Strongly Universal Reversible Gate Sets

It is well-known that the Toffoli gate and the negation gate together yield a universal gate set, in the sense that every permutation of $\{0,1\}^n$ can be implemented as a composition of these gates. Since every bit operation that does not use all of the bits performs an even permutation, we need to use at least one auxiliary bit to perform every permutation, and it is known that one bit is indeed enough. Without auxiliary bits, all even permutations can be implemented. We generalize these results to non-binary logic: If $A$ is a finite set of odd cardinality then a finite gate set can generate all permutations of $A^n$ for all $n$, without any auxiliary symbols. If the cardinality of $A$ is even then, by the same argument as above, only even permutations of $A^n$ can be implemented for large $n$, and we show that indeed all even permutations can be obtained from a finite universal gate set. We also consider the conservative case, that is, those permutations of $A^n$ that preserve the weight of the input word. The weight is the vector that records how many times each symbol occurs in the word. It turns out that no finite conservative gate set can, for all $n$, implement all conservative even permutations of $A^n$ without auxiliary bits. But we provide a finite gate set that can implement all those conservative permutations that are even within each weight class of $A^n$.Comment: Submitted to Rev Comp 201

Intención emprendedora en la agricultura de Puerto Rico: una mirada hacia el agro-cannabis

La intención emprendedora agrícola es una actividad que persigue mejorar la productividad agrícola y por ende la competitividad de los agronegocios. El ambiente cambiante del mercado unido al desarrollo de nuevas tecnologías de información y comunicación provocan que la empresa agrícola moderna deba asumir el desafío de modificar su gestión para poder competir con éxito. Los negocios de naturaleza agrícola generan importante actividad económica que es fuente de producto, empleo e ingreso. La economía de Puerto Rico ha experimentado un decrecimiento notable en años recientes. La nueva incorporación de la producción de cannabis en la agricultura de Puerto Rico ofrece un nuevo paradigma. La utilización del modelo de intención basado en la teoría del comportamiento planificado (TCP) se presenta como método en esta investigación cuantitativa para determinar si la producción de cannabis para uso medicinal forma intenciones emprendedoras en estudiantes de agricultura a nivel subgraduado. La investigación tiene como propósito responder y aportar información a la comunidad académica en relación: a si la intención emprendedora al agro cannabis está influenciada por factores exógenos que a su vez influye sobre las actitudes, normas subjetivas y control percibido de los estudiantes subgraduados de agricultura de la Universidad de Puerto Rico en Utuado y Universidad de Puerto Rico en Mayagüez

An Explicit Framework for Interaction Nets

Interaction nets are a graphical formalism inspired by Linear Logic proof-nets often used for studying higher order rewriting e.g. \Beta-reduction. Traditional presentations of interaction nets are based on graph theory and rely on elementary properties of graph theory. We give here a more explicit presentation based on notions borrowed from Girard's Geometry of Interaction: interaction nets are presented as partial permutations and a composition of nets, the gluing, is derived from the execution formula. We then define contexts and reduction as the context closure of rules. We prove strong confluence of the reduction within our framework and show how interaction nets can be viewed as the quotient of some generalized proof-nets

Topological entropy and blocking cost for geodesics in riemannian manifolds

For a pair of points $x,y$ in a compact, riemannian manifold $M$ let $n_t(x,y)$ (resp. $s_t(x,y)$) be the number of geodesic segments with length $\leq t$ joining these points (resp. the minimal number of point obstacles needed to block them). We study relationships between the growth rates of $n_t(x,y)$ and $s_t(x,y)$ as $t\to\infty$. We derive lower bounds on $s_t(x,y)$ in terms of the topological entropy $h(M)$ and its fundamental group. This strengthens the results of Burns-Gutkin \cite{BG06} and Lafont-Schmidt \cite{LS}. For instance, by \cite{BG06,LS}, $h(M)>0$ implies that $s$ is unbounded; we show that $s$ grows exponentially, with the rate at least $h(M)/2$.Comment: 13 page

Insecurity for compact surfaces of positive genus

A pair of points in a riemannian manifold $M$ is secure if the geodesics between the points can be blocked by a finite number of point obstacles; otherwise the pair of points is insecure. A manifold is secure if all pairs of points in $M$ are secure. A manifold is insecure if there exists an insecure point pair, and totally insecure if all point pairs are insecure. Compact, flat manifolds are secure. A standing conjecture says that these are the only secure, compact riemannian manifolds. We prove this for surfaces of genus greater than zero. We also prove that a closed surface of genus greater than one with any riemannian metric and a closed surface of genus one with generic metric are totally insecure.Comment: 37 pages, 11 figure

Hypoxia. HIF-mediated articular chondrocyte function: prospects for cartilage repair

In a chronically hypoxic tissue such as cartilage, adaptations to hypoxia do not merely include cell survival responses, but also promotion of its specific function. This review will focus on describing such hypoxia-mediated chondrocyte function, in particular in the permanent articular cartilage. The molecular details of how chondrocytes sense and respond to hypoxia and how this promotes matrix synthesis have recently been examined, and specific manipulation of hypoxia-induced pathways is now considered to have potential therapeutic application to maintenance and repair of articular cartilage

Paving TRAIL's Path with Ubiquitin

Despite its name, signalling induced by the tumour necrosis factor (TNF)-related apoptosis-inducing ligand (TRAIL) is versatile. Besides eliciting cell death by both apoptosis and necroptosis, TRAIL can also induce migration, proliferation, and cytokine production in cancerous and non-cancerous cells. Unravelling the mechanisms regulating the intricate balance between these different outputs could therefore facilitate our understanding of the role of TRAIL in tissue homeostasis, immunity, and cancer. Ubiquitination and its reversal, deubiquitination, are crucial modulators of immune receptor signalling. This review discusses recent progress on the orchestration of TRAIL signalling outcomes by ubiquitination of various components of the signalling complexes, our understanding of the molecular switches that decide between cell death and gene activation, and what remains to be discovered

A convenient category of locally preordered spaces

As a practical foundation for a homotopy theory of abstract spacetime, we extend a category of certain compact partially ordered spaces to a convenient category of locally preordered spaces. In particular, we show that our new category is Cartesian closed and that the forgetful functor to the category of compactly generated spaces creates all limits and colimits.Comment: 26 pages, 0 figures, partially presented at GETCO 2005; changes: claim of Prop. 5.11 weakened to finite case and proof changed due to problems with proof of Lemma 3.26, now removed; Eg. 2.7, statement before Lem. 2.11, typos, and other minor problems corrected throughout; extensive rewording; proof of Lem. 3.31, now 3.30, adde