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Livio Bioglio - One of the best experts on this subject based on the ideXlab platform.

  • Enumerated Type semantics for the calculus of looping sequences
    RAIRO - Theoretical Informatics and Applications, 2011
    Co-Authors: Livio Bioglio
    Abstract:

    The calculus of looping sequences is a formalism for describing the evolution of biological systems by means of term rewriting rules. In this paper we enrich this calculus with a Type discipline which preserves some biological properties depending on the minimum and the maximum number of elements of some Type requested by the present elements. The Type system enforces these properties and Typed reductions guarantee that evolution preserves them. As an example, we model the hemoglobin structure and the equilibrium between cell death and division: Typed reductions prevent undesirable behaviors.

Sivasubramanian Sivaramakrishnan - One of the best experts on this subject based on the ideXlab platform.

  • Eulerian Central Limit Theorems and Carlitz identities in positive elements of Classical Weyl Groups
    2020
    Co-Authors: Dey, Hiranya Kishore, Sivasubramanian Sivaramakrishnan
    Abstract:

    Central Limit Theorems are known for the Eulerian statistic "descent" (or "excedance") in the symmetric group $\SSS_n$. Recently, Fulman, Kim, Lee and Petersen gave a Central Limit Theorem for "descent" over the alternating group $\AAA_n$ and also gave a Carlitz identity in $\AAA_n$ using descents. In this paper, we give a Central Limit Theorem in $\AAA_n$ involving excedances. We extend these to the positive elements in Type B and Type D Coxeter groups. Boroweic and M\l{}otkowski Enumerated Type B descents over $\DD_n$, the Type D Coxeter group and gave similar results. We refine their results for both the positive and negative part of $\DD_n$. Our results are a consequence of signed enumeration over these subsets.Comment: Corrected a wrong spelling of an author "Borowiec". The earlier version mis-spelled all occurrences. Thanks to Prof. M\l{}otkowski for pointing this ou

Dey, Hiranya Kishore - One of the best experts on this subject based on the ideXlab platform.

  • Eulerian Central Limit Theorems and Carlitz identities in positive elements of Classical Weyl Groups
    2020
    Co-Authors: Dey, Hiranya Kishore, Sivasubramanian Sivaramakrishnan
    Abstract:

    Central Limit Theorems are known for the Eulerian statistic "descent" (or "excedance") in the symmetric group $\SSS_n$. Recently, Fulman, Kim, Lee and Petersen gave a Central Limit Theorem for "descent" over the alternating group $\AAA_n$ and also gave a Carlitz identity in $\AAA_n$ using descents. In this paper, we give a Central Limit Theorem in $\AAA_n$ involving excedances. We extend these to the positive elements in Type B and Type D Coxeter groups. Boroweic and M\l{}otkowski Enumerated Type B descents over $\DD_n$, the Type D Coxeter group and gave similar results. We refine their results for both the positive and negative part of $\DD_n$. Our results are a consequence of signed enumeration over these subsets.Comment: Corrected a wrong spelling of an author "Borowiec". The earlier version mis-spelled all occurrences. Thanks to Prof. M\l{}otkowski for pointing this ou