The Separation Principle in Stochastic Control, Redux

Over the last 50 years a steady stream of accounts have been written on the separation principle of stochastic control. Even in the context of the linear-quadratic regulator in continuous time with Gaussian white noise, subtle difficulties arise, unexpected by many, that are often overlooked. In this paper we propose a new framework for establishing the separation principle. This approach takes the viewpoint that stochastic systems are well-defined maps between sample paths rather than stochastic processes per se and allows us to extend the separation principle to systems driven by martingales with possible jumps. While the approach is more in line with "real-life" engineering thinking where signals travel around the feedback loop, it is unconventional from a probabilistic point of view in that control laws for which the feedback equations are satisfied almost surely, and not deterministically for every sample path, are excluded.Comment: 23 pages, 6 figures, 2nd revision: added references, correction

On time-reversibility of linear stochastic models

Reversal of the time direction in stochastic systems driven by white noise has been central throughout the development of stochastic realization theory, filtering and smoothing. Similar ideas were developed in connection with certain problems in the theory of moments, where a duality induced by time reversal was introduced to parametrize solutions. In this latter work it was shown that stochastic systems driven by arbitrary second-order stationary processes can be similarly time-reversed. By combining these two sets of ideas we present herein a generalization of time-reversal in stochastic realization theory.Comment: 10 pages, 4 figure

Likelihood Analysis of Power Spectra and Generalized Moment Problems

We develop an approach to spectral estimation that has been advocated by Ferrante, Masiero and Pavon and, in the context of the scalar-valued covariance extension problem, by Enqvist and Karlsson. The aim is to determine the power spectrum that is consistent with given moments and minimizes the relative entropy between the probability law of the underlying Gaussian stochastic process to that of a prior. The approach is analogous to the framework of earlier work by Byrnes, Georgiou and Lindquist and can also be viewed as a generalization of the classical work by Burg and Jaynes on the maximum entropy method. In the present paper we present a new fast algorithm in the general case (i.e., for general Gaussian priors) and show that for priors with a specific structure the solution can be given in closed form.Comment: 17 pages, 4 figure

Unsupervised machine learning for detection of phase transitions in off-lattice systems I. Foundations

We demonstrate the utility of an unsupervised machine learning tool for the detection of phase transitions in off-lattice systems. We focus on the application of principal component analysis (PCA) to detect the freezing transitions of two-dimensional hard-disk and three-dimensional hard-sphere systems as well as liquid-gas phase separation in a patchy colloid model. As we demonstrate, PCA autonomously discovers order-parameter-like quantities that report on phase transitions, mitigating the need for a priori construction or identification of a suitable order parameter--thus streamlining the routine analysis of phase behavior. In a companion paper, we further develop the method established here to explore the detection of phase transitions in various model systems controlled by compositional demixing, liquid crystalline ordering, and non-equilibrium active forces

Debugging tasked Ada programs

The applications for which Ada was developed require distributed implementations of the language and extensive use of tasking facilities. Debugging and testing technology as it applies to parallel features of languages currently falls short of needs. Thus, the development of embedded systems using Ada pose special challenges to the software engineer. Techniques for distributing Ada programs, support for simulating distributed target machines, testing facilities for tasked programs, and debugging support applicable to simulated and to real targets all need to be addressed. A technique is presented for debugging Ada programs that use tasking and it describes a debugger, called AdaTAD, to support the technique. The debugging technique is presented together with the use interface to AdaTAD. The component of AdaTAD that monitors and controls communication among tasks was designed in Ada and is presented through an example with a simple tasked program

Unsupervised machine learning for detection of phase transitions in off-lattice systems II. Applications

We outline how principal component analysis (PCA) can be applied to particle configuration data to detect a variety of phase transitions in off-lattice systems, both in and out of equilibrium. Specifically, we discuss its application to study 1) the nonequilibrium random organization (RandOrg) model that exhibits a phase transition from quiescent to steady-state behavior as a function of density, 2) orientationally and positionally driven equilibrium phase transitions for hard ellipses, and 3) compositionally driven demixing transitions in the non-additive binary Widom-Rowlinson mixture

The binary black-hole problem at the third post-Newtonian approximation in the orbital motion: Static part

Post-Newtonian expansions of the Brill-Lindquist and Misner-Lindquist solutions of the time-symmetric two-black-hole initial value problem are derived. The static Hamiltonians related to the expanded solutions, after identifying the bare masses in both solutions, are found to differ from each other at the third post-Newtonian approximation. By shifting the position variables of the black holes the post-Newtonian expansions of the three metrics can be made to coincide up to the fifth post-Newtonian order resulting in identical static Hamiltonians up the third post-Newtonian approximation. The calculations shed light on previously performed binary point-mass calculations at the third post-Newtonian approximation.Comment: LaTeX, 9 pages, to be submitted to Physical Review

Bulk gravitons from a cosmological brane

We investigate the emission of gravitons by a cosmological brane into an Anti de Sitter five-dimensional bulk spacetime. We focus on the distribution of gravitons in the bulk and the associated production of `dark radiation' in this process. In order to evaluate precisely the amount of dark radiation in the late low-energy regime, corresponding to standard cosmology, we study numerically the emission, propagation and bouncing off the brane of bulk gravitons.Comment: 27 pages, 5 figures, minor corrections. Final versio

Dihydropyrimidine-thiones and clioquinol synergize to target beta-amyloid cellular pathologies through a metal-dependent mechanism

The lack of therapies for neurodegenerative diseases arises from our incomplete understanding of their underlying cellular toxicities and the limited number of predictive model systems. It is critical that we develop approaches to identify novel targets and lead compounds. Here, a phenotypic screen of yeast proteinopathy models identified dihydropyrimidine-thiones (DHPM-thiones) that selectively rescued the toxicity caused by β-amyloid (Aβ), the peptide implicated in Alzheimer’s disease. Rescue of Aβ toxicity by DHPM-thiones occurred through a metal-dependent mechanism of action. The bioactivity was distinct, however, from that of the 8-hydroxyquinoline clioquinol (CQ). These structurally dissimilar compounds strongly synergized at concentrations otherwise not competent to reduce toxicity. Cotreatment ameliorated Aβ toxicity by reducing Aβ levels and restoring functional vesicle trafficking. Notably, these low doses significantly reduced deleterious off-target effects caused by CQ on mitochondria at higher concentrations. Both single and combinatorial treatments also reduced death of neurons expressing Aβ in a nematode, indicating that DHPM-thiones target a conserved protective mechanism. Furthermore, this conserved activity suggests that expression of the Aβ peptide causes similar cellular pathologies from yeast to neurons. Our identification of a new cytoprotective scaffold that requires metal-binding underscores the critical role of metal phenomenology in mediating Aβ toxicity. Additionally, our findings demonstrate the valuable potential of synergistic compounds to enhance on-target activities, while mitigating deleterious off-target effects. The identification and prosecution of synergistic compounds could prove useful for developing AD therapeutics where combination therapies may be required to antagonize diverse pathologies.D.F.T was funded by NRSA Fellowship NIH 5F32NS061419. D.F.T. and S.L. were supported by WIBR funds in support of research on Regenerative Disease, the Picower/JPB Foundation, and the Edward N. and Della L. Thome Foundation. G.A.C. and S.L. were funded by a Howard Hughes Medical Institute (HHMI) Collaborative Innovation Award. L.E.B., R.T., and S.E.S. were funded by NIH GM086180, NIH GM067041, and NIH GM111625. (5F32NS061419 - NRSA Fellowship NIH; WIBR funds in support of research on Regenerative Disease; Picower/JPB Foundation; Edward N. and Della L. Thome Foundation; Howard Hughes Medical Institute (HHMI) Collaborative Innovation Award; GM086180 - NIH; NIH GM067041 - NIH; NIH GM111625 - NIH)https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5705239/Accepted manuscrip