Convergence analysis of chip- and fractionally spaced LMS adaptive multiuser CDMA detectors

This paper analyzes the convergence behavior of the least mean square (LMS) filter when used in an adaptive code division multiple access (CDMA) detector consisting of a tapped delay line with adjustable tap weights. The sampling rate may be equal to or higher than the chip rate, and these correspond to chip-spaced (CS) and fractionally spaced (FS) detection, respectively. It is shown that CS and FS detectors with the same time-span exhibit identical convergence behavior if the baseband received signal is strictly bandlimited to half the chip rate. Even in the practical case when this condition is not met, deviations from this observation are imperceptible unless the initial tap-weight vector gives an extremely large mean squared error (MSE). This phenomenon is carefully explained with reference to the eigenvalues of the correlation matrix when the input signal is not perfectly bandlimited. The inadequacy of the eigenvalue spread of the tap-input correlation matrix as an indicator of the transient behavior and the influence of the initial tap weight vector on convergence speed are highlighted. Specifically, a initialization within the signal subspace or to the origin leads to very much faster convergence compared with initialization in the a noise subspace.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

On-line Gaussian mixture density estimator for adaptive minimum bit-error-rate beamforming receivers

We develop an on-line Gaussian mixture density estimator (OGMDE) in the complex-valued domain to facilitate adaptive minimum bit-error-rate (MBER) beamforming receiver for multiple antenna based space-division multiple access systems. Specifically, the novel OGMDE is proposed to adaptively model the probability density function of the beamformer’s output by tracking the incoming data sample by sample. With the aid of the proposed OGMDE, our adaptive beamformer is capable of updating the beamformer’s weights sample by sample to directly minimize the achievable bit error rate (BER). We show that this OGMDE based MBER beamformer outperforms the existing on-line MBER beamformer, known as the least BER beamformer, in terms of both the convergence speed and the achievable BER.

Strain rate of the South American lithospheric plate by SIRGAS-CON geodetic observations

A multiyear solution of the SIRGAS-CON network was used to estimate the strain rates of the earth surface from the changing directions of the velocity vectors of 140 geodetic points located in the South American plate. The strain rate was determined by the finite element method using Delaunay triangulation points that formed sub-networks; each sub-network was considered a solid and homogeneous body. The results showed that strain rates vary along the South American plate and are more significant on the western portion of the plate, as expected, since this region is close to the subduction zone of the Nazca plate beneath the South American plate. After using Euler vectors to infer Nazca plate movement and to orient the velocity vectors of the South American plate, it was possible to estimate the convergence and accommodation rates of the Nazca and South American plates, respectively. Strain rate estimates permitted determination of predominant contraction and/or extension regions and to establish that contraction regions coincide with locations with most of the high magnitude seismic events. Some areas with extension and contraction strains were found to the east within the stable South American plate, which may result from different stresses associated with different geological characteristics. These results suggest that major movements detected on the surface near the Nazca plate occur in regions with more heterogeneous geological structures and multiple rupture events. Most seismic events in the South American plate are concentrated in areas with predominant contraction strain rates oriented northeast-southwest; significant amounts of elastic strain can be accumulated on geological structures away from the plate boundary faults; and, behavior of contractions and extensions is similar to what has been found in seismological studies. © 2013 Elsevier Ltd.

Concentration of floating biogenic material in convergence zones

Some organisms that live just below the sea surface (the neuston) are known more as a matter of curiosity than as critical players in biogeochemical cycles. The hypothesis of this work is that their existence implies that they receive some food from an upward flux of organic matter. The behaviour of these organisms and of the associated organic matter, hereafter mentioned as floating biogenic material (FBM) is explored using a global physical-biogeochemical coupled model, in which its generation is fixed to 1% of primary production, and decay rate is of the order of I month. The model shows that the distribution of FBM should depart rapidly from that of primary production.. and be more sensitive to circulation patterns than to the distribution of primary production. It is trapped in convergence areas, where it reaches concentrations larger by a factor 10 than in divergences, thus enhancing and inverting the contrast between high and low primary productivity areas. Attention is called on the need to better understand the biogeochemical processes in the first meter of the ocean, as they may impact the distribution of food for fishes, as well as the conditions for air-sea exchange and for the interpretation of sea color.

Mutually catalytic branching at infinite rate

The purpose of this doctoral thesis is to prove existence for a mutually catalytic random walk with infinite branching rate on countably many sites. The process is defined as a weak limit of an approximating family of processes. An approximating process is constructed by adding jumps to a deterministic migration on an equidistant time grid. As law of jumps we need to choose the invariant probability measure of the mutually catalytic random walk with a finite branching rate in the recurrent regime. This model was introduced by Dawson and Perkins (1998) and this thesis relies heavily on their work. Due to the properties of this invariant distribution, which is in fact the exit distribution of planar Brownian motion from the first quadrant, it is possible to establish a martingale problem for the weak limit of any convergent sequence of approximating processes. We can prove a duality relation for the solution to the mentioned martingale problem, which goes back to Mytnik (1996) in the case of finite rate branching, and this duality gives rise to weak uniqueness for the solution to the martingale problem. Using standard arguments we can show that this solution is in fact a Feller process and it has the strong Markov property. For the case of only one site we prove that the model we have constructed is the limit of finite rate mutually catalytic branching processes as the branching rate approaches infinity. Therefore, it seems naturalto refer to the above model as an infinite rate branching process. However, a result for convergence on infinitely many sites remains open.

Squared Extrapolation Methods (SQUAREM): A New Class of Simple and Efficient Numerical Schemes for Accelerating the Convergence of the EM Algorithm

We derive a new class of iterative schemes for accelerating the convergence of the EM algorithm, by exploiting the connection between fixed point iterations and extrapolation methods. First, we present a general formulation of one-step iterative schemes, which are obtained by cycling with the extrapolation methods. We, then square the one-step schemes to obtain the new class of methods, which we call SQUAREM. Squaring a one-step iterative scheme is simply applying it twice within each cycle of the extrapolation method. Here we focus on the first order or rank-one extrapolation methods for two reasons, (1) simplicity, and (2) computational efficiency. In particular, we study two first order extrapolation methods, the reduced rank extrapolation (RRE1) and minimal polynomial extrapolation (MPE1). The convergence of the new schemes, both one-step and squared, is non-monotonic with respect to the residual norm. The first order one-step and SQUAREM schemes are linearly convergent, like the EM algorithm but they have a faster rate of convergence. We demonstrate, through five different examples, the effectiveness of the first order SQUAREM schemes, SqRRE1 and SqMPE1, in accelerating the EM algorithm. The SQUAREM schemes are also shown to be vastly superior to their one-step counterparts, RRE1 and MPE1, in terms of computational efficiency. The proposed extrapolation schemes can fail due to the numerical problems of stagnation and near breakdown. We have developed a new hybrid iterative scheme that combines the RRE1 and MPE1 schemes in such a manner that it overcomes both stagnation and near breakdown. The squared first order hybrid scheme, SqHyb1, emerges as the iterative scheme of choice based on our numerical experiments. It combines the fast convergence of the SqMPE1, while avoiding near breakdowns, with the stability of SqRRE1, while avoiding stagnations. The SQUAREM methods can be incorporated very easily into an existing EM algorithm. They only require the basic EM step for their implementation and do not require any other auxiliary quantities such as the complete data log likelihood, and its gradient or hessian. They are an attractive option in problems with a very large number of parameters, and in problems where the statistical model is complex, the EM algorithm is slow and each EM step is computationally demanding.

Accumulation rates and grain sizes of eolian dust in sediments of the Intertropical Convergence Zone in the northeast Pacific

A 328 cm-long piston core (KODOS 02-01-02) collected from the northeast equatorial Pacific at 16°12'N, 125°59'W was investigated for eolian mass fluxes and grain sizes to test these proxies as a tool for the paleo-position of the Intertropical Convergence Zone (ITCZ). The eolian mass fluxes of the lower interval below 250 cm (15.5-7.6 Ma) are very uniform at 5 +/- 1 mg/cm**2/kyr, while those of the upper interval above 250 cm (from 7.6 Ma) are over 2 times higher than the lower interval at 12 +/- 1 mg/cm**2/kyr. The median grain size of the eolian dusts in the lower interval increases from 8.4 Phi to 8.0 Phi downward, while that of the upper interval varies in a narrow range from 8.8 Phi to 8.6 Phi. The determined values compare well in magnitude to those of central Pacific sediments for the upper interval and equatorial and southeast Pacific sediments for the lower interval. This result suggests a possibility that the study site had been under the influence of southeast trade winds at its earlier depositional period due to the northerly position of the ITCZ, and subsequently of the northeast trade winds for a later period when the upper sediments were deposited. This interpretation is consistent with a mineralogical and geochemical study published elsewhere that assigned the provenance of the study core dust to Central/South America for the lower interval and to Asia for the upper interval. This study suggests that the distinct differences in eolian mass flux and grain size observed across the ITCZ can be used to trace the paleo-latitude of the ITCZ.

SLBN: A Scalable Max-min Fair Algorithm for Rate-Based Explicit Congestion Control

The growth of the Internet has increased the need for scalable congestion control mechanisms in high speed networks. In this context, we propose a rate-based explicit congestion control mechanism with which the sources are provided with the rate at which they can transmit. These rates are computed with a distributed max-min fair algorithm, SLBN. The novelty of SLBN is that it combines two interesting features not simultaneously present in existing proposals: scalability and fast convergence to the max-min fair rates, even under high session churn. SLBN is scalable because routers only maintain a constant amount of state information (only three integer variables per link) and only incur a constant amount of computation per protocol packet, independently of the number of sessions that cross the router. Additionally, SLBN does not require processing any data packet, and it converges independently of sessions' RTT. Finally, by design, the protocol is conservative when assigning rates, even in the presence of high churn, which helps preventing link overshoots in transient periods. We claim that, with all these features, our mechanism is a good candidate to be used in real deployments.

Overcoming performance and convergence issues of discrete transform based modeling of crosslinking classical and reversible deactivated radical polymerizations

Population balances of polymer species in terms 'of discrete transforms with respect to counts of groups lead to tractable first order partial differential equations when ali rate constants are independent of chain length and loop formation is negligible [l]. Average molecular weights in the absence ofgelation are long known to be readily found through integration of an initial value problem. The extension to size distribution prediction is also feasible, but its performance is often lower to the one provided by methods based upon real chain length domain [2]. Moreover, the absence ofagood starting procedure and a higher numerical sensitivity hás decisively impaired its application to non-linear reversibly deactivated polymerizations, namely NMRP [3].

Le role des politiques monétaires et la convergence macroeconomique sur le développement des systèmes financiers dans les pays du sud de la Méditerranée. = The role of monetary policies and macroeconomic convergence in the development of financial systems in south Mediterranean countries. MEDPRO Technical Report No. 12/April 2012

This MEDPRO Technical Report shows that the monetary and exchange rate policies conducted by central banks in the South Mediterranean region display apparent homogeneity in their operational frameworks, albeit with some specificities and differing degrees of advancement. While central banks state that price stability is their ultimate objective, failures to control interest rates as operational objectives of monetary policy result in monetary authorities resorting to quantitative approaches to monetary policy, meaning that monetary aggregates and credit targets are being used as intermediate targets of monetary policy. An econometric exercise limited to Maghreb countries (Algeria, Morocco, and Tunisia) has been conducted to analyse the potential scenarios of convergence and monetary policy coordination. Given the high structural heterogeneity and the slow pace of real convergence due to weak commercial integration in the Maghreb, results nevertheless show alternative dynamics in the integration of effective nominal exchange rates, as well as a complete convergence dynamic in exchange rate policies. Partial convergence of monetary policies regarding the stabilisation of inflation rates remains an open option for a transitional phase where financial integration is low.

A Convergence Process in Household Credit in Central and Eastern Europe. ECRI Commentary No. 16, 30 October 2015

The liberalisation of Eastern Europe’s market during the 1990s and the 2004 EU enlargement have had a great impact on the economies of Central and Eastern Europe (CEE). Indeed, prior to these events, the financial system and household credit markets in CEE were underdeveloped. Nonetheless, it appeared to numerous economists that the development of the CEE financial system and credit markets was following an intensely positive trend, raising the question of sustainability. Many variables impact the level and growth rate of credit; several economists point out that a convergence process might be one of the most important. Using a descriptive statistics approach, it seems likely that a convergence process began during the 1990s, when the CEE countries opened their economies. However, it also seems that the main driver of this household credit convergence process is the GDP per capita convergence process. Indeed, credit to households and GDP per capita have followed broadly similar tendencies over the last 20 years and it has been shown in the literature that they appear to influence each other. The consistency of this potential convergence process is also confirmed by the breakdown of household credit by type and maturity. There is a tendency towards similar household credit markets in Europe. However, it seems that this potential convergence process was slowed down by the financial crisis. Fortunately, the crisis also stabilised the share of loans in foreign currency in CEE countries. This might add more stability to credit markets in Eastern Europe.

Subgeometric rates of convergence for a class of continuous-time Markov process

Let (Phi(t))(t is an element of R+) be a Harris ergodic continuous-time Markov process on a general state space, with invariant probability measure pi. We investigate the rates of convergence of the transition function P-t(x, (.)) to pi; specifically, we find conditions under which r(t) vertical bar vertical bar P-t (x, (.)) - pi vertical bar vertical bar -> 0 as t -> infinity, for suitable subgeometric rate functions r(t), where vertical bar vertical bar - vertical bar vertical bar denotes the usual total variation norm for a signed measure. We derive sufficient conditions for the convergence to hold, in terms of the existence of suitable points on which the first hitting time moments are bounded. In particular, for stochastically ordered Markov processes, explicit bounds on subgeometric rates of convergence are obtained. These results are illustrated in several examples.

Income Ranking and convergence with physical and human capital and income equality

This paper presents an overlapping generations model with physical and human capital and income inequality. It shows that inequality impedes output growth by directly harming capital accumulation and indirectly raising the ratio of physical to human capital. The convergence speed of output growth equals the lower of the convergence speeds of the relative capital ratio and inequality, and varies with initial states. Among economies with the same balanced growth rate but different initial income levels, the ranking of income can switch in favor of those starting from low inequality and a low ratio of physical to human capital, particularly if the growth rate converges slowly. (C) 2004 Elsevier B.V. All rights reserved.

Convergence analysis of a discrete-time single-unit gradient ICA algorithm

We revisit the one-unit gradient ICA algorithm derived from the kurtosis function. By carefully studying properties of the stationary points of the discrete-time one-unit gradient ICA algorithm, with suitable condition on the learning rate, convergence can be proved. The condition on the learning rate helps alleviate the guesswork that accompanies the problem of choosing suitable learning rate in practical computation. These results may be useful to extract independent source signals on-line.