APL Functions Research Articles

Processing and presentation of (pro)‐insulin in the MHC class II pathway: the generation of antigen‐based immunomodulators in the context of type 1 diabetes mellitus

Both CD4(+) and CD8(+) T lymphocytes play a crucial role in the autoimmune process leading to T1D. Dendritic cells take up foreign antigens and autoantigens; within their endocytic compartments, proteases degrade exogenous antigens for subsequent presentation to CD4(+) T cells via MHC class II molecules. A detailed understanding of autoantigen processing and the identification of autoantigenic T cell epitopes are crucial for the development of antigen-based specific immunomodulators. APL are peptide analogues of auto-immunodominant T cell epitopes that bind to MHC class II molecules and can mediate T cell activation. However, APL can be rapidly degraded by proteases occurring in the extracellular space and inside cells, substantially weakening their efficiency. By contrast, protease-resistant APL function as specific immunomodulators and can be used at low doses to examine the functional plasticity of T cells and to potentially interfere with autoimmune responses. Here, we review the latest achievements in (pro)-insulin processing in the MHC class II pathway and the generation of APL to mitigate autoreactive T cells and to activate Treg cells.

New problem

Let us have some fun selecting out diagonals from rank 2 and 3 arrays. It is really an exercise in using some of the lesser-used but powerful primitive APL functions. There are probably several ways to arrive at the solutions. Let's see what we get.

An interface for user-defined functions in a database application

This paper describes a database application, which permits users to write their own functions in a limited way using a scripting language consisting of a set of canned functions written in APL. Inputs to the function can be database fields and/or constant values. This provides users with additional flexibility in generating reports and selection statements.The user must first define the function inputs and outputs assigning names, position, data types, default values and descriptions for each. Then the user writes a script in the database language, making reference to the named input and output fields. The scripting language is limited to a defined set of functions and certain ASCII symbols.A limited set of control structures are permitted, such as if-then-else, and while loops.The application consists of an editor, which allows the user to describe the inputs and write the script, and a "compiler", which generates an APL function, which behaves in a similar manner to the canned functions, provided with the database application. The "compiler" inserts data assignment and input checking into the function based on the data type and data structure permitted by the user.

A knowledge discovery method

The paper concentrates on one direction of Knowledge Discovery in Data Bases and Data Mining, known as automatic rule extraction from data sets.The rule extraction algorithm has been implemented in Dyalog APL. The paper presents APL functions and tests made on artificial data sets.The real life problem solution is described as an application of implemented APL code. The problem is to find automatically rules to describe the corrosion rate of steel in sodium as a function of alloy additions. The input data are experimental data of corrosion rate measured for different steel samples. The output is a set of IF-THEN rules, which describe the dependence of corrosion rate on alloy additions. An expert in corrosion has validated the rules and an example of real "discovery" has been mentioned.

An APL ompiler

Even if APL is the best-suited programming language for multi-dimensional data, nowadays computer applications additionally require complex graphical user interfaces, internet and database access. Combining software written in C, C++ or Java with interpreted APL programs is difficult. A homogeneous solution has been found by automatically converting APL programs into native C code. A complete APL2 like system including interpreter and session manager has been implemented in ISO C from scratch based on the standard C library. It is the property of the author and not yet commercially available. It has been successfully compiled on several operating systems. The built in system call APL2C allows one to compile any APL function including all referenced functions or operators within the workspace into native C code and completely removes the interpreter using direct calls to the C coded APL primitives. Only obvious restrictions (no runtime execution of character arrays or dynamic creation of functions via FX ) apply. In addition, a makefile is created to enable the simple build of standalone executable files. The C files, generated by APL2C, can be easily mixed with other C/C++ source files and compiled on any platform provided that the required library for the APL primitives is available.

EGREGION

This article describes our experience with test suites and automated branch coverage tools for APL software maintenance, based on our use of them to verify Y2K compliance of an APL-based database system. We introduce egregion, a simple, easy-to-use tool that assesses branch coverage in APL functions. The tool comprises a pair of APL functions that report detailed and summary function-level information about code coverage of test suites. The egregion tool provides a line-by-line analysis of statement coverage, labels not branched to, branches never taken, branches always taken, transfer of control via non-branches, and branches to non-labeled lines. Although we do not consider this groundbreaking work, we do believe that the coverage tool will be valuable to APL programmers who are engaged in the creation of large, reliable applications.

APL design of graphic displays for motivation in distance education

APL is used in the experimental design of graphic displays to be applied in real-time, on-line education. These graphic displays are to be integrated in instructional dialogs. Our aim is to discover displays that will motivate students while they take computer mediated and distance learning courses. During the learning process, it is especially important for a student to receive feedback about his/her progress, continually and within a few tens of seconds of the most recent interaction. This feedback may indicate student performance relative to the recent past and also relative to their peers who have interacted with the same learning items. Compact and easy-to-interpret graphical or quantitative (partly numeric) displays of student progress are designed as character arrays. The rules for constructing these arrays are described conveniently in APL functions. Such functions specify a template each display and establish design correctness. The functions also allow flexible testing that reveals how easy it is to understand each display.

Graphpak

There have been several APL Quote Quad papers published in the past few years that discuss requirements for APL graphics capabilities. The Graphpak workspace now distributed with IBM's APL2 products evolved from its 1970 roots in an environment that projected similar requirements. This paper discusses the characteristics of Graphpak that have contributed to its evolving application and its longevity. Following an introduction that describes its evolution, the paper will focus on its "tool box" approach---using APL functions that can be used to build other functions to meet custom graphics requirements. Also, some opportunities for future exploitation of APL2 are sketched.

A constructive algorithm for neural networks that generalize

APL functions were designed to describe a constructive algorithm that synthesizes a neural network while optimizing its ability to generalize. Algorithms are implemented in programs to discover networks of binary weights that assign unfamiliar, high-dimension binary patterns to their most similar classes. Constructive algorithms that create networks are important for the design of classifiers based on array-processors made from fast two-level circuits. APL is an effective tool for the exposition of a constructive algorithm that can discover a minimal neural network. APL experts can benefit from being introduced to this interesting application and demonstration of the language's potential for describing array-based software or hardware. For constructing networks, algorithms for target switching and minimizing the overlap in the separation of training patterns have been used. Typically, prototypes of constructive algorithms as commonly implemented with scalar-based procedural languages require hundreds of program statements. Array-based formulations of similar constructive algorithms with functional style programming languages like APL and J are completed with a few brief functions.

About a consistent APL notation for structured programming

For now quite a number of years, I haven't used a label or a branch within the numerous APL functions I programmed for many purposes. So, the colon symbol ":" has become free... for a brand-new use.

Using Microsoft Access to store function definitions

T HIS PAPER SUMMARISES some preliminary experimentation using Microsoft Access as a vehicle for storing APL function definitions separately from the workspace. The work appears to offer some advantages in terms of improved code portability between interpreters.

Speeding times

In a recent article [2], it was shown that function samples for all functions composed of the elementary functions can be computed using two operators, By and Times, which deliver samples of the maximum possible order for linear combinations and products of functions. The article highlighted the simplicity of the exposition, but made no attempt to modify algorithms to improve the speed of calculations. In particular, it was noted that the APL functions took around three seconds to obtain the values of the first ten derivatives of the test function ( x csc x )/ log arctan exp x while Mathematica 2.0 obtained the same results in about a second. The APL functions, however, were also able to obtain these derivatives at any number of points, and the calculation for 100 points took approximately 18 seconds. This article will show how a simple adjustment can significantly reduce these execution times.

Frequency counts, accumulations and cross-tabulations in APL

Frequency counts (how many) and accumulations (how much) are everyday programming tasks. Yet, there are no primitive APL functions for solving these problems directly. Instead, you dig into your bag of techniques and use some clever shifting or inner/outer product method to do the job. This paper proposes a primitive syntax for generally computing frequency counts, accumulations and cross-tabulations (which are multidimensional frequency counts and accumulations). The aim of the paper is not to encourage the implementation of a new primitive function; rather, it offers a mental model: a way to view this class of problems. A user-defined function that implements the model is shown on page 28.

Understanding ANOVA the APL way

Statistics text books expound the collection of techniques known as analysis of variance by using mathematical formulae. The term analysis of variance is something of a misnomer, since any analysis follows a primary exercise of partitioning sums of squares, which is entirely a matter of computation and data reorganization of the sort which APL is particularly adept at. The crux of the analysis stage then consists of making choices between what is often a bewilderingly large range of subtly different sums of squares partitions. The primitive function enclose with axis maps naturally into the data manipulations involved in sums of squares partitions for arrays. To the casual reader the latter are obscured rather clarified by the use of mathematical formulae alone. This paper explores the relationships between APL functions and ANOVA, and goes on to illustrate how these can be used in the context of a designed experiment.

Structuring functions with operators

Flow control for APL functions is limited to the simple GOTO facility supplied by the → arrow. Numerous papers have suggested enhancements to APL which provide flow control structures. This paper investigates to the extent to which control structures can be implemented in APL solely by means of features that already exist in the language, specifically by the use of primitive or defined operators. The exercise offers both a means to improve the quality of APL code and also affords an insight into the use of operators and their limitations. The paper assumes the use of APL2 or other compatible dialects such as APL.68000.

The dual structure of ordered trees

Although they were described by K. Iverson in his 1962 book [1], ordered trees have never been implemented as APL objects. However, APL2 as well as ISO-APL, provide many facilities to handle them. This paper illustrates with simple examples, the duality between the tree-structure and what will be presented as an "object-oriented definition structure". APL functions are proposed to facilitate the conversion of one form into the other one. Trees have great utility in data base processing, as well in science, as in business applications. Interfaces with the "outer world" - e.g. word processors, or LISP and PROLOG can become easy to build with the help of this simple concept of duality.

CATS

This paper describes the implementation of an automated test system for APL functions. It extends an implementation of assertive comments in APL to derive a notation for formal specification using pre and post conditions. These conditions are APL statements and so can be built into test functions. Data supplied to provide examples is captured and subjected to mutations to test behaviour under edge conditions. The techniques make extensive use of modern APL ideas such as defined operators, phrasal forms and function assignment.

Automatic synthesis of the inverses of APL functions

APL is used to facilitate the automatic inversion and execution of programs which are constructed by strict functional composition. Programs for performing high level functions and their inverses can be logically synthesized and then tested in arbitrary instances. APL is used to compose higher level functions by repeated left application of functions and operators designed expressly so that their syntax is limited to be monadic.A small system of auxiliary functions are sufficient to do the synthesis of inverse programs. This system operates on sequences of applicative functions which must be provided originally with their forward form coded in functional style APL. The system inverts higher level user-defined functions and generates correctly sequenced function calls which are used in testing the synthesized inverses.Using this system, the mechanistic re-formulation of the forward functions and either their exact or even their approximate inverses can be produced and then checked for consistency. Consistency in performance can be randomly tested by evaluating and confirming the validity of the identity R ≡ F -1 F R. This may be done for acceptable comparison tolerances over a representative number of objects named R to which the function F and its inverse F -1 are applied in tandem.

APL2 as a specification language for statistics

APL has had a dedicated following for many years among some sections of the academic and industrial statistical communities. One of its greatest strengths is its value as a specification language. Not only can algorithms be described consistently and unambiguously, but also, given an appropriate interpreter, the specifications can be immediately executed. A group of academic and industrial statisticians in the United Kingdom recognized these capabilities and embarked on a project called ASL (APL Statistics Library) with the support of the British APL Association. ASL aims to provide a collection of coherent APL functions for widely used statistical calculations, thereby creating stan-dards for the unambiguous expression of statistical algorithms. A natural consequence of this is that discussions of more complex algorithms and methods can occur without the need to revisit and redefine basic functions and the ways in which they interpret data.

Object-oriented programming of X Window System graphical user interfaces

An object-oriented programming style facilitates programming graphical user interfaces with APL and an external processor interface to the X Window System interface library of C functions. Objects are represented by global nested variables. Methods are represented by APL functions whose names are stored in the objects.