Discrete Gravitational Dimensions

We study the physics of a single discrete gravitational extra dimension using the effective field theory for massive gravitons. We first consider a minimal discretization with 4D gravitons on the sites and nearest neighbor hopping terms. At the linear level, 5D continuum physics is recovered correctly, but at the non-linear level the theory becomes highly non-local in the discrete dimension. There is a peculiar UV/IR connection, where the scale of strong interactions at high energies is related to the radius of the dimension. These new effects formally vanish in the limit of zero lattice spacing, but do not do so quickly enough to reproduce the continuum physics consistently in an effective field theory up to the 5D Planck scale. Nevertheless, this model does make sense as an effective theory up to energies parametrically higher than the compactification scale. In order to have a discrete theory that appears local in the continuum limit, the lattice action must have interactions between distant sites. We speculate on the relevance of these observations to the construction of finite discrete theories of gravity in four dimensions.Comment: 5 pages, 4 diagrams. Important typos in some equations corrected; conclusion s unchange

Constructing Gravitational Dimensions

It would be extremely useful to know whether a particular low energy effective theory might have come from a compactification of a higher dimensional space. Here, this problem is approached from the ground up by considering theories with multiple interacting massive gravitons. It is actually very difficult to construct discrete gravitational dimensions which have a local continuum limit. In fact, any model with only nearest neighbor interactions is doomed. If we could find a non-linear extension for the Fierz-Pauli Lagrangian for a graviton of mass mg which does not break down until the scale Lambda_2=(mg Mpl)^(1/2), this could be used to construct a large class of models whose continuum limit is local in the extra dimension. But this is shown to be impossible: a theory with a single graviton must break down by Lambda_3 = (mg^2 Mpl)^(1/3). Next, we look at how the discretization prescribed by the truncation of the KK tower of an honest extra diemsinon rasies the scale of strong coupling. It dictates an intricate set of interactions among various fields which conspire to soften the strongest scattering amplitudes and allow for a local continuum limit. A number of canditate symmetries associated with locality in the discretized dimension are also discussed.Comment: 21 pages, 6 diagrams, 1 figur

Fault tolerant architectures for integrated aircraft electronics systems

Work into possible architectures for future flight control computer systems is described. Ada for Fault-Tolerant Systems, the NETS Network Error-Tolerant System architecture, and voting in asynchronous systems are covered

Fault tolerant architectures for integrated aircraft electronics systems, task 2

The architectural basis for an advanced fault tolerant on-board computer to succeed the current generation of fault tolerant computers is examined. The network error tolerant system architecture is studied with particular attention to intercluster configurations and communication protocols, and to refined reliability estimates. The diagnosis of faults, so that appropriate choices for reconfiguration can be made is discussed. The analysis relates particularly to the recognition of transient faults in a system with tasks at many levels of priority. The demand driven data-flow architecture, which appears to have possible application in fault tolerant systems is described and work investigating the feasibility of automatic generation of aircraft flight control programs from abstract specifications is reported

Tensors Mesons in AdS/QCD

We explore tensor mesons in AdS/QCD focusing on f2 (1270), the lightest spin-two resonance in QCD. We find that the f2 mass and the partial width for f2 -> gamma gamma are in very good agreement with data. In fact, the dimensionless ratio of these two quantities comes out within the current experimental bound. The result for this ratio depends only on Nc and Nf, and the quark and glueball content of the operator responsible for the f2; more importantly, it does not depend on chiral symmetry breaking and so is both independent of much of the arbitrariness of AdS/QCD and completely out of reach of chiral perturbation theory. For comparison, we also explore f2 -> pi pi, which because of its sensitivity to the UV corrections has much more uncertainty. We also calculate the masses of the higher spin resonances on the Regge trajectory of the f2, and find they compare favorably with experiment.Comment: 21 pages, 1 figure; Li's correcte

Complement protein levels in plasma astrocyte-derived exosomes are abnormal in conversion from mild cognitive impairment to Alzheimer's disease dementia.

IntroductionLevels of complement proteins (CPs) in plasma astrocyte-derived exosomes (ADEs) that are abnormal in Alzheimer's disease (AD) have not been assessed in mild cognitive impairment (MCI).MethodsParticipants (n = 20 per group) had either MCI converting to dementia within 3 years (MCIC), MCI remaining stable over 3 years (MCIS), Alzheimer's disease, or were controls. CPs of ADEs isolated from plasmas by anti-human glutamine aspartate transporter antibody absorption were quantified by ELISAs.ResultsADE levels of C1q and C4b of the classical pathway, factor D and fragment Bb of the alternative pathway, and C5b, C3b, and C5b-C9 of both pathways were significantly higher in patients with MCIC than those with MCIS. ADE levels of inhibitory CPs decay-accelerating factor, CD46, CD59, and type 1 complement receptor were significantly lower in patients with MCIC than those with MCIS.DiscussionADE CPs are components of neurotoxic neuroinflammation that may be predictive biomarkers of MCI conversion to Alzheimer's disease

Some closure operations in Zariski-Riemann spaces of valuation domains: a survey

In this survey we present several results concerning various topologies that were introduced in recent years on spaces of valuation domains

Using The Student Research Project To Integrate Macroeconomics And Statistics In An Advanced Cost Accounting Course

This paper discusses a student research project that is part of an advanced cost accounting class. The project emphasizes active learning, integrates cost accounting with macroeconomics and statistics by “learning by doing” using real world data. Students analyze sales data for a publically listed company by focusing on the company’s growth rates in sales, and their growth rates in real sales by adjusting for inflation using the various consumer price indices or producer price indices that are available, and regressing the sales growth rates against macroeconomic variables such as gross domestic product and the various types of personal consumption expenditure items

Temporal behavior of two-wave-mixing in photorefractive InP:Fe versus temperature

The temporal response of two-wave-mixing in photorefractive InP:Fe under a dc electric field at different temperatures has been studied. In particular, the temperature dependence of the characteristic time constant has been studied both theoretically and experimentally, showing a strongly decreasing time constant with increasing temperature