Stable Norm Research Articles

Carapace Scute Variations of the Olive Ridley Sea Turtle (<i>Lepidochelys olivacea</i>): Polymerization as an Evolutionary Trend

The carapace scute pattern is an important morphological feature of turtles that, along with the phylogenetic stability, has a high level of intraspecific variability. The olive ridley sea turtle (Lepidochelys olivacea; Cheloniidae) demonstrates extreme instability of pholidosis, and the aim of our study is to identify the range of the carapace scute variations in this species. We studied 655 L. olivacea hatchlings from nine natural clutches on the Southern coast of Sri Lanka and identified 120 different patterns of carapace scutes. The vertebral and pleural scutes were the most variable, ranging in number from four or five to ten. Five pairs of pleural scutes, a normal condition for some species of sea turtles, were found in only 11.9% of individuals. The hatchlings with six and seven scutes in the vertebral and pleural series were the most numerous. 13 pairs of marginal scutes were the stable norm in 92.7% of individuals. Newborn turtles with symmetrical scute patterns predominated (60.9%). Comparison of the pholidosis variability in hatchlings from different clutches revealed the presence of specific scute patterns. We assume that the clutch differences are more related to the genetic characteristics of the breeding turtles than to the influence of environmental factors. The unique variable pholidosis of L. olivacea demonstrates a trend toward scute polymerization, a rare phenomenon in turtle evolution.

Rules of recognition? Explaining diplomatic representation since the Congress of Vienna

The aim of this article is to explore the establishment of diplomatic representation as a measure of de facto recognition by other state units and to explain its causes in the “long 19th century” (1817–1914) and the post–World War II (WWII) era (1950–2000). Drawing on the Correlates of War diplomatic exchange data, the article explores the underlying drivers of dyadic acts of recognition in two series of logistic regression analyses, one for each time period. The results indicate that, also when taking alternative explanations into account, recognition of other states in the international system was in the 19th century at least based on one general principle: that of recognizing other de facto states. In the post-WWII era, contrary to expectations, this principle was still in effect. De facto statehood can thus be argued to constitute a rather stable norm for recognition in the international system.

Boundary slopes for the Markov ordering on relatively prime pairs

Following McShane, we employ the stable norm on the homology of the modular torus to investigate the Markov ordering on the set of relatively prime integer pairs (q,p) with q≥p≥0. Our main theorem is a characterization of slopes along which the Markov ordering is monotone with respect to q, confirming conjectures of Lee-Li-Rabideau-Schiffler that refine conjectures of Aigner. The main tool is an explicit computation of the slopes at the corners of the stable norm ball for the modular torus.

Region social capital: institutional and social and cultural resources for the development of human capital in the republics of Tyva and Khakassia

Social capital, which is considered as a resource of human and physical capital, is increasingly positioned as one of the most significant factors in the development of modern society, especially local, regional, striving, in view of objective reasons and limitations, to use all available development resources. The South Siberian republics of Tyva and Khakassia, which still show low indicators of economic growth and the human development index, rarely fell into the focus of research interest in terms of analyzing the characteristics and dynamics of the functioning of social capital. The article examines the general conceptual approaches and particular methodological developments of domestic and foreign authors to the analysis of social capital. The main goal of the study, which is to analyze the features of the functioning of the components of the regional social capital of the South Siberian republics, is achieved by combining private indicators (index of trust capital, norms and values, social networks). As an empirical basis for the study, we used the results of opinion polls in 2013, 2016 and 2019 in the Republics of Tyva and Khakassia according to a standardized program (sample population: Khakassia — 520 people, Tuva — 290 people). The results of the study allow us to draw a well-grounded conclusion that the strongest component of the region’s social capital is the capital of values and norms, which is a consequence of the formation of a stable norm of tolerance and universal morality system, a stable complementarity of interethnic and cultural relations. The processes of actualization of alternative national identities, the preservation of tension in interethnic relations remain the risk space with low indices of the development of open social capital; decrease in trust and satisfaction with the activities of the authorities and preservation of a predominantly conformist model of social and political behavior of the region inhabitants. The priority of the federal and regional authorities, as well as civil society institutions and local self-government bodies, should be to increase the level of trust in them by the residents of the region.

When does ‖f(A)‖ = f(‖A‖) hold true?

Let a strongly stable norm on the set of complex n-by-n matrices be given, which means that for all and all . Furthermore, let be a power series with nonnegative coefficients and radius of convergence R>0. If , we additionally suppose that . We aim to characterize those A with , which fulfil . We first show how to reduce the discussion of f to Neumann series. For matrix norms induced by uniformly convex vector norms, like the -norms, , it follows from known results of the Daugavet equation that holds true if, and only if, is an eigenvalue of A, provided that for some . Under adapted assumptions on the we prove that this equivalence remains true for the - and the -norm, for unitarily invariant matrix norms and for the numerical radius. We conjecture this equivalence to be valid for all strongly stable norms if for all .

A Story of us: A New Look at Human Evolution

A Story of us: A New Look at Human Evolution

When does an advantage become unfair? Empirical and normative concerns in Semenya’s case

There is a fundamental tension in many sports: human sex is not binary, but there are only two categories in which people can compete: male and female. Over the past...

Markov numbers, Mather’s β function and stable norm

Fock (1997 (arXiv:dg-ga/9702018v3); Fock et al 2007 Handbook of Teichmüller Theory (Zürich: European Mathematical Society)) introduced an interesting function related to Markov numbers. We explain its relation to Federer–Gromov’s stable norm and Mather’s -function, and use this to study its properties. We prove that and its natural generalisations are differentiable at every irrational x and non-differentiable otherwise, by exploiting the relation with length of simple closed geodesics on the punctured or one-holed tori with the hyperbolic metric and the results by Bangert (1994 Calculus Variations Partial Differ. Equ. 2 49–63) and McShane–Rivin (1995 C. R. Acad. Sci. Paris I 320).

Off-line synthesis of evolutionarily stable normative systems

Within the area of multi-agent systems, normative systems are a widely used framework for the coordination of interdependent activities. A crucial problem associated with normative systems is that of synthesising norms that will effectively accomplish a coordination task and that the agents will comply with. Many works in the literature focus on the on-line synthesis of a single, evolutionarily stable norm (convention) whose compliance forms a rational choice for the agents and that effectively coordinates them in one particular coordination situation that needs to be identified and modelled as a game in advance. In this work, we introduce a framework for the automatic off-line synthesis of evolutionarily stable normative systems that coordinate the agents in multiple interdependent coordination situations that cannot be easily identified in advance nor resolved separately. Our framework roots in evolutionary game theory. It considers multi-agent systems in which the potential conflict situations can be automatically enumerated by employing MAS simulations along with basic domain information. Our framework simulates an evolutionary process whereby successful norms prosper and spread within the agent population, while unsuccessful norms are discarded. The outputs of such a natural selection process are sets of codependent norms that, together, effectively coordinate the agents in multiple interdependent situations and are evolutionarily stable. We empirically show the effectiveness of our approach through empirical evaluation in a simulated traffic domain.

A quantitative bounded distance theorem and a Margulis’ lemma for $\mathbb Z^n$-actions, with applications to homology

We consider the stable norm associated to a discrete, torsionless abelian group of isometries \Gamma \cong \mathbb Z^n of a geodesic space (X,d) . We show that the difference between the stable norm \| \;\, \|_{\mathrm {st}} and the distance d is bounded by a constant only depending on the rank n and on upper bounds for the diameter of \bar X=\Gamma \backslash X and the asymptotic volume \omega(\Gamma, d) . We also prove that the upper bound on the asymptotic volume is equivalent to a lower bound for the stable systole of the action of \Gamma on (X,d) ; for this, we establish a lemma à la Margulis for \mathbb{Z}^n -actions, which gives optimal estimates of \omega(\Gamma,d) in terms of stsys (\Gamma,d) , and vice versa, and characterize the cases of equality. Moreover, we show that all the parameters n , diam (\bar X) and \omega (\Gamma, d) (or stsys (\Gamma,d) ) are necessary to bound the difference d -\| \;\, \|_{\mathrm {st}} , by providing explicit counterexamples for each case. As an application in Riemannian geometry, we prove that the number of connected components of any optimal, integral 1-cycle in a closed Riemannian manifold \bar X either is bounded by an explicit function of the first Betti number, diam (\bar X) and \omega(H_1(\bar X, \mathbb{Z})) , or is a sublinear function of the mass.

The stable norm on the 2-torus at irrational directions

We study properties of the stable norm on the first homology group of the 2-torus with respect to Riemannian or Finsler metrics, focusing on points with irrational slope. Our results show that the stable norm detects KAM-tori and hyperbolicity in the geodesic flow. Along the way, we shall prove new inequalities for the stable norm near rational directions. Moreover, we study the stable norm in some natural examples reflecting the new results in this paper.

Socially Enforced Nepotism: How Norms and Reputation Can Amplify Kin Altruism.

Kin selection, which can lead organisms to behave altruistically to their genetic relatives, works differently when—as is often the case in human societies—altruism can be boosted by social pressure. Here I present a model of social norms enforced by indirect reciprocity. In the model there are many alternative stable allocations of rewards (“distributional norms”); a stable norm is stable in the sense that each player is best off following the norm if other players do the same. Stable norms vary widely in how equally they reward players with unequal abilities. In a population of mixed groups (some group members follow one norm, some follow another, and some compromise) with modest within-group coefficients of relatedness, selection within groups favors those who compromise, and selection between groups favors generous generalized reciprocity rather than balanced reciprocity. Thus evolved social norms can amplify kin altruism, giving rise to a uniquely human mode of kin-based sociality distinct from spontaneous altruism among close kin, or cooperation among non-kin.

Adaptive Norm Selection for Regularized Image Restoration and Super-Resolution.

In the commonly employed regularization models of image restoration and super-resolution (SR), the norm determination is often challenging. This paper proposes a method to adaptively determine the optimal norms for both fidelity term and regularization term in the (SR) restoration model. Inspired by a generalized likelihood ratio test, a piecewise function is proposed to solve the norm of the fidelity term. This function can find the stable norm value in a certain number of iterations, regardless of whether the noise type is Gaussian, impulse, or mixed. For the regularization norm, the main advantage of the proposed method is that it is locally adaptive. Specifically, it assigns different norms for different pixel locations, according to the local activity measured by a structure tensor metric. The proposed method was tested using different types of images. The experimental results and error analyses verify the efficacy of the method.

Variability of Structural and Biomechanical Parameters of Pelophylax Esculentus (Amphibia, Anura) Limb Bones

Abstract Variability of Structural and Biomechanical Prameters of Pelophylax esculentus (Amphibia, Anura) Limb Bones. Broshko Ye. O. — Structural and biomechanical parameters of Edible Frog, Pelophylax esculentus (Linnaeus, 1758), limb bones, namely, mass, linear dimensions, parameters of the shaft’s cross-sectional shape (cross-sectional area, moments of inertia, radiuses of inertia) were investigated. Some coefficients were also estimated: diameters ratio (df/ds), cross-sectional index (ik), principal moments of inertia ratio (Imax/Imin.). Coefficients of variation of linear dimensions (11.9-20.0 %) anrelative bone mass (22-35 %) were established. Moments of inertia of various bones are more variable (CV = 41.67-56.35 %) in relation to radii of inertia (CV = 9.68-14.67 %). Shaft’s cross-sectional shape is invariable in all cases. However, there is high individual variability of structural and biomechanical parameters of P. esculentus limb bones. Variability of parameters was limited by the certain range. We suggest the presence of stable norm in bone structure. Stylopodium bones have the primary biomechanical function among the elements of limb skeleton, because their parameters most clearly responsive to changes in body mass.

On the intersection form of surfaces

Given a closed, oriented surface M, the algebraic intersection of closed curves induces a symplectic form Int(.,.) on the first homology group of M. If M is equipped with a Riemannian metric g, the first homology group of M inherits a norm, called the stable norm. We study the norm of the bilinear form Int(.,.), with respect to the stable norm.

Plane-Like Minimizers and Differentiability of the Stable Norm

In this paper we investigate the strict convexity and the differentiability properties of the stable norm, which corresponds to the homogenized surface tension for a periodic perimeter homogenization problem (in a regular and uniformly elliptic case). We prove that it is always differentiable in totally irrational directions, while in other directions, it is differentiable if and only if the corresponding plane-like minimizers satisfying a strong Birkhoff property foliate the torus. We also discuss the issue of the uniqueness of the correctors for the corresponding homogenization problem.

Constructing metrics on a 2-torus with a partially prescribed stable norm

A result of Bangert states that the stable norm associated to any Riemannian metric on the 2-torus T 2 is strictly convex. We demonstrate that the space of stable norms associated to metrics on T 2 forms a proper dense subset of the space of strictly convex norms on $${{\mathbb R}^2}$$ . In particular, given a strictly convex norm || · ||∞ on $${{\mathbb R}^2}$$ we construct a sequence $${\langle {\| \cdot \|}_j \rangle_{j=1}^{\infty}}$$ of stable norms that converge to || · ||∞ in the topology of compact convergence and have the property that for each r > 0 there is an $${N \equiv N(r)}$$ such that || · || j agrees with || · ||∞ on $${{\mathbb Z}^2 \cap \{(a,b) : a^2 + b^2 \leq r \}}$$ for all j ≥ N. Using this result, we are able to derive results on multiplicities which arise in the minimum length spectrum of 2-tori and in the simple length spectrum of hyperbolic tori.

Institutional Traps and Transition

Two myths have harmed many economies throughout the world. One is the theory of absolute advantage of central planning over the market mechanism, and the other is the belief that efficient markets develop spontaneously and quickly enough if appropriate economic legislation is established. Volumes have been written to debunk the first myth. The falsity of the second needs to be better understood. The problem is that inside of any legislated change there exists a room for development of different institutions, or behavior norms, and it is not simple to predict which direction will be chosen by an economy. The hypothesis that efficient institutions must arise because of natural selection does not prove to be truthful. Inefficient development can be self-supporting and stable. The supporting mechanisms were systematically investigated by Arthur (1988) for technological changes. North (1990) pointed out that the same mechanisms plaid an important role in the evolution of institutions. A number of examples have been studied in different branches of economics. The most striking examples can be found in recent history of economic reforms in Russia and East European countries. This chapter uses the ideas by Arthur and North to describe a general scheme for the formation of inefficient yet stable norm or institutions, referred herein as institutional traps. The scheme is substantially based on the concepts of transaction costs, transformation costs, and transitional rent discussed below. Then the theory developed is applied to explain emergence in Russia of barter, mutual arrears, tax evasion, corruption, and some other institutional traps. Implications for reform strategy are explored. The analysis shows that the formation of institutional traps is a major risk in any reform process, and avoidance of these traps is an urgent task during transition.

Metric techniques for convex stationary ergodic Hamiltonians

We adapt the metric approach to the study of stationary ergodic Hamilton–Jacobi equations, for which a notion of admissible random (sub)solution is defined. For any level of the Hamiltonian greater than or equal to a distinguished critical value, we define an intrinsic random semidistance and prove that an asymptotic norm does exist. Taking as source region a suitable class of closed random sets, we show that the Lax formula provides admissible subsolutions. This enables us to relate the degeneracies of the critical stable norm to the existence/nonexistence of exact or approximate critical admissible solutions.

Hedlund metrics and the stable norm

The real homology of a compact Riemannian manifold M is naturally endowed with the stable norm. The stable norm on H 1 ( M , R ) arises from the Riemannian length functional by homogenization. It is difficult and interesting to decide which norms on the finite-dimensional vector space H 1 ( M , R ) are stable norms of a Riemannian metric on M. If the dimension of M is at least three, I. Babenko and F. Balacheff proved in [I. Babenko, F. Balacheff, Sur la forme de la boule unité de la norme stable unidimensionnelle, Manuscripta Math. 119 (3) (2006) 347–358] that every polyhedral norm ball in H 1 ( M , R ) , whose vertices are rational with respect to the lattice of integer classes in H 1 ( M , R ) , is the stable norm ball of a Riemannian metric on M. This metric can even be chosen to be conformally equivalent to any given metric. In [I. Babenko, F. Balacheff, Sur la forme de la boule unité de la norme stable unidimensionnelle, Manuscripta Math. 119 (3) (2006) 347–358], the stable norm induced by the constructed metric is computed by comparing the metric with a polyhedral one. Here we present an alternative construction for the metric, which remains in the geometric framework of smooth Riemannian metrics.