Quaternion Electromagnetism and the Relation with 2-Spinor Formalism

By using complex quaternion, which is the system of quaternion representation extended to complex numbers, we show that the laws of electromagnetism can be expressed much more simply and concisely. We also derive the quaternion representation of rotations and boosts from the spinor representation of Lorentz group. It is suggested that the imaginary 'i' should be attached to the spatial coordinates, and observe that the complex conjugate of quaternion representation is exactly equal to parity inversion of all physical quantities in the quaternion. We also show that using quaternion is directly linked to the two-spinor formalism. Finally, we discuss meanings of quaternion, octonion and sedenion in physics as n-fold rotationComment: Version published in journal Universe (2019

Robustness of the avalanche dynamics in data packet transport on scale-free networks

We study the avalanche dynamics in the data packet transport on scale-free networks through a simple model. In the model, each vertex is assigned a capacity proportional to the load with a proportionality constant $1+a$. When the system is perturbed by a single vertex removal, the load of each vertex is redistributed, followed by subsequent failures of overloaded vertices. The avalanche size depends on the parameter $a$ as well as which vertex triggers it. We find that there exists a critical value $a_c$ at which the avalanche size distribution follows a power law. The critical exponent associated with it appears to be robust as long as the degree exponent is between 2 and 3, and is close in value to that of the distribution of the diameter changes by single vertex removal.Comment: 5 pages, 7 figures, final version published in PR

Evolution of the Protein Interaction Network of Budding Yeast: Role of the Protein Family Compatibility Constraint

Understanding of how protein interaction networks (PIN) of living organisms have evolved or are organized can be the first stepping stone in unveiling how life works on a fundamental ground. Here we introduce a hybrid network model composed of the yeast PIN and the protein family interaction network. The essential ingredient of the model includes the protein family identity and its robustness under evolution, as well as the three previously proposed ones: gene duplication, divergence, and mutation. We investigate diverse structural properties of our model with parameter values relevant to yeast, finding that the model successfully reproduces the empirical data.Comment: 5 pages, 5 figures, 1 table. Title changed. Final version published in JKP

Inclusive angular distribution of alpha and Li fragments produced in the Fe-C and Fe-Pb collisions at 1.88 GeV/u

The LS (laboratory system) emission angles theta for 2188 and 298 Li fragments, produced inclusively in relativistic Fe-C and Fe-Pb collisions, have been measured in reference to incident Fe-ion beam tracks nearby in nuclear emulsion. An empirical differential frequency formula, dN(cot theta) = exp (a + b cot theta)d(cot theta) is obtained with the constant b approx. = -0.026 at 1.88 GeV/u, which seems to be independent on the kinds of target nucleus as well as on the kinds of projectile fragments

Quantum network architecture of tight-binding models with substitution sequences

We study a two-spin quantum Turing architecture, in which discrete local rotations \alpha_m of the Turing head spin alternate with quantum controlled NOT-operations. Substitution sequences are known to underlie aperiodic structures. We show that parameter inputs \alpha_m described by such sequences can lead here to a quantum dynamics, intermediate between the regular and the chaotic variant. Exponential parameter sensitivity characterizing chaotic quantum Turing machines turns out to be an adequate criterion for induced quantum chaos in a quantum network.Comment: Accepted for publication in J. mod. Optics [Proc. Workshop "Entanglement and Decoherence", Gargnano (Italy), Sept 1999], 3 figure

Betweenness centrality correlation in social networks

Scale-free (SF) networks exhibiting a power-law degree distribution can be grouped into the assortative, dissortative and neutral networks according to the behavior of the degree-degree correlation coefficient. Here we investigate the betweenness centrality (BC) correlation for each type of SF networks. While the BC-BC correlation coefficients behave similarly to the degree-degree correlation coefficients for the dissortative and neutral networks, the BC correlation is nontrivial for the assortative ones found mainly in social networks. The mean BC of neighbors of a vertex with BC $g_i$ is almost independent of $g_i$, implying that each person is surrounded by almost the same influential environments of people no matter how influential the person is.Comment: 4 pages, 4 figures, 1 tabl