q-Legendre Transformation: Partition Functions and Quantization of the Boltzmann Constant

In this paper we construct a q-analogue of the Legendre transformation, where q is a matrix of formal variables defining the phase space braidings between the coordinates and momenta (the extensive and intensive thermodynamic observables). Our approach is based on an analogy between the semiclassical wave functions in quantum mechanics and the quasithermodynamic partition functions in statistical physics. The basic idea is to go from the q-Hamilton-Jacobi equation in mechanics to the q-Legendre transformation in thermodynamics. It is shown, that this requires a non-commutative analogue of the Planck-Boltzmann constants (hbar and k_B) to be introduced back into the classical formulae. Being applied to statistical physics, this naturally leads to an idea to go further and to replace the Boltzmann constant with an infinite collection of generators of the so-called epoch\'e (bracketing) algebra. The latter is an infinite dimensional noncommutative algebra recently introduced in our previous work, which can be perceived as an infinite sequence of "deformations of deformations" of the Weyl algebra. The generators mentioned are naturally indexed by planar binary leaf-labelled trees in such a way, that the trees with a single leaf correspond to the observables of the limiting thermodynamic system

On Iterated Twisted Tensor Products of Algebras

We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We find conditions for constructing an iterated product of three factors, and prove that they are enough for building an iterated product of any number of factors. As an example of the geometrical aspects of our construction, we show how to construct differential forms and involutions on iterated products starting from the corresponding structures on the factors, and give some examples of algebras that can be described within our theory. We prove a certain result (called ``invariance under twisting'') for a twisted tensor product of two algebras, stating that the twisted tensor product does not change when we apply certain kind of deformation. Under certain conditions, this invariance can be iterated, containing as particular cases a number of independent and previously unrelated results from Hopf algebra theory.Comment: 44 pages, 21 figures. More minor typos corrections, one more example and some references adde

Dual Effect of Wasp Queen Pheromone in Regulating Insect Sociality

SummaryEusocial insects exhibit a remarkable reproductive division of labor between queens and largely sterile workers [1, 2]. Recently, it was shown that queens of diverse groups of social insects employ specific, evolutionarily conserved cuticular hydrocarbons to signal their presence and inhibit worker reproduction [3]. Workers also recognize and discriminate between eggs laid by the queen and those laid by workers, with the latter being destroyed by workers in a process known as “policing” [4, 5]. Worker policing represents a classic example of a conflict-reducing mechanism, in which the reproductive monopoly of the queen is maintained through the selective destruction of worker-laid eggs [5, 6]. However, the exact signals used in worker policing have thus far remained elusive [5, 7]. Here, we show that in the common wasp, Vespula vulgaris, the pheromone that signals egg maternity and enables the workers to selectively destroy worker-laid eggs is in fact the same as one of the sterility-inducing queen signals that we identified earlier [3]. These results imply that queen pheromones regulate insect sociality in two distinct and complementary ways, i.e., by signaling the queen’s presence and inhibiting worker reproduction, and by facilitating the recognition and policing of worker-laid eggs

Conserved Class of Queen Pheromones Stops Social Insect Worker Reproduction

Dissertação de mestrado em Gestão, apresentada à Faculdade de Economia da Universidade de Coimbra, sob a orientação de Patrícia Pereira da SilvaEm 2011, a crise política e financeira de Portugal atingiu um nível crítico, levando à queda do governo, assim como ao pedido de ajuda à denominada Troika, constituída pelo (Fundo Monetário Internacional, Banco Central Europeu e Comunidade Europeia). As recomendações da Troika sobre a política energética Portuguesa basearam-se em torno de medidas que potenciem a eficiência energética, ou seja, medidas que permitam poupar e otimizar consumo de energia. No entanto, sobre as energias renováveis, foi pedida especial atenção, em particular, em tecnologias menos desenvolvidas (incluindo o fotovoltaico), nas quais se deverá efetuar uma análise rigorosa em termos de custos e consequências para o preço da energia. Outra das recomendações da Troika passou por uma revisão em baixo do preço pago pela tarifa (Feed-in tariff), com o intuito de que esse valor não produza compensações alegadamente excessivas para os investidores neste setor. Atendendo às novas constrições anteriormente apresentadas, e aos elevados custo de investimento que as Fontes de Energias Renováveis apresentam, nomeadamente, no setor fotovoltaico, a respetiva avaliação económica assume um papel primordial. É, assim, objetivo desta dissertação estimar da forma mais correta a rendibilidade do investimento, sendo, para tal, desenvolvida uma metodologia de análise de projetos de investimento, usando o método discounted cash flow (DCF) – Free Cash Flow to the firm, bem como, compreender e analisar quais os principais fatores que estão inerentes a um projeto de Fontes de Energia Renovável, nomeadamente, na análise do Levelized Cost Of Electricity (LCOE) e paridade com a rede elétrica. Deste modo, pretende-se uma reanálise do ponto de vista económico de projetos com origem em fontes de energia renovável

Perverse coherent t-structures through torsion theories

Bezrukavnikov (later together with Arinkin) recovered the work of Deligne defining perverse $t$-structures for the derived category of coherent sheaves on a projective variety. In this text we prove that these $t$-structures can be obtained through tilting torsion theories as in the work of Happel, Reiten and Smal\o. This approach proves to be slightly more general as it allows us to define, in the quasi-coherent setting, similar perverse $t$-structures for certain noncommutative projective planes.Comment: New revised version with important correction

Obstructing extensions of the functor Spec to noncommutative rings

In this paper we study contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a common characteristic of these functors: every such functor assigns the empty set to M_n(C) for n >= 3. The proof relies, in part, on the Kochen-Specker Theorem of quantum mechanics. The analogous result for noncommutative extensions of the Gelfand spectrum functor for C*-algebras is also proved.Comment: 23 pages. To appear in Israel J. Math. Title was changed; introduction was rewritten; old Section 2 was removed to streamline the exposition; final section was rewritten to omit an error in the earlier proof of Theorem 1.

Generalized diagonal crossed products and smash products for quasi-Hopf algebras. Applications

In this paper we introduce generalizations of diagonal crossed products, two-sided crossed products and two-sided smash products, for a quasi-Hopf algebra H. The results we obtain may be applied to H^*-Hopf bimodules and generalized Yetter-Drinfeld modules. The generality of our situation entails that the "generating matrix" formalism cannot be used, forcing us to use a different approach. This pays off because as an application we obtain an easy conceptual proof of an important but very technical result of Hausser and Nill concerning iterated two-sided crossed products.Comment: 41 pages, no figure

At the brink of eusociality: transcriptomic correlates of worker behaviour in a small carpenter bee

Background: There is great interest in understanding the genomic underpinnings of social evolution, in particular, the evolution of eusociality (caste-containing societies with non-reproductives that care for siblings). Subsociality is a key precursor for the evolution of eusociality and characterized by prolonged parental care and parent-offspring interaction. Here, we provide the first transcriptomic data for the small carpenter bee, Ceratina calcarata. This species is of special interest because it is subsocial and in the same family as the highly eusocial honey bee, Apis mellifera. In addition, some C. calcarata females demonstrate alloparental care without reproduction, which provides a unique opportunity to study worker behaviour in a non-eusocial species. Results: We uncovered similar gene expression patterns related to maternal care and sibling care in different groups of females. This agrees with the maternal heterochrony hypothesis, specifically, that changes in timing of offspring care gene expression are related to worker behaviour in incipient insect societies. In addition, we also detected some similarity to caste-related gene expression patterns in highly eusocial honey bees, and uncovered large lifetime changes in gene expression that accompany shifts in reproductive and maternal care behaviour. Conclusions: For Ceratina calcarata, we found that transcript expression profiles were most similar between sibling care and maternal care females. The maternal care behaviour exhibited post-reproductively by Ceratina mothers is concordant in terms of transcript expression with the alloparental care exhibited by workers. In line with theoretical predictions, our data are consistent with the maternal heterochrony hypothesis for the evolutionary development of worker behaviour in subsocial bees