Michael Hardy

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The natural forms of the Leibniz rule for the kth derivative of a product and of Faà di Bruno’s formula for the kth derivative of a composition involve the differential operator ∂/∂x1 · · · ∂xk rather than dk/dxk, with no assumptions about whether the variables x1, . . . , xk are all distinct, or all identical, or partitioned into several distinguishable(More)
CcO (cytochrome c oxidase) is a multisubunit bigenomic protein complex which catalyses the last step of the mitochondrial electron transport chain. The nuclear-encoded subunits are thought to have roles either in regulation or in the structural stability of the enzyme. Subunit Vb is a peripheral nuclear-encoded subunit of mammalian CcO that is dramatically(More)
Scaled Boolean algebras are a category of mathematical objects that arose from attempts to understand why the conventional rules of probability should hold when probabilities are construed, not as frequencies or proportions or the like, but rather as degrees of belief in uncertain propositions. This paper separates the study of these objects from that not(More)
because S is “unbiased” and T 2 is “biased.” That means E(S) = σ 6= E(T ), i.e., an “unbiased estimator” is a statistic whose expected value is the quantity to be estimated. The goodness of an estimator is sometimes measured by the smallness of its “mean squared error,” defined as E ( ([estimator]− [quantity to be estimated]) ) . By that criterion the(More)
This study used a wildfire loss simulation model to evaluate how different land use policies are likely to influence wildfire risk in the wildland urban interface (WUI) for Flathead County, Montana. The model accounts for the complex socio-ecological interactions among climate change, economic growth, land use change and policy, homeowner mitigations, and(More)
Cell membranes are dynamic structures found in all living organisms. There have been numerous constructs that model phospholipid membranes. However, unlike natural membranes, these biomimetic systems cannot sustain growth owing to an inability to replenish phospholipid-synthesizing catalysts. Here we report on the design and synthesis of artificial(More)
Transmembrane proteins are critical for signaling, transport, and metabolism, yet their reconstitution in synthetic membranes is often challenging. Non-enzymatic and chemoselective methods to generate phospholipid membranes in situ would be powerful tools for the incorporation of membrane proteins. Herein, the spontaneous reconstitution of functional(More)
As more methodologies for generating and manipulating biomimetic cellular systems are developed, opportunities arise for combining different methods to create more complex synthetic biological constructs. This necessitates an increasing need for tools to selectively trigger individual methodologies. Here we demonstrate ruthenium tris-bipyridine mediated(More)
There has been increasing interest in utilizing bottom-up approaches to develop synthetic cells. A popular methodology is the integration of functionalized synthetic membranes with biological systems, producing "hybrid" artificial cells. This Concept article covers recent advances and the current state-of-the-art of such hybrid systems. Specifically, we(More)
The natural forms of the Leibniz rule for the kth derivative of a product and of Faà di Bruno’s formula for the kth derivative of a composition involve the differential operator ∂/∂x1 · · · ∂xk rather than d /dx, with no assumptions about whether the variables x1, . . . , xk are all distinct, or all identical, or partitioned into several distinguishable(More)