(p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters

Instanton partition functions of $\mathcal{N}=1$ 5d Super Yang-Mills reduced on $S^1$ can be engineered in type IIB string theory from the $(p,q)$-branes web diagram. To this diagram is superimposed a web of representations of the Ding-Iohara-Miki (DIM) algebra that acts on the partition function. In this correspondence, each segment is associated to a representation, and the (topological string) vertex is identified with the intertwiner operator constructed by Awata, Feigin and Shiraishi. We define a new intertwiner acting on the representation spaces of levels $(1,n)\otimes(0,m)\to(1,n+m)$, thereby generalizing to higher rank $m$ the original construction. It allows us to use a folded version of the usual $(p,q)$-web diagram, bringing great simplifications to actual computations. As a result, the characterization of Gaiotto states and vertical intertwiners, previously obtained by some of the authors, is uplifted to operator relations acting in the Fock space of horizontal representations. We further develop a method to build qq-characters of linear quivers based on the horizontal action of DIM elements. While fundamental qq-characters can be built using the coproduct, higher ones require the introduction of a (quantum) Weyl reflection acting on tensor products of DIM generators.Comment: 42 page

Parallel machine architecture and compiler design facilities

The objective is to provide an integrated simulation environment for studying and evaluating various issues in designing parallel systems, including machine architectures, parallelizing compiler techniques, and parallel algorithms. The status of Delta project (which objective is to provide a facility to allow rapid prototyping of parallelized compilers that can target toward different machine architectures) is summarized. Included are the surveys of the program manipulation tools developed, the environmental software supporting Delta, and the compiler research projects in which Delta has played a role

Low harmonic distortion flash A/D converters incorporating dynamic element matching techniques

New dynamic element matching techniques are shown to reduce the harmonic distortion and improve the spurious-free dynamic range of flash ADCs. Resistor chain mismatch errors are negated by randomly rearranging the resistors each sample by utilizing 5(2{dollar}\sp{b}{dollar}-1) digital switches and b + 1 random control signals for a b-bit flash ADC. The integral and differential nonlinearity of a non-ideal flash ADC are derived for three common resistor chain mismatch errors; namely, geometric mismatches, linear gradient mismatches, and dynamic mismatches. The transfer function of a non-ideal flash ADC is also derived and the converter output is shown to consist of a scaled copy of the input, a DC gain, and conversion noise that is a function of the resistor mismatches. A comprehensive summary of dynamic element matching techniques given in literature is provided. In addition, the DEM network introduced by Galton and Jensen is shown to be equivalent to the generalized-cube network used in parallel processing architectures. An alternative version of this network that uses logic gates is also proposed

Sorting networks using k-comparators

Bibliography: leaves 160-167

NASA Tech Briefs, August 1994

Topics covered include: Computer Hardware; Electronic Components and Circuits; Electronic Systems; Physical Sciences; Materials; Computer Programs; Mechanics; Machinery; Fabrication Technology; Mathematics and Information Sciences; Life Sciences; Books and Reports

Numerical aerodynamic simulation facility feasibility study

There were three major issues examined in the feasibility study. First, the ability of the proposed system architecture to support the anticipated workload was evaluated. Second, the throughput of the computational engine (the flow model processor) was studied using real application programs. Third, the availability reliability, and maintainability of the system were modeled. The evaluations were based on the baseline systems. The results show that the implementation of the Numerical Aerodynamic Simulation Facility, in the form considered, would indeed be a feasible project with an acceptable level of risk. The technology required (both hardware and software) either already exists or, in the case of a few parts, is expected to be announced this year. Facets of the work described include the hardware configuration, software, user language, and fault tolerance

A chaos theory and nonlinear dynamics approach to the analysis of financial series : a comparative study of Athens and London stock markets

This dissertation presents an effort to implement nonlinear dynamic tools adapted from chaos theory in financial applications. Chaos theory might be useful in explaining the dynamics of financial markets, since chaotic models are capable of exhibiting behaviour similar to that observed in empirical financial data. In this context, the scope of this research is to provide an insight into the role that nonlinearities and, in particular, chaos theory may play in explaining the dynamics of financial markets. From a theoretical point of view, the basic features of chaos theory, as well as, the rationales for bringing chaos theory to the attention of financial researchers are discussed. Empirically, the fundamental issue of determining whether chaos can be observed in financial time series is addressed. Regarding the latter, empirical literature has been controversial. A quite exhaustive analysis of the existing literature is provided, revealing the inadequacies in terms of methodology and the testing framework adopted, so far. A new "multiple testing" methodology is developed combining methods and techniques from the fields of both Natural Sciences and the Economics, most of which have not been applied to financial data before. A serious effort has been made to fill, as much as possible, the gap which results from the lack of a proper statistical framework for the chaotic methods. To achieve this the bootstrap methodology is adopted. The empirical part of this work focuses on the comparison of two markets with different levels of maturity; the Athens Stock Exchange (ASE), an emerging market, and London Stock Exchange (LSE). Our aim is to determine whether structural differences exist in these markets in terms of chaotic dynamics. In the empirical level we find nonlinearities in both markets by the use of the BDS test. R/S analysis reveals fractality and long term memory for the ASE series only. Chaotic methods, such as the correlation dimension (and related methods and techniques) and the largest Lyapunov exponent estimation, cannot rule out a chaotic explanation for the ASE market, but no such indication could be found for the LSE market. Noise filtering by the SVD method does not alter these findings. Alternative techniques based on nonlinear nearest neighbour forecasting methods, such as the "piecewise polynomial approximation" and the "simplex" methods, support our aforementioned conclusion concerning the ASE series. In all, our results suggest that, although nonlinearities are present, chaos is not a widespread phenomenon in financial markets and it is more likely to exist in less developed markets such as the ASE. Even then, chaos is strongly mixed with noise and the existence of low-dimensional chaos is highly unlikely. Finally, short-term forecasts trying to exploit the dependencies found in both markets seem to be of no economic importance after accounting for transaction costs, a result which supports further our conclusions about the limited scope and practical implications of chaos in Finance

Association of Christians in the Mathematical Sciences Proceedings 2019

The conference proceedings of the Association of Christians in the Mathematical Sciences biannual conference, May 29-June 1, 2019 at Indiana Wesleyan University