Nonconventional Large Deviations Theorems

We obtain large deviations theorems for nonconventional sums with underlying process being a Markov process satisfying the Doeblin condition or a dynamical system such as subshift of finite type or hyperbolic or expanding transformation

Emergency Farm Adjustments in the Wheat Area of South Dakota

SummaryThis circular tells briefly the story of some farmers in the Spring Wheat section of South Dakota. It shows the strenuous effort being made by these men to reduce expenses or to shift their production so that their income will equal their expenses.It illustrates certain adjustments that are being followed on some of the farms and suggests some changes that might be profitable on these and other farms.The most serious difficulty arises from the effort to pay the fixed charges-interest, taxes, and payments on indebtedness. On nearly all farms some adjustments are being made to obtain a farm income large enough to meet the immediately pressing expenses. These adjustments have taken the form of:1. Reducing cash expenses as much as is possible, sometimes to the extent that production is restricted or is carried on at greater risk. The effort to reduce expenses has in most cases led to a lower standard of living for the farm family.2. Reducing capital assets to meet payment demanded on indebtedness even though this means the abandonment of a practical long time system of farming.3. Family labor and the equipment is used to the limit of its capacity in an effort to increase the livestock enterprises and the acreage of crops so that the cash income can be increased.4. In some cases the acreage of cash grain has been increased at the expense of feed grains, legumes, or a cropping system that would be advantageous over the long period of time.5. In other cases, herd of stock cattle have been shifted to dairy production. In others, the practice of selling cattle as feeders has been changed to sale as finished or “warmed up cattle.”6. Farmers with low priced feed surplus have sometime found it necessary to shift from a conservative production program to the more speculative one of feeding livestock.7. In extreme cases, the operators have found it necessary to relinquish title to their farms and to continue operation as tenants to preserve their working capital and continue farming.8. Only farmers relatively free of debt can reduce operations and wait for an improvement of prices

The livestock system in Iowa County

The livestock and livestock products accounted for about 80 percent of the total farm income on 28 Iowa county farms for which records are available during 1925 to 1927. The importance of efficient feeding is emphasized by the fact that the value of feeds consumed comprised about three-fourths of the livestock expenses. Bach of the livestock enterprises tended to fill definite functions in the farm business. The nature of the cattle and hog enterprises tended to vary from farm to farm depending on the type of land, acreages in feed crops and the labor supply. The size of the hog enterprise varied widely but tended to be adjusted to the number of acres in corn and the amount of labor available. On the smaller farms more fall pigs were raised than on those large farms where the crops needed all available labor in the late summer and fall. Spring pigs were produced with an average of about 50 pounds less of concentrates but with a month more pasturage than fall pigs

Information system support in construction industry with semantic web technologies and/or autonomous reasoning agents

Information technology support is hard to find for the early design phases of the architectural design process. Many of the existing issues in such design decision support tools appear to be caused by a mismatch between the ways in which designers think and the ways in which information systems aim to give support. We therefore started an investigation of existing theories of design thinking, compared to the way in which design decision support systems provide information to the designer. We identify two main strategies towards information system support in the early design phase: (1) applications for making design try-outs, and (2) applications as autonomous reasoning agents. We outline preview implementations for both approaches and indicate to what extent these strategies can be used to improve information system support for the architectural designer

Infinitely Many Stochastically Stable Attractors

Let f be a diffeomorphism of a compact finite dimensional boundaryless manifold M exhibiting infinitely many coexisting attractors. Assume that each attractor supports a stochastically stable probability measure and that the union of the basins of attraction of each attractor covers Lebesgue almost all points of M. We prove that the time averages of almost all orbits under random perturbations are given by a finite number of probability measures. Moreover these probability measures are close to the probability measures supported by the attractors when the perturbations are close to the original map f.Comment: 14 pages, 2 figure

Private Multiplicative Weights Beyond Linear Queries

A wide variety of fundamental data analyses in machine learning, such as linear and logistic regression, require minimizing a convex function defined by the data. Since the data may contain sensitive information about individuals, and these analyses can leak that sensitive information, it is important to be able to solve convex minimization in a privacy-preserving way. A series of recent results show how to accurately solve a single convex minimization problem in a differentially private manner. However, the same data is often analyzed repeatedly, and little is known about solving multiple convex minimization problems with differential privacy. For simpler data analyses, such as linear queries, there are remarkable differentially private algorithms such as the private multiplicative weights mechanism (Hardt and Rothblum, FOCS 2010) that accurately answer exponentially many distinct queries. In this work, we extend these results to the case of convex minimization and show how to give accurate and differentially private solutions to *exponentially many* convex minimization problems on a sensitive dataset

Stochastic stability at the boundary of expanding maps

We consider endomorphisms of a compact manifold which are expanding except for a finite number of points and prove the existence and uniqueness of a physical measure and its stochastical stability. We also characterize the zero-noise limit measures for a model of the intermittent map and obtain stochastic stability for some values of the parameter. The physical measures are obtained as zero-noise limits which are shown to satisfy Pesin?s Entropy Formula

Metastability in Interacting Nonlinear Stochastic Differential Equations II: Large-N Behaviour

We consider the dynamics of a periodic chain of N coupled overdamped particles under the influence of noise, in the limit of large N. Each particle is subjected to a bistable local potential, to a linear coupling with its nearest neighbours, and to an independent source of white noise. For strong coupling (of the order N^2), the system synchronises, in the sense that all oscillators assume almost the same position in their respective local potential most of the time. In a previous paper, we showed that the transition from strong to weak coupling involves a sequence of symmetry-breaking bifurcations of the system's stationary configurations, and analysed in particular the behaviour for coupling intensities slightly below the synchronisation threshold, for arbitrary N. Here we describe the behaviour for any positive coupling intensity \gamma of order N^2, provided the particle number N is sufficiently large (as a function of \gamma/N^2). In particular, we determine the transition time between synchronised states, as well as the shape of the "critical droplet", to leading order in 1/N. Our techniques involve the control of the exact number of periodic orbits of a near-integrable twist map, allowing us to give a detailed description of the system's potential landscape, in which the metastable behaviour is encoded

The Continuum Directed Random Polymer

Motivated by discrete directed polymers in one space and one time dimension, we construct a continuum directed random polymer that is modeled by a continuous path interacting with a space-time white noise. The strength of the interaction is determined by an inverse temperature parameter beta, and for a given beta and realization of the noise the path evolves in a Markovian way. The transition probabilities are determined by solutions to the one-dimensional stochastic heat equation. We show that for all beta > 0 and for almost all realizations of the white noise the path measure has the same Holder continuity and quadratic variation properties as Brownian motion, but that it is actually singular with respect to the standard Wiener measure on C([0,1]).Comment: 21 page

Convergence of invariant densities in the small-noise limit

This paper presents a systematic numerical study of the effects of noise on the invariant probability densities of dynamical systems with varying degrees of hyperbolicity. It is found that the rate of convergence of invariant densities in the small-noise limit is frequently governed by power laws. In addition, a simple heuristic is proposed and found to correctly predict the power law exponent in exponentially mixing systems. In systems which are not exponentially mixing, the heuristic provides only an upper bound on the power law exponent. As this numerical study requires the computation of invariant densities across more than 2 decades of noise amplitudes, it also provides an opportunity to discuss and compare standard numerical methods for computing invariant probability densities.Comment: 27 pages, 19 figures, revised with minor correction