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

Investigating reliable amyloid accumulation in Centiloids: Results from the AMYPAD Prognostic and Natural History Study.

To support clinical trial designs focused on early interventions, our study determined reliable early amyloid-β (Aβ) accumulation based on Centiloids (CL) in pre-dementia populations. A total of 1032 participants from the Amyloid Imaging to Prevent Alzheimer's Disease-Prognostic and Natural History Study (AMYPAD-PNHS) and Insight46 who underwent [ F]flutemetamol, [ F]florbetaben or [ F]florbetapir amyloid-PET were included. A normative strategy was used to define reliable accumulation by estimating the 95 percentile of longitudinal measurements in sub-populations (N  = 101/750, N  = 35/382) expected to remain stable over time. The baseline CL threshold that optimally predicts future accumulation was investigated using precision-recall analyses. Accumulation rates were examined using linear mixed-effect models. Reliable accumulation in the PNHS was estimated to occur at >3.0 CL/year. Baseline CL of 16 [12,19] best predicted future Aβ-accumulators. Rates of amyloid accumulation were tracer-independent, lower for APOE ε4 non-carriers, and for subjects with higher levels of education. Our results support a 12-20 CL window for inclusion into early secondary prevention studies. Reliable accumulation definition warrants further investigations. [Abstract copyright: © 2024 The Authors. Alzheimer's & Dementia published by Wiley Periodicals LLC on behalf of Alzheimer's Association.

Recruitment of pre-dementia participants: main enrollment barriers in a longitudinal amyloid-PET study

Background: The mismatch between the limited availability versus the high demand of participants who are in the pre-dementia phase of Alzheimer’s disease (AD) is a bottleneck for clinical studies in AD. Nevertheless, potential enrollment barriers in the pre-dementia population are relatively under-reported. In a large European longitudinal biomarker study (the AMYPAD-PNHS), we investigated main enrollment barriers in individuals with no or mild symptoms recruited from research and clinical parent cohorts (PCs) of ongoing observational studies. Methods: Logistic regression was used to predict study refusal based on sex, age, education, global cognition (MMSE), family history of dementia, and number of prior study visits. Study refusal rates and categorized enrollment barriers were compared between PCs using chi-squared tests. Results: 535/1856 (28.8%) of the participants recruited from ongoing studies declined participation in the AMYPAD-PNHS. Only for participants recruited from clinical PCs (n = 243), a higher MMSE-score (β = − 0.22, OR = 0.80, p <.05), more prior study visits (β = − 0.93, OR = 0.40, p <.001), and positive family history of dementia (β = 2.08, OR = 8.02, p <.01) resulted in lower odds on study refusal. General study burden was the main enrollment barrier (36.1%), followed by amyloid-PET related burden (PCresearch = 27.4%, PCclinical = 9.0%, X 2 = 10.56, p =.001), and loss of research interest (PCclinical = 46.3%, PCresearch = 16.5%, X 2 = 32.34, p <.001). Conclusions: The enrollment rate for the AMYPAD-PNHS was relatively high, suggesting an advantage of recruitment via ongoing studies. In this observational cohort, study burden reduction and tailored strategies may potentially improve participant enrollment into trial readiness cohorts such as for phase-3 early anti-amyloid intervention trials. The AMYPAD-PNHS (EudraCT: 2018–002277-22) was approved by the ethical review board of the VU Medical Center (VUmc) as the Sponsor site and in every affiliated site

Neuropsychiatric profiles and conversion to dementia in mild cognitive impairment, a latent class analysis

Altres ajuts: Fondo Europeo de Desarrollo Regional (FEDER)Altres ajuts: Generalitat de Catalunya. Programa CERCAAltres ajuts: Instituto de Salud Carlos III (CIBERSAM i CIBERNED)Altres ajuts: Fundació "La Caixa"Altres ajuts: Grífols SA (GR@ACE project)Neuropsychiatric symptoms (NPS) have been recently addressed as risk factors of conversion to Alzheimer's disease (AD) and other dementia types in patients diagnosed with Mild Cognitive Impairment (MCI). Our aim was to determine profiles based on the prominent NPS in MCI patients and to explore the predictive value of these profiles on conversion to specific types of dementia. A total of 2137 MCI patients monitored in a memory clinic were included in the study. Four NPS profiles emerged (classes), which were defined by preeminent symptoms: Irritability, Apathy, Anxiety/Depression and Asymptomatic. Irritability and Apathy were predictors of conversion to dementia (HR = 1.43 and 1.56, respectively). Anxiety/depression class showed no risk effect of conversion when compared to Asymptomatic class. Irritability class appeared as the most discriminant neuropsychiatric condition to identify non-AD converters (i.e., frontotemporal dementia, vascular dementia, Parkinson's disease and dementia with Lewy Bodies). The findings revealed that consistent subgroups of MCI patients could be identified among comorbid basal NPS. The preeminent NPS showed to behave differentially on conversion to dementia, beyond AD. Therefore, NPS should be used as early diagnosis facilitators, and should also guide clinicians to detect patients with different illness trajectories in the progression of MCI

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.