On a generalization of Abelian equivalence and complexity of infinite words

In this paper we introduce and study a family of complexity functions of infinite words indexed by k \in \ints ^+ \cup {+\infty}. Let k \in \ints ^+ \cup {+\infty} and $A$ be a finite non-empty set. Two finite words $u$ and $v$ in $A^*$ are said to be $k$-Abelian equivalent if for all $x\in A^*$ of length less than or equal to $k,$ the number of occurrences of $x$ in $u$ is equal to the number of occurrences of $x$ in $v.$ This defines a family of equivalence relations $\thicksim_k$ on $A^*,$ bridging the gap between the usual notion of Abelian equivalence (when $k=1$) and equality (when $k=+\infty).$ We show that the number of $k$-Abelian equivalence classes of words of length $n$ grows polynomially, although the degree is exponential in $k.$ Given an infinite word \omega \in A^\nats, we consider the associated complexity function \mathcal {P}^{(k)}_\omega :\nats \rightarrow \nats which counts the number of $k$-Abelian equivalence classes of factors of $\omega$ of length $n.$ We show that the complexity function $\mathcal {P}^{(k)}$ is intimately linked with periodicity. More precisely we define an auxiliary function q^k: \nats \rightarrow \nats and show that if $\mathcal {P}^{(k)}_{\omega}(n)<q^k(n)$ for some k \in \ints ^+ \cup {+\infty} and $n\geq 0,$ the $\omega$ is ultimately periodic. Moreover if $\omega$ is aperiodic, then $\mathcal {P}^{(k)}_{\omega}(n)=q^k(n)$ if and only if $\omega$ is Sturmian. We also study $k$-Abelian complexity in connection with repetitions in words. Using Szemer\'edi's theorem, we show that if $\omega$ has bounded $k$-Abelian complexity, then for every D\subset \nats with positive upper density and for every positive integer $N,$ there exists a $k$-Abelian $N$ power occurring in $\omega$ at some position $j\in D.

Information theoretic novelty detection

We present a novel approach to online change detection problems when the training sample size is small. The proposed approach is based on estimating the expected information content of a new data point and allows an accurate control of the false positive rate even for small data sets. In the case of the Gaussian distribution, our approach is analytically tractable and closely related to classical statistical tests. We then propose an approximation scheme to extend our approach to the case of the mixture of Gaussians. We evaluate extensively our approach on synthetic data and on three real benchmark data sets. The experimental validation shows that our method maintains a good overall accuracy, but significantly improves the control over the false positive rate

A Study of Quantum Error Correction by Geometric Algebra and Liquid-State NMR Spectroscopy

Quantum error correcting codes enable the information contained in a quantum state to be protected from decoherence due to external perturbations. Applied to NMR, quantum coding does not alter normal relaxation, but rather converts the state of a ``data'' spin into multiple quantum coherences involving additional ancilla spins. These multiple quantum coherences relax at differing rates, thus permitting the original state of the data to be approximately reconstructed by mixing them together in an appropriate fashion. This paper describes the operation of a simple, three-bit quantum code in the product operator formalism, and uses geometric algebra methods to obtain the error-corrected decay curve in the presence of arbitrary correlations in the external random fields. These predictions are confirmed in both the totally correlated and uncorrelated cases by liquid-state NMR experiments on 13C-labeled alanine, using gradient-diffusion methods to implement these idealized decoherence models. Quantum error correction in weakly polarized systems requires that the ancilla spins be prepared in a pseudo-pure state relative to the data spin, which entails a loss of signal that exceeds any potential gain through error correction. Nevertheless, this study shows that quantum coding can be used to validate theoretical decoherence mechanisms, and to provide detailed information on correlations in the underlying NMR relaxation dynamics.Comment: 33 pages plus 6 figures, LaTeX article class with amsmath & graphicx package

Filtering graphs to check isomorphism and extracting mapping by using the Conductance Electrical Model

© 2016. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/This paper presents a new method of filtering graphs to check exact graph isomorphism and extracting their mapping. Each graph is modeled by a resistive electrical circuit using the Conductance Electrical Model (CEM). By using this model, a necessary condition to check the isomorphism of two graphs is that their equivalent resistances have the same values, but this is not enough, and we have to look for their mapping to find the sufficient condition. We can compute the isomorphism between two graphs in O(N-3), where N is the order of the graph, if their star resistance values are different, otherwise the computational time is exponential, but only with respect to the number of repeated star resistance values, which usually is very small. We can use this technique to filter graphs that are not isomorphic and in case that they are, we can obtain their node mapping. A distinguishing feature over other methods is that, even if there exists repeated star resistance values, we can extract a partial node mapping (of all the nodes except the repeated ones and their neighbors) in O(N-3). The paper presents the method and its application to detect isomorphic graphs in two well know graph databases, where some graphs have more than 600 nodes. (C) 2016 Elsevier Ltd. All rights reserved.Postprint (author's draft

Monte Carlo simulation of single spin asymmetries in pion-proton collisions

We present Monte Carlo simulations of both the Sivers and the Boer-Mulders effects in the polarized Drell-Yan $\pi^\pm p^\uparrow \to \mu^+ \mu^- X$ process at the center-of-mass energy $\sqrt{s} \sim 14$ GeV reachable at COMPASS with pion beams of energy 100 GeV. For the Sivers effect, we adopt two different parametrizations for the Sivers function to explore the statistical accuracy required to extract unambiguous information on this parton density. In particular, we verify the possibility of checking its predicted sign change between Semi-Inclusive Deep-Inelastic Scattering (SIDIS) and Drell-Yan processes, a crucial test of nonperturbative QCD. For the Boer-Mulders effect, because of the lack of parametrizations we can make only guesses. The goal is to explore the possibility of extracting information on the transversity distribution, the missing piece necessary to complete the knowledge of the nucleon spin structure at leading twist, and the Boer-Mulders function, which is related to the long-standing problem of the violation of the Lam-Tung sum rule in the unpolarized Drell-Yan cross section.Comment: RevTeX, 13 pages, 7 figures included in .eps forma

The IBMAP approach for Markov networks structure learning

In this work we consider the problem of learning the structure of Markov networks from data. We present an approach for tackling this problem called IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC algorithm, designed for avoiding important limitations of existing independence-based algorithms. These algorithms proceed by performing statistical independence tests on data, trusting completely the outcome of each test. In practice tests may be incorrect, resulting in potential cascading errors and the consequent reduction in the quality of the structures learned. IBMAP contemplates this uncertainty in the outcome of the tests through a probabilistic maximum-a-posteriori approach. The approach is instantiated in the IBMAP-HC algorithm, a structure selection strategy that performs a polynomial heuristic local search in the space of possible structures. We present an extensive empirical evaluation on synthetic and real data, showing that our algorithm outperforms significantly the current independence-based algorithms, in terms of data efficiency and quality of learned structures, with equivalent computational complexities. We also show the performance of IBMAP-HC in a real-world application of knowledge discovery: EDAs, which are evolutionary algorithms that use structure learning on each generation for modeling the distribution of populations. The experiments show that when IBMAP-HC is used to learn the structure, EDAs improve the convergence to the optimum

Thermal Infrared Observations of Asteroid (99942) Apophis with Herschel

The near-Earth asteroid (99942) Apophis is a potentially hazardous asteroid. We obtained far-infrared observations of this asteroid with the Herschel Space Observatory's PACS instrument at 70, 100, and 160 micron. These were taken at two epochs in January and March 2013 during a close Earth encounter. These first thermal measurements of Apophis were taken at similar phase angles before and after opposition. We performed a detailed thermophysical model analysis by using the spin and shape model recently derived from applying a 2-period Fourier series method to a large sample of well-calibrated photometric observations. We find that the tumbling asteroid Apophis has an elongated shape with a mean diameter of 375$^{+14}_{-10}$ m (of an equal volume sphere) and a geometric V-band albedo of 0.30$^{+0.05}_{-0.06}$. We find a thermal inertia in the range 250-800 Jm$^{-2}$s$^{-0.5}$K$^{-1}$ (best solution at 600 Jm$^{-2}$s$^{-0.5}$K$^{-1}$), which can be explained by a mixture of low conductivity fine regolith with larger rocks and boulders of high thermal inertia on the surface. The thermal inertia, and other similarities with (25143) Itokawa indicate that Apophis might also have a rubble-pile structure. If we combine the new size value with the assumption of an Itokawa-like density and porosity we estimate a mass between 4.4 and 6.2 10$^{10}$ kg which is more than 2-3 times larger than previous estimates. We expect that the newly derived properties will influence impact scenario studies and influence the long-term orbit predictions of Apophis.Comment: Accepted for publication in Astronomy & Astrophysics, 21 pages, 8 figures, 2 table

Private Multi-party Matrix Multiplication and Trust Computations

This paper deals with distributed matrix multiplication. Each player owns only one row of both matrices and wishes to learn about one distinct row of the product matrix, without revealing its input to the other players. We first improve on a weighted average protocol, in order to securely compute a dot-product with a quadratic volume of communications and linear number of rounds. We also propose a protocol with five communication rounds, using a Paillier-like underlying homomorphic public key cryptosystem, which is secure in the semi-honest model or secure with high probability in the malicious adversary model. Using ProVerif, a cryptographic protocol verification tool, we are able to check the security of the protocol and provide a countermeasure for each attack found by the tool. We also give a randomization method to avoid collusion attacks. As an application, we show that this protocol enables a distributed and secure evaluation of trust relationships in a network, for a large class of trust evaluation schemes.Comment: Pierangela Samarati. SECRYPT 2016 : 13th International Conference on Security and Cryptography, Lisbonne, Portugal, 26--28 Juillet 2016. 201

Calibration of <i>Herschel</i> SPIRE FTS observations at different spectral resolutions

The SPIRE Fourier Transform Spectrometer on-board the Herschel Space Observatory had two standard spectral resolution modes for science observations: high resolution (HR) and low resolution (LR), which could also be performed in sequence (H+LR). A comparison of the HR and LR resolution spectra taken in this sequential mode revealed a systematic discrepancy in the continuum level. Analysing the data at different stages during standard pipeline processing demonstrates that the telescope and instrument emission affect HR and H+LR observations in a systematically different way. The origin of this difference is found to lie in the variation of both the telescope and instrument response functions, while it is triggered by fast variation of the instrument temperatures. As it is not possible to trace the evolution of the response functions using housekeeping data from the instrument subsystems, the calibration cannot be corrected analytically. Therefore, an empirical correction for LR spectra has been developed, which removes the systematic noise introduced by the variation of the response functions