Stream computing is often seen to be embodied in compute-intensive kernel functions that are applied to each element in the data stream one at a time. These kernel functions operate in sequence in a pipelined fashion in what is essentially SIMD (single instruction multiple data) architecture. The advantage of doing this is the simplification of interconnects to get large increase in performance and in simplified programming. This processing is a take off on the style of computing that is found in DSP applications such as in voice, images, and video applied to a much larger range of applications. Here we speak of stream computing in a much larger philosophical setting that is sometimes expressed in the idea of stream of consciousness. In literature, this idea is meant to imply the internal monologue that goes on in the mind.

We give an overview of two approaches to probability theory where lower and upper probabilities, rather than probabilities, are used: Walley's behavioural theory of imprecise probabilities, and Shafer and Vovk's game-theoretic account of probability. We show that the two theories are more closely related than would be suspected at first sight, and we establish a correspondence between them that (i) has an interesting interpretation, and (ii) allows us to freely import results from one theory into the other. Our approach leads to an account of probability trees and random processes in the framework of Walley's theory. We indicate how our results can be used to reduce the computational complexity of dealing with imprecision in probability trees, and we prove an interesting and quite general version of the weak law of large numbers.

Most definitions of ontology, viewed as a "specification of a conceptualization", agree on the fact that if an ontology can take different forms, it necessarily includes a vocabulary of terms and some specification of their meaning in relation to the domain's conceptualization. And as domain knowledge is mainly conveyed through scientific and technical texts, we can hope to extract some useful information from them for building ontology. But is it as simple as this? In this article we shall see that the lexical structure, i.e. the network of words linked by linguistic relationships, does not necessarily match the domain conceptualization. We have to bear in mind that writing documents is the concern of textual linguistics, of which one of the principles is the incompleteness of text, whereas building ontology - viewed as task-independent knowledge - is concerned with conceptualization based on formal and not natural languages. Nevertheless, the famous Sapir and Whorf hypothesis, concerning the interdependence of thought and language, is also applicable to formal languages. This means that the way an ontology is built and a concept is defined depends directly on the formal language which is used; and the results will not be the same. The introduction of the notion of ontoterminology allows to take into account epistemological principles for formal ontology building.

Institut de Mathématiques, Université de Toulouse et CNRS (UMR 5219), 118 route de Narbonne, 31062 Toulouse cedex 9, France Abstract Large graphs are natural mathematical models for describing the structure of the data in a wide variety of fields, such as web mining, social networks, information retrieval, biological networks, etc. For all these applications, automatic tools are required to get a synthetic view of the graph and to reach a good understanding of the underlying problem. In particular, discovering groups of tightly connected vertices and understanding the relations between those groups is very important in practice. This paper shows how a kernel version of the batch Self Organizing Map can be used to achieve these goals via kernels derived from the Laplacian matrix of the graph, especially when it is used in conjunction with more classical methods based on the spectral analysis of the graph. The proposed method is used to explore the structure of a medieval social network modeled through a weighted graph that has been directly built from a large corpus of agrarian contracts. This work was partially supported by ANR Project "Graph-Comp". Preprint submitted to Neurocomputing 19 March 2018 1 Introduction Complex networks are large graphs with a non trivial organization. They arise naturally in numerous context [7], such as, to name a few, the World Wide Web (which gives a perfect example of how large and complex such a network may grow), metabolic pathways, citation networks between scientific articles or more general social networks that model interaction between individuals and/or organizations, etc. Complex networks share common properties that have allowed the emergence of mathematical descriptions such as small world graphs or power law graphs. The structure of these graphs often gives some keys to understand the complex network underlined. To study such a structure, one often begins with a metrology process applied to the graph that describes the degree distribution, the number of components, the density, etc. However, it should be noted that dealing with very large graphs (millions of vertices) is still an open question (see [9] for an example of an efficient algorithm to explore that kind of data sets). Several ways have been explored to cluster the vertices of the graph into communities [43] and some of them have in common the use of the Laplacian matrix. Indeed, there are important relationships between the spectrum of the Laplacian and the graph invariants that characterize its structure (see, e.g. These properties can be used for building, from the eigen-decomposition of the Laplacian, a similarity measure or a metric space such that the induced dissimilarities between vertices of the graph are related to its community structure (see [13], among others).

We consider how a search engine should select advertisements to display with search results, in order to maximize its revenue. Under the standard "pay-per-click" arrangement, revenue depends on how well the displayed advertisements appeal to users. The main difficulty stems from new advertisements whosedegree of appeal has yet to be determined. Often the only reliable way of determining appeal is exploration via display to users, which detracts from exploitation of other advertisements known to have high appeal. Budget constraints and finite advertisement lifetimes make it necessary to explore as well as exploit. In this paper we study the tradeoff between exploration and exploitation, modeling advertisement placement as a multi-armed bandit problem. We extend traditional bandit formulations to account for budget constraints that occur in search engine advertising markets, and derive theoretical bounds on the performance of a family of algorithms.

We consider how a search engine should select advertisements to display with search results, in order to maximize its revenue. Under the standard "pay-per-click" arrangement, revenue depends on how well the displayed advertisements appeal to users. The main difficulty stems from new advertisements whose degree of appeal has yet to be determined. Often the only reliable way of determining appeal is exploration via display to users, which detracts from exploitation of other advertisements known to have high appeal. Budget constraints and finite advertisement lifetimes make it necessary to explore as well as exploit. In this paper we study the tradeoff between exploration and exploitation, modeling advertisement placement as a multi-armed bandit problem. We extend traditional bandit formulations to account for budget constraints that occur in search engine advertising markets, and derive theoretical bounds on the performance of a family of algorithms.

We consider how a search engine should select advertisements to display with search results, in order to maximize its revenue. Under the standard "pay-per-click" arrangement, revenue depends on how well the displayed advertisements appeal to users. The main difficulty stems from new advertisements whose degree of appeal has yet to be determined. Often the only reliable way of determining appeal is exploration via display to users, which detracts from exploitation of other advertisements known to have high appeal. Budget constraints and finite advertisement lifetimes make it necessary to explore as well as exploit. In this paper we study the tradeoff between exploration and exploitation, modeling advertisement placement as a multi-armed bandit problem. We extend traditional bandit formulations to account for budget constraints that occur in search engine advertising markets, and derive theoretical bounds on the performance of a family of algorithms.

We propose a generic algorithm for computation of similarity measures for sequential data. The algorithm uses generalized suffix trees for efficient calculation of various kernel, distance and non-metric similarity functions. Its worst-case run-time is linear in the length of sequences and independent of the underlying embedding language, which can cover words, k-grams or all contained subsequences. Experiments with network intrusion detection, DNA analysis and text processing applications demonstrate the utility of distances and similarity coefficients for sequences as alternatives to classical kernel functions.

The locally linear embedding (LLE) is improved by introducing multiple linearly independent local weight vectors for each neighborhood. We characterize the reconstruction weights and show the existence of the linearly independent weight vectors at each neighborhood. The modified locally linear embedding (MLLE) proposed in this paper is much stable. It can retrieve the ideal embedding if MLLE is applied on data points sampled from an isometric manifold. MLLE is also compared with the local tangent space alignment (LTSA). Numerical examples are given that show the improvement and efficiency of MLLE.

Princeton Center for Theoretical Physics, Princeton University, Princeton, New Jersey 08544 USA (Dated: December 13, 2021) We consider words as a network of interacting letters, and approximate the probability distribution of states taken on by this network. Despite the intuition that the rules of English spelling are highly combinatorial (and arbitrary), we find that maximum entropy models consistent with pairwise correlations among letters provide a surprisingly good approximation to the full statistics of four letter words, capturing 92% of the multi-information among letters and even'discovering' real words that were not represented in the data from which the pairwise correlations were estimated. The maximum entropy model defines an energy landscape on the space of possible words, and local minima in this landscape account for nearly two-thirds of words used in written English. Many complex systems convey an impression of order into these controversies about language in the broad that is not so easily captured by the traditional tools of sense, but rather to test the power of pairwise interactions theoretical physics. Thus, it is not clear what sort of to capture seemingly complex structure.