The quantitation of buffering action I. A formal & general approach

BACKGROUND: Although "buffering" as a homeostatic mechanism is a universal phenomenon, the quantitation of buffering action remains controversial and problematic. Major shortcomings are: lack of a buffering strength unit for some buffering phenomena, multiple and mutually incommensurable units for others, and lack of a genuine ratio scale for buffering strength. Here, I present a concept of buffering that overcomes these shortcomings. THEORY: Briefly, when, for instance, some "free" H(+ )ions are added to a solution (e.g. in the form of strong acid), buffering is said to be present when not all H(+ )ions remain "free" (i.e., bound to H(2)O), but some become "bound" (i.e., bound to molecules other than H(2)O). The greater the number of H(+ )ions that become "bound" in this process, the greater the buffering action. This number can be expressed in two ways: 1) With respect to the number of total free ions added as "buffering coefficient b", defined in differential form as b = d(bound)/d(total). This measure expresses buffering action from nil to complete by a dimensionless number between 0 and 1, analogous to probabilites. 2) With respect to the complementary number of added ions that remain free as "buffering ratio B", defined as the differential B = d(bound)/d(free). The buffering ratio B provides an absolute ratio scale, where buffering action from nil to perfect corresponds to dimensionless numbers between 0 and infinity, and where equal differences of buffering action result in equal intervals on the scale. Formulated in purely mathematical, axiomatic form, the concept reveals striking overlap with the mathematical concept of probability. However, the concept also allows one to devise simple physical models capable of visualizing buffered systems and their behavior in an exact yet intuitive way. CONCLUSION: These two measures of buffering action can be generalized easily to any arbitrary quantity that partitions into two compartments or states, and are thus suited to serve as standard units for buffering action. Some exemplary treatments of classical and non-classical buffering phenomena are presented in the accompanying paper

Implicit Peer Triplets in Gradient-Based Solution Algorithms for ODE Constrained Optimal Control

It is common practice to apply gradient-based optimization algorithms to numerically solve large-scale ODE constrained optimal control problems. Gradients of the objective function are most efficiently computed by approximate adjoint variables. High accuracy with moderate computing time can be achieved by such time integration methods that satisfy a sufficiently large number of adjoint order conditions and supply gradients with higher orders of consistency. In this paper, we upgrade our former implicit two-step Peer triplets constructed in [Algorithms, 15:310, 2022] to meet those new requirements. Since Peer methods use several stages of the same high stage order, a decisive advantage is their lack of order reduction as for semi-discretized PDE problems with boundary control. Additional order conditions for the control and certain positivity requirements now intensify the demands on the Peer triplet. We discuss the construction of 4-stage methods with order pairs (4,3) and (3,3) in detail and provide three Peer triplets of practical interest. We prove convergence for s-stage methods, for instance, order s for the state variables even if the adjoint method and the control satisfy the conditions for order s-1, only. Numerical tests show the expected order of convergence for the new Peer triplets.Comment: 47 pages, 5 figure

Long-term outcome of ten children with opsoclonus-myoclonus syndrome

Opsoclonus-myoclonus syndrome (OMS) in children is a rare neurological condition with opsoclonus, myoclonus, ataxia and irritability in the first 2 years of life. It can be idiopathic, parainfectious, or paraneoplastic with tumours of the neural crest. Few studies of long-term follow-up after OMS have been published. We investigated the motor, cognitive and behavioural outcome of ten patients (eight girls and two boys) seen between 1987 and 2002. We reviewed the records and reassessed the patients. A ganglioneuroma was found in one patient and a neuroblastoma in another. Tumour resection did not influence the OMS. The age at diagnosis was 10-24months and the follow-up period 1-17years (average 6.5years). The interval between the first signs and symptoms and starting treatment was 2-12weeks: treatment consisted of different immunosupressants. Remission was achieved within 5months in seven, and relapses were present in seven of ten. At follow-up, only one child had mild ataxia. IQ testing was performed in nine with scores below 75 in four and above 85 in four. Attention deficit and visuomotor difficulties led to school problems with special needs, also in those three children with normal IQs. Only two children were attending regular schools. Behavioural problems were reported in seven, and speech difficulties were present in five. In conclusion, the long-term outcome in our patients with OMS was dominated by cognitive and behavioural problems and not by ataxia. Compared with previous reports, our patients were treated earlier. Larger studies and uniform treatment protocols are needed to demonstrate whether early and prolonged immunosupressant therapy has a favourable influence on outcom

Vehicular Cooperative Maneuvers -- Quo Vaditis?

Vehicles will not only get more and more automated, but they will also cooperate in new ways. Currently, human-driven vehicles begin to communicate with each other using vehicle-to-everything technology. Future vehicles will use communication to share sensor data and even negotiate cooperative maneuvers. This lets them learn more about the environment and improves traffic flow and passenger comfort as more predictable maneuvers are likely to lead to a smoother ride. This paper introduces the most important concepts around cooperative vehicular maneuvers. We also summarize currently open challenges and questions to answer before a deployment can begin. Afterward, we give some perspectives on the further evolution of cooperative maneuvers and beyond.Comment: 8 pages incl. references and author biographies, 4 figures incl. multiple sub-figure

High Rate Proton Irradiation of 15mm Muon Drifttubes

Future LHC luminosity upgrades will significantly increase the amount of background hits from photons, neutrons and protons in the detectors of the ATLAS muon spectrometer. At the proposed LHC peak luminosity of 5*10^34 1/cm^2s, background hit rates of more than 10 kHz/cm^2 are expected in the innermost forward region, leading to a loss of performance of the current tracking chambers. Based on the ATLAS Monitored Drift Tube chambers, a new high rate capable drift tube detecor using tubes with a reduced diameter of 15mm was developed. To test the response to highly ionizing particles, a prototype chamber of 46 15mm drift tubes was irradiated with a 20 MeV proton beam at the tandem accelerator at the Maier-Leibnitz Laboratory, Munich. Three tubes in a planar layer were irradiated while all other tubes were used for reconstruction of cosmic muon tracks through irradiated and non-irradiated parts of the chamber. To determine the rate capability of the 15mm drift-tubes we investigated the effect of the proton hit rate on pulse height, efficiency and spatial resolution of the cosmic muon signals

Implicit A-Stable Peer Triplets for ODE Constrained Optimal Control Problems

This paper is concerned with the construction and convergence analysis of novel implicit Peer triplets of two-step nature with four stages for nonlinear ODE constrained optimal control problems. We combine the property of superconvergence of some standard Peer method for inner grid points with carefully designed starting and end methods to achieve order four for the state variables and order three for the adjoint variables in a first-discretize-then-optimize approach together with A-stability. The notion triplets emphasize that these three different Peer methods have to satisfy additional matching conditions. Four such Peer triplets of practical interest are constructed. In addition, as a benchmark method, the well-known backward differentiation formula BDF4, which is only A(73.3°)-stable, is extended to a special Peer triplet to supply an adjoint consistent method of higher order and BDF type with equidistant nodes. Within the class of Peer triplets, we found a diagonally implicit A(84°)-stable method with nodes symmetric in [0, 1] to a common center that performs equally well. Numerical tests with four well established optimal control problems confirm the theoretical findings also concerning A-stability

The Diabetes Self-Management Questionnaire (DSMQ): development and evaluation of an instrument to assess diabetes self-care activities associated with glycaemic control

BACKGROUND: Though several questionnaires on self-care and regimen adherence have been introduced, the evaluations do not always report consistent and substantial correlations with measures of glycaemic control. Small ability to explain variance in HbA(1c) constitutes a significant limitation of an instrument’s use for scientific purposes as well as clinical practice. In order to assess self-care activities which can predict glycaemic control, the Diabetes Self-Management Questionnaire (DSMQ) was designed. METHODS: A 16 item questionnaire to assess self-care activities associated with glycaemic control was developed, based on theoretical considerations and a process of empirical improvements. Four subscales, ‘Glucose Management’ (GM), ‘Dietary Control’ (DC), ‘Physical Activity’ (PA), and ‘Health-Care Use’ (HU), as well as a ‘Sum Scale’ (SS) as a global measure of self-care were derived. To evaluate its psychometric quality, 261 patients with type 1 or 2 diabetes were assessed with the DSMQ and an established analogous scale, the Summary of Diabetes Self-Care Activities Measure (SDSCA). The DSMQ’s item and scale characteristics as well as factorial and convergent validity were analysed, and its convergence with HbA(1c) was compared to the SDSCA. RESULTS: The items showed appropriate characteristics (mean item-total-correlation: 0.46 ± 0.12; mean correlation with HbA(1c): -0.23 ± 0.09). Overall internal consistency (Cronbach’s alpha) was good (0.84), consistencies of the subscales were acceptable (GM: 0.77; DC: 0.77; PA: 0.76; HU: 0.60). Principal component analysis indicated a four factor structure and confirmed the designed scale structure. Confirmatory factor analysis indicated appropriate fit of the four factor model. The DSMQ scales showed significant convergent correlations with their parallel SDSCA scales (GM: 0.57; DC: 0.52; PA: 0.58; HU: n/a; SS: 0.57) and HbA(1c) (GM: -0.39; DC: -0.30; PA: -0.15; HU: -0.22; SS: -0.40). All correlations with HbA(1c) were significantly stronger than those obtained with the SDSCA. CONCLUSIONS: This study provides preliminary evidence that the DSMQ is a reliable and valid instrument and enables an efficient assessment of self-care behaviours associated with glycaemic control. The questionnaire should be valuable for scientific analyses as well as clinical use in both type 1 and type 2 diabetes patients