A Descriptive and analytic look at Marx's own explanations of the falling rate of profit (second version)

This paper examines, both descriptively and analytically, Marx's arguments for the falling rate of profit from the Hodgskin section of Theories of Surplus Value, The General Law section of the recently published Volume 33 of the Collected Works and Chapter 3 of Volume III of Capital. The conclusions are as follows: First, Marx realised that his main attempt to give an intrinsic explanation of the falling rate of profit, which occurred in the General Law section, had failed; but he still hoped that he would be able to demonstrate it in the future. Second, the Hodgskin and General Law sections contain a number of subsidiary explanations, mostly related to resource scarcity, some of which are correct. Third, Part III of volume III does not contain a demonstration of the falling rate of profit, but a description of the role of the falling rate of profit in capitalist development. Forth, it also contains suppressed references to resource scarcity. And finally, in Chapter 3 of Volume III, Marx says that it is resource scarcity that causes the fall in the rate of profit described in Part III of the same volume. The key to all these conclusions in the careful analysis of the General Law section.

The agreement between ipsative and normative questionnaires using compositional data analysis techniques

The main instrument used in psychological measurement is the self-report questionnaire. One of its majordrawbacks however is its susceptibility to response biases. A known strategy to control these biases hasbeen the use of so-called ipsative items. Ipsative items are items that require the respondent to makebetween-scale comparisons within each item. The selected option determines to which scale the weight ofthe answer is attributed. Consequently in questionnaires only consisting of ipsative items everyrespondent is allotted an equal amount, i.e. the total score, that each can distribute differently over thescales. Therefore this type of response format yields data that can be considered compositional from itsinception.Methodological oriented psychologists have heavily criticized this type of item format, since the resultingdata is also marked by the associated unfavourable statistical properties. Nevertheless, clinicians havekept using these questionnaires to their satisfaction. This investigation therefore aims to evaluate bothpositions and addresses the similarities and differences between the two data collection methods. Theultimate objective is to formulate a guideline when to use which type of item format.The comparison is based on data obtained with both an ipsative and normative version of threepsychological questionnaires, which were administered to 502 first-year students in psychology accordingto a balanced within-subjects design. Previous research only compared the direct ipsative scale scoreswith the derived ipsative scale scores. The use of compositional data analysis techniques also enables oneto compare derived normative score ratios with direct normative score ratios. The addition of the secondcomparison not only offers the advantage of a better-balanced research strategy. In principle it also allowsfor parametric testing in the evaluation

Sherali-Adams Relaxations and Indistinguishability in Counting Logics

Two graphs with adjacency matrices $\mathbf{A}$ and $\mathbf{B}$ are isomorphic if there exists a permutation matrix $\mathbf{P}$ for which the identity $\mathbf{P}^{\mathrm{T}} \mathbf{A} \mathbf{P} = \mathbf{B}$ holds. Multiplying through by $\mathbf{P}$ and relaxing the permutation matrix to a doubly stochastic matrix leads to the linear programming relaxation known as fractional isomorphism. We show that the levels of the Sherali--Adams (SA) hierarchy of linear programming relaxations applied to fractional isomorphism interleave in power with the levels of a well-known color-refinement heuristic for graph isomorphism called the Weisfeiler--Lehman algorithm, or, equivalently, with the levels of indistinguishability in a logic with counting quantifiers and a bounded number of variables. This tight connection has quite striking consequences. For example, it follows immediately from a deep result of Grohe in the context of logics with counting quantifiers that a fixed number of levels of SA suffice to determine isomorphism of planar and minor-free graphs. We also offer applications in both finite model theory and polyhedral combinatorics. First, we show that certain properties of graphs, such as that of having a flow circulation of a prescribed value, are definable in the infinitary logic with counting with a bounded number of variables. Second, we exploit a lower bound construction due to Cai, Fürer, and Immerman in the context of counting logics to give simple explicit instances that show that the SA relaxations of the vertex-cover and cut polytopes do not reach their integer hulls for up to $\Omega(n)$ levels, where $n$ is the number of vertices in the graph.

Self-reported sitting time and physical activity: interactive associations with mental well-being and productivity in office employees

Abstract Background: Little is known about how sitting time, alone or in combination with markers of physical activity (PA), influences mental well-being and work productivity. Given the need to develop workplace PA interventions that target employees’ health related efficiency outcomes; this study examined the associations between self-reported sitting time, PA, mental well-being and work productivity in office employees. Methods: Descriptive cross-sectional study. Spanish university office employees (n = 557) completed a survey measuring socio-demographics, total and domain specific (work and travel) self-reported sitting time, PA (International Physical Activity Questionnaire short version), mental well-being (Warwick-Edinburg Mental Well-Being Scale) and work productivity (Work Limitations Questionnaire). Multivariate linear regression analyses determined associations between the main variables adjusted for gender, age, body mass index and occupation. PA levels (low, moderate and high) were introduced into the model to examine interactive associations. Results: Higher volumes of PA were related to higher mental well-being, work productivity and spending less time sitting at work, throughout the working day and travelling during the week, including the weekends (p < 0.05). Greater levels of sitting during weekends was associated with lower mental well-being (p < 0.05). Similarly, more sitting while travelling at weekends was linked to lower work productivity (p < 0.05). In highly active employees, higher sitting times on work days and occupational sitting were associated with decreased mental well-being (p < 0.05). Higher sitting times while travelling on weekend days was also linked to lower work productivity in the highly active (p < 0.05). No significant associations were observed in low active employees. Conclusions: Employees’ PA levels exerts different influences on the associations between sitting time, mental well-being and work productivity. The specific associations and the broad sweep of evidence in the current study suggest that workplace PA strategies to improve the mental well-being and productivity of all employees should focus on reducing sitting time alongside efforts to increase PA.

Visual impairment and multimorbidity in a representative sample of the Spanish population

BACKGROUND: In the context of population aging, visual impairment has emerged as a growing concern in public health. However, there is a need for further research into the relationship between visual impairment and chronic medical conditions in the elderly. The aim of our study was to examine the relationship between visual impairment and three main types of co-morbidity: chronic physical conditions (both at an independent and additive level), mental health and cognitive functioning. METHODS: Data were collected from the COURAGE in Europe project, a cross-sectional study. A total of 4,583 participants from Spain were included. Diagnosis of chronic medical conditions included self-reported medical diagnosis and symptomatic algorithms. Depression and anxiety were assessed using CIDI algorithms. Visual assessment included objective distance/near visual acuity and subjective visual performance. Descriptive analyses included the whole sample (n = 4,583). Statistical analyses included participants aged over 50 years (n = 3,625; mean age = 66.45 years) since they have a significant prevalence of chronic conditions and visual impairment. Crude and adjusted binary logistic regressions were performed to identify independent associations between visual impairment and chronic medical conditions, physical multimorbidity and mental conditions. Covariates included age, gender, marital status, education level, employment status and urbanicity. RESULTS: The number of chronic physical conditions was found to be associated with poorer results in both distance and near visual acuity [OR 1.75 (CI 1.38-2.23); OR 1.69 (CI 1.27-2.24)]. At an independent level, arthritis, stroke and diabetes were associated with poorer distance visual acuity results after adjusting for covariates [OR 1.79 (CI 1.46-2.21); OR 1.59 (CI 1.05-2.42); OR 1.27 (1.01-1.60)]. Only stroke was associated with near visual impairment [OR 3.01 (CI 1.86-4.87)]. With regard to mental health, poor subjective visual acuity was associated with depression [OR 1.61 (CI 1.14-2.27); OR 1.48 (CI 1.03-2.13)]. Both objective and subjective poor distance and near visual acuity were associated with worse cognitive functioning. CONCLUSIONS: Arthritis, stroke and the co-occurrence of various chronic physical diseases are associated with higher prevalence of visual impairment. Visual impairment is associated with higher prevalence of depression and poorer cognitive function results. There is a need to implement patient-centered care involving special visual assessment in these cases.