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The inflationary paradigm is an important cornerstone of the concordance cosmological model. However, standard inflation cannot fully address the transition from an early homogeneous and isotropic stage, to another one lacking such…
Observations of the temperature anisotropies in the Cosmic Microwave Background (CMB) radiation show that the models of inflation with the monomial potentials are inconsistent with the allowed $n_s-r$ bounds. However certain monomial…
Given a first-order sentence, a model-checking computation tests whether the sentence holds true in a given finite structure. Data provenance extracts from this computation an abstraction of the manner in which its result depends on the…
This review summarizes the historical development of probability measures in asset pricing, from early mathematical finance and state price theory to risk-neutral valuation, martingale measures, forward measures, stochastic discount…
This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite…
Quality-designed consumer products are easy to recognize. Wouldn't it be great if the quality of financial products became just as apparent? This paper is addressed to financial practitioners. It provides an informal introduction to…
This is the author's Ph.D. Thesis. It contains results from four years of research into realizability and categorical logic. The main subjects are the axiomatisation of realizable propositions, and a characterization of realizability…
Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…
The first aim of this lecture is to highlight two areas of recent progress in inflationary cosmology, namely reheating and the quantum theory of cosmological perturbations. The second aim is to discuss important conceptual problems for the…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
This report introduces a novel class of reasoning architectures, termed Quantum Circuit Reasoning Models (QCRM), which extend the concept of Variational Quantum Circuits (VQC) from energy minimization and classification tasks to structured…
We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for…
The early Universe inflation is well known as a promising theory to explain the origin of large scale structure of Universe and to solve the early universe pressing problems. For a resonable inflation model, the potential during inflation…
A simple statement and accessible proof of a version of the Fundamental Theorem of Asset Pricing in discrete time is provided. Careful distinction is made between prices and cash flows in order to provide uniform treatment of all…
This is a review article for The Review of Particle Physics 2026 (aka the Particle Data Book), appearing as Chapter 23. It forms a compact review of our understanding of cosmological inflation near the end of 2025. Topics included are…
A correction to the Quartic Hilltop inflationary model is proposed to account for stabilising terms in the potential. We derive analytical predictions for the spectral index $n_s$ and tensor-scalar ratio $r$ which lie within the Planck 2018…
In this article, we introduce a new general definition of fractional derivative and fractional integral, which depends on an unknown kernel. By using these definitions, we obtain the basic properties of fractional integral and fractional…
Computational models are quantitative representations of systems. By analyzing and comparing the outputs of such models, it is possible to gain a better understanding of the system itself. Though as the complexity of model outputs…
We provide a pedagogical overview of inflation in string theory. Our theme is the sensitivity of inflation to Planck-scale physics, which we argue provides both the primary motivation and the central theoretical challenge for the subject.…
In the field of language modeling, models augmented with retrieval components have emerged as a promising solution to address several challenges faced in the natural language processing (NLP) field, including knowledge grounding,…