On the Complex Dimensions of Nonlattice Fractal Strings in Connection with Dirichlet Polynomials

In this paper we give a new characterization of the closure of the set of the real parts of the zeros of a particular class of Dirichlet polynomials that is associated with the set of dimensions of fractality of certain fractal strings. We show, for some representative cases of nonlattice Dirichlet polynomials, that the real parts of their zeros are dense in their associated critical intervals, confirming the conjecture and the numerical experiments made by M. Lapidus and M. van Frankenhuysen in several papers.

Democratic Contestation, Accountability, and Citizen Satisfaction at the Regional Level. CES Germany & Europe Working Papers, No. 04.2, 2004

Democratic theory tells us that competition between political parties fosters more responsive government by disciplining elected leaders. Yet party competition may not always attain the levels desirable for holding leaders accountable, notably at the sub-national level. This paper hypothesizes that variations in competition-induced accountability affect regional, or state, government behavior, and that this variation is reflected in citizen satisfaction with regional government performance. The hypothesis is confirmed using survey data from sixty-eight German state election studies. Specifically, a widening of the gap between the two main parties of each state is shown to affect subsequent individual-level satisfaction negatively. This finding presents a conjecture that should be generalizable to other countries with strong sub-national units.

Why Do Some International Institutions Contain Strong Dispute Settlement Provisions: New Evidence from Preferential Trade Agreements

To understand why some international institutions have stronger dispute settlement mechanisms (DSMs) than others, we investigate the dispute settlement provisions of nearly 600 preferential trade agreements (PTAs), which possess several desirable case-selection features and are evoked more than is realized. We broaden the study of dispute settlement design beyond “legalization” and instead reorient theorizing around a multi-faceted conceptualization of the strength of DSMs. We posit that strong DSMs are first and foremost a rational response to features of agreements that require stronger dispute settlement, such as depth and large memberships. Multivariate empirical tests using a new data set on PTA design confirm these expectations and reveal that depth – the amount of policy change specified in an agreement – is the most powerful and consistent predictor of DSM strength, providing empirical support to a long-posited but controversial conjecture. Yet power also plays a sizeable role, since agreements among asymmetric members are more likely to have strong DSMs due to their mutual appeal, as are those involving the United States. Important regional differences also emerge, as PTAs across the Americas are designed with strong dispute settlement, as are Asian PTAs, which contradicts the conventional wisdom about Asian values and legalization. Our findings demonstrate that rationalism explains much of international institutional design, yet it can be enhanced by also incorporating power-based and regional explanations.

Annibal dans les Alpes,

On cover: Ouvrage renfermant dix-sept cartes et six photographies. Paris, A. Picard, 1902.

Aspects of Markov Chains and Particle Systems

Thesis (Ph.D.)--University of Washington, 2016-06

Irreducible cyclic presentations of the trivial group

We produce families of irreducible cyclic presentations of the trivial group. These families comprehensively answer questions about such presentations asked by Dunwoody and by Edjvet, Hammond, and Thomas. Our theorems are purely theoretical, but their derivation is based on practical computations. We explain how we chose the computations and how we deduced the theorems.

Testing integrability with a single bit of quantum information

We show that deterministic quantum computing with a single bit can determine whether the classical limit of a quantum system is chaotic or integrable using O(N) physical resources, where N is the dimension of the Hilbert space of the system under study. This is a square-root improvement over all known classical procedures. Our study relies strictly on the random matrix conjecture. We also present numerical results for the nonlinear kicked top.

Decompositions of complete graphs into triangles and Hamilton cycles

For all odd integers n greater than or equal to 1, let G(n) denote the complete graph of order n, and for all even integers n greater than or equal to 2 let G,, denote the complete graph of order n with the edges of a 1-factor removed. It is shown that for all non-negative integers h and t and all positive integers n, G, can be decomposed into h Hamilton cycles and t triangles if and only if nh + 3t is the number of edges in G(n). (C) 2004 Wiley Periodicals, Inc.

A note on execution costs for stock index futures: Information versus liquidity effects

This paper examines execution costs and the impact of trade size for stock index futures using price-volume transaction data from the London International Financial Futures and Options Exchange. Consistent with Subrahmanyam [Rev. Financ. Stud. 4 (1991) 11] we find that effective half spreads in the stock index futures market are small compared to stock markets, and that trades in stock index futures have only a small permanent price impact. This result is important as it helps to better understand the success of equity index products such as index futures and Exchange Traded Funds. We also find that there is no asymmetry in the post-trade price reaction between purchases and sales for stock index futures across various trade sizes. This result is consistent with the conjecture in Chan and Lakonishok [J. Financ. Econ. 33 (1993) 173] that the asymmetry surrounding block trades in stock markets is due to the high cost of short selling and the general reluctance of traders to short sell on stock markets. (C) 2004 Elsevier B.V. All rights reserved.

Quantum entanglement and fixed-point bifurcations

How does the classical phase-space structure for a composite system relate to the entanglement characteristics of the corresponding quantum system? We demonstrate how the entanglement in nonlinear bipartite systems can be associated with a fixed-point bifurcation in the classical dynamics. Using the example of coupled giant spins we show that when a fixed point undergoes a supercritical pitchfork bifurcation, the corresponding quantum state-the ground state-achieves its maximum amount of entanglement near the critical point. We conjecture that this will be a generic feature of systems whose classical limit exhibits such a bifurcation.

Decomposition of complete graphs into 5-cubes

Necessary conditions for the complete graph on n vertices to have a decomposition into 5-cubes are that 5 divides it - 1 and 80 divides it (it - 1)/2. These are known to be sufficient when n is odd. We prove them also sufficient for it even, thus completing the spectrum problem for the 5-cube and lending further weight to a long-standing conjecture of Kotzig. (c) 2005 Wiley Periodicals, Inc.

Do different surrogate methods detect lateral genetic transfer events of different relative ages?

Non-tree-based ('surrogate') methods have been used to identify instances of lateral genetic transfer in microbial genomes but agreement among predictions of different methods can be poor. It has been proposed that this disagreement arises because different surrogate methods are biased towards the detection of certain types of transfer events. This conjecture is supported by a rigorous phylogenetic analysis of 3776 proteins in Escherichia coli K12 MG1655 to map the ages of transfer events relative to one another.

Flexible proof reuse for software verification

Proof reuse, or analogical reasoning, involves reusing the proof of a source theorem in the proof of a target conjecture. We have developed a method for proof reuse that is based on the generalisation replay paradigm described in the literature, in which a generalisation of the source proof is replayed to construct the target proof. In this paper, we describe the novel aspects of our method, which include a technique for producing more accurate source proof generalisations (using knowledge of the target goal), as well as a flexible replay strategy that allows the user to set various parameters to control the size and the shape of the search space. Finally, we report on the results of applying this method to a case study from the realm of software verification.

Estimating buffer overflows in three stages using cross-entropy

In this paper we propose a fast adaptive Importance Sampling method for the efficient simulation of buffer overflow probabilities in queueing networks. The method comprises three stages. First we estimate the minimum Cross-Entropy tilting parameter for a small buffer level; next, we use this as a starting value for the estimation of the optimal tilting parameter for the actual (large) buffer level; finally, the tilting parameter just found is used to estimate the overflow probability of interest. We recognize three distinct properties of the method which together explain why the method works well; we conjecture that they hold for quite general queueing networks. Numerical results support this conjecture and demonstrate the high efficiency of the proposed algorithm.

The dynamics of matrix momentum

We analyse the matrix momentum algorithm, which provides an efficient approximation to on-line Newton's method, by extending a recent statistical mechanics framework to include second order algorithms. We study the efficacy of this method when the Hessian is available and also consider a practical implementation which uses a single example estimate of the Hessian. The method is shown to provide excellent asymptotic performance, although the single example implementation is sensitive to the choice of training parameters. We conjecture that matrix momentum could provide efficient matrix inversion for other second order algorithms.