Improving PARMA Trailing

Taylor introduced a variable binding scheme for logic variables in his PARMA system, that uses cycles of bindings rather than the linear chains of bindings used in the standard WAM representation. Both the HAL and dProlog languages make use of the PARMA representation in their Herbrand constraint solvers. Unfortunately, PARMA's trailing scheme is considerably more expensive in both time and space consumption. The aim of this paper is to present several techniques that lower the cost. First, we introduce a trailing analysis for HAL using the classic PARMA trailing scheme that detects and eliminates unnecessary trailings. The analysis, whose accuracy comes from HAL's determinism and mode declarations, has been integrated in the HAL compiler and is shown to produce space improvements as well as speed improvements. Second, we explain how to modify the classic PARMA trailing scheme to halve its trailing cost. This technique is illustrated and evaluated both in the context of dProlog and HAL. Finally, we explain the modifications needed by the trailing analysis in order to be combined with our modified PARMA trailing scheme. Empirical evidence shows that the combination is more effective than any of the techniques when used in isolation. To appear in Theory and Practice of Logic Programming.Comment: 36 pages, 7 figures, 8 table

Observing The Hidden Sector

We study the effects of renormalization due to hidden-sector dynamics on observable soft supersymmetry-breaking parameters in the minimal supersymmetric extension of the Standard Model (MSSM), under various hypotheses about their universality at a high input scale. We show that hidden-sector renormalization effects may induce the spurious appearance of unification of the scalar masses at some lower scale, as in mirage unification scenarios. We demonstrate in simple two-parameter models of the hidden-sector dynamics that the parameters may in principle be extracted from experimental measurements, rendering the hidden sector observable. We also discuss the ingredients that would be necessary to carry this programme out in practice.Comment: 38 pages, 13 figures, uses UApreprint.cls and subfigure.sty (included

Nominal Unification from a Higher-Order Perspective

Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as distinct entities. Moreover, atoms are capturable by instantiations, breaking a fundamental principle of lambda-calculus. Despite these differences, nominal unification can be seen from a higher-order perspective. From this view, we show that nominal unification can be reduced to a particular fragment of higher-order unification problems: Higher-Order Pattern Unification. This reduction proves that nominal unification can be decided in quadratic deterministic time, using the linear algorithm for Higher-Order Pattern Unification. We also prove that the translation preserves most generality of unifiers

Split Supersymmetry in String Theory

Type I string theory in the presence of internal magnetic fields provides a concrete realization of split supersymmetry. To lowest order, gauginos are massless while squarks and sleptons are superheavy. For weak magnetic fields, the correct Standard Model spectrum guarantees gauge coupling unification with \sin^2{\theta_W}=3/8 at the compactification scale of M_{\rm GUT}\simeq 2 \times 10^{16} GeV. I discuss mechanisms for generating gaugino and higgsino masses at the TeV scale, as well as generalizations to models with split extended supersymmetry in the gauge sector.Comment: 7 pages, 3 figures, prepared for the Proceedings of PASCOS-05 and of CORFU2005 Summer Institut

Unification of Gauge, Higgs and Matter in Extra Dimensions

We consider the unification of gauge, Higgs as well as the matter fields in a 6D N=2 supersymmetric SU(8) gauge theory. The gauge symmetry SU(8) is broken down to SU(4) x SU(2)_L x SU(2)_R x U(1)^2 in 4D through T^2/Z_6 orbifold compactification, and the theory is reduced to 4D N=1 supersymmetric Pati-Salam model. The electroweak Higgs fields as well as the third family of fermions are unified in the 6D N=2 gauge multiplet. The 6D bulk gauge interaction provides both gauge and Yukawa interactions for the third family predicting \alpha_1 = \alpha_2 = \alpha_3 = \alpha_t = \alpha_b = \alpha_tau at the unification scale, in good agreement with experiment. Incorporation of the first and second family as well as other orbifolds are also briefly discussed.Comment: 13 pages and 1 figure, some minor corrections and references adde

Nominal Logic Programming

Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, alpha-equivalence). This article investigates logic programming based on nominal logic. We describe some typical nominal logic programs, and develop the model-theoretic, proof-theoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via examples.Comment: 46 pages; 19 page appendix; 13 figures. Revised journal submission as of July 23, 200

Does the unification of BL Lac and FR I radio galaxies require jet velocity structures?

We explore the viability of the unification of BL Lacs and FR I radio galaxies by comparing the core emission of radio galaxies with those of BL Lacs of similar extended radio power, taking advantage of the newly measured optical nuclear luminosity of FR I sources. The spectral properties of complete samples are also studied in the radio-optical luminosity plane: starting from the Spectral Energy Distribution (SED) of BL Lacs, we calculate the predicted luminosity of FR I nuclei in the frame of a simple one--zone model, by properly taking into account the relativistic transformations. We find that the bulk Lorentz factors required by the spread in the observed luminosities in all bands are significantly smaller than those implied by other, both observational and theoretical, considerations. This discrepancy is also reflected in the fact that FR I nuclei are over-luminous by a factor of 10-10^4, with respect to the predictions, both in the radio and in the optical band. In order to reconcile these results with the unification scheme, velocity structures in the jet are suggested, where a fast spine is surrounded by a slow (but still relativistic) layer so that the emission at different angles is dominated by different velocity components: the fast one dominates the emission in BL Lacs while the slow layer dominates the emission in misaligned objects. Furthermore for the lowest luminosity BL Lacs it has to be also postulated that their beaming factor in the radio band is lower than in the optical (and X-ray), as would result from deceleration of the jet. The self-consistency of the unification model therefore requires that both intrinsic differences in the SED and different beaming properties play a substantial role in characterizing the phenomenology of these sources.Comment: 10 pages, 11 figures, revised version, to be published in A&