The Measurement Calculus

Measurement-based quantum computation has emerged from the physics community as a new approach to quantum computation where the notion of measurement is the main driving force of computation. This is in contrast with the more traditional circuit model which is based on unitary operations. Among measurement-based quantum computation methods, the recently introduced one-way quantum computer stands out as fundamental. We develop a rigorous mathematical model underlying the one-way quantum computer and present a concrete syntax and operational semantics for programs, which we call patterns, and an algebra of these patterns derived from a denotational semantics. More importantly, we present a calculus for reasoning locally and compositionally about these patterns. We present a rewrite theory and prove a general standardization theorem which allows all patterns to be put in a semantically equivalent standard form. Standardization has far-reaching consequences: a new physical architecture based on performing all the entanglement in the beginning, parallelization by exposing the dependency structure of measurements and expressiveness theorems. Furthermore we formalize several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. This allows us to transfer all the theory we develop for the one-way model to these models. This shows that the framework we have developed has a general impact on measurement-based computation and is not just particular to the one-way quantum computer.Comment: 46 pages, 2 figures, Replacement of quant-ph/0412135v1, the new version also include formalization of several other measurement-based models: Teleportation, Phase and Pauli models and present compositional embeddings of them into and from the one-way model. To appear in Journal of AC

Theory of Chiral Order in Random Copolymers

Recent experiments have found that polyisocyanates composed of a mixture of opposite enantiomers follow a chiral ``majority rule:'' the chiral order of the copolymer, measured by optical activity, is dominated by whichever enantiomer is in the majority. We explain this majority rule theoretically by mapping the random copolymer onto the random-field Ising model. Using this model, we predict the chiral order as a function of enantiomer concentration, in quantitative agreement with the experiments, and show how the sharpness of the majority-rule curve can be controlled.Comment: 13 pages, including 4 postscript figures, uses REVTeX 3.0 and epsf.st

Thurston's pullback map on the augmented Teichm\"uller space and applications

Let $f$ be a postcritically finite branched self-cover of a 2-dimensional topological sphere. Such a map induces an analytic self-map $\sigma_f$ of a finite-dimensional Teichm\"uller space. We prove that this map extends continuously to the augmented Teichm\"uller space and give an explicit construction for this extension. This allows us to characterize the dynamics of Thurston's pullback map near invariant strata of the boundary of the augmented Teichm\"uller space. The resulting classification of invariant boundary strata is used to prove a conjecture by Pilgrim and to infer further properties of Thurston's pullback map. Our approach also yields new proofs of Thurston's theorem and Pilgrim's Canonical Obstruction theorem.Comment: revised version, 28 page

Order and Frustration in Chiral Liquid Crystals

This paper reviews the complex ordered structures induced by chirality in liquid crystals. In general, chirality favors a twist in the orientation of liquid-crystal molecules. In some cases, as in the cholesteric phase, this favored twist can be achieved without any defects. More often, the favored twist competes with applied electric or magnetic fields or with geometric constraints, leading to frustration. In response to this frustration, the system develops ordered structures with periodic arrays of defects. The simplest example of such a structure is the lattice of domains and domain walls in a cholesteric phase under a magnetic field. More complex examples include defect structures formed in two-dimensional films of chiral liquid crystals. The same considerations of chirality and defects apply to three-dimensional structures, such as the twist-grain-boundary and moire phases.Comment: 39 pages, RevTeX, 14 included eps figure

The Role of Bilayer Tilt Difference in Equilibrium Membrane Shapes

Lipid bilayer membranes below their main transition have two tilt order parameters, corresponding to the two monolayers. These two tilts may be strongly coupled to membrane shape but only weakly coupled to each other. We discuss some implications of this observation for rippled and saddle phases, bilayer tubules, and bicontinuous phases. Tilt difference introduces a length scale into the elastic theory of tilted fluid membranes. It can drive an instability of the flat phase; it also provides a simple mechanism for the spontaneous breaking of inversion symmetry seen in some recent experiments.Comment: Latex file; .ps available at http://dept.physics.upenn.edu/~nelson/saddle.p

A lambda calculus for quantum computation with classical control

The objective of this paper is to develop a functional programming language for quantum computers. We develop a lambda calculus for the classical control model, following the first author's work on quantum flow-charts. We define a call-by-value operational semantics, and we give a type system using affine intuitionistic linear logic. The main results of this paper are the safety properties of the language and the development of a type inference algorithm.Comment: 15 pages, submitted to TLCA'05. Note: this is basically the work done during the first author master, his thesis can be found on his webpage. Modifications: almost everything reformulated; recursion removed since the way it was stated didn't satisfy lemma 11; type inference algorithm added; example of an implementation of quantum teleportation adde

Chiral molecule adsorption on helical polymers

We present a lattice model for helicity induction on an optically inactive polymer due to the adsorption of exogenous chiral amine molecules. The system is mapped onto a one-dimensional Ising model characterized by an on-site polymer helicity variable and an amine occupancy one. The equilibrium properties are analyzed at the limit of strong coupling between helicity induction and amine adsorption and that of non-interacting adsorbant molecules. We discuss our results in view of recent experimental results

Pregnancy and inflammatory bowel disease: Do we provide enough patient education? A British study of 1324 women

AIM: To examine patient knowledge and factors influencing knowledge about pregnancy in British women with inflammatory bowel disease (IBD). METHODS: This is a post hoc analysis of a study of female members of Crohn’s and Colitis United Kingdom, aged 18-45 years who were sent an online questionnaire recording patient demographics, education, employment, marital status, and disease characteristics. Disease related pregnancy knowledge was recorded using Crohn’s and colitis pregnancy knowledge score (CCPKnow). RESULTS: Of 1324 responders, 776 (59%) suffered from Crohn’s disease, 496 (38%) from ulcerative colitis and 52 (4%) from IBD-uncategorised. CCPKnow scores were poor (0-7) in 50.8%, adequate (8-10) in 23.6%, good (11-13) in 17.7% and very good (≥ 14) in 7.8%. Multiple linear regression analysis revealed that higher CCPKnow scores were independently associated with higher educational achievement (P < 0.001), younger age at diagnosis (P = 0.003) and having consulted a health care professional about pregnancy and IBD (P = 0.001). CONCLUSION: Knowledge was poor in 50%. Speaking with health-care professionals was a modifiable factor associated with better knowledge. This illustrates the importance of disease related pregnancy educatio

Theory of Chiral Modulations and Fluctuations in Smectic-A Liquid Crystals Under an Electric Field

Chiral liquid crystals often exhibit periodic modulations in the molecular director; in particular, thin films of the smectic-C* phase show a chiral striped texture. Here, we investigate whether similar chiral modulations can occur in the induced molecular tilt of the smectic-A phase under an applied electric field. Using both continuum elastic theory and lattice simulations, we find that the state of uniform induced tilt can become unstable when the system approaches the smectic-A--smectic-C* transition, or when a high electric field is applied. Beyond that instability point, the system develops chiral stripes in the tilt, which induce corresponding ripples in the smectic layers. The modulation persists up to an upper critical electric field and then disappears. Furthermore, even in the uniform state, the system shows chiral fluctuations, including both incipient chiral stripes and localized chiral vortices. We compare these predictions with observed chiral modulations and fluctuations in smectic-A liquid crystals.Comment: 11 pages, including 9 postscript figures, uses REVTeX 3.0 and epsf.st

Deep Reinforcement Learning for Join Order Enumeration

Join order selection plays a significant role in query performance. However, modern query optimizers typically employ static join enumeration algorithms that do not receive any feedback about the quality of the resulting plan. Hence, optimizers often repeatedly choose the same bad plan, as they do not have a mechanism for "learning from their mistakes". In this paper, we argue that existing deep reinforcement learning techniques can be applied to address this challenge. These techniques, powered by artificial neural networks, can automatically improve decision making by incorporating feedback from their successes and failures. Towards this goal, we present ReJOIN, a proof-of-concept join enumerator, and present preliminary results indicating that ReJOIN can match or outperform the PostgreSQL optimizer in terms of plan quality and join enumeration efficiency