Technical Report: Voltage Source Converter MPC with Optimized Pulse Patterns and minimization of Integrated Squared Tracking Error

Model predictive control schemes for power electronic applications are characterized by a great variety of problem formulations. In this paper, we consider a three phase voltage source converter with an arbitrary number of voltage levels and derive a model predictive control scheme involving a combination of optimized pulse patterns and the integral of squared predicted tracking error as a cost function. We obtain a nonlinear optimization problem with the switching times as optimization variables, and solve it using gradient projection algorithm. To obtain an easier optimization problem to be solved on-line, a linearization around nominal switching instants is performed bringing the problem to a quadratic programming form. Simulation results demonstrating the performance of the derived scheme are provided for the case of a grid-tied converter with LCL filter

Certification of Bounds of Non-linear Functions: the Templates Method

The aim of this work is to certify lower bounds for real-valued multivariate functions, defined by semialgebraic or transcendental expressions. The certificate must be, eventually, formally provable in a proof system such as Coq. The application range for such a tool is widespread; for instance Hales' proof of Kepler's conjecture yields thousands of inequalities. We introduce an approximation algorithm, which combines ideas of the max-plus basis method (in optimal control) and of the linear templates method developed by Manna et al. (in static analysis). This algorithm consists in bounding some of the constituents of the function by suprema of quadratic forms with a well chosen curvature. This leads to semialgebraic optimization problems, solved by sum-of-squares relaxations. Templates limit the blow up of these relaxations at the price of coarsening the approximation. We illustrate the efficiency of our framework with various examples from the literature and discuss the interfacing with Coq.Comment: 16 pages, 3 figures, 2 table

Finding polynomial loop invariants for probabilistic programs

Quantitative loop invariants are an essential element in the verification of probabilistic programs. Recently, multivariate Lagrange interpolation has been applied to synthesizing polynomial invariants. In this paper, we propose an alternative approach. First, we fix a polynomial template as a candidate of a loop invariant. Using Stengle's Positivstellensatz and a transformation to a sum-of-squares problem, we find sufficient conditions on the coefficients. Then, we solve a semidefinite programming feasibility problem to synthesize the loop invariants. If the semidefinite program is unfeasible, we backtrack after increasing the degree of the template. Our approach is semi-complete in the sense that it will always lead us to a feasible solution if one exists and numerical errors are small. Experimental results show the efficiency of our approach.Comment: accompanies an ATVA 2017 submissio

Sharper and Simpler Nonlinear Interpolants for Program Verification

Interpolation of jointly infeasible predicates plays important roles in various program verification techniques such as invariant synthesis and CEGAR. Intrigued by the recent result by Dai et al.\ that combines real algebraic geometry and SDP optimization in synthesis of polynomial interpolants, the current paper contributes its enhancement that yields sharper and simpler interpolants. The enhancement is made possible by: theoretical observations in real algebraic geometry; and our continued fraction-based algorithm that rounds off (potentially erroneous) numerical solutions of SDP solvers. Experiment results support our tool's effectiveness; we also demonstrate the benefit of sharp and simple interpolants in program verification examples

Transcriptome bioinformatic analysis identifies potential therapeutic mechanism of pentylenetetrazole in down syndrome

<p>Abstract</p> <p>Background</p> <p>Pentylenetetrazole (PTZ) has recently been found to ameliorate cognitive impairment in rodent models of Down syndrome (DS). The mechanism underlying PTZ's therapeutic effect in DS is however not clear. Microarray profiling has previously reported differential expression, both up- and down-regulation, of genes in DS. Given this, transcriptomic data related to PTZ treatment, if available, could be used to understand the drug's therapeutic mechanism in DS. No such mammalian data however exists. Nevertheless, a <it>Drosophila </it>model inspired by PTZ induced kindling plasticity in rodents has recently been described. Microarray profiling has shown PTZ's downregulatory effect on gene expression in the fly heads.</p> <p>Methods</p> <p>In a comparative transcriptomics approach, I have analyzed the available microarray data in order to identify potential therapeutic mechanism of PTZ in DS. In the analysis, summary data of up- and down-regulated genes reported in human DS studies and of down-regulated genes reported in the <it>Drosophila </it>model has been used.</p> <p>Results</p> <p>I find that transcriptomic correlate of chronic PTZ in <it>Drosophila </it>counteracts that of DS. Genes downregulated by PTZ significantly over-represent genes upregulated in DS and under-represent genes downregulated in DS. Further, the genes which are common in the downregulated and upregulated DS set show enrichment for MAP kinase pathway.</p> <p>Conclusion</p> <p>My analysis suggests that downregulation of MAP kinase pathway may mediate therapeutic effect of PTZ in DS. Existing evidence implicating MAP kinase pathway in DS supports this observation.</p

On the Generation of Positivstellensatz Witnesses in Degenerate Cases

One can reduce the problem of proving that a polynomial is nonnegative, or more generally of proving that a system of polynomial inequalities has no solutions, to finding polynomials that are sums of squares of polynomials and satisfy some linear equality (Positivstellensatz). This produces a witness for the desired property, from which it is reasonably easy to obtain a formal proof of the property suitable for a proof assistant such as Coq. The problem of finding a witness reduces to a feasibility problem in semidefinite programming, for which there exist numerical solvers. Unfortunately, this problem is in general not strictly feasible, meaning the solution can be a convex set with empty interior, in which case the numerical optimization method fails. Previously published methods thus assumed strict feasibility; we propose a workaround for this difficulty. We implemented our method and illustrate its use with examples, including extractions of proofs to Coq.Comment: To appear in ITP 201

A convex polynomial that is not sos-convex

A multivariate polynomial $p(x)=p(x_1,...,x_n)$ is sos-convex if its Hessian $H(x)$ can be factored as $H(x)= M^T(x) M(x)$ with a possibly nonsquare polynomial matrix $M(x)$. It is easy to see that sos-convexity is a sufficient condition for convexity of $p(x)$. Moreover, the problem of deciding sos-convexity of a polynomial can be cast as the feasibility of a semidefinite program, which can be solved efficiently. Motivated by this computational tractability, it has been recently speculated whether sos-convexity is also a necessary condition for convexity of polynomials. In this paper, we give a negative answer to this question by presenting an explicit example of a trivariate homogeneous polynomial of degree eight that is convex but not sos-convex. Interestingly, our example is found with software using sum of squares programming techniques and the duality theory of semidefinite optimization. As a byproduct of our numerical procedure, we obtain a simple method for searching over a restricted family of nonnegative polynomials that are not sums of squares.Comment: 15 page

Fenofibrate Reduces Mortality and Precludes Neurological Deficits in Survivors in Murine Model of Japanese Encephalitis Viral Infection

Background: Japanese encephalitis (JE), the most common form of viral encephalitis occurs periodically in endemic areas leading to high mortality and neurological deficits in survivors. It is caused by a flavivirus, Japanese encephalitis virus (JEV), which is transmitted to humans through mosquitoes. No effective cure exists for reducing mortality and morbidity caused by JEV infection, which is primarily due to excessive inflammatory response. Fenofibrate, a peroxisome proliferator-activated receptor-a (PPARa) agonist is known to resolve inflammation by repressing nuclear factor-kB (NF-kB) and enhancing transcription of anti-oxidant and anti-inflammatory genes. In addition, fenofibrate also up-regulates a class of proteins, cytochrome P4504Fs (Cyp4fs), which are involved in detoxification of the potent pro-inflammatory eicosanoid, leukotriene B4 (LTB4) to 20-hydroxy LTB4. Methodology/Principal Findings: The neuroprotective effect of fenofibrate was examined using in vitro (BV-2 microglial cell line) and in vivo (BALB/c mice) models of JEV infection. Mice were treated with fenofibrate for 2 or 4 days prior to JEV exposure. Pretreatment with fenofibrate for 4 but not 2 days reduced mortality by 80 % and brain LTB4 levels decreased concomitantly with the induction of Cyp4f15 and 4f18, which catalyze detoxification of LTB4 through hydroxylation. Expression of cytokines and chemokine decreased significantly as did microglial activation and replication of the JEV virus. Conclusions/Significance: Fenofibrate confers neuroprotection against Japanese encephalitis, in vivo, in mouse model o