State Inequality Research Articles

Entanglement polygon inequalities for a class of mixed states

Abstract The study on the entanglement polygon inequality of multipartite systems has attracted much attention. However, most of the results are on pure states. Here we consider the property for a class of mixed states, which are the reduced density matrices of generalized W-class states in multipartite higher dimensional systems. First we show the class of mixed states satisfies the entanglement polygon inequalities in terms of Tsallis-q entanglement, then we propose a class of tighter inequalities for mixed states in terms of Tsallis-q entanglement. At last, we get an inequality for the mixed states, which can be regarded as a relation for bipartite entanglement.

New method for stability of probabilistic Boolean networks with inequality constraints

This paper studies the stability of probabilistic Boolean networks (PBNs) with state inequality constraints by establishing a new algebraic representation. On one hand, combining with the semi-tensor product (STP) of matrices and the law of total expectation, the algebraic representation of PBNs is established. On the other hand, based on the STP of matrices, an algorithm is proposed to determine the solution set of the state inequality constraints. Then, based on the algebraic representation and the inequality constrained solution set, a new form of transition probability matrix is constructed for PBNs. Finally, by the proposed transition probability matrix, new criteria are proposed for the finite-time stability with positive probability of PBNs. Several simulation examples are used to illustrate the effectiveness of the obtained results.

Concurrent learning for adaptive pontryagin's maximum principle of nonlinear systems with inequality constraints

AbstractIn this article, a finite‐horizon adaptive Pontryagin's maximum principle is presented for nonlinear systems with state inequality constraints. Concurrent learning (CL) technique is adopted to identify the unknown parameters of the dynamic systems. Based on the identification model, a novel adaptive iterative algorithm under the Pontryagin's framework is introduced to learn the finite‐horizon optimal control solution. Convergence analysis of the algorithm is provided by showing that the cost function sequence is monotonically decreasing. Furthermore, we extend the adaptive iterative algorithm to time‐varying nonlinear systems. The new algorithm overcomes the technical obstacles of the existing adaptive/approximate dynamic programming (ADP) approaches to deal with the time‐varying characteristic of Hamilton–Jacobi–Bellman (HJB) partial differential equation (PDE), especially when state constraints exist. Simulation examples are carried out to validate the effectiveness of the theoretical results.

Within the cracks of the cosmic race: Income inequalities by race and ethnicity in Latin America

While a considerable body of literature has studied ethnic inequalities and discrimination in Latin America, it is only in recent years that a growing number of studies examine income inequalities by race, defined as a skin color gradation. Furthermore, most research equates ethnic self-identification with race, leading to confusion on the root of the discrimination. Hardly any studies have addressed ethnicity and race as separate but intertwined characteristics to examine income disparities. It is crucial to address this scarcity to properly comprehend the effect miscegenation narratives have had in the region and the current state of wage inequalities. Hence, in this paper, I employ data from the Americas Barometer to investigate race and ethnicity income gaps in 17 Latin American countries. To do so, I applied non-linear regressions and decomposition methods, which allowed me to (i) separate the observable and non-observable factors of the income gap and (ii) decompose them by race and ethnicity and look at their intersection. In addition to the principal analyses, I conducted a series of robustness checks to evaluate the results’ consistency and perform heterogeneity analysis to examine income inequalities per country. The results show substantial differences in the average income of the different ethnic and racial groups, mainly driven by differences in observable characteristics like years of education and employment status. In addition, the heterogeneity analyses indicate that ethnic and racial disparities vary across Latin America and can be explained partially by unobserved variables like discrimination. Overall, the results suggest that skin color and ethnic self-identification should be accounted for simultaneously when evaluating inequality.

Trusting others in a divided country: The determinants of social trust in South Africa

AbstractThis study investigates three key determinants of social trust to explain South Africa's social trust deficit: income inequality, confidence in institutions, and racial diversity. Despite the country's racially heterogenous society and segregated history, racial diversity arguments overlook alternative theories on the determinants of low social trust. We instead argue that the decline in social trust in South Africa can be explained by worsening levels of income inequality and declines in institutional trust in recent decades. Using the 2019 South African Reconciliation Barometer citizen survey data, the empirical analysis confirms that South Africans' confidence in institutions and their subjective perceptions of income distribution (or income inequality) have the strongest influence on social trust levels while racial diversity has a negligible effect. This is encouraging for a country with South Africa's racial diversity and troubled history. Instead, efforts to address South Africa's social trust deficit should focus on increasing citizens' confidence in institutions and addressing the high levels of income inequality. However, given the dire state of institutional confidence and income inequality in the country, it remains unlikely that these conditions will improve in the short term.

The sharp form of the Kolmogorov–Rogozin inequality and a conjecture of Leader–Radcliffe

AbstractLet be a random variable and define its concentration function by For a sum of independent real‐valued random variables, the Kolmogorov–Rogozin inequality states that In this paper, we give an optimal bound for in terms of , which settles a question posed by Leader and Radcliffe in 1994. Moreover, we show that the extremal distributions are mixtures of two uniform distributions each lying on an arithmetic progression.

After the 20th Century: Growth, Convergence and Divergence in Indian Mountainous States

This paper deals with the growth, convergence, divergence and inequalities in the mountainous states of India. The data used in this paper was collected from the RBI site, which covers two decades – the first from 2000-01 to 2010-11 and the second from 2011-12 to 2021-22. By analyzing the data, this study attempted to address the compound annual growth rates with regression equation and concluded that, Meghalaya has the lowest and Sikkim has the highest net state domestic product growth rate for the entire time period (2000-01 to 2021-22). In mountainous states, the average growth rate of per capita net state domestic product declined from 6.13 percent in 2000-01/2010-11 to 4.40 percent in 2011-12/2021-22. Higher per capita net state domestic product growth rates were estimated for Himachal Pradesh, Mizoram, Sikkim, Tripura and Uttarakhand; when compared to the average growth rate for the mountainous states and India as a whole. Over the period 2000-01/2010-11 to 2011-12/2021-22, the states with the highest compound annual growth rates on per capita net state domestic product were Assam and Mizoram. In a detailed analysis of income inequality, the gini coefficient increased from 0.122 to 0.263 during 2000-01 to 2021-22 and the coefficient of variation also showed an increase. The findings revealed that there was a significant presence of σ - divergence, β - divergence and α - divergence in the mountainous states in the first, second decades and throughout the 21st century.

Military expenditure and income inequality in European NATO Member States

The purpose of this investigation was to empirically assess the association between military expenditure and income inequality in the 19 European member states of NATO between 2011 and 2022. To achieve this, the authors carried out multivariate statistical analysis using Kaplan-Meier life tables and survival estimation techniques. The results highlighted a trend in the countries analysed that income inequality tended to decrease when investment in the military increased during the period under consideration. The association manifested itself in the shortest time in the group of countries with the lowest military spending per capita, while emerging in the longer term in the countries with the highest. Furthermore, under high threat of war, the association tends to be shortest in relative terms in countries with the lowest military expenditure per capita. The results also revealed that the association between military spending and income inequality is more pronounced in the smallest countries by population and those with the lowest military expenditure per capita. The authors believe that this investigation will enrich scientific knowledge with new insights.

Challenges in Achieving Consensus on Data Localization: Digital Inequality of Digital Service Trade

The disagreements on data localization policies significantly hamper the progression of digital service trade and free cross-border data flow. This study adopts the Theory of Comparative Advantage and the Heckscher-Ohlin Theory (H-O Theory) to construct an analytical model that investigates the inequality of digital service trade on the well-being of nations and the valuation of digital factors. Our findings suggest that digital service trade exacerbates the terms of trade for developing countries. In an environment of unrestricted data flow, developed countries capitalize on the data resources from developing nations, thereby augmenting their digital comparative advantages and factor endowments. The dynamics foster a state of digital inequality or digital poverty, where late-developing countries are disadvantaged in keeping pace with their developed counterparts. Notably, data localization, while seemingly a protective measure for developing countries, may not be the optimal strategy. It potentially undermines the overall well-being of all participants by diminishing network effects. The paper argues that the path towards the liberalization of digital trade and data flows will be a lengthy and complex one, demanding concerted international efforts to overcome entrenched trade barriers.

A sharper bound of the Hotelling–Solomons inequality

AbstractThe original Hotelling–Solomons inequality states that an upper bound of the absolute difference between the mean and median, standardised by the standard deviation, is 1. However, in this paper, we introduce a new bound that depends on the sample size, which is strictly smaller than 1.

Rearrangement inequalities on the lattice graph

AbstractThe Polya–Szegő inequality in states that, given a nonnegative function , its spherically symmetric decreasing rearrangement is ‘smoother’ in the sense of for all . We study analogues on the lattice grid graph . The spiral rearrangement is known to satisfy the Polya–Szegő inequality for , the Wang‐Wang rearrangement satisfies it for and no rearrangement can satisfy it for . We develop a robust approach to show that both these rearrangements satisfy the Polya–Szegő inequality up to a constant for all . In particular, the Wang‐Wang rearrangement satisfies for all . We also show the existence of (many) rearrangements on such that for all .

Bound‐based control design for permanent magnet linear motor servo system with inequality constraints and uncertainties

AbstractThe permanent magnet linear motor (PMLM) systems are widely applied in various engineering fields. However, the state inequality constraints and uncertainties of parameters and unknown external disturbances need to be further explored. In this article, first, a state transformation method is proposed for converting bounded states to unbounded states. As a result, the output state of system is limited within the expected boundary constraint. Then, a new control strategy is constructed. This strategy can ensure that the controlled system with uncertainties is uniformly bounded and uniformly ultimately bounded. Finally, the effectiveness of the controller and the state transformation method are verified through simulation of PMLM system. The inequality constraints of the output state are satisfied, and the system performance is improved.

The maximal violation of the Svetlichny inequality for “X” states and the extended GHZ states

For a quantum system, violation of a Svetlichny inequality indicates the existence of genuine nonlocality. Through the same mathematical analysis approach, we derive the analytical expressions of the maximal violation of the Svetlichny inequality for certain three-qubit pure states and mixed “X” states. These pure states represented in the five-parameter form belong to extended GHZ states. It is convenient to use the obtained expression to distinguish the genuine nonlocal states in these states. We also obtain the analytical expression of the maximal violation of Svetlichny inequality for a subclass of four-qubit “X” states. We show the application potentiality of these expressions by designing two schemes where quantum resources are converted from less qubits “X” states to more qubits “X” states.

A strong subadditivity‐like inequality for quantum entropy in semifinite von Neumann algebras

AbstractLet be a semifinite von Neumann algebra with a normal faithful semifinite trace , and let , , be its subalgebras such that and that restricted to any of these subalgebras is semifinite. Denote by , , and the normal conditional expectations from onto , and , respectively, such that is invariant with respect to any of them. The quadruple , , , is said to be a commuting square if In this note, we show that the property of being a commuting square is characterized by a sort of the SSA‐like (strong subadditivity of entropy) inequality for an arbitrary normal state on , where denotes the Segal entropy of the state . The situation when we have equality in the inequality above is also investigated, and various equivalent conditions are obtained, in an especially appealing form for finite von Neumann algebras. For such algebras, one more condition is obtained under the assumption of independence of the algebras and .

Unequal unification? Income inequality and unification in nineteenth century Italy and Germany

This research provides a comprehensive study of the linkages between institutional structures, balance of power between core and peripheries, endogenous extractive policies and inequality in the context of nineteenth century unification of Germany and Italy. To conduct this analysis, the study puts forward estimates of income inequality for pre-unification German states using social tables, compiled using primary data, some of which have thus far been unexplored in economic research. The findings suggest that the power balance between core and periphery, systems of government as well as distorted policies contributed to differences between the Italian and German experiences, specifically to the rise of inequality in the former and no marked increase in the latter.

One generation apart: Individual income and life expectancy in two Swedish cohorts born before and after the expansion of the welfare state

Aims: Social inequalities in mortality persist or even increase in high-income countries. Most evidence is based on a period approach to measuring mortality – that is, data from individuals born decades apart. A cohort approach, however, provides complementary insights using data from individuals who grow up and age under similar social and institutional arrangements. This study compares income inequalities in cohort life expectancy in two Swedish cohorts, one born before and one born after the expansion of the welfare state. Methods: Data on individuals born in Sweden in 1922–1926 and 1951–1955 were obtained from total population registries. These data were linked to individual disposable income from 1970 and 1999 and mortality between 50 and 61 years of age in 1972–1987 and 2001–2016, respectively. We calculated cohort temporary life expectancies in the two cohorts by income and gender. Results: Life expectancy, income, and income inequalities in life expectancy increased between the two cohorts, for both men and women. Women born in 1922–1926 had modest income differences in life expectancy, but pronounced differences emerged in the cohort born in 1951–1955. Men with low incomes born in 1951–1955 had roughly similar life expectancy as those with low incomes born in 1922–1926. Conclusions: Compared with a period approach to life expectancy trends, the cohort approach highlights the stagnation of mortality at the lowest income groups for men and the rapid emergence of a mortality gradient for women. Future research on health inequalities in welfare states should consider underlying factors both from a cohort and period perspective.

Approaches to spatial inequalities in a Nordic welfare state – the case of Norway

In this article, the position of the core ideas of equity and equal opportunities within the Nordic model of education today is problematized, using Norway as the case of interest and spatial dividing lines as the main variable in question. I am specifically preoccupied with geographical education differences as part of the ‘unequal opportunity problem’ in Nordic education. Focusing on spatial inequalities in education, something that is rarely addressed by educational authorities, brings light to the assertion that aims that used to be the foundation for the Norwegian education system, are harder to see as guiding principles in education policy today. Through highlighting this, the aim is also to contribute to a discussion of how research related to education in rural areas is situated in the Norwegian context, viewing this in light of Norway as a representative of the Nordic model of education. In the article understanding the agential doings behind the paradox of the Nordic education equality ethos on the one side and the persisting and empirically documented spatial education inequalities on the other, represents the analytic intake.

Income inequality, economic openness and current account imbalances in new EU member states

Income inequality, economic openness and current account imbalances in new EU member states

The Pólya-Szegő inequality for smoothing rearrangements

A basic version of the Pólya-Szegő inequality states that if Φ is a Young function, the Φ-Dirichlet energy—the integral of Φ(‖∇f‖)—of a suitable function f∈V(Rn), the class of nonnegative measurable functions on Rn that vanish at infinity, does not increase under symmetric decreasing rearrangement. This fact, along with variants that apply to polarizations and to Steiner and certain other rearrangements, has numerous applications. Very general versions of the inequality are proved that hold for all smoothing rearrangements, those that do not increase the modulus of continuity of functions. The results cover all the main classes of functions previously considered: Lipschitz functions f∈V(Rn), functions f∈W1,p(Rn)∩V(Rn) (when 1≤p<∞ and Φ(t)=tp), and functions f∈Wloc1,1(Rn)∩V(Rn). In addition, anisotropic versions of these results, in which the role of the unit ball is played by a convex body containing the origin in its interior, are established. Taken together, the results bring together all the basic versions of the Pólya-Szegő inequality previously available under a common and very general framework.

Geometric interpretation and experimental test of Leggett inequalities with nonmaximally entangled states.

Leggett inequality states that nonlocal hidden-variable models might still be incompatible with the predictions of quantum physics. However, its theoretical and experimental demonstration is only in the scenario of 2-dimensional maximally entangled systems. An open question remains as to whether the Leggett inequality can be violated by nonmaximally entangled states. Here, we answer this question both in theory and experiment. Specifically, from the point of view of geometry, we theoretically map the problem of maximizing the correlation measure in the Leggett inequality to maximizing the sum of an ellipse's diameter and semi-diameter axes, accordingly, demonstrating that the violation of the Leggett inequality requires a more robust entanglement than that of Bell's theory. Experimentally, by leveraging the controllable photonic orbital angular momentum entanglement, we demonstrate the violation of Leggett-type inequalities by more than 8.7 and 4.5 standard deviations under concurrence C = 0.95 and 0.9, respectively. Our observations indicate that, the requirement for quantum correlation should be increased to exclude a particular class of non-local hidden variable theories that abide by Leggett's model, providing insights into the boundaries of quantum correlation and the limitations imposed by non-local hidden variables.