相关论文: Complex Analysis as Catalyst

The proliferation of deep learning techniques led to a wide range of advanced analytics applications in important business areas such as predictive maintenance or product recommendation. However, as the effectiveness of advanced analytics…

Representations are essential to mathematically model phenomena, but there are many options available. While each of those options provides useful properties with which to solve problems related to the phenomena in study, comparing results…

Circuit complexity has been used as a tool to study various properties in condensed matter systems, in particular as a way to probe the phase diagram. However, compared with measures based on entanglement, complexity has been found lacking.…

Classic economic science is reaching the limits of its explanatory powers. Complexity science uses an increasingly larger set of different methods to analyze physical, biological, cultural, social, and economic factors, providing a broader…

Meta-analysis is commonly used to combine results from multiple clinical trials, but traditional meta-analysis methods do not refer explicitly to a population of individuals to whom the results apply and it is not clear how to use their…

We apply methods of nonstandard mathematics in order to regard analytic geometry in a very different way. For example, complex spaces are seen to be the "standard part" of certain algebraic nonstandard schemes. We construct a category of…

Real numbers provide a sufficient description of classical physics and all measurable phenomena; however, complex numbers are occasionally utilized as a convenient mathematical tool to aid our calculations. On the other hand, the formalism…

Data analysis often involves the comparison of complex objects. With the ever increasing amounts and complexity of data, the demand for systems to help with these comparisons is also growing. Increasingly, information visualization tools…

We argue that complex systems science and the rules of quantum physics are intricately related. We discuss a range of quantum phenomena, such as cryptography, computation and quantum phases, and the rules responsible for their complexity.…

We present an overview of the decision-theoretic framework of statistical causality, which is well-suited for formulating and solving problems of determining the effects of applied causes. The approach is described in detail, and is related…

This is not a new result. Purpose of this work is to describe a method to search the analytical expression of the general real solution of the two-dimensional Laplace differential equation. This thing is not easy to find in scientific…

Complex vector analysis is widely used to analyze continuous systems in many disciplines, including physics and engineering. In this paper, we present a higher-order-logic formalization of the complex vector space to facilitate conducting…

Principles of analogical reasoning have recently been applied in the context of machine learning, for example to develop new methods for classification and preference learning. In this paper, we argue that, while analogical reasoning is…

Probabilistic programming is a growing area that strives to make statistical analysis more accessible, by separating probabilistic modelling from probabilistic inference. In practice this decoupling is difficult. No single inference…

The study of complex systems through the lens of category theory consistently proves to be a powerful approach. We propose that cognition deserves the same category-theoretic treatment. We show that by considering a highly-compact cognitive…

We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…

The domain of cluster analysis is a meeting point for a very rich multidisciplinary encounter, with cluster-analytic methods being studied and developed in discrete mathematics, numerical analysis, statistics, data analysis, data science,…

In this chapter the complex systems are discussed in the context of economic and business policy and decision making. It will be showed and motivated that social systems are typically chaotic, non-linear and/or non-equilibrium and therefore…

Causal inference plays an important role in explanatory analysis and decision making across various fields like statistics, marketing, health care, and education. Its main task is to estimate treatment effects and make intervention…

There has been growing interest in developing accurate models that can also be explained to humans. Unfortunately, if there exist multiple distinct but accurate models for some dataset, current machine learning methods are unlikely to find…