Physics-Informed with Power-Enhanced Residual Network for Interpolation and Inverse Problems

This paper introduces a novel neural network structure called the Power-Enhancing residual network, designed to improve interpolation capabilities for both smooth and non-smooth functions in 2D and 3D settings. By adding power terms to residual elements, the architecture boosts the network's expressive power. The study explores network depth, width, and optimization methods, showing the architecture's adaptability and performance advantages. Consistently, the results emphasize the exceptional accuracy of the proposed Power-Enhancing residual network, particularly for non-smooth functions. Real-world examples also confirm its superiority over plain neural network in terms of accuracy, convergence, and efficiency. The study also looks at the impact of deeper network. Moreover, the proposed architecture is also applied to solving the inverse Burgers' equation, demonstrating superior performance. In conclusion, the Power-Enhancing residual network offers a versatile solution that significantly enhances neural network capabilities. The codes implemented are available at: \url{https://github.com/CMMAi/ResNet_for_PINN}

A discrepancy principle for the source points location in using the MFS for solving the BHCP

Based on the discrepancy principle, we develop in this paper a new method of choosing the location of source points to solve the backward heat conduction problem (BHCP) by using the method of fundamental solutions (MFS). The standard Tikhonov regularization technique with the L curve method for an optimal regularized parameter is adopted for solving the resultant highly ill-conditioned system of linear equations. Numerical verifications of the proposed computational method are presented for both the onedimensional and the two-dimensional BHCP

The genetic basis of onset age in schizophrenia: evidence and models

Schizophrenia is a heritable neurocognitive disorder affecting about 1% of the population, and usually has an onset age at around 21–25 in males and 25–30 in females. Recent advances in genetics have helped to identify many common and rare variants for the liability to schizophrenia. Earlier evidence appeared to suggest that younger onset age is associated with higher genetic liability to schizophrenia. Clinical longitudinal research also found that early and very-early onset schizophrenia are associated with poor clinical, neurocognitive, and functional profiles. A recent study reported a heritability of 0.33 for schizophrenia onset age, but the genetic basis of this trait in schizophrenia remains elusive. In the pre-Genome-Wide Association Study (GWAS) era, genetic loci found to be associated with onset age were seldom replicated. In the post-Genome-Wide Association Study era, new conceptual frameworks are needed to clarify the role of onset age in genetic research in schizophrenia, and to identify its genetic basis. In this review, we first discussed the potential of onset age as a characterizing/subtyping feature for psychosis, and as an important phenotypic dimension of schizophrenia. Second, we reviewed the methods, samples, findings and limitations of previous genetic research on onset age in schizophrenia. Third, we discussed a potential conceptual framework for studying the genetic basis of onset age, as well as the concepts of susceptibility, modifier, and “mixed” genes. Fourth, we discussed the limitations of this review. Lastly, we discussed the potential clinical implications for genetic research of onset age of schizophrenia, and how future research can unveil the potential mechanisms for this trait

Drosophila LAR Regulates R1-R6 and R7 Target Specificity in the Visual System

AbstractDifferent classes of photoreceptor neurons (R cells) in the Drosophila compound eye connect to specific targets in the optic lobe. Using a behavioral screen, we identified LAR, a receptor tyrosine phosphatase, as being required for R cell target specificity. In LAR mutant mosaic eyes, R1-R6 cells target to the lamina correctly, but fail to choose the correct pattern of target neurons. Although mutant R7 axons initially project to the correct layer of the medulla, they retract into inappropriate layers. Using single cell mosaics, we demonstrate that LAR controls targeting of R1-R6 and R7 in a cell-autonomous fashion. The phenotypes of LAR mutant R cells are strikingly similar to those seen in N-cadherin mutants

Hypofractionated Stereotactic Ablative Radiotherapy for Recurrent or Oligometastatic Tumours in Children and Young Adults

AIMS Cancer remains a leading cause of death in children and adolescents in the developed world. Despite advances in oncological management, rates of primary treatment failure remain significant. Radiation of recurrent or metastatic disease improves survival in adults but there is little data to support clinical decision making in the paediatric/teenage and young adult population. Materials And Methods We present a retrospective case series of 14 patients treated with stereotactic ablative body radiotherapy or stereotactic radiosurgery at The Royal Marsden Hospital from September 2011 to December 2015. Eligible patients were aged <25 years, with Lansky/Karnofsky performance status ≥60 with confirmed relapsed or metastatic tumour in fewer than three sites. Follow-up was in accordance with standard clinical care and included regular outpatient review and radiological surveillance. Local control, progression-free survival and overall survival are presented. RESULTS Data for 14 patients with 18 treated lesions were included. The median patient age was 15 years (range 5–20 years). Nine patients were treated for local recurrence and five for metastatic lesions. All patients had already undergone multiple previous treatments. Eleven patients had undergone previous radiotherapy. The median interval between the completion of initial radiotherapy and reirradiation was 29.0 months (range 0.2–49.5 months). The median follow-up was 3.4 years (range 0.28–6.4 years). The 1-year local control rate was 78.6% and the 2-year local control rate was 57.1%. Overall median survival was 58.4 months (95% confidence interval 33.8–82.9 months). Cumulative biologically effective doses (BED) over 200 Gy were associated with late toxicity (P = 0.04). CONCLUSION Radical doses of short-course hypofractionated radiotherapy can achieve excellent local control and may contribute to the prolongation of overall survival. There is a need for prospective trials exploring the use of ablative radiotherapy in metastatic disease in paediatric/teenage and young adult patients in order to establish safe and effective treatment schedules

Optoacoustic solitons in Bragg gratings

Optical gap solitons, which exist due to a balance of nonlinearity and dispersion due to a Bragg grating, can couple to acoustic waves through electrostriction. This gives rise to a new species of ``gap-acoustic'' solitons (GASs), for which we find exact analytic solutions. The GAS consists of an optical pulse similar to the optical gap soliton, dressed by an accompanying phonon pulse. Close to the speed of sound, the phonon component is large. In subsonic (supersonic) solitons, the phonon pulse is a positive (negative) density variation. Coupling to the acoustic field damps the solitons' oscillatory instability, and gives rise to a distinct instability for supersonic solitons, which may make the GAS decelerate and change direction, ultimately making the soliton subsonic.Comment: 5 pages, 3 figure