On the Complexity of Random Quantum Computations and the Jones Polynomial

There is a natural relationship between Jones polynomials and quantum computation. We use this relationship to show that the complexity of evaluating relative-error approximations of Jones polynomials can be used to bound the classical complexity of approximately simulating random quantum computations. We prove that random quantum computations cannot be classically simulated up to a constant total variation distance, under the assumption that (1) the Polynomial Hierarchy does not collapse and (2) the average-case complexity of relative-error approximations of the Jones polynomial matches the worst-case complexity over a constant fraction of random links. Our results provide a straightforward relationship between the approximation of Jones polynomials and the complexity of random quantum computations.Comment: 8 pages, 4 figure

Approximation Algorithms for Complex-Valued Ising Models on Bounded Degree Graphs

We study the problem of approximating the Ising model partition function with complex parameters on bounded degree graphs. We establish a deterministic polynomial-time approximation scheme for the partition function when the interactions and external fields are absolutely bounded close to zero. Furthermore, we prove that for this class of Ising models the partition function does not vanish. Our algorithm is based on an approach due to Barvinok for approximating evaluations of a polynomial based on the location of the complex zeros and a technique due to Patel and Regts for efficiently computing the leading coefficients of graph polynomials on bounded degree graphs. Finally, we show how our algorithm can be extended to approximate certain output probability amplitudes of quantum circuits.Comment: 12 pages, 0 figures, published versio

On the Parameterised Complexity of Induced Multipartite Graph Parameters

We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$ and a given graph $G$, and for natural numbers $k\geq2$ and $\ell$, we must decide whether the maximum value of $p$ over all induced $k$-partite subgraphs of $G$ is at most $\ell$. We prove that this problem is W[1]-hard. Next, we consider a variant of this problem, where we must decide whether the given graph $G$ contains a sufficiently large induced $k$-partite subgraph $H$ such that $p(H)\leq\ell$. We show that for certain parameters this problem is para-NP-hard, while for others it is fixed-parameter tractable.Comment: 9 pages, 0 figure

On the Parameterised Complexity of Induced Multipartite Graph Parameters

We introduce a family of graph parameters, called induced multipartite graph parameters, and study their computational complexity. First, we consider the following decision problem: an instance is an induced multipartite graph parameter $p$ and a given graph $G$, and for natural numbers $k\geq2$ and $\ell$, we must decide whether the maximum value of $p$ over all induced $k$-partite subgraphs of $G$ is at most $\ell$. We prove that this problem is W[1]-hard. Next, we consider a variant of this problem, where we must decide whether the given graph $G$ contains a sufficiently large induced $k$-partite subgraph $H$ such that $p(H)\leq\ell$. We show that for certain parameters this problem is para-NP-hard, while for others it is fixed-parameter tractable.Comment: 9 pages, 0 figure

Chiral Fermions and Quadratic Divergences

In an approach towards naturalness without supersymmetry, renormalization properties of nonsupersymmetric abelian quiver gauge theories are studied. In the construction based on cyclic groups Z_p the gauge group is U(N)^p, the fermions are all in bifundamentals and the construction allows scalars in adjoints and bifundamentals. Only models without adjoint scalars, however, exhibit both chiral fermions and the absence of one-loop quadratic divergences in the scalar propagator.Comment: 11 page

Temporal Variation In Fecundity And Spawning In The Eastern Oyster, Crassostrea Virginica, In The Piankatank River, Virginia

Oysters of the genus Crassostrea are considered good examples of an r-selected marine invertebrate with small egg size, high fecundity, and multiple spawning events per year, each characterized by significant individual weight loss. Historical (decadal) data for the Virginia portion of the Chesapeake Bay support these generalities. We present recent (subdecadal) data, collected for natural Crassostrea virginica broodstock of populations in the Piankatank River, Virginia. The relationship is described between oyster size, fecundity, spawning periodicity, and egg viability for natural broodstock. Oysters collected throughout the summers of 2010 through 2012 and induced to spawn by thermal cycling released viable eggs on 7 dates (n = 119 oysters, 35male, 84 female; shell length (SL) range, 58-113 mm). Oysters were opened to examine sex ratio on four additional dates (total n = 242 oysters, 82 male, 160 female). Fecundity varied in the range 10(5)-1.2x10(8) eggs. When all data are considered in unison, no strong relationship with SL is evident; however, when eliminating the artifact of data corresponding to minimal egg release, a much stronger relationship, comparable with that reported in older literature, emerges. Female fraction (Female/(Female + Male)) was consistently more than 1 in oysters larger than 60 mm in SL (estimated age, \u3e= 2 y), generally in accordance with recently published literature on the species in themid-Atlantic. The size-versus-fecundity relationship does not appear to be greatly influenced by disease prevalence/intensity. The temporal sequence of spawning activity was not observed to continue after midsummer and is not commensurate with a cumulative degree-day estimator during the latter half of the well-documented historical spawning season. A size-fecundity estimator for the Piankatank River oysters provides a basis to estimate the disproportionate value of larger/older (\u3e= 3 y) oysters in the system, and provides additional input to the fine-tuning of a previously developed rotational harvest schedule for the river stock. The possible impact of recent changes in water quality, seasonal occurrence of dinoflagellate blooms, and/or long-term impacts of changing regimes were not examined in detail in this study but are suggested as worthy lines of future investigation

Evaluating Mobile Survey Tools (MSTs) for Field-Level Monitoring and Data Collection: Development of a Novel Evaluation Framework, and Application to MSTs for Rural Water and Sanitation Monitoring

Information and communications technologies (ICTs) such as mobile survey tools (MSTs) can facilitate field-level data collection to drive improvements in national and international development programs. MSTs allow users to gather and transmit field data in real time, standardize data storage and management, automate routine analyses, and visualize data. Dozens of diverse MST options are available, and users may struggle to select suitable options. We developed a systematic MST Evaluation Framework (EF), based on International Organization for Standardization/International Electrotechnical Commission (ISO/IEC) software quality modeling standards, to objectively assess MSTs and assist program implementers in identifying suitable MST options. The EF is applicable to MSTs for a broad variety of applications. We also conducted an MST user survey to elucidate needs and priorities of current MST users. Finally, the EF was used to assess seven MSTs currently used for water and sanitation monitoring, as a validation exercise. The results suggest that the EF is a promising method for evaluating MSTs