A Mathematical Theory of Quantum Sheaf Cohomology

The purpose of this paper is to present a mathematical theory of the half-twisted $(0,2)$ gauged linear sigma model and its correlation functions that agrees with and extends results from physics. The theory is associated to a smooth projective toric variety $X$ and a deformation \sheaf E of its tangent bundle $T_X$. It gives a quantum deformation of the cohomology ring of the exterior algebra of \sheaf E^*. We prove that in the general case, the correlation functions are independent of `nonlinear' deformations. We derive quantum sheaf cohomology relations that correctly specialize to the ordinary quantum cohomology relations described by Batyrev in the special case \sheaf E = T_X

A General Approach for Predicting the Behavior of the Supreme Court of the United States

Building on developments in machine learning and prior work in the science of judicial prediction, we construct a model designed to predict the behavior of the Supreme Court of the United States in a generalized, out-of-sample context. To do so, we develop a time evolving random forest classifier which leverages some unique feature engineering to predict more than 240,000 justice votes and 28,000 cases outcomes over nearly two centuries (1816-2015). Using only data available prior to decision, our model outperforms null (baseline) models at both the justice and case level under both parametric and non-parametric tests. Over nearly two centuries, we achieve 70.2% accuracy at the case outcome level and 71.9% at the justice vote level. More recently, over the past century, we outperform an in-sample optimized null model by nearly 5%. Our performance is consistent with, and improves on the general level of prediction demonstrated by prior work; however, our model is distinctive because it can be applied out-of-sample to the entire past and future of the Court, not a single term. Our results represent an important advance for the science of quantitative legal prediction and portend a range of other potential applications.Comment: version 2.02; 18 pages, 5 figures. This paper is related to but distinct from arXiv:1407.6333, and the results herein supersede arXiv:1407.6333. Source code available at https://github.com/mjbommar/scotus-predict-v

Dietary Exposure to Pesticide Residues from Commodities Alleged to Contain the Highest Contamination Levels

Probabilistic techniques were used to characterize dietary exposure of consumers to pesticides found in twelve commodities implicated as having the greatest potential for pesticide residue contamination by a United States-based environmental advocacy group. Estimates of exposures were derived for the ten most frequently detected pesticide residues on each of the twelve commodities based upon residue findings from the United States Department of Agriculture's Pesticide Data Program. All pesticide exposure estimates were well below established chronic reference doses (RfDs). Only one of the 120 exposure estimates exceeded 1% of the RfD (methamidophos on bell peppers at 2% of the RfD), and only seven exposure estimates (5.8 percent) exceeded 0.1% of the RfD. Three quarters of the pesticide/commodity combinations demonstrated exposure estimates below 0.01% of the RfD (corresponding to exposures one million times below chronic No Observable Adverse Effect Levels from animal toxicology studies), and 40.8% had exposure estimates below 0.001% of the RfD. It is concluded that (1) exposures to the most commonly detected pesticides on the twelve commodities pose negligible risks to consumers, (2) substitution of organic forms of the twelve commodities for conventional forms does not result in any appreciable reduction of consumer risks, and (3) the methodology used by the environmental advocacy group to rank commodities with respect to pesticide risks lacks scientific credibility

Nestle

Nestlé has a worldwide presence in the food industry. In spite of its market strength associated with its well-known brands, the company has been experiencing declining overall sales for several years. This case describes Nestlé’s diversification strategy and business portfolio in depth, as well as its industry and major competitors. Solving the company’s problems is challenging because of complexity and dependence on so many external factors

Venous outflow of the leg: Anatomy and physiologic mechanism of the plantar venous plexus

AbstractPurpose: Mechanisms of venous outflow from the leg and foot have not been clearly defined. The purpose of this study was to evaluate the anatomy and physiologic mechanism of the plantar venous plexus and its impact on venous drainage from the tibial veins.Methods: Fifty phlebograms that contained complete foot and calf films were reviewed. On lateral films, the number of veins in the plantar venous plexus and its tibial outflow tract were counted. The length and diameter of the longest vein in the plantar venous system and the length of the foot arch were measured. The ratio of the length of the plantar venous plexus to the arch length was calculated. The presence or absence of valves within the plexus was recorded. Plantar venous plexus outflow was evaluated by an duplex ultrasonographic scan of the posterior tibial, anterior tibial, and peroneal veins during intermittent external pneumatic compression of the plantar surface of the foot.Results: The plantar venous plexus was composed of one to four large veins (mean, 2.7 veins) within the plantar aspect of the foot. The diameter of these veins was 4.0 ± 1.2 mm. The veins coursed diagonally from a lateral position in the forefoot to a medial position at the level of the ankle, spanning 75% of the foot arch. Prominent valves were recognized within the plantar veins in 22 of 50 patients. The plexus coalesced into an outflow tract of one to four veins (mean, 2.5 veins) that flowed exclusively into the posterior tibial venous system. Small accessory veins that drained the plantar surface of the forefoot flowed into either the posterior tibial or peroneal veins. This pattern of selective drainage of the plantar venous plexus was confirmed by duplex imaging. Mechanical compression of the plantar venous plexus produced a mean peak velocity in the posterior tibial veins of 123 ± 71 cm/sec, in the anterior tibial veins of 24 ± 14 cm/sec, and in the peroneal veins of 29 ± 26 cm/sec.Conclusions: The plantar venous plexus is composed of multiple large-diameter veins that span the arch of the foot. Compression of the plantar venous plexus, such as that which occurs during ambulation, is capable of significantly increasing flow through the posterior tibial venous system into the popliteal vein. Its function may be integral to venous outflow from the calf and priming of the more proximal calf muscle pump. (J Vasc Surg 1996;24:819-24.

A-twisted heterotic Landau-Ginzburg models

In this paper, we apply the methods developed in recent work for constructing A-twisted (2,2) Landau-Ginzburg models to analogous (0,2) models. In particular, we study (0,2) Landau-Ginzburg models on topologically non-trivial spaces away from large-radius limits, where one expects to find correlation function contributions akin to (2,2) curve corrections. Such heterotic theories admit A- and B-model twists, and exhibit a duality that simultaneously exchanges the twists and dualizes the gauge bundle. We explore how this duality operates in heterotic Landau-Ginzburg models, as well as other properties of these theories, using examples which RG flow to heterotic nonlinear sigma models as checks on our methods.Comment: 31 pages, LaTe

A-twisted Landau-Ginzburg models

In this paper we discuss correlation functions in certain A-twisted Landau-Ginzburg models. Although B-twisted Landau-Ginzburg models have been discussed extensively in the literature, virtually no work has been done on A-twisted theories. In particular, we study examples of Landau-Ginzburg models over topologically nontrivial spaces - not just vector spaces - away from large-radius limits, so that one expects nontrivial curve corrections. By studying examples of Landau-Ginzburg models in the same universality class as nonlinear sigma models on nontrivial Calabi-Yaus, we obtain nontrivial tests of our methods as well as a physical realization of some simple examples of virtual fundamental class computations.Comment: 64 Pages, LaTe