Small-Signal Amplification of Period-Doubling Bifurcations in Smooth Iterated Maps

Various authors have shown that, near the onset of a period-doubling bifurcation, small perturbations in the control parameter may result in much larger disturbances in the response of the dynamical system. Such amplification of small signals can be measured by a gain defined as the magnitude of the disturbance in the response divided by the perturbation amplitude. In this paper, the perturbed response is studied using normal forms based on the most general assumptions of iterated maps. Such an analysis provides a theoretical footing for previous experimental and numerical observations, such as the failure of linear analysis and the saturation of the gain. Qualitative as well as quantitative features of the gain are exhibited using selected models of cardiac dynamics.Comment: 12 pages, 7 figure

Confluence of geodesic paths and separating loops in large planar quadrangulations

We consider planar quadrangulations with three marked vertices and discuss the geometry of triangles made of three geodesic paths joining them. We also study the geometry of minimal separating loops, i.e. paths of minimal length among all closed paths passing by one of the three vertices and separating the two others in the quadrangulation. We concentrate on the universal scaling limit of large quadrangulations, also known as the Brownian map, where pairs of geodesic paths or minimal separating loops have common parts of non-zero macroscopic length. This is the phenomenon of confluence, which distinguishes the geometry of random quadrangulations from that of smooth surfaces. We characterize the universal probability distribution for the lengths of these common parts.Comment: 48 pages, 33 color figures. Final version, with one concluding paragraph and one reference added, and several other small correction

Intrinsic functional clustering of ventral premotor F5 in the macaque brain

© 2020 Neurophysiological and anatomical data suggest the existence of several functionally distinct regions in the lower arcuate sulcus and adjacent postarcuate convexity of the macaque monkey. Ventral premotor F5c lies on the postarcuate convexity and consists of a dorsal hand-related and ventral mouth-related field. The posterior bank of the lower arcuate contains two additional premotor F5 subfields at different anterior-posterior levels, F5a and F5p. Anterior to F5a, area 44 has been described as a dysgranular zone occupying the deepest part of the fundus of the inferior arcuate. Finally, area GrFO occupies the most rostral portion of the fundus and posterior bank of inferior arcuate and extends ventrally onto the frontal operculum. Recently, data-driven exploratory approaches using resting-state fMRI data have been suggested as a promising non-invasive method for examining the functional organization of the primate brain. Here, we examined to what extent partitioning schemes derived from data-driven clustering analysis of resting-state fMRI data correspond with the proposed organization of the fundus and posterior bank of the macaque arcuate sulcus, as suggested by invasive architectonical, connectional and functional investigations. Using a hierarchical clustering analysis, we could retrieve clusters corresponding to the dorsal and ventral portions of F5c on the postarcuate convexity, F5a and F5p at different antero-posterior locations on the posterior bank of the lower arcuate, area 44 in the fundus, as well as part of area GrFO in the most anterior portion of the fundus. Additionally, each of these clusters displayed distinct whole-brain functional connectivity, in line with previous anatomical tracer and seed-based functional connectivity investigations of F5/44 subdivisions. Overall, our data suggests that hierarchical clustering analysis of resting-state fMRI data can retrieve a fine-grained level of cortical organization that resembles detailed parcellation schemes derived from invasive functional and anatomical investigations

Structural alterations in cortical and thalamocortical white matter tracts after recovery from prefrontal cortex lesions in macaques

Unilateral damage to the frontoparietal network typically impairs saccade target selection within the contralesional visual hemifield. Severity of deficits and the degree of recovery have been associated with widespread network dysfunction, yet it is not clear how these behavioural and functional brain changes relate with the underlying structural white matter tracts. Here, we investigated whether recovery after unilateral prefrontal cortex (PFC) lesions was associated with changes in white matter microstructure across large-scale frontoparietal cortical and thalamocortical networks. Diffusion-weighted imaging was acquired in four male rhesus macaques at pre-lesion, week 1, and week 8-16 post-lesion when target selection deficits largely recovered. Probabilistic tractography was used to reconstruct cortical frontoparietal fiber tracts, including the superior longitudinal fasciculus (SLF) and transcallosal fibers connecting the PFC or posterior parietal cortex (PPC), as well as thalamocortical fiber tracts connecting the PFC and PPC to thalamic nuclei. We found that the two animals with small PFC lesions showed increased fractional anisotropy in both cortical and thalamocortical fiber tracts when behaviour had recovered. However, we found that fractional anisotropy decreased in cortical frontoparietal tracts after larger PFC lesions yet increased in some thalamocortical tracts at the time of behavioural recovery. These findings indicate that behavioural recovery after small PFC lesions may be supported by both cortical and subcortical areas, whereas larger PFC lesions may have induced widespread structural damage and hindered compensatory remodeling in the cortical frontoparietal network

Frontoparietal connectivity as a product of convergent evolution in rodents and primates: functional connectivity topologies in grey squirrels, rats, and marmosets

Robust frontoparietal connectivity is a defining feature of primate cortical organization. Whether mammals outside the primate order, such as rodents, possess similar frontoparietal functional connectivity organization is a controversial topic. Previous work has primarily focused on comparing mice and rats to primates. However, as these rodents are nocturnal and terrestrial, they rely much less on visual input than primates. Here, we investigated the functional cortical organization of grey squirrels which are diurnal and arboreal, thereby better resembling primate ecology. We used ultra-high field resting-state fMRI data to compute and compare the functional connectivity patterns of frontal regions in grey squirrels (Sciurus carolinensis), rats (Rattus norvegicus), and marmosets (Callithrix jacchus). We utilized a fingerprinting analysis to compare interareal patterns of functional connectivity from seeds across frontal cortex in all three species. The results show that grey squirrels, but not rats, possess a frontoparietal connectivity organization that resembles the connectivity pattern of marmoset lateral prefrontal cortical areas. Since grey squirrels and marmosets have acquired an arboreal way of life but show no common arboreal ancestor, the expansion of the visual system and the formation of a frontoparietal connectivity architecture might reflect convergent evolution driven by similar ecological niches in primates and tree squirrels

Functional Localization of the Frontal Eye Fields in the Common Marmoset Using Microstimulation

Copyright © 2019 the authors. The frontal eye field (FEF) is a critical region for the deployment of overt and covert spatial attention. Although investigations in the macaque continue to provide insight into the neural underpinnings of the FEF, due to its location within a sulcus, the macaque FEF is virtually inaccessible to electrophysiological techniques such as high-density and laminar recordings. With a largely lissencephalic cortex, the common marmoset (Callithrix jacchus) is a promising alternative primate model for studying FEF microcircuitry. Putative homologies have been established with the macaque FEF on the basis of cytoarchitecture and connectivity; however, physiological investigation in awake, behaving marmosets is necessary to physiologically locate this area. Here, we addressed this gap using intracortical microstimulation in a broad range of frontal cortical areas in three adult marmosets (two males, one female). We implanted marmosets with 96-channel Utah arrays and applied microstimulation trains while they freely viewed video clips. We evoked short-latency fixed vector saccades at low currents (\u3c50 \u3eμA) in areas 45, 8aV, 8C, and 6DR. We observed a topography of saccade direction and amplitude consistent with findings in macaques and humans: small saccades in ventrolateral FEF and large saccades combined with contralateral neck and shoulder movements encoded in dorsomedial FEF. Our data provide compelling evidence supporting homology between marmoset and macaque FEF and suggest that the marmoset is a useful primate model for investigating FEF microcircuitry and its contributions to oculomotor and cognitive functions.SIGNIFICANCE STATEMENT The frontal eye field (FEF) is a critical cortical region for overt and covert spatial attention. The microcircuitry of this area remains poorly understood because in the macaque, the most commonly used model, it is embedded within a sulcus and is inaccessible to modern electrophysiological and imaging techniques. The common marmoset is a promising alternative primate model due to its lissencephalic cortex and potential for genetic manipulation. However, evidence for homologous cortical areas in this model remains limited and unclear. Here, we applied microstimulation in frontal cortical areas in marmosets to physiologically identify FEF. Our results provide compelling evidence for an FEF in the marmoset and suggest that the marmoset is a useful model for investigating FEF microcircuitry

Intrinsic functional boundaries of lateral frontal cortex in the common marmoset monkey

© 2019 the authors. The common marmoset (Callithrix jacchus) is a small New World primate species that has been recently targeted as a potentially powerful preclinical model of human prefrontal cortex dysfunction. Although the structural boundaries of frontal cortex were described in marmosets at the start of the 20th century (Brodmann, 1909) and refined more recently (Paxinos et al., 2012), the broad functional boundaries of marmoset frontal cortex have yet to be established. In this study, we sought to functionally derive boundaries of the marmoset lateral frontal cortex (LFC) using ultra-high field (9.4 T) resting-state functional magnetic resonance imaging (RS-fMRI). We collectedRS-fMRIdatainseven(fourfemales,threemales)lightlyanesthetizedmarmosetsandusedadata-drivenhierarchicalclustering approach to derive subdivisions of the LFC based on intrinsic functional connectivity. We then conducted seed-based analyses to assess the functional connectivity between these clusters and the rest of the brain. The results demonstrated seven distinct functional clusters withintheLFC.Thefunctionalconnectivitypatternsoftheseclusterswiththerestofthebrainwerealsofoundtobedistinctandorganized along a rostrocaudal gradient, consonant with those found in humans and macaques. Overall, these results support the view that marmosets are a promising preclinical modeling species for studying LFC dysfunction related to neuropsychiatric or neurodegenerative human brain diseases

Rate-dependent propagation of cardiac action potentials in a one-dimensional fiber

Action potential duration (APD) restitution, which relates APD to the preceding diastolic interval (DI), is a useful tool for predicting the onset of abnormal cardiac rhythms. However, it is known that different pacing protocols lead to different APD restitution curves (RCs). This phenomenon, known as APD rate-dependence, is a consequence of memory in the tissue. In addition to APD restitution, conduction velocity restitution also plays an important role in the spatiotemporal dynamics of cardiac tissue. We present new results concerning rate-dependent restitution in the velocity of propagating action potentials in a one-dimensional fiber. Our numerical simulations show that, independent of the amount of memory in the tissue, waveback velocity exhibits pronounced rate-dependence and the wavefront velocity does not. Moreover, the discrepancy between waveback velocity RCs is most significant for small DI. We provide an analytical explanation of these results, using a system of coupled maps to relate the wavefront and waveback velocities. Our calculations show that waveback velocity rate-dependence is due to APD restitution, not memory.Comment: 17 pages, 7 figure