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Subset Parking Functions [article]

Sam Spiro
2019 arXiv   pre-print
Motivated by this, we define a subset parking function (C_1,...,C_n), with each C_i a subset of {1,...,n}, by having the ith car try to park in the leftmost available element of C_i.  ...  A parking function (c_1,...  ...  For example, we say that C = (C 1 , . . . , C n ) is a k-subset parking function if C is a subset parking function and |C i | = k for all i.  ... 
arXiv:1909.10109v1 fatcat:32cppslomjckziwpowfu4erqje

Two Functional Subsets of FOXP3+ Regulatory T Cells in Human Thymus and Periphery

Tomoki Ito, Shino Hanabuchi, Yi-Hong Wang, Woong Ryeon Park, Kazuhiko Arima, Laura Bover, F. Xiao-Feng Qin, Michel Gilliet, Yong-Jun Liu
2008 Immunity  
Whereas the ICOS + FOXP3 + Treg cells used interleukin-10 to suppress dendritic cell function and transforming growth factor (TGF)-b to suppress T cell function, the ICOS À FOXP3 + Treg cells used TGF-b  ...  We found two subsets of FOXP3 + natural Treg cells defined by the expression of the costimulatory molecule ICOS in the human thymus and periphery.  ...  Therefore, the two subsets of naturally occurring FOXP3 + Treg cells may functionally mirror the two subsets of peripheral-induced Treg cells.  ... 
doi:10.1016/j.immuni.2008.03.018 pmid:18513999 pmcid:PMC2709453 fatcat:mxo7cdjvdfg3xjtrgv5pzmlkvy

CD94 Defines Phenotypically and Functionally Distinct Mouse NK Cell Subsets

J. Yu, M. Wei, H. Mao, J. Zhang, T. Hughes, T. Mitsui, I.-k. Park, C. Hwang, S. Liu, G. Marcucci, R. Trotta, D. M. Benson (+1 others)
2009 Journal of Immunology  
The lack of CD56 bright and CD56 dim NK cell subsets in mouse has resulted in some elegant studies to functionally and phenotypically separate mouse NK cells into two subsets.  ...  ., CD117 and CD69) noted in this study also suggests that the two subsets are not identical and may have some functional distinctions.  ... 
doi:10.4049/jimmunol.0900907 pmid:19801519 pmcid:PMC2924742 fatcat:ffmczkgf4vfvnmpnn3w4mwun2e

Global Transcriptional Profiling Reveals Distinct Functions of Thymic Stromal Subsets and Age-Related Changes during Thymic Involution

Sanghee Ki, Daechan Park, Hilary J. Selden, Jun Seita, Haewon Chung, Jonghwan Kim, Vishwanath R. Iyer, Lauren I.R. Ehrlich
2014 Cell Reports  
The data implicate unanticipated biological functions for a subset of thymic epithelial cells.  ...  Age-associated thymic involution results in diminished T cell output and function in aged individuals.  ...  provided in a searchable platform Graphical Abstract Highlights Authors Sanghee Ki, Daechan Park, ..., Vishwanath R.  ... 
doi:10.1016/j.celrep.2014.08.070 pmid:25284794 pmcid:PMC4194175 fatcat:ss3q6wdvtbbqlcmaofqa5uh5lm

CD94 surface density identifies a functional intermediary between the CD56bright and CD56dim human NK-cell subsets

J. Yu, H. C. Mao, M. Wei, T. Hughes, J. Zhang, I.-k. Park, S. Liu, S. McClory, G. Marcucci, R. Trotta, M. A. Caligiuri
2009 Blood  
Figure 3 . 3 CD94 identifies functionally distinct human CD56 dim NK-cell subsets with regard to IFN-␥ production.  ...  Peripheral blood NK cells are composed of CD56 bright (ϳ 10%) and CD56 dim (ϳ 90%) NK-cell subsets, which are functionally distinct.  ... 
doi:10.1182/blood-2009-04-215491 pmid:19897577 pmcid:PMC2808153 fatcat:twcxojc4o5gj3i3dl5d7cx4hdy

Adaptive Immune Response Signaling Is Suppressed in Ly6Chigh Monocyte but Upregulated in Monocyte Subsets of ApoE-/- Mice — Functional Implication in Atherosclerosis

Pingping Yang, Qinghua Wu, Lizhe Sun, Pu Fang, Lu Liu, Yong Ji, Joon-Young Park, Xuebin Qin, Xiaofeng Yang, Hong Wang
2021 Frontiers in Immunology  
ApoE-/- confers upon both subsets with augmented pro-atherogenic/inflammatory function and APC potential.  ...  Finally, we modeled immunological gene expression changes and functional implications in MC differentiation and adaptive immune response for MC subsets from control and ApoE-/- mice.ConclusionsLy6Chigh  ...  ApoE -/confers upon both subsets with augmented proatherogenic/inflammatory function and APC potential.  ... 
doi:10.3389/fimmu.2021.809208 pmid:34987524 pmcid:PMC8721109 fatcat:aulrnojscza55pscdfq4lvnfaa

Multigraph Hyperplane Arrangements and Parking Functions [article]

Mikhail Mazin
2015 arXiv   pre-print
They introduced the G-Shi arrangement and a labeling of its regions by G-parking functions.  ...  Back in the nineties Pak and Stanley introduced a labeling of the regions of a k-Shi arrangement by k-parking functions and proved its bijectivity.  ...  In which case the subset I ⊂ {1, . . . , n} violates the G-parking function condition.  ... 
arXiv:1501.01225v1 fatcat:idljuabtyjgivpixf25cly6a7q

Two-boundary lattice paths and parking functions

Joseph P.S. Kung, Xinyu Sun, Catherine Yan
2007 Advances in Applied Mathematics  
An analogous involution can be defined for parking functions with arbitrary lower and upper bounds.  ...  From this involution, we obtained determinantal formulas for the number and sum enumerator of such parking functions.  ...  Parking functions are rearrangements of lattice paths.  ... 
doi:10.1016/j.aam.2006.08.001 fatcat:mlb4umucqzdgnkbjx2x5vhswxe

Skeleton Ideals of Certain Graphs, Standard Monomials and Spherical Parking Functions

Chanchal Kumar, Gargi Lather, Sonica
2021 Electronic Journal of Combinatorics  
The standard monomials of the Artinian quotient $\frac{R}{\mathcal{M}_G}$ correspond bijectively to $G$-parking functions.  ...  Dochtermann introduced and studied skeleton ideals of the graph $G$, which are subideals of the $G$-parking function ideal with an additional parameter $k ~(0\le k \le n-1)$.  ...  In this case, spherical (K n+1 − {e 1 })-parking functions correspond bijectively with some specified subset of uprooted trees on the vertex set [n] (Theorem 23).  ... 
doi:10.37236/9874 fatcat:htn4kmkaizat5f376y6ehybyd4

Page 9645 of Mathematical Reviews Vol. , Issue 2004m [page]

2004 Mathematical Reviews  
Lev (IL-HAIF2; Tivon) 2004m:11169 11P81 05A17 Courtright, Kevin M. (1-PAS; University Park, PA); Sellers, James A. (1-PAS; University Park, PA) Arithmetic properties for hyper /-ary partition functions  ...  The series under consideration are infinite products that are either theta functions or partition functions. A typical result is that for n > 1, P(n) +25 °(-1)'D(n —k?)  ... 

On various multimap classes in the KKM theory and their applications

Sehei PARK
2018 Advances in the Theory of Nonlinear Analysis and its Applications  
spaces having sufficiently many linear functionals.  ...  and Idzik are examples of the function space A κ c .  ... 
doi:10.31197/atnaa.433869 fatcat:wh5tv747lvehdhkeg5m2qwz57a

Approximate fixed points on almost convex sets

J. E. C. Lope, R. M. Rey, M. Roque, P. W. Sy
2004 Tamkang Journal of Mathematics  
This generalizes the well-known Himmelberg fixed point theorem and also unifies recent results of Park and Tan [14] %cite{tan2} and Sy and Park [16].  ...  A multimap (or simply, a map) F : X ⊸ Y is a function from a set X into the power set 2 Y of a set Y ; that is, a function with the values F (x) ⊂ Y for x ∈ X and the fibers F − (y) := {x ∈ X : y ∈ F (  ...  (Park and Tan [14] , Theorem 1) Let X be a subset of a locally convex Hausdorff topological vector space E and Y an almost convex dense subset of X.  ... 
doi:10.5556/j.tkjm.35.2004.206 fatcat:m6s5pz73kbgathssszxdnvwqna

On power ideals of transversal matroids and their "parking functions"

Camilo Sarmiento
2019 Algebraic Combinatorics  
We dub the exponent vectors of these monomial basis elements "parking functions" of the corresponding transversal matroid.  ...  Notice that if q ∈ Z d 0 is an "A-parking function", then a collection of cars comprising q i 0 cars of brand i, for i ∈ [d], can park in a subset T ⊂ S of the parking spots, in such a way that at least  ...  they specialize to the renowned parking functions.  ... 
doi:10.5802/alco.57 fatcat:jh52fgxqjrhdvhniigy4vbhmyq

On power ideals of transversal matroids and their "parking functions" [article]

Camilo Sarmiento
2018 arXiv   pre-print
We dub the exponent vectors of these monomial basis elements "parking functions" of the corresponding transversal matroid.  ...  Notice that if q ∈ Z d ≥0 is an "A-parking function", then a collection of cars comprising q i ≥ 0 cars of brand i, for i ∈ [d], can park in a subset T ⊂ S of the parking spots, in such a way that at least  ...  they specialize to the renowned parking functions.  ... 
arXiv:1805.07210v1 fatcat:faeg3d762fa57mrxmukyeia6se

Distribution of the Number of Encryptions in Revocation Schemes for Stateless Receivers

Christopher Eagle, Zhicheng Gao, Mohamed Omar, Daniel Panario, Bruce Richmond
2008 Discrete Mathematics & Theoretical Computer Science  
International audience We study the number of encryptions necessary to revoke a set of users in the complete subtree scheme (CST) and the subset-difference scheme (SD).  ...  Park and Blake in: Journal of Discrete Algorithms, vol. 4, 2006, pp. 215―238, give the mean number of encryptions for these schemes.  ...  Using this recurrence, Park and Blake (7) give a recurrence for the generating function of the numbers a (n) ij in the CST scheme.  ... 
doi:10.46298/dmtcs.3564 fatcat:a6k73zeidbdlhflaa23vzpvqle
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