Algebraic entropy and the space of initial values for discrete dynamical systems

A method to calculate the algebraic entropy of a mapping which can be lifted to an isomorphism of a suitable rational surfaces (the space of initial values) are presented. It is shown that the degree of the $n$th iterate of such a mapping is given by its action on the Picard group of the space of initial values. It is also shown that the degree of the $n$th iterate of every Painlev\'e equation in sakai's list is at most $O(n^2)$ and therefore its algebraic entropy is zero.Comment: 10 pages, pLatex fil

Vacuum entanglement governs the bosonic character of magnons

It is well known that magnons, elementary excitations in a magnetic material, behave as bosons when their density is low. We study how the bosonic character of magnons is governed by the amount of a multipartite entanglement in the vacuum state on which magnons are excited. We show that if the multipartite entanglement is strong, magnons cease to be bosons. We also consider some examples, such as ground states of the Heisenberg ferromagnet and the transverse Ising model, the condensation of magnons, the one-way quantum computer, and Kitaev's toric code. Our result provides insights into the quantum statistics of elementary excitations in these models, and into the reason why a non-local transformation, such as the Jordan-Wigner transformation, is necessary for some many-body systems.Comment: 4 pages, no figur

A Fast Algorithm for Solving the Poisson Equation on a Nested Grid

We present a numerical method for solving the Poisson equation on a nested grid. The nested grid consists of uniform grids having different grid spacing and is designed to cover the space closer to the center with a finer grid. Thus our numerical method is suitable for computing the gravity of a centrally condensed object. It consists of two parts: the difference scheme for the Poisson equation on the nested grid and the multi-grid iteration algorithm. It has three advantages: accuracy, fast convergence, and scalability. First it computes the gravitational potential of a close binary accurately up to the quadraple moment, even when the binary is resolved only in the fine grids. Second residual decreases by a factor of 300 or more by each iteration. We confirmed experimentally that the iteration converges always to the exact solution of the difference equation. Third the computation load of the iteration is proportional to the total number of the cells in the nested grid. Thus our method gives a good solution at the minimum expense when the nested grid is large. The difference scheme is applicable also to the adaptive mesh refinement in which cells of different sizes are used to cover a domain of computation.Comment: 22 pages 21 figures. To appear in Ap

Geochemistry of shield stage basalts from Baluran volcano, East Java, Sunda arc

We report petrography and geochemistry of basaltic lava flows from the shield stage of Baluran, a Quaternary volcanic center in the rear of East Java, Sunda Arc, Indonesia. These basalts contain abundant plagioclase, clinopyroxene, olivine, and minor magnetite. Geochemically, they resemble other medium-K calc alkaline basalts from eastern Java’s volcanoes, but they are less enriched in light ion lithophile elements (LILE) and Pb. The predicted primary basalt of Baluran lavas can be sourced to a more primitive primary melt composition which may also generate medium-K calc-alkaline magmas in the region. The fractionation trajectory of these primary magmas shows the importance of plagioclase, clinopyroxene, olivine, and magnetite phase removal from the melt. Regardless of the diverse composition of the derivatives, the calculated primary basalts from the eastern Java are all in the field of nepheline-normative. This finding suggests variably small degree of melting of clinopyroxene-rich mantle source is at play in the generation of these magmas. Our result further suggests that the clinopyroxene source rock is possibly present as veins in peridotite mantle which have experienced metasomatism by addition of slab-derived fluids at differing proportion

Fragmentation of a Molecular Cloud Core versus Fragmentation of the Massive Protoplanetary Disk in the Main Accretion Phase

The fragmentation of molecular cloud cores a factor of 1.1 denser than the critical Bonnor-Ebert sphere is examined though three-dimensional numerical simulations. A nested grid is employed to resolve fine structure down to 1 AU while following the entire structure of the molecular cloud core of radius 0.14 pc. A total of 225 models are shown to survey the effects of initial rotation speed, rotation law, and amplitude of bar mode perturbation. The simulations show that the cloud fragments whenever the cloud rotates sufficiently slowly to allow collapse but fast enough to form a disk before first-core formation. The latter condition is equivalent to $\Omega_0 t_{\rm ff} \gtrsim 0.05$, where $\Omega_0$ and $t_{\rm ff}$ denote the initial central angular velocity and the freefall time measured from the central density, respectively. Fragmentation is classified into six types: disk-bar, ring-bar, satellite, bar, ring, and dumbbell types according to the morphology of collapse and fragmentation. When the outward decrease in initial angular velocity is more steep, the cloud deforms from spherical at an early stage. The cloud deforms into a ring only when the bar mode m = 2 perturbation is very minor. The ring fragments into two or three fragments via ring-bar type fragmentation and into at least three fragments via ring type fragmentation. When the bar mode is significant, the cloud fragments into two fragments via either bar or dumbbell type fragmentation. These fragments eventually merge due to their low angular momenta, after which several new fragments form around the merged fragment via satellite type fragmentation.Comment: Accepted by ApJ, 53 pages, 27 figures. Document with high quality figures and movies are available in http://meric.i.hosei.ac.jp/~matsu/fragment03

The Effects of Diuretics on Intracellular Ca2+ Dynamics of Arteriole Smooth Muscles as Revealed by Laser Confocal Microscopy

The regulation of cytosolic Ca2+ homeostasis is essential for cells, including vascular smooth muscle cells. Arterial tone, which underlies the maintenance of peripheral resistance in the circulation, is a major contributor to the control of blood pressure. Diuretics may regulate intracellular Ca2+ concentration ([Ca2+]i) and have an effect on vascular tone. In order to investigate the influence of diuretics on peripheral resistance in circulation, we investigated the alteration of [Ca2+]i in testicular arterioles with respect to several categories of diuretics using real-time confocal laser scanning microscopy. In this study, hydrochlorothiazide (100 µM) and furosemide (100 µM) had no effect on the [Ca2+]i dynamics. However, when spironolactone (300 µM) was applied, the [Ca2+]i of smooth muscles increased. The response was considerably inhibited under either extracellular Ca2+-free conditions, the presence of Gd3+, or with a treatment of diltiazem. After the thapsigargin-induced depletion of internal Ca2+ store, the spironolactone-induced [Ca2+]i dynamics was slightly inhibited. Therefore, the spironolactone-induced dynamics of [Ca2+]i can be caused by either a Ca2+ influx from extracellular fluid or Ca2+ mobilization from internal Ca2+ store, with the former being dominant. As tetraethylammonium, an inhibitor of the K+ channel, slightly inhibited the spironolactone-induced [Ca2+]i dynamics, the K+ channel might play a minor role in those dynamics. Tetrodotoxin, a neurotoxic Na+ channel blocker, had no effect, therefore the spironolactone-induced dynamics is a direct effect to smooth muscles, rather than an indirect effect via vessel nerves

Quantum reservoir computing with repeated measurements on superconducting devices

Reservoir computing is a machine learning framework that uses artificial or physical dissipative dynamics to predict time-series data using nonlinearity and memory properties of dynamical systems. Quantum systems are considered as promising reservoirs, but the conventional quantum reservoir computing (QRC) models have problems in the execution time. In this paper, we develop a quantum reservoir (QR) system that exploits repeated measurement to generate a time-series, which can effectively reduce the execution time. We experimentally implement the proposed QRC on the IBM's quantum superconducting device and show that it achieves higher accuracy as well as shorter execution time than the conventional QRC method. Furthermore, we study the temporal information processing capacity to quantify the computational capability of the proposed QRC; in particular, we use this quantity to identify the measurement strength that best tradeoffs the amount of available information and the strength of dissipation. An experimental demonstration with soft robot is also provided, where the repeated measurement over 1000 timesteps was effectively applied. Finally, a preliminary result with 120 qubits device is discussed