An Input Normal Form Homotopy for the L2 Optimal Model Order Reduction Problem

In control system analysis and design, finding a reduced order model, optimal in the L-squared sense, to a given system model is a fundamental problem. The problem is very difficult without the global convergence of homotopy methods, and a homotopy based approach has been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. A homotopy algorithm based on the input normal form characterization of the reduced order model is developed here and is compared with the homotopy algorithms based on Hyland and Bernstein's optimal projection equations. The main conclusions are that the input normal form algorithm can be very efficient, but can also be very ill conditioned or even fail

A Homotopy Algorithm for the Combined H-squared/H-to Infinity Model Reduction Problem

The problem of finding a reduced order model, optimal in the H-squared sense, to a given system model is a fundamental one in control system analysis and design. The addition of a H-to infinity constraint to the H-squared optimal model reduction problem results in a more practical yet computationally more difficult problem. Without the global convergence of probability-one homotopy methods the combined H-squared/H-to infinity model reduction problem is difficult to solve. Several approaches based on homotoppy methods have been proposed. The issues are the number of degrees of freedom, the well posedness of the finite dimensional optimization problem, and the numerical robustness of the resulting homotopy algorithm. Homotopy algorithms based on two formulations - input normal form; Ly, Bryson, and Cannon's 2 x 2 block parametrization - are developed and compared here

SynGAP isoforms exert opposing effects on synaptic strength

Peer reviewedPublisher PD

Short term doxycycline treatment induces sustained improvement in myocardial infarction border zone contractility.

Decreased contractility in the non-ischemic border zone surrounding a MI is in part due to degradation of cardiomyocyte sarcomeric components by intracellular matrix metalloproteinase-2 (MMP-2). We recently reported that MMP-2 levels were increased in the border zone after a MI and that treatment with doxycycline for two weeks after MI was associated with normalization of MMP-2 levels and improvement in ex-vivo contractile protein developed force in the myocardial border zone. The purpose of the current study was to determine if there is a sustained effect of short term treatment with doxycycline (Dox) on border zone function in a large animal model of antero-apical myocardial infarction (MI). Antero-apical MI was created in 14 sheep. Seven sheep received doxycycline 0.8 mg/kg/hr IV for two weeks. Cardiac MRI was performed two weeks before, and then two and six weeks after MI. Two sheep died prior to MRI at six weeks from surgical/anesthesia-related causes. The remaining 12 sheep completed the protocol. Doxycycline induced a sustained reduction in intracellular MMP-2 by Western blot (3649±643 MI+Dox vs 9236±114 MI relative intensity; p = 0.0009), an improvement in ex-vivo contractility (65.3±2.0 MI+Dox vs 39.7±0.8 MI mN/mm2; p<0.0001) and an increase in ventricular wall thickness at end-systole 1.0 cm from the infarct edge (12.4±0.6 MI+Dox vs 10.0±0.5 MI mm; p = 0.0095). Administration of doxycycline for a limited two week period is associated with a sustained improvement in ex-vivo contractility and an increase in wall thickness at end-systole in the border zone six weeks after MI. These findings were associated with a reduction in intracellular MMP-2 activity

Polynomial Interrupt Timed Automata

Interrupt Timed Automata (ITA) form a subclass of stopwatch automata where reachability and some variants of timed model checking are decidable even in presence of parameters. They are well suited to model and analyze real-time operating systems. Here we extend ITA with polynomial guards and updates, leading to the class of polynomial ITA (PolITA). We prove the decidability of the reachability and model checking of a timed version of CTL by an adaptation of the cylindrical decomposition method for the first-order theory of reals. Compared to previous approaches, our procedure handles parameters and clocks in a unified way. Moreover, we show that PolITA are incomparable with stopwatch automata. Finally additional features are introduced while preserving decidability

Thermal conductivity measurements of proton-heated warm dense aluminum.

Thermal conductivity is one of the most crucial physical properties of matter when it comes to understanding heat transport, hydrodynamic evolution, and energy balance in systems ranging from astrophysical objects to fusion plasmas. In the warm dense matter regime, experimental data are very scarce so that many theoretical models remain untested. Here we present the first thermal conductivity measurements of aluminum at 0.5-2.7 g/cc and 2-10 eV, using a recently developed platform of differential heating. A temperature gradient is induced in a Au/Al dual-layer target by proton heating, and subsequent heat flow from the hotter Au to the Al rear surface is detected by two simultaneous time-resolved diagnostics. A systematic data set allows for constraining both thermal conductivity and equation-of-state models. Simulations using Purgatorio model or Sesame S27314 for Al thermal conductivity and LEOS for Au/Al release equation-of-state show good agreement with data after 15 ps. Discrepancy still exists at early time 0-15 ps, likely due to non-equilibrium conditions

The Potential and Challenges of CAD with Equational Constraints for SC-Square

Cylindrical algebraic decomposition (CAD) is a core algorithm within Symbolic Computation, particularly for quantifier elimination over the reals and polynomial systems solving more generally. It is now finding increased application as a decision procedure for Satisfiability Modulo Theories (SMT) solvers when working with non-linear real arithmetic. We discuss the potentials from increased focus on the logical structure of the input brought by the SMT applications and SC-Square project, particularly the presence of equational constraints. We also highlight the challenges for exploiting these: primitivity restrictions, well-orientedness questions, and the prospect of incrementality.Comment: Accepted into proceedings of MACIS 201

Need Polynomial Systems Be Doubly-Exponential?

Polynomial Systems, or at least their algorithms, have the reputation of being doubly-exponential in the number of variables [Mayr and Mayer, 1982], [Davenport and Heintz, 1988]. Nevertheless, the Bezout bound tells us that that number of zeros of a zero-dimensional system is singly-exponential in the number of variables. How should this contradiction be reconciled? We first note that [Mayr and Ritscher, 2013] shows that the doubly exponential nature of Gr\"{o}bner bases is with respect to the dimension of the ideal, not the number of variables. This inspires us to consider what can be done for Cylindrical Algebraic Decomposition which produces a doubly-exponential number of polynomials of doubly-exponential degree. We review work from ISSAC 2015 which showed the number of polynomials could be restricted to doubly-exponential in the (complex) dimension using McCallum's theory of reduced projection in the presence of equational constraints. We then discuss preliminary results showing the same for the degree of those polynomials. The results are under primitivity assumptions whose importance we illustrate.Comment: Extended Abstract for ICMS 2016 Presentation. arXiv admin note: text overlap with arXiv:1605.0249