We examine two important measures that can be made in bioarcheology

We examine two important measures that can be made in bioarcheology on the remains of human and vertebrate animals. Like the concept that regular heart R-R interval data may indicate lack of health, low values of ApEn may indicate disrupted metabolism in individuals of archeological interest and even that a tipping point in deteriorating metabolism may have been reached just before death. This adds to the list of causes of death that can be determined from minimal data. 1. Introduction Big data sets are revolutionizing science. They promote insights, facilitate comprehension, and order priorities for further studies using models and powerful computers. In the past decade important advances have been made using big data sets; they range from astronomy to climate change and from biology to geology. Bioarcheology, however, Magnolol has not benefited from this trend, seemingly, because big data in bioarcheology are difficult to obtain. Bioarcheology, as defined here, is cross-disciplinary research encompassing the study of human and animal remains. The best preserved tissues are bones, teeth, and occasionally hair. Here we show that such archived materials provide sufficient data to model life’s activities such as metabolism, growth, and biologic rhythms of individuals who have died decades or even millennia ago. Many preserved tissues have growth marks left during life which reflect the rates of growth and by extension metabolism. For example, there are scale like markings on hair shafts which occur at more or less regular intervals which can be measured (Figure 1). Similarly on teeth surfaces or bone sections growth lines can easily be discerned. For all of these we use the term repeat intervals (RIs) from Bromage et al. [1] to denote the histological evidence on archived remains that betray life’s activities such as metabolism and growth. Figure 1 Human hair with repeat intervals (RIs) marked in green, 50?Perikymata Grooves Striae of Retzius(SR) in the enamel in human teeth and growth lines in archosaur teeth provide other time series [1, 2, 5]. In addition, there are time series of osteocyte density in bone [6]. Oxygen, hydrogen, or carbon isotope ratios as well as Magnolol other chemicals in hair measured along fixed intervals in the direction of growth provide time series. Here we use spectral analysis of such time series as proxies of metabolism, which provide insight into dynamic processes in operation in the individual’s past life. 2. Materials and Methods The annual growth rate can often be computed in the time domain. 2.1. Annual Growth Rate and Preprocessing Forensic Time Series The forensic time series may be discrete time = 1,, = = 1,, = from a continuous time process such as chemicals measured in successive sections of bone of equal length = 1, so that in both cases we have a discrete time series {versus time versus and replacing the series by its residuals thereafter. The mean of the series is subtracted; the mean corresponds to the power at the zero frequency on the spectra, but our interest in spectral analysis sets aside consideration of the mean for separate analysis. {The next step in standardizing the time series {versus distance along the hair shows an obvious annual cycle,|The next step in standardizing the right time series versus distance along the hair shows an obvious annual cycle, then we can proceed directly to computing the annual growth rate of the hair. Example 1 (mammoth). The hydrogen isotope ratio measurements (= ?158 ?0.727 ??cm + 8.69???sin (?0.196 ??cm + 3.98) as reported in [7]. The frequency of the sinusoid is 0.196 radians/cm. Epha6 Converting radians to cycles we have frequency = (0.196 radians/cm)/(2radians/cycle) = 0.0312 cycles/cm. This times the annual growth rate (cm/year) gives the number of cycles per year, which is equated to 1 cycle/year. Thus = 0.3?cm. Now we give the spectral parameter definitions. To be explicit, let the discrete time, stationary, Gaussian time series representing a series of measured intervals be {= 1, , is the frequency on the as a function of has a frequency (radians per unit of by 2radians per cycle gives Magnolol a unit of cycle per observation as an alternative scale. For heartbeat, the frequency unit would be cycles per RR interval. For teeth, frequency units would be cycles per PG deposition (SR, Lines of Anderson (LA), or GL deposition). For the mammoth hair, the frequency units would be cycles per increment. The units of the periodogram (and the spectral density) can be seen from the fact (proof not Magnolol shown) that the sum of is the variance of the gets larger. Thus, the usual (and better) estimate of = 0 by definition (definition not shown) and 2= 2and the = 2/is the coefficient in (2). Let us return to the mammoth example; the estimate of the spectral density of.