Flying-capacitor multilevel converter voltage balance dynamics for pure resistive load

Multilevel converters need voltage balancing to be able to generate an output voltage with high quality. Flying capacitor converter topology has a natural voltage balancing property. Voltage balance dynamics analytical research methods reported to date are essentially based on a frequency domain analysis using double fourier transform. These complicated methods are not truly analytical, which makes an understanding of parameter influence on time constants difficult. In this paper, a straightforward time domain approach based on stitching of switch intervals piece-wise analytical solutions to a DC modulated H-bridge flying capacitor converter is discussed. This method allows to obtain time-averaged discrete and continuous voltage balance dynamics models. Using small-parameter approximation for pure resistive loads, simple and accurate expressions for voltage balance time constants are deduced, revealing their dependence on load parameters, carrier frequency and duty ratio

Continuous-Time Random Walks at All Times

Continuous-time random walks (CTRW) play important role in understanding of a wide range of phenomena. However, most theoretical studies of these models concentrate only on stationary-state dynamics. We present a new theoretical approach, based on generalized master equations picture, that allowed us to obtain explicit expressions for Laplace transforms for all dynamic quantities for different CTRW models. This theoretical method leads to the effective description of CTRW at all times. Specific calculations are performed for homogeneous, periodic models and for CTRW with irreversible detachments. The approach to stationary states for CTRW is analyzed. Our results are also used to analyze generalized fluctuations theorem

PEALT: A reasoning tool for numerical aggregation of trust evidence

We present a tool that supports the understanding and validation of mechanisms that numerically aggregate trust evidence { which may stem from heterogenous sources such as geographical information, reputation, and threat levels. The tool is based on a policy com- position language Peal [3] and can declare Peal expressions and intended analyses of such expressions as input. The analyses include vacuity checking, sensitivity analysis of thresh- olds, and policy re nement. We develop and implement two methods for generating veri - cation conditions for analyses, using the SMT solver Z3 as backend. One method is explicit and space intense, the other one is symbolic and so linear in the analysis expressions. We experimentally investigate this space-time tradeo by observing the Z3 code generation and its running time on randomly generated analyses and on a non-random benchmark modeling majority voting. Our ndings suggest both methods have complementary value and may scale up su ciently for the analysis of most realistic case studies

Finite Expression Method for Solving High-Dimensional Partial Differential Equations

Designing efficient and accurate numerical solvers for high-dimensional partial differential equations (PDEs) remains a challenging and important topic in computational science and engineering, mainly due to the "curse of dimensionality" in designing numerical schemes that scale in dimension. This paper introduces a new methodology that seeks an approximate PDE solution in the space of functions with finitely many analytic expressions and, hence, this methodology is named the finite expression method (FEX). It is proved in approximation theory that FEX can avoid the curse of dimensionality. As a proof of concept, a deep reinforcement learning method is proposed to implement FEX for various high-dimensional PDEs in different dimensions, achieving high and even machine accuracy with a memory complexity polynomial in dimension and an amenable time complexity. An approximate solution with finite analytic expressions also provides interpretable insights into the ground truth PDE solution, which can further help to advance the understanding of physical systems and design postprocessing techniques for a refined solution

Boosting-based Construction of BDDs for Linear Threshold Functions and Its Application to Verification of Neural Networks

Understanding the characteristics of neural networks is important but difficult due to their complex structures and behaviors. Some previous work proposes to transform neural networks into equivalent Boolean expressions and apply verification techniques for characteristics of interest. This approach is promising since rich results of verification techniques for circuits and other Boolean expressions can be readily applied. The bottleneck is the time complexity of the transformation. More precisely, (i) each neuron of the network, i.e., a linear threshold function, is converted to a Binary Decision Diagram (BDD), and (ii) they are further combined into some final form, such as Boolean circuits. For a linear threshold function with $n$ variables, an existing method takes $O(n2^{\frac{n}{2}})$ time to construct an ordered BDD of size $O(2^{\frac{n}{2}})$ consistent with some variable ordering. However, it is non-trivial to choose a variable ordering producing a small BDD among $n!$ candidates. We propose a method to convert a linear threshold function to a specific form of a BDD based on the boosting approach in the machine learning literature. Our method takes $O(2^n \text{poly}(1/\rho))$ time and outputs BDD of size $O(\frac{n^2}{\rho^4}\ln{\frac{1}{\rho}})$, where $\rho$ is the margin of some consistent linear threshold function. Our method does not need to search for good variable orderings and produces a smaller expression when the margin of the linear threshold function is large. More precisely, our method is based on our new boosting algorithm, which is of independent interest. We also propose a method to combine them into the final Boolean expression representing the neural network