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

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

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

Cation-selective channel is regulated by anions according to their Hofmeister ranking

Specificity of small ions, the Hofmeister ranking, is long-known and has many applications including medicine. Yet it evades consistent theoretical description. Here we study the effect of Hofmeister anions on gramicidin A channels in lipid membranes. Counterintuitively, we find that conductance of this perfectly cation-selective channel increases about two-fold in the H2PO4−<Cl−≈Br−≈NO3−<ClO4−<SCN− series. Channel dissociation kinetics show even stronger dependence, with the dwell time increasing ~20-fold. While the conductance can be quantitatively explained by the changes in membrane surface potential due to exclusion of kosmotropes from (or accumulation of chaotropes at) the surface, the kinetics proved to be more difficult to treat. We estimate the effects of changes in the energetics at the bilayer surfaces on the channel dwell time, concluding that the change would have to be greater than typically observed for the Hofmeister effect outside the context of the lipid bilayer., Ion specificity and, in particular, the distinctive effects of anions in salt-induced protein precipitation have been known since the 1880’s, when Franz Hofmeister established the ranking of anions in their ability to regulate egg yolk protein water solubility []. Experimental and theoretical studies have given a detailed empirical picture of the phenomenon, the nature of the ionic interactions with the surfaces leading to the Hofmeister effect is still under debate []. The only consensus is that it cannot be explained by standard theories of electrolytes. For example, bromide is unique in that its salts were recognized as a drug to treat epilepsy a couple of dozen years before Hofmeister’s studies [] and they are still in use to treat specific types of refractory seizures in children [], but the mechanism of their action remains elusive., , Hofmeister effect studied with a nanopore in a neutral lipid membrane. Rather unexpectedly, we find that conductance of a purely cation-selective peptide pore is regulated by anions in correlation with their position in the Hofmeister series. Moreover, the pore conformational dynamics are highly sensitive to the anion species. We relate both effects to preferential depletion of kosmotropic anions (accumulation of chaotropic anions) at the membrane-water interface

Tilted axis rotation, candidates for chiral bands, and wobbling motion in 138Nd

High-spin states in 138Nd were investigated using the reaction 94Zr(48Ca,4n), detecting coincident γ rays with the gasp spectrometer. A rich level scheme was constructed including four bands of negative parity at low spins, eight bands of dipole transitions, and eight bands of quadrupole transitions at medium spins. The cranked shell model and the tilted-axis cranking model are used to assign configurations to the observed bands, where zero pairing is assumed. For selected configurations the case of finite pairing is also considered. A consistent notation for configuration assignment that applies for both zero and finite pairing is introduced. The observed bands are interpreted as rotation around the short and long principal axes (quadrupole bands), as well as around a tilted axis (dipole bands). The dipole bands have an intermediate character, between magnetic and collective electric rotation. A pair of dipole bands is identified as candidates for chiral partners. The possible existence of the wobbling mode at low deformation and medium spins is discussed. The consistent interpretation of the multitude of observed bands strongly supports the existence of stable triaxial deformation at medium spins in 138Nd. ©2012 American Physical Societ