Uniformity Assumptions Research Articles

A lower bound for depth-3 circuits with MOD m gates

We prove that any depth-3 circuit with MOD m gates of unbounded fan-in on the lowest level, AND gates on the second, and a weighted threshold gate on the top needs either exponential size or exponential weights to compute the inner product of two vectors of length n over GF(2). In contrast, with n AND gates at the bottom and a single MOD 2 gate at the top one can compute the inner product function. The lower-bound proof does not use any monotonicity or uniformity assumptions, also works for composite m's, and all of the gates have unbounded fan-in. Our main lemma asserts that functions, computed by depth-2 AND-MOD m circuits have low probabilistic communication complexity.

Self-spacial join selectivity estimation using fractal concepts

The problem of selectivity estimation for queries of nontraditional databases is still an open issue. In this article, we examine the problem of selectivity estimation for some types of spatial queries in databases containing real data . We have shown earlier [Faloutsos and Kamel 1994] that real point sets typically have a nonuniform distribution, violating consistently the uniformity and independence assumptions. Moreover, we demonstrated that the theory of fractals can help to describe real point sets. In this article we show how the concept of fractal dimension, i.e., (noninteger) dimension, can lead to the solution for the selectivity estimation problem in spatial databases. Among the infinite family of fractal dimensions, we consider here the Hausdorff fractal dimension D 0 and the “Correlation” fractal dimension D 2 . Specifically, we show that (a) the average number of neighbors for a given point set follows a power law, with D 2 as exponent, and (b) the average number of nonempty range queries follows a power law with E − D 0 as exponent ( E is the dimension of the embedding space). We present the formulas to estimate the selectivity for “biased” range queries, for self-spatial joins, and for the average number of nonempty range queries. The result of some experiments on real and synthetic point sets are shown. Our formulas achieve very low relative errors, typically about 10%, versus 40%–100% of the formulas that are based on the uniformity and independence assumptions.

Relaxing the Uniformity and Independence Assumptions Using the Concept of Fractal Dimension

We propose the concept of fractal dimension of a set of points, in order to quantify the deviation from the uniformity distribution. Using measurements on real data sets (road intersections of U.S. counties, population versus area of different nations, etc.) we provide evidence that real data indeed are skewed, and, moreover, we show that for several scales of interest they behave as mathematical fractals with a measurable noninteger fractal dimension. Armed with this tool, we then show its practical use in predicting the performance of spatial access methods and, specifically, of R-trees. We provide thefirstanalysis of R-trees for skewed distributions of points; we develop a formula that estimates the number of disk accesses for range queries, given only the fractal dimension of the point set and its count. Experiments on real data sets show that the formula is very accurate; the relative error is usually below 5%, and it rarely exceeds 10%. We believe that the fractal dimension will help replace the uniformity and independence assumptions, allowing more accurate analysis foranyspatial access method, as well as better estimates for query optimization on multiattribute queries.

Research Classic: “Some Myths of Psychotherapy Research and the Search for A Paradigm”: Revisited

The article considered and refuted three myths prevalent within the psychotherapy literature of the time: the patient and therapist uniformity assumptions; the assumption of spontaneous remission of psychoneurotic disorders (as promulgated by Eysenck, 1952); and the belief that theoretical formulations of the time provided adequate paradigms for guiding psychotherapy research. The author proposed a new research paradigm (advocating increased use of ANOVA factorial designs) that requires specification of patient change variables (dependent variables), and of relevant patient, therapist, and intervention dimensions (independent variables), so that the field can begin to assess the central theoretical and research question: Which therapist behaviors are more effective with which type of patients?

Evaluating the size of queries on relational databases with non-uniform distribution and stochastic dependence

The paper deals with the problem of evaluating how the originality of the attributes of a relation, i.e. the number of distinct values in each attribute, is affected by relational operations that reduce the cardinality of the relation. This is indeed an interesting problem in research areas such as database design and query optimization. Some authors have shown that non uniform distributions and stochastic dependence significantly affect the originality of the attributes. Therefore the models that have been proposed in the literature, based on uniformity and independence assumptions, in several situation can not be conveniently utilized. In this paper we propose a probabilistic model that overcomes the need of the uniformity and independence assumptions. The model is exact for non uniform distributions when the attributes are independent, and gives approximate results when stochastic dependence is considered. In the latter case the analytical results have been compared with a simulation, and proved to be quite accurate.

A general framework for computing block accesses

A physcial database system design should take account of skewed block access distributions, nonuniformly distributed attribute domains, and dependent attributes. In this paper we drive general formulas for the number of blocks accessed under these assumptions by considering a class of related occupancy problems. We then proceed to develop robust and accurate approximations for these formulas. We investigate three classes of approximation methods, respectively based on generating functions, Taylor series expansions, and majorization. These approximations are simple to use and more accurate than the cost estimate formulas generated by making uniformity and independence assumptions. Thus they are more representative of the actual database environment, and can be utilized by a query optimizer for better performance.

Can pregnancy be a placebo effect?: Terminology, designs, and conclusions in the study of psychosocial and pharmacological treatments of behavior disorders

This paper discusses several salient issues in the clinical research enterprise which were stimulated by chapters on research methods and placebo phenomena in White, Tursky and Schwartz (1985). Placebo: Theory, Research, and Mechanisms. These issues include the commonalities of questions, domains and classes of variables, and research strategies needed for the discovery, accumulation and application of knowledge regarding effective clinical treatments. Problems of unwarranted uniformity assumptions and absolute design requirements as well as the failure to attend to the conceptual relevance, strength and integrity of procedures are noted with examples from the systematic desensitization literature. Meta-analyses and indexes of effect size are also examined with examples demonstrating the need for especially cautious interpretation of these procedures. A re-emphasis of the construct validity approach with better designed and executed individual studies is endorsed as the best means to improve progress.

An investigation of passenger interchange and train standing time at LRT stations: (i) Alighting, boarding and platform distribution of passengers

AbstractThe train standing‐time at a station is a determinant of the line capacity and the necessary fleet‐size. Its determination is usually based on the assumption that boarding and alighting is uniform at all doors of a train. Uniform boarding and alighting is conceivable if passengers distribute themselves uniformly on station platforms while waiting for trains. The validity of the uniformity assumptions is tested using data from two stations (one CBD, one suburban) of the Calgary, Alberta LRT system. It is shown that passenger distribution on the platform, alighting and boarding is not uniform and is closely related to the location of platform access points. Some strategies that will encourage uniformity are discussed. However, procedures that can estimate the standing time for non‐uniform boarding and alighting need to be developed.

The psychodynamic diversity of anorexia nervosa

This paper proposes that anorexia nervosa patients are a psychodynamically heterogeneous group and can be usefully divided into three subtypes — the borderline; the empty, understructured; and the emotionally-conflicted, identity-confused. Clinical experience and the long-term outcome literature challenge any uniformity assumptions about anorexia nervosa. It is noted that anorexia nervosa appears to be a “spectrum disorder” with presentations ranging from normative adolescent concern about weight, dieting, appearance, etc. to severe psychopathology and classical anorexic symptomatology among those predisposed.

An existence theorem for observers of bilinear systems

Under suitable uniformity assumptions, the existence of nonlinear state observers with exponentially decaying error for bilinear systems is proved to be equivalent to that of observers whose corresponding error dynamics is linear with respect to the error.

Possible non-Regge behavior of electroproduction structure functions

The large-ω behavior of deep-inelastic structure functions, e.g., F2(ω,q^2), is studied in the framework of asymptotically free field theories. On the basis of certain uniformity assumptions we predict an unbounded growth with ω: slower than any power of ω but faster than any power of logω.

On the identifiability of parameters

A precise definition of identifiability of a parameter is given in terms of consistency in probability for the parameter estimate. Under some mild Uniformity assumptions on the conditional density parameterized by the unknown parameter, necessary and sufficient conditions for the unknown parameter to be identifiable are established. The assumptions and identifiability criteria are expressed in terms of the density of individual observations, conditioned upon all past observations. The results are applied to linear system identification problems.