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Towards an algorithmic synthesis of thermofluid systems
Individual technical components are usually well optimized. However, the design process of entire technical systems, especially in its early stages,...
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Biased Monte Carlo Simulation, Multilevel Paradigm
We introduce in this chapter the paradigm of multilevel simulation whose aim is to dramatically reduce the bias in a Monte Carlo simulation when the...
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Probabilistic and Bayesian Networks
This chapter introduces several important probabilistic models. Bayesian network is a well-known probabilistic model in machine learning. Hidden...
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Fpt-Reducibility to SAT
In the traditional parameterized complexity literature, the concept of fixed-parameter tractability is commonly used as a desideratum for algorithms...
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Deep Composition of Tensor-Trains Using Squared Inverse Rosenblatt Transports
Characterising intractable high-dimensional random variables is one of the fundamental challenges in stochastic computation. The recent surge of...
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Lectures on the Ising and Potts Models on the Hypercubic Lattice
Phase transitions are a central theme of statistical mechanics, and of probability more generally. Lattice spin models represent a general paradigm...
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Quite free complicated abelian groups, pcf and black boxes
We would like to build Abelian groups (or R -modules) which on the one hand are quite free, say ℵ ω+1 -free, and on the other hand are complicated in a...
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Lum**s of Algebraic Markov Chains Arise from Subquotients
A function on the state space of a Markov chain is a “lum**” if observing only the function values gives a Markov chain. We give very general...
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Stochastic Population Kinetics and Its Underlying Mathematicothermodynamics
Based on differential calculus, classical mechanics represents the natural world in terms of featureless point masses and their movements. Chemistry...
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Some Basic Mathematical Exercises
This chapter begins with drill exercises—those used to drill students until they acquire the necessary skills to move on. Drill exercises can range...
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Strong positivity for quantum theta bases of quantum cluster algebras
We construct “quantum theta bases,” extending the set of quantum cluster monomials, for various versions of skew-symmetric quantum cluster algebras....
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Network-based naive Bayes model for social network
Naive Bayes (NB) is one of the most popular classification methods. It is particularly useful when the dimension of the predictor is high and data...
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Lie–Butcher Series, Geometry, Algebra and Computation
Lie–Butcher (LB) series are formal power series expressed in terms of trees and forests. On the geometric side LB-series generalizes classical...
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Asymptotic Relative Risk Results from a Simplified Armitage and Doll Model of Carcinogenesis
We examine basic asymptotic properties of relative risk for two families of generalized Erlang processes (where each one is based off of a simplified...
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Diffusion
In the last chapter we examined how to use the kinetics of reactions to model the rate of change of populations, or concentrations. We did not...
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Ringel duality for certain strongly quasi-hereditary algebras
We study quasi-hereditary endomorphism algebras defined over a new class of finite dimensional monomial algebras with a special ideal structure. The...
