Conditional Deep Gaussian Processes: Multi-Fidelity Kernel Learning

Deep Gaussian Processes (DGPs) were proposed as an expressive Bayesian model capable of a mathematically grounded estimation of uncertainty. The expressivity of DPGs results from not only the compositional character but the distribution propagation within the hierarchy. Recently, it was pointed out that the hierarchical structure of DGP well suited modeling the multi-fidelity regression, in which one is provided sparse observations with high precision and plenty of low fidelity observations. We propose the conditional DGP model in which the latent GPs are directly supported by the fixed lower fidelity data. Then the moment matching method is applied to approximate the marginal prior of conditional DGP with a GP. The obtained effective kernels are implicit functions of the lower-fidelity data, manifesting the expressivity contributed by distribution propagation within the hierarchy. The hyperparameters are learned via optimizing the approximate marginal likelihood. Experiments with synthetic and high dimensional data show comparable performance against other multi-fidelity regression methods, variational inference, and multi-output GP. We conclude that, with the low fidelity data and the hierarchical DGP structure, the effective kernel encodes the inductive bias for true function allowing the compositional freedom.

New computer technologies to determine postmortem interval by the Henssge method

Background: The Henssge method is still the main thermometric method to determine postmortem interval. However, its existing software implementations are characterized by several disadvantages associated with copying simplified nomographic variants of the original mathematical models without any optimization attempts, as well as procedural imperfection in finding the roots of implicit functions. In this paper, methods are proposed for optimizing solutions to the Henssge mathematical models and determine their errors, as well as software application implementation. Aim: Optimization of the Henssge algorithm and development of a series of applications based on the obtained data, designed to determine postmortem interval. Material and methods: Methods for solving double exponential Henssge models and determining their errors based on computational mathematics and regression modeling using the least-squares method with subsequent implementation in the format of computer programs in C# language optimized. Results: The discrete nature of residual variance changes of the double exponential Henssge models intended to determine the postmortem interval according to rectal and cranioencephalic thermometry data under constant external temperature conditions is eliminated. The interval estimate determination of postmortem interval at any confidence probability is possible. The application program Warm Bodies HR was developed, which implements applied optimization methods. The application program Warm Bodies AHBG, designed to determine postmortem interval by the Henssge method in a single discrete decrease or increase conditions in the constant temperature of the external environment, including a change in the cooling conditions of the corpse, was developed. The search for the roots of implicit functions in programs is carried out using the Newton tangent method, which ensures continuous source data nature and eliminates errors associated with the need to round directly measured physical quantities. Conclusions: The developed programs are recommended for forensic medical expert practice to determine postmortem interval.

Early Vernacular Medical Advice Books and Their Popular Appeal in Early Modern Italy

The essay considers the explosion of medical advice publications in the vernacular thatcharacterises the first two centuries of printing, and in particular their chronology and the different textual genres that made up this literature in early modern Italy. It shows that, in spite of the almost exclusive focus on recipe books in recent scholarship, the composition of this literature was much more varied and regimens of health, food regimens, books about the medicinal properties of naturalia, and compendia of medical information of various kinds (diagnostic, preventative and therapeutic) matched and sometimes exceeded the fortune of recipe books. It then goes on to ask what made some vernacular medical advice books particularly appealing to a wide non-professional and non-Latinate audience,while apparently similar publications attracted little interest. To this end it pays unprecedented attention to the full range of elements that determined the appeal of a book: its physical and typographical features, its contents and implicit functions, its author, patron, publisher and geographical reach.

Metaphor as a means of creating a humorous effect in Bulgarian media texts

The paper is devoted to the questions of metaphor as a linguistic means and cognitive mechanism for creating a humorous effect in Bulgarian media texts. There is a similarity between the nature of metaphors and the humor, the ability of perception which refers to the evolutionary acquisition. The relationship of metaphor and humor is manifested in the comparison of the contradictory and the combination of the disproportionate. The humorous effect created by the metaphor in the media discourse is included in the general context and is the result of deliberate efforts, in accordance with pragmatic, linguistic and cultural settings. Despite the universality of humor and metaphor, the interpretation of knowledge, modeled by a comic metaphor, is governed by the sociocultural factor. The implicit functions of the metaphor fit into the functional and pragmatic parameters of media discourse, making the metaphor an integral part of media speech. The collected material allows us to conclude that there are single comic metaphors in Bulgarian media texts, or metaphors create the humorous effect of a fragment / whole media text based on one or more metaphorical models. Increasingly, in a modern Bulgarian media discourse, a metaphor is implemented as a construct script for the semantic development of the text.

On Global Solvability of Nonlinear Equations with Parameters

We consider smooth mappings acting from one Banach space to another and depending on a parameter belonging to a topological space. Under various regularity assumptions, sufficient conditions for the existence of global and semilocal continuous inverse and implicit functions are obtained. We consider applications of these results to the problem of continuous extension of implicit functions and to the problem of coincidence points of smooth and continuous compact mappings.