Metric gravity theories and cosmology:II. Stability of a ground state in f(R) theories

A fundamental criterion of viability of any gravity theory is existence of a stable ground-state solution being either Minkowski, dS or AdS space. Stability of the ground state is independent of which frame is physical. In general, a given theory has multiple ground states and splits into independent physical sectors. All metric gravity theories with the Lagrangian being a function of Ricci tensor are dynamically equivalent to Einstein gravity with a source and this allows us to study the stability problem using methods developed in GR. We apply these methods to f(R) theories. As is shown in 13 cases of Lagrangians the stability criterion works simply and effectively whenever the curvature of the ground state is determined. An infinite number of gravity theories have a stable ground state and further viability criteria are necessary.Comment: A modified and expanded version of a second part of the paper which previously appeared as gr-qc/0702097v1. The first, modified part is now published as gr-qc/0702097v2 and as a separate paper in Class. Qu. Grav. The present paper matches the published versio

Beyond Hebb: Exclusive-OR and Biological Learning

A learning algorithm for multilayer neural networks based on biologically plausible mechanisms is studied. Motivated by findings in experimental neurobiology, we consider synaptic averaging in the induction of plasticity changes, which happen on a slower time scale than firing dynamics. This mechanism is shown to enable learning of the exclusive-OR (XOR) problem without the aid of error back-propagation, as well as to increase robustness of learning in the presence of noise.Comment: 4 pages RevTeX, 2 figures PostScript, revised versio

Attentive Learning of Sequential Handwriting Movements: A Neural Network Model

Defense Advanced research Projects Agency and the Office of Naval Research (N00014-95-1-0409, N00014-92-J-1309); National Science Foundation (IRI-97-20333); National Institutes of Health (I-R29-DC02952-01)

Dependencies of Simulated Convective Cell and System Growth Biases on Atmospheric Instability and Model Resolution

This study evaluates convective cell properties and their relationships with convective and stratiform rainfall within a season‐long convection‐permitting weather research and forecasting simulation over central Argentina using radar, satellite, and radiosonde measurements from the RELAMPAGO‐CACTI field campaign. The simulation slightly underestimates radar‐estimated rainfall over the ∼3.5‐month evaluation period but underestimates stratiform rainfall by 46% and overestimates convective rainfall by 43%. As convective available potential energy (CAPE) increases, the convective rainfall overestimation decreases, but the stratiform rainfall underestimation increases such that the contribution of convective to total rainfall remains constantly high biased by ∼26%. Overestimated convective rainfall arises from the simulation generating 2.6 times more precipitating convective cells (14,299) than observed by radar (5,662) despite similar observed and simulated cell growth processes, with relatively wide cells contributing mostly to excessive convective rainfall. Relatively shallow cells, typically reaching heights of 4–7 km, contribute most to the cell number bias. This cell number bias increases as CAPE decreases, potentially because cells and their updrafts become narrower and more under‐resolved as CAPE decreases. The gross overproduction of precipitating shallow cells leads to overly efficient precipitation and inadequate detrainment of ice aloft, thereby diminishing the formation of robust stratiform rainfall regions. Decreasing model horizontal grid spacing from 3 to 1 or 0.333 km for low (1,000 J kg−1) cases results in minimal change to cell number, depth, and convective‐to‐stratiform partitioning biases. This suggests that improving prediction of these convective properties depends on factors beyond solely increasing model resolution

Theorems on existence and global dynamics for the Einstein equations

This article is a guide to theorems on existence and global dynamics of solutions of the Einstein equations. It draws attention to open questions in the field. The local-in-time Cauchy problem, which is relatively well understood, is surveyed. Global results for solutions with various types of symmetry are discussed. A selection of results from Newtonian theory and special relativity that offer useful comparisons is presented. Treatments of global results in the case of small data and results on constructing spacetimes with prescribed singularity structure or late-time asymptotics are given. A conjectural picture of the asymptotic behaviour of general cosmological solutions of the Einstein equations is built up. Some miscellaneous topics connected with the main theme are collected in a separate section.Comment: Submitted to Living Reviews in Relativity, major update of Living Rev. Rel. 5 (2002)

Context Matters: The Illusive Simplicity of Macaque V1 Receptive Fields

Even in V1, where neurons have well characterized classical receptive fields (CRFs), it has been difficult to deduce which features of natural scenes stimuli they actually respond to. Forward models based upon CRF stimuli have had limited success in predicting the response of V1 neurons to natural scenes. As natural scenes exhibit complex spatial and temporal correlations, this could be due to surround effects that modulate the sensitivity of the CRF. Here, instead of attempting a forward model, we quantify the importance of the natural scenes surround for awake macaque monkeys by modeling it non-parametrically. We also quantify the influence of two forms of trial to trial variability. The first is related to the neuron’s own spike history. The second is related to ongoing mean field population activity reflected by the local field potential (LFP). We find that the surround produces strong temporal modulations in the firing rate that can be both suppressive and facilitative. Further, the LFP is found to induce a precise timing in spikes, which tend to be temporally localized on sharp LFP transients in the gamma frequency range. Using the pseudo R[superscript 2] as a measure of model fit, we find that during natural scene viewing the CRF dominates, accounting for 60% of the fit, but that taken collectively the surround, spike history and LFP are almost as important, accounting for 40%. However, overall only a small proportion of V1 spiking statistics could be explained (R[superscript 2]~5%), even when the full stimulus, spike history and LFP were taken into account. This suggests that under natural scene conditions, the dominant influence on V1 neurons is not the stimulus, nor the mean field dynamics of the LFP, but the complex, incoherent dynamics of the network in which neurons are embedded.National Institutes of Health (U.S.) (K25 NS052422-02)National Institutes of Health (U.S.) (DP1 ODOO3646

Contact heat evoked potentials reveal distinct patterns of spinal cord impairment in degenerative cervical myelopathy beyond MRI lesions

Background: Magnetic resonance imaging may suggest spinal cord compression and structural lesions in degenerative cervical myelopathy (DCM) but cannot reveal functional impairments in spinal pathways. We aimed to assess the value of contact heat evoked potentials (CHEPs) in addition to MRI and hypothesized that abnormal CHEPs may be evident in DCM independent of MR-lesions and are related to dynamic mechanical cord stress.Methods: Individuals with DCM underwent neurologic examination including segmental sensory (pinprick, light touch) and motor testing. The presence or absence of hyperintense signal on T2-weighted MRI (T2-positive/negative) was assessed. Phase-contrast MRI was used to assess spinal cord motion as an indicator of dynamic mechanical stress. Dermatomal somatosensory evoked potentials and CHEPs were recorded after stimulation of dermatomes C6, C8, and T4 (CHEPs only) to assess spinal cord integrity.Results: Of 138 individuals included in this study (age 56 ± 13 years), 35% (N = 48) presented with T2-positive and 65% (N = 90) presented with T2-negative DCM. Abnormal CHEPs were present in T2-positive DCM (C6:41%; C8:32%; T4:24%) and T2-negative DCM (C6:35%; C8:54%; T4:26%). Multisegmental CHEP abnormalities at C6 and C8 were related to increased spinal cord motion (p = 0.030; ϵ2 = 0.072), and reduced upper extremity pinprick (p = 0.046; ϵ2 = 0.063) and motor scores (p = 0.005; ϵ2 = 0.108).Conclusions: CHEPs revealed distinct patterns of spinal cord impairment independent of structural T2-positive lesions, which were associated with measures of cord motion. CHEPs thus provide valuable complementary diagnostic insights into spinal cord integrity beyond MRI. This is especially important in incipient myelopathy to inform early diagnosis and timely interventions before the development of definite cord lesions

Potential thresholds of critically increased cardiac-related spinal cord motion in degenerative cervical myelopathy

Introduction: New diagnostic techniques are a substantial research focus in degenerative cervical myelopathy (DCM). This cross-sectional study determined the significance of cardiac-related spinal cord motion and the extent of spinal stenosis as indicators of mechanical strain on the cord.Methods: Eighty-four DCM patients underwent MRI/clinical assessments and were classified as MRI+ [T2-weighted (T2w) hyperintense lesion in MRI] or MRI- (no T2w-hyperintense lesion). Cord motion (displacement assessed by phase-contrast MRI) and spinal stenosis [adapted spinal canal occupation ratio (aSCOR)] were related to neurological (sensory/motor) and neurophysiological readouts [contact heat evoked potentials (CHEPs)] by receiver operating characteristic (ROC) analysis.Results: MRI+ patients (N = 31; 36.9%) were more impaired compared to MRI- patients (N = 53; 63.1%) based on the modified Japanese Orthopedic Association (mJOA) subscores for upper {MRI+ [median (Interquartile range)]: 4 (4-5); MRI-: 5 (5-5); p Discussion: These findings affirm cord motion measurements as a promising additional biomarker to improve the clinical workup and to enable timely surgical treatment particularly in MRI- DCM patients

The electromagnetic Christodoulou memory effect and its application to neutron star binary mergers

Gravitational waves are predicted by the general theory of relativity. It has been shown that gravitational waves have a nonlinear memory, displacing test masses permanently. This is called the Christodoulou memory. We proved that the electromagnetic field contributes at highest order to the nonlinear memory effect of gravitational waves, enlarging the permanent displacement of test masses. In experiments like LISA or LIGO which measure distances of test masses, the Christodoulou memory will manifest itself as a permanent displacement of these objects. It has been suggested to detect the Christodoulou memory effect using radio telescopes investigating small changes in pulsar’s pulse arrival times. The latter experiments are based on present-day technology and measure changes in frequency. In the present paper, we study the electromagnetic Christodoulou memory effect and compute it for binary neutron star mergers. These are typical sources of gravitational radiation. During these processes, not only mass and momenta are radiated away in form of gravitational waves, but also very strong magnetic fields are produced and radiated away. Moreover, a large portion of the energy is carried away by neutrinos. We give constraints on the conditions, where the energy transported by electromagnetic radiation is of similar or slightly higher order than the energy radiated in gravitational waves or in form of neutrinos. We find that for coalescing neutron stars, large magnetic fields magnify the Christodoulou memory as long as the gaseous environment is sufficiently rarefied. Thus the observed effect on test masses of a laser interferometer gravitational wave detector will be enlarged by the contribution of the electromagnetic field. Therefore, the present results are important for the planned experiments. Looking at the null asymptotics of spacetimes, which are solutions of the Einstein–Maxwell equations, we derive the electromagnetic Christodoulou memory effect. We obtain an exact solution of the full nonlinear problem, no approximations were used. Moreover, our results allow to answer astrophysical questions, as the knowledge about the amount of energy radiated away in a neutron star binary merger enables us to gain information about the source of the gravitational waves.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/98597/1/0264-9381_29_21_215003.pd