Formal model of internal measurement: Alternate changing between recursive definition and domain equation

We sketch a paradox generally resulting from recursivity, and propose a novel model to express evolutionary processes that requires identification of an interaction with internal measurement. In this model, a paradox is not resolved and the notion of relativity of any resolution is implicit. In a dynamical system a certain transition rule is used recursively along time. If one takes the foundation (or context) of recursivity into consideration, one obtains a fixed point or one confronts a paradox. In order to resolve this paradox, we adopt Scott's technical way to identify the form of a fixed point with a domain equation and to obtain a reflective domain, however we simultaneously show that any resolution is destined to be relative. In utilizing this notion, we construct a model of dynamical process by embedding a measurement process in one time step. Any time transition involves the process of doubting the foundation of a transition rule leading to a fixed point. Solving it and obtaining a reflexive domain is used as a new transition rule. Also, this process perpetually proceeds along time, and then the system perpetually proceeds while any solution is destined to be relative. We illustrate this type of model by using a dynamically changing contraction mapping as the interface of state and transition rule. Finally, we show that one can formalize emergent properties by using this model and discuss the relationship between endo-physics and internal measurement.     

Tunneling junction as an open system normal tunneling

The method of the tunneling Hamiltonian is reformulated in the case of normal tunneling by introducing two independent particle baths. Due to the baths, it becomes possible to realize a final stationary state where the electron numbers of the two electrodes in the tunneling system are maintained constant and where there exists a stationary current. The effect of the bath-system couplings on the current-voltage characteristics of the junction is discussed in relation to the usual expression of the current as a function of voltage.     

Origin of anomalous lattice expansion in oxide nanoparticles

Anomalous lattice expansions have been measured for the first time in monodisperse CeO2-x nanoparticles and in BaTiO3 single nanoparticles by electron diffraction. X-ray photoelectron spectroscopy studies on CeO2-x nanoparticles and ab initio computer simulation on BaTiO3 clusters show that the origin of expansion is the decrease of electrostatic force caused by valence reduction of Ce ions and the increase in ionicity of Ti ions, respectively. The lattice constant change of oxide (ionic) nanoparticles with the increase in ionicity would depend on the structure of the particles. Hence, first-principles calculations of large ionic clusters are indispensable.     

Exact estimates of regularity modulus for infinite programming

An exact estimate on the modulus of metric regularity for linear systems is given. By applying the estimate, we obtain explicit forms of the modulus for linear conical systems and differentiable nonlinear systems on the space of continuous functions.     

Enright functors for Kac-Moody superalgebras

A simple generalization of the Enright functor associated with a non-isotropic simple root of Kac-Moody superalgebras is introduced. Two applications for a Kac-Moody superalgebra without isotropic simple root are given: the uniqueness (up to scalar) of homomorphisms between Verma modules and the Malikov-Feigin-Fuks type singular vector formula. The braid relations of the Enright functors are also discussed.     

Improvement of Antibody Activity by Controlling Its Dynamics Using the Glycan–Lectin Interaction

Antibody dynamics on membranes, such as endocytosis and clustering, are vital in determining antibody functions. In this study, we demonstrated that glycan conjugation can modulate antibody dynamics through the glycan–lectin interaction to regulate its potency. The anti-HER2 antibody, an anti-breast-cancer antibody, was conjugated with galactose-containing N-glycan, and its internalization was suppressed by interaction with galectin-3, leading to enhanced complement-dependent cytotoxic (CDC) activity. This glycan–antibody conjugate is proposed as a new approach to modulate antibody activity and may provide an alternative strategy for redeveloping antibody drugs that do not exhibit sufficient activity.     

Mechanistic Studies for the Rational Design of Multivalent Glycodendrimers

We have synthesized B-antigen-displaying dendrimers (16-mers) with different sizes and evaluated their affinity to their IgM antibody in order to investigate which design features lead to effective multivalency. Unexpectedly, the smallest dendrimer, which cannot chelate the multiple binding sites of IgM, clearly exhibited multivalency, together with an affinity similar to or higher than those of the larger dendrimers. These results indicate that the statistical rebinding model, which involves the rapid exchange of clustered glycans, significantly contributes to the multivalency of glycodendrimers. Namely, in the design of glycodendrimers, high-density glycan presentation to enhance statistical rebinding should be considered in addition to the ability to chelate multiple binding sites. This notion stands in contrast to the currently prevailing scientific consensus, which prioritizes the chelation model. This study thus provides new and important guidelines for molecular design of glycodendrimers.