Using state space differential geometry for nonlinear blind source separation

Given a time series of multicomponent measurements of an evolving stimulus, nonlinear blind source separation (BSS) seeks to find a "source" time series, comprised of statistically independent combinations of the measured components. In this paper, we seek a source time series with local velocity cross correlations that vanish everywhere in stimulus state space. However, in an earlier paper the local velocity correlation matrix was shown to constitute a metric on state space. Therefore, nonlinear BSS maps onto a problem of differential geometry: given the metric observed in the measurement coordinate system, find another coordinate system in which the metric is diagonal everywhere. We show how to determine if the observed data are separable in this way, and, if they are, we show how to construct the required transformation to the source coordinate system, which is essentially unique except for an unknown rotation that can be found by applying the methods of linear BSS. Thus, the proposed technique solves nonlinear BSS in many situations or, at least, reduces it to linear BSS, without the use of probabilistic, parametric, or iterative procedures. This paper also describes a generalization of this methodology that performs nonlinear independent subspace separation. In every case, the resulting decomposition of the observed data is an intrinsic property of the stimulus' evolution in the sense that it does not depend on the way the observer chooses to view it (e.g., the choice of the observing machine's sensors). In other words, the decomposition is a property of the evolution of the "real" stimulus that is "out there" broadcasting energy to the observer. The technique is illustrated with analytic and numerical examples.Comment: Contains 14 pages and 3 figures. For related papers, see http://www.geocities.com/dlevin2001/ . New version is identical to original version except for URL in the bylin

A Role for Actin, Cdc1p, and Myo2p in the Inheritance of Late Golgi Elements in \u3cem\u3eSaccharomyces cerevisiae\u3c/em\u3e

In Saccharomyces cerevisiae, Golgi elements are present in the bud very early in the cell cycle. We have analyzed this Golgi inheritance process using fluorescence microscopy and genetics. In rapidly growing cells, late Golgi elements show an actin-dependent concentration at sites of polarized growth. Late Golgi elements are apparently transported into the bud along actin cables and are also retained in the bud by a mechanism that may involve actin. A visual screen for mutants defective in the inheritance of late Golgi elements yielded multiple alleles of CDC1. Mutations in CDC1 severely depolarize the actin cytoskeleton, and these mutations prevent late Golgi elements from being retained in the bud. The efficient localization of late Golgi elements to the bud requires the type V myosin Myo2p, further suggesting that actin plays a role in Golgi inheritance. Surprisingly, early and late Golgi elements are inherited by different pathways, with early Golgi elements localizing to the bud in a Cdc1p- and Myo2p-independent manner. We propose that early Golgi elements arise from ER membranes that are present in the bud. These two pathways of Golgi inheritance in S. cerevisiae resemble Golgi inheritance pathways in vertebrate cells

On the upper bound of the electronic kinetic energy in terms of density functionals

We propose a simple density functional expression for the upper bound of the kinetic energy for electronic systems. Such a functional is valid in the limit of slowly varying density, its validity outside this regime is discussed by making a comparison with upper bounds obtained in previous work. The advantages of the functional proposed for applications to realistic systems is briefly discussed.Comment: 10 pages, no figure

Cardioprotection by cocoa polyphenols and ω-3 fatty acids: A disease-prevention perspective on aging-associated cardiovascular risk

Cardiovascular disease (CVD) remains the leading cause of death today. Many of the biochemical alterations associated with the pathophysiology of CVD can be modified by adequate intakes of bioactive nutrients through a correct diet or supplementation. Recently, there has been growing public and clinical interest in cocoa polyphenols (CPs) and omega-3 (ω-3) fatty acids. A plethora of nutritional intervention trials and experimental studies demonstrates that consumption of these bioactive food compounds is beneficial to promote cardiovascular health. The purpose of this review is to summarize the major cardioprotective effects of CPs and ω-3 fatty acids, providing a scientific rationale for incorporating the combination of these molecules as a nutritional intervention in the prevention of CVD. Although several studies have shown the individual cardioprotective nature of these compounds, a combination treatment with CPs and ω-3 fatty acids may be a promising approach to enhance the preventive value of these molecules and reduce cardiovascular risk factors associated with aging. Therefore, this article also reviews some of the key studies on the interaction between CPs and the metabolism of ω-3 fatty acids

An analytic expression for the electronic correlation term of the kinetic functional

We propose an analytic formula for the non-local Fisher information functional, or electronic kinetic correlation term, appearing in the expression of the kinetic density functional. Such an explicit formula is constructed on the basis of well-founded physical arguments and a rigorous mathematical prescription

Precision Measurement of the n-3He Incoherent Scattering Length Using Neutron Interferometry

We report the first measurement of the low-energy neutron-$^3$He incoherent scattering length using neutron interferometry: $b_i' = (-2.512\pm 0.012{statistical}\pm0.014{systematic})$ fm. This is in good agreement with a recent calculation using the AV18+3N potential. The neutron-$^3$He scattering lengths are important for testing and developing nuclear potential models that include three nucleon forces, effective field theories for few-body nuclear systems, and neutron scattering measurements of quantum excitations in liquid helium. This work demonstrates the first use of a polarized nuclear target in a neutron interferometer.Comment: 4 figure

Spin waves and spin-state transitions in a ruthenate high-temperature antiferromagnet

Ruthenium compounds play prominent roles in materials research ranging from oxide electronics to catalysis, and serve as a platform for fundamental concepts such as spin-triplet superconductivity, Kitaev spin-liquids, and solid-state analogues of the Higgs mode in particle physics. However, basic questions about the electronic structure of ruthenates remain unanswered, because several key parameters (including the Hund's-rule, spin-orbit, and exchange interactions) are comparable in magnitude, and their interplay is poorly understood - partly due to difficulties in synthesizing sizable single crystals for spectroscopic experiments. Here we introduce a resonant inelastic x-ray scattering (RIXS) technique capable of probing collective modes in microcrystals of $4d$-electron materials. We present a comprehensive set of data on spin waves and spin-state transitions in the honeycomb antiferromagnet SrRu$_{2}$O$_{6}$, which possesses an unusually high N\'eel temperature. The new RIXS method provides fresh insight into the unconventional magnetism of SrRu$_{2}$O$_{6}$, and enables momentum-resolved spectroscopy of a large class of $4d$ transition-metal compounds.Comment: The original submitted version of the published manuscript. https://www.nature.com/articles/s41563-019-0327-

Complete positivity and entangled degrees of freedom

We study how some recently proposed noncontextuality tests based on quantum interferometry are affected if the test particles propagate as open systems in presence of a gaussian stochastic background. We show that physical consistency requires the resulting markovian dissipative time-evolution to be completely positive.Comment: 23 pages, plain-TeX, no figure

Dynamical Semigroup Description of Coherent and Incoherent Particle-Matter Interaction

The meaning of statistical experiments with single microsystems in quantum mechanics is discussed and a general model in the framework of non-relativistic quantum field theory is proposed, to describe both coherent and incoherent interaction of a single microsystem with matter. Compactly developing the calculations with superoperators, it is shown that the introduction of a time scale, linked to irreversibility of the reduced dynamics, directly leads to a dynamical semigroup expressed in terms of quantities typical of scattering theory. Its generator consists of two terms, the first linked to a coherent wavelike behaviour, the second related to an interaction having a measuring character, possibly connected to events the microsystem produces propagating inside matter. In case these events breed a measurement, an explicit realization of some concepts of modern quantum mechanics ("effects" and "operations") arises. The relevance of this description to a recent debate questioning the validity of ordinary quantum mechanics to account for such experimental situations as, e.g., neutron-interferometry, is briefly discussed.Comment: 22 pages, latex, no figure