Multiscale computational models

Vision Computing is a branch of artificial intelligence that focuses on providing computers with the functions typical of human vision. Due to recent advances made in technology, scientists have incorporate portable imagers into computer vision systems that can be connected via wireless networks. Advances in Vision Computing: An International Journal (AVC) is an open access, peer-reviewed journal that publishes articles which contribute new results in all areas of the advanced vision computing. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on understanding advances in vision computing and establishing new collaborations in these areas. Authors are solicited to contribute to the journal by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the areas of vision computing.

"This collective volume is the first to discuss systematically what are the possibilities to model different aspects of brain and mind functioning with the formal means of fractal geometry and deterministic chaos. At stake here is not an approximation to the way of actual performance, but the possibility of brain and mind to implement nonlinear dynamic patterns in their functioning. The contributions discuss the following topics (among others): the edge-of-chaos dynamics in recursively organized neural systems and in intersensory interaction, the fractal timing of the neural functioning on different scales of brain networking, aspects of fractal neurodynamics and quantum chaos in novel biophysics, the fractal maximum-power evolution of brain and mind, the chaotic dynamics in the development of consciousness, etc. It is suggested that the 'margins' of our capacity for phenomenal experience are 'fractal limit phenomena'. Here the possibilities to prove the plausibility of fractal modeling with appropriate experimentation and rational reconstruction are also discussed. A conjecture is made that the brain vs. mind differentiation becomes possible, most probably, only with the imposition of appropriate symmetry groups implementing a flowing interface of features of local vs. global brain dynamics.

Table of Contents
List of Contributors
Preface
Introduction

Edge-of-Chaos Dynamics in Recursively Organized Neural Systems
David M. Alexander and Gordon G. Globus

Fractal Time and the Foundations of Consciousness: Vertical convergence of 1/f phenomena from ion channels to behavioral states
Carl M. Anderson and Arnold J. Mandell

Fractal Thinking: Self-organizing brain processing
Earl Mac Cormac

n-Dimensional Nonlinear Psychophysics: Intersensory interaction as a network at the edge of chaos
Robert A.M. Gregson

Fractal Neurodynamics and Quantum Chaos: Resolving the mind-brain paradox through novel biophysics
Chris King

The Fractal Maximum-Power Evolution of Brain, Mind, and Consciousness
Larry Vandervert

The Fractal-Like Roots of Mind: A tutorial in direct access
Maxim I. Stamenov

Chaotic Dynamics and the Development of Consciousness
John R. Van Eenwyk

Subject Index"

In the past decades, significant advances have been made in computationalmodeling
of materials on multiple length and time scales. In particular, the finest scale (ab
initio, atomistic level) and coarsest (classic continua) are well understood and are
now fine-tuned for numerous applications. From numerous studies, the realization
has emerged that most macroscopic properties of materials depend critically on
the mesoscale: the evolving microstructure and interactions which occur on the
length and time scales much larger than atomic, yet much smaller than macroscopic
observables. These lecture notes follow the 1-week advanced course presented in
the International Centre for Mechanical Sciences (CISM), Udine, in May 2017.
The topics of the course are chosen with the following criteria in mind:
• Significant progress has been made in the past decades
• Some outstanding problems remain as a challenge for future researchers.
• The past efforts have been multidisciplinary, and future efforts are expected to
remain such, involving researchers in engineering, physics and mathematics.
Three broad areas representative of the field are selected: dislocation plasticity
and creep of crystals and polycrystals, interfaces in solids and fluids, and granular
deformation and flow.
Geometrical complexity of dislocation assemblies—a mixture of order and
disorder arising from highly constrained, yet rich, kinematics, combined with
the long-range interactions (inherent non-locality)—results in a very challenging
problem. Experimentally observed size effects indicate a size-dependent mesoscale
model, but the consensus about the correct formulation has not been reached.
The structure of crystalline interfaces, mechanisms of their motion, and their
role in the overall deformation of polycrystalline assemblies have been the subject
of intense research but many questions remain open, among which are dislocationinterface
interactions. Fluid interfaces in capillary flows exhibit topological discontinuities
(breaking and coalescence of subdomains). These are effectively handled
with the phase field formulations, so that questions arise regarding the appropriate
phase field model.
Depending on the packing density, the mechanical behavior of granular materials
may resemble that of solids or fluids, but also exhibits unique features (dilatancy,
critical state, shear localization with a characteristic width, vortex flow). Microscopically,
the geometry is strongly disordered and interparticle forces strongly
inhomogeneous. A continuum theory capable of describing all the salient features
is yet to be formulated.
The lecture notes are intended to provide answer to the following general
questions. How far have the understanding and mesoscale modeling advanced in
recent decades?What are the key open questions that require further research?What
are the mathematical and physical requirements for a mesoscale model intended to
provide either insight or a predictive engineering tool?
The book begins and ends with two perspectives on continuum theory. In chapter
“Physical Foundations of Mesoscale Continua” (Mesarovic), the relationship
between microscale physics and mesoscale continua is examined, with a goal of
providing a method for deriving the latter from the former. Chapter “Generalized
Continua and Phase-Field Models: Application to Crystal Plasticity” (Forest)
presents a comprehensive overviewof higher order continua and phase field models.
Chapters “Multiscale Dislocation-Based Plasticity” and “Statistical Theory
of Dislocation” are dedicated to dislocation plasticity. In chapter “Multiscale
Dislocation-Based Plasticity” (Zbib), computational discrete dislocation mechanics
and its relationship to continuum computational models are reviewed. In
chapter “Statistical Theory of Dislocation”, Istvan Groma brings the power of
modern statistical mechanics to bear on discrete dislocation dynamics, with the aim
of formulating a continuum model.
In chapter “Granular Materials: Micromechanical Approaches of Model Systems”,
Jean-Noël Roux gives a comprehensive review of computational experiments
on granular materials (discrete element method) and the advances in understanding
of granular deformation/flow that follows from such experiments.
In chapter “Multiscale Modeling of Interfaces, Dislocations, and Dislocation
Field Plasticity”, David McDowell provides a tour de force through the variety of
length and time scales from first principle models to macroscale continua, with a
broad scope of applications.
The editors are indebted to the CISM for funding and organizing the lectures and
to the guest lecturers for their contributions.

The objective of this work is the formulation of a multi-scale framework for electrochemically promoted systems. We have constructed a 3-Dimensional, isothermal, solid oxide single pellet, multi-scale framework, which describes the chemical and electrochemical phenomena taking place in a solid oxide single pellet under closed-circuit conditions, while the electrochemically promoted oxidation of CO over Pt/YSZ is used as an illustrative system. The proposed framework combines a 3-D macroscopic model which employs the finite element method (FEM) for the simulation of the charge transport and the electrochemical phenomena taking place in the pellet, and an in-house developed efficient implementation of a 2-D lattice kinetic Monte Carlo method (kMC) for the simulation of the reaction-diffusion micro-processes taking place on the catalytic surface. Comparison between the multi-scale framework and a macroscopic model [1] is carried out for several sets of operating conditions. Differences between the steady-state outputs of the two models are presented and discussed. A subsequent parametric study using the multi-scale framework is performed to investigate the effect of the gaseous species partial pressures and of the temperature on the CO 2 production rate.

The analysis of human crowds has widespread uses from law enforcement to urban engineering and traffic management. All of these require a crowd to first be detected, which is the problem addressed in this paper. Given an image, the algorithm we propose segments it into crowd and non-crowd regions. The main idea is to capture two key properties of crowds: (i) on a narrow scale, its basic element should look like a human (only weakly so, due to low resolution, occlusion, clothing variation etc.), while (ii) on a larger scale, a crowd inherently contains repetitive appearance elements. Our method exploits this by building a pyramid of sliding windows and quantifying how "crowd-like" each level of the pyramid is using an underlying statistical model based on quantized SIFT features. The two aforementioned crowd properties are captured by the resulting feature vector of window responses, describing the degree of crowd-like appearance around an image location as the surrounding spatial extent is increased.

During their operation, modern aircraft engine components are subjected to increasingly demanding operating conditions, especially the high pressure turbine (HPT) blades. Such conditions cause these parts to undergo different types of time-dependent degradation, one of which is creep. A model using the finite element method (FEM) was developed, in order to be able to predict the creep behaviour of HPT blades. Flight data records (FDR) for a specific aircraft, provided by a commercial aviation company, were used to obtain thermal and mechanical data for three different flight cycles. In order to create the 3D model needed for the FEM analysis, a HPT blade scrap was scanned, and its chemical composition and material properties were obtained. The data that was gathered was fed into the FEM model and different simulations were run, first with a simplified 3D rectangular block shape, in order to better establish the model, and then with the real 3D mesh obtained from the blade scrap. The overall expected behaviour in terms of displacement was observed, in particular at the trailing edge of the blade. Therefore such a model can be useful in the goal of predicting turbine blade life, given a set of FDR data. Abstract One of the recent trends in materials science and technology is the research of the behavior of the materials under the extreme conditions both on the theoretical and experimental basis. There are limitations of the experimental methods, however, theoretical approach can be used as a supplement to the experimental results. As a consequence, in the last two decades a vast number of structure prediction calculations have been performed on chemical systems, focusing on the high-pressure and high temperature phases. In this work, we would like to present several computational studies and their connection to the actual synthesis routes: lead sulfide (PbS), barium sulfide (BaS), and aluminum nitride (AlN). The investigated compounds were calculated on ab initio level using the most advanced tools in quantum chemistry and computational material science including Hartree-Fock Theory, Density Functional Theory (DFT) and Hybrid (B3LYP) Approximation. Their structural, mechanical, elastic and vibrational properties have been investigated and in addition, we show structure candidates as the function of size, pressure and temperature and not previously observed in any of the investigated materials thus creating new possibilities for synthesis of advanced materials with improved physical, chemical, and/or mechanical properties. Abstract One of the recent trends in materials science and technology is the research of the behavior of the materials under the extreme conditions both on the theoretical and experimental basis. There are limitations of the experimental methods, however, theoretical approach can be used as a supplement to the experimental results. As a consequence, in the last two decades a vast number of structure prediction calculations have been performed on chemical systems, focusing on the high-pressure and high temperature phases. In this work, we would like to present several computational studies and their connection to the actual synthesis routes: lead sulfide (PbS), barium sulfide (BaS), and aluminum nitride (AlN). The investigated compounds were calculated on ab initio level using the most advanced tools in quantum chemistry and computational material science including Hartree-Fock Theory, Density Functional Theory (DFT) and Hybrid (B3LYP) Approximation. Their structural, mechanical, elastic and vibrational properties have been investigated and in addition, we show structure candidates as the function of size, pressure and temperature and not previously observed in any of the investigated materials thus creating new possibilities for synthesis of advanced materials with improved physical, chemical, and/or mechanical properties.

It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrilla...

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This article describes a bridge between POD-based model order reduction techniques and classical Newton/Krylov solvers. This bridge is used to derive an efficient algorithm to correct, ``on-the-fly", the reduced order modelling of highly nonlinear problems undergoing strong topological changes. Damage initiation problems are addressed and tackle via a corrected hyperreduction method. It is shown that the relevancy of reduced order model can be significantly improved with reasonable additional costs when using this algorithm, even when strong topological changes are involved.

It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrilla...

It is known that in pathological conditions, physiological systems develop changes in the multiscale properties of physiological signals. However, in real life, little is known about how changes in the function of one of the two coupled physiological systems induce changes in function of the other one, especially on their multiscale behavior. Hence, in this work we aimed to examine the complexity of cardio-respiratory coupled systems control using multiscale entropy (MSE) analysis of cardiac intervals MSE (RR), respiratory time series MSE (Resp), and synchrony of these rhythms by cross multiscale entropy (CMSE) analysis, in the heart failure (HF) patients and healthy subjects. We analyzed 20 min of synchronously recorded RR intervals and respiratory signal during relaxation in the supine position in 42 heart failure patients and 14 control healthy subjects. Heart failure group was divided into three subgroups, according to the RR interval time series characteristics (atrial fibrilla...

1 Rzeszow University of Technology, Faculty of Mechanics and Technology, Department of Integrated Design and Tribology Systems al. Kwiatkowskiego 4, 37-450 Stalowa Wola, Poland 2 Rzeszow University of Technology, Faculty of Mechanical Engineering and Aeronautics, Department of Materials Forming and Processing al. Powstańców Warszawy 8, 35-959 Rzeszów, Poland *Corresponding author. E-mail: wf@prz.edu.pl

Intervertebral disc (IVD) degeneration is a major risk factor of low back pain. It is defined by a progressive loss of the IVD structure and functionality, leading to severe impairments with restricted treatment options due to the highly demanding mechanical exposure of the IVD. Degenerative changes in the IVD usually increase with age but at an accelerated rate in some individuals. To understand the initiation and progression of this disease, it is crucial to identify key top-down and bottom-up regulations’ processes, across the cell, tissue, and organ levels, in health and disease. Owing to unremitting investigation of experimental research, the comprehension of detailed cell signaling pathways and their effect on matrix turnover significantly rose. Likewise, in silico research substantially contributed to a holistic understanding of spatiotemporal effects and complex, multifactorial interactions within the IVD. Together with important achievements in the research of biomaterials, manifold promising approaches for regenerative treatment options were presented over the last years. This review provides an integrative analysis of the current knowledge about (1) the multiscale function and regulation of the IVD in health and disease, (2) the possible regenerative strategies, and (3) the in silico models that shall eventually support the development of advanced therapies.

International Journal on Computational Science & Applications (IJCSA) is a Bi-monthly peer-reviewed and refereed open access journal that publishes articles which contribute new results in all areas of the Computational Science & Applications. Computational science is interdisciplinary fields in which mathematical models are combined with scientific computing methods to study of a wide range of problems in science and engineering. Modeling and simulation tools find increasing applications not only in fundamental research, but also in real-world design and industry applications.

This paper proposes the application of the waveform relaxation method to the homogenization of mul-tiscale magnetoquasistatic problems. In the monolithic heterogeneous multiscale method, the nonlinear macroscale problem is solved using the Newton–Raphson scheme. The resolution of many mesoscale problems per Gauß point allows to compute the homogenized constitutive law and its derivative by finite di↵erences. In the proposed approach, the macroscale problem and the mesoscale problems are weakly coupled and solved separately using the finite element method on time intervals for several waveform relaxation iterations. The exchange of information between both problems is still carried out using the heterogeneous multiscale method. However, the partial derivatives can now be evaluated exactly by solving only one mesoscale problem per Gauß point.

This paper presents a multiscale approach for vibration frequency analysis of graphene/polymer composites. The graphene is modelled at the atomistic scale, and the matrix deformation is analysed by the continuum finite element method. Inter-connectivity between graphene and polymer matrix are assumed to be bonded by van der Waals interactions at the interface. The impact of geometrical configuration (armchair and zigzag), boundary conditions and length on the overall stiffness of the graphene reinforced plastics (GRP) is studied. The natural frequency and vibrational mode shapes of GRP studied have displayed dependence on the length and also the boundary conditions. The exceptional vibrational behaviour and large stiffness displayed by GRP makes them a potential replacement for conventional composite fibres such as carbon and glass fibres.

We propose a methodology to set up unifying scaling laws describing the response of multifarious random polycrystals. The methodology employed falls in the realm of stochastic micro-mechanics and is consistent with the Hill condition. Within this framework, we introduce the concept of a scaling function that describes ''finite size scaling" of both elastic and inelastic crystalline aggregates. While the finite size is represented by the mesoscale, the scaling function depends on an appropriate measure quantifying the single crystal anisotropy. Based on the scaling function, we construct a material scaling diagram, from which one can assess the approach to a representative volume element (RVE) for many different polycrystals. We demonstrate these concepts on the scaling of the fourth-rank elasticity and the second-rank thermal conductivity tensors.

Vision Computing is a branch of artificial intelligence that focuses on providing computers with the functions typical of human vision. Due to recent advances made in technology, scientists have in corporate portable imagers into computer vision systems that can be connected via wireless networks. Advances in Vision Computing: An International Journal (AVC) is an open access, peer- reviewed journal that publishes articles which contribute new results in all areas of the advanced vision computing. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on understanding advances in vision computing and establishing new collaborations in these areas. Authors are solicited to contribute to the journal by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the areas of vision computing.

Long simulation times in climate science typically require coarse grids due to computational constraints. Nonetheless, unresolved subscale information significantly influences the prog-nostic variables and cannot be neglected for reliable long-term simulations. This is typically done via parametrizations, but their coupling to the coarse grid variables often involves simple heuristics. We explore a novel upscaling approach inspired by multiscale finite element methods. These methods are well established in porous media applications, where mostly stationary or quasi stationary situations prevail. In advection-dominated problems arising in climate simulations, the approach needs to be adjusted. We do so by performing coordinate transforms that make the effect of transport milder in the vicinity of coarse element boundaries. The idea of our method is quite general, and we demonstrate it as a proof-of-concept on a one-dimensional passive advection-diffusion equation with oscillatory background velocity and diffusion.

Digital image processing for pattern recognition involves several processing and pre-processing steps. Edge detection stands a great position for accurate pattern recognition most especially in character recognition system. Many edge detection techniques were implemented with convolution mask and based on approximations to differential operators. For efficient Yoruba character recognition, compass edge detection algorithm was developed to enhance the recognition rate of Yoruba character. The algorithm
developed achieved 0.923 edge detection error rate. The level of accuracy will have been better if noise removal or reduction steps were included in the algorithm.

It is shown that tailored breaking of the translational symmetry through weak scattering in waveguides and optical fibers can control chromatic dispersions of the individual modes at any order; thereby, it overcomes the problem of coherent classical and quantum signal transmission at long distances. The methodology is based on previously developed quantum control techniques and gives an analytic solution in ideal scattering conditions; it has been also extended to incorporate and correct nonunitary effects in the presence of weak backscattering. In practice, it requires scatterers able to couple different modes and carefully designed dispersion laws giving a null average quadratic distortion in the spectral vicinity of the operational frequency.

In simulations of representative volume elements (RVEs) of materials with disordered microstructures, commonly used rigid and periodic boundary conditions (BCs) introduce additional constraints, causing: (i) boundary effects, (ii) unrealistic stiff response, (iii) artificial wavelengths in the solution fields, and (iv) suppression of solutions with localized deformation that otherwise may occur in the simulation. In this paper we define the minimal kinematic boundary conditions such that only the desired overall strain is imposed on the RVE, with no other undesirable constraints. We prove that such BCs result in a unique solution for the linear elastic case, and that the uniqueness for nonlinear problems is dependent on the pointwise positive definiteness of the incremental stiffness tensor. Upon incorporating the minimal BCs into the finite element framework, we consider, as an example, two-dimensional, linear elastic, disordered polycrystals and perform a systematic study of the effects of boundary conditions while varying the RVE size and controlling the sampling error. The results demonstrate that the minimal BCs, applicable to a RVE of any shape, are superior to other BCs, in that they give more realistic overall behaviour, reduce the required size of the RVE, and eliminate the superficial wavelengths in the solution field, ubiquitous in simulations with other boundary conditions.

This paper proposes a novel technique to reduce the computational burden associated with the simulation of localised failure. The proposed methodology affords the simulation of damage initiation and propagation whilst concentrating the computational effort where it is most needed, i.e. in the localisation zones. To do so, a local/global technique is devised where the global (slave) problem (far from the zones undergoing severe damage and cracking) is solved for in a reduced space computed by the classical Proper Orthogonal Decomposition, while the local (master) degrees of freedom (associated with the part of the structure where most of the damage is taking place) are fully resolved. Both domains are coupled through a local/global technique. This method circumvents the difficulties associated with model order reduction for the simulation of highly non-linear mechanical failure and offers an alternative or complementary approach to the development of multiscale fracture simulators.

Neural stimulation can be used as a tool to elicit natural sensations or behaviors by modulating neural activity. This can be potentially used to mitigate the damage of brain lesions or neural disorders. However, in order to obtain the optimal stimulation sequences, it is necessary to develop neural control methods, for example by constructing an inverse model of the target system. For real brains, this can be very challenging, and often unfeasible, as it requires repeatedly stimulating the neural system to obtain enough probing data, and depends on an unwarranted assumption of stationarity. By contrast, detailed brain simulations may provide an alternative testbed for understanding the interactions between ongoing neural activity and external stimulation. Unlike real brains, the artificial system can be probed extensively and precisely, and detailed output information is readily available. Here we employed a spiking network model of sensorimotor cortex trained to drive a realistic virtual musculoskeletal arm to reach a target. The network was then perturbed, in order to simulate a lesion, by either silencing neurons or removing synaptic connections. All lesions led to significant behvaioral impairments during the reaching task. The remaining cells were then systematically probed with a set of single and multiple-cell stimulations, and results were used to build an inverse model of the neural system. The inverse model was constructed using a kernel adaptive filtering method, and was used to predict the neural stimulation pattern required to recover the pre-lesion neural activity. Applying the derived neurostimulation to the lesioned network improved the reaching behavior performance. This work proposes a novel neurocontrol method, and provides theoretical groundwork on the use biomimetic brain models to develop and evaluate neurocontrollers that restore the function of damaged brain regions and the corresponding motor behaviors.

This paper presents a new numerical method for multiscale modeling of composite materials. The new numerical model, called DECM, consists of a DEM (Discrete Element Method) approach of the Cell Method (CM) and combines the main features of both the DEM and the CM. In particular, it offers the same degree of detail as the CM, on the microscale, and manages the discrete elements individually such as the DEM-allowing finite displacements and rotations-on the macroscale. Moreover, the DECM is able to activate crack propagation until complete detachment and automatically recognizes new contacts. Unlike other DEM approaches for modeling failure mechanisms in continuous media, the DECM does not require prior knowledge of the failure position. Furthermore, the DECM solves the problems in the space domain directly. Therefore, it does not require any dynamic relaxation techniques to obtain the static solution. For the sake of example, the paper shows the results offered by the DECM for axial and shear loading of a composite two-dimensional domain with periodic round inclusions. The paper also offers some insights into how the inclusions modify the stress field in composite continua.

Vision Computing is a branch of artificial intelligence that focuses on providing computers with the functions typical of human vision. Due to recent advances made in technology, scientists have incorporate portable imagers into computer vision systems that can be connected via wireless networks. Advances in Vision Computing: An International Journal (AVC) is an open access, peer-reviewed journal that publishes articles which contribute new results in all areas of the advanced vision computing. The goal of this journal is to bring together researchers and practitioners from academia and industry to focus on understanding advances in vision computing and establishing new collaborations in these areas. Authors are solicited to contribute to the journal by submitting articles that illustrate research results, projects, surveying works and industrial experiences that describe significant advances in the areas of vision computing.

In this paper a new method for segmenting medical images is presented, the Multiresolution Diffused Expectation-Maximization (MDEM) algorithm. The algorithm operates within a multiscale framework, thus taking advantage of the fact that objects/regions to be segmented usually resides at different scales. At each scale segmentation is carried out via the Expectation-Maximization algorithm, coupled with anisotropic diffusion on classes, in order to account for the spatial dependencies among pixels. This new approach is validated via experiments on a variety of medical images and its performance is compared with more standard methods.

Polypharmacology has emerged as novel means in drug discovery for improving treatment response in clinical use. However, to really capitalize on the polypharmacological effects of drugs, there is a critical need to better model and understand how the complex interactions between drugs and their cellular targets contribute to drug efficacy and possible side effects. Network graphs provide a convenient modeling framework for dealing with the fact that most drugs act on cellular systems through targeting multiple proteins both through on-target and off-target binding. Network pharmacology models aim at addressing questions such as how and where in the disease network should one target to inhibit disease phenotypes, such as cancer growth, ideally leading to therapies that are less vulnerable to drug resistance and side effects by means of attacking the disease network at the systems level through synergistic and synthetic lethal interactions. Since the exponentially increasing number of potential drug target combinations makes pure experimental approach quickly unfeasible, this review depicts a number of computational models and algorithms that can effectively reduce the search space for determining the most promising combinations for experimental evaluation. Such computational-experimental strategies are geared toward realizing the full potential of multi-target treatments in different disease phenotypes. Our specific focus is on system-level network approaches to polypharmacology designs in anticancer drug discovery, where we give representative examples of how network-centric modeling may offer systematic strategies toward better understanding and even predicting the phenotypic responses to multi-target therapies.

In this paper, a framework for diffusion of color images is presented. The method is based on the theory of thermodynamics of irreversible transformations, which provides a suitable basis for designing correlations between the different color channels. More precisely, we derive an equation for color evolution, which comprises a purely spatial diffusive term and a nonlinear term that depends on the interactions among color channels over space. We apply the proposed equation to images represented in several color spaces, such as RGB, CIELAB, Opponent colors and IHS Index terms. Color images, scale-space, vector-valued diffusion.

The evolution of information in images undergoing fine-to-coarse anisotropic transformations is analyzed by using an approach based on the theory of irreversible transformations. In particular, we show that, when an anisotropic diffusion model is used, local variation of entropy production over space and scale provides the basis for a general method to extract relevant image features.

We consider two-scale problems: the fine-scale and the coarse-scale. The coarse model is taken to be a continuum. The key question in this class of problems is related to the simulation of the fine-scale cell: How are the coarse-scale fields to be passed onto the fine scale? Often used periodic boundary conditions, have important drawbacks. The mathematical conditions that answer this question are called minimal boundary conditions (MBC). MBC are imposed on a fine-scale computational cell as a constraint derived from the coarse-scale model. They are minimal in the sense that nothing but the desired constraint is imposed - in contrast to periodic boundary conditions. Owing to their integral nature, the MBC can be applied to any shape of the fine-scale computational cell. The application to fine-scale continuum models has been discussed earlier, Mesarovic and Padbidri [1]. In this paper, we discuss application of MBC to fine-scale discrete models with local interactions - granular materials. The key to this application is the equivalent representation of kinematics of granular flow using the Delaunay network.