Arithmetic Expressions Research Articles

Calculating correct compilers

AbstractIn this article, we present a new approach to the problem of calculating compilers. In particular, we develop a simple but general technique that allows us to derive correct compilers from high-level semantics by systematic calculation, with all details of the implementation of the compilers falling naturally out of the calculation process. Our approach is based upon the use of standard equational reasoning techniques, and has been applied to calculate compilers for a wide range of language features and their combination, including arithmetic expressions, exceptions, state, various forms of lambda calculi, bounded and unbounded loops, non-determinism and interrupts. All the calculations in the article have been formalised using the Coq proof assistant, which serves as a convenient interactive tool for developing and verifying the calculations.

Impact of Operational Efficiency with Ratio Analysis A Study

Ratio is a simple arithmetical expression of the relationship of one number to another and is obtained by dividing for the former by later. Liquidity position of a firm is able to meet its current obligation as and when they mature. Firms said to be capable of meeting its current only if it has sufficient liquid funds to pay its short term obligation with interest within a period of year. In this research paper researcher want to convey how the Ratio act as important and useful tools in the hands of management to evaluate the firm’s performance over the period of time by comparing the present ratio with past ratio various activity or turnover ratio measure the operational efficiency of the firm.

PERIODIC ANALYSIS OF SOLAR ACTIVITY AND ITS LINK WITH THE ARCTIC OSCILLATION PHENOMENON

Based on spectrum analysis, we provide the arithmetic expressions of the quasi 11 yr cycle, 110 yr century cycle of relative sunspot numbers, and quasi 22 yr cycle of solar magnetic field polarity. Based on a comparative analysis of the monthly average geopotential height, geopotential height anomaly, and temperature anomaly of the northern hemisphere at locations with an air pressure of 500 hPa during the positive and negative phases of AO (Arctic Oscillation), one can see that the abnormal warming period in the Arctic region corresponds to the negative phase of AO, while the anomalous cold period corresponds to its positive phase. This shows that the abnormal change in the Arctic region is an important factor in determining the anomalies of AO. In accordance with the analysis performed using the successive filtering method, one can see that the AO phenomenon occurring in January shows a clear quasi 88 yr century cycle and quasi 22 yr decadal cycle, which are closely related to solar activities. The results of our comparative analysis show that there is a close inverse relationship between the solar activities (especially the solar magnetic field index changes) and the changes in the 22 yr cycle of the AO occurring in January, and that the two trends are basically opposite of each other. That is to say, in most cases after the solar magnetic index MI rises from the lowest value, the solar magnetic field turns from north to south, and the high-energy particle flow entering the Earth's magnetosphere increases to heat the polar atmosphere, thus causing the AO to drop from the highest value; after the solar magnetic index MI drops from the highest value, the solar magnetic field turns from south to north, and the solar high-energy particle flow passes through the top of the Earth's magnetosphere rather than entering it to heat the polar atmosphere. Thus the polar temperature drops, causing the AO to rise from the lowest value. In summary, the variance contribution rate of the changes in the quasi 110 yr century cycle and quasi 22 yr decadal cycle for the AO reaches 62.9%, indicating that solar activity is an important driving factor of the AO.

Relationship between drug structure and minimal inhibitory concentration value used for acceptable daily intake analysis.

The minimal inhibitory concentration (MIC) of an antimicrobial agent for a microbial population (MIC(50, obs) and MIC(90, obs)) is an interpolated value determined for antibacterial drugs by in vitro methods. Many studies have tried to determine the correlation between the MIC(50, obs) or MIC(90, obs) value and the physicochemical parameters to allow quantitaive structure activity relationship (QSAR) predictions of efficacy. A rigorous evaluation of approaches to this problem is presented here. In order to find a correlation between chemical structure and the derivatives of the MIC values for 9 indicatory bacterial strains, it is necessary to employ a number of physicochemical parameters in combination. Only an arithmetic expression composed of many features illustrating the chemical structure of the molecule can be linked to the ƒMIC(50, obs) value. This article demonstrated that, despite the complexity of the MIC value used as the end point, it is possible to validate the model in a limited extent.

Generalised hybrid switching topology for a single‐phase modular multilevel inverter

A modified single-phase hybrid cascaded H bridge multilevel inverter with a minimum number of power electronic devices and isolated DC sources is presented in this study. It consists of two inverters (upper and lower) coupled in cascade. The lower inverter is capable of developing a multilevel output and switches at low frequency and another inverter develops two-level output and switches at high frequency. In the proposed inverter, every additional power electronic switch in the lower inverter increases the level by four. This study also introduces a generalised hybrid modulation switching strategy, which gives arithmetical and logical expressions for switching the additional device for any required increase in levels. The voltage rating of the devices, conduction and switching loss of the proposed inverter are compared with the similarly setup topologies. The generalised hybrid modulation algorithm is simulated in MATLAB/Simulink and implemented in a SPATRAN 3A DSP board. Simulation and experimental results are presented for different loading conditions.

Effective topological degree computation based on interval arithmetic

We describe a new algorithm for calculating the topological degree deg (f, B, 0) where B \subseteq Rn is a product of closed real intervals and f : B \rightarrow Rn is a real-valued continuous function given in the form of arithmetical expressions. The algorithm cleanly separates numerical from combinatorial computation. Based on this, the numerical part provably computes only the information that is strictly necessary for the following combinatorial part, and the combinatorial part may optimize its computation based on the numerical information computed before. We also present computational experiments based on an implementation of the algorithm. Also, in contrast to previous work, the algorithm does not assume knowledge of a Lipschitz constant of the function f, and works for arbitrary continuous functions for which some notion of interval arithmetic can be defined.

Relationship between Tetracyclines' Structure and Minimal Inhibitory Concentration of Streptococcus spp.

During the past years, a growing number of bacterial strains have become resistant to tetracyclines. The problem of increasing resistance and lack of susceptibility to tetracyclines applies to strains isolated from both: animals and humans. Basic tools to design new drugs and determining the direction of the search for new molecules is the analysis of the relationship between the chemical structure and the pharmacokinetic and pharmacodynamic parameters. Purpose of this study is to determine the relationship between physicochemical parameters of tetracyclines and MIC50 and MIC90 values determined for Streptococcus spp. Analysis of physicochemical parameters of selected drugs was made using MarvinSketch 5.11.5 (ChemAxon Ltd.) and QuickProp 3.1 software from Schrödinger package v 31207. MIC50 and MIC90 values were correlated with 51 calculated physicochemical parameters and arithmetic expressions. Internal and external model validation was performed using leave-one out method. 4 arithmetic expressions fulfilled all validation criteria, but only in relation to MIC50. A new method to optimize the tetracyclines' structure in relation to Streptococcus spp. was presented. It was also shown that the relations of structure: antimicrobial activity type can have different nature depending on MIC50 or MIC90 of specific bacterial strain.

3D-ΔPDF: a routine method for analyzing diffuse scattering from single crystals.

With the recent advances in x-ray area detectors, high quality diffuse scattering became readily available. This allows to investigate local order in single crystals and provides invaluable information about real structures of disordered crystals, e.g. stacking probabilities, or structural dynamics. Recently, a new method called Three Dimensional Difference Pair Distribution Function (3D-ΔPDF) analysis was introduced [1]. It provides direct access to the short range order correlations and allows to investigate the diffuse scattering of both static and dynamic origin in a unified fashion . The method is similar to the powder PDF, but availability of three dimensional diffraction data provides several key differences. Firstly, it allows elimination of Bragg peaks and refinement of diffuse scattering alone which conveniently separates the investigation of average structure from investigation of ordering. Secondly, due to reduced overlap of PDF signals, the correlation coefficients at very long interatomic vectors become accessible. The 3D-ΔPDF analysis can be performed in the newly developed program Yell [2]. The program supports all types of correlations and contains a fast FFT-based method for diffuse scattering calculation, and the constraints of arbitrary arithmetic expressions.

Efficient Mining of Discriminating Relationships Among Attributes Involving Arithmetic Operations

Contrast patterns describe differences between two or more data sets or data classes; they have been proven to be useful for solving many kinds of problems, such as building accurate classifiers, defining clustering quality measures, and analyzing disease subtypes. This article investigates the mining of a new kind of contrast patterns, namely discriminating inter‐attribute functions (DIFs), which represent arithmetic‐expression‐based inter‐attribute relationships that distinguish classes of data. DIFs are an expressive and practical alternative of item‐based contrast patterns and can express discriminating relationships such as “weight/(height)2 is more likely to be ≤25 in one class than in another class.” Besides introducing the DIF mining problem, this article makes theoretical and algorithmic contributions on the problem. We prove that DIF mining is MAX SNP‐hard. Regarding how to efficiently mine DIFs, we present a set of rules to prune the search space of arithmetic expressions by eliminating redundant ones (equivalent to some others). We give two algorithms: one for finding all DIFs satisfying given thresholds and another for finding certain optimal DIFs using genetic computation techniques. The former is useful when the number of attributes is small, whereas the latter is useful when that number is large; both use the redundant arithmetic‐expression pruning rules. A performance study shows that our techniques are effective and efficient for finding DIFs.

Single level constraint interval arithmetic

In the present paper we propose a variant of constraint interval arithmetic that operates with a single parameter (level) in each interval operand of an expression. This results in a computationally simple interval arithmetic that has several desirable properties not shared in general by interval operations previously defined in the literature. The actualization and usefulness of this approach to fuzzy (interval) arithmetic is accomplished via alpha-levels. The evaluation of arithmetic expressions using the proposed single level constrained arithmetic is discussed in detail and we extend this theory to the fuzzy context.

Knowing right from wrong in mental arithmetic judgments: calibration of confidence predicts the development of accuracy.

Does knowing when mental arithmetic judgments are right—and when they are wrong—lead to more accurate judgments over time? We hypothesize that the successful detection of errors (and avoidance of false alarms) may contribute to the development of mental arithmetic performance. Insight into error detection abilities can be gained by examining the “calibration” of mental arithmetic judgments—that is, the alignment between confidence in judgments and the accuracy of those judgments. Calibration may be viewed as a measure of metacognitive monitoring ability. We conducted a developmental longitudinal investigation of the relationship between the calibration of children's mental arithmetic judgments and their performance on a mental arithmetic task. Annually between Grades 5 and 8, children completed a problem verification task in which they rapidly judged the accuracy of arithmetic expressions (e.g., 25+50 = 75) and rated their confidence in each judgment. Results showed that calibration was strongly related to concurrent mental arithmetic performance, that calibration continued to develop even as mental arithmetic accuracy approached ceiling, that poor calibration distinguished children with mathematics learning disability from both low and typically achieving children, and that better calibration in Grade 5 predicted larger gains in mental arithmetic accuracy between Grades 5 and 8. We propose that good calibration supports the implementation of cognitive control, leading to long-term improvement in mental arithmetic accuracy. Because mental arithmetic “fluency” is critical for higher-level mathematics competence, calibration of confidence in mental arithmetic judgments may represent a novel and important developmental predictor of future mathematics performance.

Abstractions from proofs

The success of model checking for large programs depends crucially on the ability to efficiently construct parsimonious abstractions. A predicate abstraction is parsimonious if at each control location, it specifies only relationships between current values of variables, and only those which are required for proving correctness. Previous methods for automatically refining predicate abstractions until sufficient precision is obtained do not systematically construct parsimonious abstractions: predicates usually contain symbolic variables, and are added heuristically and often uniformly to many or all control locations at once. We use Craig interpolation to efficiently construct, from a given abstract error trace which cannot be concretized, a parsominous abstraction that removes the trace. At each location of the trace, we infer the relevant predicates as an interpolant between the two formulas that define the past and the future segment of the trace. Each interpolant is a relationship between current values of program variables, and is relevant only at that particular program location. It can be found by a linear scan of the proof of infeasibility of the trace.We develop our method for programs with arithmetic and pointer expressions, and call-by-value function calls. For function calls, Craig interpolation offers a systematic way of generating relevant predicates that contain only the local variables of the function and the values of the formal parameters when the function was called. We have extended our model checker BLAST with predicate discovery by Craig interpolation, and applied it successfully to C programs with more than 130,000 lines of code, which was not possible with approaches that build less parsimonious abstractions.

Towards a [formula omitted] Semantics for OCL

We give a formal definition to a significant subset of the Object Constraint Language (ocl) in the K framework. The chosen subset includes the usual arithmetical, Boolean (including quantifiers), and string expressions; collection expressions (including iterators and navigation); and pre/post conditions for methods. Being executable, our definition provides us, for free, with an interpreter for the chosen subset of ocl. It can be used for free in K definitions of languages having ocl as a component We illustrate some of the advantages of K by comparing our semantical definition of ocl with the official semantics from the language's standard. We also report on a tool implementing our definition that users can try online.

Yell: a computer program for diffuse scattering analysisviathree-dimensional delta pair distribution function refinement

Yell, a program for routine refinement of disorder models against single-crystal diffuse scattering data, is presented. The analysis is based on the three-dimensional delta pair distribution function (3D-ΔPDF) method, which provides direct access to interatomic correlations in real crystal structures. Substitutional, displacive and size-effect disorder models are covered. The input file format supports flexible usage of arithmetic expressions for constraining dependent parameter values. The program is designed to be run on desktop computers. By using an efficient fast-Fourier-transform-based diffuse scattering calculation algorithm, full least-square refinements of medium complexity disorder models may be performed within minutes or hours, even if the experimental diffuse scattering is represented by large and fine-sampled reciprocal space volumes. The program is written in C++ and the source code is distributed under the GPL licence. Binary distributions are currently available for Mac and Windows operating systems.

Error assessment of the estimated coefficients obtained in system identification technique

System identification technique plays an important role in many electrical devices. In this technique, an adaptive filter models the unknown system with a finite impulse response or an infinite inverse response filter. This paper concentrates on the system identification technique based on the least squares criterion and evaluates the relationship between each estimated coefficient (obtained by the adaptive filter) and its corresponding coefficient in the unknown system. By logically classifying the variables, the amount of error between these two corresponding coefficients is evaluated and precisely expressed based on the autocorrelation lags of the input signal of the system and the coefficients of the unknown system. Also, the computed error is simplified for two particular cases in which the input signal of the system is an ideal zero-mean white Gaussian noise or a windowed (short-time) zero-mean white Gaussian noise. Experimental results provided in the simulation part verify the arithmetic expressions presented in the paper.

Polynomial function intervals for floating-point software verification

The focus of our work is the verification of tight functional properties of numerical programs, such as showing that a floating-point implementation of Riemann integration computes a close approximation of the exact integral. Programmers and engineers writing such programs will benefit from verification tools that support an expressive specification language and that are highly automated. Our work provides a new method for verification of numerical software, supporting a substantially more expressive language for specifications than other publicly available automated tools. The additional expressivity in the specification language is provided by two constructs. First, the specification can feature inclusions between interval arithmetic expressions. Second, the integral operator from classical analysis can be used in the specifications, where the integration bounds can be arbitrary expressions over real variables. To support our claim of expressivity, we outline the verification of four example programs, including the integration example mentioned earlier. A key component of our method is an algorithm for proving numerical theorems. This algorithm is based on automatic polynomial approximation of non-linear real and real-interval functions defined by expressions. The PolyPaver tool is our implementation of the algorithm and its source code is publicly available. In this paper we report on experiments using PolyPaver that indicate that the additional expressivity does not come at a performance cost when comparing with other publicly available state-of-the-art provers. We also include a scalability study that explores the limits of PolyPaver in proving tight functional specifications of progressively larger randomly generated programs.

Reinforcing Random Testing of Arithmetic Optimization of C Compilers by Scaling up Size and Number of Expressions

This paper presents an enhanced method of testing validity of arithmetic optimization of C compilers using randomly generated programs. Its bug detection capability is improved over an existing method by 1) generating longer arithmetic expressions and 2) accommodating multiple expressions in test programs. Undefined behavior in long expressions is successfully eliminated by modifying problematic subexpressions during computation of expected values for the expressions. A new method for including floating point operations into compiler random testing is also proposed. Furthermore, an efficient method for minimizing error inducing test programs is presented, which utilizes binary search. Experimental results show that a random test system based on our method has higher bug detection capability than existing methods; it has detected more bugs than previous method in earlier versions of GCCs and has revealed new bugs in the latest versions of GCCs and LLVMs.

Diagnosis of dementia with Lewy bodies: diagnostic performance of combined 123I-IMP brain perfusion SPECT and 123I-MIBG myocardial scintigraphy

Objective We assessed the value of combining 123I-IMP brain perfusion SPECT and 123I-MIBG myocardial scintigraphy for the discrimination of dementia with Lewy bodies (DLB) from other types of dementia. MethodsWe subjected 252 consecutive patients with clinically suspected DLB to both 123I-IMP brain perfusion SPECT and 123I-MIBG myocardial scintigraphy. Patients with Parkinson’s disease were included. The 252 patients were randomly assigned to an estimation (n = 152) or a validation group (n = 100). Using univariate analysis, we first analyzed the relationship between various variables and the presence or absence of DLB in estimation group and then proceeded to multivariate analysis to obtain a combined index that predicted the likelihood of DLB. The diagnostic value of the index was assessed by calculating the area under the receiver operating characteristic (ROC) curve (AUC) with the cutoff value selected from the ROC curve. We then tested the predictive accuracy of the index in validation group. ResultsThe combined index was an arithmetic expression that combined the age, early 123I-MIBG heart-to-mediastinum uptake (E-H/M) ratio, and the parietal lobe hypoperfusion score. Values for the AUC of the combined index, the E-H/M ratio, the parietal lobe hypoperfusion score, and the patient age in validation group were 0.95, 0.90, 0.72, and 0.73, respectively. There was a significant difference in the AUC of the combined index among other indices (p < 0.05). The sensitivity, specificity, and accuracy of the combined index for a diagnosis of probable DLB in validation group were 88, 87, and 87 %, respectively.ConclusionsThe combinational diagnosis based on 123I-IMP brain perfusion SPECT, 123I-MIBG myocardial scintigraphy, and the patient age is a simple and reliable means for predicting probable DLB.

Lightweight evaluation algorithm for infix arithmetic expression

Lightweight evaluation algorithm for infix arithmetic expression

Verification of Loop and Arithmetic Transformations of Array-Intensive Behaviors

Loop transformation techniques along with arithmetic transformations are applied extensively on array and loop intensive behaviors in design of area/energy efficient systems in the domain of multimedia and signal processing applications. Ensuring correctness of such transformations is crucial for the reliability of the designed systems. In this paper, array data dependence graphs (ADDGs) are used to represent both the input and the transformed behaviors and the correctness of the transformations is ensured by proving equivalence of the two ADDGs. A slice-based equivalence checking method of ADDGs is proposed for this purpose. The method relies on the normalization of arithmetic expressions and some simplification rules to handle arithmetic transformations. Unlike many other reported techniques, our method is strong enough to handle several arithmetic transformations along with all kinds of loop transformations. Correctness and complexity of the method have been dealt with. Experimental results on several test cases demonstrate the effectiveness of the method.