Logical activation functions for training arbitrary probabilistic Boolean operations
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96 KNOWLEDGE MANAGEMENT AND PRESERVATION↗
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Orientation reversal and the Chern-Simons natural boundary
We show that the fundamental property of preservation of relations, underlying resurgent analysis, provides a new perspective on crossing a natural boundary, an important general problem in theoretical and mathematical physics. This reveals a deeper rigidity aspect of resurgence in a quantum field theory path integral. The physical context here is the non-perturbative completion of complex Chern-Simons theory that associates to a 3-manifold a collection of q-series invariants labeled by Spinc structures, for which crossing the natural boundary corresponds to orientation reversal of the 3-manifold. Our new resurgent perspective leads to a practical numerical algorithm that generates q-series which are dual to unary q-series composed of false theta functions. Until recently, these duals were only known in a limited number of cases, essentially based on Ramanujan’s mock theta functions, and the common belief was that the duals might not even exist in the general case. Resurgence analysis identifies as primary objects Mordell integrals: up to changes of variables, they are Laplace transforms of resurgent functions. Their unique Borel summed transseries decomposition on either side of the Stokes line is simply the unique decomposition into real and imaginary parts. In turn, the latter are combinations of unary q-series in terms of q and its modular counterpart $\overset{\sim }{q}$ , and are resurgent by construction. The Mordell integral is analytic across the natural boundary of the q and $\overset{\sim }{q}$ series, and uniqueness of a similar decomposition which preserves algebraic relations on the other side of the boundary defines the unique boundary crossing of the q series. We demonstrate that this continuation can be efficiently implemented numerically. In the cases where unique mock modular identities are known, they are found by this numerical procedure, but the procedure can go well beyond the known list of identities. A particularly interesting feature of the resurgent approach is that it reveals new aspects, and is very different from other known approaches based on indefinite theta series, Appell-Lerch sums, and representation theory of logarithmic vertex operator algebras.
Chern-Simons theories↗
Climate warming enhances biodiversity and stability of grassland soil phosphorus-cycling microbial communities
Abstract Climate warming poses significant challenges to global phosphorus sustainability, an essential component of Earth biogeochemistry cycling and water-food-energy nexus. Despite the crucial role of polyphosphate-accumulating organism as key functional microbial agents in phosphorus cycling, the impacts of global climate warming on polyphosphate accumulating organism communities remain largely enigmatic. This study investigates the effects of climate warming on the taxonomic, network, and functional profiles of soil bacterial polyphosphate-accumulating organisms, leveraging fluorescence-activated cell sorting and single-cell Raman spectroscopy. Climate warming enhances both taxonomic and functional biodiversity of polyphosphate-accumulating organisms via biotic interactions and environmental filtering, with observed functionality-biodiversity relationships supporting the functional redundancy theory. Furthermore, polyphosphate-accumulating organism network complexity and stability rise under warming with strengthened positive relationships, supporting stress gradient hypothesis and the belief that complexity begets stability. Finally, polyphosphate-accumulating organisms are significantly correlated to key ecosystem functioning in carbon and phosphorus cycling under warming. Our study suggests that preserving polyphosphate-accumulating organism communities is crucial for maintaining soil ecosystem functioning and sustainable phosphorus management in a warming world and opens avenues for predicting the responses of other functional microbial groups to climate change, beneficially or maliciously.
Environmental Sciences & Ecology↗
Analysis and optimization of seismic monitoring networks with Bayesian optimal experimental design
SUMMARY Monitoring networks increasingly aim to assimilate data from a large number of diverse sensors covering many sensing modalities. Bayesian optimal experimental design (OED) seeks to identify data, sensor configurations or experiments which can optimally reduce uncertainty and hence increase the performance of a monitoring network. Information theory guides OED by formulating the choice of experiment or sensor placement as an optimization problem that maximizes the expected information gain (EIG) about quantities of interest given prior knowledge and models of expected observation data. Therefore, within the context of seismo-acoustic monitoring, we can use Bayesian OED to configure sensor networks by choosing sensor locations, types and fidelity in order to improve our ability to identify and locate seismic sources. In this work, we develop the framework necessary to use Bayesian OED to optimize a sensor network’s ability to locate seismic events from arrival time data of detected seismic phases at the regional-scale. This framework requires five elements: (i) A likelihood function that describes the distribution of detection and traveltime data from the sensor network, (ii) A prior distribution that describes a priori belief about seismic events, (iii) A Bayesian solver that uses a prior and likelihood to identify the posterior distribution of seismic events given the data, (iv) An algorithm to compute EIG about seismic events over a data set of hypothetical prior events, (v) An optimizer that finds a sensor network which maximizes EIG. Once we have developed this framework, we explore many relevant questions to monitoring such as: how to trade off sensor fidelity and earth model uncertainty; how sensor types, number and locations influence uncertainty; and how prior models and constraints influence sensor placement.
58 GEOSCIENCES↗
A Risk-Informed Approach to Trustworthiness Assessment in Digital Twins-Based Autonomous Control
In autonomous control systems, digital twins (DTs) are used to perform diagnostic and prognostic functions. The trustworthiness of these DTs is dependent on quality and coverage of the training data, model accuracy and integrity of sensor data. This work introduces a methodology to determine the trustworthiness of a DT system given faulty sensor data using a risk informed approach. Bayesian Belief Networks (BBNs) are used to propagate uncertainties and determine the probability of trustable recommendations. The decision to trust the control action provided by the DT is based on the DT output, expert opinion, and severity of problems. The performance of DTs is reliant on the data they are trained on. When they encounter out of distribution data, the trustworthiness of the recommendations decreases. To address this issue, we include an expert component that provides input on sensor degradation. For this, we utilize a generative artificial intelligence (AI) model, such as Generative Pretrained Transformer (GPT). The GPT functions as an expert with broad knowledge. The GPT is fine-tuned to understand and discriminate sensor degradation scenarios using manufactured data. This methodology is demonstrated through a case study on a Nearly Autonomous Management and Control System (NAMAC) during a steady state scenario. Various sensor degradation types with different severity levels are considered. Degraded sensor data is processed by the DT system and the fine-tuned GPT. Finally, using the BBN, we combine the GPT information and the DT output with its sources of uncertainty. This provides an output regarding the trustworthiness of the DT recommendation.
22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
Radiation-reduced diffusion of Nd in bcc Fe
Here, this study combines ab initio calculations and kinetic Monte Carlo simulations to investigate the bulk diffusion of Nd, an exemplar lanthanide element, in bcc Fe. Contrary to the conventional belief that irradiation accelerates diffusion processes, our study reveals that irradiation can unexpectedly reduce the diffusion of Nd due to the strong binding between substitutional Nd atoms and vacancies in bcc Fe. Combined with the high concentration of nonequilibrium vacancies, this promotes the abundant formation of Nd+3Va defect complexes containing a single Nd substitutional atom and three vacancies, accompanied by the depletion of Nd-vacancy pairs that mediate the diffusion of Nd.
Density functional theory (DFT)↗