1,986 research outputs found
A temporally-constrained convolutive probabilistic model for pitch detection
A method for pitch detection which models the temporal evolution of musical sounds is presented in this paper. The proposed model is based on shift-invariant probabilistic latent component analysis, constrained by a hidden Markov model. The time-frequency representation of a produced musical note can be expressed by the model as a temporal sequence of spectral templates which can also be shifted over log-frequency. Thus, this approach can be effectively used for pitch detection in music signals that contain amplitude and frequency modulations. Experiments were performed using extracted sequences of spectral templates on monophonic music excerpts, where the proposed model outperforms a non-temporally constrained convolutive model for pitch detection. Finally, future directions are given for multipitch extensions of the proposed model
Privacy-Preserving Distributed Optimization via Subspace Perturbation: A General Framework
As the modern world becomes increasingly digitized and interconnected,
distributed signal processing has proven to be effective in processing its
large volume of data. However, a main challenge limiting the broad use of
distributed signal processing techniques is the issue of privacy in handling
sensitive data. To address this privacy issue, we propose a novel yet general
subspace perturbation method for privacy-preserving distributed optimization,
which allows each node to obtain the desired solution while protecting its
private data. In particular, we show that the dual variables introduced in each
distributed optimizer will not converge in a certain subspace determined by the
graph topology. Additionally, the optimization variable is ensured to converge
to the desired solution, because it is orthogonal to this non-convergent
subspace. We therefore propose to insert noise in the non-convergent subspace
through the dual variable such that the private data are protected, and the
accuracy of the desired solution is completely unaffected. Moreover, the
proposed method is shown to be secure under two widely-used adversary models:
passive and eavesdropping. Furthermore, we consider several distributed
optimizers such as ADMM and PDMM to demonstrate the general applicability of
the proposed method. Finally, we test the performance through a set of
applications. Numerical tests indicate that the proposed method is superior to
existing methods in terms of several parameters like estimated accuracy,
privacy level, communication cost and convergence rate
(M-theory-)Killing spinors on symmetric spaces
We show how the theory of invariant principal bundle connections for
reductive homogeneous spaces can be applied to determine the holonomy of
generalised Killing spinor covariant derivatives of the form in a purely algebraic and algorithmic way, where is a left-invariant homomorphism. Specialising this
to the case of symmetric M-theory backgrounds (i.e. with a
symmetric space and an invariant closed 4-form), we derive several criteria
for such a background to preserve some supersymmetry and consequently find all
supersymmetric symmetric M-theory backgrounds.Comment: Updated abstract for clarity. Added missing geometries to section 6.
Main result stand
Counting sets with small sumset, and the clique number of random Cayley graphs
Given a set A in Z/NZ we may form a Cayley sum graph G_A on vertex set Z/NZ
by joining i to j if and only if i + j is in A. We investigate the extent to
which performing this construction with a random set A simulates the generation
of a random graph, proving that the clique number of G_A is a.s. O(log N). This
shows that Cayley sum graphs can furnish good examples of Ramsey graphs. To
prove this result we must study the specific structure of set addition on Z/NZ.
Indeed, we also show that the clique number of a random Cayley sum graph on
(Z/2Z)^n, 2^n = N, is almost surely not O(log N).
Despite the graph-theoretical title, this is a paper in number theory. Our
main results are essentially estimates for the number of sets A in {1,...,N}
with |A| = k and |A + A| = m, for various values of k and m.Comment: 18 pages; to appear in Combinatorica, exposition has been improved
thanks to comments from Imre Ruzsa and Seva Le
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