Capacity Analysis of Linear Operator Channels over Finite Fields

Motivated by communication through a network employing linear network coding, capacities of linear operator channels (LOCs) with arbitrarily distributed transfer matrices over finite fields are studied. Both the Shannon capacity $C$ and the subspace coding capacity $C_{\text{SS}}$ are analyzed. By establishing and comparing lower bounds on $C$ and upper bounds on $C_{\text{SS}}$, various necessary conditions and sufficient conditions such that $C=C_{\text{SS}}$ are obtained. A new class of LOCs such that $C=C_{\text{SS}}$ is identified, which includes LOCs with uniform-given-rank transfer matrices as special cases. It is also demonstrated that $C_{\text{SS}}$ is strictly less than $C$ for a broad class of LOCs. In general, an optimal subspace coding scheme is difficult to find because it requires to solve the maximization of a non-concave function. However, for a LOC with a unique subspace degradation, $C_{\text{SS}}$ can be obtained by solving a convex optimization problem over rank distribution. Classes of LOCs with a unique subspace degradation are characterized. Since LOCs with uniform-given-rank transfer matrices have unique subspace degradations, some existing results on LOCs with uniform-given-rank transfer matrices are explained from a more general way.Comment: To appear in IEEE Transactions on Information Theor

On Linear Operator Channels over Finite Fields

Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver. There are NO constraints on the distribution of the transformation matrix and the field size. Specifically, the optimality of subspace coding over LOCs is investigated. A lower bound on the maximum achievable rate of subspace coding is obtained and it is shown to be tight for some cases. The maximum achievable rate of constant-dimensional subspace coding is characterized and the loss of rate incurred by using constant-dimensional subspace coding is insignificant. The maximum achievable rate of channel training is close to the lower bound on the maximum achievable rate of subspace coding. Two coding approaches based on channel training are proposed and their performances are evaluated. Our first approach makes use of rank-metric codes and its optimality depends on the existence of maximum rank distance codes. Our second approach applies linear coding and it can achieve the maximum achievable rate of channel training. Our code designs require only the knowledge of the expectation of the rank of the transformation matrix. The second scheme can also be realized ratelessly without a priori knowledge of the channel statistics.Comment: 53 pages, 3 figures, submitted to IEEE Transaction on Information Theor

A DNA biochip for on-the-spot multiplexed pathogen identification

Miniaturized integrated DNA analysis systems have largely been based on a multi-chamber design with microfluidic control to process the sample sequentially from one module to another. This microchip design in connection with optics involved hinders the deployment of this technology for point-of-care applications. In this work, we demonstrate the implementation of sample preparation, DNA amplification, and electrochemical detection in a single silicon and glass-based microchamber and its application for the multiplexed detection of Escherichia coli and Bacillus subtilis cells. The microdevice has a thin-film heater and temperature sensor patterned on the silicon substrate. An array of indium tin oxide (ITO) electrodes was constructed within the microchamber as the transduction element. Oligonucleotide probes specific to the target amplicons are individually positioned at each ITO surface by electrochemical copolymerization of pyrrole and pyrrole−probe conjugate. These immobilized probes were stable to the thermal cycling process and were highly selective. The DNA-based identification of the two model pathogens involved a number of steps including a thermal lysis step, magnetic particle-based isolation of the target genomes, asymmetric PCR, and electrochemical sequence-specific detection using silver-enhanced gold nanoparticles. The microchamber platform described here offers a cost-effective and sample-to-answer technology for on-site monitoring of multiple pathogens

A DNA biochip for on-the-spot multiplexed pathogen identification

Miniaturized integrated DNA analysis systems have largely been based on a multi-chamber design with microfluidic control to process the sample sequentially from one module to another. This microchip design in connection with optics involved hinders the deployment of this technology for point-of-care applications. In this work, we demonstrate the implementation of sample preparation, DNA amplification, and electrochemical detection in a single silicon and glass-based microchamber and its application for the multiplexed detection of Escherichia coli and Bacillus subtilis cells. The microdevice has a thin-film heater and temperature sensor patterned on the silicon substrate. An array of indium tin oxide (ITO) electrodes was constructed within the microchamber as the transduction element. Oligonucleotide probes specific to the target amplicons are individually positioned at each ITO surface by electrochemical copolymerization of pyrrole and pyrrole−probe conjugate. These immobilized probes were stable to the thermal cycling process and were highly selective. The DNA-based identification of the two model pathogens involved a number of steps including a thermal lysis step, magnetic particle-based isolation of the target genomes, asymmetric PCR, and electrochemical sequence-specific detection using silver-enhanced gold nanoparticles. The microchamber platform described here offers a cost-effective and sample-to-answer technology for on-site monitoring of multiple pathogens

The impact of the ClearRT™ upgrade on target motion tracking accuracy in Radixact® Synchrony® lung treatments

Background: The objective was to investigate the change in segmentation error of Radixact® Synchrony® lung treatment after its kV imaging system was upgraded from Generation 1 to Generation 2 in the ClearRT™ installation. Materials and methods: Radixact® Lung Synchrony® plans were created for the Model 18023 Xsight® Lung Tracking “XLT” Phantom combined with different lung target inserts with densities of 0.280, 0.500, 0.943 and 1.093 g/cc. After Radixact® Synchrony® treatment delivery using the Generation 1 and Generation 2 kV systems according to each plan, the tracking performance of the two kV systems on each density insert was compared by calculating the root mean square (RMS) error (δRMS) between the Synchrony-predicted motion in the log file and the known phantom motion and by calculating δ95%, the maximum error within a 95% probability threshold. Results: The δRMS and δ95% of Radixact® Synchrony® treatment for Gen1 kV systems deteriorated as the density of the target insert decreased, from 1.673 ± 0.064 mm and 3.049 ± 0.089 mm, respectively, for the 1.093 g/cc insert to 8.355 ± 5.873 mm and 15.297 ± 10.470 mm, respectively, for the 0.280 g/cc insert. In contrast, no such trend was observed in the δRMS or δ95% of Synchrony® treatment using the Gen2 kV system. The δRMS and δ95%, respectively, fluctuated slightly from 1.586 to 1.687 mm and from 2.874 to 2.971 mm when different target inserts were tracked by the Gen2 kV system. Conclusion: With improved image contrast in kV radiographs, the Gen2 kV imaging system can enhance the ability to track targets accurately in Radixact® Lung Synchrony® treatment and reduce the segmentation error. Our study showed that lung targets with density values as low as 0.280 cc/g could be tracked correctly in Synchrony treatment with the Gen2 kV imaging system

Roles of the CHADS2 and CHA2DS2-VASc scores in post-myocardial infarction patients: Risk of new occurrence of atrial fibrillation and ischemic stroke

Background: Patients with myocardial infarction (MI) are at risk of the development of atrial fibrillation (AF) and ischemic stroke. We sought to evaluate the prognostic performance of the CHADS2 and CHA2DS2-VASc scores in predicting new AF and/or ischemic stroke in post-ST segment elevation MI (STEMI) patients. Six hundred and seven consecutive post-STEMI patients with no previously documented AF were studied.Methods and Results: After a follow-up of 63 months (3,184 patient-years), 83 (13.7%) patients developed new AF (2.8% per year). Patients with a high CHADS2 and/or CHA2DS2-VASc score were more likely to develop new AF. The annual incidence of new AF was 1.18%, 2.10%, 4.52%, and 7.03% in patients with CHADS2 of 0, 1, 2, and ≥ 3; and 0.39%, 1.72%, 1.83%, and 5.83% in patients with a CHA2DS2-VASc score of 1, 2, 3 and ≥ 4. The CHA2DS2-VASc score (C-statistic = 0.676) was superior to the CHADS2 (C-statistic = 0.632) for discriminating new AF. Ischemic stroke occurred in 29 patients (0.9% per year), the incidence increasing in line with the CHADS2 (0.41%, 1.02%, 1.11%, and 1.95% with score of 0, 1, 2, and ≥ 3) and CHA2DS2-VASc scores (0.39%, 0.49%, 1.02%, and 1.48% with score of 1, 2, 3 and ≥ 4). The C-statistic of the CHA2DS2-VASc score as a predictor of ischemic stroke was 0.601, superior to that of CHADS2 score (0.573). CHADS2 and CHA2DS2-VASc scores can identify post-STEMI patients at high risk of AF and stroke.Conclusions: The CHADS2 and CHA2DS2-VASc scores can identify post-STEMI patients at high risk of AF and ischemic stroke. This enables close surveillance and prompt anticoagulation for stroke prevention

A Brief Mindfulness-Based Family Psychoeducation Intervention for Chinese Young Adults With First Episode Psychosis: A Study Protocol

Family psychoeducation (FPE) has been recommended as a major component in the treatment of psychosis. Many previous studies have implemented an intensive program design that often only emphasized improvements in patients’ illness outcomes but the benefits for caregivers were limited. There have been calls for a time-limited but cost-effective FPE program to mitigate the looming reality of the suffering of people with psychosis and their families. A Brief Mindfulness-Based Family Psychoeducation for psychosis program is developed to reduce caregivers’ burden and promote young adult’s recovery. A randomized controlled trial will be conducted to compare this intervention with an ordinary FPE intervention. Both arms will involve six sessions, with a total contact time of 12 h. 300 caregivers of young adults who have experienced first episode psychosis within last 3 years will be recruited. Program effectiveness will be assessed by comparing outcomes measuring the caregivers’ burden, mental health symptoms, positive well-being, and the young adult’s mental health symptoms during the study and at 9-month post-randomization. The role of expressed emotions, interpersonal mindfulness, and non-attachment in mediating these outcomes will be explored. An additional qualitative approach Photovoice is selected to explore the complex family experiences and the benefits of mindfulness from the caregivers’ personal perspectives.Trial Registration: The trial is registered with the United States Clinical Trials Registry (ClinicalTrials.gov): NCT03688009