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Golomb, David. Models of neuronal transient synchrony during propagation of activity through neorcortical circuitry. J. Neurophysiol. 79: 1–12, 1998. Stereotypic paroxysmal discharges that propagate in neocortical tissues after electrical stimulations are used as a probe for studying cortical circuitry. I use modeling to investigate the effects of sparse connectivity, heterogeneity of intrinsic neuronal properties, and synaptic noise on synchronization of evoked propagating neuronal discharges in a network of excitatory, regular spiking neurons with spatially decaying connectivity. The global coherence of the traveling discharge is characterized by the correlation function between spike trains of neurons, averaged over all the pairs of neurons in the system at the same distance. Local coherence of two neurons is characterized by their correlation function averaged over many trials or, for persistent activity, over a long time interval. Spike synchronization between neurons emerges as a result of the transient activity; if activity is persistent, there is no synchrony, and cross-correlation functions are flat. During discharge propagation, system-average cross-correlation between neurons does not depend on their mutual distance except for a time shift. Spike synchronization occurs only when the average number of synapses M a cell receives is large enough. As M increases, there is a cross-over from an asynchronized to a synchronized discharge. Synaptic depression appears to help synchrony; it reduces the M value at the cross-over. The strengths of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and N-methyl-d-aspartate (NMDA) conductances affect synchrony only weakly. Spike synchronization is robust even with large levels of heterogeneity. Synaptic noise reduces synchrony, but strong synchrony is observed at a noise level that cannot evoke spontaneous discharges. System-average spike synchronization is determined by the levels of sparseness, heterogeneity, and noise, whereas trial-average spike synchronization is determined only by the noise level. Therefore, I predict that experiments will reveal local, two-cell spike synchrony, but not global synchrony.
Dynamics of cortical circuitry are determined, in a complicated way, by the intrinsic neuronal properties and the network architecture. Although experimental data about cortical dynamics have been collected recently using multielectrode recording (e.g., Gray 1994; Nicolelis et al. 1995, 1996; Singer 1993; Vaadia et al. 1995) and imaging (e.g., Grinvald et al. 1988; Prechtl et al. 1997) techniques, inferring the nature of cortical functional connectivity based on these experiments remains difficult. One possible approach to address this problem is to investigate a restricted region of cortex in various pharmacologically induced states. In cortical tissues, stereotypic propagating paroxysmal discharges are evoked by electrical stimulations when γ-aminobutyric acid-A (GABAA) inhibition is suppressed pharmacologically (Chervin et al. 1988; Connors 1984; Gutnick et al. 1982; Wadman and Gutnick 1993). These paroxysmal discharges have been studied experimentally in vitro, where they constitute models for interictal discharges in epilepsy. Investigating the discharge propagation range has led to conclusions regarding the range of connectivity in cortex (Chagnac-Amitai and Connors 1989a,b; Chervin et al. 1988; Wadman and Gutnick 1993; I. A. Fleidervish, A. M. Binshtok, and M. J. Gutnick, unpublished data). Other properties of the circuitry, such as the sparseness of synaptic connectivity, heterogeneity of intrinsic neuronal properties and synaptic noise, mainly affect the neuronal spike synchronization during the discharge. Here, modeling is used to study these effects.
Whereas recording techniques usually have revealed information about the temporal dynamics of one or a few neurons, modern recording and imaging techniques enable researchers to study the spatiotemporal dynamics of neuronal ensembles. Using such techniques, cortical propagating neuronal activity in behaving animals was discovered (Nicolelis et al. 1995, 1996; Prechtl et al. 1997). The modeling approach developed here also should be applicable for studying the relationship between the anatomic connectivity patterns and the patterns of synchrony in such in vivo systems.
Heretofore, theoretical investigations have addressed the mechanism of large-scale population synchrony in systems with long-range coupling1 (e.g., Hansel and Sompolinsky 1996; Hansel et al. 1993, 1995; Jefferys et al. 1996; Traub et al. 1996a; Wang et al. 1996; Whittington et al. 1995) and short-range coupling (Traub et al. 1996b) during persistent activity, i.e., activity that does not stop for a long time. In the present study, synchrony is investigated in a transient state of a propagating discharge, which is a pulse of depolarization upon which rides a train of action potentials. In addition to the time scale of the whole event, there is a second, faster, time scale of the interval between spikes. In this respect, the discharge differs from other, well-studied, propagating pulses in neurobiological systems, such as propagating action potentials in axons (Hodgkin and Huxley 1952), or in physical and chemical systems (Cross and Hohenberg 1993; Mikhailov 1990), that exhibit only one time scale. The typically large field potential recorded during paroxysmal discharges shows that the spikes of adjacent neurons are synchronized at the discharge time scale (Gutnick et al. 1982). However, on the basis of the existing experimental data, it is not clear whether the neuronal firing pattern is synchronized at the spike time scale.
In previous computational work (Golomb and Amitai 1997), models of homogeneous one-dimensional networks with spatially decaying synaptic strength were analyzed. It was shown that perfect spike synchrony was obtained between neurons along the slice model, except for a temporal phase shift Δx/νD, where Δx is the distance between the neurons and νD is the discharge velocity. Here I study the effects of sparseness, heterogeneity, and noise on spike synchrony by computing correlation functions. I discriminate between global, system-average correlation, which is affected by sparseness, heterogeneity, and synaptic noise, and local, trial-average correlation, which is affected only by synaptic noise. Global synchronization, which can be achieved at low levels of sparseness and heterogeneity, emerges as a result of the transient, propagating characteristics of the discharge. The global synchrony between neurons does not depend on the distance between them, except for a phase shift. Synaptic depression helps synchrony. These results help to interpret cross-correlation measurements during propagation and lead to predictions regarding the level of local and global synchrony expected in future experiments. Combining these modeling result with future experimental results will help to determine the level of sparseness, heterogeneity, and synaptic noise in cortex.
Biophysical, conductance-based models of single regular spiking (RS) neurons and of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic acid (AMPA) and N-methyl-d-aspartate (NMDA) synapses are used, as reported elsewhere (Golomb and Amitai 1997). In brief, the single cell dynamics are described by a single-compartment Hodgkin-Huxley type model, using a set of coupled differential equations Equation 1where C is the membrane capacitance, Vi (t) is the membrane potential of the ith neuron, and i = 1, ..., N is the neuron's index. Each RS cell possess a sodium current I Na, a persistent sodium current I NaP, a delayed-rectifier potassium current I Kdr, an inactivating potassium current (A current) I KA, a leak current I L, a synaptic AMPA current I AMPA, and a synaptic NMDA current I NMDA. The conductances of these currents are denoted by g with the appropriate subscript. The slow potassium current I K-slow(g K-slow = 1 mS/cm2) represents voltage- and calcium-dependent potassium currents, with kinetics slower than the action-potential time scale, that are responsible for adaptation. When heterogeneity in the strengths of intrinsic conductances is introduced, it is modeled by choosing the conductances g L, g KA, and g K-slow at random for each cell from a square distribution with a standard deviation that is α multiplied by the mean, where 0 < α < 1/ because conductances must be positive. The mean values are: g K-slow = 1 mS/cm2, g KA = 1.4 mS/cm2, g L = 0.02 mS/cm2.
A cell receives fast, AMPA-mediated excitatory postsynaptic potentials (EPSPs) and slow, NMDA-mediated EPSPs from other cells. Both types of synapses exhibit synaptic depression. A gating variable s for an AMPA or an NMDA receptor, representing the fraction of open channels, is modeled according to Equation 2where V pre is the presynaptic potential, T Glu is the normalized number of presynaptic glutamate vesicles, s ∞(V) = {1 + exp[−(V − θs)/σs]}−1, θs = −20 mV, σs = 2 mV, k f = 1 ms−1, and k r = 0.2 ms−1 for AMPA and 0.0067 ms−1 for NMDA. The variable T Glu evolves according to Equation 3where k ν = 0.001 ms−1. The network is analyzed for two values of the parameter k t that determines the strength of synaptic depression. At the reference value k t = 1 s−1, synapses exhibit depression in response to a rapid train of action potentials. Some simulations were carried out without synaptic depression (k t = 0).
The N neurons are distributed along an interval of length L, representing the slice length. The position of the ith neuron is xi = iL/N. Synaptic coupling decays exponentially with the distance between neurons with a characteristic length λ, called the footprint length. The model is studied in the regime Equation 4There are many neurons within a footprint length Equation 5The maximal AMPA conductance (with all channels open) between neurons is taken to be g AMPA w ij, where g AMPA is the total AMPA conductance a postsynaptic cell receives. Two architectures are examined. With a uniform architecture, the coefficients w ij are Equation 6They are normalized such that Σj w ij = 1. With sparse architecture, it is assumed that the probability of cell i to get input from cell j is Equation 7where M is the average number of synaptic inputs a neuron receives.2 The strength of each AMPA synapse is therefore g AMPA/M. The uniform model is obtained from the sparse model for very large N and M.
Synapses show spontaneous release (Fleidervish et al. 1996; Salin and Prince 1996). Typically, such release occurs randomly in terminals innervating cortical pyramidal cells with a rate of ∼20–50 s−1 per neuron. (I. A. Fleidervish and M. J. Gutnick, unpublished data) (recording of spontaneous events from rat slices at 33°C, where the rats were ≥3-wk old). Synaptic noise [spontaneous excitatory postsynaptic conductances (EPSCs)] is modeled by a linear synapse on each neuron (without saturation or depression) receiving a Poisson spike train (Golomb et al. 1994a) at a rate νnoise = 50 Hz. Each presynaptic spike at time t o evokes an EPSC with an amplitude g noise f (t − t o) described by an extended α function (Destexhe et al. 1994; Rall 1967) Equation 8where the rise time is τ1 = 1 ms and the decay time is τ2 = 5 ms, corresponding to the AMPA kinetics.
Numerical integration was carried out with the fourth-order Runge-Kutta method with a time step of 0.03 ms and with λ = L/32. Except for Fig. 6, N = 4096. At t = 0, all the cells are at their resting state. Evoked discharges were initialized by injecting a current pulse of 6 μA/cm2 for 18 ms into cells in an interval of length λ on the left of the slice model. The synaptic noise variables were simulated 50 ms before the beginning of the simulation to reach equilibrium.
Correlation functions
Activity of each neuron is often described by the time series of the occurrence of action potentials a neuron fires. The spike train of the ith neuron is represented by the spiking function defined as Equation 9where t 1, t 2, ..., t k are the times of the action potentials the ith neuron fires during a time interval T, and δ is the Dirac function (Fig. 1). The cross-correlation c i,j (τ) between two spike trains recorded during one trial is defined as Equation 10When i = j, c is the autocorrelation function. The trial-average cross-correlation c̄ i,j(τ) is Equation 11where 〈...〉 means average over trials. The system-average cross-correlation C k(τ) is defined as the average cross-correlation over all pairs at the same distance Equation 12When persistent activity is concerned, the cross-correlations are normalized by the time interval Equation 13In simulations, spikes of neurons close to the edges (at a distance <3λ) are not included in this average. Cross-correlations are calculated by binning (Abeles 1991), with a bin width of 0.1 ms. Global synchrony measures (see further) were calculated by averaging over 10 realizations for Fig. 6 and 3 realizations otherwise.
Sparse connectivity
I first study the effects of sparse connectivity only on the network dynamics (without heterogeneity or noise). The population-average maximal AMPA conductance a cell receives is g, and the standard deviation is g/ . Therefore, I expect the firing pattern to be more ordered as the average number of synapses M increases. Rastergrams are shown in Fig. 2 A. Stimulation of the left edge evokes a propagating discharge, during which each cell fires several action potentials. The discharge propagation velocity νD increases slightly with decreasing M, because with small M there are cells that receive relatively high synaptic input, fire faster, and transferthe information about the discharge more rapidly. With M =128 (Fig. 2 A, left), the firing pattern looks more orderedthan with M = 16 (Fig. 2 A, right), but there is no full coherence as occurs without sparseness (Golomb and Amitai 1997). The reduction of order with increasing sparseness is demonstrated by the system-average correlation function C k(t) (Fig. 2 B). Correlation functions are non-zero only for twice the discharge time, here ∼30 ms. The autocorrelation function C o is more oscillatory at larger M, implying larger resemblance between firing patterns of neurons. At M = 16, the nearest-neighbors cross-correlation C 1 has a peak near τ = 0, and it decays monotonically as ‖τ‖ increases. Therefore, neurons are synchronized at the discharge time scale, but there is no global spike-to-spike synchrony. At M = 128, C 1 has wiggles with a time period of a few milliseconds, reflecting some level of spike synchronization. The cross-correlation C 1024 between neurons 8λ apart is similar to C 1 for both M = 16 and M = 128, but with a time shift. Generally, the time shift of C k is Δx/νD, where Δx = kL/N.
To demonstrate the collective nature of the discharges, the cross-correlations between neighboring neurons averaged over four groups of pairs separately is calculated (Fig. 3). In the first group, neurons are not coupled monosynaptically; in the second group, the left neuron projects to the right neuron; in the third group, the right neuron projects to the left one; and in the forth group, the two neurons projects to each other. No significant difference was found between the average cross-correlations, indicating that the coherence between neurons is not a result of whether there is a monosynaptic coupling between them. This is expected from a system in a synchronized state (Ginzburg and Sompolinsky 1994).
To quantify the global level of spike synchrony, the synchrony measure χk is defined as follows (see Fig. 4 A). The values of the cross-correlation C k(τ) at the central three peaks are denoted, from left to right, by P −1, P 0, and P 1. The values of C k(τ) at the central two troughs are denoted by R −1 and R 1. The synchrony measure χk is defined as Equation 14The measure χk is larger when there is more global spike synchronization. With a uniform architecture (no sparseness), it is infinity, because the C k is a sum of δ peaks. With low M (high sparseness), it is very small and is governed by the numerical noise. The dependence of χk on the distance between the neurons in a pair is shown in Fig. 4 B. Except for numerical fluctuations, χ remains constant with the distance, i.e., the global correlation between neurons does not depend on distance, except for a phase shift.
Persistent activity
The emergence of global synchrony, and, in particular, that global synchrony between neurons does not depend on distance, is related to the propagating and transient characteristics of the discharge and does not hold during persistent activity. To demonstrate this, a model with no synaptic depression (kt = 0) and reduced slow potassium conductance (g K-slow = 0.4 mS/cm2) is simulated. The system parameters are tuned such that the discharge is not terminated, and instead continues indefinitely. A rastergram of neurons in a network reaching a persistent activity state is shown in Fig. 5 A, together with the voltage time trace of one neuron. The spiking patterns of the first few spikes of neurons are similar to those of neurons in Fig. 2 A (M = 128). The slow potassium current I K-slow builds up within ∼10 spikes. It is not strong enough to terminate the activity, and instead it reduces the firing rate to a steady state level. The firing pattern of each neuron is close to periodic, as indicated by the rastergram, the voltage trace, the damped oscillation seen in the system-average autocorrelation C 0 (Fig. 5 B, top) and the periodic nature of autocorrelation of a specific neuron calculated during a long time interval (29.7 s) (Fig. 5 C, top). The firing times of neurons do not show any special order. The nearest-neighbor system-average cross-correlation C 1 (Fig. 5 B, bottom), or any other cross-correlation, is flat. Similarly, the cross-correlation between two specific neurons (Fig. 5 C, bottom) is close to being flat, with fluctuations that decay with the length of the time interval over which correlation is calculated, indicating an asynchronous state. The patterns and microdomains that are seen in the rastergram (Fig. 5 A) mean only that there is locking in a brief time period, as expected in an asynchronized state when neurons have similar time periods (compare with Fig. 6 in Golomb et al. 1994b).
The appearance of an asynchronized state in a one-dimensional neuronal network during persistent activity is expected based on the following argument. In many systems that exhibit persistent firing with all-to-all coupling, excitation leads to an asynchronized state (Hansel et al. 1995). In other systems with long-range coupling, even if a homogeneous system exhibits a certain level of synchrony, small levels of sparseness, heterogeneity or noise shift the system into an asynchronous state3 (D. Hansel, personal communication). An all-to-all network with the parameter set of Fig. 5 will go to an almost-asynchronized state, with the population voltage (defined as in Golomb et al. 1994b) exhibiting low-amplitude oscillations (data not shown). Even a low sparseness level (e.g., N = 4096, M = 512) shifts the system into an asynchronized state, in which the population voltage is almost constant in time. The global synchrony during persistent activity in a one-dimensional system is expected to be not larger than the synchrony in a system in which the coupling does not decay with distance.
If the initial conditions of the neurons in a network with spatially independent coupling are close to a synchronized state, dephasing can occur within a few cycles. A similar effect is seen here in networks with spatially decaying, one-dimensional coupling, in which an asynchronized state is reached after a transient of ∼10 cycles.
Dependence of synchrony on N and M
Most simulations are carried out with N = 4096, and the number of cells within a footprint is Nλ/L = 128. In an actual slice, the number of cells is much larger. Therefore I investigate the dependence of the synchrony measure χ for propagating discharges as N varies between 211 = 2,098 and 217 = 13,1072 (Fig. 6). The reference parameter set (k t = 1 s−1) is used; M = 128. As N increases, χ decreases; the decrease is weaker as log (N) increases. These simulations indicate that χ approaches an asymptotic value at large N. In the example, χ at the reference value (4,096) is ∼30% higher than its value at N = 13,1072. Hence, I expect the numerical calculations of χ to be qualitatively correct for N in the order of the number of cells in the slice4 (of order 106), but quantitatively somewhat lower. The trial-to-trial variability of system-average magnitudes such as χ is very small at large N. As a result, only one large realization is necessary for calculating trial-average of such magnitudes.
The dependence of χ on M is accessed quantitatively in Fig. 7 A for networks with strong synaptic depression (kt = 1 s−1), including one with the reference parameter set, and in Fig. 7 B for networks without synaptic depression (k t = 0). In both cases, two values of g AMPA are examined. One g AMPA value is near the value for g AMPA,c, which is the threshold value for propagation with no sparseness [i.e., 0.28 mS/cm2 for the parameter set without synaptic depression and 0.54 mS/cm2 for the parameter set with synaptic depression (Golomb and Amitai 1997)]. The second g AMPA value is larger. For each g AMPA value, simulations were carried out with and without NMDA conductance. In all cases, two behavioral regimes are observed. At small M, χ is low, implying no global spike synchronization. At large M, χ increases with M, and the dependence of χ on M is close to linear. There is a smooth cross-over between the regimes. The number of inputs, M co, at which the cross-over between the regimes occurs, depends only weakly on the values of g AMPA and g NMDA, despite the fact that the number of spikes and the duration of the discharge both depend strongly on these parameters. Synaptic depression reduces M co and therefore increases synchrony: M co ≈ 35 for k t = 1 s−1 (Fig. 4 A), whereas M co ≈ 65 for k t = 0 (Fig. 4 B). A possible explanation for this result is that in most cases, prolonged excitation eventually precludes synchrony (Ermentrout 1996; Hansel et al. 1993, 1995; van Vreeswijk et al. 1994; see previous text). Because synaptic depression reduces the strength of consecutive EPSCs, the initial spikes evoke strong EPSCs and help to recruit more cells into the discharge, whereas subsequent spikes evoke weaker EPSCs, such that the excitatory synaptic input that leads to desynchronization diminishes.
Heterogeneity and synaptic noise
The neuronal population is heterogeneous with respect to the intrinsic properties of individual neurons. In particular, the strengths of various ionic conductances vary from cell to cell. I model heterogeneity by assuming that each of the three ionic conductances—g L, g KA, and g K-slow—is chosen separately, at random, from a square distribution with a ratio α between the standard deviation and the mean. The A current is deinactivated when the neuron is hyperpolarized and thus is effective at the beginning of the discharge. Heterogeneity in g KA affects the timing of the first spikes. In contrast, I K-slow becomes effective after the neuron has fired several spikes; heterogeneity in g K-slow affects the duration of the firing period and the timing of the later spikes. Heterogeneity in g L affects the timing of all the spikes. A rastergram for α = 0.3 is shown in Fig. 8 A. Despite the relatively high heterogeneity, the first four spikes of each neuron are well synchronized with the first four spikes of any other neuron, with a time shift that depends on the distance between them. Subsequent spikes (after the first four spikes) are much less synchronized. The dependence of χ on α is shown in Fig. 8 B. As expected, χ decreases with α. However, even at a maximal value of α (1/ ) the value of χ is ∼4 ms−1. This value is well above the value of χ at the cross-over to spike synchrony M co with the same parameter set (χ < 1 ms−1); to reach it in the sparse coupling case, M shouldbe >120. Therefore, heterogeneity in the cell intrinsic properties is a less severe cause of synchrony reduction than sparseness.
Synaptic noise has two effects. When it is weak, it reduces synchrony, and if it is strong enough, it also induces spontaneous discharges. I simulated the system with two values of ν, 20 and 50 s−1 (Fig. 8, C and D), corresponding to the borders of the experimental range for spontaneous synaptic input. A rastergram for g noise = 0.1 mS/cm2 and ν = 50 s−1 is shown in Fig. 8 C. All the spikes are very well synchronized (with a time shift). The dependence of χ on g noise is shown in Fig. 8 D. The arrows denote the g noise levels above which spontaneous discharges were generated; the dependencies of χ on the noise level below these values are shown. Increasing ν or g noise reduces χ. However, in the regime where no spontaneous discharges are observed, χ > 14 ms−1, i.e., it is much higher than the χ values obtained with sparseness for M < 200 and is higher than the χ values with large heterogeneity level α. Hence, synaptic noise contributes to synchrony reduction much less than sparseness and heterogeneity.
As with sparseness, the function Ck of a system with noise or heterogeneity depends on k only via a phase shift, while the value of wk remains unchanged.
Global and local synchrony
Sparseness and heterogeneity affect the global (system-average) synchrony of the traveling discharge. They do not, however, affect the local (trial-average) synchrony between two neurons, because they are not stochastic in time. If the network model is stimulated again and again exactly in the same manner, the two neuron will respond exactly the same, and the trial-average cross-correlation will be a sum of δ functions. Synaptic noise, which is stochastic, affects both global and local synchrony. Moreover, for a large noisy network with no heterogeneity and uniform architecture (no sparseness, Eq. 6 ), the trial-average cross-correlation between two neurons at a distance k neurons apart is equal to the system-average cross-correlation Ck (Fig. 9). In a cortical slice, there is sparseness, heterogeneity, and noise. Here the trial-average and system-average correlations are calculated for a system that has both sparseness and synaptic noise.
Examples of trial-average correlation functions between two adjacent neurons for a noisy and sparse network(g noise = 0.1 mS/cm2, v = 50 s−1, M = 48) are shown in Fig. 10 A, and the corresponding system-average correlations are shown in Fig. 10 B. Synaptic noise reduces synchrony only moderately, and hence trial-average autocorrelations show very sharp peaks, and cross-correlations reveal a decaying oscillatory pattern. The relative phase of firing varies from one pair of neurons to another. For example, the cross-correlation presented in Fig. 10 A, middle, indicates that those particular two cells fire almost in antisynchrony. The central peak of the cross-correlation presented in Fig. 10 A, bottom, is broader and the phase relationship between those two cell is less well defined. In general, even if the phase relationship between two neurons in a pair is well defined, it varies considerably from pair to pair. With a relatively low value of M (high sparseness), it is distributed almost uniformly. As a result, the system-average cross-correlation exhibits almost no wiggles in the time scale of the interspike interval, indicating that there is only a very small global (system-average) spike synchronization in the network.
The main results of this work are as follows. 1) Global spike synchronization can emerge during propagating discharges because of their propagating and transient nature. 2) This synchronization is a collective effect; it does not depend on monosynaptic connections between neurons. 3) The global correlation between neurons does not depend on the distance between them, except for a phase shift. 4) Global synchrony is obtained if the number of inputs a cell receives on average is above a certain cross-over value M co, of order 30–70. 5) Synaptic depression appears to help synchrony. The cross-over value M co is reduced by synaptic depression, but is only weakly affected by the strength of AMPA and NMDA conductances, g AMPA and g NMDA. 6) Global synchrony can exist even in very heterogeneous neuronal populations. 7) and, synaptic noise reduces synchrony only mildly.
Transient and persistent synchrony
As long as discharges propagate, they are always synchronous at the discharge time scale, and this synchrony does not decay with distance between neurons for any level of sparseness, heterogeneity and noise.5 An unexpected result of this work is that, in addition to discharge synchronization, neurons also can exhibit spike synchronization that does not decay with distance. Intuitively, this can be viewed as if the firing pattern of each neuron is locked to the pulse through the envelope of the discharge, defined by averaging the voltage of many neurons at the same location, which propagates at a constant velocity and maintains its shape. In two limiting conditions, this result could be predicted. In the homogeneous case (Golomb and Amitai 1997), there is perfect synchrony (with a time shift Δx/νD). With a small average number of synapses on a cell M, there is no spike synchronization. This modeling work shows that a certain (but not full) level of spike synchronization independent of distance exists in an intermediate regime, where M is above M co but does not need to be extremely high.
As M increases there is a cross-over between an asynchronized region and a region of spike synchronization. Another unexpected result of this work is that the cross-over value between asynchrony and synchrony, M co, depends only weakly on the strength of the synaptic coupling, but its reduction by synaptic depression is apparent. AMPA conductance strength, which strongly affects the discharge velocity (Golomb and Amitai 1997), has only a weak effect on M co. NMDA conductance strength has a negligible effect. Therefore, synchrony is much more affected by the kinetics of the synapses than by their strength. Synaptic depression decreases M co because it reduces the excitatory strength at long times and thereby removes desynchronizing forces. In the synchronized regime, the spike synchrony χ increases linearly with M for M > M co. Variability in the synaptic strength of existing synapses (not considered in the model) and heterogeneity in intrinsic neuronal properties are expected to reduce synchrony experimentally.
A network of excitatory cells will generally not exhibit spike synchrony during persistent firing even with spatially independent synaptic strength, in particular in the presence of sparseness, heterogeneity, and noise (Ermentrout 1996; Hansel et al. 1993, 1995; van Vreeswijk et al. 1994). Hence, it is not surprising to find that the global cross-correlations are flat during persistent activity even between neighboring pairs. If neurons are active for a long time [e.g., with strong NMDA conductance (Golomb and Amitai 1997)], and the sparseness level is low, the first spikes of each neuron are synchronized, but the level of synchrony gradually decreases until, within a few cycles, the system becomes asynchronous.
When neuronal firing is terminated by I K-slow or by synaptic depression, the propagating discharge exhibits global transient spike synchronization for a large enough M and not too strong heterogeneity. This synchronization emerges both from the propagating and the transient characteristics of the discharge. The synchrony of the first few spikes neurons fire results from the recruitment process. Resting neurons in front of the discharge are affected by the excitatory synaptic field moving toward them. Adjacent neurons will tend to rise together from rest and fire at least the first few spikes in a synchronous manner, unless M is too small (and in that case the two neurons may be affected by too different synaptic fields) or the heterogeneity level is very high (and then each neuron may respond differently). Distant neurons will be affected by the same discharge but at a time difference that is equal to the distance between them divided by the discharge velocity. Therefore, they will fire their first spikes synchronously with the corresponding time shift. Subsequent spikes tend to be less synchronized because of the excitation effect, but the discharge is terminated before the neurons have enough time to fire in the desynchronized state.
Axonal velocity is estimated to be ∼1 m/s in somatosensory cortex (Gil and Amitai 1996) and olfactory cortex (Haberly 1990). This value is large in comparison to the typical discharge propagation velocity, about 0.16 m/s (Golomb and Amitai 1997), and therefore axonal velocity is neglected in this work. Variability in axonal delays may be another desynchronizing factor. More experimental and computational work is needed for estimating this effect quantitatively.
It was estimated (Golomb and Amitai 1997) that the total AMPA synaptic strength gAMPA is ∼5 times stronger than the conductance needed to evoke a spike in a synchronized manner. A spike reaching a presynaptic terminal of a synapse with that conductance evokes an EPSP of ∼20 mV, which is the voltage difference between the resting potential and the threshold. Assuming a typical EPSP of 1–2 mV (Thomson et al. 1993) ∼10–20 presynaptic cells need to fire spikes together to evoke a postsynaptic spike. Therefore, the number of presynaptic cells that send input to a postsynaptic cell is ∼50–100. This number is much smaller than the number of synapses on a pyramidal cell of a rat, ∼104 (Abeles 1991; Colonnier 1981; Schuz and Palm 1989), because a cell may form more than one synaptic contact on another cell (Markram et al. 1997; Peters and Proskauer 1980; Thomson et al. 1996) and because many connections are cut during the slicing procedure. The number of synaptic inputs estimated here is close to the cross-over values obtained by the model. Hence, it is expected that in real rat cortical slices, only a low amount of global synchrony will be recorded, if any.
Comparison with other models
The synchrony measure χ used here (Fig. 4 A) is derived from the global correlation function, which is the sum of correlations between the firing patterns of neuronal pairs at the same distance (Eq. 12 ). In general, the correlation can be measured between other functions of the neuronal activity, denoted here by fi, such as the membrane potential and the synaptic variables. When the coupling does not depend on space, it is natural to sum over all the pairs. In this case, The global correlation will be Equation 15For τ = 0, C(0) = dt [Σi f 2 i(t)]2. From this value, a synchrony measure is constructed by subtracting the square of the average firing rate and then normalizing it (Golomb and Rinzel 1994). Therefore, the main difference between the synchrony measures used for a one-dimensional system and a spatially independent system is the selection of the neuronal pairs that are included in the summation.
The synchrony measure χ in my model increases continuously with M, and there is a smooth cross-over between the asynchronized and synchronized regions. In models with spatially independent architecture, the transition between the two regimes is sharp (Barkai et al. 1990; Wang and Buzsáki 1996; Wang et al. 1995). In thalamic networks, composed of excitatory and inhibitory populations (Wang et al. 1995), synchrony is achieved if M is >2–5, whereas in hippocampal networks of inhibitory neurons, the transition occurs at M of order 100 (Wang and Buzsáki 1996), a number that is similar to what is obtained here. This may indicate that synchronous activity is more robust in a network that includes coupled excitatory and inhibitory populations (D. Hansel, unpublished data). Synchrony between neurons in inhibitory networks does not depend on whether there is a monosynaptic coupling between them (Wang and Buzsáki 1996), as obtained here for global synchrony during transient discharges.
Discharge propagation in CA3 hippocampal slices with sparse and spatially decaying architecture was studied by Traub and colleagues (Miles et al. 1988; Traub et al. 1993). In these studies, all the cells received exactly the same number of inputs, and therefore their networks are expected to be much more synchronous than what is presented here. The intrinsic bursting properties of CA3 neurons introduce three time scales of synchrony (entire discharges, bursts, and spikes). Synchrony in the discharge time scale was observed in their model, but synchrony in the burst and spike time scale was not analyzed.
Experimental verifications of the model
The sparseness level, expected to be found in the neocortical slice, reduces synchrony to a small level or abolishes it completely. Heterogeneity further degrades synchrony. Both factors affect the global, system-average synchrony. Stochastic noise affects synchrony only mildly; this is the only factor that affects both the system-average and trial-average cross-correlation. As a consequence of these results I predict that in cortical coronal or sagittal slices, strong local, trial-average spike synchronization will be measured but that global, system-average spike synchrony will be low or absent. Local synchrony between two distinct neurons can be measured easily experimentally in neocortical slices by repetitively eliciting events in the slice and measuring the trial-average correlation between the spike patterns. To measure global synchrony, many pairs with a constant distance between the neurons in each pair should be recorded with a multi-electrode array. The model presented here applies mainly to regimes for which the connectivity patterns and the intrinsic neuronal properties do not change with space, for example, areas of order 0.2–1 mm in coronal slices (Chervin et al. 1988; Wadman and Gutnick 1993) or larger areas in sagittal slices (M. J. Gutnick, unpublished data).
If strong system-average spike synchrony is found experimentally, it probably will mean that the connectivity pattern is less sparse than what is assumed in the model. Even if M is small, an ordered connectivity pattern (for example, if each cell is coupled to exactly M/2 cells on its right and M/2 cells on its left) will lead to high synchrony. If only weak trial-average spike synchrony is found experimentally, it will mean that the level of stochastic noise is higher than what is expected from the model. For example, low probability of release can be another source of stochastic noise.
Another prediction is that the system-average cross-correlation of neurons does not depend on the distance between them. This prediction is expected to be valid in each cortical region separately, but systematic changes in the intrinsic and synaptic conductances of neurons, as may be found between adjacent cortical areas in a single slice (Chervin et al. 1988; Wadman and Gutnick 1993), may modify it.
Prechtl et al. (1997) have discovered plane waves, spiral-like waves and waves with more complex patterns in the turtle cortex. A model similar to the one reported here, but with a two-dimensional architecture, can be used for studying these waves.
I am grateful to M. J. Gutnick and I. A. Fleidervish for introducing me to the subject of cortical discharges and for a careful reading of this manuscript. I thank E. Barkai, B. W. Connors, G. B. Ermentrout, Z. Gil, D. Hansel, N. Kopell, M.A.L. Nicolelis, J. Rinzel, and E. L. White for helpful discussions and to D. Hansel also for a careful reading of this manuscript.
This research was supported by a grant from the Israel Science Foundation.
1 In models with long-range coupling, the coupling between neurons does not decay, or decays only weakly, with the distance between them. In models with short-range coupling, the coupling between neurons decays with the distance between them with a characteristical decay length much smaller than the system length (see Eq. 4 ).
2 Because the model neuron has only one compartment, it is assumed that one cell can send output to a second cell only through 0 or 1 synapses. If there are more synapses between two cells, they can be modeled as one stronger synapse.
3 An asynchronized state is obtained, in general, in networks with spatially independent excitatory coupling with even small levels of disorder (sparseness, heterogeneity, or noise), when only one time scale is involved (here the time scale of the interspike interval). If two time scales are involved and the neurons burst, either because of the neuronal intrinsic properties (Pinsky and Rinzel 1994), or because of population effects (Goldberg et al. 1996), then the bursts are often synchronized (although generally not fully synchronized), but the spikes within bursts are not.
4 The slice dimensions are ∼15 × 2 × 0.4 mm (Golomb and Amitai 1997), and the density of cells in rat neocortex is ∼105 mm−3 (Abeles 1991).
5 We study systems with M ≥ 8. If M is very small (≳2), propagation may stop because of lack of connectivity. Such extreme sparseness is not expected to occur in neocortex.
- Copyright © 1998 the American Physiological Society


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Ruptured cyst on left ovary, blood in toilet paper. Is this normal ?
I was diagnosed with a ruptured cyst on my left ovary 3 days ago. I have been to the ER and gyno a couple times in these last few days... But this morning when I went to the bathroom I noticed blood on the toilet paper after I wiped. Then I noticed a little in my urine . Is this normal since I have a ruptured cyst and its letting off a lot of fluid and blood? Or should I head back to the ER? Please help! (: thanks you!
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Dr. Sree Gouri SR
May 2013
Thanks for the query.
Ruptured ovarian cyst
can lead to
internal bleeding
But usually that will not come out through the uterus and cervix.
The cause for your bleeding could be
imbalance, uterine causes like endometrial abnormalities, local causes like cervical erosion etc.
So if the spotting repeats better to consult gynecologist once, get examined.
If needed go for
. By these the possible cause for your problem can be identified and treated.
Take care.
Answered: Wed, 18 Sep 2013
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Thanks for the query.
Ruptured ovarian cyst can lead to internal bleeding.
But usually that will not come out through the uterus and cervix.
The cause for your bleeding could be hormonal imbalance, uterine causes like endometrial abnormalities, local causes like cervical erosion etc.
So if the spotting repeats better to consult gynecologist once, get examined.
If needed go for ultrasound. By these the possible cause for your problem can be identified and treated.
Take care.
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Roast vegetable and houmous pie Recipe. Even my carnivorous rookie loved this - we thought it would do well on the Veggie-Menu at a restaurant
Syrup & fruit for to be added to prosecco | Photography by http://www.mandjphotos.com/ page pimp your prosecco bar
Party Inspiration - Thomas the tank Children's Party table great idea for #twin boys party shared by www.twinsgiftcompany.co.uk
Vintage Pink Rose & Pink Bridal Wedding Bouquet with Peonies | Classic Wedding | Images by Marianne Taylor Photography | http://www.rockmywedding.co.uk/james-katie/
Delicious Ham & Cheese Roll Ups made with puff pastry. They make a lovely treat tea for the family or can even be eaten cold for lunch! | My Fussy Eater blog
My name is Susie Kelly, I am the owner and creator of S K Cakes. I produce bespoke cakes and cupcakes for weddings, celebrations and every occasion. Great care is taken with every cake and cupcake created it is then decorated with great attention to detail. I enjoy working closely with my clients, listening to their ideas and needs, in order to create the perfect cake for their special occasion.
How to make the perfect afternoon tea treat – scones. Once they've baked, enjoy them with butter, jam and plenty of clotted cream.
My mother heard of Scarletts coronation now she told me " your 20 tomorrow! Its time for your coronation! Your time to be queen! Birthday party tomorrow , coronation the next day and then she says also we have some young men here you need to choose which one to marry! So birthday, coronation, wedding! I can't do that! Help!- Rose


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Gina's Italian Kitchen
$25 for a $50 Food & Beverage Voucher (value $50)
1 of your friends
already grabbed this deal:
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- Spoil your taste buds with authentic Italian cuisine.
- Grab a $50 food and beverage voucher at Gina's Italian Kitchen for $25.
- Enjoy dishes like the Tre Funghi pizza and Fettuccine Mari e Monti.
- Browse their wine menu for something to match your main.
Before you chain yourself to the oven for the rest of summer, take a well deserved post-Christmas break and have all the hard work done for you.
Pay $25 for a $50 food and beverage voucher at Gina's Italian Kitchen and enjoy an authentic Italian feast for lunch or dinner.
With a welcoming and friendly atmosphere, the team at Gina's Italian Kitchen will make you feel right at home. Allow yourself one night to be whisked away by intoxicating scents, unbelievable flavours and excellent company. You can use your voucher towards anything on their lunch and dinner menus boasting options like the Pansotti con Pollo pasta or the popular Toscana pizza with NZ pork and fennel sausage. Finish off with one of their delectable desserts like the Tiramisu and you'll be in heaven.
Gina's Italian Kitchen
(09) 302 2061
Business in trade
Opening Hours
Lunch: Tuesday - Friday: 12:00pm - 2:00pm
Dinner: Monday - Sunday: 5:30pm - Late. Please check fine print for any restrictions.
ConditionsValid from Dec 26, 2012
Expires Mar 25, 2013
Limit: 1 for you and 4 gifts for others
REDEEMABLE FROM 26TH DEC 2012. Bookings essential. Dine in only. Subject to availability. Valid for lunch or dinner seven days a week. Must book 1 week in advance is you want to book during the weekend. Max 1 coupon per 2 people. Max 2 coupons per table. No refunds, no cashback. Not to be used with any other offer.
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text:
Girl, 13, who refused to remove her brother's military photo on her binder 'threatened to be kicked out of school'
- Brianna Gentry told decorating her school binder was against her school's honour student programme she is a member of
A school binder decorated with pictures of a 13-year-old's older brother and her softball team nearly led the girl being kicked out of school, her mother claims.
Seen in his military uniform, a photograph of Brianna Gentry's older brother Derrick who is stationed in Montana as a military policeman is one of several pictures on her school binder.
'My brother is very important to me. I haven't seen him in a while,' Brianna told KTLA on her reasoning behind the photo's placement.
Scroll down for video
Problem: The mother of Brianna Gentry says her daughter was nearly kicked out of school for keeping pictures of her softball team and brother in his military uniform on her binder
Long distance: Brianna says her brother is stationed as a military policeman in Montana so rarely sees him, prompting her to keep the photo of him close to her
Around him are also pictures of her softball team.
Both pictures, however, as Brianna recently learned, do not comply with her school's rules with the eighth grader's membership of their AVID programme for top or advanced students.
'The counsellor took me out of class twice telling me that the pictures aren't AVID material,' Brianna said. 'But they haven't pulled out any other students with pictures out from their class. Just me.'
According to the school, which sent a copy of AVID's rules home for her to re-read, all students must 'maintain the AVID binder with assignments, grade sheets, and daily notes as required.'
The issue: The pictures clash with her school's rules specific for their AVID programme's students which Brianna is a member of
Angry: Finding that the AVID rules don't list pictures on binders as banned, Brianna's mother wrote a letter to the school saying her daughter will keep the pictures in place
Finding school officials' argument against her daughter's photographs absurd, and not in conflict with what they had agreed to, Brianna's mother fired back.
'These items are in her binder and will remain in her binder. The contract does not say a student cannot have pictures in the outside sleeve.
'The principal told me yesterday the rule is based on interpretation. Having a neat, clean binder is a matter of opinion.
'We will follow the rules set forth which do not include the removal of photos.'
'Her brother is a positive role model in her life,' her mother Jaima Eudy told KTLA. 'Her softball team she's very active in little league, she has been for six years. So, these are things that are happy moments for her.'
Agreement: Coming to an agreement, Brianna was allowed to keep the photo of her brother in her binder but had to remove her softball team
After some back and forth, the school came to an amended conclusion this week.
'We want our students to be successful and if this is the type of motivation that is going to help this young lady or any other student succeed, then by all means we will support her efforts,' school district spokeswoman Linda Bardere told KTLA.
But the picture of her softball team still had to be removed they decided.
'I'd rather have my brother in my pictures than have nothing at all,' Brianna said. 'So, I'm fine with the decision.'
Watch the video here:
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New Partnership Solidifies Leadership Team at Metrofuser29 Jan, 2008
New Partnership Solidifies Leadership Team at Metrofuser
Laser printer parts manufacturer Metrofuser www.metrofuser.com announced that it has implemented a new partnership agreement between co- founder and current Vice President of Marketing and Logistics, Will DeMuth, and current Chief Financial Officer, Eric Katz. Todd Katz, former Vice President of Sales has sold his share of the company. "Todd played an integral role in starting this company," Demuth remarked in a statement issued to employees. "His talents and hard work were vital to the early success of Metrofuser. We all wish him the best of success in his future endeavors."
With the new partnership agreement, Eric Katz will become Co- President with DeMuth while continuing his role as Chief Financial Officer. DeMuth will continue his role as Marketing and Logistics lead. The new partnership is intended to solidify the leadership team at Metrofuser. Mark Makuch remains the Director of Operations and Ken Lang had already stepped in and taken over Todd Katz's position as head of the sales department in 2007. "With Eric as Co-President, we can strengthen the foundation that has made Metrofuser the world-class printer parts manufacturer that it is today," DeMuth stated. "We will continue to improve upon that legacy and provide our customers with the best solutions that the industry has to offer."
Since 2005, Eric Katz has been instrumental in establishing the momentum that Metrofuser has created for itself. Katz's entrepreneurial experience began as co-founder and Director of Research of Jumar Technologies, a New York-based software company. Katz, a graduate of Yale University, also spent several years teaching math, English and creative writing at a public school in the South Bronx and currently sits on the Board of Advisors for the Bronx Academy of Letters.
Katz joined Metrofuser and his diverse skill set and versatility have been invaluable in Metrofuser's rapid development. He has helped steer the ship through three consecutive years of 60+ percent revenue growth and proved his executive value by taking the lead role in Metrofuser's expansion to the West Coast, where David Burchell currently runs Metrofuser's Santa Ana distribution center. "I don't think we could have pulled off opening our new facility in southern California without Eric's leadership and meticulousness," Demuth said. "There are so many operational, logistical and administrative challenges associated with taking a successful small business and making it a national entity, but with the team we've assembled here, I feel confident that we can handle anything."
Next on the horizon is expanding the production, engineering and distribution facilities in New Jersey. "I look forward to this partnership with Will," Eric Katz added, "and I'm really excited by the opportunities that our relocation will afford us. In a larger facility, we'll be able to service more customers and explore more markets, build our dedicated team and maintain our obsessive commitment to our customers' satisfaction."
What else will this new partnership bring? Katz and DeMuth both agree that Metrofuser must continue to explore strategic partnership and acquisition opportunities, launch incentive programs for employees and partners, and more. DeMuth added, "We will, of course, continue with our never-ending new product developments and commitment to product quality."
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Earl of Elgin's Strathspey [1]
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The Art of the Steal (2013)
- Title
- The Art of the Steal
- Year
- 2013
- Types
- Movies
- Actors
- Jay Baruchel Kurt Russell Matt Dillon Kenneth Welsh
- IDMB rating
- 6.3 (17612 votes)
- Netflix rating
- 3.0
- Release date
- June 7, 2014 (Netflix)
Crunch Calhoun (Kurt Russell), a third rate motorcycle daredevil and semi-reformed art thief, agrees to get back into the con game and pull off one final lucrative art theft with his untrustworthy brother, Nicky (Matt Dillon). Reassembling the old team, Crunch comes up with a plan to steal a priceless historical book, but the successful heist leads to another far riskier plan devised by Nicky. They fail to realize each other's separate agendas when their plan goes awry in this con movie about honor, revenge and the bonds of brotherhood.
Is The Art of the Steal (2013) on Netflix?
Yes! The Art of the Steal (2013) is available on Netflix since Saturday 7 June 2014.
Watch the trailer
Check the The Art of the Steal (2013) trailer!


text:
DescriptionMusic Genre: Folk, Indie. David Wax Museum's work is simplistic and sophisticated, elegant and plainspoken, messy and beautiful. Darlingside brings a quartet of voices to smart lyricism.
Event Details
Category: Performing Arts, Food & Drink
Event Hours: 8pm
Costs: General: $20.00, Advanced: $0.00, Children: $0.00, Senior: $0.00, Military: $0.00, Student: $0.00


text:
PHPCoder Publisher's description
from Jason Sheets
PHPCoder is a web based front-end to the Turck MMCache or eAccelerator encoding functions, both of which are similar to the Zend Encoder product.
PHPCoder is a web based front-end to the Turck MMCache or eAccelerator encoding functions, both of which are similar to the Zend Encoder product.
Turck MMCache is a free open source PHP accelerator, optimizer, encoder and dynamic content cache for PHP. It increases performance of PHP scripts by caching them in compiled state, so that the overhead of compiling is almost completely eliminated. Also it uses some optimizations to speed up execution of PHP scripts. Turck MMCache typically reduces server load and increases the speed of your PHP code by 1-10 times.
eAccelerator is a further development of MMCache.
PHPCoder enables you to encode your PHP scripts and applications into non reversible byte-code, thus preventing users of your programs from viewing or altering the source code while having full functionality. Another excellent use for PHPCoder is to encode your applications PHP configuration files, that way someone viewing your source code does not see your database login and password information.
What's New in This Release:* Gary Harris 28/2/06.
* V1.4 had been added to the SF files page but not the web page.
Many changes had been lost and the eAccelerator version was based
on the older version. Brought both versions back up to 1.4 spec.
* eAccelerator version encoded but produced incorrect output. Fixed.
* eAccelerator version also contained a number of bugs.
* The manual now covers both encoders and is called PHPCoder Manual.htm.
* Numerous additional fixes including URLs.
* NOTE: Multi-encoder version not currently updated.
System Requirements:Turck MMCache or eAccelerator must be installed (available on . Windows and Unix/Linux)
. PHP >= 4.1 (4.3.x highly recommended, 4.1 required)
. Apache 1.3/2 or other PHP compatable web-server
Program Release Status: Minor Update
Program Install Support: Install and Uninstall


text:
Biscuit Pudding
Bourbon biscuit brownies: What's better than a chocolate Bourbon biscuit? Chocolate Bourbon brownies! This is one of our favourite recipes of 2016 - trust us, you'll need to make a double batch
Viennese whirls from The Great British Bake Off
No-Bake Biscoff Cookie Butter Cheesecake!! A delicious No-Bake Biscoff Cookie Butter Cheesecake, sprinkled with more biscuits and whipped cream - Spiced Cookie Heaven.
Rolo Cookie Bars! ❤ Delicious Chocolatey & Caramel Cookie Bars that Everyone will Love - Delicious Cookie, Chocolate Chips, and Oooodles of Rolos!
Give Mary Berry's jaffa cakes from Great British Bake Off a whirl.
Millionaires' Cupcakes - Chocolate cupcakes topped with caramel buttercream with a hidden shortbread and caramel centre.
Eggless Chocolate Biscuit Pudding (No Bake Chocolate Cookie Cake) - An easy, classic Sri Lankan dessert with alternating layers of milk-soaked Maria cookies and soft, creamy chocolate buttercream.
1 Syn Raspberry and White Chocolate Muffins | Slimming World
Mary Berry's bakewell tart from The Great British Bake Off is as classic and classy as they get.
This berry and white chocolate tart from Annabel Karmel's Busy Mum's Cookbook is a show-stopping dessert that couldn't be simpler. The buttery biscuit base is covered with a delicious combination of cream cheese and smooth white chocolate, then topped with fresh berries, which you could swap for whichever fruits are in season. An indulgent, gorgeous pudding perfect for impressing at a dinner party.


text:
Stormy, the unofficial school crossing guard, dies
COSTA MESA – A crosswalk at Killybrooke Elementary School will be a little less friendly now.
Stormy, a 20-year-old black cat that helped a school crossing guard and became the unofficial mascot of the intersection of Killybrooke Lane and Stonefield Street, was put down on Thursday, owner Melanie Whittaker said.
"She was peacefully sent to that great catnip garden in the sky where we know she is happily frolicking and telling tales of Killybrooke Lane," Whittaker said. "Stormy was the most gentle cat and loved the attention she received from all the children going to school each day."
Stormy was famous for working with crossing guard Barbara Scalla.
"That was like losing a part of your family," said Scalla, a Huntington Beach resident. "She will be missed. She was one special kitty."
Stormy would wait for Scalla every morning at the school and the odd couple would work from 7:30 to 8:45 a.m., helping students cross the street. Stormy greeted the children and let them pet her while Scalla walked the students across the street – a routine the pair had for more than four years.
The cat had recently gotten thinner and was unable to keep food down, Whittaker said. After consulting a veterinarian the family decided to put the Stormy down, she said.
Scalla, Whittaker, and another neighbor hugged and cried this morning, said Scalla who wore a black ribbon in memory of Stormy. The crossing guard decided to let parents know about the cat and allow them to tell their children, she said.
In May, the Register ran an article about Scalla and Stormy with children's responses to the cat.
"She brings happiness," said Rachel Keane, a sixth-grader who has been crossing at that corner since kindergarten. "She is probably the fun of this whole corner."
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Find the Best Lifespan APK Mobile Android Apps and Games Below!
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- Increasing the profitability of existing products
- Developing new products
- At least 5 years banking experience
Salary negotiable
- Product Management
- Cards & Unsecured Lending
- See job description.
Salary negotiable
- Leading international bank
- Retail Banking Wealth Management
- Attractive package & benefits
HK$35k - 55k /month
- private banking, High Net worth clients segment
- investment products
- private equity, real estate, mutual funds
- Insurance Propositions
- Product and Campaign Strategy
- Strong Career Prospects
HK$55k - 70k /month (negotiable)
- Solid experience in FMCG
- Manage given A&P, coordinate with all vendors
- Work together with sales and supply chain
- Provide coaching, quality consultation
- Initiate marketing strategies
- At least 8 years banking experience
Salary negotiable
- At least 3 years' relevant solid experience
- University graduate in Marketing
- Provide marketing insights and analysis
- Review operational procedures
- Product training materials
- Min. 5 yrs. exp. in retail banking
- Craft a product roadmap, Define metrics and KPIs
- proactive in risk mitigation,process improvement
- Lead a growing team of analysts and managers
- Develop new products and services
- Analyze and evaluate new concepts
- Manage existing product lines
- Mobile
- payment
- manager
- Experience in consumer banking & wealth management
- Solid exposure in channel management
- Strong knowledge in Investment & Insurance product
- Responsible for the on-going development
- Support continuous growth of payment
- Responsible for proposing the business strategies
- Monitor industry trend
- Produce and share regular market updates
- Support Senior Manager in product / promotion
Salary negotiable
- Provide marketing insights and analysis
- Plan & manage ATL/BTL marketing & sales activities
- Responsible for P&L and inventory management
- Provide product marketing ideas
- Improve loyalty of existing and new customers
- Prepare regular report to management and regulator
- Bach Deg on Business, Finance or equivalent
- Exp in Financial Service, Wealth Mgt products
- Insurance products distribution channels managemen
HK$30k - 45k /month (negotiable)
- Responsible for developing offshore
- Regular review on all policies and procedures
- University graduate with major in Business Admin
- Global designer furniture retail store
- With large expansion plans
- Native English speakers, retail sales are welcomed
- All-rounded product managment
- Wealth product team
- Attractive remuneration
- 5 yrs premier banking segment marketing
- Structured Investment product mgt exp
- Good spoken & written English & Chinese
- Fantastic opportunity in High Net Worth Insurance
- Excellent Career Progression
- World's leading financial institution
Salary negotiable
- Monitor industry trend
- Produce and share regular market updates
- Support Senior Manager in product / promotion
Salary negotiable
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