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19
Fast Algorithms for Manipulating Formal Power Series
"... The classical algorithms require order n ~ operations to compute the first n terms in the reversion of a power series or the composition of two series, and order nelog n operations if the fast Founer transform is used for power series multiplication In this paper we show that the composition and r ..."
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Cited by 106 (9 self)
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The classical algorithms require order n ~ operations to compute the first n terms in the reversion of a power series or the composition of two series, and order nelog n operations if the fast Founer transform is used for power series multiplication In this paper we show that the composition and reversion problems are equivalent (up to constant factors), and we give algorithms which require only order (n log n) ~/2 operations In many cases of practical importance only order n log n operations are required, these include certain special functions of power series and power series solution of certain differential equations Applications to rootfinding methods which use inverse interpolation and to queueing theory are described, some results on multivariate power series are stated, and several open questions are mentioned.
Disk Drive Roadmap from the Thermal Perspective: A Case for Dynamic Thermal Management
 In Proceedings of the International Symposium on Computer Architecture (ISCA
, 2005
"... The importance of pushing the performance envelope of disk drives continues to grow, not just in the server market but also in numerous consumer electronics products. One of the most fundamental factors impacting disk drive design is the heat dissipation and its effect on drive reliability, since hi ..."
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Cited by 34 (9 self)
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The importance of pushing the performance envelope of disk drives continues to grow, not just in the server market but also in numerous consumer electronics products. One of the most fundamental factors impacting disk drive design is the heat dissipation and its effect on drive reliability, since high temperatures can cause offtrack errors, or even head crashes. Until now, drive manufacturers have continued to meet the 40 % annual growth target of the internal data rates (IDR) by increasing RPMs, and shrinking platter sizes, both of which have counteracting effects on the heat dissipation within a drive. As this paper will show, we are getting to a point where it is becoming very difficult to stay on this roadmap. This paper presents an integrated disk drive model that captures the close relationships between capacity, performance and thermal characteristics over time. Using this model, we quantify the drop off in IDR growth rates over the next decade if we are to adhere to the thermal envelope of drive design. We present two mechanisms for buying back some of this IDR loss with Dynamic Thermal Management (DTM). The first DTM technique exploits any available thermal slack, between what the drive was intended to support and the currently lower operating temperature, to ramp up the RPM. The second DTM technique assumes that the drive is only designed for average case behavior, thus allowing higher RPMs than the thermal envelope, and employs dynamic throttling of disk drive activities to remain within this envelope.
Understanding the PerformanceTemperature Interactions in Disk I/O of Server Workloads
 Interactions in Disk I/O of Server Workloads. In Proceedings of HPCA
, 2006
"... This paper describes the first infrastructure for integrated studies of the performance and thermal behavior of storage systems. Using microbenchmarks running on this infrastructure, we first gain insight into how I/O characteristics can affect the temperature of disk drives. We use this analysis to ..."
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Cited by 24 (8 self)
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This paper describes the first infrastructure for integrated studies of the performance and thermal behavior of storage systems. Using microbenchmarks running on this infrastructure, we first gain insight into how I/O characteristics can affect the temperature of disk drives. We use this analysis to identify the most promising, yet simple, “knobs ” for temperature optimization of high speed disks, which can be implemented on existing disks. We then analyze the thermal profiles of real workloads that use such disk drives in their storage systems, pointing out which knobs are most useful for dynamic thermal management when pushing the performance envelope.
Linear elastic chain with a hyperprestress
 Journal of the Mechanics and Physics of Solids
, 2002
"... To account for surface relaxation in ultrathin films, we consider the simplest onedimensional discrete chain with harmonic interactions of up to second nearest neighbors. We assume that the springs, describing interactions of the nearest neighbors (NN) and next to nearest neighbors (NNN) have inco ..."
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Cited by 11 (4 self)
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To account for surface relaxation in ultrathin films, we consider the simplest onedimensional discrete chain with harmonic interactions of up to second nearest neighbors. We assume that the springs, describing interactions of the nearest neighbors (NN) and next to nearest neighbors (NNN) have incompatible reference lengths, which introduce a hyperprestress and results in a formation of the exponential surface boundary layers. For a finite body loaded by a system of (double) forces at the boundary, we explicitly find the displacement field and compute the energies of the inhomogeneous stressed and reference configurations. We then obtain a simple expression for the hyperprestress related contribution to the surface energy and show an unusual scaling of the total energy with the film thickness. For ultrathin films we report an anomalous stiffness increase due to the overlapping of the surface boundary layers. Implications of the micro level hyperprestress in fracture mechanics and in the theory of nonBravais lattices are also discussed.
Linear difference operators and acceleration methods
, 1997
"... The aim of this paper is the study of the kernel and acceleration properties of sequence transformations of the form T n = L(S n =D n)=L(1=D n) , where (S n) is the sequence for which we want to compute the limit, (D n) is an error estimate and L is a linear difference operator. We will obtain thos ..."
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Cited by 3 (1 self)
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The aim of this paper is the study of the kernel and acceleration properties of sequence transformations of the form T n = L(S n =D n)=L(1=D n) , where (S n) is the sequence for which we want to compute the limit, (D n) is an error estimate and L is a linear difference operator. We will obtain those properties for different classes of operators L and we will give a procedure for constructing, for a given class of sequences, an operator for which the corresponding transformation accelerates that class.
Movable singularities of solutions of difference equations in relation to solvability, and study of a superstable fixed point Theoretical and
 Mathematical Physics
, 2002
"... Abstract. We overview applications exponential asymptotics and analyzable function theory to difference equations, in defining an analog of the Painlevé property for them and we sketch the conclusions with respect to the solvability properties of first order autonomous ones. It turns out that if the ..."
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Cited by 2 (1 self)
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Abstract. We overview applications exponential asymptotics and analyzable function theory to difference equations, in defining an analog of the Painlevé property for them and we sketch the conclusions with respect to the solvability properties of first order autonomous ones. It turns out that if the Painlevé property is present the equations are explicitly solvable and in the contrary case, under further assumptions, the integrals of motion develop singularity barriers. We apply the method to the logistic map xn+1 = axn(1 − xn) where it turns out that the only cases with the Painlevé property are a = −2, 0, 2 and 4 for which explicit solutions indeed exist; in the opposite case an associated conjugation map develops singularity barriers. 1.
Nonlinear Schrödinger lattices, I: stability of discrete solitons”, preprint: nlin/0410005
, 2004
"... We consider the discrete solitons bifurcating from the anticontinuum limit of the discrete nonlinear Schrödinger (NLS) lattice. The discrete soliton in the anticontinuum limit represents an arbitrary finite superposition of inphase or antiphase excited nodes, separated by an arbitrary sequence o ..."
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Cited by 1 (1 self)
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We consider the discrete solitons bifurcating from the anticontinuum limit of the discrete nonlinear Schrödinger (NLS) lattice. The discrete soliton in the anticontinuum limit represents an arbitrary finite superposition of inphase or antiphase excited nodes, separated by an arbitrary sequence of empty nodes. By using stability analysis, we prove that the discrete solitons are all unstable near the anticontinuum limit, except for the solitons, which consist of alternating antiphase excited nodes. We classify analytically and confirm numerically the number of unstable eigenvalues associated with each family of the discrete solitons. 1
POWER MANAGEMENT OF ENTERPRISE STORAGE SYSTEMS
, 2005
"... ⋆ Signatures are on file in the Graduate School. Datacentric services, such as transaction processing systems and searchengines, sustain the demands of millions of users each day. These services rely heavily on the I/O subsystem for their data storage and processing requirements. Technological imp ..."
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Cited by 1 (0 self)
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⋆ Signatures are on file in the Graduate School. Datacentric services, such as transaction processing systems and searchengines, sustain the demands of millions of users each day. These services rely heavily on the I/O subsystem for their data storage and processing requirements. Technological improvements in hard disk drive densities and datarates have been key enablers in the realization of these storage systems. However, server storage systems consume a large amount of power, leading to higher running costs, increased stresses on the power supply, higher failure rates and detrimental environmental impacts. This thesis makes four contributions towards understanding the nature of the power problem and developing effective solutions to combat its effects. First, it shows that power management is a challenging problem for enterprise storage systems and traditional techniques to reduce power are relatively ineffective in such systems. Second, it shows that the heat that is dissipated due to the high power consumption would significantly restrict the ability to sustain the pace of performance growth of disks in the near future. Third, it proposes a novel disk drive architec
Thermal Issues in Disk Drive Design: Challenges and Possible Solutions
"... The importance of pushing the performance envelope of disk drives continues to grow in the enterprise storage market. One of the most fundamental factors impacting disk drive design is heat dissipation, since it directly affects drive reliability. Until now, drive manufacturers have continued to mee ..."
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Cited by 1 (0 self)
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The importance of pushing the performance envelope of disk drives continues to grow in the enterprise storage market. One of the most fundamental factors impacting disk drive design is heat dissipation, since it directly affects drive reliability. Until now, drive manufacturers have continued to meet the 40 % annual growth target of the internal datarates (IDR) by increasing RPMs and shrinking platter sizes, both of which have counteracting effects on the heat dissipation within a drive. In this article, we shall show that we are getting to a point where it is going to be very difficult to stay on this roadmap. We first present detailed models that capture the close relationships between capacity, performance, and thermal characteristics over time. Using these models, we quantify the dropoff in IDR growth rates over the next decade if we are to adhere to the thermal design envelope. We motivate the need for continued improvements in IDR by showing that the response times of real workloads can be improved by 30–60 % with a 10K increase in the RPM for disks used in their respective storage systems. We then present two dynamic thermal management (DTM) techniques that can be used to buy back some of this IDR loss. The first DTM technique exploits the thermal slack between what the drive was intended to support and the currently lower operating temperature to ramp up the RPM. The second DTM technique assumes that the drive is
Marek Pycia
"... . In the present paper we give new formulas for a general solution of the linear difference equation of finite order with constant complex coefficients without necessity of solving the characteristic equation Introduction. In this paper we deal with the following difference equation of order m: (1) ..."
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. In the present paper we give new formulas for a general solution of the linear difference equation of finite order with constant complex coefficients without necessity of solving the characteristic equation Introduction. In this paper we deal with the following difference equation of order m: (1) xn+m = m X r=1 a r xn+m\Gammar with constant complex coefficients a 1 ; : : : ; am . Our Theorem gives a simple formula for the general solution depending only on the coefficients a 1 ; : : : ; am . We do not have to solve the characteristic equation as it is usually done (cf for instance [1], [2]) and, in general, it is often impossible to find the exact solutions of it. To formulate our Theorem we adopt the following convention: (\Gamma1)! \Delta 0 = 1 : Theorem. Let x 0 ; : : : ; xm\Gamma1 be arbitrary complex numbers, let h 1 ; : : : ; hm be nonnegative integers. The general solution of equation (1) is of the form (2): xn = m\Gamma1 X l=0 " X 1h1+\Delta\Delta\Delta+mh m=n\Gammal...