The Dynamics of Power laws: Fitness and Aging in Preferential Attachment Trees

Continuous-time branching processes describe the evolution of a population whose individuals generate a random number of children according to a birth process. Such branching processes can be used to understand preferential attachment models in which the birth rates are linear functions. We are motivated by citation networks, where power-law citation counts are observed as well as aging in the citation patterns. To model this, we introduce fitness and age-dependence in these birth processes. The multiplicative fitness moderates the rate at which children are born, while the aging is integrable, so that individuals receives a finite number of children in their lifetime. We show the existence of a limiting degree distribution for such processes. In the preferential attachment case, where fitness and aging are absent, this limiting degree distribution is known to have power-law tails. We show that the limiting degree distribution has exponential tails for bounded fitnesses in the presence of integrable aging, while the power-law tail is restored when integrable aging is combined with fitness with unbounded support with at most exponential tails. In the absence of integrable aging, such processes are explosive.     

Enhancement of electrochemical properties of Ca<Subscript>3</Subscript>Co<Subscript>4</Subscript>O<Subscript>9</Subscript> as anode materials for lithium-ion batteries by transition metal doping

Misfit-layered calcium cobaltites (Ca₃Co₄O₉, Ca₃Co_3.9Fe_0.1O₉, and Ca₃Co_3.9Mn_0.1O₉), as anode materials for lithium-ion batteries, were synthesized by a simple hydro-decomposition method. All synthesized samples do not show any impurity phase. They exhibited plate-like particle with the particle size of 1–2 μm. The specific capacities of doped samples showed higher electrochemical performance compared to the undoped sample. After charge/discharge of 50 cycles, the specific capacities of Ca₃Co₄O₉, Ca₃Co_3.9Fe_0.1O₉, and Ca₃Co_3.9Mn_0.1O₉ were 343, 562, and 581 mAh g^?1, respectively. The doped samples showed an increase of over 60% compared to the undoped sample. The cyclic voltammetry profile of the doped samples showed the enhanced reactivity corresponding to their improved electrochemical performance. The capacity improvement of doped samples resulted from the metal oxide/Li conversion reactions, volume change, and high reactivity.     

A Volume Inequality for Quantum Fisher Information and the Uncertainty Principle

Let A ₁,…,A _N be complex self-adjoint matrices and let ρ be a density matrix. The Robertson uncertainty principle

Comparison of shear banding in BMGs due to thermal-softening and free volume creation

This paper reports a comparative study of shear banding in BMGs resulting from thermal softening and free volume creation. Firstly, the effects of thermal softening and free volume creation on shear instability are discussed. It is known that thermal softening governs thermal shear banding, hence it is essentially energy related. However, compound free volume creation is the key factor to the other instability, though void-induced softening seems to be the counterpart of thermal softening. So, the driving force for shear instability owing to free volume creation is very different from the thermally assisted one. In particular, long wave perturbations are always unstable owing to compound free volume creation. Therefore, the shear instability resulting from coupled compound free volume creation and thermal softening may start more like that due to free volume creation. Also, the compound free volume creation implies a specific and intrinsic characteristic growth time of shear instability. Finally, the mature shear band width is governed by the corresponding diffusions (thermal or void diffusion) within the band. As a rough guide, the dimensionless numbers: Thermal softening related number B, Deborah number (denoting the relation of instability growth rate owing to compound free volume and loading time) and Lewis number (denoting the competition of different diffusions) show us their relative importance of thermal softening and free volume creation in shear banding. All these results are of particular significance in understanding the mechanism of shear banding in bulk metallic glasses (BMGs). Supported by the Chinese Academy of Sciences under the project “Multi-Scale Complex System” (Grant No. KJCX-SW-L08), the National Natural Science Foundation of China (Grant Nos. 10725211 and 10721202), and the Doctorial Start-up Fund of Hunan University of Science and Technology (Grant No. E50840)     

A Confined <Emphasis Type="Italic">N</Emphasis>-Dimensional Harmonic Oscillator

We compute the energy eigenvalues for the N-dimensional harmonic oscillator confined in an impenetrable spherical cavity. The results show their dependence on the size of the cavity and the space dimension N. The obtained results are compared with those for the free N-dimensional harmonic oscillator, and as a result, the notion of fractional dimensions is pointed out. Finally, we examine the correlation between eigenenergies for confined oscillators in different dimensions.     

A version of Stöber synthesis enabling the facile prediction of silica nanospheres size for the fabrication of opal photonic crystals

A sol-gel synthesis procedure based on the method proposed by Stöber et al. (J Colloid Interface Sci 26:302–315, 1968) has been adopted for the one-step preparation of mono-dispersed silica nanospheres. An excellent control of the particle diameter over a wide range is obtained by varying the amount of silicon alkoxide only, while the concentration of all other components is kept fixed: this allows the fabrication of artificial opals with a finely tuned and precisely predictable lattice parameter.     

Determination of the scattering coefficient of biological tissue considering the wavelength and absorption dependence of the anisotropy factor

The anisotropy factor g, one of the optical properties of biological tissues, has a strong influence on the calculation of the scattering coefficient μ _s in inverse Monte Carlo (iMC) simulations. It has been reported that g has the wavelength and absorption dependence; however, few attempts have been made to calculate μ _s using g values by taking the wavelength and absorption dependence into account. In this study, the angular distributions of scattered light for biological tissue phantoms containing hemoglobin as a light absorber were measured by a goniometric optical setup at strongly (405 nm) and weakly (664 nm) absorbing wavelengths to obtain g. Subsequently, the optical properties were calculated with the measured values of g by integrating sphere measurements and an iMC simulation, and compared with the results obtained with a conventional g value of 0.9. The μ _s values with measured g were overestimated at the strongly absorbing wavelength, but underestimated at the weakly absorbing wavelength if 0.9 was used in the iMC simulation.     

Optimization of detection device geometry for NIR spectroscopy using a three-layered model of stone fruit

The influences of detection device geometry and fiber optic parameters on near infrared spectroscopy measurements were assessed using stone fruit models based on Monte Carlo simulation. The stone fruit was modeled as concentric spherical layered tissues including the skin, the flesh and the core. The choices of the detection angle, the diameter of the detection fiber, the numerical aperture, and the height of the probe were discussed. Receiving diffuse reflectance signals at detection angles in the range of 35°–50° and normalizing the detection signals by the collection area and the solid acceptance angle prior to use are suggested. Fiber probes with diameters D = 0.06 cm or 0.1 cm, NA = 0.20 or 0.30, and height h ≤ 0.8 cm are preferred. The probe deflection angle should be limited to within ±5° to guarantee measurement accuracy.