Socio-economic inequality is characterized from data using various indices. The Gini () index, giving the overall inequality is the most common one, while the recently introduced Kolkata () index gives a measure of fraction of population who possess top fraction of wealth in the society. Here, we show t…
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48 results for “inequality indices”
The study calculates braid indices for two-bridge knots and proves inequalities.
problem Calculating the braid index of two-bridge knots.
method Proved inequalities and provided average braid index for knots of a given crossing number.
result Average braid index for two-bridge knots with a given crossing number.
New Gini indices capture more nuanced income inequality.
problem Measuring joint dispersion across multiple observations.
method Axiomatic approach to define and characterize n-th order Gini deviations.
result Higher-order Gini coefficients reveal more extreme income disparities.
Socio-economic inequality is measured using various indices. The Gini () index, giving the overall inequality is the most commonly used, while the recently introduced Kolkata () index gives a measure of fraction of population who possess top fraction of wealth in the society. This article reviews the ch…
Study analyzes financial distributions and inequality in professional cycling teams.
problem Financial inequality and concentration among cycling teams.
method Rank-size law and various inequality indices applied to Tour de France data.
result Financial gains distribution is hyperbolic with a decay exponent of about -1, contrary to Pareto principle.
We prove the existence of a knot whose braid index the Morton-Franks-Williams inequality fails to detect but a related inequality (KR-MFW inequality), which uses new information of Khovanov-Rozansky homology, detects. We also prove, by examples, that there exists infinitely many knots for which the KR-MFW inequality fa…
In this paper, we study the inequality indices for some models of wealth exchange. We calculated Gini index and newly introduced k-index and compare the results with reported empirical data available for different countries. We have found lower and upper bounds for the indices and discuss the efficiencies of the models…
New isoperimetric inequalities in the plane with radial weights identified.
problem Finding isoperimetric shapes in the plane with radial power weights.
method Analyzing the punctured plane with specific volume and perimeter densities.
result Centred balls are uniquely isoperimetric under certain conditions.
We argue that a stochastic model of economic exchange, whose steady-state distribution is a Generalized Beta Prime (also known as GB2), and some unique properties of the latter, are the reason for GB2's success in describing wealth/income distributions. We use housing sale prices as a proxy to wealth/income distributio…
Trading strategy uses Hoeffding's Inequality to predict financial regime change.
problem Predicting financial regime change for trading strategies.
method Applies Hoeffding's Inequality to trading performance data.
result Early warning of financial regime change can be detected.
Paper proves inequality linking capillary surfaces to Finsler geometry.
problem Proving a Heintze-Karcher inequality for capillary hypersurfaces.
method Introduced a Finsler metric for geodesic flow and studied the hypersurface properties.
result Established a new inequality relating capillary surfaces to Finsler geometry.
A global agreement on how to reduce and cap human footprint, especially their GHG emissions, is very unlikely in near future. At the same time, bilateral agreements would be inefficient because of their neural and balanced nature. Therefore, unilateral actions would have attracted attention as a practical option. Howev…
We point out a simple equities trading strategy that allows a sufficiently large, market-neutral, quantitative hedge fund to achieve outsized returns while simultaneously contributing significantly to increasing global wealth inequality. Overnight and intraday return distributions in major equity indices in the United …
The paper contains a short review of techniques examining regional wealth inequalities based on recently published research work but is also presenting unpublished features. The data pertains to Italy (IT), over the period 2007-2011: the number of cities in regions, the number of inhabitants in cities and in regions, a…
Signature of maturity in cryptocurrency volatilityphysics.soc-ph
Study shows cryptocurrency price fluctuations become more similar to national currencies over time.
problem Understanding the volatility and inequality in cryptocurrency prices.
method Calculated inequality measures (Gini, Kolkata indices, factor) for cryptocurrency and national currency price fluctuations over 10 years.
result Cryptocurrency price fluctuations become more similar to national currencies over time.
Develops virtual Morse-Bott indices for four-manifolds, proving inequalities.
problem Proving inequalities for four-manifolds of Seiberg-Witten simple type.
method Uses virtual Morse-Bott indices and Hirzebruch-Riemann-Roch Theorem.
result Proves positivity of virtual Morse-Bott indices, leading to inequalities.
We consider concepts and models for measuring inequality in the distribution of resources with a focus on how inequality varies as a function of covariates. Lorenz introduced a device for measuring inequality in the distribution of income that indicates how much the incomes below the u quantile fall short of the…
Let be the diffusion semigroup generated by on a complete connected Riemannian manifold with for some constants and the Riemannian distance to a fixed point. It is shown that is hypercontractive, or the log-Sobolev inequality holds for the…
We investigate the Brazilian personal income distribution using data from National Household Sample Survey (PNAD), an annual research available by the Brazilian Institute of Geography and Statistics (IBGE). It provides general characteristics of the country's population. Using PNAD data background we also confirm the e…
We propose a modified -divergence, give some of its properties, and show that this leads to the definition of a generalized Fisher information. We give generalized Cramér-Rao inequalities, involving this Fisher information, an extension of the Fisher information matrix, and arbitrary norms and power of the estimat…
The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincaré inequalities. Typically two kind of sensitivity indices are linked by a Poincaré type inequality, which provide upper bounds of the most interpretable index by using the other one, cheaper …
Twists agrarian and -Betti numbers for locally indicable groups.
problem Understanding -Betti numbers of locally indicable groups.
method Using generalised agrarian invariants and twisted Alexander-Thurston norms.
result Twisted -Betti numbers are equal to usual -Betti numbers rescaled by the dimension of the twisting representation.
The paper proves stability of eigenvalue inequalities on surfaces.
problem Stability of isoperimetric inequalities for Laplace eigenvalues on surfaces.
method Employing eigenvalues of measures and Sobolev space , the paper proves stability estimates for the first and second nonzero Laplace eigenvalues on surfaces.
result Metrics almost maximizing the normalized eigenvalue are -close to a maximal metric.
A society or country with income equally distributed among its people is truly a fiction! The phenomena of socioeconomic inequalities have been plaguing mankind from times immemorial. We are interested in gaining an insight about the co-evolution of the countries in the inequality space, from a data science perspective…
The counting function on the natural numbers defines a discrete Morse-Smale complex with a cohomology for which topological quantities like Morse indices, Betti numbers or counting functions for critical points of Morse index are explicitly given in number theoretical terms. The Euler characteristic of the Morse filtra…
The paper develops techniques to study entropy and rigidity in RCD-spaces.
problem Entropy and rigidity in RCD-spaces.
method Develops the barycenter technique for RCD-spaces and applies it to show entropy-volume inequalities.
result RCD-spaces with equality in entropy-volume inequality are locally symmetric.
Discrimination via algorithmic decision making has received considerable attention. Prior work largely focuses on defining conditions for fairness, but does not define satisfactory measures of algorithmic unfairness. In this paper, we focus on the following question: Given two unfair algorithms, how should we determine…
Linear stochastic models and discretized kinetic theory are two complementary analytical techniques used for the investigation of complex systems of economic interactions. The former employ Langevin equations, with an emphasis on stock trade; the latter is based on systems of ordinary differential equations and is bett…
Geometric tempering fails for Langevin dynamics, proving convergence limits.
problem Proving convergence and limitations of geometric tempering for Langevin dynamics.
method Theoretical investigation of geometric tempering using Langevin dynamics.
result Geometric tempering can lead to exponential time convergence and poor functional inequalities.
Gradient-enhanced GSA uses Poincaré chaos expansions for accurate sensitivity analysis.
problem Accurately estimating Sobol' indices with limited data.
method Integrates sparse, gradient-enhanced regression with Poincaré chaos expansions for derivative-based sensitivity analysis.
result Accurately estimated Sobol' indices using limited data.
Proposes counterfactual explainability for causal attribution, extending variance analysis methods.
problem Lack of mechanistic understanding in existing tools for explaining complex models.
method Extends global sensitivity analysis methods to causal explanations using directed acyclic graphs.
result Developed methods to estimate counterfactual explainability and applied to income inequality analysis.
Motivated by the sampling problems and heterogeneity issues common in high- dimensional big datasets, we consider a class of discordant additive index models. We propose method of moments based procedures for estimating the indices of such discordant additive index models in both low and high-dimensional settings. Our …
In this article, we thoroughly investigate the stability inequality for Ricci-flat cones. Perhaps most importantly, we prove that the Ricci-flat cone over CP^2 is stable, showing that the first stable non-flat Ricci-flat cone occurs in the smallest possible dimension. On the other hand, we prove that many other example…
Bounds neural network output distribution to Gaussian for random initialization.
problem Quantifying the distribution of randomly initialized deep neural networks.
method Quantitative Gaussian approximation using quadratic Wasserstein distance.
result Explicit inequalities show how network sizes affect Gaussian behavior.
The paper establishes a continuous embedding between two types of Barron spaces in neural networks.
problem Understanding the relationship between two types of Barron spaces in neural networks.
method Introduced a continuous embedding inequality between Barron and spectral Barron spaces.
result The embedding inequality holds for any function in the spaces, with constants independent of the input dimension.
On the Renyi entropy power and the Gagliardo-Nirenberg-Sobolev inequality on Riemannian manifoldsmath.DG
The paper proves properties of Renyi entropy power on Riemannian manifolds.
problem Properties of Renyi entropy power on Riemannian manifolds.
method Proof of concavity, rigidity models, Aronson-Benilan estimates, NIW formula, entropy isoperimetric inequality.
result Rigidity models and intrinsic relationships for Renyi entropy power.
New set class preserves Fourier series terms for planar ovals, leading to isoperimetric inequalities.
problem Investigate geometric properties of th Order Preserving Sets and ovals.
method Introduce and analyze th Order Preserving Sets and Midpoint Sets; study geometric properties and isoperimetric inequalities.
result Established an isoperimetric-type inequality relating perimeter and area of ovals and their associated sets.
Optimizes policies for reinforcement learning with limited data.
problem Computing reliable policies with high confidence in reinforcement learning problems.
method Robust MDPs (RMDPs) with weighted L1 and L∞ norms to minimize ambiguity set spans.
result Optimized ambiguity sets improve policy performance significantly.
The dynamic time warping (dtw) distance fails to satisfy the triangle inequality and the identity of indiscernibles. As a consequence, the dtw-distance is not warping-invariant, which in turn results in peculiarities in data mining applications. This article converts the dtw-distance to a semi-metric and shows that its…
The paper bounds growth indicator functions for discrete subgroups in algebraic groups.
problem Bounding growth indicator functions for discrete subgroups in algebraic groups.
method Pointwise bound and equality conditions for growth indicator functions.
result Strict inequalities and equality conditions for growth indicator functions.
Global inequality in energy consumption from 1980 to 2010physics.data-an
We study the global probability distribution of energy consumption per capita around the world using data from the U.S. Energy Information Administration (EIA) for 1980-2010. We find that the Lorenz curves have moved up during this time period, and the Gini coefficient G has decreased from 0.66 in 1980 to 0.55 in 2010,…
This research proves a topological inequality for symplectic four-manifolds using non-Abelian monopoles.
problem Proving the Bogomolov-Miyaoka-Yau inequality for symplectic four-manifolds.
method Using Morse theory on the moduli space of non-Abelian monopoles, focusing on the square of the norm of coupled spinors.
result Existence of a projectively anti-self-dual connection on a rank-two Hermitian vector bundle over a blow-up of the four-manifold.
New statistical test for change-point detection using relative entropy.
problem Offline change-point detection using divergence metrics.
method Study of empirical relative entropy distributions, derivation of approximations, introduction of new Berry-Esseen bounds.
result Theoretical and practical validation of relative entropy for change-point detection.
The paper introduces a penalized matrix estimation procedure aiming at solutions which are sparse and low-rank at the same time. Such structures arise in the context of social networks or protein interactions where underlying graphs have adjacency matrices which are block-diagonal in the appropriate basis. We introduce…
Unified framework for risk-aware policy learning in contextual bandits.
problem Optimizing decision rules in high-stakes domains with adverse outcomes.
method Distributional framework for Lipschitz-continuous risk functionals, with novel empirical concentration inequalities.
result Data-dependent suboptimality bounds with an rate, matching risk-neutral offline policy optimization.
New sampling bounds improve uniform coverage verification in machine learning.
problem Conservative bounds in classical coverage analyses at small failure probabilities.
method Variance-based analysis of uniform random sampling on a -dimensional unit hypercube.
result Sample complexity bound with logarithmic dependence on failure probability.
Proves inequality linking foliation indices for complex plane curves.
problem Bounding Gómez-Mont-Seade-Verjovsky index for foliations.
method Dimca-Greuel type inequality proof for foliations.
result New proof of Dimca-Greuel conjecture for plane curve singularities.
This article establishes the performance of stochastic blockmodels in addressing the co-clustering problem of partitioning a binary array into subsets, assuming only that the data are generated by a nonparametric process satisfying the condition of separate exchangeability. We provide oracle inequalities with rate of c…