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Not all (possibly) "random" sequences are created equal.

ABSTRACT: The need to assess the randomness of a single sequence, especially a finite sequence, is ubiquitous, yet is unaddressed by axiomatic probability theory. Here, we assess randomness via approximate entropy (ApEn), a computable measure of sequential irregularity, applicable to single sequences of both (even very short) finite and infinite length. We indicate the novelty and facility of the multidimensional viewpoint taken by ApEn, in contrast to classical measures. Furthermore and notably, for finite length, finite state sequences, one can identify maximally irregular sequences, and then apply ApEn to quantify the extent to which given sequences differ from maximal irregularity, via a set of deficit (def(m)) functions. The utility of these def(m) functions which we show allows one to considerably refine the notions of probabilistic independence and normality, is featured in several studies, including (i) digits of e, pi, radical2, and radical3, both in base 2 and in base 10, and (ii) sequences given by fractional parts of multiples of irrationals. We prove companion analytic results, which also feature in a discussion of the role and validity of the almost sure properties from axiomatic probability theory insofar as they apply to specified sequences and sets of sequences (in the physical world). We conclude by relating the present results and perspective to both previous and subsequent studies.

SUBMITTER: Pincus S

PROVIDER: S-EPMC20470 | biostudies-other | 1997 Apr

REPOSITORIES: biostudies-other

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Project description:Antibodies that block T cell inhibition via the immune checkpoints CTLA-4 and PD-1 have revolutionized cancer therapy during the last 15 years. T cells express additional inhibitory surface receptors that are considered to have potential as targets in cancer immunotherapy. Antibodies against LAG-3 and TIM-3 are currently clinically tested to evaluate their effectiveness in patients suffering from advanced solid tumors or hematologic malignancies. In addition, blockade of the inhibitory BTLA receptors on human T cells may have potential to unleash T cells to effectively combat cancer cells. Much research on these immune checkpoints has focused on mouse models. The analysis of animals that lack individual inhibitory receptors has shed some light on the role of these molecules in regulating T cells, but also immune responses in general. There are current intensive efforts to gauge the efficacy of antibodies targeting these molecules called immune checkpoint inhibitors alone or in different combinations in preclinical models of cancer. Differences between mouse and human immunology warrant studies on human immune cells to appreciate the potential of individual pathways in enhancing T cell responses. Results from clinical studies are not only highlighting the great benefit of immune checkpoint inhibitors for treating cancer but also yield precious information on their role in regulating T cells and other cells of the immune system. However, despite the clinical relevance of CTLA-4 and PD-1 and the high potential of the emerging immune checkpoints, there are still substantial gaps in our understanding of the biology of these molecules, which might prevent the full realization of their therapeutic potential. This review addresses PD-1, CTLA-4, BTLA, LAG-3, and TIM-3, which are considered major inhibitory immune checkpoints expressed on T cells. It provides summaries of our current conception of the role of these molecules in regulating T cell responses, and discussions about major ambiguities and gaps in our knowledge. We emphasize that each of these molecules harbors unique properties that set it apart from the others. Their distinct functional profiles should be taken into account in therapeutic strategies that aim to exploit these pathways to enhance immune responses to combat cancer.

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Not all (possibly) "random" sequences are created equal.

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