Phase transitions in optimal unsupervised learning

We determine the optimal performance of learning the orientation of the symmetry axis of a set of P = alpha N points that are uniformly distributed in all the directions but one on the N-dimensional sphere. The components along the symmetry breaking direction, of unitary vector B, are sampled from a mixture of two gaussians of variable separation and width. The typical optimal performance is measured through the overlap Ropt=B.J* where J* is the optimal guess of the symmetry breaking direction. Within this general scenario, the learning curves Ropt(alpha) may present first order transitions if the clusters are narrow enough. Close to these transitions, high performance states can be obtained through the minimization of the corresponding optimal potential, although these solutions are metastable, and therefore not learnable, within the usual bayesian scenario.Comment: 9 pages, 8 figures, submitted to PRE, This new version of the paper contains one new section, Bayesian versus optimal solutions, where we explain in detail the results supporting our claim that bayesian learning may not be optimal. Figures 4 of the first submission was difficult to understand. We replaced it by two new figures (Figs. 4 and 5 in this new version) containing more detail

Cyanogenesis inhibits active defense reactions in plants.

In the course of fungal attack on the cyanogenic rubber tree (Hevea brasiliensis Muell.-Arg.) HCN is liberated from infected tissue. The HCN interferes with plant host and fungal pathogen. It becomes inhibitory to active defense responses which are dependent on biosynthetic processes as far as a threshold concentration is transgressed

Statistical Mechanics of Learning in the Presence of Outliers

Using methods of statistical mechanics, we analyse the effect of outliers on the supervised learning of a classification problem. The learning strategy aims at selecting informative examples and discarding outliers. We compare two algorithms which perform the selection either in a soft or a hard way. When the fraction of outliers grows large, the estimation errors undergo a first order phase transition.Comment: 24 pages, 7 figures (minor extensions added

Agricultural scene understanding and supporting field research, volume 1

There are no author-identified significant results in this report

Cosmic rays at airplane altitudes

A continuation of experiments made in a B-29 airplane to investigate the properties of cosmic rays is herein reported. Part I describes results on the latitude effect at 30,000 ft measured with counter telescopes and with both shielded and unshielded ionization chambers, from 64° geomagnetic north to the magnetic equator. A considerably larger latitude effect for the shielded ionization chamber than with the unshielded one or with counter telescopes indicates a definite change in the character of the radiation as one goes toward the equator at this altitude. The "knee" of the latitude effect is investigated in detail by a number of similar flights. Part II describes measurements made on density and formation of extended air showers. The apparatus was of such a nature as to be sensitive to relatively sparse showers. The densities obtained can be fitted to an integral power law spectrum with a negative exponent of 1.50±0.05 for an altitude of 30,000 ft. Intensity-altitude curves are presented, showing that the development of smaller showers takes place nearer the top of the atmosphere than does the development of large showers. Derived zenith-angle dependencies at various altitudes are also given

Recent Studies of the Cosmic-Ray Latitude Effect at High Altitudes

With an improved Geiger counter telescope, having an angular aperture of about ±15° from its axis, a series of balloon flights was made in August and September, 1947, at seven stations extending from San Antonio, Texas, to Saskatoon, Canada. The axis of the telescope in all cases was oriented in a vertical direction. All sets of equipment were compared with a standard to reduce all results to a common basis. The standard sets, in turn, were compared with an accurately constructed telescope which had been used to make an absolute determination of cosmic-ray intensity at the vertical in Pasadena. Two flights were made from each of the seven stations. The agreement between flights made within a few hours of each other at a given station is very good. Results from two flights made at a given station several days apart are not in general as consistent. Likewise, no monotonic increase of the radiation with increase of latitude was observed. Evidence is presented for rather large fluctuations at high altitudes of the lower energy components of cosmic rays. Some of the reasons for these fluctuations are discussed

The Latitude and Longitude Effects in Cosmic Rays Over the United States and Canada at 30,000 Feet

The change with geomagnetic latitude of the ionizing particles at 310 g/cm^-2 atmospheric pressure (30,000 ft.) that could penetrate various thicknesses of absorber was measured by Biehl, Neher, and Roesch [1] over a range of latitude of 64° geomagnetic north to the geomagnetic equator along latitude 80°W. These flights show that most of the latitude effect is over at 50° as one proceeds north and this was independent of the absorber used or whether the total radiation at that altitude was measured or only that near the vertical. On the other hand, Swann, Morris and Seymour [2] find a 10 percent increase for a 10° increase in geomagnetic latitude at 30,000 feet even beyond the "knee" of the curve. Although no mention of an absorber was made, presumably their measurements were made with a lead absorber. A number of flights having a further bearing on this point have recently been made, covering the latitude range particularly from 40° to 64° geomagnetic north with counter telescopes and ionization chambers, the latter both unshielded and shielded with 10 cm of lead

Agricultural scene understanding, volume 1

There are no author-identified significant results in this report