On complex-valued 2D eikonals. Part four: continuation past a caustic

Theories of monochromatic high-frequency electromagnetic fields have been designed by Felsen, Kravtsov, Ludwig and others with a view to portraying features that are ignored by geometrical optics. These theories have recourse to eikonals that encode information on both phase and amplitude -- in other words, are complex-valued. The following mathematical principle is ultimately behind the scenes: any geometric optical eikonal, which conventional rays engender in some light region, can be consistently continued in the shadow region beyond the relevant caustic, provided an alternative eikonal, endowed with a non-zero imaginary part, comes on stage. In the present paper we explore such a principle in dimension $2.$ We investigate a partial differential system that governs the real and the imaginary parts of complex-valued two-dimensional eikonals, and an initial value problem germane to it. In physical terms, the problem in hand amounts to detecting waves that rise beside, but on the dark side of, a given caustic. In mathematical terms, such a problem shows two main peculiarities: on the one hand, degeneracy near the initial curve; on the other hand, ill-posedness in the sense of Hadamard. We benefit from using a number of technical devices: hodograph transforms, artificial viscosity, and a suitable discretization. Approximate differentiation and a parody of the quasi-reversibility method are also involved. We offer an algorithm that restrains instability and produces effective approximate solutions.Comment: 48 pages, 15 figure

Molecular mechanisms of cell death: recommendations of the Nomenclature Committee on Cell Death 2018.

Over the past decade, the Nomenclature Committee on Cell Death (NCCD) has formulated guidelines for the definition and interpretation of cell death from morphological, biochemical, and functional perspectives. Since the field continues to expand and novel mechanisms that orchestrate multiple cell death pathways are unveiled, we propose an updated classification of cell death subroutines focusing on mechanistic and essential (as opposed to correlative and dispensable) aspects of the process. As we provide molecularly oriented definitions of terms including intrinsic apoptosis, extrinsic apoptosis, mitochondrial permeability transition (MPT)-driven necrosis, necroptosis, ferroptosis, pyroptosis, parthanatos, entotic cell death, NETotic cell death, lysosome-dependent cell death, autophagy-dependent cell death, immunogenic cell death, cellular senescence, and mitotic catastrophe, we discuss the utility of neologisms that refer to highly specialized instances of these processes. The mission of the NCCD is to provide a widely accepted nomenclature on cell death in support of the continued development of the field

Melanocortin-4 Receptor Gene Mutations in Obese Slovak Children

Summary The most common etiology of non-syndromic monogenic obesit

Chronic lymphocytic leukaemia is driven by antigen-independent cell-autonomous signalling

Immunobiology of allogeneic stem cell transplantation and immunotherapy of hematological disease

Microevolution and maternal effects on tadpole Rana temporaria growth and development rate

Can variation in egg size explain the local variation in tadpole growth and development of the common frog Rana temporaria or are other mechanisms, e.g. microevolution, involved? To study this, tadpoles were raised in outdoor tanks. Each tank housed tadpoles from one clutch. Eggs were collected during 2 years from six different ponds and their sizes were measured. Large eggs gave rise to tadpoles that grew and developed faster than those hatched from small eggs. Tadpoles from large eggs thus metamorphosed earlier but, because they grew for a shorter time, size at metamorphosis was not affected by initial egg size. Tadpoles from different ponds differed in strategy; after correcting for egg size effects, tadpoles from some ponds tended to metamorphose earlier and at a larger size than those from others. These ponds occasionally dry out during or before the tadpoles period of metamorphosis. I argue that the detected pond differences are genetically based and represent a case of microevolution