Modern Approaches to Exact Diagonalization and Selected Configuration Interaction with the Adaptive Sampling CI Method.

Recent advances in selected configuration interaction methods have made them competitive with the most accurate techniques available and, hence, creating an increasingly powerful tool for solving quantum Hamiltonians. In this work, we build on recent advances from the adaptive sampling configuration interaction (ASCI) algorithm. We show that a useful paradigm for generating efficient selected CI/exact diagonalization algorithms is driven by fast sorting algorithms, much in the same way iterative diagonalization is based on the paradigm of matrix vector multiplication. We present several new algorithms for all parts of performing a selected CI, which includes new ASCI search, dynamic bit masking, fast orbital rotations, fast diagonal matrix elements, and residue arrays. The ASCI search algorithm can be used in several different modes, which includes an integral driven search and a coefficient driven search. The algorithms presented here are fast and scalable, and we find that because they are built on fast sorting algorithms they are more efficient than all other approaches we considered. After introducing these techniques, we present ASCI results applied to a large range of systems and basis sets to demonstrate the types of simulations that can be practically treated at the full-CI level with modern methods and hardware, presenting double- and triple-ζ benchmark data for the G1 data set. The largest of these calculations is Si2H6 which is a simulation of 34 electrons in 152 orbitals. We also present some preliminary results for fast deterministic perturbation theory simulations that use hash functions to maintain high efficiency for treating large basis sets

Generation, Ranking and Unranking of Ordered Trees with Degree Bounds

We study the problem of generating, ranking and unranking of unlabeled ordered trees whose nodes have maximum degree of $\Delta$. This class of trees represents a generalization of chemical trees. A chemical tree is an unlabeled tree in which no node has degree greater than 4. By allowing up to $\Delta$ children for each node of chemical tree instead of 4, we will have a generalization of chemical trees. Here, we introduce a new encoding over an alphabet of size 4 for representing unlabeled ordered trees with maximum degree of $\Delta$. We use this encoding for generating these trees in A-order with constant average time and O(n) worst case time. Due to the given encoding, with a precomputation of size and time O(n^2) (assuming $\Delta$ is constant), both ranking and unranking algorithms are also designed taking O(n) and O(nlogn) time complexities.Comment: In Proceedings DCM 2015, arXiv:1603.0053

Protein docking refinement by convex underestimation in the low-dimensional subspace of encounter complexes

We propose a novel stochastic global optimization algorithm with applications to the refinement stage of protein docking prediction methods. Our approach can process conformations sampled from multiple clusters, each roughly corresponding to a different binding energy funnel. These clusters are obtained using a density-based clustering method. In each cluster, we identify a smooth “permissive” subspace which avoids high-energy barriers and then underestimate the binding energy function using general convex polynomials in this subspace. We use the underestimator to bias sampling towards its global minimum. Sampling and subspace underestimation are repeated several times and the conformations sampled at the last iteration form a refined ensemble. We report computational results on a comprehensive benchmark of 224 protein complexes, establishing that our refined ensemble significantly improves the quality of the conformations of the original set given to the algorithm. We also devise a method to enhance the ensemble from which near-native models are selected.Published versio

Results from the Farm Behaviour Component of the Integrated Economic-Hydrologic Model for the Watershed Evaluation of Beneficial Management Practices Program

This report summarizes preliminary results from the Farm Behavior component of the South Tobacco Creek Integrated Modeling Project (STC Project) which is being undertaken as part of the Watershed Evaluation of BMPs (WEBs) Program. WEBS is a partnership between Agriculture and Agri-Food Canada (AAFC) and Ducks Unlimited Canada (DUC) established to evaluate the economic and environmental performance of BMPs for water quality at the watershed scale. Water draining from South Tobacco Creek eventually enters to Lake Winnipeg which is degraded from the cumulative effects of nutrient loading, particularly phosphorous. Many jurisdictions across the world, including Canada, use payments programs to encourage land owners to change land management practices in order to reduce non-point source pollution. BMP incentive programs in Canada, such as Greencover, rely on fixed payment schemes which pay producers a set amount for BMPs, regardless of costs or benefits. In order to improve the performance of payment programs many jurisdictions have instituted auction type mechanisms. The purpose of the Farm Behavior component of the STC project is to examine the performance of various types of payment programs for BMPs relative to reducing phosphorous loads from STC. Theoretical and empirical evidence from conservation auctions suggest that the performance of auctions depends on several factors which affect the bidding behavior of producers during the auction, and therefore the cost-effectiveness of auctions over other types of payment programs. In particular, some producers actually benefit from BMPs, however under certain auction rules these producers would be paid the same amount as high cost producers; alternatively, producers with low costs of adopting BMPs may not always provide the greatest benefits in terms of pollution abatement depending on their location in the watershed, and physical features of their land. We assessed the relative performance of different payment programs by developing producer response functions for adoption of Beneficial Management Practices (BMPs). Producer adoption responses under different incentive schemes were tested using experiments with student subjects and limited trials with producers. We examined four BMPs: construction of holding ponds, riparian management, forage conversion, and conservation till. The results of the adoption response experiments conducted under WEBS were used to draw preliminary observations on BMP policy design and form the basis for recommendations for further research. The farm behavior project focuses on addressing the following two questions: 1. Does BMP adoption at a given farm make the individual farm household better or worse off from an economic perspective? 2. How much will it cost the government to get farms to adopt BMPs under different payment programs? Since producer heterogeneity is key to understanding the performance of conservation auctions, we examined the costs and benefits of BMPs at the individual farm level and developed on-farm costs for each BMP for each producer in the watershed. The basic components of the model are described below, however the details including underlying assumptions regarding baseline farm behavior, are outlined within the body of the report. We used the on-farm cost model to generate aggregate cost functions for BMPs for the watershed and to parameterize the policy experiments related to conservation auctions. Preliminary estimates of environmental benefits of individual BMP adoption were provided by Dr. Wanhong Yang using results from a SWAT model developed under a separate component of the South Tobacco Creek WEBS project. Based on this information, we were able to evaluate the performance of various auction formats in terms of cost effectiveness, distribution of payments amongst producers, and environmental benefit. The results from the Farm behavior component of the South Tobacco Creek project are preliminary, and are currently being refined. Therefore it is difficult to draw generalized conclusions at this point. Further experiments are being conducted to complete the data collection during FY 08-09 through Interim WEBS funding. Nonetheless main findings to date are summarized below: 1. The four BMPs assessed differ in terms of their cost as well as their ability to deliver environmental benefits. Unfortunately, there is no BMP that dominates across farms at all abatement levels. Farms have heterogeneous costs in terms of BMPs, and some farms are cost effective at supplying abatement using one BMP, but not another. 2. This suggests that if water quality benefits (e.g. phosphorous reduction) can be quantified through modeling by BMP and by farm, then water quality should be the contracting unit for the auction rather than the BMP. This would allow producers to select the most cost effective BMP for supplying water quality benefits, and then decision makers could allocate contracts based on ranking the costs of abatement. 3. At the next stage of the research we will test for synergies between farms – ie., whether the joint production function for water quality between farms differs from the sum of individual production functions. This will have implications for how the payment scheme should be designed. 4. Incorporating „fairness‟ types of allocation rules for conservation dollars, such as maximum participation in conservation programs is inefficient in terms of cost and environmental benefits. If fairness, or using conservation payments as a form of extension to learn about on farm costs of BMPs is the goal of the auction, then fixed payment programs which are open to everyone may be more desirable. 5. The performance of the auction depends on the shape of the cost function for BMPs and/or pollution abatement, as well as whether uniform (pay everyone the highest bid) or discriminatory pricing (pay everyone their own bid) rules are applied. In future research we will be investigating to what extent we can generalize results about the performance of uniform versus discriminatory pricing rules in this context. In conclusion, this research has allowed us to investigate individually the performance of incentive payments for individual BMPs. The results of the analysis provide us with a baseline of information by which we can begin to assess more complex conservation program issues, such as how to optimally select multiple BMPs within the watershed, and whether/how to spatially target BMPs.watersheds, South Tobacco Creek, water quality, Environmental Economics and Policy, Land Economics/Use, Resource /Energy Economics and Policy, Q12,Q52,D44,

Tamari Lattices and the symmetric Thompson monoid

We investigate the connection between Tamari lattices and the Thompson group F, summarized in the fact that F is a group of fractions for a certain monoid F+sym whose Cayley graph includes all Tamari lattices. Under this correspondence, the Tamari lattice operations are the counterparts of the least common multiple and greatest common divisor operations in F+sym. As an application, we show that, for every n, there exists a length l chain in the nth Tamari lattice whose endpoints are at distance at most 12l/n.Comment: 35page

Forest rotation lengths under carbon sequestration payments

Carbon dioxide emissions resulting from direct human activities, primarily fossil fuel use and land clearing, have altered the global carbon cycle. Carbon is absorbed (sequestered) by plant matter during photosynthesis, so that approximately 50% of the dry weight of a forest’s biomass is carbon. This paper examines how payments to foresters for the carbon sequestered in their trees would affect harvesting decisions. It uses a theoretical multi-crop model adapted from the original Faustmann formula to consider different scenarios of the degree of carbon liability incurred at the time of harvest, and their impact on the length of the optimal crop rotation. These results are then contrasted with the equivalent output from a numerical model based on a simulated New South Wales Pinus radiata plantation. The finding of the paper provides an insight into which carbon sequestration payment policy would be the best at aligning public and private incentives.carbon sequestration