Bounded Arithmetic in Free Logic

One of the central open questions in bounded arithmetic is whether Buss' hierarchy of theories of bounded arithmetic collapses or not. In this paper, we reformulate Buss' theories using free logic and conjecture that such theories are easier to handle. To show this, we first prove that Buss' theories prove consistencies of induction-free fragments of our theories whose formulae have bounded complexity. Next, we prove that although our theories are based on an apparently weaker logic, we can interpret theories in Buss' hierarchy by our theories using a simple translation. Finally, we investigate finitistic G\"odel sentences in our systems in the hope of proving that a theory in a lower level of Buss' hierarchy cannot prove consistency of induction-free fragments of our theories whose formulae have higher complexity

The anti-sigma factor RsrA responds to oxidative stress by reburying its hydrophobic core

Redox-regulated effector systems that counteract oxidative stress are essential for all forms of life. Here we uncover a new paradigm for sensing oxidative stress centred on the hydrophobic core of a sensor protein. RsrA is an archetypal zinc-binding anti-sigma factor that responds to disulfide stress in the cytoplasm of Actinobacteria. We show that RsrA utilizes its hydrophobic core to bind the sigma factor σ R preventing its association with RNA polymerase, and that zinc plays a central role in maintaining this high-affinity complex. Oxidation of RsrA is limited by the rate of zinc release, which weakens the RsrA-σ R complex by accelerating its dissociation. The subsequent trigger disulfide, formed between specific combinations of RsrA's three zinc-binding cysteines, precipitates structural collapse to a compact state where all σ R-binding residues are sequestered back into its hydrophobic core, releasing σ R to activate transcription of anti-oxidant genes

Second asymptomatic carotid surgery trial (ACST-2): a randomised comparison of carotid artery stenting versus carotid endarterectomy

Background: Among asymptomatic patients with severe carotid artery stenosis but no recent stroke or transient cerebral ischaemia, either carotid artery stenting (CAS) or carotid endarterectomy (CEA) can restore patency and reduce long-term stroke risks. However, from recent national registry data, each option causes about 1% procedural risk of disabling stroke or death. Comparison of their long-term protective effects requires large-scale randomised evidence. Methods: ACST-2 is an international multicentre randomised trial of CAS versus CEA among asymptomatic patients with severe stenosis thought to require intervention, interpreted with all other relevant trials. Patients were eligible if they had severe unilateral or bilateral carotid artery stenosis and both doctor and patient agreed that a carotid procedure should be undertaken, but they were substantially uncertain which one to choose. Patients were randomly allocated to CAS or CEA and followed up at 1 month and then annually, for a mean 5 years. Procedural events were those within 30 days of the intervention. Intention-to-treat analyses are provided. Analyses including procedural hazards use tabular methods. Analyses and meta-analyses of non-procedural strokes use Kaplan-Meier and log-rank methods. The trial is registered with the ISRCTN registry, ISRCTN21144362. Findings: Between Jan 15, 2008, and Dec 31, 2020, 3625 patients in 130 centres were randomly allocated, 1811 to CAS and 1814 to CEA, with good compliance, good medical therapy and a mean 5 years of follow-up. Overall, 1% had disabling stroke or death procedurally (15 allocated to CAS and 18 to CEA) and 2% had non-disabling procedural stroke (48 allocated to CAS and 29 to CEA). Kaplan-Meier estimates of 5-year non-procedural stroke were 2·5% in each group for fatal or disabling stroke, and 5·3% with CAS versus 4·5% with CEA for any stroke (rate ratio [RR] 1·16, 95% CI 0·86–1·57; p=0·33). Combining RRs for any non-procedural stroke in all CAS versus CEA trials, the RR was similar in symptomatic and asymptomatic patients (overall RR 1·11, 95% CI 0·91–1·32; p=0·21). Interpretation: Serious complications are similarly uncommon after competent CAS and CEA, and the long-term effects of these two carotid artery procedures on fatal or disabling stroke are comparable. Funding: UK Medical Research Council and Health Technology Assessment Programme

Marine horizon with Dunbarella and its meaning in correlation of Carboniferous system in Lublin Coal Basin

W trakcie wieloletnich badań geologicznych karbonu lubelskiego udowodniono występowanie kilku ważnych poziomów litologicznych, które są przydatne do przeprowadzania korelacji profilu karbonu z różnych rejonów Lubelskiego Zagłębia Węglowego. Jednym z nich jest poziom iłowców z Dunbarella usytuowany w dolnej części formacji z Lublina w bezpośrednim stropie pokładu węgla 395(305). Jest to poziom jednorodny litologicznie, ale zmienny pod względem zawartości skamieniałości fauny. Część dolna, o grubości do 0,6 m, zawiera skorupy małżów słodkowodnych z rodzaju Carbonicola i Naiadites. Wyższa część, o grubości około 15 m, oddzielona cienką, 0,35 m warstwą węglanową, zawiera skamieniałości fauny morskiej reprezentowanej przez małże w tym Dunbarella, ramienionogi, głowonogi i ślimaki, a w części stropowej o grubości do około 5,0 m, oprócz fauny Lingula charakterystycznej dla środowisk przejściowych, pojawiają się skamieniałości małżów słodkowodnych Naiadites i Anthracosia. Poziom ten definiuje spąg serii węglonośnej z ekonomicznymi pokładami węgla, a ponadto granicę między westfalem A i B.Several lithological horizons of correlative importance have been distinguished in the Carboniferous section of the Lublin Coal Basin (Poland). One of them is the marine horizon with Dunbarella, that occurs as a claystone horizon in the lower part of the Lublin Formation, close to the coal seam no. 395 (305). Marine horizon with Dunbarella is lithologicaly unified but unique as it refers to the presence of fauna fossils. In the lower part of this horizon of 0,6m in thickness, shells of freshwater molluscs of Anthracosia and Naiadites occur. In the upper part of 15m in thickness, fossils of marine fauna occur, which are represented by: molluscs (including Dunbarella), brachiopods, cephalopods and gastropods. At the top part of the horizon of 5m in thickness, fossils of Lingula characteristic for brackish water environments occur. The presence of freshwater molluscs of Naiadites and Anthracosia is also indicative of the top part of the horizon. The boundary of marine horizon with Dunbarella between Westphalian A and Westphalian B is acknowledged as the indicative horizon of the bottom part of economic coal-bearing formation of the Carboniferous in the Lublin Coal Basin

The quality of coal from the Lublin Coal Basin

Stan rozpoznania jakości węgla w Lubelskim Zagłębiu Węglowym (LZW) jest odzwierciedleniem rozpoznania geologicznego złóż węgla zlokalizowanych głównie w centralnej części zagłębia. Analizie jakościowej i technologicznej poddano próbki węgla pobrane z pokładów przewierconych w ponad 500 otworach wiertniczych. Zdecydowana większość utworów pochodzi z formacji z Lublina, w której występuje podstawowe, wielopokładowe złoże węgla. Węgiel z formacji starszych, ze względu na brak pokładów bilansowych jest słabiej rozpoznany, ale wyniki przeprowadzonych badań są wystarczające do oceny jakości węgla w całym zagłębiu. Jakość węgla oceniono na podstawie następujących parametrów: Wa, Qsdaf, Hdaf, Cdaf, Vdaf i RI. Wymienione parametry wykazują pewne prawidłowości rozkładu w otworach. Prawidłowości te pozwoliły wydzielić trzy strefy metamorfizmu z : węglem płomiennym typu 31, gazowo-płomiennym typu 32 i gazowo-koksowym typu 34. Brakuje podstaw do wydzielenia węgla gazowego typu 33 i ortokoksowego typu 35. Węgiel typu 31 występuje od stropu karbonu tylko w północnej części LZW, węgiel typu 32 – w centralnej części, a typ 34 dominuje w części południowej. Powierzchnie ograniczające wymienione strefy są niezgodne z powierzchniami stratygraficznymi, a także z poziomami głębokościowymi w odniesieniu do poziomu morza. Parametry technologiczne oceniono na podstawie zawartości: popiołu, siarki całkowitej oraz wartości opałowej. W LZW występuje węgiel nisko- (średnio około 10,5% popiołu) i wysokopopiołowy (średnio >25,0% popiołu). Zawartość popiołu ma decydujący wpływ na wartość opałową. Zawartość siarki całkowitej w węglu pokładów bilansowych tylko lokalnie przekracza 2,0%, ale w pokładach cienkich poniżej formacji z Lublina zawartość siarki często przekracza 5,0%, osiągając wartości maksymalne powyżej 13,0%.The state of knowledge of the Lublin Coal Basin’s coal quality reflects the geological exploration level of the coal deposits located within the central part of the Basin. The coal samples, collected from the coal seams encountered in over 500 boreholes, underwent qualitative and technological analyses. Majority of the samples has been taken from the Lublin Formation that contains the most important, multi-seamed coal deposit. Coals from the older formations are much less recognised, as their coal seams have no economic value. However, the existing analytical results are sufficient to assess the coal quality of the whole Basin. The coal quality has been assessed based on the following parameters: Wa, Qsdaf, Hdaf, Cdaf, Vdaf i RI. The above mentioned parameters reveal some distribution regularities within the boreholes. Those regularities allowed to distinguish three zones of the coals metamorphism: flame coals of the 31 type, flame-gaseous coals of the 32 type, and coking-gaseous coals of the 34 type. There is no data, however, allowing to determine gaseous coals of the 33 type and/or ortho-coking coals of the 35 type. Coals of the 31 type occur in the northern part of the Lublin Coal Basin, only. Coals of the 32 type occur in its central part, and coals of the 34 type dominate in its southern part. The surfaces limiting the above mentioned zones are lying unconformably to the stratigraphic surfaces as well as to the depth levels measured from the sea level. The coals technological parameters have been assessed based on the ash and total sulphur content, and on the coals’ net calorific values. In the Lublin Coal Basin occur low-ash (10.5% in average) and high-ash (>25.0% in average) coals. The ash content is crucial as far as the coals’ net calorific values are concerned. The total sulphur content of the coal seams with the economic thickness exceeds 2,0% locally, only. However, the total sulphur content of the thinner coal seams, occurring below the Lublin Formation, exceeds very often 5,0%, reaching even 13,0%, maximally