Expectation Invariants for Probabilistic Program Loops as Fixed Points

Abstract. We present static analyses for probabilistic loops using expectation in-variants. Probabilistic loops are imperative while-loops augmented with calls to random variable generators. Whereas, traditional program analysis uses Floyd-Hoare style invariants to over-approximate the set of reachable states, our ap-proach synthesizes invariant inequalities involving the expected values of pro-gram expressions at the loop head. We first define the notion of expectation invari-ants, and demonstrate their usefulness in analyzing probabilistic program loops. Next, we present the set of expectation invariants for a loop as a fixed point of the pre-expectation operator over sets of program expressions. Finally, we use exist-ing concepts from abstract interpretation theory to present an iterative analysis that synthesizes expectation invariants for probabilistic program loops. We show how the standard polyhedral abstract domain can be used to synthesize expecta-tion invariants for probabilistic programs, and demonstrate the usefulness of our approach on some examples of probabilistic program loops.

Hybrid Modeling and Simulation of Biomolecular Networks

In a biological cell, cellular functions and the genetic regulatory apparatus are implemented and controlled by a network of chemical reactions in which regulatory proteins can control genes that produce other regulators, which in turn control other genes. Further, the feedback pathways appear to incorporate switches that result in changes in the dynamic behavior of the cell. This paper describes a hybrid systems approach to modeling the intra-cellular network using continuous di#erential equations to model the feedback mechanisms and mode-switching to describe the changes in the underlying dynamics. We use two case studies to illustrate a modular approach to modeling such networks and describe the architectural and behavioral hierarchy in the underlying models. We describe these models using Charon [2], a language that allows formal description of hybrid systems. We provide preliminary simulation results that demonstrate how our approach can help biologists in their analysis of noisy genetic circuits. Finally we describe our agenda for future work that includes the development of models and simulation for stochastic hybrid systems

Science goals and overview of the radiation belt storm probes (RBSP) energetic particle, composition, and thermal plasma (ECT) suite on NASA's Van Allen Probes mission

The Radiation Belt Storm Probes (RBSP)-Energetic Particle, Composition, and Thermal Plasma (ECT) suite contains an innovative complement of particle instruments to ensure the highest quality measurements ever made in the inner magnetosphere and radiation belts. The coordinated RBSP-ECT particle measurements, analyzed in combination with fields and waves observations and state-of-the-art theory and modeling, are necessary for understanding the acceleration, global distribution, and variability of radiation belt electrons and ions, key science objectives of NASA’s Living With a Star program and the Van Allen Probes mission. The RBSP-ECT suite consists of three highly-coordinated instruments: the Magnetic Electron Ion Spectrometer (MagEIS), the Helium Oxygen Proton Electron (HOPE) sensor, and the Relativistic Electron Proton Telescope (REPT). Collectively they cover, continuously, the full electron and ion spectra from one eV to 10’s of MeV with sufficient energy resolution, pitch angle coverage and resolution, and with composition measurements in the critical energy range up to 50 keV and also from a few to 50 MeV/nucleon. All three instruments are based on measurement techniques proven in the radiation belts. The instruments use those proven techniques along with innovative new designs, optimized for operation in the most extreme conditions in order to provide unambiguous separation of ions and electrons and clean energy responses even in the presence of extreme penetrating background environments. The design, fabrication and operation of ECT spaceflight instrumentation in the harsh radiation belt environment ensure that particle measurements have the fidelity needed for closure in answering key mission science questions. ECT instrument details are provided in companion papers in this same issue. In this paper, we describe the science objectives of the RBSP-ECT instrument suite on the Van Allen Probe spacecraft within the context of the overall mission objectives, indicate how the characteristics of the instruments satisfy the requirements to achieve these objectives, provide information about science data collection and dissemination, and conclude with a description of some early mission results

A Machine Learning Algorithm to Identify Patients at Risk of Unplanned Subsequent Surgery After Intramedullary Nailing for Tibial Shaft Fractures

Objectives: In the SPRINT trial, 18% of patients with a tibial shaft fracture (TSF) treated with intramedullary nailing (IMN) had one or more unplanned subsequent surgical procedures. It is clinically relevant for surgeon and patient to anticipate unplanned secondary procedures, other than operations that can be readily expected such as reconstructive procedures for soft tissue defects. Therefore, the objective of this study was to develop a machine learning (ML) prediction model using the SPRINT data that can give individual patients and their care team an estimate of their particular probability of an unplanned second surgery. Methods: Patients from the SPRINT trial with unilateral TSFs were randomly divided into a training set (80%) and test set (20%). Five ML algorithms were trained in recognizing patterns associated with subsequent surgery in the training set based on a subset of variables identified by random forest algorithms. Performance of each ML algorithm was evaluated and compared based on (1) area under the ROC curve, (2) calibration slope and intercept, and (3) the Brier score. Results: Total data set comprised 1198 patients, of whom 214 patients (18%) underwent subsequent surgery. Seven variables were used to train ML algorithms: (1) Gustilo-Anderson classification, (2) Tscherne classification, (3) fracture location, (4) fracture gap, (5) polytrauma, (6) injury mechanism, and (7) OTA/AO classification. The best-performing ML algorithm had an area under the ROC curve, calibration slope, calibration intercept, and the Brier score of 0.766, 0.954, -0.002, and 0.120 in the training set and 0.773, 0.922, 0, and 0.119 in the test set, respectively. Conclusions: An ML algorithm was developed to predict the probability of subsequent surgery after IMN for TSFs. This ML algorithm may assist surgeons to inform patients about the probability of subsequent surgery and might help to identify patients who need a different perioperative plan or a more intensive approach.Orthopaedics, Trauma Surgery and Rehabilitatio

Enhanced performance in fusion plasmas through turbulence suppression by megaelectronvolt ions

© 2022, The Author(s), under exclusive licence to Springer Nature Limited.Alpha particles with energies on the order of megaelectronvolts will be the main source of plasma heating in future magnetic confinement fusion reactors. Instead of heating fuel ions, most of the energy of alpha particles is transferred to electrons in the plasma. Furthermore, alpha particles can also excite Alfvénic instabilities, which were previously considered to be detrimental to the performance of the fusion device. Here we report improved thermal ion confinement in the presence of megaelectronvolts ions and strong fast ion-driven Alfvénic instabilities in recent experiments on the Joint European Torus. Detailed transport analysis of these experiments reveals turbulence suppression through a complex multi-scale mechanism that generates large-scale zonal flows. This holds promise for more economical operation of fusion reactors with dominant alpha particle heating and ultimately cheaper fusion electricity.N

Disruption prediction with artificial intelligence techniques in tokamak plasmas

In nuclear fusion reactors, plasmas are heated to very high temperatures of more than 100 million kelvin and, in so-called tokamaks, they are confined by magnetic fields in the shape of a torus. Light nuclei, such as deuterium and tritium, undergo a fusion reaction that releases energy, making fusion a promising option for a sustainable and clean energy source. Tokamak plasmas, however, are prone to disruptions as a result of a sudden collapse of the system terminating the fusion reactions. As disruptions lead to an abrupt loss of confinement, they can cause irreversible damage to present-day fusion devices and are expected to have a more devastating effect in future devices. Disruptions expected in the next-generation tokamak, ITER, for example, could cause electromagnetic forces larger than the weight of an Airbus A380. Furthermore, the thermal loads in such an event could exceed the melting threshold of the most resistant state-of-the-art materials by more than an order of magnitude. To prevent disruptions or at least mitigate their detrimental effects, empirical models obtained with artificial intelligence methods, of which an overview is given here, are commonly employed to predict their occurrence—and ideally give enough time to introduce counteracting measures