Local Universality Research Articles

MSHHOTSA: A variant of tunicate swarm algorithm combining multi-strategy mechanism and hybrid Harris optimization.

This paper proposes a novel hybrid algorithm, named Multi-Strategy Hybrid Harris Hawks Tunicate Swarm Optimization Algorithm (MSHHOTSA). The primary objective of MSHHOTSA is to address the limitations of the tunicate swarm algorithm, which include slow optimization speed, low accuracy, and premature convergence when dealing with complex problems. Firstly, inspired by the idea of the neighborhood and thermal distribution map, the hyperbolic tangent domain is introduced to modify the position of new tunicate individuals, which can not only effectively enhance the convergence performance of the algorithm but also ensure that the data generated between the unknown parameters and the old parameters have a similar distribution. Secondly, the nonlinear convergence factor is constructed to replace the original random factor c1 to coordinate the algorithm's local exploitation and global exploration performance, which effectively improves the ability of the algorithm to escape extreme values and fast convergence. Finally, the swarm update mechanism of the HHO algorithm is introduced into the position update of the TSA algorithm, which further balances the local exploitation and global exploration performance of the MSHHOTSA. The proposed algorithm was evaluated on eight standard benchmark functions, CEC2019 benchmark functions, four engineering design problems, and a PID parameter optimization problem. It was compared with seven recently proposed metaheuristic algorithms, including HHO and TSA. The results were analyzed and discussed using statistical indicators such as mean, standard deviation, Wilcoxon's rank sum test, and average running time. Experimental results demonstrate that the improved algorithm (MSHHOTSA) exhibits higher local convergence, global exploration, robustness, and universality than BOA, GWO, MVO, HHO, TSA, ASO, and WOA algorithms under the same experimental conditions.

Random orthonormal polynomials: Local universality and expected number of real roots

We consider random orthonormal polynomials F n ( x ) = ∑ i = 0 n ξ i p i ( x ) , \begin{equation*} F_{n}(x)=\sum _{i=0}^{n}\xi _{i}p_{i}(x), \end{equation*} where ξ 0 \xi _{0} , …, ξ n \xi _{n} are independent random variables with zero mean, unit variance and uniformly bounded ( 2 + ε ) (2+\varepsilon ) moments, and ( p n ) n = 0 ∞ (p_n)_{n=0}^{\infty } is the system of orthonormal polynomials with respect to a fixed compactly supported measure on the real line. Under mild technical assumptions satisfied by many classes of classical polynomial systems, we establish universality for the leading asymptotics of the average number of real roots of F n F_n , both globally and locally. Prior to this paper, these results were known only for random orthonormal polynomials with Gaussian coefficients (see D. D. Lubinsky, I. E. Pritsker, and X. Xie [Proc. Amer. Math. Soc. 144 (2016), pp. 1631–1642]) using the Kac-Rice formula, a method that does not extend to the generality of our paper.

Spherical Induced Ensembles with Symplectic Symmetry

We consider the complex eigenvalues of the induced spherical Ginibre ensemble with symplectic symmetry and establish the local universality of these point processes along the real axis. We derive scaling limits of all correlation functions at regular points both in the strong and weak non-unitary regimes as well as at the origin having spectral singularity. A key ingredient of our proof is a derivation of a differential equation satisfied by the correlation kernels of the associated Pfaffian point processes, thereby allowing us to perform asymptotic analysis.

Distributed Universal Adaptive Networks

Adaptive networks (ANs) are effective real time techniques to process and track events observed by sensor networks and, more recently, to equip Internet of Things (IoT) applications. ANs operate over nodes equipped with collaborative adaptive filters that solve distributively an estimation problem common to the whole network. However, they <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">do not</i> guarantee that nodes do not lose from cooperation, as compared to its non-cooperative operation; that poor nodes are rejected and exceptional nodes estimates reach the entire network; and that performance is uniform over all nodes. In order to enforce such properties, this work introduces the concept of distributed universal estimation, which encompasses the new concepts of local universality, global universality and universality with respect to the non-cooperative operation. We then construct a new cooperation protocol that is proven to be distributively universal, outperforming direct competitors from the literature, as shown by several simulations. Mean and mean-square analytical models are developed, with good agreement between theory and simulations.

Universal scaling limits of the symplectic elliptic Ginibre ensemble

We consider the eigenvalues of symplectic elliptic Ginibre matrices which are known to form a Pfaffian point process whose correlation kernel can be expressed in terms of the skew-orthogonal Hermite polynomials. We derive the scaling limits and the convergence rates of the correlation functions at the real bulk/edge of the spectrum, which in particular establishes the local universality at strong non-Hermiticity. Furthermore, we obtain the subleading corrections of the edge correlation kernels, which depend on the non-Hermiticity parameter contrary to the universal leading term. Our proofs are based on the asymptotic behavior of the complex elliptic Ginibre ensemble due to Lee and Riser as well as on a version of the Christoffel–Darboux identity, a differential equation satisfied by the skew-orthogonal polynomial kernel.

Roots of random functions: A framework for local universality

:We investigate the local distribution of roots of random functions of the form $F_n(z)=\sum_{i=1}^n\xi_i\phi_i(z)$, where $\xi_i$ are independent random variables and $\phi_i(z)$ are arbitrary analytic functions. Starting with the fundamental works of Kac and Littlewood-Offord in the 1940s, random functions of this type have been studied extensively in many fields of mathematics.We develop a robust framework to solve the problem by reducing, via universality theorems, the calculation of the distribution of the roots and the interaction between them to the case where $\xi_i$ are Gaussian. In this special case, one can use the Kac-Rice formula and various other tools to obtain precise answers.Our framework has a wide range of applications, which include the most popular models of random functions, such as random trigonometric polynomials and all basic classes of random algebraic polynomials (Kac, Weyl, and elliptic). Each of these ensembles has been studied heavily by deep and diverse methods. Our method, for the first time, provides a unified treatment for all of them.Among the applications, we derive the first local universality result for random trigonometric polynomials with arbitrary coefficients. When restricted to the study of real roots, this result extends several recent results, proved for less general ensembles. For random algebraic polynomials, we strengthen several recent results of Tao and the second author, with significantly simpler proofs. As a corollary, we sharpen a classical result of Erd\"{o}s and Offord on real roots of Kac polynomials, providing an optimal error estimate. Another application is a refinement of a recent result of Flasche and Kabluchko on the roots of random Taylor series.

Universality and least singular values of random matrix products: A simplified approach

In this note, we show how to provide sharp control on the least singular value of a certain translated linearization matrix arising in the study of the local universality of products of independent random matrices. This problem was first considered in a recent work of Kopel, O’Rourke, and Vu, and compared to their work, our proof is substantially simpler and established in much greater generality. In particular, we only assume that the entries of the ensemble are centered, and have second and fourth moments uniformly bounded away from 0 and infinity, whereas previous work assumed a uniform subgaussian decay condition and that the entries within each factor of the product are identically distributed. A consequence of our least singular value bound is that the four moment matching universality results for the products of independent random matrices, recently obtained by Kopel, O’Rourke, and Vu, hold under much weaker hypotheses. Our proof technique is also of independent interest in the study of structured sparse matrices.

The Contingency of the Lifeworld in a World of Standards. Repertoires of Resignification in (Evidence-Based) Healthcare Organization

In this article I discuss the irremediable tension between the universalistic dimension of contemporary medicine, represented by the paradigm of evidence-based medicine (EBM), and local daily practices in specific healthcare organizations. This tension constantly challenges the unitary, universalistic vision to which modern medicine and science aspire. The EBM paradigm, which is currently the most prevalent in every medical-nursing discipline, aims to standardize care procedures through the process of constant scientific literature review and the production of operational guidelines based on what epistemic communities define as the most reliable and effective results: the so-called gold standards. In everyday clinical, therapeutic, and care activities, these procedures are intertwined with the multiplicity of elements that make up the lifeworld. “Universalistic” premises are never merely “applied” to “local” interactive contexts but are always creatively “implicated” in them. Using data collected during a year of ethnographic research in an intensive care unit in Northern Italy, I discuss how the abstract indications of EBM and the formal dimension of health organizations are incorporated, through socially located interactive repertoires, in actual care trajectories. Following the Science and Technology Study perspective in a practice-based analysis of daily work, I show how interactions between human actors, technological artifacts and organizational apparatus in daily practices constituterepertoires of resignificationthrough which local universality emerges, resolving the tension between medicine's universalistic aspirations and the unpredictable, situated nature of the lifeworld. I consider two repertoires: the interpretative (examining the production and dissemination of knowledge) and the relational (focusing on informal interactions between different professional groups and communities of practice). The article shows how care practices cannot disregard the specific organizational conditions in which they unfold and suggests that research should develop reflective analysis skills on what Annemarie Mol calls thelogic of care, thus ceasing to treat the local dimension as a disturbing element in formal systems but, on the contrary, taking note of its impact and unavoidability in actual practice.

Особливості реформування системи територіальної організації влади в Україні в умовах децентралізації

Problem statement in general and its connection with important scientific and practical tasks. Power decentralization as a component of public policy is one of the key reforms on the agenda in Ukraine, which creates the basis for radicalization of institutional change, improving the quality of citizens life and is important for the continuation of sectoral reforms. The aim of decentralization policy is to move away from the centralized model of governance in the country, ensure the capacity of local self-government and build an effective system of territorial organization of power in Ukraine, fully implement the European Charter of Local Self-Government, subsidiarity, universality and financial self-sufficiency of local self-government.The aim of the article is to study the peculiarities of reforming the system of territorial organization of power in Ukraine in the context of decentralization through modeling the effective financial activities of local governments of united territorial communities.The paper main body. The article analyzes the features of reforming the system of territorial organization of power in Ukraine, which implies a departure from the centralized model of government in the state, ensuring the capacity of local self-governance and building an effective system of territorial organization of power in Ukraine; full implementation of the provisions of the European Charter of Local Self-Government, the principles of subsidiarity, universality and financial self-sufficiency of local self-governance.Changes in the administrative-territorial structure of Ukraine are analyzed. In particular, the draft Law of Ukraine "On the principles of administrative-territorial organization of Ukraine", register. № 8051 dated February 22, 2018; draft Law of Ukraine "On Amendments to Certain Legislative Acts of Ukraine Concerning the Regulation of Certain Issues of Activity and Organization of Public Authorities, Local Self-Government Bodies in Connection with the Formation (Liquidation) of Districts", Register. № 3651 dated 12.06.2020.Conclusions of the research. It was established that the process of consolidation of administrative-territorial units of the basic level, aimed at the formation of capable and viable local self-governance, has led to the transformation of the territorial structure and subregional level – the next stage of improving the territorial organization of power. It was proved that modeling of effective financial activity of local self-government authorities of united territorial communities in the conditions of decentralization consists of search by local authorities of own budgeting tools and real sources of receipts in the subordinate territory. The author’s position that the reorganization of authorities of the State Fiscal Service should take into account the European experience, including the EU NUTS Standard (Nomenclature of Territorial Units for Statistics), was substantiated.The idea of the reorganization of controlling authorities by analogy with approaches to the administrative-territorial structure, for example with the application of the EU NUTS Standard, was substantiated.

On the Zeros of Non-Analytic Random Periodic Signals

Abstract In this paper, we investigate the local universality of the number of zeros of a random periodic signal of the form $S_n(t)=\sum _{k=1}^n a_k f(k t)$, where $f$ is a $2\pi -$periodic function satisfying weak regularity conditions and where the coefficients $a_k$ are i.i.d. random variables, which are centered with unit variance. In particular, our results hold for continuous piecewise linear functions. We prove that the number of zeros of $S_n(t)$ in a shrinking interval of size $1/n$ converges in law as $n$ goes to infinity to the number of zeros of a Gaussian process whose explicit covariance only depends on the function $f$ and not on the common law of the random coefficients $(a_k)$. As a byproduct, this entails that the point measure of the zeros of $S_n(t)$ converges in law to an explicit limit on the space of locally finite point measures on $\mathbb R$ endowed with the vague topology. The standard tools involving the regularity or even the analyticity of $f$ to establish such kind of universality results are here replaced by some high-dimensional Berry–Esseen bounds recently obtained in [ 7]. The latter allow us to prove functional Central Limit Theorems in $C^1$ or Lipschitz topology in situations where usual criteria cannot be applied due to the lack of regularity.

Local Universality for Zeros and Critical Points of Monochromatic Random Waves

This paper concerns the asymptotic behavior of zeros and critical points for monochromatic random waves $$\phi _\lambda $$ of frequency $$\lambda $$ on a compact, smooth, Riemannian manifold (M, g) as $$\lambda \rightarrow \infty .$$ We prove global variance estimates for the measures of integration over the zeros and critical points of $$\phi _\lambda .$$ These global estimates hold for a wide class of manifolds—for example when (M, g) has no conjugate points—and rely on new local variance estimates on zeros and critical points of $$\phi _\lambda $$ in balls of radius $$\approx \lambda ^{-1}$$ around a fixed point. Our local results hold under conditions about the structure of geodesics that are generic in the space of all metrics on M.

Random matrix products: Universality and least singular values

We establish, under a moment matching hypothesis, the local universality of the correlation functions associated with products of $M$ independent i.i.d. random matrices, as $M$ is fixed, and the sizes of the matrices tend to infinity. This generalizes an earlier result of Tao and the third author for the case $M=1$. We also prove Gaussian limits for the centered linear spectral statistics of products of $M$ independent i.i.d. random matrices. This is done in two steps. First, we establish the result for product random matrices with Gaussian entries, and then extend to the general case of non-Gaussian entries by another moment matching argument. Prior to our result, Gaussian limits were known only for the case $M=1$. In a similar fashion, we establish Gaussian limits for the centered linear spectral statistics of products of independent truncated random unitary matrices. In both cases, we are able to obtain explicit expressions for the limiting variances. The main difficulty in our study is that the entries of the product matrix are no longer independent. Our key technical lemma is a lower bound on the least singular value of the translated linearization matrix associated with the product of $M$ normalized independent random matrices with independent and identically distributed sub-Gaussian entries. This lemma is of independent interest.

Contextuality as a resource for measurement-based quantum computation beyond qubits

Contextuality—the obstruction to describing quantum mechanics in a classical statistical way—has been proposed as a resource that powers quantum computing. The measurement-based model provides a concrete manifestation of contextuality as a computational resource, as follows. If local measurements on a multi-qubit state can be used to evaluate nonlinear boolean functions with only linear control processing, then this computation constitutes a proof of strong contextuality—the possible local measurement outcomes cannot all be pre-assigned. However, this connection is restricted to the special case when the local measured systems are qubits, which have unusual properties from the perspective of contextuality. A single qubit cannot allow for a proof of contextuality, unlike higher-dimensional systems, and multiple qubits can allow for state-independent contextuality with only Pauli observables, again unlike higher-dimensional generalisations. Here we identify precisely that strong non-locality is necessary in a qudit measurement-based computation (MBC) that evaluates high-degree polynomial functions with only linear control. We introduce the concept of local universality, which places a bound on the space of output functions accessible under the constraint of single-qudit measurements. Thus, the partition of a physical system into subsystems plays a crucial role for the increase in computational power. A prominent feature of our setting is that the enabling resources for qubit and qudit MBC are of the same underlying nature, avoiding the pathologies associated with qubit contextuality.

Roots of random polynomials with coefficients of polynomial growth

In this paper, we prove optimal local universality for roots of random polynomials with arbitrary coefficients of polynomial growth. As an application, we derive, for the first time, sharp estimates for the number of real roots of these polynomials, even when the coefficients are not explicit. Our results also hold for series; in particular, we prove local universality for random hyperbolic series.

On Expanding Neighborhoods of Local Universality of Gaussian Unitary Ensembles

The classical universality theorem states that the Christoffel–Darboux kernel of the Hermite polynomials scaled by a factor of \(1/\sqrt n\) tends to the sine kernel in local variables \(\tilde x,\tilde y\) in a neighborhood of a point \(x^*\in(-\sqrt 2,\sqrt 2)\)). This classical result is well known for \(\tilde x,\tilde y\in{K}\Subset\mathbb{R}\). In this paper, we show that this classical result remains valid for expanding compact sets K = K(n). An interesting phenomenon of admissible dependence of the expansion rate of compact sets K(n) on x* is established. For \(x^*\in(-\sqrt 2,\sqrt 2)\backslash\left\{0\right\}\)) and for x* = 0, there are different growth regimes of compact sets K(n). A transient regime is found.

Products of random matrices from fixed trace and induced Ginibre ensembles

We investigate the microcanonical version of the complex induced Ginibre ensemble, by introducing a fixed trace constraint for its second moment. Like for the canonical Ginibre ensemble, its complex eigenvalues can be interpreted as a two-dimensional Coulomb gas, which are now subject to a constraint and a modified, collective confining potential. Despite the lack of determinantal structure in this fixed trace ensemble, we compute all its density correlation functions at finite matrix size and compare to a fixed trace ensemble of normal matrices, representing a different Coulomb gas. Our main tool of investigation is the Laplace transform, that maps back the fixed trace to the induced Ginibre ensemble. Products of random matrices have been used to study the Lyapunov and stability exponents for chaotic dynamical systems, where the latter are based on the complex eigenvalues of the product matrix. Because little is known about the universality of the eigenvalue distribution of such product matrices, we then study the product of m induced Ginibre matrices with a fixed trace constraint—which are clearly non-Gaussian—and M − m such Ginibre matrices without constraint. Using an m-fold inverse Laplace transform, we obtain a concise result for the spectral density of such a mixed product matrix at finite matrix size, for arbitrary fixed m and M. Very recently local and global universality was proven by the authors and their coworker for a more general, single elliptic fixed trace ensemble in the bulk of the spectrum. Here, we argue that the spectral density of mixed products is in the same universality class as the product of M independent induced Ginibre ensembles.

The Hypothesis and a supercompact cardinal

AbstractIn this paper, we prove that: if κ is supercompact and the Hypothesis holds, then there is a proper class of regular cardinals in which are measurable in . Woodin also proved this result independently . As a corollary, we prove Woodin's Local Universality Theorem. This work shows that under the assumption of the Hypothesis and supercompact cardinals, large cardinals in are reflected to be large cardinals in in a local way, and reveals the huge difference between ‐supercompact cardinals and supercompact cardinals under the Hypothesis.

Universality for random matrix flows with time-dependent density

Nous démontrons que le mouvement Brownien de Dyson établit l’universalité des statistiques spectrales locales après un temps très court, en supposant la rigidité locale et la répulsion de valeurs propres. Ces conditions sont satisfaites, et donc l’universalité spectrale est démontrée au centre du spectre, pour une large classe des matrices aléatoires du type Wigner, y compris les ensembles de Wigner deformés et des ensembles dont la matrice des variances est non-stochastique, dont les densités asymptotiques diffèrent de la loi du demi-cercle de Wigner.

Policy translation through localisation: implementing national policy in the UK

This paper builds on policy implementation studies, which seek to explain how policies undergo some form of ‘translation’ from general policy guidelines to implementation in practice at the local level. The paper makes two contributions to the policy implementation literature. First, it draws on the concept of ‘local universality’ to suggest that the translation of policy by central actors is not simply transmitted but is iteratively transformed through multiple distributed agencies including local actors, infrastructure, data sets and organisational practices. Second, empirical findings show how structural policy design features influence implementation and (re)shape policy content by incorporating knowledge from practice.

An Update on Local Universality Limits for Correlation Functions Generated by Unitary Ensembles

We survey the current status of universality limits for $m$-point correlation functions in the bulk and at the edge for unitary ensembles, primarily when the limiting kernels are Airy, Bessel, or Sine kernels. In particular, we consider underlying measures on compact intervals, and fixed and varying exponential weights, as well as universality limits for a variety of orthogonal systems. The scope of the survey is quite narrow: we do not consider $\beta$ ensembles for $\beta \neq 2$, nor general Hermitian matrices with independent entries, let alone more general settings. We include some open problems.