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At least 865 records · Page 48Linked to original sources
PubMed2006

Graph transformation method for calculating waiting times in Markov chains.

We describe an exact approach for calculating transition probabilities and waiting times in finite-state discrete-time Markov processes. All the states and the rules for transitions between them must be known in advance. We can then calculate averages over a given ensemble of paths for both additive and multiplicative properties in a nonstochastic and noniterative fashion. In particular, we can calculate the mean first-passage time between arbitrary groups of stationary points for discrete path sampling databases, and hence extract phenomenological rate constants. We present a number of examples to demonstrate the efficiency and robustness of this approach.

Journal Article↗
PubMed1980

The graph-paper effect: subjective stereoscopic patterns induced by moving gratings.

Smooth tracking across an oblique grid pattern produced hallucinations of vertical and/or horizontal striations which moved with the eyes. The effect was produced by single or multiple gratings, monocularly or binocularly, but in the latter case it appeared to lie steresoscopically in the plane of fixation. Gratings containing thin lines or sawtooth edges of moderate contrast were particularly effective stimuli but sine or square waves were not. The subjective stripes had an apparent edge polarity which was opposite to that of the inducing edges or, with thin inducing lines, was determined by the lines' polarity and movement direction. Conventional explanations (eg strobe, afterimage, or moiré effects) can be ruled out. Neither the present effect nor the "pincushion-grid illusion" are due to the presence of spurious Fourier components in the stimulus pattern. An extension of a previous model, involving disinhibitory interaction between movement and pattern channels, accounts for many aspects of this elaborate phenomenon. The detailed dependence of polarity on spatial waveform and movement direction implies: (i) the spatial second harmonic is a necessary component, (ii) the generating is approximately linear and has 90 degree phase preference, and (iii) there is a movement-induced phase lag of about 45 degrees in the response to the second harmonic.

Depth Perception↗
PubMed2004

From paragraph to graph: latent semantic analysis for information visualization.

Most techniques for relating textual information rely on intellectually created links such as author-chosen keywords and titles, authority indexing terms, or bibliographic citations. Similarity of the semantic content of whole documents, rather than just titles, abstracts, or overlap of keywords, offers an attractive alternative. Latent semantic analysis provides an effective dimension reduction method for the purpose that reflects synonymy and the sense of arbitrary word combinations. However, latent semantic analysis correlations with human text-to-text similarity judgments are often empirically highest at approximately 300 dimensions. Thus, two- or three-dimensional visualizations are severely limited in what they can show, and the first and/or second automatically discovered principal component, or any three such for that matter, rarely capture all of the relations that might be of interest. It is our conjecture that linguistic meaning is intrinsically and irreducibly very high dimensional. Thus, some method to explore a high dimensional similarity space is needed. But the 2.7 x 10(7) projections and infinite rotations of, for example, a 300-dimensional pattern are impossible to examine. We suggest, however, that the use of a high dimensional dynamic viewer with an effective projection pursuit routine and user control, coupled with the exquisite abilities of the human visual system to extract information about objects and from moving patterns, can often succeed in discovering multiple revealing views that are missed by current computational algorithms. We show some examples of the use of latent semantic analysis to support such visualizations and offer views on future needs.

Animals↗