Mathematical constraints on a theory of human memory - Response

Colonius suggests that, in using standard set theory as the language in which to express our computational-level theory of human memory, we would need to violate the axiom of foundation in order to express meaningful memory bindings in which a context is identical to an item in the list. We circumvent Colonius's objection by allowing that a list item may serve as a label for a context without being identical to that context. This debate serves to highlight the value of specifying memory operations in set theoretic notation, as it would have been difficult if not impossible to formulate such an objection at the algorithmic level.

Odorant-induced currents in intact patches from rat olfactory receptor neurons: Theory and experiment

Odorant-induced currents in mammalian olfactory receptor neurons have proved difficult to obtain reliably using conventional whole-cell recording. By using a mathematical model of the electrical circuit of the patch and rest-of-cell, we demonstrate how cell-attached patch measurements can be used to quantitatively analyze responses to odorants or a high (100 mM) K+ solution. High K+ induced an immediate current flux from cell to pipette, which was modeled as a depolarization of similar to 52 mV, close to that expected from the Nernst equation (56 mV), and no change in the patch conductance. By contrast, a cocktail of cAMP-stimulating odorants induced a current flux from pipette into cell following a significant (4-10 s) delay. This was modeled as an average patch conductance increase of 36 pS and a depolarization of 13 mV, Odorant-induced single channels had a conductance of 16 pS. In cells bathed with no Mg2+ and 0.25 mM Ca2+, odorants induced a current flow from cell to pipette, which was modeled as a patch conductance increase of similar to 115 pS and depolarization of similar to 32 mV, All these results are consistent with cAMP-gated cation channels dominating the odorant response, This approach, which provides useful estimates of odorant-induced voltage and conductance changes, is applicable to similar measurements in any small cells.

White matter microstructure underlying default mode network connectivity in the human brain

Resting state functional magnetic resonance imaging (fMRI) reveals a distinct network of correlated brain function representing a default mode state of the human brain The underlying structural basis of this functional connectivity pattern is still widely unexplored We combined fractional anisotropy measures of fiber tract integrity derived from diffusion tensor imaging (DTI) and resting state fMRI data obtained at 3 Tesla from 20 healthy elderly subjects (56 to 83 years of age) to determine white matter microstructure e 7 underlying default mode connectivity We hypothesized that the functional connectivity between the posterior cingulate and hippocampus from resting state fMRI data Would be associated with the white matter microstructure in the cingulate bundle and fiber tracts connecting posterior cingulate gyrus With lateral temporal lobes, medial temporal lobes, and precuneus This was demonstrated at the p<0001 level using a voxel-based multivariate analysis of covariance (MANCOVA) approach In addition, we used a data-driven technique of joint independent component analysis (ICA) that uncovers spatial pattern that are linked across modalities. It revealed a pattern of white matter tracts including cingulate bundle and associated fiber tracts resembling the findings from the hypothesis-driven analysis and was linked to the pattern of default mode network (DMN) connectivity in the resting state fMRI data Out findings support the notion that the functional connectivity between the posterior cingulate and hippocampus and the functional connectivity across the entire DMN is based oil distinct pattern of anatomical connectivity within the cerebral white matter (C) 2009 Elsevier Inc All rights reserved

A mathematical model for Escherichia coli debris size reduction during high pressure homogenisation based on grinding theory

Experimental data for E. coli debris size reduction during high-pressure homogenisation at 55 MPa are presented. A mathematical model based on grinding theory is developed to describe the data. The model is based on first-order breakage and compensation conditions. It does not require any assumption of a specified distribution for debris size and can be used given information on the initial size distribution of whole cells and the disruption efficiency during homogenisation. The number of homogeniser passes is incorporated into the model and used to describe the size reduction of non-induced stationary and induced E. coil cells during homogenisation. Regressing the results to the model equations gave an excellent fit to experimental data ( > 98.7% of variance explained for both fermentations), confirming the model's potential for predicting size reduction during high-pressure homogenisation. This study provides a means to optimise both homogenisation and disc-stack centrifugation conditions for recombinant product recovery. (C) 1997 Elsevier Science Ltd.

Scale-free network of a dengue epidemic

In this work we show that the dengue epidemic in the city of Singapore organized itself into a scale-free network of transmission as the 2000-2005 outbreaks progressed. This scale-free network of cluster comprised geographical breeding places for the aedes mosquitoes, acting as super-spreaders nodes in a network of transmission. The geographical organization of the network was analysed by the corresponding distribution of weekly number of new cases. Therefore, our hypothesis is that the distribution of dengue cases reflects the geographical organization of a transmission network, which evolved towards a power law as the epidemic intensity progressed until 2005. (c) 2007 Elsevier Inc. All rights reserved.