Next-order asymptotic expansion for N-marginal optimal transport with Coulomb and Riesz costs

Motivated by a problem arising from Density Functional Theory, we provide the sharp next-order asymptotics for a class of multimarginal optimal transport problems with cost given by singular, long-range pairwise interaction potentials. More precisely, we consider an N-marginal optimal transport problem with N equal marginals supported on Rd and with cost of the form ∑i≠j|xi−xj|−s. In this setting we determine the second-order term in the N→∞ asymptotic expansion of the minimum energy, for the long-range interactions corresponding to all exponents 0<s<d. We also prove a small oscillations property for this second-order energy term. Our results can be extended to a larger class of models than power-law-type radial costs, such as non-rotationally-invariant costs. The key ingredient and main novelty in our proofs is a robust extension and simplification of the Fefferman–Gregg decomposition [20], [26], extended here to our class of kernels, and which provides a unified method valid across our full range of exponents. Our first result generalizes a recent work of Lewin, Lieb and Seiringer [36], who dealt with the second-order term for the Coulomb case s=1,d=3

Kolmogorov-Smirnov method for the determination of signal time-shifts

A new method for the determination of electric signal time-shifts is introduced. As the Kolmogorov-Smirnov test, it is based on the comparison of the cumulative distribution functions of the reference signal with the test signal. This method is very fast and thus well suited for on-line applications. It is robust to noise and its performances in terms of precision are excellent for time-shifts ranging from a fraction to several sample durations. PACS. 29.40.Gx (Tracking and position-sensitive detectors), 29.30.Kv (X- and -ray spectroscopy), 07.50.Qx (Signal processing electronics)Comment: 8 pages, 7 figure

Fast analytical methods for the correction of signal random time-shifts and application to segmented HPGe detectors

Detection systems rely more and more on on-line or off-line comparison of detected signals with basis signals in order to determine the characteristics of the impinging particles. Unfortunately, these comparisons are very sensitive to the random time shifts that may alter the signal delivered by the detectors. We present two fast algebraic methods to determine the value of the time shift and to enhance the reliability of the comparison to the basis signals.Comment: 13 pages, 8 figure

Structural Characterization of the ACCH Domain of Angiomotin Family Members

poster abstractThe Angiomotin (Amot) family of adaptor proteins directly coordinates signaling events during cellular and neural differentiation and proliferation. A critical feature of all Amot proteins is a novel lipid binding domain, the Amot coiled-coil homology (ACCH) domain, which confers its association with membranes and affects membrane curvature and deformation. Specifically, this domain has the unique ability to selectively bind monophosphorylated phosphatidylinositols (PIs) and cholesterol. Furthermore, Amot family members bind core polarity proteins that control the organization of the apical domain of epithelial cells as well as Yap, a transcriptional coactivator that appears to be the key regulator of cell growth. Amots have been shown to have a critical role in endothelial and epithelial cell migration, invasion, and tubule formation, and they are believed to regulate angiogenesis, which promotes tumor growth and metastasis. Amot overexpression and mutations have been linked to neuroepithelial tumors, such as glioblastomas, brain hemangioendotheliomas, neurofibromatosis, and many other cancers, such as breast cancer. The role of Amots in epithelial and endothelial cancer growth and metastasis have been linked to poor prognosis and unfavorable clinical outcomes. Understanding the structure-function relationship of the ACCH domain may provide pathways to modulate protein sorting and downstream signaling events inducing cellular differentiation, cancer cell proliferation, and cell migration. The goal of this project is to generate a solution structure of the Amot80/130 and AmotL2 (Mascot) ACCH domains using SAXS and WAXS data as well as various protein modeling software, thereby suggesting possible routes to modulate their activity associated with various tumors. Additionally, this structure will be compared against theoretical models to determine the statistical accuracy of the theoretical models. Furthermore, we hypothesize that generating these models will allow us to determine the structure of another analogue of A80/130, the Angiomotin-like 1 (JEAP) ACCH domain

Reorganization of Ternary Lipid Mixtures of Non-Phosphorylated Phosphatidylinositol Interacting with Angiomotin

Phosphatidylinositol (PI) lipids are necessary for many cellular signaling pathways of membrane associated proteins, such as Angiomotin (Amot). The Amot family regulates cellular polarity, growth, and migration. Given the low concentration of PI lipids in these membranes, it is likely that such protein-membrane interactions are stabilized by lipid domains or small lipid clusters. By small-angle x-ray scattering, we show that non-phosphorylated PI lipids induce lipid de-mixing in ternary mixtures of phosphatidylcholine (PC) and phosphatidylethanolamine (PE), likely due to preferential interactions between the head groups of PE and PI. These results were obtained in the presence of buffer containing concentrations of Tris, HEPES, NaCl, EDTA, DTT, and Benzamidine at pH 8.0 that in previous work showed an ability to cause PC to phase separate but are necessary to stabilize Amot for in vitro experimentation. Collectively, this provided a framework for determining the effect of Amot on lipid organization. Using fluorescence spectroscopy, we were able to show that the association of Amot with this lipid platform causes significant reorganization of the lipid into a more homogenous organization. This reorganization mechanism could be the basis for Amot membrane association and fusigenic activity previously described in the literature and should be taken into consideration in future protein-membrane interaction studies

Conductance of Ideally Cation Selective Channel Depends on Anion Type

poster abstractGramicidin A (gA) is a transmembrane, cation selective ion channel that has been used in many biophysical studies of lipid bilayers, in particular for investigations of lipid-protein interactions and membrane electrostatics. In addition, it was found that ionic interactions with neutral lipid membranes also affect the kinetics of gA channels. Here we report measurements of gA ion-channels for a series of sodium and potassium salts that show an anion-dependence of gA conductance. We find that gA conductance varies significantly with the anion type with ClO4 and SCN producing distinctly larger conductance values than Cl, F, and H2PO4. These results can provide new insights into ion-lipid membrane interactions and ion channel functions in general

Chiral bands in 135Nd: The interacting boson-fermion model approach

The chiral interpretation of negative-parity twin bands in the odd-A 135Nd nucleus was investigated in the interacting boson fermion model. The IBFM calculation shows that the dominant role in the formation of the chiral pattern has the exchange interaction, i.e. the antisymmetrization of odd fermions with the fermion structure of the bosons. The structure of the twin bands in 137Nd has also been investigated, concluding that it is determined by shape fluctuations and prolate-oblate coexistence rather than by chirality

Phase Coexistence in Single-Lipid Membranes Induced by Buffering Agents

Recent literature has shown that buffers affect the interaction between lipid bilayers through a mechanism that involves van der Waals forces, electrostatics, hydration forces and membrane bending rigidity. This letter shows an additional peculiar effect of buffers on the mixed chain 1-palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine (POPC) lipid bilayers, namely phase coexistence similar to what was reported by Rappolt et al. for alkali chlorides. The data presented suggest that one phase appears to dehydrate below the value in pure water, while the other phase swells as the concentration of buffer is increased. However, since the two phases must be in osmotic equilibrium with one another, this behavior challenges theoretical models of lipid interactions