Rigidity, natural kind terms and metasemantics

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Detection of a signal in linear subspace with bounded mismatch

We consider the problem of detecting a signal of interest in a background of noise with unknown covariance matrix, taking into account a possible mismatch between the actual steering vector and the presumed one. We assume that the former belongs to a known linear subspace, up to a fraction of its energy. When the subspace of interest consists of the presumed steering vector, this amounts to assuming that the angle between the actual steering vector and the presumed steering vector is upper bounded. Within this framework, we derive the generalized likelihood ratio test (GLRT). We show that it involves solving a minimization problem with the constraint that the signal of interest lies inside a cone. We present a computationally efficient algorithm to find the maximum likelihood estimator (MLE) based on the Lagrange multiplier technique. Numerical simulations illustrate the performance and the robustness of this new detector, and compare it with the adaptive coherence estimator which assumes that the steering vector lies entirely in a subspace

Adaptive detection with bounded steering vectors mismatch angle

We address the problem of detecting a signal of interest (SOI), using multiple observations in the primary data, in a background of noise with unknown covariance matrix. We consider a situation where the signal signature is not known perfectly, but its angle with a nominal and known signature is bounded. Furthermore, we consider a possible scaling inhomogeneity between the primary and the secondary noise covariance matrix. First, assuming that the noise covariance matrix is known, we derive the generalized-likelihood ratio test (GLRT), which involves solving a semidefinite programming problem. Next, we substitute the unknown noise covariance matrix for its estimate obtained from secondary data, to yield the final detector. The latter is compared with a detector that assumes a known signal signature

Observation of a Narrow Resonance of Mass 2.46 GeV/c^2 in the D_s^*+\pi^0 Final State, and Confirmation of the D_sJ^*(2317)

Using 13.5 fb^{-1} of e^+e^- annihilation data collected with the CLEO-II detector, we have observed a new narrow resonance in the D_s^*\pi^0 final state, with a mass near 2.46 GeV/c^2. The search for such a state was motivated by the recent discovery by the BaBar Collaboration of a narrow state at 2.32 GeV/c^2, the D_{sJ}^*(2317)^+, that decays to D_s\pi^0. Reconstructing the D_s\pi^0 and D_s^*\pi^0 final states in CLEO data, we observe a peak in each of the corresponding reconstructed mass difference distributions, \Delta M_{D_s\pi^0} = M(D_s\pi^0) - M(D_s) and \Delta M_{D_s^*\pi^0} = M(D_s^*\pi^0) - M(D_s^*), both of them at values around 350 MeV/c^2. These peaks constitute statistically significant evidence for two distinct states, at 2.32 and 2.46 GeV/c^2, taking into account the background source that each state comprises for the other in light of the nearly identical values of \Delta M observed for the two peaks. We have measured the mean mass differences \Delta M_{D_s\pi^0} = 350.4 \pm 1.2[stat.] \pm 1.0 [syst.] MeV/c^2 for the $D_{sJ}^*(2317)^+$ state, and \Delta M_{D_s^*\pi^0} = 351.6 \pm 1.7[stat.] \pm 1.0 [syst.] MeV/c^2 for the new state at 2.46 GeV/c^2. We have also searched, but find no evidence, for decays of D_{sJ}^*(2317) into the alternate final states D_s^*\gamma, D_s\gamma, and D_s\pi^+\pi^-. The observations of the two states at 2.32 and 2.46 GeV/c^2, in the D_s\pi^0 and D_s^*\pi^0 decay channels respectively, are consistent with their possible interpretations as c s-bar mesons with orbital angular momentum L=1, and spin-parity J^P = 0^+ and 1^+.Comment: 12 pages postscript, Updated Author List, also available through http://w4.lns.cornell.edu/public/CLNS, submitted to 8th CIPANP May 200

Detection in the presence of surprise or undernulled interference

We consider the problem of detecting a signal of interest in the presence of colored noise, in the case of a covariance mismatch between the test cell and the training samples. More precisely, we consider a situation where an interfering signal (e.g., a sidelobe target or an undernulled interference) is present in the test cell and not in the secondary data. We show that the adaptive coherence estimator (ACE) is the generalized likelihood ratio test for such a problem, which may explain the previously observed fact that theACE has excellent sidelobe rejection capability, at the price of low mainlobe target sensitivity

Externalism, internalism and logical truth

The aim of this paper is to show what sorts of logics are required by externalist and internalist accounts of the meanings of natural kind nouns. These logics give us a new perspective from which to evaluate the respective positions in the externalist--internalist debate about the meanings of such nouns. The two main claims of the paper are the following: first, that adequate logics for internalism and externalism about natural kind nouns are second-order logics; second, that an internalist second-order logic is a free logic—a second order logic free of existential commitments for natural kind nouns, while an externalist second-order logic is not free of existential commitments for natural kind nouns—it is existentially committed

CFAR matched direction detector

In a previously published paper by Besson et al., we considered the problem of detecting a signal whose associated spatial signature is known to lie in a given linear subspace, in the presence of subspace interference and broadband noise of known level. We extend these results to the case of unknown noise level. More precisely, we derive the generalized-likelihood ratio test (GLRT) for this problem, which provides a constant false-alarm rate (CFAR) detector. It is shown that the GLRT involves the largest eigenvalue and the trace of complex Wishart matrices. The distribution of the GLRT is derived under the hypothesis. Numerical simulations illustrate its performance and provide a comparison with the GLRT when the noise level is known