Motivation Minimal perfect hashing is the problem of mapping a static set of n distinct keys into the address space {1,…,n} bijectively. It is well-known that n log 2(e) bits are necessary to specify a minimal perfect hash function (MPHF) f, when no additional knowledge of the input keys is to be used. However, it is often the case in practice that the input keys have intrinsic relationships that we can exploit to lower the bit complexity of f. For example, consider a string and the set of all its distinct k-mers as input keys: since two consecutive k-mers share an overlap of k−1 symbols, it seems possible to beat the classic log 2(e) bits/key barrier in this case. Moreover, we would like f to map consecutive k-mers to consecutive addresses, as to also preserve as much as possible their relationship in the codomain. This is a useful feature in practice as it guarantees a certain degree of locality of reference for f, resulting in a better evaluation time when querying consecutive k-mers. Results Motivated by these premises, we initiate the study of a new type of locality-preserving MPHF designed for k-mers extracted consecutively from a collection of strings. We design a construction whose space usage decreases for growing k and discuss experiments with a practical implementation of the method: in practice, the functions built with our method can be several times smaller and even faster to query than the most efficient MPHFs in the literature.
Plasma renin activity (PRA) and urinary electrolyte excretion were measured in 137 healthy children aged 6 to 14 years. Plasma aldosterone concentration (PAC) was measured in 52 of the children. Nocturnal 12-hour urine was collected in 110 of the children. Spot urine was collected on two occasions, once just before lying down, once after 90-min supine rest in another 27. Na/K ratio and fractional Na excretion rate (FENa) in 12-hour urine showed a significant inverse correlation with PRA or PAC. Na excretion (mmol/min, mmol/mmol creatinine), Na/K ratio and FENa in the spot urine following 90 min in a supine position showed a significant inverse correlation with PRA or PAC, but they failed to show a significant relationship to PRA or PAC in the spot urine preceding supine rest. A spot urine after 90 min in the supine position is collected easily and hence most appropriate to study the relationship between Na excretion and PRA or PAC clinically.
Couplings of asymmetric two impurities, either magnetic or nonmagnetic, are studied in the singleorbital Alexander-Anderson model with boson interaction. All the possible solutions are obtained by exactly solving it numerically within the Hartree-Fock approximation for arbitrary impurity pair~ with asymmetric localized levels but with the same level-broadening. The phase diagrams constructed in the parameter space and the moment and charge configurations of asymmetric two impurities explain well the observed behaviors of magnetic couplings and moments in the transition-metal alloys. § 1. IntroductionIf iron Fe is alloyed with cobalt Co (or nickel Ni), the ferromagnetic (parallel) coupling develops between Fe and Co (or Ni) moments while if Fe is alloyed with manganese Mn, the anti ferromagnetic (antiparallel) coupling arises. The magnetic moments of Fe are enhanced in the neighborhood of the alloying elements. Mn, however, develops the ferromagnetic coupling with Ni as opposed to the cases with Fe and Co. Another example is the alloys of the nonmagnetic transition metals V, Pd with Fe, where the coupling of Fe with V is antiferromagnetic, while that of Fe with Pd is well known to be ferromagnetic. These magnetic couplings of binary alloys are our motivation here, which we study in the two-impurity model: What type of magnetic (or nonmagnetic) coupling is stabilized as a ground state when arbitrary two atoms (magnetic or nonmagnetic) are immersed to interact in an otherwise free-electron sea?The two-impurity model that has short-range, direct coupling of transfer offers basic mechanisms for magnetic interactions of atoms in concentrated systems. It has been a subject of long history since Alexander and Anderson l ) first started the problem and Moriya 2 ),3) then developed it extensively two decades ago. In the case of identical (symmetric) two impurities the model corresponds to coupling in the pure systems and had clarified the ferro-and antiferromagnetic exchange mechanisms l )-3) in the d-band metals. The model also applies, when a boson coupling 4 ),S) is included, to the rare-earth systems and was recently shown to lead to a new magneticcoupling, broken-symmetrystateS)-S) (which corresponds to the mixed-valence state of the rare-earth metals).In the case of different (asymmetric) two impurities the model corresponds to coupling in the binary alloys of transition and rare-earth elements. The asymmetric model has also been investigated for the degenerate d-orbital case by Moriya 2 ),3) who could explain beautifully the overall trends of observed magnetic couplings in transition-metal alloys. However, the employed second-order expansion treatment in electron transfer V in the Hartree-Fock (HF) theory enabled his explicit calculations only for the limited cases.Recently we succeeded in solving numerically the symmetric two-impurity model for an arbitrary set of the parameters. 7 )In this paper using the same technique we solve at East Tennessee State University on July 1, 2015 http://ptp.oxfordjournals.org/ Down...
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