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**1**-**20**of**328**| Next »## Search Results

- Author:
- Sussman, Daniel M.; Cho, Yigil; Castle, Toen; Gong, Xingting; Jung, Euiyeon; Yang, Shu; Kamien, Randall D.
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2015 v.112 no.24 pp. 7449-7453
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; cutting; deformation; materials; Show all 4 Subjects- Abstract:
- ... We use a regular arrangement of kirigami elements to demonstrate an inverse design paradigm for folding a flat surface into complex target configurations. We first present a scheme using arrays of disclination defect pairs on the dual to the honeycomb lattice; by arranging these defect pairs properly with respect to each other and choosing an appropriate fold pattern a target stepped surface can b ...
- DOI:
- 10.1073/pnas.1506048112
- PubMed:
- 26015582
- PubMed Central:
- PMC4475981
- http://dx.doi.org/10.1073/pnas.1506048112

- Author:
- Lü, Linyuan; Pan, Liming; Zhou, Tao; Zhang, Yi-Cheng; Stanley, H. Eugene
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2015 v.112 no.8 pp. 2325-2330
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; evolution; prediction; Show all 3 Subjects- Abstract:
- ... The organization of real networks usually embodies both regularities and irregularities, and, in principle, the former can be modeled. The extent to which the formation of a network can be explained coincides with our ability to predict missing links. To understand network organization, we should be able to estimate link predictability. We assume that the regularity of a network is reflected in th ...
- DOI:
- 10.1073/pnas.1424644112
- PubMed:
- 25659742
- PubMed Central:
- PMC4345601
- http://dx.doi.org/10.1073/pnas.1424644112

- Author:
- Zhang, Pan; Moore, Cristopher
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.51 pp. 18144-18149
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; models; physics; Show all 3 Subjects- Abstract:
- ... Modularity is a popular measure of community structure. However, maximizing the modularity can lead to many competing partitions, with almost the same modularity, that are poorly correlated with each other. It can also produce illusory ‘‘communities’’ in random graphs where none exist. We address this problem by using the modularity as a Hamiltonian at finite temperature and using an efficient bel ...
- DOI:
- 10.1073/pnas.1409770111
- PubMed:
- 25489096
- PubMed Central:
- PMC4280643
- http://dx.doi.org/10.1073/pnas.1409770111

- Author:
- Thurston, Dylan Paul
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.27 pp. 9725-9732
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; equations; mathematical models; Show all 3 Subjects- Abstract:
- ... We show that the twisted SL ₂ skein algebra of a surface has a natural basis (the bracelets basis) that is positive, in the sense that the structure constants for multiplication are positive integers. ...
- DOI:
- 10.1073/pnas.1313070111
- PubMed:
- 24982193
- PubMed Central:
- PMC4103368
- http://dx.doi.org/10.1073/pnas.1313070111

- Author:
- Fomin, Sergey; Pylyavskyy, Pavlo
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.27 pp. 9680-9687
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; cluster analysis; equations; Show all 3 Subjects- Abstract:
- ... We construct and study cluster algebra structures in rings of invariants of the special linear group action on collections of 3D vectors, covectors, and matrices. The construction uses Kuperberg’s calculus of webs on marked surfaces with boundary. ...
- DOI:
- 10.1073/pnas.1313068111
- PubMed:
- 24982186
- PubMed Central:
- PMC4103320
- http://dx.doi.org/10.1073/pnas.1313068111

- Author:
- Majda, Andrew J.; Qi, Di; Sapsis, Themistoklis P.
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.21 pp. 7511-7516
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; models; uncertainty; Show all 3 Subjects- Abstract:
- ... A major challenge in contemporary data science is the development of statistically accurate particle filters to capture non-Gaussian features in large-dimensional chaotic dynamical systems. Blended particle filters that capture non-Gaussian features in an adaptively evolving low-dimensional subspace through particles interacting with evolving Gaussian statistics on the remaining portion of phase s ...
- DOI:
- 10.1073/pnas.1405675111
- PubMed:
- 24825886
- PubMed Central:
- PMC4040593
- http://dx.doi.org/10.1073/pnas.1405675111

- Author:
- Pincus, Steve; Singer, Burton H.
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.15 pp. 5485-5490
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; certification; models; Show all 3 Subjects- Abstract:
- ... The certification, construction, and delineation of individual, infinite-length “random” sequences have been longstanding yet incompletely resolved problems. We address this topic via the study of normal numbers, which often have been viewed as reasonable proxies for randomness, given their limiting equidistribution of subblocks of all lengths. However, limitations arise within this perspective. F ...
- DOI:
- 10.1073/pnas.1402621111
- PubMed:
- 24706776
- PubMed Central:
- PMC3992646
- http://dx.doi.org/10.1073/pnas.1402621111

- Author:
- Lee, Jeehyung; Kladwang, Wipapat; Lee, Minjae; Cantu, Daniel; Azizyan, Martin; Kim, Hanjoo; Limpaecher, Alex; Yoon, Sungroh; Treuille, Adrien; Das, Rhiju
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.6 pp. 2122-2127
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; RNA; artificial intelligence; Show all 3 Subjects- Abstract:
- ... Self-assembling RNA molecules present compelling substrates for the rational interrogation and control of living systems. However, imperfect in silico models—even at the secondary structure level—hinder the design of new RNAs that function properly when synthesized. Here, we present a unique and potentially general approach to such empirical problems: the Massive Open Laboratory. The EteRNA projec ...
- DOI:
- 10.1073/pnas.1313039111
- PubMed:
- 24469816
- PubMed Central:
- PMC3926058
- http://dx.doi.org/10.1073/pnas.1313039111

- Author:
- Krzakala, Florent; Moore, Cristopher; Mossel, Elchanan; Neeman, Joe; Sly, Allan; Zdeborová, Lenka; Zhang, Pan
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2013 v.110 no.52 pp. 20935-20940
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; community structure; models; Show all 3 Subjects- Abstract:
- ... Spectral algorithms are classic approaches to clustering and community detection in networks. However, for sparse networks the standard versions of these algorithms are suboptimal, in some cases completely failing to detect communities even when other algorithms such as belief propagation can do so. Here, we present a class of spectral algorithms based on a nonbacktracking walk on the directed edg ...
- DOI:
- 10.1073/pnas.1312486110
- PubMed:
- 24277835
- PubMed Central:
- PMC3876200
- http://dx.doi.org/10.1073/pnas.1312486110

- Author:
- Ozoliņš, Vidvuds; Lai, Rongjie; Caflisch, Russel; Osher, Stanley
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2013 v.110 no.46 pp. 18368-18373
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; equations; mechanics; Show all 3 Subjects- Abstract:
- ... This article describes a general formalism for obtaining spatially localized (“sparse”) solutions to a class of problems in mathematical physics, which can be recast as variational optimization problems, such as the important case of Schrödinger’s equation in quantum mechanics. Sparsity is achieved by adding an [Formula] regularization term to the variational principle, which is shown to yield sol ...
- DOI:
- 10.1073/pnas.1318679110
- PubMed:
- 24170861
- PubMed Central:
- PMC3831964
- http://dx.doi.org/10.1073/pnas.1318679110

- Author:
- McClean, Jarrod R.; Parkhill, John A.; Aspuru-Guzik, Alán
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2013 v.110 no.41 pp. E3901
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; evolution; hydrogen; Show all 3 Subjects- Abstract:
- ... We introduce a discrete-time variational principle inspired by the quantum clock originally proposed by Feynman and use it to write down quantum evolution as a ground-state eigenvalue problem. The construction allows one to apply ground-state quantum many-body theory to quantum dynamics, extending the reach of many highly developed tools from this fertile research area. Moreover, this formalism na ...
- DOI:
- 10.1073/pnas.1308069110
- PubMed:
- 24062428
- PubMed Central:
- PMC3799300
- http://dx.doi.org/10.1073/pnas.1308069110

- Author:
- Calderhead, Ben
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.49 pp. 17408-17413
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; Markov chain; probability distribution; Show all 3 Subjects- Abstract:
- ... Markov chain Monte Carlo methods (MCMC) are essential tools for solving many modern-day statistical and computational problems; however, a major limitation is the inherently sequential nature of these algorithms. In this paper, we propose a natural generalization of the Metropolis−Hastings algorithm that allows for parallelizing a single chain using existing MCMC methods. We do so by proposing mul ...
- DOI:
- 10.1073/pnas.1408184111
- PubMed:
- 25422442
- PubMed Central:
- PMC4267367
- http://dx.doi.org/10.1073/pnas.1408184111

- Author:
- Papadimitriou, Christos
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.45 pp. 15881-15887
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; evolution; markets; social problems; Show all 4 Subjects- Abstract:
- ... Algorithms, perhaps together with Moore’s law, compose the engine of the information technology revolution, whereas complexity—the antithesis of algorithms—is one of the deepest realms of mathematical investigation. After introducing the basic concepts of algorithms and complexity, and the fundamental complexity classes P (polynomial time) and NP (nondeterministic polynomial time, or search proble ...
- DOI:
- 10.1073/pnas.1416954111
- PubMed:
- 25349382
- PubMed Central:
- PMC4234620
- http://dx.doi.org/10.1073/pnas.1416954111

- Author:
- Deift, Percy A.; Menon, Govind; Olver, Sheehan; Trogdon, Thomas
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.42 pp. 14973-14978
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; equations; models; stochastic processes; Show all 4 Subjects- Abstract:
- ... The authors present evidence for universality in numerical computations with random data. Given a (possibly stochastic) numerical algorithm with random input data, the time (or number of iterations) to convergence (within a given tolerance) is a random variable, called the halting time. Two-component universality is observed for the fluctuations of the halting time—i.e., the histogram for the halt ...
- DOI:
- 10.1073/pnas.1413446111
- PubMed:
- 25253892
- PubMed Central:
- PMC4210305
- http://dx.doi.org/10.1073/pnas.1413446111

- Author:
- Lee, Kyungyong; Li, Li; Rupel, Dylan; Zelevinsky, Andrei
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.27 pp. 9712-9716
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; cluster analysis; mathematical models; Show all 3 Subjects- Abstract:
- ... We identify a quantum lift of the greedy basis for rank 2 coefficient-free cluster algebras. Our main result is that our construction does not depend on the choice of initial cluster, that it builds all cluster monomials, and that it produces bar-invariant elements. We also present several conjectures related to this quantum greedy basis and the triangular basis of Berenstein and Zelevinsky. ...
- DOI:
- 10.1073/pnas.1313078111
- PubMed:
- 24982182
- PubMed Central:
- PMC4103316
- http://dx.doi.org/10.1073/pnas.1313078111

- Author:
- Goodearl, Kenneth R.; Yakimov, Milen T.
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.27 pp. 9696-9703
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; cluster analysis; mathematical models; Show all 3 Subjects- Abstract:
- ... A major direction in the theory of cluster algebras is to construct (quantum) cluster algebra structures on the (quantized) coordinate rings of various families of varieties arising in Lie theory. We prove that all algebras in a very large axiomatically defined class of noncommutative algebras possess canonical quantum cluster algebra structures. Furthermore, they coincide with the corresponding u ...
- DOI:
- 10.1073/pnas.1313071111
- PubMed:
- 24982197
- PubMed Central:
- PMC4103338
- http://dx.doi.org/10.1073/pnas.1313071111

- Author:
- Donatelli, Jeffrey J.; Sethian, James A.
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2014 v.111 no.2 pp. 593-598
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; X-radiation; crystallography; nanocrystals; Show all 4 Subjects- Abstract:
- ... X-ray nanocrystallography allows the structure of a macromolecule to be determined from a large ensemble of nanocrystals. However, several parameters, including crystal sizes, orientations, and incident photon flux densities, are initially unknown and images are highly corrupted with noise. Autoindexing techniques, commonly used in conventional crystallography, can determine orientations using Bra ...
- DOI:
- 10.1073/pnas.1321790111
- PubMed:
- 24344317
- PubMed Central:
- PMC3896154
- http://dx.doi.org/10.1073/pnas.1321790111

- Author:
- Baxa, Michael C.; Yu, Wookyung; Adhikari, Aashish N.; Ge, Liang; Xia, Zhen; Zhou, Ruhong; Freed, Karl F.; Sosnick, Tobin R.
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2015 v.112 no.27 pp. 8302-8307
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; mutants; prediction; simple proteins; topology; Show all 5 Subjects- Abstract:
- ... Experimental and computational folding studies of Proteins L & G and NuG2 typically find that sequence differences determine which of the two hairpins is formed in the transition state ensemble (TSE). However, our recent work on Protein L finds that its TSE contains both hairpins, compelling a reassessment of the influence of sequence on the folding behavior of the other two homologs. We character ...
- DOI:
- 10.1073/pnas.1503613112
- PubMed:
- 26100906
- PubMed Central:
- PMC4500205
- http://dx.doi.org/10.1073/pnas.1503613112

- Author:
- Riolo, Maria A.; Rohani, Pejman
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2015 v.112 no.5 pp. E472
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; public health; secondary immunization; vaccines; Show all 4 Subjects- Abstract:
- ... Pertussis has reemerged as a major public health concern in many countries where it was once considered well controlled. Although the mechanisms responsible for continued pertussis circulation and resurgence remain elusive and contentious, many countries have nevertheless recommended booster vaccinations, the timing and number of which vary widely. Here, using a stochastic, age-stratified transmis ...
- DOI:
- 10.1073/pnas.1415573112
- PubMed:
- 25605878
- PubMed Central:
- PMC4321240
- http://dx.doi.org/10.1073/pnas.1415573112

- Author:
- Anderson, Ross; Ashlagi, Itai; Gamarnik, David; Roth, Alvin E.
- Source:
- Proceedings of the National Academy of Sciences of the United States of America 2015 v.112 no.3 pp. 663-668
- ISSN:
- 0027-8424
- Subject:
**algorithms**, etc ; kidney transplant; kidneys; patients; United States; Show all 5 Subjects- Abstract:
- ... As of May 2014 there were more than 100,000 patients on the waiting list for a kidney transplant from a deceased donor. Although the preferred treatment is a kidney transplant, every year there are fewer donors than new patients, so the wait for a transplant continues to grow. To address this shortage, kidney paired donation (KPD) programs allow patients with living but biologically incompatible d ...
- DOI:
- 10.1073/pnas.1421853112
- PubMed:
- 25561535
- PubMed Central:
- PMC4311855
- http://dx.doi.org/10.1073/pnas.1421853112