Ranking Functions for Size-Change Termination II

Size-Change Termination is an increasingly-popular technique for verifying program termination. These termination proofs are deduced from an abstract representation of the program in the form of "size-change graphs". We present algorithms that, for certain classes of size-change graphs, deduce a global ranking function: an expression that ranks program states, and decreases on every transition. A ranking function serves as a witness for a termination proof, and is therefore interesting for program certification. The particular form of the ranking expressions that represent SCT termination proofs sheds light on the scope of the proof method. The complexity of the expressions is also interesting, both practicaly and theoretically. While deducing ranking functions from size-change graphs has already been shown possible, the constructions in this paper are simpler and more transparent than previously known. They improve the upper bound on the size of the ranking expression from triply exponential down to singly exponential (for certain classes of instances). We claim that this result is, in some sense, optimal. To this end, we introduce a framework for lower bounds on the complexity of ranking expressions and prove exponential lower bounds.Comment: 29 pages

Lifetime of Surface Features and Stellar Rotation: A Wavelet Time-Frequency Approach

We explore subtle variations in disk-integrated measurements spanning \lsim 18 years of stellar surface magnetism by using a newly developed time-frequency gapped wavelet algorithm. We present results based on analysis of the Mount Wilson Ca II H and K emission fluxes in four, magnetically-active stars (HD 1835 [G2V], 82885 [G8IV-V], 149661 [K0V] and 190007 [K4V]) and sensitivity tests using artificial data. When the wavelet basis is appropriately modified (i.e., when the time-frequency resolution is optimized), the results are consistent with the existence of spatially localized and long-lived Ca II features (assumed here as activity regions that tend to recur in narrowly-confined latitude bands), especially in HD 1835 and 82885. This interpretation is based on the observed persistence of relatively localized Ca II wavelet power at a narrow range of rotational time scales, enduring as long as \gsim 10 years.Comment: to appear in THE ASTROPHYSICAL JOURNAL LETTER

BRST extension of the Faddeev model

The Faddeev model is a second class constrained system. Here we construct its nilpotent BRST operator and derive the ensuing manifestly BRST invariant Lagrangian. Our construction employs the structure of Stuckelberg fields in a nontrivial fashion.Comment: 4 pages, new references adde

CS 801: Advanced Database Systems

Introduction of current trends and research issues in database systems

BRST invariance and de Rham-type cohomology of 't Hooft-Polyakov monopole

We exploit the 't Hooft-Polyakov monopole to define closed algebra of the quantum field operators and the BRST charge $Q_{BRST}$. In the first-class configuration of the Dirac quantization, by including the $Q_{BRST}$-exact gauge fixing term and the Faddeev-Popov ghost term, we find the BRST invariant Hamiltonian to investigate the de Rham-type cohomology group structure for the monopole system. The Bogomol'nyi bound is also discussed in terms of the first-class topological charge defined on the extended internal 2-sphere.Comment: 8 page

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CS 801: Advanced Database Systems

Introduction of current trends and research issues in database systems

CEG 820-01: Computer Architecture II

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CS 701: Database Systems and Design

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