Theory for the optimal control of time-averaged quantities in open quantum systems

We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal control field fulfills a high order differential equation, which we solve analytically for some limiting cases. We determine quantitatively how relaxation effects limit the control of the system. The theory is applied to open two level quantum systems. An approximate analytical solution for the level occupations in terms of the applied fields is presented. Different other applications are discussed

A Machine Learning Approach to Predict Metabolic Pathway Dynamics from Time Series Multiomics Data

New synthetic biology capabilities hold the promise of dramatically improving our ability to engineer biological systems. However, a fundamental hurdle in realizing this potential is our inability to accurately predict biological behavior after modifying the corresponding genotype. Kinetic models have traditionally been used to predict pathway dynamics in bioengineered systems, but they take significant time to develop, and rely heavily on domain expertise. Here, we show that the combination of machine learning and abundant multiomics data (proteomics and metabolomics) can be used to effectively predict pathway dynamics in an automated fashion. The new method outperforms a classical kinetic model, and produces qualitative and quantitative predictions that can be used to productively guide bioengineering efforts. This method systematically leverages arbitrary amounts of new data to improve predictions, and does not assume any particular interactions, but rather implicitly chooses the most predictive ones

Opportunities at the Intersection of Synthetic Biology, Machine Learning, and Automation

Our inability to predict the behavior of biological systems severely hampers progress in bioengineering and biomedical applications. We cannot predict the effect of genotype changes on phenotype, nor extrapolate the large-scale behavior from small-scale experiments. Machine learning techniques recently reached a new level of maturity, and are capable of providing the needed predictive power without a detailed mechanistic understanding. However, they require large amounts of data to be trained. The amount and quality of data required can only be produced through a combination of synthetic biology and automation, so as to generate a large diversity of biological systems with high reproducibility. A sustained investment in the intersection of synthetic biology, machine learning, and automation will drive forward predictive biology, and produce improved machine learning algorithms

Machine learning framework for assessment of microbial factory performance

Metabolic models can estimate intrinsic product yields for microbial factories, but such frameworks struggle to predict cell performance (including product titer or rate) under suboptimal metabolism and complex bioprocess conditions. On the other hand, machine learning, complementary to metabolic modeling necessitates large amounts of data. Building such a database for metabolic engineering designs requires significant manpower and is prone to human errors and bias. We propose an approach to integrate data-driven methods with genome scale metabolic model for assessment of microbial bio-production (yield, titer and rate). Using engineered E. coli as an example, we manually extracted and curated a data set comprising about 1200 experimentally realized cell factories from ~100 papers. We furthermore augmented the key design features (e.g., genetic modifications and bioprocess variables) extracted from literature with additional features derived from running the genome-scale metabolic model iML1515 simulations with constraints that match the experimental data. Then, data augmentation and ensemble learning (e.g., support vector machines, gradient boosted trees, and neural networks in a stacked regressor model) are employed to alleviate the challenges of sparse, non-standardized, and incomplete data sets, while multiple correspondence analysis/principal component analysis are used to rank influential factors on bio-production. The hybrid framework demonstrates a reasonably high cross-validation accuracy for prediction of E.coli factory performance metrics under presumed bioprocess and pathway conditions (Pearson correlation coefficients between 0.8 and 0.93 on new data not seen by the model)

Physical interpretation of gauge invariant perturbations of spherically symmetric space-times

By calculating the Newman-Penrose Weyl tensor components of a perturbed spherically symmetric space-time with respect to invariantly defined classes of null tetrads, we give a physical interpretation, in terms of gravitational radiation, of odd parity gauge invariant metric perturbations. We point out how these gauge invariants may be used in setting boundary and/or initial conditions in perturbation theory.Comment: 6 pages. To appear in PR

Precision tests of the MSSM

We present the results of a first global fit to the electroweak observables in the MSSM. The best fit selects either very low or very large values of ~$\tan\beta$ ~and, correspondingly, chargino (higgsino--like) and stop or the ~$CP-$odd Higgs boson are within the reach of LEP 2. Moreover, the best fit gives ~ $\alpha_s(M_Z)=0.118^{+0.005}_{-0.010}$, ~which is lower than the one obtained from the SM fits. The overall fit is excellent ~ ($\chi^2=7.2$ ~for 15 d.o.f. as compared to ~$\chi^2=11$ ~in the SM). Those results follow from the fact that in the MSSM one can increase the value of ~ $R_b\equiv\Gamma_{Z^0\to\bar bb}/\Gamma_{Z^0\to hadrons}$ ~ {\it without} modyfying the SM predictions for other observables.Comment: 10 pages, LaTEX, 7 figures (not included) may be obtained from [email protected] upon request. Modified version of the plenary talk given by S. Pokorski at the ``Beyond the Standard Model IV'', Lake Tahoe, CA, December 199

Rigorous conditions for the existence of bound states at the threshold in the two-particle case

In the framework of non-relativistic quantum mechanics and with the help of the Greens functions formalism we study the behavior of weakly bound states as they approach the continuum threshold. Through estimating the Green's function for positive potentials we derive rigorously the upper bound on the wave function, which helps to control its falloff. In particular, we prove that for potentials whose repulsive part decays slower than $1/r^{2}$ the bound states approaching the threshold do not spread and eventually become bound states at the threshold. This means that such systems never reach supersizes, which would extend far beyond the effective range of attraction. The method presented here is applicable in the many--body case