First Digit Distribution of Hadron Full Width

A phenomenological law, called Benford's law, states that the occurrence of the first digit, i.e., $1,2,...,9$, of numbers from many real world sources is not uniformly distributed, but instead favors smaller ones according to a logarithmic distribution. We investigate, for the first time, the first digit distribution of the full widths of mesons and baryons in the well defined science domain of particle physics systematically, and find that they agree excellently with the Benford distribution. We also discuss several general properties of Benford's law, i.e., the law is scale-invariant, base-invariant, and power-invariant. This means that the lifetimes of hadrons follow also Benford's law.Comment: 8 latex pages, 4 figures, final version in journal publicatio

Tracking the Equator Into the Paleogene (abstract of paper presented at AGU Fall Meeting, San Francisco, 8-12 Dec 2003)

Stratigraphy has been compiled for 63 tropical Pacific drill sites that sample lower Neogene and Paleogene sediments. These Sites derive from drilling on DSDP Leg 5 through ODP Leg 199. All Sites have been put on the biostratigraphic and paleomagnetic timescale refined by Leg 199 scientists. Sediment accumulation rates have been calculated for ten intervals ranging in age from 10 Ma to 56 Ma. A simple fixed hotspot model was used for Pacific lithospheric plate rotation in reconstructing the position of the selected sites for each of these ten intervals. The reconstruction of all intervals show the development of a tongue of relatively high accumulation rates associated with the oceanographic divergence at the geographic equator. The estimated position of the geographic equator based on these reconstructions lies consistently south of the position of the equator based on the rotation model used. However, the southward displacement is generally 2 degrees of latitude or less. We believe that this relatively small disagreement between the two estimates of equatorial position back to 56 Ma indicates: 1) Whatever hotspot movement that may have occurred in the interval between 40 and 56 Ma did not affect the motion of the Pacific plate; its motion after 40 Ma appears to have been approximately the same as before 40 Ma. 2) The estimated rate of true polar wander during the interval of 40 - 56 Ma must be very small (~0.125$\deg$/m.y.) and is probably not significant (i.e., well within the error of these reconstructions)

The leading digit distribution of the worldwide Illicit Financial Flows

Benford's law states that in data sets from different phenomena leading digits tend to be distributed logarithmically such that the numbers beginning with smaller digits occur more often than those with larger ones. Particularly, the law is known to hold for different types of financial data. The Illicit Financial Flows (IFFs) exiting the developing countries are frequently discussed as hidden resources which could have been otherwise properly utilized for their development. We investigate here the distribution of the leading digits in the recent data on estimates of IFFs to look for the existence of a pattern as predicted by Benford's law and establish that the frequency of occurrence of the leading digits in these estimates does closely follow the law.Comment: 13 pages, 10 figures, 6 tables, additional data analyi

Site 1216

Site 1216 (21°27.16´N, 139°28.79´W; 5152 meters below sea level [mbsl]; Fig. F1) is situated in abyssal hill topography south of the Molokai Fracture Zone and two small associated unnamed parasitic fracture zones (Fig. F2). Based on magnetic lineations, Site 1216 appears to be situated on normal ocean crust formed during the C25r magnetic anomaly (~57 Ma; Atwater and Severinghaus, 1989). Site 1216 was chosen for drilling because it is near the thickest section of lower Eocene sediments along the 56-Ma transect, which was based upon the seismic stratigraphy of seismic reflection data acquired on site survey cruise EW9709 during transits between the proposed drill sites (Lyle et al., this volume; Moore et al., 2002). The Cenozoic history of sedimentation in this region was poorly constrained prior to Leg 199, being largely based on two Deep Sea Drilling Project (DSDP) drill sites (40 and 41) and piston core data (EW9709-3PC) from ~1.5° in latitude to the south. Based on data from these drill sites, we expected the sedimentary sequence at Site 1216 to comprise red clays (a mixture of wind-blown dust and authigenic precipitates) overlying a biogenic sediment section composed of an upper middle Eocene radiolarian ooze and lower carbonate ooze deposited when the site was near the ridge crest in the late Paleocene and early Eocene. The broad paleoceanographic objectives of drilling the sedimentary sequence anticipated at Site 1216 are as follows: (1) to help define the shift in the Intertropical Convergence Zone through the Paleogene by following the change in eolian-dust composition and flux through time (red clays) and (2) to help define the latitudinal extent, composition, and mass accumulation of plankton communities in the north equatorial Pacific region thereby constraining ocean circulation patterns and the extent of the equatorial high-productivity belt in the Eocene ocean. Results from Site 1216 will also provide important information to test whether there was significant motion of the Hawaiian hotspot with respect to the Earth's spin axis during the early Cenozoic. At 56 Ma, the backtracked location of Site 1216 based upon a hotspot reference frame (Gripp and Gordon, 1990, for 0- to 5-Ma Pacific hotspot rotation pole; Engebretson et al., 1985, for older poles) is about 9°N, 108°W. If significant hotspot motion or true polar wander occurred since 57 Ma (Petronotis et al., 1994), this drill site could have been much nearer to the equator

Site 1220

Site 1220 (10°10.600´N, 142°45.503´W; 5218 meters below sea level (mbsl); Fig. F1) forms a southerly component of the 56-Ma transect drilled during Leg 199. It is situated about midway between the Clipperton and Clarion Fracture Zones in typical abyssal hill topography. On the basis of regional magnetic anomalies, we anticipated basement age at Site 1220 to be equivalent to Chron C25n (~56 Ma; Cande et al., 1989), slightly older than at Site 1219. At the outset of drilling at Site 1220, our estimate for total sediment depth was ~225 meters below seafloor (mbsf) (Fig. F2). Based upon a fixed hotspot model (Gripp and Gordon, 1990, for 0- to 5-Ma Pacific hotspot rotation pole; Engebretson et al., 1985, for older poles), Site 1220 should have been located ~3° south of the equator at 56 Ma and in an equatorial position at 40 Ma. Thus, Site 1220 should have been situated underneath the South Equatorial Current in the early Eocene. A nearby piston core (EW9709-13PC) taken during the site survey cruise recovered >16 m of red clay, with the base of the core dated as middle-early Miocene on the basis of radiolarian biostratigraphy (Lyle, 2000). Site 1220 will be used to study equatorial ocean circulation from the late Paleocene through the late Eocene during the early Cenozoic thermal maximum. Sediment records from this site will help to define the calcite compensation depth (CCD) and lysocline during the Paleocene-Eocene and Eocene-Oligocene transitions. In this and other respects, Site 1220 will act as an interesting analog to Site 1218. Both sites are thought to have been located on the equator at ~40 Ma, but the older crustal age anticipated at Site 1220 dictates a greater paleowater depth than for contemporaneous sediments accumulating at Site 1218

Site 1222

Site 1222 (13°48.98´N, 143°53.35´W; 4989 meters below sea level [mbsl]; Fig. F1) forms a south-central component of the 56-Ma transect drilled during Leg 199 and is situated ~2° south of the Clarion Fracture Zone in typical abyssal hill topography. On the basis of regional magnetic anomalies, we anticipated basement age at Site 1222 to be equivalent to Chron C25r or Chron C25n (~56-57 Ma) (Cande et al., 1989), which is slightly older than at Site 1219. At the outset of drilling at Site 1222, our estimate for total sediment thickness was ~115 m (Fig. F2). Based upon a fixed hotspot model (Gripp and Gordon, 1990, for 0- to 5-Ma Pacific hotspot rotation pole; Engebretson et al., 1985, for older poles) Site 1222 should have been located ~1° north of the equator at 56 Ma and ~4°N at 40 Ma. A nearby gravity core (EW9709-17GC), taken during the site survey cruise, recovered >5 m of red clay with a late-middle Miocene age on the basis of radiolarian biostratigraphy (Lyle, 2000). Deep Sea Drilling Project (DSDP) Site 42 located ~4° east of Site 1222, was not drilled to basement but contains a thin sedimentary section (~100 m thick) of upper Oligocene nannofossil ooze through middle Eocene radiolarian nannofossil ooze. In turn, DSDP Site 162 lies ~1° north of DSDP Site 42 and is situated on young crust (49 Ma) that contains ~150 m of clayey radiolarian and nannofossil oozes of early Oligocene-middle Eocene age. Site 1222 will be used to study the position of the Intertropical Convergence Zone in the late Eocene and Oligocene, to sample late Paleocene and early Eocene sediments in the central tropical Pacific Ocean, and to help determine whether or not there has been significant southward movement of the hotspots with respect to the spin axis prior to 40 Ma

Site 1217

Site 1217 (16°52.02´N, 138°06.00´W; 5342 meters below sea level [mbsl]; Fig. F1) is one of seven sites drilled to target upper Paleocene crust along a latitudinal transect during Leg 199 and will be used to investigate paleoceanographic processes in the northern tropical early Eocene Pacific Ocean. Site 1217 is situated ~1° north of the Clarion Fracture Zone on abyssal hill topography typical of the central Pacific. Based on magnetic lineations, basement age at Site 1217 should be in magnetic Anomaly C25r or ~57 Ma (Cande et al., 1989; timescale of Cande and Kent, 1995). The Cenozoic history of sedimentation in this region was poorly constrained prior to Leg 199 drilling because the nearest drill site (Deep Sea Drilling Project [DSDP] Site 162) is situated ~300 km south and west on 48-Ma crust. Based on data from this early rotary-cored hole, magnetic anomaly maps, a shallow-penetration piston core near Site 1217 (EW9709-4PC), and seismic profiling (Fig. F2), we expected the sedimentary sequence at Site 1217 to comprise a relatively thick (25 to 35 m thick) section of red clays overlying a radiolarian ooze and a basal carbonate section with possible chert near basement (estimated total depth ~125-150 meters below seafloor [mbsf]) deposited when the site was near the ridge crest in the late Paleocene and early Eocene. Site 1217 was chosen because it is anticipated to have been located just outside of the equatorial region at 56 Ma, ~5°N, 106°W based upon a fixed hotspot model (Gripp and Gordon, 1990, for 0- to 5-Ma Pacific hotspot rotation pole; Engebretson et al., 1985, for older poles). On the same basis at 40 Ma, the site was located at ~8°N, 111°W. Thus, Site 1217 should help define the paleoceanography of the northern tropical Pacific, in particular locating the ancient North Equatorial Countercurrent (NECC) region. General circulation-model experiments for the early Eocene (see Huber, this volume) suggest that the NECC was a well-developed current during this time period. Other paleoceanographic and paleoclimatic objectives of drilling the sedimentary sequence anticipated at Site 1217 are as follows: (1) to help define the shift in the Intertropical Convergence Zone through the Paleogene by following the change in eolian dust composition and flux through time (red clays); (2) to help constrain the middle-late Eocene calcite compensation depth (CCD); and (3) to sample the Paleocene/Eocene (P/E) boundary, one of the most climatologically critical intervals of Cenozoic time. Recovery of deep-sea sediments from this time interval during Leg 199 is a high priority because the P/E boundary has never before been sampled in the central tropical Pacific Ocean. Results from Site 1217 will also provide important information to test whether there was significant motion of the Hawaiian hotspot, with respect to the Earth's spin axis during the early Cenozoic. At 56 Ma, the backtracked location based upon a hotspot reference frame is ~5°N, 106°W, and at 40 Ma is ~8°N, 106°W. If significant hotspot motion or true polar wander occurred since 57 Ma (Petronotis et al., 1994), this drill site could have been much nearer to the equator

Geochemical analysis of bulk marine sediment by Inductively Coupled Plasma–Atomic Emission Spectroscopy on board the JOIDES Resolution

Geochemical analyses on board the JOIDES Resolution have been enhanced with the addition of a Jobin-Yvon Ultrace inductively coupled plasma-atomic emission spectrometer (ICP-AES) as an upgrade from the previous X-ray fluorescence facility. During Leg 199, we sought to both challenge and utilize the capabilities of the ICP-AES in order to provide an extensive bulk-sediment geochemical database during the cruise. These near real-time analyses were then used to help characterize the recovered sedimentary sequences, calculate mass accumulation rates of the different sedimentary components, and assist with cruise and postcruise sampling requests. The general procedures, sample preparation techniques, and basic protocol for ICP-AES analyses on board ship are outlined by Murray et al. (2000) in Ocean Drilling Program Tech Note, 29. We expand on those concepts and offer suggestions for ICP-AES methodology, calibration by standard reference materials, data reduction procedures, and challenges that are specific to the analysis of bulk-sediment samples. During Leg 199, we employed an extensive bulk-sediment analytical program of ~600 samples of varying lithologies, thereby providing several opportunities for refinement of techniques. We also discuss some difficulties and challenges that were faced and suggest how to alleviate such occurrences for sedimentary chemical analyses during future legs

Diversité des familles de radiolaires au cours du temps

L’examen de la biodiversité des radiolaires, au niveau de la famille au cours du Phanérozoïque révèle quelques tendances générales connues chez d’autres groupes d’organismes, surtout dans le plancton, alors que d’autres tendances leur sont particulières. La crise permo-triasique, l’une des plus importantes dans l’évolution des organismes marins, est marquée chez les radiolaires par l’extinction de deux familles (Albaillellaria et Latentifistularia) vers la fin du Permien, mais surtout par une énorme diversification des spumellaires et nassellaires au Trias inférieur et moyen. La diversité des radiolaires s’accroît du Cambrien au Jurassique, reste relativement stable au Crétacé et décroît légèremen

Benford's law predicted digit distribution of aggregated income taxes: the surprising conformity of Italian cities and regions

The yearly aggregated tax income data of all, more than 8000, Italian municipalities are analyzed for a period of five years, from 2007 to 2011, to search for conformity or not with Benford's law, a counter-intuitive phenomenon observed in large tabulated data where the occurrence of numbers having smaller initial digits is more favored than those with larger digits. This is done in anticipation that large deviations from Benford's law will be found in view of tax evasion supposedly being widespread across Italy. Contrary to expectations, we show that the overall tax income data for all these years is in excellent agreement with Benford's law. Furthermore, we also analyze the data of Calabria, Campania and Sicily, the three Italian regions known for strong presence of mafia, to see if there are any marked deviations from Benford's law. Again, we find that all yearly data sets for Calabria and Sicily agree with Benford's law whereas only the 2007 and 2008 yearly data show departures from the law for Campania. These results are again surprising in view of underground and illegal nature of economic activities of mafia which significantly contribute to tax evasion. Some hypothesis for the found conformity is presented.Comment: 18 pages, 5 tables, 4 figures, 61 references, To appear in European Physical Journal