Increasing subsequences and the hard-to-soft edge transition in matrix ensembles

Our interest is in the cumulative probabilities Pr(L(t) \le l) for the maximum length of increasing subsequences in Poissonized ensembles of random permutations, random fixed point free involutions and reversed random fixed point free involutions. It is shown that these probabilities are equal to the hard edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively. The gap probabilities can be written as a sum over correlations for certain determinantal point processes. From these expressions a proof can be given that the limiting form of Pr(L(t) \le l) in the three cases is equal to the soft edge gap probability for matrix ensembles with unitary, orthogonal and symplectic symmetry respectively, thereby reclaiming theorems due to Baik-Deift-Johansson and Baik-Rains.Comment: LaTeX, 19 page

Spatial correlations of the 1D KPZ surface on a flat substrate

We study the spatial correlations of the one-dimensional KPZ surface for the flat initial condition. It is shown that the multi-point joint distribution for the height is given by a Fredholm determinant, with its kernel in the scaling limit explicitly obtained. This may also describe the dynamics of the largest eigenvalue in the GOE Dyson's Brownian motion model. Our analysis is based on a reformulation of the determinantal Green's function for the totally ASEP in terms of a vicious walk problem.Comment: 11 pages, 2 figure

Eynard-Mehta theorem, Schur process, and their pfaffian analogs

We give simple linear algebraic proofs of Eynard-Mehta theorem, Okounkov-Reshetikhin formula for the correlation kernel of the Schur process, and Pfaffian analogs of these results. We also discuss certain general properties of the spaces of all determinantal and Pfaffian processes on a given finite set.Comment: AMSTeX, 21 pages, a new section adde

On the Form Factor for the Unitary Group

We study the combinatorics of the contributions to the form factor of the group U(N) in the large $N$ limit. This relates to questions about semiclassical contributions to the form factor of quantum systems described by the unitary ensemble.Comment: 35 page

Decoherence and Entanglement in Two-mode Squeezed Vacuum States

I investigate the decoherence of two-mode squeezed vacuum states by analyzing the relative entropy of entanglement. I consider two sources of decoherence: (i) the phase damping and (ii) the amplitude damping due to the coupling to the thermal environment. In particular, I give the exact value of the relative entropy of entanglement for the phase damping model. For the amplitude damping model, I give an upper bound for the relative entropy of entanglement, which turns out to be a good approximation for the entanglement measure in usual experimental situations.Comment: 5 pages, RevTex, 3 eps figure

Abelian varieties isogenous to a power of an elliptic curve

Let $E$ be an elliptic curve over a field $k$. Let $R:= \text{End}\, E$. There is a functor $\mathscr{H}\!\!\mathit{om}_R(-,E)$ from the category of finitely presented torsion-free left $R$-modules to the category of abelian varieties isogenous to a power of $E$, and a functor $\text{Hom}(-,E)$ in the opposite direction. We prove necessary and sufficient conditions on $E$ for these functors to be equivalences of categories.Comment: 21 pages, comments welcom

Hiding bits in Bell states

We present a scheme for hiding bits in Bell states that is secure even when the sharers Alice and Bob are allowed to carry out local quantum operations and classical communication. We prove that the information that Alice and Bob can gain about a hidden bit is exponentially small in $n$, the number of qubits in each share, and can be made arbitrarily small for hiding multiple bits. We indicate an alternative efficient low-entanglement method for preparing the shared quantum states. We discuss how our scheme can be implemented using present-day quantum optics.Comment: 4 pages RevTex, 1 figure, various small changes and additional paragraph on optics implementatio

A randomised controlled trial of the clinical and cost-effectiveness of a contingency management intervention for reduction of cannabis use and of relapse in early psychosis (CIRCLE): a study protocol for a randomised controlled trial

Background: Around 35–45 % of people in contact with services for a first episode of psychosis are using cannabis. Cannabis use is associated with delays in remission, poorer clinical outcomes, significant increases in the risk of relapse, and lower engagement in work or education. While there is a clear need for effective interventions, so far only very limited benefits have been achieved from psychological interventions. Contingency management (CM) is a behavioural intervention in which specified desired behavioural change is reinforced through financial rewards. CM is now recognised to have a substantial evidence base in some contexts and its adoption in the UK is advocated by the National Institute for Health and Care Excellence (NICE) guidance as a treatment for substance or alcohol misuse. However, there is currently little published data testing its effectiveness for reducing cannabis use in early psychosis. Methods: CIRCLE is a two-arm, rater-blinded randomised controlled trial (RCT) investigating the clinical and cost-effectiveness of a CM intervention for reducing cannabis use among young people receiving treatment from UK Early Intervention in Psychosis (EIP) services. EIP service users (n = 544) with a recent history of cannabis use will be recruited. The experimental group will receive 12 once-weekly CM sessions, and a voucher reward if urinalysis shows that they have not used cannabis in the previous week. Both the experimental and the control groups will be offered an Optimised Treatment as Usual (OTAU) psychoeducational package targeting cannabis use. Assessment interviews will be performed at consent, at 3 months, and at 18 months. The primary outcome is time to relapse, defined as admission to an acute mental health service. Secondary outcomes include proportion of cannabis-free urine samples during the intervention period, severity of positive psychotic symptoms, quality-adjusted life years, and engagement in work or education. Discussion: CIRCLE is a RCT of CM for cannabis use in young people with a recent history of psychosis (EIP service users) and recent cannabis use. It is designed to investigate whether the intervention is a clinically and cost-effective treatment for cannabis use. It is intended to inform future treatment delivery, particularly in EIP settings

The asymptotic entanglement cost of preparing a quantum state

We give a detailed proof of the conjecture that the asymptotic entanglement cost of preparing a bipartite state \rho is equal to the regularized entanglement of formation of \rho.Comment: 7 pages, no figure