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COURSE OBJECTIVES: Intense competition and continually increasing customer expectations continue to force firms to become more efficient and more responsive in order to thrive. This, together with continuing advances in transportation and communication technology, and rapidly evolving internet-based strategy, has motivated the continuous evolution of the(More)
The tool FLOW* performs Taylor model-based flowpipe construction for non-linear (polynomial) hybrid systems. FLOW* combines well-known Tay-lor model arithmetic techniques for guaranteed approximations of the continuous dynamics in each mode with a combination of approaches for handling mode invariants and discrete transitions. FLOW* supports a wide variety(More)
The stochastic cash balance problem is a periodic review inventory problem faced by a firm in which the customer demands might be positive or negative. At the beginning of each time period, the firm may decide to replenish the inventory or return excess stock. Both the ordering cost and the return cost include a fixed component and a variable component. A(More)
—We propose an approach for verifying non-linear hybrid systems using higher-order Taylor models that are a combination of bounded degree polynomials over the initial conditions and time, bloated by an interval. Taylor models are an effective means for computing rigorous bounds on the complex time trajectories of non-linear differential equations. As a(More)
We investigate linear programming relaxations to synthesize Lyapunov functions that establish the stability of a given system over a bounded region. In particular, we attempt to discover functions that are more readily useful inside symbolic verification tools for proving the correctness of control systems. Our approach searches for a Lyapunov function,(More)
PURPOSE Subtraction ictal single photon emission computed tomography (SPECT) co-registered to magnetic resonance imaging (MRI) (SISCOM) is a useful modality to identify epileptogenic focus. Using this technique, several studies have generally considered the area of highest ictal hyperperfusion, as outlined by thresholding the difference images with a(More)
We examine linear programming (LP) based relaxations for synthesizing polynomial Lyapunov functions to prove the stability of polynomial ODEs. Our approach starts from a desired parametric polynomial form of the polynomial Lyapunov function. Subsequently, we encode the positive-definiteness of the function, and the negation of its derivative, over the(More)
This paper studies the effect of parameter variation on the behavior of analog circuits at the transistor (netlist) level. It is well known that variation in key circuit parameters can often adversely impact the correctness and performance of analog circuits during fabrication. An important problem lies in characterizing a <i>safe subset</i> of the(More)
How does the visual system recognize a camouflaged object? Obviously, the brain cannot afford to learn all possible camouflaged scenes or target objects. However, it may learn the general statistical properties of backgrounds of interest, which would enable it to break camouflage by comparing the statistics of a background with a target versus the(More)