Double sweep preconditioner for optimized Schwarz methods applied to the Helmholtz problem This paper presents a preconditioner for non-overlapping Schwarz methods applied to the Helmholtz problem. Starting from a simple analytic example, we show how such a preconditioner can be designed by approximating the inverse of the iteration operator for a layered partitioning of the domain. The preconditioner works by propagating information globally by concurrently sweeping in both directions over the subdomains, and can be interpreted as a coarse grid for the domain decomposition method. The resulting algorithm is shown to converge very fast, independently of the number of subdomains and frequency. The preconditioner has the advantage that, like the original Schwarz algorithm, it can be implemented as a matrix-free routine, with no additional preprocessing. Solving the Helmholtz equation numerically is a notoriously difficult problem, especially in the highfrequency regime, when the wavelength is much smaller than the size of the domain under study [1] . When solving the problem using a grid-based volume approach like the Finite Element Method (FEM), the number of unknowns becomes so large that the direct solution of the resulting linear system is computationally intractable. On the other hand, most iterative methods that have proved successful for elliptic problems become inefficient when applied to problems with highly oscillatory solutions [1] . Domain Decomposition Methods (DDM) try to combine both direct and iterative approaches, by decomposing the original domain into smaller subdomains over which a direct solution of the Helmholtz problem is possible, and then iterating over the subdomains until the solutions match. When the subdomains do not overlap, the problem can be reformulated in terms of unknown sources on the boundaries between the subdomains, linked to impedance-type transmission conditions between the subdomains. The solution produced by these sources inside the individual subdomains must match the restriction of the solution of the full problem on the subdomains. Such a formulation falls into the framework of Schwarz methods [2, 3, 4, 5] ; recent improvements in the approximation of the transmission operators have made its convergence rate little sensitive to the wavenumber and discretization density [6, 7] .. However, a remaining limitation of Schwarz methods is that, even with optimal transmission conditions, the number of iterations increases linearly with the number of subdomains. This limitation has been successfully addressed for certain classes of problems, by adding a component to the algorithm that is known in the DDM community as a "coarse grid" [8, 9, 10, 11, 12] . This generic name refers to any technique that enables global sharing of information between subdomains, while the basic additive algorithm only allows local exchange of information, hence hampering convergence (note that multiplicative Schwarz algorithms enable long range exchange of information in one direction only, and cannot guarantee a convergence rate independent of the number of subdomains.) While coarse grids have proven to be very effective for Laplace-type problems, designing effective coarse grids for high-frequency Helmholtz problems proves difficult [11, 12] .. Another way to look at the problem is to recast the DDM as the solution of a linear system, in which case it is natural to search for a preconditioner that would efficiently speed up the convergence of the solver. This paper explores that idea and contributes a way to precondition optimized Schwarz algorithms by taking advantage of recent advances in the development of efficient absorbing boundary conditions for the Helmholtz problem, used as transmission conditions. Starting from a propagation problem for which an exact expression of the optimal transmission condition exists, we will show how such a preconditioner can be designed by approximating the inverse of the iteration operator. It will be interpreted as a double sweep over the subdomains and works by propagating information, just as a coarse grid would. The resulting algorithm is shown to converge very fast, independently of the number of subdomains and frequency. This idea of sweeping to speed up the convergence of iterative Helmholtz solvers, yet not in the context of Schwarz methods, has been proposed in recent works [13, 14, 15] where it has shown a comparable effect on the rate of convergence. Our preconditioner has the advantage that, like the original algorithm, it can be implemented as a matrix-free routine and requires no additional preprocessing.. The paper is organized as follows. In Section 2 we begin by formulating the Schwarz algorithm as a linear problem amenable to a solution by Krylov subspace techniques. We then show in Section 3 that the iteration operator that corresponds to the problem formulated in terms of surface unknowns has different properties than the Helmholtz operator, that are especially interesting when a good approximation of the optimal transmission operator (the Dirichlet-to-Neuman map, or DtN map) is available. An iterative solution of this problem can be quickly obtained by means of an efficient preconditioner that exploits these properties, as detailed in Section 4. In Section 5, we summarize the different approximations of the DtN map that will be used as transmission conditions in the algorithm. Section 6 presents numerical results obtained with the proposed method on a variety of test cases. In this paper we presented a double-sweep preconditioner for non-overlapping Schwarz methods applied to the Helmholtz problem. For a layered partitioning of the domain, the preconditioner works by propagating information by sweeping in both directions over the subdomains. The preconditioned algorithm can be implemented fully in a matrix-free fashion, requiring 2N − 2 subdomain solutions per iteration instead of N for the classical unpreconditioned Schwarz algorithm. The resulting algorithm, which can be interpreted as a coarse grid for the domain decomposition method, was shown to converge very fast, independently of the number of subdomains and frequency, provided that a good approximation of the DtN map on the interfaces between the subdomains is available.. Many perspectives exist for further investigation. First, since very accurate approximations of the DtN allow to obtain convergence in a constant number of iterations, one could investigate techniques that reduce the evaluation cost of accurate non-local DtN approximations, in particular the matrix probing technique [45] that takes advantage of a priori information on the structure of the DtN map [39] . Such a technique would shift most of the computational burden offline, in a preprocessing step. Second, by construction the algorithm would be particularly suitable for (quasi)-periodic problems, where most domains and DtN maps are identical. In such cases, the factorizations of the systems to be solved on each domain are identical and must be computed only once, as well as the DtN maps on their boundaries, leading to substantial savings in the preprocessing step and memory usage. The homogeneous and gaussian waveguides considered as test cases in Section 6 are simple examples of such problems. Third, partial sweeps can also be envisioned on smaller groups of domains, which can restore some parallel efficiency [27] . Finally, the algorithm can be applied in a straightforward manner to other harmonic wave-type problems, like the propagation of electromagnetic waves [27] .. Here we detail how the matrix of the iteration operator F A (8) was formed in Section 3.1, when analytical solutions of the PDEs in the Schwarz algorithm are used. Applying algorithm (3-4) with Krylov acceleration, we have to solve the subproblems (recall that external sources are cancelled in the definition of operator F and that we use S = D = −ık, so we apply the same condition on the artificial interfaces than on the external boundaries):. −(∂ xx + k 2 )u j = 0 in Ω j (∂ n − ık)u j = g ji on Σ ij (∂ n − ık)u j = 0 on {x l , x r }.. (A.1). The solutions of these problems are a superposition of a forward and a backward wave:. u j (x, g l , g r ) = A f,j e ıkx + A b,j e −ıkx , x ∈ Ω j , j = 1, . . . , N, with respective amplitudes given as functions of the impedance data g l and g r on the artificial boundary (we suffix by l and r quantities or coordinates associated with resp. the left and right side of the considered domain):. While the matrix is easy to form numerically, its formal expression is rather technical and requires some definitions. We first number the unknowns of the Schwarz algorithm as g = [g 12 , g 21 , g 23 , .. . . ] T , where an unknown g ij corresponds to the impedance data of the boundary condition for problem i, on Σ ij . There are two unknowns per artificial interface, for a total of M = 2(N − 1) unknowns. Then, we classically number the entries of the matrix as: Each unknown g ij has a companion unknown g ji associated to the same interface Σ ij . In the matrix indexing, we will write g m the unknown associated to g m , with the index relation:. The column F ·,n is the output of the update relation (7) applied to the n-th column of an identity matrix as source vector g k , so the m-th entry of that column will be: In the n-th column, at most 3 entries have a non-zero contribution from at least one of its terms: the n-th entry (the one on the diagonal of the matrix) is exactly 1, as only the δ nn term contributes; the n -th is 0, because the δ m n term is exactly canceled by the problem contribution as an effect of the exact transmission condition; and the (n±2)-th only has the problem contribution alone. The matrix therefore has the following structure for N subdomains:

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AUGMENTING PLATFORM-BASED DESIGN WITH SYNTHESIS TOOLS Platform-based design faces an essential tension: it wants to reuse previous designs to leverage IP; but new designs must necessarily include work that is not complete or well-characterized. Synthesis and analysis methods are therefore important elements in platform-based design methodologies. This paper describes two aspects of this problem. First, we consider the first-generation dilemma, in which we must use additional analysis in order to create the first generation of a platform. Second, we describe a synthesis method that creates accelerators for platforms whose clock periods have been optimized for the system characteristics. Platform-based design has become a leading design methodology for systems-onchips (SoCs). Platform-based design uses existing designs as starting points for new system implementations. By building from existing designs, platform-based design leverages IP to reduce design time and risk. However, new implementations must have some new elements to modify the platform and create a unique system. This paper concerns itself with two aspects of the adaptation of new components to platform-based design.. The first problem described in this paper is the first-generation dilemma. Platform-based design works because we have an existing design that we can analyze. However, when designing the first generation of a platform for a particular application space, we do not have an existing implementation.. The second problem we consider is the synthesis of performance-tuned hardwired accelerators. Platform-based designs generally include embedded processors but may also need specialized hardware accelerators for performance and/or power considerations. Previous work has not considered how to tune the clock rate of such accelerators during synthesis. We have developed a co-synthesis algorithm that uses high-level synthesis to characterize the clock rate of the accelerator so that the accelerator's design can be tuned to the system requirements.. The next section surveys previous work. Section 3 provides some general observations on platform-based design. Section 4 concentrates on design methodologies. Section 5 describes the first-generation dilemma. Section 6 describes our work on the synthesis of accelerators with custom clock rates. Platform-based design is likely to dominate the next generation of SoC designs because it is a sound methodology for reusing hardware and software designs. However, with platforms constantly evolving, new design work always needs to be done. This paper has explored two aspects of the difficulties encountered when we do not have all the IP blocks that we would like, to complete a platform-based design.. The first-generation dilemma is one example of a situation in which we need more information from synthesis and analysis tools in order to complete the design. The accelerator synthesis method we described is one way to solve this problem, since it closely couples multiple stages of synthesis in order to optimize the overall system design. We believe that synthesis tools like this will help to make platform-based design practical.

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Fault-tolerant control of electric vehicles with in-wheel motors using actuator-grouping sliding mode controllers Although electric vehicles with in-wheel motors have been regarded as one of the promising vehicle architectures in recent years, the probability of in-wheel motor fault is still a crucial issue due to the system complexity and large number of control actuators. In this study, a modified sliding mode control (SMC) is applied to achieve fault-tolerant control of electric vehicles with four-wheel-independent-steering (4WIS) and four-wheel-independent-driving (4WID). Unlike in traditional SMC, in this approach the steering geometry is re-arranged according to the location of faulty wheels in the modified SMC. Three SMC control laws for longitudinal velocity control, lateral velocity control and yaw rate control are designed based on specific vehicle motion scenarios. In addition the actuator-grouping SMC method is proposed so that driving actuators are grouped and each group of actuators can be used to achieve the specific control target, which avoids the strong coupling effect between each control target. Simulation results prove that the proposed modified SMC can achieve good vehicle dynamics control performance in normal driving and large steering angle turning scenarios. In addition, the proposed actuator-grouping SMC can solve the coupling effect of different control targets and the control performance is improved. Although electric vehicles with in-wheel motors have been regarded as one of the promising vehicle architectures in recent years, the probability of in-wheel motor fault is still a crucial issue due to the system complexity and large number of control actuators. In this study, a modified sliding mode control (SMC) is applied to achieve fault-tolerant control of electric vehicles with four-wheel-independent-steering (4WIS) and four-wheel-independent-driving (4WID). Unlike in traditional SMC, in this approach the steering geometry is re-arranged according to the location of faulty wheels in the modified SMC. Three SMC control laws for longitudinal velocity control, lateral velocity control and yaw rate control are designed based on specific vehicle motion scenarios. In addition the actuator-grouping SMC method is proposed so that driving actuators are grouped and each group of actuators can be used to achieve the specific control target, which avoids the strong coupling effect between each control target. Simulation results prove that the proposed modified SMC can achieve good vehicle dynamics control performance in normal driving and large steering angle turning scenarios. In addition, the proposed actuator-grouping SMC can solve the coupling effect of different control targets and the control performance is improved. In recent years, due to the considerable potential in the reduction of emissions and fuel consumption, electric vehicles have been regarded as the promising vehicle architecture of the future. Because of the use of electric motors, such vehicles can have both four-wheelindependent-steering (4WIS) and four-wheel-independent-driving (4WID). In 4WID vehicles, four in-wheel motors are used to drive the four wheels and each individual wheel can be independently driven or controlled. Similarly, 4WIS electric vehicles can also have different steering angles for each wheel. Thus, for a 4WIS and 4WID electric vehicle, there is a total of eight control actuators which can be utilised to enhance the performance of traction control and direct yaw-moment control, and other advanced vehicle control strategies like energyefficient control [1] - [4] .. Compared with conventional vehicles, however, the probability of an in-wheel motor fault is a crucial issue due to the system complexity and large number of control actuators. The inwheel motor fault may be caused by mechanical problems, over-heating of the motors or a fault associated with the motor drivers [5] . In addition, uneven road conditions can cause the individual wheel to lose contact with the road, thus losing friction force and this can cause a fault in an individual wheel. The fault of the in-wheel motor compromises the vehicle's dynamic control performance when conventional controllers are applied, so the design of the fault-tolerant controllers for electric vehicles is especially important.. Previously, to improve the robustness of the vehicle traction control, the model following control (MFC) approach has been proposed. This only required the input information of vehicle torque and wheel rotation speed [6] [7] [8] . Then the maximum transmissible torque estimation (MTTE) approach was developed to further improve the robust control performance of MFC [9] . Recently, a fault-tolerant control method based on MTTE has been suggested using a proportional-integral (PI) type disturbance observer [10] , but this method only concerned the uncertainties of the mathematical model and sensor faults and did not focus on the failure of one specific wheel.. Driving actuator failure could be handled using the well-known ∞ robust control method, but the dynamic performance of the vehicle under healthy conditions was also compromised [11] . To overcome this disadvantage, various active fault-tolerant controllers (AFTC) have been proposed based on the application of a fault detection and isolation (FDI) module [12] [13] . According to the fault severity, different control structures and control parameters are selected after the fault is detected. In [14] , two control structures in the AFTC approach were proposed to achieve the fault-tolerant control of an induction-motor affected by a speedsensor fault. The first control structure was the PI controller for the healthy mode and the second controller was the ∞ robust controller for the faulty mode.. This means, however, that specific controller strategies can be implemented only after the fault has been detected and therefore fault diagnosis is important for fault-tolerant control. In the literature, a number of fault diagnosis control strategies for conventional ground vehicles have been suggested, but these control methods are not for electric vehicles [15] [16] [17] . Several fault diagnosis methods for electric vehicles have been proposed [18] [19] , but motor failures are hard to diagnose using only the current and voltage sensors in the in-wheel motor. In [5] and [20] , the faulty wheel could be identified by estimating the individual motor control gain without the knowledge of the specific tyre-road friction coefficient.. Apart from the fault of a sensor or a fault caused by the disturbance and model uncertainty, much study has been done into the failure of the specific in-wheel motor. A control method has been proposed in which the faulty wheel and its opposite side wheel were isolated but this degrades the performance and stability of the vehicle [21] . Wenbo et al. proposed a control strategy to enhance the performance of the vehicle in a small turn or at low speed, but conditions where the vehicle is moving in a sharp turn or at high speed were not discussed [22] . Xin et al. classified the control strategy into the failure-driving mode, which guaranteed the vehicle continued moving and the failure-stopping mode, which stopped the vehicle [23] . In [5] , a sliding mode controller (SMC) was implemented as the high level controller to achieve the desired longitudinal velocity, lateral velocity and yaw rate, then the four driving torques of each wheel could be generated to achieve these values. An adaptive-control-based passive fault-tolerant controller was also designed to maintain vehicle stability and track the desired vehicle motion [20] . Wang and Wang also introduced an improved passive faulttolerant controller which grouped the actuators having similar effects on the control of the system into one sub-system [24] . This control method was promising due to the direct distribution of the high-level control targets to each of the group of actuators in the lower level.. The adaptive control method, however, has the problem of high computational cost compared with the SMC method. For this reason many see SMC control in fault-tolerant control of 4WID vehicles as quite promising. In order to achieve better control performance, however, SMC needs large control gains and this will cause a large chattering effect. Alipour et al. suggested the proportional-integral sliding mode control (PISMC) strategy to improve the fault-tolerant control performance of the traditional SMC so that a smaller control gain could be selected and the chattering effect could be reduced [25] . Although the SMC control gain can be reduced significantly, however, the improvement of the actual dynamics control performance over the traditional SMC is not assured. Song et al. applied terminal sliding mode control (TSMC) to achieve the finite-time convergence and quick responsiveness on the terminal sliding manifold [26] . If the SMC method is applied in a 4WID vehicle to achieve multiple control targets, the control effort is allocated into the driving actuators of four wheels. One big problem is the coupling effect between different control targets and grouping the driving actuators is one of the solutions to solve this problem. For instance, the two front wheels can be considered as one group in order to control the body slip angle only, while the two rear wheels can also be regarded as one group in order to achieve the desired yaw rate. In this way, the control actuators related to the body slip angle will not have a strong effect on the control performance of the yaw rate. Except for [25] however, it appears that few researchers have examined the grouping of the driving actuators. Actuators having a similar control effect were grouped in [25] , but this was not related to the coupling effect between different control targets. This paper focuses on the fault-tolerant control method and the location of the specific faulty wheel is assumed to be known. This assumption is reasonable according to the literature [5] [19] [20] [24] . The newly proposed SMC fault-tolerant controller focuses primarily on 4WIS-4WID electric vehicles. The main contribution of this paper is to solve the coupling effect of different control targets by grouping the actual driving actuators in fault-tolerant control of a 4WID vehicle. In addition, due to the fault of one specific wheel, the steering geometry of the whole vehicle will be re-arranged and the actual steering actuators will be adjusted in the 4WIS vehicle.. The rest of this paper is organised as follows. Vehicle modelling is presented in Section 2. The steering geometry during the wheel fault is discussed in Section 3. The SMC method and its modification are shown in Section 4. The simulation results of comparing the SMC method with other stability controllers are shown in Section 5. Section 6 describes the strategy of grouping driving actuators in the SMC method to achieve better control performance. Section 7 shows the advantage of grouping the driving actuators in SMC over the traditional SMC methods. Finally, the conclusion is given in Section 8.

B I O O O O B I O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model This article is brought to you by Swansea University. Any person downloading material is agreeing to abide by the terms of the repository licence. Authors are personally responsible for adhering to publisher restrictions or conditions. When uploading content they are required to comply with their publisher agreement and the SHERPA RoMEO database to judge whether or not it is copyright safe to add this version of the paper to this repository. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.Three-dimensional control-volume distributed multi-point flux approximation coupled with a lower-dimensional surface fracture model Understanding of fluid flow through a fractured porous medium has immense importance in energy production and environmental problems. The oil industry has a special interest because an estimated 60% of the world's remaining oil reserves reside in fractured formations [1] . In addition to oil and gas production fracture modelling is of interest in determining carbon sequestration strategies, radioactive waste manage-5 ment in the subsurface [2] , and flow of non-aqueous-phase liquids in aquifers. Fractures are a system of rock discontinuities e.g. faults, joints and fissures, that occur in porous media with apertures having widths ranging over scales from microns to centimetres [3] . Open fractures act as preferential fluid flow paths above a certain aperture and size whereas cemented fractures can act as flow barriers. Flow, in any rock, is affected by a few large fractures, by a dense network of small fractures, or by a combination of fractures of varying 10 length scales ranging from microns to hundreds of kilometres [4, 5] . Usually the matrix provides the storage for the fluid while fractures provide the main fluid flow paths. For example in two-phase flow, fractures may form the predominant flow paths for a particular phase and the less permeable matrix may become the flow region for the other phase [6] .. Because of the importance of fractures in the reservoirs, increasing effort is being devoted to development of 15 efficient and accurate numerical methods to simulate the fluid flow through fractured porous media. Dualporosity/permeability models, developed in [7, 8, 9] , have traditionally been used for the last few decades.. Flow transfer terms are defined between the fracture and matrix systems. These transfer terms depend on the shape factor, average pressure difference between two domains and further physical parameters in the case of multi-phase flow [10] . The shape factor is not straightforward to determine and is not avail-20 able in the presence of capillarity and gravity for two-phase flow [2] . Also, barriers cannot be modelled by dual-porosity/permeability models. Moreover, these models are based on the assumption that fracture systems are dense so inaccurate results are given for large scale fractures. As a result, the discrete-fracture model(DFM) was developed; see e.g. [11, 12, 13, 14, 15, 16] , which is attractive for large scale and sparse fracture systems. In this model actual geometry and location of the fracture are honoured in the domain. 25 Unlike the dual-porosity model; the effect of individual fractures on fluid flow can be determined and fluid transfer between the fracture and matrix is more straightforward and consistent. Generally, fractures are modelled by (n-1) dimensional elements in an n-dimensional domain e.g. in two-dimensions (2D), fractures are represented by lines at the edges of the polygonal matrix elements while in three-dimensions (3D) fracture systems are modelled as polygonal surfaces between the polyhedral matrix elements. Equi-dimensional 30 representation of fractures [17] , are not popular because of complexity and computational cost contributed by thin cells. In the equi-dimensional model, the control-volume at the intersection of the fractures is of the dimensions of fracture aperture which reduces the time-step size in the numerical model [2] . Also, in our experience with this method we have observed that a small control-volume increases the condition number of the global linear system which increases the computational cost for the solution of the system, consistent 35 with [18].. In the discrete-fracture method, rock-matrix and fracture elements coincide at the interface, so an unstructured grid is used to honour the explicit fracture geometry (see [19, 20] ). Also, the matrix cells near the fracture are small enough to conform to the complex fracture-network geometry. Small cells lead to a large numerical system to be solved. Because of grid conformity, application of this model to dynamic fracture 40 networks requires a dynamic grid generator with a conforming mesh where the grid is updated because of generation of new fractures [21, p. 72] . The discrete-fracture model would be increasingly costly for small scale fractures and any cases with large numbers of fractures, which would lead to locally dense unstructured grids in-turn leading to high computational cost. Hierarchical fracture models have been presented in [22, 23] for two-dimensional flow simulation in a fractured porous medium. In this approach, small scale 45 fractures are homogenized into the matrix medium and their effects are added to the matrix permeability.. Large scale fractures are explicitly modelled as major fluid conduits embedded into a non-conforming structured mesh. Other techniques based on discontinuity finite element modelling and extended-finite element method (XFEM) for embedded fractures into non-conforming mesh are presented in [24, 25, 26] . Recently, a continuum voxel approach has been presented in [27] where hydraulic properties of a fracture network are 50 mapped onto a stair-like regular mesh to avoid the intense meshing issue for discrete-fractures. A technique of multi-scale philosophy is presented in [28] to reduce the number of degrees of freedom for the fractureonly simulations. Various numerical methods have been used with DFM for single and multiphase flow in fractured porous media. Mass conservative methods include control-volume finite-element (CVFE) [6, 29] , cell-centred finite-volume (CCFV) [30, 18] , mixed finite-element (MFE) [16, 2, 31] and recently developed 55 vertex-approximate-gradient (VAG) scheme [32] and mimetic finite-difference method [33] . CVFE is not control volume distributed and is not flux-continuous for heterogeneous porous medium. MFE is locally flux-continuous and consistent but is computationally expensive because of higher degrees of freedom per cell as compared to CCFV and CVFE.. Herein, we will focus on a locally conservative cell-centred finite-volume (CCFV) formulation coupled with 60 discrete-fracture networks, in particular we use the control-volume distributed multi-point flux approximation (CVD-MPFA) [34, 35] . We choose CVD-MPFA because the method is flux-continuous and consistent for unstructured grids and heterogeneous porous media and uses a single degree of freedom per control-volume (grid cell in this case). Note that commercial simulators also use a single degree of freedom per grid cell.. We use a conforming unstructured mesh to capture the heterogeneity of a porous medium with fractures.. would be incurred by the small size of intermediate cell in the equi-dimensional model.. In this work, we present a 3D CVD-MPFA formulation applied to a 3D matrix coupled with a 2D fracture model. The matrix is defined over a 3D unstructured mesh, and fractures are defined by 2D surface meshes. We have presented a CVD-MPFA formulation for discrete fracture-matrix simulations, in three-dimensions,

O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B


Admission control in wireless ad hoc networks: a survey Wireless mobile ad hoc networks (MANETs) have emerged as a key technology for next-generation wireless networking. Because of their advantages over other wireless networks, MANETs are undergoing rapid progress and inspiring numerous applications. However, many technical issues are still facing the deployment of this technology, and one of the most challenging aspects is the quality of service (QoS) provisioning for multimedia real-time applications. MANETs are expected to offer a diverse range of services to support real-time traffic and conventional data in an integrated fashion. Because of the diversified QoS requirements of these services, QoS models are needed for an efficient usage of network resources. One of the most crucial mechanisms for providing QoS support is admission control (AC). AC has the task of estimating the state of network's resources and thereby to decide which application data flows can be admitted without promising more resources than are available and thus violating previously made guarantees. In order to provide a better understanding of the AC research challenges in MANETs, this paper presents a detailed investigation of current state-of-the-art AC models in ad hoc networks. A brief outline of the admission function, feedback to route failures, as well as the advantages and drawbacks of each discussed model are given. Mobile ad hoc networks (MANETs) offer unique advantages and flexibility for certain environments and strategic applications. They are constructed by a set of mobile nodes which are autonomously connected via multihop wireless communications ( Figure 1 ). Without any preconfigured and centrally controlled network infrastructure, they can be created and used 'anytime, anywhere. ' In fact, since all nodes are allowed to be mobile, the composition of such networks is necessarily timevarying. Not relying on complex and expensive infrastructure, which is required by their traditional counterparts, MANETs can operate in several environments where conventional networks fail [1, 2] . Such perceived benefits elicited urgent attention in the early days among military and rescue agencies in the use of ad hoc networks, especially under disorganized or hostile environments. It is vital to note that one of the major factors in the growing interest in MANETs was the improving capacities and ubiquitous nature of mobile devices, as well as the development of the unifying IEEE 802.11 standard [3] for wireless networking. Most laptop computers and many personal digital assistants now come with 802.11-compliant air interfaces. With the option to operate them in ad hoc mode, 802.11 is the primary enabling technology of MANETs [4] [5] [6] .. Providing quality of service (QoS) to users in a MANET is a key concern for service providers. Many suggested applications consist of real-time voice and video traffic that require QoS support for effective communication. The purpose of any QoS support model is to offer services with guarantees in terms of delay, bandwidth, jitter, or packet loss. To provide such guarantees in dynamic ad hoc networks, the media access control (MAC) layer is responsible for bandwidth allocation at individual devices, while the network layer must consider resources along the whole path of transmission [7] . One of the most crucial mechanisms for providing QoS guarantees is admission control (AC). AC aims to estimate the state of network's resources and thereby to decide which application data flows can be admitted without promising more resources than are available and thus violating previously made guarantees. AC has the task of controlling the usage and allocation of network resources for various applications requiring additional services. AC is a key component in multimedia systems, which needs to allow the bandwidth to be used by flows only when it is available.. In order to provide a better understanding of the AC research challenges in MANETs, this paper presents a detailed investigation of current works regarding AC models for ad hoc networks. An outline of the admission function, feedback to route failures, as well as the advantages and drawbacks of each AC model presented in this paper are given. The rest of the paper is organized as follows: the 'Design challenges of AC models in MANETs' section aims to provide an overview of some important issues regarding the design of AC models in ad hoc networks. The ' AC models in ad hoc networks' section lists the relevant admission control models found in the literature, illustrates their classification according to the method adopted for this survey, and describes their operations, advantages, and drawbacks. Finally, the 'Conclusions' section presents some concluding remarks, summarizes the trends in the field, and highlights potential areas of future work. The admission control decision in MANETs is typically based on some predefined criteria, which depends on the network traffic state and the characteristics of incoming sessions (e.g., their required network bandwidth). The design of AC models poses several challenges as described in the 'Design challenges of AC models in MANETs' section. These challenges are potential sources of service impairment in ad hoc networks, and hence, they may degrade the QoS seen by users of the network. An AC model should guarantee a successful data delivery with a good quality under a given limited memory, buffer and processing capabilities of mobile devices, implemented algorithm complexity, and wireless environment constraints. The overhead-heavy AC models may have a significant impact on resource and battery life and hence may limit the usefulness of devices. A detailed analysis of the previous discussed AC schemes is discussed in what follows.

B I O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Quantum-like interference effect in gene expression: glucose-lactose destructive interference Abstract In this note we illustrate on a few examples of cells and proteins behavior that microscopic biological systems can exhibit a complex probabilistic behavior which cannot be described by classical probabilistic dynamics. These examples support authors conjecture that behavior of microscopic biological systems can be described by quantum-like models, i.e., models inspired by quantummechanics. At the same time we do not couple quantum-like behavior with quantum physical processes in bio-systems. We present arguments that such a behavior can be induced by information complexity of even smallest bio-systems, their adaptivity to context changes. Although our examples of the quantum-like behavior are rather simple (lactose-glucose interference in E. coli growth, interference effect for differentiation of tooth stem cell induced by the presence of mesenchymal cell, interference in behavior of PrP C and PrP Sc prions), these examples may stimulate the interest in systems biology to quantum-like models of adaptive dynamics and lead to more complex examples of nonclassical probabilistic behavior in molecular biology.Keywords Quantum-like interference Á Nonclassical probabilistic behavior Á Lactose-glucose interference Á E. coli growth Á Differentiation of tooth stem cell Á Mesenchymal cell Á Interference of PrP C and PrP Sc prions Behavior of each cell is characterized by huge complexity. It can be compared with an actor who is playing simultaneously at a few different scenes participating in different (sometimes mutually incompatible) performances (e.g., Wanke and Kilian 2009) . Even smaller biological systems, such as viruses and even proteins, also exhibit complex behavior which is characterized by nontrivial contextdependence and adaptivity to context variations. During the last ten years adaptive dynamics was successfully used to model information processing by quantum systems (Ohya 2008; Asano et al. 2007) . Behavior of such systems is extremely complex as well. It cannot be described by classical evolution, neither by classical stochastic dynamics, e.g., classical Markov chains. More tricky evolutionary processes are in usage, so called quantum stochastic processes, in particular, quantum Markov chains. The authors come with the conjecture that similar mathematical models can be applied to describe activity of biological microsystems (Accardi et al. 2009) . At the same time we do not couple quantum-like behavior with quantum physical processes in bio-systems. We present arguments that such behavior can be induced by information complexity of even smallest bio-systems, their adaptivity to context changes. Although our examples of the quantum-like behavior are rather simple (lactose-glucose interference in E. coli growth, interference effect for differentiation of tooth stem cell induced by the presence of mesenchymal cell, interference in behavior of PrP C and PrP Sc prions), these examples may stimulate the interest in systems biology to quantum-like models of adaptive dynamics and lead to more complex examples of nonclassical probabilistic behavior in molecular biology.. Recently a few authors started to explore quantum-like statistical models in psychology and cognitive science (Khrennikov 2003 (Khrennikov , 2004 (Khrennikov , 2006 (Khrennikov , 2010 Busemeyer et al. , 2008 Acacio de Barros and Suppes 2009; Accardi et al. 2008 Accardi et al. , 2009 Conte et al 2008 Conte et al . 2009 Fichtner et al. 2008; Khrennikov and Haven 2009; Cheon and Takahashi 2010) . The notion of a quantum-like model was invented (Khrennikov 2003) to distinguish models in which information processing can be formally described by the mathematical formalism of quantum mechanics (QM) from really quantum physical models-models which are based on physical carriers of information (Penrose 1989 (Penrose , 1994 Homeroff 1994) . The usage of quantum-like models extends essentially the domain of applications. There is no need to worry about conditions of applicability of quantum physics.. 1 A crucial point is that the mathematical formalism of quantum mechanics presents a version of probability theory which differs from classical probability theory. The difference between laws of classical and quantum probabilities is so large and quantum laws are so counter-intuitive that some people speak about mysteries and paradoxes.. It was shown (Accardi et al. 2008 ) that such ''quantumlike'' probabilistic models can be applied in situations characterized by context dependence of behavior. 2 The contextual viewpoint to quantum and more general quantum-like probabilistic models demystified their laws (at least partially). This stimulate applications of the mathematical formalism of QM outside of physics, especially in biology.. One of the most important nonclassical features of quantum-like models is interference of probabilities. Interference can be either constructive or destructive. In the latter case (which will be considered in this paper) the reaction of a system to one factor, say B ? , can destroy its reaction to another factor, say B -. Thus the presence of both factors, B = B ? [ B -, can, in principle, minimize practically to zero the activity induced by B ? . Such destructive interference is well known in quantum physics.. In the famous two slit experiment a quantum particle passes a screen with two slits (numerated as s = 1,2), before to approach another screen covered by photoemulsion. The latter is used for registration of system's position. Experiment is done under three contexts. In the first two cases only one slit of two is open and in the last case both slits are open. Denote the first two contexts by B s , s = 1, 2. It is possible to find regions on the registration screen covered by photo-emulsion such that they attract a large number of systems under the context B ? (i.e., only s = 1 slit is open), but they attract a small number of systems when the second slit is also open. Typically this behavior is coupled to wave-particle duality. However, we interpret it in a more general framework, namely, as a consequence of contextuality. A change of context changes behavior. In this way we can proceed to contextual nonphysical models.. It was shown that interference effects can be demonstrated by cognitive systems. We can mention experiments with recognition of ambiguous figures (Conte et al. 2009 ). Moreover, recently such effects had been found in known statistical data from cognitive psychology (Hofstader 1983 (Hofstader , 1985 Shafir and Tversky 1992; Tversky and Shafir 1992; Croson 1999 )-in experiments on so called disjunction effect. For the latter it was shown (Busemeyer et al. , 2008 Accardi et al. 2009 ) that it is impossible to construct a classical Markovian model reproducing the experimental data from experiments in cognitive psychology (Shafir and Tversky 1992; Tversky and Shafir 1992) . At the same time a quantum Markov chain reproducing statistical data from cognitive psychology was constructed (Accardi et al. 2009 ).. The aim of this paper is to show that quantum-like interference (at least destructive) can be found in microbiology; in particular, as effects of activity of genetic systems. A possibility that not only humans, but even animals can ''behave in quantum-like way'' had been already discussed (Khrennikov 2006) . However, it was always emphasized that quantum-like behavior is a feature of advanced cognitive systems having the nervous system of high complexity. In this note we consider the simplest biological system, a cell, and we shall see that it can exhibit (under some special contexts) quantum-like behavior. Of course, we understood well that gene expression regulation is behind this behavior. And the genome is an advanced information system. From this viewpoint, it is not surprising that genome's activity can induce quantum-like behavior of a cell.. Although, from the biological viewpoint, we discuss a rather simple phenomenon (the glucose effect on E. coli growth), our example of destructive interference in cell's activity, interference of two factors: the presence of lactose and glucose in a E. coli cell (Inada et al. 1996) 3 , is very important from foundational viewpoint. It demonstrates that laws of classical probability can be violated not only by advanced cognitive systems (human beings in mentioned cognitive experiments), but even by cells.. The interference test is one of the basic tests in quantum physics to confirm that a system behaves in a quantum way (''nonclassically''). It played an important role in cognitive science to motivate applications of quantum-like models (Khrennikov 2004; Conte 2009 ). In this paper we apply this test to statistical data on the glucose effect on E. coli growth (Inada et al. 1996) . It is demonstrated that these data is nonclassical, i.e., quantum-like interference of probabilities is found.. Moreover, we show that quantum-like probabilistic behavior can be exhibited by even simpler molecular structures, namely, by proteins: interference of prions (PrP C ) and mutant prions PrP Sc . As was shown (Khrennikov 2004) , in statistical tests the interference effect can be found through violation of the formula of total probability. And we shall demonstrate that the formula of total probability is really violated by real experimental statistical data (Inada et al. 1996) . The formula of total probability is the base of the Bayesian approach. Thus, the story about quantum-like behavior is, in fact, about impossibility to use the Bayesian methods in some contexts (and these methods are very popular in genetics and bioinformatics). The main source of violation of the formula of total probability is contextuality-existence of incompatible contexts (in the same way as in QM). Incompatible contexts cannot be described by a single probability space (as it is done in classical theory). As a consequence, the basic formula of Bayesian approach is violated. Hence, in general (i.e., without the direct connection with quantum-like modelling) the result of this paper supports usage of nonBayesian methods in genetics and cell's biology.. We hope that this paper will motivate researches towards quantum-like models in genetics and cell-biology. It is a good place to state once again that we are not looking for really quantum effects in gene and cell activities, i.e., effects generated by quantum physical processes going on quantum scales of space and time. We are in search of quantum-like models of information processing by genes and more generally cells.. One of complications in the application of quantum-like probabilistic models outside of physics is that the standard calculus of quantum probabilities which is applicable to e.g. photons and electrons is too restrictive to describe probabilistic behavior of biological systems. Biological systems are not only nonclassical (from the probabilistic viewpoint), but they are even ''worse'' than quantum systems. They react to combinations of incompatible contexts by exhibiting stronger interference than quantum physical systems. Instead of standard trigonometric interference of the cos h-type which is well known in quantum physics, hyperbolic interference of the cosh h-type can be exhibited in experiments with cognitive systems. Experiments of the latter type cannot be described by the standard mathematical formalism of QM. A generalization of the QMformalism based on so called hyperbolic amplitudes should be applied (Khrennikov 2010) . Formally, the hyperbolic quantum-like formalism is constructed by using an imaginary element j such that j 2 = ?1, instead of the usual imaginary element i such that i 2 = -1, see Appendix. In the experiment discussed in this paper gene expression generates hyperbolic interference, i.e., interference which is essentially stronger than the standard quantumlike interference. In any event the data collected in the mentioned experiment (Inada et al. 1996) violates basic laws of classical probability theory.. We really hope that this paper will explain researchers working in genetics, molecular biology and in general biology the basic ideas of quantum probability, i.e., representation of probabilities by amplitudes (complex or more general). It will stimulate the usage of quantum and more general quantum-like probabilistic methods. Basic ideas are presented in a simple form. We hope that this paper will be readable for biologists. We demonstrated that statistical data from molecular biology can violate the basic law of classical probability theory; the formula of total probability. This can stimulate applications of quantum probability or its quantum-like generalizations, i.e., operating with amplitudes, instead of classical probabilities. In particular, quantum decision theory may be used, instead of classical Baysian decision making.. As was emphasized, we do not connect the quantum-like probabilistic behavior in molecular biology with quantum physical processes in cells or protein molecules. We pointed to a possibility to couple quantum-like probabilistic models with contextuality of biological processeswell developed ability of even microscopic biological systems to adapt their behavior to context variations. Contexts under consideration can vary due to variations in the chemical environment (as in the example with interference of lactose and glucose) or due to arrival of new microbilogical systems, e.g., cells (as in the example with appearance of mesenchymal cells in a population of tooth stem cells) or even smaller systems such as proteins (as in the example with interference of two types of prions). Dynamics of one bio-system is adapted to new context. Therefore the quantum-like probabilistic behavior can be considered as an exhibition of adaptive dynamics of microsystems. The general theory of adaptive dynamical systems was developed by one of the coauthors of this paper (Ohya 2008) . The main message of this note to the community of molecular biology is that the theory of adaptive dynamical systems can be used to describe behavior of cells, viruses, genes, and proteins.. One of referees of this paper formulated a number of important questions on expected impact of quantum-like modelling in molecular biology:. Why computing the coefficient of interference (lambda parameter) important in molecular biology? How to use it to predict phenomena of molecular biological interest? Can it predict the existence or nature of unknown biological elements (e.g., new proteins, microorganisms in the cell) or structures of biological machineries? Does QM-like model lead us to a better mechanistic understanding of the molecular biological phenomena?. The coefficient of interference provides a measure of incompatibility of contexts. Thus, e.g., in the example of the glucose effect on E. coli growth, we found that the lactosecontext exhibits a very strong destructive interference with the glucose context. Starting with the coefficient of interference we can reconstruct the wave function (complex or more general) probabilistic amplitude, see ''Classical law of total probability and its quantum-like modification'' (Khrennikov 2010) . However, further application of this ''wave function'' confronts with the following complicated problem. This wave function can be used as the initial condition for the Schrödinger equation for the probability amplitude. This equation will provide a probabilistic description of microbilogical processes. However, at the moment it is not clear at all how to construct quantum-like Hamiltonians in microbilogy. (We remark that we discuss not really quantum physical processes in cells, but quantumlike dynamics of some observables used in molecular biology.) Hence, at the moment the main value of calculation of the coefficient of interference is to show that processes are really quantum-like and, hence, stimulate future research in creation of quantum-like dynamical models, cf. cognitive science (Asano et al. 2010) . Regarding the last question on a better mechanistic understanding of the molecular biological phenomena we can say that the ordinary QM provides only a probabilistic description. The orthodox Copenhagen viewpoint is that it cannot say anything about dynamics of individual quantum particles. Nevertheless, some nonorthodox approaches provide a possibility to present a detailed mechanistic description matching QM. We can mention Bohmian mechanics. Unfortunately, majority of such mechanistic ''prequantum models'' are nonlocal. Although many people speculate about nonlocality in quantum mechanics and cognitive science and even psychology, we prefer to stop here and not proceed towards a discussion on nonlocal effects in molecular biology.. We also hope that this publication will stimulate experimental activity to provide quantitative statistical data on quantum-like interference in molecular biology. Finally, we state once again that from our viewpoint quantum-like probabilistic effect is a consequence of context-dependent behavior of cells, viruses, proteins.

B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I I O O O B I I I I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O B I O B I I O B I O B I I O B I I I I O B I O B I I I I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B I I O O O B I I I I O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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Channel condition self-clocked packet scheduling scheme for wireless networks Since mobile hosts suffer from burst and location-dependent channel errors in wireless networks, packet fair queueing algorithm in wireline networks cannot be applied directly to wireless networks. Generally, a fair scheduler in a wireless network retains the virtual time of flow when the flow encounters channel errors. This results to the flow having higher priority when it exits from errors, and the system can compensate the lost service for the flow. This causes the lagging flows to capture the shared channel and affects the queueing delay of flows perceiving a clean channel. In this paper, we present a channel condition self-clocked packet scheduling scheme. This algorithm can address the problem and achieve the following goals: (1) steady delay and jitter for flows perceiving an error-free environment, (2) delay and throughput guarantees in an error-free environment, (3) short-term fairness among flows perceiving an error-free environment, and (4) long-term fairness for error system. Our algorithm is based on start-time fair queueing, and the virtual time of flows is reset to contend for forwarding its packet the next time when errors happen for the flow. Multimedia streaming services are becoming increasingly popular in third-generation (3G) and fourth-generation (4G) mobile networks. One important characteristic of multimedia streaming services is the load asymmetry between downlink and uplink, and the services are mostly used in the downlink. In order to enhance downlink performance, some systems have been proposed. It includes the high data rate system, high-speed downlink packet access (HSDPA), and [3G partnership project technical report (3GPP TR) 25.848; 3GPP TR 25.308] system. These systems introduce many schemes such as adaptive modulation and coding technique (AMC), hybrid automatic repeat request (HARQ) scheme, the high-speed channel shared by multiple users, quality of service (QoS) control for packet services [1, 2] . In recent years, worldwide interoperability for microwave access (WiMAX) had been proposed to be a candidate of the 4G network system. WiMAX aims at providing long distance and high data rate in various metropolitan areas of wireless network. Although WiMAX applies many new techniques such as use of orthogonal frequency division multiple access, time and frequency division duplexing (TDD and FDD), multiple QoS classes for a combination of data, and voice and video service, WiMAX leaves the packet scheduling algorithm for uplink and downlink as an open issue [3, 4] .. The packet scheduler plays a key role in the system especially for the downlink because it can provide the quality of service targets that should be met for applications [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] . Scheduler designers need to consider the allocations logically and physically. Logically, the scheduler should calculate the number of slots based on QoS service classes. Physically, the scheduler needs to select which subchannels and time intervals are suitable for each user. The goals of schedulers are basically to meet QoS guarantees for all service classes, to minimize bit error rate, to maximize the system throughput, to maintain the fairness, to have as less a complexity as possible, and finally, to ensure the system scalability.. Some types of QoS parameters are delay, jitter, loss rate, or throughput. For real-time applications (e.g., audio/video streams), in additional to delay and throughput, it requires the guarantee of the jitter.. In many wireless fair queueing, the system gives higher priority to the flow that exits the error state for fairness among flows. This may cause the lagging flows to capture the channel, and the delay of flow in the clean channel becomes longer. Also, the jitter of flow in the clean channel is affected. For real-time application, the quality of service such as delay and jitter must be guaranteed [17, 18] . In order to provide quality of service such as delay and jitter for the mobile host in the clean channel among flows' fairness, the channel condition aware scheme must be designed for real-time application. Packet fair queueing has long been popular and provides delay bound and fairness in wireline networks. While these algorithms cannot be applied directly to wireless networks because there are some characteristics of location-dependent and burst channel errors in wireless networks, this may result unfairness among flows and makes it difficult to provide delay guarantees. In this paper, we provided a general and practical packet scheduling algorithm which can take the wireless channel condition into account of packet scheduling in a general wireless transmission. CSCPS provides delay guarantees and short-term fairness for the error-free system and long-term fairness for flow perceiving channel errors. Aside from the mentioned properties, CSCPS improves the flows in the clean channel, which are affected by flows perceiving channel errors, and makes the queue delay and jitter of flows in the clean channel steady. Furthermore, the queue delay of flow, which is the worst case delay bound for packets, is unaffected by lagging flows.. The further work of CSCPS is to determine the interval time of flow precisely. For traffic, such as hypertext transfer protocol (http) traffic and file transfer protocol (FTP) traffic, the rate of packet arrival in the system is not good as that in UDP/CBR traffic with a constant bitrate. When errors happen, it is difficult to set the virtual time of packet for http and FTP traffic and for other traffic types. This may result in later packet arrival in the system which has higher priority than the packet of flow that suffered from error previously. In wireline networks, many packet fair queueing [21] [22] [23] have been proposed which can provide fairness and delay bound. Because there are some characteristics of the wireless network such as location conditiondependent error, channel contention, and burst errors, packet fair queueing in the wireline network cannot be applied directly in the wireless network. Several wireless fair queueing [3, 20, [24] [25] [26] [27] [28] [29] [30] have been developed, and they can provide short-term fairness for an error-free system, long-term fairness, graceful degradation in service for flows perceiving clean channel, and delay bound.

B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Minimal founded semantics for disjunctive logic programs and deductive databases In this paper, we propose a variant of stable model semantics for disjunctive logic programming and deductive databases. The semantics, called minimal founded, generalizes stable model semantics for normal (i.e. non disjunctive) programs but differs from disjunctive stable model semantics (the extension of stable model semantics for disjunctive programs). Compared with disjunctive stable model semantics, minimal founded semantics seems to be more intuitive, it gives meaning to programs which are meaningless under stable model semantics and is no harder to compute. More specifically, minimal founded semantics differs from stable model semantics only for disjunctive programs having constraint rules or rules working as constraints. We study the expressive power of the semantics and show that for general disjunctive datalog programs it has the same power as disjunctive stable model semantics. Several different semantics have been proposed for normal and disjunctive logic programs. Stable model semantics, first proposed for normal (i.e. disjunction free) programs, has been subsequently extended to disjunctive programs. For normal programs, stable model semantics has been widely accepted since it captures the intuitive meaning of programs and, for stratified programs it coincides with perfect model semantics which is the standard semantics for this class of programs (?; ?; ?; ?). For positive programs, stable model semantics coincides with minimal model semantics which is the standard semantics for positive disjunctive programs.. For general disjunctive programs several semantics have been proposed. We mention here the generalized closed world assumption (GCWA) (?), the weak generalized closed world assumption (WGCWA) (?; ?), the possible model semantics (?), the perfect model semantics (?), particularly suited to stratified programs, the disjunctive well-founded semantics (?), the disjunctive stable model semantics (?; ?) and the partial stable model semantics (?; ?).. Disjunctive stable model semantics is widely accepted since i) it gives a good intuition of the meaning of programs, ii) for normal programs it coincides with stable model semantics and for stratified (resp. positive) programs it coincides with the perfect (resp. minimal) model semantics. However, disjunctive stable model semantics has some drawbacks. It is defined for a restricted class of programs and there are several reasonable programs which are meaningless, i.e. they do not have stable models. The semantics proposed in this paper is essentially a variant of stable model semantics for normal programs. The aim of our proposal is the solution of some drawbacks of disjunctive stable model semantics which, in some cases, interpret inclusive disjunction as exclusive disjunction.. As disjunction is not interpreted as exclusive, the proposed semantics is not invariant if rules which are subsumed by other rules (under stable model semantics) are removed from the program; for instance, the first rule in the program of Example 7 can be deleted under stable model semantics as it is subsumed by the second rule, whereas under the minimal founded model semantics it cannot be deleted.. Several questions which need further investigation have been left open. For instance, further research could be devoted to i) the identification of fragments of disjunctive datalog for which one minimal founded model can be computed in polynomial time; ii) the use of two different types of disjunctive rule (inclusive disjunction and exclusive disjunction), iii) the investigation of abstract properties for disjunctive datalog under minimal founded semantics (?).

O O B O B I I O O O O O O O O O O O O O B O O O O O O O O B O O O O O O B O O O O O O O O O O O O B O O O O O B O O O O O O O O B O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O B O O B O O O O O O B I I O O B O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O B O O O O B O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O B O O O O O O O O O B O O O O O B O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B I O B O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O