Some two-process models for memory

Two-process models for memory and learnin

Some speculations on storage and retrieval processes in long term memory

Speculations on storage and retrieval processes in long term memor

The dynamics of decision making when probabilities are vaguely specified

Consider a multi-trial game with the goal of maximizing a quantity Q(N). At each trial N, the player doubles the accumulated quantity, unless the trial number is Y, in which case all is lost and the game ends. The expected quantity for the next trial will favor continuing play, as long as the probability that the next trial is Y is less than one half. Y is vaguely specified (e.g., someone is asked to fill a sheet of paper with digits, which are then permuted to produce Y). Conditional on reaching trial N, we argue that the probability that the next trial is Y is extremely small (much less than one half), and that this holds for any N. Thus, single trial reasoning recommends one should always play, but this guarantees eventual ruin in the game. It is necessary to stop, but how can a decision to stop on N be justified, and how can N be chosen? The paradox and the conflict between what seem to be two equally plausible lines of reasoning are caused by the vagueness in the specification of the critical trial Y. Many everyday reasoning situations involve analogous situations of vagueness, in specifying probabilities, values, and/or alternatives, whether in the context of sequential decisions or single decisions. We present a computational scheme for addressing the problem of vagueness in the above game, based on quantum probability theory. The key aspect of our proposal is the idea that the range of stopping rules can be represented as a superposition state, in which the player cannot be assumed to believe in any specific stopping rule. This scheme reveals certain interesting properties, regarding the dynamics of when to stop to play

The rational status of quantum cognition

Classic probability theory (CPT) is generally considered the rational way to make inferences, but there have been some empirical findings showing a divergence between reasoning and the principles of classical probability theory (CPT), inviting the conclusion that humans are irrational. Perhaps the most famous of these findings is the conjunction fallacy (CF). Recently, the CF has been shown consistent with the principles of an alternative probabilistic framework, quantum probability theory (QPT). Does this imply that QPT is irrational or does QPT provide an alternative interpretation of rationality? Our presentation consists of three parts. First, we examine the putative rational status of QPT using the same argument as used to establish the rationality of CPT, the Dutch Book (DB) argument, according to which reasoners should not commit to bets guaranteeing a loss. We prove the rational status of QPT by formulating it as a particular case of an extended form of CPT, with separate probability spaces produced by changing context. Second, we empirically examine the key requirement for whether a CF can be rational or not; the results show that participants indeed behave rationally, at least relative to the representations they employ. Finally, we consider whether the conditions for the CF to be rational are applicable in the outside (non-mental) world. Our discussion provides a general and alternative perspective for rational probabilistic inference, based on the idea that contextuality requires either reasoning in separate CPT probability spaces or reasoning with QPT principles

Quantum Aspects of Semantic Analysis and Symbolic Artificial Intelligence

Modern approaches to semanic analysis if reformulated as Hilbert-space problems reveal formal structures known from quantum mechanics. Similar situation is found in distributed representations of cognitive structures developed for the purposes of neural networks. We take a closer look at similarites and differences between the above two fields and quantum information theory.Comment: version accepted in J. Phys. A (Letter to the Editor

Uncovering the overlapping community structure of complex networks in nature and society

Many complex systems in nature and society can be described in terms of networks capturing the intricate web of connections among the units they are made of. A key question is how to interpret the global organization of such networks as the coexistence of their structural subunits (communities) associated with more highly interconnected parts. Identifying these a priori unknown building blocks (such as functionally related proteins, industrial sectors and groups of people) is crucial to the understanding of the structural and functional properties of networks. The existing deterministic methods used for large networks find separated communities, whereas most of the actual networks are made of highly overlapping cohesive groups of nodes. Here we introduce an approach to analysing the main statistical features of the interwoven sets of overlapping communities that makes a step towards uncovering the modular structure of complex systems. After defining a set of new characteristic quantities for the statistics of communities, we apply an efficient technique for exploring overlapping communities on a large scale. We find that overlaps are significant, and the distributions we introduce reveal universal features of networks. Our studies of collaboration, word-association and protein interaction graphs show that the web of communities has non-trivial correlations and specific scaling properties.Comment: The free academic research software, CFinder, used for the publication is available at the website of the publication: http://angel.elte.hu/clusterin