Law of the leading digits and the ideological struggle for numbers

Benford's law states that the occurrence of significant digits in many data sets is not uniform but tends to follow a logarithmic distribution such that the smaller digits appear as first significant digits more frequently than the larger ones. We investigate here numerical data on the country-wise adherent distribution of seven major world religions i.e. Christianity, Islam, Buddhism, Hinduism, Sikhism, Judaism and Baha'ism to see if the proportion of the leading digits occurring in the distribution conforms to Benford's law. We find that the adherent data of all the religions, except Christianity, excellently does conform to Benford's law. Furthermore, unlike the adherent data on Christianity, the significant digit distribution of the three major Christian denominations i.e. Catholicism, Protestantism and Orthodoxy obeys the law. Thus in spite of their complexity general laws can be established for the evolution of the religious groups.Comment: 11 pages, 11 figures, 3 tables, title changed to "The law of the leading digits and the world religions" for journal version in publicatio

Rational tuning of the reactivity of three-membered heterocycle ring-openings via SN2 reactions

The development of small molecule covalent inhibitors and probes continuously pushes the rapidly evolving field of chemical biology forward. A key element in these molecular tool compounds is the "electrophilic trap" that allows for a covalent linkage with the target enzyme. The reactivity of this entity needs to be well balanced to effectively trap the desired enzyme, while not being attacked by off-target nucleophiles. We here investigate the intrinsic reactivity of substrates containing a class of widely used electrophilic traps, the three-membered heterocycles with an N- (aziridine), P- (phosphirane), O- (epoxide) and S-atom (thiirane) as heteroatom. Using quantum chemical approaches, we studied the conformational flexibility and nucleophilic ring-opening reaction of a series of model substrates, in which these electrophilic traps are mounted on a cyclohexene scaffold (C6H10Y with Y = NH, PH, O, S). It is revealed that the activation energy of the ring-opening reaction does not necessarily follow the trend that is expected from C-Y leaving-group bond strength, but steeply decreases from NH, to PH, to O, to S. We illustrate that the HOMONu-LUMOSubstrate interaction is an all-important factor for the observed reactivity. In addition, we show that the activation energy of aziridines and phosphiranes can be tuned far below that of the corresponding epoxides and thiiranes by the addition of proper electron-withdrawing ring substituents. Our results provide mechanistic insights to rationally tune the reactivity of this class of popular electrophilic traps and can guide the experimental design of covalent inhibitors and probes for enzymatic activity.NWONWO-Rekentijd grant 17569 and 11116Bio-organic Synthesi

A mean-field kinetic lattice gas model of electrochemical cells

We develop Electrochemical Mean-Field Kinetic Equations (EMFKE) to simulate electrochemical cells. We start from a microscopic lattice-gas model with charged particles, and build mean-field kinetic equations following the lines of earlier work for neutral particles. We include the Poisson equation to account for the influence of the electric field on ion migration, and oxido-reduction processes on the electrode surfaces to allow for growth and dissolution. We confirm the viability of our approach by simulating (i) the electrochemical equilibrium at flat electrodes, which displays the correct charged double-layer, (ii) the growth kinetics of one-dimensional electrochemical cells during growth and dissolution, and (iii) electrochemical dendrites in two dimensions.Comment: 14 pages twocolumn, 17 figure

Magnetic and quantum entanglement properties of the distorted diamond chain model for azurite

We present the results of magnetic properties and entanglement of the distorted diamond chain model for azurite using pure quantum exchange interactions. The magnetic properties and concurrence as a measure of pairwise thermal entanglement have been studied by means of variational mean-field like treatment based on Gibbs-Bogoliubov inequality. Such a system can be considered as an approximation of the natural material azurite, Cu3(CO3)2(OH)2. For values of exchange parameters, which are taken from experimental results, we study the thermodynamic properties, such as azurite specific heat and magnetic susceptibility. We also have studied the thermal entanglement properties and magnetization plateau of the distorted diamond chain model for azurite

Restricted three body problems at the nanoscale

In this paper, we investigate some of the classical restricted three body problems at the nanoscale, such as the circular planar restricted problem for three C60 fullerenes, and a carbon atom and two C60 fullerenes. We model the van der Waals forces between the fullerenes by the Lennard-Jones potential. In particular, the pairwise potential energies between the carbon atoms on the fullerenes are approximated by the continuous approach, so that the total molecular energy between two fullerenes can be determined analytically. Since we assume that such interactions between the molecules occur at sufficiently large distance, the classical three body problems analysis is legitimate to determine the collective angular velocity of the two and three C60 fullerenes at the nanoscale. We find that the maximum angular frequency of the two and three fullerenes systems reach the terahertz range and we determine the stationary points and the points which have maximum velocity for the carbon atom for the carbon atom and the two fullerenes system

Fall Risk and Utilization of Balance Training for Adults with Symptomatic Knee Osteoarthritis: Secondary Analysis from a Randomized Clinical Trial

Knee osteoarthritis (KOA) is a common disease that hinders activity participation in older adults. Associated symptoms and physiological changes can increase risk of falling in individuals with KOA. Balance training can decrease fall risks in older adults. Limited evidence exists regarding utilization of balance training in physical therapy (PT) for this population. This secondary data analysis investigated the proportion of participants at high risk for falling in the PhysicAl THerapy vs. INternet-based Exercise Training for Patients with Osteoarthritis (PATH-IN) study and the frequency with which balance training was utilized as an intervention in PT. Methods: PATH-IN study participants (N = 344) performed the Four-Stage Balance Test and the Timed Up and Go (TUG) test during baseline assessment. Participants were randomly allocated to PT, an Internet-based exercise program, or a control group. Participants were classified as being at high risk for falling if they did not progress to the single-leg stance (SLS) during the Four-Stage Balance Test, were unable to maintain SLS for 5 seconds, or took longer than 13.5 seconds to complete the TUG test. The proportion of participants at high risk for falling was calculated for all participants and separately for those allocated to PT. In addition, PT notes were coded for balance training and the frequency of balance training utilization was calculated. Results and Discussion: Upon enrollment, 35.5% (N = 122) of all participants and 36.2% (N = 50) of those allocated to PT were at high risk for falling. Of participants allocated to PT with documentation available for coding (N = 118), 35.5% (N = 42) were at high risk for falling. Balance training was provided to 62.7% (N = 74) during at least one PT session. Of those classified as being at high risk for falling, 33.3% (N = 14) did not receive balance training. Conclusions: The finding of high fall risks in more than one-third of all participants with KOA is consistent with previous reports of a higher risk of falling in this population. Many PT participants did receive some balance training; however, one-third of participants at high risk for falling did not. Balance training for individuals with KOA at high risk for falling may be underutilized

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

Multiple tier fuel cycle studies for waste transmutation.

As part of the U.S. Department of Energy Advanced Accelerator Applications Program, a systems study was conducted to evaluate the transmutation performance of advanced fuel cycle strategies. Three primary fuel cycle strategies were evaluated: dual-tier systems with plutonium separation, dual-tier systems without plutonium separation, and single-tier systems without plutonium separation. For each case, the system mass flow and TRU consumption were evaluated in detail. Furthermore, the loss of materials in fuel processing was tracked including the generation of new waste streams. Based on these results, the system performance was evaluated with respect to several key transmutation parameters including TRU inventory reduction, radiotoxicity, and support ratio. The importance of clean fuel processing ({approx}0.1% losses) and inclusion of a final tier fast spectrum system are demonstrated. With these two features, all scenarios capably reduce the TRU and plutonium waste content, significantly reducing the radiotoxicity; however, a significant infrastructure (at least 1/10 the total nuclear capacity) is required for the dedicated transmutation system

Topological Defects and CMB anisotropies : Are the predictions reliable ?

We consider a network of topological defects which can partly decay into neutrinos, photons, baryons, or Cold Dark Matter. We find that the degree-scale amplitude of the cosmic microwave background (CMB) anisotropies as well as the shape of the matter power spectrum can be considerably modified when such a decay is taken into account. We conclude that present predictions concerning structure formation by defects might be unreliable.Comment: 14 pages, accepted for publication in PR