Numerical operator calculus in higher dimensions.

Abstract:

:When an algorithm in dimension one is extended to dimension d, in nearly every case its computational cost is taken to the power d. This fundamental difficulty is the single greatest impediment to solving many important problems and has been dubbed the curse of dimensionality. For numerical analysis in dimension d, we propose to use a representation for vectors and matrices that generalizes separation of variables while allowing controlled accuracy. Basic linear algebra operations can be performed in this representation using one-dimensional operations, thus bypassing the exponential scaling with respect to the dimension. Although not all operators and algorithms may be compatible with this representation, we believe that many of the most important ones are. We prove that the multiparticle Schrödinger operator, as well as the inverse Laplacian, can be represented very efficiently in this form. We give numerical evidence to support the conjecture that eigenfunctions inherit this property by computing the ground-state eigenfunction for a simplified Schrödinger operator with 30 particles. We conjecture and provide numerical evidence that functions of operators inherit this property, in which case numerical operator calculus in higher dimensions becomes feasible.

authors

Beylkin G,Mohlenkamp MJ

doi

10.1073/pnas.112329799

keywords:

subject

Has Abstract

pub_date

2002-08-06 00:00:00

pages

10246-51

issue

16

eissn

0027-8424

issn

1091-6490

pii

112329799

journal_volume

99

pub_type

杂志文章
  • Declining survival probability threatens the North Atlantic right whale.

    abstract::The North Atlantic northern right whale (Eubalaena glacialis) is considered the most endangered large whale species. Its population has recovered only slowly since the cessation of commercial whaling and numbers about 300 individuals. We applied mark-recapture statistics to a catalog of photographically identified ind...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.96.6.3308

    authors: Caswell H,Fujiwara M,Brault S

    更新日期:1999-03-16 00:00:00

  • Analysis of human tumors and human malignant cell lines for BK virus-specific DNA sequences.

    abstract::Most humans in the United States have been infected with BK virus (BKV), a human papovavirus. Because BKV has oncogenic properties, we have investigated whether it may be a cause of human cancer. Basic principles of tumor virology imply that BKV-induced tumors should contain BKV DNA sequences. Therefore, we assayed (b...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.75.1.454

    authors: Wold WS,Mackey JK,Brackmann KH,Takemori N,Rigden P,Green M

    更新日期:1978-01-01 00:00:00

  • In vitro suicide inhibition of self-splicing of a group I intron from Pneumocystis carinii by an N3' --> P5' phosphoramidate hexanucleotide.

    abstract::Binding enhancement by tertiary interactions is a strategy that takes advantage of the higher order folding of functionally important RNAs to bind short nucleic acid-based compounds tightly and more specifically than possible by simple base pairing. For example, tertiary interactions enhance binding of specific hexame...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.96.6.2734

    authors: Testa SM,Gryaznov SM,Turner DH

    更新日期:1999-03-16 00:00:00

  • Interference of the complex between NCS-1 and Ric8a with phenothiazines regulates synaptic function and is an approach for fragile X syndrome.

    abstract::The protein complex formed by the Ca2+ sensor neuronal calcium sensor 1 (NCS-1) and the guanine exchange factor protein Ric8a coregulates synapse number and probability of neurotransmitter release, emerging as a potential therapeutic target for diseases affecting synapses, such as fragile X syndrome (FXS), the most co...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1611089114

    authors: Mansilla A,Chaves-Sanjuan A,Campillo NE,Semelidou O,Martínez-González L,Infantes L,González-Rubio JM,Gil C,Conde S,Skoulakis EM,Ferrús A,Martínez A,Sánchez-Barrena MJ

    更新日期:2017-02-07 00:00:00

  • AMPK blocks starvation-inducible transgenerational defects in Caenorhabditis elegans.

    abstract::Life history events, such as traumatic stress, illness, or starvation, can influence us through molecular changes that are recorded in a pattern of characteristic chromatin modifications. These modifications are often associated with adaptive adjustments in gene expression that can persist throughout the lifetime of t...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1616171114

    authors: Demoinet E,Li S,Roy R

    更新日期:2017-03-28 00:00:00

  • Mechanism by which arylamine N-acetyltransferase 1 ablation causes insulin resistance in mice.

    abstract::A single-nucleotide polymorphism in the human arylamine N-acetyltransferase 2 (Nat2) gene has recently been identified as associated with insulin resistance in humans. To understand the cellular and molecular mechanisms by which alterations in Nat2 activity might cause insulin resistance, we examined murine ortholog N...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1716990115

    authors: Camporez JP,Wang Y,Faarkrog K,Chukijrungroat N,Petersen KF,Shulman GI

    更新日期:2017-12-26 00:00:00

  • Spontaneous molecular reactivation of herpes simplex virus type 1 latency in mice.

    abstract::Infection of the mouse trigeminal ganglia (TG) is the most commonly used model for the study of herpes simplex virus type 1 (HSV-1) latency. Its popularity is caused, at least in part, by the perception that latent infection can be studied in this system in the absence of spontaneous viral reactivation. However, this ...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.022301899

    authors: Feldman LT,Ellison AR,Voytek CC,Yang L,Krause P,Margolis TP

    更新日期:2002-01-22 00:00:00

  • Bivalent domains enforce transcriptional memory of DNA methylated genes in cancer cells.

    abstract::Silencing of multiple cancer-related genes is associated with de novo methylation of linked CpG islands. Additionally, bivalent histone modification profiles characterized by the juxtaposition of active and inactive histone marks have been observed in genes that become hypermethylated in cancer. It is unknown how thes...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.0810133105

    authors: Rodriguez J,Muñoz M,Vives L,Frangou CG,Groudine M,Peinado MA

    更新日期:2008-12-16 00:00:00

  • Reduced vacuolar β-1,3-glucan synthesis affects carbohydrate metabolism as well as plastid homeostasis and structure in Phaeodactylum tricornutum.

    abstract::The β-1,3-glucan chrysolaminarin is the main storage polysaccharide of diatoms. In contrast to plants and green algae, diatoms and most other algal groups do not accumulate storage polysaccharides in their plastids. The diatom Phaeodactylum tricornutum possesses only a single gene encoding a putative β-1,3-glucan synt...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1719274115

    authors: Huang W,Haferkamp I,Lepetit B,Molchanova M,Hou S,Jeblick W,Río Bártulos C,Kroth PG

    更新日期:2018-05-01 00:00:00

  • Tissue-specific regulation of bovine heart cytochrome-c oxidase activity by ADP via interaction with subunit VIa.

    abstract::The activity of reconstituted cytochrome-c oxidase (EC 1.9.3.1) from bovine heart is stimulated by intraliposomal ADP but not by NaCl of the same ionic strength. A monoclonal antibody which reacts with subunits VIa-H (heart-type) and VIc, due to the evolutionary relationship between these subunits, also stimulates the...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.90.5.1652

    authors: Anthony G,Reimann A,Kadenbach B

    更新日期:1993-03-01 00:00:00

  • Picosecond photodissociation and subsequent recombination processes in carbon monoxide hemoglobin.

    abstract::Excitation of HbCO by a single 6-psec 530-nm pulse results in photodissociation with a first-order constant of 0.89 X 10(11) sec-1. The kinetics of photodissociation, monitored by following absorbance changes in the Soret band at 440 nm, are interpreted as corresponding to predissociation followed by a corssing into a...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.75.2.573

    authors: Noe LJ,Eisert WG,Rentzepis PM

    更新日期:1978-02-01 00:00:00

  • Selection of catalytic antibodies for a biosynthetic reaction from a combinatorial cDNA library by complementation of an auxotrophic Escherichia coli: antibodies for orotate decarboxylation.

    abstract::Antibodies capable of decarboxylating orotate were sought by immunization with a hapten designed to elicit antibodies with combining sites that resemble the orotate-binding and catalytic portion of the active site of the enzyme orotidine 5'-monophosphate (OMP) decarboxylase (orotidine-5'-monophosphate carboxy-lyase, E...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.91.18.8319

    authors: Smiley JA,Benkovic SJ

    更新日期:1994-08-30 00:00:00

  • In vitro translation of hypoxanthine/guanine phosphoribosyltransferase mRNA: characterization of a mouse neuroblastoma cell line that has elevated levels of hypoxanthine/guanine phosphoribosyltransferase protein.

    abstract::Antibody specific for the native form of Chinese hamster hypoxanthine/guanine phosphoribosyltransferase (HPRT; IMP:pyrophosphate phosphoribosyltransferase, EC 2.4.2.8) was used to detect the synthesis of HPRT protein in a rabbit reticulocyte lysate translation system primed with mRNA from Chinese hamster tissues and c...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.78.11.6977

    authors: Melton DW,Konecki DS,Ledbetter DH,Hejtmancik JF,Caskey CT

    更新日期:1981-11-01 00:00:00

  • Effect of anti-HLA antisera on macrophage-T-cell interactions.

    abstract::Human T lymphocytes were shown to proliferate in response to tetanus toxoid antigen only in the presence of macrophages. This response was inhibited by anti-DRw but not by anti-HLA (A and B loci) antisera added to the cultures and by pretreatment of macrophages but not of T cells with anti-DRw antisera and complement....

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.76.8.4038

    authors: Geha RS,Milgrom H,Broff M,Alpert S,Martin S,Yunis EJ

    更新日期:1979-08-01 00:00:00

  • Allosteric effects in the marginally stable von Hippel-Lindau tumor suppressor protein and allostery-based rescue mutant design.

    abstract::Many multifunctional tumor suppressor proteins have low stability, a property linked to cancer development. The von Hippel-Lindau tumor suppressor protein (pVHL) is one of these proteins. pVHL forms part of the E3 ubiquitin ligase complex that regulates the degradation of the hypoxia-inducible factor (HIF). Under nati...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.0707401105

    authors: Liu J,Nussinov R

    更新日期:2008-01-22 00:00:00

  • Complex formation between stage-specific oocyte factors and a Xenopus mRNA localization element.

    abstract::It is a long-standing proposal that localization of maternal factors in eggs can provide the basis for pattern formation in the early embryo. The localized information can be stored as RNA, one example being Vg1 RNA, which is localized exclusively to the vegetal hemisphere of Xenopus oocytes and eggs. Localization of ...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.93.25.14608

    authors: Mowry KL

    更新日期:1996-12-10 00:00:00

  • Energy coupling in the lactose transport system of Escherichia coli.

    abstract::A mutant (ML 308-22) was isolated from Escherichia coli ML 308, which had lost the normal capacity to accumulate lactose analogs despite an increase in the membrane carrier activity. The exit of thiomethylgalactoside was much faster than normal, accounting for the inability of the cell to maintain high intracellular c...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.65.1.63

    authors: Wong PT,Kashket ER,Wilson TH

    更新日期:1970-01-01 00:00:00

  • Digoxin derivatives with selectivity for the α2β3 isoform of Na,K-ATPase potently reduce intraocular pressure.

    abstract::The ciliary epithelium in the eye consists of pigmented epithelial cells that express the α1β1 isoform of Na,K-ATPase and nonpigmented epithelial cells that express mainly the α2β3 isoform. In principle, a Na,K-ATPase inhibitor with selectivity for α2β3 that penetrates the cornea could effectively reduce intraocular p...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1514569112

    authors: Katz A,Tal DM,Heller D,Habeck M,Ben Zeev E,Rabah B,Bar Kana Y,Marcovich AL,Karlish SJ

    更新日期:2015-11-03 00:00:00

  • Role of antibody and T cells in the long-term inhibition of IgE synthesis.

    abstract::We have shown that the long-term inhibition of IgE synthesis associated with perinatal inoculation of syngeneic IgE is accompanied by the synthesis of autoantibodies to IgE. Synthesis of IgE can also be inhibited by passive transfer of syngeneic anti-IgE antibodies. In the present investigation we made use of adoptive...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.91.2.604

    authors: Haba S,Nisonoff A

    更新日期:1994-01-18 00:00:00

  • Iridescence in nematics: Photonic liquid crystals of nanoplates in absence of long-range periodicity.

    abstract::Photonic materials with positionally ordered structure can interact strongly with light to produce brilliant structural colors. Here, we found that the nonperiodic nematic liquid crystals of nanoplates can also display structural color with only significant orientational order. Owing to the loose stacking of the nemat...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1906511116

    authors: Zeng M,King D,Huang D,Do C,Wang L,Chen M,Lei S,Lin P,Chen Y,Cheng Z

    更新日期:2019-09-10 00:00:00

  • Disruption of Lrp4 function by genetic deletion or pharmacological blockade increases bone mass and serum sclerostin levels.

    abstract::We identified previously in vitro LRP4 (low-density lipoprotein receptor-related protein 4) as a facilitator of the WNT (Wingless-type) antagonist sclerostin and found mutations disrupting this function to be associated with high bone mass in humans similar to patients lacking sclerostin. To further delineate the role...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1413828111

    authors: Chang MK,Kramer I,Huber T,Kinzel B,Guth-Gundel S,Leupin O,Kneissel M

    更新日期:2014-12-02 00:00:00

  • Estradiol modulates the efficacy of synaptic inhibition by decreasing the dwell time of GABAA receptors at inhibitory synapses.

    abstract::Estrogen plays a critical role in many physiological processes and exerts profound effects on behavior by regulating neuronal excitability. While estrogen has been established to exert effects on dendritic morphology and excitatory neurotransmission its role in regulating neuronal inhibition is poorly understood. Fast...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1705075114

    authors: Mukherjee J,Cardarelli RA,Cantaut-Belarif Y,Deeb TZ,Srivastava DP,Tyagarajan SK,Pangalos MN,Triller A,Maguire J,Brandon NJ,Moss SJ

    更新日期:2017-10-31 00:00:00

  • Insulin receptors in beta-cells are critical for islet compensatory growth response to insulin resistance.

    abstract::Insulin and insulin-like growth factor 1 (IGF1) are ubiquitous growth factors that regulate proliferation in most mammalian tissues including pancreatic islets. To explore the specificity of insulin receptors in compensatory beta-cell growth, we examined two models of insulin resistance. In the first model, we used li...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.0608703104

    authors: Okada T,Liew CW,Hu J,Hinault C,Michael MD,Krtzfeldt J,Yin C,Holzenberger M,Stoffel M,Kulkarni RN

    更新日期:2007-05-22 00:00:00

  • Analogs of palmitoyl-CoA that are substrates for myristoyl-CoA:protein N-myristoyltransferase.

    abstract::Saccharomyces cerevisiae myristoyl-CoA:protein N-myristoyltransferase (Nmt1p; EC 2.3.1.97) is an essential enzyme that is highly selective for myristoyl-CoA in vivo. It is unclear why myristate (C14:0), a rare cellular fatty acid, has been selected for this covalent protein modification over more abundant fatty acids ...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.89.21.10507

    authors: Rudnick DA,Lu T,Jackson-Machelski E,Hernandez JC,Li Q,Gokel GW,Gordon JI

    更新日期:1992-11-01 00:00:00

  • Differences in alpha and beta polypeptide chains of tubulin resolved by electron microscopy with image reconstruction.

    abstract::Electron microscopic techniques have been used to reveal two classes of subunits of tubulin in ordered arrays. Presumably the two classes correspond to the alpha and beta polypeptide chains of tubulin that have been distinguished by chemical criteria. The two types of subunits alternate along individual protofilaments...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.75.10.5006

    authors: Crepeau RH,McEwen B,Edelstein SJ

    更新日期:1978-10-01 00:00:00

  • Mechanism of integrating foreign DNA during transformation of Bacillus subtilis.

    abstract::Genes encoding thymidylate synthetase from Bacillus subtilis bacteriophages were cloned in Escherichia coli. Chimeric plasmids pCD1 and pCD3 were constructed from site-specific endonuclease digests of bacteriophage phi3T DNA cloned in pMB9 in E. coli. Similar cloning techniques with bacteriophage beta22 DNA yielded ch...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.75.8.3664

    authors: Duncan CH,Wilson GA,Young FE

    更新日期:1978-08-01 00:00:00

  • Dimer formation drives the activation of the cell death protease caspase 9.

    abstract::A critical step in the induction of apoptosis is the activation of the apoptotic initiator caspase 9. We show that at its normal physiological concentration, caspase 9 is primarily an inactive monomer (zymogen), and that activity is associated with a dimeric species. At the high concentrations used for crystal formati...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.231465798

    authors: Renatus M,Stennicke HR,Scott FL,Liddington RC,Salvesen GS

    更新日期:2001-12-04 00:00:00

  • P-hacking in clinical trials and how incentives shape the distribution of results across phases.

    abstract::Clinical research should conform to high standards of ethical and scientific integrity, given that human lives are at stake. However, economic incentives can generate conflicts of interest for investigators, who may be inclined to withhold unfavorable results or even tamper with data in order to achieve desired outcom...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1919906117

    authors: Adda J,Decker C,Ottaviani M

    更新日期:2020-06-16 00:00:00

  • Genome-wide network model capturing seed germination reveals coordinated regulation of plant cellular phase transitions.

    abstract::Seed germination is a complex trait of key ecological and agronomic significance. Few genetic factors regulating germination have been identified, and the means by which their concerted action controls this developmental process remains largely unknown. Using publicly available gene expression data from Arabidopsis th...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.1100958108

    authors: Bassel GW,Lan H,Glaab E,Gibbs DJ,Gerjets T,Krasnogor N,Bonner AJ,Holdsworth MJ,Provart NJ

    更新日期:2011-06-07 00:00:00

  • Quorum decision-making facilitates information transfer in fish shoals.

    abstract::Despite the growing interest in collective phenomena such as "swarm intelligence" and "wisdom of the crowds," little is known about the mechanisms underlying decision-making in vertebrate animal groups. How do animals use the behavior of others to make more accurate decisions, especially when it is not possible to ide...

    journal_title:Proceedings of the National Academy of Sciences of the United States of America

    pub_type: 杂志文章

    doi:10.1073/pnas.0710344105

    authors: Ward AJ,Sumpter DJ,Couzin ID,Hart PJ,Krause J

    更新日期:2008-05-13 00:00:00