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Complexity and Intractability: Limitations to Implementation in Analytical Cartography

2000
*
Cartography and Geographic Information Science
*

The three sub-areas are

doi:10.1559/152304000783547849
fatcat:pf6nayh4lvfipo7uzaq4jndury
*map*projections,*map*feature*labeling*, and*map*generalization. ... The computational complexity of algorithms*is*an important consideration for all computer systems, including geographic information systems and*mapping*systems. ... The inverse transformation*is*estimable on an entire regularly spaced grid of*n*(= m-by-m) (x, y) points*in*O(*n**log**n*) time. ...##
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Spike sorting: Bayesian clustering of non-stationary data

2006
*
Journal of Neuroscience Methods
*

At a second stage transition probabilities between candidate mixtures are computed, and a globally optimal clustering

doi:10.1016/j.jneumeth.2006.04.023
pmid:16828167
fatcat:dhy2v44sj5aslmuu566vers6my
*is*found as the*MAP*solution of the resulting probabilistic model. ... We propose an automated technique for the clustering of non-stationary Gaussian sources*in*a Bayesian framework. ... ,π*n*(P 1 , .., P*n*) =*n*i=1 π i D kl (G(x|µ i , Σ i ), G(x|µ * , Σ * )) (5) = H(G(x|µ * , Σ * )) −*n*i=1 π i H(G(x|µ i , Σ i )) = 1 2 (*log*|Σ * | −*n*i=1 π i*log*|Σ i |) using this identity*in*(3) , ...##
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Generative Model for Proposing Drug Candidates Satisfying Anticancer Properties Using a Conditional Variational Autoencoder

2020
*
ACS Omega
*

We confirm that the generated fingerprints, not included

doi:10.1021/acsomega.0c01149
pmid:32775866
pmcid:PMC7407547
fatcat:imivtfpi2va5fcymmngtphnefi
*in*the training data set, represent the desired property using the CVAE model. ...*In*addition, our method can be used as a query expansion method for searching databases because fingerprints generated using our method can be regarded as expanded queries. ... Mean −*log*GI50 of molecules*in*the test set that*is*highly similar to FPs generated from the model. We used five different segments of the target*label*to train the model and generate FPs. ...##
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An Algorithmic Study of Fully Dynamic Independent Sets for Map Labeling

2022
*
ACM Journal of Experimental Algorithmics
*

We conclude with an algorithm that maintains a 2-

doi:10.1145/3514240
fatcat:tekdybdy6bdbrfapw6of7ev2by
*approximate*Max-*IS*for dynamic sets of unit-height and arbitrary-width rectangles with \( O(\*log*^2*n*+ \*omega*\*log**n*) \) update time, where \( \*omega*\ ...*In*a subsequent algorithm, we establish the trade-off between*approximation*quality \( 2(1+\frac{1}{k}) \) and update time \( O(k^2\*log**n*) \) , for \( k\*in*\mathbb {*N*} \) . ... Corollary 5 . 5 We can maintain a 4-*approximate*Max-*IS*of a dynamic set of unit squares,*in*amortized O (*log**n**log**log**n*) update time. 1. 8 : 8 S 88 .Bhore et al. ...##
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Solving the symmetric tridiagonal eigenvalue problem on hypercubes

1993
*
Computers and Mathematics with Applications
*

The corresponding eigenvectors problem can be solved

doi:10.1016/0898-1221(93)90135-i
fatcat:3zkqh37eabdchktbypzyvjsyma
*in*O(*log**n*) time on the same networks. ... O(ml logn) time using O(n2/logn) processors, where ml*is*the number of iterations. ... .,*n*= 2 r. Therefore, there are*log**n*+ 2 stages*in*this network, and the computation time*is*only O(*log**n*) time. ...##
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On the Rigidity of Sparse Random Graphs

2016
*
Journal of Graph Theory
*

We show that

doi:10.1002/jgt.22073
fatcat:6sxkbmwvbraofoyidzaqzbwpom
*in*the sparser case $\*omega*(\frac 1*n*)\leq p\leq \frac{\*log**n*}{*n*}+\*omega*(\frac 1n)$, it holds whp that $G$'s $2$-core*is*rigid. ... A graph with a trivial automorphism group*is*said to be rigid. Wright proved that for $\frac{\*log**n*}{*n*}+\*omega*(\frac 1n)\leq p\leq \frac 12$ a random graph $G\*in*G(*n*,p)$*is*rigid whp. ... The most interesting range of this statement*is*p ≤*log**n*+(1+ )*log**log**n**n*. ...##
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Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix-Vector Products

2021
*
SIAM Journal on Mathematics of Data Science
*

*In*particular, we test the performance of our method on data sets with up to 10 million nodes per layer as well as up to 104 dimensions, resulting

*in*graphs with up to 52 layers. ... Besides the treatment of various applications with an inherent multilayer structure, we present a very flexible approach that interprets high-dimensional data

*in*a low-dimensional multilayer graph representation ... functional (5.1)

*in*the multiclass case, where \

*omega*(x i )

*is*a penalty parameter that

*is*equal to the constant \

*omega*0 \gg 0 for

*labeled*vertices x i and 0 for unlabeled vertices. ...

##
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From Gap-Exponential Time Hypothesis to Fixed Parameter Tractable Inapproximability: Clique, Dominating Set, and More

2020
*
SIAM journal on computing (Print)
*

By outputting any single vertex, we get a trivial polynomial-time

doi:10.1137/18m1166869
fatcat:cfjriedfenae7escnsgsb3xvuu
*n*-*approximation*algorithm. The bound can be improved to O(*n**log**n*) and even to O(*n*(*log**log**n*) 2*log*3*n*) with clever ideas [41] . ... f that are independent of*N*(for Clique, we want f (OPT) = \*omega*(1))? ... Furthermore, 2 \*Omega*(*log*2/3*n*) -factor inapproximability*is*known under the planted clique hypothesis [4] and, under ETH (respectively, Gap-ETH),*n*1/ poly*log**log**n*(respectively,*n*o(1) ) factor ...##
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Counting Solutions to Random CNF Formulas

2021
*
SIAM journal on computing (Print)
*

We give the first efficient algorithm to

doi:10.1137/20m1351527
fatcat:zzdf76xssngipefh5khhqr73kq
*approximately*count the number of solutions*in*the random k-SAT model when the density of the formula scales exponentially with k. ... The main challenge*in*our setting*is*to account for the presence of high-degree variables whose marginal distributions are hard to control and which cause significant correlations within the formula. ...*In*contrast, for a random k-CNF formula, although the average degree of variables*is*low, with high probability there are variables with degrees as high as \*Omega*(*log**n*/*log**log**n*). ...##
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Moments of Uniform Random Multigraphs with Fixed Degree Sequences

2020
*
SIAM Journal on Mathematics of Data Science
*

We study the expected adjacency matrix of a uniformly random multigraph with fixed degree sequence \bfd \

doi:10.1137/19m1288772
fatcat:sqpg5kntafgbpk6berbeb6qls4
*in*\BbbZ*n*+ . ... Its structure*is*well understood for large, sparse, simple graphs: the expected number of edges between nodes i and j*is*roughly Many network data sets are neither large, sparse, nor simple, and*in*these ... (f)*Approximation*of \sigma ij = \sigma (Wij) via (3.16). Note the*log*-*log*axis. ...##
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Artificial Neural Networks for Galaxy Clustering. Learning from the two-point correlation function of BOSS galaxies
[article]

2021
*
arXiv
*
pre-print

The training set

arXiv:2107.11397v1
fatcat:uk2nrpv6orgsdhpet4d6rorw5u
*is*constructed from*log*-normal mock catalogues which reproduce the clustering of the Baryon Oscillation Spectroscopic Survey (BOSS) galaxies. ... We test this new Artificial Neural Network on real BOSS data, finding*Omega*m=0.309p/m0.008, which*is*remarkably consistent with standard analysis results. ... During the training process, the interval of the*labels*, that*is*0.24 ≤ Ω m ≤ 0.38, has been*mapped*into [0, 1] through the following linear operation: L = l − 0.24 0.14 , (9) where l*is*the original*label*...##
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Inapproximability of the Independent Set Polynomial in the Complex Plane

2020
*
SIAM journal on computing (Print)
*

It

doi:10.1137/18m1184485
fatcat:ajevdohpnbeubidanwvxv7aa7u
*is*known that if \lambda*is*a real number*in*the interval ( - \lambda \ast , \lambda c) then there*is*a fully polynomial time*approximation*scheme (FPTAS) for*approximating*Z G (\lambda ) on graphs ...*In*fact, when \lambda*is*outside of \Lambda \Delta and*is*not a positive real number, we give the stronger result that*approximating*Z G (\lambda )*is*actually \#P-hard. ... If \lambda*is**in*the interval - \lambda \ast < \lambda < \lambda c , there*is*a fully polynomial time*approximation*scheme (FPTAS) for*approximating*Z G (\lambda ) on graphs G \*in*\scrG \Delta . ...##
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On approximate decidability of minimal programs
[article]

2014
*
arXiv
*
pre-print

We investigate whether the task of determining minimal indices can be solved

arXiv:1409.0496v1
fatcat:ukz6f6krrjb23gn4ockvrde6ny
*in*an*approximate*sense. ... Our first question, regarding the set of minimal indices,*is*whether there exists an algorithm which can correctly*label*1 out of k indices as either minimal or non-minimal. ... The authors thank Sanjay Jain for useful comments on the presentation of this work and are grateful to Sasha Shen and Nikolay Vereshchagin for their help with the "warm-up"*in*Section 2. ...##
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On the benefits for model regularization of a variational formulation of GTM

2008
*
2008 IEEE International Joint Conference on Neural Networks (IEEE World Congress on Computational Intelligence)
*

*In*this formulation, GTM

*is*prone to data overfitting unless a regularization mechanism

*is*included. ... Generative Topographic

*Mapping*(GTM)

*is*a manifold learning model for the simultaneous visualization and clustering of multivariate data. ... The original three-class structure of the Wine data

*is*only recognized by

*labelling*each class differently

*in*the display. ...

##
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Minimum Label s-t Cut has Large Integrality Gaps
[article]

2019
*
arXiv
*
pre-print

As Min

arXiv:1908.11491v1
fatcat:axgcdul3lncgtewearlrinukqu
*Label*s-t Cut*is*NP-hard and the linear programming technique*is*a main approach to design*approximation*algorithms, our results give negative answer to the hope that designs better*approximation*...*In*this paper, we study two linear programs for Min*Label*s-t Cut, proving that both of them have large integrality gaps, namely,*Omega*(m) and*Omega*(m^1/3-epsilon) for the respective linear programs, where ... Acknowledgements Peng Zhang*is*supported by the National Natural Science Foundation of China (61672323), the Natural Science Foundation of Shandong Province (ZR2016AM28), and the Fundamental Research Funds ...
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