A Spectral Approach to Consecutive Pattern-Avoiding Permutations

We consider the problem of enumerating permutations in the symmetric group on $n$ elements which avoid a given set of consecutive pattern $S$, and in particular computing asymptotics as $n$ tends to infinity. We develop a general method which solves this enumeration problem using the spectral theory of integral operators on $L^{2}([0,1]^{m})$, where the patterns in $S$ has length $m+1$. Kre\u{\i}n and Rutman's generalization of the Perron--Frobenius theory of non-negative matrices plays a central role. Our methods give detailed asymptotic expansions and allow for explicit computation of leading terms in many cases. As a corollary to our results, we settle a conjecture of Warlimont on asymptotics for the number of permutations avoiding a consecutive pattern.Comment: a reference is added; corrected typos; to appear in Journal of Combinatoric

A Builder's Guide to Water and Energy

The work on which this report is based was supported in part by funds provided by the Office of Water Research and Technology (Project A-Q65-ALAS), US. Department of the interior, Washington, D.C., as authorized by the Water Research and Development Act of 1978

An Experimental Investigation of Alternative Wave Attenuation Mechanisms for a Modular Breakwater

Global warming and sea level rise threaten to render traditional coastal protection structures as less effective. Floating breakwaters offer the advantages of adapting to rising sea level, allowing important material transport to occur, and being able to deploy and adapt to varying environmental conditions (seabed, depth, etc.). Traditional floating breakwaters typically consist of reflective concrete structures that are limited semi-sheltered locations. This research aimed to construct floating breakwaters out of lightweight materials with a smaller footprint while utilizing alternative attenuation mechanisms. Three breakwaters consisting of a box, beach, and pipe designs were constructed at 1:40 scale and tested in a Wind and Wave Basin located in the Advanced Structures and Composites Center at the University of Maine. All three were designed to be constructed of lightweight composite sandwich material as opposed to concrete. The pipe breakwater was designed to utilize drag and vortex shedding as wave attenuation mechanisms, while the beach was designed to utilize wave breaking to induce turbulence. The target operation environment for the breakwaters was a period of 3-6 s, and within this range, the beach breakwater was able to attenuate 50% of the energy up to a period of 5.5 s. This was comparable to the box, which attenuated 50% of the energy up to a period of 7.5 s. The beach was able to utilize an alternative to reflection to attenuate wave energy, with greater than 50% of the attenuation coming from dissipation. The beach also had the advantage of being half the full-scale width of the box, 8.56 m wide compared to 16.9 m for the box. The overall weight of the full scale box breakwater constructed from composite sandwich materials was 88% less (200 metric tons vs 1548 metric tons) than the same design made of conventional concrete. This work demonstrates the possibility to reduce the size, weight, and attenuation mechanism of a breakwater, while maintaining its overall effectiveness

Dissatisfaction theory and superintendent turnover: An exception to the rule

The cycle of change and superintendent replacement in a public school district was documented and later named Dissatisfaction Theory by Iannaccone and Lutz (1970). Since then there have been multiple studies that have further documented failed relationships between the values of the community, the school board, and the superintendent. The research has demonstrated that dissatisfied voters replace school board members who in turn replace the superintendent with someone who will reflect the ideology and policies desired by the community. The purposes of this study were to a) Better understand the dynamics of the position of superintendent, b) Inform superintendents, school boards and community members to extend their knowledge, and c) Advance the knowledge of Dissatisfaction Theory. The purposes were accomplished by investigating events that occurred in a single school and community. In that community, incumbent school board members were replaced during several periods of politicization. The propositions of Dissatisfaction Theory predicted that the school board would have replaced the superintendent but they did not, and instead the superintendent retained his position until retirement. The conceptual framework of Dissatisfaction Theory developed by Iannaccone and his student Lutz, based upon the writings of Mosca, Michaels, and Key, prompted the researcher to consider exploring further a situation that appeared to be an exception to the theory. The study utilized a research methodology based upon the perspective of the interpretivist paradigm. The Parson and Thompson conceptual model for the study of an organization; institutional leadership activities, managerial activities, and technical activities were considered to examine and make sense of the data. The multiple eras of the Portage area; beginning with the Potawatomi Indians through the retirement of the Superintendent in 2002, were investigated and described. The earlier eras were used to better understand the final era, when the exception to the rule seemed to occur. Data analysis of primary and secondary source documents, interviews, and participant observations indicated that the area was dominated by two primary groups, the Yankees who arrived first and later the Dutch who together formed the dominant culture. As the area grew, it changed but still retained a strong presence of the Yankees and Dutch. The agricultural economy changed to a community of professionals that expected an educational system that provided elite academic, athletic, and fine arts programs. The research concluded that Dissatisfaction Theory did hold in Portage but that it was delayed through a skilled superintendent who employed a variety of tactics to manage conflict at all organizational levels and by the lack of action by the board. The research also concluded that dissatisfaction occurs at all levels of the organization -- institutional, managerial, and activity -- and that all contribute to the removal of the superintendent. Finally, the study concluded that if a board fails to act, powerful community members will eventually come forward to force their values on the superintendent

Commentary on Professor Sutton's paper

The author provides commentary on Professor Sutton's paper presented in the symposium on Family Property, Law and Policy found in this issue of the Victoria University of Wellington Law Review (RJ Sutton "Law Commission succession project: Communal family property?" (1995) 25 VUWLR 53). The commentary comes from discussions with a group of six practitioners drawn from both family law litigators and property lawyers interested in family property matters. The article first discusses how the concept of communal property can earn legitimacy. The author then agrees with Professor Sutton in that New Zealand does not have a dynastic approach to property, as well as noting the broader definition of "family" adopted in New Zealand. The author believes that, increasingly, there will be a trend that the larger part of the wealth of more substantial testators will not find its way into the probated estate of that testator. It is concluded that the concept of communal family property is a useful analytical technique in consideration of new succession law regimes, but would caution against a reform structure which is driven by desire for pure application of this philosophy

Volumetric Muscle Loss: The Role of Physical Activity and Autologous Repair on Force Recovery and Signaling Pathways

Volumetric muscle loss affects both military and civilian persons. The hallmark of this injury is incomplete muscle regeneration, excessive fibrosis, and chronic inflammatory signaling resulting in permanent functional loss. Since permanent functional loss drastically reduces quality of life, many studies have been conducted to improve force recovery. Current scientific literature considers a repair strategy of either devitalized scaffolds infused with growth factors or viable tissue plus activating factors to be the more promising interventions for optimal force recovery. PURPOSE The purpose of this study is to incorporate autologous repair and physical activity and observe the effects of muscle force recovery and regeneration, fibrosis, and inflammatory signaling. METHODS 32 male Sprague-Dawley rats had 20% of their LTA removed then replaced to act as autologous repair. Half of the rats utilized wheel running, and at 2 and 8 weeks, the autologous tissue was excised from the LTA from both wheel running and sedentary rats. Electrophysiology measured peak tetanic force. Histology was used to measure CSA, centrally-located nuclei, percent of non-contractile tissue, and collagen deposition. qRT-PCR evaluated the gene expression of myogenic, ECM remodeling, and inflammatory signaling markers. RESULTS Wheel activity promoted force recovery at 2 weeks, but both groups had similar force output by 8 weeks. Myogenic gene expression did not differ in the LTA between groups at either time point. Wheel activity caused differential effects of collagen deposition in the defect and intact LTA tissue. Wheel activity differentially altered ECM remodeling markers at the 2 and 8 week time points in the wheel activity and sedentary groups. Wheel activity appeared to attenuate inflammatory signaling markers at 2 weeks, but showed evidence of a pro-inflammatory environment by 8 weeks. DISCUSSION Wheel activity promoted early beneficial responses in force recovery, ECM remodeling, and inflammatory signaling markers. These responses were not evident by 8 weeks, however, the same early patterns of these markers were observed at 8 weeks in the sedentary group. Force recovery equalizes by 8 weeks with autologous repair but is expedited using wheel activity