Trans-floating-point arithmetic removes nine quadrillion redundancies from 64-bit IEEE 754 floating-point arithmetic

IEEE 754 floating-point arithmetic is widely used in modern, general-purpose computers. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. Modifying the IEEE arithmetic so that it uses transreal arithmetic has a number of advantages. It removes one redundant binade from IEEE floating-point objects, doubling the numerical precision of the arithmetic. It removes eight redundant, relational,floating-point operations and removes the redundant total order operation. It replaces the non-reflexive, floating-point, equality operator with a reflexive equality operator and it indicates that some of the exceptions may be removed as redundant { subject to issues of backward compatibility and transient future compatibility as programmers migrate to the transreal paradigm.

Transreal limits expose category errors in IEEE 754 floating-point arithmetic and in mathematics

The IEEE 754 standard for oating-point arithmetic is widely used in computing. It is based on real arithmetic and is made total by adding both a positive and a negative infinity, a negative zero, and many Not-a-Number (NaN) states. The IEEE infinities are said to have the behaviour of limits. Transreal arithmetic is total. It also has a positive and a negative infinity but no negative zero, and it has a single, unordered number, nullity. We elucidate the transreal tangent and extend real limits to transreal limits. Arguing from this firm foundation, we maintain that there are three category errors in the IEEE 754 standard. Firstly the claim that IEEE infinities are limits of real arithmetic confuses limiting processes with arithmetic. Secondly a defence of IEEE negative zero confuses the limit of a function with the value of a function. Thirdly the definition of IEEE NaNs confuses undefined with unordered. Furthermore we prove that the tangent function, with the infinities given by geometrical con- struction, has a period of an entire rotation, not half a rotation as is commonly understood. This illustrates a category error, confusing the limit with the value of a function, in an important area of applied mathe- matics { trigonometry. We brie y consider the wider implications of this category error. Another paper proposes transreal arithmetic as a basis for floating- point arithmetic; here we take the profound step of proposing transreal arithmetic as a replacement for real arithmetic to remove the possibility of certain category errors in mathematics. Thus we propose both theo- retical and practical advantages of transmathematics. In particular we argue that implementing transreal analysis in trans- floating-point arith- metic would extend the coverage, accuracy and reliability of almost all computer programs that exploit real analysis { essentially all programs in science and engineering and many in finance, medicine and other socially beneficial applications.

Proposal of a floating mechanism based on magnetic levitation method toward EEG-driven robotic system

We discussed a floating mechanism based on quasi-magnetic levitation method that can be attached at the endpoint of a robot arm in order to construct a novel redundant robot arm for producing compliant motions. The floating mechanism can be composed of magnets and a constraint mechanism such that the repelling force of the magnets floats the endpoint part of the mechanism stable for the guided motions. The analytical and experimental results show that the proposed floating mechanism can produce stable floating motions with small inertia and viscosity. The results also show that the proposed mechanism can detect small force applied to the endpoint part because the friction force of the mechanism is very small.

EMD performance comparison: single vs double floating points

Empirical mode decomposition (EMD) is a data-driven method used to decompose data into oscillatory components. This paper examines to what extent the defined algorithm for EMD might be susceptible to data format. Two key issues with EMD are its stability and computational speed. This paper shows that for a given signal there is no significant difference between results obtained with single (binary32) and double (binary64) floating points precision. This implies that there is no benefit in increasing floating point precision when performing EMD on devices optimised for single floating point format, such as graphical processing units (GPUs).

Generic construction of monitors for floating point unit designs

This paper proposes a set of well defined steps to design functional verification monitors intended to verify Floating Point Units (FPU) described in HDL. The first step consists on defining the input and output domain coverage. Next, the corner cases are defined. Finally, an already verified reference model is used in order to test the correctness of the Device Under Verification (DUV). As a case study a monitor for an IEEE754-2008 compliant design is implemented. This monitor is built to be easily instantiated into verification frameworks such as OVM. Two different designs were verified reaching complete input coverage and successful compliant results.

A Floating-point Extended Kalman Filter Implementation for Autonomous Mobile Robots

Localization and Mapping are two of the most important capabilities for autonomous mobile robots and have been receiving considerable attention from the scientific computing community over the last 10 years. One of the most efficient methods to address these problems is based on the use of the Extended Kalman Filter (EKF). The EKF simultaneously estimates a model of the environment (map) and the position of the robot based on odometric and exteroceptive sensor information. As this algorithm demands a considerable amount of computation, it is usually executed on high end PCs coupled to the robot. In this work we present an FPGA-based architecture for the EKF algorithm that is capable of processing two-dimensional maps containing up to 1.8 k features at real time (14 Hz), a three-fold improvement over a Pentium M 1.6 GHz, and a 13-fold improvement over an ARM920T 200 MHz. The proposed architecture also consumes only 1.3% of the Pentium and 12.3% of the ARM energy per feature.

Chromium ions phytoaccumulation by three floating aquatic macrophytes from a nutrient medium

In the present work, the trivalent and hexavalent chromium phytoaccumulation by three living free floating aquatic macrophytes Salvinia auriculata, Pistia stratiotes, and Eicchornia crassipes was investigated in greenhouse. These plants were grown in hydroponic solutions supplied with non-toxic Cr3+ and Cr6+ chromium concentrations, performing six collections of nutrient media and plants in time from a batch system. The total chromium concentrations into Cr-doped hydroponic media and dry roots and aerial parts were assayed, by using the Synchrotron radiation X-ray fluorescence technique. The aquatic plant-based chromium removal data were described by using a nonstructural kinetic model, obtaining different bioaccumulation rate, ranging from 0.015 to 0.837 1 mg(-1) d(-1). The Cr3+ removal efficiency was about 90%, 50%, and 90% for the E. crassipes, P. stratiotes, and S. auriculata, respectively; while it was rather different for Cr6+ one, with values about 50%, 70%, and 90% for the E. crassipes, P. stratiotes, and S. auriculata.

The trasition from fixed to floating exchange rate regimes: the case of Brazil

This dissertation evaluates macroeconomic management in Brazil from 1994 to the present, with particular focus on exchange rate policy. It points out that while Brazil's Real Plan succeeded in halting the hyperinflation that had reached more than 2000 percent in 1993, it also caused significant real appreciation of the exchange rate situation that was only made worse by the extremely high interest rates and ensuing bout of severe financial crises in the intemational arena. By the end of 1998, the accumulation of internai and externai imbalances led the authorities to drop foreign exchange controls and allow the currency to float. In spite of some initial scepticism, the flexible rate regime cum inflation target proved to work well. Inflation was kept under control; the current account position improved significantly, real interest rates fell and GDP growth resumed. Thus, while great challenges still lie ahead, the recent successes bestow some optimism on the well functioning of this exchange rate regime. The Brazilian case suggests that successful transition from one foreign exchange system to another, particularly during financial crisis, does not depend only on one variable be it fiscal or monetary. In reality, it depends on whole set of co-ordinated policies aimed at resuming price stability with as little exchange rate and output volatility as possible.

Modified value stream mapping of airport check-in procedures

In June 2014 Brazil hosted the FIFA World Cup and in August 2016 Rio de Janeiro hosts the Summer Olympics. These two seminal sporting events will draw tens of thousands of air travelers through Brazil’s airports, airports that are currently in the midst of a national modernization program to address years of infrastructure neglect and insufficient capacity. Raising Brazil’s major airports up to the standards air travelers experience at major airports elsewhere in the world is more than just a case of building or remodeling facilities, processes must also be examined and reworked to enhance traveler experience and satisfaction. This research paper examines the key interface between airports and airline passengers—airport check-in procedures—according to how much value and waste there is associated with them. In particular, the paper makes use of a value stream mapping construct for services proposed by Martins, Cantanhede, and Jardim (2010). The uniqueness of this construct is that it attributes each activity with a certain percentage and magnitude of value or waste which can then be ordered and prioritized for improvement. Working against a fairly commonly expressed notion in Brazil that Brazil’s airports are inferior to the airports of economically advanced countries, the paper examines Rio’s two major airports, Galeão International and Santos Dumont in comparison to Washington D.C.’s Washington National and Dulles International airports. The paper seeks to accomplish three goals: - Determine whether there are differences in airport passenger check-in procedures between U.S. and Brazilian airports in terms of passenger value - Present options for Brazilian government or private sector authorities to consider adopting or implementing at Brazilian airports to maximize passenger value - Validate the Martins et al. construct for use in evaluating the airport check-in procedures Observations and analysis proved surprising in that all airports and service providers follow essentially the same check-in processes but execute them differently yet still result in similar overall performance in terms of value and waste. Although only a few activities are categorized as completely wasteful (and therefore removed in the revised value stream map of check-in activities), the weighting and categorization of individual activities according to their value (or waste) presents decision-makers a means to prioritize possible corrective actions. Various overall recommendations are presented based on this analysis. Most importantly, this paper demonstrates the viability of using the construct developed by Martins et al to examine airport operations, as well as its applicability to the study of other service industry processes.

De touch: extending service channels in an airport through touch technologies

This project aimed to create a communication and interaction channel between Madeira Airport and its passengers. We used the pre-existent touch enabled screens at the terminal since their potential was not being utilised to their full capacity. To achieve our goal, we have followed an agile strategy to create a testable prototype and take advantages of its results. The developed prototype is based on a plugin architecture turning it into a maintainable and highly customisable system. The collected usage data suggests that we have achieved the initially defined goals. There is no doubt that this new interaction channel is an improvement regarding the provided services and, supported by the usage data, there is an opportunity to explore additional developments to the channel.

Utilization of macrophyte biofilter in effluent from aquaculture: I. Floating plant

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Preliminary results of a floating subirrigation system (Aquaforest system) as an alternative to conventional tree nurseries

A new methodology for tree seedling production (Aquaforest system) based on a continuous floating subirrigation system was developed and tested using creeks with different nutrient levels. Eucalyptus grandis seedlings were produced in water from polluted and clean creeks, and compared to conventional tree nursery production. The growth variables analyzed in the seedling phase were: survival, height, diameter, shoot and root dry weight, leaf area, and root/shoot ratio. Water and substrate were analyzed, as well as leaf nutritional status. Plant survival was 100% in all treatments. Height and diameter were greater in the higher nutrient water treatment. Leaf area and dry weight of plants produced in the higher nutrient water treatment were similar to those of the control. The results showed that polluted water can represent a good nutrient source. The preliminary results show that the Aquaforest system can be a viable alternative for tree seedling production. (C) 2004 Elsevier B.V. All rights reserved.

Growth of free-floating aquatic macrophytes in different concentrations of nutrients

The objective of the study was to evaluate the effect of different concentrations of nitrogen and phosphorus on the growth of the free-floating aquatic macrophytes Eichhornia crassipes, Pistia stratiotes, and Salvinia molesta. The plants were cultured in 2,000-l outdoor concrete tanks. Triplicate tanks, with a continuous flow of effluent from culture ponds containing Nile tilapia, were used for each plant type (n = 3). The plant material was collected monthly from 0.25 m(2) floating quadrats, at the two ends of the tanks (higher nutrient concentrations near the inflow and lower nutrient concentrations near the outflow). In low nutrient concentrations, the maximum relative growth rates (RGRs) for E. crassipes (0.016/day) and P. stratiotes (0.016/day) were significantly lower (P <= 0.05) than for S. molesta (0.029/day). There were no significant differences between the RGRs of S. molesta in the different nutrient concentrations. Eichhornia crassipes and P. stratiotes had their growth limited by nitrogen and phosphorus concentrations. The increase in plant density during the experiment probably also affected the growth of these species. In this context, E. crassipes and P. stratiotes can cause problems in nutrient-rich waterbodies, but under these experimental conditions their growth was limited by nitrogen and/or phosphorus concentrations. The growth of S. molesta was not influenced by the different nutrient concentrations.