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Jiazu Zhou

Publications and source records attributed to Jiazu Zhou.

9 recordsLinked to original sources
arXiv2026

System optimality versus self-organization in metro networks: An optimal transport analysis

Urban transportation network design is typically approached through top-down planning grounded in engineering and economics. Yet cities are complex systems characterized by feedback loops between infrastructure and mobility demand: network structure shapes origin-destination (OD) flows, while OD flows adapt and in turn affect network development. Despite this interdependence, computational tools to benchmark real-world networks against alternative generative principles remain limited. Here, we introduce a data-driven framework to compare three types of metro networks: a self-organized (desire-path) network derived from local rules, a system-optimal network derived from global optimization, and the empirical real-world network. We quantify similarities and discrepancies using geometric comparisons and optimal transport theory. Applying the framework to Singapore's Mass Rapid Transit system, we find that the empirical metro network is substantially closer to the self-organized benchmark than to the system-optimal benchmark, with remaining discrepancies largely explained by geographic constraints. These findings highlight that system-wide optimality alone may be inadequate for guiding practical interventions, motivating planning approaches that explicitly incorporate local service needs. The framework is transferable across regions and can diagnose design-use misalignments to support adaptive infrastructure planning.

physics.soc-ph↗
arXiv2025

FloGAN: Scenario-Based Urban Mobility Flow Generation via Conditional GANs and Dynamic Region Decoupling

The mobility patterns of people in cities evolve alongside changes in land use and population. This makes it crucial for urban planners to simulate and analyze human mobility patterns for purposes such as transportation optimization and sustainable urban development. Existing generative models borrowed from machine learning rely heavily on historical trajectories and often overlook evolving factors like changes in population density and land use. Mechanistic approaches incorporate population density and facility distribution but assume static scenarios, limiting their utility for future projections where historical data for calibration is unavailable. This study introduces a novel, data-driven approach for generating origin-destination mobility flows tailored to simulated urban scenarios. Our method leverages adaptive factors such as dynamic region sizes and land use archetypes, and it utilizes conditional generative adversarial networks (cGANs) to blend historical data with these adaptive parameters. The approach facilitates rapid mobility flow generation with adjustable spatial granularity based on regions of interest, without requiring extensive calibration data or complex behavior modeling. The promising performance of our approach is demonstrated by its application to mobile phone data from Singapore, and by its comparison with existing methods.

cs.LG↗
arXiv2024

Asymptotic theory of $C$-pseudo-cones

In this paper, we study the non-degenerated $C$-pseudo-cones which can be uniquely decomposed into the sum of a $C$-asymptotic set and a $C$-starting point. Combining this with the novel work in \cite{Schneider-A_weighted_Minkowski_theorem}, we introduce the asymptotic weighted co-volume functional $T_Θ(E)$ of the non-degenerated $C$-pseudo-cone $E$, which is also a generalized function with the singular point $o$ (the origin). Using our convolution formula for $T_Θ(E)$, we establish a decay estimate for $T_Θ(E)$ at infinity and present some interesting results. As applications of this asymptotic theory, we prove a weighted Brunn-Minkowski type inequality and study the solutions to the weighted Minkowski problem for pseudo-cones. Moreover, we pose an open problem regarding $T_Θ(E)$, which we call the asymptotic Brunn-Minkowski inequality for $C$-pseudo-cones.

math.MG↗
arXiv2023

An affine isoperimetric inequality for log-concave functions

The authors gave an affine isoperimetric inequality \cite{LYZ2010} that gives a lower bound for the volume of a polar body and the equality holds if and only if the body is a simplex. In this paper, we give a functional isoperimetric inequality for log-concave functions that contains the affine isoperimetric inequality of Lutwak, Yang and Zhang in \cite{LYZ2010}.

math.MG↗
arXiv2021

Dual curvature measures on convex functions and associated Minkowski problems

In this paper, the $q$-th dual curvature measure is extended to convex functions and the associated Minkowski problem is posed. A special case includes the $q$-th dual curvature measure of convex bodies which defined by Huang, Lutwak, Yang and Zhang. Existence for the functional dual Minkowski problem is showed when $q\leq0$ and the uniqueness part is obtained with some assumptions.

math.FA↗
arXiv2021

Uniqueness and continuity of the solution to $L_p$ dual Minkowski problem

Lutwak, Yang and Zhang \cite{LYZ2018} introduced the $L_p$ dual curvature measure that unifies several other geometric measures in dual Brunn-Minkowski theory and Brunn- Minkowski theory. Motivated by works in \cite{LYZ2018}, we consider the uniqueness and continuity of the solution to the $L_p$ dual Minkowski problem. To extend the important work (Theorem \ref{uniquepolytope}) of LYZ to the case for general convex bodies, we establish some new Minkowski-type inequalities which are closely related to the optimization problem associated with the $L_p$ dual Minkowski problem. When $q< p$, the uniqueness of the solution to the $L_p$ dual Minkowski problem for general convex bodies is obtained. Moreover, we obtain the continuity of the solution to the $L_p$ dual Minkowski problem for convex bodies.

math.MG↗
arXiv2020

The Busemann-Petty problem on entropy of log-concave functions

The Busemann-Petty problem asks whether symmetric convex bodies in the Euclidean space $\mathbb{R}^n$ with smaller central hyperplane sections necessarily have smaller volume. The solution has been completed and the answer is affirmative if $n \le 4$ and negative if $n\ge 5$. In this paper, we investigate the Busemann-Petty problem on entropy of log-concave functions: For even log-concave functions $f$ and $g$ with finite positive integrals in $\mathbb{R}^n$, if the marginal $\int_{\mathbb{R}^n\cap H}f(x)dx$ of $f$ is smaller than the marginal $\int_{\mathbb{R}^n\cap H}g(x)dx$ of $g$ for every hyperplane $H$ passing through the origin, whether the entropy ${\rm Ent}(f)$ of $f$ is bigger than the entropy ${\rm Ent}(g)$ of $g$? The Busemann-Petty problem on entropy of log-concave functions includes the Busemann-Petty problem, hence, its answer is negative when $n\geq5$. For $2\leq n\leq4$ we give a positive answer to the Busemann-Petty problem on entropy of log-concave functions.

math.FA↗
arXiv2013

The mixed $L_p$ geominimal surface areas for multiple convex bodies

In this paper, we introduce several mixed $L_p$ geominimal surface areas for multiple convex bodies for all $p\neq -n$. Our definitions are motivated from an equivalent formula for the mixed $p$-affine surface area. Some properties, such as the affine invariance, for these mixed $L_p$ geominimal surface areas are proved. Related inequalities, such as, Alexander-Fenchel type inequality, Santaló style inequality, affine isoperimetric inequalities, and cyclic inequalities are established. Moreover, we also study some properties and inequalities for the $i$-th mixed $L_p$ geominimal surface areas for two convex bodies.

math.MG↗