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Concept: Complex number


Multi-level fission-fusion societies, characteristic of a number of large brained mammal species including some primates, cetaceans and elephants, are among the most complex and cognitively demanding animal social systems. Many free-ranging populations of these highly social mammals already face severe human disturbance, which is set to accelerate with projected anthropogenic environmental change. Despite this, our understanding of how such disruption affects core aspects of social functioning is still very limited.

Concepts: Human, Species, Sociology, Mammal, Primate, Complex number, Hippopotamus, Incisor


Optical manipulation in the vicinity of optical micro- and nanofibres has shown potential across several fields in recent years, including microparticle control, and cold atom probing and trapping. To date, most work has focussed on the propagation of the fundamental mode through the fibre. However, along the maximum mode intensity axis, higher order modes have a longer evanescent field extension and larger field amplitude at the fibre waist compared to the fundamental mode, opening up new possibilities for optical manipulation and particle trapping. We demonstrate a microfibre/optical tweezers compact system for trapping and propelling dielectric particles based on the excitation of the first group of higher order modes at the fibre waist. Speed enhancement of polystyrene particle propulsion was observed for the higher order modes compared to the fundamental mode for particles ranging from 1 μm to 5 μm in diameter. The optical propelling velocity of a single, 3 μm polystyrene particle was found to be 8 times faster under the higher order mode than the fundamental mode field for a waist power of 25 mW. Experimental data are supported by theoretical calculations. This work can be extended to trapping and manipulation of laser-cooled atoms with potential for quantum networks.

Concepts: Scientific method, Photon, Quantum mechanics, Optics, Atom, Complex number, Intensity, Evanescent wave


The complexity of chess matches has attracted broad interest since its invention. This complexity and the availability of large number of recorded matches make chess an ideal model systems for the study of population-level learning of a complex system. We systematically investigate the move-by-move dynamics of the white player’s advantage from over seventy thousand high level chess matches spanning over 150 years. We find that the average advantage of the white player is positive and that it has been increasing over time. Currently, the average advantage of the white player is [Formula: see text]0.17 pawns but it is exponentially approaching a value of 0.23 pawns with a characteristic time scale of 67 years. We also study the diffusion of the move dependence of the white player’s advantage and find that it is non-Gaussian, has long-ranged anti-correlations and that after an initial period with no diffusion it becomes super-diffusive. We find that the duration of the non-diffusive period, corresponding to the opening stage of a match, is increasing in length and exponentially approaching a value of 15.6 moves with a characteristic time scale of 130 years. We interpret these two trends as a resulting from learning of the features of the game. Additionally, we find that the exponent [Formula: see text] characterizing the super-diffusive regime is increasing toward a value of 1.9, close to the ballistic regime. We suggest that this trend is due to the increased broadening of the range of abilities of chess players participating in major tournaments.

Concepts: Emergence, Complexity, Systems theory, Trend, Complex number, Complex system, Chess, The Advantage


The cylindrical Bessel differential equation and the spherical Bessel differential equation in the interval [Formula: see text] with Neumann boundary conditions are considered. The eigenfunctions are linear combinations of the Bessel function [Formula: see text] or linear combinations of the spherical Bessel functions [Formula: see text]. The orthogonality relations with analytical expressions for the normalization constant are given. Explicit expressions for the Lommel integrals in terms of Lommel functions are derived. The cross product zeros [Formula: see text] and [Formula: see text] are considered in the complex plane for real as well as complex values of the index [Formula: see text] and approximations for the exceptional zero [Formula: see text] are obtained. A numerical scheme based on the discretization of the two-dimensional and three-dimensional Laplace operator with Neumann boundary conditions is presented. Explicit representations of the radial part of the Laplace operator in form of a tridiagonal matrix allow the simple computation of the cross product zeros.

Concepts: Mathematics, Derivative, Fourier transform, Complex number, Laplace transform, Bessel function, Helmholtz equation, Neumann polynomial


The assessment of body hydration is a complex process, and no measurement is valid for all situations. Bioelectrical impedance vector analysis (BIVA) has emerged as a relatively novel technique for assessing hydration status in sports. We applied BIVA a) to determine hydration changes evoked by an intense synchronized swimming (SS) training session; b) to characterize the sample of young elite swimmers in relation with a nonathletic reference population; and c) to generate its 50%, 75% and 95% percentiles of the bioelectrical variables.

Concepts: Measurement, Psychometrics, Hilbert space, 2000s music groups, Complex number, 1990s music groups, Swimming, Synchronized swimming


Information routing is one of the main tasks in many complex networks with a communication function. Maps produced by embedding the networks in hyperbolic space can assist this task enabling the implementation of efficient navigation strategies. However, only static maps have been considered so far, while navigation in more realistic situations, where the network structure may vary in time, remains largely unexplored. Here, we analyze the navigability of real networks by using greedy routing in hyperbolic space, where the nodes are subject to a stochastic activation-inactivation dynamics. We find that such dynamics enhances navigability with respect to the static case. Interestingly, there exists an optimal intermediate activation value, which ensures the best trade-off between the increase in the number of successful paths and a limited growth of their length. Contrary to expectations, the enhanced navigability is robust even when the most connected nodes inactivate with very high probability. Finally, our results indicate that some real networks are ultranavigable and remain highly navigable even if the network structure is extremely unsteady. These findings have important implications for the design and evaluation of efficient routing protocols that account for the temporal nature of real complex networks.

Concepts: Mathematics, Real number, Metaphysics, Complex number, Computer network, Social network, RealNetworks, Hyperbolic space


Controlling acoustic fields is crucial in diverse applications such as loudspeaker design, ultrasound imaging and therapy or acoustic particle manipulation. The current approaches use fixed lenses or expensive phased arrays. Here, using a process of analogue-to-digital conversion and wavelet decomposition, we develop the notion of quantal meta-surfaces. The quanta here are small, pre-manufactured three-dimensional units-which we call metamaterial bricks-each encoding a specific phase delay. These bricks can be assembled into meta-surfaces to generate any diffraction-limited acoustic field. We apply this methodology to show experimental examples of acoustic focusing, steering and, after stacking single meta-surfaces into layers, the more complex field of an acoustic tractor beam. We demonstrate experimentally single-sided air-borne acoustic levitation using meta-layers at various bit-rates: from a 4-bit uniform to 3-bit non-uniform quantization in phase. This powerful methodology dramatically simplifies the design of acoustic devices and provides a key-step towards realizing spatial sound modulators.

Concepts: Quantum mechanics, Physics, Medical ultrasonography, Acoustics, Ultrasound, Sound, Complex number, Acoustic levitation


A direct link between Ca(2+) and lipid homeostasis has not been definitively demonstrated. In this study, we show that manipulation of ER Ca(2+) causes the re-distribution of a portion of the intracellular unesterified cholesterol to a pool that is not available to the SCAP-SREBP complex. The SREBP processing pathway in ER Ca(2+) depleted cells remained fully functional and responsive to changes in cellular cholesterol status but differed unexpectedly in basal activity. These findings establish the role of Ca(2+) in determining the reference set-point for controlling cellular lipid homeostasis. We propose that ER Ca(2+) status is an important determinant of the basal sensitivity of the sterol sensing mechanism inherent to the SREBP processing pathway.

Concepts: Cholesterol, Cell membrane, Steroid, Metaphysics, Lipid bilayer, Complex number, Sterol regulatory element binding protein, Determine


During epithelial morphogenesis, a complex comprising the βPIX (PAK-interacting exchange factor β) and class I PAKs (p21-activated kinases) is recruited to adherens junctions. Scrib, the mammalian ortholog of the Drosophila polarity determinant and tumor suppressor Scribble, binds βPIX directly. Scrib is also targeted to adherens junctions by E-cadherin, where Scrib strengthens cadherin-mediated cell-cell adhesion. Although a role for the Scrib-βPIX-PAK signaling complex in promoting membrane protrusion at wound edges has been elucidated, a function for this complex at adherens junctions remains unknown.

Concepts: Cancer, Species, P53, Complex number, Class I railroad, Adherens junction


There exists several numerical approaches to describe the active contractile behaviour of skeletal muscles. These models range from simple one-dimensional to more advanced three-dimensional ones; especially, three-dimensional models take up the cause of describing complex contraction modes in a realistic way. However, the validation of such concepts is challenging, as the combination of geometry, material and force characteristics is so far not available from the same muscle. To this end, we present in this study a comprehensive data set of the rabbit soleus muscle consisting of the muscles' characteristic force responses (active and passive), its three-dimensional shape during isometric, isotonic and isokinetic contraction experiments including the spatial arrangement of muscle tissue and aponeurosis-tendon complex, and the fascicle orientation throughout the whole muscle at its optimal length. In this way, an extensive data set is available giving insight into the three-dimensional geometry of the rabbit soleus muscle and, further, allowing to validate three-dimensional numerical models.

Concepts: Mathematics, Cardiac muscle, Glycogen, Muscle contraction, Muscular system, Manifold, Real number, Complex number