Separable Physics-informed Neural Networks for Solving the BGK Model of the Boltzmann Equation

In this study, we introduce a method based on Separable Physics-Informed Neural Networks (SPINNs) for effectively solving the BGK model of the Boltzmann equation. While the mesh-free nature of PINNs offers significant advantages in handling high-dimensional partial differential equations (PDEs), challenges arise when applying quadrature rules for accurate integral evaluation in the BGK operator, which can compromise the mesh-free benefit and increase computational costs. To address this, we leverage the canonical polyadic decomposition structure of SPINNs and the linear nature of moment calculation, achieving a substantial reduction in computational expense for quadrature rule application. The multi-scale nature of the particle density function poses difficulties in precisely approximating macroscopic moments using neural networks. To improve SPINN training, we introduce the integration of Gaussian functions into SPINNs, coupled with a relative loss approach. This modification enables SPINNs to decay as rapidly as Maxwellian distributions, thereby enhancing the accuracy of macroscopic moment approximations. The relative loss design further ensures that both large and small-scale features are effectively captured by the SPINNs. The efficacy of our approach is demonstrated through a series of five numerical experiments, including the solution to a challenging 3D Riemann problem. These results highlight the potential of our novel method in efficiently and accurately addressing complex challenges in computational physics

Nasal Hemangiopericytoma Causing Oncogenic Osteomalacia

Oncogenic osteomalacia is a rare cause that makes abnormalities of bone metabolism. Our case arose in a 47-year-old woman presenting a nasal mass associated with osteomalacia. We excised the mass carefully. After surgery, it was diagnosed as hemangiopericytoma and her symptoms related with osteomalacia were relieved and biochemical abnormalities were restored to normal range. We report and review a rare case of nasal hemangiopericytoma that caused osteomalacia

Antimicrobial peptide from Bacillus subtilis CSB138: characterization, killing kinetics, and synergistic potency

We studied the prospect of synergy between the antimicrobial peptide p138c and non-peptide antibiotics for increasing the potency and bacterial killing kinetics of these agents. The production of p138c was maximized in the late exponential growth phase of Bacillus subtilis CSB138. Purification of p138c resulted in a total of 4800 arbitrary units (AU) with 19.15-fold and 3.2% recovery. Peptide p138c was thermo-tolerant up to 50 °C and stable at pH 5.8 to 11. The biochemical nature of p138c was determined by a bioassay, similar to tricine-SDS-PAGE, indicating inhibition at 3 kDa. The amino acid sequence of p138c was Gly-Leu-Glu-Glu-Thr-Val-Tyr-Ile-Tyr-Gly-Ala-Asn-Met-X-Ser. Potency and killing kinetics against vancomycin-resistant Staphylococcus aureus improved considerably when p138c was synergized with oxacillin, ampicillin, and penicillin G. The minimal inhibitory concentration (MIC) of p138c showed a 4-, 8-, and 16-fold improvement when p138c was combined with oxacillin, ampicillin, and penicillin G, respectively. The fractional inhibitory concentration index for the combination of p138c and oxacillin, ampicillin, and penicillin G was 0.3125, 0.25, and 0.09, respectively. Synergy with non-peptide antibiotics resulted in enhanced killing kinetics of p138c. Hence, the synergy between antimicrobial peptide and non-peptide antibiotics may enhance the potency and bacterial killing kinetics, providing more potent and rapidly acting agents for therapeutic use. [Int Microbiol 20(1):43-53 (2017)]Keywords: Bacillus subtilis · antimicrobial peptides · killing kinetic