This paper introduces a local-to-unity/small sigma process for a stationary time series with strong persistence and non-negligible long run risk. This process represents the stationary long run component in an unobserved short- and long-run components model involving different time scales. More specifically, the short run component evolves in the calendar time and the long run component evolves in an ultra long time scale. We develop the methods of estimation and long run prediction for the univariate and multivariate Structural VAR (SVAR) models with unobserved components and reveal the impossibility to consistently estimate some of the long run parameters. The approach is illustrated by a Monte-Carlo study and an application to macroeconomic data.
Optimization of design parameters of a transformer is a crucial task to increase efficiency and lower the material cost. This research presents an approach to model a three-phase transformer and optimize design parameters to minimize the volume and loss. ANSYS Maxwell 2D is used to model the transformer and analyze it for different design parameters. The multi-objective differential evolution algorithm is used to find optimum design parameters that minimize the volume and loss. In this paper, we present the optimum design parameters for a 1 kVA transformer with a particular input and output voltage specification. The transformer with these optimum design parameters is then tested for different loading conditions and power factor values. The results show that the maximum efficiency is obtained for 75% loading condition with unity power factor. As the power factor decreases, the efficiency decreases as well.
We study a general class of consumption-savings problems with recursive preferences. We characterize the sign of the consumption response to arbitrary shocks in terms of the product of two sufficient statistics: the elasticity of intertemporal substitution between contemporaneous consumption and continuation utility (EIS), and the relative elasticity of the marginal value of wealth (REMV). Under homotheticity, the REMV always equals one, so the propensity of the agent to save or dis-save is always signed by the relationship of the EIS with unity. We apply our results to derive comparative statics in classical problems of portfolio allocation, consumption-savings with income risk, and entrepreneurial investment. Our results suggest empirical identification strategies for both the value of the EIS and its relationship with unity.
Humans communicate non-verbally by sharing physical rhythms, such as nodding and gestures, to involve each other. This sharing of physicality creates a sense of unity and makes humans feel involved with others. In this paper, we developed a new body motion generation system based on the free-energy principle (FEP), which not only responds passively but also prompts human actions. The proposed system consists of two modules, the sampling module, and the motion selection module. We conducted a subjective experiment to evaluate the "feeling of interacting with the agent" of the FEP based behavior. The results suggested that FEP based behaviors show more "feeling of interacting with the agent". Furthermore, we confirmed that the agent's gestures elicited subject gestures. This result not only reinforces the impression of feeling interaction but could also realization of agents that encourage people to change their behavior.
We propose Unity Smoothing (US) for handling inconsistencies between a Bayesian network model and new unseen observations. We show that prediction accuracy, using the junction tree algorithm with US is comparable to that of Laplace smoothing. Moreover, in applications were sparsity of the data structures is utilized, US outperforms Laplace smoothing in terms of memory usage. Furthermore, we detail how to avoid redundant calculations that must otherwise be performed during the message passing scheme in the junction tree algorithm which we refer to as Unity Propagation (UP). Experimental results shows that it is always faster to exploit UP on top of the Lauritzen-Spigelhalter message passing scheme for the junction tree algorithm.
Taking advantage of both vehicle-to-everything (V2X) communication and automated driving technology, connected and automated vehicles are quickly becoming one of the transformative solutions to many transportation problems. However, in a mixed traffic environment at signalized intersections, it is still a challenging task to improve overall throughput and energy efficiency considering the complexity and uncertainty in the traffic system. In this study, we proposed a hybrid reinforcement learning (HRL) framework which combines the rule-based strategy and the deep reinforcement learning (deep RL) to support connected eco-driving at signalized intersections in mixed traffic. Vision-perceptive methods are integrated with vehicle-to-infrastructure (V2I) communications to achieve higher mobility and energy efficiency in mixed connected traffic. The HRL framework has three components: a rule-based driving manager that operates the collaboration between the rule-based policies and the RL policy; a multi-stream neural network that extracts the hidden features of vision and V2I information; and a deep RL-based policy network that generate both longitudinal and lateral eco-driving actions. In order to evaluate our approach, we developed a Unity-based simulator and designed a mixed-traffic intersection scenario. Moreover, several baselines were implemented to compare with our new design, and numerical experiments were conducted to test the performance of the HRL model. The experiments show that our HRL method can reduce energy consumption by 12.70% and save 11.75% travel time when compared with a state-of-the-art model-based Eco-Driving approach.
Quantum machine learning is a fast-emerging field that aims to tackle machine learning using quantum algorithms and quantum computing. Due to the lack of physical qubits and an effective means to map real-world data from Euclidean space to Hilbert space, most of these methods focus on quantum analogies or process simulations rather than devising concrete architectures based on qubits. In this paper, we propose a novel hybrid quantum-classical algorithm for graph-structured data, which we refer to as the Ego-graph based Quantum Graph Neural Network (egoQGNN). egoQGNN implements the GNN theoretical framework using the tensor product and unity matrix representation, which greatly reduces the number of model parameters required. When controlled by a classical computer, egoQGNN can accommodate arbitrarily sized graphs by processing ego-graphs from the input graph using a modestly-sized quantum device. The architecture is based on a novel mapping from real-world data to Hilbert space. This mapping maintains the distance relations present in the data and reduces information loss. Experimental results show that the proposed method outperforms competitive state-of-the-art models with only 1.68\% parameters compared to those models.
Initial access in millimeter-wave (mmW) wireless is critical toward successful realization of the fifth-generation (5G) wireless networks and beyond. Limited bandwidth in existing standards and use of phase-shifters in analog/hybrid phased-antenna arrays (PAA) are not suited for these emerging standards demanding low-latency direction finding. This work proposes a reconfigurable true-time-delay (TTD) based spatial signal processor (SSP) with frequency-division beam training methodology and wideband beam-squint less data communications. Discrete-time delay compensated clocking technique is used to support 800~MHz bandwidth with a large unity-gain bandwidth ring-amplifier (RAMP)-based signal combiner. To extensively characterize the proposed SSP across different SSP modes and frequency-angle pairs, an automated testbed is developed using computer-vision techniques that significantly speeds up the testing progress and minimize possible human errors. Using seven levels of time-interleaving for each of the 4 antenna elements, the TTD SSP has a delay range of 3.8 ns over 800 MHz and achieves unique frequency-to-angle mapping in the beamtraining mode with nearly 12 dB frequency-independent gain in the beamforming mode. The SSP is prototyped in 65nm CMOS with an area of 1.98mm$^2$ consuming only 29 mW excluding buffers. Further, an error vector magnitude (EVM) of 9.8% is realized for 16-QAM modulation at a speed of 122.8 Mb/s.
The stability condition for Hawkes processes and their non-linear extensions usually relies on the condition that the mean intensity is a finite constant. It follows that the total endogeneity ratio needs to be strictly smaller than unity. In the present note we argue that it is possible to have a total endogeneity ratio greater than unity without rendering the process unstable. In particular, we show that, provided the endogeneity ratio of the linear Hawkes component is smaller than unity, Quadratic Hawkes processes are always stationary, although with infinite mean intensity when the total endogenity ratio exceeds one. This results from a subtle compensation between the inhibiting realisations (mean-reversion) and their exciting counterparts (trends).
This work investigates the effects of Curriculum Learning (CL)-based approaches on the agent's performance. In particular, we focus on the safety aspect of robotic mapless navigation, comparing over a standard end-to-end (E2E) training strategy. To this end, we present a CL approach that leverages Transfer of Learning (ToL) and fine-tuning in a Unity-based simulation with the Robotnik Kairos as a robotic agent. For a fair comparison, our evaluation considers an equal computational demand for every learning approach (i.e., the same number of interactions and difficulty of the environments) and confirms that our CL-based method that uses ToL outperforms the E2E methodology. In particular, we improve the average success rate and the safety of the trained policy, resulting in 10% fewer collisions in unseen testing scenarios. To further confirm these results, we employ a formal verification tool to quantify the number of correct behaviors of Reinforcement Learning policies over desired specifications.
In this letter we propose a data-driven approach to optimizing the algebraic connectivity of a team of robots. While a considerable amount of research has been devoted to this problem, we lack a method that scales in a manner suitable for online applications for more than a handful of agents. To that end, we propose a supervised learning approach with a convolutional neural network (CNN) that learns to place communication agents from an expert that uses an optimization-based strategy. We demonstrate the performance of our CNN on canonical line and ring topologies, 105k randomly generated test cases, and larger teams not seen during training. We also show how our system can be applied to dynamic robot teams through a Unity-based simulation. After training, our system produces connected configurations over an order of magnitude faster than the optimization-based scheme for teams of 10-20 agents.
With the rapid development of intelligent vehicles and Advanced Driver-Assistance Systems (ADAS), a new trend is that mixed levels of human driver engagements will be involved in the transportation system. Therefore, necessary visual guidance for drivers is vitally important under this situation to prevent potential risks. To advance the development of visual guidance systems, we introduce a novel vision-cloud data fusion methodology, integrating camera image and Digital Twin information from the cloud to help intelligent vehicles make better decisions. Target vehicle bounding box is drawn and matched with the help of the object detector (running on the ego-vehicle) and position information (received from the cloud). The best matching result, a 79.2% accuracy under 0.7 intersection over union threshold, is obtained with depth images served as an additional feature source. A case study on lane change prediction is conducted to show the effectiveness of the proposed data fusion methodology. In the case study, a multi-layer perceptron algorithm is proposed with modified lane change prediction approaches. Human-in-the-loop simulation results obtained from the Unity game engine reveal that the proposed model can improve highway driving performance significantly in terms of safety, comfort, and environmental sustainability.
Dance choreography for a piece of music is a challenging task, having to be creative in presenting distinctive stylistic dance elements while taking into account the musical theme and rhythm. It has been tackled by different approaches such as similarity retrieval, sequence-to-sequence modeling and generative adversarial networks, but their generated dance sequences are often short of motion realism, diversity and music consistency. In this paper, we propose a Music-to-Dance with Optimal Transport Network (MDOT-Net) for learning to generate 3D dance choreographies from music. We introduce an optimal transport distance for evaluating the authenticity of the generated dance distribution and a Gromov-Wasserstein distance to measure the correspondence between the dance distribution and the input music. This gives a well defined and non-divergent training objective that mitigates the limitation of standard GAN training which is frequently plagued with instability and divergent generator loss issues. Extensive experiments demonstrate that our MDOT-Net can synthesize realistic and diverse dances which achieve an organic unity with the input music, reflecting the shared intentionality and matching the rhythmic articulation. Sample results are found at https://www.youtube.com/watch?v=dErfBkrlUO8.
We use deep neural networks to machine learn correlations between knot invariants in various dimensions. The three-dimensional invariant of interest is the Jones polynomial $J(q)$, and the four-dimensional invariants are the Khovanov polynomial $\text{Kh}(q,t)$, smooth slice genus $g$, and Rasmussen's $s$-invariant. We find that a two-layer feed-forward neural network can predict $s$ from $\text{Kh}(q,-q^{-4})$ with greater than $99\%$ accuracy. A theoretical explanation for this performance exists in knot theory via the now disproven knight move conjecture, which is obeyed by all knots in our dataset. More surprisingly, we find similar performance for the prediction of $s$ from $\text{Kh}(q,-q^{-2})$, which suggests a novel relationship between the Khovanov and Lee homology theories of a knot. The network predicts $g$ from $\text{Kh}(q,t)$ with similarly high accuracy, and we discuss the extent to which the machine is learning $s$ as opposed to $g$, since there is a general inequality $|s| \leq 2g$. The Jones polynomial, as a three-dimensional invariant, is not obviously related to $s$ or $g$, but the network achieves greater than $95\%$ accuracy in predicting either from $J(q)$. Moreover, similar accuracy can be achieved by evaluating $J(q)$ at roots of unity. This suggests a relationship with $SU(2)$ Chern--Simons theory, and we review the gauge theory construction of Khovanov homology which may be relevant for explaining the network's performance.
A key challenge in computer vision and deep learning is the definition of robust strategies for the detection of adversarial examples. Here, we propose the adoption of ensemble approaches to leverage the effectiveness of multiple detectors in exploiting distinct properties of the input data. To this end, the ENsemble Adversarial Detector (ENAD) framework integrates scoring functions from state-of-the-art detectors based on Mahalanobis distance, Local Intrinsic Dimensionality, and One-Class Support Vector Machines, which process the hidden features of deep neural networks. ENAD is designed to ensure high standardization and reproducibility to the computational workflow. Importantly, extensive tests on benchmark datasets, models and adversarial attacks show that ENAD outperforms all competing methods in the large majority of settings. The improvement over the state-of-the-art and the intrinsic generality of the framework, which allows one to easily extend ENAD to include any set of detectors, set the foundations for the new area of ensemble adversarial detection.
May and Leonard (SIAM J. Appl. Math 1975) introduced a three-species Lotka-Volterra type population model that exhibits heteroclinic cycling. Rather than producing a periodic limit cycle, the trajectory takes longer and longer to complete each "cycle", passing closer and closer to unstable fixed points in which one population dominates and the others approach zero. Aperiodic heteroclinic dynamics have subsequently been studied in ecological systems (side-blotched lizards; colicinogenic E. coli), in the immune system, in neural information processing models ("winnerless competition"), and in models of neural central pattern generators. Yet as May and Leonard observed "Biologically, the behavior (produced by the model) is nonsense. Once it is conceded that the variables represent animals, and therefore cannot fall below unity, it is clear that the system will, after a few cycles, converge on some single population, extinguishing the other two." Here, we explore different ways of introducing discrete stochastic dynamics based on May and Leonard's ODE model, with application to ecological population dynamics, and to a neuromotor central pattern generator system. We study examples of several quantitatively distinct asymptotic behaviors, including total extinction of all species, extinction to a single species, and persistent cyclic dominance with finite mean cycle length.
Using neural networks to solve variational problems, and other scientific machine learning tasks, has been limited by a lack of consistency and an inability to exactly integrate expressions involving neural network architectures. We address these limitations by formulating a novel neural network architecture that combines a polynomial mixture-of-experts model with free knot B1-spline basis functions. Effectively, our architecture performs piecewise polynomial approximation on each cell of a trainable partition of unity. Our architecture exhibits both $h$- and $p$- refinement for regression problems at the convergence rates expected from approximation theory, allowing for consistency in solving variational problems. Moreover, this architecture, its moments, and its partial derivatives can all be integrated exactly, obviating a reliance on sampling or quadrature and enabling error-free computation of variational forms. We demonstrate the success of our network on a range of regression and variational problems that illustrate the consistency and exact integrability of our network architecture.
Signed distance transforms of sampled signals can be constructed better than the traditional exact signed distance transform. Such a transform is termed the high-order signed distance transform and is defined as satisfying three conditions: the Eikonal equation, recovery by a Heaviside function, and has an order of accuracy greater than unity away from the medial axis. Such a transform is an improvement to the classic notion of an exact signed distance transform because it does not exhibit artifacts of quantization. A large constant, linear time complexity high-order signed distance transform for arbitrary dimensionality sampled signals is developed based on the high order fast sweeping method. The transform is initialized with an exact signed distance transform and quantization corrected through an upwind solver for the boundary value Eikonal equation. The proposed method cannot attain arbitrary order of accuracy and is limited by the initialization method and non-uniqueness of the problem. However, meshed surfaces are visually smoother and do not exhibit artifacts of quantization in local mean and Gaussian curvature.
In this work we apply deep reinforcement learning to the problems of navigating a three-dimensional environment and inferring the locations of human speaker audio sources within, in the case where the only available information is the raw sound from the environment, as a simulated human listener placed in the environment would hear it. For this purpose we create two virtual environments using the Unity game engine, one presenting an audio-based navigation problem and one presenting an audio source localization problem. We also create an autonomous agent based on PPO online reinforcement learning algorithm and attempt to train it to solve these environments. Our experiments show that our agent achieves adequate performance and generalization ability in both environments, measured by quantitative metrics, even when a limited amount of training data are available or the environment parameters shift in ways not encountered during training. We also show that a degree of agent knowledge transfer is possible between the environments.
Automated surgical instrument localization is an important technology to understand the surgical process and in order to analyze them to provide meaningful guidance during surgery or surgical index after surgery to the surgeon. We introduce a new dataset that reflects the kinematic characteristics of surgical instruments for automated surgical instrument localization of surgical videos. The hSDB(hutom Surgery DataBase)-instrument dataset consists of instrument localization information from 24 cases of laparoscopic cholecystecomy and 24 cases of robotic gastrectomy. Localization information for all instruments is provided in the form of a bounding box for object detection. To handle class imbalance problem between instruments, synthesized instruments modeled in Unity for 3D models are included as training data. Besides, for 3D instrument data, a polygon annotation is provided to enable instance segmentation of the tool. To reflect the kinematic characteristics of all instruments, they are annotated with head and body parts for laparoscopic instruments, and with head, wrist, and body parts for robotic instruments separately. Annotation data of assistive tools (specimen bag, needle, etc.) that are frequently used for surgery are also included. Moreover, we provide statistical information on the hSDB-instrument dataset and the baseline localization performances of the object detection networks trained by the MMDetection library and resulting analyses.