Riggs on strong justification

In 'The Weakness of Strong Justification' Wayne Riggs claims that the requirement that justified beliefs be truth conducive (likely to be true) is not always compatible with the requirement that they be epistemically responsible (arrived at in an epistemically responsible manner)1. He supports this claim by criticising Alvin Goldman's view that if a belief is strongly justified, it is also epistemically responsible. In light of this, Riggs recommends that we develop two independent conceptions of justification, one that insists upon the requirement that beliefs be truth conducive and another that insists that they be epistemically responsible. It will then, on his view, be possible to properly evaluate beliefs with regard to each conception of justification. Riggs, however, is mistaken in supposing that the two epistemic requirements are independent. If a belief is responsibly arrived at, it is therefore likely to be true. He is thus also mistaken in supposing that the two epistemic requirements are incompatible. This mistake arises because Riggs assumes that justification is possible or, at least, that it involves standards that are akin to our own. Moreover, once this assumption is made explicit, we can see why a notion of justification that connects epistemic practice with likely truth is significant

Large Deviations of the Smallest Eigenvalue of the Wishart-Laguerre Ensemble

We consider the large deviations of the smallest eigenvalue of the Wishart-Laguerre Ensemble. Using the Coulomb gas picture we obtain rate functions for the large fluctuations to the left and the right of the hard edge. Our findings are compared with known exact results for $\beta=1$ finding good agreement. We also consider the case of almost square matrices finding new universal rate functions describing large fluctuations.Comment: 4 pages, 2 figure

Roughness of moving elastic lines - crack and wetting fronts

We investigate propagating fronts in disordered media that belong to the universality class of wetting contact lines and planar tensile crack fronts. We derive from first principles their nonlinear equations of motion, using the generalized Griffith criterion for crack fronts and three standard mobility laws for contact lines. Then we study their roughness using the self-consistent expansion. When neglecting the irreversibility of fracture and wetting processes, we find a possible dynamic rough phase with a roughness exponent of $\zeta=1/2$ and a dynamic exponent of z=2. When including the irreversibility, we conclude that the front propagation can become history dependent, and thus we consider the value $\zeta=1/2$ as a lower bound for the roughness exponent. Interestingly, for propagating contact line in wetting, where irreversibility is weaker than in fracture, the experimental results are close to 0.5, while for fracture the reported values of 0.55--0.65 are higher.Comment: 15 pages, 6 figure

A comparative study of crumpling and folding of thin sheets

Crumpling and folding of paper are at rst sight very di erent ways of con ning thin sheets in a small volume: the former one is random and stochastic whereas the latest one is regular and deterministic. Nevertheless, certain similarities exist. Crumpling is surprisingly ine cient: a typical crumpled paper ball in a waste-bin consists of as much as 80% air. Similarly, if one folds a sheet of paper repeatedly in two, the necessary force becomes so large that it is impossible to fold it more than 6 or 7 times. Here we show that the sti ness that builds up in the two processes is of the same nature, and therefore simple folding models allow to capture also the main features of crumpling. An original geometrical approach shows that crumpling is hierarchical, just as the repeated folding. For both processes the number of layers increases with the degree of compaction. We nd that for both processes the crumpling force increases as a power law with the number of folded layers, and that the dimensionality of the compaction process (crumpling or folding) controls the exponent of the scaling law between the force and the compaction ratio.Comment: 5 page

The spectrum of large powers of the Laplacian in bounded domains

We present exact results for the spectrum of the Nth power of the Laplacian in a bounded domain. We begin with the one dimensional case and show that the whole spectrum can be obtained in the limit of large N. We also show that it is a useful numerical approach valid for any N. Finally, we discuss implications of this work and present its possible extensions for non integer N and for 3D Laplacian problems.Comment: 13 pages, 2 figure

Longest increasing subsequence as expectation of a simple nonlinear stochastic PDE with a low noise intensity

We report some new observation concerning the statistics of Longest Increasing Subsequences (LIS). We show that the expectation of LIS, its variance, and apparently the full distribution function appears in statistical analysis of some simple nonlinear stochastic partial differential equation (SPDE) in the limit of very low noise intensity.Comment: 6 pages, 4 figures, reference adde

Оппозиция концептов жизнь-смерть в смысловой организации петербургского текста русской культуры

Цель исследования – рассмотрение ведущей для организации Петербургского текста оппозиции концептов жизнь-смерть, члены которой получают репрезентацию в составляющих единство текстах А.С. Пушкина, Н.В. Гоголя, Ф.М. Достоевского, А.А. Блока, А.А. Ахматовой, О.Э. Мандельштама, Т.Н. Толстой и др. и участвуют в создании их общего смыслового пространства. Данные концепты оказываются ключевыми для понимания сверхтекста, герои которого вынуждены выбирать между смертью и жизнью, полной страданий.The article is devoted to the opposition of concepts life-death that plays the main part in Petersburg text’s organization. These concepts appear in texts written by A.S. Pushkin, N.V. Gogol, P.M. Dostoevsky, A.A. Blok, A.A. Ahmatova, O.E. Mandelshtam, T.N. Tolstaya etc. and help to unite their semantic space. The analysis of concepts life-death is necessary to understand the super-text which main characters have to choose between death and hard life

Fracture Roughness Scaling: a case study on planar cracks

Using a multi-resolution technique, we analyze large in-plane fracture fronts moving slowly between two sintered Plexiglas plates. We find that the roughness of the front exhibits two distinct regimes separated by a crossover length scale $\delta^*$. Below $\delta^*$, we observe a multi-affine regime and the measured roughness exponent $\zeta_{\parallel}^{-} = 0.60\pm 0.05$ is in agreement with the coalescence model. Above $\delta^*$, the fronts are mono-affine, characterized by a roughness exponent $\zeta_{\parallel}^{+} = 0.35\pm0.05$, consistent with the fluctuating line model. We relate the crossover length scale to fluctuations in fracture toughness and the stress intensity factor

Self Consistent Expansion for the Molecular Beam Epitaxy Equation

Motivated by a controversy over the correct results derived from the dynamic renormalization group (DRG) analysis of the non linear molecular beam epitaxy (MBE) equation, a self-consistent expansion (SCE) for the non linear MBE theory is considered. The scaling exponents are obtained for spatially correlated noise of the general form $D({\vec r - \vec r',t - t'}) = 2D_0 | {\vec r - \vec r'} |^{2\rho - d} \delta ({t - t'})$. I find a lower critical dimension $d_c (\rho) = 4 + 2\rho$, above, which the linear MBE solution appears. Below the lower critical dimension a r-dependent strong-coupling solution is found. These results help to resolve the controversy over the correct exponents that describe non linear MBE, using a reliable method that proved itself in the past by predicting reasonable results for the Kardar-Parisi-Zhang (KPZ) system, where DRG failed to do so.Comment: 16 page

Nonlinear field theories during homogeneous spatial dilation

The effect of a uniform dilation of space on stochastically driven nonlinear field theories is examined. This theoretical question serves as a model problem for examining the properties of nonlinear field theories embedded in expanding Euclidean Friedmann-Lema\^{\i}tre-Robertson-Walker metrics in the context of cosmology, as well as different systems in the disciplines of statistical mechanics and condensed matter physics. Field theories are characterized by the speed at which they propagate correlations within themselves. We show that for linear field theories correlations stop propagating if and only if the speed at which the space dilates is higher than the speed at which correlations propagate. The situation is in general different for nonlinear field theories. In this case correlations might stop propagating even if the velocity at which space dilates is lower than the velocity at which correlations propagate. In particular, these results imply that it is not possible to characterize the dynamics of a nonlinear field theory during homogeneous spatial dilation {\it a priori}. We illustrate our findings with the nonlinear Kardar-Parisi-Zhang equation