Tensor renormalization group approach to 2D classical lattice models

We describe a simple real space renormalization group technique for two dimensional classical lattice models. The approach is similar in spirit to block spin methods, but at the same time it is fundamentally based on the theory of quantum entanglement. In this sense, the technique can be thought of as a classical analogue of DMRG. We demonstrate the method - which we call the tensor renormalization group method - by computing the magnetization of the triangular lattice Ising model.Comment: 4 pages, 7 figure

Non-Perturbative Processes In Standard Model \& New Physics: From Standard Calculations To Machine Learning

I calculated non-perturbative processes to study the Standard Model and probe areas of new physics. I found that invisible decays of heavy mesons are not dominated by the leading order contribution in the Standard Model. I argue that this affects neutrino mass constraints and avenues for discovering new physics, such as dark photons. In addition to this, I used a novel approach to approximate a semileptonic form factor with an artificial neural network (ANN). Comparing the results from the ANN to common phenomenological parameterizations, and using it to set a lower bound constraint on the CKM matrix element, $V_{cd}$. Finally, I studied lepton flavor violating processes in electron-positron collisions. I argue that if the new physics scale is above 1 TeV, then the SM background for this process is incredibly tiny, and the discovery of new physics is highly probable. However, there is currently no experimental sensitivity for this process. In most of my works, more precise experimental measurements are required to determine the existence of new physics

Estimating Landscape Quality And Genetic Structure Of Recovering American Marten Populations In The Northeastern United States

The American marten (Martes americana) is an endangered species in Vermont and a Regional Species of Greatest Conservation Need in the northeastern United States. Though historically widespread in northeastern forests, their range presumably contracted to northern Maine and the High Peaks region of the Adirondacks by the early 1900s. Regionally, populations appear to be in recovery. Natural recolonization is believed to have occurred in New Hampshire, northeastern Vermont and the western Adirondacks. A reintroduction effort in southern Vermont that was originally declared unsuccessful is now believed to be the source of a recently detected population in the area. However, our current knowledge of distribution, population history and population connectivity relies primarily on occurrence data from harvest records, which are limited in scope and resolution. In Vermont, where population size is estimated to be extremely low, more robust estimates of population status may be critical to continued recovery. I genotyped individuals from Maine, New York, New Hampshire, northeastern Vermont and southern Vermont at ten microsatellite loci and amplified a 320 base pair segment of the control region of mtDNA to estimate the source(s) of the two Vermont populations using statistical tests of genetic differentiation. I also used Bayesian and stochastic genetic clustering methods to estimate population genetic structure in the northeastern United States. Genetic structure exists at multiple scales in the region as a result of natural barriers to gene flow, human-mediated gene flow, and lineage sorting in relic populations. My results suggest that New Hampshire is a major source of colonization of northeastern Vermont and the population in southern Vermont is either a remnant of the reintroduction or a pre-reintroduction relic that has experienced introgression from the reintroduction stock. I identified three regions where relic populations perceived to be extirpated in the 1900s may have persisted. I also developed an occupancy model for American marten in the northeastern United States using mixed-effects logistic regression based on expert opinion data. Eighteen experts from Maine, New Hampshire, Vermont and New York with backgrounds in trapping, wildlife management, and wildlife science participated in the survey. Experts were asked to estimate the probability of marten occupancy at 30 sites in the northeastern United States. Three top models described the data. Habitat covariates in those models were 1) percent canopy cover, 2) percent spruce-fir forest cover, 3) winter temperature, 4) elevation, and 5) road density. An AIC-weighted average of these three models had significant predictive ability (area under an ROC curve = 0.88) with respect to occurrence records in the northeastern United States. In addition, the model predicted that high quality habitat existed patchily along the central and northern Green Mountain spine in Vermont – where no occurrence records exist for at least a century. Top-scoring movement corridors between southern Vermont and nearby populations in northeastern Vermont/New Hampshire and New York occurred in the northern and central Green Mountains and across high resistance movement barriers in the Champlain valley. Corridors to New York were considered strong movement barriers and are unlikely to facilitate gene flow

Assessing the Rationality of Farmland Price Movements

Replaced with revised version of poster 06/03/11.Agricultural Finance, Farm Management,