Endogenizing leadership in tax competition: a timing game perspective

In this paper we extend the standard approach of horizontal tax competition by endogenizing the timing of decisions made by the competing jurisdictions. Following the literature on the endogenous timing in duopoly games, we consider a pre-play stage, where jurisdictions commit themselves to more early or late, i.e. to fix their tax rate at a first or second stage. We highlight that at least one jurisdiction experiments a second-mover advantage. We show that the Subgame Perfect Equilibria (SPEs) correspond to the two Stackelberg situations yielding to a coordination problem. In order to solve this issue, we consider a quadratic specification of the production function, and we use two criteria of selection: Pareto-dominance and risk-dominance. We emphasize that at the safer equilibrium the less productive or smaller jurisdiction leads and hence loses the second-mover advantage. If asymmetry among jurisdictions is sufficient, Pareto-dominance reinforces risk-domination in selecting the same SPE. Three results may be deduced from our analysis: (i) the downward pressure on tax rates is less severe than predicted; (ii) the smaller jurisdiction leads; (iii) the 'big-country-higher-tax-rate' rule does not always hold. Classification-JEL: H30, H87, C72.Endogenous timing; tax competition; first/second-mover advantage; strategic complements; stackelberg ; risk dominance.

Scalar Field Oscillations Contributing to Dark Energy

We use action-angle variables to describe the basic physics of coherent scalar field oscillations in the expanding universe. These analytical mechanics methods have some advantages, like the identification of adiabatic invariants. As an application, we show some instances of potentials leading to equations of state with $p<-\rho/3$, thus contributing to the dark energy that causes the observed acceleration of the universe.Comment: 17 pages, 6 figures, Latex file. Sec.II reduced, discussion on sound speed added in Sec.IV, new references added. Accepted for publication in Physical Review

Circulating adhesion molecules and arterial stiffness

Aim: VCAM-1 and ICAM-1 are two important members of the immunoglobulin gene superfamily of adhesion molecules, and their potential role as biomarkers of diagnosis, severity and prognosis of cardiovascular disease has been investigated in a number of clinical studies. The aim of the present study was to determine the relationship between circulating ICAM-1 and VCAM-1 levels and aortic stiffness in patients referred for echocardiographic examination. Methods: Aortic distensibility was determined by echocardiography using systolic and diastolic aortic diameters in 63 consecutive patients referred for echocardiography. Venous samples were collected in the morning after a 12-hour overnight fast, and serum concentrations of ICAM-1 and VCAM-1 were measured using commercial enzyme immunoassay kits. Results: Data of a total of 63 participants (mean age 55.6 ± 10.5 years, 31 male) were included in the study. Circulating levels of adhesion molecules were VCAM-1: 12.604 ± 3.904 ng/ml and ICAM-1: 45.417 ± 31.429 ng/ml. We were unable to demonstrate any correlation between indices of aortic stiffness and VCAM-1 and ICAM-1 levels. Conclusion: The role of soluble adhesion molecules in cardiovascular disease has not been fully established and clinical studies show inconsistent results. Our results indicate that levels of circulating adhesion molecules cannot be used as markers of aortic stiffness in patients

The comb jelly opsins and the origins of animal phototransduction

Opsins mediate light detection in most animals, and understanding their evolution is key to clarify the origin of vision. Despite the public availability of a substantial collection of well-characterized opsins, early opsin evolution has yet to be fully understood, in large part because of the high level of divergence observed among opsins belonging to different subfamilies. As a result, different studies have investigated deep opsin evolution using alternative data sets and reached contradictory results. Here, we integrated the data and methods of three, key, recent studies to further clarify opsin evolution. We show that the opsin relationships are sensitive to outgroup choice; we generate new support for the existence of Rhabdomeric opsins in Cnidaria (e.g., corals and jellyfishes) and show that all comb jelly opsins belong to well-recognized opsin groups (the Go-coupled opsins or the Ciliary opsins), which are also known in Bilateria (e.g., humans, fruit flies, snails, and their allies) and Cnidaria. Our results are most parsimoniously interpreted assuming a traditional animal phylogeny where Ctenophora are not the sister group of all the other animals

Spitzer's Identity and the Algebraic Birkhoff Decomposition in pQFT

In this article we continue to explore the notion of Rota-Baxter algebras in the context of the Hopf algebraic approach to renormalization theory in perturbative quantum field theory. We show in very simple algebraic terms that the solutions of the recursively defined formulae for the Birkhoff factorization of regularized Hopf algebra characters, i.e. Feynman rules, naturally give a non-commutative generalization of the well-known Spitzer's identity. The underlying abstract algebraic structure is analyzed in terms of complete filtered Rota-Baxter algebras.Comment: 19 pages, 2 figure

The Epstein-Glaser approach to pQFT: graphs and Hopf algebras

The paper aims at investigating perturbative quantum field theory (pQFT) in the approach of Epstein and Glaser (EG) and, in particular, its formulation in the language of graphs and Hopf algebras (HAs). Various HAs are encountered, each one associated with a special combination of physical concepts such as normalization, localization, pseudo-unitarity, causality and an associated regularization, and renormalization. The algebraic structures, representing the perturbative expansion of the S-matrix, are imposed on the operator-valued distributions which are equipped with appropriate graph indices. Translation invariance ensures the algebras to be analytically well-defined and graded total symmetry allows to formulate bialgebras. The algebraic results are given embedded in the physical framework, which covers the two recent EG versions by Fredenhagen and Scharf that differ with respect to the concrete recursive implementation of causality. Besides, the ultraviolet divergences occuring in Feynman's representation are mathematically reasoned. As a final result, the change of the renormalization scheme in the EG framework is modeled via a HA which can be seen as the EG-analog of Kreimer's HA.Comment: 52 pages, 5 figure

Time-ordering and a generalized Magnus expansion

Both the classical time-ordering and the Magnus expansion are well-known in the context of linear initial value problems. Motivated by the noncommutativity between time-ordering and time derivation, and related problems raised recently in statistical physics, we introduce a generalization of the Magnus expansion. Whereas the classical expansion computes the logarithm of the evolution operator of a linear differential equation, our generalization addresses the same problem, including however directly a non-trivial initial condition. As a by-product we recover a variant of the time ordering operation, known as T*-ordering. Eventually, placing our results in the general context of Rota-Baxter algebras permits us to present them in a more natural algebraic setting. It encompasses, for example, the case where one considers linear difference equations instead of linear differential equations

Hopf algebras in dynamical systems theory

The theory of exact and of approximate solutions for non-autonomous linear differential equations forms a wide field with strong ties to physics and applied problems. This paper is meant as a stepping stone for an exploration of this long-established theme, through the tinted glasses of a (Hopf and Rota-Baxter) algebraic point of view. By reviewing, reformulating and strengthening known results, we give evidence for the claim that the use of Hopf algebra allows for a refined analysis of differential equations. We revisit the renowned Campbell-Baker-Hausdorff-Dynkin formula by the modern approach involving Lie idempotents. Approximate solutions to differential equations involve, on the one hand, series of iterated integrals solving the corresponding integral equations; on the other hand, exponential solutions. Equating those solutions yields identities among products of iterated Riemann integrals. Now, the Riemann integral satisfies the integration-by-parts rule with the Leibniz rule for derivations as its partner; and skewderivations generalize derivations. Thus we seek an algebraic theory of integration, with the Rota-Baxter relation replacing the classical rule. The methods to deal with noncommutativity are especially highlighted. We find new identities, allowing for an extensive embedding of Dyson-Chen series of time- or path-ordered products (of generalized integration operators); of the corresponding Magnus expansion; and of their relations, into the unified algebraic setting of Rota-Baxter maps and their inverse skewderivations. This picture clarifies the approximate solutions to generalized integral equations corresponding to non-autonomous linear (skew)differential equations.Comment: International Journal of Geometric Methods in Modern Physics, in pres

A Hopf laboratory for symmetric functions

An analysis of symmetric function theory is given from the perspective of the underlying Hopf and bi-algebraic structures. These are presented explicitly in terms of standard symmetric function operations. Particular attention is focussed on Laplace pairing, Sweedler cohomology for 1- and 2-cochains, and twisted products (Rota cliffordizations) induced by branching operators in the symmetric function context. The latter are shown to include the algebras of symmetric functions of orthogonal and symplectic type. A commentary on related issues in the combinatorial approach to quantum field theory is given.Comment: 29 pages, LaTeX, uses amsmat

Plasma concentrations of Tapentadol and clinical evaluations of a combination of Tapentadol plus Sevoflurane for surgical anaesthesia and analgesia in rabbits (Oryctolagus cuniculus) undergoing orchiectomy

Pain is probably under-treated in animals, particularly in rabbits, due to a lack of familiarity with the species and limited information about analgesic dose, efficacy and safety. Tapentadol (TAP) is a novel opioid drug, with a proven efficacy and safety profile in humans, which could be useful as an analgesic in rabbits. In a clinical study, TAP was administered (5 mg/kg, IV) to seven male New Zealand White rabbits 5 min before anaesthetic induction with sevoflurane to perform orchiectomy. Monitoring of vital signs, including heart rate, electrocardiogram, respiratory rate, invasive blood pressure, oxygen saturation, righting reflex, palpebral reflex, jaw tone and tongue retraction, was performed throughout surgery. Pain was assessed for 8 h following surgery, using previously validated parameters, physiological assessments and behavioural assessments. Blood was also collected at regular intervals to assess the pharmacokinetic profile of the drug. TAP was rapidly distributed and eliminated in rabbits. Apnoea did not occurred in any subject. Following surgery, there were very few observable signs of pain in four rabbits and all resumed normal activities within a few hours. In conclusion, this is the first study about the clinical effects and potential utility of TAP as an adjunct drug for anaesthesia and analgesia in the rabbit. However, further studies are still needed before its use in the veterinary clinical practice