2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software, 2006
Abstract-As process technology continues to scale into the nanoscale regime and overall system co... more Abstract-As process technology continues to scale into the nanoscale regime and overall system complexity increases, the reduced order modeling of on-chip interconnect plays a crucial role in characterizing VLSI system performance. In this paper, we develop a dynamic ...
2007 IEEE Northeast Workshop on Circuits and Systems, 2007
In this paper, we developed an accurate and provably passive second order method for the model or... more In this paper, we developed an accurate and provably passive second order method for the model order reduction of passive circuit models in high performance integrated circuits. The method dynamically selects interpolation points from the system's spectral zeros and provides an automated means to simultaneously guarantee stability and passivity while generating low order models that are accurate across a specified range of frequencies. The results demonstrate that our approach provides more accurate reduced order models than second-order Krylov subspace methods.
2007 Asia and South Pacific Design Automation Conference, 2007
As process technology continues to scale into the nanoscale regime, interconnect plays an ever in... more As process technology continues to scale into the nanoscale regime, interconnect plays an ever increasing role in determining VLSI system performance. As the complexity of these systems increases, reduced order modeling becomes critical. In this paper, we develop a new method for the model order reduction of interconnect using frequency restrictive selection of interpolation points based on the spectral-zeros of the RLC interconnect model's transfer function. The methodology uses the imaginary part of spectral zeros for frequency selective projection and provides stable as well as passive reduced order models for interconnect in VLSI systems. For large order interconnect models with realistic RLC parameters, the results indicate that our method provides more accurate approximations than techniques based on balanced truncation and moment matching with excellent agreement with the original system's transfer function.
2007 Asia and South Pacific Design Automation Conference, 2007
In the paper, we develop a systematic methodology for modeling sampled interconnect frequency res... more In the paper, we develop a systematic methodology for modeling sampled interconnect frequency response data based on spline interpolation. Through piecewise polynomial interpolation, we are able to avoid the numerical problems associated with global polynomial fitting and generate higher order systems to model simulated or measured wideband frequency response data. We reduce the complexity of the generated systems using a data point pruning algorithm and by applying model order reduction based on balanced truncation. The methodology provides substantially greater accuracy than global polynomial approximation while only having O(n) growth in model complexity.
2007 IEEE International Symposium on Circuits and Systems, 2007
AbstractAs process technology continues to scale into the nanoscale regime and overall system co... more AbstractAs process technology continues to scale into the nanoscale regime and overall system complexity increases, the reduced order modeling of on-chip interconnect plays a crucial role in determining VLSI system performance. In this paper, we develop an adaptive wavelet ...
8th International Symposium on Quality Electronic Design (ISQED'07), 2007
Model order reduction plays a key role in determining VLSI system performance and the optimizatio... more Model order reduction plays a key role in determining VLSI system performance and the optimization of interconnects. In this paper, we develop an accurate and provably passive method for model order reduction using adaptive wavelet-based frequency selective projection. The waveletbased approach provides an automated means to generate low order models that are accurate in a particular range of frequencies. The results indicate that our approach provides more accurate reduced order models than the spectral zero method with uniform interpolation points and the zero-shift and multi-shift Block Arnoldi-based techniques.
As process technology continues to scale into the nanoscale regime and the overall system complex... more As process technology continues to scale into the nanoscale regime and the overall system complexity increases, the reduced order modeling of on-chip interconnect plays a crucial role in determining VLSI system performance. In this paper, we develop an adaptive wavelet interpolation method based on Krylov subspace techniques to generate reduced order interconnect models that are accurate across a wide-range of frequencies. We dynamically select interpolation points by applying an inexpensive Haar wavelet and performing irregular sampling in the frequency domain. The results indicate that our method provides greater accuracy than multi-shift Krylov subspace methods with uniform interpolation points.
In this paper, we present a new modeling technique for plasmon-based metallic nanoparticles under... more In this paper, we present a new modeling technique for plasmon-based metallic nanoparticles under the influence of an electromagnetic field. The model approximates the coefficients of the admittance rational function. The proposed model utilizes spherical wave functions to describe the field and it provides an equivalent ladder-form RLC realization. Simulation results show that our model matches very closely with the exact solution. Our newly developed model can be used as a basic building block to develop an equivalent circuit model for metallic nanoparticle-based plasmonic waveguides.
IEEE Transactions on Microwave Theory and Techniques, 2011
Recent research has demonstrated the use of plasmonic nanoparticles (e.g., a silver or a gold nan... more Recent research has demonstrated the use of plasmonic nanoparticles (e.g., a silver or a gold nanosphere) as circuit elements. In these metallic nanoparticles, an electromagnetic wave at optical frequencies excites conduction electrons resulting in a plasmon resonance. The derived values of circuit components are based on the observation that the small size of the particle compared to the wavelength leads to lumped-impedance representations under the quasi-static approximation. In this paper, we show that circuit representations based on quasi-static approximations can often result in large errors for typical nanosphere sizes. To remedy this issue, we present a new approach based on time-varying fields, which uses vector wave functions to explicitly derive accurate resonance frequency and impedance expressions for these metallic nanospheres at and around the plasmon resonance. In particular, the proposed approach accurately predicts the dependence of the resonance frequency on the size of the nanoparticle and yields more accurate expressions for the equivalent and lumped elements compared to the quasi-static model. The new impedance approach is still compatible with the process of cascading nanoparticles in series and parallel combinations to synthesize more complex nanocircuits. A comparison with Mie and full-wave finite-element simulation results demonstrates that our model provides accurate closed-form expressions, thereby extending the range of the impedance representation to larger radii nanoparticles.
Analog Integrated Circuits and Signal Processing, 2007
The efficient modeling of integrated passive components and interconnects is vital for the realiz... more The efficient modeling of integrated passive components and interconnects is vital for the realization of high performance mixed-signal systems. In this paper, we develop a dynamic multi-point rational interpolation method based on Krylov subspace techniques to generate reduced order models for passive components and interconnects that are accurate across a wide-range of frequencies. We dynamically select interpolation points by applying a cubic splinebased algorithm to detect complex regions in the system's frequency response. The results indicate that our method provides greater accuracy than techniques that apply uniform interpolation points.
In this work, we investigate the existence, uniqueness, and stability of fractional differential ... more In this work, we investigate the existence, uniqueness, and stability of fractional differential equation with multi-point integral boundary conditions involving the Caputo fractional derivative. By utilizing the Laplace transform technique, the existence of solution is accomplished. By applying the Bielecki-norm and the classical fixed point theorem, the Ulam stability results of the studied system are presented. An illustrative example is provided at the last part to validate all our obtained theoretical results.
In this paper, we investigate the existence, uniqueness and stability of coupled impulsive fracti... more In this paper, we investigate the existence, uniqueness and stability of coupled impulsive fractional integro-differential equations with Riemann-Liouville derivatives. To prove the existence and uniqueness results for afore mentioned system, we use the techniques of Kransnoselskii's type fixed point theorem. Furthermore, different kinds of Ulam stabilities are discussed along with examples, to demonstrate the validity of main results.
Mathematical Methods in the Applied Sciences, 2020
Passive brain-computer interfaces consider brain activity as an additional source of information,... more Passive brain-computer interfaces consider brain activity as an additional source of information, to augment and adapt the interface instead of controlling it. We have developed a software system that allows for real time brain signal analysis and machine learning classification of affective and workload states measured with functional near-infrared spectroscopy (fNIRS) called the online fNIRS analysis and classification (OFAC). Our system reproduces successful offline procedures, adapting them for real-time input to a user interface. Our first evaluation compares a previous offline analysis with our online analysis. While results show an accuracy decrease, they are outweighed by the new ability of interface adaptation. The second study demonstrates OFAC's online features through real-time classification of two tasks, and interface adaptation according to the predicted task. Accuracy averaged over 85%. We have created the first working real time passive BCI using fNIRS, opening the door to build adaptive user interfaces.
Herein, we predict that a 1D chain of Ti@C 32 À C 2 À Ti@C 32 (TEMF) will act as a spin switch in... more Herein, we predict that a 1D chain of Ti@C 32 À C 2 À Ti@C 32 (TEMF) will act as a spin switch in the presence of an electric field. The spin resolved density of states analyses reveal that, surprisingly, both the low-and high-spin states of TEMF are half-metal; however, the metallic density of states comes from the opposite spin channels of the two spin states. More remarkably, it is found that the electric field driven spin crossover between the low and high state in TEMF is achievable at field strength 1:04 V=nm, which eventually leads to the realization of the first ever electrically operated spin switch device.
2006 IEEE Dallas/CAS Workshop on Design, Applications, Integration and Software, 2006
Abstract-As process technology continues to scale into the nanoscale regime and overall system co... more Abstract-As process technology continues to scale into the nanoscale regime and overall system complexity increases, the reduced order modeling of on-chip interconnect plays a crucial role in characterizing VLSI system performance. In this paper, we develop a dynamic ...
2007 IEEE Northeast Workshop on Circuits and Systems, 2007
In this paper, we developed an accurate and provably passive second order method for the model or... more In this paper, we developed an accurate and provably passive second order method for the model order reduction of passive circuit models in high performance integrated circuits. The method dynamically selects interpolation points from the system's spectral zeros and provides an automated means to simultaneously guarantee stability and passivity while generating low order models that are accurate across a specified range of frequencies. The results demonstrate that our approach provides more accurate reduced order models than second-order Krylov subspace methods.
2007 Asia and South Pacific Design Automation Conference, 2007
As process technology continues to scale into the nanoscale regime, interconnect plays an ever in... more As process technology continues to scale into the nanoscale regime, interconnect plays an ever increasing role in determining VLSI system performance. As the complexity of these systems increases, reduced order modeling becomes critical. In this paper, we develop a new method for the model order reduction of interconnect using frequency restrictive selection of interpolation points based on the spectral-zeros of the RLC interconnect model's transfer function. The methodology uses the imaginary part of spectral zeros for frequency selective projection and provides stable as well as passive reduced order models for interconnect in VLSI systems. For large order interconnect models with realistic RLC parameters, the results indicate that our method provides more accurate approximations than techniques based on balanced truncation and moment matching with excellent agreement with the original system's transfer function.
2007 Asia and South Pacific Design Automation Conference, 2007
In the paper, we develop a systematic methodology for modeling sampled interconnect frequency res... more In the paper, we develop a systematic methodology for modeling sampled interconnect frequency response data based on spline interpolation. Through piecewise polynomial interpolation, we are able to avoid the numerical problems associated with global polynomial fitting and generate higher order systems to model simulated or measured wideband frequency response data. We reduce the complexity of the generated systems using a data point pruning algorithm and by applying model order reduction based on balanced truncation. The methodology provides substantially greater accuracy than global polynomial approximation while only having O(n) growth in model complexity.
2007 IEEE International Symposium on Circuits and Systems, 2007
AbstractAs process technology continues to scale into the nanoscale regime and overall system co... more AbstractAs process technology continues to scale into the nanoscale regime and overall system complexity increases, the reduced order modeling of on-chip interconnect plays a crucial role in determining VLSI system performance. In this paper, we develop an adaptive wavelet ...
8th International Symposium on Quality Electronic Design (ISQED'07), 2007
Model order reduction plays a key role in determining VLSI system performance and the optimizatio... more Model order reduction plays a key role in determining VLSI system performance and the optimization of interconnects. In this paper, we develop an accurate and provably passive method for model order reduction using adaptive wavelet-based frequency selective projection. The waveletbased approach provides an automated means to generate low order models that are accurate in a particular range of frequencies. The results indicate that our approach provides more accurate reduced order models than the spectral zero method with uniform interpolation points and the zero-shift and multi-shift Block Arnoldi-based techniques.
As process technology continues to scale into the nanoscale regime and the overall system complex... more As process technology continues to scale into the nanoscale regime and the overall system complexity increases, the reduced order modeling of on-chip interconnect plays a crucial role in determining VLSI system performance. In this paper, we develop an adaptive wavelet interpolation method based on Krylov subspace techniques to generate reduced order interconnect models that are accurate across a wide-range of frequencies. We dynamically select interpolation points by applying an inexpensive Haar wavelet and performing irregular sampling in the frequency domain. The results indicate that our method provides greater accuracy than multi-shift Krylov subspace methods with uniform interpolation points.
In this paper, we present a new modeling technique for plasmon-based metallic nanoparticles under... more In this paper, we present a new modeling technique for plasmon-based metallic nanoparticles under the influence of an electromagnetic field. The model approximates the coefficients of the admittance rational function. The proposed model utilizes spherical wave functions to describe the field and it provides an equivalent ladder-form RLC realization. Simulation results show that our model matches very closely with the exact solution. Our newly developed model can be used as a basic building block to develop an equivalent circuit model for metallic nanoparticle-based plasmonic waveguides.
IEEE Transactions on Microwave Theory and Techniques, 2011
Recent research has demonstrated the use of plasmonic nanoparticles (e.g., a silver or a gold nan... more Recent research has demonstrated the use of plasmonic nanoparticles (e.g., a silver or a gold nanosphere) as circuit elements. In these metallic nanoparticles, an electromagnetic wave at optical frequencies excites conduction electrons resulting in a plasmon resonance. The derived values of circuit components are based on the observation that the small size of the particle compared to the wavelength leads to lumped-impedance representations under the quasi-static approximation. In this paper, we show that circuit representations based on quasi-static approximations can often result in large errors for typical nanosphere sizes. To remedy this issue, we present a new approach based on time-varying fields, which uses vector wave functions to explicitly derive accurate resonance frequency and impedance expressions for these metallic nanospheres at and around the plasmon resonance. In particular, the proposed approach accurately predicts the dependence of the resonance frequency on the size of the nanoparticle and yields more accurate expressions for the equivalent and lumped elements compared to the quasi-static model. The new impedance approach is still compatible with the process of cascading nanoparticles in series and parallel combinations to synthesize more complex nanocircuits. A comparison with Mie and full-wave finite-element simulation results demonstrates that our model provides accurate closed-form expressions, thereby extending the range of the impedance representation to larger radii nanoparticles.
Analog Integrated Circuits and Signal Processing, 2007
The efficient modeling of integrated passive components and interconnects is vital for the realiz... more The efficient modeling of integrated passive components and interconnects is vital for the realization of high performance mixed-signal systems. In this paper, we develop a dynamic multi-point rational interpolation method based on Krylov subspace techniques to generate reduced order models for passive components and interconnects that are accurate across a wide-range of frequencies. We dynamically select interpolation points by applying a cubic splinebased algorithm to detect complex regions in the system's frequency response. The results indicate that our method provides greater accuracy than techniques that apply uniform interpolation points.
In this work, we investigate the existence, uniqueness, and stability of fractional differential ... more In this work, we investigate the existence, uniqueness, and stability of fractional differential equation with multi-point integral boundary conditions involving the Caputo fractional derivative. By utilizing the Laplace transform technique, the existence of solution is accomplished. By applying the Bielecki-norm and the classical fixed point theorem, the Ulam stability results of the studied system are presented. An illustrative example is provided at the last part to validate all our obtained theoretical results.
In this paper, we investigate the existence, uniqueness and stability of coupled impulsive fracti... more In this paper, we investigate the existence, uniqueness and stability of coupled impulsive fractional integro-differential equations with Riemann-Liouville derivatives. To prove the existence and uniqueness results for afore mentioned system, we use the techniques of Kransnoselskii's type fixed point theorem. Furthermore, different kinds of Ulam stabilities are discussed along with examples, to demonstrate the validity of main results.
Mathematical Methods in the Applied Sciences, 2020
Passive brain-computer interfaces consider brain activity as an additional source of information,... more Passive brain-computer interfaces consider brain activity as an additional source of information, to augment and adapt the interface instead of controlling it. We have developed a software system that allows for real time brain signal analysis and machine learning classification of affective and workload states measured with functional near-infrared spectroscopy (fNIRS) called the online fNIRS analysis and classification (OFAC). Our system reproduces successful offline procedures, adapting them for real-time input to a user interface. Our first evaluation compares a previous offline analysis with our online analysis. While results show an accuracy decrease, they are outweighed by the new ability of interface adaptation. The second study demonstrates OFAC's online features through real-time classification of two tasks, and interface adaptation according to the predicted task. Accuracy averaged over 85%. We have created the first working real time passive BCI using fNIRS, opening the door to build adaptive user interfaces.
Herein, we predict that a 1D chain of Ti@C 32 À C 2 À Ti@C 32 (TEMF) will act as a spin switch in... more Herein, we predict that a 1D chain of Ti@C 32 À C 2 À Ti@C 32 (TEMF) will act as a spin switch in the presence of an electric field. The spin resolved density of states analyses reveal that, surprisingly, both the low-and high-spin states of TEMF are half-metal; however, the metallic density of states comes from the opposite spin channels of the two spin states. More remarkably, it is found that the electric field driven spin crossover between the low and high state in TEMF is achievable at field strength 1:04 V=nm, which eventually leads to the realization of the first ever electrically operated spin switch device.
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Papers by Mehboob Alam