James Bradley

A group-select operation for relational algebra and implications for database machine design

A group-select operation has been defined for relational algebra. This operation is found to be useful for efficiently reducing expressions of nonprocedural relational languages that permit natural quantifiers. Conceptually, the operation first partitions a relation into blocks of tuples that have the same value for an attribute or attribute concatenation. It then extracts each block for which a specified number of tuples meet a specified condition. The quantity of tuples for the operation is specified by means of a natural quantifier. Performance of the group-select operation will be poor with conventional file processing, making the operation more suitable for use with a database machine with an associative memory. >

Time Period and Risk Measures in the General Risk Equation

In an earlier paper, a general risk equation, applicable to all non growth systems, and inclusive of financial systems, was derived. It related expected throughput capacity of any system to both system resources and positive risk of loss of throughput capacity. Two risk measures were required, a new MEL‐risk measure, and the conventional standard‐deviation risk measure. In this paper we show that the two apparently distinct risk measures are intimately related, and that which one is appropriate depends merely on the time period over which the risk is calculated. We show, ultimately by application of the Central Limit Theorem, that if we merely sufficiently alter the time period, at some point the need for one measure will transition into the need for the other, without any change in the underlying physical system. This leads to a comprehensive risk measure that defaults to either the MEL‐risk measure, or standard‐deviation measure, depending not on the physical system, but merely on the time period over which the risk is calculated.

A risk hypothesis and risk measures for throughput capacity in systems

A basic risk hypothesis for system throughput capacity in the presence of risk is proposed. It is expressed as a basic risk equation , derived in the paper, and governs all nongrowth, nonevolving, agent-directed systems. The basic risk equation shows how expected throughput capacity increases linearly with positive risk of loss of throughput capacity. The conventional standard deviation risk measure, from financial systems, may be used. A proposed new measure, the mean-expected loss risk measure with respect to the hazard-free case, is shown to be more appropriate for systems in general. The concept of an efficient system environment is also proposed. The well-known financial risk equation, hitherto deduced empirically, may be derived from the basic risk equation. When there is both risk exposure and resource sharing, the basic risk equation may be combined with a resource-sharing equation that governs how throughput capacity changes with the resource-sharing level. The basic risk equation also allows for risk elimination and reduction. All quantities in the equation are precisely defined, and their units are specified. The risk equation reduces to a useful numerical expression in practice.

An efficient modularized database structure for a high-resolution column-gridded Mars global terrain database

This paper discusses a modularised design for a Mars Global Terrain Database. The design provides for elevation data with respect to a triaxial ellipsoidal reference datum developed for Mars by USGS. Terrain data is recorded for 1‐second of arc almost square grid elements over the surface of Mars. A 2000‐Gigabyte column‐gridded relation called Terrain contains the surface terrain data. Data for Terrain is expected in 1999–2000 from the Mars Global Surveyor satellite currently in initial polar orbit around Mars. Each tuple of Terrain contains data for a N‐S column‐grid of 900 1‐second grid elements. There is thus a set of tuples per 1‐degree rectangle, with the number of tuples per set decreasing with the cosine of latitude. Surface resolution is 16.5 meters or better. The design constrains tuple sizes in Terrain to permit efficient blocking and manipulation of the records of the underlying storage file. Terrain contains a virtual‐attribute function for geodetic computations relating to the triaxial ellipsoidal reference datum. The database also relates Mars feature‐type relations to Terrain. Terrains gridded structure is transparent to users writing SQL expressions to retrieve Terrain data on the basis of specific features. Many different distinct feature‐type relations can be included. At least two of these participate in recursive relationships. The design also allows attachment of additional feature‐type relations in a modular manner, correctly related to Terrain, without affecting the contents of Terrain. The design is intended to enable efficient exploration of the planet at all levels of scale. Copyright

A complete L-system specification for generating an exact self-affine growth-decay function with a random walk scaling property

The existence of at least four exact self-affine time functions, called E5:3 functions, that allow for an infinite number of exact replications of Growth-Decay 12345abc structures, is demonstrated. These E5:3 functions are defined by algorithms and have no derivatiue anywhere. One of these E5:3 functions, called the standard E5:3 function, has the property of scaling like a random walk. This function also depends on the Golden Mean and rotates congruently with the Golden Spiral. A complete L-system specification for generating the standard E5:3 function is presented

Extended relational algebra for reduction of natural quantifier COOL expressions

An extended relational algebra has been developed. This extended algebra is suitable for reduction of expressions written in the object-oriented natural quantifier language COOL. The algebra consists of conventional operations, plus a group select, a subgroup select, and possibility join operation. The group select operation selects each group of related tuples where a quantity of the group obeys a condition. The subgroup-select operation selects each group of related tuples where a quantity of a subgroup of the group obeys a condition. The possibility join of relation R1 with relation R2 regenerates relation R1 but with each tuple having a logical attribute p concatenated, with p true where the R1 tuple could have been joined to an R2 tuple, otherwise p false. Generalized algebra routines for generalized COOL expressions are presented. The algebra has been successfully incorporated in an implementation of a COOL front end.