Morphological development of Corydoras aff. paleatus (Siluriformes, Callichthyidae) and correlation with the emergence of motor and social behaviors

Here we examine major anatomical characteristics of Corydoras aff. paleatus (Jenyns, 1842) post-hatching development, in parallel with its neurobehavioral evolution. Eleutheroembryonic phase, 4.3-8.8 days post-fertilization (dpf); 4.3-6.4 mm standard length (SL) encompasses from hatching to transition to exogenous feeding. Protopterygiolarval phase (8.9-10.9 dpf; 6.5-6.7 mm SL) goes from feeding transition to the commencement of unpaired fin differentiation, which marks the start of pterygiolarval phase (11-33 dpf; 6.8-10.7 mm SL) defined by appearance of lepidotrichia in the dorsal part of the median finfold. This phase ends with the full detachment and differentiation of unpaired fins, events signaling the commencement of the juvenile period (34-60 dpf; 10.8-18.0 mm SL). Eleutheroembryonic phase focuses on hiding and differentiation of mechanosensory, chemosensory and central neural systems, crucial for supplying the larval period with efficient escape and nutrient detection-capture neurocircuits. Protopterygiolarval priorities include visual development and respiratory, digestive and hydrodynamic efficiencies. Pterygiolarval priorities change towards higher swimming efficacy, including carangiform and vertical swimming, necessary for the high social interaction typical of this species. At the end of the protopterygiolarval phase, simple resting and foraging aggregations are seen. Resting and foraging shoals grow in complexity and participant number during pterygiolarval phase, but particularly during juvenile period.

Single period Markowitz portfolio selection, performance gauging and duality: a variation on Luenberger's shortage function

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

Embedding theorems of function classes, IV

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