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We introduce a new propositional proof system, which we call H, that allows quantification over permutations. In H we may write (∃ab)α and (∀ab)α, which is semantically equivalent to α(a, b) ∨ α(b, a) and α(a, b) ∧ α(b, a), respectively. We show that H with cuts restricted to Σ1 formulas (we denote this system H1) simulates efficiently the Hajós calculus (HC) for constructing graphs which are n...

The goal of this paper is to generalize certain results of Nguyen [1] (concerning the α-cuts of two-place functions defined by the Zadeh’s extension principle) to the case of extended two-place functions defined via a sup-tnorm convolution.

We extend the theorem of Balslev and Combes on the absence of singular continuous spectrum to a class of interactions including r~ (3/2 ̂ α < 2) local potentials. In addition, we note that the theory of sectorial operators allows a simplification of their proof and allows one to push the cuts through angles larger than the π/2 restriction employed by Balslev-Combes.

In this paper we are concerned with cuts in models of Samuel Buss' theories of bounded arithmetic, i.e. theories like $S_{2}^i$ and $T_{2}^i$. In correspondence with polynomial induction, we consider a rather new notion of cut that we call p-cut. We also consider small cuts, i.e. cuts that are bounded above by a small element. We study the basic properties of p-cuts and small cuts. In particula...

We investigate the angular distribution of the lepton pair in the process p¯ p → γ * + X → ℓ + ℓ − + X, where the virtual photon is produced at high transverse momentum. The angular distribution of the leptons is very sensitive to possible nonperturbative effects, such as a nontrivial vacuum structure of QCD, and offers a good chance to test such effects. We present complete O(α 2 s) calculatio...

This paper presents a new class of moves, called α-expansioncontraction, which generalizes α-expansion graph cuts for multi-label energy minimization problems. The new moves are particularly useful for optimizing the assignments in model fitting frameworks whose energies include Label Cost (LC), as well as Markov Random Field (MRF) terms. These problems benefit from the contraction moves’ great...