Amalgamation and interpolation in ordered algebras

The first part of this paper provides a comprehensive and self-contained account of the interrelationships between algebraic properties of varieties and properties of their free algebras and equational consequence relations. In particular, proofs are given of known equivalences between the amalgamation property and the Robinson property, the congruence extension property and the extension property, and the flat amalgamation property and the deductive interpolation property, as well as various dependencies between these properties. These relationships are then exploited in the second part of the paper in order to provide new proofs of amalgamation and deductive interpolation for the varieties of lattice-ordered abelian groups and MV-algebras, and to determine important subvarieties of residuated lattices where these properties hold or fail. In particular, a full description is given of all subvarieties of commutative GMV-algebras possessing the amalgamation property.

Neural analogs of associative learning in {\it Aplysia\/}: Experimental and theoretical approaches

A change in synaptic strength arising from the activation of two neuronal pathways at approximately the same time is a form of associative plasticity and may underlie classical conditioning. Previously, a cellular analog of a classical conditioning protocol has been demonstrated to produce short-term associative plasticity at the connections between sensory and motor neurons in Aplysia. A similar training protocol produced long-term (24 hour) enhancement of excitatory postsynaptic potentials (EPSPs). EPSPs produced by sensory neurons in which activity was paired with a reinforcing stimulus were significantly larger than unpaired controls 24 hours after training. To examined whether the associative plasticity observed at these synapses may be involved in higher-order forms of classical conditioning, a neural analog of contingency was developed. In addition, computer simulations were used to analyze whether the associative plasticity observed in Aplysia could, in theory, account for second-order conditioning and blocking. ^

Associative processing and paranormal belief

In the present study we introduce a novel task for the quantitative assessment of both originality and speed of individual associations. This 'BAG' (Bridge-the-Associative-Gap) task was used to investigate the relationships between creativity and paranormal belief. Twelve strong 'believers' and 12 strong 'skeptics' in paranormal phenomena were selected from a large student population (n > 350). Subjects were asked to produce single-word associations to word pairs. In 40 trials the two stimulus words were semantically indirectly related and in 40 other trials the words were semantically unrelated. Separately for these two stimulus types, response commonalities and association latencies were calculated. The main finding was that for unrelated stimuli, believers produced associations that were more original (had a lower frequency of occurrence in the group as a whole) than those of the skeptics. For the interpretation of the result we propose a model of association behavior that captures both 'positive' psychological aspects (i.e., verbal creativity) and 'negative' aspects (susceptibility to unfounded inferences), and outline its relevance for psychiatry. This model suggests that believers adopt a looser response criterion than skeptics when confronted with 'semantic noise'. Such a signal detection view of the presence/absence of judgments for loose semantic relations may help to elucidate the commonalities between creative thinking, paranormal belief and delusional ideation.

Sheaf representations of MV-algebras and lattice-ordered abelian groups via duality

We study representations of MV-algebras -- equivalently, unital lattice-ordered abelian groups -- through the lens of Stone-Priestley duality, using canonical extensions as an essential tool. Specifically, the theory of canonical extensions implies that the (Stone-Priestley) dual spaces of MV-algebras carry the structure of topological partial commutative ordered semigroups. We use this structure to obtain two different decompositions of such spaces, one indexed over the prime MV-spectrum, the other over the maximal MV-spectrum. These decompositions yield sheaf representations of MV-algebras, using a new and purely duality-theoretic result that relates certain sheaf representations of distributive lattices to decompositions of their dual spaces. Importantly, the proofs of the MV-algebraic representation theorems that we obtain in this way are distinguished from the existing work on this topic by the following features: (1) we use only basic algebraic facts about MV-algebras; (2) we show that the two aforementioned sheaf representations are special cases of a common result, with potential for generalizations; and (3) we show that these results are strongly related to the structure of the Stone-Priestley duals of MV-algebras. In addition, using our analysis of these decompositions, we prove that MV-algebras with isomorphic underlying lattices have homeomorphic maximal MV-spectra. This result is an MV-algebraic generalization of a classical theorem by Kaplansky stating that two compact Hausdorff spaces are homeomorphic if, and only if, the lattices of continuous [0, 1]-valued functions on the spaces are isomorphic.

Enhanced associative memory for colour (but not shape or location) in synaesthesia

People with grapheme-colour synaesthesia have been shown to have enhanced memory on a range of tasks using both stimuli that induce synaesthesia (e.g. words) and, more surprisingly, stimuli that do not (e.g. certain abstract visual stimuli). This study examines the latter by using multi-featured stimuli consisting of shape, colour and location conjunctions (e.g. shape A + colour A + location A; shape B + colour B + location B) presented in a recognition memory paradigm. This enables distractor items to be created in which one of these features is ‘unbound’ with respect to the others (e.g. shape A + colour B + location A; shape A + colour A + location C). Synaesthetes had higher recognition rates suggesting an enhanced ability to bind certain visual features together into memory. Importantly, synaesthetes’ false alarm rates were lower only when colour was the unbound feature, not shape or location. We suggest that synaesthetes are “colour experts” and that enhanced perception can lead to enhanced memory in very specific ways; but, not for instance, an enhanced ability to form associations per se. The results support contemporary models that propose a continuum between perception and memory.

Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Rational invariants on the space of all structures of algebras on a two-dimensional vector space

Reducing Cache Hierarchy Energy Consumption by Predicting Forwarding and Disabling Associative Sets

The first level data cache un modern processors has become a major consumer of energy due to its increasing size and high frequency access rate. In order to reduce this high energy con sumption, we propose in this paper a straightforward filtering technique based on a highly accurate forwarding predictor. Specifically, a simple structure predicts whether a load instruction will obtain its corresponding data via forwarding from the load-store structure -thus avoiding the data cache access - or if it will be provided by the data cache. This mechanism manages to reduce the data cache energy consumption by an average of 21.5% with a negligible performance penalty of less than 0.1%. Furthermore, in this paper we focus on the cache static energy consumption too by disabling a portin of sets of the L2 associative cache. Overall, when merging both proposals, the combined L1 and L2 total energy consumption is reduced by an average of 29.2% with a performance penalty of just 0.25%. Keywords: Energy consumption; filtering; forwarding predictor; cache hierarchy

Weighted composition operators on the predual and dual Banach spaces of Beurling algebras on Z

Let vv be a weight sequence on ZZ and let ψ,φψ,φ be complex-valued functions on ZZ such that φ(Z)⊂Zφ(Z)⊂Z. In this paper we study the boundedness, compactness and weak compactness of weighted composition operators Cψ,φCψ,φ on predual Banach spaces c0(Z,1/v)c0(Z,1/v) and dual Banach spaces ℓ∞(Z,1/v)ℓ∞(Z,1/v) of Beurling algebras ℓ1(Z,v)ℓ1(Z,v).