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We model the algorithmic task of geometric elimination (e.g., quantifier elimination in the elementary field theories of real and complex numbers) by means of certain constraint database queries, called geometric queries. As a particular case of such a geometric elimination task, we consider sample point queries. We show exponential lower complexity bounds for evaluating geometric queries in the general and in the particular case of sample point queries. Although this paper is of theoretical nature, its aim is to explore the possibilities and (complexity-)limits of computer implemented query evaluation algorithms for Constraint Databases, based on the principles of the most advanced geometric elimination procedures and their implementations, like, e.g., the software package "Kronecker".

In the constraint database model, spatial and spatio-temporal data are stored by boolean combinations of polynomial equalities and inequalities over the real numbers. The relational calculus augmented with polynomial constraints is the standard first-order query language for constraint databases. Although the expressive power of this query language has been studied extensively, the difficulty of the efficient evaluation of queries, usually involving some form of quantifier elimination, has received considerably less attention. The inefficiency of existing quantifier-elimination software and the intrinsic difficulty of quantifier elimination have proven to be a bottle-neck for for real-world implementations of constraint database systems. In this paper, we focus on a particular query, called the \emph{alibi query}, that asks whether two moving objects whose positions are known at certain moments in time, could have possibly met, given certain speed constraints. This query can be seen as a constraint database query and its evaluation relies on the elimination of a block of three existential quantifiers. Implementations of general purpose elimination algorithms are in the specific case, for practical purposes, too slow in answering the alibi query and fail completely in the parametric case. The main contribution of this paper is an analytical solution to the parametric alibi query, which can be used to answer this query in the specific case in constant time. We also give an analytic solution to the alibi query at a fixed moment in time. The solutions we propose are based on geometric argumentation and they illustrate the fact that some practical problems require creative solutions, where at least in theory, existing systems could provide a solution.

We propose to explore an innovative, data mining (DM) process for application in breast cancer (BC) databases. The DM process is the Constraint Satisfaction Neural Network (CSNN). Contrary to feed-toward networks and statistical models, the CSNN has a non- hierarchical architecture that allows it to be used either as a prediction/classification tool or as an analysis tool for mining association rules in databases. This is a feasibility study to investigate to what degree the CSNN can deliver the above promises for the mammographic diagnosis of breast lesion malignancy. The main objectives of the study are the following: (1) to develop a CSNN for mining a database of patients suspected with BC who underwent breast biopsy; (2) to evaluate the CSNN as a diagnostic tool; (3) to evaluate the CSNN as a patient prototype analysis tool to discover prevalent trends and associations among the variables; (4) to assess the network's robustness with missing data. Initially, the CSNN is intended as a computer-assisted diagnostic tool to help physicians optimize the decision to refer a probably benign breast lesion to short-term follow-up instead of biopsy. Ultimately, the CSNN can be applied as a support tool individualizing the decision process in BC patient management.

We propose to explore an innovative, data mining (DM) process for application in breast cancer (BC) databases. The DM process is the Constraint Satisfaction Neural Network (CSNN). Contrary to feed-toward networks and statistical models, the CSNN has a non- hierarchical architecture that allows it to be used either as a prediction/classification tool or as an analysis tool for mining association rules in databases. This is a feasibility study to investigate to what degree the CSNN can deliver the above promises for the mammographic diagnosis of breast lesion malignancy. The main objectives of the study are the following: (1) to develop a CSNN for mining a database of patients suspected with BC who underwent breast biopsy; (2) to evaluate the CSNN as a diagnostic tool; (3) to evaluate the CSNN as a patient prototype analysis tool to discover prevalent trends and associations among the variables; (4) to assess the network's robustness with missing data. Initially, the CSNN is intended as a computer-assisted diagnostic tool to help physicians optimize the decision to refer a probably benign breast lesion to short-term follow-up instead of biopsy. Ultimately, the CSNN can be applied as a support tool individualizing the decision process in BC patient management.

We propose to explore an innovative, data mining (DM) process for application in breast cancer (BC) databases. The DM process is the Constraint Satisfaction Neural Network (CSNN). Contrary to feed-toward networks and statistical models, the CSNN has a non- hierarchical architecture that allows it to be used either as a prediction/classification tool or as an analysis tool for mining association rules in databases. This is a feasibility study to investigate to what degree the CSNN can deliver the above promises for the mammographic diagnosis of breast lesion malignancy. The main objectives of the study are the following: (1) to develop a CSNN for mining a database of patients suspected with BC who underwent breast biopsy; (2) to evaluate the CSNN as a diagnostic tool; (3) to evaluate the CSNN as a patient prototype analysis tool to discover prevalent trends and associations among the variables; (4) to assess the network's robustness with missing data. Initially, the CSNN is intended as a computer-assisted diagnostic tool to help physicians optimize the decision to refer a probably benign breast lesion to short-term follow-up instead of biopsy. Ultimately, the CSNN can be applied as a support tool individualizing the decision process in BC patient management.