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The prevailing statistical approach to analyzing persistence diagrams is concerned with filtering out topological noise. In this paper, we adopt a different viewpoint and aim at estimating the actual distribution of a random persistence diagram, which captures both topological signal and noise. To that effect, Chazel and Divol (2019) proved that, under general conditions, the expected value of a random persistence diagram is a measure admitting a Lebesgue density, called the persistence intensity function. In this paper, we are concerned with estimating the persistence intensity function and a novel, normalized version of it -- called the persistence density function. We present a class of kernel-based estimators based on an i.i.d. sample of persistence diagrams and derive estimation rates in the supremum norm. As a direct corollary, we obtain uniform consistency rates for estimating linear representations of persistence diagrams, including Betti numbers and persistence surfaces. Interestingly, the persistence density function delivers stronger statistical guarantees.

Quantum computing promises transformational gains for solving some problems, but little to none for others. For anyone hoping to use quantum computers now or in the future, it is important to know which problems will benefit. In this paper, we introduce a framework for answering this question both intuitively and quantitatively. The underlying structure of the framework is a race between quantum and classical computers, where their relative strengths determine when each wins. While classical computers operate faster, quantum computers can sometimes run more efficient algorithms. Whether the speed advantage or the algorithmic advantage dominates determines whether a problem will benefit from quantum computing or not. Our analysis reveals that many problems, particularly those of small to moderate size that can be important for typical businesses, will not benefit from quantum computing. Conversely, larger problems or those with particularly big algorithmic gains will benefit from near-term quantum computing. Since very large algorithmic gains are rare in practice and theorized to be rare even in principle, our analysis suggests that the benefits from quantum computing will flow either to users of these rare cases, or practitioners processing very large data.

The generative adversarial network (GAN) is an important model developed for high-dimensional distribution learning in recent years. However, there is a pressing need for a comprehensive method to understand its error convergence rate. In this research, we focus on studying the error convergence rate of the GAN model that is based on a class of functions encompassing the discriminator and generator neural networks. These functions are VC type with bounded envelope function under our assumptions, enabling the application of the Talagrand inequality. By employing the Talagrand inequality and Borel-Cantelli lemma, we establish a tight convergence rate for the error of GAN. This method can also be applied on existing error estimations of GAN and yields improved convergence rates. In particular, the error defined with the neural network distance is a special case error in our definition.

Most of the literature on causality considers the structural framework of Pearl and the potential-outcome framework of Neyman and Rubin to be formally equivalent, and therefore interchangeably uses the do-notation and the potential-outcome subscript notation to write counterfactual outcomes. In this paper, we superimpose the two causal frameworks to prove that structural counterfactual outcomes and potential outcomes do not coincide in general -- not even in law. More precisely, we express the law of the potential outcomes in terms of the latent structural causal model under the fundamental assumptions of causal inference. This enables us to precisely identify when counterfactual inference is or is not equivalent between approaches, and to clarify the meaning of each kind of counterfactuals.

The emergence of new wireless technologies, such as the Internet of Things, allows digitalizing new and diverse urban activities. Thus, wireless traffic grows in volume and complexity, making prediction, investment planning, and regulation increasingly difficult. This article characterizes urban wireless traffic evolution, supporting operators to drive mobile network evolution and policymakers to increase national and local competitiveness. We propose a holistic method that widens previous research scope, including new devices and the effect of policy from multiple government levels. We provide an analytical formulation that combines existing complementary methods on traffic evolution research and diverse data sources. Results for a centric area of Helsinki during 2020-2030 indicate that daily volumes increase, albeit a surprisingly large part of the traffic continues to be generated by smartphones. Machine traffic gains importance, driven by surveillance video cameras and connected cars. While camera traffic is sensitive to law enforcement policies and data regulation, car traffic is less affected by transport electrification policy. High-priority traffic remains small, even under encouraging autonomous vehicle policies. We suggest that 5G small cells might be needed around 2025, albeit the utilization of novel radio technology and additional mid-band spectrum could delay this need until 2029. We argue that mobile network operators inevitably need to cooperate in constructing a single, shared small cell network to mitigate the high deployment costs of massively deploying small cells. We also provide guidance to local and national policymakers for IoT-enabled competitive gains via the mitigation of five bottlenecks. For example, local monopolies for mmWave connectivity should be facilitated on space-limited urban furniture or risk an eventual capacity crunch, slowing down digitalization.

Spiking neural network is a kind of neuromorphic computing that is believed to improve the level of intelligence and provide advantages for quantum computing. In this work, we address this issue by designing an optical spiking neural network and find that it can be used to accelerate the speed of computation, especially on combinatorial optimization problems. Here the spiking neural network is constructed by the antisymmetrically coupled degenerate optical parametric oscillator pulses and dissipative pulses. A nonlinear transfer function is chosen to mitigate amplitude inhomogeneities and destabilize the resulting local minima according to the dynamical behavior of spiking neurons. It is numerically shown that the spiking neural network-coherent Ising machines have excellent performance on combinatorial optimization problems, which is expected to offer new applications for neural computing and optical computing.

Neural oscillations are considered to be brain-specific signatures of information processing and communication in the brain. They also reflect pathological brain activity in neurological disorders, thus offering a basis for diagnoses and forecasting. Epilepsy is one of the most common neurological disorders, characterized by abnormal synchronization and desynchronization of the oscillations in the brain. About one third of epilepsy cases are pharmacoresistant, and as such emphasize the need for novel therapy approaches, where brain stimulation appears to be a promising therapeutic option. The development of brain stimulation paradigms, however, is often based on generalized assumptions about brain dynamics, although it is known that significant differences occur between patients and brain states. We developed a framework to extract individualized predictive models of epileptic network dynamics directly from EEG data. The models are based on the dominant coherent oscillations and their dynamical coupling, thus combining an established interpretation of dynamics through neural oscillations, with accurate patient-specific features. We show that it is possible to build a direct correspondence between the models of brain-network dynamics under periodic driving, and the mechanism of neural entrainment via periodic stimulation. When our framework is applied to EEG recordings of patients in status epilepticus (a brain state of perpetual seizure activity), it yields a model-driven predictive analysis of the therapeutic performance of periodic brain stimulation. This suggests that periodic brain stimulation can drive pathological states of epileptic network dynamics towards a healthy functional brain state.

We observe a large variety of robots in terms of their bodies, sensors, and actuators. Given the commonalities in the skill sets, teaching each skill to each different robot independently is inefficient and not scalable when the large variety in the robotic landscape is considered. If we can learn the correspondences between the sensorimotor spaces of different robots, we can expect a skill that is learned in one robot can be more directly and easily transferred to the other robots. In this paper, we propose a method to learn correspondences between robots that have significant differences in their morphologies: a fixed-based manipulator robot with joint control and a differential drive mobile robot. For this, both robots are first given demonstrations that achieve the same tasks. A common latent representation is formed while learning the corresponding policies. After this initial learning stage, the observation of a new task execution by one robot becomes sufficient to generate a latent space representation pertaining to the other robot to achieve the same task. We verified our system in a set of experiments where the correspondence between two simulated robots is learned (1) when the robots need to follow the same paths to achieve the same task, (2) when the robots need to follow different trajectories to achieve the same task, and (3) when complexities of the required sensorimotor trajectories are different for the robots considered. We also provide a proof-of-the-concept realization of correspondence learning between a real manipulator robot and a simulated mobile robot.

Models of complex technological systems inherently contain interactions and dependencies among their input variables that affect their joint influence on the output. Such models are often computationally expensive and few sensitivity analysis methods can effectively process such complexities. Moreover, the sensitivity analysis field as a whole pays limited attention to the nature of interaction effects, whose understanding can prove to be critical for the design of safe and reliable systems. In this paper, we introduce and extensively test a simple binning approach for computing sensitivity indices and demonstrate how complementing it with the smart visualization method, simulation decomposition (SimDec), can permit important insights into the behavior of complex engineering models. The simple binning approach computes first-, second-order effects, and a combined sensitivity index, and is considerably more computationally efficient than Sobol' indices. The totality of the sensitivity analysis framework provides an efficient and intuitive way to analyze the behavior of complex systems containing interactions and dependencies.

Knowledge graphs (KGs) of real-world facts about entities and their relationships are useful resources for a variety of natural language processing tasks. However, because knowledge graphs are typically incomplete, it is useful to perform knowledge graph completion or link prediction, i.e. predict whether a relationship not in the knowledge graph is likely to be true. This paper serves as a comprehensive survey of embedding models of entities and relationships for knowledge graph completion, summarizing up-to-date experimental results on standard benchmark datasets and pointing out potential future research directions.