On the cardinality and complexity of the set of codings for self-similar sets with positive Lebesgue measure

Let λ1,…,λn be real numbers in (0,1) and p1,…,pn be points in Rd. Consider the collection of maps fj:Rd→Rd given by fj(x)=λjx+(1−λj)pj. It is a well known result that there exists a unique nonempty compact set Λ⊂Rd satisfying Λ=∪nj=1fj(Λ). Each x∈Λ has at least one coding, that is a sequence (ϵi)∞i=1 ∈{1,…,n}N that satisfies limN→∞fϵ1…fϵN(0)=x. We study the size and complexity of the set of codings of a generic x∈Λ when Λ has positive Lebesgue measure. In particular, we show that under certain natural conditions almost every x∈Λ has a continuum of codings. We also show that almost every x∈Λ has a universal coding. Our work makes no assumptions on the existence of holes in Λ and improves upon existing results when it is assumed Λ contains no holes.

The Universal Common Good: Faith-Based Partnerships and Sustainable Development

Partnership is increasingly espoused as the best relationship between members of the sustainable development aid chain, and implies a respect for the position of all and a desire to avoid a situation where one group dominates another. It also implies a form of relationship that is not just 'better' for the sake of it but that is more able to help achieve sustainable development. However, given the inevitable inequalities in power between donors that have the resources and field partners that do not it can be hard to put this ideal into practice. This paper explores the function of partnership within a group of closely related institutions that comprise the Catholic Church development chain. The research focussed on three Catholic Church based donors (one from the USA and two from Europe) and their partners in Abuja Ecclesiastical Province, Nigeria. Relationships between and within various strata of the Church in Nigeria were also examined. Relationships were 'patchy' at all levels. One of the donors had a significant operational presence in Nigeria and this was regarded by some respondents as a parallel structure that seriously undermined local bodies. However, while problems existed, there was a sense of inter-dependence arising from a shared sense of values and Catholic Social Teaching, which allowed partners to work through their stresses and conflicts. It is the innate sustainability of the aid chain itself founded upon a set of shared values that provided the space and time for problems to be addressed. Copyright (C) 2008 John Wiley & Sons, Ltd and ERP Environment.

Moving towards a more mechanistic approach in the determination of soil heat flux from remote measurements - I. A universal approach to calculate thermal inertia

In this paper we pledge that physically based equations should be combined with remote sensing techniques to enable a more theoretically rigorous estimation of area-average soil heat flux, G. A standard physical equation (i.e. the analytical or exact method) for the estimation of G, in combination with a simple, but theoretically derived, equation for soil thermal inertia (F), provides the basis for a more transparent and readily interpretable method for the estimation of G; without the requirement for in situ instrumentation. Moreover, such an approach ensures a more universally applicable method than those derived from purely empirical studies (employing vegetation indices and albedo, for example). Hence, a new equation for the estimation of Gamma(for homogeneous soils) is discussed in this paper which only requires knowledge of soil type, which is readily obtainable from extant soil databases and surveys, in combination with a coarse estimate of moisture status. This approach can be used to obtain area-averaged estimates of Gamma(and thus G, as explained in paper II) which is important for large-scale energy balance studies that employ aircraft or satellite data. Furthermore, this method also relaxes the instrumental demand for studies at the plot and field scale (no requirement for in situ soil temperature sensors, soil heat flux plates and/or thermal conductivity sensors). In addition, this equation can be incorporated in soil-vegetation-atmosphere-transfer models that use the force restore method to update surface temperatures (such as the well-known ISBA model), to replace the thermal inertia coefficient.

Non-commutative symbolic coding

We give a non-commutative generalization of classical symbolic coding in the presence of a synchronizing word. This is done by a scattering theoretical approach. Classically, the existence of a synchronizing word turns out to be equivalent to asymptotic completeness of the corresponding Markov process. A criterion for asymptotic completeness in general is provided by the regularity of an associated extended transition operator. Commutative and non-commutative examples are analysed.

Selection of candidate coding DNA barcoding regions for use on land plants

An in silico screen of 41 of the 81 coding regions of the Nicotiana plastid genome generated a shortlist of 12 candidates as DNA barcoding loci for land plants. These loci were evaluated for amplification and sequence variation against a reference set of 98 land plant taxa. The deployment of multiple primers and a modified multiplexed tandem polymerase chain reaction yielded 85–94% amplification across taxa, and mean sequence differences between sister taxa of 6.1 from 156 bases of accD to 22 from 493 bases of matK. We conclude that loci should be combined for effective diagnosis, and recommend further investigation of the following six loci: matK, rpoB, rpoC1, ndhJ, ycf5 and accD.

Coding of visual space during motor preparation: approaching objects rapidly modulate corticospinal excitability in hand-centered coordinates

Defensive behaviors, such as withdrawing your hand to avoid potentially harmful approaching objects, rely on rapid sensorimotor transformations between visual and motor coordinates. We examined the reference frame for coding visual information about objects approaching the hand during motor preparation. Subjects performed a simple visuomanual task while a task-irrelevant distractor ball rapidly approached a location either near to or far from their hand. After the distractor ball appearance, single pulses of transcranial magnetic stimulation were delivered over the subject's primary motor cortex, eliciting motor evoked potentials (MEPs) in their responding hand. MEP amplitude was reduced when the ball approached near the responding hand, both when the hand was on the left and the right of the midline. Strikingly, this suppression occurred very early, at 70-80ms after ball appearance, and was not modified by visual fixation location. Furthermore, it was selective for approaching balls, since static visual distractors did not modulate MEP amplitude. Together with additional behavioral measurements, we provide converging evidence for automatic hand-centered coding of visual space in the human brain.

Evidence for unusual spatial location coding in Williams syndrome: an explanation for the local bias in visuo-spatial construction tasks?

Individuals with Williams syndrome (WS) display poor visuo-spatial cognition relative to verbal abilities. Furthermore, whilst perceptual abilities are delayed, visuo-spatial construction abilities are comparatively even weaker, and are characterised by a local bias. We investigated whether his differentiation in visuo-spatial abilities can be explained by a deficit in coding spatial location in WS. This can be measured by assessing participants' understanding of the spatial relations between objects within a visual scene. Coordinate and categorical spatial relations were investigated independently in four participant groups: 21 individuals with WS; 21 typically developing (TD) children matched for non-verbal ability; 20 typically developing controls of a lower non-verbal ability; and 21 adults. A third task measured understanding of visual colour relations. Results indicated first, that the comprehension of categorical and coordinate spatial relations is equally poor in WS. Second, that the comprehension of visual relations is also at an equivalent level to spatial relational understanding in this population. These results can explain the difference in performance on visuo-spatial perception and construction tasks in WS. In addition, both the WS and control groups displayed response biases in the spatial tasks. However, the direction of bias differed across the groups. This finding is explored in relation to current theories of spatial location coding. (c) 2005 Elsevier Inc. All rights reserved.

Orientation coding: a specific deficit in Williams syndrome?

Williams syndrome (WS) is a rare genetic disorder with a unique cognitive profile in which verbal abilities are markedly stronger than visuospatial abilities. This study investigated the claim that orientation coding is a specific deficit within the visuospatial domain in WS. Experiment I employed a simplified version of the Benton Judgement of Line Orientation task and a control, length-matching task. Results demonstrated comparable levels of orientation matching performance in the group with WS and a group of typically developing (TD) controls matched by nonverbal ability, although it is possible that floor effects masked group differences. A group difference was observed in the length-matching task due to stronger performance from the control group. Experiment 2 employed an orientation-discrimination task and a length-discrimination task. Contrary to previous reports, the results showed that individuals with WS were able to code by orientation to a comparable level as that of their matched controls. This demonstrates that, although some impairment is apparent, orientation coding does not represent a specific deficit in WS. Comparison between Experiments I and 2 suggests that orientation coding is vulnerable to task complexity. However, once again, this vulnerability does not appear to be specific to the population with WS, as it was also apparent in the TD controls.

Performance of GPRS coding scheme detection under severe multipath and co-channel interference as a function of soft-bit width

The General Packet Radio Service (GPRS) has been developed for the mobile radio environment to allow the migration from the traditional circuit switched connection to a more efficient packet based communication link particularly for data transfer. GPRS requires the addition of not only the GPRS software protocol stack, but also more baseband functionality for the mobile as new coding schemes have be en defined, uplink status flag detection, multislot operation and dynamic coding scheme detect. This paper concentrates on evaluating the performance of the GPRS coding scheme detection methods in the presence of a multipath fading channel with a single co-channel interferer as a function of various soft-bit data widths. It has been found that compressing the soft-bit data widths from the output of the equalizer to save memory can influence the likelihood decision of the coding scheme detect function and hence contribute to the overall performance loss of the system. Coding scheme detection errors can therefore force the channel decoder to either select the incorrect decoding scheme or have no clear decision which coding scheme to use resulting in the decoded radio block failing the block check sequence and contribute to the block error rate. For correct performance simulation, the performance of the full coding scheme detection must be taken into account.

Two-pass hexagonal algorithm with parallel implementation for video coding

This paper presents a paralleled Two-Pass Hexagonal (TPA) algorithm constituted by Linear Hashtable Motion Estimation Algorithm (LHMEA) and Hexagonal Search (HEXBS) for motion estimation. In the TPA, Motion Vectors (MV) are generated from the first-pass LHMEA and are used as predictors for second-pass HEXBS motion estimation, which only searches a small number of Macroblocks (MBs). We introduced hashtable into video processing and completed parallel implementation. We propose and evaluate parallel implementations of the LHMEA of TPA on clusters of workstations for real time video compression. It discusses how parallel video coding on load balanced multiprocessor systems can help, especially on motion estimation. The effect of load balancing for improved performance is discussed. The performance of the algorithm is evaluated by using standard video sequences and the results are compared to current algorithms.

Improved two-pass hexagonal algorithm with parallel implementation for video coding - art. no. 60630J

This paper presents an improved parallel Two-Pass Hexagonal (TPA) algorithm constituted by Linear Hashtable Motion Estimation Algorithm (LHMEA) and Hexagonal Search (HEXBS) for motion estimation. Motion Vectors (MV) are generated from the first-pass LHMEA and used as predictors for second-pass HEXBS motion estimation, which only searches a small number of Macroblocks (MBs). We used bashtable into video processing and completed parallel implementation. The hashtable structure of LHMEA is improved compared to the original TPA and LHMEA. We propose and evaluate parallel implementations of the LHMEA of TPA on clusters of workstations for real time video compression. The implementation contains spatial and temporal approaches. The performance of the algorithm is evaluated by using standard video sequences and the results are compared to current algorithms.