919 research outputs found
On the Shyr-Yu theorem
No full textInternational audienceAn alternative proof of Shyr-Yu theorem is given. Some generalizations are also considered using fractional root decompositions and fractional exponents of words
On some decompositions of r-disjunctive languages
No full textSome kinds of decompositions of r-disjunctive languages on an arbitrary alphabet will be investigated. We will show that an f-disjunctive (t-disjunctive) language can be divided into two parts and either one part of them is an f-disjunctive (t-disjunctive) language or both parts are r-disjunctive but not f-disjunctive (t-disjunctive) languages. Finally, a relevant result of H. J. Shyr and S. S. Yu concerning the disjunctive languages will be improved
Intra-abdominal adhesion formation induces anti-oxidative injury, enhances cell proliferation, and prevents complement-mediated lysis.
No full textSparse Network-regularized Nonnegative Matrix Factorization and Applications to Tumor Subtyping
No full textCancers are complex diseases and identification of clinically important subtypes has the potential to guide better prognosis and treatment. The utility of graph-regularized nonnegative matrix factorization (GNMF) has been demonstrated on tumor subtype identification based on exome-level mutation data. In a recent study, it revealed that using a panel of important genes achieved superior classification than using the full set of (exome-level) mutations. We hypothesized that combining sparse coding with GNMF will enable automatic selection of important genes to aid tumor subtyping as well as interpretations of the underlying pathways responsible for the subtypes. To test our hypothesis, we proposed a new formulation that incorporates a lasso-like penalty into GNMF to enable variable selection and sparse representation. We evaluated the proposed method for rich scenarios of simulated mutation cohorts, and further demonstrated the utility on real mutation data from large-scale sequencing studies
WS-05-02: Biostatistical and bioinformatics approaches in high dimensional data derived from high throughput assays: a consumer guide
No full textAlgebraic Properties of Primitive Related Languages
No full text本論文主要是研究與質式字有關語言的代數特質，其中包括討論規則化語言的字首質式特性、N次方字首質式相關的語言及這些語言之分隔化的特性，並討論保持質式字有關語言同態函數之間的關係，最後用函數的方法來定義一般化的二元字運算子並藉此來討論符合一般化二元字運算子的質式特性。
在這論文裡，得到下列的研究結果，知道有限的規則化元件分割語言能否由字首質式字來組成是可以被判斷出來的，N次方字首質式相關語言的特性及這些語言之分隔化的特性也被詳細討論，除此之外，另提出一個演算法來檢查給定的同態函數是否能保持字首質式之特性，並且知道在字元個數沒有限制的情形下，保持無重複字特性的同態函數就是保持字首質式特性的同態函數，及在字元個數限制只有二個的情形下，保持字首質式特性的同態函數就是保持質式特性的同態函數。The aim of this thesis is to investigate the algebraic properties
of related primitive words. There are several topics represented
in this thesis. One includes p-primitive regular languages, prefix
-power related languages, disjunctivities of prefix -power
related languages, homomorphisms and words operation closure and
primitivities.1 Preliminaries 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Basic Definitions and Notations . . . . . . . . . . . . . . . . . 7
1.3 Primitive Words . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.4 D-primitive Words . . . . . . . . . . . . . . . . . . . . . . . . 10
1.5 Regular Languages . . . . . . . . . . . . . . . . . . . . . . . . 11
1.6 Disjunctive Languages . . . . . . . . . . . . . . . . . . . . . . 12
2 P-primitive Regular Languages 14
2.1 Properties Related to P-primitive Regular Component . . . . 14
2.2 The Relations between Regular Languages and P-primitive Languages
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
3 Prefix n-Power Related Languages 20
3.1 Properties of Q(i) and D(i) Languages . . . . . . . . . . . . . 20
3.2 Properties of Prefix n-Power Related Languages . . . . . . . . 21
4 Disjunctivities 33
4.1 Disjunctivities of Q(i) and D(i) Languages . . . . . . . . . . . 33
4.2 Disjunctivities of P-primitive Related Languages . . . . . . . . 34
5 Homomorphisms 39
5.1 P-primitivity Preserving Homomorphisms . . . . . . . . . . . 39
5.2 The Relationships of Properties Preserving Homomorphisms . 45
6 Words Operation Closure and Primitivities 51
6.1 Operations of Words and Languages . . . . . . . . . . . . . . 51
6.2 0-Primitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
6.3 Q_0: The Set of 0-Primitive Words . . . . . . . . . . . . . . . . 56
7 Concluding Remarks 5
Solid m-codes and disjunctive domains
No full text令x 是一個大有限的字母集且令X* 是X 所生成的自由域(free monoid)。一個言語D
X* ,對若對任一x,y D,(X Y(RA)X (RA)，則A 是一個（若）分離型言語，其中
A X*,此時稱D 是一個（右）分離域。一種特別的有限碼，稱之為結實m 一碼，要被
提出來。本論文的目的是研究結實m 一碼的一些性質，及將分離域及右分離域特徵化
。在本論文的第二部份中，我們證明了下列定理：
令A=(S,X,M,q0,F) 是一個有限自動機且令|S|=n≧2 則，
(A)T(A)∩Q≠ 若且唯若A 接受一個質字其長度小或等於3(n-1)。
(B)T(A)∩Q|=∞若且唯若A 接受一個質字而
n≦1g(y)≦3(n-1)
此外，還證明了|T(A)∩Q|∞ 時自動機A 的一些性質。如此我們可以很清晰地來判斷
自動機與集合Q 的關係；換句話說，由自動機的觀點，我們可以清楚地判斷質字存在
一個正規言語中的狀況。
1.Hopcroft, J.E. and Ullman, J.D.,"Formal Languages and their Relation to
Automata," Addison-Wesley, Massachusetts, 1976.
2.Ito Masami, Shy, H.J. and Katsura M. Regular Domains.(Submitted for publi
cation).
3.Lallement, G. "Semigroups and Combinatorial Applications,"John Wiley and
Sons, New York(1979).
4.Lothaire. M.,Combinatorics on Words, Addision-Wesley, Reading,(1983) .
5.Shyr,H.J.,Disjunctive Languages on a Free Monoid, Information and Contro
l, Vol. 34,(1977)123-129.
6.Shyr,H.J.,"Free Monoids and Languages,"Lecture Notes, Department of Math
ematics, Soochow Unviersity, Taipei, Taiwain,(1979).
7.Shyr, H.J., Order Catenation and Regular Free Disjunctive Languages, Inf
ormation and Control, Vol. 46, No. 3, (1980)257-269.
8.Shyr, H.J., and Tseng, D.C., Some Properties of Dense Languages, Soochow
Journal of Mathematics, Vol. 10,(1984)127-131
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