The chemical master equation (CME), which describes the discrete and stochastic molecule number dynamics associated with biological processes like transcription, is difficult to solve analytically. It is particularly hard to solve for models involving bursting/gene switching, a biological feature that tends to produce heavy-tailed single cell RNA counts distributions. In this paper, we present a novel method for computing exact and analytic solutions to the CME in such cases, and use these results to explore approximate solutions valid in different parameter regimes, and to compute observables of interest. Our method leverages tools inspired by quantum mechanics, including ladder operators and Feynman-like diagrams, and establishes close formal parallels between the dynamics of bursty transcription, and the dynamics of bosons interacting with a single fermion. We focus on two problems: (i) the chemical birth-death process coupled to a switching gene/the telegraph model, and (ii) a model of transcription and multistep splicing involving a switching gene and an arbitrary number of downstream splicing steps. We work out many special cases, and exhaustively explore the special functionology associated with these problems. This is Part I in a two-part series of papers; in Part II, we explore an alternative solution approach that is more useful for numerically solving these problems, and apply it to parameter inference on simulated RNA counts data.
From nutrient uptake, to chemoreception, to synaptic transmission, many systems in cell biology depend on molecules diffusing and binding to membrane receptors. Mathematical analysis of such systems often neglects the fact that receptors process molecules at finite kinetic rates. A key example is the celebrated formula of Berg and Purcell for the rate that cell surface receptors capture extracellular molecules. Indeed, this influential result is only valid if receptors transport molecules through the cell wall at a rate much faster than molecules arrive at receptors. From a mathematical perspective, ignoring receptor kinetics is convenient because it makes the diffusing molecules independent. In contrast, including receptor kinetics introduces correlations between the diffusing molecules since, for example, bound receptors may be temporarily blocked from binding additional molecules. In this work, we present a modeling framework for coupling bulk diffusion to surface receptors with finite kinetic rates. The framework uses boundary homogenization to couple the diffusion equation to nonlinear ordinary differential equations on the boundary. We use this framework to derive an explicit formula for the cellular uptake rate and show that the analysis of Berg and Purcell significantly overestimates uptake in some typical biophysical scenarios. We confirm our analysis by numerical simulations of a many particle stochastic system.
Conventional breast cancer imaging techniques are nowadays based on the use of ionising radiations or ultrasound waves for the inspection of breast areas. Nevertheless, these conventional techniques present some drawbacks related to patient safety, processing time and resolution issues. In this framework, microwave imaging can represent a valid alternative or a complementary technique compared to other conventional medical imaging modalities since it is safe (using non-ionising radiations), relatively cheap and more comfortable from patient point of view. Unfortunately, it is slow and computationally expensive, which strongly limit its use in clinical scenarios. In this paper, an artificial neural network for effective and almost real-time breast imaging is proposed. First, a realistic breast-like phantom generator was developed for training the network. Subsequently, numerical analyses have been conducted for the optimisation and the performance evaluation of the approach. The results seem very promising in terms of recovery performance as well as for the computation burden.
In this note, I explore the implications of informational robustness under the assumption of common belief in rationality. That is, predictions for incomplete-information games which are valid across all possible information structures. First, I address this question from a global perspective and then generalize the analysis to allow for localized informational robustness.
David Gauthier in his article, Maximization constrained: the rationality of cooperation, tries to defend the joint strategy in situations in which no outcome is both equilibrium and optimal. Prisoner Dilemma is the most familiar example of these situations. He first starts with some quotes by Hobbes in Leviathan; Hobbes, in chapter 15 discusses an objection by someone is called Foole, and then will reject his view. In response to Foole, Hobbes presents two strategies (i.e. joint and individual) and two kinds of agents in such problems including Prisoner Dilemma, i.e. straightforward maximizer (SM) and constrained maximizer(CM). Then he considers two arguments respectively for SM and CM, and he will show that why in an ideal and transparent situation, the first argument fails and the second one would be the only valid argument. Likewise, in the following part of his article, he considers more realistic situations with translucency and he concludes that under some conditions, the joint strategy would be still the rational decision.
Unlike other techniques of causality inference, the use of valid instrumental variables can deal with unobserved sources of both variable errors, variable omissions, and sampling bias, and still arrive at consistent estimates of average treatment effects. The only problem is to find the valid instruments. Using the definition of Pearl (2009) of valid instrumental variables, a formal condition for validity can be stated for variables in generalized linear causal models. The condition can be applied in two different ways: As a tool for constructing valid instruments, or as a foundation for testing whether an instrument is valid. When perfectly valid instruments are not found, the squared bias of the IV-estimator induced by an imperfectly valid instrument -- estimated with bootstrapping -- can be added to its empirical variance in a mean-square-error-like reliability measure.
We consider structural vector autoregressions subject to 'narrative restrictions', which are inequality restrictions on functions of the structural shocks in specific periods. These restrictions raise novel problems related to identification and inference, and there is currently no frequentist procedure for conducting inference in these models. We propose a solution that is valid from both Bayesian and frequentist perspectives by: 1) formalizing the identification problem under narrative restrictions; 2) correcting a feature of the existing (single-prior) Bayesian approach that can distort inference; 3) proposing a robust (multiple-prior) Bayesian approach that is useful for assessing and eliminating the posterior sensitivity that arises in these models due to the likelihood having flat regions; and 4) showing that the robust Bayesian approach has asymptotic frequentist validity. We illustrate our methods by estimating the effects of US monetary policy under a variety of narrative restrictions.
This paper develops a first-stage linear regression representation for the instrumental variables (IV) quantile regression (QR) model. The quantile first-stage is analogous to the least squares case, i.e., a linear projection of the endogenous variables on the instruments and other exogenous covariates, with the difference that the QR case is a weighted projection. The weights are given by the conditional density function of the innovation term in the QR structural model, conditional on the endogeneous and exogenous covariates, and the instruments as well, at a given quantile. We also show that the required Jacobian identification conditions for IVQR models are embedded in the quantile first-stage. We then suggest inference procedures to evaluate the adequacy of instruments by evaluating their statistical significance using the first-stage result. The test is developed in an over-identification context, since consistent estimation of the weights for implementation of the first-stage requires at least one valid instrument to be available. Monte Carlo experiments provide numerical evidence that the proposed tests work as expected in terms of empirical size and power in finite samples. An empirical application illustrates that checking for the statistical significance of the instruments at different quantiles is important. The proposed procedures may be specially useful in QR since the instruments may be relevant at some quantiles but not at others.
This paper estimates the effects of non-pharmaceutical interventions - mainly, the lockdown - on the COVID-19 mortality rate for the case of Italy, the first Western country to impose a national shelter-in-place order. We use a new estimator, the Augmented Synthetic Control Method (ASCM), that overcomes some limits of the standard Synthetic Control Method (SCM). The results are twofold. From a methodological point of view, the ASCM outperforms the SCM in that the latter cannot select a valid donor set, assigning all the weights to only one country (Spain) while placing zero weights to all the remaining. From an empirical point of view, we find strong evidence of the effectiveness of non-pharmaceutical interventions in avoiding losses of human lives in Italy: conservative estimates indicate that for each human life actually lost, in the absence of lockdown there would have been on average other 1.15, the policy saved in total 20,400 human lives.
We introduce a nonparametric nonlinear VAR prewhitened long-run variance (LRV) estimator for the construction of standard errors robust to autocorrelation and heteroskedasticity that can be used for hypothesis testing in a variety of contexts including the linear regression model. Existing methods either are theoretically valid only under stationarity and have poor finite-sample properties under nonstationarity (i.e., fixed-b methods), or are theoretically valid under the null hypothesis but lead to tests that are not consistent under nonstationary alternative hypothesis (i.e., both fixed-b and traditional HAC estimators). The proposed estimator accounts explicitly for nonstationarity, unlike previous prewhitened procedures which are known to be unreliable, and leads to tests with accurate null rejection rates and good monotonic power. We also establish MSE bounds for LRV estimation that are sharper than previously established and use them to determine the data-dependent bandwidths.
Limited-information inference on New Keynesian Phillips Curves (NKPCs) and other single-equation macroeconomic relations is characterised by weak and high-dimensional instrumental variables (IVs). Beyond the efficiency concerns previously raised in the literature, I show by simulation that ad-hoc selection procedures can lead to substantial biases in post-selection inference. I propose a Sup Score test that remains valid under dependent data, arbitrarily weak identification, and a number of IVs that increases exponentially with the sample size. Conducting inference on a standard NKPC with 359 IVs and 179 observations, I find substantially wider confidence sets than those commonly found.
Measuring the prevalence of active SARS-CoV-2 infections in the general population is difficult because tests are conducted on a small and non-random segment of the population. However, people admitted to the hospital for non-COVID reasons are tested at very high rates, even though they do not appear to be at elevated risk of infection. This sub-population may provide valuable evidence on prevalence in the general population. We estimate upper and lower bounds on the prevalence of the virus in the general population and the population of non-COVID hospital patients under weak assumptions on who gets tested, using Indiana data on hospital inpatient records linked to SARS-CoV-2 virological tests. The non-COVID hospital population is tested fifty times as often as the general population, yielding much tighter bounds on prevalence. We provide and test conditions under which this non-COVID hospitalization bound is valid for the general population. The combination of clinical testing data and hospital records may contain much more information about the state of the epidemic than has been previously appreciated. The bounds we calculate for Indiana could be constructed at relatively low cost in many other states.
In autonomous applications for mobility and transport, a high-rate and highly accurate vehicle-state estimation is achieved by fusing measurements of global navigation satellite systems (GNSS) and inertial sensors. The state estimation and its protection-level generation often suffer from satellite-signal disturbances in urban environments and subsequent poor parametrization of the satellite observables. Thus, we propose an innovative scheme involving an extended H_infinity filter (EHF) for robust state estimation and zonotope for the protection-level generation. This scheme is shown as part of a tightly coupled navigation system based on an inertial navigation system and aided by the GPS/Galileo dual-constellation satellite navigation system. Specifically, GNSS pseudorange and deltarange observables are utilized. The experimental results of post-processing a real-world dataset show significant advantages of EHF against a conventional extended Kalman filter regarding the navigation accuracy and robustness under various GNSS-measurement parametrizations and environmental circumstances. The zonotope-based protection-level calculation is proven valid, computationally affordable, and feasible for real-time implementations.
Fast and accurate optimization and simulation is widely becoming a necessity for large scale transmission resiliency and planning studies such as N-1 SCOPF, batch contingency solvers, and stochastic power flow. Current commercial tools, however, prioritize speed of convergence over accuracy by relying on initial conditions that are taken from the steady state solution of similar network configurations that are not guaranteed to lie within a convex region of a valid solution. In this paper we introduce a globally convergent algorithm to facilitate fast and accurate AC steady state simulation and optimization based on prior knowledge from similar networks. The approach uses a homotopy method that gradually and efficiently translates a previously known network configuration to the current network configuration. The proposed formulation is highly scalable, and its efficacy is demonstrated for resiliency study and optimization of large networks up to 70k buses.
Learning from examples with noisy labels has attracted increasing attention recently. But, this paper will show that the commonly used CIFAR-based datasets and the accuracy evaluation metric used in the literature are both inappropriate in this context. An alternative valid evaluation metric and new datasets are proposed in this paper to promote proper research and evaluation in this area. Then, friends and foes are identified from existing methods as technical components that are either beneficial or detrimental to deep learning from noisy labeled examples, respectively, and this paper improves and combines technical components from the friends category, including self-supervised learning, new warmup strategy, instance filtering and label correction. The resulting F&F method significantly outperforms existing methods on the proposed nCIFAR datasets and the real-world Clothing1M dataset.
Artificial Intelligence (AI) covers a broad spectrum of computational problems and use cases. Many of those implicate profound and sometimes intricate questions of how humans interact or should interact with AIs. Moreover, many users or future users do have abstract ideas of what AI is, significantly depending on the specific embodiment of AI applications. Human-centered-design approaches would suggest evaluating the impact of different embodiments on human perception of and interaction with AI. An approach that is difficult to realize due to the sheer complexity of application fields and embodiments in reality. However, here XR opens new possibilities to research human-AI interactions. The article's contribution is twofold: First, it provides a theoretical treatment and model of human-AI interaction based on an XR-AI continuum as a framework for and a perspective of different approaches of XR-AI combinations. It motivates XR-AI combinations as a method to learn about the effects of prospective human-AI interfaces and shows why the combination of XR and AI fruitfully contributes to a valid and systematic investigation of human-AI interactions and interfaces. Second, the article provides two exemplary experiments investigating the aforementioned approach for two distinct AI-systems. The first experiment reveals an interesting gender effect in human-robot interaction, while the second experiment reveals an Eliza effect of a recommender system. Here the article introduces two paradigmatic implementations of the proposed XR testbed for human-AI interactions and interfaces and shows how a valid and systematic investigation can be conducted. In sum, the article opens new perspectives on how XR benefits human-centered AI design and development.
Stereo-LiDAR fusion is a promising task in that we can utilize two different types of 3D perceptions for practical usage -- dense 3D information (stereo cameras) and highly-accurate sparse point clouds (LiDAR). However, due to their different modalities and structures, the method of aligning sensor data is the key for successful sensor fusion. To this end, we propose a geometry-aware stereo-LiDAR fusion network for long-range depth estimation, called volumetric propagation network. The key idea of our network is to exploit sparse and accurate point clouds as a cue for guiding correspondences of stereo images in a unified 3D volume space. Unlike existing fusion strategies, we directly embed point clouds into the volume, which enables us to propagate valid information into nearby voxels in the volume, and to reduce the uncertainty of correspondences. Thus, it allows us to fuse two different input modalities seamlessly and regress a long-range depth map. Our fusion is further enhanced by a newly proposed feature extraction layer for point clouds guided by images: FusionConv. FusionConv extracts point cloud features that consider both semantic (2D image domain) and geometric (3D domain) relations and aid fusion at the volume. Our network achieves state-of-the-art performance on the KITTI and the Virtual-KITTI datasets among recent stereo-LiDAR fusion methods.
In this work, a non-orthogonal multiple access (NOMA) based transmission between two sources and two end-users is examined over independent non-identically distributed (i.n.i.d.) slow Nakagami-$m$ fading channels, where a single relay using decode-and-forward (DF) protocol is selected out of a set of full-duplex/half-duplex (FD/HD) multiple relays in accordance with the quality of service criterion. Two relay selection (RS) strategies, selecting a relay to maximize data rate of user 1 at selected relay and selecting a relay out of a set of relays providing service quality for user 1 to maximize data rate of user 2, are analyzed. Additionally, not only perfect successive interference cancellation (pSIC) but also imperfect SIC (ipSIC) is considered. The exact and asymptotic outage probability (OP) expressions are derived and validated via Monte Carlo simulation technique. Unlike existing works, our expressions are unique and valid for all cases such as FD and HD together with pSIC and ipSIC, i.e. expressions are not given separately but in a single compact form. Effect of each component such as pSIC, ipSIC, and self-interference (SI) for FD transmission on error floor of OP is demonstrated. Moreover, the optimum relay location is illustrated for a plenty of scenarios consisting of combination of different power allocations, data rates, pSIC/ipSIC, and total transmitted powers.
We propose a practical and robust method for making inferences on average treatment effects estimated by synthetic controls. We develop a $K$-fold cross-fitting procedure for bias correction. To avoid the difficult estimation of the long-run variance, inference is based on a self-normalized $t$-statistic, which has an asymptotically pivotal $t$-distribution. Our $t$-test is easy to implement, provably robust against misspecification, and valid with stationary and non-stationary data. It demonstrates an excellent small sample performance in application-based simulations and performs well relative to other methods. We illustrate the usefulness of the $t$-test by revisiting the effect of carbon taxes on emissions.
We introduce new inference procedures for counterfactual and synthetic control methods for policy evaluation. We recast the causal inference problem as a counterfactual prediction and a structural breaks testing problem. This allows us to exploit insights from conformal prediction and structural breaks testing to develop permutation inference procedures that accommodate modern high-dimensional estimators, are valid under weak and easy-to-verify conditions, and are provably robust against misspecification. Our methods work in conjunction with many different approaches for predicting counterfactual mean outcomes in the absence of the policy intervention. Examples include synthetic controls, difference-in-differences, factor and matrix completion models, and (fused) time series panel data models. Our approach demonstrates an excellent small-sample performance in simulations and is taken to a data application where we re-evaluate the consequences of decriminalizing indoor prostitution. Open-source software for implementing our conformal inference methods is available.