Applicability of Taylor's hypothesis in thermally driven turbulence

In this paper, we show that in the presence of large-scale circulation (LSC), Taylor's hypothesis can be invoked to deduce the energy spectrum in thermal convection using real space probes, a popular experimental tool. We perform numerical simulation of turbulent convection in a cube and observe that the velocity field follows Kolmogorov's spectrum ($k^{-5/3}$). We also record the velocity time series using real space probes near the lateral walls. The corresponding frequency spectrum exhibits Kolmogorov's spectrum ($f^{-5/3}$), thus validating Taylor's hypothesis with the steady LSC playing the role of a mean velocity field. The aforementioned findings based on real space probes provide valuable inputs for experimental measurements used for studying the spectrum of convective turbulence

Neural Packet Classification

Packet classification is a fundamental problem in computer networking. This problem exposes a hard tradeoff between the computation and state complexity, which makes it particularly challenging. To navigate this tradeoff, existing solutions rely on complex hand-tuned heuristics, which are brittle and hard to optimize. In this paper, we propose a deep reinforcement learning (RL) approach to solve the packet classification problem. There are several characteristics that make this problem a good fit for Deep RL. First, many of the existing solutions are iteratively building a decision tree by splitting nodes in the tree. Second, the effects of these actions (e.g., splitting nodes) can only be evaluated once we are done with building the tree. These two characteristics are naturally captured by the ability of RL to take actions that have sparse and delayed rewards. Third, it is computationally efficient to generate data traces and evaluate decision trees, which alleviate the notoriously high sample complexity problem of Deep RL algorithms. Our solution, NeuroCuts, uses succinct representations to encode state and action space, and efficiently explore candidate decision trees to optimize for a global objective. It produces compact decision trees optimized for a specific set of rules and a given performance metric, such as classification time, memory footprint, or a combination of the two. Evaluation on ClassBench shows that NeuroCuts outperforms existing hand-crafted algorithms in classification time by 18% at the median, and reduces both time and memory footprint by up to 3x

Optimal strategies for a game on amenable semigroups

The semigroup game is a two-person zero-sum game defined on a semigroup S as follows: Players 1 and 2 choose elements x and y in S, respectively, and player 1 receives a payoff f(xy) defined by a function f from S to [-1,1]. If the semigroup is amenable in the sense of Day and von Neumann, one can extend the set of classical strategies, namely countably additive probability measures on S, to include some finitely additive measures in a natural way. This extended game has a value and the players have optimal strategies. This theorem extends previous results for the multiplication game on a compact group or on the positive integers with a specific payoff. We also prove that the procedure of extending the set of allowed strategies preserves classical solutions: if a semigroup game has a classical solution, this solution solves also the extended game.Comment: 17 pages. To appear in International Journal of Game Theor

Rough paths in idealized financial markets

This paper considers possible price paths of a financial security in an idealized market. Its main result is that the variation index of typical price paths is at most 2, in this sense, typical price paths are not rougher than typical paths of Brownian motion. We do not make any stochastic assumptions and only assume that the price path is positive and right-continuous. The qualification "typical" means that there is a trading strategy (constructed explicitly in the proof) that risks only one monetary unit but brings infinite capital when the variation index of the realized price path exceeds 2. The paper also reviews some known results for continuous price paths and lists several open problems.Comment: 21 pages, this version adds (in Appendix C) a reference to new results in the foundations of game-theoretic probability based on Hardin and Taylor's work on hat puzzle

Fluid Particle Accelerations in Fully Developed Turbulence

The motion of fluid particles as they are pushed along erratic trajectories by fluctuating pressure gradients is fundamental to transport and mixing in turbulence. It is essential in cloud formation and atmospheric transport, processes in stirred chemical reactors and combustion systems, and in the industrial production of nanoparticles. The perspective of particle trajectories has been used successfully to describe mixing and transport in turbulence, but issues of fundamental importance remain unresolved. One such issue is the Heisenberg-Yaglom prediction of fluid particle accelerations, based on the 1941 scaling theory of Kolmogorov (K41). Here we report acceleration measurements using a detector adapted from high-energy physics to track particles in a laboratory water flow at Reynolds numbers up to 63,000. We find that universal K41 scaling of the acceleration variance is attained at high Reynolds numbers. Our data show strong intermittency---particles are observed with accelerations of up to 1,500 times the acceleration of gravity (40 times the root mean square value). Finally, we find that accelerations manifest the anisotropy of the large scale flow at all Reynolds numbers studied.Comment: 7 pages, 4 figure

On the optimal exercise boundaries of swing put options

We use probabilistic methods to characterise time-dependent optimal stopping boundaries in a problem of multiple optimal stopping on a finite time horizon. Motivated by financial applications, we consider a payoff of immediate stopping of “put” type, and the underlying dynamics follows a geometric Brownian motion. The optimal stopping region relative to each optimal stopping time is described in terms of two boundaries, which are continuous, monotonic functions of time and uniquely solve a system of coupled integral equations of Volterra-type. Finally, we provide a formula for the value function of the problem

Modeling genome-wide replication kinetics reveals a mechanism for regulation of replication timing

We developed analytical models of DNA replication that include probabilistic initiation of origins, fork progression, passive replication, and asynchrony.We fit the model to budding yeast genome-wide microarray data probing the replication fraction and found that initiation times correlate with the precision of timing.We extracted intrinsic origin properties, such as potential origin efficiency and firing-time distribution, which cannot be done using phenomenological approaches.We propose that origin timing is controlled by stochastically activated initiators bound to origin sites rather than explicit time-measuring mechanisms