On the exchange of intersection and supremum of sigma-fields in filtering theory

We construct a stationary Markov process with trivial tail sigma-field and a nondegenerate observation process such that the corresponding nonlinear filtering process is not uniquely ergodic. This settles in the negative a conjecture of the author in the ergodic theory of nonlinear filters arising from an erroneous proof in the classic paper of H. Kunita (1971), wherein an exchange of intersection and supremum of sigma-fields is taken for granted.Comment: 20 page

In vitro fermentation of different ratios of alfalfa and starch or inulin incubated with an equine faecal inoculum

The aim of this work was to assess the impact of substituting starch (S) or inulin (I) with high-temperature dried alfalfa (HTDA) as substrates for in vitro fermentation with an equine faecal inoculum. A series of experiments were conducted to assess the fermentation kinetics of HTDA (chopped [CA] or ground [GA]) and either S or I mixed in the following ratios; 100:0, 80:20, 60:40, 40:60 and 20:80S/I: CA/GA, respectively. For each experiment, a further set of bottles containing identical ratios of S/I: CA/GA were also prepared, with the exception that the alfalfa received a simulated foregut digestion treatment (SFD) as prior to incubation. Total gas production increased (P<0.05) as the ratio of S/I to alfalfa increased. Total gas production was lower in bottles containing SFD-treated alfalfa (P<0.001). Dry matter loss decreased proportionately with increasing level of alfalfa substitution of S/I (P<0.001). Values for pH were lower in bottles containing S or I, with pH values in bottles containing S alone falling to almost 6 and those with I dropping to pH 5 and under. However, the substitution of S or I with 40% alfalfa produced pH values above 6.7, which is within physiological levels encountered in the large intestine of the horse. Consequently, there appears to be considerable potential to buffer the deleterious effects of high-starch/fructan diets with the substitution of these substrates with high-temperature dried alfalfa

Sliding mode control of quantum systems

This paper proposes a new robust control method for quantum systems with uncertainties involving sliding mode control (SMC). Sliding mode control is a widely used approach in classical control theory and industrial applications. We show that SMC is also a useful method for robust control of quantum systems. In this paper, we define two specific classes of sliding modes (i.e., eigenstates and state subspaces) and propose two novel methods combining unitary control and periodic projective measurements for the design of quantum sliding mode control systems. Two examples including a two-level system and a three-level system are presented to demonstrate the proposed SMC method. One of main features of the proposed method is that the designed control laws can guarantee desired control performance in the presence of uncertainties in the system Hamiltonian. This sliding mode control approach provides a useful control theoretic tool for robust quantum information processing with uncertainties.Comment: 18 pages, 4 figure

How much time does a measurement take?

We consider the problem of measurement using the Lindblad equation, which allows the introduction of time in the interaction between the measured system and the measurement apparatus. We use analytic results, valid for weak system-environment coupling, obtained for a two-level system in contact with a measurer (Markovian interaction) and a thermal bath (non-Markovian interaction), where the measured observable may or may not commute with the system-environment interaction. Analysing the behavior of the coherence, which tends to a value asymptotically close to zero, we obtain an expression for the time of measurement which depends only on the system-measurer coupling, and which does not depend on whether the observable commutes with the system-bath interaction. The behavior of the coherences in the case of strong system-environment coupling, found numerically, indicates that an increase in this coupling decreases the measurement time, thus allowing our expression to be considered the upper limit for the duration of the process.Comment: REVISED VERSION: 17 pages, 2 figure

Topology of Chaotic Mixing Patterns

A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at least a minimum amount of stretching of material lines, which is important for chaotic mixing. We use topological considerations to describe the nature of the injection of unmixed material into a central mixing region, which takes place at injection cusps. A topological index formula allow us to predict the possible types of unstable foliations that can arise for a fixed number of rods.Comment: 15 pages, 13 figures, RevTeX4 macros. Final versio

Physical and mental health comorbidity is common in people with multiple sclerosis: nationally representative cross-sectional population database analysis

<b>Background</b> Comorbidity in Multiple Sclerosis (MS) is associated with worse health and higher mortality. This study aims to describe clinician recorded comorbidities in people with MS. <p></p> <b>Methods</b> 39 comorbidities in 3826 people with MS aged ≥25 years were compared against 1,268,859 controls. Results were analysed by age, gender, and socioeconomic status, with unadjusted and adjusted Odds Ratios (ORs) calculated using logistic regression. <p></p> <b>Results</b> People with MS were more likely to have one (OR 2.44; 95% CI 2.26-2.64), two (OR 1.49; 95% CI 1.38-1.62), three (OR 1.86; 95% CI 1.69-2.04), four or more (OR 1.61; 95% CI 1.47-1.77) non-MS chronic conditions than controls, and greater mental health comorbidity (OR 2.94; 95% CI 2.75-3.14), which increased as the number of physical comorbidities rose. Cardiovascular conditions, including atrial fibrillation (OR 0.49; 95% CI 0.36-0.67), chronic kidney disease (OR 0.51; 95% CI 0.40-0.65), heart failure (OR 0.62; 95% CI 0.45-0.85), coronary heart disease (OR 0.64; 95% CI 0.52-0.71), and hypertension (OR 0.65; 95% CI 0.59-0.72) were significantly less common in people with MS. <p></p> <b>Conclusion</b> People with MS have excess multiple chronic conditions, with associated increased mental health comorbidity. The low recorded cardiovascular comorbidity warrants further investigation

First Observation and Measurement of the Decay K+- -> pi+- e+ e- gamma

Using the full data set of the NA48/2 experiment, the decay K+- -> pi+- e+ e- gamma is observed for the first time, selecting 120 candidates with 7.3 +- 1.7 estimated background events. With K+- -> pi+- pi0D as normalisation channel, the branching ratio is determined in a model-independent way to be Br(K+- -> pi+- e+ e- gamma, m_eegamma > 260 MeV/c^2) = (1.19 +- 0.12_stat +- 0.04_syst) x 10^-8. This measured value and the spectrum of the e+ e- gamma invariant mass allow a comparison with predictions of Chiral Perturbation Theory.Comment: 13 pages, 3 figures. Accepted for publication in Phys.Lett.

Elimination of human rabies in Goa, India through an integrated One Health approach

Dog-mediated rabies kills tens of thousands of people each year in India, representing one third of the estimated global rabies burden. Whilst the World Health Organization (WHO), World Organization for Animal Health (OIE) and the Food and Agriculture Organization of the United Nations (FAO) have set a target for global dog-mediated human rabies elimination by 2030, examples of large-scale dog vaccination programs demonstrating elimination remain limited in Africa and Asia. We describe the development of a data-driven rabies elimination program from 2013 to 2019 in Goa State, India, culminating in human rabies elimination and a 92% reduction in monthly canine rabies cases. Smartphone technology enabled systematic spatial direction of remote teams to vaccinate over 95,000 dogs at 70% vaccination coverage, and rabies education teams to reach 150,000 children annually. An estimated 2249 disability-adjusted life years (DALYs) were averted over the program period at 526 USD per DALY, making the intervention ‘very cost-effective’ by WHO definitions. This One Health program demonstrates that human rabies elimination is achievable at the state level in India