Explore the vast range of titles available.

For fractional derivatives and time-fractional differential equations, we construct a framework on the basis of operator theory in fractional Sobolev spaces. Our framework provides a feasible extension of the classical Caputo and the Riemann–Liouville derivatives within Sobolev spaces of fractional orders, including negative ones. Our approach enables a unified treatment for fractional calculus and time-fractional differential equations. We formulate initial value problems for fractional ordinary differential equations and initial boundary value problems for fractional partial differential equations to prove well-posedness and other properties.

Hosts have been fighting pathogens throughout the evolution of all infectious diseases. Toxoplasma gondii is one of the most common infectious agents in humans but causes only opportunistic infection in healthy individuals. Similar to antimicrobial immunity against other organisms, the immune response against T. gondii activates innate immunity and in turn induces acquired immune responses. After activation of acquired immunity, host immune cells robustly produce the proinflammatory cytokine interferon-γ (IFN-γ), which activates a set of IFN-γ-inducible proteins, including GTPases. IFN-inducible GTPases are essential for cell-autonomous immunity and are specialized for effective clearance and growth inhibition of T. gondii by accumulating in parasitophorous vacuole membranes. Recent studies suggest that the cell-autonomous immune response plays a protective role in host defense against not only T. gondii but also various intracellular bacteria. Moreover, the negative regulatory mechanisms of such strong immune responses are also important for host survival after infection. In this review, we will discuss in detail recent advances in the understanding of host defenses against T. gondii and the roles played by cell-autonomous immune responses. Toxoplasmosis: Insights into immunity Researchers are extensively studying immune responses to the single-celled parasite Toxoplasma gondii , which infects around one-third of humans, often harmlessly, but can cause life-threatening toxoplasmosis infections in patients with weakened immune systems. Masahiro Yamamoto and Miwa Sasai at Osaka University in Japan review recent advances in understanding the interactions between the immune system and the parasite. They consider non-specific ‘innate’ immune responses and also the ‘acquired’ responses that target specific parts of the parasite, referred to as antigens. Methods that selectively switch off genes in mice are revealing details presumed to also be relevant for humans. Significant molecules, molecular signaling pathways and immune-regulating processes are being identified. Recent studies suggest cell-autonomous immunity, the ability of host cells to defend themselves against attack, plays a significant role in fighting Toxoplasma gondii infection.

Diabetic patients have a higher fracture risk than expected by their bone mineral density (BMD). Poor bone quality is the most suitable and explainable cause for the elevated fracture risk in this population. Advanced glycation end products (AGEs), which are diverse compounds generated via a non-enzymatic reaction between reducing sugars and amine residues, physically affect the properties of the bone material, one of a component of bone quality, through their accumulation in the bone collagen fibers. On the other hand, these compounds biologically act as agonists for these receptors for AGEs (RAGE) and suppress bone metabolism. The concentrations of AGEs and endogenous secretory RAGE, which acts as a “decoy receptor” that inhibits the AGEs-RAGE signaling axis, are associated with fracture risk in a BMD-independent manner. AGEs are closely associated with the pathogenesis of this unique clinical manifestation through physical and biological mechanisms in patients with diabetes mellitus.

Sensing and clearance of dysfunctional lysosomes is critical for cellular homeostasis. Here we show that transcription factor EB (TFEB)—a master transcriptional regulator of lysosomal biogenesis and autophagy—is activated during the lysosomal damage response, and its activation is dependent on the function of the ATG conjugation system, which mediates LC3 lipidation. In addition, lysosomal damage triggers LC3 recruitment on lysosomes, where lipidated LC3 interacts with the lysosomal calcium channel TRPML1, facilitating calcium efflux essential for TFEB activation. Furthermore, we demonstrate the presence and importance of this TFEB activation mechanism in kidneys in a mouse model of oxalate nephropathy accompanying lysosomal damage. A proximal tubule-specific TFEB-knockout mouse exhibited progression of kidney injury induced by oxalate crystals. Together, our results reveal unexpected mechanisms of TFEB activation by LC3 lipidation and their physiological relevance during the lysosomal damage response.Nakamura et al. find that the master transcriptional regulator of lysosomal biogenesis and autophagy TFEB is activated following LC3 lipidation during lysosomal damage and show the importance of this mechanism during kidney injury.

Chronic inflammation during many diseases is associated with bone loss. While interferons (IFNs) are often inhibitory to osteoclast formation, the complex role that IFN and interferon-stimulated genes (ISGs) play in osteoimmunology during inflammatory diseases is still poorly understood. We show that mice deficient in IFN signaling components including IFN alpha and beta receptor 1 (IFNAR1), interferon regulatory factor 1 (IRF1), IRF9, and STAT1 each have reduced bone density and increased osteoclastogenesis compared to wild type mice. The IFN-inducible guanylate-binding proteins (GBPs) on mouse chromosome 3 (GBP1, GBP2, GBP3, GBP5, GBP7) are required to negatively regulate age-associated bone loss and osteoclastogenesis. Mechanistically, GBP2 and GBP5 both negatively regulate in vitro osteoclast differentiation, and loss of GBP5, but not GBP2, results in greater age-associated bone loss in mice. Moreover, mice deficient in GBP5 or chromosome 3 GBPs have greater LPS-mediated inflammatory bone loss compared to wild type mice. Overall, we find that GBP5 contributes to restricting age-associated and inflammation-induced bone loss by negatively regulating osteoclastogenesis. The innate immune system and inflammation modulate bone homeostasis through complex regulation of bone remodelling cells including osteoblasts and osteoclasts. Here, the authors show that the type I interferon pathway and guanylate binding proteins functionally limit bone loss by inhibiting osteoclast functions.

In this survey paper, we start with a discussion of the general fractional derivative (GFD) introduced by A. Kochubei in his recent publications. In particular, a connection of this derivative to the corresponding fractional integral and the Sonine relation for their kernels are presented. Then we consider some fractional ordinary differential equations (ODEs) with the GFD including the relaxation equation and the growth equation. The main part of the paper is devoted to the fractional partial differential equations (PDEs) with the GFD. We discuss both the Cauchy problems and the initial-boundary-value problems for the time-fractional diffusion equations with the GFD. In the final part of the paper, some results regarding the inverse problems for the differential equations with the GFD are presented.

In this paper, we deal with the initial-boundary-value problems for a general time-fractional diffusion equation which generalizes the single- and the multi-term time-fractional diffusion equations as well as the time-fractional diffusion equation of the distributed order. First, important estimates for the general time-fractional derivatives of the Riemann-Liouville and the Caputo type of a function at its maximum point are derived. These estimates are applied to prove a weak maximum principle for the general time-fractional diffusion equation. As an application of the maximum principle, the uniqueness of both the strong and the weak solutions to the initial-boundary-value problem for this equation with the Dirichlet boundary conditions is established. Finally, the existence of a suitably defined generalized solution to the the initial-boundary-value problem with the homogeneous boundary conditions is proved.

This article is concerned with an inverse problem on simultaneously determining some unknown coefficients and/or an order of derivative in a multidimensional time-fractional evolution equation either in a Euclidean domain or on a Riemannian manifold. Based on a special choice of the Dirichlet boundary input, we prove the unique recovery of at most two out of four x -dependent coefficients (possibly with an extra unknown fractional order) by a single measurement of the partial Neumann boundary output. Especially, both a vector-valued velocity field of a convection term and a density can also be uniquely determined. The key ingredient turns out to be the time-analyticity of the decomposed solution, which enables the construction of Dirichlet-to-Neumann maps in the frequency domain and thus the application of inverse spectral results.

This study, derived from campaign communication mediation models, examines how incidental news exposure on social media affects political participation. Analysis of two-wave panel data collected before the 2016 US presidential election shows that incidental news exposure on social media is associated with increases in offline and online political participation (1) through online political information seeking and (2) through online political information seeking and online political expression in serial. Interestingly, results show that incidental news exposure on social media also has a direct negative relationship with offline and online political participation. Implications for the political utility of social media are discussed.

In this paper we study the null controllability property for a single population model in which the population y depends on time t, space x, age a and size τ. Moreover, the diffusion coefficient k is degenerate at a point of the domain or both extremal points. Our technique is essentially based on Carleman estimates. The τ dependence requires us to modify the weight for the Carleman estimates, and accordingly the proof of the observability inequality. Thanks to this observability inequality we obtain a null controllability result for an intermediate problem and finally for the initial system through suitable cut off functions.