Huffman’s algorithm is a procedure for constructing a binary tree with minimum weighted path length. This report presents a formal proof of the correctness of Huffman’s algorithm written using Isabelle/HOL. Our proof closely follows the sketches found in standard algorithms textbooks, uncovering a few snags in the process. Another distinguishing feature of our formalization is the use of custom...

We identified 162 roosts for 36 male Indiana bats (Myotis sodalis) across 3 study areas in the Ozarks of northern Arkansas, USA, during the autumn swarm (late Aug to late Oct, 2005 and 2006). Bats utilized 14 tree species; snags of shortleaf pine (Pinus echinata) were the most utilized (30% of roosts) and pines were selected over hardwoods. Diameter of trees and snags used for roosting ranged f...

--The habitat requirements of open nesting birds were examined in 19, five hectare, plots arranged along an altitudinal gradient in western Montana. Seven, mature forest birds were examined in detai 1. Percent shrub and low canopy cover {0.5-1.5m), mid-canopy cover {8-25m), and the number of large diameter stems {25-50 em dbh) were of major importance to this avian co11111unity. Increased avian...

The Mulligan concept encompasses a number of mobilising treatment techniques that can be applied to the spine, these include 'NAGs' (natural apophyseal glides), 'SNAGs' (sustained natural apophyseal glides), and 'SMWLMs' (spinal mobilisations with limb movements). These techniques are described and the general principles of examination and treatment are outlined. Clinical examples are used to i...

in this paper, we propose a new approach for ranking all fuzzynumbers based on revising the ranking method proposed by ezzati et al. cite{ezzati}.to this end, we present and investigate some properties of the proposed approach indetails. finally, to illustrate the advantage of the proposed method, it is applied to several groups of fuzzy numbers and the results are compared with other related a...

In the Pacific Northwest of United States, 20th century timber harvesting resulted in major declines area forests supporting large live and dead trees (i.e., snags), that are not only key habitat elements for many wildlife species but also critical components ecosystem function. Regional forest management guidance, such as Forest Plan (1994) Eastside Screens (1995), may aim to conserve foster d...