Browsing by Subject "Kernel method"
Now showing 1 - 6 of 6
- Results Per Page
- Sort Options
Item Open Access Akut koroner sendromların otomatik ST/T sınıflandırıcısı ile erken tanısı(IEEE, 2014-10) Terzi, M. Begüm; Arıkan, Orhan; Abacı, A.; Candemir, M.; Dedoğlu, MehmetIn patients with acute coronary syndrome, temporary chest pains together with changes in ECG ST segment and T wave occur shortly before the start of myocardial infarction. In order to diagnose acute coronary syndromes early, a new technique which detects changes in ECG ST/T sections is developed. As a result of implementing the developed technique to real ECG recordings, it is shown that the proposed technique provides reliable detections. Therefore, the developed technique is expected to provide early diagnosis of acute coronary syndromes which will lead to a significant decrease in heart failure and mortality rates. © 2014 IEEE.Item Embargo An algorithmic approach based on generating trees for enumerating pattern-avoiding inversion sequences(Academic Press, 2024-02) Kotsireas, Ilias; Mansour, Toufik; Yıldırım, GökhanWe introduce an algorithmic approach based on a generating tree method for enumerating the inversion sequences with various pattern-avoidance restrictions. For a given set of patterns, we propose an algorithm that outputs either an accurate description of the succession rules of the corresponding generating tree or an ansatz. By using this approach, we determine the generating trees for the pattern classes In(000,021), In(100,021), In(110,021), In(102,021), In(100,012), In(011,201), In(011,210) and In(120,210). Then we use the kernel method, obtain generating functions of each class, and find enumerating formulas. Lin and Yan studied the classification of the Wilf-equivalences for inversion sequences avoiding pairs of length-three patterns and showed that there are 48 Wilf classes among 78 pairs. In this paper, we solve six open cases for such pattern classes. Moreover, we extend the algorithm to restricted growth sequences and apply it to several classes. In particular, we present explicit formulas for the generating functions of the restricted growth sequences that avoid either {12313,12323}, {12313,12323,12333}, or {123⋯ℓ1}.Item Open Access A decomposition of column-convex polyominoes and two vertex statistics(Springer, 2022-04-27) Cakić, N.; Mansour, T.; Yıldırım, GökhanWe introduce a decomposition method for column-convex polyominoes and enumerate them in terms of two statistics: the number of internal vertices and the number of corners in the boundary. We first find the generating function for the column-convex polyominoes according to the horizontal and vertical half-perimeter, and the number of interior vertices. In particular, we show that the average number of interior vertices over all column-convex polyominoes of perimeter 2n is asymptotic to αon3 / 2 where αo≈ 0.57895563 …. We also find the generating function for the column-convex polyominoes according to the horizontal and vertical half-perimeter, and the number of corners in the boundary. In particular, we show that the average number of corners over all column-convex polyominoes of perimeter 2n is asymptotic to α1n where α1≈ 1.17157287 …. © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.Item Open Access Generating tree method and applications to pattern-avoiding inversion sequences(2024-05) Gezer, MelisAn inversion sequence of length n is an integer sequence e = e1 · · · en such that 0 ≤ ei < i for each 0 ≤ i ≤ n. We use In to denote the set of inversion sequences of length n. Let [k] := {0, 1, · · · , k − 1} denote the alphabet and τ be a word of length k over this alphabet. A pattern of length k is simply a word over the alphabet [k]. We say an inversion sequence e ∈ In contains the pattern τ of length k if it contains a sub-sequence of length k that is order isomorphic to τ; otherwise, e avoids the pattern τ . For a given pattern τ , we use In(τ ) to denote the set of all τ -avoiding inversion sequences of length n. Firstly, we review the enumeration of inversion sequences that avoid patterns of length three. We then study an enumeration method based on generating trees and the kernel method to enumerate pattern-avoiding inversion sequences for general patterns. Then, we provide sampling algorithms for pattern-avoiding inversion sequences and apply them to some specific patterns. Based on extensive simulations, we study some statistics such as the number of zeros, the number of distinct elements, the number of repeated elements, and the maximum elements. Finally, we present a bijection between In(0312) and In(0321) that preserves these statistics.Item Open Access Inversion sequences avoiding 021 and another pattern of length four(D M T C S, 2023-11-17) Toufik, M.; Yıldırım, GökhanWe study the enumeration of inversion sequences that avoid pattern 021 and another pattern of length four. We determine the generating trees for all possible pattern pairs and compute the corresponding generating functions. We introduce the concept of d-regular generating trees and conjecture that for any 021-avoiding pattern τ , the generating tree T ({021, τ }) is d-regular for some integer d.Item Open Access Smart computing for large scale visual data sensing and processing(Elsevier, 2016) Zhang, L.; Duygulu, P.; Zuo, W.; Shan, S.; Hauptmann, A.