Equivalence between Schwinger and Dirac schemes of quantization

This paper introduces the modified version of Schwinger's quantization method, in which the information on constraints and the choice of gauge conditions are included implicitly in the choice of variations used in quantization scheme. A proof of equivalence between Schwinger- and Dirac-methods for constraint systems is given.Comment: 12pages, No figures, Latex, The proof is improved and one reference is adde

Halo-Galaxy Lensing: A Full Sky Approach

The halo-galaxy lensing correlation function or the average tangential shear profile over sampled halos is a very powerful means of measuring the halo masses, the mass profile, and the halo-mass correlation function of very large separations in the linear regime. We reformulate the halo-galaxy lensing correlation in harmonic space. We find that, counter-intuitively, errors in the conventionally used flat-sky approximation remain at a % level even at very small angles. The errors increase at larger angles and for lensing halos at lower redshifts: the effect is at a few % level at the baryonic acoustic oscillation scales for lensing halos of $z\sim 0.2$, and comparable with the effect of primordial non-Gaussianity with $f_{\rm NL}\sim 10$ at large separations. Our results allow to readily estimate/correct for the full-sky effect on a high-precision measurement of the average shear profile available from upcoming wide-area lensing surveys.Comment: 12 pages, 4 figure

Sodium dynamics in pyramidal neuron dendritic spines : synaptically evoked entry predominantly through AMPA receptors and removal by diffusion

© The Author(s), 2017. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in Journal of Neuroscience 37 (2017): 9964-9976, doi:10.1523/JNEUROSCI.1758-17.2017.Dendritic spines are key elements underlying synaptic integration and cellular plasticity, but many features of these important structures are not known or are controversial. We examined these properties using newly developed simultaneous sodium and calcium imaging with single-spine resolution in pyramidal neurons in rat hippocampal slices from either sex. Indicators for both ions were loaded through the somatic patch pipette, which also recorded electrical responses. Fluorescence changes were detected with a high-speed, low-noise CCD camera. Following subthreshold electrical stimulation, postsynaptic sodium entry is almost entirely through AMPA receptors with little contribution from entry through NMDA receptors or voltage-gated sodium channels. Sodium removal from the spine head is through rapid diffusion out to the dendrite through the spine neck with a half-removal time of ∼16 ms, which suggests the neck has low resistance. Peak [Na+]i changes during single EPSPs are ∼5 mm. Stronger electrical stimulation evoked small plateau potentials that had significant longer-lasting localized [Na+]i increases mediated through NMDA receptors.This work was supported in part by National Institutes of Health Grants R21NS085729 and R01NS099122.2018-03-1

Simultaneous sodium and calcium imaging from dendrites and axons

© The Author(s), 2015. This article is distributed under the terms of the Creative Commons Attribution License. The definitive version was published in eNeuro 2 (2015): ENEURO.0092-15.2015, doi:10.1523/ENEURO.0092-15.2015.Dynamic calcium imaging is a major technique of neuroscientists. It can reveal information about the location of various calcium channels and calcium permeable receptors, the time course, magnitude, and location of intracellular calcium concentration ([Ca2+]i) changes, and indirectly, the occurrence of action potentials. Dynamic sodium imaging, a less exploited technique, can reveal analogous information related to sodium signaling. In some cases, like the examination of AMPA and NMDA receptor signaling, measurements of both [Ca2+]i and [Na+]i changes in the same preparation may provide more information than separate measurements. To this end, we developed a technique to simultaneously measure both signals at high speed and sufficient sensitivity to detect localized physiologic events. This approach has advantages over sequential imaging because the preparation may not respond identically in different trials. We designed custom dichroic and emission filters to allow the separate detection of the fluorescence of sodium and calcium indicators loaded together into a single neuron in a brain slice from the hippocampus of Sprague-Dawley rats. We then used high-intensity light emitting diodes (LEDs) to alternately excite the two indicators at the appropriate wavelengths. These pulses were synchronized with the frames of a CCD camera running at 500 Hz. Software then separated the data streams to provide independent sodium and calcium signals. With this system we could detect [Ca2+]i and [Na+]i changes from single action potentials in axons and synaptically evoked signals in dendrites, both with submicron resolution and a good signal-to-noise ratio (S/N).This work was supported by NIH grant R21 NS085729 and the New York Medical College Intramural Research Support Program

Subaru Deep Survey VI. A Census of Lyman Break Galaxies at z=4 and 5 in the Subaru Deep Fields: Clustering Properties

We investigate the clustering properties of 2,600 Lyman Break Galaxies (LBGs) at z=3.5-5.2 in two large blank fields, the Subaru Deep Field and the Subaru/XMM Deep Field (600arcmin^2 each). The angular correlation functions of these LBGs show a clear clustering at both z~4 and 5. The correlation lengths are r_0= 4.1^{+0.2}_{-0.2} and 5.9^{+1.3}_{-1.7} h_{100}^{-1} Mpc (r_0= 5.1^{+1.0}_{-1.1} and 5.9^{+1.3}_{-1.7} h_{100}^{-1} Mpc) for all the detected LBGs (for L>L* LBGs) at z~4 and 5, respectively. These correlation lengths correspond to galaxy-dark matter biases of b_g= 2.9^{+0.1}_{-0.1} and 4.6^{+0.9}_{-1.2} (b_g=3.5^{+0.6}_{-0.7} and 4.6^{+0.9}_{-1.2}), for all the detected LBGs (for L>L^* LBGs) at z~4 and 5, respectively. These results, combined with estimates for z~3 LBGs in the literature, show that the correlation length of L>L^* LBGs is almost constant, ~5 h_{100}^{-1} Mpc, over z~3-5, while the bias monotonically increases with redshift at z>3. We also find that for LBGs at z~4 the clustering amplitude increases with UV-continuum luminosity and with the amount of dust extinction. We estimate the mass of dark halos hosting various kinds of high-z galaxies including LBGs with the analytic model given by Sheth & Tormen (1999). We find that the typical mass of dark halos hosting L>L^* LBGs is about 1x10^{12} h_{70}^{-1}Msol over z~3-5, which is comparable to that of the Milky Way Galaxy. A single dark halo with ~10^{12} h_{70}^{-1} Msol is found to host 0.1-0.3 LBG on average but host about four K-band selected galaxies.Comment: 33 pages, 12 figures, ApJ in press. Paper with high resolution figures is available at http://hikari.astron.s.u-tokyo.ac.jp/~ouchi/work/astroph/SDS_V_VI/SDS_VI.pdf (PDF) (The abstract was reduced by the revision.

An exponential lower bound for Individualization-Refinement algorithms for Graph Isomorphism

The individualization-refinement paradigm provides a strong toolbox for testing isomorphism of two graphs and indeed, the currently fastest implementations of isomorphism solvers all follow this approach. While these solvers are fast in practice, from a theoretical point of view, no general lower bounds concerning the worst case complexity of these tools are known. In fact, it is an open question whether individualization-refinement algorithms can achieve upper bounds on the running time similar to the more theoretical techniques based on a group theoretic approach. In this work we give a negative answer to this question and construct a family of graphs on which algorithms based on the individualization-refinement paradigm require exponential time. Contrary to a previous construction of Miyazaki, that only applies to a specific implementation within the individualization-refinement framework, our construction is immune to changing the cell selector, or adding various heuristic invariants to the algorithm. Furthermore, our graphs also provide exponential lower bounds in the case when the $k$-dimensional Weisfeiler-Leman algorithm is used to replace the standard color refinement operator and the arguments even work when the entire automorphism group of the inputs is initially provided to the algorithm.Comment: 21 page