EFFECT ON MILK PRODUCTION AND INCOME OVER FEED COST FROM FOLLOWING LESS THAN OPTIMUM MANAGEMENT STRATEGIES RELATED TO DAIRY COW REPLACEMENT

Livestock Production/Industries,

The estimation of cell probabilites in large sparse discrete spaces

Imperial Users onl

Variational formulation of problems involving fractional order differential operators

In this work, we consider boundary value problems involving either Caputo or Riemann-Liouville fractional derivatives of order α ∈ (1, 2) on the unit interval (0, 1). These fractional derivatives lead to nonsymmetric boundary value problems, which are investigated from a variational point of view. The variational problem for the Riemann-Liouville case is coercive on the space Hα/2 0 (0, 1) but the solutions are less regular, whereas that for the Caputo case involves different test and trial spaces. The numerical analysis of these problems requires the so-called shift theorems which show that the solutions of the variational problem are more regular. The regularity pickup enables one to establish convergence rates of the finite element approximations. The analytical theory is then applied to the Sturm-Liouville problem involving a fractional derivative in the leading term. Finally, extensive numerical results are presented to illustrate the error estimates for the source problem and eigenvalue problem

A tutorial on inverse problems for anomalous diffusion processes

Over the last two decades, anomalous diffusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately described by fractional differential equations, which involves fractional derivatives in time or/and space. The fractional derivatives describe either history mechanism or long range interactions of particle motions at a microscopic level. The new physics can change dramatically the behavior of the forward problems. For example, the solution operator of the time fractional diffusion diffusion equation has only limited smoothing property, whereas the solution for the space fractional diffusion equation may contain weak singularity. Naturally one expects that the new physics will impact related inverse problems in terms of uniqueness, stability, and degree of ill-posedness. The last aspect is especially important from a practical point of view, i.e., stably reconstructing the quantities of interest. In this paper, we employ a formal analytic and numerical way, especially the two-parameter Mittag-Leffler function and singular value decomposition, to examine the degree of ill-posedness of several 'classical' inverse problems for fractional differential equations involving a Djrbashian–Caputo fractional derivative in either time or space, which represent the fractional analogues of that for classical integral order differential equations. We discuss four inverse problems, i.e., backward fractional diffusion, sideways problem, inverse source problem and inverse potential problem for time fractional diffusion, and inverse Sturm–Liouville problem, Cauchy problem, backward fractional diffusion and sideways problem for space fractional diffusion. It is found that contrary to the wide belief, the influence of anomalous diffusion on the degree of ill-posedness is not definitive: it can either significantly improve or worsen the conditioning of related inverse problems, depending crucially on the specific type of given data and quantity of interest. Further, the study exhibits distinct new features of 'fractional' inverse problems, and a partial list of surprising observations is given below. (a) Classical backward diffusion is exponentially ill-posed, whereas time fractional backward diffusion is only mildly ill-posed in the sense of norms on the domain and range spaces. However, this does not imply that the latter always allows a more effective reconstruction. (b) Theoretically, the time fractional sideways problem is severely ill-posed like its classical counterpart, but numerically can be nearly well-posed. (c) The classical Sturm–Liouville problem requires two pieces of spectral data to uniquely determine a general potential, but in the fractional case, one single Dirichlet spectrum may suffice. (d) The space fractional sideways problem can be far more or far less ill-posed than the classical counterpart, depending on the location of the lateral Cauchy data. In many cases, the precise mechanism of these surprising observations is unclear, and awaits further analytical and numerical exploration, which requires new mathematical tools and ingenuities. Further, our findings indicate fractional diffusion inverse problems also provide an excellent case study in the differences between theoretical ill-conditioning involving domain and range norms and the numerical analysis of a finite-dimensional reconstruction procedure. Throughout we will also describe known analytical and numerical results in the literature

An inverse problem for a one-dimensional time-fractional diffusion problem

Over the last two decades, anomalous diusion processes in which the mean squares variance grows slower or faster than that in a Gaussian process have found many applications. At a macroscopic level, these processes are adequately described by fractional dierential equations, which involves fractional derivatives in time or/and space. The fractional derivatives describe either history mechanism or long range interactions of particle motions at a microscopic level. The new physics can change dramatically the behavior of the forward problems. For example, the solution operator of the time fractional diusion diusion equation has only limited smoothing property, whereas the solution for the space fractional diusion equation may contain weakly singularity. Naturally one expects that the new physics will impact related inverse problems in terms of uniqueness, stability, and degree of ill-posedness. The last aspect is especially important from a practical point of view, i.e., stably reconstructing the quantities of interest. In this paper, we employ a formal analytic and numerical way, especially the two-parameter Mittag-Leer function and singular value decomposition, to examine the degree of ill-posedness of several \classical" inverse problems for fractional dierential equations involving a Djrbashian-Caputo fractional derivative in either time or space, which represent the fractional analogues of that for classical integral order dierential equations. We discuss four inverse problems, i.e., backward fractional diusion, sideways problem, inverse source problem and inverse potential problem for time fractional diusion, and inverse Sturm-Liouville problem, Cauchy problem, backward fractional diusion and sideways problem for space fractional diusion. It is found that contrary to the wide belief, the in uence of anomalous diusion on the degree of ill-posedness is not denitive: it can either signicantly improve or worsen the conditioning of related inverse problems, depending crucially on the specic type of given data and quantity of interest. Further, the study exhibits distinct new features of \fractional" inverse problems, and a partial list of surprising observations is given below. (a) Classical backward diusion is exponentially ill-posed, whereas time fractional backward diusion is only mildly ill-posed in the sense of norms on the domain and range spaces. However, this does not imply that the latter always allows a more eective reconstruction. (b) Theoretically, the time fractional sideways problem is severely ill-posed like its classical counterpart, but numerically can be nearly well-posed. (c) The classical Sturm-Liouville problem requires two pieces of spectral data to uniquely determine a general potential, but in the fractional case, one single Dirichlet spectrum may suce. (d) The space fractional sideways problem can be far more or far less ill-posed than the classical counterpart, depending on the location of the lateral Cauchy data. In many cases, the precise mechanism of these surprising observations is unclear, and awaits further analytical and numerical exploration, which requires new mathematical tools and ingenuities. Further, our ndings indicate fractional diusion inverse problems also provide an excellent case study in the dierences between theoretical ill-conditioning involving domain and range norms and the numerical analysis of a nite-dimensional reconstruction procedure. Throughout we will also describe known analytical and numerical results in the literature

Circulating emm types of Streptococcus pyogenes in Scotland: 2011-2015

No abstract available

Omega-3 Fatty Acids and Airway Hyperresponsiveness in Asthma

ABSTRACT Despite the progress that has been made in the treatment of asthma, the prevalence and burden of this disease has continued to increase. Exercise is a powerful trigger of asthma symptoms and reversible airflow obstruction and may result in the avoidance of physical activity by patients with asthma, resulting in detrimental consequences to their health. Approximately 90% of patients with asthma are hyperresponsive to exercise and experience exercise-induced bronchoconstriction (EIB). While pharmacologic treatment of asthma is usually highly effective, medications often have significant side-effects or exhibit tachyphylaxis. Alternative therapies for treatment (complementary medicine) that reduce the dose requirements of pharmacologic interventions would be beneficial, and could potentially reduce the public health burden of this disease. There is accumulating evidence that dietary modification has potential to influence the severity of asthma and reduce the prevalence and incidence of this condition. A possible contributing factor to the increased incidence of asthma in Western societies may be the consumption of a proinflammatory diet. In the typical Western diet, 20-to 25-fold more -6 polyunsaturated fatty acids (PUFA) than -3 PUFA are consumed, which causes the release of proinflammatory arachidonic acid metabolites (leukotrienes and prostanoids). This review analyzes the existing literature on -3 PUFA supplementation as a potential modifier of airway hyperresponsiveness in asthma and includes studies concerning the efficacy of -3 PUFA supplementation in EIB. While clinical data evaluating the effect of -3 PUFA supplementation in asthma has been equivocal, it has recently been shown that pharmaceuticalgrade fish oil (-3 PUFA) supplementation reduces airway hyperresponsiveness after exercise, medication use, and proinflammatory mediator generation in nonatopic elite athletes with EIB. These findings are provocative and suggest that dietary -3 PUFA supplementation may be a viable treatment modality and/or adjunct therapy in airway hyperresponsiveness. Further studies are needed to confirm these results and understand their mechanism of action. 106

Hybrid Organic–Inorganic Halide Post-Perovskite 3-Cyanopyridinium Lead Tribromide for Optoelectronic Applications

2D halide perovskite-like semiconductors are attractive materials for various optoelectronic applications, from photovoltaics to lasing. To date, the most studied families of such low-dimensional halide perovskite-like compounds are Ruddlesden–Popper, Dion–Jacobson, and other phases that can be derived from 3D halide perovskites by slicing along different crystallographic directions, which leads to the spatially isotropic corner-sharing connectivity type of metal-halide octahedra in the 2D layer plane. In this work, a new family of hybrid organic–inorganic 2D lead halides is introduced, by reporting the first example of the hybrid organic–inorganic post-perovskite 3-cyanopyridinium lead tribromide (3cp)PbBr3. The post-perovskite structure has unique octahedra connectivity type in the layer plane: a typical “perovskite-like” corner-sharing connectivity pattern in one direction, and the rare edge-sharing connectivity pattern in the other. Such connectivity leads to significant anisotropy in the material properties within the inorganic layer plane. Moreover, the dense organic cation packing results in the formation of 1D fully organic bands in the electronic structure, offering the prospects of the involvement of the organic subsystem into material's optoelectronic properties. The (3cp)PbBr3 clearly shows the 2D quantum size effect with a bandgap around 3.2 eV and typical broadband self-trapped excitonic photoluminescence at temperatures below 200 K

Inverse spectral problems for Sturm-Liouville operators with singular potentials

The inverse spectral problem is solved for the class of Sturm-Liouville operators with singular real-valued potentials from the space $W^{-1}_2(0,1)$. The potential is recovered via the eigenvalues and the corresponding norming constants. The reconstruction algorithm is presented and its stability proved. Also, the set of all possible spectral data is explicitly described and the isospectral sets are characterized.Comment: Submitted to Inverse Problem