= 1. Along the argument, we prove Mosco- and I-convergence results for discrete energy functionals, which are of independent interest for convergence of equivalent gradient flow structures in Hilbert spaces. The second part investigates L2-Wasserstein flows on metric graph. The starting point is a Benamou-Brenier formula for the L2-Wasserstein distance, which is proved via a regularisation scheme for solutions of the continuity equation, adapted to the peculiar geometric structure of metric graphs. Based on those results, we show that the L2-Wasserstein space over a metric graph admits a gradient flow which may be identified as a solution of a Fokker-Planck equation. In the third part, we focus again on the discrete gradient flows, already encountered in the first part. We propose a variational structure which extends the gradient flow structure to Markov chains violating the detailed-balance conditions. Using this structure, we characterise contraction estimates for the discrete heat flow in terms of convexity of corresponding path-dependent energy functionals. In addition, we use this approach to derive several functional inequalities for said functionals. AU - Forkert, Dominik L ID - 7629 SN - 2663-337X TI - Gradient flows in spaces of probability measures for finite-volume schemes, metric graphs and non-reversible Markov chains 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 - Assemblies of colloidal semiconductor nanocrystals (NCs) in the form of thin solid films leverage the size-dependent quantum confinement properties and the wet chemical methods vital for the development of the emerging solution-processable electronics, photonics, and optoelectronics technologies. The ability to control the charge carrier transport in the colloidal NC assemblies is fundamental for altering their electronic and optical properties for the desired applications. Here we demonstrate a strategy to render the solids of narrow-bandgap NC assemblies exclusively electron-transporting by creating a type-II heterojunction via shelling. Electronic transport of molecularly cross-linked PbTe@PbS core@shell NC assemblies is measured using both a conventional solid gate transistor and an electric-double-layer transistor, as well as compared with those of core-only PbTe NCs. In contrast to the ambipolar characteristics demonstrated by many narrow-bandgap NCs, the core@shell NCs exhibit exclusive n-type transport, i.e., drastically suppressed contribution of holes to the overall transport. The PbS shell that forms a type-II heterojunction assists the selective carrier transport by heavy doping of electrons into the PbTe-core conduction level and simultaneously strongly localizes the holes within the NC core valence level. This strongly enhanced n-type transport makes these core@shell NCs suitable for applications where ambipolar characteristics should be actively suppressed, in particular, for thermoelectric and electron-transporting layers in photovoltaic devices. AU - Miranti, Retno AU - Shin, Daiki AU - Septianto, Ricky Dwi AU - Ibáñez, Maria AU - Kovalenko, Maksym V. AU - Matsushita, Nobuhiro AU - Iwasa, Yoshihiro AU - Bisri, Satria Zulkarnaen ID - 7634 IS - 3 JF - ACS Nano TI - Exclusive electron transport in Core@Shell PbTe@PbS colloidal semiconductor nanocrystal assemblies VL - 14 ER - TY - CONF AB - Concurrent programming can be notoriously complex and error-prone. Programming bugs can arise from a variety of sources, such as operation re-reordering, or incomplete understanding of the memory model. A variety of formal and model checking methods have been developed to address this fundamental difficulty. While technically interesting, existing academic methods are still hard to apply to the large codebases typical of industrial deployments, which limits their practical impact. AU - Koval, Nikita AU - Sokolova, Mariia AU - Fedorov, Alexander AU - Alistarh, Dan-Adrian AU - Tsitelov, Dmitry ID - 7635 SN - 9781450368186 T2 - Proceedings of the ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming, PPOPP TI - Testing concurrency on the JVM with Lincheck ER - TY - CONF AB - Balanced search trees typically use key comparisons to guide their operations, and achieve logarithmic running time. By relying on numerical properties of the keys, interpolation search achieves lower search complexity and better performance. Although interpolation-based data structures were investigated in the past, their non-blocking concurrent variants have received very little attention so far. In this paper, we propose the first non-blocking implementation of the classic interpolation search tree (IST) data structure. For arbitrary key distributions, the data structure ensures worst-case O(log n + p) amortized time for search, insertion and deletion traversals. When the input key distributions are smooth, lookups run in expected O(log log n + p) time, and insertion and deletion run in expected amortized O(log log n + p) time, where p is a bound on the number of threads. To improve the scalability of concurrent insertion and deletion, we propose a novel parallel rebuilding technique, which should be of independent interest. We evaluate whether the theoretical improvements translate to practice by implementing the concurrent interpolation search tree, and benchmarking it on uniform and nonuniform key distributions, for dataset sizes in the millions to billions of keys. Relative to the state-of-the-art concurrent data structures, the concurrent interpolation search tree achieves performance improvements of up to 15% under high update rates, and of up to 50% under moderate update rates. Further, ISTs exhibit up to 2X less cache-misses, and consume 1.2 -- 2.6X less memory compared to the next best alternative on typical dataset sizes. We find that the results are surprisingly robust to distributional skew, which suggests that our data structure can be a promising alternative to classic concurrent search structures. AU - Brown, Trevor A AU - Prokopec, Aleksandar AU - Alistarh, Dan-Adrian ID - 7636 SN - 9781450368186 T2 - Proceedings of the ACM SIGPLAN Symposium on Principles and Practice of Parallel Programming TI - Non-blocking interpolation search trees with doubly-logarithmic running time 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 - 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 extent to which behavior is shaped by experience varies between individuals. Genetic differences contribute to this variation, but the neural mechanisms are not understood. Here, we dissect natural variation in the behavioral flexibility of two Caenorhabditis elegans wild strains. In one strain, a memory of exposure to 21% O2 suppresses CO2-evoked locomotory arousal; in the other, CO2 evokes arousal regardless of previous O2 experience. We map that variation to a polymorphic dendritic scaffold protein, ARCP-1, expressed in sensory neurons. ARCP-1 binds the Ca2+-dependent phosphodiesterase PDE-1 and co-localizes PDE-1 with molecular sensors for CO2 at dendritic ends. Reducing ARCP-1 or PDE-1 activity promotes CO2 escape by altering neuropeptide expression in the BAG CO2 sensors. Variation in ARCP-1 alters behavioral plasticity in multiple paradigms. Our findings are reminiscent of genetic accommodation, an evolutionary process by which phenotypic flexibility in response to environmental variation is reset by genetic change. AU - Beets, Isabel AU - Zhang, Gaotian AU - Fenk, Lorenz A. AU - Chen, Changchun AU - Nelson, Geoffrey M. AU - Félix, Marie-Anne AU - de Bono, Mario ID - 7546 IS - 1 JF - Neuron SN - 0896-6273 TI - Natural variation in a dendritic scaffold protein remodels experience-dependent plasticity by altering neuropeptide expression VL - 105 ER - TY - JOUR AB - Novelty facilitates formation of memories. The detection of novelty and storage of contextual memories are both mediated by the hippocampus, yet the mechanisms that link these two functions remain to be defined. Dentate granule cells (GCs) of the dorsal hippocampus fire upon novelty exposure forming engrams of contextual memory. However, their key excitatory inputs from the entorhinal cortex are not responsive to novelty and are insufficient to make dorsal GCs fire reliably. Here we uncover a powerful glutamatergic pathway to dorsal GCs from ventral hippocampal mossy cells (MCs) that relays novelty, and is necessary and sufficient for driving dorsal GCs activation. Furthermore, manipulation of ventral MCs activity bidirectionally regulates novelty-induced contextual memory acquisition. Our results show that ventral MCs activity controls memory formation through an intra-hippocampal interaction mechanism gated by novelty. AU - Fredes Tolorza, Felipe A AU - Silva Sifuentes, Maria A AU - Koppensteiner, Peter AU - Kobayashi, Kenta AU - Jösch, Maximilian A AU - Shigemoto, Ryuichi ID - 7551 JF - Current Biology TI - Ventro-dorsal hippocampal pathway gates novelty-induced contextual memory formation ER - TY - GEN AB - Normative theories and statistical inference provide complementary approaches for the study of biological systems. A normative theory postulates that organisms have adapted to efficiently solve essential tasks, and proceeds to mathematically work out testable consequences of such optimality; parameters that maximize the hypothesized organismal function can be derived ab initio, without reference to experimental data. In contrast, statistical inference focuses on efficient utilization of data to learn model parameters, without reference to any a priori notion of biological function, utility, or fitness. Traditionally, these two approaches were developed independently and applied separately. Here we unify them in a coherent Bayesian framework that embeds a normative theory into a family of maximum-entropy “optimization priors.” This family defines a smooth interpolation between a data-rich inference regime (characteristic of “bottom-up” statistical models), and a data-limited ab inito prediction regime (characteristic of “top-down” normative theory). We demonstrate the applicability of our framework using data from the visual cortex, and argue that the flexibility it affords is essential to address a number of fundamental challenges relating to inference and prediction in complex, high-dimensional biological problems. AU - Mlynarski, Wiktor F AU - Hledik, Michal AU - Sokolowski, Thomas R AU - Tkačik, Gašper ID - 7553 T2 - bioRxiv TI - Statistical analysis and optimality of biological systems 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 - 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 VL - 14 ER -