Spacetime and Euclidean Geometry

Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding causal domain. We use this relation to derive the Minkowski line element by two geometric proofs of the "spacetime Pythagoras theorem".Comment: 11 pages, 9 figures; for a festschrift honoring Michael P. Ryan; v.2: References to related work adde

On the spatial Markov property of soups of unoriented and oriented loops

We describe simple properties of some soups of unoriented Markov loops and of some soups of oriented Markov loops that can be interpreted as a spatial Markov property of these loop-soups. This property of the latter soup is related to well-known features of the uniform spanning trees (such as Wilson's algorithm) while the Markov property of the former soup is related to the Gaussian Free Field and to identities used in the foundational papers of Symanzik, Nelson, and of Brydges, Fr\"ohlich and Spencer or Dynkin, or more recently by Le Jan

Error bounds for expectation values: Some applications and extensions

The error‐bound procedure of Bazley and Fox is extended as in a previous paper and applied to the expectation values of some quantum‐mechanical operators of physical interest. The quality of the bounds is discussed and it is found to be possible to improve them under certain conditions. An attempt is made to use these error‐bound formulas as variational principles for expectation values. Some special cases such as Fermi contact terms and electron densities are discussed separately. Errors in Hartree—Fock expectation values are considered from the point of view of Brillouin's theorem and some qualitative predictions of their magnitudes are made. Transition probabilities are also treated and some qualitative conclusions are made concerning the accuracy of the alternative length and velocity formulas

Shift of the 21+^+_1 state of 10^{10}Be in the ternary cold fission of 252^{252}Cf

Recent experimental data indicate that in the ternary cold fission of $^{252}$Cf the energy of the first excited state of the accompanying light cluster $^{10}$Be is decreased by an amount ranging between $\approx$ 6 and 26 keV. A model is proposed to calculate the shift of the vibrational 2$^+_1$ state in $^{10}$Be when its heavy companions are the even-even nuclei $^{146}$Ba and $^{96}$Sr. The stiffness parameters of the $\beta$-vibrations are calculated within the self-consistent Hartree-Fock method with BCS pairing correlations taken into account, and its change is determined by the interaction of the light cluster with the heavy fragments. The results are pointing to a dependence of the shift magnitude and signature on the relative distance between the three clusters and their mutual orientation. Eventually it is the anharmonic perturbation of the spherical vibrator which is responsible for obtaining a negative energy shift of the 2$^+_1$ state.Comment: 4 pages, 3 figure

Fine-scale time-lapse analysis of the biphasic, dynamic behaviour of the two Vibrio cholerae chromosomes

Using fluorescent repressor-operator systems in live cells, we investigated the dynamic behaviour of chromosomal origins in Vibrio cholerae, whose genome is divided between two chromosomes. We have developed a method of analysing fine-scale motion in the curved co-ordinate system of vibrioid bacteria. Using this method, we characterized two different modes of chromosome behaviour corresponding to periods between segregation events and periods of segregation. Between segregation events, the origin positions are not fixed but rather maintained within ellipsoidal caged domains, similar to eukaryotic interphase chromosome territories. These domains are approximately 0.4 µm wide and 0.6 µm long, reflecting greater restriction in the short axis of the cell. During segregation, movement is directionally biased, speed is comparable between origins, and cell growth can account for nearly 20% of the motion observed. Furthermore, the home domain of each origin is positioned by a different mechanism. Specifically, the oriCI domain is maintained at a constant actual distance from the pole regardless of cell length, while the oriCII domain is maintained at a constant relative position. Thus the actual position of oriCII varies with cell length. While the gross behaviours of the two origins are distinct, their fine-scale dynamics are remarkably similar, indicating that both experience similar microenvironments

Evidence for a Genetic Basis of Aging in Two Wild Vertebrate Populations

SummaryAging, or senescence, defined as a decline in physiological function with age, has long been a focus of research interest for evolutionary biologists. How has natural selection failed to remove genetic effects responsible for such reduced fitness among older individuals? Current evolutionary theory explains this phenomenon by showing that, as a result of the risk of death from environmental causes that individuals experience, the force of selection inevitably weakens with age [1–3]. This in turn means that genetic mutations having detrimental effects that are only felt late in life might persist in a population. Although widely accepted, this theory rests on the assumption that there is genetic variation for aging in natural systems [4, 5], or (equivalently), that genotype-by-age interactions (GxA) occur for fitness. To date, empirical support for this assumption has come almost entirely from laboratory studies on invertebrate systems, most notably Drosophila and C. elegans [6–10], whereas tests of genetic variation for aging are largely lacking from natural populations [5]. By using data from two wild mammal populations, we perform quantitative genetic analyses of fitness and provide the first evidence for a genetic basis of senescence to come from a study in the natural environment. We find evidence that genetic differences among individuals cause variation in their rates of aging and that additive genetic variance for fitness increases with age, as predicted by the evolutionary theory of senescence

An Analytic Variational Study of the Mass Spectrum in 2+1 Dimensional SU(3) Hamiltonian Lattice Gauge Theory

We calculate the masses of the lowest lying eigenstates of improved SU(2) and SU(3) lattice gauge theory in 2+1 dimensions using an analytic variational approach. The ground state is approximated by a one plaquette trial state and mass gaps are calculated in the symmetric and antisymmetric sectors by minimising over a suitable basis of rectangular states

Light-cone QCD Sum Rules for the Λ\Lambda Baryon Electromagnetic Form Factors and its magnetic moment

We present the light-cone QCD sum rules up to twist 6 for the electromagnetic form factors of the $\Lambda$ baryon. To estimate the magnetic moment of the baryon, the magnetic form factor is fitted by the dipole formula. The numerical value of our estimation is $\mu_\Lambda=-(0.64\pm0.04)\mu_N$, which is in accordance with the experimental data and the existing theoretical results. We find that it is twist 4 but not the leading twist distribution amplitudes that dominate the results.Comment: 13 page, 7 figures, accepted for publication in Euro. Phys. J.