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 - Coxeter triangulations are triangulations of Euclidean space based on a single simplex. By this we mean that given an individual simplex we can recover the entire triangulation of Euclidean space by inductively reflecting in the faces of the simplex. In this paper we establish that the quality of the simplices in all Coxeter triangulations is O(1/d−−√) of the quality of regular simplex. We further investigate the Delaunay property for these triangulations. Moreover, we consider an extension of the Delaunay property, namely protection, which is a measure of non-degeneracy of a Delaunay triangulation. In particular, one family of Coxeter triangulations achieves the protection O(1/d2). We conjecture that both bounds are optimal for triangulations in Euclidean space.
AU - Choudhary, Aruni
AU - Kachanovich, Siargey
AU - Wintraecken, Mathijs
ID - 7567
JF - Mathematics in Computer Science
SN - 1661-8270
TI - Coxeter triangulations have good quality
ER -
TY - GEN
AB - Isomanifolds are the generalization of isosurfaces to arbitrary dimension and codimension, i.e.manifolds defined as the zero set of some multivariate multivalued functionf:Rd→Rd−n.A natural (and efficient) way to approximate an isomanifold is to consider its Piecewise-Linear(PL) approximation based on a triangulationTof the ambient spaceRd. In this paper, we giveconditions under which the PL-approximation of an isomanifold is topologically equivalent to theisomanifold. The conditions can always be met by taking a sufficiently fine triangulationT.
AU - Boissonnat, Jean-Daniel
AU - Wintraecken, Mathijs
ID - 7568
T2 - EUROCG 2020
TI - The topological correctness of the PL-approximation of isomanifolds
ER -
TY - JOUR
AB - Genes differ in the frequency at which they are expressed and in the form of regulation used to control their activity. In particular, positive or negative regulation can lead to activation of a gene in response to an external signal. Previous works proposed that the form of regulation of a gene correlates with its frequency of usage: positive regulation when the gene is frequently expressed and negative regulation when infrequently expressed. Such network design means that, in the absence of their regulators, the genes are found in their least required activity state, hence regulatory intervention is often necessary. Due to the multitude of genes and regulators, spurious binding and unbinding events, called “crosstalk”, could occur. To determine how the form of regulation affects the global crosstalk in the network, we used a mathematical model that includes multiple regulators and multiple target genes. We found that crosstalk depends non-monotonically on the availability of regulators. Our analysis showed that excess use of regulation entailed by the formerly suggested network design caused high crosstalk levels in a large part of the parameter space. We therefore considered the opposite ‘idle’ design, where the default unregulated state of genes is their frequently required activity state. We found, that ‘idle’ design minimized the use of regulation and thus minimized crosstalk. In addition, we estimated global crosstalk of S. cerevisiae using transcription factors binding data. We demonstrated that even partial network data could suffice to estimate its global crosstalk, suggesting its applicability to additional organisms. We found that S. cerevisiae estimated crosstalk is lower than that of a random network, suggesting that natural selection reduces crosstalk. In summary, our study highlights a new type of protein production cost which is typically overlooked: that of regulatory interference caused by the presence of excess regulators in the cell. It demonstrates the importance of whole-network descriptions, which could show effects missed by single-gene models.
AU - Grah, Rok
AU - Friedlander, Tamar
ID - 7569
IS - 2
JF - PLOS Computational Biology
SN - 1553-7358
TI - The relation between crosstalk and gene regulation form revisited
VL - 16
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 - This paper deals with dynamical optimal transport metrics defined by spatial discretisation of the Benamou–Benamou formula for the Kantorovich metric . Such metrics appear naturally in discretisations of -gradient flow formulations for dissipative PDE. However, it has recently been shown that these metrics do not in general converge to , unless strong geometric constraints are imposed on the discrete mesh. In this paper we prove that, in a 1-dimensional periodic setting, discrete transport metrics converge to a limiting transport metric with a non-trivial effective mobility. This mobility depends sensitively on the geometry of the mesh and on the non-local mobility at the discrete level. Our result quantifies to what extent discrete transport can make use of microstructure in the mesh to reduce the cost of transport.
AU - Gladbach, Peter
AU - Kopfer, Eva
AU - Maas, Jan
AU - Portinale, Lorenzo
ID - 7573
JF - Journal des Mathematiques Pures et Appliquees
SN - 00217824
TI - Homogenisation of one-dimensional discrete optimal transport
ER -
TY - JOUR
AB - Weak convergence of inertial iterative method for solving variational inequalities is the focus of this paper. The cost function is assumed to be non-Lipschitz and monotone. We propose a projection-type method with inertial terms and give weak convergence analysis under appropriate conditions. Some test results are performed and compared with relevant methods in the literature to show the efficiency and advantages given by our proposed methods.
AU - Shehu, Yekini
AU - Iyiola, Olaniyi S.
ID - 7577
JF - Applicable Analysis
SN - 0003-6811
TI - Weak convergence for variational inequalities with inertial-type method
ER -
TY - JOUR
AB - The eukaryotic endomembrane system is controlled by small GTPases of the Rab family, which are activated at defined times and locations in a switch-like manner. While this switch is well understood for an individual protein, how regulatory networks produce intracellular activity patterns is currently not known. Here, we combine in vitro reconstitution experiments with computational modeling to study a minimal Rab5 activation network. We find that the molecular interactions in this system give rise to a positive feedback and bistable collective switching of Rab5. Furthermore, we find that switching near the critical point is intrinsically stochastic and provide evidence that controlling the inactive population of Rab5 on the membrane can shape the network response. Notably, we demonstrate that collective switching can spread on the membrane surface as a traveling wave of Rab5 activation. Together, our findings reveal how biochemical signaling networks control vesicle trafficking pathways and how their nonequilibrium properties define the spatiotemporal organization of the cell.
AU - Bezeljak, Urban
AU - Loya, Hrushikesh
AU - Kaczmarek, Beata M
AU - Saunders, Timothy E.
AU - Loose, Martin
ID - 7580
IS - 12
JF - Proceedings of the National Academy of Sciences
SN - 0027-8424
TI - Stochastic activation and bistability in a Rab GTPase regulatory network
VL - 117
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 - 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
ER -