An improved heuristic for the far from most strings problem

The Far From Most Strings Problem (FFMSP) asks for a string that is far from as many as possible of a given set of strings. All the input and the output strings are of the same length, and two strings are far if their Hamming distance is greater than or equal to a given threshold. FFMSP belongs to the class of sequence consensus problems which have applications in molecular biology, amongst others. FFMSP is NP-hard. It does not admit a constant-ratio approximation either, unless P=NP. In the last few years, heuristic and metaheuristic algorithms have been proposed for the problem, which use local search and require a heuristic, also called an evaluation function, to evaluate candidate solutions during local search. The heuristic function used, for this purpose, in these algorithms is the problem’s objective function. However, since many candidate solutions can be of the same objective value, the resulting search landscape includes many points which correspond to local maxima. In this paper, we devise a new heuristic function to evaluate candidate solutions. We then incorporate the proposed heuristic function within a Greedy Randomized Adaptive Search Procedure (GRASP), a metaheuristic originally proposed for the problem by Festa. The resulting algorithm outperforms state-of-the-art with respect to solution quality, in some cases by orders of magnitude, on both random and real data in our experiments. The results indicate that the number of local optima is considerably reduced using the proposed heuristic.     

The Golod property for powers of ideals and Koszul ideals

Let S be a regular local ring or a polynomial ring over a field and I be an ideal of S. Motivated by a recent result of Herzog and Huneke, we study the natural question of whether $I^m$ is a Golod ideal for all $m\ge 2$. We observe that the Golod property of an ideal can be detected through the vanishing of certain maps induced in homology. This observation leads us to generalize some known results from the graded case to local rings and obtain new classes of Golod ideals.     

Convolution on L p -spaces of a locally compact group

We have recently shown that, for 2 < p < ∞, a locally compact group G is compact if and only if the convolution multiplication f * g exists for all f, g ∈ L ^p (G). Here, we study the existence of f * g for all f, g ∈ L ^p (G) in the case where 0 < p ≤ 2. Also, for 0 < p < ∞, we offer some necessary and sufficient conditions for L ^p (G) * L ^p (G) to be contained in certain function spaces on G.     

Bifurcations and distribution of limit cycles which appear from two nests of periodic orbits

In this paper, we study the distribution and simultaneous bifurcation of limit cycles bifurcated from the two periodic annuli of the holomorphic differential equation , after a small polynomial perturbation. We first show that, under small perturbations of the form , where is a polynomial of degree 2m−1 in which the power of z is odd and the power of is even, the only possible distribution of limit cycles is (u,u) for all values of u=0,1,2,…,m−3. Hence, the sharp upper bound for the number of limit cycles bifurcated from each two period annuli of is m−3, for m≥4. Then we consider a perturbation of the form , where is a polynomial of degree m in which the power of z is odd and obtain the upper bound m−5, for m≥6. Moreover, we show that the distribution (u,v) of limit cycles is possible for 0≤u≤m−5, 0≤v≤m−5 with u+v≤m−2 and m≥9.     

Enhancement of Human γ-Interferon Production in Recombinant <Emphasis Type="Italic">E. coli</Emphasis> Using Batch Cultivation

Development of inexpensive and simple culture media and appropriate induction conditions are always favorable for industry. In this research, chemical composition and stoichiometric data for γ-interferon production and recombinant Escherichia coli growth were used in order to achieve a simple medium and favorable induction conditions. To achieve this goal, the effects of medium composition and induction conditions on the production of γ-interferon were investigated in batch culture of E. coli BL21 (DE3) [pET3a-ifnγ]. These conditions were considered as suitable conditions for the production of γ-interferon: 2.5× M9 medium, supplemented with a mixture of amino acids (milligram per liter), including glutamic acid 215, aspartic acid 250, lysine 160, and phenylalanine 90, and induction at late-log phase (OD₆₀₀ = 4.5). Under these conditions, dry cell weight of 6 ± 0.2 g/l and γ-interferon concentration of 2.15 ± 0.1 g/l were obtained. Later, without changing the concentration ratio of amino acids and glucose, the effect of increase in the primary glucose concentration on productivity of γ-interferon was investigated. It was found that 25 g/l glucose will result in maximum attainable biomass and recombinant human γ-interferon. At improved conditions, a dry cell weight of 14 ± 0.2 g/l, concentration and overall productivity of γ-interferon 4.2 ± 0.1 g/l and 420 ± 10 mg/l h, respectively, were obtained.     

Comparative study of reductive amination reaction on 5-(4-formyl-3,5-dimethoxyphenoxy)valeric acid and its monomethoxy analog using the Multipin™ approach

The 5-(4-formyl-3,5-dimethoxyphenoxy)valeric acid (Barany)linker and its monomethoxy analog were applied to theMultipin method of solid phase synthesis. Acomparative assessment of reductive amination and cleavage ofthese linkers under conditions of multiple synthesis indicatedthat both were applicable to a broad range of primary aminesincluding aniline and 4-nitroaniline. Apart from the greaterlability of the dimethoxy version under TFA cleavage, there wasno observable advantage of one linker over the other within thedescribed experiment.     

Study of Phenolic Compounds Removal from Aqueous Solution by Polymeric Sorbent

This study describes preparation of polymeric sorbent and its use in removal of some phenolic compounds from aqueous solution. The polymer [poly(ethylene glycol dimethacrylate ‐ co‐methacrylic acid)] is stable both thermally and chemically. High temperature (200°C) and strong acidic or alkaline solutions (4 M HCl or NaOH) are not effective on the adsorption characteristics of polymer. Removal process of phenols is pH‐dependent and from the obtained results pH = 7.0 was selected as an optimum pH. Different parameters affecting sorption process were tested, and it was found that the kinetic of sorption is fast; therefore, column experiment at higher flow rates or batch experiment can be used. Methanol was selected as a washing solvent in column experiments. Capacity of sorbent for the studied compounds was tested and the following order was obtained: p‐chlorophenol > p‐aminophenol > phenol.     

Modulated Differential Scanning Calorimetry

The reproducibility and reliability of the TA Instruments Modulated Differential Scanning Calorimeter (MDSC) was tested over a range of conditions. The equipment base line was found to be fairly constant with a very small fluctuation (10 W), which means a 0.1 % fluctuation on the scale of a normal polymer MDSC curve. The excellent stability of the base line and the reasonable reproducibility of the curves (5%) suggest that frequent calibration is not required.The heat capacities calculated from the modulated response to the variable temperature depend on the frequency for a given cell constant. The heat capacity cell constant is a unique function of the modulation frequency:k _c =K _c ^o p/(p–6.3) wherep is the time of the periodicity expressed in seconds and K _c ^o is the heat capacity cell constant measured on a standard material and reduced to zero frequency. The cell constants depend on the flow rate of the helium according to:K(He)=K ^o(1.298–0.004424He+1.438·10^–5 He ²) whereHe is the flow rate of helium in ml min^–1 andK ^o represents a constant at 100 cm³ min^–1. There is a strong dependence of cell constant on the flow rate ranges from 10 to 80 cm³ min^–1, while above this rate (up to 135 ml min^–1) the cell constant approaches a plateau.     

Trans ligand influence in cobalt(III) Schiff base complexes: Electronic and steric effects on the kinetics of hydrolysis

Rate constants for the hydrolysis (k_h) of six different amines in trans‐[Co((BA)₂en)(amine)₂]ClO₄ complexes (amine = aniline 1a , para‐toluidine 1b , benzylamine 1c (primary amines), pyrrolidine 2a , piperidine 2b , morpholine 2c (secondary amines), and (BA)₂en = Bisbenzoylacetoneethylenediiminato) in mixed methanol/water (1:1) solvent have been determined between 30 and 55°C. The hydrolysis product of 2c , trans‐[Co((BA)₂en)(morpholine)(H₂O)]ClO₄, has been separately prepared and characterized by UV–vis and ¹H NMR spectroscopy. Depending on the nature of the axial amine ligand the limiting first‐order rate constants for the amine hydrolysis at 40°C range from (3.42 ± 0.10) × 10^?5 to (5.32 ± 0.13) × 10^?5 s^?1. At the first glance, a reasonable trend cannot be established between k_h and the basicity or the inductive trans effect of the amine ligands. However, when the complexes are classified into two groups, based on the type of the amine (primary and secondary), the values of k_h correlate well with the basicity or inductive effect of the amine in each group. The observed trend in k_h values for the complexes with primary amines is 1a (5.32 ± 0.13) × 10^?5 s^?1 > 1b (3.51 ± 0.14) × 10^?5 > 1c (1.72 ± 0.03) × 10^?5 (40°C), which is opposite to the amine basicity strength. In the case of the complexes with secondary amines, the observed trend in k_h values is in accord with amine basicity (or inductive trans effect), i.e. 2a (5.02 ± 0.22) × 10^?5 > 2b (4.18 ± 0.10) × 10^?5 > 2c (3.42 ± 0.10) × 10^?5 s^?1 (40°C). © 2002 Wiley Periodicals, Inc. Int J Chem Kinet 34: 387–393, 2002