Randomness and semimeasures

A semimeasure is a generalization of a probability measure obtained by relaxing the additivity requirement to superadditivity. We introduce and study several randomness notions for left-c.e. semimeasures, a natural class of effectively approximable semimeasures induced by Turing functionals. Among the randomness notions we consider, the generalization of weak 2-randomness to left-c.e. semimeasures is the most compelling, as it best reflects Martin-Löf randomness with respect to a computable measure. Additionally, we analyze a question of Shen, a positive answer to which would also have yielded a reasonable randomness notion for left-c.e. semimeasures. Unfortunately, though, we find a negative answer, except for some special cases

Impossibility of independence amplification in Kolmogorov complexity theory

The paper studies randomness extraction from sources with bounded independence and the issue of independence amplification of sources, using the framework of Kolmogorov complexity. The dependency of strings $x$ and $y$ is ${\rm dep}(x,y) = \max\{C(x) - C(x \mid y), C(y) - C(y\mid x)\}$, where $C(\cdot)$ denotes the Kolmogorov complexity. It is shown that there exists a computable Kolmogorov extractor $f$ such that, for any two $n$-bit strings with complexity $s(n)$ and dependency $\alpha(n)$, it outputs a string of length $s(n)$ with complexity $s(n)- \alpha(n)$ conditioned by any one of the input strings. It is proven that the above are the optimal parameters a Kolmogorov extractor can achieve. It is shown that independence amplification cannot be effectively realized. Specifically, if (after excluding a trivial case) there exist computable functions $f_1$ and $f_2$ such that ${\rm dep}(f_1(x,y), f_2(x,y)) \leq \beta(n)$ for all $n$-bit strings $x$ and $y$ with ${\rm dep}(x,y) \leq \alpha(n)$, then $\beta(n) \geq \alpha(n) - O(\log n)$

Constructive Dimension and Turing Degrees

This paper examines the constructive Hausdorff and packing dimensions of Turing degrees. The main result is that every infinite sequence S with constructive Hausdorff dimension dim_H(S) and constructive packing dimension dim_P(S) is Turing equivalent to a sequence R with dim_H(R) <= (dim_H(S) / dim_P(S)) - epsilon, for arbitrary epsilon > 0. Furthermore, if dim_P(S) > 0, then dim_P(R) >= 1 - epsilon. The reduction thus serves as a *randomness extractor* that increases the algorithmic randomness of S, as measured by constructive dimension. A number of applications of this result shed new light on the constructive dimensions of Turing degrees. A lower bound of dim_H(S) / dim_P(S) is shown to hold for the Turing degree of any sequence S. A new proof is given of a previously-known zero-one law for the constructive packing dimension of Turing degrees. It is also shown that, for any regular sequence S (that is, dim_H(S) = dim_P(S)) such that dim_H(S) > 0, the Turing degree of S has constructive Hausdorff and packing dimension equal to 1. Finally, it is shown that no single Turing reduction can be a universal constructive Hausdorff dimension extractor, and that bounded Turing reductions cannot extract constructive Hausdorff dimension. We also exhibit sequences on which weak truth-table and bounded Turing reductions differ in their ability to extract dimension.Comment: The version of this paper appearing in Theory of Computing Systems, 45(4):740-755, 2009, had an error in the proof of Theorem 2.4, due to insufficient care with the choice of delta. This version modifies that proof to fix the error

Algorithmic statistics: forty years later

Algorithmic statistics has two different (and almost orthogonal) motivations. From the philosophical point of view, it tries to formalize how the statistics works and why some statistical models are better than others. After this notion of a "good model" is introduced, a natural question arises: it is possible that for some piece of data there is no good model? If yes, how often these bad ("non-stochastic") data appear "in real life"? Another, more technical motivation comes from algorithmic information theory. In this theory a notion of complexity of a finite object (=amount of information in this object) is introduced; it assigns to every object some number, called its algorithmic complexity (or Kolmogorov complexity). Algorithmic statistic provides a more fine-grained classification: for each finite object some curve is defined that characterizes its behavior. It turns out that several different definitions give (approximately) the same curve. In this survey we try to provide an exposition of the main results in the field (including full proofs for the most important ones), as well as some historical comments. We assume that the reader is familiar with the main notions of algorithmic information (Kolmogorov complexity) theory.Comment: Missing proofs adde

Computable randomness is about more than probabilities

We introduce a notion of computable randomness for infinite sequences that generalises the classical version in two important ways. First, our definition of computable randomness is associated with imprecise probability models, in the sense that we consider lower expectations (or sets of probabilities) instead of classical 'precise' probabilities. Secondly, instead of binary sequences, we consider sequences whose elements take values in some finite sample space. Interestingly, we find that every sequence is computably random with respect to at least one lower expectation, and that lower expectations that are more informative have fewer computably random sequences. This leads to the intriguing question whether every sequence is computably random with respect to a unique most informative lower expectation. We study this question in some detail and provide a partial answer

Idiopathic hypertrophic pachymeningitis presenting with occipital neuralgia

Background: Although occipital neuralgia is usually caused by degenerative arthropathy, nearly 20 other aetiologies may lead to this condition.Methods: We present the first case report of hypertrophic pachymeningitis revealed by isolated occipital neuralgia.Results and conclusions: Idiopathic hypertrophic pachymeningitis is a plausible cause of occipital neuralgia and may present without cranial-nerve palsy. There is no consensus on the treatment for idiopathic hypertrophic pachymeningitis, but the usual approach is to start corticotherapy and then to add immunosuppressants. When occipital neuralgia is not clinically isolated or when a first-line treatment fails, another disease diagnosis should be considered. However, the cost effectiveness of extended investigations needs to be considered.Keywords: neuralgia/pathology, meningitis, neck pain/aetiology, revie

A complementary approach to estimate the internal pressure of fission gas bubbles by SEM-SIMS-EPMA in irradiated nuclear fuels

International audienceThe behaviour of gases produced by fission is of great importance for nuclear fuel in operation. Within this context, a decade ago, a general method for the characterisation of the fission gas including gas bubbles in an irradiated UO$_2$ nuclear fuel was developed and applied to determine the bubbles internal pressure. The method consists in the determination of the pressure, over a large population of bubbles, using three techniques: SEM, EPMA and SIMS. In this paper, a complementary approach using the information given by the same techniques is performed on an isolated bubble under the surface and is aiming for a better accuracy compared to the more general measurement of gas content. SEM and EPMA enable the detection of a bubble filled with xenon under the surface. SIMS enables the detection of the gas filling the bubble. The quantification is achieved using the EPMA data as reference at positions where no or nearly no bubbles are detected

Efficacy of Anakinra for Various Types of Crystal-Induced Arthritis in Complex Hospitalized Patients: A Case Series and Review of the Literature

International audienceBackground. There are few data on anakinra use after failure of conventional medications for crystal-induced peripheral arthritis and/or crowned dens syndrome among complex hospitalized patients. Methods. We retrospectively analyzed the outcome of six patients affected with subacute crystal-induced arthritis who had received anakinra in second or third line therapy, including three patients with crowned dens syndrome and three others with gouty arthritis. Patients' comorbidities, reasons for anakinra use and associated drugs, and outcomes were recorded. Results. All patients presented with elevated inflammatory syndrome, systemic symptoms with poly/oligoarthritis. Except for absolute contraindications, all patients were previously treated with full or decreased dose of NSAID, colchicine, and/or glucocorticoids, with unsatisfactory response. All three gouty patients exhibited complete responses in all acute involvements under anakinra within 3 to 5 days, including one of them who needed the reintroduction of colchicine treatment that was previously unsuccessful. Crowned dens syndrome patients, including two with pseudogout and one with subacute hydroxyapatite deposition disease, needed 9 to 11 days to achieve complete response. Tolerance to anakinra was good. Conclusion. In case series of complex hospitalized patients, anakinra showed good activity in crowned dens syndrome and associated crystal-induced peripheral arthritis, with longer treatment duration than in gouty arthritis

Variability in aerobic methane oxidation over the past 1.2 Myrs recorded in microbial biomarker signatures from Congo fan sediments

Methane (CH4) is a strong greenhouse gas known to have perturbed global climate in the past, especially when released in large quantities over short time periods from continental or marine sources. It is therefore crucial to understand and, if possible, quantify the individual and combined response of these variable methane sources to natural climate variability. However, past changes in the stability of greenhouse gas reservoirs remain uncertain and poorly constrained by geological evidence. Here, we present a record from the Congo fan of a highly specific bacteriohopanepolyol (BHP) biomarker for aerobic methane oxidation (AMO), 35-aminobacteriohopane-30,31,32,33,34-pentol (aminopentol), that identifies discrete periods of increased AMO as far back as 1.2 Ma. Fluctuations in the concentration of aminopentol, and other 35-aminoBHPs, follow a pattern that correlates with late Quaternary glacial-interglacial climate cycles, with highest concentrations during warm periods. We discuss possible sources of aminopentol, and the methane consumed by the precursor methanotrophs, within the context of the Congo River setting, including supply of methane oxidation markers from terrestrial watersheds and/or marine sources (gas hydrate and/or deep subsurface gas reservoir). Compound-specific carbon isotope values of −30‰ to −40‰ for BHPs in ODP 1075 and strong similarities between the BHP signature of the core and surface sediments from the Congo estuary and floodplain wetlands from the interior of the Congo River Basin, support a methanotrophic and likely terrigenous origin of the 35-aminoBHPs found in the fan sediments. This new evidence supports a causal connection between marine sediment BHP records of tropical deep sea fans and wetland settings in the feeding river catchments, and thus tropical continental hydrology. Further research is needed to better constrain the different sources and pathways of methane emission. However, this study identifies the large potential of aminoBHPs, in particular aminopentol, to trace and, once better calibrated and understood, quantify past methane sources and fluxes from terrestrial and potentially also marine sources

Seroprofiling of antibodies against endemic human coronaviruses and SARS-CoV-2 in an HIV cohort in Lesotho: correlates of antibody response and seropositivity.

BACKGROUND Serological data on endemic human coronaviruses (HCoVs) and SARS-CoV-2 in southern Africa are scarce. Here, we report on i) endemic HCoV seasonality, ii) SARS-CoV-2 seroprevalence, and iii) predictive factors for SARS-CoV-2 seropositivity and strength of SARS-CoV-2 and HCoV serological response during a 17-month period at the start of the COVID-19 pandemic among adults living with HIV. METHODS Plasma samples were collected from February 2020 to July 2021 within an outpatient HIV cohort in Lesotho. We used the ABCORA multiplex immunoassay to measure antibody responses to endemic HCoV (OC43, HKU1, NL63, and 229E) and SARS-CoV-2 antigens. RESULTS Results of 3'173 samples from 1'403 adults were included. Serological responses against endemic HCoVs increased over time and peaked in winter/spring. SARS-CoV-2 seropositivity reached >35% among samples collected in early 2021 and was associated with female sex (p = 0.004), obesity (p < 0.001), working outside the home (p = 0.02), and recent tiredness (p = 0.005) or fever (p = 0.007). Positive correlations were observed between the strength of response to endemic HCoVs and to SARS-CoV-2, and between older age or obesity and the IgG response to SARS-CoV-2. CONCLUSIONS These results add to our understanding of the impact of biological, clinical, and social/behavioural factors on serological responses to coronaviruses in southern Africa