Denotational Semantics of the Simplified Lambda-Mu Calculus and a New Deduction System of Classical Type Theory

Classical (or Boolean) type theory is the type theory that allows the type inference $\sigma \to \bot) \to \bot => \sigma$ (the type counterpart of double-negation elimination), where $\sigma$ is any type and $\bot$ is absurdity type. This paper first presents a denotational semantics for a simplified version of Parigot's lambda-mu calculus, a premier example of classical type theory. In this semantics the domain of each type is divided into infinitely many ranks and contains not only the usual members of the type at rank 0 but also their negative, conjunctive, and disjunctive shadows in the higher ranks, which form an infinitely nested Boolean structure. Absurdity type $\bot$ is identified as the type of truth values. The paper then presents a new deduction system of classical type theory, a sequent calculus called the classical type system (CTS), which involves the standard logical operators such as negation, conjunction, and disjunction and thus reflects the discussed semantic structure in a more straightforward fashion.Comment: In Proceedings CL&C 2016, arXiv:1606.0582

First LHCb Results from 2009 LHC Run

By the end of 2009, the Large Hadron Collider (LHC) provided a short run of pp collisions at a centre-of-mass energy of $\sqrt{s} = 900 GeV$. The LHCb Experiment has taken its first collision data with the aim to finalize the commissioning of the detector and perform the spatial and time alignments. This paper presents a collection of preliminary results of the LHCb detector obtained with the data acquired in this first LHC run. A brief outlook of the physics expected with the first data in 2010 at 7 TeV centre-of-mass energy is also presented

Experimental Determination of the Gain Distribution of an Avalanche Photodiode at Low Gains

A measurement system for determining the gain distributions of avalanche photodiodes (APDs) in a low gain range is presented. The system is based on an ultralow-noise charge--sensitive amplifier and detects the output carriers from an APD. The noise of the charge--sensitive amplifier is as low as 4.2 electrons at a sampling rate of 200 Hz. The gain distribution of a commercial Si APD with low average gains are presented, demonstrating the McIntyre theory in the low gain range.Comment: 3 pages, 4 figure