Mathematical Computing

Chaste -Cancer, Heart And Soft Tissue Environment -is an open source C++ library for the computational simulation of mathematical models developed for physiology and biology. Code development has been driven by two initial applications: cardiac electrophysiology and cancer development. A large number of cardiac electrophysiology studies have been enabled and performed, including high-performance computational investigations of defibrillation on realistic human cardiac geometries. New models for the initiation and growth of tumours have been developed. In particular, cellbased simulations have provided novel insight into the role of stem cells in the colorectal crypt. Chaste is constantly evolving and is now being applied to a far wider range of problems. The code provides modules for handling common scientific computing components, such as meshes and solvers for ordinary and partial differential equations (ODEs/PDEs). Re-use of these components avoids the need for researchers to 're-invent the wheel' with each new project, accelerating the rate of progress in new applications. Chaste is developed using industrially-derived techniques, in particular testdriven development, to ensure code quality, re-use and reliability. In this article we provide examples that illustrate the types of problems Chaste can be used to solve, which can be run on a desktop computer. We highlight some scientific studies that have used or are using Chaste, and the insights they have provided. The source code, both for specific releases and the development version, is available to download under an open source Berkeley Software Distribution (BSD) licence at , together with details of a mailing list and links to documentation and tutorials.

The NMDA receptor antagonist MK-801 produces different effects on timing tasks. In particular, MK-801 produces an underestimation of duration when animals are tested with the differential reinforcement of low rate of responding (DRL) schedule and an overestimation of duration when animals are tested with the peak-interval (PI) procedure. The goal of this study was to develop a model-based explanation for this discrepancy. Two computer simulations were conducted via an implementation of scalar expectancy theory (SET). In Simulation 1, SET was used to provide a quantitative account of PI timing data. Simulation 2 used parameter estimates from Simulation 1 to predict effects of MK-801 on the DRL task. DRL predictions provided a close match to previous empirical data. Results of the simulations suggest that differences in the literature are likely due to inherent differences between PI and DRL tasks, rather than fundamental differences in timing. Overall, the role of NMDA receptors in timing appears to be multifaceted, impacting perception, memory, and decision processes.

Acute coronary syndrome (ACS) is a major cause of morbidity and mortality in CHD patients in the world and causes around a third of total deaths in the age group >35 years. The mortality rate of patients hospitalized due to ACS in Indonesia reaches 32.3%. This figure is one of the highest in the world. Epidemiological studies show an increasing prevalence of acute coronary syndrome (ACS) worldwide. Objective of the research to analyse the RDW and PDW values which can be used as predictors of severity in patients with acute coronary syndrome. The type of research used is a descriptive analytic design with a cross-sectional approach. Analysis of RDW and PDW Levels as predictors of severity in Pure Acute Coronary Syndrome Patients (without comorbidities) There were 42% male and 58% female, average age 52.50 ± 12.62 years, RDW level correlated significantly as a predictor of severity in Acute Coronary Syndrome Patients without comorbidities, but PDW levels were not significantly correlated as predictors of severity in acute coronary syndrome patients without comorbid analysis of RDW and PDW levels in comorbid acute coronary syndrome patients. RDW and PDW are significantly correlated as predictors of severity in patients with acute coronary syndrome, comorbidities in acute coronary syndrome most of the comorbidities are diabetes mellitus, kidney disease, hypertension and sepsis. So, the levels of RDW and PDW can be a predictor of the severity of comorbid acute coronary syndrome.

Neuronal activation can be separated from other signal sources of functional magnetic resonance imaging (fMRI) data by using independent component analysis (ICA). Without deliberate neuronal activity of the brain cortex, the fMRI signal is a stochastic sum of various physiological and artifact related signal sources. The ability of spatial-domain ICA to separate spontaneous physiological signal sources was evaluated in 15 anesthetized children known to present prominent vasomotor fluctuations in the functional cortices. ICA separated multiple clustered signal sources in the primary sensory areas in all of the subjects. The spatial distribution and frequency spectra of the signal sources correspond to the known properties of 0.03-Hz very-low-frequency vasomotor waves in fMRI data. In addition, ICA was able to separate major artery and sagittal sinus related signal sources in each subject. The characteristics of the blood vessel related signal sources were different from the parenchyma sources. ICA analysis of fMRI can be used for both assessing the statistical independence of brain signals and segmenting nondeterministic signal sources for further analysis.

The grid has the potential to transform collaborative scientific investigations through the use of closely coupled computational and visualization resources, which may be geographically distributed, in order to harness greater power than is available at a single site. Scientific applications to benefit from the grid include visualization, computational science, environmental modelling and medical imaging. Unfortunately, the diversity, scale and location of the required resources can present a dilemma for the scientific worker because of the complexity of the underlying technology. As the scale of the scientific problem under investigation increases so does the nature of the scientist's interaction with the supporting infrastructure. The increased distribution of people and resources within a grid-based environment can make resource sharing and collaborative interaction a critical factor to their success. Unless the technological barriers affecting user accessibility are reduced, there is a danger that the only scientists to benefit will be those with reasonably high levels of computer literacy. This paper examines a number of important human factors of user interaction with the grid and expresses this in the context of the science undertaken by RealityGrid, a project funded by the UK e-Science programme. Critical user interaction issues will also be highlighted by comparing grid computational steering with supervisory control systems for local and remote access to the scientific environment. Finally, implications for future grid developers will be discussed with a particular emphasis on how to improve the scientists' access to what will be an increasingly important resource.

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New electron-impact differential cross-section (DCS) and DCS ratio measurements for the excitation of the four levels making up the 3p 5 4s configuration of argon are reported at incident electron energies of 14, 15, 17.5, 20, 30, 50 and 100 eV. These cross-sections were obtained using a conventional high resolution electron spectrometer. Elastic electron scattering from argon was used as a calibration standard. Electron-helium DCSs were used to determine the instrumental transmission of the spectrometer. Further checks of the relative shape of these DCS measurements were made using the method of gas mixtures (Ne mixed with Ar). We also present results from new calculations of these DCSs using the R-matrix method, the unitarized first-order manybody theory, the semi-relativistic distorted-wave Born approximation, and the relativistic distorted-wave method. Comparison with available experimental DCSs and DCS ratios is also presented.

Motivation: Protein interactions provide an important context for the understanding of function. Experimental approaches have been complemented with computational ones, such as PSIMAP, which computes domain–domain interactions for all multi-domain and multi-chain proteins in the Protein Data Bank (PDB). PSIMAP has been used to determine that superfamilies occurring in many species have many interaction partners, to show examples of convergent evolution through shared interaction partners and to uncover complexes in the interaction map. To determine an interaction, the original PSIMAP algorithm checks all residue pairs of any domain pair defined by classification systems such as SCOP. The computation takes several days for the PDB. The computation of PSIMAP has two shortcomings: first, the original PSIMAP algorithm considers only interactions of residue pairs rather than atom pairs losing information for detailed analysis of contact patterns. At the atomic level the original algorith...

The cosmological lithium-7 problem—an unresolved discrepancy between predicted and observed primordial lithium abundance—has persisted for over two decades.

This paper introduces a geometric resolution based on the Recursive Harmonic Collapse Matrix (RHCM) framework.

Instead of modeling Big Bang Nucleosynthesis as a reaction network, RHCM treats it as a sequence of phase transitions in a depth-structured field. Within this framework, helium-4, deuterium, and lithium-7 abundances all emerge from a single geometric relationship defined by fold structure.

A key result is that Be-7 and Li-7 are not separate production pathways but occupy the same geometric attractor basin, resolving the lithium discrepancy without modifying reaction rates or introducing new physics.

The framework further demonstrates:

exact encoding of nuclear charge from depth structure
a structural transition separating nuclear formation and particle stability
consistent mapping of particle masses from a unified depth coordinate
validation across 83 computational tests and a structured falsification suite

This work proposes a shift from parameter-driven cosmology to structure-driven derivation, where physical observables emerge from underlying geometric constraints.

All results are computational and presented as testable predictions.

Background: Clinicians apply posteroanterior (PA) forces to the spine for both mobility assessment and certain spinal mobilization and manipulation treatments. Commonly applied forces include lowfrequency sinusoidal oscillations (Ͻ2 Hz) as used in mobilization, single haversine thrusts (Ͻ0.5 seconds) as imparted in high-velocity, low-amplitude (HVLA) manipulation, or very rapid impulsive thrusts (Ͻ5 ms) such as those delivered in mechanical-force, manually-assisted (MFMA) manipulation. Little is known about the mechanics of these procedures. Reliable methods are sought to obtain an adequate understanding of the force-induced displacement response of the lumbar spine to PA forces. Objective: The objective of this study was to investigate the kinematic response of the lumbar spine to static and dynamic PA forces. Design: A 2-dimensional modal analysis was performed to predict the dynamic motion response of the lumbar spine. Methods: A 5-degree-of-freedom, lumped equivalent model was developed to predict the PA motion of the lumbar spine. Lumbar vertebrae were modeled as masses, massless-spring, and dampers, and the resulting equations of motion were solved by using a modal analysis approach. The sensitivity of the model to variations in the spring stiffness and damping coefficients was examined, and the model validity was determined by comparing the results to oscillatory and impulsive force measurements of vertebral motion associated with spine mobilization and 2 forms of spinal manipulation. Results: Model predictions, based on a damping ratio of 0.15 (moderate damping) and PA spring stiffness coefficient ranging from 25 to 60 kN/m, showed good agreement with in vivo human studies. Quasi-static and low-frequency (Ͻ2.0 Hz) forces at L3 produced L3 segmental and L3-L4 intersegmental displacements up to 8.1 mm and 3.0 mm, respectively. PA oscillatory motions were over 2.5-fold greater for oscillatory forces applied at the natural frequency. Impulsive forces produced much lower segmental displacements in comparison to static and oscillatory forces. Differences in intersegmental displacements resulting from impulsive, static, and oscillatory forces were much less remarkable. The latter suggests that intersegmental motions produced by spinal manipulation may play a prominent role in eliciting therapeutic responses.

Background: Computational modeling of human circulatory system has evolved significantly in recent decades. Among the various modeling strategies, one-dimensional (1D) models have emerged as alternatives to more complex models because of their balance between physiological accuracy and computational efficiency. Objective: This scoping review aimed to summarize and compare the studies on 1D computational models of the entire circulatory system, including those that incorporated additional 0D and 3D components. Methods: A systematic search was performed for studies on computational 1D models of the entire arterial tree. Studies were eligible if they employed 1D modeling either exclusively or in combination with 0D and/or 3D components. Article screening, data extraction, and analyses were conducted in accordance with the PRISMA-ScR guidelines. Results: Out of the 6,841 records, 19 studies were included. Eleven articles presented strictly 1D nonlinear models, two used linear 1D models, and six employed multiscale frameworks that integrated 1D, 0D, and/or 3D components. Nonlinear 1D models consistently outperformed linear models in simulating large elastic arteries and pathological conditions, whereas linear models were effective in simulating small vessels under low-pressure variations. Multiscale models improve local hemodynamic details, but impose significantly higher computational costs. Conclusion: 1D models provide a robust and computationally efficient framework for simulating global cardiovascular hemodynamics. Although nonlinear and multiscale models enhance the physiological fidelity and adaptability to complex scenarios, their higher computational demands should be weighed against the available resources and specific clinical or research goals.

The toxicity/efficacy of a potential drug must be examined before it can be approved for general use. Quantal dose-response experiments are conducted in both preclinical and clinical trials for this purpose. A usual practice in the design of a dose-response experiment is to divide the dosage interval evenly and allocate equal number of subjects to each of the dosage levels. It is shown here that this scheme may not be efficient. We propose multiple-objective optimal designs, including sequential designs, as a practical alternative.

Introduction Obstructive sleep apnea (OSA) affects up to 30% of the adult population and is a risk factor for coronary artery disease (CAD). The diagnostic process, involving polysomnography, may be complex. Berlin questionnaire (BQ) is a validated and economical screening tool. Purpose The aim of this study was to assess the performance of the BQ for the diagnosis of OSA in individuals with angina complaints. Methods Patients undergoing diagnostic cineangiography, portable type III polysomnography to determine the apneahypopnea index (AHI), and who answered the BQ were included. We excluded patients older than 65 years that were smokers, diabetics, and morbidly obese. High risk for OSA was based on positive responses in two of three symptom criteria of the BQ. CAD was defined by the presence of >50% lesion in coronary arteries. Results In 57 included cases, high risk in the BQ indicates significant odds ratio [95% confidence interval] for the presence of , P=0.045), adjusted for usual confounders: gender, age, and body mass index. The sensitivity and the specificity of BQ for CAD were 70% and 48%, respectively; the positive and negative predictive values are 56% and 64%. Conclusions In conclusion, simple questionnaire-based diagnostic tools can be included in the screening procedures of patients with angina to detect the need for further OSA

We present a novel approach for the analysis of transcriptomics data that integrates functional annotation of gene sets with expression values in a multivariate fashion, and directly assesses the relation of functional features to a multivariate space of response phenotypical variables. Multivariate projection methods are used to obtain new correlated variables for a set of genes that share a given function. These new functional variables are then related to the response variables of interest. The analysis of the principal directions of the multivariate regression allows for the identification of gene function features correlated with the phenotype. Two different transcriptomics studies are used to illustrate the statistical and interpretative aspects of the methodology. We demonstrate the superiority of the proposed method over equivalent approaches.

The aim of this note is to revisit the analysis of conjunctions in imaging data. We review some conceptual issues that have emerged from recent discussion (Nichols, T., Brett, M., Andersson, J., Wager, T., Poline, J.-B., this issue. Valid Conjunction Inference with the Minimum Statistic.) and reformulate the conjunction of null hypotheses as a conjunction of k or more effects. Analyses based on minimum statistics have typically used the null hypothesis that k = 0. This enables inferences about one or more effects (k N 0). However, this does not provide control over false-positive rates (FPR) for inferences about a conjunction of k = n effects, over n tests. This is the key point made by Nichols et al., who suggest a procedure based on supremum P values that provides an upper bound on FPR for k = n. Although valid, this is a very conservative procedure, particularly in the context of multiple comparisons. We suggest that an inference on a conjunction of k = n effects is generally unnecessary and distinguish between congruent contrasts that test for the same treatment and incongruent contrasts of the sort used in cognitive conjunctions. For congruent contrasts, the usual inference, k N 0, is sufficient. With incongruent contrasts it is sufficient to infer a conjunction of k N u effects, where u is the number of contrasts that share some uninteresting effect. The issues highlighted by Nichols et al., have important implications for the design and analysis of cognitive conjunction studies and have motivated a change to the SPM software, that affords a test for the more general hypothesis k N u. This more general conjunction test is described.

Mitochondrial malate dehydrogenase shows a complex regulation pattern in the presence of citrate. Previously published results indicate that this enzyme is activated by citrate in the NAD(+)----NADH direction and inhibited in the opposite direction. Moreover, high concentrations of L-malate or oxaloacetate produce deviations from the Michaelis-Menten behaviour. Results reported in this paper clearly show that citrate both activates and inhibits mitochondrial malate dehydrogenase in the same direction (NAD(+)----NADH), and in the same reaction medium, depending on substrate concentration. This surprising effect has made it necessary to propose a new kinetic mechanism that extends those previously suggested and allows us to explain both the citrate effect (activating or inhibitory) and the effect of high concentrations of L-malate and oxaloacetate.

Professionals are frequently consulted to diagnose and predict human behavior; optimal treatment and planning often hinge on the consultant's judgmental accuracy. The consultant may rely on one of two contrasting approaches to decisionmaking-the clinical and actuarial methods. Research comparing these two approaches shows the actuarial method to be superior. Factors underlying the greater accuracy of actuarial methods, sources of resistance to the scientific findings, and the benefits of increased reliance on actuarial approaches are discussed.

Vve introduce a new model of molecular computation that we call the sticker model. Like many previous proposals it makes use of DNA strands as the physical substrate in which information is represented and of separation by hybridization as a central mechanism. However , unlike previous models, the stickers model has a random access memory that requires no strand extension, uses no enzymes, and (at least in theory) its materials are reusable. The paper describes computation under the stickers model and discusses possible means for physically implementing each operation. We go on to propose a specific machine architecture for implementing the stickers model as a microprocessor-controlled parallel robotic workstation. Finally, we discuss several methods for achieving acceptable overall error rates for a computation using basic operations that are error prone. In t he course of this development a number of previous general concerns about molecular computation [36, 2 0 , 24 ) are addressed. First, it is clear that general-purpose algorithms can be implemented by DNA-based computers, potentially solving a " .. •ide class of search problems. Second, we find that there are challenging problems, for which only modest volumes of DNA should suffice. Third, we demonstrate that the formation and breaking of covalent bonds is not intrinsic to DNA-based computation. This means that costly and short-lived materials such as enzymes are not necessary, nor are energetically costly processes such as PCR. Fourth , \ .... e show that a single essential biotechnology, sequence-specific separation , suffices for constructing a general-purpose molecular computer. Fifth, we illustrate that separation errors can theoretically be reduced to tolerable levels by invoking a trade-off between time, space, and error rates at the level of algorithm design; we also outline several specific ways in which this can be done and present numerical calculations of their per formance. Despite these encouraging theoretical advances , we emphasize that sub-stantial engineering challenges remain at almost all stages and that the ultimate success or failure of DNA computing will certainly depend on whether t.hese challenges can be met in laboratory investigations.

Die Anwendungsgenauigkeit von intraoperativer Navigation hängt neben anderen Faktoren auch von der Zahl der verwendeten Fiducials ab. Nach gängiger Auffassung steigt die vorhergesagte Anwendungsgenauigkeit mit der Zahl der Fiducials. In unserer klinischen Routine hat sich deutlich gezeigt, dass durch Verwendung von mehr als fünf Punkten am Patienten für die starre Registrierung des Patienten an den präoperativen Bilddatensatz KEIN Gewinn an Anwendungsgenauigkeit gewonnen wird. Deshalb wurden im experimentellen Operationssaal der HNO unter kontrollierten Bedingungen Experimente dazu durchgeführt. Dabei wurde ein optischer Tracker (easyTrack 500, atracsys, Schweiz), ein open-source Navigationssystem (open4Dnav, voxelmaster.at) und CT und DVT Datensätzen der Studienobjekte (Plastikschädel, anatomisches Präparat, Freiwilliger) verwendet. Es wurden Messreihen mit jeweils 3-, 5-, 7und 9 Registrierungspunkten, mit je 10 Registrierungen und 10 wohldefinierten Kontrollpunkten (Targets) durch...

Authors' Contributions: Each author made an equal contribution to the conception and design of the study. All authors have reviewed and approved the final version of the manuscript for publication. Transparency: The authors affirm that this manuscript presents an honest, accurate, and transparent account of the study. All essential aspects have been included, and any deviations from the original study plan have been clearly explained. The writing process strictly adhered to established ethical standards.

The screened Coulombic potential has been shown to describe satisfactorily equilibrium properties like pA" shifts, the effects of charged groups on redox potentials and binding constants of metal ions. To test how well the screening of the electrostatic potential describes the dynamical trajectory of a macromolecular system, a series of comparative simulations have been carried out on a protein system which explicitly included water molecules and a system in vacuo. For the system without solvent the results of using (i) the standard potential form were compared with results of (ii) the potential where the Coulomb term was modified by the inclusion of a distance dependent dielectric, e(r), to model the screening effect of bulk water, and (iii) standard potential modified by reducing the charge on ionized residue side chains. All molecular dynamics simulations have been carried out on bovine pancreatic trypsin inhibitor. Comparisons between the resulting trajectories, averaged structures, hydrogen bonding patterns and properties such as solvent accessible surface area and radius of gyration are described. The results show that the dynamical behaviour of the protein calculated with a screened electrostatic term compares more favourably with the time-dependent structural changes of the full system with explicitly included water than the standard vacuum simulation.

Two approaches for calculating electrostatic effects in proteins are compared and an analysis is presented of the dependence of calculated properties on the model used to define the charge distribution. Changes in electrostatic free energy have been calculated using a screened Coulomb potential (SCP) with a distance-dependent effective dielectric permittivity to model bulk solvent effects and a finite difference approach to solve the Poisson-Boltzmann (FDPB) equation. The properties calculated include shifts in dissociation constants of ionizable groups, the effect of annihilating surface charges on the binding of metals, and shifts in redox potentials due to changes in the charge of ionizable groups. In the proteins considered the charged sites are separated by 3.5-12 A. It is shown that for the systems studied in this distance range the SCP yields calculated values which are at least as accurate as those obtained from solution of the FDPB equation. In addition, in the distance range 3-5 A the SCP gives substantially better results than the FDPB equation. Possible sources of this difference between the two methods are discussed. Shifts in binding constants and redox potentials were calculated with several standard charge sets, and the resulting values show a variation of 20-40% between the 'best' and 'worst' cases. From this study it is concluded that in most applications, changes in electrostatic free energies can be calculated economically and reliably using an SCP approach with a single functional form of the screening function.