Researcher: Demir, Alper
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Demir, Alper
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Publication Metadata only Non-Monte Carlo formulations and computational techniques for the stochastic non-linear Schrodinger equation(Academic Press Inc Elsevier Science, 2004) Department of Electrical and Electronics Engineering; Demir, Alper; Faculty Member; Department of Electrical and Electronics Engineering; College of Engineering; 3756Stochastic ordinary and partial differential equations (SOPDEs) in various forms arise and are successfully utilized in the modeling of a variety of physical and engineered systems such as telecommunication systems, electronic circuits, cosmological systems, financial systems, meteorological and climate systems. While the theory of stochastic partial and especially ordinary differential equations is more or less well understood, there has been much less work on practical formulations and computational approaches to solving these equations. In this paper, we concentrate on the stochastic non-linear Schrodinger equation (SNLSE) that arises in the analysis of wave propagation phenomena, mainly motivated by its predominant role as a modeling tool in the design of optically amplified long distance fiber telecommunication systems. We present novel formulations and computational methods for the stochastic characterization of the solution of the SNLSE. Our formulations and techniques are not aimed at computing individual realizations, i.e., sample paths, for the solution of the SNLSE A la Monte Carlo. Instead, starting with the SNLSE, we derive new systems of differential equations and develop associated computational techniques. The numerical solutions of these new equations directly produce the ensemble-averaged stochastic characterization desired for the solution of the SNLSE, in a non-Monte Carlo manner without having to compute many realizations needed for ensemble-averaging. (C) 2004 Elsevier Inc. All rights reserved.Publication Metadata only Understanding fundamental trade-offs in nanomechanical resonant sensors(Amer Inst Physics, 2021) Department of Electrical and Electronics Engineering; Demir, Alper; Faculty Member; Department of Electrical and Electronics Engineering; College of Engineering; 3756Publication Metadata only Nonlinear phase noise in optical-fiber-communication systems(IEEE-Inst Electrical Electronics Engineers Inc, 2007) Department of Electrical and Electronics Engineering; Demir, Alper; Faculty Member; Department of Electrical and Electronics Engineering; College of Engineering; 3756Gordon and Mollenauer, in their famous paper published in 1990, laid out how the interplay between the nonlinear Kerr effect in optical fibers and the amplified spontaneousemission (ASE) noise from the optical-amplifiers results In enhanced levels of noise and degrades the performance of modulation schemes that encode information in, particularly, the phase of the optical carrier. This phenomenon has been termed as nonlinear phase noise in the literature. In this paper, we first present a comparative and critical review of previous techniques that have been proposed for the analysis of nonlinear phase noise by forming a classification framework that reveals some key underlying features. We then present a unifying theory, and a comprehensive methodology and computational techniques for the analysis and characterization of nonlinear phase noise and its impact on system performance by building on and extending previous work that we identify as most favorable and systematic. In our treatment, we consider a multichannel multispan optically amplified dense wavelength-division multiplexed system and develop general techniques for the analysis of the intricate interplay among Kerr nonlinearity, chromatic dispersion, and ASE noise, and for computing the bit-error-ratio performance of differential phase-shift-keying (DPSK) systems. By means of the extensive results we present, we demonstrate and argue that correlated noise behavior plays a most significant role in understanding nonlinear phase noise and its impact on DPSK system performance.Publication Metadata only Noise analysis problems and techniques for RF electronic circuits and optical fiber communication systems(IEEE, 2007) Department of Electrical and Electronics Engineering; Demir, Alper; Faculty Member; Department of Electrical and Electronics Engineering; College of Engineering; 3756Various forms of linearized noise analysis techniques have been extensively used for analyzing the performance of electronic circuits in the presence of undesired disturbances since the early 70's. Practical numerical algorithms based on linearized perturbation formulations have been implemented in public domain and commercial electronic circuit simulators. In this paper, we describe the noise analysis problems in optical fiber communications and discuss their relationships to RF circuit noise analysis. In particular, we recognize that the noise analysis of electronic circuits with time-invariant (time-varying) large signal excitations corresponds to the analysis of noise propagation in optical fibers along with unmodulated (modulated) light carriers. We discuss how linearized perturbation formulations are used for noise analysis in both domains and draw analogies between them by providing a comparative review of the techniques that have been proposed in the literature.Publication Metadata only Numerical analysis of multidomain systems: Coupled nonlinear PDEs and DAEs with noise(IEEE-Inst Electrical Electronics Engineers Inc, 2018) Hanay, M. Selim; Department of Electrical and Electronics Engineering; Demir, Alper; Faculty Member; Department of Electrical and Electronics Engineering; College of Engineering; 3756We present a numerical modeling and simulation paradigm for multidomain, multiphysics systems with components modeled both in a lumped and distributed manner. The lumped components are modeled with a system of differential-algebraic equations (DAEs), whereas the possibly nonlinear distributed components that may belong to different physical domains are modeled using partial differential equations (PDEs) with associated boundary conditions. We address a comprehensive suite of problems for nonlinear coupled DAE-PDE systems including 1) transient simulation; 2) periodic steady-state (PSS) analysis formulated as a mixed boundary value problem that is solved with a hierarchical spectral collocation technique based on a joint Fourier-Chebyshev representation, for both forced and autonomous systems; 3) Floquet theory and analysis for coupled linear periodically time-varying DAE-PDE systems; 4) phase noise analysis for multidomain oscillators; and 5) efficient parameter sweeps for PSS and noise analyses based on first-order and pseudo-arclength continuation schemes. All of these techniques, implemented in a prototype simulator, are applied to a substantial case study: a multidomain feedback oscillator composed of distributed and lumped components in two physical domains, namely, a nano-mechanical beam resonator operating in the nonlinear regime, an electrical delay line, an electronic amplifier and a sensor-actuator for the transduction between the two physical domains.Publication Metadata only Stochastic modeling and optimization for energy management in multicore systems: a video decoding case study(IEEE-Inst Electrical Electronics Engineers Inc, 2008) Yaldız, Soner; Department of Electrical and Electronics Engineering; Department of Electrical and Electronics Engineering; Demir, Alper; Taşıran, Serdar; Faculty Member; Faculty Member; Department of Electrical and Electronics Engineering; College of Engineering; College of Engineering; 3756; N/AThis paper presents a novel stochastic modeling and optimization framework for energy minimization in multicore systems running real-time applications with tolerance to deadline misses. This framework is based on stochastic application models, which capture the variability of and the spatial and temporal correlations among the workloads of concurrent and interdependent tasks that constitute the application. These stochastic models are utilized in novel mathematical formulations to obtain optimal energy management policies. Experimental results on MPEG2 video decoding show that significant energy savings can be achieved, often close to the theoretical upper bound.Publication Metadata only Fully nonlinear oscillator noise analysis: an oscillator with no asymptotic phase(John Wiley & Sons Ltd, 2007) Department of Electrical and Electronics Engineering; Demir, Alper; Faculty Member; Department of Electrical and Electronics Engineering; College of Engineering; 3756Oscillators exist in many systems. Detailed and correct characterization and comprehension of noise in autonomous systems such as oscillators is of utmost importance. Previous approaches to oscillator noise analysis are based on some kind of perturbation analysis, some linear and some nonlinear. However, the derivations of the equations for perturbation analysis are all based on information that is produced by a linearization of the oscillator equations around the periodic steady-state solution, where it is assumed that the oscillator is orbitally stable and it has the so-called asymptotic phase property. In this paper, we first discuss these notions from a qualitative perspective, and demonstrate that the asymptotic phase property is crucial in validating all of the previous approaches. We then present the case of a simple oscillator that is orbitally stable but without asymptotic phase, for which previous approaches fail. We then present a fully nonlinear noise analysis of this oscillator. We derive and compute nonlinear, non-stationary and non-Gaussian stochastic characterizations for both amplitude and phase noise. We arrive at results that are distinctly different when compared with the ones obtained previously for oscillators with asymptotic phase. We compare and verify our analytical results against extensive Monte Carlo simulations. Copyright (C) 2006 John Wiley & Sons, Ltd.Publication Metadata only Spike timing precision of neuronal circuits(Springer, 2018) N/A; N/A; Department of Electrical and Electronics Engineering; Kılınç, Deniz; Demir, Alper; PhD Student; Faculty Member; Department of Electrical and Electronics Engineering; Graduate School of Sciences and Engineering; College of Engineering; N/A; 3756Spike timing is believed to be a key factor in sensory information encoding and computations performed by the neurons and neuronal circuits. However, the considerable noise and variability, arising from the inherently stochastic mechanisms that exist in the neurons and the synapses, degrade spike timing precision. Computational modeling can help decipher the mechanisms utilized by the neuronal circuits in order to regulate timing precision. In this paper, we utilize semi-analytical techniques, which were adapted from previously developed methods for electronic circuits, for the stochastic characterization of neuronal circuits. These techniques, which are orders of magnitude faster than traditional Monte Carlo type simulations, can be used to directly compute the spike timing jitter variance, power spectral densities, correlation functions, and other stochastic characterizations of neuronal circuit operation. We consider three distinct neuronal circuit motifs: Feedback inhibition, synaptic integration, and synaptic coupling. First, we show that both the spike timing precision and the energy efficiency of a spiking neuron are improved with feedback inhibition. We unveil the underlying mechanism through which this is achieved. Then, we demonstrate that a neuron can improve on the timing precision of its synaptic inputs, coming from multiple sources, via synaptic integration: The phase of the output spikes of the integrator neuron has the same variance as that of the sample average of the phases of its inputs. Finally, we reveal that weak synaptic coupling among neurons, in a fully connected network, enables them to behave like a single neuron with a larger membrane area, resulting in an improvement in the timing precision through cooperation.Publication Metadata only Accurate prediction of random telegraph noise effects in srams and drams(IEEE-Inst Electrical Electronics Engineers Inc, 2013) Aadithya, Karthik V.; Venugopalan, Sriramkumar; Roychowdhury, Jaijeet; Department of Electrical and Electronics Engineering; Demir, Alper; Faculty Member; Department of Electrical and Electronics Engineering; College of Engineering; 3756With aggressive technology scaling and heightened variability, circuits such as SRAMs and DRAMs have become vulnerable to random telegraph noise (RTN). The bias dependence (i.e., non-stationarity), bi-directional coupling, and high inter-device variability of RTN present significant challenges to understanding its circuit-level effects. In this paper, we present two computer-aided design (CAD) tools, SAMURAI and MUSTARD, for accurately estimating the impact of non-stationary RTN on SRAMs and DRAMs. While traditional (stationary) analysis is often overly pessimistic (e. g., it overestimates RTN-induced SRAM failure rates), the predictions made by SAMURAI and MUSTARD are more reliable by virtue of non-stationary analysis.Publication Metadata only Phase equations for quasi-periodic oscillators(Ieee, 2010) Gu, Chenjie; Roychowdhury, Jaijeet; Department of Electrical and Electronics Engineering; Demir, Alper; Faculty Member; Department of Electrical and Electronics Engineering; College of Engineering; 3756Oscillations and rhythmic activity are seen in natural and man-made systems. Dynamics of oscillators can be compactly described by phase domain models. Phase equations for periodic, single-frequency oscillators have been developed and utilized in analyzing oscillation phenomena that arise in electronic systems, circadian clocks, and the nervous system. We consider quasi-periodic oscillators and present a general phase model theory and numerical techniques for the construction of phase equations for multi-frequency oscillators. We demonstrate the utility of these phase equations in analyzing oscillators experiencing perturbations.