Decision makers best choice: a comparative investigation into the efficiency of search strategies based on ranks

Series: Working Papers on Information Systems, Information Business and Operation

Does Integrated Information Lack Subjectivity

I investigate the status of subjectivity in Integrated Information Theory. This leads me to examine if Integrated Information Theory can answer the hard problem of consciousness. On itself, Integrated Information Theory does not seem to constitute an answer to the hard problem, but could be combined with panpsychism to yield a more satisfying theory of consciousness. I will show, that even if Integrated Information Theory employs the metaphysical machinery of panpsychism, Integrated Information would still suffer from a different problem, not being able to account for the subjective character of consciousness

A framework for tropical mirror symmetry

Applying tropical geometry a framework for mirror symmetry, including a mirror construction for Calabi-Yau varieties, was proposed by the author. We discuss the conceptual foundations of this construction based on a natural mirror map identifying deformations and divisors. We show how the construction specializes to that by Batyrev for hypersurfaces and its generalization by Batyrev and Borisov to complete intersections. Based on an explicit example we comment on the implementation in the Macaulay2 package SRdeformations.Comment: 15 pages, no figure

Nucleation scaling in jigsaw percolation

Jigsaw percolation is a nonlocal process that iteratively merges connected clusters in a deterministic "puzzle graph" by using connectivity properties of a random "people graph" on the same set of vertices. We presume the Erdos--Renyi people graph with edge probability p and investigate the probability that the puzzle is solved, that is, that the process eventually produces a single cluster. In some generality, for puzzle graphs with N vertices of degrees about D (in the appropriate sense), this probability is close to 1 or small depending on whether pD(log N) is large or small. The one dimensional ring and two dimensional torus puzzles are studied in more detail and in many cases the exact scaling of the critical probability is obtained. The paper settles several conjectures posed by Brummitt, Chatterjee, Dey, and Sivakoff who introduced this model.Comment: 39 pages, 3 figures. Moved main results to the introduction and improved exposition of section

Random growth models with polygonal shapes

We consider discrete-time random perturbations of monotone cellular automata (CA) in two dimensions. Under general conditions, we prove the existence of half-space velocities, and then establish the validity of the Wulff construction for asymptotic shapes arising from finite initial seeds. Such a shape converges to the polygonal invariant shape of the corresponding deterministic model as the perturbation decreases. In many cases, exact stability is observed. That is, for small perturbations, the shapes of the deterministic and random processes agree exactly. We give a complete characterization of such cases, and show that they are prevalent among threshold growth CA with box neighborhood. We also design a nontrivial family of CA in which the shape is exactly computable for all values of its probability parameter.Comment: Published at http://dx.doi.org/10.1214/009117905000000512 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org