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.

Discrete and continuous models for dry masonry columns

The dynamic response of dry masonry columns can be approximated with finite-difference equations. Continuum models follow by replacing the difference quotients of the discrete model by corresponding differential expressions. The mathematically simplest of these models is a one-dimensional Cosserat theory. Within the presented homogenization context, the Cosserat theory is obtained by making ad hoc assumptions regarding the relative importance of certain terms in the differential expansions. The quality of approximation of the various theories is tested by comparison of the dispersion relations for bending waves with the dispersion relation of the discrete theory. All theories coincide with differences of less than 1% for wave-length-block-height (L/h) ratios bigger than 2 pi. The theory based on systematic differential approximation remains accurate up to L/h = 3 and then diverges rapidly. The Cosserat model becomes increasingly inaccurate for L/h < 2 pi. However, in contrast to the systematic approximation, the wave speed remains finite. In conclusion, considering its relative simplicity, the Cosserat model appears to be the natural starting point for the development of continuum models for blocky structures.

Sensitization to foods in gastroesophageal reflux disease and its relation to eosinophils in the esophagus: is it of clinical importance?

Background: Refractory gastroesophageal reflux disease (GERD) can be related to greater sensitization to foods. Objective: To evaluate sensitization to foods in patients with refractory GERD. Methods: Patients with refractory GERD after using at least 40 mg of a proton pump inhibitor were given a restriction diet based on the results of skin prick testing and atopy patch testing with foods. The characteristics of sensitized patients were compared with those of nonsensitized patients in relation to atopy and number of eosinophils in the esophageal mucosa. Results: The prevalence of sensitization to foods was 27.7%. Asthmatic patients showed higher sensitization to foods (P = .008). Eosinophils were determined to be present in the esophageal mucosa in 15.8% of patients, and this correlated with greater sensitization to foods (P = .01). One case of eosinophilic esophagitis was confirmed. A diet excluding identified sensitizing foods led to clinical improvement regarding GERD symptoms (P = .004). Conclusion: The presence of eosinophils in esophageal mucosa associated with greater sensitization to foods and the response to a restriction diet in patients with positive test results suggest that refractory GERD can represent an initial stage of eosinophilic esophagitis. Ann Allergy Asthma Immunol. 2010;105:359-363.

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.

Hematological indices at birth in relation to arterial and venous Doppler in small-for-gestational-age fetuses

Objective. To correlate Doppler results with hematological indices at birth in small-for-gestational-age (SGA) fetuses. Design. Prospective study. Setting. Tertiary teaching hospital, Sao Paulo, Brazil. Population. One hundred singleton pregnancies with SGA fetuses of > 27 weeks gestational age. Methods. All women had Doppler velocimetry of the umbilical arteries, middle cerebral artery, and ductus venosus within < 72 hours prior to delivery. After birth, umbilical artery blood was collected for hematological analysis. Main outcome measures. The association between fetal Doppler velocimetry pulsatility index (PI) and some hematological indices. Results. Umbilical artery PI showed a positive correlation with nucleated red blood cell count in the umbilical cord (r = 0.46; p<0.01), and a negative correlation with platelet count (r = -0.53; p<0.01) and white blood cell count (r = -0.42; p<0.01). Middle cerebral artery PI was positively correlated with platelet count (r = 0.43; p<0.01) and white blood cell count (r = 0.38; p<0.01), and was negatively correlated with nucleated red blood cell count (r = -0.39; p<0.01). The ductus venosus pulsatility index showed a positive correlation with nucleated red blood cell count (r = 0.36; p<0.01), and a negative correlation with platelet count (r = -0.37; p<0.01) and white blood cell count (r = -0.26; p<0.01). Conclusion. A significant positive or negative correlation between nucleated red blood cell, platelet and white blood cell counts, and Doppler indices suggests an association between placental insufficiency and the fetal hematological response.