On Some Applications of Nonlinear Differential Equations in Image Processing: Concepts and Electronic Implementation

International audienc

Discrete instability in nonlinear lattices

The discrete multiscale analysis for boundary value problems in nonlinear discrete systems leads to a first order discrete modulational instability above a threshold amplitude for wave numbers beyond the zero of group velocity dispersion. Applied to the electrical lattice [Phys. Rev. E, 51 (1995) 6127 ], this acurately explains the experimental instability at wave numbers beyond 1.25 . The theory is also briefly discussed for sine-Gordon and Toda lattices.Comment: 1 figure, revtex, published: Phys. Rev. Lett. 83 (1999) 232

On dissipationless shock waves in a discrete nonlinear Schr\"odinger equation

It is shown that the generalized discrete nonlinear Schr\"odinger equation can be reduced in a small amplitude approximation to the KdV, mKdV, KdV(2) or the fifth-order KdV equations, depending on values of the parameters. In dispersionless limit these equations lead to wave breaking phenomenon for general enough initial conditions, and, after taking into account small dispersion effects, result in formation of dissipationless shock waves. The Whitham theory of modulations of nonlinear waves is used for analytical description of such waves.Comment: 15 pages, 9 figure

Asymmetric gap soliton modes in diatomic lattices with cubic and quartic nonlinearity

Nonlinear localized excitations in one-dimensional diatomic lattices with cubic and quartic nonlinearity are considered analytically by a quasi-discreteness approach. The criteria for the occurence of asymmetric gap solitons (with vibrating frequency lying in the gap of phonon bands) and small-amplitude, asymmetric intrinsic localized modes (with the vibrating frequency being above all the phonon bands) are obtained explicitly based on the modulational instabilities of corresponding linear lattice plane waves. The expressions of particle displacement for all these nonlinear localized excitations are also given. The result is applied to standard two-body potentials of the Toda, Born-Mayer-Coulomb, Lennard-Jones, and Morse type. The comparison with previous numerical study of the anharmonic gap modes in diatomic lattices for the standard two-body potentials is made and good agreement is found.Comment: 24 pages in Revtex, 2 PS figure

GANDALF: Generative Adversarial Networks with Discriminator-Adaptive Loss Fine-tuning for Alzheimer's Disease Diagnosis from MRI

Positron Emission Tomography (PET) is now regarded as the gold standard for the diagnosis of Alzheimer's Disease (AD). However, PET imaging can be prohibitive in terms of cost and planning, and is also among the imaging techniques with the highest dosage of radiation. Magnetic Resonance Imaging (MRI), in contrast, is more widely available and provides more flexibility when setting the desired image resolution. Unfortunately, the diagnosis of AD using MRI is difficult due to the very subtle physiological differences between healthy and AD subjects visible on MRI. As a result, many attempts have been made to synthesize PET images from MR images using generative adversarial networks (GANs) in the interest of enabling the diagnosis of AD from MR. Existing work on PET synthesis from MRI has largely focused on Conditional GANs, where MR images are used to generate PET images and subsequently used for AD diagnosis. There is no end-to-end training goal. This paper proposes an alternative approach to the aforementioned, where AD diagnosis is incorporated in the GAN training objective to achieve the best AD classification performance. Different GAN lossesare fine-tuned based on the discriminator performance, and the overall training is stabilized. The proposed network architecture and training regime show state-of-the-art performance for three- and four- class AD classification tasks.Comment: Accepted for publication at the MICCAI 2020 conferenc

Human-Centered Design Components in Spiral Model to Improve Mobility of Older Adults

As humans grow older, their cognitive needs change more frequently due to distal and proximal life events. Designers and developers need to come up with better designs that integrate older users’ needs in a short period of time with more interaction with the users. Therefore, the positioning of human end users in the center of the design itself is not the key to the success of design artifacts while designing applications for older adults to use a smartphone as a promising tool for journey planner while using public transportation. This study analyzed the use of human-centered design (HCD) components, the spiral model, and the design for failure (DfF) approach to improve the interactions between older users and designers/developers in gathering usability needs in the concept stage and during the development of the app with short iterative cycles. To illustrate the importance of the applied approach, a case study with particular focus on older adults is presented.The results presented in this study are based on “Assistant” project funded by AAL JP, co-funded by the European Union. The authors would like to thank Dr. Stefan Carmien, my colleague in Assistant, for mentoring and for reading and making comments in the earlier versions of this chapter; participating research institutes; funding agencies; and companies from Finland, Spain, Austria, France, and the United Kingdom for their active support throughout the project

Josephson Junctions and AdS/CFT Networks

We propose a new holographic model of Josephson junctions (and networks thereof) based on designer multi-gravity, namely multi-(super)gravity theories on products of distinct asymptotically AdS spacetimes coupled by mixed boundary conditions. We present a simple model of a Josephson junction (JJ) that exhibits the well-known current-phase sine relation of JJs. In one-dimensional chains of holographic superconductors we find that the Cooper-pair condensates are described by a discretized Schrodinger-type equation. Such non-integrable equations, which have been studied extensively in the past in condensed matter and optics applications, are known to exhibit complex behavior that includes periodic and quasiperiodic solutions, chaotic dynamics, soliton and kink solutions. In our setup these solutions translate to holographic configurations of strongly-coupled superconductors in networks with weak site-to-site interactions that exhibit interesting patterns of modulated superconductivity. In a continuum limit our equations reduce to generalizations of the Gross-Pitaevskii equation. We comment on the many possible extensions and applications of this new approach.Comment: 39 pages, 11 figures; v2 clarified the nature and computation of the Josephson current in subsec. 3.2 and specific properties of the two-site system, analogous minor modifications in subsec. 4.4 and added a new subsec. 4.5 with a new fig.

Characteristics of subjective cognitive decline associated with amyloid positivity

Introduction: The evidence for characteristics of persons with subjective cognitive decline (SCD) associated with amyloid positivity is limited. Methods: In 1640 persons with SCD from 20 Amyloid Biomarker Study cohort, we investigated the associations of SCD-specific characteristics (informant confirmation, domain-specific complaints, concerns, feelings of worse performance) demographics, setting, apolipoprotein E gene (APOE) ε4 carriership, and neuropsychiatric symptoms with amyloid positivity. Results: Between cohorts, amyloid positivity in 70-year-olds varied from 10% to 76%. Only older age, clinical setting, and APOE ε4 carriership showed univariate associations with increased amyloid positivity. After adjusting for these, lower education was also associated with increased amyloid positivity. Only within a research setting, informant-confirmed complaints, memory complaints, attention/concentration complaints, and no depressive symptoms were associated with increased amyloid positivity. Feelings of worse performance were associated with less amyloid positivity at younger ages and more at older ages. Discussion: Next to age, setting, and APOE ε4 carriership, SCD-specific characteristics may facilitate the identification of amyloid-positive individuals