We consider an analogue of the well-known Riemann Hypothesis based on quantum walks on graphs with the help of the Konno-Sato theorem. Furthermore, we give some examples for complete, cycle, and star graphs.

Norio Konno

Terrestrial ecosystems are generally green and only a small part (<10%) of the plant matter is consumed by herbivores annually,but the reason has been unclear due to the lack of food web models for predicting the absolute herbivore biomass in physical units. Here, I present a simple parameterized mathematical food web model that can predict the biomass density of herbivores h (kg protein/m3) and carnivores c from ecological factors such as the nutritive values of plants np (kg protein/m3), herbivores nh, and carnivores nc, searching efficiency (volume) of carnivores S (/day), eating efficiency (speed) of herbivores eh (/day) and carnivores ec, respiratory decrease in herbivore and carnivore biomasses, dh (/day) and dc, absorption efficiency of herbivores and carnivores h (ratio) and c, and probabilities of carnivores preying on herbivores or carnivores, Phc (ratio) and Pcc.The model predicts a stable equilibrium with low herbivore biomass h sufficient to keep the world green if the food web consists of the three trophic levels, plants, herbivores and carnivores; intraguild predation of carnivores exists; np<nh,nc; S>>eh, and Phc>Pcc >0,which are well-realized in above-ground terrestrial ecosystems where plant-rich "green world" is common. The h and c calculated from our model showed good agreement with those from empirical observations in forests, where both h and c are ca. 100 mg (fresh biomass/m2), and in savannahs. The model predicts that the nutritive values and digestibility of plants are positively correlated with h and the intensity of herbivory, which theoretically explains the out-door defensive effects of the anti-nutritive or quantitative defenses (e.g., tannins, protease inhibitors) of plants, and predicts that c and c/h are positively correlated with the relative growth rate of herbivores. The present model introduced parameterized realities into food web theory.

Kotaro Konno

The Konno invariant of a projective variety X is the minimum geometric genus of the fiber of a rational pencil on X. It was computed by Konno for surfaces in P^3, and in general can be viewed as a measure of the complexity of X. We estimate Konno(X) for some natural classes of varieties, including sharp asymptotics for polarized K3 surfaces. In an appendix, we give a quick proof of a classical formula due to Deligne and Hoskin for the colength of an integrally closed ideal on a surface.

Lawrence Ein Robert Lazarsfeld

We obtain stationary measures for the one-dimensional three-state Grover walk with one defect by solving the corresponding eigenvalue problem. We clarify a relation between stationary and limit measures of the walk.

Takako Endo Hikari Kawai Norio Konno

Let $N(d,d^\perp)$ denote the minimum length $n$ of a linear code $C$ with $d$ and $d^{\bot}$, where $d$ is the minimum Hamming distance of $C$ and $d^{\bot}$ is the minimum Hamming distance of $C^{\bot}$. In this paper, we show a lower bound and an upper bound on $N(d,d^\perp)$. Further, for small values of $d$ and $d^\perp$, we determine $N(d,d^\perp)$ and give a generator matrix of the optimum linear code. This problem is directly related to the design method of cryptographic Boolean functions suggested by Kurosawa et al.

Ryutaroh Matsumoto Kaoru Kurosawa Toshiya Itoh Toshimitsu Konno Tomohiko Uyematsu

We consider a manifold X obtained by a Kahler reduction of C^n, and we define its hyperkahler analogue M as a hyperkahler reduction of T^*C^n = H^n by the same group. In the case where the group is abelian and X is a smooth toric variety, M is a toric hyperkahler manifold, as defined by Bielawski-Dancer, and further studied by Konno and Hausel-Sturmfels. The manifold M carries a natural action of S^1, induced by the scalar action of S^1 on the fibers of T^*C^n. In this paper we study this action, computing its fixed points and its equivariant cohomology. As an application, we use the associated Z/2 action on the real locus of M to compute a deformation of the Orlik-Solomon algebra of a smooth, generic, real hyperplane arrangement, depending nontrivially on the affine structure of the arrangement. This deformation is given by the Z/2-equivariant cohomology of the complement of the complexification, where Z/2 acts by complex conjugation.

Megumi Harada Nicholas J. Proudfoot

While completely self-avoiding quantum walks have the distinct property of leading to a trivial unidirectional transport of a quantum state, an interesting and non-trivial dynamics can be constructed by restricting the self-avoidance to a subspace of the complete Hilbert space. Here, we present a comprehensive study of three two-dimensional quantum walks, which are self-avoiding in coin space, in position space and in both, coin and position space. We discuss the properties of these walks and show that all result in delocalisation of the probability distribution for initial states which are strongly localised for a walk with a standard Grover coin operation. We also present analytical results for the evolution in the form of limit distributions for the self-avoiding walks in coin space and in both, coin and position space.

Takuya Machida C. M. Chandrashekar Norio Konno Thomas Busch

In order to investigate details of the superconducting (SC) gap in the iron-chalcogenide superconductors, the specific heat, C, of FeSe_1-x_Te_x_ with x=0.6-1 has been measured in magnetic fields. Using the two-gap model, it has been found that the smaller SC gap is significantly depressed by the application of magnetic field, resulting in the increase of the slope of the C/T vs T^2^ plot at low temperatures. From the specific-heat measurements at very low temperatures down to 0.4 K, it has been found that the enhancement of the residual electronic-specific-heat-coefficient in the ground state, gamma_0_, by the application of magnetic field is much smaller than that expected for superconductors with the typical s-wave or d-wave SC paring symmetry, which is in sharp contrast to the significant enhancement of gamma_0 observed in the iron-pnictide superconductors. These results are discussed in relation to the multi-band effect in the iron-based superconductors.

T. Konno T. Adachi M. Imaizumi T. Noji T. Kawamata Y. Koike

Ferromagnetism and accompanying large negative magnetoresistance in Pb-substituted Bi-Sr-Co-O misfit-layer compound are investigated in detail. Recent structural analysis of (Bi,Pb)${}_2$Sr${}_{3}$Co${}_2$O${}_9$, which has been believed to be a Co analogue of Bi${}_2$Sr${}_2$CaCu${}_2$O${}_{8+\delta}$, revealed that it has a more complex structure including a CoO${}_2$ hexagonal layer [T. Yamamoto {\it et al.}, Jpn. J. Appl. Phys. {\bf 39} (2000) L747]. Pb substitution for Bi not only introduces holes into the conducting CoO${}_2$ layers but also creates a certain amount of localized spins. Ferromagnetic transition appears at $T$ = 3.2 K with small spontaneous magnetization along the $c$ axis, and around the transition temperature large and anisotropic negative magnetoresistance was observed. This compound is the first example which shows ferromagnetic long-range order in a two-dimensional metallic hexagnonal CoO${}_2$ layer.

I. Tsukada T. Yamamoto M. Takagi T. Tsubone S. Konno K. Uchinokura

We investigate the structure of the elliptic algebra U_{q,p}(^sl_2) introduced earlier by one of the authors. Our construction is based on a new set of generating series in the quantum affine algebra U_q(^sl_2), which are elliptic analogs of the Drinfeld currents. They enable us to identify U_{q,p}(^sl_2) with the tensor product of U_q(^sl_2) and a Heisenberg algebra generated by P,Q with [Q,P]=1. In terms of these currents, we construct an L operator satisfying the dynamical RLL relation in the presence of the central element c. The vertex operators of Lukyanov and Pugai arise as `intertwiners' of U_{q,p}(^sl_2) for level one representation, in the sense to be elaborated on in the text. We also present vertex operators with higher level/spin in the free field representation.

M. Jimbo H. Konno S. Odake J. Shiraishi