Matching concepts across HOL libraries

Many proof assistant libraries contain formalizations of the same mathematical concepts. The concepts are often introduced (defined) in different ways, but the properties that they have, and are in turn formalized, are the same. For the basic concepts, like natural numbers, matching them between libraries is often straightforward, because of mathematical naming conventions. However, for more advanced concepts, finding similar formalizations in different libraries is a non-trivial task even for an expert. In this paper we investigate automatic discovery of similar concepts across libraries of proof assistants. We propose an approach for normalizing properties of concepts in formal libraries and a number of similarity measures. We evaluate the approach on HOL based proof assistants HOL4, HOL Light and Isabelle/HOL, discovering 398 pairs of isomorphic constants and types

Actual and Predicted Behavior of Large Metal Culverts

The stability of large metal culverts depends on the performance of the backfill around the pipe, which must be considered as a part of the structure when evaluating its safety. A simplified method to evaluate the current stability of such a structure on the basis of the structure\u27s shape is derived. Useful when limited amount of information is available, this method provides an economical procedure for: (1) evaluating the condition of the existing backfill and its capability to provide a safe support for the structure; (2) predicting final movements and determining if additional investigations are necessary to establish the safety of the structure; and (3) determining if measured deflections are in agreement with those predicted and, if not, determining if the safety of the structure is endangered by phenomena other than the expected behavior of surrounding soil (e.g. voids near pipe, soil erosion, non-symmetric loadings)

Spin susceptibilities, spin densities and their connection to spin-currents

We calculate the frequency dependent spin susceptibilities for a two-dimensional electron gas with both Rashba and Dresselhaus spin-orbit interaction. The resonances of the susceptibilities depends on the relative values of the Rashba and Dresselhaus spin-orbit constants, which could be manipulated by gate voltages. We derive exact continuity equations, with source terms, for the spin density and use those to connect the spin current to the spin density. In the free electron model the susceptibilities play a central role in the spin dynamics since both the spin density and the spin current are proportional to them.Comment: 6 pages, revtex4 styl

Human Activity Mediates a Trophic Cascade Caused by Wolves

Experimental evidence of trophic cascades initiated by large vertebrate predators is rare in terrestrial ecosystems. A serendipitous natural experiment provided an opportunity to test the trophic cascade hypothesis for wolves (Canis lupus) in Banff National Park, Canada. The first wolf pack recolonized the Bow Valley of Banff National Park in 1986. High human activity partially excluded wolves from one area of the Bow Valley (low-wolf area), whereas wolves made full use of an adjacent area (high-wolf area). We investigated the effects of differential wolf predation between these two areas on elk (Cervus elaphus) population density, adult female survival, and calf recruitment; aspen (Populus tremuloides) recruitment and browse intensity; willow (Salix spp.) production, browsing intensity, and net growth; beaver (Castor canadensis) density; and riparian songbird diversity, evenness, and abundance. We compared effects of recolonizing wolves on these response variables using the log response ratio between the low-wolf and high-wolf treatments. Elk population density diverged over time in the two treatments, such that elk were an order of magnitude more numerous in the low-wolf area compared to the high-wolf area at the end of the study. Annual survival of adult female elk was 62% in the high-wolf area vs. 89% in the low-wolf area. Annual recruitment of calves was 15% in the high-wolf area vs. 27% without wolves. Wolf exclusion decreased aspen recruitment, willow production, and increased willow and aspen browsing intensity. Beaver lodge density was negatively correlated to elk density, and elk herbivory had an indirect negative effect on riparian songbird diversity and abundance. These alternating patterns across trophic levels support the wolf-caused trophic cascade hypothesis. Human activity strongly mediated these cascade effects, through a depressing effect on habitat use by wolves. Thus, conservation strategies based on the trophic importance of large carnivores have increased support in terrestrial ecosystems. Read More: http://www.esajournals.org/doi/full/10.1890/04-126

Social Security Research at the University of Michigan Retirement and Disability Research Center

In 1998, the Social Security Administration established the Retirement Research Consortium to encourage research on topics related to Social Security and the well-being of older Americans, and to foster communication between the academic and policy communities. The Michigan Retirement Research Center (MRRC) participated in the Consortium from its inception until 2019, when the MRRC expanded and became the Michigan Retirement and Disability Research Center. This article surveys a selection of the MRRC’s output over its second 10 years (2008–2017), summarizes its innovative use of new data sources, and highlights several key themes in the center’s research contributions

Superposition as a logical glue

The typical mathematical language systematically exploits notational and logical abuses whose resolution requires not just the knowledge of domain specific notation and conventions, but not trivial skills in the given mathematical discipline. A large part of this background knowledge is expressed in form of equalities and isomorphisms, allowing mathematicians to freely move between different incarnations of the same entity without even mentioning the transformation. Providing ITP-systems with similar capabilities seems to be a major way to improve their intelligence, and to ease the communication between the user and the machine. The present paper discusses our experience of integration of a superposition calculus within the Matita interactive prover, providing in particular a very flexible, "smart" application tactic, and a simple, innovative approach to automation.Comment: In Proceedings TYPES 2009, arXiv:1103.311

GRUNGE: A Grand Unified ATP Challenge

This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms. The formalisms are in higher-order logic (with and without type variables) and first-order logic (possibly with multiple types, and possibly with type variables). The resultant problem sets allow us to run automated theorem provers that support different logical formats on corresponding problems, and compare their performances. This also results in a new "grand unified" large theory benchmark that emulates the ITP/ATP hammer setting, where systems and metasystems can use multiple ATP formalisms in complementary ways, and jointly learn from the accumulated knowledge.Comment: CADE 27 -- 27th International Conference on Automated Deductio

Weather and our food supply

The steep rate of increase in yield of grain crops in the United States since the mid-1950\u27s has resulted in the use of the term explosion in technology. Surplus grains piled up to such proportions after the 1960 · harvest that acreage control appeared. to be in order. But despite substantial reductions in acreages after 1960 the increased output per acre has just about compensated for acreage reductions. During this period of rapid increase in output per acre there has been a growing tendency to believe that technology has reduced the influence of weather on grain production so that we no longer need to fear shortages due to unfavorable weather. There is also a popular belief that acreage control$ fail to achieve the objective of production control, and that public funds are being wasted in storing surplus grains which we don\u27t need. There is increasing evidence, however, that a period of favorable weather interacted with technology to produce our recent high yields, and that perhaps half of the increase in yield per acre since 1950 has been due to a change to more favorable weather for grain crops. These findings have important implications in continued support for research in production technology and in the way in which we look at our surplus stocks of feed and food grains. If a period of favorable weather has been responsible for half of the increase in yields since 19501 then what can we expect if the weather trend reverses itself for a few years? Do we have periodicity in weather, and have we just passed through a run of favorable years that might be followed by a run of unfavorable years? Should we treat our surplus grains as reserves? How does our rate of growth in grain output compare with the needs of a growing world population? And of course I in the background of these questions is one big question -- how much of our recent high yields is really due to weather? To answer these important questions the Center for Agriculture and Economic Development invited outstanding authorities to present their ideas under three main headings: (1) Techniques for Evaluation of Weather Variables in Agricultural Production I (2) Periodicity in Weather Patterns: Implications in Agriculture I and (3) Weather Considerations in Agricultural Policy. The papers have been assembled in the order of their presentation under the general outline above.https://lib.dr.iastate.edu/card_reports/1021/thumbnail.jp

Model exploration and analysis for quantitative safety refinement in probabilistic B

The role played by counterexamples in standard system analysis is well known; but less common is a notion of counterexample in probabilistic systems refinement. In this paper we extend previous work using counterexamples to inductive invariant properties of probabilistic systems, demonstrating how they can be used to extend the technique of bounded model checking-style analysis for the refinement of quantitative safety specifications in the probabilistic B language. In particular, we show how the method can be adapted to cope with refinements incorporating probabilistic loops. Finally, we demonstrate the technique on pB models summarising a one-step refinement of a randomised algorithm for finding the minimum cut of undirected graphs, and that for the dependability analysis of a controller design.Comment: In Proceedings Refine 2011, arXiv:1106.348

Reduced-Intensity Conditioning Allogeneic Hematopoietic Cell Transplantation for Patients with Hematologic Malignancies Who Relapse following Autologous Transplantation: A Multi-institutional Prospective Study from the Cancer and Leukemia Group B (CALGB trial 100002)

We prospectively treated 80 patients with relapse of malignancy or secondary myelodysplasia after autologous hematopoietic cell transplantation (AHCT) with allogeneic hematopoietic cell transplantation (allo-HCT) using a reduced-intensity conditioning (RIC) regimen of fludarabine 150 mg/m2 plus intravenous busulfan 6.4 mg/kg. Both sibling (MSD) and unrelated donors (MUD) were allowed. Patients transplanted from MUD donors received more intensive graft-versus-host disease (GVHD) prophylaxis, including rabbit anti-thymocyte globulin 10 mg/kg, mycophenolate mofetil, and an extended schedule of tacrolimus. With a median follow-up of 3.1 years (0.9 to 5.8), TRM at 6 months and 2 years was 8% and 23% respectively. Neither TRM nor the rates of acute GVHD were different in those with sibling or MUD donors. Donor CD3 cell chimerism > 90% at day +30 was achieved more often in patients with MUD than with MSD donors, 70% versus 23% (p<0.0001). Median EFS was higher in patients who achieved early full donor chimerism (14.2 versus 8 mo, p = 0.0395). Allo-HCT using this RIC regimen can be performed with low TRM in patients who have received a prior AHCT. Efforts to improve early donor CD3 chimerism may improve EFS