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Chaos & graphics External arguments of Douady cauliflowers in the Mandelbrot set
"... Near to the cusp of a cardioid of the Mandelbrot set, except for the main cardioid, there is a sequence of baby Mandelbrot sets. Each baby Mandelbrot set is in the center of a Douady cauliflower, a decoration constituted by an infinity of minute Mandelbrot sets and Misiurewicz points linked by filam ..."
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by filaments. A Douady cauliflower appears to have a complicated structure, and how the external rays land without intersecting in its Misiurewicz points and minute Mandelbrot sets is not really well known. In this work we study the Douady cauliflowers, giving a binary tree model to calculate the binary
A highperformance, portable implementation of the MPI message passing interface standard
 Parallel Computing
, 1996
"... MPI (Message Passing Interface) is a specification for a standard library for message passing that was defined by the MPI Forum, a broadly based group of parallel computer vendors, library writers, and applications specialists. Multiple implementations of MPI have been developed. In this paper, we d ..."
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Cited by 888 (67 self)
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describe MPICH, unique among existing implementations in its design goal of combining portability with high performance. We document its portability and performance and describe the architecture by which these features are simultaneously achieved. We also discuss the set of tools that accompany the free
SelfSimilarity Through HighVariability: Statistical Analysis of Ethernet LAN Traffic at the Source Level
 IEEE/ACM TRANSACTIONS ON NETWORKING
, 1997
"... A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is selfsimilar or longrange dependent in nature (i.e., bursty over a wide range of time scales)  in sharp contrast to commonly made tr ..."
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Cited by 740 (24 self)
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A number of recent empirical studies of traffic measurements from a variety of working packet networks have convincingly demonstrated that actual network traffic is selfsimilar or longrange dependent in nature (i.e., bursty over a wide range of time scales)  in sharp contrast to commonly made traffic modeling assumptions. In this paper, we provide a plausible physical explanation for the occurrence of selfsimilarity in LAN traffic. Our explanation is based on new convergence results for processes that exhibit high variability (i.e., infinite variance) and is supported by detailed statistical analyses of realtime traffic measurements from Ethernet LAN's at the level of individual sources. This paper is an extended version of [53] and differs from it in significant ways. In particular, we develop here the mathematical results concerning the superposition of strictly alternating ON/OFF sources. Our key mathematical result states that the superposition of many ON/OFF sources (also k...
Statistical mechanics of complex networks
 Rev. Mod. Phys
"... Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as ra ..."
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Cited by 2083 (10 self)
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Complex networks describe a wide range of systems in nature and society, much quoted examples including the cell, a network of chemicals linked by chemical reactions, or the Internet, a network of routers and computers connected by physical links. While traditionally these systems were modeled as random graphs, it is increasingly recognized that the topology and evolution of real
Rational External Rays of the Mandelbrot Set
, 1997
"... We give a new proof that all external rays of the Mandelbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is different from the original one, given by Douady and Hubbard and refined by Lavaurs, in several w ..."
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Cited by 7 (3 self)
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We give a new proof that all external rays of the Mandelbrot set at rational angles land, and of the relation between the external angle of such a ray and the dynamics at the landing point. Our proof is different from the original one, given by Douady and Hubbard and refined by Lavaurs, in several
Extension of the DouadyHubbard’s Theorem on Convergence of Periodic External Rays of the Mandelbrot Set to Polynomials of type Ed
"... We consider the complex dynamics of a one parameter family of polynomials of type Ed [1], as fc(z) = z(z + c)d, where d ≥ 1 is a given integer and c ∈ C. In the dynamics of quadratic polynomials Pc(z) = z2 + c, Douady and Hubbard [2, 3] have proved that periodic external rays land on a parameter i ..."
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in the Mandelbrot set. This result has been extended to the parameter space of unicritical polynomials gc(z) = zd + c[8]. We extend the DouadyHubbard Theorem to the polynomials of type Ed.
Experimental Queueing Analysis with LongRange Dependent Packet Traffic
 IEEE/ACM Transactions on Networking
, 1996
"... Recent traffic measurement studies from a wide range of working packet networks have convincingly established the presence of significant statistical features that are characteristic of fractal traffic processes, in the sense that these features span many time scales. Of particular interest in packe ..."
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Cited by 347 (13 self)
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Recent traffic measurement studies from a wide range of working packet networks have convincingly established the presence of significant statistical features that are characteristic of fractal traffic processes, in the sense that these features span many time scales. Of particular interest in packet traffic modeling is a property called longrange dependence, which is marked by the presence of correlations that can extend over many time scales. In this paper, we demonstrate empirically that, beyond its statistical significance in traffic measurements, longrange dependence has considerable impact on queueing performance, and is a dominant characteristic for a number of packet traffic engineering problems. In addition, we give conditions under which the use of compact and simple traffic models that incorporate longrange dependence in a parsimonious manner (e.g., fractional Brownian motion) is justified and can lead to new insights into the traffic management of highspeed networks. 1...
The Variable Discharge of Cortical Neurons: Implications for Connectivity, Computation, and Information Coding
 J. Neurosci
, 1998
"... this paper we propose that the irregular ISI arises as a consequence of a specific problem that cortical neurons must solve: the problem of dynamic range or gain control. Cortical neurons receive 300010,000 synaptic contacts, 85% of which are asymmetric and hence presumably excitatory (Peters, 198 ..."
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Cited by 341 (3 self)
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this paper we propose that the irregular ISI arises as a consequence of a specific problem that cortical neurons must solve: the problem of dynamic range or gain control. Cortical neurons receive 300010,000 synaptic contacts, 85% of which are asymmetric and hence presumably excitatory (Peters, 1987; Braitenberg and Schuz, 1991). More than half of these contacts are thought to arise from neurons within a 100200 #m radius of the target cell, reflecting the stereotypical columnar organization of neocortex. Because neurons within a cortical column typically share similar physiological properties, the conditions that excite one neuron are likely to excite a considerable fraction of its afferent input as well (Mountcastle, 1978; Peters and Sethares, 1991), creating a scenario in which saturation of the neuron's firing rate could easily occur. This problem is exacerbated by the fact that EPSPs from individual axons appear to exert substantial impact on the membrane potential (Mason et al., 1991; Otmakhov Received Sept. 15, 1997; revised Feb. 25, 1998; accepted March 3, 1998.
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