Department of Agriculture for official use I rr Re-Evaluation of the Arizona Cloud-Seeding Experiment (randomization/timing of apparent effects)

ABSTRACT The apparent effect of cloud seeding on the average 24-hr precipitation in the Santa Catalina Moun tains during the two programs of the 7-year-long Arizona experiment was found to be a 30% loss of rain (P = 0.06). Considering rainy days only, the apparent effect is a 34% loss of rain (P = 0.03). On South-East days the apparent loss was 40% (P = 0.03). The analysis of the diurnal varia tion in the amountsof hourly precipitation brought out two suggestions: («) more active silver iodide enters the clouds through seeding at their bases than at the -6°C level; («i) the population of experimental days in cludes two categories with opposite responses to seeding: augmentations of rain in one case and losses in the other. These suggestions require independent confirmation. This is a sequel to the earlier paper (1) primarily concerned with the broad question whether "local" cloud seeding with silver iodide, intended to augment the rainfall over a limited area, can in fact affect the precipitation at relatively large distances. The specific object of study was the possible effect of cloud seeding over the Santa Catalina Mountains in Arizona (2-4) on the 24-hr precipitation at Walnut Gulch, some 65 miles to the SE. It was found that the effect averaged over all the 212 experimental days of two experimental pro grams, 1957-60 and 1961, 1962, and 1964, is represented by the apparent 40% loss of rain at Walnut Gulch (P = 0.025). Larger apparent losses of rain, some highly significant, were found for experimental days on which Walnut Gulch was downwind from the seeding site (but not on upwind days), and also on "second days" of the randomized pairs (but not on "first days"). The study of the diurnal variation in the hourly precipitation amounts on several categories of days showed two pronounced maxima of rain on not^seeded days, one at about 1800 Mountain Standard Time (MST) and the other, more pronounced, at about midnight. On seeded days, these maxima were hardly detectable. While confirming the possibility of widespread effects of local cloud seeding, the above results stimulated our interest in the apparent effects of the same seeding of the 24-hr pre cipitation that fell in the Santa Catalina Mountains, the in tended target of the seeding operations

Consensus-Halving: Does It Ever Get Easier?

In the $\varepsilon$-Consensus-Halving problem, a fundamental problem in fair division, there are $n$ agents with valuations over the interval $[0,1]$, and the goal is to divide the interval into pieces and assign a label "$+$" or "$-$" to each piece, such that every agent values the total amount of "$+$" and the total amount of "$-$" almost equally. The problem was recently proven by Filos-Ratsikas and Goldberg [2019] to be the first "natural" complete problem for the computational class PPA, answering a decade-old open question. In this paper, we examine the extent to which the problem becomes easy to solve, if one restricts the class of valuation functions. To this end, we provide the following contributions. First, we obtain a strengthening of the PPA-hardness result of [Filos-Ratsikas and Goldberg, 2019], to the case when agents have piecewise uniform valuations with only two blocks. We obtain this result via a new reduction, which is in fact conceptually much simpler than the corresponding one in [Filos-Ratsikas and Goldberg, 2019]. Then, we consider the case of single-block (uniform) valuations and provide a parameterized polynomial time algorithm for solving $\varepsilon$-Consensus-Halving for any $\varepsilon$, as well as a polynomial-time algorithm for $\varepsilon=1/2$; these are the first algorithmic results for the problem. Finally, an important application of our new techniques is the first hardness result for a generalization of Consensus-Halving, the Consensus-$1/k$-Division problem. In particular, we prove that $\varepsilon$-Consensus-$1/3$-Division is PPAD-hard

The emergence of modern statistics in agricultural science : Analysis of variance, experimental design and the reshaping of research at Rothamsted Experimental Station, 1919–1933

During the twentieth century statistical methods have transformed research in the experimental and social sciences. Qualitative evidence has largely been replaced by quantitative results and the tools of statistical inference have helped foster a new ideal of objectivity in scientific knowledge. The paper will investigate this transformation by considering the genesis of analysis of variance and experimental design, statistical methods nowadays taught in every elementary course of statistics for the experimental and social sciences. These methods were developed by the mathematician and geneticist R. A. Fisher during the 1920s, while he was working at Rothamsted Experimental Station, where agricultural research was in turn reshaped by Fisher’s methods. Analysis of variance and experimental design required new practices and instruments in field and laboratory research, and imposed a redistribution of expertise among statisticians, experimental scientists and the farm staff. On the other hand the use of statistical methods in agricultural science called for a systematization of information management and made computing an activity integral to the experimental research done at Rothamsted, permanently integrating the statisticians’ tools and expertise into the station research programme. Fisher’s statistical methods did not remain confined within agricultural research and by the end of the 1950s they had come to stay in psychology, sociology, education, chemistry, medicine, engineering, economics, quality control, just to mention a few of the disciplines which adopted them

Lectures and Conferences on Mathematical Statistics

Table of Contents – LECTURES: On the Theory of Probability, On Probability and Experimentation, On the Testing of Statistical Hypotheses. CONFERENCES: On Randomized and Systematic Arrangements of Field Experiments, On Certain Problems of Plant Breeding, On Statistical Methods in Social and Economic Research (Census by Sampling and Other Problems), On Time Series Analysis and Some Related Statistical Problems in Economics, On Statistical Estimation (Practical Problems and Various Attempts to Formulate Their Mathematical Equivalents), An Outline of the Theory of Confidence Intervals, Index

Lectures and Conferences on Mathematical Statistics and Probability

TABLE OF CONTENTS -- Chapter I: The modern viewpoint on the classical theory of probability and its applications. Tests of statistical hypotheses. Introduction. Part 1: On the theory of probability. Part 2: Probability and experimentation. Part 3: Tests of statistical hypotheses. Chapter II: Some controversial matters relating to agricultural trials. Part 1: Randomized and systematic arrangements of field experiments. Part 2: On certain problems of plant breeding. Chapter III: Some statistical problems in social and economic research. Part 1: Sampling human populations. General theory. Part 2: Theory of Friedman-Wilcox method of sampling. Part 3: On a most powerful method of discovering statistical regularities. Chapter IV: Statistical estimation. Part 1: Practical problems and various attempts to formulate their mathematical equivalents. Part 2: Outline of the theory of confidence intervals. Part 3: Fiducial argument and the theory of confidence intervals. Part 4: Stein’s sequential procedure. Index of Names. Index of Term