Search results for "Integer"
showing 10 items of 250 documents
Packing a Trunk
2003
We report on a project with a German car manufacturer. The task is to compute (approximate) solutions to a specific large-scale packing problem. Given a polyhedral model of a car trunk, the aim is to pack as many identical boxes of size 4 × 2 × 1 units as possible into the interior of the trunk. This measure is important for car manufacturers, because it is a standard in the European Union.
Markov Chains and Electrical Networks
2020
There is a natural connection between electrical networks and so called reversible Markov chains. An example for such a chain is the symmetric graph random walk which, in each step, jumps to a randomly chosen graph neighbor at equal probability. This connection is studied here in some detail. As an application, we prove the statement that if such a graph random walk is recurrent, then it is recurrent also on each subgraph. (Although this statement is rather plausible, it is hard to show by different means.) In particular, the graph random walk on a percolation cluster of the planar integer lattice is recurrent.
Groups whose real irreducible characters have degrees coprime to p
2012
Abstract In this paper we study groups for which every real irreducible character has degree not divisible by some given odd prime p .
On embedding Boolean as a subtype of integer
1990
Integer Weighted Regression Tsetlin Machines
2020
The Regression Tsetlin Machine (RTM) addresses the lack of interpretability impeding state-of-the-art nonlinear regression models. It does this by using conjunctive clauses in propositional logic to capture the underlying non-linear frequent patterns in the data. These, in turn, are combined into a continuous output through summation, akin to a linear regression function, however, with non-linear components and binary weights. However, the resolution of the RTM output is proportional to the number of clauses employed. This means that computation cost increases with resolution. To address this problem, we here introduce integer weighted RTM clauses. Our integer weighted clause is a compact r…
Optimised assembly mode reconfiguration of the 5-DOF Gantry-Tau using mixed-integer programming
2010
Pulished version of an article in the journal: Meccanica. Also available from the publisher at: http://dx.doi.org/10.1007/s11012-010-9404-y This paper presents a systematic approach based on Mixed Integer Linear Programming for finding an optimal singularity-free reconfiguration path of the 5-DOF Gantry-Tau parallel kinematic machine. The results in the paper demonstrate that singularity-free reconfiguration (change of assembly mode) of the machine is possible, which significantly increases the usable workspace. The method has been applied to a full-scale prototype and the singularity-free path has been verified both in simulations and with physical experiments using real-time control of th…
Perceived-Value-driven Optimization of Energy Consumption in Smart Homes
2020
Residential energy consumption has been rising rapidly during the last few decades. Several research efforts have been made to reduce residential energy consumption, including demand response and smart residential environments. However, recent research has shown that these approaches may actually cause an increase in the overall consumption, due to the complex psychological processes that occur when human users interact with these energy management systems. In this article, using an interdisciplinary approach, we introduce a perceived-value driven framework for energy management in smart residential environments that considers how users perceive values of different appliances and how the us…
Elementary Integration of Superelliptic Integrals
2021
Consider a superelliptic integral $I=\int P/(Q S^{1/k}) dx$ with $\mathbb{K}=\mathbb{Q}(\xi)$, $\xi$ a primitive $k$th root of unity, $P,Q,S\in\mathbb{K}[x]$ and $S$ has simple roots and degree coprime with $k$. Note $d$ the maximum of the degree of $P,Q,S$, $h$ the logarithmic height of the coefficients and $g$ the genus of $y^k-S(x)$. We present an algorithm which solves the elementary integration problem of $I$ generically in $O((kd)^{\omega+2g+1} h^{g+1})$ operations.
Reliable Propagation of Magnetic Domain Walls in Cross Structures for Advanced Multiturn Sensors
2017
[EN] We develop and analyze an advanced concept for a domain-wall-based sensing of rotations. Moving domain walls in n closed loops with n - 1 intersecting convolutions by rotating fields, we are able to sense n rotations. By combining loops with coprime numbers of rotations, we create a sensor system allowing for the total counting of millions of turns of a rotating applied magnetic field. We analyze the operation of the sensor and identify the intersecting cross structures as the critical component for reliable operation. Specifically, depending on the orientation of the applied field angle with the magnetization in the branches of the cross, a domain wall is found to propagate in an unwa…
Electrically Conductive Phthalocyanine Assemblies. Structural and Non-Integer Oxidation Number Considerations
1990
Aggregation is a well-known phenomenon in phthalocyanine chemistry. Interactions can occur between adjacent phthalocyanine rings, both in organic and aqueous phases, resulting in coupling between the electronic states of two, or more, phthalocyanine units [1].