Theory of annihilation games—I

AbstractPlace tokens on distinct vertices of an arbitrary finite digraph with n vertices which may contain cycles or loops. Each of two players alternately selects a token and moves it from its present position u to a neighboring vertex v along a directed edge which may be a loop. If v is occupied, and u ≠ v, both tokens get annihilated and phase out of the game. The player first unable to move is the loser, the other the winner. If there is no last move, the outcome is declared a draw. An O(n6) algorithm for computing the previous-player-winning, next-player-winning and draw positions of the game is given. Furthermore, an algorithm is given for computing a best strategy in O(n6) steps and winning—starting from a next-player-winning position—in O(n5) moves

Eigenfunction statistics for a point scatterer on a three-dimensional torus

In this paper we study eigenfunction statistics for a point scatterer (the Laplacian perturbed by a delta-potential) on a three-dimensional flat torus. The eigenfunctions of this operator are the eigenfunctions of the Laplacian which vanish at the scatterer, together with a set of new eigenfunctions (perturbed eigenfunctions). We first show that for a point scatterer on the standard torus all of the perturbed eigenfunctions are uniformly distributed in configuration space. Then we investigate the same problem for a point scatterer on a flat torus with some irrationality conditions, and show uniform distribution in configuration space for almost all of the perturbed eigenfunctions.Comment: Revised according to referee's comments. Accepted for publication in Annales Henri Poincar

Tight Time-Space Lower Bounds for Finding Multiple Collision Pairs and Their Applications

We consider a collision search problem (CSP), where given a parameter $C$, the goal is to find $C$ collision pairs in a random function $f:[N] \rightarrow [N]$ (where $[N] = \{0,1,\ldots,N-1\})$ using $S$ bits of memory. Algorithms for CSP have numerous cryptanalytic applications such as space-efficient attacks on double and triple encryption. The best known algorithm for CSP is parallel collision search (PCS) published by van Oorschot and Wiener, which achieves the time-space tradeoff $T^2 \cdot S = \tilde{O}(C^2 \cdot N)$ for $S = \tilde{O}(C)$. In this paper, we prove that any algorithm for CSP satisfies $T^2 \cdot S = \tilde{\Omega}(C^2 \cdot N)$ for $S = \tilde{O}(C)$, hence the best known time-space tradeoff is optimal (up to poly-logarithmic factors in $N$). On the other hand, we give strong evidence that proving similar unconditional time-space tradeoff lower bounds on CSP applications (such as breaking double and triple encryption) may be very difficult, and would imply a breakthrough in complexity theory. Hence, we propose a new restricted model of computation and prove that under this model, the best known time-space tradeoff attack on double encryption is optimal

Genetic Discovery and Risk Characterization in Type 2 Diabetes across Diverse Populations

Genomic discovery and characterization of risk loci for type 2 diabetes (T2D) have been conducted primarily in individuals of European ancestry. We conducted a multiethnic genome-wide association study of T2D among 53,102 cases and 193,679 control subjects from African, Hispanic, Asian, Native Hawaiian, and European population groups in the Population Architecture Genomics and Epidemiology (PAGE) and Diabetes Genetics Replication and Meta-analysis (DIAGRAM) Consortia. In individuals of African ancestry, we discovered a risk variant in th

Too Big to Fail — U.S. Banks’ Regulatory Alchemy: Converting an Obscure Agency Footnote into an “At Will” Nullification of Dodd-Frank’s Regulation of the Multi-Trillion Dollar Financial Swaps Market

The multi-trillion-dollar market for, what was at that time wholly unregulated, over-the-counter derivatives (“swaps”) is widely viewed as a principal cause of the 2008 worldwide financial meltdown. The Dodd-Frank Act, signed into law on July 21, 2010, was expressly considered by Congress to be a remedy for this troublesome deregulatory problem. The legislation required the swaps market to comply with a host of business conduct and anti-competitive protections, including that the swaps market be fully transparent to U.S. financial regulators, collateralized, and capitalized. The statute also expressly provides that it would cover foreign subsidiaries of big U.S. financial institutions if their swaps trading could adversely impact the U.S. economy or represent the use of extraterritorial trades as an attempt to “evade” Dodd-Frank. In July 2013, the CFTC promulgated an 80-page, triple-columned, and single-spaced “guidance” implementing Dodd-Frank’s extraterritorial reach, i.e., that manner in which Dodd-Frank would apply to swaps transactions executed outside the United States. The key point of that guidance was that swaps trading within the “guaranteed” foreign subsidiaries of U.S. bank holding company swaps dealers were subject to all of Dodd-Frank’s swaps regulations wherever in the world those subsidiaries’ swaps were executed. At that time, the standardized industry swaps agreement contemplated that, inter alia, U.S. bank holding company swaps dealers’ foreign subsidiaries would be “guaranteed” by their corporate parent, as was true since 1992. In August 2013, without notifying the CFTC, the principal U.S. bank holding company swaps dealer trade association privately circulated to its members standard contractual language that would, for the first time, “deguarantee” their foreign subsidiaries. By relying only on the obscure footnote 563 of the CFTC guidance’s 662 footnotes, the trade association assured its swaps dealer members that the newly deguaranteed foreign subsidiaries could (if they so chose) no longer be subject to Dodd-Frank. As a result, it has been reported (and it also has been understood by many experts within the swaps industry) that a substantial portion of the U.S. swaps market has shifted from the large U.S. bank holding companies swaps dealers and their U.S. affiliates to their newly deguaranteed “foreign” subsidiaries, with the attendant claim by these huge big U.S. bank swaps dealers that Dodd-Frank swaps regulation would not apply to these transactions. The CFTC also soon discovered that these huge U.S. bank holding company swaps dealers were “arranging, negotiating, and executing” (“ANE”) these swaps in the United States with U.S. bank personnel and, only after execution in the U.S., were these swaps formally “assigned” to the U.S. banks’ newly “deguaranteed” foreign subsidiaries with the accompanying claim that these swaps, even though executed in the U.S., were not covered by Dodd-Frank. In October 2016, the CFTC proposed a rule that would have closed the “deguarantee” and “ANE” loopholes completely. However, because it usually takes at least a year to finalize a “proposed” rule, this proposed rule closing the loopholes in question was not finalized prior to the inauguration of President Trump. All indications are that it will never be finalized during a Trump Administration. Thus, in the shadow of the recent tenth anniversary of the Lehman failure, there is an understanding among many market regulators and swaps trading experts that large portions of the swaps market have moved from U.S. bank holding company swaps dealers and their U.S. affiliates to their newly deguaranteed foreign affiliates where Dodd- Frank swaps regulation is not being followed. However, what has not moved abroad is the very real obligation of the lender of last resort to rescue these U.S. swaps dealer bank holding companies if they fail because of poorly regulated swaps in their deguaranteed foreign subsidiaries, i.e., the U.S. taxpayer. While relief is unlikely to be forthcoming from the Trump Administration or the Republican-controlled Senate, some other means will have to be found to avert another multi-trillion-dollar bank bailout and/or a financial calamity caused by poorly regulated swaps on the books of big U.S. banks. This paper notes that the relevant statutory framework affords state attorneys general and state financial regulators the right to bring so-called “parens patriae” actions in federal district court to enforce, inter alia, Dodd- Frank on behalf of a state’s citizens. That kind of litigation to enforce the statute’s extraterritorial provisions is now badly needed