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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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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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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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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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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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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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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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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 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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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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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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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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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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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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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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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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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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