Comparison of Alternative Meat Inspection Regimes for Pigs From Non-Controlled Housing – Considering the Cost of Error

Denmark has not had cases of bovine tuberculosis (bovTB) for more than 30 years but is obliged by trade agreements to undertake traditional meat inspection (TMI) of finisher pigs from non-controlled housing to detect bovTB. TMI is associated with higher probability of detecting bovTB but is also more costly than visual-only inspection (VOI). To identify whether VOI should replace TMI of finisher pigs from non-controlled housing, the cost of error – defined here as probability of overlooking infection and associated economic costs - should be assessed and compared with surveillance costs. First, a scenario tree model was set up to assess the ability of detecting bovTB in an infected herd (HSe) calculated for three within-herd prevalences, WHP (1, 5 and 10%), for four different surveillance scenarios (TMI and VOI with or without serological test, respectively). HSe was calculated for six consecutive 4-week surveillance periods until predicted bovTB detection (considered high-risk periods HRP). 1-HSe was probability of missing all positives by each HRP. Next, probability of spread of infection, Pspread, and number of infected animals moved were calculated for each HRP. Costs caused by overlooking bovTB were calculated taking into account Pspread, 1-HSe, eradication costs, and trade impact. Finally, the average annual costs were calculated by adding surveillance costs and assuming one incursion of bovTB in either 1, 10 or 30 years. Input parameters were based on slaughterhouse statistics, literature and expert opinion. Herd sensitivity increased by high-risk period and within-herd prevalence. Assuming WHP=5%, HSe reached median 90% by 2nd HRP for TMI, whereas for VOI this would happen after 6th HRP. Serology had limited impact on HSe. The higher the probability of infection, the higher the probability of detection and spread. TMI resulted in lowest average annual costs, if one incursion of bovTB was expected every year. However, when assuming one introduction in 10 or 30 years, VOI resulted in lowest average costs. It may be more cost-effective to focus on imported high-risk animals coming into contact with Danish livestock, instead of using TMI as surveillance on all pigs from non-controlled housing

An extension of Chaitin's halting probability \Omega to a measurement operator in an infinite dimensional quantum system

This paper proposes an extension of Chaitin's halting probability \Omega to a measurement operator in an infinite dimensional quantum system. Chaitin's \Omega is defined as the probability that the universal self-delimiting Turing machine U halts, and plays a central role in the development of algorithmic information theory. In the theory, there are two equivalent ways to define the program-size complexity H(s) of a given finite binary string s. In the standard way, H(s) is defined as the length of the shortest input string for U to output s. In the other way, the so-called universal probability m is introduced first, and then H(s) is defined as -log_2 m(s) without reference to the concept of program-size. Mathematically, the statistics of outcomes in a quantum measurement are described by a positive operator-valued measure (POVM) in the most general setting. Based on the theory of computability structures on a Banach space developed by Pour-El and Richards, we extend the universal probability to an analogue of POVM in an infinite dimensional quantum system, called a universal semi-POVM. We also give another characterization of Chaitin's \Omega numbers by universal probabilities. Then, based on this characterization, we propose to define an extension of \Omega as a sum of the POVM elements of a universal semi-POVM. The validity of this definition is discussed. In what follows, we introduce an operator version \hat{H}(s) of H(s) in a Hilbert space of infinite dimension using a universal semi-POVM, and study its properties.Comment: 24 pages, LaTeX2e, no figures, accepted for publication in Mathematical Logic Quarterly: The title was slightly changed and a section on an operator-valued algorithmic information theory was adde

Genuinely Distributed Byzantine Machine Learning

Machine Learning (ML) solutions are nowadays distributed, according to the so-called server/worker architecture. One server holds the model parameters while several workers train the model. Clearly, such architecture is prone to various types of component failures, which can be all encompassed within the spectrum of a Byzantine behavior. Several approaches have been proposed recently to tolerate Byzantine workers. Yet all require trusting a central parameter server. We initiate in this paper the study of the ``general'' Byzantine-resilient distributed machine learning problem where no individual component is trusted. We show that this problem can be solved in an asynchronous system, despite the presence of $\frac{1}{3}$ Byzantine parameter servers and $\frac{1}{3}$ Byzantine workers (which is optimal). We present a new algorithm, ByzSGD, which solves the general Byzantine-resilient distributed machine learning problem by relying on three major schemes. The first, Scatter/Gather, is a communication scheme whose goal is to bound the maximum drift among models on correct servers. The second, Distributed Median Contraction (DMC), leverages the geometric properties of the median in high dimensional spaces to bring parameters within the correct servers back close to each other, ensuring learning convergence. The third, Minimum-Diameter Averaging (MDA), is a statistically-robust gradient aggregation rule whose goal is to tolerate Byzantine workers. MDA requires loose bound on the variance of non-Byzantine gradient estimates, compared to existing alternatives (e.g., Krum). Interestingly, ByzSGD ensures Byzantine resilience without adding communication rounds (on a normal path), compared to vanilla non-Byzantine alternatives. ByzSGD requires, however, a larger number of messages which, we show, can be reduced if we assume synchrony.Comment: This is a merge of arXiv:1905.03853 and arXiv:1911.07537; arXiv:1911.07537 will be retracte

Attaining the rate-independent limit of a rate-dependent strain gradient plasticity theory

The existence of characteristic strain rates in rate-dependent material models, corresponding to rate-independent model behavior, is studied within a back stress based rate-dependent higher order strain gradient crystal plasticity model. Such characteristic rates have recently been observed for steady-state processes, and the present study aims to demonstrate that the observations in fact unearth a more widespread phenomenon. In this work, two newly proposed back stress formulations are adopted to account for the strain gradient effects in the single slip simple shear case, and characteristic rates for a selected quantity are identified through numerical analysis. Evidently, the concept of a characteristic rate, within the rate-dependent material models, may help unlock an otherwise inaccessible parameter space

A GRASP-Based Approach for Planning UAV-Assisted Search and Rescue Missions

Search and Rescue (SAR) missions aim to search and provide first aid to persons in distress or danger. Due to the urgency of these situations, it is important to possess a system able to take fast action and effectively and efficiently utilise the available resources to conduct the mission. In addition, the potential complexity of the search such as the ruggedness of terrain or large size of the search region should be considered. Such issues can be tackled by using Unmanned Aerial Vehicles (UAVs) equipped with optical sensors. This can ensure the efficiency in terms of speed, coverage and flexibility required to conduct this type of time-sensitive missions. This paper centres on designing a fast solution approach for planning UAV-assisted SAR missions. The challenge is to cover an area where targets (people in distress after a hurricane or earthquake, lost vessels in sea, missing persons in mountainous area, etc.) can be potentially found with a variable likelihood. The search area is modelled using a scoring map to support the choice of the search sub-areas, where the scores represent the likelihood of finding a target. The goal of this paper is to propose a heuristic approach to automate the search process using scarce heterogeneous resources in the most efficient manner