Junan Zhang

Universal compression of memoryless sources over unknown alphabets

It has long been known that the compression redundancy of independent and identically distributed (i.i.d.) strings increases to infinity as the alphabet size grows. It is also apparent that any string can be described by separately conveying its symbols, and its pattern-the order in which the symbols appear. Concentrating on the latter, we show that the patterns of i.i.d. strings over all, including infinite and even unknown, alphabets, can be compressed with diminishing redundancy, both in block and sequentially, and that the compression can be performed in linear time. To establish these results, we show that the number of patterns is the Bell number, that the number of patterns with a given number of symbols is the Stirling number of the second kind, and that the redundancy of patterns can be bounded using results of Hardy and Ramanujan on the number of integer partitions. The results also imply an asymptotically optimal solution for the Good-Turing probability-estimation problem.

Stopping sets and the girth of Tanner graphs

Recent work has related the error probability of iterative decoding over erasure channels to the presence of stopping sets in the Tanner graph of the code used. In particular, it was shown that the smallest number of uncorrected erasures is the size of the graphs smallest stopping set. Relating stopping sets and girths, we consider the size /spl sigma/(d,g) of the smallest stopping set in any bipartite graph of girth g and left degree d. For g/spl les/8 and any d, we determine /spl sigma/(d,g) exactly. For larger gs we bound /spl sigma/(d,g) in terms of d, showing that for fixed d, /spl sigma/(d,g) grows exponentially with g. Since constructions of high-girth graphs are known, one can therefore design codes with good erasure-correction guarantees under iterative decoding.

Dosimetric characteristics of Novalis Tx system with high definition multileaf collimator

A new Novalis Tx system equipped with a high definition multileaf collimator (HDMLC) recently became available to perform both image-guided radiosurgery and conventional radiotherapy. It is capable of delivering a highly conformal radiation dose with three energy modes: 6 MV photon energy, 15 MV photon energy, and 6 MV photon energy in a stereotactic radiosurgery mode with 1000 MU/min dose rate. Dosimetric characteristics of the new Novalis Tx treatment unit with the HDMLC are systematically measured for commissioning. A high resolution diode detector and miniion-chamber detector are used to measure dosimetric data for a range of field sizes from 4 x 4 mm to 400 x 400 mm. The commissioned Novalis Tx system has passed the RPC stereotactic radiosurgery head phantom irradiation test. The Novalis Tx system not only expands its capabilities with three energy modes, but also achieves better beam conformity and sharer beam penumbra with HDMLC. Since there is little beam data information available for the new Novalis Tx system, we present in this work the dosimetric data of the new modality for reference and comparison.

Always Good Turing: asymptotically optimal probability estimation

While deciphering the German Enigma code during World War II, I.J. Good and A.M. Turing considered the problem of estimating a probability distribution from a sample of data. They derived a surprising and unintuitive formula that has since been used in a variety of applications and studied by a number of researchers. Borrowing an information-theoretic and machine-learning framework, we define the attenuation of a probability estimator as the largest possible ratio between the per-symbol probability assigned to an arbitrarily-long sequence by any distribution, and the corresponding probability assigned by the estimator. We show that some common estimators have infinite attenuation and that the attenuation of the Good-Turing estimator is low, yet larger than one. We then derive an estimator whose attenuation is one, namely, as the length of any sequence increases, the per-symbol probability assigned by the estimator is at least the highest possible. Interestingly, some of the proofs use celebrated results by Hardy and Ramanujan on the number of partitions of an integer. To better understand the behavior of the estimator, we study the probability it assigns to several simple sequences. We show that some sequences this probability agrees with our intuition, while for others it is rather unexpected.

Regional lung density changes after radiation therapy for tumors in and around thorax.

PURPOSE To study the temporal nature of regional lung density changes and to assess whether the dose-dependent nature of these changes is associated with patient- and treatment-associated factors. METHODS AND MATERIALS Between 1991 and 2004, 118 patients with interpretable pre- and post-radiation therapy (RT) chest computed tomography (CT) scans were evaluated. Changes in regional lung density were related to regional dose to define a dose-response curve (DRC) for RT-induced lung injury using three-dimensional planning tools and image fusion. Multiple post-RT follow-up CT scans were evaluated by fitting linear-quadratic models of density changes on dose with time as the covariate. Various patient- and treatment-related factors were examined as well. RESULTS There was a dose-dependent increase in regional lung density at nearly all post-RT follow-up intervals. The population volume-weighted changes evolved over the initial 6-month period after RT and reached a plateau thereafter (p < 0.001). On univariate analysis, patient age greater than 65 years (p = 0.003) and/or the use of pre-RT surgery (p < 0.001) were associated with significantly greater changes in CT density at both 6 and 12 months after RT, but the magnitude of this effect was modest. CONCLUSIONS There appears to be a temporal nature for the dose-dependent increases in lung density. Nondosimetric clinical factors tend to have no, or a modest, impact on these changes.

Radiation-Induced Reductions in Regional Lung Perfusion: 0.1–12 Year Data From a Prospective Clinical Study

PURPOSE To assess the time and regional dependence of radiation therapy (RT)-induced reductions in regional lung perfusion 0.1-12 years post-RT, as measured by single photon emission computed tomography (SPECT) lung perfusion. MATERIALS/METHODS Between 1991 and 2005, 123 evaluable patients receiving RT for tumors in/around the thorax underwent SPECT lung perfusion scans before and serially post-RT (0.1-12 years). Registration of pre- and post-RT SPECT images with the treatment planning computed tomography, and hence the three-dimensional RT dose distribution, allowed changes in regional SPECT-defined perfusion to be related to regional RT dose. Post-RT follow-up scans were evaluated at multiple time points to determine the time course of RT-induced regional perfusion changes. Population dose response curves (DRC) for all patients at different time points, different regions, and subvolumes (e.g., whole lungs, cranial/caudal, ipsilateral/contralateral) were generated by combining data from multiple patients at similar follow-up times. Each DRC was fit to a linear model, and differences statistically analyzed. RESULTS In the overall groups, dose-dependent reductions in perfusion were seen at each time post-RT. The slope of the DRC increased over time up to 18 months post-RT, and plateaued thereafter. Regional differences in DRCs were only observed between the ipsilateral and contralateral lungs, and appeared due to tumor-associated changes in regional perfusion. CONCLUSIONS Thoracic RT causes dose-dependent reductions in regional lung perfusion that progress up to approximately 18 months post-RT and persists thereafter. Tumor shrinkage appears to confound the observed dose-response relations. There appears to be similar dose response for healthy parts of the lungs at different locations.

Comparing Digital Tomosynthesis to Cone-beam CT for Position Verification in Patients Undergoing Partial Breast Irradiation

PURPOSE To evaluate digital tomosynthesis (DTS) technology for daily positioning of patients receiving accelerated partial breast irradiation (APBI) and to compare the positioning accuracy of DTS to three-dimensional cone-beam computed tomography (CBCT). METHODS AND MATERIALS Ten patients who underwent APBI were scanned daily with on-board CBCT. A subset of the CBCT projections was used to reconstruct a stack of DTS image slices. To optimize soft-tissue visibility, the DTS images were reconstructed in oblique directions so that the tumor bed, breast tissue, ribs, and lungs were well separated. Coronal and sagittal DTS images were also reconstructed. Translational shifts of DTS images were obtained on different days from the same patients and were compared with the translational shifts of corresponding CBCT images. Seventy-seven CBCT scans and 291 DTS scans were obtained from nine evaluable patients. RESULTS Tumor beds were best visible in the oblique DTS scans. One-dimensional positioning differences between DTS and CBCT images were 0.8-1.7 mm for the six patients with clips present and 1.2-2.0 mm for the three patients without clips. Because of the limited DTS scan angle, the DTS registration accuracy along the off-plane direction is lower than the accuracy along the in-plane directions. CONCLUSIONS For patients receiving APBI, DTS localization offers comparable accuracy to CBCT localization for daily patient positioning while reducing mechanical constraints and imaging dose.

Limit results on pattern entropy

We determine the entropy rate of patterns of certain random processes including all finite-entropy stationary processes. For independent and identically distributed (i.i.d.) processes, we also bound the speed at which the per-symbol pattern entropy converges to this rate, and show that patterns satisfy an asymptotic equipartition property. To derive some of these results we upper bound the probability that the nth variable in a random process differs from all preceding ones.

Finite-length analysis of LDPC codes with large left degrees

Extending the results of Proietti et al. (see IEEE Trans. on Information Theory, vol.48, June 2002) we derive a recursion for calculating the average error probability of random bipartite graph ensembles of LDPC codes with large left degrees over erasure channels.

Association Between RT-Induced Changes in Lung Tissue Density and Global Lung Function

PURPOSE To assess the association between radiotherapy (RT)-induced changes in computed tomography (CT)-defined lung tissue density and pulmonary function tests (PFTs). METHODS AND MATERIALS Patients undergoing incidental partial lung RT were prospectively assessed for global (PFTs) and regional (CT and single photon emission CT [SPECT]) lung function before and, serially, after RT. The percent reductions in the PFT and the average changes in lung density were compared (Pearson correlations) in the overall group and subgroups stratified according to various clinical factors. Comparisons were also made between the CT- and SPECT-based computations using the Mann-Whitney U test. RESULTS Between 1991 and 2004, 343 patients were enrolled in this study. Of these, 111 patients had a total of 203 concurrent post-RT evaluations of changes in lung density and PFTs available for the analyses, and 81 patients had a total of 141 concurrent post-RT SPECT images. The average increases in lung density were related to the percent reductions in the PFTs, albeit with modest correlation coefficients (range, 0.20-0.43). The analyses also indicated that the association between lung density and PFT changes is essentially equivalent to the corresponding association with SPECT-defined lung perfusion. CONCLUSION We found a weak quantitative association between the degree of increase in lung density as defined by CT and the percent reduction in the PFTs.