On Determinism Versus Non-Determinism And Related Problems

We show that, for multi-tape Turing machines, non-deterministic linear time is more deterministic Turing machines (that receive their input on their work tape) require time Q(n2) to powerful than deterministic linear time. We also recognize non-palindromes of length n (it is easy to discuss the prospects for extending this result to see that time O(n log n) is. sufficient for a more general Turing machines. non-deterministic machine). 1. Introductio

Structure of computations in parallel complexity classes

Issued as Annual report, and Final project report, Project no. G-36-67

Predictive Golf Analytics Versus the Daily Fantasy Sports Market

This study examines the different skills necessary for PGA tour players to succeed at specific annual tournaments, in order to create a predictive model for DraftKings PGA contests. The model takes into account data from the PGA Tour ShotLink Intelligence Program. The predictive model is created each week based on past results from the specific tournament in question, with the hope of predicting a group of twenty-five players who should be successful based on their statistical profile. The results of the model are detailed in this paper, which covers the first nine weeks of the 2017 PGA Tour season, with a net profit of $45,070. Despite a positive profit there is not enough information to prove significance, so the model would need to be carried out for many more weeks to be conclusive. Ultimately, the study shows that each PGA Tour course is slightly different, which means certain players should be more successful at certain courses, which is valuable information for predicting future outcomes

The Big Match with a clock and a bit of memory

The Big Match is a multi-stage two-player game. In each stage Player 1 hides one or two pebbles in his hand, and his opponent has to guess that number; Player 1 loses a point if Player 2 is correct, and otherwise he wins a point. As soon as Player 1 hides one pebble, the players cannot change their choices in any future stage. Blackwell and Ferguson (1968) give an ε-optimal strategy for Player 1 that hides, in each stage, one pebble with a probability that depends on the entire past history. Any strategy that depends just on the clock or on a finite memory is worthless. The long-standing natural open problem has been whether every strategy that depends just on the clock and a finite memory is worthless. We prove that there is such a strategy that is ε-optimal. In fact, we show that just two states of memory are sufficient

Two-Player Graph Pebbling

Given a graph G with pebbles on the vertices, we define a pebbling move as removing two pebbles from a vertex u, placing one pebble on a neighbor v, and discarding the other pebble, like a toll. The pebbling number n(G) is the least number of pebbles needed so that every arrangement of n(G) pebbles can place a pebble on any vertex through a sequence of pebbling moves. We introduce a new variation on graph pebbling called two-player pebbling. In this, players called the mover and the defender alternate moves, with the stipulation that the defender cannot reverse the previous move. The mover wins only if they can place a pebble on a specified vertex and the defender wins if the mover cannot. We define n(G), analogously, as the minimum number of pebbles such that given every configuration of the n(G) pebbles and every specified vertex r, the mover has a winning strategy. First, we will investigate upper bounds for n(G) on various classes of graphs and find a certain structure for which the defender has a winning strategy, no matter how many pebbles are in a configuration. Then, we characterize winning configurations for both players on a special class of diameter 2 graphs. Finally, we show winning configurations for the mover on paths using a recursive argument

Sir Walter and Mr. Jones: Walter Hagen, Bobby Jones, and the Rise of American Golf. Chapter 8: The Atlanta Golf Machine and the Lion-Tamer, 1928-1929.

During the period 1914-30 Walter Hagen and Bobby Jones dominated golf. The publicity they generated contributed much to the transformation of American golf from an elite pastime to a popular spectator sport, and together they led the way in establishing the U.S. as an international golf powerhouse. Both were outstanding sports heroes, yet their backgrounds, personalities, and public images were remarkably different--even antithetical. Sir Walter and Mr. Jones are revealing enough as individuals, but taken together they provide comparisons and contrasts which illuminate a pivotal period in the history of golf and American society

The Social Network and the Crowdfund Act: Zuckerberg, Saverin, and Venture Capitalists\u27 Dilution of the Crowd

By virtue of Title III of the JOBS Act, signed into law on April 5, 2012, crowdfunding could become a powerful, even revolutionary, force to finance start-up companies. It democratizes entrepreneurs\u27 access to seed capital and converts the masses of Internet users into potential retail venture capitalists. Many have cautioned, though, that crowdfunding poses serious investment risks of start-up companies failing, committing fraud, and being mismanaged. Accordingly, the JOBS Act includes numerous disclosure obligations designed to mitigate such downside risks. But what has been overlooked, and what this Article analyzes from a venture capitalist perspective, is that even if a crowdfunded start-up company is successful, crowdfunding investors can lose the value of their investment if they lack venture capital legal protections. When successful start-up companies raise additional funds from professional venture capitalists, the value of ground-floor investments can be severely diluted, as colorfully dramatized in The Social Network. In addition, when crowdfunded companies are acquired in private transactions, crowdfunders are at risk of being left out. Therefore, under a qualitative mandates regulatory philosophy that moves beyond securities law\u27s status-quo disclosure requirements, this Article proposes substantive venture capitalist protections for crowdfunding investors. For example, down-round anti-dilution protection, tag-along rights, and preemptive rights should help safeguard the value of early-stage crowdfunding investments in successful start-up companies. Especially because many crowdfunding investors are likely to be inexperienced and unsophisticated in start-up-company investing, crowdfunding laws and regulations should go beyond disclosure requirements that warn investors of danger (to the extent investors even read or understand the disclosures) to help crowdfunders obtain market-based economic protections characteristic of venture capitalist investment contracts

Determinants of Startup Funding: The Interaction between Web Attention and Culture

Technology empowers entrepreneurs to pursue alternative funding through platforms like crowdfunding. This research explores significant startup funding factors using Crunchbase. Controlling for common factors (acquisition/funding-rounds/IPO), the research uniquely focuses on web attention - the visibility on social media - and its impact on funding. It also examines the moderating influence of startup’s home country culture (individualism/collectivism). Findings show stronger positive impact of web attention on startup funding for collectivist countries. While individualistic investors value personal goals, collectivists value collaborative goals - inclinations that align with crowdfunding behavior. Therefore while increasing web attention, crowdfunding efforts can be targeted towards collectivist countries

COMPARATIVE PERFORMANCE ANALYSIS OF PGA TOUR AND ONTARIO UNIVERSITY GOLFERS

The purposes of the study were to 1) build a model to predict scoring average for a total sample of professional (n = 82) and collegiate (n = 41) golfers using stepwise regression, 2) test the model on the samples independently using hierarchical regression, and 3); examine the significance in performance differences in the two subsamples. Both samples played two tournament rounds at the South Course of Angus Glen Golf Club; the professionals during the 2002 PGA tour Canadian Open and the collegians during the 2010 OUA championship. For the total sample, GIR percentage, putts per round, scrambling percentage and driving accuracy percentage predicted 92% of the variance in scoring average; for professionals and collegians the only the former three performance measures accounted for explained variance for scoring average (80% and 81% respectively). Professionals were significantly superior to the collegians in all four performance indices as well as scoring average