In this paper we discuss briefly some aspects of image semantics and the role that it plays for the design of Image Databases. We argue that images don't have an intrinsic meaning, but that they are endowed with a meaning by placing them in the context of other images and by the user interaction. From this observation, we conclude that in an image database users should be allowed to manipulate not only the individual images, but also the relation between them. We present an interface model based on the manipulation of configurations of images. 1 Introduction In this paper we propose some new ideas on image semantics, and study some of their consequences on the interaction with---and the organization of---image databases. Many current Content Based Image Retrieval (CBIR) systems follow a semantic model derived from traditional databases according to which the meaning of a record is a compositional function of its syntactic structure and of the meaning of its elementary constituents. W...

One method for communicating with multiple antennas is to encode the transmitted data differentially using unitary matrices at the transmitter, and to decode differentially without knowing the channel coefficients at the receiver. Since channel knowledge is not required at the receiver, differential schemes are ideal for use on wireless links where channel tracking is undesirable or infeasible, either because of rapid changes in the channel characteristics or because of limited system resources. Although this basic principle is well understood, it is not known how to generate good-performing constellations of unitary matrices, for any number of transmit and receive antennas and for any rate. This is especially true at high rates where the constellations must be rapidly encoded and decoded. We propose a class of Cayley codes that works with any number of antennas, and has efficient encoding and decoding at any rate. The codes are named for their use of the Cayley transform, which maps the highly nonlinear Stiefel manifold of unitary matrices to the linear space of skew-Hermitian matrices. This transformation leads to a simple linear constellation structure in the Cayley transform domain and to an information-theoretic design criterion based on emulating a Cauchy random matrix. Moreover, the resulting Cayley codes allow polynomial-time near-maximum-likelihood decoding based on either successive nulling/cancelling or sphere decoding. Simulations show that the Cayley codes allow efficient and effective high-rate data transmission in multi-antenna communication systems without knowing the channel.

In this paper, we define four different notions of controllability of physical interest for multilevel quantum mechanical systems. These notions involve the possibility of driving the evolution operator as well as the state of the system. We establish the connections among these different notions as well as methods to verify controllability. The paper also contains results on the relation between the controllability in arbitrary small time of a system varying on a compact transformation Lie group and the corresponding system on the associated homogeneous space. As an application, we prove that, for the system of two interacting spin 1 2 particles, not every state transfer can be obtained in arbitrary small time. 1

Abstract. We give geometric proofs of some of the basic structure theorems for compact Lie groups. The goal is to take a fresh look at these theorems, prove some that are difficult to find in the literature, and illustrate an approach to the theorems that can be imitated in the homotopy theoretic setting of p-compact groups. A compact Lie group G is a compact differentiable manifold together with a smooth multiplication map G × G → G which gives G the structure of a group. (The inverse map is automatically smooth [8, p. 22].) For instance, G might be the multiplicative group of unit complex numbers, the multiplicative group of unit

We consider quantum walks on the cycle in the non-stationary case where the ‘coin ’ operation is allowed to change at each time step. We characterize, in algebraic terms, the set of possible state transfers and prove that, as opposed to the stationary case, it is possible to reach a uniform distribution among the nodes of the associated graph. PACS: 03.65.-w, 03.67.-a

Abstract. Given a Lie algebra g, the Nahm algebra of g is the vector space g×g×g with the natural commutative, nonassociative algebra structure associated with the system of ordinary differential equations (1.1)-(1.3). Motivated by applications to these equations, we herein initiate the study of Nahm algebras. 1.

Engineers have for some time known that singularities play a significant role in the design and control of robot manipulators. Singularities of the kinematic mapping, which determines the position of the end–effector in terms of the manipulator’s joint variables, may impede control algorithms, lead to large joint velocities, forces and torques and reduce instantaneous mobility. However they can also enable fine control, and the singularities exhibited by trajectories of the points in the end–effector can be used to mechanical advantage. A number of attempts have been made to understand kinematic singularities and, more specifically, singularities of robot manipulators, using aspects of the singularity theory of smooth maps. In this survey, we describe the mathematical framework for manipulator kinematics and some of the key results concerning singularities. A transversality theorem of Gibson and Hobbs asserts that, generically, kinematic mappings give rise to trajectories that display only singularity types up to a given codimension. However this result does not take into account the specific geometry of manipulator motions or, a fortiori, to a given class of manipulator. An alternative approach, using screw systems, provides more detailed information but also shows that practical manipulators may exhibit high codimension singularities in a stable way. This exemplifies the difficulties of tailoring singularity theory’s emphasis on the generic with the specialized designs that play a key role in engineering.

Abstract not found

Abstract not found

ABSTRACT: There are a number of applications in which linear noise models are inappropriate. In this paper, the use of bilinear noise modela in circuits and devices is considered. Several physical problems are studied in this framework. These include circuils involving varying parameters (such as variable resistance circuits constructed using Jieldeffect transistors), the effect of switching jitter on sampled data system performance and communication systems involving voltage-controlled oscillators and phase-lock loops. In addition, several types of analytical techniques for stochastic bilinear systems are considered. Speci$cally, the moment equations of Brockett for bilinear systems driven by white noise are discussed, and closed-form expressions for certain bilinear systema (those that evolve on abelian or solvable Lie groups) driven by white or colored noise are derived. In addition, an approximate statistical technique involving the use of harmonic expansions is described. I. Zntroduction Although linear models are extremely useful in many applications, there are large classes of problems of practical importance for which such models