Using the memories of multiscale machines to characterize complex systems

A scheme is presented to extract detailed dynamical signatures from successive measurements of complex systems. Relative entropy based time series tools are used to quantify the gain in predictive power of increasing past knowledge. By lossy compression, data is represented by increasingly coarsened symbolic strings. Each compression resolution is modeled by a machine: a finite memory transition matrix. Applying the relative entropy tools to each machine's memory exposes correlations within many time scales. Examples are given for cardiac arrhythmias and different heart conditions are distinguished.     

Equilibrium structures and flows of polar and nonpolar liquids in different carbon nanotubes

Molecular dynamics (MD) simulations of equilibrium structures and flows of polar water and nonpolar methane confined by single-walled carbon nanotubes (SWCNTs) with circular and square cross sections and bounding walls with regular graphene structure and random (amorphous) distribution of carbon atoms have been performed. The results of these simulations show that equilibrium structures of both confined liquids depend strongly on the shape of the cross section of SWCNTs, whereas the structure of their bounding walls has a minor influence on these structures. On contrary, the external pressure driven water and methane flows through above mentioned SWCNTs depend significantly on both the shape of their cross sections and the structure of their bounding walls.     

A detailed chemical kinetic model for high temperature ethanol oxidation

A detailed chemical kinetic model for ethanol oxidation has been developed and validated against a variety of experimental data sets. Laminar flame speed data (obtained from a constant volume bomb and counterflow twin‐flame), ignition delay data behind a reflected shock wave, and ethanol oxidation product profiles from a jet‐stirred and turbulent flow reactor were used in this computational study. Good agreement was found in modeling of the data sets obtained from the five different experimental systems. The computational results show that high temperature ethanol oxidation exhibits strong sensitivity to the fall‐off kinetics of ethanol decomposition, branching ratio selection for C₂H₅OH + OH ↔ Products, and reactions involving the hydroperoxyl (HO₂) radical. The multichanneled ethanol decomposition process is analyzed by RRKM/Master Equation theory, and the results are compared with those obtained from earlier studies. The ten‐parameter Troe form is used to define the C₂H₅OH(+M) ↔ CH₃ + CH₂OH(+M) rate expression as k^∞ = 5.94E23 T^−1.68 exp(−45880 K/T) (s⁻¹) k^o = 2.88E85 T^−18.9 exp(−55317 K/T) (cm³/mol/sec) F_cent = 0.5 exp(−T/200 K) + 0.5 exp(−T/890 K) + exp(−4600 K/T) and the C₂H₅OH(+M) ↔ C₂H₄ + H₂O(+M) rate expression as k^∞ = 2.79E13 T^0.09 exp(−33284 K/T) (s⁻¹) k^o = 2.57E83 T^−18.85 exp(−43509 K/T) (cm³/mol/sec) F _cent = 0.3 exp(−T/350 K) + 0.7 exp(−T/800 K) + exp(−3800 K/T) with an applied energy transfer per collision value of <ΔE_down> = 500 cm⁻¹. An empirical branching ratio estimation procedure is presented which determines the temperature dependent branching ratios of the three distinct sites of hydrogen abstraction from ethanol. The calculated branching ratios for C₂H₅OH + OH, C₂H₅OH + O, C₂H₅OH + H, and C₂H₅OH + CH₃ are compared to experimental data. © 1999 John Wiley & Sons, Inc. Int J Chem Kinet 31: 183–220, 1999     

The Average Condition Number of Most Tensor Rank Decomposition Problems is Infinite

The tensor rank decomposition, or canonical polyadic decomposition, is the decomposition of a tensor into a sum of rank-1 tensors. The condition number of the tensor rank decomposition measures the sensitivity of the rank-1 summands with respect to structured perturbations. Those are perturbations preserving the rank of the tensor that is decomposed. On the other hand, the angular condition number measures the perturbations of the rank-1 summands up to scaling. We show for random rank-2 tensors that the expected value of the condition number is infinite for a wide range of choices of the density. Under a mild additional assumption, we show that the same is true for most higher ranks \(r\ge 3\) as well. In fact, as the dimensions of the tensor tend to infinity, asymptotically all ranks are covered by our analysis. On the contrary, we show that rank-2 tensors have finite expected angular condition number. Based on numerical experiments, we conjecture that this could also be true for higher ranks. Our results underline the high computational complexity of computing tensor rank decompositions. We discuss consequences of our results for algorithm design and for testing algorithms computing tensor rank decompositions.

     

On the probability of Magnus Carlsen reaching 2900

How likely is it that Magnus Carlsen will achieve his goal of a 2900 Elo rating? At what level of play does Magnus have a reasonable chance of reaching the 2900 goal? These two questions are of great current interest to Magnus and the chess community. The probabilistic properties of Elo's rating system are well known, and together with a Brownian motion model of rating evolution, we use simulation-based methods to address these questions. Our model assesses that Magnus has a 4.5% chance of reaching 2900 if he continues his 2020–2022 level of play. However, this increases dramatically to $80$% chance if he can repeat his hot streak performance of 2019 which is not an easy undertaking. The probabilities are intimately related to Elo's choice $K$-factor used for grandmaster chess play. Finally, we conclude with a discussion of the policy issues involved with the choice of $K$-factor.