Risk and the GP budget holder

For most individuals, the use made of health care in a given year is determined principally by unpredictable random incidents. Of course, some individuals have a predictably higher predisposition to illness than others. However, the general consensus is that only a fraction of individual variability in health care costs can be predicted. The purpose of this paper is to explore the implications of this inherent randomness for budget setting for GP purchasers. The paper argues that variability in utilization in the NHS is very high; that no formula will ever completely capture that variability, even for large populations; that the problem of variability is likely to be very acute for a GP practice; and that health authorities and GP budget holders will therefore need to adopt a range of strategies to manage the variability.fundholding

An Evolutionary Approach to the Design of Controllable Cellular Automata Structure for Random Number Generation

Cellular Automata (CA) has been used in pseudorandom number generation over a decade. Recent studies show that two-dimensional (2-d) CA Pseudorandom Number Generators (PRNGs) may generate better random sequences than conventional one-dimensional (1-d) CA PRNGs, but they are more complex to implement in hardware than 1-d CA PRNGs. In this paper, we propose a new class of 1-d CA Controllable Cellular Automata (CCA) without much deviation from the structure simplicity of conventional 1-d CA. We give a general definition of CCA first and then introduce two types of CCA – CCA0 and CCA2. Our initial study on them shows that these two CCA PRNGs have better randomness quality than conventional 1-d CA PRNGs but their randomness is affected by their structures. To find good CCA0/CCA2 structures for pseudorandom number generation, we evolve them using the Evolutionary Multi-Objective Optimization (EMOO) techniques. Three different algorithms are presented in this paper. One makes use of an aggregation function; the other two are based on the Vector Evaluated Genetic Algorithm (VEGA). Evolution results show that these three algorithms all perform well. Applying a set of randomness tests on the evolved CCA PRNGs, we demonstrate that their randomness is better than that of 1-d CA PRNGs and can be comparable to that of two-dimensional CA PRNGs

Multidimensional quantum entanglement with large-scale integrated optics

The ability to control multidimensional quantum systems is key for the investigation of fundamental science and for the development of advanced quantum technologies. Here we demonstrate a multidimensional integrated quantum photonic platform able to robustly generate, control and analyze high-dimensional entanglement. We realize a programmable bipartite entangled system with dimension up to $15 \times 15$ on a large-scale silicon-photonics quantum circuit. The device integrates more than 550 photonic components on a single chip, including 16 identical photon-pair sources. We verify the high precision, generality and controllability of our multidimensional technology, and further exploit these abilities to demonstrate key quantum applications experimentally unexplored before, such as quantum randomness expansion and self-testing on multidimensional states. Our work provides a prominent experimental platform for the development of multidimensional quantum technologies.Comment: Science, (2018

The Role of Randomness and Noise in Strategic Classification

We investigate the problem of designing optimal classifiers in the strategic classification setting, where the classification is part of a game in which players can modify their features to attain a favorable classification outcome (while incurring some cost). Previously, the problem has been considered from a learning-theoretic perspective and from the algorithmic fairness perspective. Our main contributions include 1. Showing that if the objective is to maximize the efficiency of the classification process (defined as the accuracy of the outcome minus the sunk cost of the qualified players manipulating their features to gain a better outcome), then using randomized classifiers (that is, ones where the probability of a given feature vector to be accepted by the classifier is strictly between 0 and 1) is necessary. 2. Showing that in many natural cases, the imposed optimal solution (in terms of efficiency) has the structure where players never change their feature vectors (the randomized classifier is structured in a way, such that the gain in the probability of being classified as a 1 does not justify the expense of changing one's features). 3. Observing that the randomized classification is not a stable best-response from the classifier's viewpoint, and that the classifier doesn't benefit from randomized classifiers without creating instability in the system. 4. Showing that in some cases, a noisier signal leads to better equilibria outcomes -- improving both accuracy and fairness when more than one subpopulation with different feature adjustment costs are involved. This is interesting from a policy perspective, since it is hard to force institutions to stick to a particular randomized classification strategy (especially in a context of a market with multiple classifiers), but it is possible to alter the information environment to make the feature signals inherently noisier.Comment: 22 pages. Appeared in FORC, 202

A Note on Shared Randomness and Shared Entanglement in Communication

We consider several models of 1-round classical and quantum communication, some of these models have not been defined before. We "almost separate" the models of simultaneous quantum message passing with shared entanglement and the model of simultaneous quantum message passing with shared randomness. We define a relation which can be efficiently exactly solved in the first model but cannot be solved efficiently, either exactly or in 0-error setup in the second model. In fact, our relation is exactly solvable even in a more restricted model of simultaneous classical message passing with shared entanglement. As our second contribution we strengthen a result by Yao that a "very short" protocol from the model of simultaneous classical message passing with shared randomness can be simulated in the model of simultaneous quantum message passing: for a boolean function f, QII(f) \in exp(O(RIIp(f))) log n. We show a similar result for protocols from a (stronger) model of 1-way classical message passing with shared randomness: QII(f) \in exp(O(RIp(f))) log n. We demonstrate a problem whose efficient solution in the model of simultaneous quantum message passing follows from our result but not from Yao's.Comment: Stronger separation, minor changes and fixe