Palindromic Length of Words with Many Periodic Palindromes

The palindromic length $\text{PL}(v)$ of a finite word $v$ is the minimal number of palindromes whose concatenation is equal to $v$. In 2013, Frid, Puzynina, and Zamboni conjectured that: If $w$ is an infinite word and $k$ is an integer such that $\text{PL}(u)\leq k$ for every factor $u$ of $w$ then $w$ is ultimately periodic. Suppose that $w$ is an infinite word and $k$ is an integer such $\text{PL}(u)\leq k$ for every factor $u$ of $w$. Let $\Omega(w,k)$ be the set of all factors $u$ of $w$ that have more than $\sqrt[k]{k^{-1}\vert u\vert}$ palindromic prefixes. We show that $\Omega(w,k)$ is an infinite set and we show that for each positive integer $j$ there are palindromes $a,b$ and a word $u\in \Omega(w,k)$ such that $(ab)^j$ is a factor of $u$ and $b$ is nonempty. Note that $(ab)^j$ is a periodic word and $(ab)^ia$ is a palindrome for each $i\leq j$. These results justify the following question: What is the palindromic length of a concatenation of a suffix of $b$ and a periodic word $(ab)^j$ with "many" periodic palindromes? It is known that $\lvert\text{PL}(uv)-\text{PL}(u)\rvert\leq \text{PL}(v)$, where $u$ and $v$ are nonempty words. The main result of our article shows that if $a,b$ are palindromes, $b$ is nonempty, $u$ is a nonempty suffix of $b$, $\vert ab\vert$ is the minimal period of $aba$, and $j$ is a positive integer with $j\geq3\text{PL}(u)$ then $\text{PL}(u(ab)^j)-\text{PL}(u)\geq 0$

An ecological status indicator for all time: Are AMBI and M-AMBI effective indicators of change in deep time?

Increasingly environmental management seeks to limit the impacts of human activities on ecosystems relative to some ‘reference’ condition, which is often the presumed pre-impacted state, however such information is limited. We explore how marine ecosystems in deep time (Late Jurassic) are characterised by AZTI's Marine Biotic Index (AMBI), and how the indices responded to natural perturbations. AMBI is widely used to detect the impacts of human disturbance and to establish management targets, and this study is the first application of these indices to a fossil fauna. Our results show AMBI detected changes in past seafloor communities (well-preserved fossil deposits) that underwent regional deoxygenation in a manner analogous to those experiencing two decades of organic pollution. These findings highlight the potential for palaeoecological data to contribute to reconstructions of pre-human marine ecosystems, and hence provide information to policy makers and regulators with greater temporal context on the nature of ‘pristine’ marine ecosystems

Influence of climate-induced biogeographic range shifts on mudflat ecological functioning in the subtropics

A growing volume of evidence shows that the broad-scale biogeographic redistribution of species is occurring in response to increasing global temperatures. The present study documents poleward movements of up to eight species of nominally ‘tropical’ macroinvertebrates (molluscs, polychaetes, crustaceans and foraminifera) from intertidal mudflats on the south east coast of Australia. The speed of movement was comparable with that for Australian marine fauna generally, but was particularly fast for worms and molluscs (~70–300 km decade−1) and may be facilitated by the southward flowing East Australia Current. Further, two temperate taxa appear to have extended their ranges northwards. Changes in species biogeographic ranges raises questions surrounding the response of ecological processes within the altered and novel species combinations, including processes that underpin valuable ecosystem services. Using biological traits analysis to investigate how the observed species range changes might have impacted mudflat ecosystem functioning, and to predict the possible impacts of further poleward movements of tropical taxa. Our models suggest the changes to date, and those likely to occur in the near future, are within the envelope whereby ecological functioning is maintained by functional compensation and redundancy within the mudflat assemblage. However, in the most extreme scenario the replacement of temperate by tropical taxa resulted in major changes in ecological functioning with potential impacts on nutrient cycling and C-cycling, undermining the potential of these mudflats to continue to deliver critical ecosystem services. The widespread nature of biogeographic range shifts and the value of coastal systems should add further weight to calls for global action to mitigate global temperature change

Species-Specific Effects on Ecosystem Functioning Can Be Altered by Interspecific Interactions

Biological assemblages are constantly undergoing change, with species being introduced, extirpated and experiencing shifts in their densities. Theory and experimentation suggest that the impacts of such change on ecosystem functioning should be predictable based on the biological traits of the species involved. However, interspecific interactions could alter how species affect functioning, with the strength and sign of interactions potentially depending on environmental context (e.g. homogenous vs. heterogeneous conditions) and the function considered. Here, we assessed how concurrent changes to the densities of two common marine benthic invertebrates, Corophium volutator and Hediste diversicolor, affected the ecological functions of organic matter consumption and benthic-pelagic nutrient flux. Complementary experiments were conducted within homogenous laboratory microcosms and naturally heterogeneous field plots. When the densities of the species were increased within microcosms, interspecific interactions enhanced effects on organic matter consumption and reduced effects on nutrient flux. Trait-based predictions of how each species would affect functioning were only consistently supported when the density of the other species was low. In field plots, increasing the density of either species had a positive effect on organic matter consumption (with no significant interspecific interactions) but no effect on nutrient flux. Our results indicate that species-specific effects on ecosystem functioning can be altered by interspecific interactions, which can be either facilitative (positive) or antagonistic (negative) depending on the function considered. The impacts of biodiversity change may therefore not be predictable based solely on the biological traits of the species involved. Possible explanations for why interactions were detected in microcosms but not in the field are discussed

Modelling the interior sound field of a railway vehicle using statistical energy analysis

The sound field in train compartments, treated as a series of connected air cavities, is modelled using statistical energy analysis, SEA. For the case under study, with five cavities in series and the source in the second cavity, a closed-form solution is obtained. An adjusted SEA model is used to predict the rate of spatial decay within a cavity. The SEA model is validated using results from a ray tracing method and from scale model measurements. For the octave bands 500-4000 Hz, good agreement is shown between the results from measurements, the ray tracing and the SEA model, for the two saloons closest to the source cavity (a vestibule). The SEA model was shown to slightly underestimate the rate of spatial decay within a cavity. It is concluded that a reasonable cause is the additional diffusion due to the seating