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The following learning problem arises naturally in various applications: Given a finite sample from a categorical or count time series, can we learn a function of the sample that (nearly) maximizes the probability of correctly guessing the values of a given portion of the data using the values from the remaining parts? Unlike the classical task of estimating conditional probabilities in a stochastic process, our approach avoids explicitly estimating these probabilities. We propose a non-parametric guessing function with a learning rate that is independent of the alphabet size. Our analysis focuses on a broad class of time series models that encompasses finite-order Markov chains, some hidden Markov chains, Poisson regression for count process, and one-dimensional Gibbs measures. Additionally, we establish a minimax lower bound for the rate of convergence of the risk associated with our guessing problem. This lower bound matches the upper bound achieved by our estimator up to a logarithmic factor, demonstrating its near-optimality., Comment: 21 pages, submitted

Matter distribution in the environment of galaxy clusters, from their cores to their connected cosmic filaments, must be in principle related to the underlying cluster physics and it evolutionary state. We aim to investigate how radial and azimuthal distribution of gas is affected by cluster environments, and how it can be related to cluster mass assembly history. Radial physical properties of gas (velocity, temperature, and density) is first analysed around 415 galaxy cluster environments from IllustrisTNG simulation at z = 0 (TNG300-1). Whereas hot plasma is virialised inside clusters (< R200), the dynamics of warm hot inter-galactic medium (WHIM) can be separated in two regimes: accumulating and slowly infalling gas at cluster peripheries and fast infalling motions outside clusters (> 1.5R200). The azimuthal distribution of dark matter (DM), hot and warm gas phases is secondly statistically probed by decomposing their 2-D distribution in harmonic space. Inside clusters, the azimuthal symmetries of DM and hot gas are well tracing cluster structural properties, such as their center offsets, substructure fractions and elliptical shapes. Beyond cluster virialised regions, we find that WHIM gas follows the azimuthal distribution of DM thus tracing cosmic filament patterns. Azimuthal symmetries of hot and warm gas distribution are finally shown to be imprints of cluster mass assembly history, strongly correlated with the formation time, mass accretion rate, and dynamical state of clusters. Azimuthal mode decomposition of 2-D gas distribution is a promising probe to assess the 3-D physical and dynamical cluster properties up to their connected cosmic filaments., Comment: Accepted to A&A, 16 pages, 9 figures, comments are welcome

In many dynamical systems in nature, the law of the dynamics changes along with the temporal evolution of the system. These changes are often associated with the occurrence of certain events. The timing of occurrence of these events depends, in turn, on the trajectory of the dynamical system itself, making the dynamics of the system and the timing of a change in the dynamics strongly coupled. Naturally, trajectories that take longer to satisfy the event will last longer. Therefore, we expect to observe more frequently the dominant dynamics, the ones that take longer to change in the long run. This article proposes a Markov chain model, called Self-Switching Markov Chain (SSMC), in which the emergence of dominant dynamics can be rigorously addressed. We present conditions and scaling in the SSMC under which we observe with probability one only the subset of dominant dynamics, and we characterize these dominant dynamics. Furthermore, we show that the switching between dynamics exhibits metastability-like property.

We obtain optimal Gaussian concentration bounds (GCBs) for stochastic chains of unbounded memory (SCUMs) on countable alphabets. These stochastic processes are also known as "chains with complete connections" or "$g$-measures". We consider two different conditions on the kernel: (1) when the sum of its oscillations is less than one, or (2) when the sum of its variations is finite, i.e., belongs to $\ell^1(\mathbb{N})$. We also obtain explicit constants as functions of the parameters of the model. The proof is based on maximal coupling. Our conditions are optimal in the sense that we exhibit examples of SCUMs that do not have GCB and for which the sum of oscillations is strictly larger than one, or the variation belongs to $\ell^{1+\epsilon}(\mathbb{N})$ for any $\epsilon > 0$. These examples are based on the existence of phase transitions. We also extend the validity of GCB to a class of functions which can depend on infinitely many coordinates. We illustrate our results by three applications. First, we derive a Dvoretzky-Kiefer-Wolfowitz type inequality which gives a uniform control on the fluctuations of the empirical measure. Second, in the finite-alphabet case, we obtain an upper bound on the $\bar{d}$-distance between two stationary SCUMs and, as a by-product, we obtain new (explicit) bounds on the speed of Markovian approximation in $\bar{d}$. Third, we obtain exponential rate of convergence for Birkhoff sums of a certain class of observables., Comment: 33 pages. The main difference with the first version is that Theorem 3.2 now holds for countably infinite alphabets. We corrected many typos and improved the presentation

To account for the dark matter content in our Universe, post-inflationary scenarios predict for the QCD axion a mass in the range $(10-10^3)\,\mu\mbox{eV}$. Searches with haloscope experiments in this mass range require the monitoring of resonant cavity modes with frequency above 5\,GHz, where several experimental limitations occur due to linear amplifiers, small volumes, and low quality factors of Cu resonant cavities. In this paper we deal with the last issue, presenting the result of a search for galactic axions using a haloscope based on a $36\,\mbox{cm}^3$ NbTi superconducting cavity. The cavity worked at $T=4\,\mbox{K}$ in a 2\,T magnetic field and exhibited a quality factor $Q_0= 4.5\times10^5$ for the TM010 mode at 9\,GHz. With such values of $Q$ the axion signal is significantly increased with respect to copper cavity haloscopes. Operating this setup we set the limit $g_{a\gamma\gamma}<1.03\times10^{-12}\,\mbox{GeV}^{-1}$ on the axion photon coupling for a mass of about 37\,$\mu$eV. A comprehensive study of the NbTi cavity at different magnetic fields, temperatures, and frequencies is also presented.

Let $(X_k)_{k\geq 0}$ be a stationary and ergodic process with joint distribution $\mu$ where the random variables $X_k$ take values in a finite set $\mathcal{A}$. Let $R_n$ be the first time this process repeats its first $n$ symbols of output. It is well-known that $\frac{1}{n}\log R_n$ converges almost surely to the entropy of the process. Refined properties of $R_n$ (large deviations, multifractality, etc) are encoded in the return-time $L^q$-spectrum defined as \[ \mathcal{R}(q)=\lim_n\frac{1}{n}\log\int R_n^q \,d\mu\quad (q\in\mathbb{R}) \] provided the limit exists. We consider the case where $(X_k)_{k\geq 0}$ is distributed according to the equilibrium state of a potential $\varphi:\mathcal{A}^{\mathbb{N}}\to\mathbb{R}$ with summable variation, and we prove that \[ \mathcal{R}(q) = \begin{cases} P((1-q)\varphi) & \text{for}\;\; q\geq q_\varphi^*\\ \sup_\eta \int \varphi \, d\eta & \text{for}\;\; q

The current status of the QUAX R\&D program is presented. QUAX is a feasibility study for a detection of axion as dark matter based on the coupling to the electrons. The relevant signal is a magnetization change of a magnetic material placed inside a resonant microwave cavity and polarized with a static magnetic field., Comment: Contributed to the 13th Patras Workshop on Axions, WIMPs and WISPs, Thessaloniki, May 15 to 19, 2017