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### Pseudo Unique Sink Orientations [article]

Vitor Bosshard, Bernd Gärtner
2017 arXiv   pre-print
If a cube orientation is not a USO, it contains a pseudo unique sink orientation (PUSO): an orientation of some subcube such that every proper face of it has a unique sink, but the subcube itself hasn't  ...  A unique sink orientation (USO) is an orientation of the n-dimensional cube graph (n-cube) such that every face (subcube) has a unique sink. The number of unique sink orientations is n^Θ(2^n).  ...  Pseudo unique sink orientations. If a cube orientation has a unique sink in every face except the cube itself, we call it a pseudo unique sink orientation (PUSO).  ...

### A New Combinatorial Property of Geometric Unique Sink Orientations [article]

Yuan Gao, Bernd Gärtner, Jourdain Lamperski
2022 arXiv   pre-print
A unique sink orientation (USO) is an orientation of the hypercube graph with the property that every face has a unique sink.  ...  A number of well-studied problems reduce in strongly polynomial time to finding the global sink of a USO; most notably, linear programming (LP) and the P-matrix linear complementarity problem (P-LCP).  ...  A pseudo USO is a cube orientation that does not have a unique global sink, but every proper face has a unique sink [2, Definition 2] .  ...

### Directed random walks on polytopes with few facets [article]

Malte Milatz
2017 arXiv   pre-print
We prove that the same bound holds for the more general unique sink orientations.  ...  It is known that the directed random walk along the edges of P terminates after O(^2 n) steps, if the edges are oriented in a (pseudo-)linear fashion.  ...  Now, an orientation of the edges of a polytope is a unique sink orientation if every non-empty face of the polytope has a unique sink.  ...

### Finding a Simple Polytope from Its Graph in Polynomial Time

Eric J. Friedman
2008 Discrete & Computational Geometry
In addition, we define the concept of a pseudo-polytopal-multigraph which may be of independent interest. 1 Note that if the polytope is not simple then it is not uniquely defined by its graph.  ...  Also note that IP-SD suggests that a generalization of unique sink orientations which drops the requirement that the sinks arise from an orientation, might also be of interest.  ...  An abstract objective function (AOF) on G(P ) is an acyclic orientation such that the induced directed subgraph on every face of P has a unique sink. 2-systems and Pseudo-Polytopes Now we describe a  ...

### Posets arising as 1-skeleta of simple polytopes, the nonrevisiting path conjecture, and poset topology [article]

Patricia Hersh
2019 arXiv   pre-print
Given any polytope P and any generic linear functional c, one obtains a directed graph G(P, c) by taking the 1-skeleton of P and orienting each edge e(u,v) from u to v for c (u) < c ( v).  ...  This conjecture is proven for 3-polytopes and for spindles having the two distinguished vertices as source and sink; this shows that known counterexamples to the Hirsch Conjecture will not provide counterexamples  ...  and unique sink.  ...

### On the Black-Box Complexity of Sperner's Lemma [chapter]

Katalin Friedl, Gábor Ivanyos, Miklos Santha, Yves F. Verhoeven
2005 Lecture Notes in Computer Science
We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension.  ...  The sources and sinks of the flow are the fully labelled d-simplices.  ...  A pseudo d-manifold M is said to be orientable if it − if K is oriented, then K = S∈K d (S, τ S ) ∈ C d (K, Z) where τ S is the ori- entation of S in K.  ...

### On the Black-Box Complexity of Sperner's Lemma

Katalin Friedl, Gábor Ivanyos, Miklos Santha, Yves F. Verhoeven
2008 Theory of Computing Systems
We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension.  ...  The sources and sinks of the flow are the fully labelled d-simplices.  ...  A pseudo d-manifold M is said to be orientable if it − if K is oriented, then K = S∈K d (S, τ S ) ∈ C d (K, Z) where τ S is the ori- entation of S in K.  ...

### On the black-box complexity of Sperner's Lemma [article]

Katalin Friedl, Gabor Ivanyos, Miklos Santha, Yves F. Verhoeven
2005 arXiv   pre-print
We give a deterministic algorithm for Sperner problems over pseudo-manifolds of arbitrary dimension.  ...  Moreover, if there are exactly two Oriented Sperner on Pseudo d-Manifolds (d-OSPM) Input: an oriented pseudo d-manifold M, and S ∈ M d . Oracle input: a labeling ℓ : M 0 → {0, 1, . . . , d}.  ...  We can consider an oriented d-simplex (S, τ S ) with N d [ (S, τ S ) ] = 1 as a source for the flow, and ( S ′ , τ S ′ ) with N d [ (S ′ , τ S ′ ) ] = −1 as a sink.  ...

### Collective sinking promotes selective cell pairing in planktonic pennate diatoms

Joan S. Font-Muñoz, Raphaël Jeanneret, Jorge Arrieta, Sílvia Anglès, Antoni Jordi, Idan Tuval, Gotzon Basterretxea
2019 Proceedings of the National Academy of Sciences of the United States of America
Finding a partner in an inherently unsteady 3-dimensional system, such as the planktonic marine environment, is a difficult task for nonswimming organisms with poor control over their orientation.  ...  This is, eminently, a cell abundance-dependent process, therefore being more effective when population sinking is synchronized.  ...  (B) Daily shear flow profile (γ) and cell orientation (e) with its confidence interval shown with dashed lines. Cell orientation is only estimated where Pseudo-nitzschia sp. is dominant.  ...

### Smale diffeomorphisms and surface topology

Steve Batterson, John Smillie
1985 Ergodic Theory and Dynamical Systems
This paper concerns Smale diffeomorphisms of compact oriented surfaces. Relationships are found between the isotopy class of the map and the dynamics of its basic sets.  ...  Theorem 4 describes restrictions on Smale maps in pseudo-Anosov isotopy classes. In another direction we find restrictions on which collections of subshifts can occur as basic sets of a given map.  ...  Each component of the closure of the difference is an oriented manifold with non-trivial boundary.  ...

### Depth Dependence of Nanoindentation Pile-Up Patterns in Copper Single Crystals

Stanisław Kucharski, Dariusz Jarząbek
2014 Metallurgical and Materials Transactions. A
Furthermore, a detailed analysis of residual impressions with maximal applied loads equal to 2 mN and bigger reveals that both pile-up and sink-in patterns are present.  ...  A study of the dependence of nanoindentation pile-up patterns on the indentation load and crystallographic orientation is presented.  ...  The pseudo-pile-ups can be seen. (b) (011)-oriented surface; Sink-in for greatest indentation loads, (001)-oriented surface. (a) (111)-oriented surface. (b) (001)-oriented surface.  ...

### Multiple Sink Based Compressive Data Aggregation Technique for Wireless Sensor Network

Mohamed Yacoab M.Y, V Sundaram
2011 International Journal of Wireless & Mobile Networks
Hence, in this paper, we develop a multiple sink based data aggregation technique, assuming the sinks are static. In this technique, initially a sink oriented tree is determined for each sink.  ...  In addition, the radio channel capacity close to the sink may become overloaded if the average number of hops between the source and the sink becomes excess [10] . 3] In single sink network architectures  ...  By a pseudo link, all sink nodes are connected to pseudo destination. In multiple sink network which in turn changes it to a single reverse multicast tree [12] .  ...

### A distributed prime sieving algorithm based on Scheduling by Multiple Edge Reversal [article]

Gabriel Paillard, Felipe Franca
2013 arXiv   pre-print
SER works as follows: starting from any acyclic orientation ω on G, there is at least one sink node, i.e., a node such that all its arcs are directed to itself; all sink nodes are allowed to operate while  ...  A new acyclic orientation is defined and the whole process is then repeated for the new set of sinks. Letω = g(ω) denote this greedy operation.  ...

### Grid Orientations, (d,d + 2)-Polytopes, and Arrangements of Pseudolines

Stefan Felsner, Bernd Gärtner, Falk Tschirschnitz
2005 Discrete & Computational Geometry
with all intermediate orientations being admissible or unique sink, respectively.  ...  For example, it is shown that any two admissible and more generally any two unique sink orientations of the (n, m)-grid (Definition 2.1) can be transformed into each other by a sequence of edge-flips,  ...  Theorem 4. 1 . 1 Any two unique sink orientations G and G of the (n, m)-grid can be transformed into each other by a sequence of edge-flips, with all intermediate orientations being unique sink orientations  ...

### Fast Encryption for Multi-Hop Wireless Sensor Networks using Gaussian Transposition Cipher

2020 VOLUME-8 ISSUE-10, AUGUST 2019, REGULAR ISSUE
distance of node from sink node (D i ), normalized residual energy of node (E i ) and normalized angle of orientation with respect to sink node (A i ).  ...  Sink node encrypts M cluster head unique codes as follows.  CH i = CH i ⊕ BSK  S i = Rand()  Store S i in NodeInfo < S >  S i = S i ⊕ GK1 i  CH i ' = CH i || S i 5) Finally, sink node broadcasts encrypted  ...
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