Specialising finite domain programs with polyhedra

A procedure is described for tightening domain constraints of finite domain logic programs by applying a static analysis based on convex polyhedra. Individual finite domain constraints are over-approximated by polyhedra to describe the solution space over ninteger variables as an n dimensional polyhedron. This polyhedron is then approximated, using projection, as an n dimensional bounding box that can be used to specialise and improve the domain constraints. The analysis can be implemented straightforwardly and an empirical evaluation of the specialisation technique is given

Incremental closure for systems of two variables per inequality

Subclasses of linear inequalities where each inequality has at most two vari- ables are popular in abstract interpretation and model checking, because they strike a balance between what can be described and what can be efficiently computed. This paper focuses on the TVPI class of inequalities, for which each coefficient of each two variable inequality is unrestricted. An implied TVPI in- equality can be generated from a pair of TVPI inequalities by eliminating a given common variable (echoing resolution on clauses). This operation, called result , can be applied to derive TVPI inequalities which are entailed (implied) by a given TVPI system. The key operation on TVPI is calculating closure: satisfiability can be observed from a closed system and a closed system also simplifies the calculation of other operations. A closed system can be derived by repeatedly applying the result operator. The process of adding a single TVPI inequality to an already closed input TVPI system and then finding the closure of this augmented system is called incremental closure. This too can be calcu- lated by the repeated application of the result operator. This paper studies the calculus defined by result , the structure of result derivations, and how deriva- tions can be combined and controlled. A series of lemmata on derivations are presented that, collectively, provide a pathway for synthesising an algorithm for incremental closure. The complexity of the incremental closure algorithm is analysed and found to be O (( n 2 + m 2 )lg( m )), where n is the number of variables and m the number of inequalities of the input TVPI system

Noncommutative symmetric functions and Laplace operators for classical Lie algebras

New systems of Laplace (Casimir) operators for the orthogonal and symplectic Lie algebras are constructed. The operators are expressed in terms of paths in graphs related to matrices formed by the generators of these Lie algebras with the use of some properties of the noncommutative symmetric functions associated with a matrix. The decomposition of the Sklyanin determinant into a product of quasi-determinants play the main role in the construction. Analogous decomposition for the quantum determinant provides an alternative proof of the known construction for the Lie algebra gl(N).Comment: 25 page

Mapping Observations of DNC and HN^13C in Dark Cloud Cores

We present results of mapping observations of the DNC, HN^13C, and H^13CO^+ lines (J=1-0) toward 4 nearby dark cloud cores, TMC-1, L1512, L1544, and L63, along with observations of the DNC and HN^13C lines (J=2-1) toward selected positions. By use of statistical equilibrium calculations based on the LVG model, the H_2 densities are derived to be (1.4-5.5)*10^5 cm^-3, and the [DNC]/[HN^13C] ratios are derived to be 1.25-5.44 with a typical uncertainty by a factor of 2. The observed [DNC]/[HNC] ratios range from 0.02 to 0.09, assuming the [^12C]/[^13C] ratio of 60. Distributions of DNC and HN^13C are generally similar to each other, whereas the distribution of H^13CO^+ is more extended than those of DNC and HN^13C, indicating that they reside in an inner part of the cores than HCO^+. The [DNC]/[HN^13C] ratio is rather constant within each core, although a small systematic gradients are observed in TMC-1 and L63. Particularly, no such systematic gradient is found in L1512 and L1544, where a significant effect of depletion of molecules is reported toward the central part of the cores. This suggests that the [DNC]/[HNC] ratio would not be very sensitive to depletion factor, unlike the [DCO^+]/[HCO^+] ratio. On the other hand, the core to core variation of the [DNC]/[HNC] ratio, which range an order of magnitude, is more remarkable than the variation within each core. These results are interpreted qualitatively by a combination of three competing time-dependent processes; gas-phase deuterium fractionation, depletion of molecules onto grain surface, and dynamical evolution of a core.Comment: 22 pages, 8 EPS figures, aasLaTex 5.0, accepted to The Astrophysical Journa

Understanding Algorithm Performance on an Oversubscribed Scheduling Application

The best performing algorithms for a particular oversubscribed scheduling application, Air Force Satellite Control Network (AFSCN) scheduling, appear to have little in common. Yet, through careful experimentation and modeling of performance in real problem instances, we can relate characteristics of the best algorithms to characteristics of the application. In particular, we find that plateaus dominate the search spaces (thus favoring algorithms that make larger changes to solutions) and that some randomization in exploration is critical to good performance (due to the lack of gradient information on the plateaus). Based on our explanations of algorithm performance, we develop a new algorithm that combines characteristics of the best performers; the new algorithms performance is better than the previous best. We show how hypothesis driven experimentation and search modeling can both explain algorithm performance and motivate the design of a new algorithm

Low-degree multi-spectral p-mode fitting

We combine unresolved-Sun velocity and intensity observations at multiple wavelengths from the Helioseismic and Magnetic Imager and Atmospheric Imaging Array onboard the Solar Dynamics Observatory to investigate the possibility of multi-spectral mode-frequency estimation at low spherical harmonic degree. We test a simple multi-spectral algorithm using a common line width and frequency for each mode and a separate amplitude, background and asymmetry parameter, and compare the results with those from fits to the individual spectra. The preliminary results suggest that this approach may provide a more stable fit than using the observables separately

Solar cycle induced variations in GONG p-mode frequencies and splittings

We have analysed the recently available GONG p-mode frequencies and splitting coefficients for a period of three and half years, including the rapidly rising phase of solar cycle 23. The analysis of mean frequency shift with different activity indices shows that the shift is equally correlated with both magnetic and radiative indices. During the onset of the new cycle 23, we notice that the change in $b_4$ splitting coefficient is more prominent than the change in $b_2$. We have estimated the solar rotation rate with varying depth and latitude. In the equatorial region, the rotation first increases with depth and then decreases, while an opposite behaviour is seen in the polar region. We also find a small but significant temporal variation in the rotation rate at high latitudes.Comment: Uses aastex, To appear in Astrophysical Journal, October 10, 2000 issu

Volkov-Akulov theory and D-branes

The action of supersymmetric Born-Infeld theory (D-9-brane in a Lorentz covariant static gauge) has a geometric form of the Volkov-Akulov-type. The first non-linearly realized supersymmetry can be made manifest, the second world-volume supersymmetry is not manifest. We also study the analogous 2 supersymmetries of the quadratic action of the covariantly quantized D-0-brane. We show that the Hamiltonian and the BRST operator are build from these two supersymmetry generators.Comment: 10 pages, Latex, Contribution to Supersymmetry and Quantum Field Theory, International Seminar dedicated to the memory of D. V. Volkov (Kharkov, 1997