Invariant weighted Wiener measures and almost sure global well-posedness for the periodic derivative NLS

In this paper we construct an invariant weighted Wiener measure associated to the periodic derivative nonlinear Schr\"odinger equation in one dimension and establish global well-posedness for data living in its support. In particular almost surely for data in a Fourier-Lebesgue space {\mathcal F}L^{s,r}(\T) with $s \ge \frac{1}{2}$, $2 < r < 4$, $(s-1)r <-1$ and scaling like H^{\frac{1}{2}-\epsilon}(\T), for small $\epsilon >0$. We also show the invariance of this measure.Comment: 52 page

On the Infinite Variance Problem in Fermion Models

Monte Carlo calculations of fermionic systems with continuous auxiliary fields frequently suffer from a diverging variance. If a system has the infinite variance problem, one cannot estimate observables reliably even with an infinite number of samples. In this paper, we explore a method to deal with this problem based on sampling according to the distribution of a system with an extra time-slice. The necessary reweighting factor is computed both perturbatively and through a secondary Monte Carlo. We show that the Monte Carlo reweigthing coupled to the use of a non-biased estimator of the reweigthing factor leads to a method that eliminates the infinite variance problem at a very small extra cost. We compute the double occupancy in the Hubbard model at half-filling to demonstrate the method and compare the results to well established results obtained by other methods.Comment: 9 pages, 4 figure

A solution for infinite variance problem of fermionic observables

Fermionic Monte Carlo calculations with continuous auxiliary fields often encounter infinite variance problem from fermionic observables. This issue renders the estimation of observables unreliable, even with an infinite number of samples. In this work, we show that the infinite variance problem stems from the fermionic determinant. Also, we propose an approach to address this problem by employing a reweighting method that utilizes the distribution from an extra time-slice. Two strategies to compute the reweighting factor are explored: one involves truncating and analytically calculating the reweighting factor, while the other employs a secondary Monte Carlo estimation. With Hubbard model as a testbed, we demonstrate that utilizing the sub-Monte Carlo estimation, coupled with an unbiased estimator, offers a solution that effectively mitigates the infinite variance problem at a minimal additional cost.Comment: 7 pages, 3 figures, Proceedings of the 40th International Symposium on Lattice Field Theory (Lattice 2023), July 31st - August 4th, 2023, Fermi National Accelerator Laborator

Interfacing Microfluidics and Laser Desorption/Ionization Mass Spectrometry by Continuous Deposition for Application in Single Cell Analysis

We present a simple method for continuous deposition of effluent originating from a microfluidic device on a flat metal surface for subsequent analysis by matrix-assisted laser desorption/ionization mass spectrometry (MALDI-MS). The sample is delivered using a microscale fused silica capillary and passed onto the surface of a stainless steel plate coated with a layer of a standard matrix. The key parameters optimized in order to obtain high quality and reproducible sample traces are: i) sampleflow rate, ii) speed of the XY-stage movement, and iii) distance of the capillary tip from the plate. Tapering the capillary end as well as surface functionalization to induce hydrophobicity were shown to further enhance the deposition process. The described continuous deposition method is compared with a previously published mass spectrometric method utilizing a piezoelectric microdispenser for microspotting onto the MALDI plates which enabled detection of primary metabolites at the singlecell level. Research is underway to adapt the continuous deposition as an interface for single cell metabolite detection and enhancement of quantitative abilities of the MALDI methodology. We envisage that the presented continuous deposition method may also be suitable for sensitive detection of analytes using other surface analysis tools

Novel impeller design for stem cell bioprocessing and its application in hMSC stirred-tank bioreactor cultures

Please click Additional Files below to see the full abstract

Peptidylarginine deiminase (PAD) is a mouse cortical granule protein that plays a role in preimplantation embryonic development

BACKGROUND: While mammalian cortical granules are important in fertilization, their biochemical composition and functions are not fully understood. We previously showed that the ABL2 antibody, made against zona free mouse blastocysts, binds to a 75-kDa cortical granule protein (p75) present in a subpopulation of mouse cortical granules. The purpose of this study was to identify and characterize p75, examine its distribution in unfertilized oocytes and preimplantation embryos, and investigate its biological role in fertilization. RESULTS: To identify p75, the protein was immunoprecipitated from ovarian lysates with the ABL2 antibody and analyzed by tandem mass spectrometry (MS/MS). A partial amino acid sequence (VLIGGSFY) was obtained, searched against the NCBI nonredundant database using two independent programs, and matched to mouse peptidylarginine deiminase (PAD). When PAD antibody was used to probe western blots of p75, the antibody detected a single protein band with a molecular weight of 75 kDa, confirming our mass spectrometric identification of p75. Immunohistochemistry demonstrated that PAD was present in the cortical granules of unfertilized oocytes and was released from activated and in vivo fertilized oocytes. After its release, PAD was observed in the perivitelline space, and some PAD remained associated with the oolemma and blastomeres' plasma membranes as a peripheral membrane protein until the blastocyst stage of development. In vitro treatment of 2-cell embryos with the ABL2 antibody or a PAD specific antibody retarded preimplantation development, suggesting that cortical granule PAD plays a role after its release in preimplantation cleavage and early embryonic development. CONCLUSION: Our data showed that PAD is present in the cortical granules of mouse oocytes, is released extracellularly during the cortical reaction, and remains associated with the blastomeres' surfaces as a peripheral membrane protein until the blastocyst stage of development. Our in vitro study supports the idea that extracellular PAD functions in preimplantation development

Transitions in Mathematics Education

Mathematics Education; Learning; Teachin