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The paper addresses the problem of estimation of the model parameters of the logistic exponential distribution based on progressive type-I hybrid censored sample. The maximum likelihood estimates are obtained and computed numerically using Newton-Raphson method. Further, the Bayes estimates are derived under squared error, LINEX and generalized entropy loss functions. Two types (independent and bivariate) of prior distributions are considered for the purpose of Bayesian estimation. It is seen that the Bayes estimates are not of explicit forms.Thus, Lindley's approximation technique is employed to get approximate Bayes estimates. Interval estimates of the parameters based on normal approximate of the maximum likelihood estimates and normal approximation of the log-transformed maximum likelihood estimates are constructed. The highest posterior density credible intervals are obtained by using the importance sampling method. Furthermore, numerical computations are reported to review some of the results obtained in the paper. A real life dataset is considered for the purpose of illustrations.

We propose a multidimensional smoothing spline algorithm in the context of manifold learning. We generalize the bending energy penalty of thin-plate splines to a quadratic form on the Sobolev space of a flat manifold, based on the Frobenius norm of the Hessian matrix. This leads to a natural definition of smoothing splines on manifolds, which minimizes square error while optimizing a global curvature penalty. The existence and uniqueness of the solution is shown by applying the theory of reproducing kernel Hilbert spaces. The minimizer is expressed as a combination of Green's functions for the biharmonic operator, and 'linear' functions of everywhere vanishing Hessian. Furthermore, we utilize the Hessian estimation procedure from the Hessian Eigenmaps algorithm to approximate the spline loss when the true manifold is unknown. This yields a particularly simple quadratic optimization algorithm for smoothing response values without needing to fit the underlying manifold. Analysis of asymptotic error and robustness are given, as well as discussion of out-of-sample prediction methods and applications.

We present a novel application of neural networks to design improved mixing elements for single-screw extruders. Specifically, we propose to use neural networks in numerical shape optimization to parameterize geometries. Geometry parameterization is crucial in enabling efficient shape optimization as it allows for optimizing complex shapes using only a few design variables. Recent approaches often utilize CAD data in conjunction with spline-based methods where the spline's control points serve as design variables. Consequently, these approaches rely on the same design variables as specified by the human designer. While this choice is convenient, it either restricts the design to small modifications of given, initial design features - effectively prohibiting topological changes - or yields undesirably many design variables. In this work, we step away from CAD and spline-based approaches and construct an artificial, feature-dense yet low-dimensional optimization space using a generative neural network. Using the neural network for the geometry parameterization extends state-of-the-art methods in that the resulting design space is not restricted to user-prescribed modifications of certain basis shapes. Instead, within the same optimization space, we can interpolate between and explore seemingly unrelated designs. To show the performance of this new approach, we integrate the developed shape parameterization into our numerical design framework for dynamic mixing elements in plastics extrusion. Finally, we challenge the novel method in a competitive setting against current free-form deformation-based approaches and demonstrate the method's performance even at this early stage.

In the usual Bayesian setting, a full probabilistic model is required to link the data and parameters, and the form of this model and the inference and prediction mechanisms are specified via de Finetti's representation. In general, such a formulation is not robust to model mis-specification of its component parts. An alternative approach is to draw inference based on loss functions, where the quantity of interest is defined as a minimizer of some expected loss, and to construct posterior distributions based on the loss-based formulation; this strategy underpins the construction of the Gibbs posterior. We develop a Bayesian non-parametric approach; specifically, we generalize the Bayesian bootstrap, and specify a Dirichlet process model for the distribution of the observables. We implement this using direct prior-to-posterior calculations, but also using predictive sampling. We also study the assessment of posterior validity for non-standard Bayesian calculations, and provide an efficient way to calibrate the scaling parameter in the Gibbs posterior so that it can achieve the desired coverage rate. We show that the developed non-standard Bayesian updating procedures yield valid posterior distributions in terms of consistency and asymptotic normality under model mis-specification. Simulation studies show that the proposed methods can recover the true value of the parameter efficiently and achieve frequentist coverage even when the sample size is small. Finally, we apply our methods to evaluate the causal impact of speed cameras on traffic collisions in England.

The use of high order fully implicit Runge-Kutta methods is of significant importance in the context of the numerical solution of transient partial differential equations, in particular when solving large scale problems due to fine space resolution with many millions of spatial degrees of freedom and long time intervals. In this study we consider strongly A-stable implicit Runge-Kutta methods of arbitrary order of accuracy, based on Radau quadratures, for which efficient preconditioners have been introduced. A refined spectral analysis of the corresponding matrices and matrix-sequences is presented, both in terms of localization and asymptotic global distribution of the eigenvalues. Specific expressions of the eigenvectors are also obtained. The given study fully agrees with the numerically observed spectral behavior and substantially improves the theoretical studies done in this direction so far. Concluding remarks and open problems end the current work, with specific attention to the potential generalizations of the hereby suggested general approach.

Motivated by a real-world application, we model and solve a complex staff scheduling problem. Tasks are to be assigned to workers for supervision. Multiple tasks can be covered in parallel by a single worker, with worker shifts being flexible within availabilities. Each worker has a different skill set, enabling them to cover different tasks. Tasks require assignment according to priority and skill requirements. The objective is to maximize the number of assigned tasks weighted by their priorities, while minimizing assignment penalties. We develop an adaptive large neighborhood search (ALNS) algorithm, relying on tailored destroy and repair operators. It is tested on benchmark instances derived from real-world data and compared to optimal results obtained by means of a commercial MIP-solver. Furthermore, we analyze the impact of considering three additional alternative objective functions. When applied to large-scale company data, the developed ALNS outperforms the previously applied solution approach.

Online platforms often incentivize consumers to improve user engagement and platform revenue. Since different consumers might respond differently to incentives, individual-level budget allocation is an essential task in marketing campaigns. Recent advances in this field often address the budget allocation problem using a two-stage paradigm: the first stage estimates the individual-level treatment effects using causal inference algorithms, and the second stage invokes integer programming techniques to find the optimal budget allocation solution. Since the objectives of these two stages might not be perfectly aligned, such a two-stage paradigm could hurt the overall marketing effectiveness. In this paper, we propose a novel end-to-end framework to directly optimize the business goal under budget constraints. Our core idea is to construct a regularizer to represent the marketing goal and optimize it efficiently using gradient estimation techniques. As such, the obtained models can learn to maximize the marketing goal directly and precisely. We extensively evaluate our proposed method in both offline and online experiments, and experimental results demonstrate that our method outperforms current state-of-the-art methods. Our proposed method is currently deployed to allocate marketing budgets for hundreds of millions of users on a short video platform and achieves significant business goal improvements. Our code will be publicly available.

Software is a great enabler for a number of projects that otherwise would be impossible to perform. Such projects include Space Exploration, Weather Modeling, Genome Projects, and many others. It is critical that software aiding these projects does what it is expected to do. In the terminology of software engineering, software that corresponds to requirements, that is does what it is expected to do is called correct. Checking the correctness of software has been the focus of a great deal of research in the area of software engineering. Practitioners in the field in which software is applied quite often do not assign much value to checking this correctness. Yet, as software systems become larger, potentially combined with distributed subsystems written by different authors, such verification becomes even more important. Concurrent, distributed systems are prone to dangerous errors due to different speeds of execution of their components such as deadlocks, race conditions, or violation of project-specific properties. This project describes an application of a static analysis method called model checking to verification of a distributed system for the Bioinformatics process. In it, we evaluate the efficiency of the model checking approach to the verification of combined processes with an increasing number of concurrently executed steps. We show that our experimental results correspond to analytically derived expectations. We also highlight the importance of static analysis to combined processes in the Bioinformatics field.

While most methods for solving mixed-integer optimization problems compute a single optimal solution, a diverse set of near-optimal solutions can often lead to improved outcomes. We present a new method for finding a set of diverse solutions by emphasizing diversity within the search for near-optimal solutions. Specifically, within a branch-and-bound framework, we investigated parameterized node selection rules that explicitly consider diversity. Our results indicate that our approach significantly increases the diversity of the final solution set. When compared with two existing methods, our method runs with similar runtime as regular node selection methods and gives a diversity improvement between 12% and 190%. In contrast, popular node selection rules, such as best-first search, in some instances performed worse than state-of-the-art methods by more than 35% and gave an improvement of no more than 130%. Further, we find that our method is most effective when diversity in node selection is continuously emphasized after reaching a minimal depth in the tree and when the solution set has grown sufficiently large. Our method can be easily incorporated into integer programming solvers and has the potential to significantly increase the diversity of solution sets.

Full Waveform Inversion (FWI) is a large-scale nonlinear ill-posed problem for which implementation of the Newton-type methods is computationally expensive. Moreover, these methods can trap in undesirable local minima when the starting model lacks low-wavenumber part and the recorded data lack low-frequency content. In this paper, the Gauss-Newton (GN) method is modified to address these issues. We rewrite the GN system for multisoure multireceiver FWI in an equivalent matrix equation form whose solution is a diagonal matrix, instead of a vector in the standard system. Then we relax the diagonality constraint, lifting the search direction from a vector to a matrix. This relaxation is equivalent to introducing an extra degree of freedom in the subsurface offset axis for the search direction. Furthermore, it makes the Hessian matrix separable and easy to invert. The relaxed system is solved explicitly for computing the desired search direction, requiring only inversion of two small matrices that deblur the data residual matrix along the source and receiver dimensions. Application of the Extended GN (EGN) method to solve the extended-source FWI leads to an algorithm that has the advantages of both model extension and source extension. Numerical examples are presented showing robustness and stability of EGN algorithm for waveform inversion.