Quantitative Performance Bounds in Biomolecular Circuits due to Temperature Uncertainty

Performance of biomolecular circuits is affected by changes in temperature, due to its influence on underlying reaction rate parameters. While these performance variations have been estimated using Monte Carlo simulations, how to analytically bound them is generally unclear. To address this, we apply control-theoretic representations of uncertainty to examples of different biomolecular circuits, developing a framework to represent uncertainty due to temperature. We estimate bounds on the steady-state performance of these circuits due to temperature uncertainty. Through an analysis of the linearised dynamics, we represent this uncertainty as a feedback uncertainty and bound the variation in the magnitude of the input-output transfer function, providing a estimate of the variation in frequency-domain properties. Finally, we bound the variation in the time trajectories, providing an estimate of variation in time-domain properties. These results should enable a framework for analytical characterisation of uncertainty in biomolecular circuit performance due to temperature variation and may help in estimating relative performance of different controllers

Do All BPS Black Hole Microstates Carry Zero Angular Momentum?

From the analysis of the near horizon geometry and supersymmetry algebra it has been argued that all the microstates of single centered BPS black holes with four unbroken supersymmetries carry zero angular momentum in the region of the moduli space where the black hole description is valid. A stronger form of the conjecture would be that the result holds for any sufficiently generic point in the moduli space. In this paper we set out to test this conjecture for a class of black hole microstates in type II string theory on $T^6$, represented by four stacks of D-branes wrapped on various cycles of $T^6$. For this system the above conjecture translates to the statement that the moduli space of classical vacua must be a collection of points. Explicit analysis of systems carrying a low number of D-branes supports this conjecture.Comment: LaTeX, 42 pages; v2: minor corrections, some new results adde

BPS State Counting in N=8 Supersymmetric String Theory for Pure D-brane Configurations

Exact results for the BPS index are known for a class of BPS dyons in type II string theory compactified on a six dimensional torus. In this paper we set up the problem of counting the same BPS states in a duality frame in which the states carry only Ramond-Ramond charges. We explicitly count the number of states carrying the lowest possible charges and find agreement with the result obtained in other duality frames. Furthermore, we find that after factoring out the supermultiplet structure, each of these states carry zero angular momentum. This is in agreement with the prediction obtained from a representation of these states as supersymmetric black holes.Comment: 26 pages; v2: minor corrections in section 5; v3: typos correcte

Investigation of the transient fuel preburner manifold and combustor

A computational fluid dynamics (CFD) model with finite rate reactions, FDNS, was developed to study the start transient of the Space Shuttle Main Engine (SSME) fuel preburner (FPB). FDNS is a time accurate, pressure based CFD code. An upwind scheme was employed for spatial discretization. The upwind scheme was based on second and fourth order central differencing with adaptive artificial dissipation. A state of the art two-equation k-epsilon (T) turbulence model was employed for the turbulence calculation. A Pade' Rational Solution (PARASOL) chemistry algorithm was coupled with the point implicit procedure. FDNS was benchmarked with three well documented experiments: a confined swirling coaxial jet, a non-reactive ramjet dump combustor, and a reactive ramjet dump combustor. Excellent comparisons were obtained for the benchmark cases. The code was then used to study the start transient of an axisymmetric SSME fuel preburner. Predicted transient operation of the preburner agrees well with experiment. Furthermore, it was also found that an appreciable amount of unburned oxygen entered the turbine stages

Negative Feedback Facilitates Temperature Robustness in Biomolecular Circuit Dynamics

Temporal dynamics in many biomolecular circuits can change with temperature because of the temperature dependence of underlying reaction rate parameters. It is generally unclear what circuit mechanisms can inherently facilitate robustness in the dynamics to variations in temperature. Here, we address this issue using a combination of mathematical models and experimental measurements in a cell-free transcription-translation system. We find that negative transcriptional feedback can reduce the effect of temperature variation on circuit dynamics. Further, we find that effective negative feedback due to first-order degradation mechanisms can also enable such a temperature robustness effect. Finally, we estimate temperature dependence of key parameters mediating such negative feedback mechanisms. These results should be useful in the design of temperature robust circuit dynamics

Quantitative Performance Bounds in Biomolecular Circuits due to Temperature Uncertainty

Performance of biomolecular circuits is affected by changes in temperature, due to its influence on underlying reaction rate parameters. While these performance variations have been estimated using Monte Carlo simulations, how to analytically bound them is generally unclear. To address this, we apply control-theoretic representations of uncertainty to examples of different biomolecular circuits, developing a framework to represent uncertainty due to temperature. We estimate bounds on the steady-state performance of these circuits due to temperature uncertainty. Through an analysis of the linearised dynamics, we represent this uncertainty as a feedback uncertainty and bound the variation in the magnitude of the input-output transfer function, providing a estimate of the variation in frequency-domain properties. Finally, we bound the variation in the time trajectories, providing an estimate of variation in time-domain properties. These results should enable a framework for analytical characterisation of uncertainty in biomolecular circuit performance due to temperature variation and may help in estimating relative performance of different controllers

Editorial: Special Issue on "Nonparametric Inference Under Shape Constraints"

Shape-constrained inference usually refers to nonparametric function estimation and uncertainty quantification under qualitative shape restrictions such as monotonicity, convexity, log-concavity and so on. One of the earliest contributions to the field was by Grenander (1956). Motivated by the theory of mortality measurement, he studied the nonparametric maximum likelihood estimator of a decreasing density function on the nonnegative half-line. A great attraction of this estimator is that, unlike other nonparametric density estimators such as histograms or kernel density estimators, there are no tuning parameters (e.g., bandwidths) to choose.R. J. Samworth is supported by EPSRC Grants EP/P031447/1 and EP/N031938/1. B. Sen is supported by NSF Grants DMS-17-12822 and AST-16-14743

Evaluation of Trace Alignment Quality and its Application in Medical Process Mining

Trace alignment algorithms have been used in process mining for discovering the consensus treatment procedures and process deviations. Different alignment algorithms, however, may produce very different results. No widely-adopted method exists for evaluating the results of trace alignment. Existing reference-free evaluation methods cannot adequately and comprehensively assess the alignment quality. We analyzed and compared the existing evaluation methods, identifying their limitations, and introduced improvements in two reference-free evaluation methods. Our approach assesses the alignment result globally instead of locally, and therefore helps the algorithm to optimize overall alignment quality. We also introduced a novel metric to measure the alignment complexity, which can be used as a constraint on alignment algorithm optimization. We tested our evaluation methods on a trauma resuscitation dataset and provided the medical explanation of the activities and patterns identified as deviations using our proposed evaluation methods.Comment: 10 pages, 6 figures and 5 table