Robust, Universal Tree Balance Indices

Balance indices that quantify the symmetry of branching events and the compactness of trees are widely used to compare evolutionary processes or tree-generating algorithms. Yet existing indices have important shortcomings, including that they are unsuited to the tree types commonly used to describe the evolution of tumours, microbial populations, and cell lines. The contributions of this article are twofold. First, we define a new class of robust, universal tree balance indices. These indices take a form similar to Colless’ index but account for node sizes, are defined for trees with any degree distribution, and enable more meaningful comparison of trees with different numbers of leaves. Second, we show that for bifurcating and all other full m-ary cladograms (in which every internal node has the same out-degree), one such Colless-like index is equivalent to the normalised reciprocal of Sackin’s index. Hence we both unify and generalise the two most popular existing tree balance indices. Our indices are intrinsically normalised and can be computed in linear time. We conclude that these more widely applicable indices have potential to supersede those in current use.

On the exhaustive generation of generalized ballot sequences in lexicographic and Gray code order

A generalized (resp. p-ary) ballot sequence is a sequence over the set of non-negative integers (resp. integers less than p) where in any of its prefixes each positive integer i occurs at most as often as any integer less than i. We show that the Reected Gray Code order induces a cyclic 3-adjacent Gray code on both, the set of fixed length generalized ballot sequences and p-ary ballot sequences when p is even, that is, ordered list where consecutive sequences (regarding the list cyclically) differ in at most 3 adjacent positions. Non-trivial efficient generating algorithms for these ballot sequences, in lexicographic order and for the obtained Gray codes, are also presented.

PENGAMANAN CITRA DENGAN ALGORITMA DIFFIE-HELLMAN DAN ALGORITMA SIMPLIFIED DATA ENCRYPTION STANDARD (S-DES)

Simplified Data Encryption Standard (S-DES) is a cryptographic algorithm whose data-disguise process is simple and fast enough compared to other algorithms. Because of its simplicity, the S-DES algorithm is vulnerable to statistical attacks when applied to imagery, so this study tries to minimize S-DES weaknesses in image data by modifying S-DES keys with Diffie-Hellman. Diffie-Hellman is one of the key generating algorithms and key exchange. This research uses image data that is RGB image and grayscale image. A modified S-DES key with Diffie-Hellman is then used to encrypt the image. This study also analyzed the security level of S-DES algorithm that the key has been modified with Diffie-Hellman.

Effects of DEM Generating Algorithms on Water Retention Calculations in Polders – A Case Study

Digital Elevation Models have been an important topic in the last decades in order to accurately describe one’s surroundings for various purposes. The most wide-spread applications of Digital Elevation Modelling are related to volumetric calculations over large areas, as well as to hydrographic simulations. This paper will analyse the impact of various data interpolation models on the result of volumetric calculations in a longitudinal shaped polder. In order to achieve general conclusions instead of case specific solutions, the raw parametric Digital Elevation Models have been used, rather than the specific parameters suiting the actual scenario. In order to achieve this, data smoothing has also been neglected. The result of the conducted study presents the impact of the digital elevation modelling methods over the volumetric calculations. When applied to the same dataset, the methods yielded different results, partially confirming the predicted usefulness of the algorithms.

Comparison of Instantaneous Reactive and Notch Filter Algorithms Seven Level Parallel Active Filter

<p class="Abstract">This work focused on the association of a seven level Neutral Point Clamped inverter and a parallel active filter. In order to test the efficiency of the 7 level parallel active filter, two reference current generating algorithms are used. The instantaneous reactive power algorithm and the notch filter algorithm. In this study, the instantaneous reactive power method and the notch filter method are presented. Than a section which gives a recall of the NPC multilevel inverter and PWM strategy. A comparison between the two reference current generating algorithms is made. The subjects of comparison are the total harmonic distortion (THD) and the fundamental value of the source current. The obtained simulation results have proved that the instantaneous reactive power technique is better than the notch filter technique. Simulations are carried out by PSIM program.</p>

An Assessment of Algorithms for Deriving Failure Deterministic Finite Automata

Failure deterministic finite automata (FDFAs) represent regular languages more compactly than deterministic finite automata (DFAs). Four algorithms that convert arbitrary DFAs to language-equivalent FDFAs are empirically investigated. Three are concrete variants of a previously published abstract algorithm, the DFA-Homomorphic Algorithm (DHA). The fourth builds a maximal spanning tree from the DFA to derive what it calls a delayed input DFA. A first suite of test data consists of DFAs that recognise randomised sets of finite length keywords. Since the classical Aho-Corasick algorithm builds an optimal FDFA from such a set (and only from such a set), it provides benchmark FDFAs against which the performance of the general algorithms can be compared. A second suite of test data consists of random DFAs generated by a specially designed algorithm that also builds language-equivalent FDFAs, some of which may have non-divergent cycles. These random FDFAs provide (not necessarily tight) lower bounds for assessing the effectiveness of the four general FDFA generating algorithms.