We present a constructive and self-contained approach to data driven general partition-of-unity copulas that were recently introduced in the literature. In particular, we consider Bernstein-, negative binomial and Poisson copulas and present a solution to the problem of fitting such copulas to highly asymmetric data.
To model discriminative, i.e. competition induced, self-thinning in even-aged forest stands a concept has been explored that discriminative mortality alters spatial arrangement of trees which in turn alters the mortality. Function of density was suggested to be a balance of initial density minus mortality that was dependent on initial spatial arrangement and mean horizontal size in the forest stand. Assuming initial spatial arrangement to be aggregation and performing normalizations gave the self-thinning function depending on only two parameters, initial stem density and maximal horizontal size (represented by stem diameter). Normalizations included integral of probability of trees to collide to be unity and stem density at maximal size to be zero. The self-thinning function obtained has been shown to successfully capture non-linear self-thinning dynamics in Douglas-fir long-term experiments in which competition-induced mortality prevailed.
Understanding and predicting outbreaks of contagious diseases are crucial to the development of society and public health, especially for underdeveloped countries. However, challenging problems are encountered because of complex epidemic spreading dynamics influenced by spatial structure and human dynamics (including both human mobility and human interaction intensity). We propose a systematical model to depict nationwide epidemic spreading in C\^{o}te d'Ivoire, which integrates multiple factors, such as human mobility, human interaction intensity, and demographic features. We provide insights to aid in modeling and predicting the epidemic spreading process by data-driven simulation and theoretical analysis, which is otherwise beyond the scope of local evaluation and geometrical views. We show that the requirement that the average local basic reproductive number to be greater than unity is not necessary for outbreaks of epidemics. The observed spreading phenomenon can be roughly explained as a heterogeneous diffusion-reaction process by redefining mobility distance according to the human mobility volume between nodes, which is beyond the geometrical viewpoint. However, the heterogeneity of human dynamics still poses challenges to precise prediction.
Many cell populations, exemplified by certain tumors, grow approximately according to a Gompertzian growth model which has a slower approach to an upper limit than that of logistic growth. Certain populations of animals and other organisms have also recently been analyzed with the Gompertz model. This article addresses the question of how long it takes to reduce the population from one level to a lower one under a schedule of sudden decrements, each of which removes a given fraction of the cell mass or population. A deterministic periodic schedule is first examined and yields exact results for the eradication or extinction time which is defined as that required to reduce the number of cells to less than unity. The decrements in cell mass at each hit could correspond to an approximation to reduction of a tumor by external beam radiation therapy. The effects of variations in magnitude of successive decrements, the time interval between them, the initial population size and the intrinsic growth rate are calculated and results presented graphically. With a schedule governed by a Poisson process, the number of organisms or cells satisfies a stochastic differential equation whose solution sample paths have downward jumps as random times. The moments of the exit time then satisfy a system of recurrent differential-difference equations. A simple transformation results in a simpler system which has been studied both analytically and numerically in the context of interspike intervals of a model neuron. Results are presented for the mean eradication time for various frequencies and magnitudes of hits and for various eventual and initial population sizes. The standard deviation of the eradication time is also investigated.
The number of substitutions (of nucleotides, amino acids, ...) that take place during the evolution of a sequence is a stochastic variable of fundamental importance in the field of molecular evolution. Although the mean number of substitutions during molecular evolution of a sequence can be estimated for a given substitution model, no simple solution exists for the variance of this random variable. We show in this article that the computation of the variance is as simple as that of the mean number of substitutions for both short and long times. Apart from its fundamental importance, this result can be used to investigate the dispersion index R , i.e. the ratio of the variance to the mean substitution number, which is of prime importance in the neutral theory of molecular evolution. By investigating large classes of substitution models, we demonstrate that although R\ge1 , to obtain R significantly larger than unity necessitates in general additional hypotheses on the structure of the substitution model.
(Abridged) We present palaeoeconomy reconstructions for pre-modern agriculture, with the Cucuteni-Trypillia Cultural unity (5,400-2,700 BC, modern Ukraine, Moldova and Romania) as example. The starting point of our analysis is the palaeodiet structure suggested by archaeological data, stable isotope analyses of human remains, and palynology. We allow for the archeologically attested contributions of domesticated and wild animal products to the diet, develop plausible estimates of the yield of ancient cereal varieties cultivated with ancient techniques, and quantify the yield dependence on the time after initial planting and on rainfall (as a climate proxy). Our conclusions involve analysis of the labour costs of the agricultural cycle of both an individual and a farmer's family. Finally, we put our results into the context of the exploitation territory and catchment analysis. The simplest economic complex based on cereals, domestic and wild animal products, with fallow cropping, appears to be capable of supporting an isolated, relatively small farming community of 50-300 people (2-10 ha). Our results strongly suggest that dairy products played a significant role in the dietary and labour balance. The smaller settlements are typical of the earliest Trypillia A but remain predominant at the later stages. A larger settlement of several hundred people could function in isolation only with technological innovations, such as manure fertiliser and ard tillage. Very large settlements of a few hundred hectares could function only if supported by satellite farming villages and stable exchange networks. We also discuss, quantify and assess some strategies to mitigate the risks of arable agriculture associated with strong temporal fluctuations in the cereal yield, such as manure fertilisation, increased fraction of cereals in the diet combined with producing grain surplus for emergency storage.
We construct new multivariate copulas on the basis of a generalized infinite partition-of-unity approach. This approach allows - in contrast to finite partition-of-unity copulas - for tail-dependence as well as for asymmetry. A possibility of fitting such copulas to real data from quantitative risk management is also pointed out.
Because of their tractability and their natural interpretations in term of market quantities, Hawkes processes are nowadays widely used in high-frequency finance. However, in practice, the statistical estimation results seem to show that very often, only nearly unstable Hawkes processes are able to fit the data properly. By nearly unstable, we mean that the $L^1$ norm of their kernel is close to unity. We study in this work such processes for which the stability condition is almost violated. Our main result states that after suitable rescaling, they asymptotically behave like integrated Cox-Ingersoll-Ross models. Thus, modeling financial order flows as nearly unstable Hawkes processes may be a good way to reproduce both their high and low frequency stylized facts. We then extend this result to the Hawkes-based price model introduced by Bacry et al. [Quant. Finance 13 (2013) 65-77]. We show that under a similar criticality condition, this process converges to a Heston model. Again, we recover well-known stylized facts of prices, both at the microstructure level and at the macroscopic scale.
Graph data is ubiquitous in academia and industry, from social networks to bioinformatics. The pervasiveness of graphs today has raised the demand for algorithms that can answer various questions: Which products would a user like to purchase given her order list? Which users are buying fake followers to increase their public reputation? Myriads of new graph mining algorithms are proposed every year to answer such questions - each with a distinct problem formulation, computational time, and memory footprint. This lack of unity makes it difficult for a practitioner to compare different algorithms and pick the most suitable one for a specific application. These challenges - even more severe for non-experts - create a gap in which state-of-the-art techniques developed in academic settings fail to be optimally deployed in real-world applications. To bridge this gap, we propose AUTOGM, an automated system for graph mining algorithm development. We first define a unified framework UNIFIEDGM that integrates various message-passing based graph algorithms, ranging from conventional algorithms like PageRank to graph neural networks. Then UNIFIEDGM defines a search space in which five parameters are required to determine a graph algorithm. Under this search space, AUTOGM explicitly optimizes for the optimal parameter set of UNIFIEDGM using Bayesian Optimization. AUTOGM defines a novel budget-aware objective function for the optimization to incorporate a practical issue - finding the best speed-accuracy trade-off under a computation budget - into the graph algorithm generation problem. Experiments on real-world benchmark datasets demonstrate that AUTOGM generates novel graph mining algorithms with the best speed/accuracy trade-off compared to existing models with heuristic parameters.
In the pursuit of artificial general intelligence, our most significant measurement of progress is an agent's ability to achieve goals in a wide range of environments. Existing platforms for constructing such environments are typically constrained by the technologies they are founded on, and are therefore only able to provide a subset of scenarios necessary to evaluate progress. To overcome these shortcomings, we present our use of Unity, a widely recognized and comprehensive game engine, to create more diverse, complex, virtual simulations. We describe the concepts and components developed to simplify the authoring of these environments, intended for use predominantly in the field of reinforcement learning. We also introduce a practical approach to packaging and re-distributing environments in a way that attempts to improve the robustness and reproducibility of experiment results. To illustrate the versatility of our use of Unity compared to other solutions, we highlight environments already created using our approach from published papers. We hope that others can draw inspiration from how we adapted Unity to our needs, and anticipate increasingly varied and complex environments to emerge from our approach as familiarity grows.
In video games, non-player characters (NPCs) are used to enhance the players' experience in a variety of ways, e.g., as enemies, allies, or innocent bystanders. A crucial component of NPCs is navigation, which allows them to move from one point to another on the map. The most popular approach for NPC navigation in the video game industry is to use a navigation mesh (NavMesh), which is a graph representation of the map, with nodes and edges indicating traversable areas. Unfortunately, complex navigation abilities that extend the character's capacity for movement, e.g., grappling hooks, jetpacks, teleportation, or double-jumps, increases the complexity of the NavMesh, making it intractable in many practical scenarios. Game designers are thus constrained to only add abilities that can be handled by a NavMesh if they want to have NPC navigation. As an alternative, we propose to use Deep Reinforcement Learning (Deep RL) to learn how to navigate 3D maps using any navigation ability. We test our approach on complex 3D environments in the Unity game engine that are notably an order of magnitude larger than maps typically used in the Deep RL literature. One of these maps is directly modeled after a Ubisoft AAA game. We find that our approach performs surprisingly well, achieving at least $90\%$ success rate on all tested scenarios. A video of our results is available at https://youtu.be/WFIf9Wwlq8M.
We outline the design and construction of novel robotic arms using machine perception, convolutional neural networks, and symbolic AI for logical control and affordance indexing. We describe our robotic arms built with a humanlike mechanical configuration and aesthetic, with 28 degrees of freedom, touch sensors, and series elastic actuators. The arms were modelled in Roodle and Gazebo with URDF models, as well as Unity, and implement motion control solutions for solving live games of Baccarat (the casino card game), rock paper scissors, handshaking, and drawing. This includes live interactions with people, incorporating both social control of the hands and facial gestures, and physical inverse kinematics (IK) for grasping and manipulation tasks. The resulting framework is an integral part of the Sophia 2020 alpha platform, which is being used with ongoing research in the authors work with team AHAM, an ANA Avatar Xprize effort towards human-AI hybrid telepresence. These results are available to test on the broadly released Hanson Robotics Sophia 2020 robot platform, for users to try and extend.
This paper is devoted to adaptive signal denoising in the context of Graph Signal Processing (GSP) using Spectral Graph Wavelet Transform (SGWT). This issue is addressed \emph{via} a data-driven thresholding process in the transformed domain by optimizing the parameters in the sense of the Mean Square Error (MSE) using the Stein's Unbiased Risk Estimator (SURE). The SGWT considered is built upon a partition of unity making the transform semi-orthogonal so that the optimization can be performed in the transformed domain. However, since the SGWT is over-complete, the divergence term in the SURE needs to be computed in the context of correlated noise. Two thresholding strategies called coordinatewise and block thresholding process are investigated. For each of them, the SURE is derived for a whole family of elementary thresholding functions among which the soft threshold and the James-Stein threshold. This multi-scales analysis shows better performance than the most recent methods from the literature. That is illustrated numerically for a series of signals on different graphs.
The hard problem of consciousness is the question how subjective experience arises from brain matter. I suggest exploring the possibility that quantum physics could be part of the answer. The simultaneous unity and complexity of subjective experience is difficult to understand from a classical physics perspective. In contrast, quantum entanglement is naturally both complex and unified. Moreover the concept of matter is much more subtle in quantum physics compared to classical physics, and quantum computing shows that quantum effects can be useful for information processing. Building on recent progress in quantum technology and neuroscience, I propose a concrete hypothesis as a basis for further investigation, namely that subjective experience is related to the dynamics of a complex entangled state of spins, which is continuously generated and updated through the exchange of photons. Spins in condensed matter systems at room or body temperature can have coherence times in the relevant range for subjective experience (milliseconds to seconds). Photons are well suited for distributing entanglement over macroscopic distances. Neurons emit photons, reactive oxygen species in the mitochondria being likely sources. Opsins, light-sensitive proteins that are plausible single-photon detectors, exist in the brain and are evolutionarily conserved, suggesting that they serve a function. We have recently shown by detailed numerical modeling that axons can plausibly act as photonic waveguides. The oxygen molecule, which has non-zero electronic spin and emits photons, might serve as an interface between photons and spins. The achievable photon rates seem to be more than sufficient to support the bandwidth of subjective experience. The proposed hypothesis raises many interesting experimental and theoretical questions in neuroscience, quantum physics, evolutionary biology, psychophysics, and philosophy.
State-of-the-art quadrotor simulators have a rigid and highly-specialized structure: either are they really fast, physically accurate, or photo-realistic. In this work, we propose a novel quadrotor simulator: Flightmare. Flightmare is composed of two main components: a configurable rendering engine built on Unity and a flexible physics engine for dynamics simulation. Those two components are totally decoupled and can run independently of each other. This makes our simulator extremely fast: rendering achieves speeds of up to 230 Hz, while physics simulation of up to 200,000 Hz on a laptop. In addition, Flightmare comes with several desirable features: (i) a large multi-modal sensor suite, including an interface to extract the 3D point-cloud of the scene; (ii) an API for reinforcement learning which can simulate hundreds of quadrotors in parallel; and (iii) integration with a virtual-reality headset for interaction with the simulated environment. We demonstrate the flexibility of Flightmare by using it for two different robotic tasks: quadrotor control using deep reinforcement learning and collision-free path planning in a complex 3D environment.
We study the problem of solving strongly convex and smooth unconstrained optimization problems using stochastic first-order algorithms. We devise a novel algorithm, referred to as Recursive One-Over-T SGD (ROOT-SGD), based on an easily implementable, recursive averaging of past stochastic gradients. We prove that it simultaneously achieves state-of-the-art performance in both a finite-sample, nonasymptotic sense and an asymptotic sense. On the non-asymptotic side, we prove risk bounds on the last iterate of ROOT-SGD with leading-order terms that match the optimal statistical risk with a unity pre-factor, along with a higher-order term that scales at the sharp rate of $O(n^{-3/2})$ under the Lipschitz condition on the Hessian matrix. On the asymptotic side, we show that when a mild, one-point Hessian continuity condition is imposed, the rescaled last iterate of (multi-epoch) ROOT-SGD converges asymptotically to a Gaussian limit with the Cram\'er-Rao optimal asymptotic covariance, for a broad range of step-size choices.
Sharing, downloading, and reusing software is common-place, some of which is carried out legally with open source software. When it is not legal, it is unclear just how many copyright infringements and trade secret violations have taken place: does an infringement count for the artefact as a whole or perhaps for each file of the program? To answer this question, it must first be established whether a program should be considered as an integral whole, a collection, or a mere set of distinct files, and why. We argue that a program is a functional whole, availing of, and combining, arguments from mereology, granularity, modularity, unity, and function to substantiate the claim. The argumentation and answer contributes to the ontology of software artefacts, may assist industry in litigation cases, and demonstrates that the notion of unifying relation is operationalisable. Indirectly, it provides support for continued modular design of artefacts following established engineering practices.
Convolutional neural networks (CNNs) require high throughput hardware accelerators for real time applications owing to their huge computational cost. Most traditional CNN accelerators rely on single core, linear processing elements (PEs) in conjunction with 1D dataflows for accelerating convolution operations. This limits the maximum achievable ratio of peak throughput per PE count to unity. Most of the past works optimize their dataflows to attain close to a 100% hardware utilization to reach this ratio. In this paper, we introduce a high throughput, multi-threaded, log-based PE core. The designed core provides a 200% increase in peak throughput per PE count while only incurring a 6% increase in area overhead compared to a single, linear multiplier PE core with same output bit precision. We also present a 2D weight broadcast dataflow which exploits the multi-threaded nature of the PE cores to achieve a high hardware utilization per layer for various CNNs. The entire architecture, which we refer to as NeuroMAX, is implemented on Xilinx Zynq 7020 SoC at 200 MHz processing clock. Detailed analysis is performed on throughput, hardware utilization, area and power breakdown, and latency to show performance improvement compared to previous FPGA and ASIC designs.
The Apperception Engine is an unsupervised learning system. Given a sequence of sensory inputs, it constructs a symbolic causal theory that both explains the sensory sequence and also satisfies a set of unity conditions. The unity conditions insist that the constituents of the theory - objects, properties, and laws - must be integrated into a coherent whole. Once a theory has been constructed, it can be applied to predict future sensor readings, retrodict earlier readings, or impute missing readings. In this paper, we evaluate the Apperception Engine in a diverse variety of domains, including cellular automata, rhythms and simple nursery tunes, multi-modal binding problems, occlusion tasks, and sequence induction intelligence tests. In each domain, we test our engine's ability to predict future sensor values, retrodict earlier sensor values, and impute missing sensory data. The engine performs well in all these domains, significantly outperforming neural net baselines and state of the art inductive logic programming systems. These results are significant because neural nets typically struggle to solve the binding problem (where information from different modalities must somehow be combined together into different aspects of one unified object) and fail to solve occlusion tasks (in which objects are sometimes visible and sometimes obscured from view). We note in particular that in the sequence induction intelligence tests, our system achieved human-level performance. This is notable because our system is not a bespoke system designed specifically to solve intelligence tests, but a general-purpose system that was designed to make sense of any sensory sequence.
Data simulation engines like Unity are becoming an increasingly important data source that allows us to acquire ground truth labels conveniently. Moreover, we can flexibly edit the content of an image in the engine, such as objects (position, orientation) and environments (illumination, occlusion). When using simulated data as training sets, its editable content can be leveraged to mimic the distribution of real-world data, and thus reduce the content difference between the synthetic and real domains. This paper explores content adaptation in the context of semantic segmentation, where the complex street scenes are fully synthesized using 19 classes of virtual objects from a first person driver perspective and controlled by 23 attributes. To optimize the attribute values and obtain a training set of similar content to real-world data, we propose a scalable discretization-and-relaxation (SDR) approach. Under a reinforcement learning framework, we formulate attribute optimization as a random-to-optimized mapping problem using a neural network. Our method has three characteristics. 1) Instead of editing attributes of individual objects, we focus on global attributes that have large influence on the scene structure, such as object density and illumination. 2) Attributes are quantized to discrete values, so as to reduce search space and training complexity. 3) Correlated attributes are jointly optimized in a group, so as to avoid meaningless scene structures and find better convergence points. Experiment shows our system can generate reasonable and useful scenes, from which we obtain promising real-world segmentation accuracy compared with existing synthetic training sets.