Multilevel Diversity Coding with Secure Regeneration: Separate Coding Achieves the MBR Point

The problem of multilevel diversity coding with secure regeneration (MDC-SR) is considered, which includes the problems of multilevel diversity coding with regeneration (MDC-R) and secure regenerating code (SRC) as special cases. Two outer bounds are established, showing that separate coding of different messages using the respective SRCs can achieve the minimum-bandwidth-regeneration (MBR) point of the achievable normalized storage-capacity repair-bandwidth tradeoff regions for the general MDC-SR problem. The core of the new converse results is an exchange lemma, which can be established using Han's subset inequality

Outstanding intraindividual genetic diversity in fissiparous planarians (Dugesia, Platyhelminthes) with facultative sex.

Predicted genetic consequences of asexuality include high intraindividual genetic diversity (i.e., the Meselson effect) and accumulation of deleterious mutations (i.e., Muller’s Ratchet), among others. These consequences have been largely studied in parthenogenetic organisms, but studies on fissiparous species are scarce. Differing from parthenogens, fissiparous organisms inherit part of the soma of the progenitor, including somatic mutations. Thus, in the long term, fissiparous reproduction may also result in genetic mosaicism, besides the presence of the Meselson effect and Muller’s Ratchet. Dugesiidae planarians show outstanding regeneration capabilities, allowing them to naturally reproduce by fission, either strictly or combined with sex (facultative). Therefore, they are an ideal model to analyze the genetic footprint of fissiparous reproduction, both when it is alternated with sex and when it is the only mode of reproduction

Modelling growth, recruitment and mortality to describe and simulate dynamics of subtropical rainforests following different levels of disturbance

The capacity of rainforests to recover from logging disturbance is difficult to model due to the compounding interactions between long-term disturbance effects, natural dynamics, site characteristics and tree species regeneration strategies. The aim of this study was to develop a quantitative model using over three decades of data from stands subjected to various levels of disturbance ranging from natural, through increasing intensities of tree removal to intensive logging. Data for trees >10 cm diameter at 1.3 m above the ground (dbh) in subtropical rainforest of north-east New South Wales, Australia were used. Botanical identity of trees at species level, species-specific shade tolerance and size at maturity were used to classify 117 species into five groups. These groups include the emergent and shade tolerant main canopy species, shade tolerant mid canopy species, shade tolerant understorey species, moderate shade tolerant species, and shade intolerant tree species. Multilevel nonlinear regression was used to estimate growth, recruitment and mortality parameters, based on the assumption of variations in tree species performance at both the plot and tree levels. The species group, tree size and competition from larger trees accounted for most variation at the tree level. Significant stand level variables included topography (elevation, slope and aspect), stand basal area, and time since the disturbance. The final model is a classical matrix management-oriented model with an ecological basis and maximum size-dependent parameters of ingrowth and outgrowth. The model provides a tool to simulate stand performance after logging and to assess silvicultural prescriptions before they are applied. Simulations with estimated parameters indicate that moderate harvesting (47% overstorey basal area (BA) removal) in a checkerboard of logged and unlogged patches (group selection) on a 120-year cycle could enable sustainable timber production without compromising the ecological integrity in these rainforests. This is due to reduced logging damage in group selection, which also released retained stems and facilitated recruitment of both shade tolerant and intolerant trees. Single-tree selection (35% BA removal) created small canopy gaps that resulted in low recruitment, a slight increase in the growth of retained stems and recovery time of 150 years. Intensive single-tree selection (50% BA removal) resulted in high logging damage that increased recovery time to 180 years. Intensive logging (65-80% BA removal) decreased the stem density and created larger canopy gaps allowing for high growth rates and recruitment of both shade tolerant and intolerant trees. However, few retained stems and high mortality of recruits, increased the recovery time to 180-220 years. Pre-harvest climber cutting coupled with poisoning of nontimber species followed by logging could allow harvesting on a 300-year cycle. Shorter logging cycles may lead to changes in species composition as well as in the forest structure

Weakly Secure Symmetric Multilevel Diversity Coding

Multilevel diversity coding is a classical coding model where multiple mutually independent information messages are encoded, such that different reliability requirements can be afforded to different messages. It is well known that {\em superposition coding}, namely separately encoding the independent messages, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). In the current paper, we consider weakly secure SMDC where security constraints are injected on each individual message, and provide a complete characterization of the conditions under which superposition coding is sum-rate optimal. Two joint coding strategies, which lead to rate savings compared to superposition coding, are proposed, where some coding components for one message can be used as the encryption key for another. By applying different variants of Han's inequality, we show that the lack of opportunity to apply these two coding strategies directly implies the optimality of superposition coding. It is further shown that under a set of particular security constraints, one of the proposed joint coding strategies can be used to construct a code that achieves the optimal rate region.Comment: The paper has been accepted by IEEE Transactions on Information Theor

Fundamental Limits of Exact-Repair Regenerating Codes

Understanding the fundamental limits of communication systems involves both constructing efficient coding schemes as well as proving mathematically that certain performance is impossible to achieve; the latter is known as the converse problem in information theory. This thesis focused on the converse problems for complex information systems such as self-repair distributed storage and coded caching systems, and our goal was to establish tight converse results for such systems by exploiting problem-specific combinatorial structures. The main part of this thesis dealt with exact-repair regenerating codes, which were first proposed by Dimakis et al. in 2010. In particular, we considered two extensions of the original setting of Dimakis et al., namely 1) multilevel diversity coding with regeneration and 2) secure exact-repair regenerating codes. For the problem of multilevel diversity coding with regeneration, we showed, via the proposed combinatorial approach, that the natural separate encoding strategy can achieve the optimal tradeoff between the normalized storage capacity and repair bandwidth at the minimum-bandwidth rate (MBR) point. This settled a conjecture by Tian and Liu in 2015. For the problem of secure exact-repair regenerating codes, all known results from the literature showed that the achievable tradeoff regions between the normalized storage capacity and repair bandwidth have a single corner point, achieved by a scheme proposed by Shah, Rashmi and Kumar (the SRK point). Since the achievable tradeoff regions of the exact-repair regenerating code problem without any secrecy constraints were known to have multiple corner points in general, these existing results suggested a phase-change-like behavior, i.e., enforcing a secrecy constraint immediately reduces the tradeoff region to one with a single corner point. In our work, we first showed that when the secrecy parameter is sufficiently large, the SRK point is indeed the only corner point of the tradeoff region. However, when the secrecy parameter is small, we showed that the tradeoff region can, in fact, have multiple corner points. In particular, we established a precise characterization of the tradeoff region for a particular problem instance, which has exactly two corner points. Thus, a smooth transition, instead of a phase-change-type of transition, should be expected as the secrecy constraint is gradually strengthened

Role of the social and physical neighbourhood environment in physical activity in deprived communities

Physical activity is associated with numerous physical and psychosocial health benefits, yet population levels in the United Kingdom remain low, particularly in lower socioeconomic groups. Socioecological models posit that social and physical environments have independent and interactive influences on physical activity. Although a growing body of literature has examined the independent effect of aspects of the social and physical environment, interactive effects are rarely assessed. In addition, there is limited research specifically examining independent or interactive environmental influences in populations vulnerable to lower levels of physical activity, such as those living in neighbourhoods with high levels of deprivation. This thesis examines the association between quality of the neighbourhood physical environment (aesthetics, maintenance, physical disorder) and social environment (cohesion, safety, social interaction, support, trust, empowerment) on physical activity in adults living in income-deprived communities, using Glasgow as a case study. Cross-sectional analyses, conducted using a socioecological approach, suggested independent and interactive effects of objectively measured physical environmental factors and perceived social environmental factors on neighbourhood-based walking and moderate physical activity. Longitudinal analyses found little evidence that changes in environmental measures predict change in self-reported walking. However, qualitative analyses provided insight into potential causal pathways through a system of interacting environmental factors. Together, findings from this thesis suggest a role for the quality of the neighbourhood physical and social environment on activity, providing some evidence of interactive effects of the neighbourhood social and physical environment. Further research is needed to elucidate causal relationships between the quality of the neighbourhood environment and physical activity. Findings call for a complex systems approach to understanding contextual environmental effects on physical activity in deprived communities

The Explicit Coding Rate Region of Symmetric Multilevel Diversity Coding

It is well known that {\em superposition coding}, namely separately encoding the independent sources, is optimal for symmetric multilevel diversity coding (SMDC) (Yeung-Zhang 1999). However, the characterization of the coding rate region therein involves uncountably many linear inequalities and the constant term (i.e., the lower bound) in each inequality is given in terms of the solution of a linear optimization problem. Thus this implicit characterization of the coding rate region does not enable the determination of the achievability of a given rate tuple. In this paper, we first obtain closed-form expressions of these uncountably many inequalities. Then we identify a finite subset of inequalities that is sufficient for characterizing the coding rate region. This gives an explicit characterization of the coding rate region. We further show by the symmetry of the problem that only a much smaller subset of this finite set of inequalities needs to be verified in determining the achievability of a given rate tuple. Yet, the cardinality of this smaller set grows at least exponentially fast with $L$. We also present a subset entropy inequality, which together with our explicit characterization of the coding rate region, is sufficient for proving the optimality of superposition coding