Relativistic Constraints for a Naturalistic Metaphysics of Time

The traditional metaphysical debate between static and dynamic views in the philosophy of time is examined in light of considerations concerning the nature of time in physical theory. Adapting the formalism of Rovelli (1995, 2004), I set out a precise framework in which to characterise the formal structure of time that we find in physical theory. This framework is used to provide a new perspective on the relationship between the metaphysics of time and the special theory of relativity by emphasising the dual representations of time that we find in special relativity. I extend this analysis to the general theory of relativity with a view to prescribing the constraints that must be heeded for a metaphysical theory of time to remain within the bounds of a naturalistic metaphysics

Reasoning about Cardinal Directions between Extended Objects

Direction relations between extended spatial objects are important commonsense knowledge. Recently, Goyal and Egenhofer proposed a formal model, known as Cardinal Direction Calculus (CDC), for representing direction relations between connected plane regions. CDC is perhaps the most expressive qualitative calculus for directional information, and has attracted increasing interest from areas such as artificial intelligence, geographical information science, and image retrieval. Given a network of CDC constraints, the consistency problem is deciding if the network is realizable by connected regions in the real plane. This paper provides a cubic algorithm for checking consistency of basic CDC constraint networks, and proves that reasoning with CDC is in general an NP-Complete problem. For a consistent network of basic CDC constraints, our algorithm also returns a 'canonical' solution in cubic time. This cubic algorithm is also adapted to cope with cardinal directions between possibly disconnected regions, in which case currently the best algorithm is of time complexity O(n^5)

Cross Market Effects of stocks Short-Selling Restrictions: Evidence from the September 2008 Natural Experiment

Using intraday data, this paper investigates empirically the joint stock and corporate bond markets responses to the September 2008 stocks short sell ban. The study intends to exploit the natural experiment in order to asses the impact of the stock market short sale restrictions (stock market liquidity shock) on corporate bond market variables during the nancial crisis period. The short sell ban was one of the levers that regulators pulled in order to manage the financial crisis. The economic question is whether this lever worked or should have been pulled given the complexity of financial market linkages and news dissemination. Recent financial events suggested that, when market conditions are severe, liquidity can rapidly decline or even disappear. Liquidity shocks are the potential channel through which asset prices are influenced by liquidity. However, the standard theoretical equilibrium asset pricing models do not consider trading and thus ignore the time and cost of transforming cash into financial assets and viceversa hence ignoring the impact of the liquidity shocks. Therefore, investigating liquidity shocks empirically, their transmission across markets is of high interest especially during times of high turbulence as we recently witnessed. We use vector autoregression (VAR) approach to model stock and corporate bond returns, volatilities and transaction costs simultaneously, obtaining an econometric reduced form that incorporates causal and feedback effects among the two markets variables. Using VAR tools, we found that shocks in stock market (short sell ban) had a significant negative impact on corporate bond market variables during the time under investigation.

Foundations of Relational Particle Dynamics

Relational particle dynamics include the dynamics of pure shape and cases in which absolute scale or absolute rotation are additionally meaningful. These are interesting as regards the absolute versus relative motion debate as well as discussion of conceptual issues connected with the problem of time in quantum gravity. In spatial dimension 1 and 2 the relative configuration spaces of shapes are n-spheres and complex projective spaces, from which knowledge I construct natural mechanics on these spaces. I also show that these coincide with Barbour's indirectly-constructed relational dynamics by performing a full reduction on the latter. Then the identification of the configuration spaces as n-spheres and complex projective spaces, for which spaces much mathematics is available, significantly advances the understanding of Barbour's relational theory in spatial dimensions 1 and 2. I also provide the parallel study of a new theory for which positon and scale are purely relative but orientation is absolute. The configuration space for this is an n-sphere regardless of the spatial dimension, which renders this theory a more tractable arena for investigation of implications of scale invariance than Barbour's theory itself.Comment: Minor typos corrected; references update

Hybrid quantization of an inflationary model: The flat case

We present a complete quantization of an approximately homogeneous and isotropic universe with small scalar perturbations. We consider the case in which the matter content is a minimally coupled scalar field and the spatial sections are flat and compact, with the topology of a three-torus. The quantization is carried out along the lines that were put forward by the authors in a previous work for spherical topology. The action of the system is truncated at second order in perturbations. The local gauge freedom is fixed at the classical level, although different gauges are discussed and shown to lead to equivalent conclusions. Moreover, descriptions in terms of gauge-invariant quantities are considered. The reduced system is proven to admit a symplectic structure, and its dynamical evolution is dictated by a Hamiltonian constraint. Then, the background geometry is polymerically quantized, while a Fock representation is adopted for the inhomogeneities. The latter is selected by uniqueness criteria adapted from quantum field theory in curved spacetimes, which determine a specific scaling of the perturbations. In our hybrid quantization, we promote the Hamiltonian constraint to an operator on the kinematical Hilbert space. If the zero mode of the scalar field is interpreted as a relational time, a suitable ansatz for the dependence of the physical states on the polymeric degrees of freedom leads to a quantum wave equation for the evolution of the perturbations. Alternatively, the solutions to the quantum constraint can be characterized by their initial data on the minimum-volume section of each superselection sector. The physical implications of this model will be addressed in a future work, in order to check whether they are compatible with observations.Comment: 20 pages, no figures. v2: minor changes, in particular, abstract shortened, final discussion improve