Graph-Facilitated Resonant Mode Counting in Stochastic Interaction Networks

Oscillations in a stochastic dynamical system, whose deterministic counterpart has a stable steady state, are a widely reported phenomenon. Traditional methods of finding parameter regimes for stochastically-driven resonances are, however, cumbersome for any but the smallest networks. In this letter we show by example of the Brusselator how to use real root counting algorithms and graph theoretic tools to efficiently determine the number of resonant modes and parameter ranges for stochastic oscillations. We argue that stochastic resonance is a network property by showing that resonant modes only depend on the squared Jacobian matrix $J^2$ , unlike deterministic oscillations which are determined by $J$. By using graph theoretic tools, analysis of stochastic behaviour for larger networks is simplified and chemical reaction networks with multiple resonant modes can be identified easily.Comment: 5 pages, 4 figure

A community occupational survey of a manufacturing and industrial city, suburban to Boston, to discover the jobs or occupations within the community, suited to the limited abilities of special class graduates

Thesis (Ed.M.)--Boston Universit

The Way to God or God\u27s Way to Us: The Theologies of Edward Farley and James McClendon in Critical Dialogue

A lively theological debate in recent decades has been the dispute over theological method between revisionist and narrativist theologians. To explore and evaluate this debate I consider the work of revisionist theologian Edward Farley and of narrativist theologian James William McClendon, Jr. Farley\u27s method calls, first, for an attempt to uncover faith realities that can be directly perceived, such as the faith community\u27s efforts to remove ethnic boundaries, and, second, for an endeavor to examine how such realities indirectly demonstrate the existence of additional faith realities, such as the character of God. In contrast, McClendon\u27s method calls for an attempt to ground doctrine in various sources, such as experience, community and the narrative of Christian tradition, but most especially in the narrative of Scripture, conceived of as the word of God. An endeavor to address adequately their understandings of theological method requires not only a direct analysis of the methods themselves (set forth in chapters 1 and 2) but also an examination of how these methods may be applied in the construction of doctrine. Thus, (in chapters 3 and 4) I consider the manner in which Farley\u27s and McClendon\u27s methods inform their doctrines of God. Finally, (in chapter 5) in dialog with other commentaries on their work, I present an assessment and comparative evaluation of their theological methods and doctrines of God, demonstrating strengths and potential deficiencies in each case. I conclude that there are some significant differences between Farley\u27s and McClendon\u27s projects. For instance, they vary from one another in how they conceive of the identity of Scripture. For Farley, the Bible is chiefly a text that the faith community has made, and it is one means (among others) through which one can uncover the realities of faith; for McClendon, Scripture is primarily a text in which God speaks (through humans), and it is thus a text through which God can find us. Another related difference is in where they place authority as the basis for developing doctrine. Farley locates this authority chiefly with the contemporary ecclesial community, while McClendon places it primarily with the narrative of Scripture

Phylogeny and taxonomy of the Ophiostoma piceae complex and the Dutch elm disease fungi

The Ophiostoma piceae complex forms a monophyletic group of insect-dispersed pyrenomycetes with synnemata (Pesotum) and micronematous (Sporothrix) synanamorphs. Other species of Ophios-toma outside of the O. piceae complex that form syn-nemata lack the Sporothrix state. The nine recognized species within the 0. piceae complex are delimited by synnema morphology, growth rate at 32 C, mating reactions and sequences of the internal transcribed spacer (ITS) region of the rDNA operon. Phyloge-netic analysis of the ITS region suggests two major clades in the complex, one that causes bluestain in primarily coniferous hosts and the other on primarily hardwood hosts. In the coniferous group are O. pi-ceae, O. canum, O. floccosum and the recently de-scribed O. setosum (anamorph Pesotum cupulatum sp. nov.). In the hardwood group are O. querci, O. caton-ianum, and the Dutch elm disease fungi: O. ulmi, O. novo-ulmi and O. himal-ulmi. Restriction fragment length polymorphisms of the ITS region are shown to be a convenient diagnostic tool for delimiting these species

Cardinal characteristics and countable Borel equivalence relations

Boykin and Jackson recently introduced a property of countable Borel equivalence relations called Borel boundedness, which they showed is closely related to the union problem for hyperfinite equivalence relations. In this paper, we introduce a family of properties of countable Borel equivalence relations which correspond to combinatorial cardinal characteristics of the continuum in the same way that Borel boundedness corresponds to the bounding number $\mathfrak b$. We analyze some of the basic behavior of these properties, showing for instance that the property corresponding to the splitting number $\mathfrak s$ coincides with smoothness. We then settle many of the implication relationships between the properties; these relationships turn out to be closely related to (but not the same as) the Borel Tukey ordering on cardinal characteristics

A TYPICAL FARM SERIES: DEVELOPMENT AND APPLICATION TO A MISSISSIPPI DELTA FARM

Farm Management,