A Hybrid Lagrangian Variational Method for Bose–Einstein Condensates in Optical Lattices

Solving the Gross–Pitaevskii (GP) equation describing a Bose–Einstein condensate (BEC) immersed in an optical lattice potential can be a numerically demanding task. We present a variational technique for providing fast, accurate solutions of the GP equation for systems where the external potential exhibits rapid variation along one spatial direction. Examples of such systems include a BEC subjected to a one-dimensional optical lattice or a Bragg pulse. This variational method is a hybrid form of the Lagrangian variational method for the GP equation in which a hybrid trial wavefunction assumes a Gaussian form in two coordinates while being totally unspecified in the third coordinate. The resulting equations of motion consist of a quasi-one-dimensional GP equation coupled to ordinary differential equations for the widths of the transverse Gaussians. We use this method to investigate how an optical lattice can be used to move a condensate non-adiabatically

A Hybrid Lagrangian Variation Method for Bose-Einstein Condensates in Optical Lattices

Solving the Gross--Pitaevskii (GP) equation describing a Bose--Einstein condensate (BEC) immersed in an optical lattice potential can be a numerically demanding task. We present a variational technique for providing fast, accurate solutions of the GP equation for systems where the external potential exhibits rapid varation along one spatial direction. Examples of such systems include a BEC subjected to a one--dimensional optical lattice or a Bragg pulse. This variational method is a hybrid form of the Lagrangian Variational Method for the GP equation in which a hybrid trial wavefunction assumes a gaussian form in two coordinates while being totally unspecified in the third coordinate. The resulting equations of motion consist of a quasi--one--dimensional GP equation coupled to ordinary differential equations for the widths of the transverse gaussians. We use this method to investigate how an optical lattice can be used to move a condensate non--adiabatically.Comment: 16 pages and 1 figur

Haplotypes of DNA repair and cell cycle control genes, X-ray exposure, and risk of childhood acute lymphoblastic leukemia

[[abstract]]Background: Acute leukemias of childhood are a heterogeneous group of malignancies characterized by cytogenetic abnormalities, such as translocations and changes in ploidy. These abnormalities may be influenced by altered DNA repair and cell cycle control processes. Methods: We examined the association between childhood acute lymphoblastic leukemia (ALL) and 32 genes in DNA repair and cell cycle pathways using a haplotype-based approach, among 377 childhood ALL cases and 448 controls enrolled during 1995-2002. Results: We found that haplotypes in APEX1, BRCA2, ERCC2, and RAD51 were significantly associated with total ALL, while haplotypes in NBN and XRCC4, and CDKN2A were associated with structural and numerical change subtypes, respectively. In addition, we observed statistically significant interaction between exposure to 3 or more diagnostic X-rays and haplotypes of XRCC4 on risk of structural abnormality-positive childhood ALL. Conclusions: These results support a role of altered DNA repair and cell cycle processes in the risk of childhood ALL, and show that this genetic susceptibility can differ by cytogenetic subtype and may be modified by exposure to ionizing radiation. To our knowledge, our study is the first to broadly examine the DNA repair and cell cycle pathways using a haplotype approach in conjunction with X-ray exposures in childhood ALL risk. If confirmed, future studies are needed to identify specific functional SNPs in the regions of interest identified in this analysis

The Structure of Complete Degrees

This paper surveys investigations into how strong these commonalities are. More concretely, we are concerned with: What do NP-complete sets look like? To what extent are the properties of particular NP-complete sets, e.g., SAT, shared by all NP-complete sets? If there are are structural differences between NP-complete sets, what are they and what explains the differences? We make these questions, and the analogous questions for other complexity classes, more precise below. We need first to formalize NP-completeness. There are a number of competing definitions of NP-completeness. (See [Har78a, p. 7] for a discussion.) The most common, and the one we use, is based on the notion of m-reduction, also known as polynomial-time manyone reduction and Karp reduction. A set A is m-reducible to B if and only if there is a (total) polynomial-time computable function f such that for all x, x 2 A () f(x) 2 B: (1)

Improving DNA double-strand repair inhibitor KU55933 therapeutic index in cancer radiotherapy using nanoparticle drug delivery

Radiotherapy is a key component of cancer treatment. Because of its importance, there has been high interest in developing agents and strategies to further improve the therapeutic index of radiotherapy. DNA double-strand repair inhibitors (DSBRIs) are among the most promising agents to improve radiotherapy. However, their clinical translation has been limited by their potential toxicity to normal tissue. Recent advances in nanomedicine offer an opportunity to overcome this limitation. In this study, we aim to demonstrate the proof of principle by developing and evaluating nanoparticle (NP) formulations of KU55933, a DSBRI. We engineered a NP formulation of KU55933 using nanoprecipitation method with different lipid polymer nanoparticle formulation. NP KU55933 using PLGA formulation has the best loading efficacy as well as prolonged drug release profile. We demonstrated that NP KU55933 is a potent radiosensitizer in vitro using clonogenic assay and is more effective as a radiosensitizer than free KU55933 in vivo using mouse xenograft models of non-small cell lung cancer (NSCLC). Western blots and immunofluorescence showed NP KU55933 exhibited more prolonged inhibition of DNA repair pathway. In addition, NP KU55933 leads to lower skin toxicity than KU55933. Our study supports further investigations using NP to deliver DSBRIs to improve cancer radiotherapy treatment

Discovery of PiragliatinFirst Glucokinase Activator Studied in Type 2 Diabetic Patients

Glucokinase (GK) activation as a potential strategy to treat type 2 diabetes (T2D) is well recognized. Compound <b>1</b>, a glucokinase activator (GKA) lead that we have previously disclosed, caused reversible hepatic lipidosis in repeat-dose toxicology studies. We hypothesized that the hepatic lipidosis was due to the structure-based toxicity and later established that it was due to the formation of a thiourea metabolite, <b>2</b>. Subsequent SAR studies of <b>1</b> led to the identification of a pyrazine-based lead analogue <b>3</b>, lacking the thiazole moiety. In vivo metabolite identification studies, followed by the independent synthesis and profiling of the cyclopentyl keto- and hydroxyl- metabolites of <b>3</b>, led to the selection of piragliatin, <b>4</b>, as the clinical lead. Piragliatin was found to lower pre- and postprandial glucose levels, improve the insulin secretory profile, increase β-cell sensitivity to glucose, and decrease hepatic glucose output in patients with T2D