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L’articolo racconta, a partire dal film del 2018 Stan & Ollie, il viaggio in Italia del duo comico più famoso del mondo, datato 1950. Fra il 1947 e il 1954, quando il successo in America iniziava a scemare, Stanlio e Ollio intrapresero una tournée europea in Francia, Inghilterra, Belgio e Danimarca, accolti ovunque in trionfo. Qui, infatti, il loro successo sembrava non aver mai avuto un calo; ovunque andassero, la risposta del pubblico era sempre la stessa: una grande e calorosa accoglienza.

L'associazionismo giovanile di partito č una realtŕ a tutt'oggi indagata solo in parte dalla ricerca storica. Il saggio ricostruisce, tramite una pluralitŕ di fonti, la nascita dei Gruppi giovanili della Democrazia cristiana, dal 1953 rinominati Movimento giovanile Dc, dalle origini nel 1944 al 1955, segnato dalla segreteria di Amintore Fanfani. L'intento č precisare alcune informazioni non corrette riportate da ricerche precedenti e dalla memorialistica, analizzando il dibattito interno all'organizzazione in alcuni tornanti decisivi del primo decennio repubblicano, mettendo in luce elementi di originalitŕ rispetto ai temi prevalenti fra gli "adulti" e offrendo, per quanto possibile, uno sguardo a livello europeo dell'associazionismo giovanile democristiano.

This essay explores the food discourse elaborated by Chinese intellectuals in the Song period (960–1279) and puts forward a hypothesis concerning its social function. Starting from the Bourdieusian...

We consider the problem of estimating a large rank-one tensor ${\boldsymbol u}^{\otimes k}\in({\mathbb R}^{n})^{\otimes k}$, $k\ge 3$ in Gaussian noise. Earlier work characterized a critical signal-to-noise ratio $\lambda_{Bayes}= O(1)$ above which an ideal estimator achieves strictly positive correlation with the unknown vector of interest. Remarkably no polynomial-time algorithm is known that achieved this goal unless $\lambda\ge C n^{(k-2)/4}$ and even powerful semidefinite programming relaxations appear to fail for $1\ll \lambda\ll n^{(k-2)/4}$. In order to elucidate this behavior, we consider the maximum likelihood estimator, which requires maximizing a degree-$k$ homogeneous polynomial over the unit sphere in $n$ dimensions. We compute the expected number of critical points and local maxima of this objective function and show that it is exponential in the dimensions $n$, and give exact formulas for the exponential growth rate. We show that (for $\lambda$ larger than a constant) critical points are either very close to the unknown vector ${\boldsymbol u}$, or are confined in a band of width $\Theta(\lambda^{-1/(k-1)})$ around the maximum circle that is orthogonal to ${\boldsymbol u}$. For local maxima, this band shrinks to be of size $\Theta(\lambda^{-1/(k-2)})$. These `uninformative' local maxima are likely to cause the failure of optimization algorithms., Comment: 40 pages, 20 pdf figures

Given a collection of data points, nonnegative matrix factorization (NMF) suggests expressing them as convex combinations of a small set of “archetypes” with nonnegative entries. This decomposition...

We consider the problem of learning an unknown function $f_{\star}$ on the $d$-dimensional sphere with respect to the square loss, given i.i.d. samples $\{(y_i,{\boldsymbol x}_i)\}_{i\le n}$ where ${\boldsymbol x}_i$ is a feature vector uniformly distributed on the sphere and $y_i=f_{\star}({\boldsymbol x}_i)+\varepsilon_i$. We study two popular classes of models that can be regarded as linearizations of two-layers neural networks around a random initialization: the random features model of Rahimi-Recht (RF); the neural tangent kernel model of Jacot-Gabriel-Hongler (NT). Both these approaches can also be regarded as randomized approximations of kernel ridge regression (with respect to different kernels), and enjoy universal approximation properties when the number of neurons $N$ diverges, for a fixed dimension $d$. We consider two specific regimes: the approximation-limited regime, in which $n=\infty$ while $d$ and $N$ are large but finite; and the sample size-limited regime in which $N=\infty$ while $d$ and $n$ are large but finite. In the first regime we prove that if $d^{\ell + \delta} \le N\le d^{\ell+1-\delta}$ for small $\delta > 0$, then \RF\, effectively fits a degree-$\ell$ polynomial in the raw features, and \NT\, fits a degree-$(\ell+1)$ polynomial. In the second regime, both RF and NT reduce to kernel methods with rotationally invariant kernels. We prove that, if the number of samples is $d^{\ell + \delta} \le n \le d^{\ell +1-\delta}$, then kernel methods can fit at most a a degree-$\ell$ polynomial in the raw features. This lower bound is achieved by kernel ridge regression. Optimal prediction error is achieved for vanishing ridge regularization., Comment: 65 pages; 17 pdf figures

Consider the problem of estimating a low-rank matrix when its entries are perturbed by Gaussian noise. If the empirical distribution of the entries of the spikes is known, optimal estimators that exploit this knowledge can substantially outperform simple spectral approaches. Recent work characterizes the asymptotic accuracy of Bayes-optimal estimators in the high-dimensional limit. In this paper we present a practical algorithm that can achieve Bayes-optimal accuracy above the spectral threshold. A bold conjecture from statistical physics posits that no polynomial-time algorithm achieves optimal error below the same threshold (unless the best estimator is trivial). Our approach uses Approximate Message Passing (AMP) in conjunction with a spectral initialization. AMP algorithms have proved successful in a variety of statistical estimation tasks, and are amenable to exact asymptotic analysis via state evolution. Unfortunately, state evolution is uninformative when the algorithm is initialized near an unstable fixed point, as often happens in low-rank matrix estimation. We develop a new analysis of AMP that allows for spectral initializations. Our main theorem is general and applies beyond matrix estimation. However, we use it to derive detailed predictions for the problem of estimating a rank-one matrix in noise. Special cases of this problem are closely related---via universality arguments---to the network community detection problem for two asymmetric communities. For general rank-one models, we show that AMP can be used to construct confidence intervals and control false discovery rate. We provide illustrations of the general methodology by considering the cases of sparse low-rank matrices and of block-constant low-rank matrices with symmetric blocks (we refer to the latter as to the `Gaussian Block Model')., 76 pages, 6 pdf figures; Version 4 expands the introductory material and the applications to statistical inference