The design of an optical computer must be based on the characteristics of optics and optical technology, and not on those of electronic technology. The property of optical superposition is considered and the implications it has in the design of computing systems is discussed. It can be exploited in the implementation of optical gates, interconnections, and shared memory. INTRODUCTION Fundamenta...

We present an extension of superposition that natively handles a polymorphic type system extended with type classes, thus eliminating the need for type encodings when used by an interactive theorem prover like Isabelle/HOL. We describe syntax, typing rules, semantics, the polymorphic superposition calculus and an evaluation on a problem set that is generated from Isabelle/HOL theories. Our eval...

We propose a linear-quadratic (LQ) control problem of streamflow discharge by optimizing an infinite-dimensional jump-driven stochastic differential equation (SDE). Our SDE is superposition Ornstein-Uhlenbeck processes (supOU process), generating sub-exponential autocorrelation function observed in actual data. The integral operator Riccati heuristically derived to determine the optimal system....

We investigate the superposition strategy and its usefulness in terms of achievable information theoretic rates. The achievable rate of the superposition of block Markov encoding (decode-forward) and side information encoding (compress-forward) for the three-node Gaussian relay channel is analyzed. It is generally believed that the superposition can out perform decode-forward or compress-forwar...

An operational measure to quantify the sizes of some “macroscopic quantum superpositions”, realized in recent experiments, is proposed. The measure is based on the fact that a superposition presents greater sensitivity in interferometric applications than its superposed constituent states. This enhanced sensitivity, or “interference utility”, may then be used as a size criterion among superposi...

We deene a superposition calculus specialized for abelian groups represented as integer modules, and show its refutational completeness. This allows to substantially reduce the number of inferences compared to a standard superposition prover which applies the axioms directly. Speciically, equational literals are simpliied, so that only the maximal term of the sums is on the left-hand side. Only...

The most efficient techniques that have been developed to date for equality handling in first-order theorem proving are based on superposition calculi. Superposition is a refinement of paramodulation in that various ordering constraints are imposed on inferences. For practical purposes, a key aspect of superposition is its compatibility with powerful simplification techniques. In this paper we ...

The fast-flying day-active hawkmoth Macroglossum stellatarum (Lepidoptera: Sphingidae) has a remarkable refracting superposition eye that departs radically from the classical principles of Exnerian superposition optics. Unlike its classical counterparts, this superposition eye is highly aspherical and contains extensive gradients of resolution and sensitivity. While such features are well known...

~ave energy flow conservation is demonstrated for Hermitian differential operators that arise m the Vlasov-Maxwell theory for propagation perpendicular to a magnetic field. The energy fl~w can be related ~o the. bilinear concomitant, for a solution and its complex conjugate, by usmg the Lagrange Identity ofthe operator. This bilinear form obeys a conservation law and is shown to describe the us...

• A quantum state Ψ is a linear superposition of basis states {|x〉}x and is described by the summation |Ψ〉 = ∑ x αx|x〉, with amplitudes αx ∈ C and |αx| the probability of observing the state x. • Formally, for an N dimensional system, the quantum state is represented by a "2 normalized vector in the N dimensional Hilbert with complex amplitudes. • Throughout this article we assume that our quan...