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Measurement-based quantum computation (MBQC) offers a fundamentally unique paradigm to design quantum algorithms. Indeed, due to the inherent randomness of quantum measurements, the natural operations in MBQC are not deterministic and unitary, but are rather augmented with probabilistic byproducts. Yet, the main algorithmic use of MBQC so far has been to completely counteract this probabilistic nature in order to simulate unitary computations expressed in the circuit model. In this work, we propose designing MBQC algorithms that embrace this inherent randomness and treat the random byproducts in MBQC as a resource for computation. As a natural application where randomness can be beneficial, we consider generative modeling, a task in machine learning centered around generating complex probability distributions. To address this task, we propose a variational MBQC algorithm equipped with control parameters that allow to directly adjust the degree of randomness to be admitted in the computation. Our numerical findings indicate that this additional randomness can lead to significant gains in learning performance in certain generative modeling tasks. These results highlight the potential advantages in exploiting the inherent randomness of MBQC and motivate further research into MBQC-based algorithms.

Models of complex technological systems inherently contain interactions and dependencies among their input variables that affect their joint influence on the output. Such models are often computationally expensive and few sensitivity analysis methods can effectively process such complexities. Moreover, the sensitivity analysis field as a whole pays limited attention to the nature of interaction effects, whose understanding can prove to be critical for the design of safe and reliable systems. In this paper, we introduce and extensively test a simple binning approach for computing sensitivity indices and demonstrate how complementing it with the smart visualization method, simulation decomposition (SimDec), can permit important insights into the behavior of complex engineering models. The simple binning approach computes first-, second-order effects, and a combined sensitivity index, and is considerably more computationally efficient than Sobol' indices. The totality of the sensitivity analysis framework provides an efficient and intuitive way to analyze the behavior of complex systems containing interactions and dependencies.

A new mechanical model on noncircular shallow tunnelling considering initial stress field is proposed in this paper by constraining far-field ground surface to eliminate displacement singularity at infinity, and the originally unbalanced tunnel excavation problem in existing solutions is turned to an equilibrium one of mixed boundaries. By applying analytic continuation, the mixed boundaries are transformed to a homogenerous Riemann-Hilbert problem, which is subsequently solved via an efficient and accurate iterative method with boundary conditions of static equilibrium, displacement single-valuedness, and traction along tunnel periphery. The Lanczos filtering technique is used in the final stress and displacement solution to reduce the Gibbs phenomena caused by the constrained far-field ground surface for more accurte results. Several numerical cases are conducted to intensively verify the proposed solution by examining boundary conditions and comparing with existing solutions, and all the results are in good agreements. Then more numerical cases are conducted to investigate the stress and deformation distribution along ground surface and tunnel periphery, and several engineering advices are given. Further discussions on the defects of the proposed solution are also conducted for objectivity.

We present a new framework for modelling multivariate extremes, based on an angular-radial representation of the probability density function. Under this representation, the problem of modelling multivariate extremes is transformed to that of modelling an angular density and the tail of the radial variable, conditional on angle. Motivated by univariate theory, we assume that the tail of the conditional radial distribution converges to a generalised Pareto (GP) distribution. To simplify inference, we also assume that the angular density is continuous and finite and the GP parameter functions are continuous with angle. We refer to the resulting model as the semi-parametric angular-radial (SPAR) model for multivariate extremes. We consider the effect of the choice of polar coordinate system and introduce generalised concepts of angular-radial coordinate systems and generalised scalar angles in two dimensions. We show that under certain conditions, the choice of polar coordinate system does not affect the validity of the SPAR assumptions. However, some choices of coordinate system lead to simpler representations. In contrast, we show that the choice of margin does affect whether the model assumptions are satisfied. In particular, the use of Laplace margins results in a form of the density function for which the SPAR assumptions are satisfied for many common families of copula, with various dependence classes. We show that the SPAR model provides a more versatile framework for characterising multivariate extremes than provided by existing approaches, and that several commonly-used approaches are special cases of the SPAR model. Moreover, the SPAR framework provides a means of characterising all `extreme regions' of a joint distribution using a single inference. Applications in which this is useful are discussed.

Insurers usually turn to generalized linear models for modelling claim frequency and severity data. Due to their success in other fields, machine learning techniques are gaining popularity within the actuarial toolbox. Our paper contributes to the literature on frequency-severity insurance pricing with machine learning via deep learning structures. We present a benchmark study on four insurance data sets with frequency and severity targets in the presence of multiple types of input features. We compare in detail the performance of: a generalized linear model on binned input data, a gradient-boosted tree model, a feed-forward neural network (FFNN), and the combined actuarial neural network (CANN). Our CANNs combine a baseline prediction established with a GLM and GBM, respectively, with a neural network correction. We explain the data preprocessing steps with specific focus on the multiple types of input features typically present in tabular insurance data sets, such as postal codes, numeric and categorical covariates. Autoencoders are used to embed the categorical variables into the neural network and we explore their potential advantages in a frequency-severity setting. Finally, we construct global surrogate models for the neural nets' frequency and severity models. These surrogates enable the translation of the essential insights captured by the FFNNs or CANNs to GLMs. As such, a technical tariff table results that can easily be deployed in practice.

Rational function approximations provide a simple but flexible alternative to polynomial approximation, allowing one to capture complex non-linearities without oscillatory artifacts. However, there have been few attempts to use rational functions on noisy data due to the likelihood of creating spurious singularities. To avoid the creation of singularities, we use Bernstein polynomials and appropriate conditions on their coefficients to force the denominator to be strictly positive. While this reduces the range of rational polynomials that can be expressed, it keeps all the benefits of rational functions while maintaining the robustness of polynomial approximation in noisy data scenarios. Our numerical experiments on noisy data show that existing rational approximation methods continually produce spurious poles inside the approximation domain. This contrasts our method, which cannot create poles in the approximation domain and provides better fits than a polynomial approximation and even penalized splines on functions with multiple variables. Moreover, guaranteeing pole-free in an interval is critical for estimating non-constant coefficients when numerically solving differential equations using spectral methods. This provides a compact representation of the original differential equation, allowing numeric solvers to achieve high accuracy quickly, as seen in our experiments.

In this article, we focus on the error that is committed when computing the matrix logarithm using the Gauss--Legendre quadrature rules. These formulas can be interpreted as Pad\'e approximants of a suitable Gauss hypergeometric function. Empirical observation tells us that the convergence of these quadratures becomes slow when the matrix is not close to the identity matrix, thus suggesting the usage of an inverse scaling and squaring approach for obtaining a matrix with this property. The novelty of this work is the introduction of error estimates that can be used to select a priori both the number of Legendre points needed to obtain a given accuracy and the number of inverse scaling and squaring to be performed. We include some numerical experiments to show the reliability of the estimates introduced.

Within the realm of image recognition, a specific category of multi-label classification (MLC) challenges arises when objects within the visual field may occlude one another, demanding simultaneous identification of both occluded and occluding objects. Traditional convolutional neural networks (CNNs) can tackle these challenges; however, those models tend to be bulky and can only attain modest levels of accuracy. Leveraging insights from cutting-edge neural science research, specifically the Holistic Bursting (HB) cell, this paper introduces a pioneering integrated network framework named HB-net. Built upon the foundation of HB cell clusters, HB-net is designed to address the intricate task of simultaneously recognizing multiple occluded objects within images. Various Bursting cell cluster structures are introduced, complemented by an evidence accumulation mechanism. Testing is conducted on multiple datasets comprising digits and letters. The results demonstrate that models incorporating the HB framework exhibit a significant $2.98\%$ enhancement in recognition accuracy compared to models without the HB framework ($1.0298$ times, $p=0.0499$). Although in high-noise settings, standard CNNs exhibit slightly greater robustness when compared to HB-net models, the models that combine the HB framework and EA mechanism achieve a comparable level of accuracy and resilience to ResNet50, despite having only three convolutional layers and approximately $1/30$ of the parameters. The findings of this study offer valuable insights for improving computer vision algorithms. The essential code is provided at //github.com/d-lab438/hb-net.git.

Nonignorable missing outcomes are common in real world datasets and often require strong parametric assumptions to achieve identification. These assumptions can be implausible or untestable, and so we may forgo them in favour of partially identified models that narrow the set of a priori possible values to an identification region. Here we propose a new nonparametric Bayes method that allows for the incorporation of multiple clinically relevant restrictions of the parameter space simultaneously. We focus on two common restrictions, instrumental variables and the direction of missing data bias, and investigate how these restrictions narrow the identification region for parameters of interest. Additionally, we propose a rejection sampling algorithm that allows us to quantify the evidence for these assumptions in the data. We compare our method to a standard Heckman selection model in both simulation studies and in an applied problem examining the effectiveness of cash-transfers for people experiencing homelessness.

In large-scale systems there are fundamental challenges when centralised techniques are used for task allocation. The number of interactions is limited by resource constraints such as on computation, storage, and network communication. We can increase scalability by implementing the system as a distributed task-allocation system, sharing tasks across many agents. However, this also increases the resource cost of communications and synchronisation, and is difficult to scale. In this paper we present four algorithms to solve these problems. The combination of these algorithms enable each agent to improve their task allocation strategy through reinforcement learning, while changing how much they explore the system in response to how optimal they believe their current strategy is, given their past experience. We focus on distributed agent systems where the agents' behaviours are constrained by resource usage limits, limiting agents to local rather than system-wide knowledge. We evaluate these algorithms in a simulated environment where agents are given a task composed of multiple subtasks that must be allocated to other agents with differing capabilities, to then carry out those tasks. We also simulate real-life system effects such as networking instability. Our solution is shown to solve the task allocation problem to 6.7% of the theoretical optimal within the system configurations considered. It provides 5x better performance recovery over no-knowledge retention approaches when system connectivity is impacted, and is tested against systems up to 100 agents with less than a 9% impact on the algorithms' performance.