Efficient computation of high index Sturm-Liouville eigenvalues for problems in physics

Finding the eigenvalues of a Sturm-Liouville problem can be a computationally challenging task, especially when a large set of eigenvalues is computed, or just when particularly large eigenvalues are sought. This is a consequence of the highly oscillatory behaviour of the solutions corresponding to high eigenvalues, which forces a naive integrator to take increasingly smaller steps. We will discuss some techniques that yield uniform approximation over the whole eigenvalue spectrum and can take large steps even for high eigenvalues. In particular, we will focus on methods based on coefficient approximation which replace the coefficient functions of the Sturm-Liouville problem by simpler approximations and then solve the approximating problem. The use of (modified) Magnus or Neumann integrators allows to extend the coefficient approximation idea to higher order methods

Comment on: a two-stage fourth-order “almost” P-stable method for oscillatory problems

AbstractIn Chawla and Al-Zanaidi (J. Comput. Appl. Math. 89 (1997) 115–118) a fourth-order “almost” P-stable method for y″=f(x,y) is proposed. We claim that it is possible to retrieve this combination of multistep methods by means of the theory of parameterized Runge-Kutta-Nyström (RKN) methods and moreover to generalize the method discussed by Chawla and Al-Zanaidi (J. Comput. Appl. Math. 89 (1997) 115–118)

Functional Validation of the Putative Oncogenic Activity of PLAU

Plasminogen activator, urokinase (PLAU) is involved in cell migration, proliferation and tissue remodeling. PLAU upregulation is associated with an increase in aggressiveness, metastasis, and invasion of several cancer types, including breast cancer. In patients, this translates into decreased sensitivity to hormonal treatment, and poor prognosis. These clinical findings have led to the examination of PLAU as a biomarker for predicting breast cancer prognosis and therapy responses. In this study, we investigated the functional ability of PLAU to act as an oncogene in breast cancers by modulating its expression using CRISPR-deactivated Cas9 (CRISPR-dCas9) tools. Different effector domains (e.g., transcription modulators (VP64, KRAB)) alone or in combination with epigenetic writers (DNMT3A/3L, MSssI) were fused to dCas9 and targeted to the PLAU promoter. In MDA-MB-231 cells characterized by high PLAU expression downregulation of PLAU expression by CRISPR-dCas9-DNMT3A/3L-KRAB, resulted in decreased cell proliferation. Conversely, CRISPR-dCas9-VP64 induced PLAU upregulation in low PLAU expressing MCF-7 cells and significantly increased aggressiveness and invasion. In conclusion, modulation of PLAU expression affected metastatic related properties of breast cancer cells, thus further validating its oncogenic activity in breast cancer cells.</p

Functional Validation of the Putative Oncogenic Activity of PLAU

Plasminogen activator, urokinase (PLAU) is involved in cell migration, proliferation and tissue remodeling. PLAU upregulation is associated with an increase in aggressiveness, metastasis, and invasion of several cancer types, including breast cancer. In patients, this translates into decreased sensitivity to hormonal treatment, and poor prognosis. These clinical findings have led to the examination of PLAU as a biomarker for predicting breast cancer prognosis and therapy responses. In this study, we investigated the functional ability of PLAU to act as an oncogene in breast cancers by modulating its expression using CRISPR-deactivated Cas9 (CRISPR-dCas9) tools. Different effector domains (e.g., transcription modulators (VP64, KRAB)) alone or in combination with epigenetic writers (DNMT3A/3L, MSssI) were fused to dCas9 and targeted to the PLAU promoter. In MDA-MB-231 cells characterized by high PLAU expression downregulation of PLAU expression by CRISPR-dCas9-DNMT3A/3L-KRAB, resulted in decreased cell proliferation. Conversely, CRISPR-dCas9-VP64 induced PLAU upregulation in low PLAU expressing MCF-7 cells and significantly increased aggressiveness and invasion. In conclusion, modulation of PLAU expression affected metastatic related properties of breast cancer cells, thus further validating its oncogenic activity in breast cancer cells.</p

Functional Validation of the Putative Oncogenic Activity of PLAU

Plasminogen activator, urokinase (PLAU) is involved in cell migration, proliferation and tissue remodeling. PLAU upregulation is associated with an increase in aggressiveness, metastasis, and invasion of several cancer types, including breast cancer. In patients, this translates into decreased sensitivity to hormonal treatment, and poor prognosis. These clinical findings have led to the examination of PLAU as a biomarker for predicting breast cancer prognosis and therapy responses. In this study, we investigated the functional ability of PLAU to act as an oncogene in breast cancers by modulating its expression using CRISPR-deactivated Cas9 (CRISPR-dCas9) tools. Different effector domains (e.g., transcription modulators (VP64, KRAB)) alone or in combination with epigenetic writers (DNMT3A/3L, MSssI) were fused to dCas9 and targeted to the PLAU promoter. In MDA-MB-231 cells characterized by high PLAU expression downregulation of PLAU expression by CRISPR-dCas9-DNMT3A/3L-KRAB, resulted in decreased cell proliferation. Conversely, CRISPR-dCas9-VP64 induced PLAU upregulation in low PLAU expressing MCF-7 cells and significantly increased aggressiveness and invasion. In conclusion, modulation of PLAU expression affected metastatic related properties of breast cancer cells, thus further validating its oncogenic activity in breast cancer cells.</p

Functional Validation of the Putative Oncogenic Activity of PLAU

Plasminogen activator, urokinase (PLAU) is involved in cell migration, proliferation and tissue remodeling. PLAU upregulation is associated with an increase in aggressiveness, metastasis, and invasion of several cancer types, including breast cancer. In patients, this translates into decreased sensitivity to hormonal treatment, and poor prognosis. These clinical findings have led to the examination of PLAU as a biomarker for predicting breast cancer prognosis and therapy responses. In this study, we investigated the functional ability of PLAU to act as an oncogene in breast cancers by modulating its expression using CRISPR-deactivated Cas9 (CRISPR-dCas9) tools. Different effector domains (e.g., transcription modulators (VP64, KRAB)) alone or in combination with epigenetic writers (DNMT3A/3L, MSssI) were fused to dCas9 and targeted to the PLAU promoter. In MDA-MB-231 cells characterized by high PLAU expression downregulation of PLAU expression by CRISPR-dCas9-DNMT3A/3L-KRAB, resulted in decreased cell proliferation. Conversely, CRISPR-dCas9-VP64 induced PLAU upregulation in low PLAU expressing MCF-7 cells and significantly increased aggressiveness and invasion. In conclusion, modulation of PLAU expression affected metastatic related properties of breast cancer cells, thus further validating its oncogenic activity in breast cancer cells.</p