Less entanglement exhibiting more nonlocality with noisy measurements

The Clauser–Horne–Shimony–Holt (CHSH) inequality test is widely used as a mean of invalidating the local deterministic theories. Most attempts to experimentally test nonlocality have presumed unphysical idealizations that do not hold in real experiments, namely, noiseless measurements. We demonstrate an experimental violation of the CHSH inequality that is free of idealization and rules out local models with high confidence. We show that the CHSH inequality can always be violated for any nonzero noise parameter of the measurement. Intriguingly, less entanglement exhibits more nonlocality in the CHSH test with noisy measurements. Furthermore, we theoretically propose and experimentally demonstrate how the CHSH test with noisy measurements can be used to detect weak entanglement on two-qubit states. Our results offer a deeper insight into the relation between entanglement and nonlocality.

Sequential delay and probability discounting tasks in mice reveal anchoring effects partially attributable to decision noise

Delay discounting and probability discounting decision making tasks in rodent models have high translational potential. However, it is unclear whether the discounted value of the large reward option is the main contributor to variability in animals' choices in either task, which may limit translatability to human discounting data. Male and female mice underwent sessions of delay and probability discounting in sequence to assess how choice behavior adapts over experience with each task. To control for "anchoring" (persistent choices based on the initial delay or probability), mice experienced "Worsening" schedules where the large reward was offered under initially favorable delay or probability conditions that became less favorable during testing, followed by "Improving" schedules where the large reward was offered under initially unfavorable conditions that improved over a session. During delay discounting, both male and female mice showed elimination of anchoring effects over training. In probability discounting, both sexes of mice continued to show some anchoring even after months of training. One possibility is that noisy action selection could contribute to these anchoring effects, rather than persistent fluctuations in value discounting. We fit choice behavior in individual animals using models that included both a value-based discounting parameter and a decision noise parameter that captured variability in choices deviating from value maximization. Changes in anchoring behavior over time were tracked by changes in our decision noise parameter, not the value parameter. Thus, changes in discounting behavior in mice can result from changes in exploration of the environment rather than changes in reward valuation.

Navigating in Trees with Permanently Noisy Advice

We consider a search problem on trees in which an agent starts at the root of a tree and aims to locate an adversarially placed treasure, by moving along the edges, while relying on local, partial information. Specifically, each node in the tree holds a pointer to one of its neighbors, termed advice . A node is faulty with probability q . The advice at a non-faulty node points to the neighbor that is closer to the treasure, and the advice at a faulty node points to a uniformly random neighbor. Crucially, the advice is permanent , in the sense that querying the same node again would yield the same answer. Let Δ denote the maximum degree. For the expected number of moves (edge traversals) until finding the treasure, we show that a phase transition occurs when the noise parameter q is roughly 1 √Δ. Below the threshold, there exists an algorithm with expected number of moves O ( D √Δ), where D is the depth of the treasure, whereas above the threshold, every search algorithm has an expected number of moves, which is both exponential in D and polynomial in the number of nodes n . In contrast, if we require to find the treasure with probability at least 1 − δ, then for every fixed ɛ > 0, if q < 1/Δ ɛ , then there exists a search strategy that with probability 1 − δ finds the treasure using (Δ −1 D ) O (1/ε) moves. Moreover, we show that (Δ −1 D ) Ω(1/ε) moves are necessary.

Design Space Calculation and Continuous Improvement Considering a Noise Parameter: A Case Study of Ethanol Precipitation Process Optimization for Carthami Flos Extract

The optimization of process parameters in the pharmaceutical industry is often carried out according to the Quality by Design (QbD) concept. QbD also emphasizes that continuous improvement should be performed in life cycle management. Process parameters that are difficult to control in actual production can be regarded as noise parameters. In this study, based on the QbD concept, the ethanol precipitation process of Carthami Flos extract was optimized, considering a noise parameter. The density of the concentrated extract, ethanol concentration, the volume ratio of ethanol to concentrated extract, stirring time after ethanol addition, and refrigeration temperature were selected as critical process parameters (CPPs), using a definitive screening design. The mathematical models among CPPs and evaluation indicators were established. Considering that the refrigeration temperature of industrial ethanol precipitation is often difficult to control with seasonal changes, refrigeration temperature was treated as a noise parameter. A calculation method for the design space in the presence of the noise parameter was proposed. The design space was calculated according to the probability of reaching the standards of evaluation indicators. Controlling parameters within the design space was expected to reduce the influence of noise parameter fluctuations on the quality of the ethanol precipitation supernatant. With more data obtained, the design space was updated. In industry, it is also recommended to adopt a similar idea: that is, continuing to collect industrial data and regularly updating mathematical models, which can further update the design space and make it more stable and reliable.

Design space calculation and continuous improvement considering a noise parameter: A case study of ethanol precipitation process optimization for the Carthami Flos extract

Background The optimization of process parameters in the pharmaceutical industry is often carried out according to the Quality by Design (QbD) concept. QbD also emphasizes that continuous improvement should be performed in life cycle management. Process parameters that are difficult to control in actual production could be regarded as noise parameters. In this study, a noise parameter was considered, an example of continuous improvement in the design space was provided. Methods The ethanol precipitation process of Carthami Flos (Honghua) extract was optimized based on the QbD concept. The critical process parameters (CPPs) were identified using a definitive screening design. Considering that the refrigeration temperature of industrial ethanol precipitation is often difficult to control with seasonal changes, the refrigeration temperature was treated as a noise parameter. The design space was then calculated using an exhaustive search-Monte Carlo method. The mathematical models were reestablished when more data were obtained and then the calculated probabilities of reaching the process standards were updated. Results The calculation procedure of design space based on an exhaustive search-Monte Carlo method was proposed. The density of the concentrated extract, ethanol concentration, the volume ratio of ethanol to concentrated extract, stirring time after ethanol addition, and refrigeration temperature were selected as CPPs. The mathematical models of CPPs and evaluation indicators were established, and the coefficient of determination of each model was greater than 0.81. The predictive performance of the models was good. After continuous improvement, the recalculated probability values were more reliable, the design space became larger. Conclusions The calculation of design space and the continuous improvement strategy considering a noise parameter was developed. In industrial production, it is also recommended to adopt this similar idea, that is, continuing to collect industrial data and regularly updating the mathematical models, which can further update the design space and make it more stable and reliable.