We introduce new hash functions SSInhash, n=160, 192, 256, 384, 512, 1024 and 2048, whose algorithm is, differently from many other hash functions, consisting of multiplication and shift of multiple-precision integers. The base of algorithm is a repetition of piecewise linear chaos mappings called SSR computations. We first construct a tiny hash function SSRhash which is derived from SSR algorithm directly, and then translate it into all-integer version SSInhash whose hash value is n bits. After constructing hash functions we verify randomness of hash values generated by SSInhash by applying the NIST statistical test suite and TestU01. We further discuss the security of our hash function by deriving algebraic equation of high degree.
The Object-Spatial Imagery Questionnaire (OSIQ) is a measure of individual differences in visual imagery preferences. In the present study, we attempted to develop a Japanese version of the OSIQ (J-OSIQ). On the basis of principal components analysis, we obtained two factors in the questionnaire. An object imagery scale (15 items) assesses preferences for representing colorful, pictorial, high-resolution images of individual objects or scenes. A spatial imagery scale (15 items) assesses preferences for representing schematic images of objects and spatial locations of objects. The reliabilities of these factors were similar to those of the original version. Additionally, we showed that the object imagery scale was selectively correlated with object imagery measures, whereas the spatial imagery scale was selectively correlated with spatial imagery tests. These results demonstrate that the J-OSIQ is useful for measuring preferences for object and spatial imagery in Japanese.
We give a refinement of Löwner's inequality with argument of the equality case. To this end, we establish a complete univalence criterion for meromorphic functions of special type. We also give applications of the refinement.
In this paper, we explore a strategy for recovering a PKI system without reconstructing the whole one when the trust anchor has been broken. Specifically, we propose two distributed signature schemes based on the hyper-powering discrete logarithm problem, which is a two-dimensional extension of the discrete logarithm problem. We show that these schemes are existentially unforgeable against the adaptively chosen message attack.
In this paper, we consider constructibility of simplicial 3-balls. Examining 1-dimensional subcomplexes of a simplicial 3-ball is efficient to solve the decision problem whether the simplicial 3-ball is constructible or not. From the point of view, we consider the case where a simplicial 3-ball has spanning edges and present a sufficient condition for nonconstructibility.
The Manhattan product of directed paths Pn and Pm is a digraph, where the underlying graph is the n×m lattice and each edge is given direction in such a way that left and right directed horizontal lines are placed alternately, and so are up and down directed vertical lines. Unless both m and n are even, the Manhattan product of Pn and Pm is unique up to isomorphisms, which is called standard and denoted by Pn#Pm. If both m and n are even, there is a Manhattan product which is not isomorphic to the standard one. It is called non-standard and denoted by Pn#′Pm. The characteristic polynomials of Pn#P2 and Pn#′P2 are expressed in terms of the Chebychev polynomials of the second kind, and their spectra (eigenvalues with multiplicities) are thereby determined explicitly. In particular, it is shown that ev (P2n-1#P2)=ev (P2n#P2) and ev (P2n#′P2)=ev (P2n+2#P2). The limit of the spectral distribution of Pn#P2 as n→∞ exists in the sense of weak convergence and its concrete form is obtained.
Boltzmann machines are parametric probabilistic models for the statistical machine learning, forming Markov random fields. Owing to their normalization constant, inference and learning in Boltzmann machines are generally classified under NP-hard problems. Maximum pseudo-likelihood estimation is an effective approximate learning method for Boltzmann machines. However, in principle, we cannot use this method for incomplete data sets, except for some special cases. In this paper, we propose a new learning algorithm for Boltzmann machines with incomplete data sets by generating a pseudo-complete data set from a given incomplete data using the max-product algorithm and the Markov chain Monte Carlo method, and then, by applying maximum pseudo-likelihood estimation to the pseudo-complete data set.