The role of infrequent and extraordinary deep dives in leatherback turtles (Dermochelys coriacea)

Infrequent and exceptional behaviours can provide insight into the ecology and physiology of a particular species. Here we examined extraordinarily deep (300-1250 m) and protracted (>1h) dives made by critically endangered leatherback turtles (Dermochelys coriacea) in the context of three previously suggested hypotheses: predator evasion, thermoregulation and exploration for gelatinous prey. Data were obtained via satellite relay data loggers attached to adult turtles at nesting beaches (N=11) and temperate foraging grounds (N=2), constituting a combined tracking period of 9.6 years (N=26,146 dives) and spanning the entire North Atlantic Ocean. Of the dives, 99.6% (N=26,051) were to depths <300 m with only 0.4% (N=95) extending to greater depths (subsequently termed 'deep dives'). Analysis suggested that deep dives: (1) were normally distributed around midday; (2) may exceed the inferred aerobic dive limit for the species; (3) displayed slow vertical descent rates and protracted durations; (4) were much deeper than the thermocline; and (5) occurred predominantly during transit, yet ceased once seasonal residence on foraging grounds began. These findings support the hypothesis that deep dives are periodically employed to survey the water column for diurnally descending gelatinous prey. If a suitable patch is encountered then the turtle may cease transit and remain within that area, waiting for prey to approach the surface at night. If unsuccessful, then migration may continue until a more suitable site is encountered. Additional studies using a meta-analytical approach are nonetheless recommended to further resolve this matter.

The mechanical and rheological characterisation of implantable medical devices formulated from binary mixtures of cellulose derivatives

This study highlights the potential associated with utilising multi-component polymeric gels to formulate materials that possess unique rheological and mechanical properties. The synergistic effect* and interaction between hydroxyethylcellulose (HEC) and sodium carboxymethylcellulose (NaCMC), polymers which are commonly employed as drug delivery platforms for implantable medical devices (1), have been determined using dynamic, continuous shear and texture profile analysis. * The difference between the actual response of a binary mixture and the sum of the two components comprising the mixture Increases in polymer concentration resulted in an increase in G', G? and ?' whereas tan d decreased. Similarly, significant increases were also apparent in continuous shear and texture analysis. All binary mixtures showed positive synergy values which may suggest associative interaction between the two components.

The proof of Kontsevich's periodicity conjecture on noncommutative birational transformations

For an arbitrary associative unital ring RR, let J1J1 and J2J2 be the following noncommutative, birational, partly defined involutions on the set M3(R)M3(R) of 3×33×3 matrices over RR: J1(M)=M−1J1(M)=M−1 (the usual matrix inverse) and J2(M)jk=(Mkj)−1J2(M)jk=(Mkj)−1 (the transpose of the Hadamard inverse).

We prove the surprising conjecture by Kontsevich that (J2∘J1)3(J2∘J1)3 is the identity map modulo the DiagL×DiagRDiagL×DiagR action (D1,D2)(M)=D−11MD2(D1,D2)(M)=D1−1MD2 of pairs of invertible diagonal matrices. That is, we show that, for each MM in the domain where (J2∘J1)3(J2∘J1)3 is defined, there are invertible diagonal 3×33×3 matrices D1=D1(M)D1=D1(M) and D2=D2(M)D2=D2(M) such that (J2∘J1)3(M)=D−11MD2(J2∘J1)3(M)=D1−1MD2.