Sequential importance sampling for estimating expectations over the space of perfect matchings

This paper makes three contributions to estimating the number of perfect matching in bipartite graphs. First, we prove that the popular sequential importance sampling algorithm works in polynomial time for dense bipartite graphs. More carefully, our algorithm gives a $(1-\epsilon)$-approximation for the number of perfect matchings of a $\lambda$-dense bipartite graph, using $O(n^{\frac{1-2\lambda}{8\lambda}+\epsilon^{-2}})$ samples. With size $n$ on each side and for $\frac{1}{2}>\lambda>0$, a $\lambda$-dense bipartite graph has all degrees greater than $(\lambda+\frac{1}{2})n$. Second, practical applications of the algorithm requires many calls to matching algorithms. A novel preprocessing step is provided which makes significant improvements. Third, three applications are provided. The first is for counting Latin squares, the second is a practical way of computing the greedy algorithm for a card guessing game with feedback, and the third is for stochastic block models. In all three examples, sequential importance sampling allows treating practical problems of reasonably large sizes

Speaking Stata: On numbers and strings

The great divide among data types in Stata is between numeric and string variables. Most of the time, which kind you want to use for particular variables is clear and unproblematic, but surprisingly often,users face difficulties in making the right decision or need to convert variables from one kind to another. The main problems that may arise and their possible solutions are surveyed with reference both to official Stata and to user-written programs. Copyright 2002 by Stata Corporation.binary variables,categorical variables,Data Editor,dates,decode, destring,encode,identifiers,missing values,numeric variables,spreadsheets, string functions,string variables,tostring,value labels

Entropy-Based Strategies for Multi-Bracket Pools

Much work in the March Madness literature has discussed how to estimate the probability that any one team beats any other team. There has been strikingly little work, however, on what to do with these win probabilities. Hence we pose the multi-brackets problem: given these probabilities, what is the best way to submit a set of $n$ brackets to a March Madness bracket challenge? This is an extremely difficult question, so we begin with a simpler situation. In particular, we compare various sets of $n$ randomly sampled brackets, subject to different entropy ranges or levels of chalkiness (rougly, chalkier brackets feature fewer upsets). We learn three lessons. First, the observed NCAA tournament is a "typical" bracket with a certain "right" amount of entropy (roughly, a "right" amount of upsets), not a chalky bracket. Second, to maximize the expected score of a set of $n$ randomly sampled brackets, we should be successively less chalky as the number of submitted brackets increases. Third, to maximize the probability of winning a bracket challenge against a field of opposing brackets, we should tailor the chalkiness of our brackets to the chalkiness of our opponents' brackets

Assessing The Probability Of Fluid Migration Caused By Hydraulic Fracturing; And Investigating Flow And Transport In Porous Media Using Mri

Hydraulic fracturing is used to extract oil and natural gas from low permeability formations. The potential of fluids migrating from depth through adjacent wellbores and through the production wellbore was investigated using statistical modeling and predic-tive classifiers. The probability of a hydraulic fracturing well becoming hydraulically connected to an adjacent well in the Marcellus shale of New York was determined to be between 0.00% and 3.45% at the time of the study. This means that the chance of an in-duced fracture from hydraulic fracturing intersecting an existing well is highly dependent on the area of increased permeability caused by fracturing. The chance of intersecting an existing well does not mean that fluid will flow upwards; for upward migration to occur, a pathway must exist and a pressure gradient is required to drive flow, with the exception of gas flow caused by buoyancy. Predictive classifiers were employed on a dataset of wells in Alberta Canada to identify well characteristics most associated to fluid migration along the production well. The models, specifically a random forest, were able to identify pathways better than random guessing with 78% of wells in the data set identified cor-rectly. Magnetic resonance imaging (MRI) was used to visualize and quantify contami-nant transport in a soil column using a full body scanner. T1 quantification was used to determine the concentration of a contaminant surrogate in the form of Magnevist, an MRI contrast agent. Imaging showed a strong impact from density driven convection when the density difference between the two fluids was small (0.3%). MRI also identified a buildup of contrast agent concentration at the interface between a low permeability ground silica and higher permeability AFS 50-70 testing sand when density driven con-vection was eliminated

Deduction with XOR Constraints in Security API Modelling

We introduce XOR constraints, and show how they enable a theorem prover to reason effectively about security critical subsystems which employ bitwise XOR. Our primary case study is the API of the IBM 4758 hardware security module. We also show how our technique can be applied to standard security protocols

The influence of the basic electronic calculator on the teaching and learning of mathematics in the 11-16 age range

The electronic calculator is now invariably the device used by people in employment and everyday life to deal with complicated and tedious calculations. The aim of this dissertation is to examine the effect it may have on the secondary school mathematics curriculum and, especially, to examine its potential as a powerful teaching aid which can be used to help pupils to acquire understanding of mathematical concepts. Chapter 1 investigates the contribution the basic calculator makes as a calculating aid which should cause the teacher to reassess the place of the standard pencil and paper algorithms in the curriculum. Some of the fears associated with this innovation are also discussed. The final section emphasises the importance of knowing the idiosyncrasies of different calculators. Chapter 2 suggests, in some detail, ways in which the teacher may use the calculator to enhance the understanding of certain topics such as fractions and place value. Applications of the calculator to everyday life problems, such as compound interest, are also included as well as the possibility of more interesting and enjoyable topics being introduced into the syllabus. New methods, such as iterative procedures, are discussed and the potential of the calculator as an aid to investigations is ascerted. Chapter 3 looks at the beneficial influence of the calculator on the mathematics curriculum generally and the possible effect on the mathematical content in particular with further suggestions following on from Chapter 2. Some contentious issues are considered and it is emphasised that more must be done to encourage the effective use of the calculator and not allow it to be overshadowed by its more 'glamorous' counterpart - the microcomputer