The paper proposes a method of variable-to-fixed length binary data encryption in the class of conventional cryptosystems. An encryption algorithm reduces an interval of the integers that mean candidates of cryptograph according to a key and messages. A decryption algorithm traces the trajectory of reduction of interval according to the key and cryptographs to reproduce the messages. These algorithms are executable with simple arithmetics on several registers. However, wiretappers without knowledge on the key cannot correctly reproduce messages since they cannot trace the trajectory of reduction. The exhaustive cryptanalysis identifies the correct decryption procedure only from cryptographs. The comparing cryptanalysis identifies the correct decryption procedure from some pairs of message and cryptograph. Asymptotic evaluations for the computational complexity of cryptanalysis show a satisfactory endurance against wiretapping.

This article shows construction of an asymptotically optimal source code for transmitting sentences together with truth values on a [0,1]-valued logic system.

Learning control is a new approach to the problem of skill refinement for robotic systems by repetitive training. A class of simple learning control algorithms with a forgetting factor and without use of the derivative of velocity signals for motion control of robot manipulators is proposed and the convergence property is discussed. The robustness of such a learning control scheme with respect to initialization errors, disturbances, and measurement noise is studied extensively. It is proved that motion trajectories converge to a neighborhood of the desired one and eventually remain in it. In the argument the passivity of robot dynamics and displacement robot dynamics plays a fundamental role. Relations of the size of attraction neighborhoods with the magnitudes of initialization errors and other disturbances are obtained, which suggests a rule for selection of the forgetting factor in the progress of learning. Based on these results, two classes of learning control called "interval training" and "selective learning" are proposed in order to accelerate the speed of convergence.

This paper attempts to account for intelligibility of practices-based learning (so-called 'learning control') for skill refinement from the viewpoint of Newtonian mechanics. It is shown from an axiomatic approach that an extended notion of passivity for the residual error dynamics of robots plays a crucial role in their ability of learning. More precisely, it is shown that the exponentially weighted passivity with respect to residual velocity vector and torque vector leads the robot system to the convergence of trajectory tracking errors to zero with repeating practices. For a class of tasks when the endpoint is constrained geometrically on a surface, the problem of convergence of residual tracking errors and residual contact-force errors is also discussed on the basis of passivity analysis.

This paper is concerned with analysis of nonlinear dynamics under geometric constraints that express pinching motions of a pair of multi-degrees of freedom fingers with soft tips. The dynamics of such a pair of soft fingers can be expressed by a set of complicated nonlinear differential equations with algebraic constraints, even if the motion is constrained in a plane. However, it is shown from the passivity analysis that dynamic stable grasping (pinching) can be realized by means of a feedforward input of desired internal force with coefficients composed of elements of Jacobian matrices plus a feedback of the difference between moments of rotation exerted at both sides of the object. It is shown in the case of a pair of 2 d.o.f. and 3 d.o.f. fingers (corresponding to a pair of thumb and index fingers) that a principle of linear superposition is applicable to design of additional feedback signals for controlling simultaneously the posture (rotational angle) and position of the mass center of the object, though the dynamics are nonlinear. A sufficient condition for applicability of the principle of superposition is discussed and given as a condition for unique stationary resolution of the overall motion to elementary motions (stable grasping, rotation control, x and y coordinates control). The principle implies that a skilled motion can be resolved into some of elementary motions which human can learn separately and independently.

This paper aims at challenging Bernstein's problem called the "Degrees-of-Freedom problem," which remains unsolved from both the physiological and robotics viewpoints. More than a half century ago A.N. Bernstein observed that "dexterity" residing in human limb motion emerges from accumulated involvement of multi-joint movements in surplus DOF. It is also said in robotics that redundancy of DOFs in robot mechanisms may contribute to enhancement of dexterity and versatility. However, kinematic redundancy incurs a problem of ill-posedness of inverse kinematics from task-description space to joint space. In the history of robotics research such ill-posedness problem of inverse-kinematics has not yet been attacked directly but circumvented by introducing an artificial performance index and determining uniquely an inverse kinematics solution by minimizing it. Instead of it, this paper introduces two novel concepts named "stability on a manifold" and "transferability to a submanifold" in treating the case of human multi-joint movements of reaching and shows that a sensory feedback from task space to joint space together with a set of adequate dampings enables any solution to the overall closed-loop dynamics to converge naturally and coordinately to a lower-dimensional manifold describing a set of joint states fulfilling a given motion task. This means that, without considering any type of inverse kinematics, the reaching task can be accomplished by a sensory feedback with adequate choice of a stiffness parameter and damping coefficients. It is also shown that these novel concepts can cope with annoying characteristics called "variability" of redundant joint motions seen typically in human skilled reaching. Finally, it is pointed out that the proposed control signals can be generated in a feedforward manner in case of human limb movements by referring to mechano-chemical characteristics of activation of muscles. Based on this observation, generation of human skilled movements of reaching can be interpreted in terms of the proposed "Virtual-Spring" hypothesis instead of the traditional "Equilibrium-Point" hypothesis.

A Bitplane Tree Weighting (BTW) method with arithmetic coding is proposed for lossless coding of gray scale images, which are represented with multiple bitplanes. A bitplane tree, in the same way as the context tree in the CTW method, is used to derive a weighted coding probability distribution for arithmetic coding with the first order Markov model. It is shown that the proposed method can attain better compression ratio than known schemes with MDL criterion. Furthermore, the BTW method can be extended to a high order Markov model by combining the BTW with the CTW or with prediction. The performance of these modified methods is also evaluated. It is shown that they attain better compression ratio than the original BTW method without increasing memory size and coding time, and they can beat the lossless JPEG coding.

This paper proposes () an algorithm that dynamically constructs an asymptotically-balanced binary tree to store successively-given keys without knowledge of the distribution of key occurence, and () another algorithm for quick key search over the constructed tree such that: If the tree has in memory at least a key that is inside the Δ-neighbor (in a Hamming space) of a reference key, then the algorithm can find one of such Δ-neighbor keys almost with probability 1. The memory capacity required to describe a tree in the tree construction algorithm is of order being proportional to the number l of keys already processed. For an independently and idenically distributed binary source of generating keys, the mean computation time required to update a tree for every key input can be of an order being a little higher than (log2l)2log2(log2l), and that required to search a Δ-neighbor key can be of an order being a little higher than (log2l)3.

The asymptotic behavior of the recurrence time with fidelity criterion is discussed. Let X= be a source and Y= a database. For a Δ>0 and an integer l>0 define (Y,X,Δ) as the minimum integer N satisfying dl(,) Δ subject to a fidelity criterion dl. In this paper the following two i. i. d. cases are considered: (A) Xi P and Yi Q, where P and Q are probability distributions on a finite alphabet, and (B) Xi N(0,1) and Yi N(0,1). In case (A) it is proved that (1/l)log2(Y,X,Δ) almost surely converges to a certain constant determined by P, Q and Δ as l. The Kac's lemma plays an important role in the proof on the convergence. In case (B) it is shown that there is a quantity related to (1/l)log2 (Y,X,Δ) that converges to the rate-distortion bound in almost sure sense.

Let U denote a set comprising elements called "keys." The goal of the nearest point problem is to search quickly for a key among some keys x1 , xn that is the nearest to a reference key x under a partial order relation defined as (x, y) (x, z) for x, y, zU if d(x, y)d(x, z) given a wide-sense distance measure d. This article proposes a method of rearranging x1 , xn into a binary perfectly-balanced tree for solving quickly the nearest point problems. Further, computational performances of the proposed method are evaluated experimentally.

This paper characterizes a class of optimal fixed-to-fixed length data compression codes for memoryless Gaussian sources that achieve asymptotically the rate-distortion bound under squared-error criterion. Any source output of blocklength n is encoded by two steps, i.e., 1) to quantize in gain by scholar quantizers and 2) to quantize in shape by pointsets on n-dimensional hyperspheres. To show the asymptotic optimality of the proposed codes, rate-distortion properties of the codes are analyzed in detail by using a random coding argument on the n-dimensional unit hypersphere. It is shown that asymptotic behaviors of the proposed codes are mainly determined by the choice of scalar quantizer of the gain. As a results, deep insights into not only the class of asymptotically optimal codes but also the rate-distortion bound itself are obtained.

This article proposes, given an independently-and-identically distributed binary source, an arithmetic code-like variable-to-variable length source code whose compression efficiency achieves nearly the rate function in a range of small distortion. Inheriting advantages of arithmetic codes, the proposed code requires neither large memory capacity nor large computation time for management of messages and codewords. The Elias code, which can be regarded as an antecedent of arithmetic codes, is defined originally in terms of the first-in-first-out (FIFO) coding form. The proposed code corresponds to an extension from the Elias code refined in terms of the last-in-first-out (LIFO) coding form into one considered a fidelity criterion.