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S Amari

Publications and source records attributed to S Amari.

35 records · Page 2Linked to original sources

A numerical study on learning curves in stochastic multilayer feedforward networks.

The universal asymptotic scaling laws proposed by Amari et al. are studied in large scale simulations using a CM5. Small stochastic multilayer feedforward networks trained with backpropagation are investigated. In the range of a large number of training patterns t, the asymptotic generalization error scales as 1/t as predicted. For a medium range t a faster 1/t2 scaling is observed. This effect is explained by using higher order corrections of the likelihood expansion. It is shown for small t that the scaling law changes drastically, when the network undergoes a transition from strong overfitting to effective learning.

Learning↗

Type II Supernova Matter in a Silicon Carbide Grain from the Murchison Meteorite

The circumstellar silicon carbide (SiC) grain X57 from the Murchison meteorite contains large amounts of radiogenic calcium-44 (20 times its solar system abundance) and has an anomalous silicon isotopic composition, different from other circumstellar SiC grains. Its inferred initial 44Ti/Si and 44Ti/48Ti ratios are 1.6 x 10(-4) and 0.37. In addition, it contains radiogenic magnesium-26; the inferred initial 26Al/27Al ratio is 0.11. The isotopic and elemental data of X57 can be explained by selective mixing of matter from different zones of a typical type II supernova of 25 solar masses during its explosion. The high 44Ti/Si ratio requires contributions from the innermost nickel zone of the supernova to the SiC condensation site, as similarly suggested by astronomical observations.

Journal Article↗

Small SiC grains and a nitride grain of circumstellar origin from the Murchison meteorite: implications for stellar evolution and nucleosynthesis.

We report the results of SIMS isotopic analyses of carbon, nitrogen, oxygen, and silicon made on 849 small (approximately 1 micrometer) individual silicon carbide grains from the Murchison meteorite. The isotopic compositions of the major elements carbon and silicon of most grains (mainstream) are similar to those observed in larger grain studies suggesting an AGB star origin of these grains. In contrast, the trace element nitrogen shows a clear dependency on grain size. 14N/15N ratios increase with decreasing grain size, suggesting different stellar sources for grains of different size. Typically observed 14N/15N ratios in the small grains of this study are approximately 2700, clearly larger than the values expected from model calculations of AGB stars. In addition to the three dredge-up episodes characteristic for the evolution of AGB stars, extra-mixing of CNO-processed matter in low mass AGB stars appears to be a promising possibility in order to explain the high 14N/15N ratios of the small circumstellar SiC grains. A small fraction of grains shows a silicon isotopic signature not observed in larger circumstellar SiC grains from Murchison. Their stellar origin is still uncertain. The minor type A, B, Y, and X grains were found to be present at a level of a percent, which is similar to their abundance in the larger-grain SiC separates from Murchison. Oxygen isotopic compositions are normal within the experimental uncertainties of several 10%, indicating that oxygen of stellar origin is rare or even absent in the SiC grains. We conclude that most of the oxygen is a contaminant which was introduced into the SiC grains after their formation, e.g., during sample processing in the laboratory. We identified a nitride grain, most likely Si3N4 with little carbon, with highly anomalous isotopic compositions (12C/13C = 157 +/- 33, 14N/15N = 18 +/- 1, delta 29 Si = -43 +/- 56%, delta 30 Si = -271 +/- 50%). The isotopic patterns of carbon, nitrogen, and silicon resemble those of the rare SiC X grains suggesting that these two rare constituents of circumstellar matter formed in the same type of stellar source, namely, Type II supernovae.

Carbon↗

A theory on the determination of 3D motion and 3D structure from features.

The present paper proposes a mathematical theory and a method of recognition of both the 3D structure and the motion of a moving object from its monocular image. Initially, characteristic features are extracted from the 2D perspective image of the object. Because motion of the object induces a change in its 2D perspective image, it also induces a change in the features which depends on the 3D structure and the velocity of the object. This suggests the possibility of detecting the 3D structure and the motion directly from the features and their changing rate, without the need for calculating optical flows. An analysis is made of the relation between the 3D rigid motion of a surface element and the change in local linear features. From this relation, a method is proposed for calculating the velocity of and the normal to the surface element without considering any correspondence of points. An optical flow can also be calculated by this method. Two simple computer simulations are provided.

Form Perception↗

Sensori-motor transformations in the brain (with a critique of the tensor theory of cerebellum).

Section 1 lists 12 points which must be addressed by neural models of sensorimotor coordination. Section 2 addresses the problem of extrapolating motor output from noisy data or from sensory input. The Pellionisz-Llinas cerebellar lookahead module addresses this problem for the noise-free case, and we suggest theoretical and experimental tests of the model; we then suggest the investigation of neural analogs of the Kalman-Bucy filter. Section 3 offers a brief exposition of mechanics in a tensor framework to provide the irreducible minimum of mathematical machinery to evaluate the Pellionisz-Llinás tensor theory of brain function and to suggest fruitful new hypotheses. Our critique of this theory in section 4 leads us to conclude that what they offer is based on metaphorical use of terminology from Euclidean tensors, not on rigorous application of the mathematics of tensor analysis. The central claim of their theory--that the input is a covariant intention vector transformed by a metric tensor encoded in the cerebellum to a contravariant execution vector--has not been substantiated and probably cannot be substantiated. However, we do point the way to further use of tensor analysis in the study of neural control of movement. The concluding section then returns to the points raised in section 1 with a highly selective survey of models of cerebellum and tectum.

Amphibians↗

Formation of topographic maps and columnar microstructures in nerve fields.

Topographic connections are found in many parts of the vertebrate nervous systems, known for example as retinotopy. The self-organizing ability of Hebb type modifiable synapses plays an important role in forming, at least in refining, the topographic connections. We present a mathematical analysis of a revised version of the Willshaw-Malsburg model of topographic formation, solving the equations of synaptic self-organization coupled with the field equation of neural excitations. The equilibrium solutions are obtained and their stability is studied. It is proved that two cases exist depending on parameters. In one case, the smooth topographic organization is obtained as a stable equilibrium of the equations. In the other case, this solution becomes unstable, and instead the topographic organization with columnar microstructures appears. This might explain the columnar structures in the cerebrum. The theory is confirmed by computer simulated experiments.

Computers↗

Existence and stability of local excitations in homogeneous neural fields.

Dynamics of excitation patterns is studied in one-dimensional homogeneous lateral-inhibition type neural fields. The existence of a local excitation pattern solution as well as its waveform stability is proved by the use of the Schauder fixed-point theorem and a generalized version of the Perron-Frobenius theorem of positive matrices to the fuction space. The dynamcis of the field is in general multi-stable so that the field can keep short-term memory.

Humans↗

Mutual information of sparsely coded associative memory with self-control and ternary neurons.

The influence of a macroscopic time-dependent threshold on the retrieval dynamics of attractor associative memory models with ternary neurons ¿-1, 0, +1¿ is examined. If the threshold is chosen appropriately as a function of the cross-talk noise and of the activity of the memorized patterns in the model, adapting itself in the course of the time evolution, it guarantees an autonomous functioning of the model. Especially in the limit of sparse coding, it is found that this self-control mechanism considerably improves the quality of the fixed-point retrieval dynamics, in particular the storage capacity, the basins of attraction and the information content. The mutual information is shown to be the relevant parameter to study the retrieval quality of such sparsely coded models. Numerical results confirm these observations.

Association Learning↗

[Antiphospholipid antibodies in African women presenting obstetrical complications].

The presence of antiphospholipid antibodies (APL) has been investigated in 68 African women presenting obstetrical complications versus a control group of 22 pregnant healthy women. Patients inclusion criterias were recurrent foetal loss, pre eclampsia, retroplacental haematoma and chronic foetal suffering. Eight of patients (11.8%) had a positive APL diagnosis, versus 0% in controls, using the combination of diluted thromboplastin test and Staclot LA These results argue for the systematic APL screening in African women with obstetrical complications, and could further improve the management of patients at risk.

Antibodies, Antiphospholipid↗