The Steinberg torus of a Weyl group as a module over the Coxeter complex

Associated to each irreducible crystallographic root system $\Phi$, there is a certain cell complex structure on the torus obtained as the quotient of the ambient space by the coroot lattice of $\Phi$. This is the Steinberg torus. A main goal of this paper is to exhibit a module structure on (the set of faces of) this complex over the (set of faces of the) Coxeter complex of $\Phi$. The latter is a monoid under the Tits product of faces. The module structure is obtained from geometric considerations involving affine hyperplane arrangements. As a consequence, a module structure is obtained on the space spanned by affine descent classes of a Weyl group, over the space spanned by ordinary descent classes. The latter constitute a subalgebra of the group algebra, the classical descent algebra of Solomon. We provide combinatorial models for the module of faces when $\Phi$ is of type $A$ or $C$.Comment: 36 pages, 23 figures. Extended abstract of this work appeared in proceedings of FPSAC 25 (Paris): DMTCS proceedings AS, 2013, p. 277-28

Inflation tax and deficit financing in Egypt

Although Egypt's budget deficit is far above the level found in other low-middle-income countries, the inflation rate in Egypt has never been very high. This is because the country has managed to finance these budget deficits by resorting to an inflation tax that, at 11 percent of GDP in 1987, constitutes a large share of total tax revenues. By contrast, conventional tax revenues come to only 17 percent of GDP. The authors report a large, underlying inflation-tax base - from which the Egyptian government has collected substantial revenues which exist because of money balances held by the private sector. The authors find that the private business sector, with anet borrowing position of 14 percent of GDP, has benefited from the inflation tax. Households, on the other hand, pay more of the inflation tax than other sectors, turning over 8 percent of GDP to the government. This compares with 0.5 percent of GDP that households pay in income tax. Although income tax in Egypt is fairly progressive, the greater reliance on the inflation tax makes Egypt's overall tax structure fairly regressive. The authors argue that : i) understanding the role and size of the inflation tax will help in determining the sequencing and equity aspects of any future reform program; and ii) the financial side cannot continue to bear the burden for the real side; Egypt must move swiftly to cut its budget deficit, the underlying cause of its dependence on the inflation tax.Economic Theory&Research,Public Sector Economics&Finance,Banks&Banking Reform,Environmental Economics&Policies,Macroeconomic Management

Money, inflation, and deficit in Egypt

Egypt has been able to escape high inflation by depleting its stocks of creditworthiness, money illusion, and enforceable foreign-exchange controls. These nonrecoverable assets are quickly becoming extinct and the economy is on an unsustainable path. The authors present a short- and medium-term dynamic model of the Egyptian economy and use it to simulate the effects on output and inflation of a stabilization-cum-adjustment program. Their conclusion is to make the public sector live within its means, and to do so at once. This is a demanding prescription; political and social pressure can become intolerable under adjustment. The authors show that both a slowdown in output and the initial rise in inflation associated with a tough reform program will be short-lived. And a do-nothing strategy will soon push the country into a serious crisis, the correction of which will certainly be more painful.Economic Theory&Research,Economic Stabilization,Environmental Economics&Policies,Banks&Banking Reform,Public Sector Economics&Finance

Lead extrusion analysis by finite volume method

Computational numerical simulation is nowadays largely applied in the design and analysis of metal forming process. Extrusion of metals is one main forming process largely applied in the manufacturing of metallic products or parts. Historically, the Finite Element Method has been applied for decades in metal extrusion analysis [4]. However, recently in the academy, there is a trend to use Finite Volume Method: literature suggests that metal flow by extrusion can be analyzed by the flow formulation [1, 2]. Thus, metal flow can be modelled such us an incompressible viscous fluid [2]. This hypothesis can be assumed because extrusion process is an isochoric process. The MacCormack Method is commonly used to simulate compressible fluid flow by the finite volume method [3]. However, metal extrusion and incompressible fluid flow do not present state equations for the evolution of pressure, and therefore, a velocity-pressure coupling method is necessary to obtain a consistent velocity and pressure fields [3]. Present work proposes a new numerical scheme to obtain information about metal flow in the extrusion process, in steady state. The governing equations were discretized by Finite Volume Method, using the Explicit MacCormack Method to structured and collocated mesh. The SIMPLE Method was applied to attain pressure-velocity coupling [3]. These new numerical scheme was applied to forward extrusion process of lead. The incompressible metal extrusion velocity fields achieved faster convergence and a good agreement with analytical and experimental results obtained from literature. The MacCormack Method applied for metals produced consistent results without the need of artificial viscosity as employed by the compressible flow simulation approaches. Furthermore, the present numerical results also suggest that MacCormack Method and SIMPLE can be applied in the solution of metal forming processes besides the traditional application for compressible fluid flow

Aluminium extrusion analysis by the finite volume method

Present work proposes a novel numerical scheme to calculate stress and velocity fields of metal flow in axisymmetric extrusion process in steady state. Extrusion of aluminium is one main metal forming process largely applied in manufacturing bars and products with complex cross section shape. The upper-bound, slab, slip-line methods and more recently the numerical methods such as the Finite Element Method have been commonly applied in aluminium extrusion analysis. However, recently in the academy, the Finite Volume Method has been developed for metal flow analysis: literature suggests that extrusion of metals can be modelled by the flow formulation. Hence, metal flow can be mathematically modelled such us an incompressible non linear viscous fluid, owing to volume constancy and varying viscosity in metal forming. The governing equations were discretized by the Finite Volume Method, using the Explicit MacCormack Method in structured and collocated mesh. The MacCormack Method is commonly used to simulate compressible fluid flow by the finite volume method. However, metal plastic flow and incompressible fluid flow do not present state equations for the evolution of pressure, and therefore, a velocity-pressure coupling method is necessary to obtain a consistent velocity and pressure fields. The SIMPLE Method was applied to attain pressure-velocity coupling. This new numerical scheme was applied to forward hot extrusion process of an aluminium alloy. The metal extrusion velocity fields achieved fast convergence and a good agreement with experimental results. The MacCormack Method applied to metal extrusion produced consistent results without the need of artificial viscosity as employed by the compressible flow simulation approaches. Therefore, present numerical results also suggest that MacCormack method together with SIMPLE method can be applied in the solution of metal forming processes in addition to the traditional application for compressible fluid flow

Organising metabolic networks: cycles in flux distributions

Metabolic networks are among the most widely studied biological systems. The topology and interconnections of metabolic reactions have been well described for many species, but are not sufficient to understand how their activity is regulated in living organisms. The principles directing the dynamic organisation of reaction fluxes remain poorly understood. Cyclic structures are thought to play a central role in the homeostasis of biological systems and in their resilience to a changing environment. In this work, we investigate the role of fluxes of matter cycling in metabolic networks. First, we introduce a methodology for the computation of cyclic and acyclic fluxes in metabolic networks, adapted from an algorithm initially developed to study cyclic fluxes in trophic networks. Subsequently, we apply this methodology to the analysis of three metabolic systems, including the central metabolism of wild type and a deletion mutant of Escherichia coli, erythrocyte metabolism and the central metabolism of the bacterium Methylobacterium extorquens. The role of cycles in driving and maintaining the performance of metabolic functions upon perturbations is unveiled through these examples. This methodology may be used to further investigate the role of cycles in living organisms, their pro-activity and organisational invariance, leading to a better understanding of biological entailment and information processing

Optomechanical transduction of an integrated silicon cantilever probe using a microdisk resonator

Sensitive transduction of the motion of a microscale cantilever is central to many applications in mass, force, magnetic resonance, and displacement sensing. Reducing cantilever size to nanoscale dimensions can improve the bandwidth and sensitivity of techniques like atomic force microscopy, but current optical transduction methods suffer when the cantilever is small compared to the achievable spot size. Here, we demonstrate sensitive optical transduction in a monolithic cavity-optomechanical system in which a sub-picogram silicon cantilever with a sharp probe tip is separated from a microdisk optical resonator by a nanoscale gap. High quality factor (Q ~ 10^5) microdisk optical modes transduce the cantilever's MHz frequency thermally-driven vibrations with a displacement sensitivity of ~ 4.4x10^-16 m\sqrt[2]{Hz} and bandwidth > 1 GHz, and a dynamic range > 10^6 is estimated for a 1 s measurement. Optically-induced stiffening due to the strong optomechanical interaction is observed, and engineering of probe dynamics through cantilever design and electrostatic actuation is illustrated

Universal and deterministic manipulation of the quantum state of harmonic oscillators: a route to unitary gates for Fock State qubits

We present a simple quantum circuit that allows for the universal and deterministic manipulation of the quantum state of confined harmonic oscillators. The scheme is based on the selective interactions of the referred oscillator with an auxiliary three-level system and a classical external driving source, and enables any unitary operations on Fock states, two-by-two. One circuit is equivalent to a single qubit unitary logical gate on Fock states qubits. Sequences of similar protocols allow for complete, deterministic and state-independent manipulation of the harmonic oscillator quantum state.Comment: 4 pages, 4 figure

Implications of WMAP 3 Year Data for the Sources of Reionization

New results on the anisotropy of the cosmic microwave background (CMB) and its polarization based on the first 3 years of data from the Wilkinson Microwave Anisotropy Probe (WMAP) have revised the electron scattering optical depth downward from tau_es=0.17+0.08-0.07 to tau_es=0.09+/-0.03. This implies a shift of the effective reionization redshift from z_r~17 to z_r~11. Previous attempts to explain the high redshift of reionization inferred from the WMAP 1 year data have led to widespread speculation that the sources of reionization must have been much more efficient than those associated with the star formation observed at low redshift. This is consistent, for example, with the suggestion that early star formation involved massive, Population III stars that early on produced most of the ionizing radiation escaping from halos. It is therefore tempting to interpret the new WMAP results as implying that we can now relax those previous high demands on the efficiency of the sources of reionization and perhaps even turn the argument around as evidence against such high efficiency. We show that this is not the case, however. The new WMAP results also find that the primordial density fluctuation power spectrum has a lower amplitude, sigma_8, and departs substantially from the scale-invariant spectrum. We show that these effects combine to cancel the impact of the later reionization implied by the new value of tau_es on the required ionizing efficiency per collapsed baryon. The delay of reionization is surprisingly well matched by a comparable delay (by a factor of ~1.4 in scale factor) in the formation of the halos responsible for reionization.Comment: 4 pages, 3 figures, Published in ApJ Letters, revised to match published versio