Dynamic storage allocation with known durations

This paper is concerned with a new version of on-line storage allocation in which the durations of all processes are known at their arrival time. This version of the problem is motivated by applications in communication networks and has not been studied previously. We provide an on-line algorithm for the problem with a competitive ratio of O(min{log Δ,log τ}), where Δ is the ratio between the longest and shortest duration of a process, and τ is the maximum number of concurrent active processes that have different durations. For the special case where all durations are powers of two, the competitive ratio achieved is O(loglog Δ).     

Similarity Solutions for Thawing Processes with a Heat Flux Condition at the Fixed Boundary

Similarity solutions for a mathematical model for thawing in a saturated semi-infinite porous medium is considered when change of phase induces a density jump and a heat flux condition of the type is imposed on the fixed face x=0. Different cases depending on physical parameters are analysed and the explicit solution is obtained if and only if an inequality for the thermal coefficient q ₀ is verified. An improvement for the existence of a similarity solution for the same free boundary problem with a constant temperature on the fixed face x=0 is also obtained. Sommario. Vengono considerate soluzioni di similarità per un modello matematico di disgelo di un mezzo poroso saturo semi-infinito allorquando il cambiamento di fase induce un salto di densità ed una condizione di flusso di calore del tipo viene imposta sulla faccia fissa x=0. Si analizzano differenti casi dipendenti da parametri fisici e la soluzione esplicita viene ottenuta se e solo se risulta verificata una diseguaglianzo per il coefficiente termico q ₀. Si ottiene altresi un miglioramento della condizione di esistenza di una soluzione di similarità per lo stesso problema al contorno libero con temperatura costante sulla faccia fissa x=0.     

DFT calculations induced a regiochemical outcome revision of the Diels-Alder reaction between levoglucosenone and isoprene

An appealing inversion in the regiochemical outcome of Diels-Alder reactions between levoglucosenone (1) and its α-bromo derivative (5) with isoprene (2) was studied computationally. Based on different DFT calculations we concluded that both reactions should display the same regioselectivity. This result was further validated experimentally.     

Regulating the size and stabilization of lipid raft-like domains and using calcium ions as their probe

We apply a means to probe, stabilize, and control the size of lipid raft-like domains in vitro. In biomembranes the size of lipid rafts is ca. 10-30 nm. In vitro, mixing saturated and unsaturated lipids results in microdomains, which are unstable and coalesce. This inconsistency is puzzling. It has been hypothesized that biological line-active surfactants reduce the line tension between saturated and unsaturated lipids and stabilize small domains in vivo. Using solution X-ray scattering, we studied the structure of binary and ternary lipid mixtures in the presence of calcium ions. Three lipids were used: saturated, unsaturated, and a hybrid (1-saturated-2-unsaturated) lipid that is predominant in the phospholipids of cellular membranes. Only membranes composed of the saturated lipid can adsorb calcium ions, become charged, and therefore considerably swell. The selective calcium affinity was used to show that binary mixtures, containing the saturated lipid, phase separated into large-scale domains. Our data suggests that by introducing the hybrid lipid to a mixture of the saturated and unsaturated lipids, the size of the domains decreased with the concentration of the hybrid lipid, until the three lipids could completely mix. We attribute this behavior to the tendency of the hybrid lipid to act as a line-active cosurfactant that can easily reside at the interface between the saturated and the unsaturated lipids and reduce the line tension between them. These findings are consistent with a recent theory and provide insight into the self-organization of lipid rafts, their stabilization, and size regulation in biomembranes.     

Stability and structure of mixed-ligand metal ion complexes that contain Ni2+, Cu2+, or Zn2+, and Histamine, as well as adenosine 5'-triphosphate (ATP4-) or uridine 5'-triphosphate (UTP(4-): an intricate network of equilibria

With a view on protein–nucleic acid interactions in the presence of metal ions we studied the “simple” mixed‐ligand model systems containing histamine (Ha), the metal ions Ni²⁺, Cu²⁺, or Zn²⁺ (M²⁺), and the nucleotides adenosine 5′‐triphosphate (ATP^4?) or uridine 5′‐triphosphate (UTP^4?), which will both be referred to as nucleoside 5′‐triphosphate (NTP^4?) . The stability constants of the ternary M(NTP)(Ha)^2? complexes were determined in aqueous solution by potentiometric pH titrations. We show for both ternary‐complex types, M(ATP)(Ha)^2? and M(UTP)(Ha)^2?, that intramolecular stacking between the nucleobase and the imidazole residue occurs and that the stacking intensity is approximately the same for a given M²⁺ in both types of complexes: The formation degree of the intramolecular stacks is estimated to be 20 to 50 %. Consequently, in protein–nucleic acid interactions imidazole–nucleobase stacks may well be of relevance. Furthermore, the well‐known formation of macrochelates in binary M²⁺ complexes of purine nucleotides, that is, the phosphate‐coordinated M²⁺ interacts with N7, is confirmed for the M(ATP)^2? complexes. It is concluded that upon formation of the mixed‐ligand complexes the M²⁺? N7 bond is broken and the energy needed for this process corresponds to the stability differences determined for the M(UTP)(Ha)^2? and M(ATP)(Ha)^2? complexes. It is, therefore, possible to calculate from these stability differences of the ternary complexes the formation degrees of the binary macrochelates: The closed forms amount to (65±10) %, (75±8) %, and (31±14) % for Ni(ATP)^2?, Cu(ATP)^2?, and Zn(ATP)^2?, respectively, and these percentages agree excellently with previous results obtained by different methods, confirming thus the internal validity of the data and the arguments used in the evaluation processes. Based on the overall results it is suggested that M(ATP)^2? species, when bound to an enzyme, may exist in a closed macrochelated form only, if no enzyme groups coordinate directly to the metal ion.     

Aqua ions-graphene interfacial and confinement behavior: insights from isobaric-isothermal molecular dynamics

We carry out a systematic microstructural characterization of the solid-fluid interface (SFI) of water and simple metal chloride aqueous solutions in contact with a free-standing plate or with two such plates separated by an interplate distance 0 ≤ h (?) ≤ 30 at ambient conditions via isothermal-isobaric molecular dynamics. With this characterization, we target the interrogation of the system in search for answers to fundamental questions regarding the structure of the "external" and "internal" (confined) SFIs, the effect of the differential hydration behavior among species, and its link to species expulsion from confinement. For water at ambient conditions, we found that the structure of the "external" SFIs is independent of the interplate distance h in the range 0 ≤ h (?) ≤ 30, that is, the absence of wall-mediated correlation effects between "external" and "internal" SFIs, and that for h < 9 ? the slit-pores dewet. Moreover, we observed a selective expulsion of ions caused by the differential hydration between the anion and the cations with a consequent charging of the slit-pore. All these observations were interpreted in terms of the axial profiles for precisely defined order parameters, including tetrahedral configuration, hydrogen bonding, and species coordination numbers.     

On Quillen?s Theorem A for posets

A theorem of McCord of 1966 and Quillen?s Theorem A of 1973 provide sufficient conditions for a map between two posets to be a homotopy equivalence at the level of complexes. We give an alternative elementary proof of this result and we deduce also a stronger statement: under the hypotheses of the theorem, the map is not only a homotopy equivalence but a simple homotopy equivalence. This leads then to stronger formulations of the simplicial version of Quillen?s Theorem A, the Nerve Lemma and other known results. In particular we establish a conjecture of Kozlov on the simple homotopy type of the crosscut complex and we improve a well-known result of Cohen on contractible mappings.     

A new perspective on implementation by voting trees

Voting trees describe an iterative procedure for selecting a single vertex from a tournament. They provide a very general abstract model of decision‐making among a group of individuals, and it has therefore been studied which voting rules have a tree that implements them, i.e., chooses according to the rule for every tournament. While partial results concerning implementable rules and necessary conditions for implementability have been obtained over the past 40 years, a complete characterization of voting rules implementable by trees has proven surprisingly hard to find. A prominent rule that cannot be implemented by trees is the Copeland rule, which singles out vertices with maximum degree. In this paper, we suggest a new angle of attack and re‐examine the implementability of the Copeland solution using paradigms and techniques that are at the core of theoretical computer science. We study the extent to which voting trees can approximate the maximum degree in a tournament, and give upper and lower bounds on the worst‐case ratio between the degree of the vertex chosen by a tree and the maximum degree, both for the deterministic model concerned with a single fixed tree, and for randomizations over arbitrary sets of trees. Our main positive result is a randomization over surjective trees of polynomial size that provides an approximation ratio of at least 1/2. The proof is based on a connection between a randomization over caterpillar trees and a rapidly mixing Markov chain. © 2010 Wiley Periodicals, Inc. Random Struct. Alg., 39, 59–82, 2011     

Foliations with persistent singularities

Let ω be a differential q-form defining a foliation of codimension q in a projective variety. In this article we study the singular locus of ω in various settings. We relate a certain type of singularities, which we name persistent, with the unfoldings of ω, generalizing previous work done on foliations of codimension 1 in projective space. We also relate the absence of persistent singularities with the existence of a connection in the sheaf of 1-forms defining the foliation.     

Determination of nitrate with a flow-injection system combining square-wave polarographic detection with on-line deaeration

The combination of a flow-injection system with square-wave polarography and on-line deaeration is applied to the determination of nitrate, utilizing the catalytic reaction between nitrate and uranyl ion. The method is simple, rapid (60 samples h^?1), sensitive and accurate, with a detection limit of 2 μM nitrate. The method has been applied to the determination of nitrate in drinking and river waters.