Irregular conformal blocks, with an application to the fifth and fourth Painlev\'e equations

We develop the theory of irregular conformal blocks of the Virasoro algebra. In previous studies, expansions of irregular conformal blocks at regular singular points were obtained as degeneration limits of regular conformal blocks; however, such expansions at irregular singular points were not clearly understood. This is because precise definitions of irregular vertex operators had not been provided previously. In this paper, we present precise definitions of irregular vertex operators of two types and we prove that one of our vertex operators exists uniquely. Then, we define irregular conformal blocks with at most two irregular singular points as expectation values of given irregular vertex operators. Our definitions provide an understanding of expansions of irregular conformal blocks and enable us to obtain expansions at irregular singular points. As an application, we propose conjectural formulas of series expansions of the tau functions of the fifth and fourth Painlev\'e equations, using expansions of irregular conformal blocks at an irregular singular point.Comment: 26 page

Reply to Comment on "Quantum Phase Transition of Randomly-Diluted Heisenberg Antiferromagnet on a Square Lattice"

This is a reply to the comment by A. W. Sandvik (cond-mat/0010433) on our paper Phys. Rev. Lett. 84, 4204 (2000). We show that his data do not conflict with our data nor with our conclusions.Comment: RevTeX, 1 page; Revised versio

Probing Tensor-Vector-Scalar Theory with Gravitational Wave Asteroseismology

In order to examine the gravitational waves emitted from the neutron stars in the tensor-vector-scalar (TeVeS) theory, we derive the perturbation equations for relativistic stars, where for simplicity we omit the perturbations of vector field. That is, we consider the perturbations of scalar and tensor fields. With this assumption, we find that the axial gravitational waves, which are corresponding to the oscillations of spacetime ($w$ modes), are independent from the perturbations of scalar field and the effects of scalar field can be mounted only via the background properties. Using two different equations of state, we calculate the complex eigenfrequencies of axial $w$ modes and find that the dependences of frequencies on the stellar compactness are almost independent from the adopted equation of state and the parameter in TeVeS. Additionally, these dependences of frequencies of axial $w$ modes in TeVeS is obviously different from those expected in the general relativity. Thus the direct observations of gravitational waves could reveal the gravitational theory in the strong-field regime.Comment: Accepted for publication in PR

Neutrino masses and mixing from S4 flavor twisting

We discuss a neutrino mass model based on the S4 discrete symmetry where the symmetry breaking is triggered by the boundary conditions of the bulk right-handed neutrino in the fifth spacial dimension. While the symmetry restricts bare mass parameters to flavor-diagonal forms, the viable mixing angles emerge from the wave functions of the Kaluza-Klein modes which carry symmetry breaking effect. The magnitudes of the lepton mixing angles, especially the reactor angle is related to the neutrino mass patterns and the model will be tested in future neutrino experiments, e.g., an early (late) discovery of the reactor angle favors the normal (inverted) hierarchy. The size of extra dimension has a connection to the possible mass spectrum; a small (large) volume corresponds to the normal (inverted) mass hierarchy.Comment: 22 pages, 3 figures; added references for section

Shift in Management Strategy of Yak Herding in the South of Mustang District, Nepal, Himalaya

In the Himalayan regions of Nepal, people herd yaks (Bos grunniens) under transhumant pastoralism, seasonal migrations of herds between summer highlands and winter lowlands. For several decades, the number of yaks has decreased, and the management strategy of yak herding has been altered due to the influence of substantial changes in both the social environment and their livelihoods. We conducted field surveys on yak herding in the south of Mustang District from 2012 to 2016 to examine the recent shift in management strategy and practice. The surveys were focused on fifteen yak owners and their herdsmen who lived in southernmost three villages in the district and organized a yak owners’ cooperative group. The herd scale has been constant in recent years, although the owners had a willingness to increase the scale. The herding practices were traditional and extensive, which might not have led to an increase in herd size or productivity. Dairy production has shown an obvious declining trend, whereas sales of meat and the revenue from the yak blood drinking festival hosted by the cooperative group have become more important income sources for local yak herding in association with the development of local infrastructures and livelihoods. Because the economic incentives for yak herding remained strong in the study area, the herding scale will be maintained, or expanded if the management practices are improved in the future

Theoretical framework of entangled-photon generation from biexcitons in nano-to-bulk crossover regime with planar geometry

We have constructed a theoretical framework of the biexciton-resonant hyperparametric scattering for the pursuit of high-power and high-quality generation of entangled photon pairs. Our framework is applicable to nano-to-bulk crossover regime where the center-of-mass motion of excitons and biexcitons is confined. Material surroundings and the polarization correlation of generated photons can be considered. We have analyzed the entangled-photon generation from CuCl film, by which ultraviolet entangled-photon pairs are generated, and from dielectric microcavity embedding a CuCl layer. We have revealed that in the nano-to-bulk crossover regime we generally get a high performance from the viewpoint of statistical accuracy, and the generation efficiency can be enhanced by the optical cavity with maintaining the high performance. The nano-to-bulk crossover regime has a variety of degrees of freedom to tune the entangled-photon generation, and the scattering spectra explicitly reflect quantized exciton-photon coupled modes in the finite structure.Comment: 18 pages, 10 figure

Probing Strong-Field Scalar-Tensor Gravity with Gravitational Wave Asteroseismology

We present an alternative way of tracing the existence of a scalar field based on the analysis of the gravitational wave spectrum of a vibrating neutron star. Scalar-tensor theories in strong-field gravity can potentially introduce much greater differences in the parameters of a neutron star than the uncertainties introduced by the various equations of state. The detection of gravitational waves from neutron stars can set constraints on the existence and the strength of scalar fields. We show that the oscillation spectrum is dramatically affected by the presence of a scalar field, and can provide unique confirmation of its existence.Comment: 14 pages, 7 figure

On the isomorphism problem of concept algebras

Weakly dicomplemented lattices are bounded lattices equipped with two unary operations to encode a negation on {\it concepts}. They have been introduced to capture the equational theory of concept algebras \cite{Wi00}. They generalize Boolean algebras. Concept algebras are concept lattices, thus complete lattices, with a weak negation and a weak opposition. A special case of the representation problem for weakly dicomplemented lattices, posed in \cite{Kw04}, is whether complete {\wdl}s are isomorphic to concept algebras. In this contribution we give a negative answer to this question (Theorem \ref{T:main}). We also provide a new proof of a well known result due to M.H. Stone \cite{St36}, saying that {\em each Boolean algebra is a field of sets} (Corollary \ref{C:Stone}). Before these, we prove that the boundedness condition on the initial definition of {\wdl}s (Definition \ref{D:wdl}) is superfluous (Theorem \ref{T:wcl}, see also \cite{Kw09}).Comment: 15 page

Role of BacA in Lipopolysaccharide Synthesis, Peptide Transport, and Nodulation by \u3cem\u3eRhizobium\u3c/em\u3e sp. Strain NGR234

BacA of Sinorhizobium meliloti plays an essential role in the establishment of nitrogen-fixing symbioses with Medicago plants, where it is involved in peptide import and in the addition of very-long-chain fatty acids (VLCFA) to lipid A of lipopolysaccharide (LPS). We investigated the role of BacA in Rhizobium species strain NGR234 by mutating the bacA gene. In the NGR234 bacA mutant, peptide import was impaired, but no effect on VLCFA addition was observed. More importantly, the symbiotic ability of the mutant was comparable to that of the wild type for a variety of legume species. Concurrently, an acpXL mutant of NGR234 was created and assayed. In rhizobia, AcpXL is a dedicated acyl carrier protein necessary for the addition of VLCFA to lipid A. LPS extracted from the NGR234 mutant lacked VLCFA, and this mutant was severely impaired in the ability to form functional nodules with the majority of legumes tested. Our work demonstrates the importance of VLCFA in the NGR234-legume symbiosis and also shows that the necessity of BacA for bacteroid differentiation is restricted to specific legume-Rhizobium interactions