Optimal Hebbian Learning: A Probabilistic Point of View

Abstract. Up to now, many activity dependent learning rules have been proposed in order to model long-term potentiation (LTP). Our aim is to derive a spike time dependent learning rule from a probabilistic optimality criterion. The idea is to create a model in order to obtain quantitative results in terms of a learning window. This is done by maximising a given likelihood function with respect to the synaptic weights. The results are consistent with the actual knowledge of back-propagating action potentials

GEp/GMpG_{E_p}/G_{M_p} ratio by polarization transfer in e⃗p→ep⃗\vec{e}p\rightarrow e\vec{p}

The ratio of the proton's elastic electromagnetic form factors was obtained by measuring the transverse and longitudinal polarizations of recoiling protons from the elastic scattering of polarized electrons with unpolarized protons. The ratio of the electric to magnetic form factor is proportional to the ratio of the transverse to longitudinal recoil polarizations. The ratio was measured over a range of four-momentum transfer squared between 0.5 and 3.5 GeV-squared. Simultaneous measurement of transverse and longitudinal polarizations in a polarimeter provides good control of the systematic uncertainty. The results for the ratio of the proton's electric to magnetic form factors show a systematic decrease with increasing four momentum squared, indicating for the first time a marked difference in the spatial distribution of charge and magnetization currents in the proton

Proton elastic form factor ratios to Q2Q^2=3.5 GeV2^2 by polarization transfer

PHASEThe ratio of the proton elastic electromagnetic form factors, $G_{Ep}/G_{Mp}$, was obtained by measuring $P_{t}$ and $P_{\ell}$, the transverse and longitudinal recoil proton polarization components, respectively, for the elastic $\vec e p \to e\vec p$ ~reaction in the four-momentum transfer squared range of 0.5 to 3.5 GeV$^2$. In the single-photon exchange approximation, the ratio $G_{Ep}/G_{Mp}$ is directly proportional to the ratio $P_t/P_{\ell}$. The simultaneous measurement of $P_{t}$ and $P_{\ell}$ in a polarimeter reduces systematic uncertainties. The results for the ratio $G_{Ep}/G_{Mp}$ show a systematic decrease with increasing $Q^2$, indicating for the first time a definite difference in the distribution of charge and magnetization in the proton. The data have been re-analyzed and systematic uncertainties have become significantly smaller than previously published results