Distinguishability and Disturbance in the Quantum Key Distribution Protocol Using the Mean Multi-Kings’ Problem

We introduce a quantum key distribution protocol using mean multi-kings’ problem. Using this protocol, a sender can share a bit sequence as a secret key with receivers. We consider a relation between information gain by an eavesdropper and disturbance contained in legitimate users’ information. In BB84 protocol, such relation is known as the so-called information disturbance theorem. We focus on a setting that the sender and two receivers try to share bit sequences and the eavesdropper tries to extract information by interacting legitimate users’ systems and an ancilla system. We derive trade-off inequalities between distinguishability of quantum states corresponding to the bit sequence for the eavesdropper and error probability of the bit sequence shared with the legitimate users. Our inequalities show that eavesdropper’s extracting information regarding the secret keys inevitably induces disturbing the states and increasing the error probability.     

Grammatical Verification for Mathematical Formula Recognition Based on Context-Free Tree Grammar

This paper proposes the use of a formal grammar for the verification of mathematical formulae for a practical mathematical OCR system. Like a C compiler detecting syntax errors in a source file, we want to have a verification mechanism to find errors in the output of mathematical OCR. A linear monadic context-free tree grammar (LM-CFTG) is employed as a formal framework to define “well-formed” mathematical formulae. A cubic time parsing algorithm for LM-CFTGs is presented. For the purpose of practical evaluation, a verification system for mathematical OCR is developed, and the effectiveness of the system is demonstrated by using the ground-truthed mathematical document database InftyCDB-1 and a misrecognition database newly constructed for this study.     

The effect of various calcination treatments on the photocatalytic activity of a rod-type TiO<Subscript>2</Subscript> electrode for oxidation of ethanethiol

It was found that the photoelectrochemical performance and photocatalytic activity of rod-type TiO₂ electrodes were affected by various post-calcination treatments, for example, calcination in NH₃ or under vacuum. Post-calcination treatment in NH₃ at 773 K was particularly effective in increasing the photoelectrochemical performance and photocatalytic activity of rod-type TiO₂ electrodes. A unique photoelectrochemical circuit was constructed by connecting a rod-type TiO₂ electrode to a Pt electrode through a silicon solar cell in which the negative bias was applied on the rod-type TiO₂ electrode. It was found that the photoelectrochemical circuit can effectively oxidize ethanethiol in water into CO₂.     

Probabilistic evaluation of interconnectable capacity for wind power generation

We propose a novel framework for probabilistic evaluation of interconnectable capacity for wind power generation. This is based on mathematical modeling of load frequency control systems, which captures their nonlinear (saturation and rate limiting) dynamical characteristics, and stochastic uncertainty of wind power output deviation. The method called stochastic linearization is used to analyze resulting power quality. The effectiveness of the proposed method is examined by numerical simulation.     

Toroidal surgeries on hyperbolic knots

For a hyperbolic knot in , a toroidal surgery is Dehn surgery which yields a -manifold containing an incompressible torus. It is known that a toroidal surgery on is an integer or a half-integer. In this paper, we prove that all integers occur among the toroidal slopes of hyperbolic knots with bridge index at most three and tunnel number one.

     

Supramolecular graphyne: a C(sp)-H...N hydrogen-bonded unique network structure of 2,4,6-triethynyl-1,3,5-triazine

The crystallization of 2,4,6-triethynyl-1,3,5-triazine (2) leads to a pi-stacked layered structure of a C(sp)-H...N hydrogen-bonded unique hexagonal network structure, which may be regarded as a supramolecular analogue of a hitherto unknown graphyne network: in-plane intermolecular interactions are short and linear H...N contacts (2.31 and 2.34 A) and the interlayer separation is 3.23 A.     

Induction in linear logic

Linear logic, introduced by Girardet al., has a great power of expression, but no method for induction. This paper proposes a method of induction using knowledge represented by linear logical formulas. In linear logic, the number of propositions is controlled by logical operators. When a background theory and a hypothesis prove an example, the number of propositions on each side must be equivalent.