A rotational approach to triple point obstructions

Subfactors where the initial branching point of the principal graph is 3-valent are subject to strong constraints called triple point obstructions. Since more complicated initial branches increase the index of the subfactor, triple point obstructions play a key role in the classification of small index subfactors. There are two strong triple point obstructions called the triple-single obstruction and the quadratic tangles obstruction. Although these obstructions are very closely related, neither is strictly stronger. In this paper we give a more general triple-point obstruction which subsumes both. The techniques are a mix of planar algebraic and connection-theoretic techniques with the key role played by the rotation operator.Comment: 5 page

Autonomous Boat Control Software Design Using Model-Based Systems Engineering

While there is considerable buzz about self-driving cars, self-driving boats are actually more fully developed. The Boat Hardware Control Platform Team was tasked with developing a fleet of small autonomous boats that travel to a destination while avoiding obstacles and staying in formation. The author’s specific task was to develop software used by the boats to detect obstacles and plan a route to a destination. This was done using a method inspired by self-driving cars, which shows promise, but is still being tested at the time of writing. The entire project incorporated model-based systems engineering, which proved to be useful

Bargaining Practices: Negotiating the Kampala Compromise for the International Criminal Court

At the International Criminal Court\u27s (ICC) Review Conference in 2010, the ICC\u27s Assembly of States Parties (ASP) agreed upon a definition of the crime of aggression, jurisdictional conditions, and a mechanism for its entry into force (the Kampala Compromise ). These amendments give the ICC jurisdiction to prosecute political and military leaders of states for planning, preparing, initiating, or executing illegal wars, beginning as early as January 2017. This article explains the bargaining practices of the diplomats that gave rise to this historic development in international law. This article argues that the international-practices framework, as currently conceived, does not adequately capture the role sincerity played in the negotiations. Sincerity was an international practice, but not a performance. It follows that the international practices framework should be adjusted to accommodate the decisive role of sincerity, a special nonperformative international practice, in the face-to-face interactions of international politics and diplomacy. The remainder of the article lays out the international-practices framework and explains the place of performances within it. The article then introduces the concept of sincerity as a social practice. The second half of the article discusses some ways that sincerity played a role in the negotiations. The article concludes that sincerity is a special kind of international practice: It cannot be a performance, but it can be an international practice, and an effective one at that

Problems with the "Problems" with psychophysical causation

In this essay, I defend a mind-body dualism, according to which human minds are immaterial substances that exercise non-redundant causal powers over bodies, against the notorious problem of psychophysical causation. I explicate and reply to three formulations of the problem: (i) the claim that, on dualism, psychophysical causation is inconsistent with physical causal closure, (ii) the claim that psychophysical causation on the dualist view is intolerably mysterious, and (iii) Jaegwon Kim’s claim that dualism fails to account for causal pairings. Ultimately, I conclude that these objections fail and that dualist interactionism is no more problematic or mysterious than physical causation

Schwarzschild Quantum Fluctuations from Regge-Wheeler Scattering

We apply a multichannel variable phase method to scattering from Regge-Wheeler potentials. Using a reduced version of the WKB subtraction developed by Candelas and Howard, this approach allows for efficient numerical calculations of scattering data for imaginary wave number, making it possible to compute quantum expectation values in a Schwarzschild curved spacetime background through Wick rotation to the imaginary frequency axis. These scattering theory techniques are also potentially applicable to a variety of other problems involving wave propagation in curved spacetime.Comment: 12 pages, 4 .eps figures. v2: fixed typos, added example calculatio

Resolving a Conjecture on Degree of Regularity of Linear Homogeneous Equations

A linear equation is $r$-regular, if, for every $r$-coloring of the positive integers, there exist positive integers of the same color which satisfy the equation. In 2005, Fox and Radoicic conjectured that the equation $x_1 + 2x_2 + \cdots + 2^{n-2}x_{n-1} - 2^{n-1}x_n = 0$, for any $n \geq 2$, has a degree of regularity of $n-1$, which would verify a conjecture of Rado from 1933. Rado's conjecture has since been verified with a different family of equations. In this paper, we show that Fox and Radoicic's family of equations indeed have a degree of regularity of $n-1$. We also provide a few extensions of this result.Comment: 8 page

Using Empirical Mode Decomposition to Study Periodicity and Trends in Extreme Precipitation

Classically, we look at annual maximum precipitation series from the perspective of extreme value statistics, which provides a useful statistical distribution, but does not allow much flexibility in the context of climate change. Such distributions are usually assumed to be static, or else require some assumed information about possible trends within the data. For this study, we treat the maximum rainfall series as sums of underlying signals, upon which we perform a decomposition technique, Empirical Mode Decomposition. This not only allows the study of non-linear trends in the data, but could give us some idea of the periodic forces that have an effect on our series. To this end, data was taken from stations in the New England area, from different climatological regions, with the hopes of seeing temporal and spacial effects of climate change. Although results vary among the chosen stations the results show some weak signals and in many cases a trend-like residual function is determined