On Second-Order Monadic Monoidal and Groupoidal Quantifiers

We study logics defined in terms of second-order monadic monoidal and groupoidal quantifiers. These are generalized quantifiers defined by monoid and groupoid word-problems, equivalently, by regular and context-free languages. We give a computational classification of the expressive power of these logics over strings with varying built-in predicates. In particular, we show that ATIME(n) can be logically characterized in terms of second-order monadic monoidal quantifiers

A Reduction-Preserving Completion for Proving Confluence of Non-Terminating Term Rewriting Systems

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critical pairs and it also (partially) works even if the system is not terminating modulo E. We first present confluence criteria for term rewriting systems whose rewrite rules can be partitioned into a terminating part and a possibly non-terminating part. We then give a reduction-preserving completion procedure so that the applicability of the criteria is enhanced. In contrast to the well-known Knuth-Bendix completion procedure which preserves the equivalence relation of the system, our completion procedure preserves the reduction relation of the system, by which confluence of the original system is inferred from that of the completed system

Model Checking CTL is Almost Always Inherently Sequential

The model checking problem for CTL is known to be P-complete (Clarke, Emerson, and Sistla (1986), see Schnoebelen (2002)). We consider fragments of CTL obtained by restricting the use of temporal modalities or the use of negations---restrictions already studied for LTL by Sistla and Clarke (1985) and Markey (2004). For all these fragments, except for the trivial case without any temporal operator, we systematically prove model checking to be either inherently sequential (P-complete) or very efficiently parallelizable (LOGCFL-complete). For most fragments, however, model checking for CTL is already P-complete. Hence our results indicate that, in cases where the combined complexity is of relevance, approaching CTL model checking by parallelism cannot be expected to result in any significant speedup. We also completely determine the complexity of the model checking problem for all fragments of the extensions ECTL, CTL+, and ECTL+

Simulation of the flow and the study of the effects of the surface roughness in isothermal gas flows of micro scale using Lattice Boltzmann method

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.In this paper, a lattice Boltzmann method used in the simulation of the fluid flow in micro/nano scale is introduced and studied. The method can be employed instead of NS equations in cases where the continuum assumption is no longer valid. In the present study the aim is to investigate the effects of surface roughness on flow characteristics of micro/nano gas flows. In order to compare the final results, two flow geometries were chosen for which the numerical and experimental results were available. Surface roughness was increased in each stage (from completely smooth to 12% roughness) and its influences on the flow regime, pressure and velocity distribution, slip velocity and mass flow rate were studied. It is shown that surface roughness results in a decrease in the mass flow rate as well as slip velocity. Increasing the amount of roughness causes the mass flow rate to continually decrease, however this trend is inverted for the slip velocity

Modelling of the pulsatile blood flow in an arterial tree of retinal vasculature

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.The paper presents a numerical investigation of pulsatile blood flow in arterial vasculatures of a mouse retina using a Womersley model incorporating an appropriate outlet boundary impedance at the end of the terminal vessels of the arterial tree (pre-capillary arterioles). The mouse retinal flatmount was prepared for confocal microscopy and the morphometric information of the vasculature was obtained from the confocal images. The pulsatile analysis focused on one of the arterial trees in the retinal vasculature. We included the in vivo viscosity evaluated from the mathematical models of Fahraues-Lindquist effect and the plasma skimming effect in the microcirculation. Comparative investigations of the pulsatile circulation were carried out for cases of constant viscosity, in vivo viscosity, zero and non-zero outlet boundary impedance. In addition, the dependency of the oscillating input impedance at the inlet of the arterial trees on angular frequencies of the oscillation and vessel elasticises was also studied. The study shows the pulsatile blood flow prediction is largely influenced by the outlet boundary impedance. The oscillating input impedance at the inlet of the arterial tree is also found to be significantly dependent on the angular frequency and the Young modulus of the vessel segment

Modal Logics of Topological Relations

Logical formalisms for reasoning about relations between spatial regions play a fundamental role in geographical information systems, spatial and constraint databases, and spatial reasoning in AI. In analogy with Halpern and Shoham's modal logic of time intervals based on the Allen relations, we introduce a family of modal logics equipped with eight modal operators that are interpreted by the Egenhofer-Franzosa (or RCC8) relations between regions in topological spaces such as the real plane. We investigate the expressive power and computational complexity of logics obtained in this way. It turns out that our modal logics have the same expressive power as the two-variable fragment of first-order logic, but are exponentially less succinct. The complexity ranges from (undecidable and) recursively enumerable to highly undecidable, where the recursively enumerable logics are obtained by considering substructures of structures induced by topological spaces. As our undecidability results also capture logics based on the real line, they improve upon undecidability results for interval temporal logics by Halpern and Shoham. We also analyze modal logics based on the five RCC5 relations, with similar results regarding the expressive power, but weaker results regarding the complexity

Luddites and the Demographic Transition

Technological change was unskilled-labor-biased during the early Industrial Revolution, but is skill-biased today. This is not embedded in extant unified growth models. We develop a model which can endogenously account for these facts, where factor bias reflects profit-maximizing decisions by innovators. Endowments dictate that the early Industrial Revolution be unskilled-labor-biased. Increasing basic knowledge causes a growth takeoff, an income-led demand for fewer educated children, and the transition to skill-biased technological change. The simulated model tracks British industrialization in the 18th and 19th centuries and generates a demographic transition without relying on either rising skill premia or exogenous educational supply shocks.