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Cook and Reckhow [5] pointed out that $\mathcal {N}\mathcal {P} \neq co\mathcal {N}\mathcal {P}$ iff there is no propositional proof system that admits polynomial size proofs of all tautologies. The theory of proof complexity generators aims at constructing sets of tautologies hard for strong and possibly for all proof systems. We focus on a conjecture from [16] in foundations of the theory that there is a proof complexity generator hard for all proof systems. This can be equivalently formulated (for p-time generators) without a reference to proof complexity notions as follows:
• There exists a p-time function g stretching each input by one bit such that its range $rng(g)$ intersects all infinite $\mathcal {N}\mathcal {P}$ sets.
We consider several facets of this conjecture, including its links to bounded arithmetic (witnessing and independence results), to time-bounded Kolmogorov complexity, to feasible disjunction property of propositional proof systems and to complexity of proof search. We argue that a specific gadget generator from [18] is a good candidate for g. We define a new hardness property of generators, the $\bigvee $-hardness, and show that one specific gadget generator is the $\bigvee $-hardest (w.r.t. any sufficiently strong proof system). We define the class of feasibly infinite $\mathcal {N}\mathcal {P}$ sets and show, assuming a hypothesis from circuit complexity, that the conjecture holds for all feasibly infinite $\mathcal {N}\mathcal {P}$ sets.
We present the general analytical solution of the Riemann problem (decay of a jump discontinuity) for non-convex relativistic hydrodynamics. In convex dynamics, an elementary nonlinear wave, i.e. a rarefaction or a shock, originates at the discontinuity and travels towards one of the initial states. Between the left and right waves, an equilibrium state appears represented by a contact discontinuity. The exact solution to the Riemann problem in convex relativistic hydrodynamics was first addressed by Martí & Müller (J. Fluid Mech., vol. 258, 1994, pp. 317–333). In non-convex dynamics, two sequences of elementary nonlinear waves move towards the left and right initial states. Solving the Riemann problem involves determining the types of wave developing and the equilibrium state where they coincide. The procedure consists of constructing the wave curves associated with the nonlinear waves in the pressure–velocity phase space, where the intersection of the wave curves indicates the equilibrium state. We describe the relation between the wave curves, the explicit formulas for their calculation, and the outline of the process for a correct derivation and representation of the waves in the spatial domain. We present examples of the exact solution of a Riemann problem that illustrate the complex phenomena of non-convex dynamics by using the phenomenological non-convex equation of state proposed by Ibáñez et al. (Mon. Not. R. Astron. Soc., vol. 476, 2017, pp. 1100–1110).
Subjective cognitive decline (SCD) and how much cognitive decline impacts one’s ability to perform instrumental activities of daily living (iADLs) are necessary elements of neuropsychological assessment when diagnosing mild cognitive impairment (MCI) and dementia. Though limited, the literature suggests that culture and self-appraisal of cognitive abilities are related. However, it is unclear if differences exist in the subjective elements of neuropsychological assessments between patients born in Anglosphere countries (Canada, the USA, and the UK) versus immigrants born elsewhere (International Group).
Method:
We conducted a retrospective chart review of advanced Parkinson’s disease (PD) patients (n = 764). Reports of SCD and iADL difficulties were extracted from neuropsychological reports and coded by two independent raters. We also examined responses on self- and family-rated questionnaires of executive functioning and iADL difficulties.
Results:
Anglosphere and International patients did not differ on overall, memory, or attention SCD, or overall iADL difficulties based on interviews. Anglosphere patients reported more executive and language SCD during the interview but International care-partners reported more current executive dysfunction on a questionnaire. International patients and care-partners reported more iADL difficulties on a questionnaire, which they ascribed to motor (not cognitive) symptoms. The effects on questionnaires were small and persisted after accounting for depression severity ratings.
Conclusion:
There were no consistent group differences in the number or pervasiveness of SCD or iADL difficulties reported by Anglosphere versus International groups. Immigration status has limited effect on these subjective elements and they should be given significant weight when diagnosing cognitive dysfunction in PD.
Bringing home federal spending projects to the district is a common reelection strategy for members of the U.S. Congress, and congresswomen tend to outperform congressmen in securing district spending. However, for legislators to turn distributive benefits into higher approval and electoral rewards, constituents must recognize that public spending has taken place in their community and attribute credit to the correct public official. I theorize that congresswomen face a gender bias when claiming credit for federal projects, and I test this theory through an online survey experiment. Contrary to expectations, I find no evidence that legislator gender influences the public’s reaction to congressional credit claims, indicating that congresswomen can effectively use distributive politics to counter gendered vulnerability in the U.S. Congress. This research advances the literature on gender and politics by investigating whether a gender bias in credit claiming prevents congresswomen from turning their representational efforts into electoral capital.
Using direct numerical simulations, we investigate the heat transport in bulk and boundary flows separately in rotating Rayleigh–Bénard convection in cylindrical cells. In the bulk we observe a steep scaling relationship between the Nusselt number ($Nu$) and the Rayleigh number ($Ra$), which is consistent with the results from simulations using periodic boundary conditions. For the boundary flow, we observe a power law $Nu_{BF}\sim (Ra/Ra_w)^1$ at the leading order, where $Nu_{BF}$ is the local Nusselt number of the boundary flow and $Ra_w$ is the onset Rayleigh number of the wall mode. We develop a model using the boundary layer marginal stability theory to explain this power law, and further show that a more precise description of the data can be obtained if a higher-order correction is introduced. A striking finding of our study is the observation of a sharp transition in flow state, manifested by a sudden drop in $Nu_{BF}$ with a corresponding collapse of the boundary flow coherency. After the transition, the boundary flow breaks into vortices, leading to a reduction in flow coherency and heat transport efficiency. As the physical properties of the vortices should not depend on the aspect ratio, $Nu_{BF}$ for all aspect ratios collapse together after the transition. Moreover, the centrifugal force helps trigger the breakdown of the coherent boundary flow state. For this reason, $Nu_{BF}$ for the cases with non-zero centrifugal force collapse together. We further develop a method that enables us to separate the contributions from the bulk and boundary flows in the global Nusselt number using only the global $Nu$ and it does not require the centrifugal force to be absent.
The article offers a reconstruction of Donoso's idea of political theology by analyzing his main work, the 1851 Essay on Catholicism, Socialism, and Liberalism. Commentators have often confined the role of Donoso to a footnote in the literature on Carl Schmitt. To better appreciate his original thought, this article analyzes his account of the secularization of theological ideas. Donoso understands modern politics as a confrontation between the philosophies of socialism, liberalism, and Catholicism, which diverge on questions about the nature of man, of evil, and of society. Modern worldviews are thus read through simplified Catholic dogma. Donoso's vision of politics as secularized theology develops in dialogue with Pierre-Joseph Proudhon. The Donoso-Proudhon-Schmitt rapport allows a consideration of political theology in terms of metaphor and literary device. Within this larger story, Donoso represents the moment when a traditionalist figure of thought slowly detaches itself from its historical foundations.
The study aimed to increase the understanding of the lived experience of patients during the acute phase of a coronavirus disease 2019 (COVID-19) infection.
Method:
A Web-based survey was distributed through established patient and public engagement and involvement groups and networks, social media, and by means of word of mouth. The survey covered questions relating to patient demographics, COVID-19 diagnosis, symptom profile, and patient experience during acute COVID-19.
Results:
The findings demonstrate the varying symptom profiles experienced by people in the acute stage of COVID-19 infection, with participants sharing how they managed care at home, and/or accessed medical advice. Findings also highlight themes that people were concerned with being unable to receive care and believed they needed to rely heavily on family, with extreme thoughts of death.
Conclusions:
Although the urgent threat to public health has been negated by efficacious vaccines and enhanced treatment strategies, there are key lessons from the lived experience of COVID-19 that should be used to prepare for future pandemics and public health emergencies.
The Oxford Cognitive Screen (OCS) is a screening tool to assess stroke patients for deficits in attention, executive functions, language, praxis, numeric cognition, and memory. In this study, the OCS was culturally and linguistically adapted to Tamil, for use in India (OCS TA), considering the differences between formal and spoken versions of Tamil and consideration of its phonetic complexity.
Method:
We adopted two-parallel form versions of the OCS and generated normative data for them. We recruited 181 healthy controls (Mean = 39.27 years, SD 16.52) (141 completed version A, 40 completed version B, 33 completed version A and B) and compared the data with the original UK normative sample. In addition, 28 native Tamil-speaking patients who had a stroke in the past three years (Mean = 62.76 years, SD 9.14) were assessed. Convergent validity was assessed with subtasks from Addenbrooke’s Cognitive Examination III (ACE-III).
Results:
We found significant differences between the UK normative group and the OCS TA normative group in age and education. Tamil-specific norms were used to adapt the cutoffs for the memory, gesture imitation, and executive function tasks. When domain-specific scores on the ACE-III were compared, OCS TA exhibited strong convergent validity.
Conclusions:
The OCS TA has shown the potential to be a useful screening tool for stroke survivors among Tamil speakers with the two-parallel forms demonstrating good equivalence. Further empirical evidence from larger studies is required to establish their psychometric performance and clinical validity.
The comparative analysis of three “contested truths” around COVID-19 in East Africa demonstrates that knowledge is a product of knotted, uneven, and disputed epistemological practices tied to structures of power. Lee, Meek, and Katumusiime examine: (1) the construction of a pan-African skepticism of COVID-19 that drew on anti-imperialist discourses; (2) social media posts through which Tanzanian digital publics critically evaluated steam inhalation as an alternative therapeutic for COVID-19; and (3) the resistance by many Ugandans to complying with public health measures such as lockdowns. “Contested truths” is used as an analytical framework to center the specificity and situatedness of truth-making in East Africa during the COVID-19 pandemic.