Ratio of flavour non-singlet and singlet scalar density renormalisation parameters in $$N_\mathrm {f}=3$$ QCD with Wilson quarks

We determine non-perturbatively the normalisation factor $$r_{\mathrm{m}}\equiv Z_{\mathrm{S}}/Z_{\mathrm{S}}^{0}$$ r m ≡ Z S / Z S 0 , where $$Z_{\mathrm{S}}$$ Z S and $$Z_{\mathrm{S}}^{0}$$ Z S 0 are the renormalisation parameters of the flavour non-singlet and singlet scalar densities, respectively. This quantity is required in the computation of quark masses with Wilson fermions and for instance the renormalisation of nucleon matrix elements of scalar densities. Our calculation involves simulations of finite-volume lattice QCD with the tree-level Symanzik-improved gauge action, $$N_{\mathrm{f}}= 3$$ N f = 3 mass-degenerate $${\mathrm{O}}(a)$$ O ( a ) improved Wilson fermions and Schrödinger functional boundary conditions. The slope of the current quark mass, as a function of the subtracted Wilson quark mass is extracted both in a unitary setup (where nearly chiral valence and sea quark masses are degenerate) and in a non-unitary setup (where all valence flavours are chiral and the sea quark masses are small). These slopes are then combined with $$Z \equiv Z_{\mathrm{P}}/(Z_{\mathrm{S}}Z_{\mathrm{A}})$$ Z ≡ Z P / ( Z S Z A ) in order to obtain $$r_{\mathrm{m}}$$ r m . A novel chiral Ward identity is employed for the calculation of the normalisation factor Z. Our results cover the range of gauge couplings corresponding to lattice spacings below $$0.1\,$$ 0.1 fm, for which $$N_{\mathrm{f}}= 2+1$$ N f = 2 + 1 QCD simulations in large volumes with the same lattice action are typically performed.

A comparative study of infection and mortality in COVID-19 across countries: A scaling analysis

Analysing infection and mortality data for COVID-19 as a function of days for 54 countries across all continents, we show that there is a simple scaling behaviour connecting these two quantities for any given nation when the data is segmented over few ranges of dates covering the most rapid spread of the pandemic and the recovery, wherever achieved. This scaling is described by two parameters, one representing a shift along the time axis and the other is a normalisation factor, providing a reliable definition of the mortality rate for each country in a given period. The number of segments for any country required in our analyses turns out to be surprisingly few with as many as 16 out of 54 countries being described by a single segment and no country requiring more than three segments. Estimates of the shift and mortality for these 54 countries in different periods show large spreads ranging over 0-16 days and 0.45-19.96%, respectively. Shift and mortality are found to be inversely correlated. Analyses of number of tests carried out for detecting COVID-19 and the number of infections detected due to such tests suggest that an effective way to increase the shift, and therefore, decrease mortality, is to increase number of tests per infection detected. This points to the need of a dynamic management of testing that should accelerate with the rise of the pandemic; it also suggests a basis for adjusting variations in the testing patterns in different geographical locations within a given country.

A unified accretion-ejection paradigm for black hole X-ray binaries

Context. We proposed in paper I that the spectral evolution of transient X-ray binaries (XrB) is due to an interplay between two flows: a standard accretion disk (SAD) in the outer parts and a jet-emitting disk (JED) in the inner parts. We showed in papers II, III, and IV that the spectral evolution in X-ray and radio during the 2010–2011 outburst of GX 339-4 can be recovered. However, the observed variability in X-ray was never addressed in this framework. Aims. We investigate the presence of low frequency quasi-periodic oscillations (LFQPOs) during an X-ray outburst, and address the possible correlation between the frequencies of these LFQPOs and the transition radius between the two flows, rJ. Methods. We select X-ray and radio data that correspond to 3 outbursts of GX 339-4. We use the method detailed in Paper IV to obtain the best parameters rJ(t) and ṁin(t) for each outburst. We also independently search for X-ray QPOs in each selected spectra and compare the QPO frequency to the Kepler and epicyclic frequencies of the flow in rJ. Results. We successfully reproduce the correlated evolution of the X-ray spectra and the radio emission for 3 different activity cycles of GX 339-4. We use a unique normalisation factor for the radio emission, f∼R. We also report the detection of 7 new LFQPOs (3 Type B, and 4 Type C), to go along with the ones previously reported in the literature. We show that the frequency of Type C QPOs can be linked to the dynamical JED-SAD transition radius rJ, rather than to the optically thin-thick transition radius in the disk. The scaling factor q such that νQPO ≃ νK(rJ)/q is q ≃ 70 − 130, a factor consistent during the 4 cycles, and similar to previous studies. Conclusions. The JED-SAD hybrid disk configuration not only provides a successful paradigm allowing us to describe XrB cycles, but also matches the evolution of QPO frequencies. Type C QPOs provide an indirect way to probe the JED-SAD transition radius, where an undetermined process produces secular variability. The demonstrated relation between the transition radius links Type C QPOs to the transition between two different flows, effectively tying it to the inner magnetized structure, i.e., the jets. This direct connection between the jets’ (accretion-ejection) structure and the process responsible for Type C QPOs, if confirmed, could naturally explain their puzzling multi-wavelength behavior.

Balanced Quantum-Like Bayesian Networks

Empirical findings from cognitive psychology indicate that, in scenarios under high levels of uncertainty, many people tend to make irrational decisions. To address this problem, models based on quantum probability theory, such as the quantum-like Bayesian networks, have been proposed. However, this model makes use of a Bayes normalisation factor during probabilistic inference to convert the likelihoods that result from quantum interference effects into probability values. The interpretation of this operation is not clear and leads to extremely skewed intensity waves that make the task of prediction of these irrational decisions challenging. This article proposes the law of balance, a novel mathematical formalism for probabilistic inferences in quantum-like Bayesian networks, based on the notion of balanced intensity waves. The general idea is to balance the intensity waves resulting from quantum interference in such a way that, during Bayes normalisation, they cancel each other. With this representation, we also propose the law of maximum uncertainty, which is a method to predict these paradoxes by selecting the amplitudes of the wave with the highest entropy. Empirical results show that the law of balance together with the law of maximum uncertainty were able to accurately predict different experiments from cognitive psychology showing paradoxical or irrational decisions, namely in the Prisoner’s Dilemma game and the Two-Stage Gambling Game.

Non-perturbative determination of improvement coefficients $$b_\mathrm{m}$$ and $$b_\mathrm{A}-b_\mathrm{P}$$ and normalisation factor $$Z_\mathrm{m}Z_\mathrm{P}/Z_\mathrm{A}$$ with $$N_\mathrm{f}= 3$$ Wilson fermions

We determine non-perturbatively the normalisation parameter $$Z_\mathrm{m}Z_\mathrm{P}/Z_\mathrm{A}$$ZmZP/ZA as well as the Symanzik coefficients $$b_\mathrm{m}$$bm and $$b_\mathrm{A}-b_\mathrm{P}$$bA-bP, required in $$\mathrm{O}(a)$$O(a) improved quark mass renormalisation with Wilson fermions. The strategy underlying their computation involves simulations in $$N_\mathrm{f}=3$$Nf=3 QCD with $$\mathrm{O}(a)$$O(a) improved massless sea and non-degenerate valence quarks in the finite-volume Schrödinger functional scheme. Our results, which cover the typical gauge coupling range of large-volume $$N_\mathrm{f}=2+1$$Nf=2+1 QCD simulations with Wilson fermions at lattice spacings below $$0.1\,\mathrm{fm}$$0.1fm, are of particular use for the non-perturbative calculation of $$\mathrm{O}(a)$$O(a) improved renormalised quark masses.

A Wavelet-Based Damage Detection Approach for Acousto-Ultrasonic In Situ Monitoring Systems

In this research, an advanced signal processing technique using wavelet analysis has been developed for a guided wave structural health monitoring system. The approach was applied for the detection of delamination in carbon fibre reinforced composites. A monolithic piezoceramic actuator was attached to a laminate plate for wave generation while laser vibrometry was used to facilitate the measurements of the wave response in a sensor network. This database of wave response was then processed using the continuous wavelet transform to obtain the positional frequency content. Transforms between damaged and undamaged states were compared to ascertain the presence of defects by evaluating the total energy of the time-frequency density function. Results show high damage detection indices depending on the location of the sensor and normalisation factor applied while there are positive indications that this methodology can be extended for damage characterisation.

A FOURTH ORDER REAL-SPACE ALGORITHM FOR SOLVING LOCAL SCHRÖDINGER EQUATIONS

We describe a rapidly converging algorithm for solving the Schrödinger equation with local potentials in real space. The algorithm is based on evolving the Schrödinger equation in imaginary time by factorizing the evolution operator e -εH to fourth order with purely positive coefficients. The states |ψj> and the associated energies extracted from the normalisation factor e -εEj converge as [Formula: see text]. Our algorithm is at least a factor of 100 more efficient than existing second order split operator methods. We apply the new scheme to a spherical jellium cluster with 20 electrons. We show that the low-lying eigenstates converge very rapidly and that the algorithm does not lose any of its effectiveness for very steep potentials.