Sparse {Fourier Transform} by Traversing {Cooley-Tukey FFT} Computation Graphs

Computing the dominant Fourier coefficients of a vector is a common task in many fields, such as signal processing, learning theory, and computational complexity. In the Sparse Fast Fourier Transform (Sparse FFT) problem, one is given oracle access to a $d$-dimensional vector $x$ of size $N$, and is asked to compute the best $k$-term approximation of its Discrete Fourier Transform, quickly and using few samples of the input vector $x$. While the sample complexity of this problem is quite well understood, all previous approaches either suffer from an exponential dependence of runtime on the dimension $d$ or can only tolerate a trivial amount of noise. This is in sharp contrast with the classical FFT algorithm of Cooley and Tukey, which is stable and completely insensitive to the dimension of the input vector: its runtime is $O(N\log N)$ in any dimension $d$. In this work, we introduce a new high-dimensional Sparse FFT toolkit and use it to obtain new algorithms, both on the exact, as well as in the case of bounded $\ell_2$ noise. This toolkit includes i) a new strategy for exploring a pruned FFT computation tree that reduces the cost of filtering, ii) new structural properties of adaptive aliasing filters recently introduced by Kapralov, Velingker and Zandieh'SODA'19, and iii) a novel lazy estimation argument, suited to reducing the cost of estimation in FFT tree-traversal approaches. Our robust algorithm can be viewed as a highly optimized sparse, stable extension of the Cooley-Tukey FFT algorithm. Finally, we explain the barriers we have faced by proving a conditional quadratic lower bound on the running time of the well-studied non-equispaced Fourier transform problem. This resolves a natural and frequently asked question in computational Fourier transforms. Lastly, we provide a preliminary experimental evaluation comparing the runtime of our algorithm to FFTW and SFFT 2.0

Probing a Complex of Cytochromecand Cardiolipin by Magnetic Circular Dichroism Spectroscopy: Implications for the Initial Events in Apoptosis

Oxidation of cardiolipin (CL) by its complex with cytochrome c (cyt c) plays a crucial role in triggering apoptosis. Through a combination of magnetic circular dichroism spectroscopy and potentiometric titrations, we show that both the ferric and ferrous forms of the heme group of a CL:cyt c complex exist as multiple conformers at a physiologically relevant pH of 7.4. For the ferric state, these conformers are His/Lys- and His/OH–-ligated. The ferrous state is predominantly high-spin and, most likely, His/–. Interconversion of the ferric and ferrous conformers is described by a single midpoint potential of -80 ± 9 mV vs SHE. These results suggest that CL oxidation in mitochondria could occur by the reaction of molecular oxygen with the ferrous CL:cyt c complex in addition to the well-described reaction of peroxides with the ferric form

Rubisco evolution in C₄ eudicots: an analysis of Amaranthaceae sensu lato.

BACKGROUND: Rubisco (ribulose-1,5-bisphosphate carboxylase/oxygenase) catalyses the key reaction in the photosynthetic assimilation of CO₂. In C₄ plants CO₂ is supplied to Rubisco by an auxiliary CO₂-concentrating pathway that helps to maximize the carboxylase activity of the enzyme while suppressing its oxygenase activity. As a consequence, C₄ Rubisco exhibits a higher maximum velocity but lower substrate specificity compared with the C₃ enzyme. Specific amino-acids in Rubisco are associated with C₄ photosynthesis in monocots, but it is not known whether selection has acted on Rubisco in a similar way in eudicots. METHODOLOGY/PRINCIPAL FINDINGS: We investigated Rubisco evolution in Amaranthaceae sensu lato (including Chenopodiaceae), the third-largest family of C₄ plants, using phylogeny-based maximum likelihood and Bayesian methods to detect Darwinian selection on the chloroplast rbcL gene in a sample of 179 species. Two Rubisco residues, 281 and 309, were found to be under positive selection in C₄ Amaranthaceae with multiple parallel replacements of alanine by serine at position 281 and methionine by isoleucine at position 309. Remarkably, both amino-acids have been detected in other C₄ plant groups, such as C₄ monocots, illustrating a striking parallelism in molecular evolution. CONCLUSIONS/SIGNIFICANCE: Our findings illustrate how simple genetic changes can contribute to the evolution of photosynthesis and strengthen the hypothesis that parallel amino-acid replacements are associated with adaptive changes in Rubisco

Coevolution of amino acid residues in the key photosynthetic enzyme Rubisco

<p>Abstract</p> <p>Background</p> <p>One of the key forces shaping proteins is coevolution of amino acid residues. Knowing which residues coevolve in a particular protein may facilitate our understanding of protein evolution, structure and function, and help to identify substitutions that may lead to desired changes in enzyme kinetics. Rubisco, the most abundant enzyme in biosphere, plays an essential role in the process of carbon fixation through photosynthesis, thus facilitating life on Earth. This makes Rubisco an important model system for studying the dynamics of protein fitness optimization on the evolutionary landscape. In this study we investigated the selective and coevolutionary forces acting on large subunit of land plants Rubisco using Markov models of codon substitution and clustering approaches applied to amino acid substitution histories.</p> <p>Results</p> <p>We found that both selection and coevolution shape Rubisco, and that positively selected and coevolving residues have their specifically favored amino acid composition and pairing preference. The mapping of these residues on the known Rubisco tertiary structures showed that the coevolving residues tend to be in closer proximity with each other compared to the background, while positively selected residues tend to be further away from each other. This study also reveals that the residues under positive selection or coevolutionary force are located within functionally important regions and that some residues are targets of both positive selection and coevolution at the same time.</p> <p>Conclusion</p> <p>Our results demonstrate that coevolution of residues is common in Rubisco of land plants and that there is an overlap between coevolving and positively selected residues. Knowledge of which Rubisco residues are coevolving and positively selected could be used for further work on structural modeling and identification of substitutions that may be changed in order to improve efficiency of this important enzyme in crops.</p

Positively selected amino acid replacements within the RuBisCO enzyme of oak trees are associated with ecological adaptations

Phylogenetic analysis by maximum likelihood (PAML) has become the standard approach to study positive selection at the molecular level, but other methods may provide complementary ways to identify amino acid replacements associated with particular conditions. Here, we compare results of the decision tree (DT) model method with ones of PAML using the key photosynthetic enzyme RuBisCO as a model system to study molecular adaptation to particular ecological conditions in oaks (Quercus). We sequenced the chloroplast rbcL gene encoding RuBisCO large subunit in 158 Quercus species, covering about a third of the global genus diversity. It has been hypothesized that RuBisCO has evolved differentially depending on the environmental conditions and leaf traits governing internal gas diffusion patterns. Here, we show, using PAML, that amino acid replacements at the residue positions 95, 145, 251, 262 and 328 of the RuBisCO large subunit have been the subject of positive selection along particular Quercus lineages associated with the leaf traits and climate characteristics. In parallel, the DT model identified amino acid replacements at sites 95, 219, 262 and 328 being associated with the leaf traits and climate characteristics, exhibiting partial overlap with the results obtained using PAML

Controlling the Transverse Magneto-Optical Kerr Effect in Cr/NiFe Bilayer Thin Films by Changing the Thicknesses of the Cr Layer

Here, we demonstrate the impact of ferromagnetic layer coating on controlling the magneto-optical response. We found that the transverse magneto-optical Kerr effect (TMOKE) signal and TMOKE hysteresis loops of Ni80Fe20 thin layers coated with a Cr layer show a strong dependence on the thickness of the Cr layer and the incidence angle of the light. The transmission and reflection spectra were measured over a range of incidence angles and with different wavelengths so as to determine the layers’ optical parameters and to explain the TMOKE behavior. The generalized magneto-optical and ellipsometry (GMOE) model based on modified Abeles characteristic matrices was used to examine the agreement between the experimental and theoretical results. A comprehensive theoretical and experimental analysis reveals the possibility to create a TMOKE suppression/enhancement coating at specific controllable incidence angles. This has potential for applications in optical microscopy and sensors

Phospholipid Composition Modulates Carbon Nanodiamond-Induced Alterations in Phospholipid Domain Formation

This document is the Accepted Manuscript version of a Published Work that appeared in final form in Langmuir, copyright © American Chemical Society after peer review and technical editing by the publisher. To access the final edited and published work see http://doi.org/10.1021/la504923j.The focus of this work is to elucidate how phospholipid composition can modulate lipid nanoparticle interactions in phospholipid monolayer systems. We report on alterations in lipid domain formation induced by anionically engineered carbon nanodiamonds (ECNs) as a function of lipid headgroup charge and alkyl chain saturation. Using surface pressure vs area isotherms, monolayer compressibility, and fluorescence microscopy, we found that anionic ECNs induced domain shape alterations in zwitterionic phosphatidylcholine lipids, irrespective of the lipid alkyl chain saturation, even when the surface pressure vs area isotherms did not show any significant changes. Bean-shaped structures characteristic of dipalmitoylphosphatidylcholine (DPPC) were converted to multilobed, fractal, or spiral domains as a result of exposure to ECNs, indicating that ECNs lower the line tension between domains in the case of zwitterionic lipids. For membrane systems containing anionic phospholipids, ECN-induced changes in domain packing were related to the electrostatic interactions between the anionic ECNs and the anionic lipid headgroups, even when zwitterionic lipids are present in excess. By comparing the measured size distributions with our recently developed theory derived by minimizing the free energy associated with the domain energy and mixing entropy, we found that the change in line tension induced by anionic ECNs is dominated by the charge in the condensed lipid domains. Atomic force microscopy images of the transferred anionic films confirm that the location of the anionic ECNs in the lipid monolayers is also modulated by the charge on the condensed lipid domains. Because biological membranes such as lung surfactants contain both saturated and unsaturated phospholipids with different lipid headgroup charges, our results suggest that when studying potential adverse effects of nanoparticles on biological systems the role of lipid compositions cannot be neglected

One thousand plant transcriptomes and the phylogenomics of green plants

Abstract: Green plants (Viridiplantae) include around 450,000–500,000 species1, 2 of great diversity and have important roles in terrestrial and aquatic ecosystems. Here, as part of the One Thousand Plant Transcriptomes Initiative, we sequenced the vegetative transcriptomes of 1,124 species that span the diversity of plants in a broad sense (Archaeplastida), including green plants (Viridiplantae), glaucophytes (Glaucophyta) and red algae (Rhodophyta). Our analysis provides a robust phylogenomic framework for examining the evolution of green plants. Most inferred species relationships are well supported across multiple species tree and supermatrix analyses, but discordance among plastid and nuclear gene trees at a few important nodes highlights the complexity of plant genome evolution, including polyploidy, periods of rapid speciation, and extinction. Incomplete sorting of ancestral variation, polyploidization and massive expansions of gene families punctuate the evolutionary history of green plants. Notably, we find that large expansions of gene families preceded the origins of green plants, land plants and vascular plants, whereas whole-genome duplications are inferred to have occurred repeatedly throughout the evolution of flowering plants and ferns. The increasing availability of high-quality plant genome sequences and advances in functional genomics are enabling research on genome evolution across the green tree of life

Multiple Nuclear Gene Phylogenetic Analysis of the Evolution of Dioecy and Sex Chromosomes in the Genus Silene

In the plant genus Silene, separate sexes and sex chromosomes are believed to have evolved twice. Silene species that are wholly or largely hermaphroditic are assumed to represent the ancestral state from which dioecy evolved. This assumption is important for choice of outgroup species for inferring the genetic and chromosomal changes involved in the evolution of dioecy, but is mainly based on data from a single locus (ITS). To establish the order of events more clearly, and inform outgroup choice, we therefore carried out (i) multi-nuclear-gene phylogenetic analyses of 14 Silene species (including 7 hermaphrodite or gynodioecious species), representing species from both Silene clades with dioecious members, plus a more distantly related outgroup, and (ii) a BayesTraits character analysis of the evolution of dioecy. We confirm two origins of dioecy within this genus in agreement with recent work on comparing sex chromosomes from both clades with dioecious species. We conclude that sex chromosomes evolved after the origin of Silene and within a clade that includes only S. latifolia and its closest relatives. We estimate that sex chromosomes emerged soon after the split with the ancestor of S. viscosa, the probable closest non-dioecious S. latifolia relative among the species included in our study