Cosmological Cutting Rules

Primordial perturbations in our universe are believed to have a quantum origin, and can be described by the wavefunction of the universe (or equivalently, cosmological correlators). It follows that these observables must carry the imprint of the founding principle of quantum mechanics: unitary time evolution. Indeed, it was recently discovered that unitarity implies an infinite set of relations among tree-level wavefunction coefficients, dubbed the Cosmological Optical Theorem. Here, we show that unitarity leads to a systematic set of “Cosmological Cutting Rules” which constrain wavefunction coefficients for any number of fields and to any loop order. These rules fix the discontinuity of an n-loop diagram in terms of lower-loop diagrams and the discontinuity of tree-level diagrams in terms of tree-level diagrams with fewer external fields. Our results apply with remarkable generality, namely for arbitrary interactions of fields of any mass and any spin with a Bunch-Davies vacuum around a very general class of FLRW spacetimes. As an application, we show how one-loop corrections in the Effective Field Theory of inflation are fixed by tree-level calculations and discuss related perturbative unitarity bounds. These findings greatly extend the potential of using unitarity to bootstrap cosmological observables and to restrict the space of consistent effective field theories on curved spacetimes.

Problems with graphomotorics at the beginning and the end of primary education

The study monitors two phenomena of graphomotor problems among children at the beginning and the end of primary education. The study has a character of piloting. A series of seven graphomotor tasks were submited to preschoolers (n = 51) and in the ninth grade (n = 22). For each task, tremor and number of hand move interruptions were considered as indicators of graphomotor difficulties. The results showed that the tremor was detected at 33.3% to 78.4% of preschoolers and at 18.2% to 59.1% of ninth grade pupils. In both groups, the tremor was the least prevalent in the ‘teeth’ task and the most frequent in the ‘double upper-lower loop’ task. The prevalence of tremor in the solution of graphomotor problems decreases with age, the difference is statistically insignificant. Contrary to the expectations, more interruptions were found at nineth grade pupils. Based on the study results, we recommend to note in the instruction that the templates are ‘straight lines’. Keywords: Graphomotor skills, graphomotor difficulties, tremor, number of interrupsions, preschool children, adolescents, pilot study.

The accidental ally: Nucleosomal barriers can accelerate cohesin mediated loop formation in chromatin

An important question in the context of the 3D organization of chromosomes is the mechanism of formation of large loops between distant base pairs. Recent experiments suggest that the formation of loops might be mediated by Loop Extrusion Factor proteins like cohesin. Experiments on cohesin have shown that cohesins walk diffusively on the DNA, and that nucleosomes act as obstacles to the diffusion, lowering the permeability and hence reducing the effective diffusion constant. An estimation of the times required to form the loops of typical sizes seen in Hi-C experiments using these low effective diffusion constants leads to times that are unphysically large. The puzzle then is the following, how does a cohesin molecule diffusing on the DNA backbone achieve speeds necessary to form the large loops seen in experiments? We propose a simple answer to this puzzle, and show that while at low densities, nucleosomes act as barriers to cohesin diffusion, beyond a certain concentration, they can reduce loop formation times due to a subtle interplay between the nucleosome size and the mean linker length. This effect is further enhanced on considering stochastic binding kinetics of nucleosomes on the DNA backbone, and leads to predictions of lower loop formation times than might be expected from a naive obstacle picture of nucleosomes.

Age Related Variation in Feminine Handwriting among Population Groups of Delhi, India

Background: Handwriting is a uniquely human trait which progresses and evolves during lifetime and declines with age. The aim of the present paper is to assess variation in handwriting features with age among female writers of select population groups of Delhi, India (for roman script). Method: A total of 405 handwritten samples were obtained from female (n=405) writers in the age range of 14-60 years. Writers were stratified into three age groups (≤ 18 years, 19-38 years and ≥39 years) in accordance to population group. Macro- and micro-features of handwriting were extracted from the scanned handwritten samples. These features were subjected to statistical analysis in the objective driven research. Result: The mean difference among age groups for pen pressure, height of handwriting and handwriting connectivity was statistically significant (p < 0.001). Significant difference was also observed among age groups for all micro-features of handwriting selected in the present study, namely, nature of ‘i’ – dot (p < 0.001), nature of lower loop of ‘g’ (p < 0.01); nature of‘d’- stem (p < 0.01), nature of ‘m’-hump (p < 0.05) and ‘r’- shape (p < 0.001). Conclusion: The present study showed that there was a significant variation in both macro- and micro- features of handwriting with respect to age of the writer. Pen pressure, height of handwriting and handwriting connectivity were prominent macro-features that addressed age related variation in handwriting. In addition, significant variation was observed among age groups for all micro-features of handwriting selected in the present study. The present study has immense forensic significance as it can assist to analyze age of the writer on the basis of handwriting characteristics.

Massive loops in thermal SU(2) Yang–Mills theory: Radiative corrections to the pressure beyond two loops

We address the loop expansion of the pressure in the deconfining phase of SU(2) Yang–Mills thermodynamics. We devise an efficient book-keeping of excluded energy-sign and scattering-channel combinations for the loop four-momenta associated with massive quasiparticles, circulating in (connected) bubble diagrams subject to vertex constraints inherited from the thermal ground state. These radiative corrections modify the one-loop pressure exerted by free thermal quasiparticles. Increasing the loop order in two-particle irreducible (2PI) bubble diagrams, we exemplarily demonstrate a suppressing effect of the vertex constraints on the number of valid combinations. This increasingly strong suppression gave rise to the conjecture in arXiv:hep-th/0609033 that the loop expansion would terminate at a finite order. Albeit the low-temperature dependence of the 2PI 3-loop diagram complies with this behavior, a thorough analysis of the high-temperature situation reveals that the leading power in temperature is thirteen such that this diagram dominates all lower loop orders for sufficiently high temperatures. An all-loop-order resummation of 2PI diagrams with dihedral symmetry is thus required, defining an extremely well-bounded analytical continuation of the low-temperature result.

Massive Fluctuations in Deconfining SU(2) Yang-Mills Thermodynamics

We review how vertex constraints inherited from the thermal ground state strongly reduce the integration support of loop four-momenta associated with massive quasiparticles in bubble diagrams constituting corrections to the free thermal quasiparticle pressure. In spite of the observed increasingly suppressing effect when increasing 2-particle-irreducible (2PI) loop order, a quantitative analysis enables us to disprove the conjecture voiced in hep-th/0609033 that the loop expansion would terminate at a finite order. This reveals the necessity to investigate exact expressions of (at least some) higher-loop order diagrams. Explicit calculation shows that although the behaviour of the 2PI three-loop contribution at low temperatures displays hierarchical suppression compared to lower loop orders, its high-temperature expression instead dominates all lower orders. However, an all-loop-order resummation of a class of 2PI bubble diagrams is shown to yield an analytic continuation of the low-temperature hierarchy to all temperatures in the deconfining phase.