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### Citations

1472 |
Exact stochastic simulation of coupled chemical reactions
- Gillespie
- 1977
(Show Context)
Citation Context ...Living cells are complex mixtures of a variety of complex molecules that are constantly undergoing reactions with one another, and such reactions typically have an exponential distribution associated =-=[7]-=-. Furthermore, stochastic fluctuations play a key role in biological processes, both at the molecular level, where low intracellular copy numbers of molecules can fundamentally limit the precision of ... |

913 |
Asymptotic analysis for periodic structures
- Bensoussan, Lions, et al.
- 1978
(Show Context)
Citation Context ...ples and the cell-level properties of the tissue — the macroscopic bidomain equations were not directly connected to the microstructure of the tissue. The advent of more formal homogenisation methods =-=[2]-=- paved the way for a first attempt at a rigorous derivation of the bidomain equations by Neu & Krassowska in 1993 [7]. They used a multiple-scales asymptotic expansion technique to convert the microsc... |

773 | The algorithmic analysis of hybrid systems
- Alur, Courcoubetis, et al.
- 1995
(Show Context)
Citation Context ...ng problem for the two counter machine can be reduced to the reachability problem of a particular class of hybrid automata, the reachability problem for hybrid automata itself is not always decidable =-=[1]-=-. However, if H is a T -hybrid automaton and T is a first-order decidable theory, then the reachability through a bounded number of discrete transitions can be characterized with a first-order decidab... |

679 | A.: The Theory of Hybrid Automata
- Henzinger
- 1996
(Show Context)
Citation Context ...lgebra (a subset of stochastic CCS), systems of reactions in the stoichiometric form and ODE systems. Bortolussi and Policriti [6] extend this work by defining a semantics in terms of hybrid automata =-=[11]-=-, defining the requisites according to which a set of processes can be treated as discrete control states, while others have the usual continuous interpretation. Several other methods for associating ... |

530 |
Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties.
- Gray, M, et al.
- 1989
(Show Context)
Citation Context ...] and they were observed in the thalamus [18], and in the cortex [17]. Many studies suggested that, in the mammalian visual system, neurons signals may be group together through in-phase oscillations =-=[11]-=-. Because of this, the development and analysis of models representing oscillatory phenomena assume a great importance in understanding the neurophysiological activities. A simple continuous model of ... |

411 | Control of systems integrating logic, dynamics, and constraints
- Bemporad, Morari
- 1999
(Show Context)
Citation Context ...1}. 3 Hybrid semantics and optimal control of infectious processes In this section we define the optimal control law for therapy scheduling in the SIR model by means of Model Predictive Control (MPC) =-=[4]-=-, and we report the optimally controlled solutions with parameters that are typical of the measles [20]. A similar problem has been addressed in [21] for the scheduling of hormone therapy in a model f... |

373 | What's decidable about hybrid automata
- Henzinger, Kopke, et al.
- 1995
(Show Context)
Citation Context ...hniques 3.1 Noise and Disturbed Automata The density of continuous variables provide an unbounded quantity of memory within a bounded region. As a matter of fact, the undecidability results proved in =-=[13]-=- are based on the possibility of embedding N in (0,1]⊆ R through the function f (n) = 2−n. However, Fränzle in [7] observed that noise disturbes the trajectiories of real hybrid systems, augmenting t... |

234 | PRISM: Probabilistic symbolic model checker
- Kwiatkowska, Norman, et al.
- 2002
(Show Context)
Citation Context ...s the differences in bone density by evaluating the dynamics of the bone remodeling process being in a certain state. This kind of data can be elaborated by means of automatic verification procedures =-=[11]-=-. We believe that this kind of quantitative, formal and automated analysis may represent a step ahead in the understanding of the modeling efforts of osteoporosis development, by shifting the attentio... |

226 |
Reconstruction of the action potential of ventricular myocardial fibers
- Beeler, Reuter
- 1977
(Show Context)
Citation Context ...tem, given by the modified bidomain equations (19), and the discrete system, given in [(1),(2),(3),(4)] with the transmembrane current given by (15), using a Beeler-Reuter model for the ionic current =-=[1]-=- in both cases. We use a finite element method [9] with 320 nodes per cell in the discrete case and 80 nodes covering the corresponding area in the continuum case, and use the PETSc library (http://ww... |

146 |
The functional states of the thalamus and the associated neuronal interplay.
- STERIADE, LLINAS
- 1988
(Show Context)
Citation Context ...important role in the activities of several brain regions. Some examples of brain locations in which it has been demonstrated the central role of neural oscillations are the cortex [17], the thalamus =-=[18]-=-, and the olfactory information processing [8]. With the aim of understanding neurophysiological activities, we propose the modeling of oscillatory phenomena exploiting hybrid automata. A continuous m... |

130 | Redlog: Computer algebra meets computer logic.
- Dolzmann, Sturm
- 1997
(Show Context)
Citation Context ...mplified as: φ [X,T]≡ ∃X0(Π1JX0,TK∧Π2JX0,TK∧δ (X0,X)< ε). (8) Similarly, ψ becomes: ψ[X]≡ ∃T(T> 0∧∃X0(Π1JX0,TK∧Π2JX0,TK∧δ (X0,X)< ε)). (9) So we plugged this last formula in Formula 5 and used REDLOG =-=[5]-=- to test it. The formula turns out to be true (the result is computed within few seconds), proving our conjectures. Notice that we used Maxima to compute the exact coordinates of the points on the lim... |

104 | Approximation metrics for discrete and continuous systems
- Girard, Pappas
- 2007
(Show Context)
Citation Context ...For these reasons, we study our hybrid automaton exploiting different approximation techniques that introduce noise. In the literature, several approximation techniques have been proposed (see, e.g., =-=[7, 16, 10, 3, 15]-=-). Fränzle in [7] presents a model of noise over hybrid automata. The introduction of noise ensures in many cases the (semi-)decidability of the reachability problem. Another result of (semi-)decidab... |

81 | R.: Model checking continuous time Markov chains
- Aziz, Sanwal, et al.
- 2000
(Show Context)
Citation Context ... variability of the bone density could address the investigation of metabolic syndrome, diabetes and cancer. The logical properties to verify have been formulated in CSL (Continuous Stochastic Logic) =-=[1]-=-, and are: 88 Verification instances for bone pathologies • The cumulative values of bone formation and resorption. f+(t) : R{“boneFormed′′}=?[C ≤ t], f−(t) : R{“boneResorbed′′}=?[C ≤ t], t = 0,10, . ... |

62 |
Intrinsic oscillations of neocortex generated by layer 5 pyramidal neurons.
- LR, Amitai, et al.
- 1991
(Show Context)
Citation Context ...muli which play an important role in the activities of several brain regions. Some examples of brain locations in which it has been demonstrated the central role of neural oscillations are the cortex =-=[17]-=-, the thalamus [18], and the olfactory information processing [8]. With the aim of understanding neurophysiological activities, we propose the modeling of oscillatory phenomena exploiting hybrid autom... |

58 |
Contributions to the mathematical theory of epidemics. ii. the problem of endemicity.
- Kermack, McKendrick
- 1932
(Show Context)
Citation Context ...into compartments:Susceptible, Exposed, Infected and Recovered. According to the possible flows among such compartments, different variants arises, like the SIR (Susceptible→Infected→Recovered) model =-=[12]-=-, SIS, SIRS, SEIR and SEIRS. Further compartments can be taken into account like the population of immune infants, usually indicated with M. Similar compartments can be identified not only at the huma... |

57 | Analysis of signalling pathways using continuous time Markov chains.
- Calder, Vyshemirsky, et al.
- 2006
(Show Context)
Citation Context ...listic automata, and probabilistic timed automata. The PRISM model checker have been successfully employed in a several number of biological case studies, especially for modeling biochemical pathways =-=[12, 6, 2, 16]-=-. However, our framework is not determined by the features of a specific tool, and other similar platforms could have been chosen. 2.2 Definition of the model In our settings, we use Continuous Time M... |

43 |
Role of gap junctions in the propagation of the cardiac action potential. Cardiovasc Res 62:309–322.
- Rohr
- 2004
(Show Context)
Citation Context ... potential propagation at cell-level, we therefore expect to see the conduction velocity reduce as the wave passes through the gap junction. Indeed, this is supported by experimental data as shown in =-=[11]-=- — the spatial form of the action potential is ‘stepped’, with the reduced conductivity in the gap junction causing a steep jump in membrane potential between one side of the gap junction and the othe... |

41 | Analysis of hybrid systems: an ounce of realism can save an infinity of states, in
- Fränzle
- 1999
(Show Context)
Citation Context ...For these reasons, we study our hybrid automaton exploiting different approximation techniques that introduce noise. In the literature, several approximation techniques have been proposed (see, e.g., =-=[7, 16, 10, 3, 15]-=-). Fränzle in [7] presents a model of noise over hybrid automata. The introduction of noise ensures in many cases the (semi-)decidability of the reachability problem. Another result of (semi-)decidab... |

34 |
Spatial EEG patterns, non-linear dynamics and perception. Brain Res Rev 10:147-175
- Freeman, CA
- 1985
(Show Context)
Citation Context ...in regions. Some examples of brain locations in which it has been demonstrated the central role of neural oscillations are the cortex [17], the thalamus [18], and the olfactory information processing =-=[8]-=-. With the aim of understanding neurophysiological activities, we propose the modeling of oscillatory phenomena exploiting hybrid automata. A continuous model of a single oscillator based on an ordina... |

31 |
Oscillations and synchronization in neural networks: an exploration of the labelling hypothesis
- Atiya, Baldi
- 1989
(Show Context)
Citation Context ... τ ∗λ ≤ 1, then the point 〈0,0〉 is the unique global attractor of the system, if, otherwise, τ ∗λ > 1, the origin is an unstable equilibrium and all the evolutions converge to a limit cycle attractor =-=[2]-=-. A simulation of f (3,1) is represented in Fig. 4(a). 62 Hybrid Automata and ε-Analysis on a Neural Oscillator Xe Xi Ẋe =−Xeτ Ẋi =−Xiτ +2 v0 Ẋe =−Xeτ −2 Ẋi =−Xiτ v1 Ẋe =−Xeτ Ẋi =−Xiτ −2 v2 Ẋe ... |

27 | D.: Qualitative analysis and verification of hybrid models of genetic regulatory networks: Nutritional stress response in Escherichia coli
- Batt, Ropers, et al.
- 2005
(Show Context)
Citation Context ...ance, genetic regulatory networks naturally exhibits hybrid dynamics, for which the continuous concentration of proteins is interrupted by the discrete switches dictated by changes in gene expression =-=[3, 10]-=-. Moreover in population biology it happens that some species are present in high concentration, so they can be approximately modelled by continuous variables; conversely, small populations are opport... |

25 | Using probabilistic model checking in systems biology
- Kwiatkowska, Norman, et al.
(Show Context)
Citation Context ...listic automata, and probabilistic timed automata. The PRISM model checker have been successfully employed in a several number of biological case studies, especially for modeling biochemical pathways =-=[12, 6, 2, 16]-=-. However, our framework is not determined by the features of a specific tool, and other similar platforms could have been chosen. 2.2 Definition of the model In our settings, we use Continuous Time M... |

21 | Processes to ODEs by Chemistry.
- Cardelli
- 2008
(Show Context)
Citation Context ... are a formal notation initially developed for modelling software systems, but in the last decade it has been extensively used and extended in order to describe biological systems. In a seminal paper =-=[7]-=-, Cardelli showed that a subset of stochastic CCS is powerful enough to encode both systems of reactions in the stoichiometric form and systems of ordinary differential equations. Additionally, a rece... |

14 |
Cellular and molecular mechanisms of bone remodeling
- Raggatt, Partridge
- 2010
(Show Context)
Citation Context ...units are finishing [10]. In the normal bone, the number of BMUs, the bone resorption rate, and the bone formation rate are all relatively constant depending on hormones, vascularization and genetics =-=[17]-=-. In cortical BMUs, osteoclasts excavate cylindrical tunnels in the predominant loading direction of the bone. They are followed by osteoblasts, filling the tunnel, creating secondary osteons of renew... |

13 |
Developing the use of process algebra in the derivation and analysis of mathematical models of infectious disease
- Norman, Shankland
- 2003
(Show Context)
Citation Context ...which [9, 5]. The formal modelling language employed in this paper is called Disease Chemical Ground Form (DCGF), and it is a variant of CGF for describing complex disease processes. Differently from =-=[17]-=-, where a stochastic process algebra and its continuous semantics are used to describe a classical epidemic model, we attempt to provide a framework for more generic diseases and, although the syntax ... |

9 |
A biophysical model for defibrillation of cardiac tissue
- Keener, Panfilov
- 1996
(Show Context)
Citation Context ...s is presented later in this document (see Section 2.2), and as discussed earlier it is the generally accepted model of cardiac tissue behaviour. A more formal derivation of the model can be found in =-=[5]-=-. Whilst realistic simulations using the bidomain model have been demonstrated, these studies tend to take the bidomain equations as being physiologically correct in all circumstances, and empirical p... |

8 |
Homogenization of syncytial tissues, Critical reviews in biomedical engineering 21
- Neu, Krassowska
- 1993
(Show Context)
Citation Context ...the microstructure of the tissue. The advent of more formal homogenisation methods [2] paved the way for a first attempt at a rigorous derivation of the bidomain equations by Neu & Krassowska in 1993 =-=[7]-=-. They used a multiple-scales asymptotic expansion technique to convert the microscopic problem, formulated in terms of the pointwise potentials, to a macroscopic problem formulated in terms of the le... |

7 |
2004 Qualitative simulation of genetic regulatory networks using piecewise-linear models.max satisfies the conditions for theorem 2.2 in L be a compact a or v limit set of an irreor competitive system in R3. If L contains is a closed orbit.’ Poincaré–Ben
- Jong, Gouze, et al.
(Show Context)
Citation Context ...analysis and composition can be made. Trying to linearize the non-linear components of the original continuous model, we first replace in the standard way the sigmoidal behaviours with sign functions =-=[9, 14]-=-, approximating continuos signals with discrete off-on signals. Unfortunately, the behaviour of this model differs from the original one. For this reason, we propose a more sophisticated approximation... |

7 | Safety verification of non-linear hybrid systems is quasisemidecidable.
- Ratschan
- 2010
(Show Context)
Citation Context ...For these reasons, we study our hybrid automaton exploiting different approximation techniques that introduce noise. In the literature, several approximation techniques have been proposed (see, e.g., =-=[7, 16, 10, 3, 15]-=-). Fränzle in [7] presents a model of noise over hybrid automata. The introduction of noise ensures in many cases the (semi-)decidability of the reachability problem. Another result of (semi-)decidab... |

6 |
Sguanci L (2007) Risk perception in epidemic modeling
- Bagnoli, Liò
(Show Context)
Citation Context ...ocess; or in an infection scenario, the cognitive behaviour at the human level that avoids or limits the interactions with other individuals possibly affected by the disease. A work by Bagnoli et al. =-=[1]-=- embeds this aspect of human behaviour into a SIR epidemic model by allowing individuals to perceive the risk of being infected by ill neighbours. Therefore, the use of control-theoretic tools seems p... |

6 | HYPE: a process algebra for compositional flows and emergent behaviour. In:
- Galpin, Bortolussi, et al.
- 2009
(Show Context)
Citation Context ...discrete control states, while others have the usual continuous interpretation. Several other methods for associating hybrid semantics to quantitative process algebras have been proposed, among which =-=[9, 5]-=-. The formal modelling language employed in this paper is called Disease Chemical Ground Form (DCGF), and it is a variant of CGF for describing complex disease processes. Differently from [17], where ... |

6 |
F (2010) The central regulation of bone mass, the first link between bone remodeling and energy metabolism
- Karsenty, Oury
(Show Context)
Citation Context ...echanosensing micro-fractures and to send signals to the BMU cells. This process is highly dynamic and each BMU has a finite lifetime, so new units are continuously forming as old units are finishing =-=[10]-=-. In the normal bone, the number of BMUs, the bone resorption rate, and the bone formation rate are all relatively constant depending on hormones, vascularization and genetics [17]. In cortical BMUs, ... |

5 | Inclusion dynamics hybrid automata - Casagrande, Piazza, et al. |

5 |
CJ (2001) Lateral inhibition through Delta-Notch signaling: A piecewise affine hybrid model
- Ghosh, Tomlin
(Show Context)
Citation Context ...analysis and composition can be made. Trying to linearize the non-linear components of the original continuous model, we first replace in the standard way the sigmoidal behaviours with sign functions =-=[9, 14]-=-, approximating continuos signals with discrete off-on signals. Unfortunately, the behaviour of this model differs from the original one. For this reason, we propose a more sophisticated approximation... |

5 |
Synchronization and desynchronization of neural oscillators
- Tonnelier, Meignen, et al.
- 1999
(Show Context)
Citation Context ...ogical activities, we propose the modeling of oscillatory phenomena exploiting hybrid automata. A continuous model of a single oscillator based on an ordinary differential system has been proposed in =-=[19]-=-. Even if this is a simple model, its analysis and the analysis of its composition in multiple copies is limited due to the non-linearity of the ordinary differential system involved. For this reason,... |

5 |
Osteoprotegerin, RANKL and bone turnover in postmenopausal osteoporosis
- Jabbar, Drury, et al.
- 2011
(Show Context)
Citation Context ...jor determinant of bone mass and strength [8]. In particular, recent works show that the levels of OPG and RANKL are inversely related to bone density, and may lead to the development of osteoporosis =-=[9]-=-. Our previous work [15] shows how small changes in RANKL for very long periods lead to disease conditions, especially when aging factors are involved. In particular, we have simulated the bone remode... |

3 |
Multiple Verification in Complex Biological Systems: The Bone Remodelling Case Study
- Bartocci, Liò, et al.
(Show Context)
Citation Context ...monstrates the effectiveness of a hybrid approach where a process-algebraic specification level is translated into a runnable stochastic agent-based model in the bone remodelling case study, while in =-=[2]-=- the same case study is approached with different semantics according to the biological property to analyse. Consequently, formal languages could represent a wrapping language able to homogeneously de... |

3 |
Policriti (2009): Hybrid Dynamics of Stochastic Programs
- Bortolussi, A
(Show Context)
Citation Context ...ow several encodings can be implemented among specifications in the CGF algebra (a subset of stochastic CCS), systems of reactions in the stoichiometric form and ODE systems. Bortolussi and Policriti =-=[6]-=- extend this work by defining a semantics in terms of hybrid automata [11], defining the requisites according to which a set of processes can be treated as discrete control states, while others have t... |

3 |
Multiscale Modeling of the Skeletal System
- Viceconti
- 2012
(Show Context)
Citation Context ...d of single-scale models, describing the biological process at different characteristic space-time scales, and scale bridging models, which define how the singlescale models are coupled to each other =-=[22]-=-. Higher level languages and formalisms can help in giving a general homogeneous formulation for the different scales in a multiscale biological system. In general, that formal description cannot be d... |

3 |
2010): Physiology and pathophysiology of the RANKL/RANK system
- Hanada, Hanada, et al.
- 1515
(Show Context)
Citation Context .... In this way, OPG inhibits the production of osteoclasts, thus protecting bone from excessive resorption. The relative concentration of RANKL in bone is a major determinant of bone mass and strength =-=[8]-=-. In particular, recent works show that the levels of OPG and RANKL are inversely related to bone density, and may lead to the development of osteoporosis [9]. Our previous work [15] shows how small c... |

2 |
Policriti (2009): Discrete Semantics for Hybrid Automata. Discrete Event Dynamic Systems 19(4
- Casagrande, Piazza, et al.
(Show Context)
Citation Context |

2 |
Dullerud (2009): Verifying Tolerant Systems Using Polynomial Approximations
- Prabhakar, Vladimerou, et al.
(Show Context)
Citation Context |

2 |
Zavattaro (2008): On the computational power of biochemistry. Algebraic Biology
- Cardelli, G
(Show Context)
Citation Context ...ses where discrete intervention policies has to be modelled. 2.1 The Disease Chemical Ground Form Here we present the Disease Chemical Ground Form (D-CGF), a variant of the Chemical Ground Form (CGF) =-=[8]-=-) targeted to describe complex models of disease in a process-algebraic fashion. The syntax of D-CGF is given by the grammar in Table 1. A D-CGF model is given by a set of species S, an initial popula... |

2 |
Merelli & L. Tesei (2010): Shape Calculus. A Spatial Mobile Calculus for 3D Shapes. Scientific Annals of Computer Science 20. Available at http://www.doaj.org/ doaj?func=abstract&id=655401
- Bartocci, Corradini, et al.
(Show Context)
Citation Context ...deling Liò, Merelli & Paoletti 83 approaches that can handle multiple intracellular and extracellular factors acting on different time and space scales. Previous work has focused on a Shape Calculus =-=[4, 3]-=- approach to bone remodeling [13]. In this paper new models provide a way to integrate both discrete and continuous behavior that are used to represent individual cells (as agents) and concentration o... |

2 |
Smolka (2011): Model Repair for Probabilistic Systems
- Bartocci, Grosu, et al.
(Show Context)
Citation Context ...ired direction would be reverse engineering from patient datasets, which in turn will allow to fine tuning the diagnosis. In addition, we aim at using parametric probabilistic model repair techniques =-=[5]-=- for our model. The problem of model repair is, roughly speaking, “given a probabilistic model M and a formula not satisfied by M, finding a M′ that satisfy the formula and such that the cost of modif... |

2 |
Viceconti M (2011) A combined process algebraic and stochastic approach to bone remodeling
- Liò, Merelli, et al.
(Show Context)
Citation Context ...approaches that can handle multiple intracellular and extracellular factors acting on different time and space scales. Previous work has focused on a Shape Calculus [4, 3] approach to bone remodeling =-=[13]-=-. In this paper new models provide a way to integrate both discrete and continuous behavior that are used to represent individual cells (as agents) and concentration or density fields (as environment)... |

1 |
Enderton (2001): A Mathematical Introduction to Logic, II edition
- B
(Show Context)
Citation Context ...2∧X = 3). Finally, if ϕ[X1, . . . ,Xi, . . . ,Xn] then we may denote the formula ϕJXi/~sK by writing ϕJX1, . . . ,~s, . . . ,XnK. The semantics of a formula is defined in the standard way (see. e.g., =-=[6]-=-). Given a set Γ of sentences and a sentence ϕ , we say that ϕ is a logical consequence of Γ (denoted, Γ |= ϕ) if ϕ is valid in any modelM in which each formula of Γ is valid too (M |= Γ). A theory T ... |

1 |
Bartocci (2011): From cardiac cells to genetic regulatory networks. In: Computer Aided Verification
- Grosu, Batt, et al.
(Show Context)
Citation Context ...Xe)+hλ ,α(Xi) , (4) A. Casagrande, T. Dreossi & C. Piazza 63 whose corresponding hybrid automaton is depicted in Fig. 3. A different approximation could be obtained by using the technique proposed in =-=[12]-=-. Xe Xi Xe =−αλ Xe = αλ Xi =−αλ Xi = αλ Ẋe = τ∗λ−ατ∗α Xe− λαXi Ẋi = λαXe+ τ∗λ−α τ∗α Xi v0 Ẋe =−Xeτ − λαXi−1 Ẋi = τ∗λ−ατ∗α Xi−1 v1 Ẋe =−Xeτ Ẋi =−Xiτ −2 v2 Ẋe = τ∗λ−ατ∗α Xe+1 Ẋi = λαXe− Xiτ −1 v... |

1 |
Hillston & M. Tribastone (2010): Hybrid semantics for PEPA
- Bortolussi, Galpin, et al.
(Show Context)
Citation Context ...discrete control states, while others have the usual continuous interpretation. Several other methods for associating hybrid semantics to quantitative process algebras have been proposed, among which =-=[9, 5]-=-. The formal modelling language employed in this paper is called Disease Chemical Ground Form (DCGF), and it is a variant of CGF for describing complex disease processes. Differently from [17], where ... |

1 |
Multi-Parametric Toolbox (MPT). Available at http:// control.ee.ethz.ch/~mpt
- Kvasnica, Grieder, et al.
- 2004
(Show Context)
Citation Context ...cancer. In order to cope with the nonlinear dynamics of the SIR model, the optimal scheduling of multiple therapies is computed by solving an on-line MPC problem in the Multi-Parametric Toolbox (MPT) =-=[13]-=-. P. Liò, E. Merelli & N. Paoletti 163 The optimal control law can be formulated by means of the following constrained finite-time optimal control (CFTOC) problem, where the original continuous-time ... |

1 |
2011): SHAVE: stochastic hybrid analysis of markov population models
- Lapin, Mikeev, et al.
(Show Context)
Citation Context ... some species are present in high concentration, so they can be approximately modelled by continuous variables; conversely, small populations are opportunely modelled as discrete stochastic variables =-=[14]-=-. Another crucial aspect is related to the self-regulation and control of biological systems: in normal conditions, biological entities and functions are self-regulated and several multiscale control ... |

1 |
Merelli & Viceconti M. (2012): Modelling osteomyelitis
- Liò, Paoletti, et al.
(Show Context)
Citation Context ...t acts as a bacteriostatic agent, and is usually combined with other antibiotics. Based on a recent work of the authors about the modelling of osteomyelitis and the comparison of different treatments =-=[15]-=-, we can define a hybrid version of that model and a treatment strategy combining antibiotic and anti-inflammatory therapies. The model describes how the bone remodelling dynamics of osteoblasts’ (Ob)... |

1 |
Lamnabhi-Lagarrigue et al. (2009): Handbook of hybrid systems control: theory, tools, applications
- Lunze, F
(Show Context)
Citation Context ...ets. 2.2.1 Hybrid dynamical system of D-CGF models Here we describe the semantics of a D-CGF model in terms of a particular class of hybrid dynamical systems, called controlled switched systems (CSS) =-=[16]-=-. While in the general formulation of hybrid dynamical system the external control input and the discrete operation mode are distinct, in a CSS the external controller produces a switching signal (i.e... |

1 |
Viceconti (2011): Osteoporosis: a multiscale modeling viewpoint
- Paoletti, Lió, et al.
(Show Context)
Citation Context ...TMC), ordinary/partial differential equations (ODE/PDE), agent-based models (ABM), or finite state machines (FSM). Such heterogeneous semantics can be wrapped by a common formal language. the authors =-=[18, 19]-=- demonstrates the effectiveness of a hybrid approach where a process-algebraic specification level is translated into a runnable stochastic agent-based model in the bone remodelling case study, while ... |

1 |
Merelli & M. Viceconti (2012): Multi-level Computational Modeling and Quantitative Analysis of Bone Remodeling
- Paoletti, Liò, et al.
(Show Context)
Citation Context ...TMC), ordinary/partial differential equations (ODE/PDE), agent-based models (ABM), or finite state machines (FSM). Such heterogeneous semantics can be wrapped by a common formal language. the authors =-=[18, 19]-=- demonstrates the effectiveness of a hybrid approach where a process-algebraic specification level is translated into a runnable stochastic agent-based model in the bone remodelling case study, while ... |

1 |
Agur (2000): Theoretical examination of the pulse vaccination policy
- Stone, Shulgin, et al.
(Show Context)
Citation Context ...al control law for therapy scheduling in the SIR model by means of Model Predictive Control (MPC) [4], and we report the optimally controlled solutions with parameters that are typical of the measles =-=[20]-=-. A similar problem has been addressed in [21] for the scheduling of hormone therapy in a model for prostate cancer. In order to cope with the nonlinear dynamics of the SIR model, the optimal scheduli... |

1 |
Aihara (2010): Piecewise affine systems modelling for optimizing hormone therapy of prostate cancer
- Suzuki, Bruchovsky, et al.
(Show Context)
Citation Context ...IR model by means of Model Predictive Control (MPC) [4], and we report the optimally controlled solutions with parameters that are typical of the measles [20]. A similar problem has been addressed in =-=[21]-=- for the scheduling of hormone therapy in a model for prostate cancer. In order to cope with the nonlinear dynamics of the SIR model, the optimal scheduling of multiple therapies is computed by solvin... |

1 |
Wasilewska (2008): Learning and Detecting Emergent Behavior
- Grosu, Bartocci, et al.
(Show Context)
Citation Context ...al morphology of the action potential [13]. The model was further refined to study more specific conditions associated with action potential morphology such as early depolarisation [14], spiral waves =-=[3]-=-, and tachycardia [4]. Whilst these models allow efficient and precise analysis of the conditions required for such phenomena, they are not focused on the incorporation of the cell microstructure and ... |

1 |
Bartocci (2011): From Cardiac
- Grosu, Batt, et al.
(Show Context)
Citation Context ...action potential [13]. The model was further refined to study more specific conditions associated with action potential morphology such as early depolarisation [14], spiral waves [3], and tachycardia =-=[4]-=-. Whilst these models allow efficient and precise analysis of the conditions required for such phenomena, they are not focused on the incorporation of the cell microstructure and the corresponding eff... |

1 |
Sneyd (2001): Mathematical Physiology, corrected edition
- Keener, J
(Show Context)
Citation Context ...and σi is the (scalar) conductivity of the intracellular space. The form of the current comes from Ohm’s law which states that current is the product of conductivity and the gradient of the potential =-=[6]-=-. Conservation D.A. Bruce, P. Pathmanathan & J.P. Whiteley 5 6 ff - x σi, φi y σe, φe Ω (a) A representation of cardiac cells in 2D. σi and σe are, respectively, the intracellular and extracellular co... |

1 |
Gavaghan (2010): A numerical guide to the solution of the bidomain equations of cardiac electrophysiology
- Pathmanathan, Bernabeu, et al.
(Show Context)
Citation Context ...feasible even for very small regions of tissue. It is much more efficient to solve these models using a continuum approximation to the equations, and indeed over the last 20 years many have done this =-=[8]-=-. This continuum model relies on a homogenisation technique to construct a suitable approximation to the discrete model. The homogenisation process uses a multiple-scales method which uses the fact th... |

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Introduction to the Finite Element Method, 2 edition
- Reddy
- 1993
(Show Context)
Citation Context ..., and the discrete system, given in [(1),(2),(3),(4)] with the transmembrane current given by (15), using a Beeler-Reuter model for the ionic current [1] in both cases. We use a finite element method =-=[9]-=- with 320 nodes per cell in the discrete case and 80 nodes covering the corresponding area in the continuum case, and use the PETSc library (http://www.mcs.anl.gov/petsc) to solve the resulting linear... |

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Chapman (2011): Derivation of the Bidomain Equations for a Beating Heart with a General Microstructure
- Richardson, J
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Citation Context ...ult being that the mechanism for defibrillation was clarified. It is a version of this derivation that will be presented later in this document. Following this, a recent paper by Richardson & Chapman =-=[10]-=- augmented the above derivation by introducing a co-ordinate transformation that allows for variable tissue structure and ultimately a set of bidomain equations in which the conductivity tensors syste... |

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A bi-domain model for ischemic myocardial D-C potentials
- Tung
- 1978
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Citation Context ...omputationally desirable to homogenise the microstructure to allow us to pose the problem as a continuum rather than a discrete problem. This led to the proposal of the bidomain model by Tung in 1978 =-=[12]-=- in which the homogenised potentials are solved for via two reaction-diffusion equations using averaged conductivities, where the precise form of averaging arises from the homogenisation technique. A ... |

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Smolka (2005): Efficient modeling of excitable cells using hybrid automata. In
- Ye, Entcheva, et al.
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Citation Context ...c electrophysiology In recent years, models based on hybrid automata have been developed to model networks of excitable cells, with an initial focus on the temporal morphology of the action potential =-=[13]-=-. The model was further refined to study more specific conditions associated with action potential morphology such as early depolarisation [14], spiral waves [3], and tachycardia [4]. Whilst these mod... |

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Entcheva (2008): Formal Analysis of Abnormal Excitation
- Ye, Grosu, et al.
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Citation Context ...focus on the temporal morphology of the action potential [13]. The model was further refined to study more specific conditions associated with action potential morphology such as early depolarisation =-=[14]-=-, spiral waves [3], and tachycardia [4]. Whilst these models allow efficient and precise analysis of the conditions required for such phenomena, they are not focused on the incorporation of the cell m... |

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Troina (2005): A probabilistic model for molecular systems
- Barbuti, Cataudella, et al.
(Show Context)
Citation Context ...listic automata, and probabilistic timed automata. The PRISM model checker have been successfully employed in a several number of biological case studies, especially for modeling biochemical pathways =-=[12, 6, 2, 16]-=-. However, our framework is not determined by the features of a specific tool, and other similar platforms could have been chosen. 2.2 Definition of the model In our settings, we use Continuous Time M... |

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Merelli & L. Tesei (2010): Shape Calculus: Timed Operational Semantics and Well-formedness. Scientific Annals of Computer Science 20. Available at http: //arxiv.org/abs/1011.2488
- Bartocci, Cacciagrano, et al.
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Citation Context ...deling Liò, Merelli & Paoletti 83 approaches that can handle multiple intracellular and extracellular factors acting on different time and space scales. Previous work has focused on a Shape Calculus =-=[4, 3]-=- approach to bone remodeling [13]. In this paper new models provide a way to integrate both discrete and continuous behavior that are used to represent individual cells (as agents) and concentration o... |

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2010): What old means to bone. Trends
- Manolagas, Parfitt
- 1016
(Show Context)
Citation Context ..., as a result of mechanisms involving bone remodeling, very often a net bone loss is seen. In order to maintain the mechanical properties of the bones, old bone is continuously replaced by new tissue =-=[14]-=-. However, pathological conditions can alter the equilibrium between bone resorption and bone formation; osteoporosis, and often osteomyelitis and bone cancer, are examples of pathologies with negativ... |

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Bošnački & T.M. Breit (2007): Stochastic modeling of codon bias with PRISM
- Pronk, Vink, et al.
- 2007
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