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33
Cayley differential unitary space–time codes
 IEEE Trans. Inform. Theory
, 2002
"... 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 ..."
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Cited by 70 (6 self)
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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 goodperforming 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 skewHermitian matrices. This transformation leads to a simple linear constellation structure in the Cayley transform domain and to an informationtheoretic design criterion based on emulating a Cauchy random matrix. Moreover, the resulting Cayley codes allow polynomialtime nearmaximumlikelihood decoding based on either successive nulling/cancelling or sphere decoding. Simulations show that the Cayley codes allow efficient and effective highrate data transmission in multiantenna communication systems without knowing the channel.
Emergent Semantics Through Interaction in Image Databases
 IEEE Transactions on Knowledge and Data Engineering
, 2001
"... 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. Fr ..."
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Cited by 66 (6 self)
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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 withand the organization ofimage 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...
Spatially Homogeneous Dynamics: A Unified Picture (Preprint Series No
, 1983
"... The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial homogeneity. A parameter dependent decomposition of the metric variabl ..."
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Cited by 17 (2 self)
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The Einstein equations for a perfect fluid spatially homogeneous spacetime are studied in a unified manner by retaining the generality of certain parameters whose discrete values correspond to the various Bianchi types of spatial homogeneity. A parameter dependent decomposition of the metric variables adapted to the symmetry breaking effects of the nonabelian Bianchi types on the “free dynamics ” leads to a reduction of the equations of motion for those variables to a 2dimensional time dependent Hamiltonian system containing various time dependent potentials which are explicitly described and diagrammed. These potentials are extremely useful in deducing the gross features of the evolution of the metric variables. 1
Notions of controllability for quantum mechanical systems
, 2001
"... 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 ..."
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Cited by 13 (2 self)
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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
ALGEBRAIC STRUCTURE AND FINITE DIMENSIONAL NONLINEAR ESTIMATION
, 1978
"... The algebraic structure of certain classes of nonlinear systems is exploited in order to prove that the optimal estimators for these systems are recursive and finite dimensional. These systems are represented by certain Volterra series expansions or by bilinear systems with nilpotent Lie algebras. I ..."
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Cited by 6 (0 self)
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The algebraic structure of certain classes of nonlinear systems is exploited in order to prove that the optimal estimators for these systems are recursive and finite dimensional. These systems are represented by certain Volterra series expansions or by bilinear systems with nilpotent Lie algebras. In addition, an example is presented, and the steadystate estimator for this example is discussed.
THE ELEMENTARY GEOMETRIC STRUCTURE OF COMPACT LIE GROUPS
"... 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 se ..."
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Cited by 5 (2 self)
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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 pcompact 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
Nonstationary quantum walks on the cycle
, 2007
"... We consider quantum walks on the cycle in the nonstationary 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 distribu ..."
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Cited by 3 (0 self)
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We consider quantum walks on the cycle in the nonstationary 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
NAHM ALGEBRAS
, 1999
"... 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 Nah ..."
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Cited by 2 (0 self)
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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.
Singularities of Robot Manipulators
"... 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 ..."
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Cited by 1 (0 self)
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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.
HAMILTONIAN CURVE FLOWS IN LIE GROUPS G ⊂ U(N) AND VECTOR NLS, mKdV, SINEGORDON SOLITON EQUATIONS
, 2006
"... Abstract. A biHamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of nonstretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a paralle ..."
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Abstract. A biHamiltonian hierarchy of complex vector soliton equations is derived from geometric flows of nonstretching curves in the Lie groups G = SO(N + 1), SU(N) ⊂ U(N), generalizing previous work on integrable curve flows in Riemannian symmetric spaces G/SO(N). The derivation uses a parallel frame and connection along the curves, involving the Klein geometry of the group G. This is shown to yield the two known U(N − 1)invariant vector generalizations of both the nonlinear Schrödinger (NLS) equation and the complex modified Kortewegde Vries (mKdV) equation, as well as U(N − 1)invariant vector generalizations of the sineGordon (SG) equation found in recent symmetryintegrability classifications of hyperbolic vector equations. The curve flows themselves are described in explicit form by chiral wave maps, chiral variants of Schrödinger maps, and mKdV analogs.