Learning Probability Measures with respect to Optimal Transport Metrics

We study the problem of estimating, in the sense of optimal transport metrics, a measure which is assumed supported on a manifold embedded in a Hilbert space. By establishing a precise connection between optimal transport metrics, optimal quantization, and learning theory, we derive new probabilistic bounds for the performance of a classic algorithm in unsupervised learning (k-means), when used to produce a probability measure derived from the data. In the course of the analysis, we arrive at new lower bounds, as well as probabilistic upper bounds on the convergence rate of the empirical law of large numbers, which, unlike existing bounds, are applicable to a wide class of measures.Comment: 13 pages, 2 figures. Advances in Neural Information Processing Systems, NIPS 201

Phase transitions, memory and frustration in a Sznajd-like model with synchronous updating

We introduce a consensus model inspired by the Sznajd Model. The updating is synchronous and memory plays here a decisive role in making possible the reaching of total consensus. We study the phase transition between the state with no-consensus to the state with total consensus.Comment: to be published in the IJMP

The Topological Theory of the Milnor Invariant μˉ(1,2,3)\bar{\mu}(1,2,3)

We study a topological Abelian gauge theory that generalizes the Abelian Chern-Simons one, and that leads in a natural way to the Milnor's link invariant $\bar{\mu}(1,2,3)$ when the classical action on-shell is calculated.Comment: 4 pages; corrected equatio

On the Sample Complexity of Subspace Learning

A large number of algorithms in machine learning, from principal component analysis (PCA), and its non-linear (kernel) extensions, to more recent spectral embedding and support estimation methods, rely on estimating a linear subspace from samples. In this paper we introduce a general formulation of this problem and derive novel learning error estimates. Our results rely on natural assumptions on the spectral properties of the covariance operator associated to the data distribu- tion, and hold for a wide class of metrics between subspaces. As special cases, we discuss sharp error estimates for the reconstruction properties of PCA and spectral support estimation. Key to our analysis is an operator theoretic approach that has broad applicability to spectral learning methods.Comment: Extendend Version of conference pape

Backscatter Transponder Based on Frequency Selective Surface for FMCW Radar Applications

This paper describes an actively-controlled frequency selective surface (FSS) to implement a backscatter transponder. The FSS is composed by dipoles loaded with switching PIN diodes. The transponder exploits the change in the radar cross section (RCS) of the FSS with the bias of the diodes to modulate the backscattered response of the tag to the FMCW radar. The basic operation theory of the system is explained here. An experimental setup based on a commercial X-band FMCW radar working as a reader is proposed to measure the transponders. The transponder response can be distinguished from the interference of non-modulated clutter, modulating the transponder’s RCS. Some FSS with different number of dipoles are studied, as a proof of concept. Experimental results at several distances are provided

Cosmic ray production in modified gravity

This paper is a reply to the criticism of our work on particle production in modified gravity by D. Gorbunov and A. Tokareva. We show that their arguments against efficient particle production are invalid. $F(R)$ theories can lead to an efficient generation of high energy cosmic rays in contracting systems.Comment: In response to criticism by referees several clarifying comments are added. The results of the paper remain largely unchanged. Version to appear on EPJ

Time-Evolution of the Power Spectrum of the Black Hole X-ray Nova XTE J1550-564

We have studied the time evolution of the power spectrum of XTE J1550-564, using X-ray luminosity time series data obtained by the Rossi X-Ray Timing Explorer satellite. A number of important practical fundamental issues arise in the analysis of these data, including dealing with time-tagged event data, removal of noise from a highly non-stationary signal, and comparison of different time-frequency distributions. We present two new methods to understand the time frequency variations, and compare them to the dynamic power spectrum of Homan et al. All of the approaches provide evidence that the QPO frequency varies in a systematic way during the time evolution of the signal.Comment: 4 pages, 3 figures; 2001 IEEE - EURASIP Workshop on Nonlinear Signal and Image Processing (June 3-6, 2001), and to appear in the proceeding