Mumford dendrograms and discrete p-adic symmetries

In this article, we present an effective encoding of dendrograms by embedding them into the Bruhat-Tits trees associated to $p$-adic number fields. As an application, we show how strings over a finite alphabet can be encoded in cyclotomic extensions of $\mathbb{Q}_p$ and discuss $p$-adic DNA encoding. The application leads to fast $p$-adic agglomerative hierarchic algorithms similar to the ones recently used e.g. by A. Khrennikov and others. From the viewpoint of $p$-adic geometry, to encode a dendrogram $X$ in a $p$-adic field $K$ means to fix a set $S$ of $K$-rational punctures on the $p$-adic projective line $\mathbb{P}^1$. To $\mathbb{P}^1\setminus S$ is associated in a natural way a subtree inside the Bruhat-Tits tree which recovers $X$, a method first used by F. Kato in 1999 in the classification of discrete subgroups of $\textrm{PGL}_2(K)$. Next, we show how the $p$-adic moduli space $\mathfrak{M}_{0,n}$ of $\mathbb{P}^1$ with $n$ punctures can be applied to the study of time series of dendrograms and those symmetries arising from hyperbolic actions on $\mathbb{P}^1$. In this way, we can associate to certain classes of dynamical systems a Mumford curve, i.e. a $p$-adic algebraic curve with totally degenerate reduction modulo $p$. Finally, we indicate some of our results in the study of general discrete actions on $\mathbb{P}^1$, and their relation to $p$-adic Hurwitz spaces.Comment: 14 pages, 6 figure

Experiences with and interpretation of standard test methods of building energy analysis tools

The authors separately apply ANSI/ASHRAE Standard 140-2001 to the simulation program TRNSYS, comparing not only their results but the differences in their simulation assumptions and in their interpretations of the Standard's test cases. Results of the application are presented for all three authors, showing that there is a significant amount of leeway within a complex simulation tool such asTRNSYS for users of different backgrounds to apply their own common simulating practices and still fall comfortably within the range of acceptability specified by such Standards. Included in the application results are results of sensitivity tests that demonstrate the relative importance of assumption differences

A pp-adic RanSaC algorithm for stereo vision using Hensel lifting

A $p$-adic variation of the Ran(dom) Sa(mple) C(onsensus) method for solving the relative pose problem in stereo vision is developped. From two 2-adically encoded images a random sample of five pairs of corresponding points is taken, and the equations for the essential matrix are solved by lifting solutions modulo 2 to the 2-adic integers. A recently devised $p$-adic hierarchical classification algorithm imitating the known LBG quantisation method classifies the solutions for all the samples after having determined the number of clusters using the known intra-inter validity of clusterings. In the successful case, a cluster ranking will determine the cluster containing a 2-adic approximation to the "true" solution of the problem.Comment: 15 pages; typos removed, abstract changed, computation error remove

Converging on a recommended set of interpretations and assumptions in applying standard tests to energy analysis tools

The authors, having individually applied ANSI/ASHRAE Standard 140-2001 to the simulation program TRNSYS in a previous project, compare their results, simulation assumptions, and interpretations of the Standard's test cases to arrive at a conformed set of recommended practices. Sensitivities to individual assumptions are investigated and results of applying the conformed set of assumptions are presented

Combining different validation techniques for continuous software improvement - Implications in the development of TRNSYS 16

Validation using published, high quality test suites can serve to identify different problems in simulation software: modeling and coding errors, missing features, frequent sources of user confusion. This paper discusses the application of different published validation procedures during the development of a new TRNSYS version: BESTEST/ASHRAE 140 (Building envelope), HVAC BESTEST (mechanical systems) and IEA ECBCS Annex 21 / SHC Task 12 empirical validation (performance of a test cell with a very simple mechanical system). It is shown that each validation suite has allowed to identify different types of problems. Those validation tools were also used to diagnose and fix some of the identified problems, and to assess the influence of code modifications. The paper also discusses some limitations of the selected validation tools

Vibration limiting of rotors by feedback control

Experimental findings of a three mass rotor with four channels of feedback control are reported. The channels are independently controllable with force being proportional to the velocity and/or instantaneous displacement from equilibrium of the shaft at the noncontacting probe locations (arranged in the vertical and horizontal attitudes near the support bearings). The findings suggest that automatic feedback control of rotors is feasible for limiting certain vibration levels. Control of one end of a rotor does afford some predictable vibration limiting of the rotor at the other end

Effect of Urea and Distillers Inclusion in Dry- Rolled Corn Based Diets on Heifer Performance and Carcass Characteristics

Crossbred heifers (n=96, BW = 810 ± 20) were utilized to evaluate the effects of increasing wet distillers grains plus solubles and urea inclusion in a dry rolled corn based finishing diet on performance and carcass characteristics. Heifers were individually fed using a calan gate system with a 2 × 2 factorial arrangement of treatments. Factors included distillers inclusion at either 10 or 20% of diet DM and urea inclusion at either 0.2 or 1.4% of diet DM. Th ere was no difference for final body weight, average daily gain, and feed conversion on a live or carcass adjusted basis for either urea or distillers inclusion in the diet. Dry matter intake was reduced with increased urea inclusion; however, distillers inclusion did not influence intake. Added distillers and urea in the diet had minimal impact on performance suggesting supplemental urea in a dry rolled corn based finishing diets is of minimal benefit when feeding at least 10% distillers grains

Simulation synergy : expanding TRNSYS capabilities and usability

Developers of simulation packages are now able to take advantage of the increase in available desktop computing power to expand the capabilities and usability of their programs. This paper will illustrate these opportunities by discussing the different techniques the developers of the TRNSYS software package have used to try and create a synergy between TRNSYS and external programs and between the developers and users of the program