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Yazıcı, Emine Şule

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Emine Şule

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Now showing 1 - 10 of 35
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    The triangle intersection problem for K4 - E designs
    (Utilitas Mathematica Publishing Inc., 2007) Billington, Elizabeth J.; Lindner, C. C.; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432
    An edge-disjoint decomposition of the complete graph Kn into copies of K4 - e, the simple graph with four vertices and five edges, is known to exist if and only if n ≡ 0 or 1 (mod 5) and n ≥ 6 (Bermond and Schönheim, Discrete Math. 19 (1997)). The intersection problem for K4 - e designs has also been solved (Billington, M. Gionfriddo and Lindner, J. Statist. Planning Inference 58 (1997)); this problem finds the number of common K4 - e blocks which two K4 - e designs on the same set may have. Here we answer the question: how many common triangles may two K4 - e designs on the same set have? Since it is possible for two K4 - e designs on the same set to have no common K4 - e blocks and yet some positive number of common triangles, this problem is largely independent of the earlier K4 - e intersection result.
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    On regular embedding of H-designs into G-designs
    (Utilitas Mathematica, 2013) Quattrocchi, Gaetano; Department of Mathematics; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Smith, Benjamin R.; Yazıcı, Emine Şule; Faculty Member; Researcher; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 105252; N/A; 27432
    The graph H is embedded in the graph G, if H is a subgraph of G. An H-design is a decomposition of a complete graph into edge disjoint copies of the graph H, called blocks. An H-i-design with k blocks, say H-1, H-2, ...H-k is embedded in a G-design if for every H-i, there exists a distinct block, say G(i), in the G-design that embeds H-i. If G(i) are all isomorphic for 1 <= i <= k then the embedding is called regular. This paper solves the problem of the regular embedding of H-designs into G-designs when G has at most four vertices and four edges.
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    Orthogonal trades and the intersection problem for orthogonal arrays
    (Springer Japan Kk, 2016) Demirkale, Fatih; Donovan, Diane M.; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Yazıcı, Emine Şule; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; 105252; 27432
    This work provides an orthogonal trade for all possible volumes N is an element of Z(+) \ {1, 2, 3, 4, 5, 7} for block size 4. All orthogonal trades of volume N <= 15 are classified up to isomorphism for this block size. The intersection problem for orthogonal arrays with block size 4 is solved for all but finitely many possible exceptions.
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    High-rate LDPC codes from partially balanced incomplete block designs
    (Springer, 2022) Donovan, Diane; Price, Aiden; Rao, Asha; N/A; Department of Mathematics; Üsküplü, Elif; Yazıcı, Emine Şule; PhD Student; Faculty Member; Department of Mathematics; Graduate School of Sciences and Engineering; College of Sciences; N/A; 27432
    This paper presents a combinatorial construction of low-density parity-check (LDPC) codes from partially balanced incomplete block designs. Since Gallager's construction of LDPC codes by randomly allocating bits in a sparse parity-check matrix, many researchers have used a variety of more structured combinatorial approaches. Many of these constructions start with the Galois field; however, this limits the choice of parameters of the constructed codes. Here we present a construction of LDPC codes of length 4n(2) - 2n for all n using the cyclic group of order 2n. These codes achieve high information rate (greater than 0.8) for n >= 8, have girth at least 6 and have minimum distance 6 for n odd. The results provide proof of concept and lay the groundwork for potential high performing codes.
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    Square integer Heffter arrays with empty cells
    (Springer, 2015) Archdeacon, Dan S.; Dinitz, Jeffrey H.; Donovan, Diane M.; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432
    A Heffter array is an matrix with nonzero entries from such that (i) each row contains filled cells and each column contains filled cells, (ii) every row and column sum to 0, and (iii) no element from appears twice. Heffter arrays are useful in embedding the complete graph on an orientable surface where the embedding has the property that each edge borders exactly one s-cycle and one t-cycle. Archdeacon, Boothby and Dinitz proved that these arrays can be constructed in the case when , i.e every cell is filled. In this paper we concentrate on square arrays with empty cells where every row sum and every column sum is in . We solve most of the instances of this case.
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    Embedding 4-cycle systems into octagon triple systems
    (2009) Billington, Elizabeth J.; Lindner, Curt; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Yazıcı, Emine Şule; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; 105252; 27432
    An octagon triple is the graph consisting of the four triangles (triples) {a, b,c}, {c, d,e}, {e, f,g}, and {g, h,a}, where a,b,c, d,e, f, g and h axe distinct. The 4-cycle (a, c, e, g) is called an inside 4-cycle. An octagon triple system of order n is a pair (X,O), where O is a collection of edge disjoint octagon triples which partitions the edge set of K-n with vertex set X. Let (X, O) be an octagon triple system and let P be the collection of inside 4-cycles. Then (X, P) is a partial 4-cycle system of order n. It is not possible for (X, P) to be a 4-cycle system (not enough 4-cycles). So the problem of determining for each n the smallest octagon triple system whose inside 4-cycles contain a 4-cycle system of order 8n + 1 is immediate. The object of this note is to determine the spectrum for octagon triple systems and to construct for every n a 4-cycle system of order k = 8n + 1 that can be embedded in the inside 4-cycles of some octagon triple system of order approximately 3k. This is probably not the best possible embedding (the best embedding is approximately 2k + 1), but it is a good start.
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    The full metamorphosis of lambda-fold block designs with block size four into lambda-fold kite systems
    (Utilitas Mathematica Publishing, 2013) N/A; Department of Mathematics; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Smith, Benjamin R.; Yazıcı, Emine Şule; Faculty Member; Researcher; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; College of Sciences; 105252; N/A; 27432
    Let(X,B)be a λ-fold block design with block size 4. If a path of length two is removed from each block of B the resulting collection of kites K is a partial λ-fold kite system(X,K). If the deleted edges can be arranged into a collection of kites D,then(X,K ∪ D)is a λ-fold kite system [5]. Now for each block 6 ∈ B let {P1(6),P 2(b),P3(b)} be a partition of b into paths of length two and define for each i = 1,2,3, sets Ki and Di as follows: for each b ∈ B,put the kite b\Pi(b)in Ki and the two edges belonging to the path Pi(b)in Di. If the edges in Di can be arranged into a collection of kites Di * then Mi =(X,Ki∪Di *)is a λ-fold kite system,called the ith metamorphosis of(X,B). The full metamorphosis is the set of three metamorphoses {M 1,M2,M3}. We give a complete solution of the following problem: for which n and A does there exist a λ-fold block design with block size 4 having a full metamorphosis into a λ-fold kite system?
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    Improved learning cycle assessment of stimulated wells' performance through advanced mathematical modeling
    (Soc Petroleum Eng, 2022) Donovan, Diane; Azadi, Mohsen; Ganpule, Sameer; Nuralishahi, Turaj; Smith, Andrew; Josserand, Sylvain; Thompson, Bevan; Reay, Thomas; Gay, Laura; Burrage, Kevin; Burrage, Pamela; Lawson, Brodie; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432
    In this paper, we forecast cumulative production for stimulated gas wells using a combination of fast-to-implement modeling methodologies, including polynomial chaos expansion (PCE) and Gaussian processes (GP) proxy models coupled with populations of phenomenological models (POMs). These modeling techniques allow for a reduction in forecast uncertainty and are shown to be effective techniques for extrapolating early time data for stimulated well production from a field of wells in the Surat Basin, Queensland, Australia. The proposed techniques strategically capture and capitalize on production trends across an entire gas field, even in the presence of early production transients. We demonstrate that learning cycles can be shortened, leading to reasonable forecasts, as well as meaningful and actionable insights.
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    The full metamorphosis of λ-fold block designs with block size four into A-fold 4-cycle systems
    (Charles Babbage Res Ctr, 2012) Lindner, Charles Curtis; Department of Mathematics; Department of Mathematics; Küçükçifçi, Selda; Yazıcı, Emine Şule; Faculty Member; Faculty Member; Department of Mathematics; College of Sciences; College of Sciences; 105252; 27432
    Let (X, B) be a lambda-fold block design with block size 4. If a pair of disjoint edges are removed from each block of B the resulting collection of 4-cycles C is a partial lambda-fold 4-cycle system (X, C). If the deleted edges can be arranged into a collection of 4-cycles D, then (X,C boolean OR D) is a lambda-fold 4-cycle system [10]. Now for each block b is an element of B specify a 1-factorization of b as {F-1(b), F-2(b), F-3(b)} and define for each i = 1,2,3, sets C-i and D-i as follows: for each b is an element of B, put the 4-cycle b backslash F-i(b) in C-i and the 2 edges belonging to F-i(b) in D-i. If the edges in D-i can be arranged into a collection of 4-cycles D-i* then M-i = (X, C-i boolean OR D-i*) is a lambda-fold 4-cycle system, called the ith metamorphosis of (X, B). The full metamorphosis is the set of three metamorphoses {M-1, M-2, M-3}. We give a complete solution of the following problem: for which n and lambda does there exist a lambda-fold block design with block size 4 having a full metamorphosis into a lambda-fold 4-cycle system?
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    Constructing and embedding mutually orthogonal Latin squares: reviewing both new and existing results
    (Charles University Faculty of Mathematics and Physics, 2020) Donovan, Diane M.; Grannell, Mike; Department of Mathematics; Yazıcı, Emine Şule; Faculty Member; Department of Mathematics; College of Sciences; 27432
    We review results for the embedding of orthogonal partial Latin squares in orthogonal Latin squares, comparing and contrasting these with results for embedding partial Latin squares in Latin squares. We also present a new construction that uses the existence of a set of t mutually orthogonal Latin squares of order n to construct a set of 2t mutually orthogonal Latin squares of order n(t).