Improving the efficiency of variational tensor network algorithms

We present several results relating to the contraction of generic tensor networks and discuss their application to the simulation of quantum many-body systems using variational approaches based upon tensor network states. Given a closed tensor network $\mathcal{T}$, we prove that if the environment of a single tensor from the network can be evaluated with computational cost $\kappa$, then the environment of any other tensor from $\mathcal{T}$ can be evaluated with identical cost $\kappa$. Moreover, we describe how the set of all single tensor environments from $\mathcal{T}$ can be simultaneously evaluated with fixed cost $3\kappa$. The usefulness of these results, which are applicable to a variety of tensor network methods, is demonstrated for the optimization of a Multi-scale Entanglement Renormalization Ansatz (MERA) for the ground state of a 1D quantum system, where they are shown to substantially reduce the computation time.Comment: 12 pages, 8 figures, RevTex 4.1, includes reference implementation. Software updated to v1.02: Resolved two scenarios in which multienv would generate errors for valid input

Some of the factors influencing the infection and pathogenicity of Ustilago Zeae (Beckm.) Unger on Zea Mays L.

A survey of corn smut based on visible smut galls and conducted near Ames, Iowa, from 1930 to 1934 inclusive, showed 10.6, 9.9, 13.9, 5.5 and 18.3 percent of affected plants. When the leaf sheaths were stripped from 1,985 plants, exposed to artificial and natural infection in 1934, many small smut galls aggregating 39.3 percent of the total expressed infections were found at the nodes. The symptoms of corn smut may be classed as exposed and concealed. Exposed symptoms occur as irregular yellow or reddish stripes or blotches, brownish lesions and galls. Concealed symptoms are completely hidden by the leaf sheaths and occur as small nodal galls and minute pustules of chlamydospores in the leaves of the axillary buds. A decrease in the surface tension of the inoculum increased the infectivity of the medium containing the sporidia. One percent rosin fish oil soap was found to be an effective surface tension reducing agent. The surface tension of carrot filtrate, used as a culture medium, was 47.0 dynes per centimeter; water, 72.3; carrot filtrate with 1 percent fish oil soap, 34.0. Ninety-two percent of 500 sweet corn plants (Golden Bantam) became infected when inoculated with a sporidial suspension in carrot filtrate plus 1 percent fish oil soap, while 36.6 percent of 90 similar plants became infected when inoculated with a sporidial suspension in carrot filtrate. Increased bud growth was accompanied by a larger number of nodal infections. Axillary bud growth was stimulated by injury to the corn plant, or inhibition of pollination. Injured or unpollinated inoculated plants produced approximately twice as many smut galls as the checks. Histological examination of 262 axillary buds from 50 inoculated sweet corn plants (Golden Bantam) showed 53.6 percent or 140 of the buds to be infected with smut mycelium. Mycelium was found in apparently healthy axillary buds 67 days after inoculation. The percentage of smut infection as indicated by nodal smut galls increased with lateness in planting. An average of data for 2 years showed 12 percent on May 15 plantings while approximately 40 percent of the June 4 plantings were smutted. The percentage of smut infection as indicated by nodal smut galls showed a tendency to increase both ways from the 2-3 rates of planting. During the years 1931, 1932, 1933 and 934 those plants growing one in a hill showed 40.8, 20.4, 9.0 and 22.8 percent infection, respectively; those at the rate of three per hill 22.5, 13.5, 4.3 and 14.6, while those at the rate of five per hill showed 32.4, 21.6, 5.9 and 18.5 percent infection

Essays on the Patient-Centered Medical Home in the United States Military Health System

The Patient-Centered Medical Home has been endorsed by the primary care community as the model of the future, with hopes that it will increase quality of care and the patient and provider experience while decreasing costs. Many aspects of the implementation of the Patient-Centered Medical Home model remain unexplored. This dissertation comprises three independent studies examining Patient-Centered Medical Home implementation in the Military Health System, including (1) the effects of environmental correlates on the time to implement the model, (2) the impact of differences in implementation on preventive care quality outcomes, and (3) the effect of differences in implementation on chronic care quality outcomes. Survival analysis was utilized to analyze the effect of environment, defined as resources and governance, on how long it took Military Health System clinics to adopt the Patient-Centered Medical Home model. Clinics were assumed to have adopted the model when they achieved National Committee on Quality Assurance recognition. Differences-in-differences models were created to compare both preventive and chronic care quality outcomes in Military Health System clinics by branch of service before and after Patient-Centered Medical Home implementation. Dependent variables included Chlamydia and various cancer screenings as well as heart condition and diabetes care HEDIS metrics. Measures were drawn from Military Health Mart, a patient-level utilization database, and aggregated at the clinic level. SPSS was used to analyze the data and we considered a p-value of less than .05 as statistical significance. Our research suggests that, while the environmental correlates of resources and governance did impact the time to adoption of the Patient-Centered Medical Home model, differences in how the model was implemented had mixed results on both preventive and chronic care quality outcomes. The differences in significant measures were small. More research is needed on cost, utilization and patient/provider satisfaction to assess the impact of implementation differences

Civil Rules Interpretive Theory

We contend that the Federal Rules of Civil Procedure (Rules) should be interpreted in a distinctive fashion, despite the federal courts' proclivity to interpret the Rules as if they were statutes. The Supreme Court itself promulgates the Rules. Congress does not enact them as statutes through the traditional path of bicameralism and presentment. As a result, the principle of legislative supremacy and the related notion that the federal courts should serve as a faithful agent of Congress, which undergird every traditional theory of statutory interpretation, do not apply in the Rules context. Unlike statutory interpretation, Rules interpretation is not an interbranch endeavor, but rather an intrabranch one. The Rules, therefore, require an interpretive theory that is descriptively and normatively grounded within this non-legislative framework. That said, rule-of-law norms demonstrate that the Rules are authoritative and that they are generally interpretable from a perspective that we call "jurisprudential purposivism." From these insights, we draw several conclusions: namely, the Rules should not be interpreted as if they are statutes; the nascent nonstatutory theories of civil rules interpretation are inadequate; and an administrative law approach presents the best interpretive vision for the Rules. While our proposed model may not be the last word on the subject-indeed, we hope it is not-we intend it to be the beginning of sustained judicial and scholarly inquiry in the distinctive field of civil rules interpretive theory

Institutional Competence and Civil Rules Interpretation

This essay responds to Pragmatism Rules by Professor Elizabeth Porter, which argues that the Supreme Court is justified in eschewing, at least at times, traditional tools of statutory construction when it interprets the Federal Rules of Civil Procedure. Porter devotes substantial attention in her piece to our prior work on the Supreme Court’s methods for implementing the Federal Rules. This response essay highlights some of the strengths of Porter’s article and identifies substantial areas of agreement. It also parts company with her analysis insofar as she contends that the Supreme Court is justified in supplanting the Rules drafters’ policy prescriptions with its own or crafting novel procedural policy via adjudication. The essay further argues that the Mulliszewski model of Rules interpretation is superior to her proposed alternative based on the competencies of the relevant institutional actors; namely, the Rules Advisory Committee, the lower federal courts, and the Supreme Court