Model order reduction and sensitivity analysis

The electronics industry provides the core technology for numerous industrial innovations. Progress in the area of microelectronics is highlighted by several milestones in chip technology, for example microprocessors and memory chips. The ongoing increase in performance and memory density would not have been possible without the extensive use of computer simulation techniques, especially electronic circuit simulation. The basis of the latter is formed by a sound framework of methods from the area of numerical methods. In recent years, the demands on the capabilities of circuit simulation have become even more stringent. Circuit simulators have become the core of all simulations within the electronics industry. Crosstalk effects in interconnect structures are modeled by large extracted RLC networks. Also, substrate effects that start playing a crucial role in determining the performance are modeled by extracting, again, large resistive or RC networks. New algorithms are needed to cope with such situations that are extremely crucial for designers. The complexity caused by these parasitic extractions must be reduced to facilitate the simulation of the circuit while preserving accuracy. Fortunately, highly accurate parasitic extraction is not necessary for all parts of the design. Each layout contains critical blocks or paths whose timing and performance is crucial for the overall functionality of the chip. High precision interconnect modeling must be used for these circuit parts to verify the functionality of the design. On the other hand, there is interconnect outside of critical paths which adds to the complexity but whose exact model is not necessary and can be simplified. For the critical paths a so-called sensitivity analysis can bring a major achievement in speed-up, by automatically determining the critical parasitic elements that provide the most dominant influence. Another important aspect is the fact that there is an increasing deviation between design and manufacturing. Due to the ever decreasing feature sizes in modern chips, deviations from the intended dimensions are becoming more probable. Designers need to cope with this, and design the circuits in such a way that a deviation from intended dimensions does not alter the functionality of the circuit. In order to investigate this properly, one needs to assume that all components can possibly be slightly different after manufacturing.The effects this has on the performance of the circuit can be studied by introducing many thousands or even millions of parameters, describing the deviations, and performing a sensitivity analysis of the circuit w.r.t. parameter changes. The aforementioned problems form the inspiration for the study in this thesis. Sensitivity analysis is crucial for the correctness of virtual design environments based on electronic circuit simulators, and gives designers insight in how to alter the designs in order to guarantee more robustness with respect to variability in the design. The problem is that a thorough sensitivity analysis requires derivatives of the solution with respect to a large amount of parameters. This is not feasible using classical methods, being far too time-consuming for modern circuits. Recently proposed methods using the adjoint problem to calculate sensitivities are far more efficient, and these form the basis for our methodology. Our work has concentrated on making such methods even more efficient, by mixing them with concepts from the area of model order reduction. This leads to very efficient, robust and accurate methods for sensitivity analysis, even if the underlying circuit is large and the number of parameters is excessive

Spin diffusion in perturbed isotropic Heisenberg spin chain

The isotropic Heisenberg chain represents a particular case of an integrable many-body system exhibiting superdiffusive spin transport at finite temperatures. Here, we show that this model has distinct properties also at finite magnetization $m\ne0$, even upon introducing the SU(2) invariant perturbations. Specifically, we observe nonmonotonic dependence of the diffusion constant ${\cal D}_0(\Delta)$ on the spin anisotropy $\Delta$, with a pronounced maximum at $\Delta =1$. The latter dependence remains true also in the zero magnetization sector, with superdiffusion at $\Delta=1$ that is remarkably stable against isotropic perturbation (at least in finite-size systems), consistent with recent experiments with cold atoms.Comment: 5+5 pages, 4+5 figure

Adjoint transient sensitivity analysis in circuit simulation

Sensitivity analysis is an important tool that can be used to assess and improve the design and accuracy of a model describing an electronic circuit. Given a model description in the form of a set of differential-algebraic equations it is possible to observe how a circuit's output reacts to varying input parameters, which are introduced at the requirements stage of design. In this paper we consider the adjoint method more closely. This method is efficient when the number of parameters is large.We extend the transient sensitivity work of Petzold et al., in particular we take into account the parameter dependency of the dynamic term.We also compare the complexity of the direct and adjoint sensitivity and derive some error estimates. Finally we sketch out how Model Order Reduction techniques could be used to improve the efficiency of adjoint sensitivity analysis

From thermal rectifiers to thermoelectric devices

We discuss thermal rectification and thermoelectric energy conversion from the perspective of nonequilibrium statistical mechanics and dynamical systems theory. After preliminary considerations on the dynamical foundations of the phenomenological Fourier law in classical and quantum mechanics, we illustrate ways to control the phononic heat flow and design thermal diodes. Finally, we consider the coupled transport of heat and charge and discuss several general mechanisms for optimizing the figure of merit of thermoelectric efficiency.Comment: 42 pages, 22 figures, review paper, to appear in the Springer Lecture Notes in Physics volume "Thermal transport in low dimensions: from statistical physics to nanoscale heat transfer" (S. Lepri ed.

Quasi-local conserved charges and spin transport in spin-1 integrable chains

We consider the integrable one-dimensional spin-1 chain defined by the Zamolodchikov-Fateev (ZF) Hamiltonian. The latter is parametrized, analogously to the XXZ spin-1/2 model, by a continuous anisotropy parameter and at the isotropic point coincides with the well-known spin-1 Babujian-Takhtajan Hamiltonian. Following a procedure recently developed for the XXZ model, we explicitly construct a continuous family of quasi-local conserved operators for the periodic spin-1 ZF chain. Our construction is valid for a dense set of commensurate values of the anisotropy parameter in the gapless regime where the isotropic point is excluded. Using the Mazur inequality, we show that, as for the XXZ model, these quasi-local charges are enough to prove that the high-temperature spin Drude weight is non-vanishing in the thermodynamic limit, thus establishing ballistic spin transport at high temperature

Influence of Prenatal Arsenic Exposure and Newborn Sex on Global Methylation of Cord Blood DNA

Background An emerging body of evidence indicates that early-life arsenic (As) exposure may influence the trajectory of health outcomes later in life. However, the mechanisms underlying these observations are unknown. Objective The objective of this study was to investigate the influence of prenatal As exposure on global methylation of cord blood DNA in a study of mother/newborn pairs in Matlab, Bangladesh. Design Maternal and cord blood DNA were available from a convenience sample of 101 mother/newborn pairs. Measures of As exposure included maternal urinary As (uAs), maternal blood As (mbAs) and cord blood As (cbAs). Several measures of global DNA methylation were assessed, including the [3H]-methyl-incorporation assay and three Pyrosequencing assays: Alu, LINE-1 and LUMA. Results In the total sample, increasing quartiles of maternal uAs were associated with an increase in covariate-adjusted means of newborn global DNA methylation as measured by the [3H]-methyl-incorporation assay (quartile 1 (Q1) and Q2 vs. Q4; p = 0.06 and 0.04, respectively). Sex-specific linear regression analyses, while not reaching significance level of 0.05, indicated that the associations between As exposures and Alu, LINE-1 and LUMA were positive among male newborns (N = 58) but negative among female newborns (N = 43); tests for sex differences were borderline significant for the association of cbAs and mbAs with Alu (p = 0.05 and 0.09, respectively) and for the association between maternal uAs and LINE-1 (p = 0.07). Sex-specific correlations between maternal urinary creatinine and newborn methyl-incorporation, Alu and LINE-1 were also evident (p\u3c0.05). Conclusions These results suggest that prenatal As exposure is associated with global DNA methylation in cord blood DNA, possibly in a sex-specific manner. Arsenic-induced epigenetic modifications in utero may potentially influence disease outcomes later in life. Additional studies are needed to confirm these findings and to examine the persistence of DNA methylation marks over time

Inflammatory Gene Regulatory Networks in Amnion Cells Following Cytokine Stimulation: Translational Systems Approach to Modeling Human Parturition

A majority of the studies examining the molecular regulation of human labor have been conducted using single gene approaches. While the technology to produce multi-dimensional datasets is readily available, the means for facile analysis of such data are limited. The objective of this study was to develop a systems approach to infer regulatory mechanisms governing global gene expression in cytokine-challenged cells in vitro, and to apply these methods to predict gene regulatory networks (GRNs) in intrauterine tissues during term parturition. To this end, microarray analysis was applied to human amnion mesenchymal cells (AMCs) stimulated with interleukin-1β, and differentially expressed transcripts were subjected to hierarchical clustering, temporal expression profiling, and motif enrichment analysis, from which a GRN was constructed. These methods were then applied to fetal membrane specimens collected in the absence or presence of spontaneous term labor. Analysis of cytokine-responsive genes in AMCs revealed a sterile immune response signature, with promoters enriched in response elements for several inflammation-associated transcription factors. In comparison to the fetal membrane dataset, there were 34 genes commonly upregulated, many of which were part of an acute inflammation gene expression signature. Binding motifs for nuclear factor-κB were prominent in the gene interaction and regulatory networks for both datasets; however, we found little evidence to support the utilization of pathogen-associated molecular pattern (PAMP) signaling. The tissue specimens were also enriched for transcripts governed by hypoxia-inducible factor. The approach presented here provides an uncomplicated means to infer global relationships among gene clusters involved in cellular responses to labor-associated signals

MicroMotility: State of the art, recent accomplishments and perspectives on the mathematical modeling of bio-motility at microscopic scales

Mathematical modeling and quantitative study of biological motility (in particular, of motility at microscopic scales) is producing new biophysical insight and is offering opportunities for new discoveries at the level of both fundamental science and technology. These range from the explanation of how complex behavior at the level of a single organism emerges from body architecture, to the understanding of collective phenomena in groups of organisms and tissues, and of how these forms of swarm intelligence can be controlled and harnessed in engineering applications, to the elucidation of processes of fundamental biological relevance at the cellular and sub-cellular level. In this paper, some of the most exciting new developments in the fields of locomotion of unicellular organisms, of soft adhesive locomotion across scales, of the study of pore translocation properties of knotted DNA, of the development of synthetic active solid sheets, of the mechanics of the unjamming transition in dense cell collectives, of the mechanics of cell sheet folding in volvocalean algae, and of the self-propulsion of topological defects in active matter are discussed. For each of these topics, we provide a brief state of the art, an example of recent achievements, and some directions for future research

Model order reduction and sensitivity analysis

The electronics industry provides the core technology for numerous industrial innovations. Progress in the area of microelectronics is highlighted by several milestones in chip technology, for example microprocessors and memory chips. The ongoing increase in performance and memory density would not have been possible without the extensive use of computer simulation techniques, especially electronic circuit simulation. The basis of the latter is formed by a sound framework of methods from the area of numerical methods. In recent years, the demands on the capabilities of circuit simulation have become even more stringent. Circuit simulators have become the core of all simulations within the electronics industry. Crosstalk effects in interconnect structures are modeled by large extracted RLC networks. Also, substrate effects that start playing a crucial role in determining the performance are modeled by extracting, again, large resistive or RC networks. New algorithms are needed to cope with such situations that are extremely crucial for designers. The complexity caused by these parasitic extractions must be reduced to facilitate the simulation of the circuit while preserving accuracy. Fortunately, highly accurate parasitic extraction is not necessary for all parts of the design. Each layout contains critical blocks or paths whose timing and performance is crucial for the overall functionality of the chip. High precision interconnect modeling must be used for these circuit parts to verify the functionality of the design. On the other hand, there is interconnect outside of critical paths which adds to the complexity but whose exact model is not necessary and can be simplified. For the critical paths a so-called sensitivity analysis can bring a major achievement in speed-up, by automatically determining the critical parasitic elements that provide the most dominant influence. Another important aspect is the fact that there is an increasing deviation between design and manufacturing. Due to the ever decreasing feature sizes in modern chips, deviations from the intended dimensions are becoming more probable. Designers need to cope with this, and design the circuits in such a way that a deviation from intended dimensions does not alter the functionality of the circuit. In order to investigate this properly, one needs to assume that all components can possibly be slightly different after manufacturing.The effects this has on the performance of the circuit can be studied by introducing many thousands or even millions of parameters, describing the deviations, and performing a sensitivity analysis of the circuit w.r.t. parameter changes. The aforementioned problems form the inspiration for the study in this thesis. Sensitivity analysis is crucial for the correctness of virtual design environments based on electronic circuit simulators, and gives designers insight in how to alter the designs in order to guarantee more robustness with respect to variability in the design. The problem is that a thorough sensitivity analysis requires derivatives of the solution with respect to a large amount of parameters. This is not feasible using classical methods, being far too time-consuming for modern circuits. Recently proposed methods using the adjoint problem to calculate sensitivities are far more efficient, and these form the basis for our methodology. Our work has concentrated on making such methods even more efficient, by mixing them with concepts from the area of model order reduction. This leads to very efficient, robust and accurate methods for sensitivity analysis, even if the underlying circuit is large and the number of parameters is excessive