Desynchronization in Networks of Globally Coupled Neurons with Dendritic Dynamics

This paper presents the results of a study of synchronization processes in oscillatory neural networks of various structures based on the Kuramoto model. The estimates of synchronization processes occurring in the oscillatory networks are examined. The results of studying the practical application of oscillatory networks for solving cluster analysis problems are presented.

Benefits of intensive speech treatment have been documented for a range of speech signs in English speakers with Parkinson's Disease (PD). However, the answer to a critical question that whether the same treatment benefits speech variables including intelligibility in Mandarin speakers is still unclear. In order to develop a targeted speech treatment for Mandarin speakers with PD, we reviewed the efficacy of intensive speech treatment to improve vocal loudness and functional communication and discuss possible explanations for efficacy on Mandarin speakers with PD. Literatures about intensive speech treatment for Mandarin speakers with PD were retrieved from PubMed, Web of Science, Embase, China National Knowledge Infrastructure (CNKI), Wanfang and Weipu Database for Chinese Technical Periodicals (VIP) Database. Search strategy was (voice therapy OR speech therapy OR voice treatment OR speech treatment OR voice training OR speech training OR voice rehabilitation OR speech rehabilitation OR Lee Silverman voice treatment OR intensive speech treatment) and (Parkinson's disease) and (Mandarin speakers OR Chinese OR Chinese people). Five randomized controlled trials were selected and possible explanations for efficacy on individuals with PD are discussed. Further research directions are suggested. The existing evidence from treatment efficacy studies of intensive speech treatment provides support for improving vocal loudness, speech intelligibility, pitch and rate in Mandarin speakers with PD. Our future research will continue to work to conduct a large sample multicenter randomized controlled trial to provide high quality evidence and understand the basic mechanisms accompanying treatment-related change.

The Kuramoto model in complex networks

The standard Kuramoto model has been instrumental in explaining synchronization and desynchronization, two emergent phenomena often observed in biological, neuronal, and physical systems. While the Kuramoto model has turned out effective with one-dimensional oscillators, real-world systems often involve high-dimensional interacting units, such as biological swarms, necessitating a model of multidimensional oscillators. However, existing high-dimensional generalizations of the Kuramoto model commonly rely on a scalar-valued coupling strength, which limits their ability to capture the full complexity of high-dimensional interactions. This work introduces a matrix, A, to couple the interconnected components of the oscillators in a d-dimensional space, leading to a matrix-coupled multidimensional Kuramoto model that approximates a prototypical swarm dynamics by its first-order Fourier harmonics. Moreover, the matrix A introduces an inter-dimensional higher-order interaction that partly accounts for the emergence of 2 d system modes in a d-dimensional population, where each dimension can either be synchronized or desynchronized, represented by a set of almost binary order parameters. The binary system modes capture characteristic swarm behaviors such as fish milling or polarized schooling. Additionally, our findings provides a theoretical analogy to cerebral activity, where the resting state and the activated state coexist unihemispherically. It also suggests a new possibility for information storage in oscillatory neural networks.

We devised a new method of data mining for a large-scale database. In the method, a network of locally coupled phase oscillators subject to Kuramoto's model substitutes for given multivariate data to generate major features through phase locking of the oscillators, i.e., phase transition of the data set. We applied the method to the national database of care needs certification for the Japanese public long-term care insurance program, and found three major patterns in the aging process of the frail elderly. This work revealed the latent utility of Kuramoto's model for data processing.

Event-related potentials and reaction time measures to auditory discrimination tasks of graded difficulty were used to separate cognitive from motor processing time in 27 patients with newly diagnosed, previously untreated Parkinson's disease and later on optimal levodopa treatment. Before treatment event-related potential P3 and task performance were normal but the reaction time was prolonged compared with age matched controls. After treatment P3 latency was significantly prolonged and the reaction time reduced suggesting a dopamine induced dissociation between cognitive and motor processing. In early Parkinson's disease cognitive processing time remains normal but the motor processing time is prolonged. Dopamine replacement is followed by significantly reduced motor processing time despite increased cognitive processing time. Motor processing may reflect the dopamine status of the putamen whereas dopaminergic over-stimulation of other regions may adversely affect cognitive processing in patients treated with levodopa.

Altered Cerebellar Oscillations in Parkinson’s Disease Patients during Cognitive and Motor Tasks

Cognitive processes and neurophysiological mechanisms of time processing in Parkinson's disease: A narrative review.

Networks of phase oscillators have become a widely established paradigmatic model for studying emergent collective behavior across several real-world systems, including neuronal networks, populations of chemical oscillators, and power grids. The Kuramoto model, involving one-dimensional or two-dimensional phase oscillators, demonstrates the potential for networks to showcase exceptional collective dynamics. This encompasses various outcomes such as full, partial, explosive, and asymmetry-induced synchronization, clusters, chimeras, solitary states, and generalized splay states. Notably, increasing all-to-all coupling in the classical Kuramoto model induces full synchronization as the most probable outcome and dominant rhythm. Kuramoto networks with repulsive coupling usually display splay, generalized, and cluster splay states, but the conditions under which a certain rhythm can arise and prevail are not entirely understood. Equally important for connecting Kuramoto networks to practical physical systems is understanding the function of higher-order coupling terms. These terms display a Fourier decomposition of a general 2π-periodic interaction function [1]. Previous studies have demonstrated that the inclusion of higher-order terms in the classical Kuramoto model of oscillators with all-to-all attractive coupling can lead to multiple synchronous states and switching between synchronization clusters. However, the impact of higher-order coupling modes on rhythm generation in repulsive networks remains unexplored. In this work, we present significant progress in addressing the critical issue related to repulsive Kuramoto–Sakaguchi networks of phase oscillators with phase-lagged first-order and higher-order coupling. We demonstrate that weakly repulsive networks of even and odd numbers of oscillators with first-order coupling are dominated by two-cluster and three-cluster splay states, respectively. The three-cluster splay states consist of two distinct coherent clusters and one solitary oscillator. These tripod states can be considered a fusion of a two-body chimera and a solitary state. We have dubbed these patterns of three oscillators as “Cyclops states” in reference to the Greek mythological giant with a single eye. The solitary oscillator and synchronous clusters respectively represent the Cyclops’ eye and shoulders. We present a remarkable discovery that the inclusion of higher-order coupling modes leads to worldwide stability of cyclops states across almost the entire range of the phase-lag parameter controlling repulsion [2]. Beyond the Kuramoto oscillators, we demonstrate the robust presence of this effect in networks of canonical theta-neurons with adaptive coupling. Furthermore, our results provide insight into identifying dominant rhythms within repulsive physical and biological networks.

Human cognitive and perception processes have a great tolerance for imprecision or uncertainty. For this reason, the notions of perception and cognition have great importance in solving many decision making problems in engineering, medicine, science, and social science as there are innumerable uncertainties in real-world phenomena. These uncertainties can be broadly classified as either type one uncertainty arising from the random behavior of physical processes or type two uncertainty arising from human perception and cognition processes. Statistical theory can be used to model the former, but lacks the sophistication to process the latter. The theory of fuzzy logic has proven to be very effective in processing type two uncertainty. New computing methods based on fuzzy logic can lead to greater adaptability, tractability, robustness, a lower cost solution, and better rapport with reality in the development of intelligent systems. Fuzzy logic is needed to properly pose and answer queries about quantitatively defining imprecise linguistic terms like middle class, poor, low inflation, medium inflation, and high inflation. Imprecise terms like these in natural languages should be considered to have qualitative definitions, quantitative definitions, crisp quantitative definitions, fuzzy quantitative definitions, type-one fuzzy quantitative definitions, and interval type-two fuzzy quantitative definitions. There can be crisp queries, crisp answers, type-one fuzzy queries, type-one fuzzy answers, interval type-two fuzzy queries, and interval type-two fuzzy answers.

In an attempt to improve the gait of people with Parkinson disease (PD), researchers have examined the effect of visual cues placed on the floor. These studies typically have used a single session of training with such cues and have not examined the long-term carryover of such training. In the present study, therefore, gait was analyzed during uncued, cued, and retention phases, each lasting 1 month. A 78-year-old woman who had been diagnosed with PD 12 years previously (Hoehn and Yahr classification of disability, stage III) volunteered for the study. During the initial uncued gait phase, the subject was required to walk a distance of 10 m as many times as she could in 30 minutes, 3 times per week for 4 weeks. During the 4-week cued gait phase, visual cues were placed on the floor along the 10-m walkway. The cues were initially 110% of the uncued step length and were later increased to 120%. Following this cued gait phase, the subject's gait was recorded periodically for 1 month without cues available. Step length, gait speed, and 2-dimensional lower-limb kinematics were compared within and across the 3 experimental phases. Celeration lines were calculated for the initial uncued phase and then extrapolated across the cued training and uncued retention phases. Binomial tests were used to analyze the significance of changes from the initial phase of the experiment. Step length (0.53-0.56 m) and gait speed (0.77-0.82 m x s(-1)) were essentially unchanged during uncued gait training after the first day; however, during the cued gait phase, gait speed improved, from 0.87 m x s(-1) to 1.13 m x s(-1), as step length was increased with visual cues. Improvements in step length (0.68 m) and gait speed (1.08 m x s(-1)) were still evident 1 month following the removal of the cues. Analyses of angle-angle diagrams and phase-plane portraits revealed that training with visual cues increased hip and knee range of motion and engendered more stable motor control of the lower limb. In contrast to previous studies in which the benefits of visual cueing were relatively short-lived, in this study, 1 month of gait training with visual cues was successful in establishing a lasting improvement in gait speed and step length while increasing the stability of the underlying motor control system.

See Bell et al. (doi:10.1093/awx063) for a scientific commentary on this article. Impaired dual tasking, namely the inability to concurrently perform a cognitive and a motor task (e.g. 'stops walking while talking'), is a largely unexplained and frequent symptom of Parkinson's disease. Here we consider two circuit-level accounts of how striatal dopamine depletion might lead to impaired dual tasking in patients with Parkinson's disease. First, the loss of segregation between striatal territories induced by dopamine depletion may lead to dysfunctional overlaps between the motor and cognitive processes usually implemented in parallel cortico-striatal circuits. Second, the known dorso-posterior to ventro-anterior gradient of dopamine depletion in patients with Parkinson's disease may cause a funnelling of motor and cognitive processes into the relatively spared ventro-anterior putamen, causing a neural bottleneck. Using functional magnetic resonance imaging, we measured brain activity in 19 patients with Parkinson's disease and 26 control subjects during performance of a motor task (auditory-cued ankle movements), a cognitive task (implementing a switch-stay rule), and both tasks simultaneously (dual task). The distribution of task-related activity respected the known segregation between motor and cognitive territories of the putamen in both groups, with motor-related responses in the dorso-posterior putamen and task switch-related responses in the ventro-anterior putamen. During dual task performance, patients made more motor and cognitive errors than control subjects. They recruited a striatal territory (ventro-posterior putamen) not engaged during either the cognitive or the motor task, nor used by controls. Relatively higher ventro-posterior putamen activity in controls was associated with worse dual task performance. These observations suggest that dual task impairments in Parkinson's disease are related to reduced spatial focusing of striatal activity. This pattern of striatal activity may be explained by a loss of functional segregation between neighbouring striatal territories that occurs specifically in a dual task context.

Computational simulations of flocks and crowds have typically been processed by a set of logic or syntactic rules. In recent decades, a new generation of systems has emerged from dynamicist approaches in which the agents and the environment are treated as a pair of dynamical systems coupled informationally and mechanically. Their spontaneous interactions allow them to achieve the desired behavior. The main proposition assumes that the agent does not need a full model or to make inferences before taking actions; rather, the information necessary for any action can be derived from the environment with simple computations and very little internal state. In this paper, we present a simulation framework in which the agents are endowed with a sensing device, an oscillator network as controller and actuators to interact with the environment. The perception device is designed as an optic array emulating the principles of the animal retina, which assimilates stimuli resembling optic flow to be captured from the environment. The controller modulates informational variables to action variables in a sensory‐motor flow. Our approach is based on the Kuramoto model that describes mathematically a network of coupled phase oscillators and the use of evolutionary algorithms, which is proved to be capable of synthesizing minimal synchronization strategies based on the dynamical coupling between agents and environment. We carry out a comparative analysis with classical implementations taking into account several criteria. It is concluded that we should consider replacing the metaphor of symbolic information processing by that of sensory‐motor coordination in problems of multi‐agent organizations. Copyright © 2015 John Wiley & Sons, Ltd.

In this paper, we introduce a programmable particle swarm evolving on a sphere called swarm on sphere system. This model is a polynomial dynamical system obtained from a consensus algorithm that exhibits a rich set of synchronous behaviors with close connections to the Kuramoto model of coupled oscillators, coalition formation in social networks, small-words, integer programming problems such as max-cut, and networks of self-synchronous oscillators with applications to synthetic biology. We prove the generalized Kuramoto model can be obtained as a special case of this model in dimension two. Moreover, we provide formal stability analysis of aligned, bipolar, and dispersed synchronous modes of the system. As a byproduct of this stability analysis, we obtain simple algorithms for programming the weights of the swarm enabling it to exhibit various desired patterns of synchrony. Simulation results are provided that demonstrate 3-D in-phase synchrony, coalition formation for interacting agents with mixed-sign couplings, and dispersal behavior with spatial order.

Asymptotic formation and orbital stability of phase-locked states for the Kuramoto model