arXiv subjects

Matheus Santos

Publications and source records attributed to Matheus Santos.

3 recordsLinked to original sources

arXiv2026

Blow-up for a Semilinear Tricomi-type Equation with Scale-Invariant Mass in the Oscillatory Regime

We investigate the finite-time blow-up of solutions to a Tricomi-type equation with scale-invariant potential and power nonlinearities in the oscillatory regime. For smooth, compactly supported, nonnegative initial data, we prove nonexistence of global-in-time solutions when the power nonlinearity lies below the positive root of an explicit Strauss-type polynomial naturally associated with the equation. The proof combines two main ingredients. The first is the construction of a positive adjoint temporal profile, which yields a weighted monotonicity formula and, consequently, a quantitative lower bound for the nonlinear term. The second is a phase-localized test function argument on logarithmic time shells, fitted to capture the oscillatory effects induced by the scale-invariant potential and to derive a complementary upper bound for the same quantity. The existence of global solutions when the power nonlinearity is equal to the polynomial root is still an open problem.

math.AP↗

arXiv2025

SSCATeR: Sparse Scatter-Based Convolution Algorithm with Temporal Data Recycling for Real-Time 3D Object Detection in LiDAR Point Clouds

This work leverages the continuous sweeping motion of LiDAR scanning to concentrate object detection efforts on specific regions that receive a change in point data from one frame to another. We achieve this by using a sliding time window with short strides and consider the temporal dimension by storing convolution results between passes. This allows us to ignore unchanged regions, significantly reducing the number of convolution operations per forward pass without sacrificing accuracy. This data reuse scheme introduces extreme sparsity to detection data. To exploit this sparsity, we extend our previous work on scatter-based convolutions to allow for data reuse, and as such propose Sparse Scatter-Based Convolution Algorithm with Temporal Data Recycling (SSCATeR). This operation treats incoming LiDAR data as a continuous stream and acts only on the changing parts of the point cloud. By doing so, we achieve the same results with as much as a 6.61-fold reduction in processing time. Our test results show that the feature maps output by our method are identical to those produced by traditional sparse convolution techniques, whilst greatly increasing the computational efficiency of the network.

cs.CV↗

arXiv2023

Rethinking Financial Service Promotion With Hybrid Recommender Systems at PicPay

The fintech PicPay offers a wide range of financial services to its 30 million monthly active users, with more than 50 thousand items recommended in the PicPay mobile app. In this scenario, promoting specific items that are strategic to the company can be very challenging. In this work, we present a Switching Hybrid Recommender System that combines two algorithms to effectively promote items without negatively impacting the user's experience. The results of our A/B tests show an uplift of up to 3.2\% when compared to a default recommendation strategy.

cs.IR↗