Data analysis and data mining are concerned with unsupervised pattern finding and structure determination in data sets. "Structure" can be understood as symmetry and a range of symmetries are expressed by hierarchy. Such symmetries directly point to invariants, that pinpoint intrinsic properties of the data and of the background empirical domain of interest. We review many aspects of hierarchy here, including ultrametric topology, generalized ultrametric, linkages with lattices and other discrete algebraic structures and with p-adic number representations. By focusing on symmetries in data we have a powerful means of structuring and analyzing massive, high dimensional data stores. We illustrate the powerfulness of hierarchical clustering in case studies in chemistry and finance, and we provide pointers to other published case studies.

The plasmodium feeds on microscopic food particles, including microbial life forms. The plasmodium placed in an environment with distributed nutrients develops a network of protoplasmic tubes spanning the nutrients' sources. Te topology of the plasmodium's protoplasmic network optimizes the plasmodium's harvesting on the scattered sources of nutrients and makes more efficient flow and transport of intracellular components [8,9,10,11]. The plasmodium is capable for approximation of shortest path [10], computation of planar proximity graphs [2] and plane tessellations [13], primitive memory [12], basic logical computing [15], and control of robot navigation[16]. The plasmodium can be considered as a general-purpose computer because the plasmodium simulates Kolmogorov-Uspenskii machine -- the storage modification machine operating on a colored set of graph nodes [1]. Preprint submitted to Elsevier Science 17 May 2014 The paper is structured as follows. In Sect. 2 we introduce the experimental gates invented in [15] and reinterpret the gates as multi-output logical gates.

We develop a novel advanced Particle Markov chain Monte Carlo algorithm that is capable of sampling from the posterior distribution of non-linear state space models for both the unobserved latent states and the unknown model parameters. We apply this novel methodology to five population growth models, including models with strong and weak Allee effects, and test if it can efficiently sample from the complex likelihood surface that is often associated with these models. Utilising real and also synthetically generated data sets we examine the extent to which observation noise and process error may frustrate efforts to choose between these models. Our novel algorithm involves an Adaptive Metropolis proposal combined with an SIR Particle MCMC algorithm (AdPMCMC). We show that the AdPMCMC algorithm samples complex, high-dimensional spaces efficiently, and is therefore superior to standard Gibbs or Metropolis Hastings algorithms that are known to converge very slowly when applied to the non-linear state space ecological models considered in this paper. Additionally, we show how the AdPMCMC algorithm can be used to recursively estimate the Bayesian Cram\'er-Rao Lower Bound of Tichavsk\'y (1998). We derive expressions for these Cram\'er-Rao Bounds and estimate them for the models considered. Our results demonstrate a number of important features of common population growth models, most notably their multi-modal posterior surfaces and dependence between the static and dynamic parameters. We conclude by sampling from the posterior distribution of each of the models, and use Bayes factors to highlight how observation noise significantly diminishes our ability to select among some of the models, particularly those that are designed to reproduce an Allee effect.

Probabilistic databases play a crucial role in the management and understanding of uncertain data. However, incorporating probabilities into the semantics of incomplete databases has posed many challenges, forcing systems to sacrifice modeling power, scalability, or restrict the class of relational algebra formula under which they are closed. We propose an alternative approach where the underlying relational database always represents a single world, and an external factor graph encodes a distribution over possible worlds; Markov chain Monte Carlo (MCMC) inference is then used to recover this uncertainty to a desired level of fidelity. Our approach allows the efficient evaluation of arbitrary queries over probabilistic databases with arbitrary dependencies expressed by graphical models with structure that changes during inference. MCMC sampling provides efficiency by hypothesizing {\em modifications} to possible worlds rather than generating entire worlds from scratch. Queries are then run over the portions of the world that change, avoiding the onerous cost of running full queries over each sampled world. A significant innovation of this work is the connection between MCMC sampling and materialized view maintenance techniques: we find empirically that using view maintenance techniques is several orders of magnitude faster than naively querying each sampled world. We also demonstrate our system's ability to answer relational queries with aggregation, and demonstrate additional scalability through the use of parallelization.

Modern solvers for Boolean Satisfiability (SA T) and Answer Set Programming (ASP) are based on sophisticated Boolean constraint solving techniques. In both areas, conflict-driven learning and related techniques constitute key features whose application is enabled by conflict analysis. Although various conflict analysis schemes have been proposed, implemented, and studied both theoretically and practically in the SA T area, the heuristic aspects involved in conflict analysis have not yet received much attention. Assuming a fixed conflict analysis scheme, we address the open question of how to identify "good" reasons for conflicts, and we investigate several heuristics for conflict analysis in ASP solving. To our knowledge, a systematic study like ours has not yet been performed in the SA T area, thus, it might be beneficial for both the field of ASP as well as the one of SA T solving.

We present tropical games, a generalization of combinatorial min-max games based on tropical algebras. Our model breaks the traditional symmetry of rational zero-sum games where players have exactly opposed goals (min vs. max), is more widely applicable than min-max and also supports a form of pruning, despite it being less effective than alpha-beta. Actually, min-max games may be seen as particular cases where both the game and its dual are tropical: when the dual of a tropical game is also tropical, the power of alpha-beta is completely recovered. We formally develop the model and prove that the tropical pruning strategy is correct, then conclude by showing how the problem of approximated parsing can be modeled as a tropical game, profiting from pruning.

It is hypothesized that creativity arises from the self-mending capacity of an internal model of the world, or worldview. The uniquely honed worldview of a creative individual results in a distinctive style that is recognizable within and across domains. It is further hypothesized that creativity is domaingeneral in the sense that there exist multiple avenues by which the distinctiveness of one's worldview can be expressed. These hypotheses were tested using art students and creative writing students. Art students guessed significantly above chance both which painting was done by which of five famous artists, and which artwork was done by which of their peers. Similarly, creative writing students guessed significantly above chance both which passage was written by which of five famous writers, and which passage was written by which of their peers. These findings support the hypothesis that creative style is recognizable. Moreover, creative writing students guessed significantly above chance which of their peers produced particular works of art, supporting the hypothesis that creative style is recognizable not just within but across domains.

Existing action calculi provide rich, declarative formalisms for reasoning about actions. BDI-based programming languages like AgentSpeak, on the other hand, are procedural and geared towards practical applications of cognitive agents. In this paper, we close the gap between these two lines of research by integrating action calculi and AgentSpeak programs. Specifically, we develop a new and purely declarative semantics for AgentSpeak, which paves the way for combining this language with any suitable action calculus in a strictly modular fashion. As the main technical result, we prove that the new declarative semantics is correct wrt. the standard operational semantics for AgentSpeak. This provides the basis for a modular integration of a BDI-based agent programming language with sophisticated methods for reasoning about actions.

Levesque introduced the notion of only-knowing to precisely capture the beliefs of a knowledge base. He also showed how only-knowing can be used to formalize non-monotonic behavior within a monotonic logic. Despite its appeal, all attempts to extend only-knowing to the many agent case have undesirable properties. A belief model by Halpern and Lakemeyer, for instance, appeals to proof-theoretic constructs in the semantics and needs to axiomatize validity as part of the logic. It is also not clear how to generalize their ideas to a first-order case. In this paper, we propose a new account of multi-agent only-knowing which, for the first time, has a natural possible-world semantics for a quantified language with equality. We then provide, for the propositional fragment, a sound and complete axiomatization that faithfully lifts Levesque's proof theory to the many agent case. We also discuss comparisons to the earlier approach by Halpern and Lakemeyer. 

In this paper, I defend a multiplicative approach that distinguishes statues from amounts of matter, political entities from physical ones, qua entities (e.g. John qua Alitalia passenger) from players (e.g. John), etc. I develop a theory of levels which is based on the primitive notions of level, parthood, and grounding (a kind of existential dependence) and that is used to characterize more specific relations like constitution, inherence, and abstraction. I neither aim to propose a `definitive' theory of levels nor to commit to their ontological or conceptual nature. Hence, the adjective `ontological' used in the title does not qualify the nature of the entities that belong to levels but the way the notion of level is characterized, i.e. in terms of general and philosophically well-founded notions. By keeping away from a purely realist attitude, I can then discuss the adequacy of some alternative first-order theories to account for three puzzling scenarios.