Asymptotic Learning Curve and Renormalizable Condition in Statistical Learning Theory

Bayes statistics and statistical physics have the common mathematical structure, where the log likelihood function corresponds to the random Hamiltonian. Recently, it was discovered that the asymptotic learning curves in Bayes estimation are subject to a universal law, even if the log likelihood function can not be approximated by any quadratic form. However, it is left unknown what mathematical property ensures such a universal law. In this paper, we define a renormalizable condition of the statistical estimation problem, and show that, under such a condition, the asymptotic learning curves are ensured to be subject to the universal law, even if the true distribution is unrealizable and singular for a statistical model. Also we study a nonrenormalizable case, in which the learning curves have the different asymptotic behaviors from the universal law

Dynamical stabilization of matter-wave solitons revisited

We consider dynamical stabilization of Bose-Einstein condensates (BEC) by time-dependent modulation of the scattering length. The problem has been studied before by several methods: Gaussian variational approximation, the method of moments, method of modulated Townes soliton, and the direct averaging of the Gross-Pitaevskii (GP) equation. We summarize these methods and find that the numerically obtained stabilized solution has different configuration than that assumed by the theoretical methods (in particular a phase of the wavefunction is not quadratic with $r$). We show that there is presently no clear evidence for stabilization in a strict sense, because in the numerical experiments only metastable (slowly decaying) solutions have been obtained. In other words, neither numerical nor mathematical evidence for a new kind of soliton solutions have been revealed so far. The existence of the metastable solutions is nevertheless an interesting and complicated phenomenon on its own. We try some non-Gaussian variational trial functions to obtain better predictions for the critical nonlinearity $g_{cr}$ for metastabilization but other dynamical properties of the solutions remain difficult to predict

Muon spin relaxation and rotation study on the solid solution of the two spin-gap systems (CH3)2CHNH3-CuCl3 and (CH3)2CHNH3-CuBr3

Muon-spin-rotation and relaxation studies have been performed on (CH$_3$)$_2$CHNH$_3$Cu(Cl$_x$Br$_{1-x}$)$_3$ with $x$=0.85 and 0.95, which are solid solutions of the two isomorphic spin-gap systems (CH$_3$)$_2$CHNH$_3$CuCl$_3$ and (CH$_3$)$_2$CHNH$_3$CuBr$_3$ with different spin gaps. The sample with $x$=0.85 showed a clear muon spin rotation under zero-field below $T_{\rm N}$=11.65K, indicating the existence of a long-range antiferromagnetic order. A critical exponent of the hyperfine field was obtained to be $\beta$=0.33, which agrees with 3D-Ising model. In the other sample with $x$=0.95, an anomalous enhancement of the muon spin relaxation was observed at very low temperatures indicating a critical slowing down due to a magnetic instability of the ground state

Signatures of pairing mechanisms and order parameters in ferromagnetic superconductors

Two predictions are made for properties of the ferromagnetic superconductors discovered recently. The first one is that spin-triplet, p-wave pairing in such materials will give the magnons a mass inversely proportional to the square of the magnetization. The second one is based on a specific mechanism for p-wave pairing, and predicts that the observed broad anomaly in the specific heat of URhGe will be resolved into a split transition with increasing sample quality. These predictions will help discriminate between different possible mechanisms for ferromagnetic superconductivity.Comment: 4 pp., 1 ps fi

Measuring Hall Viscosity of Graphene's Electron Fluid

Materials subjected to a magnetic field exhibit the Hall effect, a phenomenon studied and understood in fine detail. Here we report a qualitative breach of this classical behavior in electron systems with high viscosity. The viscous fluid in graphene is found to respond to non-quantizing magnetic fields by producing an electric field opposite to that generated by the classical Hall effect. The viscous contribution is large and identified by studying local voltages that arise in the vicinity of current-injecting contacts. We analyze the anomaly over a wide range of temperatures and carrier densities and extract the Hall viscosity, a dissipationless transport coefficient that was long identified theoretically but remained elusive in experiment. Good agreement with theory suggests further opportunities for studying electron magnetohydrodynamics.Comment: 18 pages, 9 figure

Gold-plated processes at photon colliders

We review the most important topics and objectives of the physics program of the gamma-gamma, gamma-electron collider (photon collider) option for an e+e- linear collider.Comment: 36 pages, Latex, 11 figures(ps,eps), Talk at Intern. Workshop on High Energy Photon Colliders; June 14-17, 2000, DESY, Hamburg, Germany; to be published in Nucl. Instr. and Methods

Anatomical and molecular properties of long descending propriospinal neurons in mice

Long descending propriospinal neurons (LDPNs) are interneurons that form direct connections between cervical and lumbar spinal circuits. LDPNs are involved in interlimb coordination and are important mediators of functional recovery after spinal cord injury (SCI). Much of what we know about LDPNs comes from a range of species, however, the increased use of transgenic mouse lines to better define neuronal populations calls for a more complete characterisation of LDPNs in mice. In this study, we examined the cell body location, inhibitory neurotransmitter phenotype, developmental provenance, morphology and synaptic inputs of mouse LDPNs throughout the cervical and upper thoracic spinal cord. LDPNs were retrogradely labelled from the lumbar spinal cord to map cell body locations throughout the cervical and upper thoracic segments. Ipsilateral LDPNs were distributed throughout the dorsal, intermediate and ventral grey matter as well as the lateral spinal nucleus and lateral cervical nucleus. In contrast, contralateral LDPNs were more densely concentrated in the ventromedial grey matter. Retrograde labelling in GlyT2GFP and GAD67GFP mice showed the majority of inhibitory LDPNs project either ipsilaterally or adjacent to the midline. Additionally, we used several transgenic mouse lines to define the developmental provenance of LDPNs and found that V2b positive neurons form a subset of ipsilaterally projecting LDPNs. Finally, a population of Neurobiotin (NB) labelled LDPNs were assessed in detail to examine morphology and plot the spatial distribution of contacts from a variety of neurochemically distinct axon terminals. These results provide important baseline data in mice for future work on their role in locomotion and recovery from SCI

Spin susceptibility and fluctuation corrections in the BCS-BEC crossover regime of an ultracold Fermi gas

We investigate magnetic properties and effects of pairing fluctuations in the BCS (Bardeen-Cooper-Schrieffer)-BEC (Bose-Einstein condensation) crossover regime of an ultracold Fermi gas. Recently, Liu and Hu, and Parish, pointed out that the strong-coupling theory developed by Nozi\`eres and Schmitt-Rink (NSR), which has been extensively used to successfully clarify various physical properties of cold Fermi gases, unphysically gives negative spin susceptibility in the BCS-BEC crossover region. The same problem is found to also exist in the ordinary non-self-consistent T-matrix approximation. In this paper, we clarify that this serious problem comes from incomplete treatment in term of pseudogap phenomena originating from strong pairing fluctuations, as well as effects of spin fluctuations on the spin susceptibility. Including these two key issues, we construct an extended T-matrix theory which can overcome this problem. The resulting positive spin susceptibility agrees well with the recent experiment on a 6Li Fermi gas done by Sanner and co-workers. We also apply our theory to a polarized Fermi gas to examine the superfluid phase transition temperature Tc, as a function of the polarization rate. Since the spin susceptibility is an important physical quantity, especially in singlet Fermi superfluids, our results would be useful in considering how singlet pairs appear above and below Tc in the BCS-BEC crossover regime of cold Fermi gases.Comment: 21 pages, 9 figure

Nodal gap structure of BaFe_2(As_{1-x}P_x)_2 from angle-resolved thermal conductivity in a magnetic field

The structure of the superconducting order parameter in the iron-pnictide superconductor BaFe$_2$(As$_{0.67}$P$_{0.33}$)$_2$ ($T_c=31$\,K) with line nodes is studied by the angle-resolved thermal conductivity measurements in a magnetic field rotated within the basal plane. We find that the thermal conductivity displays distinct fourfold oscillations with minima when the field is directed at $\pm45^\circ$ with respect to the tetragonal a-axis. We discuss possible gap structures that can account for the data, and conclude that the observed results are most consistent with the closed nodal loops located at the flat parts of the electron Fermi surface with high Fermi velocity.Comment: 4 pages, 4 figure