Learning with Algebraic Invariances, and the Invariant Kernel Trick

When solving data analysis problems it is important to integrate prior knowledge and/or structural invariances. This paper contributes by a novel framework for incorporating algebraic invariance structure into kernels. In particular, we show that algebraic properties such as sign symmetries in data, phase independence, scaling etc. can be included easily by essentially performing the kernel trick twice. We demonstrate the usefulness of our theory in simulations on selected applications such as sign-invariant spectral clustering and underdetermined ICA

Decoherence and Entropy Production in Relativistic Nuclear Collisions

Short thermalization times of less than 1 fm/c for quark and gluon matter have been suggested by recent experiments at the Relativistic Heavy Ion Collider (RHIC). It has been difficult to justify this rapid thermalization in first-principle calculations based on perturbation theory or the color glass condensate picture. Here, we address the related question of the decoherence of the gluon field, which is a necessary component of thermalization. We present a simplified leading-order computation of the decoherence time of a gluon ensemble subject to an incoming flux of Weizsacker-Williams gluons. We also discuss the entropy produced during the decoherence process and its relation to the entropy in the final state which has been measured experimentally.Comment: 8 pages, 3 figure

Benchmarking a semiclassical impurity solver for dynamical-mean-field theory: self-energies and magnetic transitions of the single-orbital Hubbard model

An investigation is presented of the utility of semiclassical approximations for solving the quantum-impurity problems arising in the dynamical-mean-field approach to the correlated-electron models. The method is based on performing a exact numerical integral over the zero-Matsubara-frequency component of the spin part of a continuous Hubbard-Stratonovich field, along with a spin-field-dependent steepest descents treatment of the charge part. We test this method by applying it to one or two site approximations to the single band Hubbard model with different band structures, and comparing the results to quantum Monte-Carlo and simplified exact diagonalization calculations. The resulting electron self-energies, densities of states and magnetic transition temperatures show reasonable agreement with the quantum Monte-Carlo simulation over wide parameter ranges, suggesting that the semiclassical method is useful for obtaining a reasonable picture of the physics in situations where other techniques are too expensive.Comment: 14 pages, 15 figure

Platelet lysate as a serum substitute for 2D static and 3D perfusion culture of stromal vascular fraction cells from human adipose tissue

Fetal bovine serum (FBS) and fibroblast growth factor (FGF)-2 are key supplements for the culture of stromal vascular fraction (SVF) cells from adipose tissue, both for typical monolayer (2D) expansion and for streamlined generation of osteogenic-vasculogenic grafts in 3D perfusion culture. The present study investigates whether factors present in human platelet lysate (PL) could substitute for FBS and FGF-2 in 2D and 3D culture models of SVF cells from human lipoaspirates. SVF cells were grown in medium supplemented with 10% FBS+FGF-2 or with 5% PL. In 2D cultures, PL initially supported SVF cell proliferation, but resulted in growth arrest shortly after the first passage. Freshly isolated SVF cells cultured with both media under perfusion for 5 days within 3D ceramic scaffolds induced bone formation after subcutaneous implantation in nude mice. However, blood vessels of donor origin were generated only using FBS+FGF-2-cultured cells. This was unexpected, because the proportion of CD34+/CD31+ endothelial lineage cells was significantly higher with PL than that of FBS+FGF-2 (33% vs. 3%, respectively). These results support the use of PL as a substitute of FBS+FGF-2 for short-term culture of human SVF cells, and indicate that more specific serum-free formulations are required to maintain a functionally vasculogenic fraction of SVF cells expanded under 3D perfusion

Probing molecular free energy landscapes by periodic loading

Single molecule pulling experiments provide information about interactions in biomolecules that cannot be obtained by any other method. However, the reconstruction of the molecule's free energy profile from the experimental data is still a challenge, in particular for the unstable barrier regions. We propose a new method for obtaining the full profile by introducing a periodic ramp and using Jarzynski's identity for obtaining equilibrium quantities from non-equilibrium data. Our simulated experiments show that this method delivers significant more accurate data than previous methods, under the constraint of equal experimental effort.Comment: 4 pages, 3 figure

Imaging the Electrostatic Potential of Transmembrane Channels: Atomic Probe Microscopy of OmpF Porin

This is the published version. Copyright 2002 by Elsevier.The atomic force microscope (AFM) was used to image native OmpF porin and to detect the electrostatic potential generated by the protein. To this end the OmpF porin trimers from Escherichia coli was reproducibly imaged at a lateral resolution of ∼0.5 nm and a vertical resolution of ∼0.1 nm at variable electrolyte concentrations of the buffer solution. At low electrolyte concentrations the charged AFM probe not only contoured structural details of the membrane protein surface but also interacted with local electrostatic potentials. Differences measured between topographs recorded at variable ionic strength allowed mapping of the electrostatic potential of OmpF porin. The potential map acquired by AFM showed qualitative agreement with continuum electrostatic calculations based on the atomic OmpF porin embedded in a lipid bilayer at the same electrolyte concentrations. Numerical simulations of the experimental conditions showed the measurements to be reproduced quantitatively when the AFM probe was included in the calculations. This method opens a novel avenue to determine the electrostatic potential of native protein surfaces at a lateral resolution better than 1 nm and a vertical resolution of ∼0.1 nm