Log Nk Research Articles

Randomized counter-based algorithms for frequency estimation over data streams in [formula omitted] space

This note studies the problem of estimating frequencies of items over data streams. We propose a simple streaming algorithm for the problem in small space complexity. Our algorithm is a counter-based algorithm with the aid of probabilistic counting. We show that our algorithm with k counters computes, with probability at least 1−δ, the estimation with relative error at most (1+ε)N/k, taking O(klog⁡log⁡Nk+klog⁡(ε−1δ−1k)+klog⁡ℓ) space in expectation, where N is the total number of items and ℓ is the number of different items.

Half-plane point retrieval queries with independent and dependent geometric uncertainties

This paper addresses a family of geometric half-plane retrieval queries of points in the plane in the presence of geometric uncertainty. The problems include exact and uncertain point sets and half-plane queries defined by an exact or uncertain line whose location uncertainties are independent or dependent and are defined by k real-valued parameters. Point coordinate uncertainties are modeled with the Linear Parametric Geometric Uncertainty Model (LPGUM), an expressive and computationally efficient worst-case, first order linear approximation of geometric uncertainty that supports parametric dependencies between point locations. We present an efficient O(k2) time and space algorithm for computing the envelope of the LPGUM line that defines the half-plane query. For an exact line and an LPGUM n points set, we present an O(log⁡nk+mk) time query and O(nk) space algorithm, where m is the number of LPGUM points on or above the half-plane line. For a LPGUM line and an exact points set, we present a O(k2+(klog⁡nlog⁡log⁡n)ε+m) time and O(n2log⁡n+kε) space approximation algorithm, where 0<ε≤1 is the desired approximation error. For a LPGUM line and an LPGUM points set, we present two O(k2+(klog⁡nklog⁡log⁡nk)ε+mk) and O(mk2+(klog⁡nklog⁡log⁡nk)ε) time query and O((nk)2log⁡nk+kε) space approximation algorithms for the independent and dependent case, respectively.

INTERSTELLAR ABSORPTION TOWARDS THE NOVAE V339 DEL AND V5668 SGR

We present a search and study of interstellar (IS) absorption features in the observed spectra of two Novae V339 Del and V5668 Sgr. We obtained high resolution spectra (R ≈ 20, 000) in the wavelength range between 3800 and 8800 Å of both novae with the TIGRE telescope. Common IS features of Na I and Ca II were identified in both novae, and the Ca II H and K features of Nova V339 Del show substructures, while a blueshifted absorption feature was found in the spectra of Nova V5668 Sgr. Absorption of K I was identified only in the spectra of Nova V5668 Sgr. The DIBs 6196, 6203, 6379, 6614 and 7562 were found in both novae, and in the spectra of Nova V5668 Sgr we could also identify the DIBs 5780, 5797 and 6660. We present the equivalent widths of all features and determined the column densities of Ca II, K I and hydrogen in the direction of Nova V5668 Sgr (log NCa II = 12.50, log NK I = 11.55, log NH = 18.5).

On balanced separators, treewidth, and cycle rank

We investigate relations between different width parameters of graphs, in particular balanced separator number, treewidth, and cycle rank. Our main result states that a graph with balanced separator number k has treewidth at least k but cycle rank at most k · ( 1 + log nk ) , thus refining the previously known bounds, as stated by Robertson and Seymour (1986) and by Bodlaender et al. (1995). Furthermore, we show that the improved bounds are best possible.

Quenched limits for transient, zero speed one-dimensional random walk in random environment

We consider a nearest-neighbor, one dimensional random walk {Xn}n≥0 in a random i.i.d. environment, in the regime where the walk is transient but with zero speed, so that Xn is of order ns for some s<1. Under the quenched law (i.e., conditioned on the environment), we show that no limit laws are possible: There exist sequences {nk} and {xk} depending on the environment only, such that Xnk−xk=o(log nk)2 (a localized regime). On the other hand, there exist sequences {tm} and {sm} depending on the environment only, such that logsm/log tm→s<1 and Pω(Xtm/sm≤x)→1/2 for all x>0 and →0 for x≤0 (a spread out regime).

Evaluation of Measuring Methods of Human Serum Albumin-Drug Binding Affinity

This study evaluated the feasibility of measuring HSA-drug binding affinity by ordinary (free solution) method. NMR is used to identify where a drug binds. An HSA-immobilized column and mimic ion-exchange columns were developed to measure HSA-drug binding affinity. The correlation between capacity ratios (log k) measured using these columns and HSA-drug binding affinity (log nK) was not perfect. The log k values measured using the mimic ion-exchangers well correlated with log nK values measured by a modified Hummer-Dreyer method with purified HSA. The log k (log KHSA) of basic drugs correlated well with the log nK values measured by the modified Hummer-Dreyer method, but not for the acidic drugs. Simple measurement as the percent concentration of bound drug is another matter. Computational chemical prediction methods were proposed. One uses the molecular properties of drugs. Another involves the direct calculation of binding energy required using model phases. Further study is necessary to develop quick measurement and prediction method to accelerate the drug discovery process.

Molecular Modeling for Quantitative Analysis of Molecular Interaction&amp;#x2020;

The binding affinity (log nK) between human serum albumin and acidic drugs was quantitatively analyzed using a computational chemical method with several model phases. A flat guanidino-phase was the most efficient for calculating log nK values, and docking was easily performed. A flowerpot type model phase bonded a guanidino group at the center bottom demonstrating that ion-ion interaction was the main driving force. A large molecule pushed aside the hydrophobic wall of log P = 5, and reached the guanidino group. Ionized acidic compounds may reach the guanidino group inside a protein by ion-ion interaction through a narrow channel of length 10Å.

Prediction of human serum albumin–drug binding affinity without albumin

A new liquid chromatographic system was developed to measure protein–drug binding affinity indirectly without albumin and was evaluated using log nK values of drugs measured by a modified Hummel–Dreyer method using purified human serum albumin. The retention factors of acidic and basic drugs were measured by reversed-phase and ion-exchange liquid chromatography in sodium phosphate buffer, pH 7.40, containing 50 vol.% methanol at 37 °C. The bonded phases were pentyl, guanidino and carboxyl phases. The combined retention factors were correlated with the log nK values measured by a modified Hummel–Dreyer method because glycosylation of human serum albumin did not significantly affect log nK value. The correlation coefficients were 0.949 ( n=7) for acidic drugs and 0.978 ( n=5) for basic drugs. The log nK values of 26 acidic and 18 basic drugs were predicted from their retention factors measured by reversed-phase and ion-exchange liquid chromatography.

Quantitative analysis of human serum albumin–drug interactions using reversed-phase and ion-exchange liquid chromatography

A new liquid chromatographic system was developed to measure protein-drug binding affinity indirectly and evaluated using log nK values of acidic drugs measured by a modified Hummer–Dryer method using purified human serum albumin. The retention factors of acidic drugs were measured in two reversed-phases and an ion-exchange liquid chromatography. The bonded phases were butyl, phenylpropyl and guanidino phases, and their retention factors were measured in sodium phosphate buffer of pH 7.5. The combined retention factors were correlated with the measured log nK values; the correlation coefficient was 0.948.

Sensitivity Profiles of Diversity Indices

AbstractThe author previously described special sensitivity measures for diversity indices. These measures make possible on analytical treatment of the index sensitivity. In the article a detailed analysis of sensitivity properties of the Hurlbert indices is presented. In the first step the abundances nk were sequenced in an increasing order. Plotting the sensitivity against nk or log nk, essential sensitivity properties can be observed. For example, one can study the sensitivities to changes in the dominant and subdominant abundances, the site of the “nearly neutral” abundance and the site of local sensitivity maxima in the domain of the relatively rare categories. The observations are supported by mathematical reasoning.

On an Estimate of the Partial Sums of Vilenkin-Fourier

AbstractWe show that the partial sums Snf of the Vilenkin-Fourier series of f ∊ L1 are of exponential type off any set where the Hardy-Littlewood maximal function of f is bounded. It then follows that Snkf(x) = o(log log nk) a.e. for any lacunary sequence {nk}. Our results are Vilenkin-Fourier series analogues of those of R. A. Hunt [1].

Phosphatidylserine as a determinant for the tissue distribution of weakly basic drugs in rats.

Interogan variation in tissue distribution of weakly basic drugs such as quinidine, propranolol, and imipramine was investigated as a function of binding to phosphatidylserine (PhS) in tissues. Tissue distributions of these drugs were determined using 10 different tissues at a steady-state plasma concentration and were expressed as tissue-to-plasma partition coefficients (Kp values). The concentration of PhS in the tissue was determined by two-dimensional thin-layer chromatography. Plotting of Kp values, except for brain, against the tissue PhS concentrations showed a linear relationship, indicating that PhS is a determinant in the interorgan variation of these tissue distributions. Further, differences in tissue distribution among the drugs was considered to be due to the difference in binding potency to PhS. Drug binding parameters to individual standard phospholipid were determined using a hexane-pH 4.0 buffer partition system. Binding was highest to PhS, and a linear relationship was found between the log nK [product of the number of binding sites (n) and the association constant (K) for PhS binding] obtained in vitro and Kp values of drugs in tissues in vivo. The empirically derived equation, Kp = 14.3 x (log nK) x (PhS conc.) - 8.09, was found to predict Kp values in vivo of weakly basic drugs. Thus, a determinant of interorgan variation in the tissue distribution of the weakly basic drugs studied was the tissue concentration of PhS and the drug binding affinity to PhS.

The binding characteristics of some adrenergic beta-receptor antagonists to human serum proteins

Binding of pindolol and 8 related compounds was studied in vitro by equilibrium dialysis. The overall binding in serum was compared with the binding to the main, isolated, serum proteins. Most substances show both saturable and non-saturable binding in serum. The saturable and main binding is to α 1-AGP, the low non-saturable binding corresponds to albumin and lipoprotein binding. The binding to α 1 AGP is characterized by approximately one binding site and association constants K ranging from 10 4 to 10 6M −1. The binding of pindolol to α 1-AGP is strongly inhibited by propranolol, lidocaine, erythromycin, imipramine and TBEP. Significant correlations were found between log NK and log partition coefficient octanol-phosphate buffer suggesting that the protein binding of the 9 adrenergic beta-receptor antagonists to all serum proteins, including (α 1-AGP, is predominantly hydrophobic in nature.

A comment on Horton's law of stream numbers

Horton's Law of Stream Numbers is shown to be internally inconsistent in the following sense: If there exists a large channel network of order S, with stream numbers that satisfy Horton's Law exactly, then the mean stream numbers for lower order networks contained in the large one will show definite deviations from Horton's Law. These mean stream numbers can be expressed by a recursive formula, which involves the probabilities Pij that a stream of order i terminates in a stream of order j &gt; i. Reasonable assumptions about the nature of the Pij suggest that Horton curves (log Nk versus k) for the small order basins should be concave upwards, a result which is in general agreement with observation.

On the logarithmic mean of the derived conjugate series of a Fourier series

n k (j) +1 2 E (log I n |Cn 2 < Ek(,) log nk(t)+1 < 2D,. In I nk (A)+' We choose the corresponding Fourier coefficients to define as before a new function g(x), whose Fourier series converges almost everywhere since E .. 1D,, < co. Now we define { m, } to take on the values m, fnk(,) <m fnk(,,)+l for each ,. Since the sequence {nk(,) } is lacunary, the almost everywhere convergence of sm,,,(x; f) to f(x) follows as before. For the sequence { my I, q(nk(A)+1) flnk(,)+1 nk(,) nk (t)+1 nk (r)+1 sh