Arithmetic Expressions Research Articles

Applying Multidimensional Geometry to Basic Data Centre Designs

Fog computing deployments are catching up by the day due to their advantages on latency and bandwidth compared to cloud implementations. Furthermore, the number of required hosts is usually far smaller, and so are the amount of switches needed to make the interconnections among them. In this paper, an approach based on multidimensional geometry is proposed for building up basic switching architectures for Data Centres, in a way that the most common convex regular N-polytopes are first introduced, where N is treated in an incremental manner in order to reach a generic high-dimensional N, and in turn, those resulting shapes are associated with their corresponding switching topologies. This way, N-simplex is related to a full mesh pattern, N-orthoplex is linked to a quasi full mesh structure and N-hypercube is referred to as a certain type of partial mesh layout. In each of those three contexts, a model is to be built up, where switches are first identified, afterwards, their downlink ports leading to the end hosts are exposed, along with those host identifiers, as well as their uplink ports leading to their neighboring switches, and eventually, a pseudocode algorithm is designed, exposing how a packet coming in from any given port of a switch is to be forwarded through the proper outgoing port on its way to the destination host by using the appropriate arithmetic expressions in each particular case. Therefore, all those algorithmic models represent how their corresponding switches may work when dealing with user data traffic within a Data Centre, guiding it towards its destination.

Presenting the Meta-Performance Test, a Metacognitive Battery based on Performance

<p style="text-align:justify">The self-report and think-aloud approaches are the two dominant methodologies to measure metacognition. This is problematic, since they generate respondent and confirmation biases, respectively. The Meta-Performance Test is an innovative battery, which evaluates metacognition based on the respondent's performance, mitigating the aforementioned biases. The Meta-Performance Test consists of two tests, the Meta-text, which evaluates metacognition in the domain of reading comprehension, and Meta-number, in the domain of arithmetic expressions solving. The main focus of this article is to present the development of the battery, in terms of its conceptual basis, development strategies and structure. Evidence of its content validity is also presented, through the evaluation of three experts in metacognition, two experts in Spanish language, two experts in mathematics and five students who represent the target population. The results of the judges' evaluations attested to the Meta-Performance Test content validity, and the target population declared that both the battery understanding and taking are adequate. Contributions and future research perspectives of the Meta-Performance Test in the field of metacognition are discussed.</p>

MODELING OF MAXIMALLY PARALLEL STRUCTURES OF ALGORITHMS FOR SOLVING THERMAL PROBLEMS

The paper demonstrates the possibility of creating a maximum parallel form of computational algorithms to solve thermal problems and their mapping to the architecture of multiprocessor systems based on solving thermal problems of mathematical physics. It is shown that an effective tool for studying heat and mass transfer problems in metallurgical production could be parallel computing technologies on distributed cluster systems with a relatively low cost and reasonably easily scalable both in the number of processors and in the amount of RAM. Tridiagonal structure systems' parallelization was implemented by a numerical-analytical approach, which predetermined their maximally parallel algorithmic form. That approach is facilitated by the minimum possible implementation time of the developed algorithm on parallel computing systems. Furthermore, during the arithmetic expressions parallel computations, the developed algorithm separates the error in the output data from rounding operations. Thus, the parallelization of tridiagonal systems based on numerical-analytical discretization methods does not impose any restrictions on the topology of the mesh nodes of the computational domain.Furthermore, as applied to the parallel computation of arithmetic expressions, it separates the initial data error from a real PC's rounding operations. That approach eliminates the recurrent structure of computing the sought-for decision vectors, which, as a rule, leads to the round-off errors accumulation. Such a parallel form of the constructed algorithm is maximal and has the shortest possible implementation time of the algorithm on parallel computing systems. The developed approach to parallelizing the mathematical model is stable for various types of input data. It has the most parallel form and is distinguished by the minimum time for solving the problem as applied to multiprocessor computing systems. That is explained as follows. If it is hypothesized that one processor can be assigned to one processor and one processor can be assigned to one node of the computational mesh domain, the computations can be processed in parallel and simultaneously for all nodes of the computational mesh domain. The simulation process was implemented on a PC cluster. It follows from the simulation results analysis that the developed method for solving the heat conduction problem effectively minimizes residuals.

A divided differences based medium to analyze smoothness of the binary bivariate refinement schemes

In this article, we present the continuity analysis of the 3D models produced by the tensor product scheme of (m+1)-point binary refinement scheme. We use differences and divided differences of the bivariate refinement scheme to analyze its smoothness. The C^{0}, C^{1} and C^{2} continuity of the general bivariate scheme is analyzed in our approach. This gives us some simple conditions in the form of arithmetic expressions and inequalities. These conditions require the mask and the complexity of the given refinement scheme to analyze its smoothness. Moreover, we perform several experiments by using these conditions on established schemes to verify the correctness of our approach. These experiments show that our results are easy to implement and are applicable for both interpolatory and approximating types of the schemes.

Numerical Markov Logic Network: A Scalable Probabilistic Framework for Hybrid Knowledge Inference

In recent years, the Markov Logic Network (MLN) has emerged as a powerful tool for knowledge-based inference due to its ability to combine first-order logic inference and probabilistic reasoning. Unfortunately, current MLN solutions cannot efficiently support knowledge inference involving arithmetic expressions, which is required to model the interaction between logic relations and numerical values in many real applications. In this paper, we propose a probabilistic inference framework, called the Numerical Markov Logic Network (NMLN), to enable efficient inference of hybrid knowledge involving both logic and arithmetic expressions. We first introduce the hybrid knowledge rules, then define an inference model, and finally, present a technique based on convex optimization for efficient inference. Built on decomposable exp-loss function, the proposed inference model can process hybrid knowledge rules more effectively and efficiently than the existing MLN approaches. Finally, we empirically evaluate the performance of the proposed approach on real data. Our experiments show that compared to the state-of-the-art MLN solution, it can achieve better prediction accuracy while significantly reducing inference time.

Latent Compositional Representations Improve Systematic Generalization in Grounded Question Answering

AbstractAnswering questions that involve multi-step reasoning requires decomposing them and using the answers of intermediate steps to reach the final answer. However, state-of-the-art models in grounded question answering often do not explicitly perform decomposition, leading to difficulties in generalization to out-of-distribution examples. In this work, we propose a model that computes a representation and denotation for all question spans in a bottom-up, compositional manner using a CKY-style parser. Our model induces latent trees, driven by end-to-end (the answer) supervision only. We show that this inductive bias towards tree structures dramatically improves systematic generalization to out-of- distribution examples, compared to strong baselines on an arithmetic expressions benchmark as well as on C losure, a dataset that focuses on systematic generalization for grounded question answering. On this challenging dataset, our model reaches an accuracy of 96.1%, significantly higher than prior models that almost perfectly solve the task on a random, in-distribution split.

Toward Unseating the Unsafe C Programming Language

Reflecting on content that I taught in a recent security course about software-based vulnerabilities, I wondered: Am I giving too much focus to the C programming language? C-based examples get straight to the point, allowing compact illustrations of the concepts underlying stack-and heap-based buffer overruns and return-oriented programming, aside from integer-based vulnerabilities, related to arithmetic underflow, conversions between signed and unsigned values, and errors due to the compiler promotion of short-integer data types in arithmetic expressions.1 But are these relevant for today's students, given the wide availability of modern languages with strong language safety properties? Unfortunately, the answer is still yes.

Conversion-based aggregation algorithms for linear ordinal rankings combined with granular computing

This paper proposes two aggregation algorithms for aggregating individuals’ linear ordinal rankings (LORs) in group decision-making environment, which improves the computability of LORs. At first, in order to represent the position information of alternatives, we depict LORs by extended preference map, and then analyze the basic statistical quantitative characteristics of the LORs. Subsequently, combining with the concept of granular computing, we derive the arithmetic expressions of interval utility values for alternatives, in which the information granularity indices are introduced to determine the interval lengths. Later on, two programming​ models are established with the aim of minimizing the differences between individual opinions and the corresponding collective one. Besides, in the two models, we propose the methods to determine experts’ weights according to the differences of experts’ knowledge backgrounds. Both information granularity index and the aggregated interval utility value can be calculated by solving the models, based on which the final aggregated ranking can be determined. Furthermore, a numerical case concerning the electric vehicle charging station site selection problem is presented to illustrate the usage of the proposed algorithms, and finally, the efficiency and features of the two algorithms are exhibited through comparative analyses and simulation experiment.

Midazolam and hydroxymidazolam plasma concentrations can be monitored with selected biochemical and physiological parameters of palliative care patients

Rationale & objectiveMidazolam is one of top three drugs used in palliative care. Its use increases in the last days of hospice patients’ lives while safe dosage can be challenging. Equations currently used to estimate glomerular filtration rate, e.g: the Cockroft-Gault (eGFRCR) and the Modification of Diet in Renal Disease (eGFRMDRD) ones, do not generate precise calculations, especially in palliative patients exhibiting variations in body parameters. Our aim was to seek new relationships between mean midazolam (Mavg) and alfahydroxymidazolam (OH-Mavg) concentrations in plasma, and selected biochemical and physiological parameters of palliative patients, to enable optimal midazolam pharmacotherapy. Study design, participants and interventionsThe pilot study included 11 Caucasians, aged 42–95, with advanced cancer disease, receiving midazolam in a hospice in-patient unit. We tested correlations among Mavg, BMI, eGFRMDRD, midazolam clearance (CL), OH-Mavg, bilirubin (Bil) and blood creatinine concentration (Cr). F test and leave-one out (LOO) validation was applied to verify the correlations’ significance and predictive ability. ResultsWe found ten statistically significant (p < 0.05) correlations related to midazolam pharmacokinetics and physiological factors. We formulated two equations with high degree of predictive ability, based on the eGFRMDRD→CL and the (Bil + BMI × Ln(Cr))→Mavg-(OH-Mavg) correlations.The limitations of the study mainly revolve around its pilot nature and the need to continue testing the results on a bigger population.No funding to disclose. ConclusionsThe significance of correlations corresponding to the arithmetic expressions confirms that Bil, BMI, Ln(Cr) analyzed simultaneously report a series of processes on which midazolam metabolism depends. Two of ten correlations proposed came close to meet all LOO validation criteria. Current findings can help optimize midazolam treatment in palliative therapy.

Similarity-preserving hash for content-based audio retrieval using unsupervised deep neural networks

Due to its efficiency in storage and search speed, binary hashing has become an attractive approach for a large audio database search. However, most existing hashing-based methods focus on data-independent scheme where random linear projections or some arithmetic expression are used to construct hash functions. Hence, the binary codes do not preserve the similarity and may degrade the search performance. In this paper, an unsupervised similarity-preserving hashing method for content-based audio retrieval is proposed. Different from data-independent hashing methods, we develop a deep network to learn compact binary codes from multiple hierarchical layers of nonlinear and linear transformations such that the similarity between samples is preserved. The independence and balance properties are included and optimized in the objective function to improve the codes. Experimental results on the Extended Ballroom dataset with 8 genres of 3,000 musical excerpts show that our proposed method significantly outperforms state-of-the-art data-independent method in both effectiveness and efficiency.

What Counts? Sources of Knowledge in Children’s Acquisition of the Successor Function

Although many U.S. children can count sets by 4years, it is not until 5½-6years that they understand how counting relates to number-that is, that adding 1 to a set necessitates counting up one number. This study examined two knowledge sources that 3½- to 6-year-olds (N=136) may leverage to acquire this "successor function": (a) mastery of productive rules governing count list generation; and (b) training with "+1" math facts. Both productive counting and "+1" math facts were related to understanding that adding 1 to sets entails counting up one number in the count list; however, even children with robust successor knowledge struggled with its arithmetic expression, suggesting they do not generalize the successor function from "+1" math facts.

Third Grade Students’ Use of Relational Thinking

Current mathematics curricula have as one of their fundamental objectives the development of number sense. This is understood as a set of skills. Some of them have an algebraic nature such as acquiring an abstract understanding of relations between numbers, developing awareness of properties and of the structure of the decimal number system and using it in a strategic manner. In this framework, the term relational thinking directs attention towards a way of working with arithmetic expressions that promotes relations between their terms and the use of properties. A teaching experiment has allowed to characterize the way in which third grade students use this type of thinking for solving number equalities by distinguishing four profiles of use. These profiles inform about how students employ relations and arithmetic properties to solve the equalities. They also ease the description of the evolution of the use of relational thinking along the sessions in the classroom. Uses of relational thinking of different sophistication are distinguished depending on whether a general known rule is applied, or relations and properties are used in a flexible way. Results contribute to understanding the process of developing the algebraic component of number sense.

Modelovanje ekvivalencije matematičkih izraza u početnoj nastavi

The notion of expression equivalence is one of the terms that has been recognized in the literature as key to understanding algebraic ideas. To understand this term, the context used as a basis for developing meaning is important, as well as the language in which generalizations are expressed. The aim of this paper is twofold: a) to examine whether the context of a textual task and modeling activities influence the understanding of the transformation of expressions into equivalent forms; b) determine whether the understanding of the equivalence of the expression is affected by the level of abstractness of the expression (algebraic or arithmetic). The research is of a quasi-experimental design with two experimental groups and one control group. The sample consists of 148 fourth-graders. The existence of statistically significant differences between the students of the experimental groups and the control group suggests that the modeling process influences the development of the notion of expression equivalence. This research did not show any differences in the results of the students who were taught using algebraic or arithmetic expressions. This implies that the understanding of equivalence developed through the modeling process is not related to the level of abstractness of the mathematical language used, but that, based on understanding the meaning of the term, students can transform arithmetic and algebraic expressions with equal success.

Determination of the ball mills performance, taking into account the particle size of the finished product

The article discusses the issue of determining the newly formed specific surface of the cement clinker taking into account the lateral surface of the seal area. When developing this technique, the assumption that the newly formed particles have a shape close to spherical, has been made. The obtained ratio determines the work that considers the formation of thecement clinker material new surface, depending on the size of the original and newly formed material. An arithmetic expression is given, defined as the minimum amount of energy that must be introduced into the deformation zone for the destruction of a cement clinker particle to occur. The presented technique is specified taking into account the fact that defects are introduced into the crushed material particle. Taking into account the fact that the grinding ball makes an impact in one cycle of its movement, the value of the newly formed surface of the material in the ball mill is determined in one hour of its operation.

Quantitative Server Sizing Model for Performance Satisfaction in Secure U2L Migration

There are many challenges in measuring capacity size using units such as transaction per minute (TPM) and operation per second (OPS) for all server hardware, which are increasingly obsolete due to the shortening of hardware life cycle and the advent of microprocessors. Thus, the results of accredited performance measurements are used to measure these standards, which are then used as references in the capacity sizing method employed by industries. Generally, in industries, the capacity sizing of a web application server is defined by OPS, for which no clear transition criterion exists for calculating tpmC using an empirical verification method. In particular, considering secure Unix to Linux (U2L) x86-based servers migration, there are no methods to compare and verify the max-jOPS value of Standard Performance Evaluation Corp., which is an industry-recognized performance measurement standard, to Unix-based benchmark tpmC. In this study, scenario-based U2L migration was empirically verified by analyzing and comparing pre-to-post with the interpretation of Census statistics system log data, which was conducted on approximately 1.7M households over 21 days with 25,288 maximum concurrent users. Thus, we present the correlation through pre-to-post comparison and analysis of Unix-to-Linux for each Census statistics system log data by measuring the maximum CPU utilization as U2L migration between heterogeneous CPUs. These are applied to OPS by TPC-C proportional equation and quantified as derived conversion ratio of OPS to max-jOPS. As a result, we formulated and normalized an arithmetic expression, which is derived the CPU core conversion ratio of 0.165 as facile in U2L migration from a Unix-based legacy platform to a x86-based server. Therefore, we propose a new server sizing model for secure U2L migration between heterogeneous CPUs architecture, which results in an average of 14.3% improvement in data processing time.

LL (1) Parser versus GNF inducted LL (1) Parser on Arithmetic Expressions Grammar: A Comparative Study

The prime objective of the proposed study is to determine the induction of Greibach Normal Form (GNF) in Arithmetic Expression Grammars to improve the processing speed of conventional LL(1) parser. Conventional arithmetic expression grammar and its equivalent LL(1) is used in the study which is converted. A transformation method is defined which converts the selected grammar into a Greibach normal form that is further converted into a GNF based parser through a method proposed in the study. These two parsers are analyzed by considering 399 cases of arithmetic expressions. During statistical analysis, the results are initially examined with the Kolmogorov-Smirnov and Shapiro-Wilk test. The statistical significance of the proposed method is evaluated with the Mann-Whitney U test. The study described that GNF based LL(1) parser for arithmetic take fewer steps than conventional LL(1) grammar. The ranks and asymptotic significance depict that the GNF based LL(1) method is significant than the conventional LL(1) approach. The study adds to the knowledge of parsers itself, parser expression grammars (PEG’s), LL(1) grammars, Greibach Normal Form (GNF) induced grammar structure, and the induction of Arithmetic PEG’s LL(1) to GNF based grammar.

Prediction of electrochemical characteristics of practical-size solid oxide fuel cells based on database of unit cell performance

A novel numerical methodology for predicting the electrochemical characteristics of a practical-size solid oxide fuel cell (SOFC) is proposed. The core idea is to divide the practical-size cell into independent one-dimensional (1D) unit cells and to evaluate the characteristics of the practical-size cell as an aggregation of the performance of local unit cells. The proposed methodology consists of two steps. The first is to construct a database of the electrochemical performance of the unit cells under a comprehensive range of operating conditions. For this purpose, a 1D numerical simulation model is developed and validated by comparing the predicted values with experimental data. It is confirmed that not only the current–voltage characteristics but also the impedance characteristics are accurately reproduced by the developed unit cell model. The second is to reproduce the performance of the practical-size cell using the constructed database. The cell is considered as an assembly of unit cells and the electrochemical performance of each unit cell is determined by referring to the constructed database. Subsequently, the macroscopic characteristics of the entire cell are evaluated by using the derived theoretical expressions correlating the macroscopic characteristics with the local electrochemical performance. The predicted cell characteristics fairly agree with the experimental data found in the literature. Since the macroscopic characteristics of the practical-size cell is evaluated with simple arithmetic expressions, the computational cost is significantly reduced, which realizes an exhaustive parametric study of the practical-size cell to identify the optimal operation conditions.

Lpopt: A Rule Optimization Tool for Answer Set Programming

State-of-the-art answer set programming (ASP) solvers rely on a program called a grounder to convert non-ground programs containing variables into variable-free, propositional programs. The size of this grounding depends heavily on the size of the non-ground rules, and thus, reducing the size of such rules is a promising approach to improve solving performance. To this end, in this paper we announce lpopt, a tool that decomposes large logic programming rules into smaller rules that are easier to handle for current solvers. The tool is specifically tailored to handle the standard syntax of the ASP language (ASP-Core) and makes it easier for users to write efficient and intuitive ASP programs, which would otherwise often require significant handtuning by expert ASP engineers. It is based on an idea proposed by Morak and Woltran (2012) that we extend significantly in order to handle the full ASP syntax, including complex constructs like aggregates, weak constraints, and arithmetic expressions. We present the algorithm, the theoretical foundations on how to treat these constructs, as well as an experimental evaluation showing the viability of our approach.

Error detection of arithmetic expressions

Inspecting floating-point errors is essential to floating-point operations. In this paper, we present floating-point error detector (FPED), an inspector of floating-point errors for arithmetic expressions. FPED can pick a suitable benchmark generation approach by analyzing the distribution of the expression of a floating-point operation, thereby minimizing the possibilities of underreporting floating-point errors. FPED is also able to determine the significant sources of errors in a floating-point operation according to the frequencies of computation building blocks that contribute most to the floating-point errors, benefiting the follow-up optimizations of computation accuracies. We validate the correctness and functionalities of FPED by conducting experiments on the FPBench benchmark suite. The experimental results demonstrate that FPED can obtain more accurate detection results than the random detecting approach with respect to floating-point error detection. We also compare FPED with the existing dynamic error detection tools. The experimental results show that in most of the 33 test benchmarks, the maximum error results of FPED are greater than Herbgrind and the detection performance is higher than Herbgrind.

Use of Arithmetic Operation Skills in Block Based Programming Environments: A Comparative Case Study

The purpose of this study is to examine the 7th grade middle school students' processes of creating and calculating arithmetic expressions in the code.org block based coding environments. For this purpose, the reasons of students' behaviors in coding environments are tried to be revealed by comparing them with student behaviors in traditional environments. The participants of the study, which was conducted as a comparative case study, are composed of 10 students studying at a public school. Arithmetic Operation Test developed by the researchers, Student Screen Records taken from the code.org platform, Student Opinion Form consisting of three open-ended questions, Unstructured Interviews held with the students and Field Notes were used as data collection tools in this study. Descriptive analyzes were performed in order to compare the data obtained from different cases and the analysis results were expressed in different categories. In conclusion, it has been observed that the students were not as successful in coding environments as expected and use arithmetical operation skills more successfully in traditional environments than block based coding environments. In particular, it has been revealed that the use of blocks and the way in which code.org handles arithmetic operations cause the students cannot transfer their existing knowledge to the coding environments.