Kenneth B. Keating to John D. Feerick

Letter from Senator Kenneth B. Keating to Dean John D. Feerick, regarding his scholarly article on presidential inability.https://ir.lawnet.fordham.edu/twentyfifth_amendment_correspondence/1015/thumbnail.jp

Getting peasants organised : peasants, the Communist-party and village organisations in Northwest China, 1934-45

Organising peasants was a Chinese Communist strategy for 'democratising' rural China. In the view of most western historians, the Communists’ grassroots organisations have been the means through which a hegemonising Partystate penetrated rural society to an extent that no state power in China has done before. This paper argues that, if 'democracy' is understood as community activism arising from a measure of local autonomy, there is not necessarily a contradiction between the goals of democratisation and overall state control at the national level. The paper makes a close study of the Communists’ rural organisational work in northwest China in the early 1940s for the purpose of demonstrating the dynamic interplay between the two goals. And it draws three broad conclusions: first, that getting peasants organised was very difficult, and many of the early grassroots organisations failed; second, that local conditions largely determined whether village democracy ever made it to the starter’s block; and third, that farmer mutualaid teams in districts close to Yan’an city serve as the best examples of the autonomycontrol dynamic at work

Intermediate wave-function statistics

We calculate statistical properties of the eigenfunctions of two quantum systems that exhibit intermediate spectral statistics: star graphs and Seba billiards. First, we show that these eigenfunctions are not quantum ergodic, and calculate the corresponding limit distribution. Second, we find that they can be strongly scarred by short periodic orbits, and construct sequences of states which have such a limit. Our results are illustrated by numerical computations.Comment: 4 pages, 3 figures. Final versio

Value distribution of the eigenfunctions and spectral determinants of quantum star graphs

We compute the value distributions of the eigenfunctions and spectral determinant of the Schrodinger operator on families of star graphs. The values of the spectral determinant are shown to have a Cauchy distribution with respect both to averages over bond lengths in the limit as the wavenumber tends to infinity and to averages over wavenumber when the bond lengths are fixed and not rationally related. This is in contrast to the spectral determinants of random matrices, for which the logarithm is known to satisfy a Gaussian limit distribution. The value distribution of the eigenfunctions also differs from the corresponding random matrix result. We argue that the value distributions of the spectral determinant and of the eigenfunctions should coincide with those of Seba-type billiards.Comment: 32 pages, 9 figures. Final version incorporating referee's comments. Typos corrected, appendix adde

Autocorrelation of Random Matrix Polynomials

We calculate the autocorrelation functions (or shifted moments) of the characteristic polynomials of matrices drawn uniformly with respect to Haar measure from the groups U(N), O(2N) and USp(2N). In each case the result can be expressed in three equivalent forms: as a determinant sum (and hence in terms of symmetric polynomials), as a combinatorial sum, and as a multiple contour integral. These formulae are analogous to those previously obtained for the Gaussian ensembles of Random Matrix Theory, but in this case are identities for any size of matrix, rather than large-matrix asymptotic approximations. They also mirror exactly autocorrelation formulae conjectured to hold for L-functions in a companion paper. This then provides further evidence in support of the connection between Random Matrix Theory and the theory of L-functions

Europe as a multilevel federation

Peer reviewedPublisher PD

Using Big Bang Nucleosynthesis to Extend CMB Probes of Neutrino Physics

We present calculations showing that upcoming Cosmic Microwave Background (CMB) experiments will have the power to improve on current constraints on neutrino masses and provide new limits on neutrino degeneracy parameters. The latter could surpass those derived from Big Bang Nucleosynthesis (BBN) and the observationally-inferred primordial helium abundance. These conclusions derive from our Monte Carlo Markov Chain (MCMC) simulations which incorporate a full BBN nuclear reaction network. This provides a self-consistent treatment of the helium abundance, the baryon number, the three individual neutrino degeneracy parameters and other cosmological parameters. Our analysis focuses on the effects of gravitational lensing on CMB constraints on neutrino rest mass and degeneracy parameter. We find for the PLANCK experiment that total (summed) neutrino mass $M_{\nu} > 0.29$ eV could be ruled out at $2\sigma$ or better. Likewise neutrino degeneracy parameters $\xi_{\nu_{e}} > 0.11$ and $| \xi_{\nu_{\mu/\tau}} | > 0.49$ could be detected or ruled out at $2\sigma$ confidence, or better. For POLARBEAR we find that the corresponding detectable values are $M_\nu > 0.75 {\rm eV}$, $\xi_{\nu_{e}} > 0.62$, and $| \xi_{\nu_{\mu/\tau}}| > 1.1$, while for EPIC we obtain $M_\nu > 0.20 {\rm eV}$, $\xi_{\nu_{e}} > 0.045$, and $|\xi_{\nu_{\mu/\tau}}| > 0.29$. Our forcast for EPIC demonstrates that CMB observations have the potential to set constraints on neutrino degeneracy parameters which are better than BBN-derived limits and an order of magnitude better than current WMAP-derived limits.Comment: 27 pages, 11 figures, matches published version in JCA