There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

To study the operational behaviour of λ-terms, we will use the denotational (mathematical) approach. A denotational semantics for a language is based on the choice of a space of semantics values, or denotations, where terms are to be interpreted. Choosing a space with nice mathematical properties can help in proving the semantic properties of terms, since to this aim standard mathematical techniques can be used.

λ Δ -Models

The pancreatic islets are richly innervated by parasympathetic, sympathetic and sensory nerves. Several different neurotransmitters are stored within the terminals of these nerves, both the classical neurotransmitters, acetylcholine and noradrenaline, and several neuropeptides. The neuropeptides, vasoactive intestinal polypeptide, pituitary adenlyate cyclase activating polypeptide and gastrin releasing peptide are constituents of the parasympathetic nerves, whereas the neuropeptides galanin and neuropeptide Y are localised to sympathetic nerve terminals. Furthermore, the neuropeptide calcitonin gene-related peptide is localised to sensory nerves and cholecystokinin is also an islet neuropeptide, although the nature of the cholecystokinin nerves is not established. Stimulation of the autonomic nerves and treatment with neurotransmitters affect islet hormone secretion. Thus, insulin secretion is stimulated by parasympathetic nerves or their neurotransmitters and inhibited by sympathetic nerves or their neurotransmitters. The islet autonomic nerves seem to be of physiological importance in mediating the cephalic phase of insulin secretion, in synchronising the islets to function as a unit allowing oscillations of islet hormone secretion, and in optimising islet hormone secretion during metabolic stress, e.g. hypoglycaemia and neuroglycopenia. The autonomic nerves could also be involved in the islet adaptation to insulin resistance with possible implication for the development of glucose intolerance and Type II (non-insulin-dependent) diabetes mellitus. It is concluded that islet innervation, through the contribution of all branches of the autonomic nerves and several different neurotransmitters is of importance both for the physiology and pathophysiology of the islets.

/pdf/autonomic-regulation-of-islet-hormone-secretion-implications-3sqmygpev5.pdf

Autonomic regulation of islet hormone secretion--implications for health and disease.

The prognostic value of central systolic blood pressure has been established recently. At present, its noninvasive assessment is limited by the need of dedicated equipment and trained operators. Mo...

Validation of a Brachial Cuff-Based Method for Estimating Central Systolic Blood Pressure

In the European Society of Cardiology–European Society of Hypertension guidelines of the year 2007, the consequences of arterial stiffness and wave reflection on cardiovascular mortality have a major role. But the investigators claimed the poor availability of devices/methods providing easy and widely suitable measuring of arterial wall stiffness or their surrogates like augmentation index (AIx) or aortic systolic blood pressure (aSBP). The aim of this study was the validation of a novel method determining AIx and aSBP based on an oscillometric method using a common cuff (ARCSolver) against a validated tonometric system (SphygmoCor). aSBP and AIx measured with the SphygmoCor and ARCSolver method were compared for 302 subjects. The mean age was 56 years with an s.d. of 20 years. At least two iterations were performed in each session. This resulted in 749 measurements. For aSBP the mean difference was −0.1 mm Hg with an s.d. of 3.1 mm Hg. The mean difference for AIx was 1.2% with an s.d. of 7.9%. There was no significant difference in reproducibility of AIx for both methods. The variation estimate of inter- and intraobserver measurements was 6.3% for ARCSolver and 7.5% for SphygmoCor. The ARCSolver method is a novel method determining AIx and aSBP based on an oscillometric system with a cuff. The results agree with common accepted tonometric measurements. Its application is easy and for widespread use.

/pdf/a-new-oscillometric-method-for-pulse-wave-analysis-38e4r8nc3g.pdf

A new oscillometric method for pulse wave analysis: comparison with a common tonometric method.

Modeling arterial and left ventricular coupling for non-invasive measurements

Modelling SIR-type epidemics by ODEs, PDEs, difference equations and cellular automata – A comparative study

Laura, a very beautiful but also mysterious lady, inspired the famous poet Petrarch for poems, which express ecstatic love as well as deep despair. F. J. Jones – a scientist for literary work – recognized in these changes between love and despair an oscillating behaviour – from 1328 to 1350 – which he called Petrarch’s emotional cycle. The mathematician S. Rinaldi investigated this cycle and established a mathematical model based on ordinary differential equation: two coupled nonlinear ODEs, reflecting Laura’s and Petrarch’s emotions for each other, drive an inspiration variable, which coincides with Petrarch’s emotional cycle. These ODEs were the starting point for the investigations in two directions: mapping the mathematical model to a suitable modelling concept, and trying to extend the model for love dynamics in modern times (F. Breitenecker et al.). This contribution introduces and investigates amodelling approach for love dynamics and inspiration by means of System Dynamics, for Laura’s and Petrarch’s emotions as well as for a modern couple in love. In principle, emotions and inspiration emerge from a source and are fading into a sink. But the controlling parameters for increase and decrease of emotion create a broad variety of emotional behaviour and of degree of inspiration, because of the nonlinearities. Experiments including an implementation of this model approach and selected simulations provide interesting case studies for different kinds of love dynamics - attraction, rejection and neglect – stable equilibria and chaotic cycles.

/pdf/love-emotions-between-laura-and-petrarch-an-approach-by-31sjk7v61j.pdf

Love Emotions between Laura and Petrarch – an Approach by Mathematics and System Dynamics

To elucidate in vitro the transience of glucagon-induced hepatic glucose release, the effects of glucagon on hepatic glucose production and cAMP release were evaluated in the isolated rat liver preparation perfused by a nonrecirculating system. Glucagon was added to the infusate in stepwise increasing concentrations at 0, 60, and 100 min to give final concentrations of 2.5 X 10(-11), 10(-9), and 5 X 10(-8) M, respectively. Glucagon at 2.5 X 10(-11) M caused cAMP release [basal (mean +/- SD), 11.2 +/- 3.0 pmol/(min X 100 g BW)] to rise rapidly and plateau at 23.3 +/- 7.0 pmol/(min X 100 g BW), whereas hepatic glucose production [basal, 3.7 +/- 1.6 mumol/(min X 100 g BW)] increased only transiently to a maximum of 15.3 +/- 3.1 mumol/(min X 100 g BW) and fell thereafter. The enhanced cAMP release during the consecutive glucagon infusion was accompanied by a transient rise in hepatic glucose production during the second, but not during a third, glucagon infusion. When 3-isobutyl-1-methylxanthine, a potent phosphodiesterase inhibitor, was added to the perfusion medium (0.5 mM), the cAMP response to 2.5 X 10(-11) M glucagon was enhanced [247 +/- 124 pmol/(min X 100 g BW)] as was hepatic glucose production (+ 21%; P less than 0.05). Further augmentation of the glucagon concentration was followed by an increase in hepatic cAMP, but not glucose, release. When glucagon infusion (2.5 X 10(-11) M) was repeated with a glucagon-free period of 30 min in between, no stimulation of cAMP and consecutive glucose release was found during the second period. However, when the second glucagon dose was increased to 10(-9) M, glucose and cAMP release were again stimulated to the same extent as in experiments with no glucagon-free period in between. We conclude that the size of the glycogen pool and the cAMP concentration directly modulate hepatic glucose production and are responsible for evanescent glucagon action. This mechanism can be described by computer simulation.

Contribution by the glycogen pool and adenosine 3',5'-monophosphate release to the evanescent effect of glucagon on hepatic glucose production in vitro.

With the progress in modeling dynamic systems new extensions in model coupling are needed. The models in classical engineering are described by differential equations. Depending on the general condition of the system the description of the model and thereby the state space is altered. This change of system behavior can be implemented in different ways. In this work we focus on three state-of-the-art DAE simulation environments, Dymola, Mosilab and AnyLogic, and compare the possibilities of coupling of different state spaces. This can be done either using a parallel model setup, a serial model setup, or a combined model setup. The analogies and discrepancies are figured out on the basis of the classical constrained pendulum as defined in ARGESIM comparison C7.

/pdf/modeling-structural-dynamics-systems-in-modelica-dymola-1jtnllsrkv.pdf

Felix Breitenecker

Papers

Modeling arterial and left ventricular coupling for non-invasive measurements

Modelling SIR-type epidemics by ODEs, PDEs, difference equations and cellular automata – A comparative study

Love Emotions between Laura and Petrarch – an Approach by Mathematics and System Dynamics

Contribution by the glycogen pool and adenosine 3',5'-monophosphate release to the evanescent effect of glucagon on hepatic glucose production in vitro.

Modeling Structural - Dynamics Systems in MODELICA/Dymola; MODELICA/Mosilab and AnyLogic