Applying quantitative semantics to higher-order quantum computing

Finding a denotational semantics for higher order quantum computation is a long-standing problem in the semantics of quantum programming languages. Most past approaches to this problem fell short in one way or another, either limiting the language to an unusably small finitary fragment, or giving up important features of quantum physics such as entanglement. In this paper, we propose a denotational semantics for a quantum lambda calculus with recursion and an infinite data type, using constructions from quantitative semantics of linear logic

Atlas of common complications associated with R.G.P. and S.C.L wear

Contact lenses are a popular and frequently used mode of correcting refractive error and are occasionally used to treat diseased and degenerative processes. As both Rigid Gas Permeable (RGP) and Soft Contact Lenses (SCL) lie directly on the cornea buffered only by the tear layer. it is the cornea that shows the first signs of adverse effects of contact lens wear. Contact lenses can affect the cornea both mechanically, due to their physical presence on the eye, as well as indirectly through interference with the normal physiology of the cornea. As the mode of contact lens wear increases through new materials and designs, so too do the needs of the patient. The population trend is moving toward the older patient and this group of patients are less tolerant to mild corneal hypoxia and mechanical trauma than the younger population. At the same time, as their corneal topography and physiology is more fragile, there is an increased need for thicker contact lenses (e.g. bifocal lenses). With this situation, the early detection of contact lens complications is critical in order to preserve a healthy visual system. A good patient evaluation assessing the ocular health. combined with strong patient motivation is the first step in successful contact lens wear. Secondly. a thorough knowledge of materials, lens design, fits and care solutions also contribute to successful long term contact lens wear. Once a patient has been fitted with their lenses, the recognition of early contact lens complications is essential. The earlier the identification and correct treatment is undertaken, the better the prognosis for continued success in contact lens wear. Optometry students and new practitioners (who may have had little experience with contact lens complications). often find it difficult to correctly identify the problems and implement the correct treatment. This thesis was developed to provide a pictorial reference guide with an accompanying written identification and treatment guideline for eight of the most common contact lens complications. The early identification. and implementation of appropriate treatment will usually stop the progression of the corneal/lid problem. preserving and/ or re-establishing a healthy ocular system. while still maintaining good visual acuity. Successful treatment of contact lens associated ocular problems can lead to continued healthy contact lens wear by the patient

Environment and classical channels in categorical quantum mechanics

We present a both simple and comprehensive graphical calculus for quantum computing. In particular, we axiomatize the notion of an environment, which together with the earlier introduced axiomatic notion of classical structure enables us to define classical channels, quantum measurements and classical control. If we moreover adjoin the earlier introduced axiomatic notion of complementarity, we obtain sufficient structural power for constructive representation and correctness derivation of typical quantum informatic protocols.Comment: 26 pages, many pics; this third version has substantially more explanations than previous ones; Journal reference is of short 14 page version; Proceedings of the 19th EACSL Annual Conference on Computer Science Logic (CSL), Lecture Notes in Computer Science 6247, Springer-Verlag (2010

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

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

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

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

An extremal model for amorphous media plasticity

An extremal model for the plasticity of amorphous materials is studied in a simple two-dimensional anti-plane geometry. The steady-state is analyzed through numerical simulations. Long-range spatial and temporal correlations in local slip events are shown to develop, leading to non-trivial and highly anisotropic scaling laws. In particular, the plastic strain is shown to statistically concentrate over a region which tends to align perpendicular to the displacement gradient. By construction, the model can be seen as giving rise to a depinning transition, the threshold of which (i.e. the macroscopic yield stress) also reveal scaling properties reflecting the localization of the activity.Comment: 4 pages, 5 figure

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