Gaussian process approximations of stochastic differential equations

Stochastic differential equations arise naturally in a range of contexts, from financial to environmental modeling. Current solution methods are limited in their representation of the posterior process in the presence of data. In this work, we present a novel Gaussian process approximation to the posterior measure over paths for a general class of stochastic differential equations in the presence of observations. The method is applied to two simple problems: the Ornstein-Uhlenbeck process, of which the exact solution is known and can be compared to, and the double-well system, for which standard approaches such as the ensemble Kalman smoother fail to provide a satisfactory result. Experiments show that our variational approximation is viable and that the results are very promising as the variational approximate solution outperforms standard Gaussian process regression for non-Gaussian Markov processes.

Some aspects of the solution of non-linear differential equations

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Variational mean-field algorithm for efficient inference in large systems of stochastic differential equations

This work introduces a Gaussian variational mean-field approximation for inference in dynamical systems which can be modeled by ordinary stochastic differential equations. This new approach allows one to express the variational free energy as a functional of the marginal moments of the approximating Gaussian process. A restriction of the moment equations to piecewise polynomial functions, over time, dramatically reduces the complexity of approximate inference for stochastic differential equation models and makes it comparable to that of discrete time hidden Markov models. The algorithm is demonstrated on state and parameter estimation for nonlinear problems with up to 1000 dimensional state vectors and compares the results empirically with various well-known inference methodologies.

Differential impact of posterior lesions in the left and right hemisphere on visual category learning and generalization to contrast reversal

Hemispheric differences in the learning and generalization of pattern categories were explored in two experiments involving sixteen patients with unilateral posterior, cerebral lesions in the left (LH) or right (RH) hemisphere. In each experiment participants were first trained to criterion in a supervised learning paradigm to categorize a set of patterns that either consisted of simple geometric forms (Experiment 1) or unfamiliar grey-level images (Experiment 2). They were then tested for their ability to generalize acquired categorical knowledge to contrast-reversed versions of the learning patterns. The results showed that RH lesions impeded category learning of unfamiliar grey-level images more severely than LH lesions, whereas this relationship appeared reversed for categories defined by simple geometric forms. With regard to generalization to contrast reversal, categorization performance of LH and RH patients was unaffected in the case of simple geometric forms. However, generalization to of contrast-reversed grey-level images distinctly deteriorated for patients with LH lesions relative to those with RH lesions, with the latter (but not the former) being consistently unable to identify the pattern manipulation. These findings suggest a differential use of contrast information in the representation of pattern categories in the two hemispheres. Such specialization appears in line with previous distinctions between a predominantly lefthemispheric, abstract-analytical and a righthemispheric, specific-holistic representation of object categories, and their prediction of a mandatory representation of contrast polarity in the RH. Some implications for the well-established dissociation of visual disorders for the recognition of faces and letters are discussed.

Differential localization of GABAA receptor subunits in relation to rat striatopallidal and pallidopallidal synapses

As a central integrator of basal ganglia function, the external segment of the globus pallidus (GP) plays a critical role in the control of voluntary movement. The GP is composed of a network of inhibitory GABA-containing projection neurons which receive GABAergic input from axons of the striatum (Str) and local collaterals of GP neurons. Here, using electrophysiological techniques and immunofluorescent labeling we have investigated the differential cellular distribution of a1, a2 and a3 GABAA receptor subunits in relation to striatopallidal (Str-GP) and pallidopallidal (GP-GP) synapses. Electrophysiological investigations showed that zolpidem (100 nm; selective for the a1 subunit) increased the amplitude and the decay time of both Str-GP and GP-GP IPSCs, indicating the presence of the a1 subunits at both synapses. However, the application of drugs selective for the a2, a3 and a5 subunits (zolpidem at 400 nm, L-838,417 and TP003) revealed differential effects on amplitude and decay time of IPSCs, suggesting the nonuniform distribution of non-a1 subunits. Immunofluorescence revealed widespread distribution of the a1 subunit at both soma and dendrites, while double- and triple-immunofluorescent labeling for parvalbumin, enkephalin, gephyrin and the ?2 subunit indicated strong immunoreactivity for GABAAa3 subunits in perisomatic synapses, a region mainly targeted by local axon collaterals. In contrast, immunoreactivity for synaptic GABAAa2 subunits was observed in dendritic compartments where striatal synapses are preferentially located. Due to the kinetic properties which each GABAAa subunit confers, this distribution is likely to contribute differentially to both physiological and pathological patterns of activity.

Differential perception of innovation with particular reference to the organisational context

Differential perception of innovation is a research area which has been advocated as a suitable topic for study in recent years. It developed from the problems encountered within earlier perception of innovation studies which sought to establish what characteristics of an innovation affected the ease of its adoption. While some success was achieved In relating perception of innovation to adoption behaviour, variability encountered Within groups expected - to fercelve innovation similarly suggested that the needs and experiences of the potential adopter were significantly affecting the research findings. Such analysis being supported by both sociological and psychological perceptual research. The present study sought to identify the presence of differential perception of innovation and explore the nature of the process. It was decided to base the research in an organisational context and to concentrate upon manufacturing innovation. It has been recognised that such adoption of technological innovation is commonly the product of a collective decision-making process, involving individuals from a variety of occupational backgrounds, both in terms of occupational speciality and level within the hierarchy. Such roles appeared likely to significantly influence perception of technological innovation, as gathered through an appropriate measure and were readily identifiable. Data vas collected by means of a face-to-face card presentation technique, a questionnaire and through case study material. Differential perception of innovation effects were apparent In the results, many similarities and differences of perception being related to the needs and experiences of the individuals studied. Phenomenological analysis, which recognises the total nature of experience in infiuencing behaviour, offered the best means of explaining the findings. It was also clear that the bureaucratic model of role definition was not applicable to the area studied, it seeming likely that such definitions are weaker under conditions of uncertainty, such as encountered in innovative decision-making.

Differential patterns of activity and functional connectivity in emotion processing neural circuitry to angry and happy faces in adolescents with and without suicide attempt

Background - Neural substrates of emotion dysregulation in adolescent suicide attempters remain unexamined. Method - We used functional magnetic resonance imaging to measure neural activity to neutral, mild or intense (i.e. 0%, 50% or 100% intensity) emotion face morphs in two separate emotion-processing runs (angry and happy) in three adolescent groups: (1) history of suicide attempt and depression (ATT, n = 14); (2) history of depression alone (NAT, n = 15); and (3) healthy controls (HC, n = 15). Post-hoc analyses were conducted on interactions from 3 group × 3 condition (intensities) whole-brain analyses (p < 0.05, corrected) for each emotion run. Results - To 50% intensity angry faces, ATT showed significantly greater activity than NAT in anterior cingulate gyral–dorsolateral prefrontal cortical attentional control circuitry, primary sensory and temporal cortices; and significantly greater activity than HC in the primary sensory cortex, while NAT had significantly lower activity than HC in the anterior cingulate gyrus and ventromedial prefrontal cortex. To neutral faces during the angry emotion-processing run, ATT had significantly lower activity than NAT in the fusiform gyrus. ATT also showed significantly lower activity than HC to 100% intensity happy faces in the primary sensory cortex, and to neutral faces in the happy run in the anterior cingulate and left medial frontal gyri (all p < 0.006,corrected). Psychophysiological interaction analyses revealed significantly reduced anterior cingulate gyral–insula functional connectivity to 50% intensity angry faces in ATT v. NAT or HC. Conclusions - Elevated activity in attention control circuitry, and reduced anterior cingulate gyral–insula functional connectivity, to 50% intensity angry faces in ATT than other groups suggest that ATT may show inefficient recruitment of attentional control neural circuitry when regulating attention to mild intensity angry faces, which may represent a potential biological marker for suicide risk.

Differential effects of value consciousness and coupon proneness on consumers’ persuasion knowledge of pricing tactics

Pricing tactics persuasion knowledge (PTPK) is a relatively new concept that seeks to extend the research on persuasion knowledge to the pricing domain. Pricing tactics persuasion knowledge refers to the persuasion knowledge of consumers about marketers’ pricing tactics. Employing an acquisition–transaction utility theoretic perspective, this study examines the differential effects of value consciousness and coupon proneness on the accuracy, confidence, and calibration of consumers’ pricing tactics persuasion knowledge. The study finds that coupon proneness is negatively related to accuracy, confidence, and calibration of PTPK, while value consciousness is positively related to accuracy, confidence, and calibration of PTPK. The implications of the study are outlined.

Eye movement problems and differential diagnosis of the parkinsonian syndromes

Differential clinical diagnosis of the parkinsonian syndromes, viz., Parkinson’s disease (PD), progressive supranuclear palsy (PSP), dementia with Lewy bodies (DLB), and multiple system atrophy (MSA) can be difficult. Eye movement problems, however, are a chronic complication of many of these disorders and may be a useful aid to diagnosis. Hence, the presence in PSP of vertical supranuclear gaze palsy, fixation instability, lid retraction, blepharospasm, and apraxia of eyelid opening and closing is useful in separating PD from PSP. Moreover, atypical features of PSP include slowing of upward saccades, moderate slowing of downward saccades, the presence of a full range of voluntary vertical eye movements, a curved trajectory of oblique saccades, and absence of square-wave jerks. Downgaze palsy is probably the most useful diagnostic clinical symptom of PSP. By contrast, DLB patients are specifically impaired in both reflexive and saccadic execution and in the performance of more complex saccadic eye movement tasks. Problems in convergence in DLB are also followed by akinesia and rigidity. Abnormal ocular fixation may occur in a significant proportion of MSA patients along with excessive square-wave jerks, a mild supranuclear gaze palsy, a gaze-evoked nystagmus, a positioning down-beat nystagmus, mild-moderate saccadic hypometria, impaired smooth pursuit movements, and reduced vestibulo-ocular reflex (VOR) suppression. There may be considerable overlap between the eye movement problems characteristic of the various parkinsonian disorders, but taken together with other signs and symptoms, can be a useful aid in differential diagnosis, especially in the separation of PD and PSP.

Differential effects of chlorinated and oxidized phospholipids in vascular tissue:implications for neointima formation

The presence of inflammatory cells and MPO (myeloperoxidase) in the arterial wall after vascular injury could increase neointima formation by modification of phospholipids. The present study investigates how these phospholipids, in particular oxidized and chlorinated species, are altered within injured vessels and how they affect VSMC (vascular smooth muscle cell) remodelling processes. Vascular injury was induced in C57BL/6 mice and high fat-fed ApoE-/- (apolipoprotein E) mice by wire denudation and ligation of the left carotid artery (LCA). Neointimal and medial composition was assessed using immunohistochemistry and ESI-MS. Primary rabbit aortic SMCs (smooth muscle cells) were utilized to examine the effects of modified lipids on VSMC proliferation, viability and migration at a cellular level. Neointimal area, measured as intima-to-media ratio, was significantly larger in wire-injured ApoE-/- mice (3.62±0.49 compared with 0.83±0.25 in C57BL/6 mice, n=3) and there was increased oxidized low-density lipoprotein (oxLDL) infiltration and elevated plasma MPO levels. Relative increases in lysophosphatidylcholines and unsaturated phosphatidylcholines (PCs) were also observed in wire-injured ApoE-/- carotid arteries. Chlorinated lipids had no effect on VSMC proliferation, viability or migration whereas chronic incubation with oxidized phospholipids stimulated proliferation in the presence of fetal calf serum [154.8±14.2% of viable cells at 1 μM PGPC (1-palmitoyl-2-glutaroyl-sn-glycero-3-phosphocholine) compared with control, n=6]. In conclusion, ApoE-/- mice with an inflammatory phenotype develop more neointima in wire-injured arteries and accumulation of oxidized lipids in the vessel wall may propagate this effect.

Differential control of two forms of glutamate release by group III metabotropic glutamate receptors at rat entorhinal synapses

Neurotransmitter release at CNS synapses occurs via both action potential-dependent and independent mechanisms, and it has generally been accepted that these two forms of release are regulated in parallel. We examined the effects of activation of group III metabotropic glutamate receptors (mGluRs) on stimulus-evoked and spontaneous glutamate release onto entorhinal cortical neurones in rats, and found a differential regulation of action potential-dependent and independent forms of release. Activation of presynaptic mGluRs depressed the amplitude of stimulus-evoked excitatory postsynaptic currents, but concurrently enhanced the frequency of spontaneous excitatory currents. Moreover, these differential effects on glutamate release were mediated by pharmacologically separable mechanisms. Application of the specific activator of adenylyl cyclase, forskolin, mimicked the effect of mGluR activation on spontaneous, but not evoked release, and inhibition of adenylyl cyclase with 9-tetrahydro-2-furanyl)-9H-purin-6-amine (SQ22536) blocked mGluR-mediated enhancement of spontaneous release, but not depression of evoked release. Occlusion studies with calcium channel blockers suggested that the group III mGluRs might depress evoked release through inhibition of both N and P/Q, but not R-type calcium channels. We suggest that the concurrent depression of action potential-evoked, and enhancement of action potential-independent glutamate release operate through discrete second messenger/effector systems at excitatory entorhinal terminals in rat brain. © 2007 IBRO.

Background synaptic activity in rat entorhinal cortical neurones:differential control of transmitter release by presynaptic receptors

The entorhinal cortex (EC) is a key brain area controlling both hippocampal input and output via neurones in layer II and layer V, respectively. It is also a pivotal area in the generation and propagation of epilepsies involving the temporal lobe. We have previously shown that within the network of the EC, neurones in layer V are subject to powerful synaptic excitation but weak inhibition, whereas the reverse is true in layer II. The deep layers are also highly susceptible to acutely provoked epileptogenesis. Considerable evidence now points to a role of spontaneous background synaptic activity in control of neuronal, and hence network, excitability. In the present article we describe results of studies where we have compared background release of the excitatory transmitter, glutamate, and the inhibitory transmitter, GABA, in the two layers, the role of this background release in the balance of excitability, and its control by presynaptic auto- and heteroreceptors on presynaptic terminals. © The Physiological Society 2004.

Species differential regulation of COX2 can be described by an NFκB-dependent logic AND gate

Cyclooxygenase 2 (COX2), a key regulatory enzyme of the prostaglandin/eicosanoid pathway, is an important target for anti-inflammatory therapy. It is highly induced by pro-inflammatory cytokines in a Nuclear factor kappa B (NFκB)-dependent manner. However, the mechanisms determining the amplitude and dynamics of this important pro-inflammatory event are poorly understood. Furthermore, there is significant difference between human and mouse COX2 expression in response to the inflammatory stimulus tumor necrosis factor alpha (TNFα). Here, we report the presence of a molecular logic AND gate composed of two NFκB response elements (NREs) which controls the expression of human COX2 in a switch-like manner. Combining quantitative kinetic modeling and thermostatistical analysis followed by experimental validation in iterative cycles, we show that the human COX2 expression machinery regulated by NFκB displays features of a logic AND gate. We propose that this provides a digital, noise-filtering mechanism for a tighter control of expression in response to TNFα, such that a threshold level of NFκB activation is required before the promoter becomes active and initiates transcription. This NFκB-regulated AND gate is absent in the mouse COX2 promoter, most likely contributing to its differential graded response in promoter activity and protein expression to TNFα. Our data suggest that the NFκB-regulated AND gate acts as a novel mechanism for controlling the expression of human COX2 to TNFα, and its absence in the mouse COX2 provides the foundation for further studies on understanding species-specific differential gene regulation.

Differential impact of amino acid substitutions on critical residues of the human glucagon-like peptide-1 receptor involved in peptide activity and small-molecule allosterys

The glucagon-like peptide-1 receptor (GLP-1R) is a class B G protein-coupled receptor that has a critical role in the regulation of glucose homeostasis, principally through the regulation of insulin secretion. The receptor systemis highly complex, able to be activated by both endogenous [GLP-1(1-36)NH2, GLP-1(1-37), GLP-1(7-36)NH2, GLP-1(7-37), oxyntomodulin], and exogenous (exendin-4) peptides in addition to small-molecule allosteric agonists (compound 2 [6,7-dichloro-2-methylsulfonyl-3-tertbutylaminoquinoxaline], BETP [4-(3-benzyloxy)phenyl)-2-ethylsulfinyl-6-(trifluoromethyl)pyrimidine]). Furthermore, the GLP-1R is subject to single-nucleotide polymorphic variance, resulting in amino acid changes in the receptor protein. In this study, we investigated two polymorphic variants previously reported to impact peptidemediated receptor activity (M149) and small-molecule allostery (C333). These residues were mutated to a series of alternate amino acids, and their functionality was monitored across physiologically significant signaling pathways, including cAMP, extracellular signal-regulated kinase 1 and 2 phosphorylation, and intracellular Ca2+ mobilization, in addition to peptide binding and cell-surface expression. We observed that residue 149 is highly sensitive to mutation, with almost all peptide responses significantly attenuated at mutated receptors. However, most reductions in activity were able to be restored by the small-molecule allosteric agonist compound 2. Conversely, mutation of residue 333 had little impact on peptide-mediated receptor activation, but this activity could not be modulated by compound 2 to the same extent as that observed at the wild-type receptor. These results provide insight into the importance of residues 149 and 333 in peptide function and highlight the complexities of allosteric modulation within this receptor system.