Maximum Entropy Criterion for Moment Indeterminacy of Probability Densities

We deal with absolutely continuous probability distributions with finite all-positive integer-order moments. It is well known that any such distribution is either uniquely determined by its moments (M-determinate), or it is non-unique (M-indeterminate). In this paper, we follow the maximum entropy approach and establish a new criterion for the M-indeterminacy of distributions on the positive half-line (Stieltjes case). Useful corollaries are derived for M-indeterminate distributions on the whole real line (Hamburger case). We show how the maximum entropy is related to the symmetry property and the M-indeterminacy.

Plaque-infiltrating T lymphocytes in patients with carotid atherosclerosis: an insight into the cellular mechanisms associated to plaque destabilization

AIM

Inflammation plays a crucial role in the progression of atherosclerotic plaques. The aim of the present study was to investigate phenotypic and functional characteristics of plaque-infiltrating T lymphocytes associated with a complicated phenotype of carotid atherosclerotic lesions.

METHODS

Atherosclerotic plaques were obtained from 17 patients undergoing carotid endarterectomy and cultured to isolate infiltrating T lymphocytes. Blood samples were obtained from patients and from 20 sex- and age-matched healthy subjects. The presence of lymphocytes (CD3+ cells) within atherosclerotic plaques was determined by immunohistochemistry. Phenotypic characteristics and intracellular cytokine expression of plaque-infiltrating and circulating T lymphocytes were determined by flow cytometry. Cytokine levels in supernatants from infiltrating T cell cultures were evaluated by enzyme-linked immunosorbent assay.

RESULTS

A higher number of CD3+ cells was detected in complicated than in uncomplicated plaques. Complicated plaques had higher percentages of tumor necrosis factor (TNF)-α- and interferon (IFN)-γ- positive cells than uncomplicated ones, especially in CD4+ subpopulation. In patients the percentages of TNF-α-positive cells were higher in infiltrating than in circulating lymphocyte samples. Intracellular TNF-α, IFN-γ, interleukin (IL)-4 and IL-10 expression resulted higher in circulating lymphocyte samples from patients than in those from healthy subjects. Supernatants of infiltrating T cell cultures from complicated plaques showed higher levels of TNF-α and lower levels of IL-4 than those from uncomplicated plaques.

CONCLUSION

Our data provide new information on the presence of increased percentages of pro-inflammatory T lymphocytes in complicated plaques with respect to uncomplicated ones and support the concept of the key role played by activated T cells in the progression of atherosclerotic lesions.