Constructive Gelfand duality for C*-algebras

We present a constructive proof of Gelfand duality for C*-algebras by reducing the problem to Gelfand duality for real C*-algebras.Comment: 6page

Wilis: Architectural Modeling of Wireless Systems

The performance of a wireless system depends on the wireless channel as well as the algorithms used in the transceiver pipelines. Because physical phenomena affect transceiver pipelines in difficult to predict ways, detailed simulation of the entire transceiver system is needed to evaluate even a single processing block. Further, some protocol validations require simulation of rare events (say, 1 bit error in 109 bits), which means the protocol must simulate for a long enough time for such events to materialize. This requirement coupled with the heavy computation typical of most physical-layer processing, rules out pure software solutions. In this paper we describe WiLIS, an FPGA-based hybrid hardware-software system designed to facilitate the development of wireless protocols. We then use WiLIS to evaluate several microarchitectures for measuring very low bit-error rates (BER). We demonstrate, for the first time, that the recently proposed SoftPHY can be implemented efficiently in hardware

Classification of Extensions of Classifiable C*-algebras

We classify extensions of certain classifiable C*-algebras using the six term exact sequence in K-theory together with the positive cone of the K_0-groups of the distinguished ideal and quotient. We then apply our results to a class of C*-algebras arising from substitutional shift spaces.Comment: 22 pages, Reordered some sections, an application involving graph algebras is adde

A Test of the Adaptive Market Hypothesis using a Time-Varying AR Model in Japan

This study examines the adaptive market hypothesis (AMH) in Japanese stock markets (TOPIX and TSE2). In particular, we measure the degree of market efficiency by using a time-varying model approach. The empirical results show that (1) the degree of market efficiency changes over time in the two markets, (2) the level of market efficiency of the TSE2 is lower than that of the TOPIX in most periods, and (3) the market efficiency of the TOPIX has evolved, but that of the TSE2 has not. We conclude that the results support the AMH for the more qualified stock market in Japan.Comment: 10 pages, 2 figure, 2 table

Identifying and Supporting Financially Vulnerable Consumers in a Privacy-Preserving Manner: A Use Case Using Decentralised Identifiers and Verifiable Credentials

Vulnerable individuals have a limited ability to make reasonable financial decisions and choices and, thus, the level of care that is appropriate to be provided to them by financial institutions may be different from that required for other consumers. Therefore, identifying vulnerability is of central importance for the design and effective provision of financial services and products. However, validating the information that customers share and respecting their privacy are both particularly important in finance and this poses a challenge for identifying and caring for vulnerable populations. This position paper examines the potential of the combination of two emerging technologies, Decentralized Identifiers (DIDs) and Verifiable Credentials (VCs), for the identification of vulnerable consumers in finance in an efficient and privacy-preserving manner.Comment: Published in the ACM CHI 2021 workshop on Designing for New Forms of Vulnerabilit

Comparison theory and smooth minimal C*-dynamics

We prove that the C*-algebra of a minimal diffeomorphism satisfies Blackadar's Fundamental Comparability Property for positive elements. This leads to the classification, in terms of K-theory and traces, of the isomorphism classes of countably generated Hilbert modules over such algebras, and to a similar classification for the closures of unitary orbits of self-adjoint elements. We also obtain a structure theorem for the Cuntz semigroup in this setting, and prove a conjecture of Blackadar and Handelman: the lower semicontinuous dimension functions are weakly dense in the space of all dimension functions. These results continue to hold in the broader setting of unital simple ASH algebras with slow dimension growth and stable rank one. Our main tool is a sharp bound on the radius of comparison of a recursive subhomogeneous C*-algebra. This is also used to construct uncountably many non-Morita-equivalent simple separable amenable C*-algebras with the same K-theory and tracial state space, providing a C*-algebraic analogue of McDuff's uncountable family of II_1 factors. We prove in passing that the range of the radius of comparison is exhausted by simple C*-algebras.Comment: 30 pages, no figure

The Dixmier property and tracial states for C*-algebras

A.T. was partially supported by an NSERC Postdoctoral Fellowship and through the EPSRC grant EP/N00874X/1. Acknowledgements We are grateful to Luis Santiago for helpful discussions at an early stage of this investigation. We would also like to thank the referee for providing helpful comments, which have led to a number of improvements.Peer reviewedPublisher PD