FJMP: Factorized Joint Multi-Agent Motion Prediction over Learned Directed Acyclic Interaction Graphs

Predicting the future motion of road agents is a critical task in an autonomous driving pipeline. In this work, we address the problem of generating a set of scene-level, or joint, future trajectory predictions in multi-agent driving scenarios. To this end, we propose FJMP, a Factorized Joint Motion Prediction framework for multi-agent interactive driving scenarios. FJMP models the future scene interaction dynamics as a sparse directed interaction graph, where edges denote explicit interactions between agents. We then prune the graph into a directed acyclic graph (DAG) and decompose the joint prediction task into a sequence of marginal and conditional predictions according to the partial ordering of the DAG, where joint future trajectories are decoded using a directed acyclic graph neural network (DAGNN). We conduct experiments on the INTERACTION and Argoverse 2 datasets and demonstrate that FJMP produces more accurate and scene-consistent joint trajectory predictions than non-factorized approaches, especially on the most interactive and kinematically interesting agents. FJMP ranks 1st on the multi-agent test leaderboard of the INTERACTION dataset.Comment: CVPR 202

Shift-Symmetric Configurations in Two-Dimensional Cellular Automata: Irreversibility, Insolvability, and Enumeration

The search for symmetry as an unusual yet profoundly appealing phenomenon, and the origin of regular, repeating configuration patterns have long been a central focus of complexity science and physics. To better grasp and understand symmetry of configurations in decentralized toroidal architectures, we employ group-theoretic methods, which allow us to identify and enumerate these inputs, and argue about irreversible system behaviors with undesired effects on many computational problems. The concept of so-called configuration shift-symmetry is applied to two-dimensional cellular automata as an ideal model of computation. Regardless of the transition function, the results show the universal insolvability of crucial distributed tasks, such as leader election, pattern recognition, hashing, and encryption. By using compact enumeration formulas and bounding the number of shift-symmetric configurations for a given lattice size, we efficiently calculate the probability of a configuration being shift-symmetric for a uniform or density-uniform distribution. Further, we devise an algorithm detecting the presence of shift-symmetry in a configuration. Given the resource constraints, the enumeration and probability formulas can directly help to lower the minimal expected error and provide recommendations for system's size and initialization. Besides cellular automata, the shift-symmetry analysis can be used to study the non-linear behavior in various synchronous rule-based systems that include inference engines, Boolean networks, neural networks, and systolic arrays.Comment: 22 pages, 9 figures, 2 appendice

MRI-based Quantification of Optic Nerve Tortuosity and Subarachnoid Space 3D Geometry: Reliability Assessment

In some astronauts, long-duration space flight results in ophthalmic structure changes such as optic nerve (ON) kinking, ON distention, and globe flattening. Assessment of the ON and ON sheath (ONS) may provide insight into the mechanisms responsible for ophthalmic structure changes seen in a subset of astronauts. Automated and manual methods were developed to quantify 3D ON/ONS geometry and ON tortuosity

Fluctuations in an Evolutional Model of Two-Dimensional Young Diagrams

We discuss the non-equilibrium fluctuation problem, which corresponds to the hydrodynamic limit established in \cite{FS}, for the dynamics of two-dimensional Young diagrams associated with the uniform and restricted uniform statistics, and derive linear stochastic partial differential equations in the limit. We show that their invariant measures are identical to the Gaussian measures which appear in the fluctuation limits in the static situations.Comment: 43 pages, 2 figure

Stationary distributions for diffusions with inert drift

Consider reflecting Brownian motion in a bounded domain in $${\mathbb R^d}$$ that acquires drift in proportion to the amount of local time spent on the boundary of the domain. We show that the stationary distribution for the joint law of the position of the reflecting Brownian motion and the value of the drift vector has a product form. Moreover, the first component is uniformly distributed on the domain, and the second component has a Gaussian distribution. We also consider more general reflecting diffusions with inert drift as well as processes where the drift is given in terms of the gradient of a potential

A Multi-Country Trade and Tourism with Endogenous Capital and Knowledge

Background: The study models a dynamic interaction among economic growth, structural change, knowledge accumulation, international trade and tourist flows. Objective: The purpose of this study is to introduce endogenous knowledge into a multi-country growth model with trade and tourism proposed by Zhang. The study models a dynamic interaction among economic growth, structural change, knowledge accumulation, international trade and tourist flows. Methods/Approach: The model is based on Arrow’s learning by doing, the Solow one-sector growth model, the Oniki-Uzawa neoclassical trade model, and the Uzawa two-sector growth model. We first build the multi-country neoclassical growth model of endogenous knowledge with international tourism. Then we show that we can follow the motion of the -country world economy with differential equations. Results: We simulate the motion of the three-country global economy. We carry out a comparative dynamic analysis by simulation with regard to the knowledge utilization efficiency, the efficiency of learning by doing, the propensity to save, the propensity to tour other countries, and the population. Conclusions: The global economy has a unique equilibrium

Analysis of fracture processes in cortical bone tissue

This article has been published in the journal, Engineering Fracture Mechanics [© Elsevier Ltd]. The definitive version is available at: http://dx.doi.org/10.1016/j.engfracmech.2012.11.020Bones are the principal structural components of a skeleton; they play unique roles in the body providing its shape maintenance, protection of internal organs and transmission of forces. Ultimately, their structural integrity is vital for the quality of life. Unfortunately, bones can only sustain loads until a certain limit, beyond which they fail. Understanding a fracture behaviour of bone is necessary for prevention and diagnosis of trauma; this can be achieved by studying mechanical properties of bone, such as its fracture toughness. Generally, most of bone fractures occur in long bones consisting mostly of cortical bone tissue. Therefore, in this paper, an experimental study and numerical simulations of fracture processes in a bovine femoral cortical bone tissue were considered. A set of experiments was conducted to characterise fracture toughness of the bone tissue in order to gain basic understanding of spatial variability and anisotropy of its resistance to fracture and its link to an underlying microstructure. The data was obtained using single-edge-notch-bending specimens of cortical bone tested in a three-point bending setup; fracture surfaces of specimens were studied using scanning electron microscopy. Based on the results of those experiments, a number of finite-element models were developed in order to analyse its deformation and fracture using the extended finite-element method (X-FEM). Experimental results of this study demonstrate both variability and anisotropy of fracture toughness of the cortical bone tissue; the developed models adequately reflected the experimental data