Matrix product approximations to multipoint functions in two-dimensional conformal field theory

Matrix product states (MPS) illustrate the suitability of tensor networks for the description of interacting many-body systems: ground states of gapped $1$-D systems are approximable by MPS as shown by Hastings [J. Stat. Mech. Theor. Exp., P08024 (2007)]. In contrast, whether MPS and more general tensor networks can accurately reproduce correlations in critical quantum systems, respectively quantum field theories, has not been established rigorously. Ample evidence exists: entropic considerations provide restrictions on the form of suitable Ansatz states, and numerical studies show that certain tensor networks can indeed approximate the associated correlation functions. Here we provide a complete positive answer to this question in the case of MPS and $2D$ conformal field theory: we give quantitative estimates for the approximation error when approximating correlation functions by MPS. Our work is constructive and yields an explicit MPS, thus providing both suitable initial values as well as a rigorous justification of variational methods.Comment: 5 pages, 1 figure. See long companion paper arXiv:1509.07414 for full technical detail

Constructed wetlands: Treatment of concentrated storm water runoff (part A)

The aim of this research was to assess the treatment efficiencies for gully pot liquor of experimental vertical- flow constructed wetland filters containing Phragmites australis (Cav.) Trin. ex Steud. (common reed) and filter media of different adsorption capacities. Six out of 12 filters received inflow water spiked with metals. For 2 years, hydrated nickel and copper nitrate were added to sieved gully pot liquor to simulate contaminated primary treated storm runoff. For those six constructed wetland filters receiving heavy metals, an obvious breakthrough of dissolved nickel was recorded after road salting during the first winter. However, a breakthrough of nickel was not observed, since the inflow pH was raised to eight after the first year of operation. High pH facilitated the formation of particulate metal compounds such as nickel hydroxide. During the second year, reduction efficiencies of heavy metal, 5-days at 20°C N-Allylthiourea biochemical oxygen demand (BOD) and suspended solids (SS) improved considerably. Concentrations of BOD were frequently �20 mg/L. However, concentrations for SS were frequently �30 mg/L. These are the two international thresholds for secondary wastewater treatment. The BOD removal increased over time due to biomass maturation, and the increase of pH. An analysis of the findings with case-based reasoning can be found in the corresponding follow-up paper (Part B)

Quantum-proof randomness extractors via operator space theory

Quantum-proof randomness extractors are an important building block for classical and quantum cryptography as well as device independent randomness amplification and expansion. Furthermore they are also a useful tool in quantum Shannon theory. It is known that some extractor constructions are quantum-proof whereas others are provably not [Gavinsky et al., STOC'07]. We argue that the theory of operator spaces offers a natural framework for studying to what extent extractors are secure against quantum adversaries: we first phrase the definition of extractors as a bounded norm condition between normed spaces, and then show that the presence of quantum adversaries corresponds to a completely bounded norm condition between operator spaces. From this we show that very high min-entropy extractors as well as extractors with small output are always (approximately) quantum-proof. We also study a generalization of extractors called randomness condensers. We phrase the definition of condensers as a bounded norm condition and the definition of quantum-proof condensers as a completely bounded norm condition. Seeing condensers as bipartite graphs, we then find that the bounded norm condition corresponds to an instance of a well studied combinatorial problem, called bipartite densest subgraph. Furthermore, using the characterization in terms of operator spaces, we can associate to any condenser a Bell inequality (two-player game) such that classical and quantum strategies are in one-to-one correspondence with classical and quantum attacks on the condenser. Hence, we get for every quantum-proof condenser (which includes in particular quantum-proof extractors) a Bell inequality that can not be violated by quantum mechanics.Comment: v3: 34 pages, published versio

Modular design of data-parallel graph algorithms

Amorphous Data Parallelism has proven to be a suitable vehicle for implementing concurrent graph algorithms effectively on multi-core architectures. In view of the growing complexity of graph algorithms for information analysis, there is a need to facilitate modular design techniques in the context of Amorphous Data Parallelism. In this paper, we investigate what it takes to formulate algorithms possessing Amorphous Data Parallelism in a modular fashion enabling a large degree of code re-use. Using the betweenness centrality algorithm, a widely popular algorithm in the analysis of social networks, we demonstrate that a single optimisation technique can suffice to enable a modular programming style without loosing the efficiency of a tailor-made monolithic implementation

Constructed wetlands: Prediction of performance with case-based reasoning (part B)

The aim of this research was to assess the treatment efficiencies for gully pot liquor of experimental vertical- flow constructed wetland filters containing Phragmites australis (Cav.) Trin. ex Steud. (common reed) and filter media of different adsorption capacities. Six out of 12 filters received inflow water spiked with metals. For 2 years, hydrated nickel and copper nitrate were added to sieved gully pot liquor to simulate contaminated primary treated storm runoff. The findings were analyzed and discussed in a previous paper (Part A). Case-based reasoning (CBR) methods were applied to predict 5 days at 20°C N-Allylthiourea biochemical oxygen demand (BOD) and suspended solids (SS), and to demonstrate an alternative method of analyzing water quality performance indicators. The CBR method was successful in predicting if outflow concentrations were either above or below the thresholds set for water-quality variables. Relatively small case bases of approximately 60 entries are sufficient to yield relatively high predictions of compliance of at least 90% for BOD. Biochemical oxygen demand and SS are expensive to estimate, and can be cost-effectively controlled by applying CBR with the input variables turbidity and conductivity

Private Saving and Public Policy

The evidence presented in this paper supports the view that many Americans, particularly those without a college education, save too little. Our analysis also indicates that it should be possible to increase total personal saving among lower income households by encouraging the formation and expansion of private pension plans. It is doubtful that favorable tax treatment of capital income would stimulate significant additional saving by this group. Conversely, the expansion of private pensions would probably have little effect on saving by higher income households. However, these households are more likely to increase saving significantly in response to favorable tax treatment of capital income. Currently, eligibility for IRAs is linked to an AGI cap, and pension coverage is more common among higher income households than among low income households. The most effective system for promoting personal saving would have precisely the opposite features. Extending tax incentives for saving to higher income households is problematic. We discuss three competing policy options, IRAs with AGI caps, the universal IRA, and the Premium Saving Account (PSA). Our analysis reveals that the PSA system is a more cost-effective vehicle for providing saving incentives to, all households, particularly those in the top quintile of the income distribution.

Uncertainty relations: An operational approach to the error-disturbance tradeoff

The notions of error and disturbance appearing in quantum uncertainty relations are often quantified by the discrepancy of a physical quantity from its ideal value. However, these real and ideal values are not the outcomes of simultaneous measurements, and comparing the values of unmeasured observables is not necessarily meaningful according to quantum theory. To overcome these conceptual difficulties, we take a different approach and define error and disturbance in an operational manner. In particular, we formulate both in terms of the probability that one can successfully distinguish the actual measurement device from the relevant hypothetical ideal by any experimental test whatsoever. This definition itself does not rely on the formalism of quantum theory, avoiding many of the conceptual difficulties of usual definitions. We then derive new Heisenberg-type uncertainty relations for both joint measurability and the error-disturbance tradeoff for arbitrary observables of finite-dimensional systems, as well as for the case of position and momentum. Our relations may be directly applied in information processing settings, for example to infer that devices which can faithfully transmit information regarding one observable do not leak any information about conjugate observables to the environment. We also show that Englert's wave-particle duality relation [PRL 77, 2154 (1996)] can be viewed as an error-disturbance uncertainty relation.Comment: v3: title change, accepted in Quantum; v2: 29 pages, 7 figures; improved definition of measurement error. v1: 26.1 pages, 6 figures; supersedes arXiv:1402.671