Abstract: Two models are first presented, of a one-dimensional discrete-time quantum walk (DTQW) with temporal noise on the internal degree of freedom (i.e., the coin): (i) a model with both a coin-flip and a phase-flip channel, and (ii) a model with random coin unitaries. It is then shown that both these models admit a common limit in the spacetime continuum, namely, a Lindblad equation with Dirac-fermion Hamiltonian part and, as Lindblad jumps, a chirality flip and a chirality-dependent phase flip, which are two of the three standard error channels for a two-level quantum system. This, as one may call it, Dirac Lindblad equation, provides a model of quantum relativistic spatial diffusion, which is evidenced both analytically and numerically. This model of spatial diffusion has the intriguing specificity of making sense only with original unitary models which are relativistic in the sense that they have chirality, on which the noise is introduced: the diffusion arises via the by-construction (quantum) coupling of chirality to the position. For a particle with vanishing mass, the model of quantum relativistic diffusion introduced in the present work, reduces to the well-known telegraph equation, which yields propagation at short times, diffusion at long times, and exhibits no quantumness. Finally, the results are extended to temporal noises which depend smoothly on position.

Abstract: Importance Mammography screening currently relies on subjective human interpretation. Artificial intelligence (AI) advances could be used to increase mammography screening accuracy by reducing missed cancers and false positives. Objective To evaluate whether AI can overcome human mammography interpretation limitations with a rigorous, unbiased evaluation of machine learning algorithms. Design, Setting, and Participants In this diagnostic accuracy study conducted between September 2016 and November 2017, an international, crowdsourced challenge was hosted to foster AI algorithm development focused on interpreting screening mammography. More than 1100 participants comprising 126 teams from 44 countries participated. Analysis began November 18, 2016. Main Outcomes and Measurements Algorithms used images alone (challenge 1) or combined images, previous examinations (if available), and clinical and demographic risk factor data (challenge 2) and output a score that translated to cancer yes/no within 12 months. Algorithm accuracy for breast cancer detection was evaluated using area under the curve and algorithm specificity compared with radiologists' specificity with radiologists' sensitivity set at 85.9% (United States) and 83.9% (Sweden). An ensemble method aggregating top-performing AI algorithms and radiologists' recall assessment was developed and evaluated. Results Overall, 144231 screening mammograms from 85580 US women (952 cancer positive <= 12 months from screening) were used for algorithm training and validation. A second independent validation cohort included 166578 examinations from 68008 Swedish women (780 cancer positive). The top-performing algorithm achieved an area under the curve of 0.858 (United States) and 0.903 (Sweden) and 66.2% (United States) and 81.2% (Sweden) specificity at the radiologists' sensitivity, lower than community-practice radiologists' specificity of 90.5% (United States) and 98.5% (Sweden). Combining top-performing algorithms and US radiologist assessments resulted in a higher area under the curve of 0.942 and achieved a significantly improved specificity (92.0%) at the same sensitivity. Conclusions and Relevance While no single AI algorithm outperformed radiologists, an ensemble of AI algorithms combined with radiologist assessment in a single-reader screening environment improved overall accuracy. This study underscores the potential of using machine learning methods for enhancing mammography screening interpretation. Question How do deep learning algorithms perform compared with radiologists in screening mammography interpretation? Findings In this diagnostic accuracy study using 144231 screening mammograms from 85580 women from the United States and 166578 screening mammograms from 68008 women from Sweden, no single artificial intelligence algorithm outperformed US community radiologist benchmarks; including clinical data and prior mammograms did not improve artificial intelligence performance. However, combining best-performing artificial intelligence algorithms with single-radiologist assessment demonstrated increased specificity. Meaning Integrating artificial intelligence to mammography interpretation in single-radiologist settings could yield significant performance improvements, with the potential to reduce health care system expenditures and address resource scarcity experienced in population-based screening programs. This diagnostic accuracy study evaluates whether artificial intelligence can overcome human mammography interpretation limits with a rigorous, unbiased evaluation of machine learning algorithms.