Requirements of IPv6 over Low Power WPAN (6LoWPAN) are energy conservation and low protocol complexity. Incorporating the desirable features, potential-field-based routing known as ALFA (autonomous load-balancing field-based any cast routing) achieves autonomous load-balancing and efficient path-length provisioning with little control overhead in a wireless mesh network (WMN), which is a hub-and-spoke type network similarly to 6LoWPAN. In this paper, we provide the protocol architecture of ALFA for 6LoWPAN to consider energy consumption. Distinct from the case of ALFA in a WMN, when the energy level of a sensor node declines to a threshold, the exchange of its potential information holds and its energy shortage is reported to a sink node.

The q-analogues of many well known formulas are derived by using several results of q-Bernoulli, q-Euler numbers and polynomials. The q-analogues of ζ-type functions are given by using generating functions of q-Bernoulli, q-Euler numbers and polynomials. Finally, their values at non-positive integers are also been computed.

2010 Mathematics Subject Classification: 11B68; 11S40; 11S80.

Lex X be a normed space and Y be a Banach fuzzy space. Let D = {(x, y) ∈ X × X : ||x|| + ||y|| ≥ d} where d > 0. We prove that the Pexiderized Jensen functional equation is stable in the fuzzy norm for functions defined on D and taking values in Y. We consider also the Pexiderized Cauchy functional equation.

2000 Mathematics Subject Classification: 39B22; 39B82; 46S10.

Information theories for the general time-dependent harmonic oscillator are described on the basis of invariant operator method. We obtained entropic uncertainty relation of the system and discussed whether it is always larger than or equal to the physically allowed minimum value. Shannon information and Fisher information are derived by means of density operator that satisfies Liouville–von Neumann equation and their characteristics are investigated. Shannon information is independent of time, but Fisher information is explicitly dependent on time as the time functions of the Hamiltonian vary. We can regard that the Fisher information is a local measure since its time behavior is largely affected by local arrangements of the density, whilst the Shannon information plays the role of a global measure of the spreading of density. To promote the understanding, our theory is applied to special systems, the so-called quantum oscillator with time-dependent frequency and strongly pulsating mass system.

Motivated by therapeutic deep brain stimulation, we carried out a model study on the effects of periodic stimulation on an overly activated neuronal circuit. Our neuronal circuit, modeled as a small-world network of noisy Hodgkin-Huxley neurons, is controlled to undergo the mechanism of coherence resonance to exhibit spontaneous synchronization of neuronal firing. This state of energy burst is then directly modulated by a chain of electric pulses. Our study shows that (i) the stimulation blocks the synchronization by generating traveling waves, (ii) only the pulse with proper frequency can block the synchronization, and (iii) the effects of stimulation are completely reversible. It is also found that the stimulation is effective only when the network maintains fairly good structural regularity.

We investigated the possibility of estimating network link weights from the multivariate time series of phase oscillators on a complex network. The inverse phase synchronization index of the coupled oscillator network is found to grow in proportion to the corresponding link weight, as network synchronization occurs for a strong coupling strength. This implies that the network link weights can be estimated from the measurement of the inverse phase synchronization indices. By adopting this estimation method, we successfully reconstructed the minimal spanning tree of the original network from the inverse phase synchronization indices. Even for the weak coupling case, the estimation of the network link weights could be improved significantly by taking the average of a sufficiently large number of configurations.

The coordinated motion of a cell is fundamental to many important biological processes such as development, wound healing, and phagocytosis. For eukaryotic cells, such as amoebae or animal cells, the cell motility is based on crawling and involves a complex set of internal biochemical events. A recent study reported very interesting crawling behavior of single cell amoeba: in the absence of an external cue, free amoebae randomly with a noisy, yet, discernible sequence of ‘run-and-turns’ analogous to the ‘run-and-tumbles’ of swimming bacteria. Interestingly, amoeboid trajectories favor zigzag turns. In other words, the cells bias their crawling by making a turn in the opposite direction to a previous turn. This property enhances the long range directional persistence of the moving trajectories. This study proposes that such a zigzag crawling behavior can be a general property of any crawling cells by demonstrating that 1) microglia, which are the immune cells of the brain, and 2) a simple rule-based model cell, which incorporates the actual biochemistry and mechanics behind cell crawling, both exhibit similar type of crawling behavior. Almost all legged animals walk by alternating their feet. Similarly, all crawling cells appear to forward by alternating the direction of their ment, even though the regularity and degree of zigzag preference vary from one type to the other.