Super-Brownian motion with extra birth at one point

A super-Brownian motion in two and three dimensions is constructed where "particles" give birth at a higher rate, if they approach the origin. Via a log-Laplace approach, the construction is based on Albeverio et al. (1995) who calculated the fundamental solutions of the heat equation with one-point potential in dimensions less than four

On the large scale behavior of super-Brownian motion in three dimensions with a single point source

In a recent work, Fleischmann and Mueller (2004) showed the existence of a super-Brownian motion in R^d, d=2,3, with extra birth at the origin. Their construction made use of an analytical approach based on the fundamental solution of the heat equation with a one point potential worked out by Albeverio et al. (1995). The present note addresses two properties of this measure-valued process in the three-dimensional case, namely the scaling of the process and the large scale behavior of its mean

Force Statistics and Correlations in Dense Granular Packings

In dense, static, polydisperse granular media under isotropic pressure, the probability density and the correlations of particle-wall contact forces are studied. Furthermore, the probability density functions of the populations of pressures measured with different sized circular pressure cells is examined. The questions answered are: (i) What is the number of contacts that has to be considered so that the measured pressure lies within a certain error margin from its expectation value? (ii) What is the statistics of the pressure probability density as function of the size of the pressure cell? Astonishing non-random correlations between contact forces are evidenced, which range at least 10 to 15 particle diameter. Finally, an experiment is proposed to tackle and better understand this issue.Comment: 10 pages, 12 figure

East European studies, neo-totalitarianism and social science theory

The relevance of sociological theory for explaining the recent dramatic changes in Eastern Europe is at hand. The impact of the downfall of communism has been compared with those Great Transformations along which sociology evolved as a science of crisis par excellence (Habermas). The actual elaboration of a sociological theory of post-communist transformation and its relation to East European studies is, nevertheless, anything but clear. The unexpected collapse of socialism was perceived as a failure of prognosis and led to self-critical debates in all social science disciplines. In this rethinking its basic concepts, sociology is exposed to pressure from different sides - above all from the polemic launched with the surprising revival of the theory of totalitarianism against the ,,liberalist social sciences across the board. Influential historians like Robert Pipes, Martin Malia, Robert Conquest, and Francois Furet followed by sociologists from Robert Nisbet to Seymour Lipset hold the fatal influence exerted by social science concepts on Eastern European and Soviet Studies during the last decades responsible for the whole intellectual disaster in Western Academe which became apparent after 1989. These approaches, as the neo-totalitarian accusation runs, elevated Soviet socialism to a modernization strategy and conceded a reform capacity which, in fact, was not available. Target of this critique are all attempts of a social history from below, sociological theories of action and especially the positivist illusion of modernization theory. Blinded by political motives, it is said, the insights of (neo-)totalitarianism theory into the inevitable collapse of communism were dismissed. In order to correctly draw the lines in the controversies between neototalitarianism theory and the social science approach, it is helpful to follow them along the changing career of the concept of totalitarianism thereby reconstructing the sociological arguments involved in the current discussion on the disintegration of socialist societies. On this line it will be argued (section 2), that the crisis of the classic theory of totalitarianism and the social science approach in Soviet studies did not follow from a politically motivated revisionism since the 1960s and 1970s. Analysing the socialist societies after 1945 was shaped from the very beginning by sociological, political science and economic models, which contrasted with fundamental assumptions of the classic concept of totalitarianism (section 3). The findings generated by this type of research as well as its limits are revealed when it comes to explaining the disintegration of Soviet socialism. The neo-totalitarianist's objection is correct that ranging socialism in an evolutionary scheme of ascending forms of society was problematic. This construction seems highly inadequate in view of the postcommunist crises and regressions (section 4). On the other hand, a coherent and self-reliant neo-totalitarianism theory is not visible (section 5). Instead the research on Eastern Europe after 1989 has seen an explosive growth of the social science approach in the course of which many revisionist theorems have been refuted, modified or confirmed. Nevertheless, the wave of social science theories entering the post-communist studies does not imply a way back to the golden age of classic modernization theory. The lesson to be learned from (neo-)totalitarianism theory concerns the stress it lays on domination and its specific irrationalities, variables which were indeed neglected by mainstream sociology and, after the Soviet breakdown, are ignored by the liberalist optimism of neoclassic reform programmes. The drama of the post-communist crises reminds us that there are no hidden hands and no evolutionary universals which would lead, quasi automatically, to modernity. On the other hand, the lesson to be learned from the social science approach is that even the most total totalitarianism did not result from a logic of history, but from certain constellations of interests, reciprocities between rulers and ruled, institutions of administration and value commitments, etc. which are quite accessible to a reconstruction in sociological terms

Two interacting particles in a random potential: mapping onto one parameter localization theories without interaction

We consider two models for a pair of interacting particles in a random potential: (i) two particles with a Hubbard interaction in arbitrary dimensions and (ii) a strongly bound pair in one dimension. Establishing suitable correpondences we demonstrate that both cases can be described in terms familiar from theories of noninteracting particles. In particular, these two cases are shown to be controlled by a single scaling variable, namely the pair conductance $g_2$. For an attractive or repulsive Hubbard interaction and starting from a certain effective Hamiltonian we derive a supersymmetric nonlinear $\sigma$ model. Its action turns out to be closely related to the one found by Efetov for noninteracting electrons in disordered metals. This enables us to describe the diffusive motion of the particle pair on scales exceeding the one-particle localization length $L_1$ and to discuss the corresponding level statistics. For tightly bound pairs in one dimension, on the other hand, we follow early work by Dorokhov and exploit the analogy with the transfer matrix approach to quasi 1d conductors. Extending our study to M particles we obtain a M-particle localization length scaling like the Mth power of the one-particle localization length.Comment: 29 pages, Revtex, no figure

Beyond saliency: understanding convolutional neural networks from saliency prediction on layer-wise relevance propagation

Despite the tremendous achievements of deep convolutional neural networks (CNNs) in many computer vision tasks, understanding how they actually work remains a significant challenge. In this paper, we propose a novel two-step understanding method, namely Salient Relevance (SR) map, which aims to shed light on how deep CNNs recognize images and learn features from areas, referred to as attention areas, therein. Our proposed method starts out with a layer-wise relevance propagation (LRP) step which estimates a pixel-wise relevance map over the input image. Following, we construct a context-aware saliency map, SR map, from the LRP-generated map which predicts areas close to the foci of attention instead of isolated pixels that LRP reveals. In human visual system, information of regions is more important than of pixels in recognition. Consequently, our proposed approach closely simulates human recognition. Experimental results using the ILSVRC2012 validation dataset in conjunction with two well-established deep CNN models, AlexNet and VGG-16, clearly demonstrate that our proposed approach concisely identifies not only key pixels but also attention areas that contribute to the underlying neural network's comprehension of the given images. As such, our proposed SR map constitutes a convenient visual interface which unveils the visual attention of the network and reveals which type of objects the model has learned to recognize after training. The source code is available at https://github.com/Hey1Li/Salient-Relevance-Propagation.Comment: 35 pages, 15 figure