On the emergence of the Λ{\bf\Lambda}CDM model from self-interacting Brans-Dicke theory in d=5{\bf d= 5}

We investigate whether a self-interacting Brans-Dicke theory in $d=5$ without matter and with a time-dependent metric can describe, after dimensional reduction to $d=4$, the FLRW model with accelerated expansion and non-relativistic matter. By rewriting the effective 4-dimensional theory as an autonomous three-dimensional dynamical system and studying its critical points, we show that the $\Lambda$CDM cosmology cannot emerge from such a model. This result suggests that a richer structure in $d=5$ may be needed to obtain the accelerated expansion as well as the matter content of the 4-dimensional universe.Comment: 7 pages, 7 figure

Recurrent myocardial infarction: Mechanisms of free-floating adaptation and autonomic derangement in networked cardiac neural control - Fig 4

<p>In Fig 4 through <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0180194#pone.0180194.g014" target="_blank">Fig 14</a> inclusive the simulation results are depicted as solid lines for four variables: (i) efferent sympathetic activity (red), (ii) heart rate (green), (iii) central drive (black), and (iv) parasympathetic efferent (blue). The simulation timeline definitions described here are further explained in Simulation Design. Each of the red vertical lines <i>E</i>_<i>j</i>, <i>j</i> = 1, 2, 3 indicates the beginning of the <i>j</i>^<i>th</i> episode. Three sub-events within each episode are the red, blue, and black vertical lines that respectively correspond to the onset of infarction (or unstable angina), recovery, and demand. The last vertical dashed line indicates the beginning of the aftermath of the recurrent pathology. In this figure, a stratified network with low neural diversity is shown. Local circuit neurons are affected and remain alive. Neurons that transduce heart rate and blood flow demand are affected and remain alive. There is no autonomic derangement.</p

Schematic of mathematical model.

<p>Closed-loop control of cardiac output is shown as a networked 3-level hierarchy.</p

Hierarchical networked model for cardiac control.

<p>Network interactions occur within the local circuit neural (LCN) populations. These integrate activities within and between peripheral ganglia and the central nervous system subserve reflex control of the heart. The intrinsic cardiac nervous system possesses sympathetic (Sympath) and parasympathetic (Parasym) efferent post-ganglionic neurons, local circuit neurons (LCN) and afferent (Aff.) neurons. The intrathoracic extracardiac nervous system is comprised of ganglia containing afferent neurons, LCN and sympathetic efferent post-ganglionic neurons. Cardiovascular heart rate and demand inputs are conveyed centrally via dorsal root (DRG), nodose and petrosal ganglia subserving spinal cord (C-cervical, T-thoracic), brainstem and higher center reflexes for hemostatic maintenance.</p

Central model of cardiac control.

<p>The classical view of the neuronal populations making up the cardiac neuronal hierarchy. In this view the cardiac neuroaxis is made up of two main neuronal groupings based on their anatomic locations: i) higher center neurons, including those in the medulla and spinal cord (C1-T4 primarily) up to the level of the insular cortex. ii) peripheral ganglia—a) neural somata in intrathoracic extracardiac ganglia (adrenergic postganglionic motor neurons) and b) those on the heart (cholinergic postganglionic motor neurons). In this model, these peripheral neuronal populations are under the control of central neuronal command.</p

Changes that occur in this control system in response to ischemic/infarct stress predicate the degree of hyperactivity that cardiac sympathetic efferent neurons undergo.

<p>The transition of the benchmark balance from before (black bars) to the onset of recurrent MI or unstable angina and in the aftermath period of a new normal (white bars) is depicted for stratified networks with high neural diversity. The top half of the figure illustrates this transition for the sympathetic tone and the bottom half for the central drive tone. The first three pairs of bars in the top and bottom halves, starting from the left, represent the benchmark balance without autonomic derangement (’ANS derangement’ labelled ‘N’) while the remaining four pairs of bars refer to the system with autonomic derangement (’Y’). Details of how LCN neurons (’LCN Neurons’) and neurons that transduce heart rate and demand neurons are affected (’Sensory Neurons’) appears in the second and third rows. As a result of the pathology, these neurons are considered to die (’D’), become stressed (’S’), or are unaffected (’N’). In the presence of autonomic derangement (last four pairs of bars) the final state of the system becomes sensitive the extent to which local circuit neurons (’LCN neuron’) versus those transducing heart rate and blood flow demand are influenced by pathology. The vertical scales on the left represent relative neuronal activity states.</p

A top-down network with high neural diversity.

<p>Local circuit neurons are affected and remain alive. Neurons that transduce heart rate and blood flow demand are affected and survive. There is no autonomic derangement.</p

A top-down network with low neural diversity.

<p>Local circuit neurons are affected and survive. Neurons that transduce heart rate and blood flow demand are affected and also survive. There is no autonomic derangement.</p

Endo- and epicardial ATa maps in the computer model (A–C) and in the experiments (D–I).

<p>(A) Color-coded simulated endocardial ATa map in the presence of repolarization heterogeneity with a radius of 3 mm around the white star. White dots represent epicardial electrode positions. (B) Simulated epicardial ATa map for the same beat. (C) Epi- vs endocardial simulated ATa for all simulations with different repolarization heterogeneity distributions, along with the linear regression curve and 50% confidence interval. Data point density estimated by kernel-based method is displayed as contour lines. (D) and (G) Examples of experimental endocardial ATa maps in two different dogs. (E) and (H) Experimental epicardial ATa map for the same beat. (F) and (I) Epi- vs endocardial ATa for all beats combined in each of the two dogs. SVC: superior vena cava; IVC: inferior vena cava; RAA: right atrium appendage; BB: Bachmann’s bundle; RAGP: right atrium ganglionated plexus.</p

Right atrium geometry and electrode configuration.

<p>(A) Endocardial surface of a canine right atrium as reconstructed by the EnSite NavX system (<i>left side</i>: anterior view; <i>right side</i>: posterior view). Anatomical features identified by the catheter localization system are shown in red. Blue stars represent recording sites of the direct-contact endocardial catheter (B) 3D geometrical model (same views as panel A) of the right atrium after processing. Dashed circles represent the location of heterogeneity regions, shown here with a radius of 3 mm. (C) Epicardial electrode position for the two plaques in the computer model. (D) <i>Left side</i>: Balloon catheter with its 64 electrode. <i>Right side</i>: closed endocardial surface used for the inverse problem. RAA: right atrium appendage; SVC: superior vena cava; IVC: inferior vena cava; TV: tricuspid valve; CS: coronary sinus; SAN: sino-atrial node; RAGP: right atrium ganglionated plexus; IA: inter-atrial bundles.</p