Interdependent Durations

This paper studies the identification of a simultaneous equation model where the variable of interest is a duration measure. It proposes a game theoretic model in which durations are determined by strategic agents. In the absence of strategic motives, the model delivers a version of the generalized accelerated failure time model. In its most general form, the system resembles a classical simultaneous equation model in which endogenous variables interact with observable and unobservable exogenous components to characterize a certain economic environment. In this paper, the endogenous variables are the individually chosen equilibrium durations. Even though a unique solution to the game is not always attainable in this context, the structural elements of the economic system are shown to be semiparametrically point identified. We also present a brief discussion of estimation ideas and a set of simulation studies on the model.duration, empirical games, identification

Statistics of seismic cluster durations

Using the standard ETAS model of triggered seismicity, we present a rigorous theoretical analysis of the main statistical properties of temporal clusters, defined as the group of events triggered by a given main shock of fixed magnitude m that occurred at the origin of time, at times larger than some present time t. Using the technology of generating probability function (GPF), we derive the explicit expressions for the GPF of the number of future offsprings in a given temporal seismic cluster, defining, in particular, the statistics of the cluster's duration and the cluster's offsprings maximal magnitudes. We find the remarkable result that the magnitude difference between the largest and second largest event in the future temporal cluster is distributed according to the regular Gutenberg-Richer law that controls the unconditional distribution of earthquake magnitudes. For earthquakes obeying the Omori-Utsu law for the distribution of waiting times between triggering and triggered events, we show that the distribution of the durations of temporal clusters of events of magnitudes above some detection threshold \nu has a power law tail that is fatter in the non-critical regime $n<1$ than in the critical case n=1. This paradoxical behavior can be rationalised from the fact that generations of all orders cascade very fast in the critical regime and accelerate the temporal decay of the cluster dynamics.Comment: 45 pages, 15 figure

The Visual Mechanisms of Tenebrio Molitor: Changes in the Electro-Retinogram as Function of the Stimulus Duration

The ERG complex of the compound eye of the yellow mealworm bettle Tenebrimolitor (L.) separates into two components with stimulus durations of longer than 100 ms. These are the ‘on’ and the ‘off’ effects. Above stimulus durations of 1 s the positive potential following the ‘on’ is faster and the positive ‘off’ is followed by a small negative one. The latent period of the ‘on’ is independent of the stimulus duration while for stimulus durations of longer than 300 ms the ‘off’ latency is coupled with the end of the stimulus. If measured after the extinction of the stimulus the ‘off’ latency is affected by the stimulus duration. The ‘on’ and ‘off’ amplitudes behave similarly for various stimulus durations. Both originate in the receptor cells. The Bunsen-Roscoe Law of photochemistry holds for stimulus durations of 10-40 ms. For a given intensity, the amplitudes diminished for durations longer than 300 ms

Detrended fluctuation analysis of intertrade durations

The intraday pattern, long memory, and multifractal nature of the intertrade durations, which are defined as the waiting times between two consecutive transactions, are investigated based upon the limit order book data and order flows of 23 liquid Chinese stocks listed on the Shenzhen Stock Exchange in 2003. An inverse $U$-shaped intraday pattern in the intertrade durations with an abrupt drop in the first minute of the afternoon trading is observed. Based on the detrended fluctuation analysis, we find a crossover of power-law scaling behaviors for small box sizes (trade numbers in boxes) and large box sizes and strong evidence in favor of long memory in both regimes. In addition, the multifractal nature of intertrade durations in both regimes is confirmed by a multifractal detrended fluctuation analysis for individual stocks with a few exceptions in the small-duration regime. The intraday pattern has little influence on the long memory and multifractaility.Comment: 15 Elsart pages including 4 figures and 1 tabl

Does the value of quality of life depend on duration?

The aims of this study are to investigate the feasibility of eliciting Time Trade Off (TTO) valuations using short durations; to determine the effect of contrasting durations on individuals’ responses to the TTO; to examine variations within and between respondents’ values with respect to duration; and to consider the insights provided by participants’ comments and explanations regarding their reaction to duration in the valuation task. 27 participants provided TTO values using short and long durations for three EQ-5D states. Feedback was sought using a series of open ended questions. Of the 81 opportunities to observe it, strict constant proportionality was satisfied twice. 11 participants had no systematic relationship between duration and value; 11 provided consistently lower valuations in long durations, while 5 had higher valuations in long durations. Comments provided by participants were consistent with the values they provided. Mean TTO values did not differ markedly between alternative durations. We conclude that it is feasible to elicit TTO values for short durations. There is considerable heterogeneity in individuals’ responses to the time frames used to elicit values. Further research is required to ensure that the values used in cost effectiveness analysis adequately represent preferences about quality and length of life

Dissociable neuroanatomical correlates of subsecond and suprasecond time perception

The ability to estimate durations varies across individuals. Although previous studies have reported that individual differences in perceptual skills and cognitive capacities are reflected in brain structures, it remains unknown whether timing abilities are also reflected in the brain anatomy. Here, we show that individual differences in the ability to estimate subsecond and suprasecond durations correlate with gray matter (GM) volume in different parts of cortical and subcortical areas. Better ability to discriminate subsecond durations was associated with a larger GM volume in the bilateral anterior cerebellum, whereas better performance in estimating the suprasecond range was associated with a smaller GM volume in the inferior parietal lobule. These results indicate that regional GM volume is predictive of an individual's timing abilities. These morphological results support the notion that subsecond durations are processed in the motor system, whereas suprasecond durations are processed in the parietal cortex by utilizing the capacity of attention and working memory to keep track of time

Human comfort in relation to sinusoidal vibration

An investigation was made to assess the overall subjective comfort levels to sinusoidal excitations over the range 1 to 19 Hz using a two axis electrohydraulic vibration simulator. Exposure durations of 16 minutes, 25 minutes, 1 hour, and 2.5 hours have been considered. Subjects were not exposed over such durations, but were instructed to estimate the overall comfort levels preferred had they been constantly subjected to vibration over such durations