain open in the proposed mathematical framework, we demonstrate the computational viability of the new modeling constructs over a sample set of problems to illustrate the rapid production of end-to-end TSP solutions to extensively-constrained practical problems.Comment: 24 pages, 8 figure