Symbolic Comparison Research Articles

The Epoch of the Constellations on the Farnese Atlas and Their Origin in Hipparchus's Lost Catalogue

1. BACKGROUND The Farnese Atlas is a Roman statue depicting the Titan Atlas holding up a celestial globe that displays an accurate representation of the ancient Greek constellations (see Figures 1 and 2). This is the oldest surviving depiction of this set of the original Western constellations, and as such can be a valuable resource for studying their early development. The globe places the celestial fi gures against a grid of circles (including the celestial equator, the tropics, the colures, the ecliptic, the Arctic Circle, and the Antarctic Circle) that allows for the accurate positioning of the constellations. The positions shift with time due to precession, so the observed positions on the Farnese Atlas correspond to some particular date. Also, the declination of the Arctic and Antarctic Circles will correspond to a particular latitude for the observer whose observations were adopted by the sculptor. Thus, a detailed analysis of the globe will reveal the latitude and epoch for the observations incorporated in the Atlas; and indeed these will specify enough information that we can identify the observer. Independently, a detailed comparison of the constellation symbols on the Atlas with those from the other surviving ancient material also uniquely points to the same origin for the fi gures. The Farnese Atlas 1 fi rst came to modern attention in the early sixteenth century when it became part of the collection of antiquities in the Farnese Palace in Rome, hence its name. The statue was later transferred to the museum in Naples now called the Museo Archeologico Nazionale di Napoli. It is carved in white marble and depicts the bearded Atlas crouched down on one knee with a cloak over his shoulder and holding the celestial globe on his shoulder with both hands. The globe is 65cm in diameter. Its top has a substantial hole knocked into it and this has obliterated the constellations of Ursa Major and Ursa Minor. A total of 41 constellations 2 are depicted, each drawn in positive relief as the classical fi gure, with no individual stars shown. Art historians conclude that the statue is a Roman copy from the second century A.D. of a Greek original dating to before the birth of Christ. 3 What is the date of the observations used for depicting the constellation positions on the Farnese Atlas? A very wide range of plausible answers is possible. First, the Roman sculptor could have updated the constellation positions with his own observations (or those of a contemporary), hence suggesting a date of c. 150 A.D. Second, the Roman sculptor could have used the latest star catalogue to place the constellations accurately onto the coordinate grid of the sky, and this would be from the Almagest of Ptolemy,

Selective Interference With the Use of Visual Images in the Symbolic Distance Paradigm.

Eight experiments investigated the effects of visual, spatial, auditory, and executive interference on the symbolic comparison of animal size and ferocity, semantic goodness of words, and numbers. Dynamic visual noise (DVN) and the reading of visually presented stimulus items were shown to selectively interfere with response times on the animal size comparison task, though the slope of the symbolic distance function remained unchanged. Increased change of DVN significantly increased interference, but interference was reduced by equiluminant DVN. Spatial tracking reduced the slope of the symbolic distance function in contrast to an executive task that only increased mean latency and errors for all comparisons. Results suggest that the generation of an image is necessary for size comparison, but neither imagery nor executive function is responsible for the frequently observed distance-time function.

A response time model for judging order relationship between two symbolic stimuli

The response time to judge the order relationship between two symbolic stimuli is frequently modeled as the time spent in a (constant-rate) accumulative sampling process until a threshold is reached. We will show that empirical descriptions of observed effects in number comparisons suggest an accrual process that reaches the threshold at an exponential rate. The model accrual equations and stopping conditions have an immediate interpretation in terms of a simple quantitative connectionist network. The encoded stimuli and thresholds are inputs to the network. The former are considered to result from the participant's learning history, and the latter modulate the rearrangement of the network parts; each arrangement models a different task. We have found a good correlation between model predictions and other authors' experimental data, both in number comparisons and in experiments in which the ordering of the symbolic stimuli has been artificially induced. Incorrect answers are discussed, and predictions are compared with data. We will explore differences and similarities with other approaches, such as random walk and the symbolic comparison model. In a limit case, our model becomes identical to the discriminability model.

From cutting an object to a clear cut analysis

The representation of the concrete world is an abstraction. The elements that are physically pertinent to reality are synthesized in a gestural, schematic and ergonomic representation. Although schematic, this representation is nuanced: the gestural variants are numerous in order to account for the way we cut things: differences in size and configuration of blades as well as in their manipulation in a single or repeated movement. Representing an abstract notion derived from the act itself, gesture evolves towards increasing simplification and integrates the representation of other notions that enrich the first: cf. the semantic nuances supplied by the plane of the hand and the orientation of the palm in order to evoke ‘cut plus division’, ‘cut plus obstacle’, etc. Moreover, on the semantic level one witnesses a process of generalization: the passage from concrete to abstract, and in the abstract world, from one domain to another: the individual knows how ‘trancher / to decide’ and is ‘tranchant / abrupt’. From the physical and symbolic comparison of the gestural variants referring to all kinds of cuts, a common percept emerges: a gap in a continuum, a representative schema explaining the cut as an interruption. The question addressed is: does gesture not directly account for the abstract schema loaded with imagery from diverse perceptual experiences (representation of acts and their results) at the basis of the concept (representation of the notion)?

A Comparison of Symbols for Preferred Behaviors

The number of persons traveling to and working in locations where their native language is not used has increased significantly. Thus, communication via symbols has become important for many reasons, including safety. Previous research has shown that a symbol indicating that something is to be done may significantly increase understanding of symbols indicating behavior to be avoided (Leonard, 2000). The symbol indicating that an activity was permitted or to be done was the enclosure of the symbol for the activity in a pentagon. One of the present studies expanded on this result by examining the ability of individuals to learn the meaning of the symbol from a small number of presentations. The second study compared the usefulness of the pentagon symbol with another approach to presenting to do information. The pentagon was superior in drawing attention to the behavior to be performed, especially when no negative symbol was involved. Taken together the two studies provide further support for the usefulness of the pentagon symbol as an indicator of the acceptability or need to perform an activity.

Revisiting the picture-superiority effect in symbolic comparisons: Do pictures provide privileged access?

In 4 experiments, symbolic comparisons were investigated to test semantic-memory retrieval accounts espousing processing advantages for picture over word stimuli. In Experiment 1, participants judged pairs of animal names or pictures by responding to questions probing concrete or abstract attributes (texture or size, ferocity or intelligence). Per pair, attributes were salient or nonsalient concerning their prerated relevance to animals being compared. Distance (near or far) between attribute magnitudes was also varied. Pictures did not significantly speed responding relative to words across all other variables. Advantages were found forfar attribute magnitudes (i.e., the distance effect) and salient attributes. The distance effect was much less for salient than nonsalient concrete-attribute comparisons. These results were consistently found in additional experiments with increased statistical power to detect modality effects. Our findings argue against dual-coding and some common-code accounts of conceptual attribute processing, urging reexamination of the assumption that pictures confer privileged access to long-term knowledge.

The locus and nature of semantic congruity in symbolic comparison: evidence from the Stroop effect.

Pictures of animals with names of animals printed within the pictures were presented for comparative judgments of size based on either the pictures or the names. The picture-word compounds were compared faster with picture than with word as the relevant dimension. The comparisons of pictures were free of interference from the irrelevant names, but the comparisons of names suffered considerable Stroop interference from the irrelevant pictures. Large effects of semantic congruity characterized the comparisons of both pictures and words. Stroop congruity and semantic congruity did not interact even for comparison of words in which both were present, leading instead to additive effects. The results support theories that (1) place semantic congruity in the decision stage and (2) minimize the role of semantic processing as the basis of the semantic congruity effect.

Revisiting the picture-superiority effect in symbolic comparisons: Do pictures provide privileged access?

Revisiting the picture-superiority effect in symbolic comparisons: Do pictures provide privileged access?

A model of response time effects in symbolic comparison.

A model of response time effects in symbolic comparison.

A model of response time effects in symbolic comparison.

A model of response time effects in symbolic comparison.

A model of response time effects in symbolic comparison.

A cognitive process model is developed that predicts the 3 major symbolic comparison response time effects (distance, end, and semantic congruity) found in the results of the linear syllogistic reasoning task. The model includes a simple connectionist learning component and dual evidence accumulation decision-making components. It assumes that responses can be based either on information concerning the positional difference between the presented stimulus items or on information concerning the endpoint status of each of these items. The model provides an excellent quantitative account of the mean correct response times obtained from 16 participants who performed paired comparisons of 6 ordered symbolic stimuli (3-letter names).

Fast practical multi-pattern matching

The multi-pattern matching problem consists in finding all occurrences of the patterns from a finite set X in a given text T of length n. We present a new and simple algorithm combining the ideas of the Aho–Corasick algorithm and the directed acyclic word graphs. The algorithm has time complexity which is linear in the worst case (it makes at most 2n symbol comparisons) and has good average-case time complexity assuming the shortest pattern is sufficiently long. Denote the length of the shortest pattern by m, and the total length of all patterns by M. Assume that M is polynomial with respect to m, the alphabet contains at least 2 symbols and the text (in which the pattern is to be found) is random, for each position each letter occurs independently with the same probability. Then the average number of comparisons is O((n/m)· logm) , which matches the lower bound of the problem. For sufficiently large values of m the algorithm has a good behavior in practice.

On the Comparison Complexity of the String Prefix-Matching Problem

In this paper we study the exact comparison complexity of the string prefix-matching problem in the deterministic sequential comparison model with equality tests. We derive almost tight lower and upper bounds on the number of symbol comparisons required in the worst case by on-line prefix-matching algorithms for any fixed pattern and variable text. Unlike previous results on the comparison complexity of string-matching and prefix-matching algorithms, our bounds are almost tight for any particular pattern. We also consider the special case where the pattern and the text are the same string. This problem, which we call thestring self-prefixproblem, is similar to the pattern preprocessing step of the Knuth–Morris–Pratt string-matching algorithm that is used in several comparison efficient string-matching and prefix-matching algorithms, including in our new algorithm. We obtain roughly tight lower and upper bounds on the number of symbol comparisons required in the worst case by on-line self-prefix algorithms. Our algorithms can be implemented in linear time and space in the standard uniform-cost random-access-machine model.

Saving comparisons in the Crochemore-Perrin string-matching algorithm

Crochemore and Perrin discovered an elegant linear-time constant-space string-matching algorithm that makes at most 2 n − m symbol comparisons. This paper shows how to modify their algorithm to use fewer comparisons. Given any fixed ε > 0, the new algorithm takes linear time, uses constant space and makes at most n + [ 1 + ε 2 (n − m)] symbol comparisons. If O( log m) space is available, then the algorithm makes at most n + [ 1 2 (n − m)] symbol comparisons. The pattern preprocessing step also takes linear time and uses constant space. These are the first string-matching algorithms that make fewer than 2 n − m symbol comparisons and use sub-linear space.

On the Comparison Complexity of the String Prefix-Matching Problem

In this paper we study the exact comparison complexity of the string<br />prefix-matching problem in the deterministic sequential comparison model<br />with equality tests. We derive almost tight lower and upper bounds on<br />the number of symbol comparisons required in the worst case by on-line<br />prefix-matching algorithms for any fixed pattern and variable text. Unlike<br />previous results on the comparison complexity of string-matching and<br />prefix-matching algorithms, our bounds are almost tight for any particular pattern.<br />We also consider the special case where the pattern and the text are the<br />same string. This problem, which we call the string self-prefix problem, is<br />similar to the pattern preprocessing step of the Knuth-Morris-Pratt string-matching<br />algorithm that is used in several comparison efficient string-matching<br />and prefix-matching algorithms, including in our new algorithm.<br />We obtain roughly tight lower and upper bounds on the number of symbol<br />comparisons required in the worst case by on-line self-prefix algorithms.<br />Our algorithms can be implemented in linear time and space in the<br />standard uniform-cost random-access-machine model.

Dictionary-Matching on Unbounded Alphabets: Uniform Length Dictionaries

In the string-matching problem one is interested in all occurrences of a short pattern string in a longer text string. Dictionary-matching is a generalization of this problem where one is looking simultaneously for all occurrences of several patterns in a single text. This paper presents an efficient on-line dictionary-matching algorithm for the case where the patterns have uniform length and the input alphabet is unbounded. A tight lower bound establishes that our approach is optimal if the only access the algorithm has to the input strings is by pairwise symbol comparisons. In an immediate application, the new dictionary-matching algorithm can be used in a previously known higher dimensional array-matching algorithm, improving the performance of this algorithm on unbounded alphabets. The resulting algorithm is currently the fastest known algorithm for k-dimensional array-matching on unbounded alphabets, for k ≥ 3.

Precise compile-time performance prediction for superscalar-based computers

Optimizing compilers (particularly parallel compilers) are constrained by their ability to predict performance consequences of the transformations they apply. Many factors, such as unknowns in control structures, dynamic behavior of programs, and complexity of the underlying hardware, make it very difficult for compilers to estimate the performance of the transformations accurately and efficiently. In this paper, we present a performance prediction framework that combines several innovative approaches to solve this problem. First, the framework employs a detailed, architecture-specific, but portable, cost model that can be used to estimate the cost of straight line code efficiently. Second, aggregated costs of loops and conditional statements are computed and represented symbolically. This avoids unnecessary, premature guesses and preserves the precision of the prediction. Third, symbolic comparison allows compilers to choose the best transformation dynamically and systematically. Some methodologies for applying the framework to optimizing parallel compilers to support automatic, performance-guided program restructuring are discussed.

Logic Verification System for Power Plant Sequence Diagrams.

A logic verification system for sequence diagrams of power plants has been developed. The system's main function is to verify correctness of the logic realized by sequence diagrams for power plant control systems. The verification is based on a symbolic comparison of the logic of the sequence diagrams with the logic of the corresponding IBDs (Interlock Block. Diagrams) in combination with reference to design knowledge. The developed system points out the sub-circuit which is responsible for any existing mismatches between the IBD logic and the logic realized by the sequence diagrams. Applications to the verification of actual sequence diagrams of power plants confirmed that the developed system is practical and effective.

Efficient Comparison Based String Matching

We study the exact number of symbol comparisons that are required to solve the string matching problem and present a family of efficient algorithms. Unlike previous string matching algorithms, the algorithms in this family do not "forget" results of comparisons, what makes their analysis much simpler. In particular, we give a linear-time algorithm that finds all occurrences of a pattern of length m in a text of length n in [formula] comparisons. The pattern preprocessing takes linear time and makes at most 2 m comparisons. This algorithm establishes that, in general, searching for a long pattern is easier than searching for a short one. We also show that any algorithm in the family of the algorithms presented must make at least [formula] symbol comparisons, for m = 2 k − 1 and any integer k ≥ 1.

Development of a Connectivity Verification System for Sequence Diagrams of Power Plants

A design verification system for sequence diagrams of power plants has been developed. Its main function is to verify component connectivities in power plant control systems. The verification is achieved through both a symbolic comparison of sequence diagrams against their corresponding one-line diagrams and by reference to design knowledge. The verification of actual nuclear power plant sequence diagrams confirms the system's practical effectiveness.