Based on 1712.09990 which handles the 4-particle amplituhedron at 3-loop, we have found an extremely simple pattern, yet far more non-trivial than one might naturally expect: the all-loop Mondrian diagrammatics. By further simplifying and rephrasing the key relation of positivity in the amplituhedron setting, remarkably, we find a completeness relation unifying all diagrams of the Mondrian types for the 4-particle integrand of planar N = 4 SYM to all loop orders, each of which can be mapped to a simple product following a few plain rules designed for this relation. The explicit examples we investigate span from 3-loop to 7-loop order, and based on them, we classify the basic patterns of Mondrian diagrams into four types: the ladder, cross, brick-wall and spiral patterns. Interestingly, for some special combinations of ordered subspaces (a concept defined in the previous work), we find failed exceptions of the completeness relation which are called "anomalies", nevertheless, they substantially give hints on the all-loop recursive proof of this relation. These investigations are closely related to the combinatoric knowledge of separable permutations and Schröder numbers, and go even further from a diagrammatic perspective. For physical relevance, we need to further consider dual conformal invariance for two basic diagrammatic patterns to correct the numerator for a local integrand involving one or both of such patterns, while the denominator encoding its pole structure and also the sign factor, are already fixed by rules of the completeness relation. With this extra treatment to ensure the integrals are dual conformally invariant, each Mondrian diagram can be exactly translated to its corresponding physical loop integrand after being summed over all ordered subspaces that admit it.
A series of novel solid-solid phase change materials, namely, cellulose-g-polyoxyethylene (2) hexadecyl ether (Cellulose-g-E 2 C 16 ) copolymers, were synthesized using toluene 2,4-diisocyanate (TDI) as a coupling reagent in the ionic liquid 1-allyl-3-methylimidazolium chloride (AmimCl). The optimum prepolymerization conditions were determined to be 25°C and 75 min without catalyst, and the optimum reaction conditions of the grafting step were 90°C, 6 h and 0.1 wt% dibutyltin dilaurate (DBTDL, weight percent of TDI). The successful grafting was confirmed by FTIR and 1 H-NMR. The properties of the Cellulose-g-E 2 C 16 copolymers were investigated by DSC, TG and XRD. It is shown that the heat storage ability and phase change temperature of Cellulose-g-E 2 C 16 copolymers depended on the degree of substitution. The crystalline type of the grafted E 2 C 16 was not affected by the cellulosic backbone. Compared with E 2 C 16 , Cellulose-g-E 2 C 16 copolymers showed better thermal stability. They are expected to be widely applied in the area of thermal energy storage.
Remote monitoring of heart disease provides the means to keep patients under continuous supervision. In this paper, we introduce the design and implementation of a remote monitoring medical system for heart failure prediction and management. The three-part system includes a patient-end for data collection, a medical data center as data storage and analysis, and a doctor-end to diagnosis and intervention. The main objective of the system is to prognose the occurrence risk of heart failure (HF) confirmed by the level of N-terminal prohormone of brain natriuretic peptide (NT-proBNP) based on the changes of the patients’ (systolic and diastolic) blood pressure and body weight that are measured noninvasively in a home environment. The prediction of HF and non-HF patients was achieved by a structured support vector machine (SVM) classification algorithm. With the present system, we also proposed a scoring method to interpret the long-term risk of HF. We demonstrated the efficiency of the system with a pilot clinical study of 34 samples, where the NT-proBNP test was used to help train the prediction model as well as check the prediction results for our system. Results showed an accuracy of 79.4% for predicting HF on day 7 based on daily body weight and blood pressure data acquired over 30 days.
Cardiovascular disease (CVD) is a major issue to public health. It contributes 41% to the Chinese death rate each year. This huge loss encouraged us to develop a Wearable Efficient teleCARdiology systEm (WE-CARE) for early warning and prevention of CVD risks in real time. WE-CARE is expected to work 24/7 online for mobile health (mHealth) applications. Unfortunately, this purpose is often disrupted in system experiments and clinical trials, even if related enabling technologies work properly. This phenomenon is rooted in the overload issue of complex Electrocardiogram (ECG) data in terms of system integration. In this study, our main objective is to get a system light-loading technology to enable mHealth with a benchmarked ECG anomaly recognition rate. To achieve this objective, we propose an approach to purify clinical features from ECG raw data based on manifold learning, called the Manifold-based ECG-feature Purification algorithm. Our clinical trials verify that our proposal can detect anomalies with a recognition rate of up to 94% which is highly valuable in daily public health-risk alert applications based on clinical criteria. Most importantly, the experiment results demonstrate that the WE-CARE system enabled by our proposal can enhance system reliability by at least two times and reduce false negative rates to 0.76%, and extend the battery life by 40.54%, in the system integration level.
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