9,923 research outputs found
Closed Form Discrete Unimodular MIMO Waveform Design Using Block Circulant Decomposition
This paper deals with the waveform design under the constraint of discrete multiphase unimodular sequences. It relies on Block Circulant decomposition of the slow-time transmitted waveform. The presented closed-form solution is capable of designing orthogonal signals, such that the virtual MIMO paradigm is enabled leading to enhanced angular resolution. On the other hand, the proposed method is also capable of approximating any desired radiation pattern within the physical limits of the transmitted array size. Simulation results prove the effectiveness in terms computational complexity, orthogonal signal design and the transmit beam pattern design under constant modulus constraint
On the Lagrangian Structure of Reduced Dynamics Under Virtual Holonomic Constraints
This paper investigates a class of Lagrangian control systems with
degrees-of-freedom (DOF) and n-1 actuators, assuming that virtual
holonomic constraints have been enforced via feedback, and a basic regularity
condition holds. The reduced dynamics of such systems are described by a
second-order unforced differential equation. We present necessary and
sufficient conditions under which the reduced dynamics are those of a
mechanical system with one DOF and, more generally, under which they have a
Lagrangian structure. In both cases, we show that typical solutions satisfying
the virtual constraints lie in a restricted class which we completely
characterize.Comment: 23 pages, 5 figures, published online in ESAIM:COCV on April 28th,
201
A vector equilibrium problem for the two-matrix model in the quartic/quadratic case
We consider the two sequences of biorthogonal polynomials (p_{k,n})_k and
(q_{k,n})_k related to the Hermitian two-matrix model with potentials V(x) =
x^2/2 and W(y) = y^4/4 + ty^2. From an asymptotic analysis of the coefficients
in the recurrence relation satisfied by these polynomials, we obtain the
limiting distribution of the zeros of the polynomials p_{n,n} as n tends to
infinity. The limiting zero distribution is characterized as the first measure
of the minimizer in a vector equilibrium problem involving three measures which
for the case t=0 reduces to the vector equilibrium problem that was given
recently by two of us. A novel feature is that for t < 0 an external field is
active on the third measure which introduces a new type of critical behavior
for a certain negative value of t. We also prove a general result about the
interlacing of zeros of biorthogonal polynomials.Comment: 60 pages, 9 figure
A non-squeezing theorem for convex symplectic images of the Hilbert ball
We prove that the non-squeezing theorem of Gromov holds for
symplectomorphisms on an infinite-dimensional symplectic Hilbert space, under
the assumption that the image of the ball is convex. The proof is based on the
construction by duality methods of a symplectic capacity for bounded convex
neighbourhoods of the origin. We also discuss some examples of
symplectomorphisms on infinite-dimensional spaces exhibiting behaviours which
would be impossible in finite dimensions.Comment: Added application to the nonlinear Schr\"odinger equatio
Pattern Matching for sets of segments
In this paper we present algorithms for a number of problems in geometric
pattern matching where the input consist of a collections of segments in the
plane. Our work consists of two main parts. In the first, we address problems
and measures that relate to collections of orthogonal line segments in the
plane. Such collections arise naturally from problems in mapping buildings and
robot exploration.
We propose a new measure of segment similarity called a \emph{coverage
measure}, and present efficient algorithms for maximising this measure between
sets of axis-parallel segments under translations. Our algorithms run in time
O(n^3\polylog n) in the general case, and run in time O(n^2\polylog n) for
the case when all segments are horizontal. In addition, we show that when
restricted to translations that are only vertical, the Hausdorff distance
between two sets of horizontal segments can be computed in time roughly
O(n^{3/2}{\sl polylog}n). These algorithms form significant improvements over
the general algorithm of Chew et al. that takes time . In the
second part of this paper we address the problem of matching polygonal chains.
We study the well known \Frd, and present the first algorithm for computing the
\Frd under general translations. Our methods also yield algorithms for
computing a generalization of the \Fr distance, and we also present a simple
approximation algorithm for the \Frd that runs in time O(n^2\polylog n).Comment: To appear in the 12 ACM Symposium on Discrete Algorithms, Jan 200
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