Improved Upper Bounds to the Causal Quadratic Rate-Distortion Function for Gaussian Stationary Sources

We improve the existing achievable rate regions for causal and for zero-delay source coding of stationary Gaussian sources under an average mean squared error (MSE) distortion measure. To begin with, we find a closed-form expression for the information-theoretic causal rate-distortion function (RDF) under such distortion measure, denoted by $R_{c}^{it}(D)$, for first-order Gauss-Markov processes. Rc^{it}(D) is a lower bound to the optimal performance theoretically attainable (OPTA) by any causal source code, namely Rc^{op}(D). We show that, for Gaussian sources, the latter can also be upper bounded as Rc^{op}(D)\leq Rc^{it}(D) + 0.5 log_{2}(2\pi e) bits/sample. In order to analyze $R_{c}^{it}(D)$ for arbitrary zero-mean Gaussian stationary sources, we introduce \bar{Rc^{it}}(D), the information-theoretic causal RDF when the reconstruction error is jointly stationary with the source. Based upon \bar{Rc^{it}}(D), we derive three closed-form upper bounds to the additive rate loss defined as \bar{Rc^{it}}(D) - R(D), where R(D) denotes Shannon's RDF. Two of these bounds are strictly smaller than 0.5 bits/sample at all rates. These bounds differ from one another in their tightness and ease of evaluation; the tighter the bound, the more involved its evaluation. We then show that, for any source spectral density and any positive distortion D\leq \sigma_{x}^{2}, \bar{Rc^{it}}(D) can be realized by an AWGN channel surrounded by a unique set of causal pre-, post-, and feedback filters. We show that finding such filters constitutes a convex optimization problem. In order to solve the latter, we propose an iterative optimization procedure that yields the optimal filters and is guaranteed to converge to \bar{Rc^{it}}(D). Finally, by establishing a connection to feedback quantization we design a causal and a zero-delay coding scheme which, for Gaussian sources, achieves...Comment: 47 pages, revised version submitted to IEEE Trans. Information Theor

Design and Analysis of LT Codes with Decreasing Ripple Size

In this paper we propose a new design of LT codes, which decreases the amount of necessary overhead in comparison to existing designs. The design focuses on a parameter of the LT decoding process called the ripple size. This parameter was also a key element in the design proposed in the original work by Luby. Specifically, Luby argued that an LT code should provide a constant ripple size during decoding. In this work we show that the ripple size should decrease during decoding, in order to reduce the necessary overhead. Initially we motivate this claim by analytical results related to the redundancy within an LT code. We then propose a new design procedure, which can provide any desired achievable decreasing ripple size. The new design procedure is evaluated and compared to the current state of the art through simulations. This reveals a significant increase in performance with respect to both average overhead and error probability at any fixed overhead

Hartree-Fock theory for pseudorelativistic atoms

We study the Hartree-Fock model for pseudorelativistic atoms, that is, atoms where the kinetic energy of the electrons is given by the pseudorelativistic operator \sqrt{(pc)^2+(mc^2)^2}-mc^2. We prove the existence of a Hartree-Fock minimizer, and prove regularity away from the nucleus and pointwise exponential decay of the corresponding orbitals

Sources of Regional Resilience in the Danish ICT Sector

In this paper the use of the term “resilience” is discussed and a definition for use in quantitative studies of industrial evolution is suggested. Resilience is the ability of an industry in a region to exploit the possibilities arising from external events and adapt to thrive under new selection environments. An econometric analysis is undertaken to uncover the effects of the change in selection environment that the ICT industry faced from the burst of the ICT bubble in the year 2000. It is shown that some characteristics of regional industry structure are associated with growth over the whole period while other characteristics have varying effects pre and post burst. Special attention is given to the responsiveness of growth to the evolution of sales of ICT goods and services in Denmark and it is found that the industry structures that restrain growth also are the ones, which make the regional industry better able to exploit changes in sales at the national level.Resilience; Business cycle; ICT sector; Regional growth

Knowledge Flows Through Social Networks in a Cluster Interfirm versus University-Industry Contacts

Knowledge spillovers from a university to the local industry play an important role in clusters, but we know little about these spillovers. This paper examines empirically the extent of university-industry informal contacts. Furthermore, it analyses the characteristics of an engineer that acquire knowledge from informal contacts with university researchers. The university-industry contacts are compared with results for interfirm contacts. The research shows that the interfirm informal contacts are more numerous than university informal contacts. Likewise, knowledge is more frequently acquired from other firms than through university-industry contacts. Engineers that have participated in formal projects with university researchers and engineers that are educated at the university have a higher likelihood of acquiring knowledge from informal contacts with university researchers.Knowledge flows; informal contacts

Beyond Technological Diversification: The Impact of Employee Diversity on Innovation

This paper investigates the effect of employee diversity in terms of gender, age, ethnicity and education on the firm’s likelihood of introducing an innovation. The analysis draws on data from a recent innovation survey. This data is merged with a linked employer-employee dataset that allow us to identify the employee composition of each firm. We test the hypothesis that employee diversity is associated with better innovative performance. The econometric analysis reveals positive, negative and non-significant effects of the different employee characteristics on the likelihood of introducing an innovation.Diversity, Innovation, Education, Gender, Cultural Backgrund

On the convergence of eigenfunctions to threshold energy states

We prove the convergence in certain weighted spaces in momentum space of eigenfunctions of H = T-lambda*V as the energy goes to an energy threshold. We do this for three choices of kinetic energy T, namely the non-relativistic Schr"odinger operator, the pseudorelativistc operator sqrt{-\Delta+m^2}-m, and the Dirac operator.Comment: 15 pages; references and comments added (e.g., Remark 3