Stability and convergence of an implicit numerical method for the non-linear fractional reaction-subdiffusion process

In this paper, we consider the following non-linear fractional reaction–subdiffusion process (NFR-SubDP): Formula where f(u, x, t) is a linear function of u, the function g(u, x, t) satisfies the Lipschitz condition and 0Dt1–{gamma} is the Riemann–Liouville time fractional partial derivative of order 1 – {gamma}. We propose a new computationally efficient numerical technique to simulate the process. Firstly, the NFR-SubDP is decoupled, which is equivalent to solving a non-linear fractional reaction–subdiffusion equation (NFR-SubDE). Secondly, we propose an implicit numerical method to approximate the NFR-SubDE. Thirdly, the stability and convergence of the method are discussed using a new energy method. Finally, some numerical examples are presented to show the application of the present technique. This method and supporting theoretical results can also be applied to fractional integrodifferential equations.

An implicit RBF meshless approach for time fractional diffusion equations

This paper aims to develop an implicit meshless approach based on the radial basis function (RBF) for numerical simulation of time fractional diffusion equations. The meshless RBF interpolation is firstly briefed. The discrete equations for two-dimensional time fractional diffusion equation (FDE) are obtained by using the meshless RBF shape functions and the strong-forms of the time FDE. The stability and convergence of this meshless approach are discussed and theoretically proven. Numerical examples with different problem domains and different nodal distributions are studied to validate and investigate accuracy and efficiency of the newly developed meshless approach. It has proven that the present meshless formulation is very effective for modeling and simulation of fractional differential equations.

An implicit RBF meshless method for a fractal mobile/immobile transport model

Fractional differential equation is used to describe a fractal model of mobile/immobile transport with a power law memory function. This equation is the limiting equation that governs continuous time random walks with heavy tailed random waiting times. In this paper, we firstly propose a finite difference method to discretize the time variable and obtain a semi-discrete scheme. Then we discuss its stability and convergence. Secondly we consider a meshless method based on radial basis functions (RBF) to discretize the space variable. By contrast to conventional FDM and FEM, the meshless method is demonstrated to have distinct advantages: calculations can be performed independent of a mesh, it is more accurate and it can be used to solve complex problems. Finally the convergence order is verified from a numerical example is presented to describe the fractal model of mobile/immobile transport process with different problem domains. The numerical results indicate that the present meshless approach is very effective for modeling and simulating of fractional differential equations, and it has good potential in development of a robust simulation tool for problems in engineering and science that are governed by various types of fractional differential equations.

Relationship among CFH and ARMS2 genotypes, macular pigment optical density, and neuroretinal function in persons without age-related macular degeneration

Purpose: To determine whether there is a difference in neuroretinal function and in macular pigment optical density between persons with high- and low-risk gene variants for age-related macular degeneration (AMD) and no ophthalmoscopic signs of AMD, and to compare the results on neuroretinal function to patients with manifest early AMD. Methods and Participants: Neuroretinal function was assessed with the multifocal electroretinogram (mfERG) for 32 participants (22 healthy persons with no AMD and 10 early AMD patients). The 22 healthy participants with no AMD had high- or low-risk genotypes for either CFH (rs380390) and/or ARMS2 (rs10490924). Trough-to-peak response densities and peak-implicit times were analyzed in 5 concentric rings. Macular pigment optical densitometry was assessed by customized heterochromatic flicker photometry. Results: Trough-to-peak response densities for concentric rings 1 to 3 were, on average, significantly greater in participants with high-risk genotypes than in participants with low-risk genotypes and in persons with early AMD after correction for age and smoking (p<0.05). The group peak- implicit times for ring 1 were, on average, delayed in the patients with early AMD compared with the participants with high- or low-risk genotypes, although these differences were not significant. There was no significant correlation between genotypes and macular pigment optical density. Conclusion: Increased neuroretinal activity in persons who carry high-risk AMD genotypes may be due to genetically determined subclinical inflammatory and/or histological changes in the retina. Neuroretinal function in healthy persons genetically susceptible to AMD may be a useful additional early biomarker (in combination with genetics) before there is clinical manifestation.

The relationship between CFH and ARMS2 genotypes and neuroretinal function in persons without age-related macular degeneration

Purpose: To determine whether neuroretinal function differs in healthy persons with and without common risk gene variants for age- related macular degeneration (AMD) and no ophthalmoscopic signs of AMD, and to compare those findings in persons with manifest early AMD. Methods and Participants: Neuroretinal function was assessed with the multifocal electroretinogram (mfERG) (VERIS, Redwood City, CA,) in 32 participants (22 healthy persons with no clinical signs of AMD and 10 early AMD patients). The 22 healthy participants with no AMD were risk genotypes for either the CFH (rs380390) and/or ARMS2 (rs10490920). We used a slow flash mfERG paradigm (3 inserted frames) and a 103 hexagon stimulus array. Recordings were made with DTL electrodes; fixation and eye movements were monitored online. Trough N1 to peak P1 (N1P1) response densities and P1-implicit times (IT) were analysed in 5 concentric rings. Results: N1P1 response densities (mean ± SD) for concentric rings 1-3 were on average significantly higher in at-risk genotypes (ring 1: 17.97 nV/deg2 ± 1.9, ring 2: 11.7 nV/deg2 ±1.3, ring 3: 8.7 nV/deg2 ± 0.7) compared to those without risk (ring 1: 13.7 nV/deg2 ± 1.9, ring 2: 9.2 nV/deg2 ±0.8, ring 3: 7.3 nV/deg2 ± 1.1) and compared to persons with early AMD (ring 1: 15.3 nV/deg2 ± 4.8, ring 2: 9.1 nV/deg2 ±2.3, ring 3 nV/deg2: 7.3± 1.3) (p<0.5). The group implicit times, P1-ITs for ring 1 were on average delayed in the early AMD patients (36.4 ms ± 1.0) compared to healthy participants with (35.1 ms ± 1.1) or without risk genotypes (34.8 ms ±1.3), although these differences were not significant. Conclusion: Neuroretinal function in persons with normal fundi can be differentiated into subgroups based on their genetics. Increased neuroretinal activity in persons who carry AMD risk genotypes may be due to genetically determined subclinical inflammatory and/or histological changes in the retina. Assessment of neuroretinal function in healthy persons genetically susceptible to AMD may be a useful early biomarker before there is clinical manifestation of AMD.

Mode coupling theory analysis of electrolyte solutions: Time dependent diffusion, intermediate scattering function, and ion solvation dynamics

A self-consistent mode coupling theory (MCT) with microscopic inputs of equilibrium pair correlation functions is developed to analyze electrolyte dynamics. We apply the theory to calculate concentration dependence of (i) time dependent ion diffusion, (ii) intermediate scattering function of the constituent ions, and (iii) ion solvation dynamics in electrolyte solution. Brownian dynamics with implicit water molecules and molecular dynamics method with explicit water are used to check the theoretical predictions. The time dependence of ionic self-diffusion coefficient and the corresponding intermediate scattering function evaluated from our MCT approach show quantitative agreement with early experimental and present Brownian dynamic simulation results. With increasing concentration, the dispersion of electrolyte friction is found to occur at increasingly higher frequency, due to the faster relaxation of the ion atmosphere. The wave number dependence of intermediate scattering function, F(k, t), exhibits markedly different relaxation dynamics at different length scales. At small wave numbers, we find the emergence of a step-like relaxation, indicating the presence of both fast and slow time scales in the system. Such behavior allows an intriguing analogy with temperature dependent relaxation dynamics of supercooled liquids. We find that solvation dynamics of a tagged ion exhibits a power law decay at long times-the decay can also be fitted to a stretched exponential form. The emergence of the power law in solvation dynamics has been tested by carrying out long Brownian dynamics simulations with varying ionic concentrations. The solvation time correlation and ion-ion intermediate scattering function indeed exhibit highly interesting, non-trivial dynamical behavior at intermediate to longer times that require further experimental and theoretical studies. (c) 2015 AIP Publishing LLC.

Visual function and dysfunction in early and late age-related maculopathy

Late age-related maculopathy (ARM) is responsible for the majority of blind registrations in the Western world among persons over 50 years of age. It has devastating effects on quality of life and independence and is becoming a major public health concern. Current treatment options are limited and most aim to slow progression rather than restore vision; therefore, early detection to identify those patients most suitable for these interventions is essential. In this work, we review the literature encompassing the investigation of visual function in ARM in order to highlight those visual function parameters which are affected very early in the disease process. We pay particular attention to measures of acuity, contrast sensitivity (CS), cone function, electrophysiology, visual adaptation, central visual field sensitivity and metamorphopsia. We also consider the impact of bilateral late ARM on visual function as well as the relationship between measures of vision function and self-reported visual functioning. Much interest has centred on the identification of functional changes which may predict progression to neovascular disease; therefore, we outline the longitudinal studies, which to date have reported dark-adaptation time, short-wavelength cone sensitivity, colour-match area effect, dark-adapted foveal sensitivity, foveal flicker sensitivity, slow recovery from glare and slower foveal electroretinogram implicit time as functional risk factors for the development of neovascular disease. Despite progress in this area, we emphasise the need for longitudinal studies designed in light of developments in disease classification and retinal imaging, which would ensure the correct classification of cases and controls, and provide increased understanding of the natural course and progression of the disease and further elucidate the structure-function relationships in this devastating disorder.

Flavonoids and cognitive function: a review of human randomized controlled trial studies and recommendations for future studies

Evidence in support of the neuroprotective effects of flavonoids has increased significantly in recent years, although to date much of this evidence has emerged from animal rather than human studies. Nonetheless, with a view to making recommendations for future good practice, we review 15 existing human dietary intervention studies that have examined the effects of particular types of flavonoid on cognitive performance. The studies employed a total of 55 different cognitive tests covering a broad range of cognitive domains. Most studies incorporated at least one measure of executive function/working memory, with nine reporting significant improvements in performance as a function of flavonoid supplementation compared to a control group. However, some domains were overlooked completely (e.g. implicit memory, prospective memory), and for the most part there was little consistency in terms of the particular cognitive tests used making across study comparisons difficult. Furthermore, there was some confusion concerning what aspects of cognitive function particular tests were actually measuring. Overall, while initial results are encouraging, future studies need to pay careful attention when selecting cognitive measures, especially in terms of ensuring that tasks are actually sensitive enough to detect treatment effects.

Dissociating word stem completion and cued recall as a function of divided attention at retrieval

The aim of this study was to investigate the widely held, but largely untested, view that implicit memory (repetition priming) reflects an automatic form of retrieval. Specifically, in Experiment 1 we explored whether a secondary task (syllable monitoring), performed during retrieval, would disrupt performance on explicit (cued recall) and implicit (stem completion) memory tasks equally. Surprisingly, despite substantial memory and secondary costs to cued recall when performed with a syllable-monitoring task, the same manipulation had no effect on stem completion priming or on secondary task performance. In Experiment 2 we demonstrated that even when using a particularly demanding version of the stem completion task that incurred secondary task costs, the corresponding disruption to implicit memory performance was minimal. Collectively, the results are consistent with the view that implicit memory retrieval requires little or no processing capacity and is not seemingly susceptible to the effects of dividing attention at retrieval.

Entrepreneurial opportunities, implicit contracts and market making for complex consumer goods

This article extends the theory of entrepreneurial opportunity exploitation, outlining how under certain conditions, opportunity exploitation is dependent on market making innovations. Where adverse selection and moral hazard characterize markets, consumers are likely to withdraw regardless of product quality. In order to overcome consumer resistance, entrepreneurs must signal credible commitments. But because consumers purchase without fully specifying requirements, entrepreneurs' commitments take the partial form of implicit contracts, creating strong mutual commitments to repeated transactions. These commitments enable novel markets to function, but introduce additional costs. This article illustrates the theory with the historic case of Singer in sewing machines

INDEX OF AN IMPLICIT DIFFERENTIAL EQUATION

In this paper we introduce the concept of the index of an implicit differential equation F(x,y,p) = 0, where F is a smooth function, p = dy/dx, F(p) = 0 and F(pp) = 0 at an isolated singular point. We also apply the results to study the geometry of surfaces in R(5).

Second person : a point of view? The function of the second person pronoun in narrative prose fiction

This thesis looks at the functions and effects of the ‘second-person’ pronoun in narrative prose fiction, with particular focus on the fluidity and ambiguity of the mode that I will call Protean-'you.' It is a mode in which it is unclear whether the ‘you’ is a character, the narrator, a reader/narratee, or no-one in particular—or a combination of these—so that readers find ‘second-person’ utterances at once familiar and deeply strange. I regard the ‘second person’ as a special case of narrative ‘person’ that, at its most fluid, can produce an experience of reading quite unlike that of reading traditional ‘first-‘ and ‘third-person’ narrative. Essentially, this unique experience comes about because Protean-‘you’ neglects to constitute the stable modes of subjectivity that readers expect to find within narrative textuality. These stable modes of subjectivity, modelled on what I will refer to as Cartesianism’s hegemonic notion of the self, have been thoroughly formalised and naturalised within the practices of ‘first-‘ and ‘third-person’ narrative. The Protean-‘you’ form of ‘second-person’ narrative, conversely, is a mode of narrative discourse that puts readers in a place of doubt and uncertainty, its unsettling equivocations forcefully disrupting accustomed, mimetic explanations of narrative and denying us access to the foundational, authorising subject of classical Cartesian thought. Rather than founding a notion of ‘second-person’ narrative and narrative ‘person’ generally on Cartesianism's ‘self-ish’ logic of unified, privatised identity, I turn to C.S, Peirce's notion of the semiotic self and to developments in post-structuralist thought. Essentially, the conception of subjectivity underpinning my arguments is Peirce's proposition that the self is to be conceived of not as a cogito, but as a sign by which the conscious entity knows itself. It is a sign, moreover, that is constantly being re-read, reinterpreted, so that identity is never self-complete. This reconception of subjectivity is necessary because 1 will argue that the effects of Protean-‘you’ arise in some part from a tension between Cartesianism's hegemony and what philosophical pragmatism and post-structuralism glimpse as the actual condition of the human subject—the subject as dispersed and contingent rather than unified and authoritative. Most discussions of ‘second-person’ narrative conceive of the mode in terms of implicit communicative relations, in some measure instituting Cartesianism's notion of the intentionalist self at the centre of literary meaning. I contrast the paradigmatic address model that arises from this conception against a model that approaches the analysis of ‘second-person’ narrative modality in terms of a referential function, that is, in terms of the object or objects referred to deictically by the ‘second-person’ pronoun. Two principal functions of ‘second-person’ textuality are identified and discussed at length. The first is generalisation, which is rarely dissipated altogether, a situation that contributes to the ambiguities of the pronoun's reference in much ‘second-person’ fiction. The second principal function is that of address, that is, the allocutionary function. Clearly, although stories that continually refer to a ‘you’ can seem quite baffling and unnatural, not all ‘second-person’ narratives unsettle the reader. In order to make the ‘second person's’ outlandish narratives knowable and stable, we bring to bear on them in our habits of reading whatever hermeneutic frames, whatever interpretive keys, come to hand, including a large number of unexceptional forms of literary and ‘natural’ discourse that employ the ‘second-person’ pronoun. These forms include letter writing and internal dialogue (i.e., talking to one's self), the language of the courtroom, the travelogue, the maxim, and so on. In looking at the ways in which the radicalising potentials of ‘second-person’ discourse are contained or recuperated, I focus on issues of vraisemblance and mimesis. Vraisemblance can be described as the ‘system of conventions and expectations which rests on/reinforces that more general system of ‘mutual knowledge’ produced within a community for the realisation and maintenance of a whole social world’. All of the forms of the vraisemblable are already instituted within social, cultural relations, so that what vraisemblance describes is the way we fit the inscriptions we read-that is, the way in which we naturalise what we read-into those given cultural and social forms. I also look at the conventionalising and naturalising work done by notions of mimesis in explaining relations between the world, our being in it, and texts, proposing that mimesis provides a principle buttress by which the good standing of the metaphor of ‘person’ is preserved in traditional and pre-critical modes of analysis. Indeed, the critic’s recourse to ‘person’ is in some measure always an engagement with mimesis. Any discussion that maintains that mimesis is in some way productive of meaning-which this thesis in fact does-must identify mimesis as a merely conventional category within practices of reading and semiosis more generally, and at the very least remove that term from its traditional position of transparent primacy and authority. Some of the most interesting and insightful arguments about ‘second-person’ narrative propose that the ‘second person’s’ most striking effects derive from the constitution of an ‘intersubjective’ experience of reading in which the subject positions of the ‘you’-protagonist, reader-narratee and narrator are combined into a fluid and indeterminate multiple subjectivity. Notions of intersubjectivity frequently position themselves as liberating the reader from Cartesianism's fixed, authoritative modes of subjectivity, Frequently, however, they tend implicitly to reinstate Cartesianism's notion of the self at the centre of textual practice and subjectivity. I look at Daniel Gunn's novel ‘Almost You’, at length in this context, illustrating the constant overdetermination of the ‘you’ and the novel's narrating voice, and demonstrating that this overdetermination leaves the origin of the narrative discourse, the identity of the narrator, and the ontological nature of both principal protagonists utterly ambiguous. The fluidity and ambiguity of Protean-‘you’ in ‘Almost You’ is discussed in terms of ‘second-person’ intersubjectivity, but with a view to demonstrating the indebtedness by the notion of intersubjectivity to Cartesianism's hegemony of ‘person’. I then turn to a discussion of what might be a more ‘old fashioned’ if perhaps ultimately more far-reaching approach to the ‘second person’s’ often startling ambiguities. This is Keats's notion of negative capability, a capacity or quality in which a person ‘is capable of being in uncertainties, Mysteries, doubts, without any irritable reaching after fact and reason.’ I suggest that Protean-‘you’ texts will license all of the readings of ambiguity and fluidity proposed in my discussion of ‘Almost You’, but conclude that the instances of indeterminacy illustrate no more than that: the fluidity and deep ambiguity, and thus, finally, the lack of coherence, of Protean-‘you’ discourse. This has particular implications for how we are to consider readers’ experiences of narrative texts. More fundamentally, it has implications for how we are to consider readers as subjects. I suggest that unstable, ambiguous instances of ‘second-person’ narrative can tear the complex and systematic embroidery of ideological suture that unifies Cretinism’s experience or sense of subjectivity, leaving the reader in a condition of epistemological and ontological havoc. I go on to argue that much of the deeply unsettling effect of Protean-‘you’ discourse anises because its utterances explicitly gesture towards Cretinism’s notion of self. Protean-‘you’ involves a sense of address that is much more pronounced than we are accustomed to facing when reading literary narrative, alerting us to the presence of inscribed anthropomorphic subjects. At the very same time, protean-‘you’ leaves its inscribed subjects indeterminate, ambiguous. This conflict generates a tension between the anticipation of the emergence of speaking and listening selves and our inability to find them. I go on to propose that Protean-‘you’ narrative's lack of coherence is also to be understood as the condition of narrative actuality generally, but a condition that is vigorously mediated against by dominant practices of reading and writing, hocusing my discussion in this respect on the issue of narrative ‘person,’ I argue that narrative ‘person’ is constituted within texts as an apparent unity, but that it is in fact, produced as unitary solely within the practice of making sense, that is, Within our habits of reading, and so is never finally unified. I propose that this is the case for ‘first-‘ and ‘third-person’ modes no less than for the ‘second.’ Where ‘second-person’ narrative at its most radical and Protean differs from conventional ‘first-‘ and ‘third-person’ narratives is the degree to which each has been circumscribed by practices of tantalization, containment and limit, and, in particular, Cretinism’s hegemony of ‘person.’ It may be that the most significant insights ‘second-person’ narrative has to offer are to be found within its capacity to reveal to the engaged reader the underlying condition of narrative discourse, and more generally, its capacity to reveal the actual condition of the human subject-a condition in which, exactly like its textual corollary of narrative ‘person,’ the self is glimpsed as thoroughly dispersed and contingent.

Function-based approach to mixed haptic effects rendering

Commonly, surface and solid haptic effects are defined in such a way that they hardly can be rendered together. We propose a method for defining mixed haptic effects including surface, solid, and force fields. These haptic effects can be applied to virtual scenes containing various objects, including polygon meshes, point clouds, impostors, and layered textures, voxel models as well as function-based shapes. Accordingly, we propose a way how to identify location of the haptic tool in such virtual scenes as well as consistently and seamlessly determine haptic effects when the haptic tool moves in the scenes with objects having different sizes, locations, and mutual penetrations. To provide for an efficient and flexible rendering of haptic effects, we propose to concurrently use explicit, implicit and parametric functions, and algorithmic procedures.

Discovering implicit criteria preferences reflected in tourism journal ranking lists using the Choquet Integral

Variations between journal rankings may cause confusion. As such, prior attempts were made to compare and evaluate journal ranking criteria for obtaining insightful knowledge on how different research communities have ranked journals. However, existing approaches are unable to model the journal ranking process closely enough as they are incapable of considering the relationship between multiple criteria simultaneously. In this paper, we address the challenges by introducing the Choquet Integral (CI) for evaluating journal ranking criteria. The new approach is able to account for interactions between criteria in relation to overall ranking score, using a fuzzy measure in its computation. Its properties, the Shapley value and the Interaction index, allow for good representations of importance and interactions between criteria. We demonstrate the efficiency of the CI through a case study of journal ranking lists in tourism and service journals.