Analog perceptrons: On additive representation of functions

The theory of computational geometry in Perceptrons (Rosenblatt, 1962), developed by M. Minsky and S. Papert (1969), is extended to “Analog Perceptrons” with real-valued input and out-put. Mathematically, our problem is to determine the order of a function, i.e., the smallest number of variables necessary to make an additive representation of the function by employing partial functions of the smaller number of variables.Mathematical tools, called the group-invariance theorem, the classification theorem and the collapsing theorem, are given which are useful for evaluating the order of analog Perceptrons. These are also applied for several analog Perceptrons

Thermal Conductivity of the Quasi One-Dimensional Spin System Sr_2_V_3_O_9_

We have measured the thermal conductivity along the [101] direction, kappa_[101]_, along the [10-1] direction, kappa_[10-1]_, and along the b-axis, kappa_b_, of the quasi one-dimensional S=1/2 spin system Sr_2_V_3_O_9_ in magnetic fields up to 14 T, in order to find the thermal conductivity due to spinons and to clarify whether the spin-chains run along the [101] or [10-1] direction. It has been found that both kappa_[101]_, kappa_[10-1]_ and kappa_b_ show one peak around 10 K in zero field and that the magnitude of kappa_[10-1]_ is larger than those of kappa_[101]_ and kappa_b_. By the application of magnetic field along the heat current, the peak of kappa_[10-1]_ is markedly suppressed, while the peaks of kappa_[101]_ and kappa_b_ little change. These results indicate that there is a large contribution of spinons to kappa_[10-1]_ and suggest that the spin-chains run along the [10-1] direction.Comment: 3 pages, 4 figure

Electron wave functions in beta-decay formulas revisited (II): Completion including recoil-order and induced currents

We present complete formulas of the allowed and first-forbidden transitions of the nuclear beta decay taking into account the recoil-order and induced currents up to the next-to-leading order (NLO). The longitudinal part of the vector current is cleared away by the use of the conservation of the vector current for the multipole operators of the natural-parity transitions, which makes the effect of the meson exchange current for the vector current as small as possible. The formula is transparent enough to be applied to various beta-decay processes. As a numerical demonstration, we apply our formulas to the beta decay of a neutron-rich nucleus $^{160}$Sn. We find that the NLO corrections amount to 10--20\% of the total decay rate, whereas the induced currents alter the rate at most 5\%.Comment: 25 pages, 2 figure

Total reaction cross section on a deuteron target and the eclipse effect of the constituent neutron and proton

Background: Eclipse effect of the neutron and proton in a deuteron target is essential to correctly describe high-energy deuteron scattering. The nucleus-deuteron scattering needs information not only on the nucleus-proton but also the nucleus-neutron interaction, for which no direct measurement of the nucleus-neutron cross sections is available for unstable nuclei. Purpose: We systematically evaluated the total reaction cross sections by a deuteron target to explore the feasibility of extracting the nucleus-neutron interaction from measurable cross sections. Methods: High-energy nucleus-deuteron collision is described by the Glauber model, in which the proton and neutron configuration of the deuteron is explicitly taken into account. Results: Our calculation reproduces available experimental total reaction cross section data on the nucleus-deuteron scattering. The possibility of extracting the nucleus-neutron total reaction cross section from nucleus-deuteron and nucleus-proton total reaction cross sections is explored. The total reaction cross sections of a nucleus by proton, neutron, and deuteron targets can be expressed, to good accuracy, in terms of the nuclear matter radius and neutron skin thickness. Incident-energy dependence of the total reaction cross sections is examined. Conclusions: The total reaction cross section on a deuteron target includes information on both the nucleus-neutron and nucleus-proton profile functions. Measuring the cross sections by deuteron and proton targets is a promising tool to extract the nuclear size properties.Comment: 9 pages, 5 figures, to appear in Phys. Rev.

Shallow and diffuse spin-orbit potential for proton elastic scattering from neutron-rich helium isotopes at 71 MeV/nucleon

Vector analyzing powers for proton elastic scattering from 8He at 71 MeV/nucleon have been measured using a solid polarized proton target operated in a low magnetic field of 0.1 T. The spin-orbit potential obtained from a phenomenological optical model analysis is found to be significantly shallower and more diffuse than the global systematics of stable nuclei, which is an indication that the spin-orbit potential is modified for scattering involving neutron-rich nuclei. A close similarity between the matter radius and the root-mean-square radius of the spin-orbit potential is also identified.Comment: 6 pages, 4 figures, accepted for publication in Physical Review C Rapid Communicatio

Measurement of the tensor analyzing power T20 in the dd->^3Hen and dd->^3Hp at intermediate energies and at zero degree

The data on the tensor analyzing power T20 in the dd->^3Hen and dd-> ^3Hp reactions at 140, 200 and 270 MeV of the deuteron kinetic energy and at zero degree obtained at RIKEN Accelerator Research Facility are presented. The observed positive sign of T20 clearly demonstrates the sensitivity to the D/S wave ratios in the ^3He and ^3H in the energy domain of the measurements. The T20 data for the ^3He-n and ^3H-p channels are in agreement within experimental accuracy.Comment: 9 pages, 3 figures, submitted in Phys.Lett.

Convergence of simulated annealing by the generalized transition probability

We prove weak ergodicity of the inhomogeneous Markov process generated by the generalized transition probability of Tsallis and Stariolo under power-law decay of the temperature. We thus have a mathematical foundation to conjecture convergence of simulated annealing processes with the generalized transition probability to the minimum of the cost function. An explicitly solvable example in one dimension is analyzed in which the generalized transition probability leads to a fast convergence of the cost function to the optimal value. We also investigate how far our arguments depend upon the specific form of the generalized transition probability proposed by Tsallis and Stariolo. It is shown that a few requirements on analyticity of the transition probability are sufficient to assure fast convergence in the case of the solvable model in one dimension.Comment: 11 page

Existence of Dynamical Scaling in the Temporal Signal of Time Projection Chamber

The temporal signals from a large gas detector may show dynamical scaling due to many correlated space points created by the charged particles while passing through the tracking medium. This has been demonstrated through simulation using realistic parameters of a Time Projection Chamber (TPC) being fabricated to be used in ALICE collider experiment at CERN. An interesting aspect of this dynamical behavior is the existence of an universal scaling which does not depend on the multiplicity of the collision. This aspect can be utilised further to study physics at the device level and also for the online monitoring of certain physical observables including electronics noise which are a few crucial parameters for the optimal TPC performance.Comment: 5 pages, 6 figure