Metropolia

Niniejszy artykuł stanowi fragment czwartego rozdziału ostatniej książki Michaela Hardta i Antonia Negriego Commonwealth, w znacznie większej mierze niż ich poprzednie prace zainteresowanej wątkami miejskimi. Zawarta w nim propozycja to próba ujęcia współczesnego miasta w kategoriach biopolitycznych, co odróżniałoby je od wcześniejszych form organizacji przestrzennej, np. miasta przemysłowego i pozwalało na przejście od formy miejskiej do formy metropolitalnej. Główna teza tekstu głosi, że z uwagi na zachodzące współcześnie zmiany na gruncie produkcji i pracy, metropolia zajmuje miejsce zarezerwowane wcześniej dla fabryki („metropolia jest tym dla wielości, czym fabryka dla klasy robotników przemysłowych”). Staje się zarazem nieograniczonym ścianami obszarem produkcji tego, co wspólne, jak i obiektem kontestacji ogniskującej się w obliczu władzy imperialnej i kapitalistycznego wyzysku. Autorzy analizują w tym miejscu również dwie kolejne jakości de&niujące metropolię: kwestie nieprzewidywalnych spotkań oraz organizacji oporu (w formie miejskich rebelii zwanych żakeriami). Gdy ująć te cechy wspólnie, przekonują Hardt i Negri, należy zgodzić się z tezą, że metropolia jest miejscem, w którym wielość znajduje swój dom

The effective shear and dilatational viscosity of a particle-laden interface in the dilute limit

The effective dilatational and shear viscosities of a particle-laden fluid interface are computed in the dilute limit under the assumption of an asymptotically vanishing viscosity ratio between both fluids. Spherical particles with a given contact angle of the fluid interface at the particle surface are considered. A planar fluid interface and a small Reynolds number are assumed. The theoretical analysis is based on a domain perturbation expansion in the deviation of the contact angle from $90^\circ$ up to the second order. The resulting effective dilatational viscosity shows a stronger dependence on the contact angle than the effective shear viscosity, and its magnitude is larger for all contact angles. As an application of the theory, the stability of a liquid cylinder decorated with particles is considered. The limits of validity of the theory and possible applications in terms of numerical simulations of particle-laden interfaces are discussed.Comment: 28 pages, 4 figure

Learning Mixtures of Gaussians in High Dimensions

Efficiently learning mixture of Gaussians is a fundamental problem in statistics and learning theory. Given samples coming from a random one out of k Gaussian distributions in Rn, the learning problem asks to estimate the means and the covariance matrices of these Gaussians. This learning problem arises in many areas ranging from the natural sciences to the social sciences, and has also found many machine learning applications. Unfortunately, learning mixture of Gaussians is an information theoretically hard problem: in order to learn the parameters up to a reasonable accuracy, the number of samples required is exponential in the number of Gaussian components in the worst case. In this work, we show that provided we are in high enough dimensions, the class of Gaussian mixtures is learnable in its most general form under a smoothed analysis framework, where the parameters are randomly perturbed from an adversarial starting point. In particular, given samples from a mixture of Gaussians with randomly perturbed parameters, when n > {\Omega}(k^2), we give an algorithm that learns the parameters with polynomial running time and using polynomial number of samples. The central algorithmic ideas consist of new ways to decompose the moment tensor of the Gaussian mixture by exploiting its structural properties. The symmetries of this tensor are derived from the combinatorial structure of higher order moments of Gaussian distributions (sometimes referred to as Isserlis' theorem or Wick's theorem). We also develop new tools for bounding smallest singular values of structured random matrices, which could be useful in other smoothed analysis settings

Is your model predicting the past?

When does a machine learning model predict the future of individuals and when does it recite patterns that predate the individuals? In this work, we propose a distinction between these two pathways of prediction, supported by theoretical, empirical, and normative arguments. At the center of our proposal is a family of simple and efficient statistical tests, called backward baselines, that demonstrate if, and to what extent, a model recounts the past. Our statistical theory provides guidance for interpreting backward baselines, establishing equivalences between different baselines and familiar statistical concepts. Concretely, we derive a meaningful backward baseline for auditing a prediction system as a black box, given only background variables and the system's predictions. Empirically, we evaluate the framework on different prediction tasks derived from longitudinal panel surveys, demonstrating the ease and effectiveness of incorporating backward baselines into the practice of machine learning.Comment: Code available at: https://github.com/socialfoundations/backward_baseline