Ordinary and Generalized Circulation Algebras for Regular Matroids

Let E be a finite set, and let R(E) denote the algebra of polynomials in indeterminates (x_e)_{e in E}, modulo the squares of these indeterminates. Subalgebras of R(E) generated by homogeneous elements of degree 1 have been studied by many authors and can be understood combinatorially in terms of the matroid represented by the linear equations satisfied by these generators. Such an algebra is related to algebras associated to deletions and contractions of the matroid by a short exact sequence, and can also be written as the quotient of a polynomial algebra by certain powers of linear forms. We study such algebras in the case that the matroid is regular, which we term circulation algebras following Wagner. In addition to surveying the existing results on these algebras, we give a new proof of Wagner's result that the structure of the algebra determines the matroid, and construct an explicit basis in terms of basis activities in the matroid. We then consider generalized circulation algebras in which we mod out by a fixed power of each variable, not necessarily equal to 2. We show that such an algebra is isomorphic to the circulation algebra of a "subdivided" matroid, a variation on a result of Nenashev, and derive from this generalized versions of many of the results on ordinary circulation algebras, including our basis result. We also construct a family of short exact sequences generalizing the deletion-contraction decomposition

Groping for Intimacy: Modern Man\u27s Pressure and the Onanistic Inversion of Christianity, Marriage, and the Nuclear Family in Three American Novels

Several critics have suggested that modernity\u27s most fundamental theme is autonomy. Yet, few critics have considered Søren Kierkegaard\u27s thought in relation to autonomous notions of freedom, and even fewer literary critics have considered Kierkegaard\u27s vast influence - particularly on twentieth-century American authors - through this thematic lens. Michelle Kosch has argued that Kierkegaard\u27s notion of despair essentially involves the self\u27s misunderstanding of the nature of his freedom, while Samuel Loncar has argued that Kierkegaard\u27s thought in this regard can be traced back through the German Enlightenment to Immanuel Kant\u27s notion of autonomy. Yet, while Kierkegaard offers a fine critique of autonomous notions of freedom in favor of the self\u27s necessity of God\u27s revelation, he ultimately fails to affirm the implications of his own thought for community life. My argument is that the dialectic of freedom and alienation is compellingly relevant for three Kierkegaard-influenced, mid-twentieth century novels which are concerned with a peculiarly American form of individualism. Flannery O\u27Connor\u27s Wise Blood, Walker Percy\u27s The Moviegoer, and John Updike\u27s Rabbit, Run are not only Kierkegaardian in the sense that they depict increasingly alienated protagonists pursuing excessive personal freedoms, they are also Kierkegaardian in that they ultimately lack significant depictions of communal reconciliation between self and other. For the three protagonists - Hazel Motes, Jack Binx Bolling, and Harry Rabbit Angstrom - autonomous notions of freedom degenerate into onanistic forms of identity whereby they manipulate others toward the end of their own fulfillment, producing the waste of both an incoherent, dissatisfying identity, and the inhumane diminishment of others. Instead, this thesis argues that the self must be situated within a sense of communal narrative - one which is particularly capable of producing fruitful, unifying, and generative intercourse between self and other, and calls into question those among us whose freedom or rights would severely undermine it

A Comprehensive Biophysical Description of Pairwise Epistasis throughout an Entire Protein Domain

SummaryBackgroundNonadditivity in fitness effects from two or more mutations, termed epistasis, can result in compensation of deleterious mutations or negation of beneficial mutations. Recent evidence shows the importance of epistasis in individual evolutionary pathways. However, an unresolved question in molecular evolution is how often and how significantly fitness effects change in alternative genetic backgrounds.ResultsTo answer this question, we quantified the effects of all single mutations and double mutations between all positions in the IgG-binding domain of protein G (GB1). By observing the first two steps of all possible evolutionary pathways using this fitness profile, we were able to characterize the extent and magnitude of pairwise epistasis throughout an entire protein molecule. Furthermore, we developed a novel approach to quantitatively determine the effects of single mutations on structural stability (ΔΔGU). This enabled determination of the importance of stability effects in functional epistasis.ConclusionsOur results illustrate common biophysical mechanisms for occurrences of positive and negative epistasis. Our results show pervasive positive epistasis within a conformationally dynamic network of residues. The stability analysis shows that significant negative epistasis, which is more common than positive epistasis, mostly occurs between combinations of destabilizing mutations. Furthermore, we show that although significant positive epistasis is rare, many deleterious mutations are beneficial in at least one alternative mutational background. The distribution of conditionally beneficial mutations throughout the domain demonstrates that the functional portion of sequence space can be significantly expanded by epistasis

An In Vivo

Infection is the leading complication associated with intravascular devices, and these infections develop when a catheter becomes colonized by microorganisms. To combat this issue, medical device manufacturers seek to provide healthcare facilities with antimicrobial medical devices to prevent or reduce the colonization. In order to adequately evaluate these devices, an in vivo model is required to accurately assess the performance of the antimicrobial devices in a clinical setting. The model presented herein was designed to provide a simulation of the subcutaneous tunnel environment to evaluate the ability of an antimicrobial peripherally inserted central catheter (PICC), coated with chlorhexidine based technology, to reduce microbial migration and colonization compared to an uncoated PICC. Three samples of control, uncoated PICCs and three samples of coated PICCs were surgically tunneled into the backs of female New Zealand White rabbits. The insertion sites were then challenged with Staphylococcus aureus at the time of implantation. Animals were evaluated out to thirty days and sacrificed. Complete en bloc dissection and evaluation of the catheter and surrounding tissue demonstrated that the chlorhexidine coated catheter was able to significantly reduce microbial colonization and prevent microbial migration as compared to the standard, un-treated catheter

Canagliflozin lowers blood sugar, but does it also lower cardiovascular risk? Maybe not

For the last 25 years it has been widely accepted that diabetes mellitus is associated with a twofold or greater risk of clinical atherosclerotic disease. Long-standing elevated blood sugar levels, as measured by the hemoglobin A1c level, have been shown to be independent of major cardiovascular risk factors including age, body mass index, systolic blood pressure, serum cholesterol, cigarette smoking, or history of cardiovascular disease