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关键词： Caputo fractional derivative   fractional differential equations   fractional integrals   impulsive differential equations   non-instantaneous impulses   Volterra integral equations  

摘要： Real-world processes that display non-local behaviours or interactions, and that are subject to external impulses over non-zero periods, can potentially be modelled using non-instantaneous impulsive fractional differential equations or systems. These have been the subject of many recent papers, which rely on re-formulating fractional differential equations in terms of integral equations, in order to prove results such as existence, uniqueness, and stability. However, specifically in the non-instantaneous impulsive case, some of the existing papers contain invalid re-formulations of the problem, based on a misunderstanding of how fractional operators behave. In this work, we highlight the correct ways of writing non-instantaneous impulsive fractional differential equations as equivalent integral equations, considering several different cases according to the lower limits of the integro-differential operators involved.

关键词： Codes   Decoding   Reed-Solomon codes   Additives   Kernel   Convolutional codes   Linear codes   Linear codes   convolutional codes   decoding   skew codes  

摘要： A large class of MDS linear codes is constructed. These codes are endowed with an efficient decoding algorithm. Both the definition of the codes and the design of their decoding algorithm only require from Linear Algebra methods, making them fully accessible for everyone. Thus, the first part of the paper develops a direct presentation of the codes by means of parity-check matrices, and the decoding algorithm rests upon matrix and linear maps manipulations. The somewhat more sophisticated mathematical context (non-commutative rings) needed for the proof of the correctness of the decoding algorithm is postponed to the second part. A final section locates the Reed-Solomon skew-differential codes introduced here within the general context of codes defined by means of skew polynomial rings.

关键词： Data compression   differential encoding   Huffman encoding   smart agriculture   IoT  

摘要： Agriculture faces several uncertain problems in terms of making the best use of its natural resources. As a result, and in light of the growing threat of changing weather conditions, we must closely track local soil conditions and meteorological data to expedite the adoption of culture-friendly decisions. In the Internet of Things (IoT) era, deploying Wireless Sensor Networks (WSN) as a low-cost remote monitoring and management system for these types of features is a viable choice. However, the WSN is hampered by the motes' insufficient energy sources, which reduces the network's overall lifespan. Each mote collects the tracked feature regularly and sends the data to the sink for further analysis. This method of transmitting large amounts of data requires the sensor node to use a lot of energy and a lot of network bandwidth. We propose a lightweight lossless compression algorithm based on Differential Encoding (DE) and Huffman techniques in this paper, which is especially useful for IoT sensor nodes that track environmental features, especially those with limited computing and memory resources. Rather than attempting to create novel ad hoc algorithms, we show that, given a general understanding of the features to be monitored, classical Huffman coding can be used to effectively represent the same features that measure at different times and locations. Even though the proposed system does not achieve the theoretical limit, results using temperature measurements show that it outperforms standard methods built specifically for WSNs.

关键词： Diagnostic markers   Prognostic markers   Schizophrenia   Medicine/Public Health   general   Psychiatry   Neurosciences   Behavioral Sciences   Pharmacotherapy   Biological Psychology  

摘要： Psychotic disorders are common and disabling mental conditions. The relative importance of immune-related mechanisms in psychotic disorders remains subject of debate. Here, we present a large-scale retrospective study of blood and cerebrospinal fluid (CSF) immune cell profiles of psychosis spectrum patients. We performed basic CSF analysis and multi-dimensional flow cytometry of CSF and blood cells from 59 patients with primary psychotic disorders (F20, F22, F23, and F25) in comparison to inflammatory (49 RRMS and 16 NMDARE patients) and non-inflammatory controls (52 IIH patients). We replicated the known expansion of monocytes in the blood of psychosis spectrum patients, that we identified to preferentially affect classical monocytes. In the CSF, we found a relative shift from lymphocytes to monocytes, increased protein levels, and evidence of blood-brain barrier disruption in psychosis. In fact, these CSF features confidently distinguished autoimmune encephalitis from psychosis despite similar (initial) clinical features. We then constructed machine learning models incorporating blood and CSF parameters and demonstrated their superior ability to differentiate psychosis from non-inflammatory controls compared to individual parameters. Multi-dimensional and multi-compartment immune cell signatures can thus support the diagnosis of psychosis spectrum disorders with the potential to accelerate diagnosis and initiation of therapy.

关键词： Third kind Volterra integro-differential equations   Spectral collocation method   Noncompact   Smoothing transformation   Convergence analysis  

摘要： This work is to analyze a Legendre collocation approximation for third-kind Volterra integro-differential equations. The rigorous error analysis in the L-infinity and L-omega(.0,0)2-norms is provided for the proposed method. In fact when converting the original equation to an equivalent second kind one, the integral operator of the obtained equation contains two singularities and may become non-compact under certain conditions. In addition, in order to avoid the low-order accuracy caused by the singularity of the solution at the initial point, we adopted the idea of smooth transformation at the beginning to convert the original equation into a new equation with a more regular solution. Finally, the validity and applicability of the method are verified by several numerical experiments.

关键词： rational function model   differential evolution algorithm   E-plane filter   waveguide   radio frequency filters  

摘要： The article presents a stochastic population-based optimization algorithm, called Differential Evolution Algorithm, to optimally approximate Radio-Frequency filters into a compact mathematical form consisting of poles and residues. The methodology enables reduced-order rational function models, generated by minimizing a frequency domain least square error function. The article presents numerical examples of various filter prototypes to illustrate the accuracy of the Differential Evolution Algorithm in terms of its system identification capability. The results show that Differential Evolution Algorithm is capable of identifying the poles and residues of filters accurately. It is also observed that Differential Evolution Algorithm approximates the systems with a reduced-order of approximation compared with the existing modeling algorithm. Further, Differential Evolution Algorithm is applied to determine the pole-zero model of a Ka-band waveguide E-Plane Bandpass Filter (EPF). We have observed that the proposed methodology is capable of generating accurate reduced-order rational function models of microwave filters from their frequency domain responses.

关键词： Machine learning   Breast cancer   Ultrasound  

摘要： Objectives We aimed to assess the performance of radiomics and machine learning (ML) for classification of non-cystic benign and malignant breast lesions on ultrasound images, compare ML's accuracy with that of a breast radiologist, and verify if the radiologist's performance is improved by using ML. Methods Our retrospective study included patients from two institutions. A total of 135 lesions from Institution 1 were used to train and test the ML model with cross-validation. Radiomic features were extracted from manually annotated images and underwent a multistep feature selection process. Not reproducible, low variance, and highly intercorrelated features were removed from the dataset. Then, 66 lesions from Institution 2 were used as an external test set for ML and to assess the performance of a radiologist without and with the aid of ML, using McNemar's test. Results After feature selection, 10 of the 520 features extracted were employed to train a random forest algorithm. Its accuracy in the training set was 82% (standard deviation, SD, +/- 6%), with an AUC of 0.90 (SD +/- 0.06), while the performance on the test set was 82% (95% confidence intervals (CI) = 70-90%) with an AUC of 0.82 (95% CI = 0.70-0.93). It resulted in being significantly better than the baseline reference (p = 0.0098), but not different from the radiologist (79.4%, p = 0.815). The radiologist's performance improved when using ML (80.2%), but not significantly (p = 0.508). Conclusions A radiomic analysis combined with ML showed promising results to differentiate benign from malignant breast lesions on ultrasound images.

关键词： non-front-fanged colubroids   nonvenomous snake   antivenom  

摘要： Bites of "nonvenomous" snakes can sometimes be mistaken for the bites of venomous snakes. As an example of this confusion, this report describes confirmed bites by Philodryas olfersii and Bothrops jararaca. In the first case, a 55-y-old man with a history of controlled hypertension was bitten on his right forearm by P olfersii. Physical examination revealed extensive edema, erythema, and widespread ecchymoses throughout his right upper limb. Laboratory tests indicated leukocytosis and high D-dimer levels, but normal coagulation, suggestive of a resolved recent coagulopathy. He received only supportive treatment. In the second case, a healthy 35-y-old man was bitten by B jararaca. Although the anatomic region of the bite and the results of physical examination were similar to those in the first case, laboratory tests showed mild coagulopathy, leukocytosis, and high D-dimer levels. The patient was treated with antivenom. In both cases, the 20-min whole blood clotting test results were normal. Patients bitten by P olfersii may present with local symptoms resembling B jararaca envenomation. Without snake identification and the detection of venom-induced consumption coagulopathy, especially in places where the 20-min whole blood clotting test is the only clotting test available, it is almost impossible to establish an accurate and safe differential diagnosis. In this context, the best alternative is to take the risk of prescribing antivenom for a possible P olfersii bite rather than failing to do so for a real Bothrops bite. Late treatment for Bothrops bite can result in severe complications and sequelae.

关键词： Reachability analysis   Uncertainty quantification   Interval methods   Sensitivity analysis   Verification  

摘要： This paper presents a new method for bounding the set of trajectories consistent with a system of nonlinear ordinary differential equations, a compact set of admissible time-invariant uncertainties, and a set of state constraints. Such reachability bounds are important in set-based state estimation, fault detection, robust control, etc. Interval reachability methods based on differential inequalities (DI) are desirable in these applications due to their high efficiency, but they often produce extremely conservative bounds. Here, we extend the DI approach to compute tighter enclosures using the mean value form, which is widely used to mitigate the conservatism of interval methods in non-dynamic settings. We present a general mean-value DI bounding theorem along with an efficient algorithmic implementation. We also prove that the overestimation error of mean-value DI converges to zero quadratically as the uncertainty set diminishes, rather than linearly as for interval DI methods, which is important for algorithms based on uncertainty set partitioning. Finally, we present numerical results for two challenging test problems. (C) 2021 Elsevier Ltd. All rights reserved.

关键词： anaemia of chronic disease   hepcidin   Iron deficiency anaemia   reticulocyte haemoglobin equivalent  

摘要： Introduction Iron deficiency anaemia (IDA) and anaemia of chronic disease (ACD) are common causes of anaemia with similar clinical and laboratory features. IDA is caused by low iron stores while ACD is due to iron-restricted erythropoiesis occurring in inflammatory states. Differential diagnosis requires analysis of multiple biochemical and haematological parameters. IDA can occur simultaneously to ACD (mixed aetiology). It is essential that true iron deficiency is identified, as these patients will require iron therapy. This preliminary study investigated whether hepcidin, the master regulator of iron homeostasis, in conjunction with reticulocyte haemoglobin equivalent (RetHe) has the potential to differentiate IDA from ACD, and to exclude IDA in patients with mixed aetiology. Methods Hepcidin concentration (measured using a commercially available ELISA method), RetHe, and iron parameters along with C-reactive protein (CRP) were analysed in 77 Gastroenterology patients with anaemia in a secondary care setting. Results Receiver operator characteristic (ROC) analysis showed that hepcidin at an optimal cut-off concentration of 46ng/ml. Identifying true IDA in mixed aetiology patients could be achieved by RetHe analysis and applying an optimal cut-off of <30pg. Conclusion Hepcidin, in conjunction with RetHe, offers a new simplified diagnostic pathway for differential diagnosis of IDA and ACD, thereby reducing the diagnostic turnaround time and allowing appropriate treatment of patients with a true iron deficiency.