Slow feature analysis (SFA) is an information processing method proposed by Wiskott and Sejnowski (WS02) which allows to extract slowly varying signals from complex multidimensional time series. Wiskott (Wis98) formulated a similar idea already before as a model of unsupervised learning of invariances in the visual system of vertebrates. SFA has been applied successfully to numerous different tasks: to reproduce a wide range of properties of complex cells in primary visual cortex (BW05), to model the self-organized formation of place cells in the hippocampus (FSW07), to classify handwritten digits (Ber05) and to extract driving forces from nonstationary time series (Wis03). The analysis of nonstationary time series plays an important role in the data understanding of various phenomena such as temperature drift in experimental setup, global warming in climate data or varying heart rate in cardiology. Such nonstationarities can be modeled by underlying parameters, referred to as driving forces, that change the dynamics of the system smoothly on a slow time scale or abruptly but rarely, e.g. if the dynamics switches between different discrete states.

Logics of knowledge based on possible-world semantics are u seful in many areas of knowledge representation and reasoning, ranging from security t o distributed computing to game theory. In these models, an agent is said to know a fact ϕ if ϕ is true in all the worlds she considers possible. While reasoning about knowledge with t his semantics has proved useful, as is well known, it suffers from what is known in the literature as the logical omniscience problem: under possible-world semantics, agents know all t autologies and know the logical consequences of their knowledge. While logical omniscience is certainly not always an issue, in many applications it is. For example, in the context of distributed computing, we are interested in polynomial-time algorithms, although in some cases the knowledge needed to p erform optimally may require calculations that cannot be performed in polynomial time (u nless P=NP) [Moses and Tuttle 1988]; in the context of security, we may want to reason about computationally bounded adversaries who cannot factor a large composite number, and thus cannot be logically omniscient; in game theory, we may be interested in the impac t of computational resources on solution concepts (for example, what will agents do if com puting a Nash equilibrium is difficult). Not surprisingly, many approaches for dealing with the logi cal omniscience problem have been suggested (see [Fagin, Halpern, Moses, and Vardi 1 995, Chapter 9] and [Moreno 1998]).

Probabilistic sampling methods have become very popular to solve single-shot path planning problems. Rapidly-exploring Random Trees (RRTs) in particular have been shown to be very efficient in solving high dimensional problems. Even though several RRT variants have been proposed to tackle the dynamic replanning problem, these methods only perform well in environments with infrequent changes. This paper addresses the dynamic path planning problem by combining simple techniques in a multi-stage probabilistic algorithm. This algorithm uses RRTs as an initial solution, informed local search to fix unfeasible paths and a simple greedy optimizer. The algorithm is capable of recognizing when the local search is stuck, and subsequently restart the RRT. We show that this combination of simple techniques provides better responses to a highly dynamic environment than the dynamic RRT variants.

The present paper investigates consequence relations that are both non-monotonic and paraconsistent. More precisely, we put the focus on preferential consequence relations, i.e. those relations that can be defined by a binary preference relation on states labelled by valuations. We worked with a general notion of valuation that covers e.g. the classical valuations as well as certain kinds of many-valued valuations. In the many-valued cases, preferential consequence relations are paraconsistant (in addition to be non-monotonic), i.e. they are capable of drawing reasonable conclusions which contain contradictions. The first purpose of this paper is to provide in our general framework syntactic characterizations of several families of preferential relations. The second and main purpose is to provide, again in our general framework, characterizations of several families of preferential discriminative consequence relations. They are defined exactly as the plain version, but any conclusion such that its negation is also a conclusion is rejected (these relations bring something new essentially in the many-valued cases).

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.