AutoBayes: A System for Generating Data Analysis Programs from Statistical Models

Data analysis is an important scientific task which is required whenever information needs to be extracted from raw data. Statistical approaches to data analysis, which use methods from probability theory and numerical analysis, are well-founded but difficult to implement: the development of a statistical data analysis program for any given application is time-consuming and requires substantial knowledge and experience in several areas. In this paper, we describe AutoBayes, a program synthesis system for the generation of data analysis programs from statistical models. A statistical model specifies the properties for each problem variable (i.e., observation or parameter) and its dependencies in the form of a probability distribution. It is a fully declarative problem description, similar in spirit to a set of differential equations. From such a model, AutoBayes generates optimized and fully commented C/C++ code which can be linked dynamically into the Matlab and Octave environments. Code is produced by a schema-guided deductive synthesis process. A schema consists of a code template and applicability constraints which are checked against the model during synthesis using theorem proving technology. AutoBayes augments schema-guided synthesis by symbolic-algebraic computation and can thus derive closed-form solutions for many problems. It is well-suited for tasks like estimating best-fitting model parameters for the given data. Here, we describe AutoBayes's system architecture, in particular the schema-guided synthesis kernel. Its capabilities are illustrated by a number of advanced textbook examples and benchmarks

Concurrent processing simulation of the space station

The development of a new capability for the time-domain simulation of multibody dynamic systems and its application to the study of a large angle rotational maneuvers of the Space Station is described. The effort was divided into three sequential tasks, which required significant advancements of the state-of-the art to accomplish. These were: (1) the development of an explicit mathematical model via symbol manipulation of a flexible, multibody dynamic system; (2) the development of a methodology for balancing the computational load of an explicit mathematical model for concurrent processing; and (3) the implementation and successful simulation of the above on a prototype Custom Architectured Parallel Processing System (CAPPS) containing eight processors. The throughput rate achieved by the CAPPS operating at only 70 percent efficiency, was 3.9 times greater than that obtained sequentially by the IBM 3090 supercomputer simulating the same problem. More significantly, analysis of the results leads to the conclusion that the relative cost effectiveness of concurrent vs. sequential digital computation will grow substantially as the computational load is increased. This is a welcomed development in an era when very complex and cumbersome mathematical models of large space vehicles must be used as substitutes for full scale testing which has become impractical

Numerical simulation of the stress-strain state of the dental system

We present mathematical models, computational algorithms and software, which can be used for prediction of results of prosthetic treatment. More interest issue is biomechanics of the periodontal complex because any prosthesis is accompanied by a risk of overloading the supporting elements. Such risk can be avoided by the proper load distribution and prediction of stresses that occur during the use of dentures. We developed the mathematical model of the periodontal complex and its software implementation. This model is based on linear elasticity theory and allows to calculate the stress and strain fields in periodontal ligament and jawbone. The input parameters for the developed model can be divided into two groups. The first group of parameters describes the mechanical properties of periodontal ligament, teeth and jawbone (for example, elasticity of periodontal ligament etc.). The second group characterized the geometric properties of objects: the size of the teeth, their spatial coordinates, the size of periodontal ligament etc. The mechanical properties are the same for almost all, but the input of geometrical data is complicated because of their individual characteristics. In this connection, we develop algorithms and software for processing of images obtained by computed tomography (CT) scanner and for constructing individual digital model of the tooth-periodontal ligament-jawbone system of the patient. Integration of models and algorithms described allows to carry out biomechanical analysis on three-dimensional digital model and to select prosthesis design.Comment: 19 pages, 9 figure

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table

Connections Between Mathematics and Computational Thinking: Kindergarten Students\u27 Demonstration of Mathematics Knowledge in a Computational Thinking Assessment

Research shows that computational thinking can be used with kindergarten mathematics instruction, however we still do not know much about how specific math knowledge is related to computational thinking and if (and if so, how) children\u27s mathematical knowledge is related to students\u27 performance on computational thinking assessments. This student fills this knowledge gap by examining the following research questions: (1) How are kindergarten students\u27 mathematical knowledge (MK) and computational thinking (CT)MK and CT operationalized during a CT assessment? In what ways, if any, do MK and CT co-occur, and (2) How do students\u27 mathematical knowledge and co-occurring mathematical knowledge and computational thinking relate to their performance on individual assessment items? To answer these questions, I analyzed video data that was originally collected for a larger research study (NSF project award #DRL-1842116), which showed 60 kindergarten students taking an interview-based, computational thinking assessment. I coded and notated the data to describe how students demonstrate their mathematical knowledge and computational thinking, then analyzed the coded data to identify how students\u27 mathematical knowledge and computational thinking co-occurred. Lastly, I described how, for four assessment items, students\u27 co-occurring knowledge related to their assessment item performance. The results show that students demonstrated different levels of mathematical knowledge and computational thinking through their gestures, language, and interactions with the assessment materials. Students\u27 spatial and unit measurement knowledge most frequently co-occurred with computational thinking, and most often when students built and read/enacted programs. I categorized the co-occurrences as independent or dependent, depending on if the co-occurrence related to the students\u27 correct or incorrect response to the assessment items. These findings show that mathematical knowledge and computational thinking are strongly connected, and that students\u27 mathematical knowledge is related to how they performed on the assessment. These findings have implications for computational thinking curriculum and assessment design, mathematics curriculum design, and theory. Based on the results of this present study, I recommend that mathematics curriculum developers take advantage of the particularly strong connections of spatial and unit measurement knowledge with computational thinking to design experiences for children develop their spatial reasoning and measurement knowledge

All Advanced Placement (AP) Computer Science is Not Created Equal: A Comparison of AP Computer Science A and Computer Science Principles

This article compares the two most prominent courses of Advanced Placement (AP) computer science study offered throughout 9-12 grades in the U.S. The structure, guidelines, components, and exam formats of the traditional AP Computer Science A course and the relatively newer AP Computer Science Principles course were compared to examine differences in content and emphases. A depth-of-learning analysis was conducted employing Bloom’s Revised Taxonomy to examine potential differences in rigor and challenge represented by the two options, particularly as it relates to acquiring computer programming proficiency. Analyses suggest structural differences in both course content and end-of-course exam components likely result in less depth and rigor in the new Computer Science Principles course as compared to the Computer Science A course. A lower minimum standard for learning programming skills in the Computer Science Principles course was observed, making it a less viable option for students looking to acquire skills transferable to future computer science study or employment. The potential implications for students choosing the new course over the traditional offering, as well as for schools opting for the new course as its sole or primary offering are discussed