In this paper, first, we introduce a new concept, called the norm-to-weak continuous semigroup in a Banach space, and give a technical theorem to verify this notion of continuity. Then we establish a general method which is necessary and sufficient to obtain the existence of the global attractor for this kind of semigroup. As an application, we obtain the existence of the global attractor for a nonlinear reaction-diffusion equation with a polynomial growth nonlinearity of arbitrary order and with some weak derivatives in the inhomogeneous term, the global attractors are obtained in L p ( ), H 1 0 ( ) and H 2 ( )∩H 1 0 ( ), respectively. A new a priori estimate method, called asymptotic a priori estimate, has been introduced. Since the solutions of the equation has no higher regularity and the semigroup associated the solutions is not continuous in L p ( ), H 1 0 ( ) and H 2 ( ) ∩ H 1 0 ( ), the results in this part are new and appear to be optimal.

BackgroundLate Gadolinium enhancement (LGE) cardiovascular magnetic resonance (CMR) imaging can be used to visualise regions of fibrosis and scarring in the left atrium (LA) myocardium. This can be important for treatment stratification of patients with atrial fibrillation (AF) and for assessment of treatment after radio frequency catheter ablation (RFCA). In this paper we present a standardised evaluation benchmarking framework for algorithms segmenting fibrosis and scar from LGE CMR images. The algorithms reported are the response to an open challenge that was put to the medical imaging community through an ISBI (IEEE International Symposium on Biomedical Imaging) workshop.MethodsThe image database consisted of 60 multicenter, multivendor LGE CMR image datasets from patients with AF, with 30 images taken before and 30 after RFCA for the treatment of AF. A reference standard for scar and fibrosis was established by merging manual segmentations from three observers. Furthermore, scar was also quantified using 2, 3 and 4 standard deviations (SD) and full-width-at-half-maximum (FWHM) methods. Seven institutions responded to the challenge: Imperial College (IC), Mevis Fraunhofer (MV), Sunnybrook Health Sciences (SY), Harvard/Boston University (HB), Yale School of Medicine (YL), King’s College London (KCL) and Utah CARMA (UTA, UTB). There were 8 different algorithms evaluated in this study.ResultsSome algorithms were able to perform significantly better than SD and FWHM methods in both pre- and post-ablation imaging. Segmentation in pre-ablation images was challenging and good correlation with the reference standard was found in post-ablation images. Overlap scores (out of 100) with the reference standard were as follows: Pre: IC = 37, MV = 22, SY = 17, YL = 48, KCL = 30, UTA = 42, UTB = 45; Post: IC = 76, MV = 85, SY = 73, HB = 76, YL = 84, KCL = 78, UTA = 78, UTB = 72.ConclusionsThe study concludes that currently no algorithm is deemed clearly better than others. There is scope for further algorithmic developments in LA fibrosis and scar quantification from LGE CMR images. Benchmarking of future scar segmentation algorithms is thus important. The proposed benchmarking framework is made available as open-source and new participants can evaluate their algorithms via a web-based interface.

First we establish some necessary and sufficient conditions for the existence of the global attractor of an infinite dimensional dynamical system, using the measure of noncompactness. Then we give a new method/recipe for proving the existence of the global attractor. The main advantage of this new method/recipe is that one needs only to verify a necessary compactness condition with the same type of energy estimates as those for establishing the absorbing set. In other words, one doesn't need to obtain estimates in function spaces of higher regularity. In particular, this property is useful when higher regularity is not available, as demonstrated in the example on the Navier-Stokes equations on nonsmooth domains.

Content caching at the edge nodes is a promising technique to reduce the data traffic in next-generation wireless networks. Inspired by the success of Deep Reinforcement Learning (DRL) in solving complicated control problems, this work presents a DRL-based framework with Wolpertinger architecture for content caching at the base station. The proposed framework is aimed at maximizing the long-term cache hit rate, and it requires no knowledge of the content popularity distribution. To evaluate the proposed framework, we compare the performance with other caching algorithms, including Least Recently Used (LRU), Least Frequently Used (LFU), and First-In First-Out (FIFO) caching strategies. Meanwhile, since the Wolpertinger architecture can effectively limit the action space size, we also compare the performance with Deep Q-Network to identify the impact of dropping a portion of the actions. Our results show that the proposed framework can achieve improved short-term cache hit rate and improved and stable long-term cache hit rate in comparison with LRU, LFU, and FIFO schemes. Additionally, the performance is shown to be competitive in comparison to Deep Q-learning, while the proposed framework can provide significant savings in runtime.

The existence and structure of uniform attractors in V is proved for nonautonomous 2D Navier-stokes equations on bounded domain with a new class of external forces, termed normal in L 2 loc (R; H) (see Definition 3.1), which are translation bounded but not translation compact in L 2 loc (R; H). To this end, some abstract results are established. First, a characterization on the existence of uniform attractor for a family of processes is presented by the concept of measure of noncompactness as well as a method to verify it. Then, the structure of the uniform attractor is obtained by constructing skew product flow on the extended phase space with weak topology. Finally, the uniform attractor of a process is identified with that of a family of processes with symbols in the closure of the translation family of the original symbol in a Banach space with weak topology.