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On Merge Trees and Discrete Morse Functions on Paths and Trees [article]

Julian Brüggemann
2022 arXiv   pre-print
We show that each merge tree is represented by a discrete Morse function on a path.  ...  Furthermore, we present explicit constructions for two different but related kinds of discrete Morse functions on paths that induce any given merge tree.  ...  This is one of the main differences between merge trees in [JS22] and the merge trees in [Cur19] . We consider one way to keep some information provided by the induced labeling on M(X, f ).  ... 
arXiv:2112.01311v3 fatcat:zm5pgo5gtrabdbnom2io2yxcne

An inequality on paths in a grid

István Beck, Stein Krogdahl
1992 Journal of combinatorial theory. Series A  
In this figure there is a one-to-one correspondence between paths from 1 (lower left) to x1x1x3 y, y, (upper right) and mergings of the sequences {xi} and { yj}.  ...  . + x, "'X,, and we defined a merging of two sequences in the obvious way. and bj=nLl\yk (2 <j < m + 1). Let ci, j = a,bj. Theorem 1 applied to the matrix (Ci, j) proves Corollary 1.  ...  The sorted merging is the one that maximizes the value of cz zn+m I, . . . . 1. Thus Corollary 1 implies Corollary 2. Remark.  ... 
doi:10.1016/0097-3165(92)90026-q fatcat:ukpzmrb4sne3fmxo75e5nt2fpe

Merging regular processes by means of fixed-point theory

J.-J.Ch. Meyer
1986 Theoretical Computer Science  
Finally, we use this to prove the correctness of a formalism similar to the one for arbitrary merge in order to calculate the fair merge of two regular sequential (nondeterrainistic) processes with g-recursion  ...  Hereafter we define the semantics of the fair merge of these processes.  ...  Bergstra for their comments on earlier drafts.  ... 
doi:10.1016/0304-3975(86)90045-9 fatcat:d2as4lexwvg4rfxogltphthc7i

Sorting an Array Using the Topological Sort of a Corresponding Comparison Graph [article]

Balaram Behera
2020 arXiv   pre-print
In the process, we construct a new merge process for graphs with relevant invariant properties for our use.  ...  Also let's conclude some properties of sequences of merges on a particular forest along with DFS. Lemma 3.  ...  Hence our path P will eventually contain all the vertices, so it is a Hamiltonian path by definition in H as claimed. Remark.  ... 
arXiv:2009.00098v1 fatcat:h6aigcfaprctvoicandpsdk7tm

Toric grammars: a new statistical approach to natural language modeling [article]

Olivier Catoni, Thomas Mainguy
2013 arXiv   pre-print
This Markov chain, that we call a communication model, recombines at each step randomly the set of sentences forming its current state, using some grammar rules.  ...  Although the toric grammars we use are closely related to Context Free Grammars, the way we generate the language from the grammar is qualitatively different.  ...  This proof is a bit lengthy and is based on some invariants in the split and merge operations. It has been put off to appendix A.1 on page 29.  ... 
arXiv:1302.2569v1 fatcat:dpyyltfb4jgxzpzcntkdvpznr4

A New Merging Process for Data Integration Based on the Discrete Fréchet Distance [chapter]

Thomas Devogele
2002 Advances in Spatial Data Handling  
It also merges an ordered set of pairs of matching points (vertices) into a single geometry.  ...  This paper proposes a new merging process to complement the vector overlay for data integration of several layers.  ...  We can remark that: · The "From-To" is a one-to-one relationship. A point cannot relate to many points. Section 3 will show that these relationships can be one-to-many or many-to-one.  ... 
doi:10.1007/978-3-642-56094-1_13 fatcat:wojacg32nzcplctcp54n6gnx5y

Moment inequalities for random variables in computational geometry

L. Devroye
1983 Computing  
We show that for all p ? 1, there exists a universal constant C, > 0 such that E(N)_CC p max (1, E~( N,)) where q ='. This complements Jensen's lower bound for the p-th moment : E (Nn) ? E' (N n) .  ...  We also give necessary and sufficient conditions on E (Nn) for linear expected time behavior of divide-and-conquer methods for finding A n .  ...  ., Xn , and let us merge and edit in step (ii) in the most trivial possible way : merge to the two sets, consider all d-tuples of elements, and check if all the remaining elements fall on the same side  ... 
doi:10.1007/bf02280782 fatcat:budwfvmwlnck3m3zfq77zo35a4

The Fiber of the Persistence Map for Functions on the Interval [article]

Justin Curry
2019 arXiv   pre-print
In this paper we study functions on the interval that have the same persistent homology.  ...  The equivalence classes used here are indexed by chiral merge trees, which are binary merge trees where a left-right ordering of the children of each vertex is given.  ...  Remark 6.6. For a general ordered merge tree it's not clear how to specify a total ordering on the vertices.  ... 
arXiv:1706.06059v2 fatcat:57vhs3ya7fb5veubdyg6byswzy

Principles to control autonomous formation merging

Changbin Yu, B. Fidan, B.D.O. Anderson
2006 2006 American Control Conference  
A strategy is developed based on simplification of the merging problem to a problem of growing a minimally or globally rigid graph.  ...  Based on this strategy, three principles are provided to control the merging efficiently and optimally, in the sense of minimizing the number of added edges and the number of vertices incident to these  ...  In this case, one need to develop strategies and/or operations that construct all possible ways of merging multiple sub-formations. • Consider the scenario that there are common vertices shared by more  ... 
doi:10.1109/acc.2006.1655448 fatcat:sxq7xpu24nbexlpjdru2xty77m

Effective intervals and regular Dirichlet subspaces [article]

Liping Li, Wenjie Sun, Jiangang Ying
2018 arXiv   pre-print
This paper focuses on how to operate on effective intervals to obtain regular Dirichlet subspaces.  ...  Then we give an explicit road map how to obtain all regular Dirichlet subspaces from a local and regular Dirichlet form on an interval, by a series of intuitive operations on the effective intervals in  ...  and then merged according to some rule into new ones.  ... 
arXiv:1805.09499v1 fatcat:aofhqmjflrgo7oagkc6f7tr6om

Resource cost results for one-way entanglement distillation and state merging of compound and arbitrarily varying quantum sources

H. Boche, G. Janßen
2014 Journal of Mathematical Physics  
We consider one-way quantum state merging and entanglement distillation under compound and arbitrarily varying source models.  ...  We determine the one-way entanglement distillation capacity for AVQS, where we invoke the famous robustification and elimination techniques introduced by R. Ahlswede.  ...  Remark 9.  ... 
doi:10.1063/1.4893635 fatcat:6afldznl75bc7acx3qugbqkbga

Process algebra for synchronous communication

J.A. Bergstra, J.W. Klop
1984 Information and Control  
Further, some relationships are shown to hold between the four concepts of merging.  ...  Four cases are considered: free merge or interleaving, merging with communication, merging with mutual exclusion of tight regions, and synchronous process cooperation.  ...  ., a process P sends a message c! to a process Q such that P can proceed while the message c! to Q is "on the way."  ... 
doi:10.1016/s0019-9958(84)80025-x fatcat:g7i2a4o57rcn7fnkyhdnqxrg3m

E-values: Calibration, combination, and applications [article]

Vladimir Vovk, Ruodu Wang
2020 arXiv   pre-print
Multiple testing of a single hypothesis and testing multiple hypotheses are usually done in terms of p-values.  ...  We demonstrate that e-values are often mathematically more tractable; in particular, in multiple testing of a single hypothesis, e-values can be merged simply by averaging them.  ...  On the other hand, we can check that any procedure satisfying (A.3) will satisfy (A.2) for some conditional p-variable (P Q ): indeed, we can set P Q := min Q∈H k P * k . Remark A.1.  ... 
arXiv:1912.06116v4 fatcat:6qexl46x2rekpn5q4wnn6anm5u

Boost Symbolic Execution Using Dynamic State Merging and Forking

Chao Zhang, Weiliang Yin, Zhiqiang Lin
2018 Asia-Pacific Software Engineering Conference  
In this way we can reveal how state merging efficiently joins branches and decrease paths. It is remarkable that paths getting through a certain location might enclose a large gap in time.  ...  The second way is to apply some imprecise techniques from static analysis, such as abstract interpretation and summary.  ... 
dblp:conf/apsec/ZhangYL18 fatcat:bmbs7miuare2vgk4c3osqijuz4

Adaptive strategies to platoon merging with vehicle engine uncertainty

Vishrut Jain, Di Liu, Simone Baldi
2020 IFAC-PapersOnLine  
dynamics, while the bidirectional error seamlessly allows the vehicle that wants to merge to interact with both the front and the rear vehicles, in a similar way as humans do.  ...  This work shows how such challenges can be tackled via a newly proposed strategy based on adaptive control with bidirectional error: the adaptive control framework autonomously adapts to different engine  ...  CONCLUSIONS The problem of synchronized merging of cooperative vehicles is more challenging than the one of formation-keeping, due to some challenges associated to the merging scenario, such as the need  ... 
doi:10.1016/j.ifacol.2020.12.2027 fatcat:j3pfdsr4tnamrjcv2gamuqct2a
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