On the Phase Space of Block-Hiding Strategies in Bitcoin-like networks

We calculate the probability of success of block-hiding mining strategies in Bitcoin-like networks. These strategies involve building a secret branch of the block-tree and publishing it opportunistically, aiming to replace the top of the main branch and rip the reward associated with the secretly mined blocks. We identify two types of block-hiding strategies and chart the parameter space where those are more beneficial than the standard mining strategy described in Nakamoto's paper. Our analysis suggests a generalization of the notion of the relative hashing power as a measure for a miner's influence on the network. Block-hiding strategies are beneficial only when this measure of influence exceeds a certain threshold.Comment: 28 pages, 7 figure

Comparing Profitability for Game Developers: Xbox vs PlayStation vs PC

Ever since the beginning of the video game industry, consoles have come and gone such as the Atari 2600 and the Nintendo Gameboy. However, there are two main series of consoles that have continued to modern day: the Xbox’s and the PlayStation’s. These two series of consoles have been rivals for more than a decade, consistently releasing systems to compete with each other. Furthermore, similar to consoles coming and going, many companies have gone bankrupt due to significant gaming failures and losses. Because of this, there are only few major companies still producing games, along with some independent game developers struggling to succeed. However, more successful, independent companies and developers means a greater variety of games for consumers to play. Therefore, I determined which series of consoles appears to be the more profitable series for small companies and individual developers. Along with these series of consoles, the gaming industry for the PC has recently expanded rapidly and appears to be more friendly to low-budget games. Therefore, I analyzed PC game sales and concluded where should new video-game developers invest their time and money for producing games: for Xbox’s, PlayStation’s, or the PC

The Mathematics of Chinese Checkers

Our goal for this project was to expand and improve upon the findings of George I. Bell and Nicholas Fonseca, who have both written papers on optimization in Chinese Checkers. While their work focuses mainly on cooperative games between one, two, and three players, we have considered games for six players. While doing this, we have redefined the playing board in a more intuitive manner, while developing and proving its associated distance formula. As well, we have found the shortest game for six players, and are working to generalize a formula for the number of moves required to finish a six player game as fast as possible. This could further incite research to generalize a lower bound for any number of players

Superstring Theory on AdS_3 x G/H and Boundary N=3 Superconformal Symmetry

Superstrings propagating on backgrounds of the form AdS_3 x G/H are studied using the coset CFT approach. We focus on seven dimensional cosets which have a semiclassical limit, and which give rise to N=3 superconformal symmetry in the dual CFT. This is realized for the two cases AdS_3 x SU(3)/U(1) and AdS_3 x SO(5)/SO(3), for which we present an explicit construction. We also provide sufficient conditions on a CFT background to enable a similar construction, and comment on the geometrical interpretation of our results.Comment: 22 pages, harvmac; added reference

Superstrings on AdS_3 and Symmetric Products

Some properties of N=2 superstrings on AdS_3 x N are studied. Their spectrum has the same pattern as 2-d CFTs in the moduli space of symmetric products M^p/S_p, where p is associated with the number of long fundamental strings required to construct the AdS_3 background, and M is the spacetime CFT corresponding to short string excitations of a single long string. Worldsheet operators associated with w long strings correspond to twisted sectors of M^p/S_p.Comment: 43 pages, harvma

Towards observable signatures of other bubble universes

We evaluate the possibility of observable effects arising from collisions between vacuum bubbles in a universe undergoing false-vacuum eternal inflation. Contrary to conventional wisdom, we find that under certain assumptions most positions inside a bubble should have access to a large number of collision events. We calculate the expected number and angular size distribution of such collisions on an observer's "sky," finding that for typical observers the distribution is anisotropic and includes many bubbles, each of which will affect the majority of the observer's sky. After a qualitative discussion of the physics involved in collisions between arbitrary bubbles, we evaluate the implications of our results, and outline possible detectable effects. In an optimistic sense, then, the present paper constitutes a first step in an assessment of the possible effects of other bubble universes on the cosmic microwave background and other observables.Comment: 17 PRD-style pages including 13 embedded figures. Minor corrections to figures 4 and 7 and added discussion in Sec. III.E.2 and

Electoral Systems and Intra-Party Candidate Selection Processes: Influences on Legislators\u27 Behavior

How legislators behave and how cohesively parties act are influenced, to a great extent, by the institutional environment within which they operate. While most research has regarded each institution separately, this dissertation project seeks to theorize and to empirically examine the complex institutional context that affects legislators\u27 behavior and representation styles. I specifically shed light on how electoral systems and intra-party candidate selection processes, separately and in combination, influence how much legislators emphasize their unique individualistic behaviors at the expense of their parties\u27 collective unified reputations. I argue that electoral systems and candidate selection procedures conditionally structure the incentives and institutional environment within which a legislator operates. Chapter 2 presents a theoretical/conceptual distinction between electoral systems and intra-party candidate selection processes and critiques the current literature that usually amalgamates them into a single factor. I further justify this distinction by empirically showing the lack of a strong association between the two institutions. Chapter 3 presents my theory concerning the distinct and combined conditional effect of electoral systems and selection processes on legislators\u27 behavior. I support my assertions using party-level models that use Rice cohesion scores and Weighted Rice cohesion scores as outcome variables. Chapter 4 tests my theory using individual level analysis which uses the ideological distance of a legislator from the median position of his or her party as a measure of behavior. To this end, I have collected a number of unique data sets that include information about parties\u27 candidate selection processes, parties\u27 cohesion measures, and individual legislators\u27 ideological distances. Using these original data sets, I can support my theory concerning the conditional combined effect of electoral systems and intra-party candidate selection processes on legislators\u27 behavior. The incentives and constraints legislators face are more convoluted than scholars previously assumed