MCMC inference for Markov Jump Processes via the Linear Noise Approximation

Bayesian analysis for Markov jump processes is a non-trivial and challenging problem. Although exact inference is theoretically possible, it is computationally demanding thus its applicability is limited to a small class of problems. In this paper we describe the application of Riemann manifold MCMC methods using an approximation to the likelihood of the Markov jump process which is valid when the system modelled is near its thermodynamic limit. The proposed approach is both statistically and computationally efficient while the convergence rate and mixing of the chains allows for fast MCMC inference. The methodology is evaluated using numerical simulations on two problems from chemical kinetics and one from systems biology

Clustering via kernel decomposition

Spectral clustering methods were proposed recently which rely on the eigenvalue decomposition of an affinity matrix. In this letter, the affinity matrix is created from the elements of a nonparametric density estimator and then decomposed to obtain posterior probabilities of class membership. Hyperparameters are selected using standard cross-validation methods

Quantum discord for general two--qubit states: Analytical progress

We present a reliable algorithm to evaluate quantum discord for general two--qubit states, amending and extending an approach recently put forward for the subclass of X--states. A closed expression for the discord of arbitrary states of two qubits cannot be obtained, as the optimization problem for the conditional entropy requires the solution to a pair of transcendental equations in the state parameters. We apply our algorithm to run a numerical comparison between quantum discord and an alternative, computable measure of non-classical correlations, namely the geometric discord. We identify the extremally non-classically correlated two--qubit states according to the (normalized) geometric discord, at fixed value of the conventional quantum discord. The latter cannot exceed the square root of the former for systems of two qubits.Comment: 8 pages, 2 figure

Probabilistic Numerics and Uncertainty in Computations

We deliver a call to arms for probabilistic numerical methods: algorithms for numerical tasks, including linear algebra, integration, optimization and solving differential equations, that return uncertainties in their calculations. Such uncertainties, arising from the loss of precision induced by numerical calculation with limited time or hardware, are important for much contemporary science and industry. Within applications such as climate science and astrophysics, the need to make decisions on the basis of computations with large and complex data has led to a renewed focus on the management of numerical uncertainty. We describe how several seminal classic numerical methods can be interpreted naturally as probabilistic inference. We then show that the probabilistic view suggests new algorithms that can flexibly be adapted to suit application specifics, while delivering improved empirical performance. We provide concrete illustrations of the benefits of probabilistic numeric algorithms on real scientific problems from astrometry and astronomical imaging, while highlighting open problems with these new algorithms. Finally, we describe how probabilistic numerical methods provide a coherent framework for identifying the uncertainty in calculations performed with a combination of numerical algorithms (e.g. both numerical optimisers and differential equation solvers), potentially allowing the diagnosis (and control) of error sources in computations.Comment: Author Generated Postprint. 17 pages, 4 Figures, 1 Tabl

Sustainability and welfare of Podolian cattle

The aim of the present study was to evaluate the sustainability and welfare of extensively farmed Podolian cattle. A trained interviewer visited 50 farms and filled in a checklist which included four cards corresponding to the following animal categories: calves, replacements, feeders and adults. The analysis of the farming system showed that animals were able to express their main behavioural patterns. In addition, recorded animal-related variables indicated that Podolian cattle could benefit from high standards of welfare. Sustainability of the Podolian farming system in terms of human edible returns was evaluated for two production systems producing 10-month-old calves (10 month) and 18-month-old young bulls (18 month), respectively. Edible returns for humans were low when all animal intakes were considered for both production systems. However, if returns were computed using not only the amount of food used by the animals but also consumable by humans, yields were much higher for 18-month systems [103% crude protein (CP) and 37.1% gross energy (GE)] and so high that they could not be computed for 10-month systems. These results indicate either a low degree of competition (18-month system) or no competition (10-month system) between humans and Podolian cattle. Perceptions of sustainability and welfare of Podolian cattle may promote a favourable positioning of products in premium-price markets and help preserving this breed and the related traditional farming system

Congenital factor XI and factor VII deficiencies assure an apparent opposite protection against arterial or venous thrombosis: An intriguing observation.

To investigate the prevalence and type of thrombotic events reported in patients with congenital factor XI (FXI) or factor VII (FVII) deficiency.Data on all patients with congenital FXI or FVII deficiency and a thrombotic event were gathered by means of a time unlimited PubMed search carried out in June 2014 and in February 2015. Appropriate keywords including the medical subject headings were used in both instances. Side tables were also consulted and cross-checking of the references was carried out to avoid omissions. The thrombosis event had to be proven by objective methods.Forty-three patients with FXI deficiency had arterial thrombosis and only eight had venous thrombosis. On the contrary, only five patients with FVII deficiency had arterial thrombosis whereas 31 patients had venous thrombosis. The arterial/venous ratios were 5.37 and 0.17 for FXI or FVII, respectively.Arterial thrombosis is frequent in FXI deficiency whereas venous thrombosis is rare. The reverse is true for FVII deficiency. The significance of these findings is discussed especially in view of the recent use of synthetic anti-FXI compounds in the prophylaxis of post-orthopedic surgery of venous thrombosis complications

Interplay between computable measures of entanglement and other quantum correlations

Composite quantum systems can be in generic states characterized not only by entanglement, but also by more general quantum correlations. The interplay between these two signatures of nonclassicality is still not completely understood. In this work we investigate this issue focusing on computable and observable measures of such correlations: entanglement is quantified by the negativity N, while general quantum correlations are measured by the (normalized) geometric quantum discord D_G. For two-qubit systems, we find that the geometric discord reduces to the squared negativity on pure states, while the relationship $D_G \geq N^2$ holds for arbitrary mixed states. The latter result is rigorously extended to pure, Werner and isotropic states of two-qudit systems for arbitrary d, and numerical evidence of its validity for arbitrary states of a qubit and a qutrit is provided as well. Our results establish an interesting hierarchy, that we conjecture to be universal, between two relevant and experimentally friendly nonclassicality indicators. This ties in with the intuition that general quantum correlations should at least contain and in general exceed entanglement on mixed states of composite quantum systems.Comment: 10 pages, 4 figure