Executable Refinement Types

This dissertation introduces executable refinement types, which refine structural types by semi-decidable predicates, and establishes their metatheory and accompanying implementation techniques. These results are useful for undecidable type systems in general. Particular contributions include: (1) Type soundness and a logical relation for extensional equivalence for executable refinement types (though type checking is undecidable); (2) hybrid type checking for executable refinement types, which blends static and dynamic checks in a novel way, in some sense performing better statically than any decidable approximation; (3) a type reconstruction algorithm - reconstruction is decidable even though type checking is not, when suitably redefined to apply to undecidable type systems; (4) a novel use of existential types with dependent types to ensure that the language of logical formulae is closed under type checking (5) a prototype implementation, Sage, of executable refinement types such that all dynamic errors are communicated back to the compiler and are thenceforth static errors.Comment: Ph.D. dissertation. Accepted by the University of California, Santa Cruz, in March 2014. 278 pages (295 including frontmatter

Refinement Types for Logical Frameworks and Their Interpretation as Proof Irrelevance

Refinement types sharpen systems of simple and dependent types by offering expressive means to more precisely classify well-typed terms. We present a system of refinement types for LF in the style of recent formulations where only canonical forms are well-typed. Both the usual LF rules and the rules for type refinements are bidirectional, leading to a straightforward proof of decidability of typechecking even in the presence of intersection types. Because we insist on canonical forms, structural rules for subtyping can now be derived rather than being assumed as primitive. We illustrate the expressive power of our system with examples and validate its design by demonstrating a precise correspondence with traditional presentations of subtyping. Proof irrelevance provides a mechanism for selectively hiding the identities of terms in type theories. We show that LF refinement types can be interpreted as predicates using proof irrelevance, establishing a uniform relationship between two previously studied concepts in type theory. The interpretation and its correctness proof are surprisingly complex, lending support to the claim that refinement types are a fundamental construct rather than just a convenient surface syntax for certain uses of proof irrelevance

Relativistic MHD with Adaptive Mesh Refinement

This paper presents a new computer code to solve the general relativistic magnetohydrodynamics (GRMHD) equations using distributed parallel adaptive mesh refinement (AMR). The fluid equations are solved using a finite difference Convex ENO method (CENO) in 3+1 dimensions, and the AMR is Berger-Oliger. Hyperbolic divergence cleaning is used to control the $\nabla\cdot {\bf B}=0$ constraint. We present results from three flat space tests, and examine the accretion of a fluid onto a Schwarzschild black hole, reproducing the Michel solution. The AMR simulations substantially improve performance while reproducing the resolution equivalent unigrid simulation results. Finally, we discuss strong scaling results for parallel unigrid and AMR runs.Comment: 24 pages, 14 figures, 3 table

Efficient Downlink Channel Reconstruction for FDD Multi-Antenna Systems

In this paper, we propose an efficient downlink channel reconstruction scheme for a frequency-division-duplex multi-antenna system by utilizing uplink channel state information combined with limited feedback. Based on the spatial reciprocity in a wireless channel, the downlink channel is reconstructed by using frequency-independent parameters. We first estimate the gains, delays, and angles during uplink sounding. The gains are then refined through downlink training and sent back to the base station (BS). With limited overhead, the refinement can substantially improve the accuracy of the downlink channel reconstruction. The BS can then reconstruct the downlink channel with the uplink-estimated delays and angles and the downlink-refined gains. We also introduce and extend the Newtonized orthogonal matching pursuit (NOMP) algorithm to detect the delays and gains in a multi-antenna multi-subcarrier condition. The results of our analysis show that the extended NOMP algorithm achieves high estimation accuracy. Simulations and over-the-air tests are performed to assess the performance of the efficient downlink channel reconstruction scheme. The results show that the reconstructed channel is close to the practical channel and that the accuracy is enhanced when the number of BS antennas increases, thereby highlighting that the promising application of the proposed scheme in large-scale antenna array systems

Atomic structures and deletion mutant reveal different capsid-binding patterns and functional significance of tegument protein pp150 in murine and human cytomegaloviruses with implications for therapeutic development.

Cytomegalovirus (CMV) infection causes birth defects and life-threatening complications in immunosuppressed patients. Lack of vaccine and need for more effective drugs have driven widespread ongoing therapeutic development efforts against human CMV (HCMV), mostly using murine CMV (MCMV) as the model system for preclinical animal tests. The recent publication (Yu et al., 2017, DOI: 10.1126/science.aam6892) of an atomic model for HCMV capsid with associated tegument protein pp150 has infused impetus for rational design of novel vaccines and drugs, but the absence of high-resolution structural data on MCMV remains a significant knowledge gap in such development efforts. Here, by cryoEM with sub-particle reconstruction method, we have obtained the first atomic structure of MCMV capsid with associated pp150. Surprisingly, the capsid-binding patterns of pp150 differ between HCMV and MCMV despite their highly similar capsid structures. In MCMV, pp150 is absent on triplex Tc and exists as a "Λ"-shaped dimer on other triplexes, leading to only 260 groups of two pp150 subunits per capsid in contrast to 320 groups of three pp150 subunits each in a "Δ"-shaped fortifying configuration. Many more amino acids contribute to pp150-pp150 interactions in MCMV than in HCMV, making MCMV pp150 dimer inflexible thus incompatible to instigate triplex Tc-binding as observed in HCMV. While pp150 is essential in HCMV, our pp150-deletion mutant of MCMV remained viable though with attenuated infectivity and exhibiting defects in retaining viral genome. These results thus invalidate targeting pp150, but lend support to targeting capsid proteins, when using MCMV as a model for HCMV pathogenesis and therapeutic studies

Generation of folk song melodies using Bayes transforms

The paper introduces the `Bayes transform', a mathematical procedure for putting data into a hierarchical representation. Applicable to any type of data, the procedure yields interesting results when applied to sequences. In this case, the representation obtained implicitly models the repetition hierarchy of the source. There are then natural applications to music. Derivation of Bayes transforms can be the means of determining the repetition hierarchy of note sequences (melodies) in an empirical and domain-general way. The paper investigates application of this approach to Folk Song, examining the results that can be obtained by treating such transforms as generative models

Image classification by visual bag-of-words refinement and reduction

This paper presents a new framework for visual bag-of-words (BOW) refinement and reduction to overcome the drawbacks associated with the visual BOW model which has been widely used for image classification. Although very influential in the literature, the traditional visual BOW model has two distinct drawbacks. Firstly, for efficiency purposes, the visual vocabulary is commonly constructed by directly clustering the low-level visual feature vectors extracted from local keypoints, without considering the high-level semantics of images. That is, the visual BOW model still suffers from the semantic gap, and thus may lead to significant performance degradation in more challenging tasks (e.g. social image classification). Secondly, typically thousands of visual words are generated to obtain better performance on a relatively large image dataset. Due to such large vocabulary size, the subsequent image classification may take sheer amount of time. To overcome the first drawback, we develop a graph-based method for visual BOW refinement by exploiting the tags (easy to access although noisy) of social images. More notably, for efficient image classification, we further reduce the refined visual BOW model to a much smaller size through semantic spectral clustering. Extensive experimental results show the promising performance of the proposed framework for visual BOW refinement and reduction