Both soybean composition and processing conditions impact the nutritional quality of soybean meal. The objective of this experiment was to compare nutrient compositions of soybeans grown under diverse environmental conditions in a variety of locations. Dry matter, organic matter, and ash concentrations differed in soybeans collected within the countries of Brazil, China, and the United States, ...

In “Bulgarian Solitaire”, a player divides a deck of n cards into piles. Each move consists of taking a card from each pile to form a single new pile. One is concerned only with how many piles there are of each size. Starting from any division into piles, one always reaches some cycle of partitions of n. Brandt proved that for n = 1+2+ · · ·+k, the cycle is just the single partition into piles ...

In crisp approximation theory the operations that are used are only the usual sum and product of reals. We propose the following problem: are sum and product the only operations that can be used in approximation theory? As an answer to this problem we propose max-product Shepard Approximation operators and we prove that these operators have very similar properties to those provided by the crisp...

Sum-Product Networks (SPNs) were recently proposed as a new class of probabilistic graphical models that guarantee tractable inference, even on models with high-treewidth. In this paper, we propose a new extension to SPNs, called Decision Sum-Product-Max Networks (Decision-SPMNs), that makes SPNs suitable for discrete multi-stage decision problems. We present an algorithm that solves Decision-S...

The Max Product (MP) is a local, iterative, message passing style algorithm that has been developed for finding the maximum a posteriori (MAP) assignment of discrete probability distribution specified by a graphical model. The scope of application of MP is vast and in particular it can serve as a heuristic to solve any combinatorial optimization problem. Despite the success of MP algorithm in t...

Finding the maximum a posteriori (MAP) assignment of a discrete-state distribution specified by a graphical model requires solving an integer program. The max-product algorithm, also known as the max-plus or min-sum algorithm, is an iterative method for (approximately) solving such a problem on graphs with cycles. We provide a novel perspective on the algorithm, which is based on the idea of re...

Monomials function has always been considered as a significant and most extensively used function in real living. Resource allocation, structure optimization and technology management can often apply these functions. In optimization problems the objective functions can be considered by monomials. In this paper, we present monomials geometric programming with fuzzy relation inequalities constrai...

⎯It is well known that the solution set of fuzzy relational equations with max-product composition can be determined by the maximum solution and a finite number of minimal solutions. There exists an analytic expression for the maximum solution and it can be yielded easily, but finding the complete set of minimal solutions is not trivial. In this paper we first provide a necessary condition for ...