pwc-archive/papers-with-abstracts huggingface dataset:
A Safe Control Architecture Based on Robust Model Predictive Control for Autonomous Driving
Authors: Maryam Nezami, Ngoc Thinh Nguyen, Georg Männel, Hossam Seddik Abbas, Georg Schildbach
Date: 2022-06-20 00:00:00
Tasks: Autonomous Driving, Decision Making, Model Predictive Control

This paper proposes a Robust Safe Control Architecture (RSCA) for safe-decision making. The system to be controlled is a vehicle in the presence of bounded disturbances. The RSCA consists of two parts: a Supervisor MPC and a Controller MPC. Both the Supervisor and the Controller are tube MPCs (TMPCs). The Supervisor MPC provides a safety certificate for an operating controller and a backup control input in every step. After an unsafe action by the operating controller is predicted, the Controller MPC takes over the system. In this paper, a method for the computation of a terminal set is proposed, which is robust against changes in road curvature and forces the vehicle to reach a safe reference. Moreover, two important proofs are provided in this paper. First, it is shown that the backup control input is safe to be applied to the system to lead the vehicle to a safe state. Next, the recursive feasibility of the RSCA is proven. By simulating some obstacle avoidance scenarios, the effectiveness of the proposed RSCA is confirmed.
Analysis of Electric Vehicle Charging Station Usage and Profitability in Germany based on Empirical Data
Authors: Christopher Hecht, Jan Figgener, Dirk Uwe Sauer
Date: 2022-06-20 00:00:00

Electric vehicles are booming and with them the required public charging stations. Knowing how charging stations are used is crucial for operators of the charging stations themselves, navigation systems, electricity grids, and many more. Given that there are now 2.5 as many vehicles per charging station compared to 2017, the system needs to allocate charging points intelligently and efficiently. This paper presents representative data on energy consumption, arrival times, occupation, and profitability of charging stations in Germany by combining usage data of 27,800 installations. Charging happens mainly during the day and on weekdays for AC charging stations while DC fast-charging stations are more popular on the weekend. Fast-chargers service approximately 3 times as many vehicles per connection point while also being substantially more profitable due to higher achieved margins. For AC chargers, up to 20 kWh of energy are charged in an average charge event while DC fast-chargers supply approximately 40 kWh.
Data-Driven Synthesis of Symbolic Abstractions with Guaranteed Confidence
Authors: Abolfazl Lavaei, Emilio Frazzoli
Date: 2022-06-19 00:00:00

In this work, we propose a data-driven approach for the construction of finite abstractions (a.k.a., symbolic models) for discrete-time deterministic control systems with unknown dynamics. We leverage notions of so-called alternating bisimulation functions (ABF), as a relation between each unknown system and its symbolic model, to quantify the mismatch between state behaviors of two systems. Accordingly, one can employ our proposed results to perform formal verification and synthesis over symbolic models and then carry the results back over unknown original systems. In our data-driven setting, we first cast the required conditions for constructing ABF as a robust optimization program (ROP). Solving the provided ROP is not tractable due to the existence of unknown models in the constraints of ROP. To tackle this difficulty, we collect finite numbers of data from trajectories of unknown systems and propose a scenario optimization program (SOP) corresponding to the original ROP. By establishing a probabilistic relation between optimal values of SOP and ROP, we formally construct ABF between unknown systems and their symbolic models based on the number of data and a required confidence level. We verify the effectiveness of our data-driven results over two physical case studies with unknown models including (i) a DC motor and (ii) a nonlinear jet engine compressor. We construct symbolic models from data as appropriate substitutes of original systems and synthesize policies maintaining states of unknown systems in a safe set within infinite time horizons with some guaranteed confidence levels.
A Note on Comparator-Overdrive-Delay Conditioning for Current-Mode Control
Authors: Xiaofan Cui, Al-Thaddeus Avestruz
Date: 2022-06-19 00:00:00

Comparator-overdrive-delay conditioning is a new control conditioning approach for high-frequency current-mode control. No existing literature rigorously studies the effect of the comparator overdrive delay on the current-mode control. The results in this paper provide insights into the mechanism of comparator-overdrive-delay conditioning.
Multi-period Optimal Control for Mobile Agents Considering State Unpredictability
Authors: Chendi Qu, Jianping He, Jialun Li
Date: 2022-06-19 00:00:00
Tasks: Stochastic Optimization

The optimal control for mobile agents is an important and challenging issue. Recent work shows that using randomized mechanism in agents' control can make the state unpredictable, and thus improve the security of agents. However, the unpredictable design is only considered in single period, which can lead to intolerable control performance in long time horizon. This paper aims at the trade-off between the control performance and state unpredictability of mobile agents in long time horizon. Utilizing random perturbations consistent with uniform distributions to maximize the attackers' prediction errors of future states, we formulate the problem as a multi-period convex stochastic optimization problem and solve it through dynamic programming. Specifically, we design the optimal control strategy considering both unconstrained and input constrained systems. The analytical iterative expressions of the control are further provided. Simulation illustrates that the algorithm increases the prediction errors under Kalman filter while achieving the control performance requirements successfully.
Automatic Self-Adaptive Local Voltage Control Under Limited Reactive Power
Authors: Rui Cheng, Naihao Shi, Salish Maharjan, Zhaoyu Wang
Date: 2022-06-18 00:00:00

The increasing proliferation of distributed energy resources has posed new challenges to Volt/VAr control problems in distribution networks. To this end, this paper proposes an automatic self-adaptive local voltage control (ASALVC) by locally controlling VAr outputs of distributed energy resources. In this ASALVC strategy, each bus agent can locally and dynamically adjust its voltage droop function in accordance with time-varying system changes. The voltage droop function is associated with the bus-specific time-varying slope and intercept, which can be locally updated, merely based on local voltage measurements, without requiring communication. Stability, convergence, and optimality properties of this local voltage control are analytically established. In addition, the online implementation of ASALVC is further proposed to address the real-time system changes by adjusting VAr outputs of DERs online. Numerical test cases are performed to validate and demonstrate the effectiveness and superiority of ASALVC.
Enabling Undergrounding of Long-Distance Transmission Lines with Low Frequency AC Technology
Authors: David K. Sehloff, Line A. Roald
Date: 2022-06-17 00:00:00

With increasing prevalence of severe natural hazards and the ignition of wildfires by power lines, many power system planners are considering converting overhead lines to underground cables to mitigate risks related to these events. Systems with a large proportion of underground cables can bring challenges due to the capacitance and losses of the cables, factors which may limit the potential for hardening in critical areas. Low frequency AC (LFAC) transmission solves these problems, as lowering the frequency decreases both the effects of capacitance and the losses. This paper presents a tractable frequency-dependent model for underground cables and incorporates it into the open source optimal power flow tool VariableFrequencyOPF.jl. The model and implementation are used to demonstrate the benefits of LFAC in a case study involving two multi-terminal cable upgrades with LFAC, including a comparison with HVDC. The results demonstrate the value of LFAC systems for both power flow control and reduction of losses.
Orthogonal Rational Approximation of Transfer Functions for High-Frequency Circuits
Authors: Andrew Ma, Arif Ege Engin
Date: 2022-06-17 00:00:00
Tasks: Vocal Bursts Intensity Prediction

Rational function approximations find applications in many areas including macro-modeling of high-frequency circuits, model order reduction for controller design, interpolation and extrapolation of system responses, surrogate models for high-energy physics, and approximation of elementary mathematical functions. The unknown denominator polynomial of the model results in a non-linear problem, which can be replaced with successive solutions of linearized problems following the Sanathanan-Koerner (SK) iteration. An orthogonal basis can be obtained based on Arnoldi resulting in a stabilized SK iteration. We present an extension of the stabilized SK, called Orthogonal Rational Approximation (ORA), which ensures real polynomial coefficients and stable poles for realizability of electrical networks. We also introduce an efficient implementation of ORA for multi-port networks based on a block QR decomposition.
A theory of learning with constrained weight-distribution
Authors: Weishun Zhong, Ben Sorscher, Daniel D Lee, Haim Sompolinsky
Date: 2022-06-14 00:00:00

A central question in computational neuroscience is how structure determines function in neural networks. The emerging high-quality large-scale connectomic datasets raise the question of what general functional principles can be gleaned from structural information such as the distribution of excitatory/inhibitory synapse types and the distribution of synaptic weights. Motivated by this question, we developed a statistical mechanical theory of learning in neural networks that incorporates structural information as constraints. We derived an analytical solution for the memory capacity of the perceptron, a basic feedforward model of supervised learning, with constraint on the distribution of its weights. Our theory predicts that the reduction in capacity due to the constrained weight-distribution is related to the Wasserstein distance between the imposed distribution and that of the standard normal distribution. To test the theoretical predictions, we use optimal transport theory and information geometry to develop an SGD-based algorithm to find weights that simultaneously learn the input-output task and satisfy the distribution constraint. We show that training in our algorithm can be interpreted as geodesic flows in the Wasserstein space of probability distributions. We further developed a statistical mechanical theory for teacher-student perceptron rule learning and ask for the best way for the student to incorporate prior knowledge of the rule. Our theory shows that it is beneficial for the learner to adopt different prior weight distributions during learning, and shows that distribution-constrained learning outperforms unconstrained and sign-constrained learning. Our theory and algorithm provide novel strategies for incorporating prior knowledge about weights into learning, and reveal a powerful connection between structure and function in neural networks.
Multivariate Quadratic Hawkes Processes -- Part I: Theoretical Analysis
Authors: Cécilia Aubrun, Michael Benzaquen, Jean-Philippe Bouchaud
Date: 2022-06-21 00:00:00

Quadratic Hawkes (QHawkes) processes have proved effective at reproducing the statistics of price changes, capturing many of the stylised facts of financial markets. Motivated by the recently reported strong occurrence of endogenous co-jumps (simultaneous price jumps of several assets) we extend QHawkes to a multivariate framework (MQHawkes), that is considering several financial assets and their interactions. Assuming that quadratic kernels write as the sum of a time-diagonal component and a rank one (trend) contribution, we investigate endogeneity ratios and the resulting stationarity conditions. We then derive the so-called Yule-Walker equations relating covariances and feedback kernels, which are essential to calibrate the MQHawkes process on empirical data. Finally, we investigate the volatility distribution of the process and find that, as in the univariate case, it exhibits power-law behavior, with an exponent that can be exactly computed in some limiting cases.
A new generation of reduction methods for networks of neurons with complex dynamic phenotypes
Authors: Inês C. Guerreiro, Matteo di Volo, Boris Gutkin
Date: 2022-06-21 00:00:00

Collective dynamics of spiking networks of neurons has been of central interest to both computation neuroscience and network science. Over the past years a new generation of neural population models based on exact reductions (ER) of spiking networks have been developed. However, most of these efforts have been limited to networks of neurons with simple dynamics (e.g. the quadratic integrate and fire models). Here, we present an extension of ER to conductance-based networks of two-dimensional Izhikevich neuron models. We employ an adiabatic approximation, which allows us to analytically solve the continuity equation describing the evolution of the state of the neural population and thus to reduce model dimensionality. We validate our results by showing that the reduced mean-field description we derived can qualitatively and quantitatively describe the macroscopic behaviour of populations of two-dimensional QIF neurons with different electrophysiological profiles (regular firing, adapting, resonator and type III excitable). Most notably, we apply this technique to develop an ER for networks of neurons with bursting dynamics.
Bayesian neural networks for the probabilistic forecasting of wind direction and speed using ocean data
Authors: Mariana C A Clare, Matthew D Piggott
Date: 2022-06-14 00:00:00

Neural networks are increasingly being used in a variety of settings to predict wind direction and speed, two of the most important factors for estimating the potential power output of a wind farm. However, these predictions are arguably of limited value because classical neural networks lack the ability to express uncertainty. Here we instead consider the use of Bayesian Neural Networks (BNNs), for which the weights, biases and outputs are distributions rather than deterministic point values. This allows for the evaluation of both epistemic and aleatoric uncertainty and leads to well-calibrated uncertainty predictions of both wind speed and power. Here we consider the application of BNNs to the problem of offshore wind resource prediction for renewable energy applications. For our dataset, we use observations recorded at the FINO1 research platform in the North Sea and our predictors are ocean data such as water temperature and current direction. The probabilistic forecast predicted by the BNN adds considerable value to the results and, in particular, informs the user of the network's ability to make predictions of out-of-sample datapoints. We use this property of BNNs to conclude that the accuracy and uncertainty of the wind speed and direction predictions made by our network are unaffected by the construction of the nearby Alpha Ventus wind farm. Hence, at this site, networks trained on pre-farm ocean data can be used to accurately predict wind field information from ocean data after the wind farm has been constructed.
Open Problems in Mathematical Biology
Authors: Sean T. Vittadello, Michael P. H. Stumpf
Date: 2022-06-20 00:00:00

Biology is data-rich, and it is equally rich in concepts and hypotheses. Part of trying to understand biological processes and systems is therefore to confront our ideas and hypotheses with data using statistical methods to determine the extent to which our hypotheses agree with reality. But doing so in a systematic way is becoming increasingly challenging as our hypotheses become more detailed, and our data becomes more complex. Mathematical methods are therefore gaining in importance across the life- and biomedical sciences. Mathematical models allow us to test our understanding, make testable predictions about future behaviour, and gain insights into how we can control the behaviour of biological systems. It has been argued that mathematical methods can be of great benefit to biologists to make sense of data. But mathematics and mathematicians are set to benefit equally from considering the often bewildering complexity inherent to living systems. Here we present a small selection of open problems and challenges in mathematical biology. We have chosen these open problems because they are of both biological and mathematical interest.
Statistical inference of lead-lag at various timescales between asynchronous time series from p-values of transfer entropy
Authors: Christian Bongiorno, Damien Challet
Date: 2022-06-21 00:00:00
Tasks: Time Series, Time Series Analysis

Symbolic transfer entropy is a powerful non-parametric tool to detect lead-lag between time series. Because a closed expression of the distribution of Transfer Entropy is not known for finite-size samples, statistical testing is often performed with bootstraps whose slowness prevents the inference of large lead-lag networks between long time series. On the other hand, the asymptotic distribution of Transfer Entropy between two time series is known. In this work, we derive the asymptotic distribution of the test for one time series having a larger Transfer Entropy than another one on a target time series. We then measure the convergence speed of both tests in the small sample size limits via benchmarks. We then introduce Transfer Entropy between time-shifted time series, which allows to measure the timescale at which information transfer is maximal and vanishes. We finally apply these methods to tick-by-tick price changes of several hundreds of stocks, yielding non-trivial statistically validated networks.
Photoelectric Factor Prediction Using Automated Learning and Uncertainty Quantification
Authors: Khalid L. Alsamadony, Ahmed Farid Ibrahim, Salaheldin Elkatatny, Abdulazeez Abdulraheem
Date: 2022-06-17 00:00:00
Tasks: GPR, Uncertainty Quantification

The photoelectric factor (PEF) is an important well logging tool to distinguish between different types of reservoir rocks because PEF measurement is sensitive to elements with high atomic number. Furthermore, the ratio of rock minerals could be determined by combining PEF log with other well logs. However, PEF log could be missing in some cases such as in old well logs and wells drilled with barite-based mud. Therefore, developing models for estimating missing PEF log is essential in those circumstances. In this work, we developed various machine learning models to predict PEF values using the following well logs as inputs: bulk density (RHOB), neutron porosity (NPHI), gamma ray (GR), compressional and shear velocity. The predictions of PEF values using adaptive-network-fuzzy inference system (ANFIS) and artificial neural network (ANN) models have errors of about 16% and 14% average absolute percentage error (AAPE) in the testing dataset, respectively. Thus, a different approach was proposed that is based on the concept of automated machine learning. It works by automatically searching for the optimal model type and optimizes its hyperparameters for the dataset under investigation. This approach selected a Gaussian process regression (GPR) model for accurate estimation of PEF values. The developed GPR model decreases the AAPE of the predicted PEF values in the testing dataset to about 10% AAPE. This error could be further decreased to about 2% by modeling the potential noise in the measurements using the GPR model.
New possibilities in identification of binary choice models with fixed effects
Authors: Yinchu Zhu
Date: 2022-06-21 00:00:00

We study the identification of binary choice models with fixed effects. We propose a condition called sign saturation and show that this condition is sufficient for identifying the model. In particular, this condition can guarantee identification even when all the regressors are bounded, including multiple discrete regressors. We also establish that without this condition, the model is not identified unless the error distribution belongs to a special class. Moreover, we show that sign saturation is also essential for identifying the sign of treatment effects. Finally, we introduce a measure for sign saturation and develop tools for its estimation and inference.
Policy Learning under Endogeneity Using Instrumental Variables
Authors: Yan Liu
Date: 2022-06-20 00:00:00

This paper studies the identification and estimation of individualized intervention policies in observational data settings characterized by endogenous treatment selection and the availability of instrumental variables. We introduce encouragement rules that manipulate an instrument. Incorporating the marginal treatment effects (MTE) as policy invariant structural parameters, we establish the identification of the social welfare criterion for the optimal encouragement rule. Focusing on binary encouragement rules, we propose to estimate the optimal policy via the Empirical Welfare Maximization (EWM) method and derive convergence rates of the regret (welfare loss). We consider extensions to accommodate multiple instruments and budget constraints. Using data from the Indonesian Family Life Survey, we apply the EWM encouragement rule to advise on the optimal tuition subsidy assignment. Our framework offers interpretability regarding why a certain subpopulation is targeted.
Unbiased estimation of the OLS covariance matrix when the errors are clustered
Authors: Tom Boot, Gianmaria Niccodemi, Tom Wansbeek
Date: 2022-06-20 00:00:00

When data are clustered, common practice has become to do OLS and use an estimator of the covariance matrix of the OLS estimator that comes close to unbiasedness. In this paper we derive an estimator that is unbiased when the random-effects model holds. We do the same for two more general structures. We study the usefulness of these estimators against others by simulation, the size of the $t$-test being the criterion. Our findings suggest that the choice of estimator hardly matters when the regressor has the same distribution over the clusters. But when the regressor is a cluster-specific treatment variable, the choice does matter and the unbiased estimator we propose for the random-effects model shows excellent performance, even when the clusters are highly unbalanced.
Optimal data-driven hiring with equity for underrepresented groups
Authors: Yinchu Zhu, Ilya O. Ryzhov
Date: 2022-06-19 00:00:00
Tasks: Attribute

We present a data-driven prescriptive framework for fair decisions, motivated by hiring. An employer evaluates a set of applicants based on their observable attributes. The goal is to hire the best candidates while avoiding bias with regard to a certain protected attribute. Simply ignoring the protected attribute will not eliminate bias due to correlations in the data. We present a hiring policy that depends on the protected attribute functionally, but not statistically, and we prove that, among all possible fair policies, ours is optimal with respect to the firm's objective. We test our approach on both synthetic and real data, and find that it shows great practical potential to improve equity for underrepresented and historically marginalized groups.