The Experts below are selected from a list of 303 Experts worldwide ranked by ideXlab platform
Ushio Tanaka - One of the best experts on this subject based on the ideXlab platform.
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GSI - On Geometric Properties of the Textile Set and Strict Textile Set
Lecture Notes in Computer Science, 2019Co-Authors: Tomonari Sei, Ushio TanakaAbstract:The textile plot is a tool for data visualisation proposed by Kumasaka and Shibata (2008). The textile set is a geometric object constructed to understand the textile plot outputs. In this study, we find additional facts on a Proper Subset called the strict textile set. Furthermore, we investigate differential and analytical geometric Properties of the textile set.
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On Geometric Properties of the Textile Set and Strict Textile Set
Geometric Science of Information, 2019Co-Authors: Tomonari Sei, Ushio TanakaAbstract:The textile plot is a tool for data visualisation proposed by Kumasaka and Shibata (2008). The textile set is a geometric object constructed to understand the textile plot outputs. In this study, we find additional facts on a Proper Subset called the strict textile set. Furthermore, we investigate differential and analytical geometric Properties of the textile set.
Tomonari Sei - One of the best experts on this subject based on the ideXlab platform.
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GSI - On Geometric Properties of the Textile Set and Strict Textile Set
Lecture Notes in Computer Science, 2019Co-Authors: Tomonari Sei, Ushio TanakaAbstract:The textile plot is a tool for data visualisation proposed by Kumasaka and Shibata (2008). The textile set is a geometric object constructed to understand the textile plot outputs. In this study, we find additional facts on a Proper Subset called the strict textile set. Furthermore, we investigate differential and analytical geometric Properties of the textile set.
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On Geometric Properties of the Textile Set and Strict Textile Set
Geometric Science of Information, 2019Co-Authors: Tomonari Sei, Ushio TanakaAbstract:The textile plot is a tool for data visualisation proposed by Kumasaka and Shibata (2008). The textile set is a geometric object constructed to understand the textile plot outputs. In this study, we find additional facts on a Proper Subset called the strict textile set. Furthermore, we investigate differential and analytical geometric Properties of the textile set.
Dong Wan Shin - One of the best experts on this subject based on the ideXlab platform.
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On geometric ergodicity of the MTAR process
Statistics & Probability Letters, 2000Co-Authors: Dong Wan ShinAbstract:We consider the momentum threshold autoregressive (MTAR) process and characterize the region of the autoregressive coefficients for geometric ergodicity. The region is a Proper Subset of the ergodic region of the TAR process. We show that the process is geometrically ergodic inside the region and is transient outside the closure of the region.
Wb Vasantha Kandasamy - One of the best experts on this subject based on the ideXlab platform.
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A Smarandache Weak Structure
viXra, 2014Co-Authors: Wb Vasantha KandasamyAbstract:A Smarandache Weak Structure on a set S means a structure on S that has a Proper Subset P with a weaker structure. By Proper Subset of a set S, we mean a Subset P of S, different from the empty set, from the original set S, and from the idempotent elements if any.
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Smarandache Rings
2003Co-Authors: Wb Vasantha KandasamyAbstract:Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a Proper Subset B which is embedded with a stronger structure S. By Proper Subset one understands a set included in A, different from the empty set, from the unit element if any, and from A. These types of structures occur in our everyday's life thats why we study them in this book. Thus, as two particular cases: A Smarandache Ring of level I (S-ring I) is a ring R that contains a Proper Subset that is a field with respect to the operations induced. A Smarandache Ring of level II (S-ring II) is a ring R that contains a Proper Subset A that verifies: A is an additive abelian group; A is a semigroup under multiplication, for a, b belonging to A, a . b = 0 if and only if a = 0 or b = 0.
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Smarandache Loops
2003Co-Authors: Wb Vasantha KandasamyAbstract:Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a Proper Subset B which is embedded with a stronger structure S. By Proper Subset one understands a set included in A, different from the empty set, from the unit element if any, and from A. These types of structures occur in our everyday's life, thats why we study them in this book. As an example: A non-empty set L is said to form a loop, if on L is defined a binary operation called product, denoted by '.' such that: for all a, b belonging to L we have a . b belonging to L (closure Property); there exists an element e belonging to L such that a . e = e . a = a for all a belonging to L (e is the identity element of L); for every ordered pair (a, b) belonging to L x L there exists a unique pair (p, q) in L such that ap = b and qa = b. Whence: A Smarandache Loop (or S-Loop) is a loop L such that a Proper Subset M of L is a subgroup (with respect to the same induced operation).
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Smarandache Non-associative rings
2002Co-Authors: Wb Vasantha KandasamyAbstract:Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a Proper Subset B contained in A which is embedded with a stronger structure S. These types of structures occur in our everyday's life, that's why we study them in this book. Thus, as a particular case: A non-associative ring is a non-empty set R together with two binary operations '+' and '.' such that (R, +) is an additive abelian group and (R, .) is a groupoid. For all a, b, c belonging to R we have (a + b) . c = a . c + b . c and c . (a + b) = c . a + c . b. A Smarandache non-associative ring is a non-associative ring (R, +, .) which has a Proper Subset P contained in R, that is an associative ring (with respect to the same binary operations on R).
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Smarandache Semigroups
2002Co-Authors: Wb Vasantha KandasamyAbstract:Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a Proper Subset B contained in A which is embedded with a stronger structure S. These types of structures occur in our everyday life, that's why we study them in this book. Thus, as a particular case: A Smarandache semigroup is a semigroup A which has a Proper Subset B contained in A that is a group (with respect to the same binary operation on A).
David Fernández-baca - One of the best experts on this subject based on the ideXlab platform.
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Incompatible quartets, triplets, and characters
Algorithms for molecular biology : AMB, 2013Co-Authors: Brad Shutters, Sudheer Vakati, David Fernández-bacaAbstract:We study a long standing conjecture on the necessary and sufficient conditions for the compatibility of multi-state characters: There exists a function f(r) such that, for any set C of r-state characters, C is compatible if and only if every Subset of f(r) characters of C is compatible. We show that for every r≥2, there exists an incompatible set C of Ω(r2)r-state characters such that every Proper Subset of C is compatible. This improves the previous lower bound of f(r)≥r given by Meacham (1983), and f(4)≥5 given by Habib and To (2011). For the case when r=3, Lam, Gusfield and Sridhar (2011) recently showed that f(3)=3. We give an independent proof of this result and completely characterize the sets of pairwise compatible 3-state characters by a single forbidden intersection pattern. Our lower bound on f(r) is proven via a result on quartet compatibility that may be of independent interest: For every n≥4, there exists an incompatible set Q of Ω(n2) quartets over n labels such that every Proper Subset of Q is compatible. We show that such a set of quartets can have size at most 3 when n=5, and at most O(n3) for arbitrary n. We contrast our results on quartets with the case of rooted triplets: For every n≥3, if R is an incompatible set of more than n−1 triplets over n labels, then some Proper Subset of R is incompatible. We show this bound is tight by exhibiting, for every n≥3, a set of n−1 triplets over n taxa such that R is incompatible, but every Proper Subset of R is compatible.
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Improved Lower Bounds on the Compatibility of Multi-State Characters ⋆
arXiv: Combinatorics, 2012Co-Authors: Brad Shutters, Sudheer Vakati, David Fernández-bacaAbstract:We study a long standing conjecture on the necessary and sufficient conditions for the compatibility of multi-state c There exists a function f(r) such that, for any set C of r-state characters, C is compatible if and only if every Subset of f(r) characters of C is compatible. We show that for every r ≥ 2, there exists an incompatible set C of ⌊ r ⌋·⌈ r ⌉+1 r-state characters such that every Proper Subset of C is compatible. Thus, f(r) ≥ ⌊ r ⌋ · ⌈ r ⌉ + 1 for every r ≥ 2. This improves the previous lower bound of f(r) ≥ r given by Meacham (1983), and generalizes the construction showing that f(4) ≥ 5 given by Habib and To (2011). We prove our result via a result on quartet compatibility that may be of independent interest: For every integer n ≥ 4, there exists an incompatible set Q of ⌊ n 2 2 ⌋·⌈ n 2 2 ⌉+ 1 quartets over n labels such that every Proper Subset of Q is compatible. We contrast this with a result on the compatibility of triplets: For every n ≥ 3, if R is an incompatible set of more than n−1 triplets over n labels, then some Proper Subset of R is incompatible. We show this upper bound is tight by exhibiting, for every n ≥ 3, a set of n − 1 triplets over n taxa such that R is incompatible, but every Proper Subset of R is compatible.
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WABI - Improved lower bounds on the compatibility of quartets, triplets, and multi-state characters
Lecture Notes in Computer Science, 2012Co-Authors: Brad Shutters, Sudheer Vakati, David Fernández-bacaAbstract:We study a long standing conjecture on the necessary and sufficient conditions for the compatibility of multi-state characters: There exists a function f(r) such that, for any set C of r-state characters, C is compatible if and only if every Subset of f(r) characters of C is compatible. We show that for every r≥2, there exists an incompatible set C of $\lfloor\frac{r}{2}\rfloor\cdot\lceil\frac{r}{2}\rceil + 1$ r-state characters such that every Proper Subset of C is compatible. Thus, f(r) ≥ $\lfloor\frac{r}{2}\rfloor\cdot\lceil\frac{r}{2}\rceil + 1$ for every r≥2. This improves the previous lower bound of f(r)≥r given by Meacham (1983), and generalizes the construction showing that f(4)≥5 given by Habib and To (2011). We prove our result via a result on quartet compatibility that may be of independent interest: For every integer n≥4, there exists an incompatible set Q of $\lfloor\frac{n-2}{2}\rfloor\cdot\lceil\frac{n-2}{2}\rceil + 1$ quartets over n labels such that every Proper Subset of Q is compatible. We contrast this with a result on the compatibility of triplets: For every n≥3, if R is an incompatible set of more than n−1 triplets over n labels, then some Proper Subset of R is incompatible. We show this bound is tight by exhibiting, for every n≥3, a set of n−1 triplets over n taxa such that R is incompatible, but every Proper Subset of R is compatible.
