algebraic abstract data type

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The combinatorics of abstract container data types

The combinatorics of abstract container data types

Abstract data types are central to the point of view adopted in object-oriented programming which now permeates all large software projects. Although abstract data typing was initially adopted primarily for its use as a software design tool it has always been recognised that each data type has a rigorous mathematical definition. Each abstract data type is characterised by the set of operations that can be per­ formed on it. Therefore an abstract data type can be regarded as an abstract machine whose instruction set is the set of operations it supports. Some of these op­ erations may supply input or output while others may examine or change the state of the abstract data type. The precise specification of these instruction sets has been studied in considerable depth by algebraic means, see [BMC092a, EMC092b] for a survey. However, the classical abstract machines are studied at a much deeper level; their behaviour in response to arbitrary sequences of instructions, or programs, is studied and this behaviour is captured by the idea of the language recognised by the machine. As yet, such a study has hardly begun for abstract data types although, as indicated below, there is a very natural extension of the language notion to abstract data types.
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GRAPHIC SPECIFICATION OF ABSTRACT DATA TYPES

GRAPHIC SPECIFICATION OF ABSTRACT DATA TYPES

Formally specifying software requirements using algebraic specifications has all the advantages of formal specifications. This type of specifications is usually textual. Most modern specification languages have a graphical representation in an attempt to improve usability. This is also the case for algebraic specifications .Here we present a survey on how abstract data types are represented graphically. We propose a structure containing a superset of all elements surveyed. We also show an application example, and we report some experimental results when using this graphical representation.
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Translating Generalized Algebraic Data Types to System F

Translating Generalized Algebraic Data Types to System F

Abstract. Generalized algebraic data types (GADTs) extend ordinary algebraic data types by refining the types of constructors with syntactic equality constraints. This is highly useful and allows for novel applica- tions such as strongly-typed evaluators, typed LR parsing etc. To trans- late GADTs we need to enrich the System F style typed intermediate languages of modern language implementations to capture these equality constraints. We show that GADTs can be translated to a minor exten- sion of System F where type equality proofs are compiled into System F typable proof terms. At run-time proof terms evaluate to the identity. Hence, they can be safely erased before execution of the program. We provide evidence that our approach scales to deal with extensions where equality is not anymore syntactic. The benefit of our method is that type checking of target programs remains as simple as type checking in Sys- tem F. Thus, we can offer a light-weight approach to integrate GADTs and extensions of it into existing implementations.
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ABSTRACT : Digital terrain model (DTM) represents a very important geospatial data type. In the Czech Republic, the

ABSTRACT : Digital terrain model (DTM) represents a very important geospatial data type. In the Czech Republic, the

raster models represents the value of the whole pixel with the given size (area), whereas the resolution of the resulting DTM with the pixel size 5 × 5 m was selected. The position component of control pixels was located with GPS Trimble GeoExplorer XT, namely by the code measurement by a static method with 10-minute observation length (120 re- cords with 5-second interval). The postprocessing method of corrections was used for the specification of measured points after termination of measure- ments, applying data from a permanent GPS station in TUBO point situated at an appropriate distance ca. 7 km from the experimental locality. The data are provided by the Faculty of Civil Engineering (University of Technology Brno) freely to download on web sites. Measured data processing was done in GPS Pathfinder Office 3.00, which allows both working with the measured data and their correc- tion and the export into common vector formats. The error in the accuracy of determination of the position component after corrections did not exceed 2 m, which is absolutely suitable in terms of the pixel size. Unfortunately, it is not possible to reach the ac- curacy usable for control in the height component because it was verified that this error made a double to quadruple of the position measurement inaccu- racy. Therefore it was necessary to locate the height component in control points in a levelling way with the usage of the data of the nearest trigonometric points by the method of geometric levelling from the centre using the instrument Topcon AT-64 with a levelling stick and an underlay. The error in the accuracy of determination of the height component did not exceed 10 cm, which is fully sufficient in terms of terrain characteristics in forest ecosystems. In total 250 points were located uniformly over the experimental locality. The points were recorded in the format of a vector point area with an attached database. This vector file was transferred into a raster form as necessary with the pixel size appropriate to DTM created for further analysis.
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Abstract Convexity and Hermite Hadamard Type Inequalities

Abstract Convexity and Hermite Hadamard Type Inequalities

Abstract convex function is one of this type of function classes. Hermite-Hadamard type inequalities are studied for some important classes of abstract convex functions, and the concrete results are found 6–9. For example, increasing convex-along-rays ICAR functions, which are defined in R 2

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Obfuscation of Abstract Data-Types

Obfuscation of Abstract Data-Types

We present a fresh approach to obfuscation by obfuscating abstract data- types allowing us to develop structure-dependent obfuscations that would other- wise (traditionally) not be available. We regard obfuscation as data refinement enabling us to produce equations for proving correctness and we model the data- type operations as functional programs making our proofs easy to construct. For case studies, we examine different data-types exploring different areas of computer science. We consider lists letting us to capture array-based obfusca- tions, sets reflecting specification based software engineering, trees demonstrat- ing standard programming techniques and as an example of numerical methods we consider matrices.
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INTERACTIVE VISUALIZATION OF ABSTRACT DATA

INTERACTIVE VISUALIZATION OF ABSTRACT DATA

The most cited visual investigation technique, and not only related to abstract data, is the visualization seeking mantra - Overview first, zoom, filter, and then focus details-on demand [22]. Users first see data in general view, then select subset of his/her interest and finally focus on particular attributes of selected data objects. Visualization mantra is an interactive process requiring fast response of computer, which is especially in case of large data sets not trivial. However new multi-core processors and GPU allows to render complex scenes and new forms of interactive visualization are possible. In this paper we discus the visualization process, show several experimental methods of graph visualizations and present applications in software visualization.
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Network Modulation: An Algebraic Approach to Enhancing Network Data Persistence

Network Modulation: An Algebraic Approach to Enhancing Network Data Persistence

Copyright © 2010 Xiaoli Ma et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Large-scale distributed systems such as sensor networks usually experience dynamic topology changes, data losses, and node failures in various catastrophic or emergent environments. As such, maintaining data persistence in a scalable fashion has become critical and essential for such systems. The existing major efforts such as coding, routing, and traditional modulation all have their own limitations. In this work, we propose a novel network modulation (NeMo) approach to significantly improve the data persistence. Built on algebraic number theory, NeMo operates at the level of modulated symbols (so-called “modulation over modulation”). Its core notion is to mix data at intermediate network nodes and meanwhile guarantee the symbol recovery at the sink(s) without prestoring or waiting for other symbols. In contrast to the traditional thought that n linearly independent equations are needed to solve for n unknowns, NeMo opens a new regime to boost the convergence speed of achieving persistence. Different performance criteria (e.g., modulation and demodulation complexity, convergence speed, finite-bit representation, and noise robustness) have been evaluated in the comprehensive simulations and real experiments to show that the proposed approach is efficient to enhance the network data persistence.
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Array Abstract Data Type

Array Abstract Data Type

The value of defining arrays as an abstract data type is primarily for systems programmers, who work behind the scenes and bring you all the wonderful software that comes with an operating system, such as compilers, linkers, file managers, text editors, etc. For most of us mortal people, we simply use arrays in our programming languages without thought of the more abstract nature of arrays.

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Algebraic dynamic programming over general data structures

Algebraic dynamic programming over general data structures

 | S ∗ (11) A first glance, this grammar looks odd. It is not the grammar for the suffix-version of Gotoh’s algorithm. Instead, it refers to a rather unusual way of solving the affine gap cost problem. Here the distinction is not made between opening or extending a gap, but rather between closing or extending it. The nonterminals on the r.h.s. of the rule thus refer to the type of alignment that is reached after extending the one on the l.h.s. of the rule by the terminal symbol appearing on the r.h.s. Since our forward recursion (10) is set up to separately score gap opening, i.e., the left-most gapped position in the alignment, the same must be true for the backward recursion. Since it proceeds from right to left on the input string, we naturally arrive at the algorithmic var- iant that scores gap closing separately. The correspond- ing non-terminals therefore depend on how the alignment is continued in the subsequent step.
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Sampling real algebraic varieties for topological data analysis

Sampling real algebraic varieties for topological data analysis

Our approach for sampling varieties is based on numerical algebraic geometry, with the books [5], [55] providing a general overview. The algorithm addresses the first point above by constructing provably dense samples with points very close to the underlying variety. The theoretical version of the algorithm can be readily adjusted to incorporate geometric heuristics which significantly reduce the number of points in the final output, thereby addressing the second point. An implementation is publicly available as the Python package tdasampling on PyPI and the package source code is available at https://github.com/P-Edwards/tdasampling.
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On transcendental meromorphic solutions of certain type of nonlinear algebraic differential equations

On transcendental meromorphic solutions of certain type of nonlinear algebraic differential equations

On transcendental meromorphic solutions of certain type of nonlinear algebraic differential equations Zhang Advances in Difference Equations (2016) 2016 300 DOI 10 1186/s13662 016 1030 0 R E S E A R C[.]

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Isomorphy Classes of k-involutions of Algebraic Groups of Type G2 and F4.

Isomorphy Classes of k-involutions of Algebraic Groups of Type G2 and F4.

Groups of type F 4 over a field k can be thought of as the automorphism group of an Albert algebra, where an Albert algebra is a 3 × 3 matrix that is Hermitian up to a diagonal matrix γ,[r]

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Integral Representations and Algebraic Decompositions of the Fox-Wright Type of Special Functions

Integral Representations and Algebraic Decompositions of the Fox-Wright Type of Special Functions

These multiple integrals can be denoted as generalized fractional differeitegrals [6], however this line of representation is superfluous to the necessities of the numerical (i.e. Euler [r]

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Algorithms and Abstract Data Types

Algorithms and Abstract Data Types

Some modern languages provide specific mechanisms for building first-class ADTs. Being able to manipulate instances of ADTs in much the same way that of built-in data types int or float, it allows any application program to be written such that the program manipulates the objects of central concern to the application; it allows many programmers to work simultaneously on large systems, all using a precisely defined set of abstract operations, and it provides for those abstract operations to be implemented in many different ways without any changes to the applications code - for example for new machines and programming environments. Some languages even allow operator overloading, to use basic symbols such as + or * to define operators.
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Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra

Non-Hermitian systems of Euclidean Lie algebraic type with real energy spectra

Once η is identified the metric operators needed for a consistent quantum mechanical formulation can in general be taken to be ρ = η † η. Let us now construct isospectral counterparts, if they exist, for non-Hermitian Hamiltonians symmetric with regard to the various different types of PT -symmetries. It should be noted that exact computations of this type remain a rare exception and even for some of the simplest potentials the answer is only known perturbatively, as for instance even for the simple prototype non-Hermitian potential V = iεx 3 [22, 23, 24].

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Data Mining at FDA ABSTRACT INTRODUCTION

Data Mining at FDA ABSTRACT INTRODUCTION

disproportionately associated with drugs and events. This “mechanism mining” tool generates enzymatic, pathway, and molecular target hypotheses that warrant further evaluation. The program was recently used to study infusion reactions. 18 Beyond the Office of Crisis Management’s experiences with geographical information systems (GIS) technology to manage product quality threats due to natural disasters, 19 FDA is also exploring GIS technology to enable safety data analysis for routine circumstances. Product surveillance using GIS will allow analysts to capture, store, retrieve, analyze, manage, and display safety data geographically and/or temporally. Tracking potential safety signals in this manner can provide new opportunities for real-time interventions, and identification of:
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Abstract Visualization of Algorithms and Data Structures

Abstract Visualization of Algorithms and Data Structures

JavaScript Object Notation (JSON) is a human-readable markup language. The highly extensible and widely used format stores data in key-value pairs. Be- cause of its widespread use, libraries parsing JSON have been developed by most languages in use today. JSON is language independent, but developers experienced in C-family languages will likely recognize the format and syntax. JSON supports objects, arrays, strings and values. Values is a string, number, boolean, object, or array [10]. This means that you technically could have an unlimited number of layers wrapping and organizing the data. In reality however, many parsers are unable to deserialize data which is stored "too deep".
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C++ Support for Abstract Data Types

C++ Support for Abstract Data Types

 The C++ parameterized type scheme allows “lazy instantiation” – i.e., the compiler need not generate definitions for template methods that are not used (or non-template methods)  ANSI/ISO C++ allows a programmer to explicitly instantiate parameterized types, e.g., template class Vector<int>;

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Discretisation of abstract linear evolution equations of parabolic type

Discretisation of abstract linear evolution equations of parabolic type

Our motivation lies in the numerical approximation of multidimensional PDE pro- blems arising in European financial option pricing. Let us consider the stochastic mod- eling of a multi-asset financial option of European type under the framework of a general version of Black-Scholes model, where the vector of asset appreciation rates and the volatility matrix are taken time and space-dependent. Owing to a Feynman- Kač type formula, pricing this option can be reduced to solving the Cauchy problem (with terminal condition) for a second-order linear parabolic PDE of nondivergent type, with null term and unbounded coefficients, degenerating in the space variables (see, e.g., [1]).
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