Understanding the complexity in low dimensional systems

Complex System is any system that presents involved behavior, and is hard to be modeled by using the reductionist approach of successive subdivision, searching for ''elementary'' constituents. Nature provides us with plenty of examples of these systems, in fields as diverse as biology, chemistry, geology, physics, and fluid mechanics, and engineering. What happens, in general, is that for these systems we have a situation where a large number of both attracting and unstable chaotic sets coexist. As a result, we can have a rich and varied dynamical behavior, where many competing behaviors coexist. In this work, we present and discuss simple mechanical systems that are nice paradigms of Complex System, when they are subjected to random external noise. We argue that systems with few degrees of freedom can present the same complex behavior under quite general conditions.

Clinical signs of pneumonia in children: association with and prediction of diagnosis by fuzzy sets theory

The present study compares the performance of stochastic and fuzzy models for the analysis of the relationship between clinical signs and diagnosis. Data obtained for 153 children concerning diagnosis (pneumonia, other non-pneumonia diseases, absence of disease) and seven clinical signs were divided into two samples, one for analysis and other for validation. The former was used to derive relations by multi-discriminant analysis (MDA) and by fuzzy max-min compositions (fuzzy), and the latter was used to assess the predictions drawn from each type of relation. MDA and fuzzy were closely similar in terms of prediction, with correct allocation of 75.7 to 78.3% of patients in the validation sample, and displaying only a single instance of disagreement: a patient with low level of toxemia was mistaken as not diseased by MDA and correctly taken as somehow ill by fuzzy. Concerning relations, each method provided different information, each revealing different aspects of the relations between clinical signs and diagnoses. Both methods agreed on pointing X-ray, dyspnea, and auscultation as better related with pneumonia, but only fuzzy was able to detect relations of heart rate, body temperature, toxemia and respiratory rate with pneumonia. Moreover, only fuzzy was able to detect a relationship between heart rate and absence of disease, which allowed the detection of six malnourished children whose diagnoses as healthy are, indeed, disputable. The conclusion is that even though fuzzy sets theory might not improve prediction, it certainly does enhance clinical knowledge since it detects relationships not visible to stochastic models.

Selection of patients for myocardial perfusion scintigraphy based on fuzzy sets theory applied to clinical-epidemiological data and treadmill test results

Coronary artery disease (CAD) is a worldwide leading cause of death. The standard method for evaluating critical partial occlusions is coronary arteriography, a catheterization technique which is invasive, time consuming, and costly. There are noninvasive approaches for the early detection of CAD. The basis for the noninvasive diagnosis of CAD has been laid in a sequential analysis of the risk factors, and the results of the treadmill test and myocardial perfusion scintigraphy (MPS). Many investigators have demonstrated that the diagnostic applications of MPS are appropriate for patients who have an intermediate likelihood of disease. Although this information is useful, it is only partially utilized in clinical practice due to the difficulty to properly classify the patients. Since the seminal work of Lotfi Zadeh, fuzzy logic has been applied in numerous areas. In the present study, we proposed and tested a model to select patients for MPS based on fuzzy sets theory. A group of 1053 patients was used to develop the model and another group of 1045 patients was used to test it. Receiver operating characteristic curves were used to compare the performance of the fuzzy model against expert physician opinions, and showed that the performance of the fuzzy model was equal or superior to that of the physicians. Therefore, we conclude that the fuzzy model could be a useful tool to assist the general practitioner in the selection of patients for MPS.

Publication Statistics Sets of slides, transparents and microfiche 1991-

Vapaakappalekartuntaan perustuva tilasto Suomessa julkaistuista dia-, kalvo- ja filmikorttisarjoista vuodesta 1991 lähtien

Improving the Scalability of Reduct Determination in Rough Sets

Rough Set Data Analysis (RSDA) is a non-invasive data analysis approach that solely relies on the data to find patterns and decision rules. Despite its noninvasive approach and ability to generate human readable rules, classical RSDA has not been successfully used in commercial data mining and rule generating engines. The reason is its scalability. Classical RSDA slows down a great deal with the larger data sets and takes much longer times to generate the rules. This research is aimed to address the issue of scalability in rough sets by improving the performance of the attribute reduction step of the classical RSDA - which is the root cause of its slow performance. We propose to move the entire attribute reduction process into the database. We defined a new schema to store the initial data set. We then defined SOL queries on this new schema to find the attribute reducts correctly and faster than the traditional RSDA approach. We tested our technique on two typical data sets and compared our results with the traditional RSDA approach for attribute reduction. In the end we also highlighted some of the issues with our proposed approach which could lead to future research.

Ranking Sets of Objects

We provide a survey of the literature on ranking sets of objects. The interpretations of those set rankings include those employed in the theory of choice under complete uncertainty, rankings of opportunity sets, set rankings that appear in matching theory, and the structure of assembly preferences. The survey is prepared for the Handbook of Utility Theory, vol. 2, edited by Salvador Barberà, Peter Hammond, and Christian Seidl, to be published by Kluwer Academic Publishers. The chapter number is provisional.

Von Neumann-Morgenstern Stable Sets in Matching Problems

The following properties of the core of a one well-known: (i) the core is non-empty; (ii) the core is a lattice; and (iii) the set of unmatched agents is identical for any two matchings belonging to the core. The literature on two-sided matching focuses almost exclusively on the core and studies extensively its properties. Our main result is the following characterization of (von Neumann-Morgenstern) stable sets in one-to-one matching problem only if it is a maximal set satisfying the following properties : (a) the core is a subset of the set; (b) the set is a lattice; (c) the set of unmatched agents is identical for any two matchings belonging to the set. Furthermore, a set is a stable set if it is the unique maximal set satisfying properties (a), (b) and (c). We also show that our main result does not extend from one-to-one matching problems to many-to-one matching problems.

Anomaly Detection Using System Call Sequence Sets.

This paper discusses our research in developing a generalized and systematic method for anomaly detection. The key ideas are to represent normal program behaviour using system call frequencies and to incorporate probabilistic techniques for classification to detect anomalies and intrusions. Using experiments on the sendmail system call data, we demonstrate that concise and accurate classifiers can be constructed to detect anomalies. An overview of the approach that we have implemented is provided.

Computing median and antimedian sets in median graphs

The median (antimedian) set of a profile π = (u1, . . . , uk) of vertices of a graphG is the set of vertices x that minimize (maximize) the remoteness i d(x,ui ). Two algorithms for median graphs G of complexity O(nidim(G)) are designed, where n is the order and idim(G) the isometric dimension of G. The first algorithm computes median sets of profiles and will be in practice often faster than the other algorithm which in addition computes antimedian sets and remoteness functions and works in all partial cubes

Prediction of Key Symptoms of Learning Disabilities in School-Age Children Using Rough Sets

This paper highlights the prediction of learning disabilities (LD) in school-age children using rough set theory (RST) with an emphasis on application of data mining. In rough sets, data analysis start from a data table called an information system, which contains data about objects of interest, characterized in terms of attributes. These attributes consist of the properties of learning disabilities. By finding the relationship between these attributes, the redundant attributes can be eliminated and core attributes determined. Also, rule mining is performed in rough sets using the algorithm LEM1. The prediction of LD is accurately done by using Rosetta, the rough set tool kit for analysis of data. The result obtained from this study is compared with the output of a similar study conducted by us using Support Vector Machine (SVM) with Sequential Minimal Optimisation (SMO) algorithm. It is found that, using the concepts of reduct and global covering, we can easily predict the learning disabilities in children

Median Sets and Median Number of a Graph

A profile is a finite sequence of vertices of a graph. The set of all vertices of the graph which minimises the sum of the distances to the vertices of the profile is the median of the profile. Any subset of the vertex set such that it is the median of some profile is called a median set. The number of median sets of a graph is defined to be the median number of the graph. In this paper, we identify the median sets of various classes of graphs such as Kp − e, Kp,q forP > 2, and wheel graph and so forth. The median numbers of these graphs and hypercubes are found out, and an upper bound for the median number of even cycles is established.We also express the median number of a product graph in terms of the median number of their factors.

On The Center Sets and Center Numbers of Some Graph Classes

For a set S of vertices and the vertex v in a connected graph G, max x2S d(x, v) is called the S-eccentricity of v in G. The set of vertices with minimum S-eccentricity is called the S-center of G. Any set A of vertices of G such that A is an S-center for some set S of vertices of G is called a center set. We identify the center sets of certain classes of graphs namely, Block graphs, Km,n, Kn −e, wheel graphs, odd cycles and symmetric even graphs and enumerate them for many of these graph classes. We also introduce the concept of center number which is defined as the number of distinct center sets of a graph and determine the center number of some graph classes

Fair Sets of Some Classes of Graphs

Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S is the di erence between maximum and minimum of the distances of the vertex to the vertices of S. The vertices with minimum partiality constitute the fair center of the set. Any vertex set which is the fair center of some set of vertices is called a fair set. In this paper we prove that the induced subgraph of any fair set is connected in the case of trees and characterise block graphs as the class of chordal graphs for which the induced subgraph of all fair sets are connected. The fair sets of Kn, Km;n, Kn e, wheel graphs, odd cycles and symmetric even graphs are identi ed. The fair sets of the Cartesian product graphs are also discussed