The on-line shortest path problem is considered under various mode ls of partial monitoring. Given a weighted directed acyclic graph whose edge weights can c hange in an arbitrary (adversarial) way, a decision maker has to choose in each round of a game a path between two distinguished vertices such that the loss of the chosen path (defin ed as the sum of the weights of its composing edges) be as small as possible. In a setting generalizing the multi-armed bandit problem, after choosing a path, the decision maker learns only the w eights of those edges that belong to the chosen path. For this problem, an algorithm is given who se average cumulative loss in n rounds exceeds that of the best path, matched off-line to the ent ire sequence of the edge weights, by a quantity that is proportional to 1 / n and depends only polynomially on the number of edges of the graph. The algorithm can be implemented with linear complexity in the number of rounds n and in the number of edges. An extension to the so-called label efficie nt setting is also given, in which the decision maker is informed about the w eights of the edges corresponding to the chosen path at a total of m n time instances. Another extension is shown where the decision maker competes against a time-varying pa th, a generalization of the problem of tracking the best expert. A version of the multi-armed b andit setting for shortest path is also discussed where the decision maker learns only the total weight of the chosen path but not the weights of the individual edges on the path. Applications to routing in packet switched networks along with simulation results are also presented.

The models of statistical physics used to study collective phenomena in some interdisciplinary contexts, such as social dynamics and opinion spreading, do not consider the effects of the memory on individual decision processes. On the contrary, in the Naming Game, a recently proposed model of Language formation, each agent chooses a particular state, or opinion, by means of a memory-based negotiation process, during which a variable number of states is collected and kept in memory. In this perspective, the statistical features of the number of states collected by the agents becomes a relevant quantity to understand the dynamics of the model, and the influence of topological properties on memory-based models. By means of a master equation approach, we analyze the internal agent dynamics of Naming Game in populations embedded on networks, finding that it strongly depends on very general topological properties of the system (e.g. average and fluctuations of the degree). However, the influence of topological properties on the microscopic individual dynamics is a general phenomenon that should characterize all those social interactions that can be modeled by memory-based negotiation processes.

Some alternatives to probability in the literature include sets of probability measure [Huber 1981; Walley 1991], Dempster-Shafer belief functions [Shafer 1976] and the closely related nonadditive measures [Schmeidler 1989], and possibility measures [Dubois and Prade 1990]. In this paper, we consider the notion of expectation for all these representations of uncertainty. We do not take a stand here on what the "right" way is to represent uncertainty; we simply investigate characterizations of expectation and reasoning about expectation, both for probability and for other representations of uncertainty. It is well known that a probability measure determines a unique expectation function that is linear (i.e., E (aX + bY) = aE (X) + bE (Y)), monotone (i.e., X Y implies E ( X) E (Y)), and maps constant functions to their value. Conversely, given an expectation function E (that is, a function from random variables to the reals) that is linear, monotone, and maps constant functions to their value, there is a unique probability measure µ such that E = E µ. That is, there is a 1-1 mapping from probability measures to (probabilistic) expectation functions. One of the goals of this paper is to provide similar characterizations of expectation for other representations of uncertainty. Some work along these lines has already been done, particulary with regard to sets of probability measures [Huber 1981; Walley 1991; 1981]. 1 However, there seems to be surprisingly little work on characterizing expectation in the context of other measures of uncertainty, such as belief functions [Shafer 1976] and possibility measures [Dubois and Prade 1990].

This paper includes a reflection on the role of networks in the study of English language acquisition, as well as a collection of practical criteria to annotate free-speech corpora from children utterances. At the theoretical level, the main claim of this paper is that syntactic networks should be interpreted as the outcome of the use of the syntactic machinery. Thus, the intrinsic features of such machinery are not accessible directly from (known) network properties. Rather, what one can see are the global patterns of its use and, thus, a global view of the power and organization of the underlying grammar. Taking a look into more practical issues, the paper examines how to build a net from the projection of syntactic relations. Recall that, as opposed to adult grammars, early-child language has not a well-defined concept of structure. To overcome such difficulty, we develop a set of systematic criteria assuming constituency hierarchy and a grammar based on lexico-thematic relations. At the end, what we obtain is a well defined corpora annotation that enables us i) to perform statistics on the size of structures and ii) to build a network from syntactic relations over which we can perform the standard measures of complexity. We also provide a detailed example.

Probability-like parameters appearing in some statistical models, and their prior distributions, are reinterpreted through the notion of `circumstance', a term which stands for any piece of knowledge that is useful in assigning a probability and that satisfies some additional logical properties. The idea, which can be traced to Laplace and Jaynes, is that the usual inferential reasonings about the probability-like parameters of a statistical model can be conceived as reasonings about equivalence classes of `circumstances' - viz., real or hypothetical pieces of knowledge, like e.g. physical hypotheses, that are useful in assigning a probability and satisfy some additional logical properties - that are uniquely indexed by the probability distributions they lead to.

An approach to induction is presented, based on the idea of analysing the context of a given problem into `circumstances'. This approach, fully Bayesian in form and meaning, provides a complement or in some cases an alternative to that based on de Finetti's representation theorem and on the notion of infinite exchangeability. In particular, it gives an alternative interpretation of those formulae that apparently involve `unknown probabilities' or `propensities'. Various advantages and applications of the presented approach are discussed, especially in comparison to that based on exchangeability. Generalisations are also discussed.

This text provides with an introduction to the modern approach of artificiality and simulation in social sciences. It presents the relationship between complexity and artificiality, before introducing the field of artificial societies which greatly benefited from the computer power fast increase, gifting social sciences with formalization and experimentation tools previously owned by "hard" sciences alone. It shows that as "a new way of doing social sciences", artificial societies should undoubtedly contribute to a renewed approach in the study of sociality and should play a significant part in the elaboration of original theories of social phenomena.

For graphs $G$ and $H$, a mapping $f: V(G)\dom V(H)$ is a homomorphism of $G$ to $H$ if $uv\in E(G)$ implies $f(u)f(v)\in E(H).$ If, moreover, each vertex $u \in V(G)$ is associated with costs $c_i(u), i \in V(H)$, then the cost of the homomorphism $f$ is $\sum_{u\in V(G)}c_{f(u)}(u)$. For each fixed graph $H$, we have the {\em minimum cost homomorphism problem}, written as MinHOM($H)$. The problem is to decide, for an input graph $G$ with costs $c_i(u),$ $u \in V(G), i\in V(H)$, whether there exists a homomorphism of $G$ to $H$ and, if one exists, to find one of minimum cost. Minimum cost homomorphism problems encompass (or are related to) many well studied optimization problems. We describe a dichotomy of the minimum cost homomorphism problems for graphs $H$, with loops allowed. When each connected component of $H$ is either a reflexive proper interval graph or an irreflexive proper interval bigraph, the problem MinHOM($H)$ is polynomial time solvable. In all other cases the problem MinHOM($H)$ is NP-hard. This solves an open problem from an earlier paper. Along the way, we prove a new characterization of the class of proper interval bigraphs.

Introduction In the last years, many useful NLP tools have been developed and many of them are now even available commercially. Most of these tools are monolingual or multi-monolingual, meaning that the software can deal with more than one language, but that the re sults will al ways be displayed in the same language as the text. We therefore distinguish these applications from cross-lingual software, which is software that helps to transgress the language bound ary. Examples for such applications are machine translation and cross-lingual document retrieval, i.e. retrieval using search engines which allow to en ter a search term in one language and which also yield results in other languages, usually because the query is translated in one way or another. In our eyes, cross-lingual applications are currently the bottleneck of available NLP tools. To our knowledge, there are no applications that allow comparing documents written in dif ferent languages with each other and there are very few which give users a quick overview of the ap proximate contents of documents written in different languages.

Automatic annotation of documents with controlled vocabulary terms (descriptors) from a conceptual thesaurus is not only useful for document indexing and retrieval. The mapping of texts onto the same thesaurus furthermore allows to establish links between similar documents. This is also a substantial requirement of the Semantic Web. This paper presents an almost language-independent system that maps documents written in different languages onto the same multilingual conceptual thesaurus, EUROVOC. Conceptual thesauri differ from Natural Language Thesauri in that they consist of relatively small controlled lists of words or phrases with a rather abstract meaning. To automatically identify which thesaurus descriptors describe the contents of a document best, we developed a statistical, associative system that is trained on texts that have previously been indexed manually. In addition to describing the large number of empirically optimised parameters of the fully functional application, we present the performance of the software according to a human evaluation by professional indexers.