TY - JOUR
AB - In pipe, channel, and boundary layer flows turbulence first occurs intermittently in space and time: at moderate Reynolds numbers domains of disordered turbulent motion are separated by quiescent laminar regions. Based on direct numerical simulations of pipe flow we argue here that the spatial intermittency has its origin in a nearest neighbor interaction between turbulent regions. We further show that in this regime turbulent flows are intrinsically intermittent with a well-defined equilibrium turbulent fraction but without ever assuming a steady pattern. This transition scenario is analogous to that found in simple models such as coupled map lattices. The scaling observed implies that laminar intermissions of the turbulent flow will persist to arbitrarily large Reynolds numbers.
AU - Avila, Marc
AU - Hof, Björn
ID - 2811
IS - 6
JF - Physical Review E
TI - Nature of laminar-turbulence intermittency in shear flows
VL - 87
ER -
TY - CONF
AB - We consider the problem of deciding whether the persistent homology group of a simplicial pair (K, L) can be realized as the homology H* (X) of some complex X with L ⊂ X ⊂ K. We show that this problem is NP-complete even if K is embedded in ℝ3. As a consequence, we show that it is NP-hard to simplify level and sublevel sets of scalar functions on S3 within a given tolerance constraint. This problem has relevance to the visualization of medical images by isosurfaces. We also show an implication to the theory of well groups of scalar functions: not every well group can be realized by some level set, and deciding whether a well group can be realized is NP-hard.
AU - Attali, Dominique
AU - Bauer, Ulrich
AU - Devillers, Olivier
AU - Glisse, Marc
AU - Lieutier, André
ID - 2812
T2 - Proceedings of the 29th annual symposium on Computational Geometry
TI - Homological reconstruction and simplification in R3
ER -
TY - JOUR
AB - Turbulence is ubiquitous in nature, yet even for the case of ordinary Newtonian fluids like water, our understanding of this phenomenon is limited. Many liquids of practical importance are more complicated (e.g., blood, polymer melts, paints), however; they exhibit elastic as well as viscous characteristics, and the relation between stress and strain is nonlinear. We demonstrate here for a model system of such complex fluids that at high shear rates, turbulence is not simply modified as previously believed but is suppressed and replaced by a different type of disordered motion, elasto-inertial turbulence. Elasto-inertial turbulence is found to occur at much lower Reynolds numbers than Newtonian turbulence, and the dynamical properties differ significantly. The friction scaling observed coincides with the so-called "maximum drag reduction" asymptote, which is exhibited by a wide range of viscoelastic fluids.
AU - Samanta, Devranjan
AU - Dubief, Yves
AU - Holzner, Markus
AU - Schäfer, Christof
AU - Morozov, Alexander
AU - Wagner, Christian
AU - Hof, Björn
ID - 2813
IS - 26
JF - PNAS
TI - Elasto-inertial turbulence
VL - 110
ER -
TY - JOUR
AB - We study the problem of generating a test sequence that achieves maximal coverage for a reactive system under test. We formulate the problem as a repeated game between the tester and the system, where the system state space is partitioned according to some coverage criterion and the objective of the tester is to maximize the set of partitions (or coverage goals) visited during the game. We show the complexity of the maximal coverage problem for non-deterministic systems is PSPACE-complete, but is NP-complete for deterministic systems. For the special case of non-deterministic systems with a re-initializing "reset" action, which represent running a new test input on a re-initialized system, we show that the complexity is coNP-complete. Our proof technique for reset games uses randomized testing strategies that circumvent the exponentially large memory requirement of deterministic testing strategies. We also discuss the memory requirement for deterministic strategies and extensions of our results to other models, such as pushdown systems and timed systems.
AU - Chatterjee, Krishnendu
AU - Alfaro, Luca
AU - Majumdar, Ritankar
ID - 2814
IS - 2
JF - International Journal of Foundations of Computer Science
TI - The complexity of coverage
VL - 24
ER -
TY - JOUR
AB - The fact that a sum of isotropic Gaussian kernels can have more modes than kernels is surprising. Extra (ghost) modes do not exist in ℝ1 and are generally not well studied in higher dimensions. We study a configuration of n+1 Gaussian kernels for which there are exactly n+2 modes. We show that all modes lie on a finite set of lines, which we call axes, and study the restriction of the Gaussian mixture to these axes in order to discover that there are an exponential number of critical points in this configuration. Although the existence of ghost modes remained unknown due to the difficulty of finding examples in ℝ2, we show that the resilience of ghost modes grows like the square root of the dimension. In addition, we exhibit finite configurations of isotropic Gaussian kernels with superlinearly many modes.
AU - Edelsbrunner, Herbert
AU - Fasy, Brittany Terese
AU - Rote, Günter
ID - 2815
IS - 4
JF - Discrete & Computational Geometry
TI - Add isotropic Gaussian kernels at own risk: More and more resilient modes in higher dimensions
VL - 49
ER -
TY - JOUR
AB - In solid tumors, targeted treatments can lead to dramatic regressions, but responses are often short-lived because resistant cancer cells arise. The major strategy proposed for overcoming resistance is combination therapy. We present a mathematical model describing the evolutionary dynamics of lesions in response to treatment. We first studied 20 melanoma patients receiving vemurafenib. We then applied our model to an independent set of pancreatic, colorectal, and melanoma cancer patients with metastatic disease. We find that dual therapy results in long-term disease control for most patients, if there are no single mutations that cause cross-resistance to both drugs; in patients with large disease burden, triple therapy is needed. We also find that simultaneous therapy with two drugs is much more effective than sequential therapy. Our results provide realistic expectations for the efficacy of new drug combinations and inform the design of trials for new cancer therapeutics.
AU - Božić, Ivana
AU - Reiter, Johannes
AU - Allen, Benjamin
AU - Antal, Tibor
AU - Chatterjee, Krishnendu
AU - Shah, Preya
AU - Moon, Yo
AU - Yaqubie, Amin
AU - Kelly, Nicole
AU - Le, Dung
AU - Lipson, Evan
AU - Chapman, Paul
AU - Diaz, Luis
AU - Vogelstein, Bert
AU - Nowak, Martin
ID - 2816
JF - eLife
TI - Evolutionary dynamics of cancer in response to targeted combination therapy
VL - 2
ER -
TY - JOUR
AB - The basic idea of evolutionary game theory is that payoff determines reproductive rate. Successful individuals have a higher payoff and produce more offspring. But in evolutionary and ecological situations there is not only reproductive rate but also carrying capacity. Individuals may differ in their exposure to density limiting effects. Here we explore an alternative approach to evolutionary game theory by assuming that the payoff from the game determines the carrying capacity of individual phenotypes. Successful strategies are less affected by density limitation (crowding) and reach higher equilibrium abundance. We demonstrate similarities and differences between our framework and the standard replicator equation. Our equation is defined on the positive orthant, instead of the simplex, but has the same equilibrium points as the replicator equation. Linear stability analysis produces the classical conditions for asymptotic stability of pure strategies, but the stability properties of internal equilibria can differ in the two frameworks. For example, in a two-strategy game with an internal equilibrium that is always stable under the replicator equation, the corresponding equilibrium can be unstable in the new framework resulting in a limit cycle.
AU - Novak, Sebastian
AU - Chatterjee, Krishnendu
AU - Nowak, Martin
ID - 2817
JF - Journal of Theoretical Biology
TI - Density games
VL - 334
ER -
TY - JOUR
AB - Models of neural responses to stimuli with complex spatiotemporal correlation structure often assume that neurons are selective for only a small number of linear projections of a potentially high-dimensional input. In this review, we explore recent modeling approaches where the neural response depends on the quadratic form of the input rather than on its linear projection, that is, the neuron is sensitive to the local covariance structure of the signal preceding the spike. To infer this quadratic dependence in the presence of arbitrary (e.g., naturalistic) stimulus distribution, we review several inference methods, focusing in particular on two information theory–based approaches (maximization of stimulus energy and of noise entropy) and two likelihood-based approaches (Bayesian spike-triggered covariance and extensions of generalized linear models). We analyze the formal relationship between the likelihood-based and information-based approaches to demonstrate how they lead to consistent inference. We demonstrate the practical feasibility of these procedures by using model neurons responding to a flickering variance stimulus.
AU - Rajan, Kanaka
AU - Marre, Olivier
AU - Tkacik, Gasper
ID - 2818
IS - 7
JF - Neural Computation
TI - Learning quadratic receptive fields from neural responses to natural stimuli
VL - 25
ER -
TY - CONF
AB - We introduce quantatitive timed refinement metrics and quantitative timed simulation functions, incorporating zenoness checks, for timed systems. These functions assign positive real numbers between zero and infinity which quantify the timing mismatches between two timed systems, amongst non-zeno runs. We quantify timing mismatches in three ways: (1) the maximum timing mismatch that can arise, (2) the "steady-state" maximum timing mismatches, where initial transient timing mismatches are ignored; and (3) the (long-run) average timing mismatches amongst two systems. These three kinds of mismatches constitute three important types of timing differences. Our event times are the global times, measured from the start of the system execution, not just the time durations of individual steps. We present algorithms over timed automata for computing the three quantitative simulation functions to within any desired degree of accuracy. In order to compute the values of the quantitative simulation functions, we use a game theoretic formulation. We introduce two new kinds of objectives for two player games on finite state game graphs: (1) eventual debit-sum level objectives, and (2) average debit-sum level objectives. We present algorithms for computing the optimal values for these objectives for player 1, and then use these algorithms to compute the values of the quantitative timed simulation functions.
AU - Chatterjee, Krishnendu
AU - Prabhu, Vinayak
ID - 2819
T2 - Proceedings of the 16th International Conference on Hybrid Systems: Computation and Control
TI - Quantitative timed simulation functions and refinement metrics for real-time systems
VL - 1
ER -
TY - CONF
AB - In this paper, we introduce the powerful framework of graph games for the analysis of real-time scheduling with firm deadlines. We introduce a novel instance of a partial-observation game that is suitable for this purpose, and prove decidability of all the involved decision problems. We derive a graph game that allows the automated computation of the competitive ratio (along with an optimal witness algorithm for the competitive ratio) and establish an NP-completeness proof for the graph game problem. For a given on-line algorithm, we present polynomial time solution for computing (i) the worst-case utility; (ii) the worst-case utility ratio w.r.t. a clairvoyant off-line algorithm; and (iii) the competitive ratio. A major strength of the proposed approach lies in its flexibility w.r.t. incorporating additional constraints on the adversary and/or the algorithm, including limited maximum or average load, finiteness of periods of overload, etc., which are easily added by means of additional instances of standard objective functions for graph games.
AU - Chatterjee, Krishnendu
AU - Kößler, Alexander
AU - Schmid, Ulrich
ID - 2820
SN - 978-1-4503-1567-8
T2 - Proceedings of the 16th International conference on Hybrid systems: Computation and control
TI - Automated analysis of real-time scheduling using graph games
ER -