A sequence x1, . . . , xn, . . . of discrete-valued observations is generated according to some unknown probabilistic law (measure) μ. After observing each outcome, it is required to give the conditional probabilities of the next observation. The realizable case is when the measure μ belongs to an arbitrary but known class C of process measures. The nonrealizable case is when μ is completely ar...

A logical calculus, not unlike Gentzen's sequent calculus for intuitionist logic, is described which is sound for polynomial-time realizability as deened by Crossley and Remmel. The sequent calculus admits cut elimination, thus giving a decision procedure for the propositional fragment. 0 Introduction In 4], a restricted notion of realizability is introduced, a special case of which is polynomi...

We present a robust arrangement algorithm for algebraic curves based on floating point arithmetic. The algorithm performs a line sweep, tests the consistency of each sweep update, and modifies the input to prevent inconsistent updates. The output arrangement is realizable by semi-algebraic curves that are close to the input curves. We present a new performance model for robust computational geo...

We show that every uniform state on the sphere is essentially a superposition of regular graphs. In addition, we develop graph-based ansatz to construct trial FHQ ground states sharing local properties Jack polynomials. particular, our graphic have (k,r) clustering property. Moreover, subclass construction realizable as densest zero-energy model modifies projection Hamiltonian.