bluuebunny/crossref_metadata_2025 huggingface dataset:
Starvation Induces Vacuolar Targeting and Degradation of the Tryptophan Permease in Yeast
Authors: Beck Thomas , Schmidt Anja , Hall Michael N.
Published: July 2002

In Saccharomyces cerevisiae, amino acid permeases are divided into two classes. One class, represented by the general amino acid permease GAP1, contains permeases regulated in response to the nitrogen source. The other class, including the high affinity tryptophan permease, TAT2, consists of the so-called constitutive permeases. We show that TAT2 is regulated at the level of protein stability. In exponentially growing cells, TAT2 is in the plasma membrane and also accumulates in internal compartments of the secretory pathway. Upon nutrient deprivation or rapamycin treatment, TAT2 is transported to and degraded in the vacuole. The ubiquitination machinery and lysine residues within the NH2-terminal 31 amino acids of TAT2 mediate ubiquitination and degradation of the permease. Starvation-induced degradation of internal TAT2 is blocked in sec18, sec23, pep12, and vps27 mutants, but not in sec4, end4, and apg1 mutants, suggesting that, upon nutrient limitation, internal TAT2 is diverted from the late secretory pathway to the vacuolar pathway. Furthermore, our results suggest that TAT2 stability and sorting are controlled by the TOR signaling pathway, and regulated inversely to that of GAP1.
Sphingolipid–Cholesterol Rafts Diffuse as Small Entities in the Plasma Membrane of Mammalian Cells
Authors: Pralle A. , Keller P. , Florin E.-L. , Simons K. , Hörber J.K.H.
Published: July 2002

To probe the dynamics and size of lipid rafts in the membrane of living cells, the local diffusion of single membrane proteins was measured. A laser trap was used to confine the motion of a bead bound to a raft protein to a small area (diam ≤ 100 nm) and to measure its local diffusion by high resolution single particle tracking. Using protein constructs with identical ectodomains and different membrane regions and vice versa, we demonstrate that this method provides the viscous damping of the membrane domain in the lipid bilayer. When glycosylphosphatidylinositol (GPI) -anchored and transmembrane proteins are raft-associated, their diffusion becomes independent of the type of membrane anchor and is significantly reduced compared with that of nonraft transmembrane proteins. Cholesterol depletion accelerates the diffusion of raft-associated proteins for transmembrane raft proteins to the level of transmembrane nonraft proteins and for GPI-anchored proteins even further. Raft-associated GPI-anchored proteins were never observed to dissociate from the raft within the measurement intervals of up to 10 min. The measurements agree with lipid rafts being cholesterol-stabilized complexes of 26 ± 13 nm in size diffusing as one entity for minutes.
Components of a Ubiquitin Ligase Complex Specify Polyubiquitination and Intracellular Trafficking of the General Amino Acid Permease
Authors: Helliwell Stephen B. , Losko Sascha , Kaiser Chris A.
Published: July 2002

Gap1p, the general amino acid permease of Saccharomyces cerevisiae, is regulated by intracellular sorting decisions that occur in either Golgi or endosomal compartments. Depending on nitrogen source, Gap1p is transported to the plasma membrane, where it functions for amino acid uptake, or to the vacuole, where it is degraded. We found that overexpression of Bul1p or Bul2p, two nonessential components of the Rsp5p E3–ubiquitin ligase complex, causes Gap1p to be sorted to the vacuole regardless of nitrogen source. The double mutant bul1Δ bul2Δ has the inverse phenotype, causing Gap1p to be delivered to the plasma membrane more efficiently than in wild-type cells. In addition, bul1Δ bul2Δ can reverse the effect of lst4Δ, a mutation that normally prevents Gap1p from reaching the plasma membrane. Evaluation of Gap1p ubiquitination revealed a prominent polyubiquitinated species that was greatly diminished in a bul1Δ bul2Δ mutant. Both a rsp5-1 mutant and a COOH-terminal truncation of Gap1p behave as bul1Δ bul2Δ, causing constitutive delivery of Gap1p to the plasma membrane and decreasing Gap1p polyubiquitination. These results indicate that Bul1p and Bul2p, together with Rsp5p, generate a polyubiquitin signal on Gap1p that specifies its intracellular targeting to the vacuole.
Lipid raft microdomain compartmentalization of TC10 is required for insulin signaling and GLUT4 translocation
Authors: Watson Robert T. , Shigematsu Satoshi , Chiang Shian-Huey , Mora Silvia , Kanzaki Makoto , Macara Ian G. , Saltiel Alan R. , Pessin Jeffrey E.
Published: July 2002

Recent studies indicate that insulin stimulation of glucose transporter (GLUT)4 translocation requires at least two distinct insulin receptor–mediated signals: one leading to the activation of phosphatidylinositol 3 (PI-3) kinase and the other to the activation of the small GTP binding protein TC10. We now demonstrate that TC10 is processed through the secretory membrane trafficking system and localizes to caveolin-enriched lipid raft microdomains. Although insulin activated the wild-type TC10 protein and a TC10/H-Ras chimera that were targeted to lipid raft microdomains, it was unable to activate a TC10/K-Ras chimera that was directed to the nonlipid raft domains. Similarly, only the lipid raft–localized TC10/ H-Ras chimera inhibited GLUT4 translocation, whereas the TC10/K-Ras chimera showed no significant inhibitory activity. Furthermore, disruption of lipid raft microdomains by expression of a dominant-interfering caveolin 3 mutant (Cav3/DGV) inhibited the insulin stimulation of GLUT4 translocation and TC10 lipid raft localization and activation without affecting PI-3 kinase signaling. These data demonstrate that the insulin stimulation of GLUT4 translocation in adipocytes requires the spatial separation and distinct compartmentalization of the PI-3 kinase and TC10 signaling pathways.
Contraction and polymerization cooperate to assemble and close actomyosin rings around Xenopus oocyte wounds
Authors: Mandato Craig A. , Bement William M.
Published: July 2002

Xenopus oocytes assemble an array of F-actin and myosin 2 around plasma membrane wounds. We analyzed this process in living oocytes using confocal time-lapse (four-dimensional) microscopy. Closure of wounds requires assembly and contraction of a classic “contractile ring” composed of F-actin and myosin 2. However, this ring works in concert with a 5–10-μm wide “zone” of localized actin and myosin 2 assembly. The zone forms before the ring and can be uncoupled from the ring by inhibition of cortical flow and contractility. However, contractility and the contractile ring are required for the stability and forward movement of the zone, as revealed by changes in zone dynamics after disruption of contractility and flow, or experimentally induced breakage of the contractile ring. We conclude that wound-induced contractile arrays are provided with their characteristic flexibility, speed, and strength by the combined input of two distinct components: a highly dynamic zone in which myosin 2 and actin preferentially assemble, and a stable contractile actomyosin ring.
Elevating the level of Cdc34/Ubc3 ubiquitin-conjugating enzyme in mitosis inhibits association of CENP-E with kinetochores and blocks the metaphase alignment of chromosomes
Authors: Topper Leana M. , Bastians Holger , Ruderman Joan V. , Gorbsky Gary J.
Published: July 2002

Cdc34/Ubc3 is a ubiquitin-conjugating enzyme that functions in targeting proteins for proteasome-mediated degradation at the G1 to S cell cycle transition. Elevation of Cdc34 protein levels by microinjection of bacterially expressed Cdc34 into mammalian cells at prophase inhibited chromosome congression to the metaphase plate with many chromosomes remaining near the spindle poles. Chromosome condensation and nuclear envelope breakdown occurred normally, and chromosomes showed oscillatory movements along mitotic spindle microtubules. Most injected cells arrested in a prometaphase-like state. Kinetochores, even those of chromosomes that failed to congress, possessed the normal trilaminar plate ultrastructure. The elevation of Cdc34 protein levels in early mitosis selectively blocked centromere protein E (CENP-E), a mitotic kinesin, from associating with kinetochores. Other proteins, including two CENP-E–associated proteins, BubR1 and phospho-p42/p44 mitogen-activated protein kinase, and mitotic centromere-associated kinesin, cytoplasmic dynein, Cdc20, and Mad2, all exhibited normal localization to kinetochores. Proteasome inhibitors did not affect the prometaphase arrest induced by Cdc34 injection. These studies suggest that CENP-E targeting to kinetochores is regulated by ubiquitylation not involving proteasome-mediated degradation.
Nuclear Factor (NF)-κB2 (p100/p52) Is Required for Normal Splenic Microarchitecture and B Cell–mediated Immune Responses
Authors: Caamaño Jorge H. , Rizzo Cheryl A. , Durham Stephen K. , Barton Debra S. , Raventós-Suárez Carmen , Snapper Clifford M. , Bravo Rodrigo
Published: July 2002

The nfkb2 gene is a member of the Rel/NF-κB family of transcription factors. COOH-terminal deletions and rearrangements of this gene have been associated with the development of human cutaneous T cell lymphomas, chronic lymphocytic leukemias, and multiple myelomas. To further investigate the function of NF-κB2, we have generated mutant mice carrying a germline mutation of the nfkb2 gene by homologous recombination. NF-κB2–deficient mice showed a marked reduction in the B cell compartment in spleen, bone marrow, and lymph nodes. Moreover, spleen and lymph nodes of mutant mice presented an altered architecture, characterized by diffuse, irregular B cell areas and the absence of discrete perifollicular marginal and mantle zones; the formation of secondary germinal centers in spleen was also impaired. Proliferation of NF-κB2–deficient B cells was moderately reduced in response to lipopolysaccharide, anti-IgD-dextran, and CD40, but maturation and immunoglobulin switching were normal. However, nfkb2 (−/−) animals presented a deficient immunological response to T cell–dependent and –independent antigens. These findings indicate an important role of NF-κB2 in the maintenance of the peripheral B cell population, humoral responses, and normal spleen architecture.
Absence of Epithelial Immunoglobulin a Transport, with Increased Mucosal Leakiness, in Polymeric Immunoglobulin Receptor/Secretory Component–Deficient Mice
Authors: Johansen Finn-Eirik , Pekna Marcela , Norderhaug Inger Natvig , Haneberg Bjørn , Hietala Max Albert , Krajci Peter , Betsholtz Christer , Brandtzaeg Per
Published: July 2002

Mucosal surfaces are protected specifically by secretory immunoglobulin A (SIgA) and SIgM generated through external translocation of locally produced dimeric IgA and pentameric IgM. Their active transport is mediated by the epithelial polymeric Ig receptor (pIgR), also called the transmembrane secretory component. Paracellular passive external transfer of systemic and locally produced antibodies also provides mucosal protection, making the biological importance of secretory immunity difficult to assess. Here we report complete lack of active external IgA and IgM translocation in pIgR knockout mice, indicating no redundancy in epithelial transport mechanisms. The knockout mice were of normal size and fertility but had increased serum IgG levels, including antibodies to Escherichia coli, suggesting undue triggering of systemic immunity. Deterioration of their epithelial barrier function in the absence of SIgA (and SIgM) was further attested to by elevated levels of albumin in their saliva and feces, reflecting leakage of serum proteins. Thus, SIgA did not appear to be essential for health under the antigen exposure conditions of these experimental animals. Nevertheless, our results showed that SIgA contributes to maintenance of mucosal homeostasis. Production of SIgA might therefore be a variable in the initiation of human immunopathology such as inflammatory bowel disease or gluten-sensitive enteropathy.
The N-Glycans Determine the Differential Blood Clearance and Hepatic Uptake of Human Immunoglobulin (Ig)a1 and Iga2 Isotypes
Authors: Rifai Abdalla , Fadden Kim , Morrison Sherie L. , Chintalacharuvu Koteswara R.
Published: July 2002

Human immunoglobulin (Ig)A exists in blood as two isotypes, IgA1 and IgA2, with IgA2 present as three allotypes: IgA2m(1), IgA2m(2), and IgA2m(n). We now demonstrate that recombinant, chimeric IgA1 and IgA2 differ in their pharmacokinetic properties. The major pathway for the clearance of all IgA2 allotypes is the liver. Liver-mediated uptake is through the asialoglycoprotein receptor (ASGR), since clearance can be blocked by injection of excess galactose-Ficoll ligand and suppressed in ASGR-deficient mice. In contrast, only a small percentage of IgA1 is cleared through this pathway. The clearance of IgA1 lacking the hinge region with its associated O-linked carbohydrate was more rapid than that of wild-type IgA1. IgA1 and IgA2 that are not rapidly eliminated by the ASGR are both removed through an undefined ASGR-independent pathway with half-lives of 14 and 10 h, respectively. The rapid clearance of IgA2 but not IgA1 through the liver may in part explain why the serum levels of IgA1 are greater than those of IgA2. In addition, dysfunction of the ASGR or altered N-linked glycosylation, but not O-glycans, that affects recognition by this receptor may account for the elevated serum IgA seen in liver disease and IgA nephropathy.
Salmonella-Induced Caspase-2 Activation in Macrophages
Authors: Jesenberger Veronika , Procyk Katarzyna J. , Yuan Junying , Reipert Siegfried , Baccarini Manuela
Published: July 2002

The enterobacterial pathogen Salmonella induces phagocyte apoptosis in vitro and in vivo. These bacteria use a specialized type III secretion system to export a virulence factor, SipB, which directly activates the host's apoptotic machinery by targeting caspase-1. Caspase-1 is not involved in most apoptotic processes but plays a major role in cytokine maturation. We show that caspase-1–deficient macrophages undergo apoptosis within 4–6 h of infection with invasive bacteria. This process requires SipB, implying that this protein can initiate the apoptotic machinery by regulating components distinct from caspase-1. Invasive Salmonella typhimurium targets caspase-2 simultaneously with, but independently of, caspase-1. Besides caspase-2, the caspase-1–independent pathway involves the activation of caspase-3, -6, and -8 and the release of cytochrome c from mitochondria, none of which occurs during caspase-1–dependent apoptosis. By using caspase-2 knockout macrophages and chemical inhibition, we establish a role for caspase-2 in both caspase-1–dependent and –independent apoptosis. Particularly, activation of caspase-1 during fast Salmonella-induced apoptosis partially relies on caspase-2. The ability of Salmonella to induce caspase-1–independent macrophage apoptosis may play a role in situations in which activation of this protease is either prevented or uncoupled from the induction of apoptosis.
Sodium Channel Inactivation Is Altered by Substitution of Voltage Sensor Positive Charges
Authors: Kontis Kris J. , Goldin Alan L.
Published: July 2002

The role of the voltage sensor positive charges in fast and slow inactivation of the rat brain IIA sodium channel was investigated by mutating the second and fourth conserved positive charges in the S4 segments of all four homologous domains. Both charge-neutralizing mutations (by glutamine substitution) and charge-conserving mutations were constructed in a cDNA encoding the sodium channel α subunit. To determine if fast inactivation altered the effects of the mutations on slow inactivation, the mutations were also constructed in a channel that had fast inactivation removed by the incorporation of the IFMQ3 mutation in the III–IV linker (West, J.W., D.E. Patton, T. Scheuer, Y. Wang, A.L. Goldin, and W.A. Catterall. 1992. Proc. Natl. Acad. Sci. USA. 89:10910– 10914). Most of the mutations shifted the v1/2 of fast inactivation in the negative direction, with the largest effects resulting from mutations in domains I and II. These shifts were in the opposite direction compared with those observed for activation. The effects of the mutations on slow inactivation depended on whether fast inactivation was intact or not. When fast inactivation was eliminated, most of the mutations resulted in positive shifts in the v1/2 of slow inactivation. The largest effects again resulted from mutations in domains I and II. When fast inactivation was intact, the mutations in domains II and III resulted in negative shifts in the v1/2 of slow inactivation. Neutralization of the fourth charge in domain I or II resulted in the appearance of a second component in the voltage dependence of slow inactivation that was only observable when fast inactivation was intact. These results suggest the S4 regions of all four domains of the sodium channel are involved in the voltage dependence of inactivation, but to varying extents. Fast inactivation is not strictly coupled to activation, but it derives some independent voltage sensitivity from the charges in the S4 domains. Finally, there is an interaction between the fast and slow inactivation processes.
Glutamine Substitution at Alanine1649 in the S4–S5 Cytoplasmic Loop of Domain 4 Removes the Voltage Sensitivity of Fast Inactivation in the Human Heart Sodium Channel
Authors: Tang Lihui , Chehab Nabil , Wieland Steven J. , Kallen Roland G.
Published: July 2002

Normal activation–inactivation coupling in sodium channels insures that inactivation is slow at small but rapid at large depolarizations. M1651Q/M1652Q substitutions in the cytoplasmic loop connecting the fourth and fifth transmembrane segments of Domain 4 (S4–S5/D4) of the human heart sodium channel subtype 1 (hH1) affect the kinetics and voltage dependence of inactivation (Tang, L., R.G. Kallen, and R. Horn. 1996. J. Gen. Physiol. 108:89–104.). We now show that glutamine substitutions NH2-terminal to the methionines (L1646, L1647, F1648, A1649, L1650) also influence the kinetics and voltage dependence of inactivation compared with the wild-type channel. In contrast, mutations at the COOH-terminal end of the S4–S5/D4 segment (L1654, P1655, A1656) are without significant effect. Strikingly, the A1649Q mutation renders the current decay time constants virtually voltage independent and decreases the voltage dependences of steady state inactivation and the time constants for the recovery from inactivation. Single-channel measurements show that at negative voltages latency times to first opening are shorter and less voltage dependent in A1649Q than in wild-type channels; peak open probabilities are significantly smaller and the mean open times are shorter. This indicates that the rate constants for inactivation and, probably, activation are increased at negative voltages by the A1649Q mutation reminiscent of Y1494Q/ Y1495Q mutations in the cytoplasmic loop between the third and fourth domains (O'Leary, M.E., L.Q. Chen, R.G. Kallen, and R. Horn. 1995. J. Gen. Physiol. 106:641–658.). Other substitutions, A1649S and A1649V, decrease but fail to eliminate the voltage dependence of time constants for inactivation, suggesting that the decreased hydrophobicity of glutamine at either residues A1649 or Y1494Y1495 may disrupt a linkage between S4–S5/D4 and the interdomain 3–4 loop interfering with normal activation–inactivation coupling.
Mechanism of Auxiliary Subunit Modulation of Neuronal α1E Calcium Channels
Authors: Jones Lisa P. , Wei Shao-kui , Yue David T.
Published: July 2002

Voltage-gated calcium channels are composed of a main pore-forming α1 moiety, and one or more auxiliary subunits (β, α2δ) that modulate channel properties. Because modulatory properties may vary greatly with different channels, expression systems, and protocols, it is advantageous to study subunit regulation with a uniform experimental strategy. Here, in HEK 293 cells, we examine the expression and activation gating of α1E calcium channels in combination with a β (β1–β4) and/or the α2δ subunit, exploiting both ionic- and gating-current measurements. Furthermore, to explore whether more than one auxiliary subunit can concomitantly specify gating properties, we investigate the effects of cotransfecting α2δ with β subunits, of transfecting two different β subunits simultaneously, and of COOH-terminal truncation of α1E to remove a second β binding site. The main results are as follows. (a) The α2δ and β subunits modulate α1E in fundamentally different ways. The sole effect of α2δ is to increase current density by elevating channel density. By contrast, though β subunits also increase functional channel number, they also enhance maximum open probability (Gmax/Qmax) and hyperpolarize the voltage dependence of ionic-current activation and gating-charge movement, all without discernible effect on activation kinetics. Different β isoforms produce nearly indistinguishable effects on activation. However, β subunits produced clear, isoform-specific effects on inactivation properties. (b) All the β subunit effects can be explained by a gating model in which subunits act only on weakly voltage-dependent steps near the open state. (c) We find no clear evidence for simultaneous modulation by two different β subunits. (d) The modulatory features found here for α1E do not generalize uniformly to other α1 channel types, as α1C activation gating shows marked β isoform dependence that is absent for α1E. Together, these results help to establish a more comprehensive picture of auxiliary-subunit regulation of α1E calcium channels.
Unitary Ca2+ Current through Cardiac Ryanodine Receptor Channels under Quasi-Physiological Ionic Conditions
Authors: Mejía-Alvarez Rafael , Kettlun Claudia , Ríos Eduardo , Stern Michael , Fill Michael
Published: July 2002

Single canine cardiac ryanodine receptor channels were incorporated into planar lipid bilayers. Single-channel currents were sampled at 1–5 kHz and filtered at 0.2–1.0 kHz. Channel incorporations were obtained in symmetrical solutions (20 mM HEPES-Tris, pH 7.4, and pCa 5). Unitary Ca2+ currents were monitored when 2–30 mM Ca2+ was added to the lumenal side of the channel. The relationship between the amplitude of unitary Ca2+ current (at 0 mV holding potential) and lumenal [Ca2+] was hyperbolic and saturated at ∼4 pA. This relationship was then defined in the presence of different symmetrical CsCH3SO3 concentrations (5, 50, and 150 mM). Under these conditions, unitary current amplitude was 1.2 ± 0.1, 0.65 ± 0.1, and 0.35 ± 0.1 pA in 2 mM lumenal Ca2+; and 3.3 ± 0.4, 2.4 ± 0.2, and 1.63 ± 0.2 pA in 10 mM lumenal Ca2+ (n > 6). Unitary Ca2+ current was also defined in the presence of symmetrical [Mg2+] (1 mM) and low [Cs+] (5 mM). Under these conditions, unitary Ca2+ current in 2 and 10 mM lumenal Ca2+ was 0.66 ± 0.1 and 1.52 ± 0.06 pA, respectively. In the presence of higher symmetrical [Cs+] (50 mM), Mg2+ (1 mM), and lumenal [Ca2+] (10 mM), unitary Ca2+ current exhibited an amplitude of 0.9 ± 0.2 pA (n = 3). This result indicates that the actions of Cs+ and Mg2+ on unitary Ca2+ current were additive. These data demonstrate that physiological levels of monovalent cation and Mg2+ effectively compete with Ca2+ as charge carrier in cardiac ryanodine receptor channels. If lumenal free Ca2+ is 2 mM, then our results indicate that unitary Ca2+ current under physiological conditions should be <0.6 pA.
Controversial medical and agri-food biotechnology: a cultivation analysis
Authors: Bauer Martin W.
Published: July 2002

Whether biotechnology is one or several developments is not clear. Once distinctions are required, the question is: Which one prevails? When the good, the bad, and the ugly settle, where do they fall? Evaluation implies distinction, and representation drives attitude. The controversies over biotechnology are fertile ground on which to study these issues. The imports of genetically modified (GM) soya into Europe in 1996-97 and the cloning of Dolly the sheep from adult cells in 1997 changed the symbolic environment for genetic engineering. The ensuing public controversies came to focus mainly on field trials of GM crops and food labeling. This paper will explore the relationship between quality press coverage and public perception, in particular the cultivation of the contrast between “desirable” biomedical (RED) and “undesirable” agri-food (GREEN) biotechnology in Britain. The argument draws on a systematic analysis of the British press coverage of biotechnology from 1973 to 1999 and analysis of public perceptions in 1996 and 1999. The paper concludes that the debate over GM crops and food ingredients fostered the RED-GREEN contrast among the newspaper-reading public, thereby shielding RED biotechnology from public controversy, and ushered in a realignment of the regulatory framework in 2000.
The face(t)s of biotech in the nineties: how the German press framed modern biotechnology
Authors: Kohring Matthias , Matthes Jörg
Published: July 2002

The following article deals with the different images of modern biotechnology created by the German press in the last decade of the twentieth century. To describe these images we have chosen the theoretical concept of framing, which in general denotes the idea that the media deal with certain issues in different ways and that therefore the coverage offers different perspectives to the reader. We understand a frame as a certain pattern of a text that is composed of several different text elements. We assume that some of these text elements group together systematically in a specific way, thereby forming a certain pattern that can be identified across several texts in a sample. These patterns we call frames. By means of cluster analysis we are able to identify not only predefined but also newly emerging frames and the way framing of an issue changes over time. This methodological approach allows us to give a dynamic overview of how the German press dealt with biotechnology in the early and late nineties.
A Characterization of Finitely Decidable Congruence Modular Varieties
Authors: Idziak Paweł
Published: July 2002

For every finitely generated, congruence modular varietyV\mathcal {V}of finite type we find a finite familyR\mathcal {R}of finite rings such that the varietyV\mathcal {V}is finitely decidable if and only ifV\mathcal {V}is congruence permutable and residually small, all solvable congruences in finite algebras fromV\mathcal {V}are Abelian, each congruence above the centralizer of the monolith of a subdirectly irreducible algebraA\mathbf {A}fromV\mathcal {V}is comparable with all congruences ofA\mathbf {A}, each homomorphic image of a subdirectly irreducible algebra with a non-Abelian monolith has a non-Abelian monolith, and, for each ringRRfromR\mathcal {R}, the variety ofRR–modules is finitely decidable.
Period of the power generator and small values of Carmichael’s function
Authors: Friedlander John , Pomerance Carl , Shparlinski Igor
Published: July 2002

Consider the pseudorandom number generator<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u Subscript n Baseline identical-to u Subscript n minus 1 Superscript e Baseline left-parenthesis mod m right-parenthesis comma 0 less-than-or-equal-to u Subscript n Baseline less-than-or-equal-to m minus 1 comma n equals 1 comma 2 comma ellipsis comma">un≡un−1e(modm),0≤un≤m−1,n=1,2,…,\begin{equation*} u_n\equiv u_{n-1}^e\pmod {m},\quad 0\le u_n\le m-1,\quad n=1,2,\ldots , \end{equation*}where we are given the modulusmm, the initial valueu0=ϑu_0=\varthetaand the exponentee. One case of particular interest is when the modulusmmis of the formplpl, wherep,lp,lare different primes of the same magnitude. It is known from work of the first and third authors that for modulim=plm=pl, if the period of the sequence(un)(u_n)exceedsm3/4+εm^{3/4+\varepsilon }, then the sequence is uniformly distributed. We show rigorously that for almost all choices ofp,lp,lit is the case that for almost all choices ofϑ,e\vartheta ,e, the period of the power generator exceeds(pl)1−ε(pl)^{1-\varepsilon }. And so, in this case, the power generator is uniformly distributed. We also give some other cryptographic applications, namely, to ruling-out the cycling attack on the RSA cryptosystem and to so-called time-release crypto. The principal tool is an estimate related to the Carmichael functionλ(m)\lambda (m), the size of the largest cyclic subgroup of the multiplicative group of residues modulomm. In particular, we show that for anyΔ≥(log⁡log⁡N)3\Delta \ge (\log \log N)^3, we haveλ(m)≥Nexp⁡(−Δ)\lambda (m)\ge N\exp (-\Delta )for all integersmmwith1≤m≤N1\le m\le N, apart from at mostNexp⁡(−0.69(Δlog⁡Δ)1/3)N\exp \left (-0.69\left (\Delta \log \Delta \right )^{1/3}\right )exceptions.
A capitulation problem and Greenberg’s conjecture on real quadratic fields
Authors: Fukuda T. , Komatsu K.
Published: July 2002

We give a sufficient condition in order that an ideal of a real quadratic field

F
F

capitulates in the cyclotomic

Z

3

\mathbb {Z}_3

-extension of

F
F

by using a unit of an intermediate field. Moreover, we give new examples of

F
F

’s for which Greenberg’s conjecture holds by calculating units of fields of degree 6, 18, 54 and 162.
An extrapolation method for a class of boundary integral equations
Authors: Xu Yuesheng , Zhao Yunhe
Published: July 2002

Boundary value problems of the third kind are converted into boundary integral equations of the second kind with periodic logarithmic kernels by using Green’s formulas. For solving the induced boundary integral equations, a Nyström scheme and its extrapolation method are derived for periodic Fredholm integral equations of the second kind with logarithmic singularity. Asymptotic expansions for the approximate solutions obtained by the Nyström scheme are developed to analyze the extrapolation method. Some computational aspects of the methods are considered, and two numerical examples are given to illustrate the acceleration of convergence.
Spontaneous generation of modular invariants
Authors: Cohn Harvey , McKay John
Published: July 2002

It is possible to compute

j
(
τ
)

j(\tau )

and its modular equations with no perception of its related classical group structure except at

∞
\infty

. We start by taking, for

p
p

prime, an unknown “

p
p

-Newtonian” polynomial equation

g
(
u
,
v
)
=
0

g(u,v)=0

with arbitrary coefficients (based only on Newton’s polygon requirements at

∞
\infty

for

u
=
j
(
τ
)

u=j(\tau )

and

v
=
j
(
p
τ
)

v=j(p\tau )

). We then ask which choice of coefficients of

g
(
u
,
v
)

g(u,v)

leads to some consistent Laurent series solution

u
=
u
(
q
)
≈
1

/

q

u=u(q)\approx 1/q

,

v
=
u
(

q

p

)

v=u(q^{p})

(where

q
=
exp
⁡
2
π
i
τ
)

q=\exp 2\pi i\tau )

. It is conjectured that if the same Laurent series

u
(
q
)

u(q)

works for

p
p

-Newtonian polynomials of two or more primes

p
p

, then there is only a bounded number of choices for the Laurent series (to within an additive constant). These choices are essentially from the set of “replicable functions,” which include more classical modular invariants, particularly

u
=
j
(
τ
)

u=j(\tau )

. A demonstration for orders

p
=
2

p=2

and

3
3

is done by computation. More remarkably, if the same series

u
(
q
)

u(q)

works for the

p
p

-Newtonian polygons of 15 special “Fricke-Monster” values of

p
p

, then

(
u
=
)
j
(
τ
)

(u=)j(\tau )

is (essentially) determined uniquely. Computationally, this process stands alone, and, in a sense, modular invariants arise “spontaneously.”
A note on entropy inequalities and error estimates for higher-order accurate finite volume schemes on irregular families of grids
Authors: Noelle Sebastian
Published: July 2002

Recently, Cockburn, Coquel and LeFloch proved convergence and error estimates for higher-order finite volume schemes. Their result is based on entropy inequalities which are derived under restrictive assumptions on either the flux function or the numerical fluxes. Moreover, they assume that the spatial grid satisfies a standard regularity assumption. Using instead entropy inequalities derived in previous work by Kröner, Noelle and Rokyta and a weaker condition on the grid, we can generalize and simplify the error estimates.
Computing canonical heights with little (or no) factorization
Authors: Silverman Joseph
Published: July 2002

Let

E

/

Q

E/ \mathbb {Q}

be an elliptic curve with discriminant 

Δ
\Delta

, and let

P
∈
E
(

Q

)

P\in E( \mathbb {Q})

. The standard method for computing the canonical height

h
^

(
P
)

\hat h(P)

is as a sum of local heights
<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="ModifyingAbove h With caret left-parenthesis upper P right-parenthesis equals ModifyingAbove lamda With caret Subscript normal infinity Baseline left-parenthesis upper P right-parenthesis plus sigma-summation Underscript p Endscripts ModifyingAbove lamda With caret Subscript p Baseline left-parenthesis upper P right-parenthesis">

h
^

(
P
)
=

λ
^

∞

(
P
)
+

∑

p

λ
^

p

(
P
)

\hat h (P)= \hat \lambda _{\infty }(P)+\sum _{p} \hat \lambda _{p}(P)

. There are well-known series for computing the archimedean height 

λ
^

∞

(
P
)

\hat \lambda _{\infty }(P)

, and the non-archimedean heights 

λ
^

p

(
P
)

\hat \lambda _{p}(P)

are easily computed as soon as all prime factors of 

Δ
\Delta

have been determined. However, for curves with large coefficients it may be difficult or impossible to factor 

Δ
\Delta

. In this note we give a method for computing the non-archimedean contribution to 

h
^

(
P
)

\hat h (P)

which is quite practical and requires little or no factorization. We also give some numerical examples illustrating the algorithm.
On quasi-Monte Carlo simulation of stochastic differential equations
Authors: Hofmann Norbert , Mathé Peter
Published: July 2002

In a number of problems of mathematical physics and other fields stochastic differential equations are used to model certain phenomena. Often the solution of those problems can be obtained as a functional of the solution of some specific stochastic differential equation. Then we may use the idea of weak approximation to carry out numerical simulation. We analyze some complexity issues for a class of linear stochastic differential equations (Langevin type), which can be given by
\[

d

X

t

=
−
α

X

t

d
t
+
β
(
t
)
d

W

t

,

X

0

:=
0
,

dX_{t}=-\alpha X_{t}dt+\beta (t)dW_{t}, \quad X_{0}:= 0,

\]
where

α
>
0

\alpha >0

and

β
:
[
0
,
T
]
→

R

\beta : [0,T]\to \mathbb {R}

. It turns out that for a class of input data which are not more than Lipschitz continuous the explicit Euler scheme gives rise to an optimal (by order) numerical method. Then we study numerical phenomena which occur when switching from (real) Monte Carlo simulation to quasi–Monte Carlo simulation, which is the case when we carry out the simulation on computers. It will easily be seen that completely uniformly distributed sequences yield good substitutes for random variates, while not all uniformly distributed (mod 1) sequences are suited. In fact we provide necessary conditions on a sequence in order to serve quasi–Monte Carlo purposes. This condition is expressed in terms of the measure of well-distributions. Numerical examples complement the theoretical analysis.
The exponent of discrepancy is at most 1.4778...
Authors: Wasilkowski Grzegorz , Woźniakowski Henryk
Published: July 2002

We study discrepancy with arbitrary weights in theL2L_2norm over thedd-dimensional unit cube. The exponentp∗p^*of discrepancy is defined as the smallestppfor which there exists a positive numberKKsuch that for allddand allε≤1\varepsilon \le 1there existKε−pK\varepsilon ^{-p}points with discrepancy at mostε\varepsilon. It is well known thatp∗∈(1,2]p^*\in (1,2]. We improve the upper bound by showing that\[p∗≤1.4778842.p^*\le 1.4778842.\]This is done by using relations between discrepancy and integration in the average case setting with the Wiener sheet measure. Our proof isnotconstructive. The known constructive bound on the exponentp∗p^*is2.4542.454.
On the asymptotic spectrum of Hermitian block Toeplitz matrices with Toeplitz blocks
Authors: Tilli Paolo
Published: July 2002

We study the asymptotic behaviour of the eigenvalues of Hermitian

n
×
n

n\times n

block Toeplitz matrices

A

n
,
m

A_{n,m}

, with

m
×
m

m\times m

Toeplitz blocks. Such matrices are generated by the Fourier coefficients of an integrable bivariate function

f
f

, and we study their eigenvalues for large

n
n

and

m
m

, relating their behaviour to some properties of

f
f

as a function; in particular we show that, for any fixed

k
k

, the first

k
k

eigenvalues of

A

n
,
m

A_{n,m}

tend to

inf
f

\inf f

, while the last

k
k

tend to

sup
f

\sup f

, so extending to the block case a well-known result due to Szegö. In the case the

A

n
,
m

A_{n,m}

’s are positive-definite, we study the asymptotic spectrum of

P

n
,
m

−
1

A

n
,
m

P_{n,m}^{-1}A_{n,m}

, where

P

n
,
m

P_{n,m}

is a block Toeplitz preconditioner for the conjugate gradient method, applied to solve the system

A

n
,
m

x
=
b

A_{n,m}x=b

, obtaining strict estimates, when

n
n

and

m
m

are fixed, and exact limit values, when

n
n

and

m
m

tend to infinity, for both the condition number and the conjugate gradient convergence factor of the previous matrices. Extensions to the case of a deeper nesting level of the block structure are also discussed.
Extension theorems for plate elements with applications
Authors: Gu Jinsheng , Hu Xiancheng
Published: July 2002

Extension theorems for plate elements are established. Their applications to the analysis of nonoverlapping domain decomposition methods for solving the plate bending problems are presented. Numerical results support our theory.
Computing ray class groups, conductors and discriminants
Authors: Cohen H. , y Diaz F. , Olivier M.
Published: July 2002

We use the algorithmic computation of exact sequences of Abelian groups to compute the complete structure of

(

Z

K

/

m

)

∗

(\mathbb {Z}_{K}/\mathfrak {m})^{*}

for an ideal

m

\mathfrak {m}

of a number field

K
K

, as well as ray class groups of number fields, and conductors and discriminants of the corresponding Abelian extensions. As an application we give several number fields with discriminants less than previously known ones.
On divisibility of the class number ℎ⁺ of the real cyclotomic fields of prime degree 𝑙
Authors: Jakubec Stanislav
Published: July 2002

In this paper, criteria of divisibility of the class number

h
+

h^+

of the real cyclotomic field

Q

(

ζ
p

+

ζ
p

−
1

)

\mathbf {Q}(\zeta _p+\zeta _p^{-1})

of a prime conductor

p
p

and of a prime degree

l
l

by primes

q
q

the order modulo

l
l

of which is

l
−
1

2

\frac {l-1}{2}

, are given. A corollary of these criteria is the possibility to make a computational proof that a given

q
q

does not divide

h
+

h^+

for any

p
p

(conductor) such that both

p
−
1

2

,

p
−
3

4

\frac {p-1}{2},\frac {p-3}{4}

are primes. Note that on the basis of Schinzel’s hypothesis there are infinitely many such primes

p
p

.
The 𝑑₂-transformation for infinite double series and the 𝐷₂-transformation for infinite double integrals
Authors: Greif Chen , Levin David
Published: July 2002

New transformations for accelerating the convergence of infinite double series and infinite double integrals are presented. These transformations are generalizations of the univariate

d
d

- and

D
D

-transformations. The

D
2

D_2

-transformation for infinite double integrals is efficient if the integrand satisfies a p.d.e. of a certain type. Similarly, the

d
2

d_2

-transformation for double series works well for series whose terms satisfy a difference equation of a certain type. In both cases, the application of the transformation does not require an explicit knowledge of the differential or the difference equation. Asymptotic expansions for the remainders in the infinite double integrals and series are derived, and nonlinear transformations based upon these expansions are presented. Finally, numerical examples which demonstrate the efficiency of these transformations are given.
Accelerated spectral approximation
Authors: Alam Rafikul , Kulkarni Rekha , Limaye Balmohan
Published: July 2002

A systematic development of higher order spectral analysis, introduced by Dellwo and Friedman, is undertaken in the framework of an appropriate product space. Accelerated analogues of Osborn’s results about spectral approximation are presented. Numerical examples are given by considering an integral operator.
The number of primes is finite
Authors: Živković Miodrag
Published: July 2002

For a positive integer

n
n

let

A

n
+
1

=

∑

i
=
1

n

(
−
1

)

n
−
i

i
!
,

A_{n+1}=\sum _{i=1}^n (-1)^{n-i} i!,

!
n
=

∑

i
=
0

n
−
1

i
!

!n = \sum _{i=0}^{n-1} i!

and let

p
1

=
3612703

p_1=3612703

. The number of primes of the form

A
n

A_n

is finite, because if

n
≥

p
1

n\geq p_1

, then

A
n

A_n

is divisible by

p
1

p_1

. The heuristic argument is given by which there exists a prime

p
p

such that

p
∣
!
n

p\mid !n

for all large

n
n

; a computer check however shows that this prime has to be greater than

2

23

2^{23}

. The conjecture that the numbers

!
n

!n

are squarefree is not true because

54503
2

∣

!
26541

{54503^2}\mid {!26541}

.
Elliptic binomial diophantine equations
Authors: Stroeker Roelof , de Weger Benjamin
Published: July 2002

The complete sets of solutions of the equation(nk)=(mℓ)\binom {n}{k} = \binom {m}{\ell }are determined for the cases(k,ℓ)=(2,3)(k,\ell ) = (2,3),(2,4)(2,4),(2,6)(2,6),(2,8)(2,8),(3,4)(3,4),(3,6)(3,6),(4,6)(4,6),(4,8)(4,8). In each of these cases the equation is reduced to an elliptic equation, which is solved by using linear forms in elliptic logarithms. In all but one case this is more or less routine, but in the remaining case ((k,ℓ)=(3,6)(k,\ell ) = (3,6)) we had to devise a new variant of the method.
On the number of zero-patterns of a sequence of polynomials
Authors: Rónyai Lajos , Babai László , Ganapathy Murali
Published: July 2002

Letf=(f1,…,fm)\mathbf {f} =(f_1,\dots ,f_m)be a sequence of polynomials of degree≤d\le dinnnvariables(m≥n)(m\ge n)over a fieldFF. Thezero-patternoff\mathbf {f}atu∈Fnu\in F^nis the set of thoseii(1≤i≤m1\le i\le m) for whichfi(u)=0f_i(u)=0. LetZF(f)Z_F(\mathbf {f})denote the number of zero-patterns off\mathbf {f}asuuranges overFnF^n. We prove thatZF(f)≤∑j=0n(mj)Z_F(\mathbf {f}) \le \sum _{j=0}^n \binom {m}{j}ford=1d=1and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="StartLayout 1st Row with Label left-parenthesis asterisk right-parenthesis EndLabel upper Z Subscript upper F Baseline left-parenthesis bold f right-parenthesis less-than-or-equal-to StartBinomialOrMatrix m d Choose n EndBinomialOrMatrix EndLayout">(∗)ZF(f)≤(mdn)\begin{equation*} Z_F(\mathbf {f})\le \binom {md}{n}\tag {$*$} \end{equation*}ford≥2d\ge 2. Form≥ndm\ge nd, these bounds are optimal within a factor of(7.25)n(7.25)^n. The bound (∗*) improves the bound(1+md)n(1+md)^nproved by J. Heintz (1983) using the dimension theory of affine varieties. Over the field of real numbers, bounds stronger than Heintz’s but slightly weaker than (∗*) follow from results of J. Milnor (1964), H. E.  Warren (1968), and others; their proofs use techniques from real algebraic geometry. In contrast, our half-page proof is a simple application of the elementary “linear algebra bound”. Heintz applied his bound to estimate the complexity of his quantifier elimination algorithm for algebraically closed fields. We give several additional applications. The first two establish the existence of certain combinatorial objects. Our first application, motivated by the “branching program” model in the theory of computing, asserts that over any fieldFF, most graphs withvvvertices haveprojective dimensionΩ(v/log⁡v)\Omega (\sqrt {v/\log v})(the implied constant is absolute). This result was previously known over the reals (Pudlák–Rödl). The second application concerns a lower bound in thespan programmodel for computing Boolean functions. The third application, motivated by a paper by N. Alon, gives nearly tightRamsey boundsfor matrices whose entries are defined by zero-patterns of a sequence of polynomials. We conclude the paper with a number of open problems.
The Δ₃⁰-automorphism method and noninvariant classes of degrees
Authors: Harrington Leo , Soare Robert
Published: July 2002

A setAAof nonnegative integers iscomputably enumerable (c.e.), also calledrecursively enumerable (r.e.), if there is a computable method to list its elements. LetE\mathcal {E}denote the structure of the computably enumerable sets under inclusion,E=({We}e∈ω,⊆)\mathcal {E} = ( \{ W_e \}_{e\in \omega }, \subseteq ). Most previously known automorphismsΦ\Phiof the structureE\mathcal {E}of sets were effective (computable) in the sense thatΦ\Phihas an effective presentation. We introduce here a new method for generating noneffective automorphisms whose presentation isΔ30\Delta ^0_3, and we apply the method to answer a number of long open questions about the orbits of c.e. sets under automorphisms ofE\mathcal {E}. For example, we show that the orbit of every noncomputable (i.e., nonrecursive) c.e. set contains a set of high degree, and hence that for alln>0n>0the well-known degree classesLn\mathbf {L}_n(the lown_nc.e. degrees) andH¯n=R−Hn\overline {\mathbf {H}}_n = \mathbf {R} - \mathbf {H}_n(the complement of the highn_nc.e. degrees) are noninvariant classes.
On an 𝑛-manifold in 𝐂ⁿ near an elliptic complex tangent
Authors: Huang Xiaojun
Published: July 2002

In this paper, we study the local biholomorphic property of a real

n
n

-manifold

M
⊂

C

n

M\subset \mathbf C^n

near an elliptic complex tangent point

p
∈
M

p\in M

. In particular, we are interested in the regularity and the unique disk-filling problem of the local hull of holomorphy

M
~

\widetilde {M}

of

M
M

near

p
p

, first considered in a paper of Bishop. When

M
M

is a

C

∞

C^{\infty }

-smooth submanifold, using a result established by Kenig-Webster, we show that near

p
p

,

M
~

\widetilde {M}

is a smooth Levi-flat

(
n
+
1
)

(n+1)

-manifold with a neighborhood of

p
p

in

M
M

as part of its

C

∞

C^{\infty }

boundary. Moreover, near

p
p

,

M
~

\widetilde {M}

is foliated by a family of disjoint embedded complex analytic disks. We also prove a uniqueness theorem for the analytic disks attached to

M
M

. This result was proved in the previous work of Kenig-Webster when

n
=
2

n=2

. When

M
M

is real analytic, we show that

M
~

\widetilde {M}

is real analytic with a neighborhood of

p
p

in

M
M

as part of its real analytic boundary. Equivalently, we prove the convergence of the formal solutions of a certain functional equation. When

n
=
2

n=2

or when

n
>
2

n>2

but the Bishop invariant does not vanish at the point under study, the analyticity was then previously obtained in the work of Moser-Webster, Moser, and in the author’s joint work with Krantz.
Integral crystalline cohomology over very ramified valuation rings
Authors: Faltings Gerd
Published: July 2002

We explain how to set up an integral version (

Z

p

\mathbb {Z}_{p}

as opposed to

Q

p

\mathbb {Q}_{p}

) of Fontaine’s comparison between crystalline and étale cohomology, over

p
p

-adic fields with arbitrary ramification index. The main results then are that Fontaine’s map respects integrality of Tate-cycles, and a construction of versal deformations of

p
p

-divisible groups with Tate-cycles. An appendix deals with finite generation of crystalline cohomology.
Characterization of the range of the Radon transform on homogeneous trees
Authors: Tarabusi Enrico , Cohen Joel , Colonna Flavia
Published: July 2002

This article contains results on the range of the Radon transform

R
R

on the set

H

\mathcal {H}

of horocycles of a homogeneous tree

T
T

. Functions of compact support on

H

\mathcal {H}

that satisfy two explicit Radon conditions constitute the image under

R
R

of functions of finite support on

T
T

. Replacing functions on

H

\mathcal {H}

by distributions, we extend these results to the non-compact case by adding decay criteria.