Geometry of contours and Peierls estimates in d=1 Ising models

Following Fr\"ohlich and Spencer, we study one dimensional Ising spin systems with ferromagnetic, long range interactions which decay as $|x-y|^{-2+\alpha}$, $0\leq \alpha\leq 1/2$. We introduce a geometric description of the spin configurations in terms of triangles which play the role of contours and for which we establish Peierls bounds. This in particular yields a direct proof of the well known result by Dyson about phase transitions at low temperatures.Comment: 28 pages, 3 figure

Detection of variations in aspen forest habitat from LANDSAT digital data: Bear River Range, Utah

The aspen forests of the Bear River Range were analyzed and mapped using data recorded on July 2, 1979 by the LANDSAT III satellite; study efforts yielded sixty-seven light signatures for the study area, of which three groups were identified as aspen and mapped at a scale of 1:24,000. Analysis and verification of the three groups were accomplished by random location of twenty-six field study plots within the LANDSAT-defined aspen areas. All study plots are included within the Cache portion of the Wasatch-Cache National Forest. The following selected site characteristics were recorded for each study plot: a list of understory species present; average percent cover density for understory species; aspen canopy cover estimates and stem measurements; and general site topographic characteristics. The study plot data were then analyzed with respect to corresponding Landsat spectral signatures. Field studies show that all twenty-six study plots are associated with one of the three aspen groups. Further study efforts concentration on characterizing the differences between the site characteristics of plots falling into each of the three aspen groups

Detection of aspen/conifer forest mixes from multitemporal LANDSAT digital data

Aspen, conifer and mixed aspen/conifer forests were mapped for a 15-quadrangle study area in the Utah-Idaho Bear River Range using LANDSAT multispectral scanner (MSS) data. The digital MSS data were utilized to devise quantitative indices which correlate with apparently stable and seral aspen forests. The extent to which a two-date LANDSAT MSS analysis may permit the delineation of different categories of aspen/conifer forest mix was explored. Multitemporal analyses of MSS data led to the identification of early, early to mid, mid to late, and late seral stages of aspen/conifer forest mixing

Cyclic cycle systems of the complete multipartite graph

In this paper, we study the existence problem for cyclic $\ell$-cycle decompositions of the graph $K_m[n]$, the complete multipartite graph with $m$ parts of size $n$, and give necessary and sufficient conditions for their existence in the case that $2\ell \mid (m-1)n$

Detecting agricultural to urban land use change from multi-temporal MSS digital data

Conversion of agricultural land to a variety of urban uses is a major problem along the Wasatch Front, Utah. Although LANDSAT MSS data is a relatively coarse tool for discriminating categories of change in urban-size plots, its availability prompts a thorough test of its power to detect change. The procedures being applied to a test area in Salt Lake County, Utah, where the land conversion problem is acute are presented. The identity of land uses before and after conversion was determined and digital procedures for doing so were compared. Several algorithms were compared, utilizing both raw data and preprocessed data. Verification of results involved high quality color infrared photography and field observation. Two data sets were digitally registered, specific change categories internally identified in the software, results tabulated by computer, and change maps printed at 1:24,000 scale

An integrated LANDSAT/ancillary data classification of desert rangeland

Range inventorying methods using LANDSAT MSS data, coupled with ancillary data were examined. The study area encompassed nearly 20,000 acres in Rush Valley, Utah. The vegetation is predominately desert shrub and annual grasses, with some annual forbs. Three LANDSAT scenes were evaluated using a Kauth-Thomas brightness/greenness data transformation (May, June, and August dates). The data was classified using a four-band maximum-likelihood classifier. A print map was taken into the field to determine the relationship between print symbols and vegetation. It was determined that classification confusion could be greatly reduced by incorporating geomorphic units and soil texture (coarse vs fine) into the classification. Spectral data, geomorphic units, and soil texture were combined in a GIS format to produce a final vegetation map identifying 12 vegetation types

Deep learning-based parameter mapping for joint relaxation and diffusion tensor MR Fingerprinting

Magnetic Resonance Fingerprinting (MRF) enables the simultaneous quantification of multiple properties of biological tissues. It relies on a pseudo-random acquisition and the matching of acquired signal evolutions to a precomputed dictionary. However, the dictionary is not scalable to higher-parametric spaces, limiting MRF to the simultaneous mapping of only a small number of parameters (proton density, T1 and T2 in general). Inspired by diffusion-weighted SSFP imaging, we present a proof-of-concept of a novel MRF sequence with embedded diffusion-encoding gradients along all three axes to efficiently encode orientational diffusion and T1 and T2 relaxation. We take advantage of a convolutional neural network (CNN) to reconstruct multiple quantitative maps from this single, highly undersampled acquisition. We bypass expensive dictionary matching by learning the implicit physical relationships between the spatiotemporal MRF data and the T1, T2 and diffusion tensor parameters. The predicted parameter maps and the derived scalar diffusion metrics agree well with state-of-the-art reference protocols. Orientational diffusion information is captured as seen from the estimated primary diffusion directions. In addition to this, the joint acquisition and reconstruction framework proves capable of preserving tissue abnormalities in multiple sclerosis lesions