Yaoran Yang

Current Organizations / Institutes

The organizations/institutes from the scholar's latest article

Sichuan University

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Research Interests

Yaoran Yang has a total of 2 co-authors. Here are the top co-authors by number of shared publications:

Yutong Zhang
School of Mathematics, Sichuan University, Chengdu, China
13 shared publications
Wentao Zhang
Tsinghua University
1 shared publication

Latest Publications

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- 16 October 2026
- Published by Springer Nature in Journal of Applied Mathematics and Computing
Interior-free beta tails for convex scenario programs
by Yutong Zhang, Yaoran Yang
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- 16 October 2026
- Published by Springer Nature in Journal of Applied Mathematics and Computing
Interior-free beta tails for convex scenario programs
by Yutong Zhang, Yaoran Yang
Open Access
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- 14 October 2026
- Published by Elsevier in SSRN Electronic Journal
Drift-blind Frostman disintegration for Gaussian fibers and a solution of the Balka--Darji--Elekes Brownian-drift problem
by Yutong Zhang, Yaoran Yang
Let $G$ be a $d$-dimensional Gaussian process whose coordinates are independent copies of a centered scalar process that is strongly locally nondeterministic with index $H$. Fix a continuous deterministic drift $f$ and an $s$-Frostman measure $\mu$ on $[0,1]$, with $s>Hd$. We construct, simultaneously for every spatial level $z$, a conditional occupation measure $\ell_z$ supported on $(G+f)^{-1}(z)\cap\supp\mu$. In the Fourier representations, the drift contributes only unimodular phases, so all deterministic moment constants are independent of $f$. Almost surely, for every $0<\gamma0$, the set $\{z:\ell_z(J)>0\}$ is nonempty and open, captures full $\mu$-occupation in $J$, and every corresponding fiber has Hausdorff dimension at least $s-Hd$. For one-dimensional Brownian motion, $s=1$ and $H=1/2$; this answers both clauses of Problem 9.1 of Balka, Darji and Elekes, including full occupation for the samplewise largest open good-level set. The probability-one event is chosen after the deterministic drift is fixed.
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- 14 October 2026
- Published by Elsevier in SSRN Electronic Journal
Open Access
Drift-blind Frostman disintegration for Gaussian fibers and a solution of the Balka--Darji--Elekes Brownian-drift problem
by Yutong Zhang, Yaoran Yang
Let $G$ be a $d$-dimensional Gaussian process whose coordinates are independent copies of a centered scalar process that is strongly locally nondeterministic with index $H$. Fix a continuous deterministic drift $f$ and an $s$-Frostman measure $\mu$ on $[0,1]$, with $s>Hd$. We construct, simultaneously for every spatial level $z$, a conditional occupation measure $\ell_z$ supported on $(G+f)^{-1}(z)\cap\supp\mu$. In the Fourier representations, the drift contributes only unimodular phases, so all deterministic moment constants are independent of $f$. Almost surely, for every $0<\gamma0$, the set $\{z:\ell_z(J)>0\}$ is nonempty and open, captures full $\mu$-occupation in $J$, and every corresponding fiber has Hausdorff dimension at least $s-Hd$. For one-dimensional Brownian motion, $s=1$ and $H=1/2$; this answers both clauses of Problem 9.1 of Balka, Darji and Elekes, including full occupation for the samplewise largest open good-level set. The probability-one event is chosen after the deterministic drift is fixed.
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Google Scholar
- 7 October 2026
- Published by Springer Nature in Journal of Fixed Point Theory and Applications
Continuous P-contractive mappings on compact metric spaces are Picard operators
by Yutong Zhang, Yaoran Yang
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- 7 October 2026
- Published by Springer Nature in Journal of Fixed Point Theory and Applications
Continuous P-contractive mappings on compact metric spaces are Picard operators
by Yutong Zhang, Yaoran Yang
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- 7 September 2026
- Published by Springer Nature
Learning Under Heavy-Tailed Covariate Shift: Rényi-Moment Guarantees, Sharp Rates, and Near-Minimax Optimality
by Yutong Zhang, Yaoran Yang, Wentao Zhang
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- 7 September 2026
- Published by Springer Nature
Learning Under Heavy-Tailed Covariate Shift: Rényi-Moment Guarantees, Sharp Rates, and Near-Minimax Optimality
by Yutong Zhang, Yaoran Yang, Wentao Zhang
Open Access
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- 15 August 2026
- Published by Elsevier in SSRN Electronic Journal
A traveling-wave proof of the tight runtime of the compact genetic algorithm on LeadingOnes
by Yutong Zhang, Yaoran Yang
The first rigorous analysis of the compact genetic algorithm (cGA) on $\mathrm{LeadingOnes}$ established an $O(\mu n\log n)$ high-probability upper bound and left open an asymptotically matching lower bound. We show that the logarithmic factor is not intrinsic. For the standard cGA with borders $[1/n,1-1/n]$, a lattice-aligned update parameter $\mu$, and $\mu\ge Cn\log n$, the optimization time $\tau_{\mathrm{opt}}$ satisfies $\Pp(\tau_{\mathrm{opt}}>C'\mu n)\le\exp(-c\mu/n)$. For every fixed $\eta\in(0,1)$ and every such parameter with $\mu\le(2-\eta)^n/n$, a matching lower bound holds with probability $1-\exp(-\Omega_\eta(\mu/n))-\exp(-\Omega_\eta(n))$. Consequently, $\tau_{\mathrm{opt}}=\Theta(\mu n)$ with high probability throughout every polynomially bounded low-genetic-drift regime covered by the theorem. The proof derives the exact coordinate transition kernel, establishes a localized multiscale contraction theorem for adaptive reflected biased walks, and advances all marginals along diagonals in coordinate--accuracy space. A deterministic log-odds flow reveals the associated traveling wave. An independent aggregate-mass martingale argument yields the lower bound and explains why an exponential-order upper restriction on $\mu$ is unavoidable in any uniform high-probability $\Omega(\mu n)$ statement.
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- 15 August 2026
- Published by Elsevier in SSRN Electronic Journal
Open Access
A traveling-wave proof of the tight runtime of the compact genetic algorithm on LeadingOnes
by Yutong Zhang, Yaoran Yang
The first rigorous analysis of the compact genetic algorithm (cGA) on $\mathrm{LeadingOnes}$ established an $O(\mu n\log n)$ high-probability upper bound and left open an asymptotically matching lower bound. We show that the logarithmic factor is not intrinsic. For the standard cGA with borders $[1/n,1-1/n]$, a lattice-aligned update parameter $\mu$, and $\mu\ge Cn\log n$, the optimization time $\tau_{\mathrm{opt}}$ satisfies $\Pp(\tau_{\mathrm{opt}}>C'\mu n)\le\exp(-c\mu/n)$. For every fixed $\eta\in(0,1)$ and every such parameter with $\mu\le(2-\eta)^n/n$, a matching lower bound holds with probability $1-\exp(-\Omega_\eta(\mu/n))-\exp(-\Omega_\eta(n))$. Consequently, $\tau_{\mathrm{opt}}=\Theta(\mu n)$ with high probability throughout every polynomially bounded low-genetic-drift regime covered by the theorem. The proof derives the exact coordinate transition kernel, establishes a localized multiscale contraction theorem for adaptive reflected biased walks, and advances all marginals along diagonals in coordinate--accuracy space. A deterministic log-odds flow reveals the associated traveling wave. An independent aggregate-mass martingale argument yields the lower bound and explains why an exponential-order upper restriction on $\mu$ is unavoidable in any uniform high-probability $\Omega(\mu n)$ statement.
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Cited by 1
- 4 August 2026
- Published by Springer Nature in European Journal of Mathematics
A compensation theorem for the Sylow-integral invariant and counterexamples to an $A_5$-characterization conjecture
by Yutong Zhang, Yaoran Yang
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- 4 August 2026
- Published by Springer Nature in European Journal of Mathematics
A compensation theorem for the Sylow-integral invariant and counterexamples to an $A_5$-characterization conjecture
by Yutong Zhang, Yaoran Yang
Cited by 1
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- 17 July 2026
- Published by Elsevier in Fuzzy Sets and Systems
Measure-inducing quasi-copulas with self-similar fractal supports
by Yutong Zhang, Yaoran Yang
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- 17 July 2026
- Published by Elsevier in Fuzzy Sets and Systems
Measure-inducing quasi-copulas with self-similar fractal supports
by Yutong Zhang, Yaoran Yang
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- 6 July 2026
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
A DETERMINANT CONGRUENCE CONJECTURED BY SUN
by Yutong Zhang, Yaoran Yang
We prove a strengthened form of a conjecture of Sun on a determinant attached to a binary quadratic form. Let $n > 3$ $n>3$ n greater than 3 and let $c, d \in Z$ $c,d\in \mathbb Z$ c comma d element of double struck upper Z . If n is composite, then $\begin{array}{r} det [(i^{2} + c i j + d j^{2})^{n - 2}]_{0 \leq i, j \leq n - 1} \equiv 0 (\mod n^{2}) \end{array}$ $$ \begin{align*} \det [(i^2+cij+dj^2)^{n-2}]_{0\leq i,j\leq n-1}\equiv 0 \pmod {n^2} \end{align*} $$ with no condition on c and d . If $n = p$ $n=p$ n equals p is prime, the same congruence holds whenever the Legendre symbol $(d / p)$ $({d}/{p})$ left parenthesis d divided by p right parenthesis is $- 1$ $-1$ negative 1 . For composite n , a polynomial determinant is divisible by two Vandermonde factors; after specialisation, their product already yields the required square divisor. For prime $n = p$ $n=p$ n equals p , we estimate the rank of the matrix modulo p . The required rank defect follows from a coefficient cancellation obtained from the involution $t \mapsto d / t$ $t\mapsto d/t$ t right arrow from bar d divided by t on $F_{p}^{\times}$ $\mathbb F_p^\times $ double struck upper F Subscript p Superscript times and the condition $(d / p) = - 1$ $({d}/{p})=-1$ left parenthesis d divided by p right parenthesis equals negative 1 .
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- 6 July 2026
- Published by Cambridge University Press (CUP) in Bulletin of the Australian Mathematical Society
A DETERMINANT CONGRUENCE CONJECTURED BY SUN
by Yutong Zhang, Yaoran Yang
We prove a strengthened form of a conjecture of Sun on a determinant attached to a binary quadratic form. Let $n > 3$ $n>3$ n greater than 3 and let $c, d \in Z$ $c,d\in \mathbb Z$ c comma d element of double struck upper Z . If n is composite, then $\begin{array}{r} det [(i^{2} + c i j + d j^{2})^{n - 2}]_{0 \leq i, j \leq n - 1} \equiv 0 (\mod n^{2}) \end{array}$ $$ \begin{align*} \det [(i^2+cij+dj^2)^{n-2}]_{0\leq i,j\leq n-1}\equiv 0 \pmod {n^2} \end{align*} $$ with no condition on c and d . If $n = p$ $n=p$ n equals p is prime, the same congruence holds whenever the Legendre symbol $(d / p)$ $({d}/{p})$ left parenthesis d divided by p right parenthesis is $- 1$ $-1$ negative 1 . For composite n , a polynomial determinant is divisible by two Vandermonde factors; after specialisation, their product already yields the required square divisor. For prime $n = p$ $n=p$ n equals p , we estimate the rank of the matrix modulo p . The required rank defect follows from a coefficient cancellation obtained from the involution $t \mapsto d / t$ $t\mapsto d/t$ t right arrow from bar d divided by t on $F_{p}^{\times}$ $\mathbb F_p^\times $ double struck upper F Subscript p Superscript times and the condition $(d / p) = - 1$ $({d}/{p})=-1$ left parenthesis d divided by p right parenthesis equals negative 1 .
Open Access
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- 29 June 2026
- Published by AccScience Publishing in An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
Flat lower envelopes solve bounded monomial convexification on two-variable cones
by Yaoran Yang, Yutong Zhang
Bounded monomial sets are basic relaxable objects in deterministic global optimization. Belotti's 2025 Mathematical Programming article established the upper envelope for two-variable cones and the lower envelope in dimension two, while leaving the lower envelope open in dimensions greater than two. We close this gap by proving that, in every dimension of at least three, the lower convex envelope over the bounded monomial set intersected with a two-variable cone is flat: after convexifying the restricted epigraph, the only lower constraint on the graph variable is the imposed lower value bound. The formula is independent of the upper value bound and the total homogeneity degree. The proof is based on a level-set convexification identity: every point in the monomial superlevel set inside the cone is either on the target level or an explicit convex combination of two points on that level. A single coordinate outside the constrained pair supplies the required compensation, which also explains why the result fails sharply in dimension two. Combining this lower-envelope formula with Belotti's known upper envelope yields the complete convex hull of the bounded graph for all homogeneity regimes in dimensions of at least three. We also give constructive certificates, separation conditions, a notation summary in the back matter, and reproducible numerical diagnostics showing that the two-point certificates are recovered to roundoff-level reconstruction accuracy over representative regimes.
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- 29 June 2026
- Published by AccScience Publishing in An International Journal of Optimization and Control: Theories & Applications (IJOCTA)
Open Access
Flat lower envelopes solve bounded monomial convexification on two-variable cones
by Yaoran Yang, Yutong Zhang
Bounded monomial sets are basic relaxable objects in deterministic global optimization. Belotti's 2025 Mathematical Programming article established the upper envelope for two-variable cones and the lower envelope in dimension two, while leaving the lower envelope open in dimensions greater than two. We close this gap by proving that, in every dimension of at least three, the lower convex envelope over the bounded monomial set intersected with a two-variable cone is flat: after convexifying the restricted epigraph, the only lower constraint on the graph variable is the imposed lower value bound. The formula is independent of the upper value bound and the total homogeneity degree. The proof is based on a level-set convexification identity: every point in the monomial superlevel set inside the cone is either on the target level or an explicit convex combination of two points on that level. A single coordinate outside the constrained pair supplies the required compensation, which also explains why the result fails sharply in dimension two. Combining this lower-envelope formula with Belotti's known upper envelope yields the complete convex hull of the bounded graph for all homogeneity regimes in dimensions of at least three. We also give constructive certificates, separation conditions, a notation summary in the back matter, and reproducible numerical diagnostics showing that the two-point certificates are recovered to roundoff-level reconstruction accuracy over representative regimes.
Open Access
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- 26 May 2026
- Published by Elsevier in SSRN Electronic Journal
A first-moment improvement for unshifted rank-one lattice rules in unanchored Sobolev spaces
by Yaoran Yang, Yutong Zhang
A recent note of Goda disproves the Kazashi--Sloan counting conjecture and proves, without that conjecture, the dimension-independent averaged squared worst-case-error estimate $\eav^2(n)=O(n^{-1/2}\log n)$ for unshifted rank-one lattice rules in weighted unanchored Sobolev spaces of smoothness one, under the corresponding summability condition on the weights. The same note asks whether this rate can be improved. We give an affirmative answer. The key observation is the exact identity $\sum_{\kappa=1}^{n-1}T_n(\kappa)=2H_{(n-1)/2}^2$, combined with the uniform Kazashi--Sloan estimate $T_n(\kappa)\le \pi^2/6$. This replaces threshold counting by a first-moment-to-all-moments estimate. Consequently, for every odd prime $n$ and every finite dimension $d$, the averaged squared worst-case error is bounded by $n^{-1}(\log n)^2$ times an explicit weighted subset sum. For product weights, this proves the existence of an unshifted rank-one lattice rule satisfying $e(n,\bm z)=O_\gamma(n^{-1/2}\log n)$, uniformly in $d$, whenever $\sum_{j\ge1}\gamma_j<\infty$. Numerical experiments confirm the exact arithmetic identity, illustrate the resulting moment conversion, and compare the new bounds with the previous rate scale.
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Google Scholar
- 26 May 2026
- Published by Elsevier in SSRN Electronic Journal
Open Access
A first-moment improvement for unshifted rank-one lattice rules in unanchored Sobolev spaces
by Yaoran Yang, Yutong Zhang
A recent note of Goda disproves the Kazashi--Sloan counting conjecture and proves, without that conjecture, the dimension-independent averaged squared worst-case-error estimate $\eav^2(n)=O(n^{-1/2}\log n)$ for unshifted rank-one lattice rules in weighted unanchored Sobolev spaces of smoothness one, under the corresponding summability condition on the weights. The same note asks whether this rate can be improved. We give an affirmative answer. The key observation is the exact identity $\sum_{\kappa=1}^{n-1}T_n(\kappa)=2H_{(n-1)/2}^2$, combined with the uniform Kazashi--Sloan estimate $T_n(\kappa)\le \pi^2/6$. This replaces threshold counting by a first-moment-to-all-moments estimate. Consequently, for every odd prime $n$ and every finite dimension $d$, the averaged squared worst-case error is bounded by $n^{-1}(\log n)^2$ times an explicit weighted subset sum. For product weights, this proves the existence of an unshifted rank-one lattice rule satisfying $e(n,\bm z)=O_\gamma(n^{-1/2}\log n)$, uniformly in $d$, whenever $\sum_{j\ge1}\gamma_j<\infty$. Numerical experiments confirm the exact arithmetic identity, illustrate the resulting moment conversion, and compare the new bounds with the previous rate scale.

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