Approximating Nash Equilibria in Tree Polymatrix Games

We develop a quasi-polynomial time Las Vegas algorithm for approximating Nash equilibria in polymatrix games over trees, under a mild renormalizing assumption. Our result, in particular, leads to an expected polynomial-time algorithm for computing approximate Nash equilibria of tree polymatrix games in which the number of actions per player is a fixed constant. Further, for trees with constant degree, the running time of the algorithm matches the best known upper bound for approximating Nash equilibria in bimatrix games (Lipton, Markakis, and Mehta 2003). Notably, this work closely complements the hardness result of Rubinstein (2015), which establishes the inapproximability of Nash equilibria in polymatrix games over constant-degree bipartite graphs with two actions per player

A categorical foundation for Bayesian probability

Given two measurable spaces $H$ and $D$ with countably generated $\sigma$-algebras, a perfect prior probability measure $P_H$ on $H$ and a sampling distribution $S: H \rightarrow D$, there is a corresponding inference map $I: D \rightarrow H$ which is unique up to a set of measure zero. Thus, given a data measurement $\mu: 1 \rightarrow D$, a posterior probability $\widehat{P_H}= I \circ \mu$ can be computed. This procedure is iterative: with each updated probability $P_H$, we obtain a new joint distribution which in turn yields a new inference map $I$ and the process repeats with each additional measurement. The main result uses an existence theorem for regular conditional probabilities by Faden, which holds in more generality than the setting of Polish spaces. This less stringent setting then allows for non-trivial decision rules (Eilenberg--Moore algebras) on finite (as well as non finite) spaces, and also provides for a common framework for decision theory and Bayesian probability.Comment: 15 pages; revised setting to more clearly explain how to incorporate perfect measures and the Giry monad; to appear in Applied Categorical Structure

Asymmetric triplex metallohelices with high and selective activity against cancer cells

Small cationic amphiphilic α-helical peptides are emerging as agents for the treatment of cancer and infection, but they are costly and display unfavourable pharmacokinetics. Helical coordination complexes may offer a three-dimensional scaffold for the synthesis of mimetic architectures. However, the high symmetry and modest functionality of current systems offer little scope to tailor the structure to interact with specific biomolecular targets, or to create libraries for phenotypic screens. Here, we report the highly stereoselective asymmetric self-assembly of very stable, functionalized metallohelices. Their anti-parallel head-to-head-to-tail ‘triplex’ strand arrangement creates an amphipathic functional topology akin to that of the active sub-units of, for example, host-defence peptides and ​p53. The metallohelices display high, structure-dependent toxicity to the human colon carcinoma cell-line HCT116 ​p53++, causing dramatic changes in the cell cycle without DNA damage. They have lower toxicity to human breast adenocarcinoma cells (MDA-MB-468) and, most remarkably, they show no significant toxicity to the bacteria methicillin-resistant Staphylococcus aureus and Escherichia coli. At a glanc

Uist Lagoons Survey

Scotland has around a hundred saline lagoons, coastal lochs that are not quite as saline as the sea. A small number of organisms are confined to these lochs, but most of these are very small and belong to groups that are difficult to identify. A consortium of specialists in identification at the National Museum of Scotland and ecologists sampled most of the saline lagoons on designated sites (SSSI and SAC) in the Uists, the area believed to have the best biodiversity of lagoon organisms in Scotland. The study not only confirmed the presence of these specialist species, but also that they were more widely distributed in the Uists than had been believed. Samples of the organisms have been placed in the permanent collections of the National Museum of Scotland and (for plants) in the Royal Botanic Gardens Edinburgh, where they will be available for future study

China\u27s Acquisitions Abroad - Global Ambitions, Domestic Effects

In the past year or so, the world has observed with seeming trepidation what appears to be a new phenomenon-China\u27s stepping out into the world economy. The move, labeled the Going Out Strategy by Chinese policy makers, sees China acting in the world not just as a trader of commodities and raw materials, or the provider of inexpensively-produced consumer goods for every corner of the globe, but as a driven and sophisticated acquirer of foreign assets and the equity interests in the legal entities that control such assets. The New Yorker magazine, ever topical and appropriately humorous, highlighted this attention with a cartoon in its October 17,2005 edition. That drawing shows two prosperous and no doubt Upper East Side-dwelling matrons holding cocktails before a fireplace. Above the fireplace hangs the formal portrait of a balding, well-fed, elderly, man. Looking at the portrait, one lady says matter-of-factly to the other: That\u27s Karl, before he was purchased by the Chinese

\u27Quack Corporate Governance\u27 as Traditional Chinese Medicine – The Securities Regulation Cannibalization of China\u27s Corporate Law and a State Regulator\u27s Battle Against Party State Political Economic Power

From the start of the People’s Republic of China’s (PRC) “corporatization ” project in the late 1980s, a Chinese corporate governance regime subject to increasingly enabling legal norms has been determined by mandatory regulations imposed by the PRC securities regulator, the China Securities Regulatory Commission (CSRC). Indeed, the Chinese corporate law system has been cannibalized by all - encompassing securities regulation directed at corporate governance, at least for companies with listed stock. This Article traces the path of that sustained intervention and makes a case — wholly contrary to the “quack corporate governance” critique much aired in the United States — that for the PRC this phenomenon is necessary, appropriate, and benign. That analysis, in turn, reveals a great deal about the following: the development of Chinese law and legal institutions after 1979; China’s contemporary political economy; the true identity of the firm under the PRC “corporatization without privatization” program; the normative character and function of corporate law across increasingly globalized capital markets; and the ways in which state intervention may protect against state abuse of power and enable greater private autonomy. For analysts of China’s contemporary political system, this Article uncovers a new identity of the Chinese party state’s horizontally oriented “fragmented authoritarianism,” where a central government agency has instituted pre-enforcement designs that systemically constrain the economic and directorial power of the PRC’s most powerful, formally non-governmental, political economic actors

Enforcement Without Foundation? Insider Trading and China\u27s Administrative Law Crisis

China\u27s securities regulator enforces insider trading prohibitions pursuant to non-legal and non-regulatory internal guidance. Reported agency decisions indicate that enforcement against insider trading is often possible only pursuant to this guidance, as the behavior identified is far outside of the scope of insider trading liability provided for in statute or regulation. I argue that the agency guidance is itself unlawful and unenforceable, because: (i) the guidance is not the regulatory norm required by the statutory delegation of power; and (ii) the guidance is ultra vires because (a) it addresses something substantively different from what is authorized under the statutory delegation, and (b) because the guidance radically transforms the underlying basis for the breach of insider trading under Chinese law-from a modified classical Ifiduciary duty plus misappropriation theory to an extremely robust equal access I mere possession of inside information theory. I then outline potential Chinese law challenges to the norms and their enforcement, and analyze why there is such marked tolerance to plainly illegal rule-making and enforcement by what is commonly understood to be one of China\u27s best administrative agencies. The infirmity underlying the basis for well-governed and investor- attracting capital markets identified here has implications not only for China\u27s securities regulation regime and healthy market development, but also for the entirety of China\u27s legal and administrative law system in the reform era

When \u27Good\u27 Corporate Governance Makes \u27Bad\u27 (Financial) Firms: The Global Crisis and the Limits of Private Law

In the aftermath of the global financial crisis of 2008–2009, investors, analysts, legislators, and pundits have spotlighted “good” or “improved” corporate governance as a remedy for all that presently ails us. It is one remedy in a long wish list that includes tougher requirements for risk capital, liquidity, and leverage; compensation and bonus reform; reimposition ofthe Glass-Steagall-like separation of bank “utility” and “casino” functions; the downsizing or breakup of institutions deemed “too big to fail;” enhanced consumer protection; securities law liability for secondary violators (like credit rating agencies); direct taxation of proprietary trading; “macroprudential” regulation; and new transparency requirements for derivatives trading and clearance. This time, the proposed objects of corporate governance reform are not Michael Eisner’s personal “magic kingdom” at the Walt Disney Company or Andy Fastow’s self-dealing and ultimately self-deceiving Enron Corporation, but the global financial institutions that saw their balance sheets degraded—and the global credit markets put at risk—by proprietary tradingin so-called “toxic” assets and other high-risk, high-reward, “casino” activities. The renewed focus on good corporate governance pertains not only to the perceived asymmetry between the outlandish compensation dished out at now bankrupt or massively bailed-out firms, but also to the traditional, broader roster of corporate governance mechanisms designed to enhance director-manager accountability to firm “owners”—the shareholders. In this case, however, more effective corporate governance may not be a serious part of the solution; instead, “good” (or effectively functioning) corporate governance may have been one of the major factors that contributed to the global financial meltdown. This insight highlights the existence of unalterable constraints on any corporate governance system, and emphasizes the need for even more robust government regulation of private businesses—especially firms that function at the core of a global capital allocation system