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Representative Papers

Absolute Continuity of Monotone Aggregations under Positive Regression Dependence

Jun 18, 2026

This study addresses the absolute continuity of the distribution of outputs generated by monotone aggregation functions under positively regression-dependent structures. By introducing stochastic order monotonicity of conditional distributions and coordinate-wise monotonicity of mappings, the authors establish sufficient conditions that do not require independence or joint density assumptions, allowing for arbitrary marginal distributions. The results are extended to general measurable spaces equipped with reflexive binary relations. Leveraging tools from stochastic orders, conditional distributions, measure theory, and monotone functions, the paper proves the absolute continuity of the distribution of the aggregated variable \(g(X,Y)\). This extends the applicability of convolution regularization techniques and provides theoretical foundations for applications such as risk aggregation.

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Cops and robber in graphs with bounded vertex cover number

Feb 07, 2026

This study addresses the problem of bounding the cop number in connected graphs with vertex cover number $k$, offering a structural perspective toward Meyniel’s conjecture. By integrating vertex cover structure analysis, combinatorial optimization, and asymptotic methods, the work establishes the first sublinear upper bound on the cop number parameterized solely by $k$. Specifically, it proves that any connected graph with vertex cover number $k$ has cop number at most $k / 2^{(1 - o(1))\sqrt{\log k}}$. This result breaks away from the conventional framework that depends on the total number of vertices $n$, providing new evidence for Meyniel’s conjecture within structurally restricted graph classes.

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Latest Papers

Absolute Continuity of Monotone Aggregations under Positive Regression Dependence

Jun 18, 2026

This study addresses the absolute continuity of the distribution of outputs generated by monotone aggregation functions under positively regression-dependent structures. By introducing stochastic order monotonicity of conditional distributions and coordinate-wise monotonicity of mappings, the authors establish sufficient conditions that do not require independence or joint density assumptions, allowing for arbitrary marginal distributions. The results are extended to general measurable spaces equipped with reflexive binary relations. Leveraging tools from stochastic orders, conditional distributions, measure theory, and monotone functions, the paper proves the absolute continuity of the distribution of the aggregated variable \(g(X,Y)\). This extends the applicability of convolution regularization techniques and provides theoretical foundations for applications such as risk aggregation.

0 citationsRead paper

Cops and robber in graphs with bounded vertex cover number

Feb 07, 2026

This study addresses the problem of bounding the cop number in connected graphs with vertex cover number $k$, offering a structural perspective toward Meyniel’s conjecture. By integrating vertex cover structure analysis, combinatorial optimization, and asymptotic methods, the work establishes the first sublinear upper bound on the cop number parameterized solely by $k$. Specifically, it proves that any connected graph with vertex cover number $k$ has cop number at most $k / 2^{(1 - o(1))\sqrt{\log k}}$. This result breaks away from the conventional framework that depends on the total number of vertices $n$, providing new evidence for Meyniel’s conjecture within structurally restricted graph classes.

0 citationsRead paper