Integral Equations with Hypersingular Kernels -- Theory and Applications to Fracture Mechanics

Hypersingular integrals of the type I_{\alpha}(T_n,m,r) = \int_{-1}^{1} \hpsngAbs \frac{T_n(s)(1-s^2)^{m-{1/2}}}{(s-r)^\alpha}ds |r|<1 and I_{\alpha}(U_n,m,r) = \int_{-1}^{1} \hpsngAbs \frac{U_n(s)(1-s^2)^{m-{1/2}}}{(s-r)^\alpha}ds |r|<1 are investigated for general integers $\alpha$ (positive) and $m$ (non-negative), where $T_n(s)$ and $U_n(s)$ are the Tchebyshev polynomials of the 1st and 2nd kinds, respectively. Exact formulas are derived for the cases $\alpha = 1, 2, 3, 4$ and $m = 0, 1, 2, 3$; most of them corresponding to new solutions derived in this paper. Moreover, a systematic approach for evaluating these integrals when $\alpha > 4$ and $m>3$ is provided. The integrals are also evaluated as $|r|>1$ in order to calculate stress intensity factors (SIFs). Examples involving crack problems are given and discussed with emphasis on the linkage between mathematics and mechanics of fracture. The examples include classical linear elastic fracture mechanics (LEFM), functionally graded materials (FGM), and gradient elasticity theory. An appendix, with closed form solutions for a broad class of integrals, supplements the paper

Efficacy of laser interstitial thermal therapy for biopsy-proven radiation necrosis in radiographically recurrent brain metastases

BACKGROUND: Laser interstitial thermal therapy (LITT) in the setting of post-SRS radiation necrosis (RN) for patients with brain metastases has growing evidence for efficacy. However, questions remain regarding hospitalization, local control, symptom control, and concurrent use of therapies. METHODS: Demographics, intraprocedural data, safety, Karnofsky performance status (KPS), and survival data were prospectively collected and then analyzed on patients who consented between 2016-2020 and who were undergoing LITT for biopsy-proven RN at one of 14 US centers. Data were monitored for accuracy. Statistical analysis included individual variable summaries, multivariable Fine and Gray analysis, and Kaplan-Meier estimated survival. RESULTS: Ninety patients met the inclusion criteria. Four patients underwent 2 ablations on the same day. Median hospitalization time was 32.5 hours. The median time to corticosteroid cessation after LITT was 13.0 days (0.0, 1229.0) and cumulative incidence of lesional progression was 19% at 1 year. Median post-procedure overall survival was 2.55 years [1.66, infinity] and 77.1% at one year as estimated by KaplanMeier. Median KPS remained at 80 through 2-year follow-up. Seizure prevalence was 12% within 1-month post-LITT and 7.9% at 3 months; down from 34.4% within 60-day prior to procedure. CONCLUSIONS: LITT for RN was not only again found to be safe with low patient morbidity but was also a highly effective treatment for RN for both local control and symptom management (including seizures). In addition to averting expected neurological death, LITT facilitates ongoing systemic therapy (in particular immunotherapy) by enabling the rapid cessation of steroids, thereby facilitating maximal possible survival for these patients

Panel: Teaching To Increase Diversity and Equity in STEM

TIDES (Teaching to Increase Diversity and Equity in STEM) is a three-year initiative to transform colleges and universities by changing what STEM faculty, especially CS instructors, are doing in the classroom to encourage the success of their students, particularly those that have been traditionally underrepresented in computer science. Each of the twenty projects selected proposed new interdisciplinary curricula and adopted culturally sensitive pedagogies, with an eye towards departmental and institutional change. The four panelists will each speak about their TIDES projects, which all involved educating faculty about cultural competency. Three of the panelists infused introductory CS courses with applications from other disciplines, while one of the projects taught computational skills in natural science courses

Panel: Teaching To Increase Diversity and Equity in STEM

TIDES (Teaching to Increase Diversity and Equity in STEM) is a three-year initiative to transform colleges and universities by changing what STEM faculty, especially CS instructors, are doing in the classroom to encourage the success of their students, particularly those that have been traditionally underrepresented in computer science. Each of the twenty projects selected proposed new interdisciplinary curricula and adopted culturally sensitive pedagogies, with an eye towards departmental and institutional change. The four panelists will each speak about their TIDES projects, which all involved educating faculty about cultural competency. Three of the panelists infused introductory CS courses with applications from other disciplines, while one of the projects taught computational skills in natural science courses

Stereotactic ablative radiotherapy for medically inoperable early stage lung cancer: early outcomes

Objective To evaluate the clinical outcome and safety of stereotactic ablative radiotherapy for medically inoperable stage I non- small-cell lung carcinoma. Design Retrospective case series. Setting Pamela Youde Nethersole Eastern Hospital, Hong Kong. Patients All patients with medically inoperable stage I non-small-cell lung carcinoma receiving stereotactic ablative radiotherapy since its establishment in 2008. Main outcome measures Disease control rate, overall survival, and treatment toxicities. Results Sixteen stage I non-small-cell lung carcinoma patients underwent the procedure from June 2008 to November 2011. The median patient age was 82 years and the majority (81%) had moderate-tosevere co-morbidity based on the Adult Comorbidity Evaluation 27 index. With a median follow-up of 22 months, the 2-year primary tumour control rate, disease-free survival and overall survival rates were 91%, 71% and 87%, respectively. No grade 3 (National Cancer Institute Common Terminology Criteria for Adverse Events) or higher treatment-related complications were reported. Conclusion Stereotactic ablative radiotherapy can achieve a high degree of local control safely in medically inoperable patients with early lung cancer.published_or_final_versio

Survival Analysis of Re-resection Versus Radiofrequency Ablation for Intrahepatic Recurrence After Hepatectomy for Hepatocellular Carcinoma

Ó The Author(s) 2011. This article is published with open access at Springerlink.com Background Tumor recurrence after resection of hepatocellular carcinoma is a common phenomenon. Re-resection and radiofrequency ablation (RFA) are good options for treating recurrent HCC. This study compared the efficacy of these two modalities in the treatment of intrahepatic HCC recurrence after hepatectomy. Methods From January 2001 to December 2008, a total of 179 patients developed intrahepatic HCC recurrence after hepatectomy. To treat the recurrence, 29 patients underwent re-resection and 45 patients had RFA. Patient characteristics, clinicopathologic data, and survival outcomes were reviewed. Results Child-Pugh status, time to develop first recurrence (12.2 vs. 8.7 months), and recurrent tumor size (2.1 vs. 2.1 cm) were comparable for the two groups. Time to develop a second intrahepatic recurrence after re-resection and RFA was 5.9 and 4.0 months respectively. The 1-, 3-, and 5-year disease-free survival rates were 41.4%, 24.2%, and 24.2 % after re-resection and 32.2%, 12.4%, and 9.3% after RFA (p = 0.14). The 1-, 3-, and 5-year overall survival rates were 89.7%, 56.5%, and 35.2 % after re-resection and 83.7%, 43.1%, and 29.1 % after RFA (p = 0.48). For the second recurrence, 33.3 % of patients underwent a second round of RFA and 10.0 % underwent a third resection

Lorentz-CPT violation, radiative corrections and finite temperature

In this work we investigate the radiatively induced Chern-Simons-like terms in four-dimensions at zero and finite temperature. We use the approach of rationalizing the fermion propagator up to the leading order in the CPT-violating coupling $b_\mu$. In this approach, we have shown that although the coefficient of Chern-Simons term can be found unambiguously in different regularization schemes at zero or finite temperature, it remains undetermined. We observe a correspondence among results obtained at finite and zero temperature.Comment: To appear in JHEP, 10 pages, 1 eps figure, minor changes and references adde

The PRE-Derived NMR Model of the 38.8-kDa Tri-Domain IsdH Protein from Staphylococcus aureus Suggests That It Adaptively Recognizes Human Hemoglobin

Staphylococcus aureus is a medically important bacterial pathogen that, during infections, acquires iron from human hemoglobin (Hb). It uses two closely related iron-regulated surface determinant (Isd) proteins to capture and extract the oxidized form of heme (hemin) from Hb, IsdH and IsdB. Both receptors rapidly extract hemin using a conserved tri-domain unit consisting of two NEAT (near iron transporter) domains connected by a helical linker domain. To gain insight into the mechanism of extraction, we used NMR to investigate the structure and dynamics of the 38.8-kDa tri-domain IsdH protein (IsdHN2N3, A326–D660 with a Y642A mutation that prevents hemin binding). The structure was modeled using long-range paramagnetic relaxation enhancement (PRE) distance restraints, dihedral angle, small-angle X-ray scattering, residual dipolar coupling and inter-domain NOE nuclear Overhauser effect data. The receptor adopts an extended conformation wherein the linker and N3 domains pack against each other via a hydrophobic interface. In contrast, the N2 domain contacts the linker domain via a hydrophilic interface and, based on NMR relaxation data, undergoes inter-domain motions enabling it to reorient with respect to the body of the protein. Ensemble calculations were used to estimate the range of N2 domain positions compatible with the PRE data. A comparison of the Hb-free and Hb-bound forms reveals that Hb binding alters the positioning of the N2 domain. We propose that binding occurs through a combination of conformational selection and induced-fit mechanisms that may promote hemin release from Hb by altering the position of its F helix

Structural Studies and Structure Activity Relationships for Novel Computationally Designed Non-nucleoside Inhibitors and Their Interactions With HIV-1 Reverse Transcriptase

Reverse transcriptase (RT) from the human immunodeficiency virus continues to be an attractive drug target for antiretroviral therapy. June 2022 will commemorate the 30th anniversary of the first Human Immunodeficiency Virus (HIV) RT crystal structure complex that was solved with non-nucleoside reverse transcriptase inhibitor nevirapine. The release of this structure opened opportunities for designing many families of non-nucleoside reverse transcriptase inhibitors (NNRTIs). In paying tribute to the first RT-nevirapine structure, we have developed several compound classes targeting the non-nucleoside inhibitor binding pocket of HIV RT. Extensive analysis of crystal structures of RT in complex with the compounds informed iterations of structure-based drug design. Structures of seven additional complexes were determined and analyzed to summarize key interactions with residues in the non-nucleoside inhibitor binding pocket (NNIBP) of RT. Additional insights comparing structures with antiviral data and results from molecular dynamics simulations elucidate key interactions and dynamics between the nucleotide and non-nucleoside binding sites.Fil: Frey, Kathleen M.. University of Yale; Estados UnidosFil: Bertoletti, Nicole. University of Yale; Estados UnidosFil: Chan, Albert H.. University of Yale; Estados UnidosFil: Ippolito, Joseph A.. University of Yale; Estados UnidosFil: Bollini, Mariela. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Centro de Investigaciones en Bionanociencias "Elizabeth Jares Erijman"; Argentina. University of Yale; Estados UnidosFil: Spasov, Krasimir A.. University of Yale; Estados UnidosFil: Jorgensen, William L.. University of Yale; Estados UnidosFil: Anderson, Karen S.. University of Yale; Estados Unido