THE DUAL OF A COST MINIMIZING LINEAR TRANSSHIPMENT MODEL: AN ECONOMIC INTERPRETATION OF AN ASSEMBLY-PLANT PROCESSING-DISTRIBUTION NETWORK FOR A FIRM

Agribusiness,

Hierarchical control over effortful behavior by rodent medial frontal cortex : a computational model

The anterior cingulate cortex (ACC) has been the focus of intense research interest in recent years. Although separate theories relate ACC function variously to conflict monitoring, reward processing, action selection, decision making, and more, damage to the ACC mostly spares performance on tasks that exercise these functions, indicating that they are not in fact unique to the ACC. Further, most theories do not address the most salient consequence of ACC damage: impoverished action generation in the presence of normal motor ability. In this study we develop a computational model of the rodent medial prefrontal cortex that accounts for the behavioral sequelae of ACC damage, unifies many of the cognitive functions attributed to it, and provides a solution to an outstanding question in cognitive control research-how the control system determines and motivates what tasks to perform. The theory derives from recent developments in the formal study of hierarchical control and learning that highlight computational efficiencies afforded when collections of actions are represented based on their conjoint goals. According to this position, the ACC utilizes reward information to select tasks that are then accomplished through top-down control over action selection by the striatum. Computational simulations capture animal lesion data that implicate the medial prefrontal cortex in regulating physical and cognitive effort. Overall, this theory provides a unifying theoretical framework for understanding the ACC in terms of the pivotal role it plays in the hierarchical organization of effortful behavior

Finitely dependent coloring

We prove that proper coloring distinguishes between block-factors and finitely dependent stationary processes. A stochastic process is finitely dependent if variables at sufficiently well-separated locations are independent; it is a block-factor if it can be expressed as an equivariant finite-range function of independent variables. The problem of finding non-block-factor finitely dependent processes dates back to 1965. The first published example appeared in 1993, and we provide arguably the first natural examples. More precisely, Schramm proved in 2008 that no stationary 1-dependent 3-coloring of the integers exists, and conjectured that no stationary k-dependent q-coloring exists for any k and q. We disprove this by constructing a 1-dependent 4-coloring and a 2-dependent 3-coloring, thus resolving the question for all k and q. Our construction is canonical and natural, yet very different from all previous schemes. In its pure form it yields precisely the two finitely dependent colorings mentioned above, and no others. The processes provide unexpected connections between extremal cases of the Lovasz local lemma and descent and peak sets of random permutations. Neither coloring can be expressed as a block-factor, nor as a function of a finite-state Markov chain; indeed, no stationary finitely dependent coloring can be so expressed. We deduce extensions involving d dimensions and shifts of finite type; in fact, any non-degenerate shift of finite type also distinguishes between block-factors and finitely dependent processes

Forms of early walking

Children in the first weeks of independent locomotion display a wide variety of walking forms. The walking forms differ in mechanical strategy and concern with balance. Three extreme walking forms are presented: the Twister, who uses trunk twist, the Faller, who uses gravity, and the Stepper, who remains balanced as much as possible. Each walking form is presented as a ''d-space'', a mathematical format combining continuous and discrete aspects, developed to express the sequence and pattern of a movement without the inappropriate precision of a physical trajectory. The three d-spaces represent analyses of three extreme modes of early walking. They are used to generate the variety of early walking forms and to predict mixtures of mechanical strategies as children mature and converge to more similar walking forms over the first few months of independent locomotion. (C) 1995 Academic Press Limite

Integrals, Partitions, and Cellular Automata

We prove that $$\int_0^1\frac{-\log f(x)}xdx=\frac{\pi^2}{3ab}$$ where $f(x)$ is the decreasing function that satisfies $f^a-f^b=x^a-x^b$, for $0<a<b$. When $a$ is an integer and $b=a+1$ we deduce several combinatorial results. These include an asymptotic formula for the number of integer partitions not having $a$ consecutive parts, and a formula for the metastability thresholds of a class of threshold growth cellular automaton models related to bootstrap percolation.Comment: Revised version. 28 pages, 2 figure

PLANT LOCATION MODELS FOR A HONEY PACKER: SENSITIVITY OF FINDINGS TO SOME ALTERNATIVE SPECIFICATIONS WITH REFERENCE TO THE SOUTH

Agribusiness,

Percolation in invariant Poisson graphs with i.i.d. degrees

Let each point of a homogeneous Poisson process in R^d independently be equipped with a random number of stubs (half-edges) according to a given probability distribution mu on the positive integers. We consider translation-invariant schemes for perfectly matching the stubs to obtain a simple graph with degree distribution mu. Leaving aside degenerate cases, we prove that for any mu there exist schemes that give only finite components as well as schemes that give infinite components. For a particular matching scheme that is a natural extension of Gale-Shapley stable marriage, we give sufficient conditions on mu for the absence and presence of infinite components