pwc-archive/papers-with-abstracts huggingface dataset:
On Complexity Bounds for the Maximal Admissible Set of Linear Time-Invariant Systems
Authors: Hamid R. Ossareh, Ilya Kolmanovsky
Date: 2023-02-04 00:00:00

Given a dynamical system with constrained outputs, the maximal admissible set (MAS) is defined as the set of all initial conditions such that the output constraints are satisfied for all time. It has been previously shown that for discrete-time, linear, time-invariant, stable, observable systems with polytopic constraints, this set is a polytope described by a finite number of inequalities (i.e., has finite complexity). However, it is not possible to know the number of inequalities apriori from problem data. To address this gap, this contribution presents two computationally efficient methods to obtain upper bounds on the complexity of the MAS. The first method is algebraic and is based on matrix power series, while the second is geometric and is based on Lyapunov analysis. The two methods are rigorously introduced, a detailed numerical comparison between the two is provided, and an extension to systems with constant inputs is presented. Knowledge of such upper bounds can speed up the computation of MAS, and can be beneficial for defining the memory and computational requirements for storing and processing the MAS, as well as the control algorithms that leverage the MAS.
Perimeter Defense using a Turret with Finite Range and Service Times
Authors: Shivam Bajaj, Shaunak D. Bopardikar, Alexander Von Moll, Eric Torng, David W. Casbeer
Date: 2023-02-04 00:00:00

We consider a perimeter defense problem in a planar conical environment comprising a single turret that has a finite range and non-zero service time. The turret seeks to defend a concentric perimeter against $N\geq 2$ intruders. Upon release, each intruder moves radially towards the perimeter with a fixed speed. To capture an intruder, the turret's angle must be aligned with that of the intruder's angle and must spend a specified service time at that orientation. We address offline and online versions of this optimization problem. Specifically, in the offline version, we establish that in general parameter regimes, this problem is equivalent to solving a Travelling Repairperson Problem with Time Windows (TRP-TW). We then identify specific parameter regimes in which there is a polynomial time algorithm that maximizes the number of intruders captured. In the online version, we present a competitive analysis technique in which we establish a fundamental guarantee on the existence of at best $(N-1)$-competitive algorithms. We also design two online algorithms that are provably $1$ and $2$-competitive in specific parameter regimes.
Towards a modeling, optimization and predictive control framework for fed-batch metabolic cybergenetics
Authors: Sebastián Espinel-Ríos, Bruno Morabito, Johannes Pohlodek, Katja Bettenbrock, Steffen Klamt, Rolf Findeisen
Date: 2023-02-04 00:00:00
Tasks: Cultural Vocal Bursts Intensity Prediction, Model Predictive Control

Biotechnology offers many opportunities for the sustainable manufacturing of valuable products. The toolbox to optimize bioprocesses includes \textit{extracellular} process elements such as the bioreactor design and mode of operation, medium formulation, culture conditions, feeding rates, etc. However, these elements are frequently insufficient for achieving optimal process performance or precise product composition. One can use metabolic and genetic engineering methods for optimization at the intracellular level. Nevertheless, those are often of static nature, failing when applied to dynamic processes or if disturbances occur. Furthermore, many bioprocesses are optimized empirically and implemented with little-to-no feedback control to counteract disturbances. The concept of cybergenetics has opened new possibilities to optimize bioprocesses by enabling online modulation of the gene expression of metabolism-relevant proteins via external inputs (e.g., light intensity in optogenetics). Here, we fuse cybergenetics with model-based optimization and predictive control for optimizing dynamic bioprocesses. To do so, we propose to use dynamic constraint-based models that integrate the dynamics of metabolic reactions, resource allocation, and inducible gene expression. We formulate a model-based optimal control problem to find the optimal process inputs. Furthermore, we propose using model predictive control to address uncertainties via online feedback. We focus on fed-batch processes, where the substrate feeding rate is an additional optimization variable. As a simulation example, we show the optogenetic control of the ATPase enzyme complex for dynamic modulation of enforced ATP wasting to adjust product yield and productivity.
Stability Constrained OPF in Microgrids: A Chance Constrained Optimization Framework with Non-Gaussian Uncertainty
Authors: Jun Wang, Yue Song, David John Hill, Yunhe Hou, Feilong Fan
Date: 2023-02-04 00:00:00
Tasks: Benchmarking

To figure out the stability issues brought by renewable energy sources (RES) with non-Gaussian uncertainties in isolated microgrids, this paper proposes a chance constrained stability constrained optimal power flow (CC-SC-OPF) model. Firstly, we propose a bi-level optimization problem, of which the upper level aims to minimize the expected generation cost without violating the stability chance constraint; the lower level concerns about the stability index given by a semi-definite program (SDP). Secondly, we apply the Gaussian mixture model (GMM) to handle the non-Gaussian RES uncertainties and introduce analytical sensitivity analysis to reformulate chance constraints with respect to stability index and operational variables into linear deter-ministic versions. By incorporating linearized constraints, the bi-level model can be efficiently solved by Benders decomposition-based approach. Thirdly, we design a supplementary corrective countermeasure to compensate the possible control error caused by the linear approximation. Simulation results on the 33-bus microgrid reveal that compared to benchmarking approaches, the proposed model converges 30 times faster with more accurate solutions.
Hybrid path-lifting algorithm and Equivalence of Stability results for MRP-based control strategies
Authors: Luís Martins, Carlos Cardeira, Paulo Oliveira
Date: 2023-02-03 00:00:00

The modified Rodrigues parameters (MRP) consist of two numerically different triplets that, by switching between them, yield a minimal globally non-singular attitude description with advantageous properties. The MRP space results from the Alexandroff compactification of the three-dimensional Euclidean space and is a double cover of $\mathrm{SO(3)}$. By capitalizing on instrumental properties of the covering map, this paper proposes a novel hybrid dynamic path-lifting mechanism to unambiguously and robustly extract the MRP from the attitude space. This hybrid solution allows applying an MRP-based feedback controller to the attitude dynamics in the base space while preserving its asymptotic and exponential stability properties. Furthermore, by profiting from the distinct characteristics of the MRP, the resulting interconnection is impervious to the unwinding phenomenon. The design and validation of an MRP-based controller exemplify the application of the proposed algorithm alongside the novel results for equivalence of stability between spaces. The solution renders the attitude space tracking dynamics robustly globally exponentially stable, demonstrating the potential of this novel methodology.
Quantifying tissue growth, shape and collision via continuum models and Bayesian inference
Authors: Carles Falcó, Daniel J. Cohen, José A. Carrillo, Ruth E. Baker
Date: 2023-02-06 00:00:00
Tasks: Bayesian Inference

Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues, and organs, coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach combining data from recent experiments, mathematical modelling, and Bayesian parameter inference, to describe the self-assembly of multiple epithelial sheets by growth and collision. We use two simple and well-studied continuum models, where cells move either randomly or following population pressure gradients. After suitable calibration, both models prove to be practically identifiable, and can reproduce the main features of single tissue expansions. However, our findings reveal that whenever tissue-tissue interactions become relevant, the random motion assumption can lead to unrealistic behaviour. Under this setting, a model accounting for population pressure from different cell populations is more appropriate and shows a better agreement with experimental measurements. Finally, we discuss how tissue shape and pressure affect multi-tissue collisions. Our work thus provides a systematic approach to quantify and predict complex tissue configurations with applications in the design of tissue composites and more generally in tissue engineering.
Spike-by-Spike Frequency Analysis of Amperometry Traces Provides Statistical Validation of Observations in the Time Domain
Authors: Jeyashree Krishnan, Zeyu Lian, Pieter E. Oomen, Xiulan He, Soodabeh Majdi, Andreas Schuppert, Andrew Ewing
Date: 2023-02-06 00:00:00

Amperometry is a commonly used electrochemical method for studying the process of exocytosis in real-time. Given the high precision of recording that amperometry procedures offer, the volume of data generated can span over several hundreds of megabytes to a few gigabytes and therefore necessitates systematic and reproducible methods for analysis. Though the spike characteristics of amperometry traces in the time domain hold information about the dynamics of exocytosis, these biochemical signals are, more often than not, characterized by time-varying signal properties. Such signals with time-variant properties may occur at different frequencies and therefore analyzing them in the frequency domain may provide statistical validation for observations already established in the time domain. This necessitates the use of time-variant, frequency-selective signal processing methods as well, which can adeptly quantify the dominant or mean frequencies in the signal. The Fast Fourier Transform (FFT) is a well-established computational tool that is commonly used to find the frequency components of a signal buried in noise. In this work, we outline a method for spike-based frequency analysis of amperometry traces using FFT that also provides statistical validation of observations on spike characteristics in the time domain. We demonstrate the method by utilizing simulated signals and by subsequently testing it on diverse amperometry datasets generated from different experiments with various chemical stimulations. To our knowledge, this is the first fully automated open-source tool available dedicated to the analysis of spikes extracted from amperometry signals in the frequency domain.
Characterization and Generation of 3D Realistic Geological Particles with Metaball Descriptor based on X-Ray Computed Tomography
Authors: Yifeng Zhao, Xiangbo Gao, Pei Zhang, Liang Lei, S. A. Galindo-Torres, Stan Z. Li
Date: 2023-02-05 00:00:00

The morphology of geological particles is crucial in determining its granular characteristics and assembly responses. In this paper, Metaball-function based solutions are proposed for morphological characterization and generation of three-dimensional realistic particles according to the X-ray Computed Tomography (XRCT) images. For characterization, we develop a geometric-based Metaball-Imaging algorithm. This algorithm can capture the main contour of parental particles with a series of non-overlapping spheres and refine surface-texture details through gradient search. Four types of particles, hundreds of samples, are applied for evaluations. The result shows good matches on key morphological indicators(i.e., volume, surface area, sphericity, circularity, corey-shape factor, nominal diameter and surface-equivalent-sphere diameter), confirming its characterization precision. For generation, we propose the Metaball Variational Autoencoder. Assisted by deep neural networks, this method can generate 3D particles in Metaball form, while retaining coessential morphological features with parental particles. Additionally, this method allows for control over the generated shapes through an arithmetic pattern, enabling the generation of particles with specific shapes. Two sets of XRCT images different in sample number and geometric features are chosen as parental data. On each training set, one thousand particles are generated for validations. The generation fidelity is demonstrated through comparisons of morphologies and shape-feature distributions between generated and parental particles. Examples are also provided to demonstrate controllability on the generated shapes. With Metaball-based simulations frameworks previously proposed by the authors, these methods have the potential to provide valuable insights into the properties and behavior of actual geological particles.
Modeling and Simulation of Financial Returns under Non-Gaussian Distributions
Authors: Federica De Domenico, Giacomo Livan, Guido Montagna, Oreste Nicrosini
Date: 2023-02-06 00:00:00
Tasks: Management

It is well known that the probability distribution of high-frequency financial returns is characterized by a leptokurtic, heavy-tailed shape. This behavior undermines the typical assumption of Gaussian log-returns behind the standard approach to risk management and option pricing. Yet, there is no consensus on what class of probability distributions should be adopted to describe financial returns and different models used in the literature have demonstrated, to varying extent, an ability to reproduce empirically observed stylized facts. In order to provide some clarity, in this paper we perform a thorough study of the most popular models of return distributions as obtained in the empirical analyses of high-frequency financial data. We compare the statistical properties and simulate the dynamics of non-Gaussian financial fluctuations by means of Monte Carlo sampling from the different models in terms of realistic tail exponents. Our findings show a noticeable consistency between the considered return distributions in the modeling of the scaling properties of large price changes. We also discuss the convergence rate to the asymptotic distributions of the non-Gaussian stochastic processes and we study, as a first example of possible applications, the impact of our results on option pricing in comparison with the standard Black and Scholes approach.
Penalized Quasi-likelihood Estimation and Model Selection in Time Series Models with Parameters on the Boundary
Authors: Heino Bohn Nielsen, Anders Rahbek
Date: 2023-02-06 00:00:00
Tasks: Model Selection, Time Series, Time Series Analysis

We extend the theory from Fan and Li (2001) on penalized likelihood-based estimation and model-selection to statistical and econometric models which allow for non-negativity constraints on some or all of the parameters, as well as time-series dependence. It differs from classic non-penalized likelihood estimation, where limiting distributions of likelihood-based estimators and test-statistics are non-standard, and depend on the unknown number of parameters on the boundary of the parameter space. Specifically, we establish that the joint model selection and estimation, results in standard asymptotic Gaussian distributed estimators. The results are applied to the rich class of autoregressive conditional heteroskedastic (ARCH) models for the modelling of time-varying volatility. We find from simulations that the penalized estimation and model-selection works surprisingly well even for a large number of parameters. A simple empirical illustration for stock-market returns data confirms the ability of the penalized estimation to select ARCH models which fit nicely the autocorrelation function, as well as confirms the stylized fact of long-memory in financial time series data.
Out of Sample Predictability in Predictive Regressions with Many Predictor Candidates
Authors: Jesus Gonzalo, Jean-Yves Pitarakis
Date: 2023-02-06 00:00:00

This paper is concerned with detecting the presence of out of sample predictability in linear predictive regressions with a potentially large set of candidate predictors. We propose a procedure based on out of sample MSE comparisons that is implemented in a pairwise manner using one predictor at a time and resulting in an aggregate test statistic that is standard normally distributed under the global null hypothesis of no linear predictability. Predictors can be highly persistent, purely stationary or a combination of both. Upon rejection of the null hypothesis we subsequently introduce a predictor screening procedure designed to identify the most active predictors. An empirical application to key predictors of US economic activity illustrates the usefulness of our methods and highlights the important forward looking role played by the series of manufacturing new orders.
Testing Quantile Forecast Optimality
Authors: Jack Fosten, Daniel Gutknecht, Marc-Oliver Pohle
Date: 2023-02-06 00:00:00

Quantile forecasts made across multiple horizons have become an important output of many financial institutions, central banks and international organisations. This paper proposes misspecification tests for such quantile forecasts that assess optimality over a set of multiple forecast horizons and/or quantiles. The tests build on multiple Mincer-Zarnowitz quantile regressions cast in a moment equality framework. Our main test is for the null hypothesis of autocalibration, a concept which assesses optimality with respect to the information contained in the forecasts themselves. We provide an extension that allows to test for optimality with respect to larger information sets and a multivariate extension. Importantly, our tests do not just inform about general violations of optimality, but may also provide useful insights into specific forms of sub-optimality. A simulation study investigates the finite sample performance of our tests, and two empirical applications to financial returns and U.S. macroeconomic series illustrate that our tests can yield interesting insights into quantile forecast sub-optimality and its causes.
Testing for Structural Change under Nonstationarity
Authors: Christis Katsouris
Date: 2023-02-05 00:00:00
Tasks: regression

This Appendix (dated: July 2021) includes supplementary derivations related to the main limit results of the econometric framework for structural break testing in predictive regression models based on the OLS-Wald and IVX-Wald test statistics, developed by Katsouris C (2021). In particular, we derive the asymptotic distributions of the test statistics when the predictive regression model includes either mildly integrated or persistent regressors. Moreover, we consider the case in which a model intercept is included in the model vis-a-vis the case that the predictive regression model has no model intercept. In a subsequent version of this study we reexamine these particular aspects in more depth with respect to the demeaned versions of the variables of the predictive regression.
NPV, IRR, PI, PP, and DPP: a unified view
Authors: Mikhail V. Sokolov
Date: 2023-02-06 00:00:00
Tasks: valid

This paper introduces a class of investment project's profitability metrics that includes the net present value (NPV) criterion (which labels a project as weakly profitable if its NPV is nonnegative), internal rate of return (IRR), profitability index (PI), payback period (PP), and discounted payback period (DPP) as special cases. We develop an axiomatic characterization of this class, as well as of the mentioned conventional metrics within the class. The proposed approach offers several key contributions. First, it provides a unified interpretation of profitability metrics as indicators of a project's financial stability across various economic scenarios. Second, it reveals that, except for the NPV criterion, a profitability metric is inherently undefined for some projects. In particular, this implies that any extension of IRR to the space of all projects does not meet a set of reasonable conditions. A similar conclusion is valid for the other mentioned conventional metrics. For each of these metrics, we offer a characterization of the pairs of comparable projects and identify the largest set of projects to which the metric can be unequivocally extended. Third, our study identifies conditions under which the application of one metric is superior to others, helping to guide decision-makers in selecting the most appropriate metric for specific investment contexts.
Adaptive local VAR for dynamic economic policy uncertainty spillover
Authors: Niels Gillmann, Ostap Okhrin
Date: 2023-02-06 00:00:00

The availability of data on economic uncertainty sparked a lot of interest in models that can timely quantify episodes of international spillovers of uncertainty. This challenging task involves trading off estimation accuracy for more timely quantification. This paper develops a local vector autoregressive model (VAR) that allows for adaptive estimation of the time-varying multivariate dependency. Under local, we mean that for each point in time, we simultaneously estimate the longest interval on which the model is constant with the model parameters. The simulation study shows that the model can handle one or multiple sudden breaks as well as a smooth break in the data. The empirical application is done using monthly Economic Policy Uncertainty data. The local model highlights that the empirical data primarily consists of long homogeneous episodes, interrupted by a small number of heterogeneous ones, that correspond to crises. Based on this observation, we create a crisis index, which reflects the homogeneity of the sample over time. Furthermore, the local model shows superiority against the rolling window estimation.
Being at the core: firm product specialisation
Authors: Filippo Bontadini, Mercedes Campi, Marco Dueñas
Date: 2023-02-06 00:00:00

We propose a novel measure to investigate firms' product specialisation: product coreness, that captures the centrality of exported products within the firm's export basket. We study product coreness using firm-product level data between 2018 and 2020 for Colombia, Ecuador, and Peru. Three main findings emerge from our analysis. First, the composition of firms' export baskets changes relatively little from one year to the other, and products far from the firm's core competencies, with low coreness, are more likely to be dropped. Second, higher coreness is associated with larger export flows at the firm level. Third, such firm-level patterns also have implications at the aggregate level: products that are, on average, exported with higher coreness have higher export flows at the country level, which holds across all levels of product complexity. Therefore, the paper shows that how closely a product fits within a firm's capabilities is important for economic performance at both the firm and country level. We explore these issues within an econometric framework, finding robust evidence both across our three countries and for each country separately.
A quantification of how much crypto-miners are driving up the wholesale cost of energy in Texas
Authors: Jangho Lee, Lily Wu, Andrew E. Dessler
Date: 2023-02-04 00:00:00

The use of energy by cryptocurrency mining comes not just with an environmental cost but also an economic one through increases in electricity prices for other consumers. Here we investigate the increase in wholesale price on Texas ERCOT grid due to energy consumption from cryptocurrency mining. For every GW of cryptocurrency mining load on the grid, we find that the wholesale price of electricity on the ERCOT grid increases by 2 per Cent. Given that todays cryptocurrency mining load on the ERCOT grid is around 1 GW, it suggests that wholesale prices have already risen this amount. There are 27 GW of mining load waiting to be hooked up to the ERCOT grid. If cryptocurrency mining increases rapidly, the price of energy in Texas could skyrocket.