Filters








36,115 Hits in 2.6 sec

Binary Non-tiles [article]

Don Coppersmith, Victor S. Miller
2011 arXiv   pre-print
In some problems in coding theory and hashing we are given a putative tile V, and wish to know whether or not it is a tile.  ...  We apply both criteria to a list of putative tiles given by Gordon, Miller, and Ostapenko in that none of them are, in fact, tiles.  ...  Resolving the existence of fullrank tiling of binary Hamming spaces. SIAM J. Discrete Math., 18:382-387, 2004. [7] Ari Trachtenberg and Alexander Vardy. Full-rank tiling of F 8 2 do not exist.  ... 
arXiv:0911.1388v2 fatcat:nsm4bqzkbzglzj4ahyxwdee26i

Diffraction of a binary non-Pisot inflation tiling

Michael Baake, Uwe Grimm
2017 Journal of Physics, Conference Series  
A one-parameter family of binary inflation rules in one dimension is considered. Apart from the first member, which is the well-known Fibonacci rule, no inflation factor is a unit.  ...  Let us close by commenting on the other non-Pisot members of our inflation tiling family.  ...  In all remaining cases, the PF eigenvalue is irrational, but fails to be a Pisot-Vijayaraghavan (PV) number, which means that none of the corresponding tilings can have non-trivial point spectrum [9,  ... 
doi:10.1088/1742-6596/809/1/012026 fatcat:zcqorvfn7bexfcf543a7mccgoe

Page 3424 of Mathematical Reviews Vol. , Issue 97F [page]

1997 Mathematical Reviews  
In particular, the authors prove that if M is a non-binary, non-ternary 3-connected matroid having neither U2; nor U35 as minors, then M is not representable over any field.  ...  set of distinct polyominoes such that copies of members of the set can be used to tile the whole plane, but only non-periodically?”  ... 

A Combinatorial Approach to Positional Number Systems [article]

Andrew Vince
2013 arXiv   pre-print
Our combinatorial approach is to construct infinitely many binary radix systems, each one from a single pair of binary strings.  ...  This paper concerns binary radix systems, i.e., positional number systems with digits 0 and 1.  ...  Then T is a collection of non-overlapping intervals whose union is R + . The set T will be referred to as the tiling of R + for the binary radix system.  ... 
arXiv:1205.6460v2 fatcat:fmikgbhggrh7pdhlf4dtwcrigu

Exact holographic tensor networks for the Motzkin spin chain [article]

Rafael N. Alexander, Glen Evenbly, Israel Klich
2021 arXiv   pre-print
In particular, our network offers a two-dimensional representation of this state by a correspondence between walks and a type of tiling of a square lattice.  ...  Thus, the binary height tensor network can be modified to include non-unit values of t by introducing a layerdependent reweighing of the tiles.  ...  We find it convenient to encode both the walk and the binary addition using a set of tiles, as explained below.  ... 
arXiv:1806.09626v4 fatcat:ewmjty7bnrfxvk2q3sjykddb7i

Exact holographic tensor networks for the Motzkin spin chain

Rafael N. Alexander, Glen Evenbly, Israel Klich
2021 Quantum  
In particular, our network offers a two-dimensional representation of this state by a correspondence between walks and a type of tiling of a square lattice.  ...  Thus, the binary height tensor network can be modified to include non-unit values of t by introducing a layerdependent reweighing of the tiles.  ...  We find it convenient to encode both the walk and the binary addition using a set of tiles, as explained below.  ... 
doi:10.22331/q-2021-09-21-546 fatcat:vyemm7iwkrhvfftgpzxbmvva7u

Self assembly of rectangular shapes on concentration programming and probabilistic tile assembly models

Vamsi Kundeti, Sanguthevar Rajasekaran
2012 Natural Computing  
This technique eliminates the need for sub-tiles which perform binary arithmetic, reduces the constant in the asymptotic bound, and eliminates the need for approximate frames (Kao et al.  ...  In: proceedings of the 50th annual IEEE symposium on foundations of computer science (FOCS), IEEE, Atlanta. pp 85-94, 2009)-which can only self assembly squares and rely on tiles which perform binary arithmetic  ...  At any stage i, the non-determinism part is induced by tiles and (green colored tile, see Fig. 6 ) which compete to bind with .  ... 
doi:10.1007/s11047-012-9313-1 pmid:24311993 pmcid:PMC3848893 fatcat:lupyp767hnhqzkye273gibztt4

Bit-GraphBLAS: Bit-Level Optimizations of Matrix-Centric Graph Processing on GPU [article]

Jou-An Chen, Hsin-Hsuan Sung, Xipeng Shen, Nathan Tallent, Kevin Barker, Ang Li
2022 arXiv   pre-print
Figure 3a shows that when the tile size equals 4×4, there are less than 30% non-empty tiles; when the tile size equals 32×32, non-empty tiles reach more than 80% for some matrices.  ...  The reason is that although increasing tile size can decrease the number of non-empty tiles, the reduction is often less than 4× (the times of per tile size increment), causing the ratio of non-empty tiles  ... 
arXiv:2201.08560v2 fatcat:odfeqnu525ch5btls2ajvaera4

Infinite-pressure phase diagram of binary mixtures of (non)additive hard disks [article]

Etienne Fayen, Anuradha Jagannathan, Giuseppe Foffi, Frank Smallenburg
2020 arXiv   pre-print
Increasing non-additivity both gives rise to additional crystal phases and broadens the stability regime for crystal structures involving a large number of large-small contacts, including random tilings  ...  Additionally, we identify random tiling regions to predict random tiling quasicrystal stability ranges.  ...  BINARY NON-ADDITIVE HARD DISK MIXTURES We now turn our attention to non-additive binary hard-disk mixtures, focusing on non-additivity parameters ∆ = 0.03, 0.05 and 0.1.  ... 
arXiv:2003.08889v1 fatcat:ly2pgcmxb5bbtikt7g2pawqcqy

Translationally Invariant Universal Classical Hamiltonians

Tamara Kohler, Toby Cubitt
2019 Journal of statistical physics  
The proof draws on techniques from theoretical computer science, in particular recent complexity theoretic results on tiling problems.  ...  binary counter Turing machine, and we could simply run the non-universal Turing machine on poly(n) spins.  ...  Any non-optimal tiling will incur an energy penalty of Δ, so provided Δ > E max (H ) any spin configuration which corresponds to an non-optimal tiling will not have energy below the energy cut-off.  ... 
doi:10.1007/s10955-019-02295-3 fatcat:kaeafmsxvraxrb4apnavfp6zoa

Universal Computation and Optimal Construction in the Chemical Reaction Network-Controlled Tile Assembly Model [chapter]

Nicholas Schiefer, Erik Winfree
2015 Lecture Notes in Computer Science  
We introduce a new model of tile-based self-assembly in which a well-mixed chemical reaction network interacts with self-assembling tiles to exert non-local control on the self-assembly process.  ...  Although tile self-assembly provides a powerful framework for describing Turing-universal self-assembling systems, assembly logic in tile selfassembly is localized, so that only the nearby environment  ...  Consequently, we aim to leverage the non-local information transfer offered by chemical reaction networks to exercise non-local control over a two-dimensional (or, in principle, three-dimensional) tile  ... 
doi:10.1007/978-3-319-21999-8_3 fatcat:zaemkuudwjhzhexedkc4lrabfm

Resiliency to Multiple Nucleation in Temperature-1 Self-Assembly [chapter]

Matthew J. Patitz, Trent A. Rogers, Robert T. Schweller, Scott M. Summers, Andrew Winslow
2016 Lecture Notes in Computer Science  
The construction uses "cyclic, colliding" binary counters, and assembles the shape non-deterministically.  ...  We consider problems in variations of the two-handed abstract Tile Assembly Model (2HAM), a generalization of Erik Winfree's abstract Tile Assembly Model (aTAM).  ...  A counter for a non-power-of-2 value n involves concatenating up to O(log n) distinct cyclic counters, one for each 1-bit of the binary representation of n.  ... 
doi:10.1007/978-3-319-43994-5_7 fatcat:oh5wi3r7ivfd3drzr4xe5r2fza

Resiliency to multiple nucleation in temperature-1 self-assembly

Matthew J. Patitz, Robert Schweller, Trent A. Rogers, Scott M. Summers, Andrew Winslow
2017 Natural Computing  
The construction uses "cyclic, colliding" binary counters, and assembles the shape non-deterministically.  ...  We consider problems in variations of the two-handed abstract Tile Assembly Model (2HAM), a generalization of Erik Winfree's abstract Tile Assembly Model (aTAM).  ...  A counter for a non-power-of-2 value n involves concatenating up to O(log n) distinct cyclic counters, one for each 1-bit of the binary representation of n.  ... 
doi:10.1007/s11047-017-9662-x fatcat:is54wlcyijaqnad5cx64wvfpxa

Matrix Tile Analysis [article]

Inmar Givoni, Vincent Cheung, Brendan J. Frey
2012 arXiv   pre-print
We introduce a general computational problem, 'matrix tile analysis' (MTA), which consists of decomposing a matrix into a set of non-overlapping tiles, each of which is defined by a subset of usually nonadjacent  ...  MTA does not require an algebra for combining tiles, but must search over discrete combinations of tile assignments.  ...  In order for the model to fully describe the constraints requiring tile elements to be non-overlapping, we introduce an additional set of binary random variables, s t ij whose purpose is to restrict each  ... 
arXiv:1206.6833v1 fatcat:tni5eca65jf4fmnwupcoaii4xu

A divide-and-conquer algorithm for binary matrix completion [article]

Melanie Beckerleg, Andrew Thompson
2019 arXiv   pre-print
Our algorithm, which we call TBMC (Tiling for Binary Matrix Completion), gives interpretable output in the form of binary factors which represent a decomposition of the matrix into tiles.  ...  We propose an algorithm for low rank matrix completion for matrices with binary entries which obtains explicit binary factors.  ...  non-integer.  ... 
arXiv:1907.04251v1 fatcat:pfmtpsl7gfehldtkspmaxezfmm
« Previous Showing results 1 — 15 out of 36,115 results