TY - JOUR AB - We introduce “state space persistence analysis” for deducing the symbolic dynamics of time series data obtained from high-dimensional chaotic attractors. To this end, we adapt a topological data analysis technique known as persistent homology for the characterization of state space projections of chaotic trajectories and periodic orbits. By comparing the shapes along a chaotic trajectory to those of the periodic orbits, state space persistence analysis quantifies the shape similarity of chaotic trajectory segments and periodic orbits. We demonstrate the method by applying it to the three-dimensional Rössler system and a 30-dimensional discretization of the Kuramoto–Sivashinsky partial differential equation in (1+1) dimensions. One way of studying chaotic attractors systematically is through their symbolic dynamics, in which one partitions the state space into qualitatively different regions and assigns a symbol to each such region.1–3 This yields a “coarse-grained” state space of the system, which can then be reduced to a Markov chain encoding all possible transitions between the states of the system. While it is possible to obtain the symbolic dynamics of low-dimensional chaotic systems with standard tools such as Poincaré maps, when applied to high-dimensional systems such as turbulent flows, these tools alone are not sufficient to determine symbolic dynamics.4,5 In this paper, we develop “state space persistence analysis” and demonstrate that it can be utilized to infer the symbolic dynamics in very high-dimensional settings. AU - Yalniz, Gökhan AU - Budanur, Nazmi B ID - 7563 IS - 3 JF - Chaos SN - 1054-1500 TI - Inferring symbolic dynamics of chaotic flows from persistence VL - 30 ER - TY - JOUR AB - Slicing a Voronoi tessellation in ${R}^n$ with a $k$-plane gives a $k$-dimensional weighted Voronoi tessellation, also known as a power diagram or Laguerre tessellation. Mapping every simplex of the dual weighted Delaunay mosaic to the radius of the smallest empty circumscribed sphere whose center lies in the $k$-plane gives a generalized discrete Morse function. Assuming the Voronoi tessellation is generated by a Poisson point process in ${R}^n$, we study the expected number of simplices in the $k$-dimensional weighted Delaunay mosaic as well as the expected number of intervals of the Morse function, both as functions of a radius threshold. As a by-product, we obtain a new proof for the expected number of connected components (clumps) in a line section of a circular Boolean model in ${R}^n$. AU - Edelsbrunner, Herbert AU - Nikitenko, Anton ID - 7554 IS - 4 JF - Theory of Probability and its Applications SN - 0040585X TI - Weighted Poisson–Delaunay mosaics VL - 64 ER - TY - JOUR AB - The relaxation of few-body quantum systems can strongly depend on the initial state when the system’s semiclassical phase space is mixed; i.e., regions of chaotic motion coexist with regular islands. In recent years, there has been much effort to understand the process of thermalization in strongly interacting quantum systems that often lack an obvious semiclassical limit. The time-dependent variational principle (TDVP) allows one to systematically derive an effective classical (nonlinear) dynamical system by projecting unitary many-body dynamics onto a manifold of weakly entangled variational states. We demonstrate that such dynamical systems generally possess mixed phase space. When TDVP errors are small, the mixed phase space leaves a footprint on the exact dynamics of the quantum model. For example, when the system is initialized in a state belonging to a stable periodic orbit or the surrounding regular region, it exhibits persistent many-body quantum revivals. As a proof of principle, we identify new types of “quantum many-body scars,” i.e., initial states that lead to long-time oscillations in a model of interacting Rydberg atoms in one and two dimensions. Intriguingly, the initial states that give rise to most robust revivals are typically entangled states. On the other hand, even when TDVP errors are large, as in the thermalizing tilted-field Ising model, initializing the system in a regular region of phase space leads to a surprising slowdown of thermalization. Our work establishes TDVP as a method for identifying interacting quantum systems with anomalous dynamics in arbitrary dimensions. Moreover, the mixed phase space classical variational equations allow one to find slowly thermalizing initial conditions in interacting models. Our results shed light on a link between classical and quantum chaos, pointing toward possible extensions of the classical Kolmogorov-Arnold-Moser theorem to quantum systems. AU - Michailidis, Alexios AU - Turner, C. J. AU - Papić, Z. AU - Abanin, D. A. AU - Serbyn, Maksym ID - 7570 IS - 1 JF - Physical Review X SN - 2160-3308 TI - Slow quantum thermalization and many-body revivals from mixed phase space VL - 10 ER - TY - JOUR AB - Small RNAs (smRNA, 19–25 nucleotides long), which are transcribed by RNA polymerase II, regulate the expression of genes involved in a multitude of processes in eukaryotes. miRNA biogenesis and the proteins involved in the biogenesis pathway differ across plant and animal lineages. The major proteins constituting the biogenesis pathway, namely, the Dicers (DCL/DCR) and Argonautes (AGOs), have been extensively studied. However, the accessory proteins (DAWDLE (DDL), SERRATE (SE), and TOUGH (TGH)) of the pathway that differs across the two lineages remain largely uncharacterized. We present the first detailed report on the molecular evolution and divergence of these proteins across eukaryotes. Although DDL is present in eukaryotes and prokaryotes, SE and TGH appear to be specific to eukaryotes. The addition/deletion of specific domains and/or domain-specific sequence divergence in the three proteins points to the observed functional divergence of these proteins across the two lineages, which correlates with the differences in miRNA length across the two lineages. Our data enhance the current understanding of the structure–function relationship of these proteins and reveals previous unexplored crucial residues in the three proteins that can be used as a basis for further functional characterization. The data presented here on the number of miRNAs in crown eukaryotic lineages are consistent with the notion of the expansion of the number of miRNA-coding genes in animal and plant lineages correlating with organismal complexity. Whether this difference in functionally correlates with the diversification (or presence/absence) of the three proteins studied here or the miRNA signaling in the plant and animal lineages is unclear. Based on our results of the three proteins studied here and previously available data concerning the evolution of miRNA genes in the plant and animal lineages, we believe that miRNAs probably evolved once in the ancestor to crown eukaryotes and have diversified independently in the eukaryotes. AU - Moturu, Taraka Ramji AU - Sinha, Sansrity AU - Salava, Hymavathi AU - Thula, Sravankumar AU - Nodzyński, Tomasz AU - Vařeková, Radka Svobodová AU - Friml, Jiří AU - Simon, Sibu ID - 7582 IS - 3 JF - Plants TI - Molecular evolution and diversification of proteins involved in miRNA maturation pathway VL - 9 ER - TY - JOUR AB - Heterozygous loss of human PAFAH1B1 (coding for LIS1) results in the disruption of neurogenesis and neuronal migration via dysregulation of microtubule (MT) stability and dynein motor function/localization that alters mitotic spindle orientation, chromosomal segregation, and nuclear migration. Recently, human induced pluripotent stem cell (iPSC) models revealed an important role for LIS1 in controlling the length of terminal cell divisions of outer radial glial (oRG) progenitors, suggesting cellular functions of LIS1 in regulating neural progenitor cell (NPC) daughter cell separation. Here we examined the late mitotic stages NPCs in vivo and mouse embryonic fibroblasts (MEFs) in vitro from Pafah1b1-deficient mutants. Pafah1b1-deficient neocortical NPCs and MEFs similarly exhibited cleavage plane displacement with mislocalization of furrow-associated markers, associated with actomyosin dysfunction and cell membrane hyper-contractility. Thus, it suggests LIS1 acts as a key molecular link connecting MTs/dynein and actomyosin, ensuring that cell membrane contractility is tightly controlled to execute proper daughter cell separation. AU - Moon, Hyang Mi AU - Hippenmeyer, Simon AU - Luo, Liqun AU - Wynshaw-Boris, Anthony ID - 7593 JF - eLife SN - 2050-084X TI - LIS1 determines cleavage plane positioning by regulating actomyosin-mediated cell membrane contractility VL - 9 ER - TY - JOUR AB - Directional intercellular transport of the phytohormone auxin mediated by PIN FORMED (PIN) efflux carriers plays essential roles in both coordinating patterning processes and integrating multiple external cues by rapidly redirecting auxin fluxes. Multilevel regulations of PIN activity under internal and external cues are complicated; however, the underlying molecular mechanism remains elusive. Here we demonstrate that 3’-Phosphoinositide-Dependent Protein Kinase1 (PDK1), which is conserved in plants and mammals, functions as a molecular hub integrating the upstream lipid signalling and the downstream substrate activity through phosphorylation. Genetic analysis uncovers that loss-of-function Arabidopsis mutant pdk1.1 pdk1.2 exhibits a plethora of abnormalities in organogenesis and growth, due to the defective PIN-dependent auxin transport. Further cellular and biochemical analyses reveal that PDK1 phosphorylates D6 Protein Kinase to facilitate its activity towards PIN proteins. Our studies establish a lipid-dependent phosphorylation cascade connecting membrane composition-based cellular signalling with plant growth and patterning by regulating morphogenetic auxin fluxes. AU - Tan, Shutang AU - Zhang, Xixi AU - Kong, Wei AU - Yang, Xiao-Li AU - Molnar, Gergely AU - Vondráková, Zuzana AU - Filepová, Roberta AU - Petrášek, Jan AU - Friml, Jiří AU - Xue, Hong-Wei ID - 7600 JF - Nature Plants TI - The lipid code-dependent phosphoswitch PDK1–D6PK activates PIN-mediated auxin efflux in Arabidopsis VL - 6 ER - TY - JOUR AB - Plants are exposed to a variety of abiotic and biotic stresses that may result in DNA damage. Endogenous processes - such as DNA replication, DNA recombination, respiration, or photosynthesis - are also a threat to DNA integrity. It is therefore essential to understand the strategies plants have developed for DNA damage detection, signaling, and repair. Alternative splicing (AS) is a key post-transcriptional process with a role in regulation of gene expression. Recent studies demonstrate that the majority of intron-containing genes in plants are alternatively spliced, highlighting the importance of AS in plant development and stress response. Not only does AS ensure a versatile proteome and influence the abundance and availability of proteins greatly, it has also emerged as an important player in the DNA damage response (DDR) in animals. Despite extensive studies of DDR carried out in plants, its regulation at the level of AS has not been comprehensively addressed. Here, we provide some insights into the interplay between AS and DDR in plants. AU - Nimeth, Barbara Anna AU - Riegler, Stefan AU - Kalyna, Maria ID - 7603 JF - Frontiers in Plant Science TI - Alternative splicing and DNA damage response in plants VL - 11 ER - TY - JOUR AB - CLC chloride/proton exchangers may support acidification of endolysosomes and raise their luminal Cl− concentration. Disruption of endosomal ClC‐3 causes severe neurodegeneration. To assess the importance of ClC‐3 Cl−/H+ exchange, we now generate Clcn3unc/unc mice in which ClC‐3 is converted into a Cl− channel. Unlike Clcn3−/− mice, Clcn3unc/unc mice appear normal owing to compensation by ClC‐4 with which ClC‐3 forms heteromers. ClC‐4 protein levels are strongly reduced in Clcn3−/−, but not in Clcn3unc/unc mice because ClC‐3unc binds and stabilizes ClC‐4 like wild‐type ClC‐3. Although mice lacking ClC‐4 appear healthy, its absence in Clcn3unc/unc/Clcn4−/− mice entails even stronger neurodegeneration than observed in Clcn3−/− mice. A fraction of ClC‐3 is found on synaptic vesicles, but miniature postsynaptic currents and synaptic vesicle acidification are not affected in Clcn3unc/unc or Clcn3−/− mice before neurodegeneration sets in. Both, Cl−/H+‐exchange activity and the stabilizing effect on ClC‐4, are central to the biological function of ClC‐3. AU - Weinert, Stefanie AU - Gimber, Niclas AU - Deuschel, Dorothea AU - Stuhlmann, Till AU - Puchkov, Dmytro AU - Farsi, Zohreh AU - Ludwig, Carmen F. AU - Novarino, Gaia AU - López-Cayuqueo, Karen I. AU - Planells-Cases, Rosa AU - Jentsch, Thomas J. ID - 7586 JF - EMBO Journal SN - 02614189 TI - Uncoupling endosomal CLC chloride/proton exchange causes severe neurodegeneration VL - 39 ER - TY - JOUR AB - This short note aims to study quantum Hellinger distances investigated recently by Bhatia et al. (Lett Math Phys 109:1777–1804, 2019) with a particular emphasis on barycenters. We introduce the family of generalized quantum Hellinger divergences that are of the form ϕ(A,B)=Tr((1−c)A+cB−AσB), where σ is an arbitrary Kubo–Ando mean, and c∈(0,1) is the weight of σ. We note that these divergences belong to the family of maximal quantum f-divergences, and hence are jointly convex, and satisfy the data processing inequality. We derive a characterization of the barycenter of finitely many positive definite operators for these generalized quantum Hellinger divergences. We note that the characterization of the barycenter as the weighted multivariate 1/2-power mean, that was claimed in Bhatia et al. (2019), is true in the case of commuting operators, but it is not correct in the general case. AU - Pitrik, Jozsef AU - Virosztek, Daniel ID - 7618 IS - 8 JF - Letters in Mathematical Physics SN - 0377-9017 TI - Quantum Hellinger distances revisited VL - 110 ER - TY - JOUR AB - The posterior parietal cortex (PPC) and frontal motor areas comprise a cortical network supporting goal-directed behaviour, with functions including sensorimotor transformations and decision making. In primates, this network links performed and observed actions via mirror neurons, which fire both when individuals perform an action and when they observe the same action performed by a conspecific. Mirror neurons are believed to be important for social learning, but it is not known whether mirror-like neurons occur in similar networks in other social species, such as rodents, or if they can be measured in such models using paradigms where observers passively view a demonstrator. Therefore, we imaged Ca2+ responses in PPC and secondary motor cortex (M2) while mice performed and observed pellet-reaching and wheel-running tasks, and found that cell populations in both areas robustly encoded several naturalistic behaviours. However, neural responses to the same set of observed actions were absent, although we verified that observer mice were attentive to performers and that PPC neurons responded reliably to visual cues. Statistical modelling also indicated that executed actions outperformed observed actions in predicting neural responses. These results raise the possibility that sensorimotor action recognition in rodents could take place outside of the parieto-frontal circuit, and underscore that detecting socially-driven neural coding depends critically on the species and behavioural paradigm used. AU - Tombaz, Tuce AU - Dunn, Benjamin A. AU - Hovde, Karoline AU - Cubero, Ryan J AU - Mimica, Bartul AU - Mamidanna, Pranav AU - Roudi, Yasser AU - Whitlock, Jonathan R. ID - 7632 IS - 1 JF - Scientific reports TI - Action representation in the mouse parieto-frontal network VL - 10 ER - TY - JOUR AB - The International Young Physicists' Tournament (IYPT) continued in 2018 in Beijing, China and 2019 in Warsaw, Poland with its 31st and 32nd editions. The IYPT is a modern scientific competition for teams of high school students, also known as the Physics World Cup. It involves long-term theoretical and experimental work focused on solving 17 publicly announced open-ended problems in teams of five. On top of that, teams have to present their solutions in front of other teams and a scientific jury, and get opposed and reviewed by their peers. Here we present a brief information about the competition with a specific focus on one of the IYPT 2018 tasks, the 'Ring Oiler'. This seemingly simple mechanical problem appeared to be of such a complexity that even the dozens of participating teams and jurying scientists were not able to solve all of its subtleties. AU - Plesch, Martin AU - Plesník, Samuel AU - Ruzickova, Natalia ID - 7622 IS - 3 JF - European Journal of Physics SN - 01430807 TI - The IYPT and the 'Ring Oiler' problem VL - 41 ER - TY - JOUR AB - A two-dimensional mathematical model for cells migrating without adhesion capabilities is presented and analyzed. Cells are represented by their cortex, which is modeled as an elastic curve, subject to an internal pressure force. Net polymerization or depolymerization in the cortex is modeled via local addition or removal of material, driving a cortical flow. The model takes the form of a fully nonlinear degenerate parabolic system. An existence analysis is carried out by adapting ideas from the theory of gradient flows. Numerical simulations show that these simple rules can account for the behavior observed in experiments, suggesting a possible mechanical mechanism for adhesion-independent motility. AU - Jankowiak, Gaspard AU - Peurichard, Diane AU - Reversat, Anne AU - Schmeiser, Christian AU - Sixt, Michael K ID - 7623 IS - 3 JF - Mathematical Models and Methods in Applied Sciences SN - 02182025 TI - Modeling adhesion-independent cell migration VL - 30 ER - TY - JOUR AB - In plant cells, environmental stressors promote changes in connectivity between the cortical ER and the PM. Although this process is tightly regulated in space and time, the molecular signals and structural components mediating these changes in inter-organelle communication are only starting to be characterized. In this report, we confirm the presence of a putative tethering complex containing the synaptotagmins 1 and 5 (SYT1 and SYT5) and the Ca2+ and lipid binding protein 1 (CLB1/SYT7). This complex is enriched at ER-PM contact sites (EPCS), have slow responses to changes in extracellular Ca2+, and display severe cytoskeleton-dependent rearrangements in response to the trivalent lanthanum (La3+) and gadolinium (Gd3+) rare earth elements (REEs). Although REEs are generally used as non-selective cation channel blockers at the PM, here we show that the slow internalization of REEs into the cytosol underlies the activation of the Ca2+/Calmodulin intracellular signaling, the accumulation of phosphatidylinositol-4-phosphate (PI4P) at the PM, and the cytoskeleton-dependent rearrangement of the SYT1/SYT5 EPCS complexes. We propose that the observed EPCS rearrangements act as a slow adaptive response to sustained stress conditions, and that this process involves the accumulation of stress-specific phosphoinositides species at the PM. AU - Lee, E AU - Vila Nova Santana, B AU - Samuels, E AU - Benitez-Fuente, F AU - Corsi, E AU - Botella, MA AU - Perez-Sancho, J AU - Vanneste, S AU - Friml, Jiří AU - Macho, A AU - Alves Azevedo, A AU - Rosado, A ID - 7646 IS - 14 JF - Journal of Experimental Botany SN - 0022-0957 TI - Rare earth elements induce cytoskeleton-dependent and PI4P-associated rearrangement of SYT1/SYT5 ER-PM contact site complexes in Arabidopsis VL - 71 ER - TY - JOUR AB - We propose that correlations among neurons are generically strong enough to organize neural activity patterns into a discrete set of clusters, which can each be viewed as a population codeword. Our reasoning starts with the analysis of retinal ganglion cell data using maximum entropy models, showing that the population is robustly in a frustrated, marginally sub-critical, or glassy, state. This leads to an argument that neural populations in many other brain areas might share this structure. Next, we use latent variable models to show that this glassy state possesses well-defined clusters of neural activity. Clusters have three appealing properties: (i) clusters exhibit error correction, i.e., they are reproducibly elicited by the same stimulus despite variability at the level of constituent neurons; (ii) clusters encode qualitatively different visual features than their constituent neurons; and (iii) clusters can be learned by downstream neural circuits in an unsupervised fashion. We hypothesize that these properties give rise to a “learnable” neural code which the cortical hierarchy uses to extract increasingly complex features without supervision or reinforcement. AU - Berry, Michael J. AU - Tkačik, Gašper ID - 7656 JF - Frontiers in Computational Neuroscience TI - Clustering of neural activity: A design principle for population codes VL - 14 ER - TY - JOUR AB - Following on from our recent work, we investigate a stochastic approach to non-equilibrium quantum spin systems. We show how the method can be applied to a variety of physical observables and for different initial conditions. We provide exact formulae of broad applicability for the time-dependence of expectation values and correlation functions following a quantum quench in terms of averages over classical stochastic processes. We further explore the behavior of the classical stochastic variables in the presence of dynamical quantum phase transitions, including results for their distributions and correlation functions. We provide details on the numerical solution of the associated stochastic differential equations, and examine the growth of fluctuations in the classical description. We discuss the strengths and limitations of the current implementation of the stochastic approach and the potential for further development. AU - De Nicola, Stefano AU - Doyon, B. AU - Bhaseen, M. J. ID - 7638 IS - 1 JF - Journal of Statistical Mechanics: Theory and Experiment TI - Non-equilibrium quantum spin dynamics from classical stochastic processes VL - 2020 ER - TY - JOUR AB - The evolution of finitely many particles obeying Langevin dynamics is described by Dean–Kawasaki equations, a class of stochastic equations featuring a non-Lipschitz multiplicative noise in divergence form. We derive a regularised Dean–Kawasaki model based on second order Langevin dynamics by analysing a system of particles interacting via a pairwise potential. Key tools of our analysis are the propagation of chaos and Simon's compactness criterion. The model we obtain is a small-noise stochastic perturbation of the undamped McKean–Vlasov equation. We also provide a high-probability result for existence and uniqueness for our model. AU - Cornalba, Federico AU - Shardlow, Tony AU - Zimmer, Johannes ID - 7637 IS - 2 JF - Nonlinearity SN - 09517715 TI - From weakly interacting particles to a regularised Dean-Kawasaki model VL - 33 ER - TY - JOUR AB - Metabotropic γ-aminobutyric acid (GABAB) receptors contribute to the control of network activity and information processing in hippocampal circuits by regulating neuronal excitability and synaptic transmission. The dysfunction in the dentate gyrus (DG) has been implicated in Alzheimer´s disease (AD). Given the involvement of GABAB receptors in AD, to determine their subcellular localisation and possible alteration in granule cells of the DG in a mouse model of AD at 12 months of age, we used high-resolution immunoelectron microscopic analysis. Immunohistochemistry at the light microscopic level showed that the regional and cellular expression pattern of GABAB1 was similar in an AD model mouse expressing mutated human amyloid precursor protein and presenilin1 (APP/PS1) and in age-matched wild type mice. High-resolution immunoelectron microscopy revealed a distance-dependent gradient of immunolabelling for GABAB receptors, increasing from proximal to distal dendrites in both wild type and APP/PS1 mice. However, the overall density of GABAB receptors at the neuronal surface of these postsynaptic compartments of granule cells was significantly reduced in APP/PS1 mice. Parallel to this reduction in surface receptors, we found a significant increase in GABAB1 at cytoplasmic sites. GABAB receptors were also detected at presynaptic sites in the molecular layer of the DG. We also found a decrease in plasma membrane GABAB receptors in axon terminals contacting dendritic spines of granule cells, which was more pronounced in the outer than in the inner molecular layer. Altogether, our data showing post- and presynaptic reduction in surface GABAB receptors in the DG suggest the alteration of the GABAB-mediated modulation of excitability and synaptic transmission in granule cells, which may contribute to the cognitive dysfunctions in the APP/PS1 model of AD AU - Martín-Belmonte, Alejandro AU - Aguado, Carolina AU - Alfaro-Ruíz, Rocío AU - Moreno-Martínez, Ana Esther AU - De La Ossa, Luis AU - Martínez-Hernández, José AU - Buisson, Alain AU - Shigemoto, Ryuichi AU - Fukazawa, Yugo AU - Luján, Rafael ID - 7664 IS - 7 JF - International journal of molecular sciences TI - Density of GABAB receptors is reduced in granule cells of the hippocampus in a mouse model of Alzheimer's disease VL - 21 ER - TY - JOUR AB - Acute brain slice preparation is a powerful experimental model for investigating the characteristics of synaptic function in the brain. Although brain tissue is usually cut at ice-cold temperature (CT) to facilitate slicing and avoid neuronal damage, exposure to CT causes molecular and architectural changes of synapses. To address these issues, we investigated ultrastructural and electrophysiological features of synapses in mouse acute cerebellar slices prepared at ice-cold and physiological temperature (PT). In the slices prepared at CT, we found significant spine loss and reconstruction, synaptic vesicle rearrangement and decrease in synaptic proteins, all of which were not detected in slices prepared at PT. Consistent with these structural findings, slices prepared at PT showed higher release probability. Furthermore, preparation at PT allows electrophysiological recording immediately after slicing resulting in higher detectability of long-term depression (LTD) after motor learning compared with that at CT. These results indicate substantial advantages of the slice preparation at PT for investigating synaptic functions in different physiological conditions. AU - Eguchi, Kohgaku AU - Velicky, Philipp AU - Hollergschwandtner, Elena AU - Itakura, Makoto AU - Fukazawa, Yugo AU - Danzl, Johann G AU - Shigemoto, Ryuichi ID - 7665 JF - Frontiers in Cellular Neuroscience SN - 16625102 TI - Advantages of acute brain slices prepared at physiological temperature in the characterization of synaptic functions VL - 14 ER - TY - JOUR AB - Wood, as the most abundant carbon dioxide storing bioresource, is currently driven beyond its traditional use through creative innovations and nanotechnology. For many properties the micro- and nanostructure plays a crucial role and one key challenge is control and detection of chemical and physical processes in the confined microstructure and nanopores of the wooden cell wall. In this study, correlative Raman and atomic force microscopy show high potential for tracking in situ molecular rearrangement of wood polymers during compression. More water molecules (interpreted as wider cellulose microfibril distances) and disentangling of hemicellulose chains are detected in the opened cell wall regions, whereas an increase of lignin is revealed in the compressed areas. These results support a new more “loose” cell wall model based on flexible lignin nanodomains and advance our knowledge of the molecular reorganization during deformation of wood for optimized processing and utilization. AU - Felhofer, Martin AU - Bock, Peter AU - Singh, Adya AU - Prats Mateu, Batirtze AU - Zirbs, Ronald AU - Gierlinger, Notburga ID - 7663 IS - 4 JF - Nano Letters TI - Wood deformation leads to rearrangement of molecules at the nanoscale VL - 20 ER - TY - JOUR AB - Generalizing the decomposition of a connected planar graph into a tree and a dual tree, we prove a combinatorial analog of the classic Helmholtz–Hodge decomposition of a smooth vector field. Specifically, we show that for every polyhedral complex, K, and every dimension, p, there is a partition of the set of p-cells into a maximal p-tree, a maximal p-cotree, and a collection of p-cells whose cardinality is the p-th reduced Betti number of K. Given an ordering of the p-cells, this tri-partition is unique, and it can be computed by a matrix reduction algorithm that also constructs canonical bases of cycle and boundary groups. AU - Edelsbrunner, Herbert AU - Ölsböck, Katharina ID - 7666 JF - Discrete and Computational Geometry SN - 01795376 TI - Tri-partitions and bases of an ordered complex VL - 64 ER -