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Complexity and Intractability: Limitations to Implementation in Analytical Cartography

Alan Saalfeld
2000 Cartography and Geographic Information Science  
The three sub-areas are 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.  ... 
doi:10.1559/152304000783547849 fatcat:pf6nayh4lvfipo7uzaq4jndury

Spike sorting: Bayesian clustering of non-stationary data

Aharon Bar-Hillel, Adam Spiro, Eran Stark
2006 Journal of Neuroscience Methods  
At a second stage transition probabilities between candidate mixtures are computed, and a globally optimal clustering 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.  ...  ,πn (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) ,  ... 
doi:10.1016/j.jneumeth.2006.04.023 pmid:16828167 fatcat:dhy2v44sj5aslmuu566vers6my

Generative Model for Proposing Drug Candidates Satisfying Anticancer Properties Using a Conditional Variational Autoencoder

Sunghoon Joo, Min Soo Kim, Jaeho Yang, Jeahyun Park
2020 ACS Omega  
We confirm that the generated fingerprints, not included 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.  ... 
doi:10.1021/acsomega.0c01149 pmid:32775866 pmcid:PMC7407547 fatcat:imivtfpi2va5fcymmngtphnefi

An Algorithmic Study of Fully Dynamic Independent Sets for Map Labeling

Sujoy Bhore, Guangping Li, Martin Nöllenburg
2022 ACM Journal of Experimental Algorithmics  
We conclude with an algorithm that maintains a 2-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.  ... 
doi:10.1145/3514240 fatcat:tekdybdy6bdbrfapw6of7ev2by

Solving the symmetric tridiagonal eigenvalue problem on hypercubes

Kuo-Liang Chung, Wen-Ming Yan
1993 Computers and Mathematics with Applications  
The corresponding eigenvectors problem can be solved 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.  ... 
doi:10.1016/0898-1221(93)90135-i fatcat:3zkqh37eabdchktbypzyvjsyma

On the Rigidity of Sparse Random Graphs

Nati Linial, Jonathan Mosheiff
2016 Journal of Graph Theory  
We show that 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 .  ... 
doi:10.1002/jgt.22073 fatcat:6sxkbmwvbraofoyidzaqzbwpom

Semi-supervised Learning for Aggregated Multilayer Graphs Using Diffuse Interface Methods and Fast Matrix-Vector Products

Kai Bergermann, Martin Stoll, Toni Volkmer
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.  ... 
doi:10.1137/20m1352028 fatcat:3wrtqnekbnghllv6anwq5lk3wa

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

Parinya Chalermsook, Marek Cygan, Guy Kortsarz, Bundit Laekhanukit, Pasin Manurangsi, Danupon Nanongkai, Luca Trevisan
2020 SIAM journal on computing (Print)  
By outputting any single vertex, we get a trivial polynomial-time 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  ... 
doi:10.1137/18m1166869 fatcat:cfjriedfenae7escnsgsb3xvuu

Counting Solutions to Random CNF Formulas

Andreas Galanis, Leslie Ann Goldberg, Heng Guo, Kuan Yang
2021 SIAM journal on computing (Print)  
We give the first efficient algorithm to 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).  ... 
doi:10.1137/20m1351527 fatcat:zzdf76xssngipefh5khhqr73kq

Moments of Uniform Random Multigraphs with Fixed Degree Sequences

Philip S. Chodrow
2020 SIAM Journal on Mathematics of Data Science  
We study the expected adjacency matrix of a uniformly random multigraph with fixed degree sequence \bfd \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.  ... 
doi:10.1137/19m1288772 fatcat:sqpg5kntafgbpk6berbeb6qls4

Artificial Neural Networks for Galaxy Clustering. Learning from the two-point correlation function of BOSS galaxies [article]

Niccolò Veronesi, Federico Marulli, Alfonso Veropalumbo, Lauro Moscardini
2021 arXiv   pre-print
The training set 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  ... 
arXiv:2107.11397v1 fatcat:uk2nrpv6orgsdhpet4d6rorw5u

Inapproximability of the Independent Set Polynomial in the Complex Plane

Ivona Bezáková, Andreas Galanis, Leslie Ann Goldberg, Daniel Štefankovič
2020 SIAM journal on computing (Print)  
It 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 .  ... 
doi:10.1137/18m1184485 fatcat:ajevdohpnbeubidanwvxv7aa7u

On approximate decidability of minimal programs [article]

Jason Teutsch, Marius Zimand
2014 arXiv   pre-print
We investigate whether the task of determining minimal indices can be solved 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.  ... 
arXiv:1409.0496v1 fatcat:ukz6f6krrjb23gn4ockvrde6ny

On the benefits for model regularization of a variational formulation of GTM

Ivan Olier, Alfredo Vellido
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.  ... 
doi:10.1109/ijcnn.2008.4634005 dblp:conf/ijcnn/OlierV08a fatcat:6o5msr7okzhinluxr3hff24sv4

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

Peng Zhang, Linqing Tang
2019 arXiv   pre-print
As Min 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  ... 
arXiv:1908.11491v1 fatcat:axgcdul3lncgtewearlrinukqu
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