Transfer Matrices for the Partition Function of the Potts Model on Toroidal Lattice Strips

We present a method for calculating transfer matrices for the $q$-state Potts model partition functions $Z(G,q,v)$, for arbitrary $q$ and temperature variable $v$, on strip graphs $G$ of the square (sq), triangular (tri), and honeycomb (hc) lattices of width $L_y$ vertices and of arbitrarily great length $L_x$ vertices, subject to toroidal and Klein bottle boundary conditions. For the toroidal case we express the partition function as $Z(\Lambda, L_y \times L_x,q,v) = \sum_{d=0}^{L_y} \sum_j b_j^{(d)} (\lambda_{Z,\Lambda,L_y,d,j})^m$, where $\Lambda$ denotes lattice type, $b_j^{(d)}$ are specified polynomials of degree $d$ in $q$, $\lambda_{Z,\Lambda,L_y,d,j}$ are eigenvalues of the transfer matrix $T_{Z,\Lambda,L_y,d}$ in the degree-$d$ subspace, and $m=L_x$ ($L_x/2$) for $\Lambda=sq, tri (hc)$, respectively. An analogous formula is given for Klein bottle strips. We exhibit a method for calculating $T_{Z,\Lambda,L_y,d}$ for arbitrary $L_y$. In particular, we find some very simple formulas for the determinant $det(T_{Z,\Lambda,L_y,d})$, and trace $Tr(T_{Z,\Lambda,L_y})$. Corresponding results are given for the equivalent Tutte polynomials for these lattice strips and illustrative examples are included.Comment: 52 pages, latex, 10 figure

Steroid induced osteonecrosis: An analysis of steroid dosing risk.

Osteonecrosis is a serious condition involving bone destruction that frequently requires surgical treatment to rebuild the joint. While there is an abundance of literature documenting corticosteroid related osteonecrosis, there is no consensus as to the relative risk of osteonecrosis after administration of steroids via parenteral, oral, topical, inhaled and other routes. This risk is an important prognostic indicator because identification and conservative intervention can potentially reduce morbidity associated with aggressive surgical treatment of osteonecrosis. This paper provides insight into establishing guidelines related to the risk of developing osteonecrosis as a result of corticosteroid use. Case studies, retrospective studies and prospective studies in humans on different corticosteroids and varied dosages were assessed. Most cases of osteonecrosis are secondary to systemically administered corticosteroids and/or high dose daily therapy, particularly in patients with underlying comorbidities including connective tissue diseases, hyperlipidemia, or previous trauma. Previous case reports of osteonecrosis related to inhaled or topical use of steroids are complicated by the fact that in the great majority of cases, the patients are also treated with systemic steroids prior to the development of osteonecrosis. Based on the literature, a set of recommendations regarding the risk of osteonecrosis in patients on steroids was formulated

A cyberciege traffic analysis extension for teaching network security

CyberCIEGE is an interactive game simulating realistic scenarios that teaches the players Information Assurance (IA) concepts. The existing game scenarios only provide a high-level abstraction of the networked environment, e.g., nodes do not have Internet protocol (IP) addresses or belong to proper subnets, and there is no packet-level network simulation. This research explored endowing the game with network level traffic analysis, and implementing a game scenario to take advantage of this new capability. Traffic analysis is presented to players in a format similar to existing tools such that learned skills may be easily transferred to future real-world situations. A network traffic analysis tool simulation within CyberCIEGE was developed and this new tool provides the player with traffic analysis capability. Using existing taxonomies of cyber-attacks, the research identified a subset of network-based attacks most amenable to modeling and representation within CyberCIEGE. From the attacks identified, a complementary CyberCIEGE scenario was developed to provide the player with new educational opportunities for network analysis and threat identification. From the attack scenario, players also learn about the effects of these cyber-attacks and glean a more informed understanding of appropriate mitigation measures.http://archive.org/details/acyberciegetraff109451057

PC-CUBE: A Personal Computer Based Hypercube

PC-CUBE is an ensemble of IBM PCs or close compatibles connected in the hypercube topology with ordinary computer cables. Communication occurs at the rate of 115.2 K-band via the RS-232 serial links. Available for PC-CUBE is the Crystalline Operating System III (CrOS III), Mercury Operating System, CUBIX and PLOTIX which are parallel I/O and graphics libraries. A CrOS performance monitor was developed to facilitate the measurement of communication and computation time of a program and their effects on performance. Also available are CXLISP, a parallel version of the XLISP interpreter; GRAFIX, some graphics routines for the EGA and CGA; and a general execution profiler for determining execution time spent by program subroutines. PC-CUBE provides a programming environment similar to all hypercube systems running CrOS III, Mercury and CUBIX. In addition, every node (personal computer) has its own graphics display monitor and storage devices. These allow data to be displayed or stored at every processor, which has much instructional value and enables easier debugging of applications. Some application programs which are taken from the book Solving Problems on Concurrent Processors (Fox 88) were implemented with graphics enhancement on PC-CUBE. The applications range from solving the Mandelbrot set, Laplace equation, wave equation, long range force interaction, to WaTor, an ecological simulation

Potts Model Partition Functions for Self-Dual Families of Strip Graphs

We consider the $q$-state Potts model on families of self-dual strip graphs $G_D$ of the square lattice of width $L_y$ and arbitrarily great length $L_x$, with periodic longitudinal boundary conditions. The general partition function $Z$ and the T=0 antiferromagnetic special case $P$ (chromatic polynomial) have the respective forms $\sum_{j=1}^{N_{F,L_y,\lambda}} c_{F,L_y,j} (\lambda_{F,L_y,j})^{L_x}$, with $F=Z,P$. For arbitrary $L_y$, we determine (i) the general coefficient $c_{F,L_y,j}$ in terms of Chebyshev polynomials, (ii) the number $n_F(L_y,d)$ of terms with each type of coefficient, and (iii) the total number of terms $N_{F,L_y,\lambda}$. We point out interesting connections between the $n_Z(L_y,d)$ and Temperley-Lieb algebras, and between the $N_{F,L_y,\lambda}$ and enumerations of directed lattice animals. Exact calculations of $P$ are presented for $2 \le L_y \le 4$. In the limit of infinite length, we calculate the ground state degeneracy per site (exponent of the ground state entropy), $W(q)$. Generalizing $q$ from ${\mathbb Z}_+$ to ${\mathbb C}$, we determine the continuous locus ${\cal B}$ in the complex $q$ plane where $W(q)$ is singular. We find the interesting result that for all $L_y$ values considered, the maximal point at which ${\cal B}$ crosses the real $q$ axis, denoted $q_c$ is the same, and is equal to the value for the infinite square lattice, $q_c=3$. This is the first family of strip graphs of which we are aware that exhibits this type of universality of $q_c$.Comment: 36 pages, latex, three postscript figure

Accounting Ethics Education: A Comparison with Buddhist Ethics Education Framework

Accounting educators such as Mintz and Mele have argued about the importance of virtues in moral behavior. Mele presented a conceptual model of moral behavior that integrated professional rules of conduct, moral values, and moral virtues. Moral virtues are defined as “permanent attitudes and interior strength for moral behavior.” A major shortcoming of the Mele’s model is that the model does not provide any discussion on the methodologies facilitating the cultivation of virtues. This paper describes the framework and process of Buddhist ethics education and compares the similarities and differences of the Buddhist ethics education framework with the mainstream accounting ethics education framework. Compared with the mainstream ethics education model, the Buddhist ethics education framework appears to be comprehensive and systematic. In addition, to delineate the constituent factors that contribute to moral behavior, it renders several methodological discussions on how to cultivate moral sentiment, practical wisdom, and transitive and self-mastering virtues. Its systematic nature is exhibited by the line-up or formulation of necessary steps leading to the final achievement of moral behavior. Taken as a whole, the framework provides practitioners with practical guidance for what they need to work on sequentially or simultaneously in the moral development process. We sincerely hope that our discussion and comparison of the framework benefit accounting educators who are concerned with instilling long-term values and virtues into the lives of their students