For all integers $k,d$ such that $k \geq 3$ and $k/2\leq d \leq k-1$, let $n$ be a sufficiently large integer ( which may not be divisible by $k$ ) , and let $s\le \lfloor n/k\rfloor-1$. We show that if $H$ is a $k$-uniform hypergraph on $n$ vertices with $\delta_{d}(H)>\binom{n-d}{k-d}-\binom{n-d-s+1}{k-d}$, then $H$ contains a matching of size $s$. This improves a recent result of Lu, Yu, and Yuan and also answers a question of Kühn, Osthus, and Townsend. In many cases, our result can be strengthened to $s\leq \lfloor n/k\rfloor$, which then covers the entire possible range of $s$. On the other hand, there are examples showing that the result does not hold for certain $n, k, d$, and $s= \lfloor n/k\rfloor$.

The goal of sample-data-based origin-destination (O-D) demand estimation is to aggregate the location data into the traffic network. Inevitably, the scaling rate, which expands the estimated O-D demands to the population level, should be generated. In this paper, a two-stage optimization model is explored for determining the sensor location and stochastic scaling rate. In the first stage, a sensor deployment model identifies the optimal sensor location strategy by minimizing the variability of the scaling rate under a budget constraint. In the second stage, a Bayesian-based scaling rate inference model leverages the prior information and the data that were observed at the identified sensor locations to derive the stochastic scaling rate. The Bayesian-based scaling rate inference model is a bilevel program, which seeks the maximum a posteriori (MAP) scaling rate conditioned by the observed link flows in the upper level and optimizes the stochastic user equilibrium (SUE) in the lower level. To reflect the interactive relationships between the sensor location and the stochastic scaling rate inference, an integrating model is built. A sequential identifying sensor location algorithm that avoids matrix inversions was proposed to solve the sensor deployment model, and an iterative solution algorithm was developed to solve the Bayesian-based scaling rate inference model. The results from numerical experiments demonstrate that the sensor deployment model could provide the most reliable scheme of sensor locations, thereby contributing to the reliable estimation of the stochastic scaling rate. The results also demonstrate that both the endogenous information (prior information on the scaling rate) and exogenous factors (link flows) can facilitate a more accurate scaling rate inference.