We find by applying MacMahons partition analysis that all magic labellings of the cube are of eight types, each generated by six basis elements. A combinatorial proof of this fact is given. The number of magic labellings of the cube is thus reobtaine
d as a polynomial in the magic sum of degree $5$. Then we enumerate magic distinct labellings, the number of which turns out to be a quasi-polynomial of period 720720. We also find the group of symmetry can be used to significantly simplify the computation.
This paper presents the Rail-5k dataset for benchmarking the performance of visual algorithms in a real-world application scenario, namely the rail surface defects detection task. We collected over 5k high-quality images from railways across China, a
nd annotated 1100 images with the help from railway experts to identify the most common 13 types of rail defects. The dataset can be used for two settings both with unique challenges, the first is the fully-supervised setting using the 1k+ labeled images for training, fine-grained nature and long-tailed distribution of defect classes makes it hard for visual algorithms to tackle. The second is the semi-supervised learning setting facilitated by the 4k unlabeled images, these 4k images are uncurated containing possible image corruptions and domain shift with the labeled images, which can not be easily tackle by previous semi-supervised learning methods. We believe our dataset could be a valuable benchmark for evaluating robustness and reliability of visual algorithms.
Market by order (MBO) data - a detailed feed of individual trade instructions for a given stock on an exchange - is arguably one of the most granular sources of microstructure information. While limit order books (LOBs) are implicitly derived from it
, MBO data is largely neglected by current academic literature which focuses primarily on LOB modelling. In this paper, we demonstrate the utility of MBO data for forecasting high-frequency price movements, providing an orthogonal source of information to LOB snapshots and expanding the universe of alpha discovery. We provide the first predictive analysis on MBO data by carefully introducing the data structure and presenting a specific normalisation scheme to consider level information in order books and to allow model training with multiple instruments. Through forecasting experiments using deep neural networks, we show that while MBO-driven and LOB-driven models individually provide similar performance, ensembles of the two can lead to improvements in forecasting accuracy - indicating that MBO data is additive to LOB-based features.
Deep neural models have hitherto achieved significant performances on numerous classification tasks, but meanwhile require sufficient manually annotated data. Since it is extremely time-consuming and expensive to annotate adequate data for each class
ification task, learning an empirically effective model with generalization on small dataset has received increased attention. Existing efforts mainly focus on transferring task-relevant knowledge from other similar data to tackle the issue. These approaches have yielded remarkable improvements, yet neglecting the fact that the task-irrelevant features could bring out massive negative transfer effects. To date, no large-scale studies have been performed to investigate the impact of task-irrelevant features, let alone the utilization of this kind of features. In this paper, we firstly propose Task-Irrelevant Transfer Learning (TIRTL) to exploit task-irrelevant features, which mainly are extracted from task-irrelevant labels. Particularly, we suppress the expression of task-irrelevant information and facilitate the learning process of classification. We also provide a theoretical explanation of our method. In addition, TIRTL does not conflict with those that have previously exploited task-relevant knowledge and can be well combined to enable the simultaneous utilization of task-relevant and task-irrelevant features for the first time. In order to verify the effectiveness of our theory and method, we conduct extensive experiments on facial expression recognition and digit recognition tasks. Our source code will be also available in the future for reproducibility.
