We give a new proof of the theorem of Joszéf Dénes: If L1 and L2 are distinct latin squares of order n ≥ 2, n / ∈ {4, 6}, that satisfy the quadrangle criterion, then L1 and L2 differ in at least 2n entries.

In this note we explain the use of the Akiake Information Criterion and its related model comparison indices (usually derived for maximum likelihood estimator inverse problem formulations) for use with least squares (ordinary, weighted, iterative weighted or ”generalized”, etc.) based inverse problem formulations. The ideas are illustrated with several examples of interest in biology.

We investigated the benefit of incorporating a negativity penalty into a least-squares criterion used to reconstruct 3-D radiotracer distributions in cardiac SPECT studies. B-spline spatial basis functions were used to provide a continuous model for the 3-D tracer distribution. Spline coefficients that tended to have negative values were identified and were constrained to stay near zero with us...

The Total least squares error criterion is considered for estimation problems. Exact necessary conditions for the total error criterion have been derived. Several solution methodologies are presented to solve the modified normal equations obtained from the necessary conditions. A monte-carlo simulation depicting the effect of parameter variations on the coefficients of the resulting characteris...

AbstructThis paper presents a color image segmentation method which divides color space into clusters. Competitive learning is used as a tool for clustering color space based on the least sum of squares criterion. We show that competitive learning converges to approximate the optimum solution based on this criterion theoretically and experimentally. We applied this method to various color scene...

A new model adaptive method is presented for restoration of blurred and noise corrupted images by exploiting information available from observed data to choose the apprcpriate optimization criterion. The derived maximum likelihood solution is based on the 1 , minimization criterion that naturally arises from the adoption of the generalized p-Gaussian family of probability distributions as an ad...

In this paper adaptive least-squares type algorithms are introduced for blind source separation. They are based on minimizing a criterion used in context with nonlinear PCA (Principal Component Analysis) networks. The new algorithms converge clearly faster and provide more accurate results than typical current adaptive blind separation algorithms based on instantaneous gradients. They are also ...

This paper is on tilings of polygons by rectangles. A celebrated physical interpretation of such tilings due to R.L. Brooks, C.A.B. Smith, A.H. Stone and W.T. Tutte uses directcurrent circuits. The new approach of the paper is an application of alternating-current circuits. The following results are obtained: • a necessary condition for a rectangle to be tilable by rectangles of given shapes; •...

The purpose of this paper is to reveal the Charles-Edouard Jeannert’s urban morphology theory squares in unpublished manuscript “La construction des villes” and clarify its ideological background. We found that Jeanneret uses 19 partis, which means type element city, criteria evaluate partis squares. Among them a criterion “visual closure” dominant, treats “volume” as visible space if “surface”...