@article{dobric_gundy_hitczenko_2000, title={Stability properties for a compactly supported prescale function}, volume={31}, ISSN={["0036-1410"]}, DOI={10.1137/S003614109732746X}, abstractNote={We show that if $\phi$ is a continuous, minimally supported prescale function, then its translates are linearly independent on any set of positive measure in the unit interval. This generalizes results of Y. Meyer and P. G. Lemari{e.This result implies that a stability condition, introduced by Gundy and Kazarian for the study of local convergence of spline wavelet expansions, is satisfied for all expansions arising from multiresolution analyses generated by such prescale functions $\phi$.}, number={3}, journal={SIAM JOURNAL ON MATHEMATICAL ANALYSIS}, author={Dobric, V and Gundy, RF and Hitczenko, P}, year={2000}, month={Mar}, pages={574–580} }
 @article{chalker_godbole_hitchzenko_radcliff_ruehr_1999, title={On the size of a random sphere of influence graph}, volume={31}, ISSN={["1475-6064"]}, DOI={10.1017/S0001867800009307}, abstractNote={We approach sphere of influence graphs (SIGs) from a probabilistic perspective. Ordinary SIGs were first introduced by Toussaint as a type of proximity graph for use in pattern recognition, computer vision and other low-level vision tasks. A random sphere of influence graph (RSIG) is constructed as follows. Consider n points uniformly and independently distributed within the unit square in d dimensions. Around each point,
X
               
                  i
               , draw an open ball (‘sphere of influence’) with radius equal to the distance to X
               
                  i
               's nearest neighbour. Finally, draw an edge between two points if their spheres of influence intersect. Asymptotically exact values for the expected number of edges in a RSIG are determined for all values of d; previously, just upper and lower bounds were known for this quantity. A modification of the Azuma-Hoeffding exponential inequality is employed to exhibit the sharp concentration of the number of edges around its expected value.}, number={3}, journal={ADVANCES IN APPLIED PROBABILITY}, author={Chalker, TK and Godbole, AP and Hitchzenko, P and Radcliff, J and Ruehr, OG}, year={1999}, month={Sep}, pages={596–609} }
 @article{hitczenko_janson_yukich_1999, title={On the variance of the random sphere of influence graph}, volume={14}, ISSN={["1042-9832"]}, DOI={10.1002/(SICI)1098-2418(199903)14:2<139::AID-RSA2>3.0.CO;2-E}, abstractNote={We show that the variance of the number of edges in the random sphere of influence graph built on n i.i.d. sites which are uniformly distributed over the unit cube in Rd, grows linearly with n. This is then used to establish a central limit theorem for the number of edges in the random sphere of influence graph built on a Poisson number of sites. Some related proximity graphs are discussed as well. ©1999 John Wiley & Sons, Inc. Random Struct. Alg., 14, 139–152, 1999}, number={2}, journal={RANDOM STRUCTURES & ALGORITHMS}, author={Hitczenko, P and Janson, S and Yukich, JE}, year={1999}, month={Mar}, pages={139–152} }
 @article{figiel_hitczenko_johnson_schechtman_zinn_1997, title={Extremal properties of Rademacher functions with applications to the Khintchine and Rosenthal inequalities}, volume={349}, ISSN={["0002-9947"]}, DOI={10.1090/S0002-9947-97-01789-3}, abstractNote={. The best constant and the extreme cases in an inequality of H.P. Rosenthal, relating the p moment of a sum of independent symmetric random variables to that of the p and 2 moments of the individual variables, are computed in the range 2 < p (cid:20) 4. This complements the work of Utev who has done the same for p > 4. The qualitative nature of the extreme cases turns out to be di(cid:11)erent for p < 4 than for p > 4. The method developed yields results in some more general and other related moment inequalities.}, number={3}, journal={TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY}, author={Figiel, T and Hitczenko, P and Johnson, WB and Schechtman, G and Zinn, J}, year={1997}, month={Mar}, pages={997–1027} }
 @article{muralidharan_rinker_hirsh_bouwer_kelly_1997, title={Hydrogen transfer between methanogens and fermentative heterotrophs in hyperthermophilic cocultures}, volume={56}, DOI={10.1002/(sici)1097-0290(19971105)56:3<268::aid-bit4>3.0.co;2-h}, abstractNote={Interactions involving hydrogen transfer were studied in a coculture of two hyperthermophilic microorganisms: Thermotoga maritima, an anaerobic heterotroph, and Methanococcus jannaschii, a hydrogenotrophic methanogen. Cell densities of T. maritima increased 10-fold when cocultured with M. jannaschii at 85 degrees C, and the methanogen was able to grow in the absence of externally supplied H(2) and CO(2). The coculture could not be established if the two organisms were physically separated by a dialysis membrane, suggesting the importance of spatial proximity. The significance of spatial proximity was also supported by cell cytometry, where the methanogen was only found in cell sorts at or above 4.5 microm in samples of the coculture in exponential phase. An unstructured mathematical model was used to compare the influence of hydrogen transport and metabolic properties on mesophilic and hyperthermophilic cocultures. Calculations suggest the increases in methanogenesis rates with temperature result from greater interactions between the methanogenic and fermentative organisms, as evidenced by the sharp decline in H(2) concentration in the proximity of a hyperthermophilic methanogen. The experimental and modeling results presented here illustrate the need to consider the interactions within hyperthermophilic consortia when choosing isolation strategies and evaluating biotransformations at elevated temperatures.}, number={3}, journal={Biotechnology and Bioengineering}, author={Muralidharan, V. and Rinker, K. D. and Hirsh, I. S. and Bouwer, E. J. and Kelly, Robert}, year={1997}, pages={268–278} }