On Prediction Properties of Kriging: Uniform Error Bounds and Robustness

Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict for a range of untried points simultaneously. In this work we obtain some error bounds for the (simple) kriging predictor under the uniform metric. It works for a scattered set of input points in an arbitrary dimension, and also covers the case where the covariance function of the Gaussian process is misspecified. These results lead to a better understanding of the rate of convergence of kriging under the Gaussian or the Mat\'ern correlation functions, the relationship between space-filling designs and kriging models, and the robustness of the Mat\'ern correlation functions

Nonvolatile memory with molecule-engineered tunneling barriers

We report a novel field-sensitive tunneling barrier by embedding C60 in SiO2 for nonvolatile memory applications. C60 is a better choice than ultra-small nanocrystals due to its monodispersion. Moreover, C60 provides accessible energy levels to prompt resonant tunneling through SiO2 at high fields. However, this process is quenched at low fields due to HOMO-LUMO gap and large charging energy of C60. Furthermore, we demonstrate an improvement of more than an order of magnitude in retention to program/erase time ratio for a metal nanocrystal memory. This shows promise of engineering tunnel dielectrics by integrating molecules in the future hybrid molecular-silicon electronics.Comment: to appear in Applied Physics Letter

Brainstem metastases treated with Gamma Knife stereotactic radiosurgery: the Indiana University Health experience

Brainstem metastases offer a unique challenge in cancer treatment, yet stereotactic radiosurgery (SRS) has proven to be an effective modality in treating these tumors. This report discusses the clinical outcomes of patients with brainstem metastases treated at Indiana University with Gamma Knife (GK) radiosurgery from 2008 to 2016. 19 brainstem metastases from 14 patients who had follow-up brain imaging were identified. Median tumor volume was 0.04 cc (range: 0.01-2.0 cc). Median prescribed dose was 17.5 Gy to the 50% isodose line (range: 14-22 Gy). Median survival after GK SRS treatment to brainstem lesion was 17.2 months (range: 2.8-45.6 months). The experience at Indiana University confirms the safety and efficacy of range of GK SRS prescription doses (14-22 Gy) to brainstem metastases

Acute and Subacute Toxic Study of Aqueous Leaf Extract of Combretum Molle

Purpose: The purpose of the present study was to evaluate the acute and subacute toxicity of the aqueous leaf extract of Combretum molle.Methods: The acute toxicity of the extract was evaluated in rats. The animals were orally administered with doses ranging from 2000 to 8000 mg/kg and observed continuously for the first 4 h, then hourly for the next 24 h, and finally, 6-hourly for 72 h. Control animals received orally normal saline. The rats were observed carefully for mortality, pain as well as respiratory movements. For subacute toxicity, 6 groups of 6 rats (3 male and 3 female) each received intraperitoneally, normal saline (control), 400, 600, 800, 1000 and 1200 mg/kg of the extract, respectively, thrice daily for 15 days. At the end of the treatment period, the animals were sacrificed and their organs (liver, heart and kidney) removed for macroscopic examination.Results: For the acute toxicit test, no death and signs of poisoning were observed in the treated groups. In the subacute tstudy, LD50 in the rats after intraperitoneal administration was 700 mg/kg (456 - 896, 95 % confidence interval). The clinical signs of poisoning (motor difficulties, decreased respiratory rate, and tremor preceding death) were observed, suggesting overt toxicity throughout the neuromuscular system. However, histological examination of vital organs showed normal architecture suggesting no morphological abnormalities in the heart, kidney and liver.Conclusion: The results show that the aqueous leaf extract of C. molle is moderately toxic when given intraperitoneally.Keywords: Combretum molle, Acute/subacute toxicity, Histopathology, Rat