On the relation between input and output distributions of scRNA-seq experiments

Single-cell RNA sequencing determines RNA copy numbers per cell for a given gene. However, technical noise poses the question how observed distributions (output) are connected to their cellular distributions (input). We model a single-cell RNA sequencing setup consisting of PCR amplification and sequencing, and derive probability distribution functions for the output distribution given an input distribution. We provide copy number distributions arising from single transcripts during PCR amplification with exact expressions for mean and variance. We prove that the coefficient of variation of the output of sequencing is always larger than that of the input distribution. Experimental data reveals the variance and mean of the input distribution to obey characteristic relations, which we specifically determine for a HeLa data set. We can calculate as many moments of the input distribution as are known of the output distribution (up to all). This, in principle, completely determines the input from the output distribution.

Agency Contracts under Maximum-Entropy

This article proposes the application of the maximum-entropy principle (MEP) to agency contracting (where a principal hires an agent to make decisions on their behalf) in situations where the principal and agent only have partial knowledge on the probability distribution of the output conditioned on the agent’s actions. The paper characterizes the second-best agency contract from a maximum entropy distribution (MED) obtained from applying the MEP to the agency situation consistently with the information available. We show that, with the minimum shared information about the output distribution for the agency relationship to take place, the second-best compensation contract is (a monotone transformation of) an increasing affine function of output. With additional information on the output distribution, the second-best optimal contracts can be more complex. The second-best contracts obtained theoretically from the MEP cover many compensation schemes observed in real agency relationships.

Remote Sensing Image Scene Classification via Label Augmentation and Intra-Class Constraint

In recent years, many convolutional neural network (CNN)-based methods have been proposed to address the scene classification tasks of remote sensing images. Since the number of training samples in RS datasets is generally small, data augmentation is often used to expand the training set. It is, however, not appropriate when original data augmentation methods keep the label and change the content of the image at the same time. In this study, label augmentation (LA) is presented to fully utilize the training set by assigning a joint label to each generated image, which considers the label and data augmentation at the same time. Moreover, the output of images obtained by different data augmentation is aggregated in the test process. However, the augmented samples increase the intra-class diversity of the training set, which is a challenge to complete the following classification process. To address the above issue and further improve classification accuracy, Kullback–Leibler divergence (KL) is used to constrain the output distribution of two training samples with the same scene category to generate a consistent output distribution. Extensive experiments were conducted on widely-used UCM, AID and NWPU datasets. The proposed method can surpass the other state-of-the-art methods in terms of classification accuracy. For example, on the challenging NWPU dataset, competitive overall accuracy (i.e., 91.05%) is obtained with a 10% training ratio.

Quantum Divide and Compute: Exploring the Effect of Different Noise Sources

Our recent work (Ayral et al. in Proceedings of IEEE computer society annual symposium on VLSI, ISVLSI, pp 138–140, 2020. 10.1109/ISVLSI49217.2020.00034) showed the first implementation of the Quantum Divide and Compute (QDC) method, which allows to break quantum circuits into smaller fragments with fewer qubits and shallower depth. This accommodates the limited number of qubits and short coherence times of quantum processors. This article investigates the impact of different noise sources—readout error, gate error and decoherence—on the success probability of the QDC procedure. We perform detailed noise modeling on the Atos Quantum Learning Machine, allowing us to understand tradeoffs and formulate recommendations about which hardware noise sources should be preferentially optimized. We also describe in detail the noise models we used to reproduce experimental runs on IBM’s Johannesburg processor. This article also includes a detailed derivation of the equations used in the QDC procedure to compute the output distribution of the original quantum circuit from the output distribution of its fragments. Finally, we analyze the computational complexity of the QDC method for the circuit under study via tensor-network considerations, and elaborate on the relation the QDC method with tensor-network simulation methods.

How Should Performance Signals Affect Contracts?

The informativeness principle states that a contract should depend on informative signals. This paper studies how it should do so. Signals indicating that the output distribution has shifted to the left (e.g., weak industry performance) reduce the threshold for the manager to be paid; those indicating that output is a precise measure of effort (e.g., low volatility) decrease high thresholds and increase low thresholds. Surprisingly, “good” signals of performance need not reduce the threshold. Applying our model to performance-based vesting, we show that performance measures should affect the strike price, rather than the number of vesting options, contrary to practice.

On the classical complexity of sampling from quantum interference of indistinguishable bosons

Experimental demonstration of the quantum advantage over classical simulations with Boson Sampling is currently under intensive investigation. There seems to be a scalability issue to the necessary number of bosons on the linear optical platforms and the experiments, such as the recent Boson Sampling with 20 photons on 60-port interferometer by H. Wang et al., Phys. Rev. Lett. 123 (2019) 250503, are usually carried out on a small interferometer, much smaller than the size necessary for the no-collision regime. Before demonstration of quantum advantage, it is urgent to estimate exactly how the classical computations necessary for sampling from the output distribution of Boson Sampling are reduced when a smaller-size interferometer is used. This work supplies such a result, valid with arbitrarily close to 1 probability, which reduces in the no-collision regime to the previous estimate by Clifford and Clifford. One of the results with immediate application to current experiments with Boson Sampling is that classically sampling from the interference of [Formula: see text] single bosons on an [Formula: see text]-port interferometer is at least as hard as that with [Formula: see text] single bosons in the no-collision regime, i.e. on a much larger interferometer with at least [Formula: see text] ports.