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.

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.

Risk Estimates of Dengue in Travelers to Dengue Endemic Areas Using Mathematical Models

Dengue has emerged as a frequent problem in international travelers. The risk depends on destination, duration, and season of travel. However, data to quantify the true risk for travelers to acquire dengue are lacking. We used mathematical models to estimate the risk of nonimmune persons to acquire dengue when traveling to Singapore. From the force of infection, we calculated the risk of dengue dependent on duration of stay and season of arrival. Our data highlight that the risk for nonimmune travelers to acquire dengue in Singapore is substantial but varies greatly with seasons and epidemic cycles. For instance, for a traveler who stays in Singapore for 1 week during the high dengue season in 2005, the risk of acquiring dengue was 0.17%, but it was only 0.00423% during the low season in a nonepidemic year such as 2002. Risk estimates based on mathematical modeling will help the travel medicine provider give better evidence-based advice for travelers to dengue endemic countries.

Placental Volumes Measured by 3-Dimensional Ultrasonography in Normal Pregnancies From 12 to 40 Weeks` Gestation

Objective. The purpose of this study was to construct nomograms of placental volumes according to gestational age and estimated fetal weight. Methods. From March to November 2007, placental volumes were prospectively measured by ultrasonography in 295 normal pregnancies from 12 to 40 weeks` gestation and correlated with gestational age and estimated fetal weight. Inclusion criteria were healthy women, singleton pregnancies with normal fetal morphologic characteristics on ultrasonography, and confirmed gestational age by first-trimester ultrasonography. Results. The mean placental volume ranged from 83 cm(3) at 12 weeks to 427.7 cm(3) at 40 weeks. Linear regression yielded the following formula for the expected placental volumes (ePV) according to gestational age (GA): ePV` (cm(3)) = -64.68 + 12.31 x GA (r = 0.572; P < .001). Placental volumes also varied according to estimated fetal weight (EFW), and the following mathematical equation was also obtained by linear regression: ePV = 94.19 + 0.09 x EFW (r = 0.505; P < 0.001). Conclusions. Nomograms of placental volumes according to gestational age and estimated fetal weight were constructed, generating reference values.

Effect of PaCO(2) variation on standard base excess value in critically ill patients

Purpose: The aim of this study was to investigate the impact of acute PaCO(2) temporal variation on the standard base excess (SBE) value in critically ill patients. Methods: A total of 265 patients were prospectively observed; 158 were allocated to the modeling group, and 107 were allocated to the validation group. Two models were developed in the modeling group (one including and one excluding PaCO(2) as a variable determinant of SBE), and both were tested in the validation group. Results: In the modeling group, the mathematical model including SIDai, SIG, L-lactate, albumin, phosphate, and PaCO(2) had a predictive superiority in comparison with the model without PaCO(2) (R(2) = 0.978 and 0.916, respectively). In the validation group, the results were confirmed with significant F change statistics (R(2) change = 0.059, P < .001) between the model with and without PaCO(2). A high correlation (R = 0.99, P < .001) and agreement (bias = -0.25 mEq/L, limits of agreement 95% = -0.72 to 0.22 mEq/L) were found between the model-predicted SBE value and the SBE calculated using the Van Slyke equation. Conclusions: Acute PaCO(2), temporal variation is related to SBE changes in critically ill patients. (C) 2009 Elsevier Inc. All rights reserved.

A decision support system to facilitate management of patients with acute gastrointestinal bleeding

Objective: To develop a model to predict the bleeding source and identify the cohort amongst patients with acute gastrointestinal bleeding (GIB) who require urgent intervention, including endoscopy. Patients with acute GIB, an unpredictable event, are most commonly evaluated and managed by non-gastroenterologists. Rapid and consistently reliable risk stratification of patients with acute GIB for urgent endoscopy may potentially improve outcomes amongst such patients by targeting scarce health-care resources to those who need it the most. Design and methods: Using ICD-9 codes for acute GIB, 189 patients with acute GIB and all. available data variables required to develop and test models were identified from a hospital medical records database. Data on 122 patients was utilized for development of the model and on 67 patients utilized to perform comparative analysis of the models. Clinical data such as presenting signs and symptoms, demographic data, presence of co-morbidities, laboratory data and corresponding endoscopic diagnosis and outcomes were collected. Clinical data and endoscopic diagnosis collected for each patient was utilized to retrospectively ascertain optimal management for each patient. Clinical presentations and corresponding treatment was utilized as training examples. Eight mathematical models including artificial neural network (ANN), support vector machine (SVM), k-nearest neighbor, linear discriminant analysis (LDA), shrunken centroid (SC), random forest (RF), logistic regression, and boosting were trained and tested. The performance of these models was compared using standard statistical analysis and ROC curves. Results: Overall the random forest model best predicted the source, need for resuscitation, and disposition with accuracies of approximately 80% or higher (accuracy for endoscopy was greater than 75%). The area under ROC curve for RF was greater than 0.85, indicating excellent performance by the random forest model Conclusion: While most mathematical models are effective as a decision support system for evaluation and management of patients with acute GIB, in our testing, the RF model consistently demonstrated the best performance. Amongst patients presenting with acute GIB, mathematical models may facilitate the identification of the source of GIB, need for intervention and allow optimization of care and healthcare resource allocation; these however require further validation. (c) 2007 Elsevier B.V. All rights reserved.

Regression of glomerular injury by losartan in experimental diabetic nephropathy

Many features of chronic kidney disease may be reversed, but it is unclear whether advanced lesions, such as adhesions of sclerotic glomerular tufts to Bowman`s capsule (synechiae), can resolve during treatment. We previously showed, using a renal ablation model, that the renoprotective effect of the AT-1 receptor blocker, losartan, is dose-dependent. Here we determined if moderate and advanced glomerular lesions, associated with streptozotocin-induced diabetes, regress with conventional or high-dose losartan treatment. Using daily insulin injection for 10 months, we maintained diabetic adult male Munich-Wistar rats in a state of moderate hyperglycemia. Following this period, some rats continued to receive insulin with or without conventional or high-dose losartan for an additional 2 months. Diabetic rats pretreated with insulin for 10 months and age-matched non-diabetic rats served as controls. Mesangial expansion was found in the control diabetic rats and was exacerbated in those rats maintained on only insulin for an additional 2 months. Conventional and high-dose losartan treatments reduced this mesangial expansion and the severity of synechiae lesions below that found prior to treatment; however, the frequency of the latter was unchanged. There was no dose-response effect of losartan. Our results show that regression of mesangial expansion and contraction of sclerotic lesions is feasible in the treatment of diabetes, but complete resolution of advanced glomerulosclerosis may be hard to achieve.

Expression of fibroblast growth factor receptors during development and regression of the bovine corpus luteum

There is evidence that fibroblast growth factors (FGFs) are involved in the regulation of growth and regression of the corpus luteum (CL). However, the expression pattern of most FGF receptors (FGFRs) during CL lifespan is still unknown. The objective of the present study was to determine the pattern of expression of `B` and `C` splice variants of FGFRs in the bovine CL. Bovine CL were collected from an abattoir and classed as corpora hemorrhagica (Stage I), developing (Stage II), developed (Stage III) or regressed (Stage IV) CL. Expression of FGFR mRNA was measured by semiquantitative reverse transcription-polymerase chain reaction and FGFR protein was localised by immunohistochemistry. Expression of mRNA encoding the `B` and `C` spliced forms of FGFR1 and FGFR2 was readily detectable in the bovine CL and was accompanied by protein localisation. FGFR1C and FGFR2C mRNA expression did not vary throughout CL lifespan, whereas FGFR1B was upregulated in the developed (Stage III) CL. FGFR3B, FGFR3C and FGFR4 expression was inconsistent in the bovine CL. The present data indicate that FGFR1 and FGFR2 splice variants are the main receptors for FGF action in the bovine CL.

Long-term survivor mixture model with random effects: application to a multi-centre clinical trial of carcinoma

A mixture model incorporating long-term survivors has been adopted in the field of biostatistics where some individuals may never experience the failure event under study. The surviving fractions may be considered as cured. In most applications, the survival times are assumed to be independent. However, when the survival data are obtained from a multi-centre clinical trial, it is conceived that the environ mental conditions and facilities shared within clinic affects the proportion cured as well as the failure risk for the uncured individuals. It necessitates a long-term survivor mixture model with random effects. In this paper, the long-term survivor mixture model is extended for the analysis of multivariate failure time data using the generalized linear mixed model (GLMM) approach. The proposed model is applied to analyse a numerical data set from a multi-centre clinical trial of carcinoma as an illustration. Some simulation experiments are performed to assess the applicability of the model based on the average biases of the estimates formed. Copyright (C) 2001 John Wiley & Sons, Ltd.

Proximal arterial vasoconstriction precedes regression of the hyaloid vasculature

Purpose: To determine whether constriction of proximal arterial vessels precedes involution of the distal hyaloid vasculature in the mouse, under normal conditions, and whether this vasoconstriction is less pronounced when the distal hyaloid network persists, as it does in oxygen-induced retinopathy (OIR). Methods: Photomicrographs of the vasa hyaloidea propria were analysed from pre-term pups (1-2 days prior to birth), and on Days 1-11 post-birth. The OIR model involved exposing pups to similar to 90% O-2 from D1-5, followed by return to ambient air. At sampling times pups were anaesthetised and perfused with india ink. Retinal flatmounts were also incubated with FITC-lectin (BS-1, G. simplicifolia,); this labels all vessels, allowing identification of vessels not patent to the perfusate. Results: Mean diameter of proximal hyaloid vessels in preterm pups was 25.44 +/- 1.98 mum; +/-1 SEM). Within 3-12 hrs of birth, significant vasoconstriction was evident (diameter:12.45 +/- 0.88 mum), and normal hyaloid regression subsequently occurred. Similar vasoconstriction occurred in the O-2-treated group, but this was reversed upon return to room air, with significant dilation of proximal vessels by D7 (diameter: 31.75 +/- 11.99 mum) and distal hyaloid vessels subsequently became enlarged and tortuous. Conclusions: Under normal conditions, vasoconstriction of proximal hyaloid vessels occurs at birth, preceding attenuation of distal hyaloid vessels. Vasoconstriction also occurs in O-2-treated pups during treatment, but upon return to room air, the remaining hyaloid vessels dilate proximally, and the distal vessels become dilated and tortuous. These observations support the contention that regression of the hyaloid network is dependent, in the first instance, on proximal arterial vasoconstriction.