title: How to generalise demonic composition

authors: Stokes, Tim E.

abstract: Demonic composition is defined on the set of binary relations over the non-empty set X, 𝑅𝑒𝑙𝑋, and is a variant of standard or “angelic” composition. It arises naturally in the setting of the theory of non-deterministic computer programs, and shares many of the nice features of ordinary composition (it is associative, and generalises composition of functions). When equipped with the operations of demonic composition and domain, 𝑅𝑒𝑙𝑋 is a left restriction semigroup (like 𝑃𝑇𝑋, the semigroup of partial functions on X), whereas usual composition and domain give a unary semigroup satisfying weaker laws. By viewing 𝑅𝑒𝑙𝑋 under a restricted version of its usual composition and domain as a constellation (a kind of “one-sided” category), we show how this demonic left restriction semigroup structure arises on 𝑅𝑒𝑙𝑋, placing it in a more general context. The construction applies to any unary semigroup with a “domain-like” operation satisfying certain minimal conditions which we identify. In particular it is shown that using the construction, any Baer ∗-semigroup S can be given a left restriction semigroup structure which is even an inverse semigroup if S is ∗-regular. It follows that the semigroup of 𝑛×𝑛 matrices over the real or complex numbers is an inverse semigroup with respect to a modified notion of product that almost always agrees with the usual matrix product, and in which inverse is pseudoinverse (Moore–Penrose inverse).

text: How to generalise demonic composition Demonic composition is defined on the set of binary relations over the non-empty set X, 𝑅𝑒𝑙𝑋, and is a variant of standard or “angelic” composition. It arises naturally in the setting of the theory of non-deterministic computer programs, and shares many of the nice features of ordinary composition (it is associative, and generalises composition of functions). When equipped with the operations of demonic composition and domain, 𝑅𝑒𝑙𝑋 is a left restriction semigroup (like 𝑃𝑇𝑋, the semigroup of partial functions on X), whereas usual composition and domain give a unary semigroup satisfying weaker laws. By viewing 𝑅𝑒𝑙𝑋 under a restricted version of its usual composition and domain as a constellation (a kind of “one-sided” category), we show how this demonic left restriction semigroup structure arises on 𝑅𝑒𝑙𝑋, placing it in a more general context. The construction applies to any unary semigroup with a “domain-like” operation satisfying certain minimal conditions which we identify. In particular it is shown that using the construction, any Baer ∗-semigroup S can be given a left restriction semigroup structure which is even an inverse semigroup if S is ∗-regular. It follows that the semigroup of 𝑛×𝑛 matrices over the real or complex numbers is an inverse semigroup with respect to a modified notion of product that almost always agrees with the usual matrix product, and in which inverse is pseudoinverse (Moore–Penrose inverse).

year: 2020

title: Caffeine Modifies the Immune and Anti-inflammatory Responses to Short Incremental Cycling Exercise Until Exhaustion in Humans: A Pilot Study

authors: Rahimi, Mohammad Rahman

abstract: Exercise has well-documented effects on immune function with both positive and negative sequelae dependent on intensity, volume, and duration. The immunosuppressive effects of exercise are mediated, in part, by the complex interaction of cytokines, catecholamines, and nutrition. Caffeine has been reported to modulate immune function; however, the interaction with brief exhaustive exercise is not well characterized. It was hypothesized that caffeine would upregulate the cytokine response to intense exercise. Seven male students volunteered to participate in a randomized, double-blinded crossover study where they ingested either caffeine (6 mg/kg) or a maltodextrin placebo (6 mg/kg) 1 h prior to a cycling exercise. The exercise protocol started at 100 W and the intensity was increased by 50 W every two minutes until exhaustion. Serum samples were collected pre-, post-, and 1-h post-exercise and analyzed for IL-4, IL-10, and TGF-<jats:italic>β</jats:italic>1. Caffeine ingestion increased time to exhaustion (<jats:italic>P</jats:italic> = 0.005; Effect Size [ES] = 1.33), IL-4 (<jats:italic>P</jats:italic> = 0.004; ES = 2.34), IL-10 (<jats:italic>P</jats:italic> = 0.047; ES = 0.41 ± 0.57), and TGF-<jats:italic>β</jats:italic>1 (<jats:italic>P</jats:italic> = 0.013; ES = 0.76). The accentuated response of the cytokines may have important ramifications due to their potent anti-inflammatory and immunoregulatory properties. Specifically, the 6 mg/kg caffeine dose not only improved exercise performance but the cytokine data is indicative of an upregulated inflammatory response and an enhancement of the anti-inflammatory benefits of exercise.

text: Caffeine Modifies the Immune and Anti-inflammatory Responses to Short Incremental Cycling Exercise Until Exhaustion in Humans: A Pilot Study Exercise has well-documented effects on immune function with both positive and negative sequelae dependent on intensity, volume, and duration. The immunosuppressive effects of exercise are mediated, in part, by the complex interaction of cytokines, catecholamines, and nutrition. Caffeine has been reported to modulate immune function; however, the interaction with brief exhaustive exercise is not well characterized. It was hypothesized that caffeine would upregulate the cytokine response to intense exercise. Seven male students volunteered to participate in a randomized, double-blinded crossover study where they ingested either caffeine (6 mg/kg) or a maltodextrin placebo (6 mg/kg) 1 h prior to a cycling exercise. The exercise protocol started at 100 W and the intensity was increased by 50 W every two minutes until exhaustion. Serum samples were collected pre-, post-, and 1-h post-exercise and analyzed for IL-4, IL-10, and TGF-<jats:italic>β</jats:italic>1. Caffeine ingestion increased time to exhaustion (<jats:italic>P</jats:italic> = 0.005; Effect Size [ES] = 1.33), IL-4 (<jats:italic>P</jats:italic> = 0.004; ES = 2.34), IL-10 (<jats:italic>P</jats:italic> = 0.047; ES = 0.41 ± 0.57), and TGF-<jats:italic>β</jats:italic>1 (<jats:italic>P</jats:italic> = 0.013; ES = 0.76). The accentuated response of the cytokines may have important ramifications due to their potent anti-inflammatory and immunoregulatory properties. Specifically, the 6 mg/kg caffeine dose not only improved exercise performance but the cytokine data is indicative of an upregulated inflammatory response and an enhancement of the anti-inflammatory benefits of exercise.

year: 2023-03-07

title: 'Waitangi and indigenous rights: Revolution, law and legitimacy' by F.M. Brookfield

authors: Melbourne, Hirini

subjects: indigenous rights

abstract: 'Waitangi and Indigenous Rights: Revolution, Law and Legitimacy' book review by Hirini Melbourne.

text: 'Waitangi and indigenous rights: Revolution, law and legitimacy' by F.M. Brookfield 'Waitangi and Indigenous Rights: Revolution, Law and Legitimacy' book review by Hirini Melbourne.

year: 2000-10