An Efficient Representation Format for Fuzzy Intervals Based on Symmetric Membership Functions

International audienceThis paper proposes a novel implementation of fuzzy arithmetics that exploits both fuzzy intervals and hardware specificities. First, we propose and evaluate the benefit of an alternative representation format to the traditional lower-upper and midpoint-radius representation formats for intervals. Thanks to the proposed formats, we show that it is possible to halve the number of operations and memory requirements compared to conventional methods. Then, we show that operations on fuzzy intervals are sensitive to hardware specificities of accelerators such as GPU. These include static rounding, memory usage, instruction level parallelism (ILP) and thread-level parallelism (TLP). We develop a library of fuzzy arithmetic operations in CUDA and C++ over several formats. The proposed library is evaluated using compute-bound and memory-bound benchmarks on Nvidia GPUs, and shows a performance gain of 2 to 20 over traditional approaches

Semiclassical quantization of the diamagnetic hydrogen atom with near action-degenerate periodic-orbit bunches

The existence of periodic orbit bunches is proven for the diamagnetic Kepler problem. Members of each bunch are reconnected differently at self-encounters in phase space but have nearly equal classical action and stability parameters. Orbits can be grouped already on the level of the symbolic dynamics by application of appropriate reconnection rules to the symbolic code in the ternary alphabet. The periodic orbit bunches can significantly improve the efficiency of semiclassical quantization methods for classically chaotic systems, which suffer from the exponential proliferation of orbits. For the diamagnetic hydrogen atom the use of one or few representatives of a periodic orbit bunch in Gutzwiller's trace formula allows for the computation of semiclassical spectra with a classical data set reduced by up to a factor of 20.Comment: 10 pages, 9 figure

Unums 2.0: An Interview with John L. Gustafson

In an earlier interview (April 2016), Ubiquity spoke with John Gustafson about the unum, a new format for floating point numbers. The unique property of unums is that they always know how many digits of accuracy they have. Now Gustafson has come up with yet another format that, like the unum 1.0, always knows how accurate it is. But it also allows an almost arbitrary mapping of bit patterns to the reals. In doing so, it paves the way for custom number systems that squeeze the maximum accuracy out of a given number of bits. This new format could have prime applications in deep learning, big data, and exascale computing

Music Expectation by Cognitive Rule-Mapping

Iterative rules appear everywhere in music cognition, creating strong expectations. Consequently, denial of rule projection becomes an important compositional strategy, generating numerous possibilities for musical affect. Other rules enter the musical aesthetic through reflexive game playing. Still other kinds are completely constructivist in nature and may be uncongenial to cognition, requiring much training to be recognized, if at all. Cognitive rules are frequently found in contexts of varied repetition (AA), but they are not necessarily bounded by stylistic similarity. Indeed, rules may be especially relevant in the processing of unfamiliar contexts (AB), where only abstract coding is available. There are many kinds of deduction in music cognition. Typical examples include melodic sequence, partial melodic sequence, and alternating melodic sequence (which produces streaming). These types may coexist in the musical fabric, involving the invocation of both simultaneous and nested rules. Intervallic expansion and reduction in melody also involve higherorder abstractions. Various mirrored forms in music entail rule-mapping as well, although these may be more difficult to perceive than their analogous visual symmetries. Listeners can likewise deduce additivity and subtractivity at work in harmony, tempo, texture, pace, and dynamics. Rhythmic augmentation and diminution, by contrast, rely on multiplication and division. The examples suggest numerous hypotheses for experimental research

How to Model Condensate Banking in a Simulation Model to Get Reliable Forecasts? Case Story of Elgin/Franklin

Imperial Users onl

The developmental onset of symbolic approximation: beyond nonsymbolic representations, the language of numbers matters

Symbolic (i.e., with Arabic numerals) approximate arithmetic with large numerosities is an important predictor of mathematics. It was previously evidenced to onset before formal schooling at the kindergarten age (Gilmore et al., 2007) and was assumed to map onto pre-existing nonsymbolic (i.e., abstract magnitudes) representations. With a longitudinal study (Experiment 1), we show, for the first time, that nonsymbolic and symbolic arithmetic demonstrate different developmental trajectories. In contrast to Gilmore et al.’s (2007) findings, Experiment 1 showed that symbolic arithmetic onsets in grade 1, with the start of formal schooling, not earlier. Gilmore et al. (2007) had examined English-speaking children, whereas we assessed a large Dutch-speaking sample. The Dutch language for numbers can be cognitively more demanding, for example, due to the inversion property in numbers above 20. Thus, for instance, the number 48 is named in Dutch “achtenveertig” (eight and forty) instead of “forty eight.” To examine the effect of the language of numbers, we conducted a cross-cultural study with English- and Dutch-speaking children that had similar SES and math achievement skills (Experiment 2). Results demonstrated that Dutch-speaking kindergarteners lagged behind English-speaking children in symbolic arithmetic, not nonsymbolic and demonstrated a working memory overload in symbolic arithmetic, not nonsymbolic. Also, we show for the first time that the ability to name two-digit numbers highly correlates with symbolic approximate arithmetic not nonsymbolic. Our experiments empirically demonstrate that the symbolic number system is modulated more by development and education than the nonsymbolic system. Also, in contrast to the nonsymbolic system, the symbolic system is modulated by language

George Perle’s Twelve–Tone Tonality: some developments for CAC using PWGL

This paper presents a description and some developments on Perle’s theory and compositional system known as Twelve-Tone Tonality, a system that, because of its characteristics and fundamentals, is currently associated with Schoenberg dodecaphonic system. Some research has been made in the last few decades in order to develop his model in a Computer Assisted Composition (CAC) environment. After some efforts in order to analyse these prototypes, we realize that in general they were discontinued or outdated. A three-scope proposal is so outlined: Firstly, to simplify the grasp of a system that presents an easily understandable starting premise but afterwards enters a world of unending lists and arrays of letters and numbers; Secondly, to present the implementation process already started using PWGL [1] (see Laurson, 1996; Laurson, 2003; Laurson, 2009). Finally, the model is applied in a short original compositional work, and it is presented and analysed emphasizing the standpoints properties of the system. Some further considerations were made regarding the continuity of this project where the construction of a dedicated PWGL library of Perle’s model reveals a pre-compositional necessary tool. PWGL software was selected due to its specific fitting features: it is based on Common Lisp - perfectly powerful and suitable to process lists of integers — and it is specialized in CAC

Faster convergence in seismic history matching by dividing and conquering the unknowns

The aim in reservoir management is to control field operations to maximize both the short and long term recovery of hydrocarbons. This often comprises continuous optimization based on reservoir simulation models when the significant unknown parameters have been updated by history matching where they are conditioned to all available data. However, history matching of what is usually a high dimensional problem requires expensive computer and commercial software resources. Many models are generated, particularly if there are interactions between the properties that update and their effects on the misfit that measures the difference between model predictions to observed data. In this work, a novel 'divide and conquer' approach is developed to the seismic history matching method which efficiently searches for the best values of uncertain parameters such as barrier transmissibilities, net:gross, and permeability by matching well and 4D seismic predictions to observed data. The ‘divide’ is carried by applying a second order polynomial regression analysis to identify independent sub-volumes of the parameters hyperspace. These are then ‘conquered’ by searching separately but simultaneously with an adapted version of the quasi-global stochastic neighbourhood algorithm. This 'divide and conquer' approach is applied to the seismic history matching of the Schiehallion field, located on the UK continental shelf. The field model, supplied by the operator, contained a large number of barriers that affect flow at different times during production, and their transmissibilities were largely unknown. There was also some uncertainty in the petrophysical parameters that controlled permeability and net:gross. Application of the method was accomplished because it is found that the misfit function could be successfully represented as sub-misfits each dependent on changes in a smaller number of parameters which then could be searched separately but simultaneously. Ultimately, the number of models required to find a good match reduced by an order of magnitude. Experimental design was used to contribute to the efficiency and the ‘divide and conquer’ approach was also able to separate the misfit on a spatial basis by using time-lapse seismic data in the misfit. The method has effectively gained a greater insight into the reservoir behaviour and has been able to predict flow more accurately with a very efficient 'divide and conquer' approach