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, PPOPP
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 growth of snail shells can be described by simple mathematical rules. Variation in a few parameters can explain much of the diversity of shell shapes seen in nature. However, empirical studies of gastropod shell shape variation typically use geometric morphometric approaches, which do not capture this growth pattern. We have developed a way to infer a set of developmentally descriptive shape parameters based on three-dimensional logarithmic helicospiral growth and using landmarks from two-dimensional shell images as input. We demonstrate the utility of this approach, and compare it to the geometric morphometric approach, using a large set of Littorina saxatilis shells in which locally adapted populations differ in shape. Our method can be modified easily to make it applicable to a wide range of shell forms, which would allow for investigations of the similarities and differences between and within many different species of gastropods.
AU - Larsson, J.
AU - Westram, Anja M
AU - Bengmark, S.
AU - Lundh, T.
AU - Butlin, R. K.
ID - 7651
IS - 163
JF - Journal of The Royal Society Interface
SN - 1742-5689
TI - A developmentally descriptive method for quantifying shape in gastropod shells
VL - 17
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 -