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About 1,106 papers for “Sublinear function”
G. N. Chhatria, Said R. Grace, John R. Graef · Greater South Information System · 2021
Abstract The authors present necessary and sufficient conditions for the oscillation of a class of second order non-linear neutral dynamic equations with non-positive neutral coefficients by using Krasnosel'skii's fixed point theorem on time scales. The nonlinear function may be strongly sublinear or strongly superlinear.
Cited by 0Open access
Amir Abboud, Greg Bodwin, Seth Pettie · arXiv (Cornell University) · 2016
Spanners, emulators, and approximate distance oracles can be viewed as lossy compression schemes that represent an unweighted graph metric in small space, say $\tilde{O}(n^{1+δ})$ bits. There is an inherent tradeoff between the sparsity parameter $δ$ and the stretch function $f$ of the compression scheme, but the qualitative nature of this tradeoff has remained a persistent open problem. In this paper we show that the recent additive spanner lower bound of Abboud and Bodwin is just the first step in a hierarchy of lower bounds that fully characterize the asymptotic behavior of the optimal stretch function $f$ as a function of $δ\in (0,1/3)$. Specifically, for any integer $k\ge 2$, any compression scheme with size $O(n^{1+\frac{1}{2^k-1} - ε})$ has a sublinear additive stretch function $f$: $$f(d) = d + Ω(d^{1-\frac{1}{k}}).$$ This lower bound matches Thorup and Zwick's (2006) construction of sublinear additive emulators. It also shows that Elkin and Peleg's $(1+ε,β)$-spanners have an essentially optimal tradeoff between $δ,ε,$ and $β$, and that the sublinear additive spanners of Pettie (2009) and Chechik (2013) are not too far from optimal. To complement these lower bounds we present a new construction of $(1+ε, O(k/ε)^{k-1})$-spanners with size $O((k/ε)^{h_k} kn^{1+\frac{1}{2^{k+1}-1}})$, where $h_k < 3/4$. This size bound improves on the spanners of Elkin and Peleg (2004), Thorup and Zwick (2006), and Pettie (2009). According to our lower bounds neither the size nor stretch function can be substantially improved.
Cited by 0Open access
Ryuji Kajikiya · Transactions of the American Mathematical Society · 2009
In this paper, a priori estimates of positive solutions for sublinear elliptic equations are given in terms of thicknesses of domains. To this end, a supersolution is constructed by a composite function of a solution to an ordinary differential equation and a distance function. The results work efficiently in the case where the domain is an exterior or an interior of a convex set.
Cited by 7Open access
Fengnan Gao, Aad van der Vaart, Rui M. Castro et al. · Electronic Journal of Statistics · 2017
We propose an empirical estimator of the preferential attachment function $f$ in the setting of general sublinear preferential attachment trees. Using a supercritical continuous-time branching process framework, we prove the almost sure consistency of the proposed estimator. We perform simulations to study the empirical properties of our estimators.
Cited by 12Open access
Qingfeng Wu, Xili Tan, Shuang Guo et al. · AIMS Mathematics · 2024
<p>In this article, using the Fuk-Nagaev type inequality, we studied general strong law of large numbers for weighted sums of $ m $-widely acceptable ($ m $-WA, for short) random variables under sublinear expectation space with the integral condition</p><p><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \hat{\mathbb{E}} \left ( f^-\left ( \left | X \right | \right ) \right ) \le \mathrm{C}_\mathbb{V}\left ( f^-\left ( \left | X \right | \right ) \right )&lt; \infty $\end{document} </tex-math></disp-formula></p><p>and $ Choquet $ integrals existence, respectively, where</p><p><disp-formula> <label/> <tex-math id="FE2"> \begin{document}$ f\left ( x \right ) = x^{1/\beta }L\left ( x \right ) $\end{document} </tex-math></disp-formula></p><p>for $ \beta &gt; 1 $, $ L\left (x \right) &gt; 0 $ $ \left(x &gt; 0\right) $ was a monotonic nondecreasing slowly varying function, and $ f^-\left (x \right) $ was the inverse function of $ f\left(x\right) $. One of the results included the Kolmogorov-type strong law of large numbers and the partial Marcinkiewicz-type strong law of large numbers for $ m $-WA random variables under sublinear expectation space. Besides, we obtained almost surely convergence for weighted sums of $ m $-WA random variables under sublinear expectation space. These results improved the corresponding results of Ma and Wu under sublinear expectation space.</p>
Cited by 0Open access
Seongmin Jeon, Yu Sang Chang · International Journal of Environment and Sustainable Development · 2020
The high level of urbanisation in the USA may have led to the generation of very high emissions of carbon dioxide (CO2) in cities. This study examines the scaling relationship of CO2 emission as a function of population size across a large number of US cities, conducting scaling analyses on multiple subgroups of cities with varying population sizes. The findings indicate that while superlinear or linear scaling can be applied to the total sample of cities, these changes to sublinear scaling for the subgroups of more populous cities. In addition, this study finds that the tipping point toward said sublinear scaling lies at the subgroup of the 75 most populous cities. The implications of the findings will be discussed.
Cited by 1
Sebastián Donoso, Andreas Koutsogiannis, Wenbo Sun · Ergodic Theory and Dynamical Systems · 2018
For any measure-preserving system $(X,{\mathcal{B}},\unicode[STIX]{x1D707},T_{1},\ldots ,T_{d})$ with no commutativity assumptions on the transformations $T_{i},$ $1\leq i\leq d,$ we study the pointwise convergence of multiple ergodic averages with iterates of different growth coming from a large class of sublinear functions. This class properly contains important subclasses of Hardy field functions of order zero and of Fejér functions, i.e., tempered functions of order zero. We show that the convergence of the single average, via an invariant property, implies the convergence of the multiple one. We also provide examples of sublinear functions which are, in general, bad for convergence on arbitrary systems, but good for uniquely ergodic systems. The case where the fastest function is linear is addressed as well, and we provide, in all the cases, an explicit formula of the limit function.
Cited by 7Open access
Fatma Kılınç Karzan · 2013
We study mixed integer conic sets involving a general regular (closed, convex, full dimensional, and pointed) cone K such as the nonnegative orthant, the Lorentz cone or the positive semidefinite cone. In a unified framework, we introduce K-minimal inequalities and show that under mild assumptions, these inequalities together with the trivial cone-implied inequalities are sufficient to describe the convex hull. We study the properties of K-minimal inequalities by establishing necessary conditions for an inequality to be K-minimal. This characterization leads to a broader class of K-sublinear inequalities, which includes K-minimal inequalities as a subclass. We establish a close connection between K-sublinear inequalities and the support functions of sets with certain structure. This leads to practical ways of showing that a given inequality is K-sublinear and K-minimal. We provide examples to show how our framework can be applied. Our framework generalizes the results from the mixed integer linear case, such as the minimal inequalities for mixed integer linear programs are generated by sublinear (positively homogeneous, subadditive and convex) functions that are also piecewise linear. So whenever possible we highlight the connections to the existing literature. However our study reveals that such a cut generating function view is not possible for in the conic case even when the cone involved is the Lorentz cone.
Cited by 0
Min Meng, Xiuxian Li, Jie Chen · IEEE Transactions on Automatic Control · 2023
This article studies distributed online bandit learning of generalized Nash equilibria for online games, where the cost functions of all players and coupled constraints are time-varying. The function values, rather than full information about cost and local constraint functions, are revealed to local players with time delays. The goal of each player is to selfishly minimize its own cost function with no future information, subject to a strategy set constraint and time-varying coupled inequality constraints. To this end, a distributed online algorithm based on mirror descent and one-point delayed bandit feedback is designed for seeking generalized Nash equilibria in the online game. It is shown that the devised online algorithm achieves sublinear expected regrets and accumulated constraint violation if the path variation of the generalized Nash equilibrium sequence is sublinear. Simulations are presented to illustrate the efficiency of the theoretical result.
Cited by 25
Jianli Bai, Xiangfu Song, Xiaowu Zhang et al. · Annual Computer Security Applications Conference · 2023
A private decision tree evaluation (PDTE) protocol allows a feature vector owner (FO) to classify its data using a tree model from a model owner (MO) and only reveals an inference result to the FO. This paper proposes Mostree, a PDTE protocol secure in the presence of malicious parties with sublinear communication. We design Mostree in the three-party honest-majority setting, where an (untrusted) computing party (CP) assists the FO and MO in the secure computation. We propose two low-communication oblivious selection (OS) protocols by exploiting nice properties of three-party replicated secret sharing (RSS) and distributed point function. Mostree combines OS protocols with a tree encoding method and three-party secure computation to achieve sublinear communication. We observe that most of the protocol components already maintain privacy even in the presence of a malicious adversary, and what remains to achieve is correctness. To ensure correctness, we propose a set of lightweight consistency checks and seamlessly integrate them into Mostree. As a result, Mostree achieves sublinear communication and malicious security simultaneously. We implement Mostree and compare it with the state-of-the-art. Experimental results demonstrate that Mostree is efficient and comparable to semi-honest PDTE schemes with sublinear communication. For instance, when evaluated on the MNIST dataset in a LAN setting, Mostree achieves an evaluation using approximately 768 ms with communication of around 168 KB.
Cited by 12
Jianli Bai, Xiangfu Song, Xiaowu Zhang et al. · arXiv (Cornell University) · 2023
A private decision tree evaluation (PDTE) protocol allows a feature vector owner (FO) to classify its data using a tree model from a model owner (MO) and only reveals an inference result to the FO. This paper proposes Mostree, a PDTE protocol secure in the presence of malicious parties with sublinear communication. We design Mostree in the three-party honest-majority setting, where an (untrusted) computing party (CP) assists the FO and MO in the secure computation. We propose two low-communication oblivious selection (OS) protocols by exploiting nice properties of three-party replicated secret sharing (RSS) and distributed point function. Mostree combines OS protocols with a tree encoding method and three-party secure computation to achieve sublinear communication. We observe that most of the protocol components already maintain privacy even in the presence of a malicious adversary, and what remains to achieve is correctness. To ensure correctness, we propose a set of lightweight consistency checks and seamlessly integrate them into Mostree. As a result, Mostree achieves sublinear communication and malicious security simultaneously. We implement Mostree and compare it with the state-of-the-art. Experimental results demonstrate that Mostree is efficient and comparable to semi-honest PDTE schemes with sublinear communication. For instance, when evaluated on the MNIST dataset in a LAN setting, Mostree achieves an evaluation using approximately 768 ms with communication of around 168 KB.
Cited by 0Open access
Fengyu XUE · Proceedings of the Romanian Academy Series A Mathematics Physics Technical Sciences Information Science · 2025
In this paper, we investigated two different kinds of commutators associated with the multi-sublinear maximal function $\mathcal{M}_{\alpha}$ when symbol functions belong to Lipschitz spaces. We give some necessary and sufficient conditions for the boundedness of these two different kinds of commutators on the products of Slice space.
Cited by 0Open access
Bin Ge, Jianfang Lü · Mathematische Nachrichten · 2022
Abstract In this paper, we study the ‐curl problem of the type: where is a bounded simply connected domain with a C 1, 1 boundary denoted by , , is a continuous function, , and is a Carathéodory function. We obtain the existence and multiplicity of solutions for a class of ‐curl systems in the absence of Ambrosetti–Rabinowitz condition under superlinear case. Besides, we also obtain infinitely many solutions under sublinear case.
Cited by 1
Eiichi Nakai, Takuya Sobukawa · arXiv (Cornell University) · 2014
We introduce $B_w^u$-function spaces which unify Lebesgue, Morrey-Campanato, Lipschitz, $B^p$, CMO, local Morrey-type spaces, etc., and investigate the interpolation property of $B_w^u$-function spaces. We also apply it to the boundedness of linear and sublinear operators, for example, the Hardy-Littlewood maximal and fractional maximal operators, singular and fractional integral operators with rough kernel, the Littlewood-Paley operator, Marcinkiewicz operator, and so on.
Cited by 2Open access
Elisa Sovrano, Fabio Zanolin · OpenstarTs (Univeristy of Trieste https://www.units.it/) · 2015
We present some existence and multiplicity results for positive solutions to the Dirichlet problem associated with; under suitable conditions on the nonlinearity g(u)and thew eight function a(x): The assumptions considered are related to classical theorems about positive solutions to a sublinear elliptic equation due to Brezis-Oswald and Brown-Hess.
Cited by 2Open access
Davide Mattiolo, Giuseppe Mazzuoccolo, Vahan Mkrtchyan · arXiv (Cornell University) · 2021
If $f:\mathbb{N}\rightarrow \mathbb{N}$ is a function, then let us say that $f$ is sublinear if \[\lim_{n\rightarrow +\infty}\frac{f(n)}{n}=0.\] If $G=(V,E)$ is a cubic graph and $c:E\rightarrow \{1,...,k\}$ is a proper $k$-edge-coloring of $G$, then an edge $e=uv$ of $G$ is poor (rich) in $c$, if the edges incident to $u$ and $v$ are colored with three (five) colors. An edge is abnormal if it is neither rich nor poor. The Petersen coloring conjecture of Jaeger states that any bridgeless cubic graph admits a proper 5-edge-coloring $c$, such that there is no an abnormal edge of $G$ with respect to $c$. For a proper 5-edge-coloring $c$ of $G$, let $N_G(c)$ be the set of abnormal edges of $G$ with respect to $c$. In this paper we show that (a) The Petersen coloring conjecture is equivalent to the statement that there is a sublinear function $f:\mathbb{N}\rightarrow \mathbb{N}$, such that all bridgeless cubic graphs admit a proper 5-edge-coloring $c$ with $|N_G(c)|\leq f(|V|)$; (b) for $k=2,3,4$, the statement that there is a sublinear function $f:\mathbb{N}\rightarrow \mathbb{N}$, such that all (cyclically) $k$-edge-connected cubic graphs admit a proper 5-edge-coloring $c$ with $|N_G(c)|\leq f(|V|)$ is equivalent to the statement that all (cyclically) $k$-edge-connected cubic graphs admit a proper 5-edge-coloring $c$ with $|N_G(c)|\leq 2k+1$.
Cited by 0Open access
Kouijzer, S Sandra, Li, W Weiwei, Wienk, MM Martijn et al. · TU/e Research Portal (Eindhoven University of Technology) · 2015
In ternary bulk heterojunction solar cells based on a semiconducting biphenyl-dithienyldiketopyrrolopyrrole copolymer donor and two different fullerene acceptors that distinctly differ in electron affinity, the open-circuit voltage is found to depend in a slightly sublinear fashion on the relative ratio of the two fullerenes in the blend. Similar effects have previously been observed and have been attributed to the formation of an alloyed fullerene phase possessing electronic levels that are the weighted average of the two components. By analyzing the contribution of the charge transfer (CT)-state absorption to the external quantum efficiency of the ternary blend solar cells as a function of composition, we find no evidence for a CT state formed between the polymer and an alloyed fullerene phase. Rather, the results are consistent with the presence of two distinct CT states, one for each polymer–fullerene combination. The two-state CT model does not, however, explain the sublinear behavior of the open-circuit voltage as a function of the blend composition.
Cited by 0
Sandra Kouijzer, Weiwei Li, Martijn M. Wienk et al. · Journal of Photonics for Energy · 2014
In ternary bulk heterojunction solar cells based on a semiconducting biphenyl-dithienyldiketopyrrolopyrrole copolymer donor and two different fullerene acceptors that distinctly differ in electron affinity, the open-circuit voltage is found to depend in a slightly sublinear fashion on the relative ratio of the two fullerenes in the blend. Similar effects have previously been observed and have been attributed to the formation of an alloyed fullerene phase possessing electronic levels that are the weighted average of the two components. By analyzing the contribution of the charge transfer (CT)-state absorption to the external quantum efficiency of the ternary blend solar cells as a function of composition, we find no evidence for a CT state formed between the polymer and an alloyed fullerene phase. Rather, the results are consistent with the presence of two distinct CT states, one for each polymer–fullerene combination. The two-state CT model does not, however, explain the sublinear behavior of the open-circuit voltage as a function of the blend composition.
Cited by 37Open access
Kaiying Guo, Chunrong Zhu, G Minty et al. · Journal of Nonlinear and Variational Analysis · 2022
In this paper, we study a Bregman proximal point algorithm (BPPA) for convex optimization problems.Though the convergence and sublinear convergence rate for BPPA are well-understand, the linear convergence rate for BPPA has yet been thoroughly studied in the literature.In this paper, we analyze the linear convergence rate of BPPA.Under the assumption that the objective function is strongly convex relative to a Legendre function, we establish the linear convergence for the function values sequence.Moreover, if the Legendre function is strongly convex and smooth, the linear convergence for the iterative sequence of BPPA is obtained.
Cited by 3Open access
Le Van Hien · Mathematical Methods in the Applied Sciences · 2025
ABSTRACT In this paper, the problem of global attractivity of a neoclassical model with sublinear Ricker‐type Cobb‐Douglas growth function and variable time‐lag in the production function is investigated. By novel comparison techniques based on the fluctuation lemma and differential inequalities, the permanence property of positive solutions and global convergence to a unique positive equilibrium are established. The obtained results encompass existing ones in the literature as some special cases.
Cited by 0