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Binary Non-tiles
[article]

2011
*
arXiv
*
pre-print

In some problems in coding theory and hashing we are given a putative

arXiv:0911.1388v2
fatcat:nsm4bqzkbzglzj4ahyxwdee26i
*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. ...##
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Diffraction of a binary non-Pisot inflation tiling

2017
*
Journal of Physics, Conference Series
*

A one-parameter family of

doi:10.1088/1742-6596/809/1/012026
fatcat:zcqorvfn7bexfcf543a7mccgoe
*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, ...##
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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?” ...##
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A Combinatorial Approach to Positional Number Systems
[article]

2013
*
arXiv
*
pre-print

Our combinatorial approach is to construct infinitely many

arXiv:1205.6460v2
fatcat:fmikgbhggrh7pdhlf4dtwcrigu
*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. ...##
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Exact holographic tensor networks for the Motzkin spin chain
[article]

2021
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arXiv
*
pre-print

In particular, our network offers a two-dimensional representation of this state by a correspondence between walks and a type of

arXiv:1806.09626v4
fatcat:ewmjty7bnrfxvk2q3sjykddb7i
*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. ...##
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Exact holographic tensor networks for the Motzkin spin chain

2021
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Quantum
*

In particular, our network offers a two-dimensional representation of this state by a correspondence between walks and a type of

doi:10.22331/q-2021-09-21-546
fatcat:vyemm7iwkrhvfftgpzxbmvva7u
*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. ...##
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Self assembly of rectangular shapes on concentration programming and probabilistic tile assembly models

2012
*
Natural Computing
*

This technique eliminates the need for sub-

doi:10.1007/s11047-012-9313-1
pmid:24311993
pmcid:PMC3848893
fatcat:lupyp767hnhqzkye273gibztt4
*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 . ...##
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Bit-GraphBLAS: Bit-Level Optimizations of Matrix-Centric Graph Processing on GPU
[article]

2022
*
arXiv
*
pre-print

Figure 3a shows that when the

arXiv:2201.08560v2
fatcat:odfeqnu525ch5btls2ajvaera4
*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*...##
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Infinite-pressure phase diagram of binary mixtures of (non)additive hard disks
[article]

2020
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arXiv
*
pre-print

Increasing

arXiv:2003.08889v1
fatcat:ly2pgcmxb5bbtikt7g2pawqcqy
*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. ...##
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Translationally Invariant Universal Classical Hamiltonians

2019
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Journal of statistical physics
*

The proof draws on techniques from theoretical computer science, in particular recent complexity theoretic results on

doi:10.1007/s10955-019-02295-3
fatcat:kaeafmsxvraxrb4apnavfp6zoa
*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. ...##
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Universal Computation and Optimal Construction in the Chemical Reaction Network-Controlled Tile Assembly Model
[chapter]

2015
*
Lecture Notes in Computer Science
*

We introduce a new model of

doi:10.1007/978-3-319-21999-8_3
fatcat:zaemkuudwjhzhexedkc4lrabfm
*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*...##
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Resiliency to Multiple Nucleation in Temperature-1 Self-Assembly
[chapter]

2016
*
Lecture Notes in Computer Science
*

The construction uses "cyclic, colliding"

doi:10.1007/978-3-319-43994-5_7
fatcat:oh5wi3r7ivfd3drzr4xe5r2fza
*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. ...##
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Resiliency to multiple nucleation in temperature-1 self-assembly

2017
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Natural Computing
*

The construction uses "cyclic, colliding"

doi:10.1007/s11047-017-9662-x
fatcat:is54wlcyijaqnad5cx64wvfpxa
*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. ...##
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Matrix Tile Analysis
[article]

2012
*
arXiv
*
pre-print

We introduce a general computational problem, 'matrix

arXiv:1206.6833v1
fatcat:tni5eca65jf4fmnwupcoaii4xu
*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 ...##
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A divide-and-conquer algorithm for binary matrix completion
[article]

2019
*
arXiv
*
pre-print

Our algorithm, which we call TBMC (

arXiv:1907.04251v1
fatcat:pfmtpsl7gfehldtkspmaxezfmm
*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. ...
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