Barium isotope fractionation during experimental formation of the double carbonate BaMn[CO3]2 at ambient temperature

In this study, we present the first experimental results for stable barium (Ba) isotope (¹³⁷Ba/¹³⁴Ba) fractionation during low-temperature formation of the anhydrous double carbonate BaMn[CO₃]₂. This investigation is part of an ongoing work on Ba fractionation in the natural barium cycle. Precipitation at a temperature of 21±1°C leads to an enrichment of the lighter Ba isotope described by an enrichment factor of?0.11±0.06‰ in the double carbonate than in an aqueous barium-manganese(II) chloride/sodium bicarbonate solution, which is within the range of previous reports for synthetic pure BaCO ₃ (witherite) formation.     

Maximizing Complementary Quantities by Projective Measurements

In this work, we study the so-called quantitative complementarity quantities. We focus in the following physical situation: two qubits (q _A and q _B ) are initially in a maximally entangled state. One of them (q _B ) interacts with a N-qubit system (R). After the interaction, projective measurements are performed on each of the qubits of R, in a basis that is chosen after independent optimization procedures: maximization of the visibility, the concurrence, and the predictability. For a specific maximization procedure, we study in detail how each of the complementary quantities behave, conditioned on the intensity of the coupling between q _B and the N qubits. We show that, if the coupling is sufficiently “strong,” independent of the maximization procedure, the concurrence tends to decay quickly. Interestingly enough, the behavior of the concurrence in this model is similar to the entanglement dynamics of a two qubit system subjected to a thermal reservoir, despite that we consider finite N. However, the visibility shows a different behavior: its maximization is more efficient for stronger coupling constants. Moreover, we investigate how the distinguishability, or the information stored in different parts of the system, is distributed for different couplings.     

Non-linear model parameter estimation–estimating a feasible parameter set with respect to model use

This article deals with non-linear model parameter estimation from experimental data. As for non-linear models a rigorous identifiability analysis is difficult to perform, parameter estimation is performed in such a way that uncertainty in the estimated parameter values is represented by the range of model use results when the model is used for a certain purpose. Using this approach, the article presents a simulation study where the objective is to discover whether the estimation of model parameters can be improved, so that a small enough range of model use results is obtained. The results of the study indicate that from plant measurements available for the estimation of model parameters, it is possible to extract data that are important for the estimation of model parameters relative to a certain model use. If these data are improved by a proper measurement campaign (e.g. proper choice of measured variables, better accuracy, higher measurement frequency) it is to be expected that a valid model for a certain model use will be obtained. The simulation study is performed for an activated sludge model from wastewater treatment, while the estimation of model parameters is done by Monte Carlo simulation.     

A mathematical insight in the epithelial-mesenchymal-like transition in cancer cells and its effect in the invasion of the extracellular matrix

Current biological knowledge supports the existence of a secondary group of cancer cells within the body of the tumour that exhibits stem cell-like properties. These cells are termed cancer stem cells, and as opposed to themore usual differentiated cancer cells, they exhibit highermotility, they are more resilient to therapy, and are able to metastasize to secondary locations within the organism and produce new tumours. The origin of the cancer stem cells is not completely clear; they seem to stem from the differentiated cancer cells via a transition process related to the epithelial-mesenchymal transition that can also be found in normal tissue. In the current work we model and numerically study the transition between these two types of cancer cells, and the resulting “ensemble” invasion of the extracellular matrix. This leads to the derivation and numerical simulation of two systems: an algebraic-elliptic system for the transition and an advection-reaction-diffusion system of Keller-Segel taxis type for the invasion.     

Bayesian Multivariate Distributional Regression With Skewed Responses and Skewed Random Effects

The normal and the t distribution are classical tools for building random effects regression models where both can be used for the specification of either the conditional response distribution or the random effects distribution. However, the underlying assumption of symmetry can be questionable in many applications. We, therefore, propose regression models where the skew-normal and skew-t distribution are considered for both the response and the random effects specification and embed these models in the framework of distributional regression such that regression predictors can be specified for all distributional parameters. The distributional regression framework also allows us to consider multivariate versions of the skew-normal and the skew-t distribution. For Bayesian inference, we adapt iteratively weighted least-square proposals within Markov chain Monte Carlo simulations such that they can also facilitate the inclusion of nonnormal random effects specifications. Model choice is based on the Watanabe–Akaike information criterion, in particular, to differentiate between skew and nonskew distributional specifications in a number of simulation studies. Finally, to illustrate their practical applicability, the developed models are applied to a study on cholesterol levels originating from the Framingham Heart Study and a dataset from the Demographic and Health Surveys on undernutrition among children in Nigeria. Supplementary material for this article is available online.     

Barium isotope fractionation during the experimental transformation of aragonite to witherite and of gypsum to barite,and the effect of ion (de)solvation

In this study, we present the experimental results for stable barium (Ba) isotope fractionation (¹³⁷Ba/¹³⁴Ba) during the transformation of aragonite (CaCO₃) and gypsum (CaSO₄·2H₂O) in Ba-bearing aqueous solution to witherite (BaCO₃) and barite (BaSO₄), respectively. The process was studied at three temperatures between 4 and 60?°C. In all cases, the transformation leads to a relative enrichment of the lighter ¹³⁴Ba isotope in the solid compared to the aqueous solution, with ^137/134Ba enrichment factors between –0.11 and ?0.17?‰ for BaCO₃, and –0.21 and –0.26?‰ for BaSO₄. The corresponding mass-dependent ^138/134Ba enrichment factors are ?0.15 to –0.23?‰ for BaCO₃, and –0.28 to –0.35?‰ for BaSO₄. The magnitude of isotope fractionation is within the range of recent reports for witherite and barite formation, as well as trace Ba incorporation into orthorhombic aragonite, and no substantial impact of temperature can be found between 4 and 80?°C. In previous studies, ion (de)solvation has been suggested to impact both the crystallization process of Ba-bearing solids and associated Ba isotope fractionation. Precipitation experiments of BaSO₄ and BaCO₃ using an methanol-containing aqueous solution indicate only a minor effect of ion and crystal surface (de)solvation on the overall Ba isotope fractionation process.     

Faster algorithms for computing longest common increasing subsequences

We present algorithms for finding a longest common increasing subsequence of two or more input sequences. For two sequences of lengths n and m, where m?n, we present an algorithm with an output-dependent expected running time of and O(m) space, where ? is the length of an LCIS, σ is the size of the alphabet, and Sort is the time to sort each input sequence. For k?3 length-n sequences we present an algorithm which improves the previous best bound by more than a factor k for many inputs. In both cases, our algorithms are conceptually quite simple but rely on existing sophisticated data structures. Finally, we introduce the problem of longest common weakly-increasing (or non-decreasing) subsequences (LCWIS), for which we present an -time algorithm for the 3-letter alphabet case. For the extensively studied longest common subsequence problem, comparable speedups have not been achieved for small alphabets.     

The vibrations of formaldehyde

A new six-dimensional variational code is presented for the determination of the vibrational energy levels of four-atom molecules which are either linearly connected or centrally connected. Internal (displacement) coordinates are used. It is demonstrated for the CCSD(T) surface of formaldehyde, due to Martin, Lee and Taylor, and it is shown that a small scaling of the force constants leads to a high-accuracy surface.