Regularity Properties and Pathologies of Position-Space Renormalization-Group Transformations

We reconsider the conceptual foundations of the renormalization-group (RG) formalism, and prove some rigorous theorems on the regularity properties and possible pathologies of the RG map. Regarding regularity, we show that the RG map, defined on a suitable space of interactions (= formal Hamiltonians), is always single-valued and Lipschitz continuous on its domain of definition. This rules out a recently proposed scenario for the RG description of first-order phase transitions. On the pathological side, we make rigorous some arguments of Griffiths, Pearce and Israel, and prove in several cases that the renormalized measure is not a Gibbs measure for any reasonable interaction. This means that the RG map is ill-defined, and that the conventional RG description of first-order phase transitions is not universally valid. For decimation or Kadanoff transformations applied to the Ising model in dimension $d \ge 3$, these pathologies occur in a full neighborhood $\{ \beta > \beta_0 ,\, |h| < \epsilon(\beta) \}$ of the low-temperature part of the first-order phase-transition surface. For block-averaging transformations applied to the Ising model in dimension $d \ge 2$, the pathologies occur at low temperatures for arbitrary magnetic-field strength. Pathologies may also occur in the critical region for Ising models in dimension $d \ge 4$. We discuss in detail the distinction between Gibbsian and non-Gibbsian measures, and give a rather complete catalogue of the known examples. Finally, we discuss the heuristic and numerical evidence on RG pathologies in the light of our rigorous theorems.Comment: 273 pages including 14 figures, Postscript, See also ftp.scri.fsu.edu:hep-lat/papers/9210/9210032.ps.

Different ways to die: cell death modes of the unicellular chlorophyte Dunaliella viridis exposed to various environmental stresses are mediated by the caspase-like activity DEVDase

Programmed cell death is necessary for homeostasis in multicellular organisms and it is also widely recognized to occur in unicellular organisms. However, the mechanisms through which it occurs in unicells, and the enzymes involved within the final response is still the subject of heated debate. It is shown here that exposure of the unicellular microalga Dunaliella viridis to several environmental stresses, induced different cell death morphotypes, depending on the stimulus received. Senescent cells demonstrated classical and unambiguous apoptotic-like characteristics such as chromatin condensation, DNA fragmentation, intact organelles, and blebbing of the cell membrane. Acute heat shock caused general swelling and altered plasma membrane, but the presence of chromatin clusters and DNA strand breaks suggested a necrotic-like event. UV irradiated cells presented changes typical for necrosis, together with apoptotic characteristics resembling an intermediate cell-death phenotype termed aponecrosis-like. Cells subjected to hyperosmotic shock revealed chromatin spotting without DNA fragmentation, and extensive cytoplasmic swelling and vacuolization, comparable to a paraptotic-like cell death phenotype. Nitrogen-starved cells showed pyknosis, blebbing, and cytoplasmic consumption, indicating a similarity to autophagic/vacuolar-like cell death. The caspase-like activity DEVDase was measured by using the fluorescent substrate Ac-DEVD-AMC and antibodies against the human caspase-3 active enzyme cross-reacted with bands, the intensity of which paralleled the activity. All the environmental stresses tested produced a substantial increase in both DEVDase activity and protein levels. The irreversible caspase-3 inhibitor Z-DEVD-FMK completely inhibited the enzymatic activity whereas serine and aspartyl proteases inhibitors did not. These results show that cell death in D. viridis does not conform to a single pattern and that environmental stimuli may produce different types of cell death depending on the type and intensity of the stimulus, all of which help to understand the cell death-dependent and cell death-independent functions of caspase-like proteins. Hence, these data support the theory that alternative, non-apoptotic programmed cell death (PCDs), exist either in parallel or in an independent manner with apoptosis and were already present in single-celled organisms that evolved some 1.2-1.6 billion years ago