Empirical evidence for ultrametric structure in multi-layer perceptron error surfaces

Combinatorial optimization problems share an interesting property with spin glass systems in that their state spaces can exhibit ultrametric structure. We use sampling methods to analyse the error surfaces of feedforward multi-layer perceptron neural networks learning encoder problems. The third order statistics of these points of attraction are examined and found to be arranged in a highly ultrametric way. This is a unique result for a finite, continuous parameter space. The implications of this result are discussed.

Hand-assisted laparoscopic adrenalectomy: An alternative minimal invasive surgical technique for the adrenal gland

Background: Presently the surgical approach to the adrenal gland is in a state of flux. While the traditional approach to the adrenal gland has been the open transabdominal technique, more recently laparoscopic approaches, particularly via the transabdominal route, have increasingly been utilized. However, laparoscopic intervention for the adrenal gland can be problematic in certain circumstances, particularly for large adrenal masses and in instances of adrenal malignancies. Methods: In this report we describe the use of hand-assisted laparoscopic adrenalectomy as an alternative minimal invasive surgical approach to the adrenal gland. Hand-assisted laparoscopic adrenalectomy using the HandPort system (Smith & Nephew, Sydney, Australia) was undertaken in three patients requiring adrenalectomy for mass lesions including one patient with Conn's syndrome. Results: In all three cases, surgery proceeded promptly and uneventfully. In the present paper, the details of the technique of hand-assisted adrenalectomy are described. This is the first report in the world literature of this new technique for the adrenal gland. Conclusions: Hand-assisted laparoscopic adrenalectomy is an easily performed technique, which can be completed within a short operative time span and which has the advantage of providing intraoperative tactile localization for the adrenal gland. It may be particularly applicable for large adrenal tumours, yet only involves the performance of a small abdominal incision. Postoperative recovery is comparable with that reported for the laparoscopic-only technique. Hand-assisted adrenalectomy is a new technique which has great potential and which warrants further evaluation.

Exploring complex fitness surfaces: Multiple ornamentation and polymorphism in male guppies

The sexual ornamentation used by male guppies to attract females comprises many components, each of which varies considerably among males. Although natural and sexual selection have been shown to contribute to divergence among populations in male sexual ornaments, the role of sexual selection in maintaining polymorphism within populations is less clear. We used both parametric quadratic regression and nonparametric projection pursuit regression techniques to reveal the major axes of non-linear sexual selection on male ornaments. We visualized the fitness surfaces defined by these axes using thin-plate splines to allow a direct comparison of the two methodologies. Identification of the major axes of selection and their visualization was critical in determining the form and strength of nonlinear selection. Both types of analysis revealed fitness surfaces comprising three peaks, suggesting that there is more than one way to make an attractive guppy. Disruptive selection may be an important process underlying the presence of multiple sexual ornaments and may contribute to the maintenance of the high levels of polymorphism in male sexual ornaments found in guppy populations.

The spectrum of minimal defining sets of some Steiner systems

For a design D, define spec(D) = {\M\ \ M is a minimal defining set of D} to be the spectrum of minimal defining sets of D. In this note we give bounds on the size of an element in spec(D) when D is a Steiner system. We also show that the spectrum of minimal defining sets of the Steiner triple system given by the points and lines of PG(3,2) equals {16,17,18,19,20,21,22}, and point out some open questions concerning the Steiner triple systems associated with PG(n, 2) in general. (C) 2002 Elsevier Science B.V. All rights reserved.

Link invariants associated with gauge equivalent solutions of the Yang-Baxter equation: The one-parameter family of minimal typical representations of Uq[gl(2|1)]

In this paper we investigate the construction of state models for link invariants using representations of the braid group obtained from various gauge choices for a solution of the trigonometric Yang-Baxter equation. Our results show that it is possible to obtain invariants of regular isotopy (as defined by Kauffman) which may not be ambient isotopic. We illustrate our results with explicit computations using solutions of the trigonometric Yang-Baxter equation associated with the one-parameter family of minimal typical representations of the quantum superalgebra U-q,[gl(2/1)]. We have implemented MATHEMATICA code to evaluate the invariants for all prime knots up to 10 crossings.