Relationship Between Time-constants and 3dB Cutoff of High-Order Damped LTI Systems

This paper deals with linear time-invariant (LTI) systems and examines the link between the 3dB cutoff and time-constants. It shows that the cutoff frequency of a low-pass damped network can be estimated from the reciprocal of a p-norm calculated from the system\u27s time-constants. Furthermore, to achieve good accuracy the p factor must have a fractional value, for example, p=1.7. Two formulas are derived, and their performance evaluated using Monte Carlo simulations which reveal a sub-3% error for most cases

The westward drift of the lithosphere. A tidal ratchet?

Is the westerly rotation of the lithosphere an ephemeral accidental recent phenomenon or is it a stable process of Earth’s geodynamics? The reason why the tidal drag has been questioned as the mechanism determining the lithospheric shift relative to the underlying mantle is the apparent too high viscosity of the asthenosphere. However, plate boundaries asymmetries are a robust indication of the ‘westerly’ decoupling of the entire Earth’s outer lithospheric shell and new studies support lower viscosities in the low-velocity layer (LVZ) atop the asthenosphere. Since the solid Earth tide oscillation is longer in one side relative to the other due to the contemporaneous Moon’s revolution, we demonstrate that a non-linear rheological behavior is expected in the lithosphere mantle interplay. This may provide a sort of ratchet favoring lowering of the LVZ viscosity under shear, allowing decoupling in the LVZ and triggering the westerly motion of the lithosphere relative to the mantle

Computational study of the mechanism of Bcl-2 apoptotic switch

Programmed cell death - apoptosis is one of the most studied biological phenomenon of recent years. Apoptotic regulatory network contains several significant control points, including probably the most important one - Bcl--2 apoptotic switch. There are two proposed hypotheses regarding its internal working - the indirect activation and direct activation models. Since these hypotheses form extreme poles of full continuum of intermediate models, we have constructed more general model with these two models as extreme cases. By studying relationship between model parameters and steady-state response ultrasensitivity we have found optimal interaction pattern which reproduces behavior of Bcl-2 apoptotic switch. Our results show, that stimulus-response ultrasensitivity is negatively related to spontaneous activation of Bcl-2 effectors - subgroup of Bcl-2 proteins. We found that ultrasensitivity requires effector's activation, mediated by another subgroup of Bcl-2 proteins - activators. We have shown that the auto-activation of effectors forms ultrasensitivity enhancing feedback loop, only if mediated by monomers, but not by oligomers. Robustness analysis revealed that interaction pattern proposed by direct activation hypothesis is able to conserve stimulus-response dependence and preserve ultrasensitivity despite large changes of its internal parameters. This ability is strongly reduced as for the intermediate to indirect side of the models. Computer simulation of the more general model presented here suggest, that stimulus-response ultrasensitivity is an emergent property of the direct activation model, that cannot originate within model of indirect activation. Introduction of indirect-model-specific interactions does not provide better explanation of Bcl-2 functioning compared to direct model

Fast Repeater Tree Construction

Repeaters are used during physical design of chips to improve the electrical and timing properties of interconnections. They are added along Steiner trees that connect root gates to sinks, creating repeater trees. Their construction became a crucial part of chip design. We present a new algorithm to solve the repeater tree construction problem. We first present an extensive version of the Repeater Tree Problem. Our problem formulation encapsulates most of the constraints that have been studied so far. We also consider several aspects for the first time, for example, slew dependent required arrival times at repeater tree sinks. The employed technology, the properties of available repeaters and metal wires, the shape of the chip, the temperature, the voltages, and many other factors highly influence the results of repeater tree construction. To take all this into account, we extensively preprocess the environment to extract parameters for our algorithms. We first present an algorithm for Steiner tree creation and prove that our algorithm is able to create timing-efficient as well as cost-efficient trees. Our algorithm is based on a delay model that accurately describes the timing that one can achieve after repeater insertion upfront. Next, we deal with the problem of adding repeaters to a given Steiner tree. The predominantly used algorithms to solve this problem use dynamic programming. However, they have several drawbacks. Firstly, potential repeater positions along the Steiner tree have to be chosen upfront. Secondly, the algorithms strictly follow the given Steiner tree and miss optimization opportunities. Finally, dynamic programming causes high running times. We present our new buffer insertion algorithm, Fast Buffering, that overcomes these limitations. It is able to produce results with similar quality to a dynamic programming approach but a much better running time. In addition, we also present improvements to the dynamic programming approach that allows us to push the quality at the expense of a high running time. We have implemented our algorithms as part of the BonnTools physical design optimization suite developed at the Research Institute for Discrete Mathematics in cooperation with IBM. Our implementation deals with all tedious details of a grown real-world chip optimization environment. We have created extensive experimental results on challenging real-world test cases provided by our cooperation partner. Our algorithm can solve about 5.7 million instances per hour

Small-scale solar magnetic fields

As we resolve ever smaller structures in the solar atmosphere, it has become clear that magnetism is an important component of those small structures. Small-scale magnetism holds the key to many poorly understood facets of solar magnetism on all scales, such as the existence of a local dynamo, chromospheric heating, and flux emergence, to name a few. Here, we review our knowledge of small-scale photospheric fields, with particular emphasis on quiet-sun field, and discuss the implications of several results obtained recently using new instruments, as well as future prospects in this field of research.Comment: 43 pages, 18 figure

Algorithms for Circuit Sizing in VLSI Design

One of the key problems in the physical design of computer chips, also known as integrated circuits, consists of choosing a  physical layout  for the logic gates and memory circuits (registers) on the chip. The layouts have a high influence on the power consumption and area of the chip and the delay of signal paths.  A discrete set of predefined layouts  for each logic function and register type with different physical properties is given by a library. One of the most influential characteristics of a circuit defined by the layout is its size. In this thesis we present new algorithms for the problem of choosing sizes for the circuits and its continuous relaxation,  and  evaluate these in theory and practice. A popular approach is based on Lagrangian relaxation and projected subgradient methods. We show that seemingly heuristic modifications that have been proposed for this approach can be theoretically justified by applying the well-known multiplicative weights algorithm. Subsequently, we propose a new model for the sizing problem as a min-max resource sharing problem. In our context, power consumption and signal delays are represented by resources that are distributed to customers. Under certain assumptions we obtain a polynomial time approximation for the continuous relaxation of the sizing problem that improves over the Lagrangian relaxation based approach. The new resource sharing algorithm has been implemented as part of the BonnTools software package which is developed at the Research Institute for Discrete Mathematics at the University of Bonn in cooperation with IBM. Our experiments on the ISPD 2013 benchmarks and state-of-the-art microprocessor designs provided by IBM illustrate that the new algorithm exhibits more stable convergence behavior compared to a Lagrangian relaxation based algorithm. Additionally, better timing and reduced power consumption was achieved on almost all instances. A subproblem of the new algorithm consists of finding sizes minimizing a weighted sum of power consumption and signal delays. We describe a method that approximates the continuous relaxation of this problem in polynomial time under certain assumptions. For the discrete problem we provide a fully polynomial approximation scheme under certain assumptions on the topology of the chip. Finally, we present a new algorithm for timing-driven optimization of registers. Their sizes and locations on a chip are usually determined during the clock network design phase, and remain mostly unchanged afterwards although the timing criticalities on which they were based can change. Our algorithm permutes register positions and sizes within so-called  clusters  without impairing the clock network such that it can be applied late in a design flow. Under mild assumptions, our algorithm finds an optimal solution which maximizes the worst cluster slack. It is implemented as part of the BonnTools and improves timing of registers on state-of-the-art microprocessor designs by up to 7.8% of design cycle time. </div

Dynamics of the Solar Chromosphere. II. Ca II H2V and K2V Grains versus Internetwork Fields

We use the Advanced Stokes Polarimeter at the NSO/Sacramento Peak Vacuum Tower Telescope to search for spatio- temporal correlations between enhanced magnetic fields in the quiet solar internetwork photosphere and the occurrence of Ca II H2v grains in the overlying chromosphere.We address the question of whether the shocks that produce the latter are caused by magnetism-related processes,or whether they are of purely hydrodynamic nature. The observations presented here are the first in which sensitive Stokes polarimetry is combined synchronously with high- resolution Ca II H spectrometry. We pay particular attention to the nature and significance of weak polarization signals from the internetwork domain,obtaining a robust estimate of our magnetographic noise level at an apparent flux density of only 3 Mxcm^-2 . For the quiet Sun internetwork area analyzed here,we find no direct correlation between the presence of magnetic features with apparent flux density above this limit and the occurrence of H2v brightenings.This result contradicts the one-to-one correspondence claimed by Sivaraman &Livingston (1982).We also find no correspondence between H2v grains and the horizontal-?eld internetwork features discovered by Lites et al.(1996)

Advanced modelling and design considerations for interconnects in ultra- low power digital system

PhD ThesisAs Very Large Scale Integration (VLSI) is progressing in very Deep submicron (DSM) regime without decreasing chip area, the importance of global interconnects increases but at the cost of performance and power consumption for advanced System-on- Chip (SoC)s. However, the growing complexity of interconnects behaviour presents a challenge for their adequate modelling, whereby conventional circuit theoretic approaches cannot provide sufficient accuracy. During the last decades, fractional differential calculus has been successfully applied to modelling certain classes of dynamical systems while keeping complexity of the models under acceptable bounds. For example, fractional calculus can help capturing inherent physical effects in electrical networks in a compact form, without following conventional assumptions about linearization of non-linear interconnect components. This thesis tackles the problem of interconnect modelling in its generality to simulate a wide range of interconnection configurations, its capacity to emulate irregular circuit elements and its simplicity in the form of responsible approximation. This includes modelling and analysing interconnections considering their irregular components to add more flexibility and freedom for design. The aim is to achieve the simplest adaptable model with the highest possible accuracy. Thus, the proposed model can be used for fast computer simulation of interconnection behaviour. In addition, this thesis proposes a low power circuit for driving a global interconnect at voltages close to the noise level. As a result, the proposed circuit demonstrates a promising solution to address the energy and performance issues related to scaling effects on interconnects along with soft errors that can be caused by neutron particles. The major contributions of this thesis are twofold. Firstly, in order to address Ultra-Low Power (ULP) design limitations, a novel driver scheme has been configured. This scheme uses a bootstrap circuitry which boosts the driver’s ability to drive a long interconnect with an important feedback feature in it. Hence, this approach achieves two objectives: improving performance and mitigating power consumption. Those achievements are essential in designing ULP circuits along with occupying a smaller footprint and being immune to noise, observed in this design as well. These have been verified by comparing the proposed design to the previous and traditional circuits using a simulation tool. Additionally, the boosting based approach has been shown beneficial in mitigating the effects of single event upset (SEU)s, which are known to affect DSM circuits working under low voltages. Secondly, the CMOS circuit driving a distributed RLC load has been brought in its analysis into the fractional order domain. This model will make the on-chip interconnect structure easy to adjust by including the effect of fractional orders on the interconnect timing, which has not been considered before. A second-order model for the transfer functions of the proposed general structure is derived, keeping the complexity associated with second-order models for this class of circuits at a minimum. The approach here attaches an important trait of robustness to the circuit design procedure; namely, by simply adjusting the fractional order we can avoid modifying the circuit components. This can also be used to optimise the estimation of the system’s delay for a broad range of frequencies, particularly at the beginning of the design flow, when computational speed is of paramount importance.Iraqi Ministry of Higher Education and Scientific Researc