For P a poset or lattice, let Id(P ) denote the poset, respectively, lattice, of upward directed downsets in P, including the empty set, and let id(P ) = Id(P )−{∅}. This note obtains various results to the effect that Id(P ) is always, and id(P ) often, “essentially larger” than P. In the first vein, we find that a poset P admits no <-respecting map (and so in particular, no one-to-one isotone...

This paper shows that any compactly generated lattice is a subdirect product of subdirectly irreducible lattices which are complete and upper continuous. An example of a compactly generated lattice which cannot be subdirectly decomposed into subdirectly irreducible compactly generated lattices is given. In the case of an ideal lattice of a lattice L, the decomposition into subdirectly irreducib...

In this paper, we describe new methods to compute the radical (resp. real radical) of an ideal, assuming it complex (resp. real) variety is finte. The aim is to combine approaches for solving a system of polynomial equations with dual methods which involve moment matrices and semi-definite programming. While the border basis algorithms of [17] are efficient and numerically stable for computing ...

Feedback neural architectures have addressed a myriad of optimization problems—almost exclusively in slow software simulation. Speed is promised only when implemented in high-speed recurrent hardware. Unfortunately, hardware’s discrepancies from ideal conspire to produce poor solutions. This paper describes a recurrent hardware-in-the-loop learning procedure that maps idealized solutions of opt...

Dear Sir: Gary-Bobo and Solomon (1968, 1971) have employed Gibbs-Donnan equilibrium studies in the assessment o f the anomalous osmotic behavior o f the red cell. In these studies, the interpretation was based on thermodynamic equations for ideal solutions. During the course of recent investigations, we have found that it is necessary to consider the nonideal aspects o f concentrated hemoglobin...

Many real life decision making problems can be modeled as stochastic multi-attribute decision making (MADM) problems. A novel method for stochastic MADM problems is developed based on the ideal and nadir solutions as in the classical TOPSIS method. In a stochastic MADM problem, the evaluations of the alternatives with respect to the different attributes are represented by discrete stochastic va...

Exploiting the analogy between exemplar models and population coding schemes, we characterize, by means of information theoretic tools, the efficiency of a large but finite population of cells coding for a discrete set of categories (e.g. vowels). The optimal code is shown to typically allocate more cells to class boundaries than to regions further apart. We then discuss the predicted perceptua...

We consider the problem of designing reliable and confidential lattice codes, known as wiretap lattice codes, for fast fading channels. We identify as code design criterion for finite lattice constellations a finite sum of inverse of algebraic norms, in fact the analogous for finite sums of the known criterion for infinite constellations, which motivates us to study totally real number fields w...