A C`adl`ag Rough Path Foundation for Robust Finance

Using rough path theory, we provide a pathwise foundation for stochastic It^o integration, which covers most commonly applied trading strategies and mathematical models of financial markets, including those under Knightian uncertainty. To this end, we introduce the so-called Property (RIE) for c`adl`ag paths, which is shown to imply the existence of a c`adl`ag rough path and of quadratic variation in the sense of Follmer. We prove that the corresponding rough integrals exist as limits of left-point Riemann sums along a suitable sequence of partitions. This allows one to treat integrands of non-gradient type, and gives access to the powerful stability estimates of rough path theory. Additionally, we verify that (path-dependent) functionally generated trading strategies and Covers universal portfolio are admissible integrands, and that Property (RIE) is satisfied by both (Young) semimartingales and typical price paths.

Higher Order Kernel Mean Embeddings to Capture Filtrations of Stochastic Processes

Stochastic processes are random variables with values in some space of paths. However, reducing a stochastic process to a path-valued random variable ignores its filtration, i.e. the flow of information carried by the process through time. By conditioning the process on its filtration, we introduce a family of higher order kernel mean embeddings (KMEs) that generalizes the notion of KME and captures additional information related to the filtration. We derive empirical estimators for the associated higher order maximum mean discrepancies (MMDs) and prove consistency. We then construct a filtration-sensitive kernel two-sample test able to pick up information that gets missed by the standard MMD test. In addition, leveraging our higher order MMDs we construct a family of universal kernels on stochastic processes that allows to solve real-world calibration and optimal stopping problems in quantitative finance (such as the pricing of American options) via classical kernel-based regression methods. Finally, adapting existing tests for conditional independence to the case of stochastic processes, we design a causal-discovery algorithm to recover the causal graph of structural dependencies among interacting bodies solely from observations of their multidimensional trajectories.

Model-free Portfolio Theory: A Rough Path Approach

Based on a rough path foundation, we develop a model-free approach to stochastic portfolio theory (SPT). Our approach allows to handle significantly more general portfolios compared to previous model-free approaches based on Follmer integration. Without the assumption of any underlying probabilistic model, we prove pathwise Master formulae analogous to those of classical SPT, describing the growth of wealth processes associated to functionally generated portfolios relative to the market portfolio. We show that the appropriately scaled asymptotic growth rate of a far reaching generalization of Covers universal portfolio based on controlled paths coincides with that of the best retrospectively chosen portfolio within this class. We provide several novel results concerning rough integration, and highlight the advantages of the rough path approach by considering (non-functionally generated) log-optimal portfolios in an ergodic It^o diffusion setting.

Graph Convolution for Re-ranking in Person Re-identification

Nowadays, deep learning is widely applied to extract features for similarity computation in person re-identification (re-ID) and have achieved great success. However, due to the non-overlapping between training and testing IDs, the difference between the data used for model training and the testing data makes the performance of learned feature degraded during testing. Hence, re-ranking is proposed to mitigate this issue and various algorithms have been developed. However, most of existing re-ranking methods focus on replacing the Euclidean distance with sophisticated distance metrics, which are not friendly to downstream tasks and hard to be used for fast retrieval of massive data in real applications. In this work, we propose a graph-based re-ranking method to improve learned features while still keeping Euclidean distance as the similarity metric. Inspired by graph convolution networks, we develop an operator to propagate features over an appropriate graph. Since graph is the essential key for the propagation, two important criteria are considered for designing the graph, and three different graphs are explored accordingly. Furthermore, a simple yet effective method is proposed to generate a profile vector for each tracklet in videos, which helps extend our method to video re-ID. Extensive experiments on three benchmark data sets, e.g., Market-1501, Duke, and MARS, demonstrate the effectiveness of our proposed approach.

Vision-Language Navigation with Random Environmental Mixup

Vision-language Navigation (VLN) tasks require an agent to navigate step-by-step while perceiving the visual observations and comprehending a natural language instruction. Large data bias, which is caused by the disparity ratio between the small data scale and large navigation space, makes the VLN task challenging. Previous works have proposed various data augmentation methods to reduce data bias. However, these works do not explicitly reduce the data bias across different house scenes. Therefore, the agent would overfit to the seen scenes and achieve poor navigation performance in the unseen scenes. To tackle this problem, we propose the Random Environmental Mixup (REM) method, which generates cross-connected house scenes as augmented data via mixuping environment. Specifically, we first select key viewpoints according to the room connection graph for each scene. Then, we cross-connect the key views of different scenes to construct augmented scenes. Finally, we generate augmented instruction-path pairs in the cross-connected scenes. The experimental results on benchmark datasets demonstrate that our augmentation data via REM help the agent reduce its performance gap between the seen and unseen environment and improve the overall performance, making our model the best existing approach on the standard VLN benchmark.

Phase-field modeling of rock fractures with roughness

Phase-field modeling -- a continuous approach to discontinuities -- is gaining popularity for simulating rock fractures due to its ability to handle complex, discontinuous geometry without an explicit surface tracking algorithm. None of the existing phase-field models, however, incorporates the impact of surface roughness on the mechanical response of fractures -- such as elastic deformability and shear-induced dilation -- despite the importance of this behavior for subsurface systems. To fill this gap, here we introduce the first framework for phase-field modeling of rough rock fractures. The framework transforms a displacement-jump-based discrete constitutive model for discontinuities into a strain-based continuous model, and then casts it into a phase-field formulation for frictional interfaces. We illustrate the framework by constructing a particular phase-field form employing a rock joint model originally formulated for discrete modeling. The results obtained by the new formulation show excellent agreement with those of a well-established discrete method for a variety of problems ranging from shearing of a single discontinuity to compression of fractured rocks. Consequently, our phase-field framework provides an unprecedented bridge between a discrete constitutive model for rough discontinuities -- common in rock mechanics -- and the continuous finite element method -- standard in computational mechanics -- without any algorithm to explicitly represent discontinuity geometry.

The topological phase of bright solitons

We study the topological phase of bright soliton with arbitrary velocity under the self-steepening effect. Such topological phase can be described by the topological vector potential and effective magnetic field. We find that the point-like magnetic fields corresponds to the density peak of such bright solitons, where each elementary magnetic flux is {pi}. Remarkably, we show that two bright solitons can generate an additional topological field due to the phase jump between them. Our research provided the possibility to use bright solitons to explore topological properties.

City-Scale Multi-Camera Vehicle Tracking Guided by Crossroad Zones

Multi-Target Multi-Camera Tracking has a wide range of applications and is the basis for many advanced inferences and predictions. This paper describes our solution to the Track 3 multi-camera vehicle tracking task in 2021 AI City Challenge (AICITY21). This paper proposes a multi-target multi-camera vehicle tracking framework guided by the crossroad zones. The framework includes: (1) Use mature detection and vehicle re-identification models to extract targets and appearance features. (2) Use modified JDETracker (without detection module) to track single-camera vehicles and generate single-camera tracklets. (3) According to the characteristics of the crossroad, the Tracklet Filter Strategy and the Direction Based Temporal Mask are proposed. (4) Propose Sub-clustering in Adjacent Cameras for multi-camera tracklets matching. Through the above techniques, our method obtained an IDF1 score of 0.8095, ranking first on the leaderboard. The code have released: https://github.com/LCFractal/AIC21-MTMC.

A Sobolev rough path extension theorem via regularity structures

We show that every $mathbb{R}^d$-valued Sobolev path with regularity $alpha$ and integrability $p$ can be lifted to a Sobolev rough path provided $alpha < 1/p<1/3$. The novelty of our approach is its use of ideas underlying Hairers reconstruction theorem generalized to a framework allowing for Sobolev models and Sobolev modelled distributions. Moreover, we show that the corresponding lifting map is locally Lipschitz continuous with respect to the inhomogeneous Sobolev metric.

Generalized fractional grey system models: Memory effects perspective

As an essential characteristics of fractional calculus, the memory effect is served as one of key factors to deal with diverse practical issues, thus has been received extensive attention since it was born. By combining the fractional derivative with memory effects and grey modeling theory, this paper aims to construct an unified framework for the commonly-used fractional grey models already in place. In particular, by taking different kernel and normalization functions, this framework can deduce some other new fractional grey models. To further improve the prediction performance, the four popular intelligent algorithms are employed to determine the emerging coefficients for the UFGM(1,1) model. Two published cases are then utilized to verify the validity of the UFGM(1,1) model and explore the effects of fractional accumulation order and initial value on the prediction accuracy, respectively. Finally, this model is also applied to dealing with two real examples so as to further explain its efficacy and equally show how to use the unified framework in practical applications.