Calculation of Reliability Characteristics for Regenerative Models

If a regenerative process is represented as semi-regenerative, we derive formulae enabling us to calculate basic characteristics associated with the first occurrence time starting from corresponding characteristics for the semi-regenerative process. Recursive equations, integral equations, and Monte-Carlo algorithms are proposed for practical solving of the problem.

Algebraic and geometric intersection numbers for free groups

We show that the algebraic intersection number of Scott and Swarup for splittings of free groups Coincides With the geometric intersection number for the sphere complex of the connected sum of copies of S-2 x S-1. (C) 2009 Elsevier B.V. All rights reserved.

A geometric analysis of convex demixing

Demixing is the task of identifying multiple signals given only their sum and prior information about their structures. Examples of demixing problems include (i) separating a signal that is sparse with respect to one basis from a signal that is sparse with respect to a second basis; (ii) decomposing an observed matrix into low-rank and sparse components; and (iii) identifying a binary codeword with impulsive corruptions. This thesis describes and analyzes a convex optimization framework for solving an array of demixing problems.

Our framework includes a random orientation model for the constituent signals that ensures the structures are incoherent. This work introduces a summary parameter, the statistical dimension, that reflects the intrinsic complexity of a signal. The main result indicates that the difficulty of demixing under this random model depends only on the total complexity of the constituent signals involved: demixing succeeds with high probability when the sum of the complexities is less than the ambient dimension; otherwise, it fails with high probability.

The fact that a phase transition between success and failure occurs in demixing is a consequence of a new inequality in conic integral geometry. Roughly speaking, this inequality asserts that a convex cone behaves like a subspace whose dimension is equal to the statistical dimension of the cone. When combined with a geometric optimality condition for demixing, this inequality provides precise quantitative information about the phase transition, including the location and width of the transition region.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Composite control of non-linear singularly perturbed systems: a geometric approach

Using a geometric approach, a composite control—the sum of a slow control and a fast control—is derived for a general class of non-linear singularly perturbed systems. A new and simpler method of composite control design is proposed whereby the fast control is completely designed at the outset. The slow control is then free to be chosen such that the slow integral manifold of the original system approximates a desired design manifold to within any specified order of ε accuracy.

Improved geometric parameterisation techniques for continuation power flow

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Bivariate gamma-geometric law and its induced Levy process

In this article we introduce a three-parameter extension of the bivariate exponential-geometric (BEG) law (Kozubowski and Panorska, 2005) [4]. We refer to this new distribution as the bivariate gamma-geometric (BGG) law. A bivariate random vector (X, N) follows the BGG law if N has geometric distribution and X may be represented (in law) as a sum of N independent and identically distributed gamma variables, where these variables are independent of N. Statistical properties such as moment generation and characteristic functions, moments and a variance-covariance matrix are provided. The marginal and conditional laws are also studied. We show that BBG distribution is infinitely divisible, just as the BEG model is. Further, we provide alternative representations for the BGG distribution and show that it enjoys a geometric stability property. Maximum likelihood estimation and inference are discussed and a reparametrization is proposed in order to obtain orthogonality of the parameters. We present an application to a real data set where our model provides a better fit than the BEG model. Our bivariate distribution induces a bivariate Levy process with correlated gamma and negative binomial processes, which extends the bivariate Levy motion proposed by Kozubowski et al. (2008) [6]. The marginals of our Levy motion are a mixture of gamma and negative binomial processes and we named it BMixGNB motion. Basic properties such as stochastic self-similarity and the covariance matrix of the process are presented. The bivariate distribution at fixed time of our BMixGNB process is also studied and some results are derived, including a discussion about maximum likelihood estimation and inference. (C) 2012 Elsevier Inc. All rights reserved.

Geometric Integrability of the Camassa-Holm Equation. II

It is known that the Camassa–Holm (CH) equation describes pseudo-spherical surfaces and that therefore its integrability properties can be studied by geometrical means. In particular, the CH equation admits nonlocal symmetries of “pseudo-potential type”: the standard quadratic pseudo-potential associated with the geodesics of the pseudo-spherical surfaces determined by (generic) solutions to CH, allows us to construct a covering π of the equation manifold of CH on which nonlocal symmetries can be explicitly calculated. In this article, we present the Lie algebra of (first-order) nonlocal π-symmetries for the CH equation, and we show that this algebra contains a semidirect sum of the loop algebra over sl(2,R) and the centerless Virasoro algebra. As applications, we compute explicit solutions, we construct a Darboux transformation for the CH equation, and we recover its recursion operator. We also extend our results to the associated Camassa–Holm equation introduced by J. Schiff.

A geometric characterization of the upper bound for the span of the jones polynomial

Let D be a link diagram with n crossings, sA and sB be its extreme states and |sAD| (respectively, |sBD|) be the number of simple closed curves that appear when smoothing D according to sA (respectively, sB). We give a general formula for the sum |sAD| + |sBD| for a k-almost alternating diagram D, for any k, characterizing this sum as the number of faces in an appropriate triangulation of an appropriate surface with boundary. When D is dealternator connected, the triangulation is especially simple, yielding |sAD| + |sBD| = n + 2 - 2k. This gives a simple geometric proof of the upper bound of the span of the Jones polynomial for dealternator connected diagrams, a result first obtained by Zhu [On Kauffman brackets, J. Knot Theory Ramifications6(1) (1997) 125–148.]. Another upper bound of the span of the Jones polynomial for dealternator connected and dealternator reduced diagrams, discovered historically first by Adams et al. [Almost alternating links, Topology Appl.46(2) (1992) 151–165.], is obtained as a corollary. As a new application, we prove that the Turaev genus is equal to the number k of dealternator crossings for any dealternator connected diagram

Geometric Stable Laws Through Series Representations

Let (Xi ) be a sequence of i.i.d. random variables, and let N be a geometric random variable independent of (Xi ). Geometric stable distributions are weak limits of (normalized) geometric compounds, SN = X1 + · · · + XN , when the mean of N converges to infinity. By an appropriate representation of the individual summands in SN we obtain series representation of the limiting geometric stable distribution. In addition, we study the asymptotic behavior of the partial sum process SN (t) = ⅀( i=1 ... [N t] ) Xi , and derive series representations of the limiting geometric stable process and the corresponding stochastic integral. We also obtain strong invariance principles for stable and geometric stable laws.

Algebraic geometric codes over rings

The techniques of algebraic geometry have been widely and successfully applied to the study of linear codes over finite fields since the early 1980's. Recently, there has been an increased interest in the study of linear codes over finite rings. In this thesis, we combine these two approaches to coding theory by introducing and studying algebraic geometric codes over rings.

Is the sum more than the corporate entrepreneurship parts? the different effects of social capital on innovation, venturing, and renewal processes

Principal Topic Although corporate entrepreneurship is of vital importance for long-term firm survival and growth (Zahra and Covin, 1995), researchers still struggle with understanding how to manage corporate entrepreneurship activities. Corporate entrepreneurship consists of three parts: innovation, venturing, and renewal processes (Guth and Ginsberg, 1990). Innovation refers to the development of new products, venturing to the creation of new businesses, and renewal to redefining existing businesses (Sharma, and Chrisman, 1999; Verbeke et al., 2007). Although there are many studies focusing on one of these aspects (cf. Burgelman, 1985; Huff et al., 1992), it is very difficult to compare the outcomes of these studies due to differences in contexts, measures, and methodologies. This is a significant lack in our understanding of CE, as firms engage in all three aspects of CE, making it important to compare managerial and organizational antecedents of innovation, venturing and renewal processes. Because factors that may enhance venturing activities may simultaneously inhibit renewal activities. The limited studies that did empirically compare the individual dimensions (cf. Zahra, 1996; Zahra et al., 2000; Yiu and Lau, 2008; Yiu et al., 2007) generally failed to provide a systematic explanation for potential different effects of organizational antecedents on innovation, venturing, and renewal. With this study we aim to investigate the different effects of structural separation and social capital on corporate entrepreneurship activities. The access to existing and the development of new knowledge has been deemed of critical importance in CE-activities (Floyd and Wooldridge, 1999; Covin and Miles, 2007; Katila and Ahuja, 2002). Developing new knowledge can be facilitated by structurally separating corporate entrepreneurial units from mainstream units (cf. Burgelman, 1983; Hill and Rothaermel, 2003; O'Reilly and Tushman, 2004). Existing knowledge and resources are available through networks of social relationships, defined as social capital (Nahapiet and Ghoshal, 1998; Yiu and Lau, 2008). Although social capital has primarily been studied at the organizational level, it might be equally important at top management level (Belliveau et al., 1996). However, little is known about the joint effects of structural separation and integrative mechanisms to provide access to social capital on corporate entrepreneurship. Could these integrative mechanisms for example connect the separated units to facilitate both knowledge creation and sharing? Do these effects differ for innovation, venturing, and renewal processes? Are the effects different for organizational versus top management team integration mechanisms? Corporate entrepreneurship activities have for example been suggested to take place at different levels. Whereas innovation is suggested to be a more bottom-up process, strategic renewal is a more top-down process (Floyd and Lane, 2000; Volberda et al., 2001). Corporate venturing is also a more bottom-up process, but due to the greater required resource commitments relative to innovation, it ventures need to be approved by top management (Burgelman, 1983). As such we will explore the following key research question in this paper: How do social capital and structural separation on organizational and TMT level differentially influence innovation, venturing, and renewal processes? Methodology/Key Propositions We investigated our hypotheses on a final sample of 240 companies in a variety of industries in the Netherlands. All our measures were validated in previous studies. We targeted a second respondent in each firm to reduce problems with single-rater data (James et al., 1984). We separated the measurement of the independent and the dependent variables in two surveys to create a one-year time lag and reduce potential common method bias (Podsakoff et al., 2003). Results and Implications Consistent with our hypotheses, our results show that configurations of structural separation and integrative mechanisms have different effects on the three aspects of corporate entrepreneurship. Innovation was affected by organizational level mechanisms, renewal by integrative mechanisms on top management team level and venturing by mechanisms on both levels. Surprisingly, our results indicated that integrative mechanisms on top management team level had negative effects on corporate entrepreneurship activities. We believe this paper makes two significant contributions. First, we provide more insight in what the effects of ambidextrous organizational forms (i.e. combinations of differentiation and integration mechanisms) are on venturing, innovation and renewal processes. Our findings show that more valuable insights can be gained by comparing the individual parts of corporate entrepreneurship instead of focusing on the whole. Second, we deliver insights in how management can create a facilitative organizational context for these corporate entrepreneurship activities.

FPGA implementation of dual-microphone delay-and-sum beamforming for in-car speech enhancement and recognition

In an automotive environment, the performance of a speech recognition system is affected by environmental noise if the speech signal is acquired directly from a microphone. Speech enhancement techniques are therefore necessary to improve the speech recognition performance. In this paper, a field-programmable gate array (FPGA) implementation of dual-microphone delay-and-sum beamforming (DASB) for speech enhancement is presented. As the first step towards a cost-effective solution, the implementation described in this paper uses a relatively high-end FPGA device to facilitate the verification of various design strategies and parameters. Experimental results show that the proposed design can produce output waveforms close to those generated by a theoretical (floating-point) model with modest usage of FPGA resources. Speech recognition experiments are also conducted on enhanced in-car speech waveforms produced by the FPGA in order to compare recognition performance with the floating-point representation running on a PC.