Boolean algebras and Lubell functions

Let $2^{[n]}$ denote the power set of $[n]:=\{1,2,..., n\}$. A collection \B\subset 2^{[n]} forms a $d$-dimensional {\em Boolean algebra} if there exist pairwise disjoint sets $X_0, X_1,..., X_d \subseteq [n]$, all non-empty with perhaps the exception of $X_0$, so that \B={X_0\cup \bigcup_{i\in I} X_i\colon I\subseteq [d]}. Let $b(n,d)$ be the maximum cardinality of a family \F\subset 2^X that does not contain a $d$-dimensional Boolean algebra. Gunderson, R\"odl, and Sidorenko proved that $b(n,d) \leq c_d n^{-1/2^d} \cdot 2^n$ where $c_d= 10^d 2^{-2^{1-d}}d^{d-2^{-d}}$. In this paper, we use the Lubell function as a new measurement for large families instead of cardinality. The Lubell value of a family of sets \F with \F\subseteq \tsupn is defined by h_n(\F):=\sum_{F\in \F}1/{{n\choose |F|}}. We prove the following Tur\'an type theorem. If \F\subseteq 2^{[n]} contains no $d$-dimensional Boolean algebra, then h_n(\F)\leq 2(n+1)^{1-2^{1-d}} for sufficiently large $n$. This results implies $b(n,d) \leq C n^{-1/2^d} \cdot 2^n$, where $C$ is an absolute constant independent of $n$ and $d$. As a consequence, we improve several Ramsey-type bounds on Boolean algebras. We also prove a canonical Ramsey theorem for Boolean algebras.Comment: 10 page

Rhetoricizing Habermas: The Restoration of Legitimacy as a Theme in the 1992 Televised Presidential Debates.

During the past twenty years, scholars have posited the emergence of a legitimacy crisis in the American political system. Symptoms of the crisis were low voter turn out and a culture of withdrawal, cynicism, alienation, and a widespread perception of institutional incompetence and indifference. At the very least, the widespread mood of apathy and decline have been seized upon by various candidates seeking political office, in particular the presidency, who routinely engage in discourse targeting legitimacy restoration. This discourse echoed the general theme of the Jeffersonian Myth. This myth, which predates Jefferson in its old Roman roots, targets the citizen as the primary source of political power and moral authority. Working from Habermas\u27 writings regarding legitimacy crises and his ideal speech situation, this study developed three legitimacy topoi which were used as a critical method for understanding candidate discourse. These topoi were used to explore the discourse of the 1992 televised presidential debates. The debates were selected because of their economy of statements and voter impact, and because legitimacy had become a central theme of the 1992 elections. The study found that the third party candidate indicted the legitimacy of the system and argued for restoration far more than the other two candidates. The incumbent used legitimacy appeals the least. The exhaling Democratic challenger affirmed and vilified the legitimacy of the government showing that rhetorical strategy and logic do not always coincide

Sesame-Style Decomposition of KS-DFT Molecular Dynamics for Direct Interrogation of Nuclear Models

A common paradigm used in the construction of equations of state is to decompose the thermodynamics into a superposition of three terms: a static-lattice cold curve, a contribution from the thermal motion of the nuclei, and a contribution from the thermal excitation of the electrons. While statistical mechanical models for crystals provide tractable framework for the nuclear contribution in the solid phase, much less is understood about the nuclear contribution above the melt temperature ($C_v^{(\text{nuc})}\approx 3R$) and how it should transition to the high-temperature limit ($C_v^{(\text{nuc})} \sim \frac{3}{2}R$). In this work, we describe an algorithm for extracting both the thermal nuclear and thermal electronic contributions from quantum molecular dynamics (QMD). We then use the VASP QMD package to probe thermal nuclear behavior of liquid aluminum at normal density to compare the results to semi-empirical models -- the Johnson generic model, the Chisolm high-temperature liquid model, and the CRIS model.Comment: 6 pages, 4 figures, APS Shock Compression of Condensed Matter Conference Proceedings 201

Ecohydrological implications of woody plant encroachment

Journal ArticleIncreases in the abundance or density of woody plants in historically semiarid and arid grassland ecosystems have important ecological, hydrological, and socioeconomic implications. Using a simplified water-balance model, we propose a framework for conceptualizing how woody plant encroachment is likely to affect components of the water cycle within these ecosystems

Model-guided design of ligand-regulated RNAi for programmable control of gene expression

Progress in constructing biological networks will rely on the development of more advanced components that can be predictably modified to yield optimal system performance. We have engineered an RNA-based platform, which we call an shRNA switch, that provides for integrated ligand control of RNA interference (RNAi) by modular coupling of an aptamer, competing strand, and small hairpin (sh) RNA stem into a single component that links ligand concentration and target gene expression levels. A combined experimental and mathematical modelling approach identified multiple tuning strategies and moves towards a predictable framework for the forward design of shRNA switches. The utility of our platform is highlighted by the demonstration of fine-tuning, multi-input control, and model-guided design of shRNA switches with an optimized dynamic range. Thus, shRNA switches can serve as an advanced component for the construction of complex biological systems and offer a controlled means of activating RNAi in disease therapeutics

Americans’ support for college financial aid for prisoners depends on how the benefits are described

Allowing prisoners to access college-level education reduces the risk of reoffending and can save state governments money because of the reduction in future crime. But Americans, by contrast, often oppose providing prisoners such benefits. With the recent overturning of the ban on prisoners’ receiving Pell Grants, Travis M. Johnston and Kevin H. Wozniak look at how the public reacts to prison education reform, depending on how its benefits are described. They find that when the benefits to the incarcerated and to society are noted, Americans were more likely to support providing college aid to prisoners

Synthetic control of a fitness tradeoff in yeast nitrogen metabolism

Background: Microbial communities are involved in many processes relevant to industrial and medical biotechnology, such as the formation of biofilms, lignocellulosic degradation, and hydrogen production. The manipulation of synthetic and natural microbial communities and their underlying ecological parameters, such as fitness, evolvability, and variation, is an increasingly important area of research for synthetic biology. Results: Here, we explored how synthetic control of an endogenous circuit can be used to regulate a tradeoff between fitness in resource abundant and resource limited environments in a population of Saccharomyces cerevisiae. We found that noise in the expression of a key enzyme in ammonia assimilation, Gdh1p, mediated a tradeoff between growth in low nitrogen environments and stress resistance in high ammonia environments. We implemented synthetic control of an endogenous Gdh1p regulatory network to construct an engineered strain in which the fitness of the population was tunable in response to an exogenously-added small molecule across a range of ammonia environments. Conclusion: The ability to tune fitness and biological tradeoffs will be important components of future efforts to engineer microbial communities

A Comparison of Statistical Approaches for Predicting Stream Temperatures Across Heterogeneous Landscapes 1

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/73725/1/j.1752-1688.2009.00341.x.pd