Scaling properties of complex networks: Toward Wilsonian renormalization for complex networks

Nowadays, scaling methods for general large-scale complex networks have been developed. We proposed a new scaling scheme called "two-site scaling". This scheme was applied iteratively to various networks, and we observed how the degree distribution of the network changes by two-site scaling. In particular, networks constructed by the BA algorithm behave differently from the networks observed in the nature. In addition, an iterative scaling scheme can define a new renormalizing method. We investigated the possibility of defining the Wilsonian renormalization group method on general complex networks and its application to the analysis of the dynamics of complex networks.Comment: 4pages, 6 figures, submitted to PHYSCOMNET0

Constructing families of elliptic curves with prescribed mod 3 representation via Hessian and Cayleyan curves

For a given elliptic curve $E_0$ defined over a number field $k$, we construct two families of elliptic curves whose mod 3 representations are isomorphic to that of $E_0$. The isomorphisms in the first family are symplectic, and those in the second family are anti-symplectic. Our construction is based on the notion of Hessian and Cayleyan curves in classical geometry.Comment: After submitting the first version of this paper on the arXiv, the author was informed that the main observation of this paper had already been made by Tom Fisher, "The Hessian of a genus one curve", Proc. Lond. Math. Soc. (3) 104 (2012), 613-648 (arXiv:math/0610403v2

On AGT-W Conjecture and q-Deformed W-Algebra

We propose an extension of the Alday-Gaiotto-Tachikawa-Wyllard conjecture to 5d SU(N) gauge theories. A Nekrasov partition function then coincides with the scalar product of the corresponding Gaiotto-Whittaker vectors of the q-deformed W_N algebra.Comment: 18 page

Solutions in the generalized Proca theory with the nonminimal coupling to the Einstein tensor

We investigate the static and spherically symmetric solutions in a class of the generalized Proca theory with the nonminimal coupling to the Einstein tensor. First, we show that the solutions in the scalar-tensor theory with the nonminimal derivative coupling to the Einstein tensor can be those in the generalized Proca theory with the vanishing field strength. We then show that when the field strength takes the nonzero value the static and spherically symmetric solutions can be found only for the specific value of the nonminimal coupling constant. Second, we investigate the first-order slow-rotation corrections to the static and spherically symmetric background. We find that for the background with the vanishing electric field strength the slowly rotating solution is identical to the Kerr- (anti-) de Sitter solutions in general relativity. On the other hand, for the background with the nonvanishing electric field strength the stealth property can realized at the first order in the slow-rotation approximation.Comment: 11 pages, no figure, the journal versio

Linearized gravity in flat braneworlds with anisotropic brane tension

We study the four-dimensional gravitational fluctuation on anisotropic brane tension embedded in braneworlds with vanishing bulk cosmological constant. In this setup, warp factors have two types (A and B) and we point out that the two types correspond to positive and negative tension brane, respectively. We show that volcano potential in the model of type A has singularity and the usual Newton's law is reproduced by the existence of normalizable zero mode. While, in the case of type B, the effective Planck scale is infinite so that there is no normalizable zero mode.Comment: 7 pages, 2 figure

Five-Dimensional Gauge Theories and Whitham-Toda Equation

The five-dimensional supersymmetric SU(N) gauge theory is studied in the framework of the relativistic Toda chain. This equation can be embedded in two-dimensional Toda lattice hierarchy. This system has the conjugate structure. This conjugate structure corresponds to the charge conjugation.Comment: 9 pages, LaTex, section 3 and 4 are change

Invitation to higher local fields, Part I, section 9: Exponential maps and explicit formulas

An exponential homomorphism for a complete discrete valuation field of characteristic zero which relates differential forms and the Milnor K-groups of the field is studied. An application to explicit formulas is included.Comment: For introduction and notation, see math.NT/0012131 . Published by Geometry and Topology Monographs at http://www.maths.warwick.ac.uk/gt/GTMon3/m3-I-9.abs.htm

Efficient quantum key distribution with practical sources and detectors

We consider the security of a system of quantum key distribution (QKD) using only practical devices. Currently, attenuated laser pulses are widely used and considered to be the most practical light source. For the receiver of photons, threshold (or on/off) photon detectors are almost the only choice. Combining the decoy-state idea and the security argument based on the uncertainty principle, we show that a QKD system composed of such practical devices can achieve the unconditional security without any significant penalty in the key rate and the distance limitation.Comment: 4 pages, 3 figure

Strong algebraization of fixed point properties

The following natural question arises from Shalom's innovational work (1999, Publ. IHES): "Can we establish an intrinsic criterion to synthesize relative fixed point properties into the whole fixed point property without assuming Bounded Generation?" This paper resolves this question in the affirmative. Our criterion works for ones with respect to certain classes of Busemann NPC spaces. It, moreover, suggests a further step toward constructing super-expanders from finite simple groups of Lie type.Comment: Major revision (v2), 27 pages. Results contain ones with respect to certain Busemann NPC spaces; old title is "Strong algebraization of fixed point properties"; 14 pages (v1), no figur

Weighted counting of inversions on alternating sign matrices

We extend the author's formula (2011) of weighted counting of inversions on permutations to the one on alternating sign matrices. The proof is based on the sequential construction of alternating sign matrices from the unit matrix recently shown by Brualdi-Schroeder and the author (both 2017) independently.Comment: 19 page