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

Some Aspects of New CDM Models and CDM Detection Methods

We briefly review some recent Cold Dark Matter (CDM) models. Our main focus are charge symmetric models of WIMPs which are not the standard SUSY LSP's (Lightest Supersymmetric Partners). We indicate which experiments are most sensitive to certain aspects of the models. In particular we discuss the manifestations of the new models in neutrino telescopes and other set-ups. We also discuss some direct detection experiments and comment on measuring the direction of recoil ions--which is correlated with the direction of the incoming WIMP. This could yield daily variations providing along with the annual modulation signatures for CDM.Comment: 14 page

Supersymmetry-Breaking Loops from Analytic Continuation into Superspace

We extend to all orders in perturbation theory a method to calculate supersymmetry-breaking effects by analytic continuation of the renormalization group into superspace. A central observation is that the renormalized gauge coupling can be extended to a real vector superfield, thereby including soft breaking effects in the gauge sector. We explain the relation between this vector superfield coupling and the "holomorphic" gauge coupling, which is a chiral superfield running only at 1 loop. We consider these issues for a number of regulators, including dimensional reduction. With this method, the renormalization group equations for soft supersymmetry breaking terms are directly related to supersymmetric beta functions and anomalous dimensions to all orders in perturbation theory. However, the real power of the formalism lies in computing finite soft breaking effects corresponding to high-loop component calculations. We prove that the gaugino mass in gauge-mediated supersymmetry breaking is ``screened'' from strong interactions in the messenger sector. We present the complete next-to-leading calculation of gaugino masses (2 loops) and sfermion masses (3 loops) in minimal gauge mediation, and several other calculations of phenomenological relevance.Comment: 50 pages, 1 ps and 1 eps figure, LaTe

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

Effect of Learning Rate on the Recognition of Images

This paper presents a study for the effect of learning rate on an approach for texture classification and detection based on the neural network principle. This neural network consists of three layers, which are input, output, and hidden layers. The back propagation technique is considered. A computer algorithm is deduced and applied. In this work, the synthetic textures are generated. The results are taken for the modern computer of AT 486 type. The mathematical analysis is summarized in order to illustrate the effect of learning rate parameter on the exact discrimination during processing. This effect is studied through applications. The minimum consumed time for the computational time of classification in industry is correlated to correspond only the use of only 2 units in the hidden layer of a neural network for real images instead of 11 units

Quantum Key Distribution over Probabilistic Quantum Repeaters

A feasible route towards implementing long-distance quantum key distribution (QKD) systems relies on probabilistic schemes for entanglement distribution and swapping as proposed in the work of Duan, Lukin, Cirac, and Zoller (DLCZ) [Nature 414, 413 (2001)]. Here, we calculate the conditional throughput and fidelity of entanglement for DLCZ quantum repeaters, by accounting for the DLCZ self-purification property, in the presence of multiple excitations in the ensemble memories as well as loss and other sources of inefficiency in the channel and measurement modules. We then use our results to find the generation rate of secure key bits for QKD systems that rely on DLCZ quantum repeaters. We compare the key generation rate per logical memory employed in the two cases of with and without a repeater node. We find the cross-over distance beyond which the repeater system outperforms the non-repeater one. That provides us with the optimum inter-node distancing in quantum repeater systems. We also find the optimal excitation probability at which the QKD rate peaks. Such an optimum probability, in most regimes of interest, is insensitive to the total distance.Comment: 12 pages, 6 figures; Fig. 5(a) is replace