Glück Auf! Fortuna und Risiko im frühneuzeitlichen Bergbau

As mining became more popular as a form of investment in the 16th century, the number of representations of mining scenes depicting the goddess Fortuna increased. She became a popular emblem of the promises, risks, and uncertainties of mining. The discursive and iconographical traditions of chance in the context of mining are borrowed from the fortuna di mare. The popularity of the maritime Fortuna stood in a close context with the emergence of the term risk in the late Middle Ages, which is closely connected to the sea trade and the social group of merchants and sailors. In the context of mining this image of fragile stability seems to have captured the imagination of those who, like the goddess, had to make quick moves to keep on top in the new world of 16th-century business with mineral resources. In this article I show how the concepts of hope, risk and chance were mediated through the figure of Fortuna between the sea and the mountains. In current research, however, a modernist perspective often connects the emergence of risk with the processes of secularization and growing self-awareness of tradesmen and merchants. My investigation instead concentrates on discourses about successful and failed mining investments, both in textual and visual sources, in order to investigate the vast semantic field of risk, hope and chances. This analysis reveals that the notion of Fortune in mining was inextricably tied up with Christian discourses on moral values and hope

The effect of wound instillation of a novel purified capsaicin formulation on postherniotomy pain: a double-blind, randomized, placebo-controlled study

BACKGROUND: Acute postoperative pain is common after most surgical procedures. Despite the availability of many analgesic options, postoperative pain management is often unsatisfactory. Purified capsaicin (ALGRX 4975 98% pure) has demonstrated prolong inhibition of C-fiber function in in vitro, preclinical, and clinical studies, and may be an effective adjunct to postoperative pain management. METHODS: We performed a single-center, randomized, double-blind, placebo-controlled study of the analgesic efficacy of a single intraoperative wound instillation of 1000 mu g ultrapurified capsaicin (ALGRX 4975) after open mesh groin hernia repair in 41 adult male patients. The primary end-point was average daily visual analog scale (VAS) pain scores during the first week after surgery assessed as area under the curve (AUC). Pain was recorded twice daily in a pain diary for 4 wk. Physical examination and laboratory tests were done before and I wk after surgery, together with recordings of adverse events up to 28 days. Adverse events were recorded. Data were also analyzed using a mixed-effects analysis with NONMEM. RESULTS: VAS AUC was significantly lower during the first 3 days postoperatively (P < 0.05), but not for the whole I or 4 wk postoperatively. Mixed-effects analysis with NONMEM revealed that pain scores were significantly lower (P < 0.05) in the capsaicin group during the first 4 days. No clinically significant serious adverse events were observed, although a mild transient increase in liver enzymes was seen more often in the capsaicin-treated group. CONCLUSION: In the setting of a well-defined analgesic protocol standard, VAS AUC analysis and a mixed-effect analysis showed superior analgesia of capsaicin relative to placebo during the first 3-4 days after inguinal hernia repair

Large deviations for a damped telegraph process

In this paper we consider a slight generalization of the damped telegraph process in Di Crescenzo and Martinucci (2010). We prove a large deviation principle for this process and an asymptotic result for its level crossing probabilities (as the level goes to infinity). Finally we compare our results with the analogous well-known results for the standard telegraph process

Tail asymptotics of light-tailed Weibull-like sums

Abstract: We consider sums of n i.i.d. random variables with tails close to exp{−x^β} for some β &gt; 1. Asymptotics developed by Rootzén (1987) and Balkema, Klüppelberg, and Resnick (1993) are discussed from the point of view of tails rather than of densities, using a somewhat different angle, and supplemented with bounds, results on a random number N of terms, and simulation algorithms

On Compound Poisson Processes Arising in Change-Point Type Statistical Models as Limiting Likelihood Ratios

Different change-point type models encountered in statistical inference for stochastic processes give rise to different limiting likelihood ratio processes. In a previous paper of one of the authors it was established that one of these likelihood ratios, which is an exponential functional of a two-sided Poisson process driven by some parameter, can be approximated (for sufficiently small values of the parameter) by another one, which is an exponential functional of a two-sided Brownian motion. In this paper we consider yet another likelihood ratio, which is the exponent of a two-sided compound Poisson process driven by some parameter. We establish, that similarly to the Poisson type one, the compound Poisson type likelihood ratio can be approximated by the Brownian type one for sufficiently small values of the parameter. We equally discuss the asymptotics for large values of the parameter and illustrate the results by numerical simulations

Convergence of the all-time supremum of a L\'evy process in the heavy-traffic regime

In this paper we derive a technique of obtaining limit theorems for suprema of L\'evy processes from their random walk counterparts. For each $a>0$, let $\{Y^{(a)}_n:n\ge 1\}$ be a sequence of independent and identically distributed random variables and $\{X^{(a)}_t:t\ge 0\}$ be a L\'evy processes such that $X_1^{(a)}\stackrel{d}{=} Y_1^{(a)}$, $\mathbb E X_1^{(a)}<0$ and $\mathbb E X_1^{(a)}\uparrow0$ as $a\downarrow0$. Let $S^{(a)}_n=\sum_{k=1}^n Y^{(a)}_k$. Then, under some mild assumptions, $\Delta(a)\max_{n\ge 0} S_n^{(a)}\stackrel{d}{\to} R\iff\Delta(a)\sup_{t\ge 0} X^{(a)}_t\stackrel{d}{\to} R$, for some random variable $R$ and some function $\Delta(\cdot)$. We utilize this result to present a number of limit theorems for suprema of L\'evy processes in the heavy-traffic regime

Quantum algorithm and circuit design solving the Poisson equation

The Poisson equation occurs in many areas of science and engineering. Here we focus on its numerical solution for an equation in d dimensions. In particular we present a quantum algorithm and a scalable quantum circuit design which approximates the solution of the Poisson equation on a grid with error \varepsilon. We assume we are given a supersposition of function evaluations of the right hand side of the Poisson equation. The algorithm produces a quantum state encoding the solution. The number of quantum operations and the number of qubits used by the circuit is almost linear in d and polylog in \varepsilon^{-1}. We present quantum circuit modules together with performance guarantees which can be also used for other problems.Comment: 30 pages, 9 figures. This is the revised version for publication in New Journal of Physic

Forecasting Player Behavioral Data and Simulating in-Game Events

Understanding player behavior is fundamental in game data science. Video games evolve as players interact with the game, so being able to foresee player experience would help to ensure a successful game development. In particular, game developers need to evaluate beforehand the impact of in-game events. Simulation optimization of these events is crucial to increase player engagement and maximize monetization. We present an experimental analysis of several methods to forecast game-related variables, with two main aims: to obtain accurate predictions of in-app purchases and playtime in an operational production environment, and to perform simulations of in-game events in order to maximize sales and playtime. Our ultimate purpose is to take a step towards the data-driven development of games. The results suggest that, even though the performance of traditional approaches such as ARIMA is still better, the outcomes of state-of-the-art techniques like deep learning are promising. Deep learning comes up as a well-suited general model that could be used to forecast a variety of time series with different dynamic behaviors

Area distribution and the average shape of a L\'evy bridge

We consider a one dimensional L\'evy bridge x_B of length n and index 0 < \alpha < 2, i.e. a L\'evy random walk constrained to start and end at the origin after n time steps, x_B(0) = x_B(n)=0. We compute the distribution P_B(A,n) of the area A = \sum_{m=1}^n x_B(m) under such a L\'evy bridge and show that, for large n, it has the scaling form P_B(A,n) \sim n^{-1-1/\alpha} F_\alpha(A/n^{1+1/\alpha}), with the asymptotic behavior F_\alpha(Y) \sim Y^{-2(1+\alpha)} for large Y. For \alpha=1, we obtain an explicit expression of F_1(Y) in terms of elementary functions. We also compute the average profile < \tilde x_B (m) > at time m of a L\'evy bridge with fixed area A. For large n and large m and A, one finds the scaling form = n^{1/\alpha} H_\alpha({m}/{n},{A}/{n^{1+1/\alpha}}), where at variance with Brownian bridge, H_\alpha(X,Y) is a non trivial function of the rescaled time m/n and rescaled area Y = A/n^{1+1/\alpha}. Our analytical results are verified by numerical simulations.Comment: 21 pages, 4 Figure