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 $\text{PL}(u(ab)^j)-\text{PL}(u)\geq 0$

Canonical Representatives of Morphic Permutations

An infinite permutation can be defined as a linear ordering of the set of natural numbers. In particular, an infinite permutation can be constructed with an aperiodic infinite word over $\{0,\ldots,q-1\}$ as the lexicographic order of the shifts of the word. In this paper, we discuss the question if an infinite permutation defined this way admits a canonical representative, that is, can be defined by a sequence of numbers from [0, 1], such that the frequency of its elements in any interval is equal to the length of that interval. We show that a canonical representative exists if and only if the word is uniquely ergodic, and that is why we use the term ergodic permutations. We also discuss ways to construct the canonical representative of a permutation defined by a morphic word and generalize the construction of Makarov, 2009, for the Thue-Morse permutation to a wider class of infinite words.Comment: Springer. WORDS 2015, Sep 2015, Kiel, Germany. Combinatorics on Words: 10th International Conference. arXiv admin note: text overlap with arXiv:1503.0618

Composition of fish communities in macrotidal salt marshes of the Mont Saint-Michel bay (France)

At least 100 fish species are known to be present in the intertidal areas (estuaries, mudflats and salt marshes) of Mont Saint-Michel Bay. These and other comparable shallow marine coastal waters, such as estuaries and lagoons, play a nursery role for many fish species. However, in Europe little attention has been paid to the value of tidal salt marshes for fishes. Between March 1996 and April 1999, 120 tides were sampled in a tidal creek. A total of 31 species were caught. This community was largely dominated by mullets (Liza ramada represent 87% of the total biomass) and sand gobies(Pomatoschistus minutus and P. lozanoi represent 82% of the total numbers). These species and also Gasterosteus aculeatus, Syngnathus rostellatus, Dicentrarchus labrax, Mugil spp., Liza aurata and Sprattus sprattus were the most frequent species (>50% of monthly frequency of occurrence). In Europe, salt marshes and their creeks are flooded only during high spring tides. So, fishes only invade this environment during short immersion periods, and no species can be considered as marsh resident. But, the salt marsh was colonized by fish every time the tide reached the creek, and during the short time of flood, dominant fishes fed actively and exploited the high productivity. Nevertheless, this study shows that there is little interannual variation in the fish community and there are three ‘ seasons ’ in the fish fauna of the marsh. Marine straggler and marine estuarine dependent species colonize marshes between spring (recruitment period in the bay) and autumn before returning into deeper adjacent waters. Estuarine fishes are present all year round with maximum abundances in the end of summer. The presence of fishes confirms that this kind of wetland plays an important trophic and nursery role for these species. Differences in densities and stages distribution of these species into Mont Saint-Michel systems (tidal mudflats, estuaries and tidal salt marshes) can reduce the trophic competition

Building development and roads: implications for the distribution of stone curlews across the Brecks

Background: Substantial new housing and infrastructure development planned within England has the potential to conflict with the nature conservation interests of protected sites. The Breckland area of eastern England (the Brecks) is designated as a Special Protection Area for a number of bird species, including the stone curlew (for which it holds more than 60% of the UK total population). We explore the effect of buildings and roads on the spatial distribution of stone curlew nests across the Brecks in order to inform strategic development plans to avoid adverse effects on such European protected sites. Methodology: Using data across all years (and subsets of years) over the period 1988 – 2006 but restricted to habitat areas of arable land with suitable soils, we assessed nest density in relation to the distances to nearest settlements and to major roads. Measures of the local density of nearby buildings, roads and traffic levels were assessed using normal kernel distance-weighting functions. Quasi-Poisson generalised linear mixed models allowing for spatial auto-correlation were fitted. Results: Significantly lower densities of stone curlew nests were found at distances up to 1500m from settlements, and distances up to 1000m or more from major (trunk) roads. The best fitting models involved optimally distance-weighted variables for the extent of nearby buildings and the trunk road traffic levels. Significance : The results and predictions from this study of past data suggests there is cause for concern that future housing development and associated road infrastructure within the Breckland area could have negative impacts on the nesting stone curlew population. Given the strict legal protection afforded to the SPA the planning and conservation bodies have subsequently agreed precautionary restrictions on building development within the distances identified and used the modelling predictions to agree mitigation measures for proposed trunk road developments

Whey protein lowers systolic blood pressure and Ca-caseinate reduces serum TAG after a high-fat meal in mildly hypertensive adults

Epidemiological studies show an inverse association between dairy consumption and blood pressure (BP) but there are few data on the postprandial effects of milk proteins. This study examined their effects, compared to maltodextrin, on postprandial BP and other CVD risk markers in volunteers with mild and pre-hypertension over an 8 h period. In this double-blinded, randomised, cross-over, controlled study 27 adults ingested a high-fat, isoenergetic breakfast and lunch with 28 g whey protein, 28 g Ca-caseinate or 27 g maltodextrin. Whey protein reduced systolic BP compared with Ca-caseinate (−15.2 ± 13.6 mmHg) and maltodextrin (−23.4 ± 10.5 mmHg) up to 5 h post-ingestion. There was an improvement in arterial stiffness after whey protein compared with maltodextrin (incremental Area Under the Curve- iAUC0–8h: +14.4 ± 6.2%). Despite similar glucose levels after both whey protein and Ca-caseinate, whey protein induced a higher insulin response than Cacaseinate (iAUC0–8h: +219.5 ± 54.6 pmol/L). Ca-caseinate induced less suppression of non-esterified fatty acids than whey protein (iAUC0–5h: −58.9 ± 135.5 μmol/L) and maltodextrin (iAUC0–5h: −106.9 ± 89.4 μmol/L) and induced a smaller postprandial triacylglycerol response than whey protein (iAUC0–8h: −1.68 ± 0.6 mmol/L). Milk proteins co-ingestion with high-fat meals may have the potential to maintain or improve CVD risk factors

Setback distances as a conservation tool in wildlife-human interactions : testing their efficacy for birds affected by vehicles on open-coast sandy beaches

In some wilderness areas, wildlife encounter vehicles disrupt their behaviour and habitat use. Changing driver behaviour has been proposed where bans on vehicle use are politically unpalatable, but the efficacy of vehicle setbacks and reduced speeds remains largely untested. We characterised bird-vehicle encounters in terms of driver behaviour and the disturbance caused to birds, and tested whether spatial buffers or lower speeds reduced bird escape responses on open beaches. Focal observations showed that: i) most drivers did not create sizeable buffers between their vehicles and birds; ii) bird disturbance was frequent; and iii) predictors of probability of flushing (escape) were setback distance and vehicle type (buses flushed birds at higher rates than cars). Experiments demonstrated that substantial reductions in bird escape responses required buffers to be wide (> 25 m) and vehicle speeds to be slow (< 30 km h-1). Setback distances can reduce impacts on wildlife, provided that they are carefully designed and derived from empirical evidence. No speed or distance combination we tested, however, eliminated bird responses. Thus, while buffers reduce response rates, they are likely to be much less effective than vehicle-free zones (i.e. beach closures), and rely on changes to current driver behaviou

Setback distances as a conservation tool in wildlife-human interactions : testing their efficacy for birds affected by vehicles on open-coast sandy beaches

In some wilderness areas, wildlife encounter vehicles disrupt their behaviour and habitat use. Changing driver behaviour has been proposed where bans on vehicle use are politically unpalatable, but the efficacy of vehicle setbacks and reduced speeds remains largely untested. We characterised bird-vehicle encounters in terms of driver behaviour and the disturbance caused to birds, and tested whether spatial buffers or lower speeds reduced bird escape responses on open beaches. Focal observations showed that: i) most drivers did not create sizeable buffers between their vehicles and birds; ii) bird disturbance was frequent; and iii) predictors of probability of flushing (escape) were setback distance and vehicle type (buses flushed birds at higher rates than cars). Experiments demonstrated that substantial reductions in bird escape responses required buffers to be wide (> 25 m) and vehicle speeds to be slow (< 30 km h-1). Setback distances can reduce impacts on wildlife, provided that they are carefully designed and derived from empirical evidence. No speed or distance combination we tested, however, eliminated bird responses. Thus, while buffers reduce response rates, they are likely to be much less effective than vehicle-free zones (i.e. beach closures), and rely on changes to current driver behaviou

Milk and dairy products: good or bad for human health? An assessment of the totality of scientific evidence

Background: There is scepticism about health effects of dairy products in the public, which is reflected in an increasing intake of plant-based drinks, for example, from soy, rice, almond, or oat. Objective: This review aimed to assess the scientific evidence mainly from meta-analyses of observational studies and randomised controlled trials, on dairy intake and risk of obesity, type 2 diabetes, cardiovascular disease, osteoporosis, cancer, and all-cause mortality. Results: The most recent evidence suggested that intake of milk and dairy products was associated with reduced risk of childhood obesity. In adults, intake of dairy products was shown to improve body composition and facilitate weight loss during energy restriction. In addition, intake of milk and dairy products was associated with a neutral or reduced risk of type 2 diabetes and a reduced risk of cardiovascular disease, particularly stroke. Furthermore, the evidence suggested a beneficial effect of milk and dairy intake on bone mineral density but no association with risk of bone fracture. Among cancers, milk and dairy intake was inversely associated with colorectal cancer, bladder cancer, gastric cancer, and breast cancer, and not associated with risk of pancreatic cancer, ovarian cancer, or lung cancer,while the evidence for prostate cancer risk was inconsistent.Finally,consumption of milk and dairy products was not associated with all-cause mortality. Calcium-fortified plant-based drinks have been included as an alternative to dairy products in the nutrition recommendations in several countries. However, nutritionally, cow’s milk and plant-based drinks are completely different foods,and an evidence-based conclusion on the health value of the plant-based drinks requires more studies in humans. Conclusion: The totality of available scientific evidence supports that intake of milk and dairy products contribute to meet nutrient recommendations, and may protect against the most prevalent chronic diseases, whereas very few adverse effects have been reported