Uniform Margin Research Articles

Growing integer partitions with uniform marginals and the equivalence of partition ensembles

We present an explicit construction of a Markovian random growth process on integer partitions such that given it visits some level n, it passes through any partition λ of n with equal probabilities. The construction has continuous time, but we also investigate its discrete time jump chain. The jump probabilities are given by explicit but complicated expressions, so we find their asymptotic behavior as the partition becomes large. This allows us to explain how the limit shape is formed.Using the known connection of the considered probabilistic objects to Poisson point processes, we give an alternative description of the partition growth process in these terms. Then we apply the constructed growth process to find sufficient conditions for a phenomenon known as equivalence of two ensembles of random partitions for a finite number of partition characteristics. This result allows to show that counts of odd and even parts in a random partition of n are asymptotically independent as n→∞ and to find their limiting distributions, which are, somewhat surprisingly, different.

A novel internal target volume definition based on velocity and time of respiratory target motion for external beam radiotherapy.

This study aimed to develop a novel internal target volume (ITV) definition for respiratory motion targets, considering target motion velocity and time. The proposed ITV was evaluated in respiratory-gated radiotherapy. An ITV modified with target motion velocity and time (ITVvt) was defined as an ITV that includes a target motion based on target motion velocity and time. The target motion velocity was calculated using four-dimensional computed tomography (4DCT) images. The ITVvts were created from phantom and clinical 4DCT images. The phantom 4DCT images were acquired using a solid phantom that moved with a sinusoidal waveform (peak-to-peak amplitudes of 10 and 20mm and cycles of 2-6s). The clinical 4DCT images were obtained from eight lung cancer cases. In respiratory-gated radiotherapy, the ITVvt was compared with conventional ITVs for beam times of 0.5-2s within the gating window. The conventional ITV was created by adding a uniform margin as the maximum motion within the gating window. In the phantom images, the maximum volume difference between the ITVvt and conventional ITV was -81.9%. In the clinical images, the maximum volume difference was -53.6%. Shorter respiratory cycles and longer BTs resulted in smaller ITVvt compared with the conventional ITV. Therefore, the proposed ITVvt plan could be used to reduce treatment volumes and doses to normal tissues.

Balance-Sheet Netting in U.S. Treasury Markets and Central Clearing

In this paper, we provide a comprehensive investigation of the potential for expanded central clearing to reduce the costs of the supplementary leverage ratio (SLR) on Treasury market intermediation in both cash and repo markets. Combining a detailed analysis of the rules involved in calculating the SLR with a unique set of regulatory data, we conclude that expanding central clearing would have relatively limited effects on the level of SLRs. We do find intermediaries’ increase their balance sheet netting when their regulatory balance sheet costs are higher. Our data permits us to establish a number of empirical facts related to the noncentrally cleared bilateral (NCCB) repo segment, and to repo activity overall, at the bank holding company level. We find that sizeable amounts of bilaterally-cleared activity would not be nettable even if centrally cleared. We also find that a significant portion of activity is already nettable outside of central clearing because dealers are structuring their NCCB trades to net. While expanded central clearing could have other benefits, such as imposing a more uniform margin regime on Treasury market intermediation, the scope of its effects on reducing balance sheet costs associated with the leverage ratio is limited.

Abstract PO1-22-02: Optimal intra-fraction PTV margins for patients receiving stereotactic partial breast radiation (SPBI) using cone beam adaptive radiation therapy

Abstract Objectives To quantify the intra-fraction tumor bed motion using image guidance and fiducial markers to determine optimal PTV margins in early-stage breast cancer patients receiving adaptive radiation therapy SPBI after partial mastectomy. Methods A retrospective cohort of five patients with pT1a-pT2N0, grade 1-2, ER+/PR+ early-stage invasive ductal carcinoma of either the right breast or left breast underwent partial mastectomy and adjuvant five-fraction SPBI using cone beam based online adaptation. A total of 62 CBCTs and 22 total fractions were analyzed after post-processing with an average time span of 39.1±8.9 minutes. Two methods were utilized to determine optimal CTV to PTV margins: one contouring-based and another fiducial-based. Our contouring-based method involved independently contouring on each fraction’s CBCTs including pre-treatment CBCT, intra-treatment CBCT, and post-treatment CBCT. After image registration with the original simulation CT image, these contours were propagated to and combined to create a new union CTV. Using the original CTV on the simulation CT, optimal PTV margin was determined to achieve 95% overlap of the union CTV created from fractionated CBCTs. In addition to the contouring-based method, our fiducial-based method utilized an in-house script to calculate the centroid of all fiducials per CBCT. The average and maximum anterior-posterior, medial-lateral, superior-inferior shifts of fiducials between intra-fraction CBCTs were recorded. Results Using our contouring-based method, we calculated and determined that a uniform 3.5 mm expansion around the original CT simulation CTV is needed to achieve 95% PTV overlap encompassing the pre-treatment, intra-treatment, and post-treatment union CTV. Furthermore, with our fiducial-based method, we calculated average centroid anterior-posterior, medial-lateral and superior-inferior shifts to be the following: 1.51±0.79mm, 1.04±0.55 mm, 1.78±0.94 mm respectively. Average maximum shifts were determined to be 2.13±1.18mm anterior-posterior, 1.45±0.76mm medial-lateral and 2.47±1.40mm superior-inferior shifts. Conclusion With our contouring-based analysis, this preliminarily study suggests CTV to PTV margin of 3.5mm is adequate. On the other hand, our fiducial-based method suggests decreased movement and smaller asymmetric margin. Further CBCT adaptation images will be analyzed. In conjunction with these two methods, we currently recommend utilizing a 3.5mm uniform margin for intrafraction motion and to assess adequate coverage with image guidance during daily adaptation for patients with early-stage breast cancer receiving SPBI. Citation Format: Meng-Lun Hsieh, Justin Visak, Sean Domal, Gabrielle Gard, Steven Montalvo, Liyuan Chen, Xinran Zhong, Zohaib Iqbal, Tingliang Zhuang, Bin Cai, Heejung Kim, Mona Arbab, Prasanna Alluri, Nathan Kim, Mu-Han Lin, David Parsons, Asal Rahimi. Optimal intra-fraction PTV margins for patients receiving stereotactic partial breast radiation (SPBI) using cone beam adaptive radiation therapy [abstract]. In: Proceedings of the 2023 San Antonio Breast Cancer Symposium; 2023 Dec 5-9; San Antonio, TX. Philadelphia (PA): AACR; Cancer Res 2024;84(9 Suppl):Abstract nr PO1-22-02.

Pelvic target volume inter-fractional motion during radiotherapy for cervical cancer with daily iterative cone beam computed tomography.

Tumor regression and organ movements indicate that a large margin is used to ensure target volume coverage during radiotherapy. This study aimed to quantify inter-fractional movements of the uterus and cervix in patients with cervical cancer undergoing radiotherapy and to evaluate the clinical target volume (CTV) coverage. This study analyzed 303 iterative cone beam computed tomography (iCBCT) scans from 15 cervical cancer patients undergoing external beam radiotherapy. CTVs of the uterus (CTV-U) and cervix (CTV-C) contours were delineated based on each iCBCT image. CTV-U encompassed the uterus, while CTV-C included the cervix, vagina, and adjacent parametrial regions. Compared with the planning CTV, the movement of CTV-U and CTV-C in the anterior-posterior, superior-inferior, and lateral directions between iCBCT scans was measured. Uniform expansions were applied to the planning CTV to assess target coverage. The motion (mean ± standard deviation) in the CTV-U position was 8.3 ± 4.1mm in the left, 9.8 ± 4.4mm in the right, 12.6 ± 4.0mm in the anterior, 8.8 ± 5.1mm in the posterior, 5.7 ± 5.4mm in the superior, and 3.0 ± 3.2mm in the inferior direction. The mean CTV-C displacement was 7.3 ± 3.2mm in the left, 8.6 ± 3.8mm in the right, 9.0 ± 6.1mm in the anterior, 8.4 ± 3.6mm in the posterior, 5.0 ± 5.0mm in the superior, and 3.0 ± 2.5mm in the inferior direction. Compared with the other tumor (T) stages, CTV-U and CTV-C motion in stage T1 was larger. A uniform CTV planning treatment volume margin of 15mm failed to encompass the CTV-U and CTV-C in 11.1% and 2.2% of all fractions, respectively. The mean volume change of CTV-U and CTV-C were 150% and 51%, respectively, compared with the planning CTV. Movements of the uterine corpus are larger than those of the cervix. The likelihood of missing the CTV is significantly increased due to inter-fractional motion when utilizing traditional planning margins. Early T stage may require larger margins. Personal radiotherapy margining is needed to improve treatment accuracy.

Daily Online Adaptive Radiation Therapy of Postoperative Endometrial and Cervical Cancer With PTV Margin Reduction to 5 mm: Dosimetric Outcomes, Acute Toxicity, and First Clinical Experience

PurposeThis study evaluated the first clinical implementation of daily iterative cone-beam computed tomography (iCBCT)-guided online adaptive radiotherapy (oART) in the postoperative treatment of endometrial and cervical cancer. Methods and MaterialsSeventeen consecutive patients treated with daily iCBCT-guided oART were enrolled in this prospective study, with a reduced uniform three-dimensional PTV margin of 5 mm. Treatment plans were designed to deliver 45 or 50.4 Gy in 1.8 Gy daily fractions to PTV. Pre- and posttreatment ultrasound and iCBCT scans were performed to record intrafractional bladder and rectal volume changes. The accuracy of contouring, oART procedure time, dosimetric outcomes and acute toxicity were evaluated. ResultsThe average time from first iCBCT acquisition to completion of treatment was 22 min and 26 s. During this period, bladder volume increased by 44 cm3 using iCBCT contouring, while rectal volume remained stable (62.9 cm3 pretreatment vs. 61.9 cm3 posttreatment). A total of 91.6% of influencers and 88.1% of CTVs required no or minor edits. The adapted plan was selected in all (434) fractions and significantly improved the dosimetry coverage for CTV and PTV, especially the vaginal PTV coverage by nearly 7% (p<0.05). The adapted bladder Dmean was 104.61 cGy, and the rectum Dmean was 123.67 cGy, significantly lower than the scheduled plan of 108.24 and 128.19 cGy, respectively. The bone marrow, femur head left and right dosimetry were also improved with adaptation. Grade 2 acute gastrointestinal and genitourinary toxicities were 24% and 0, respectively. There was a Grade 3 acute toxicity of decreased white blood cell count in one patient. ConclusionsDaily oART was associated with favourable dosimetry improvement and low acute toxicity, supporting its safety and efficacy for postoperative treatment of endometrial and cervical cancer. These results need to be validated in a larger prospective randomized controlled cohort.

Sketching Approximability of All Finite CSPs

A constraint satisfaction problem (CSP), \(\textsf {Max-CSP}(\mathcal {F})\) , is specified by a finite set of constraints \(\mathcal {F}\subseteq \lbrace [q]^k \rightarrow \lbrace 0,1\rbrace \rbrace\) for positive integers q and k . An instance of the problem on n variables is given by m applications of constraints from \(\mathcal {F}\) to subsequences of the n variables, and the goal is to find an assignment to the variables that satisfies the maximum number of constraints. In the (γ ,β)-approximation version of the problem for parameters 0 ≤ β ≤ γ ≤ 1, the goal is to distinguish instances where at least γ fraction of the constraints can be satisfied from instances where at most β fraction of the constraints can be satisfied. In this work, we consider the approximability of this problem in the context of sketching algorithms and give a dichotomy result. Specifically, for every family \(\mathcal {F}\) and every β &lt; γ, we show that either a linear sketching algorithm solves the problem in polylogarithmic space or the problem is not solvable by any sketching algorithm in \(o(\sqrt {n})\) space. In particular, we give non-trivial approximation algorithms using polylogarithmic space for infinitely many constraint satisfaction problems. We also extend previously known lower bounds for general streaming algorithms to a wide variety of problems, and in particular the case of q = k =2, where we get a dichotomy, and the case when the satisfying assignments of the constraints of \(\mathcal {F}\) support a distribution on \([q]^k\) with uniform marginals. Prior to this work, other than sporadic examples, the only systematic classes of CSPs that were analyzed considered the setting of Boolean variables q = 2, binary constraints k =2, and singleton families \(|\mathcal {F}|=1\) and only considered the setting where constraints are placed on literals rather than variables. Our positive results show wide applicability of bias-based algorithms used previously by [ 47 ] and [ 41 ], which we extend to include richer norm estimation algorithms, by giving a systematic way to discover biases. Our negative results combine the Fourier analytic methods of [ 56 ], which we extend to a wider class of CSPs, with a rich collection of reductions among communication complexity problems that lie at the heart of the negative results. In particular, previous works used Fourier analysis over the Boolean cube to initiate their results and the results seemed particularly tailored to functions on Boolean literals (i.e., with negations). Our techniques surprisingly allow us to get to general q -ary CSPs without negations by appealing to the same Fourier analytic starting point over Boolean hypercubes.

The impact of preferential market access: British imports into Canada, 1892–1903

AbstractCanada initiated the formation of the (modern) imperial trade bloc in 1897 when it extended preferential market access to imports from Britain. British goods initially received a preferential reduction of one eighth of the applicable duty, rising to one quarter in 1898 and one third in 1900. Because duties varied across imported commodities, the uniform relative margins of preference resulted in cross‐commodity variation in the absolute margins of preference. This cross‐commodity variation is exploited in our paper. Relying on a data set that includes over 32,000 Canadian import products, we find that a 1 percentage‐point increase in the absolute margin of preference was associated with a 5.4% increase in the value of imports from Britain. Counterfactually, if Canada had not adopted a preferential trade policy, by 1903, the value of British imports into Canada would have been reduced by approximately one half.

The influence of anisotropy on the clinical target volume of brain tumor patients

Objective. Current radiotherapy guidelines for glioma target volume definition recommend a uniform margin expansion from the gross tumor volume (GTV) to the clinical target volume (CTV), assuming uniform infiltration in the invaded brain tissue. However, glioma cells migrate preferentially along white matter tracts, suggesting that white matter directionality should be considered in an anisotropic CTV expansion. We investigate two models of anisotropic CTV expansion and evaluate their clinical feasibility. Approach. To incorporate white matter directionality into the CTV, a diffusion tensor imaging (DTI) atlas is used. The DTI atlas consists of water diffusion tensors that are first spatially transformed into local tumor resistance tensors, also known as metric tensors, and secondly fed to a CTV expansion algorithm to generate anisotropic CTVs. Two models of spatial transformation are considered in the first step. The first model assumes that tumor cells experience reduced resistance parallel to the white matter fibers. The second model assumes that the anisotropy of tumor cell resistance is proportional to the anisotropy observed in DTI, with an ‘anisotropy weighting parameter’ controlling the proportionality. The models are evaluated in a cohort of ten brain tumor patients. Main results. To evaluate the sensitivity of the model, a library of model-generated CTVs was computed by varying the resistance and anisotropy parameters. Our results indicate that the resistance coefficient had the most significant effect on the global shape of the CTV expansion by redistributing the target volume from potentially less involved gray matter to white matter tissue. In addition, the anisotropy weighting parameter proved useful in locally increasing CTV expansion in regions characterized by strong tissue directionality, such as near the corpus callosum. Significance. By incorporating anisotropy into the CTV expansion, this study is a step toward an interactive CTV definition that can assist physicians in incorporating neuroanatomy into a clinically optimized CTV.

Developments in Quantifying the Response Factors Required for Linear Analytical and Seismic Design Procedures

Despite the recent initiatives and developments in building design provisions using performance-based design, practicing engineers frequently adopt force-based design approaches, irrespective of the structural system or building irregularity. Modern seismic building codes adopt the concept of simplifying the complex nonlinear response of a structure under seismic loading to an equivalent linear response through elastic analytical procedures using seismic design response factors. Nevertheless, code-recommended seismic design response factors may not result in a cost-effective design with a uniform margin of safety for different structural systems. Previous studies also adopted different methodologies for quantifying the seismic response factors. Hence, there is a pressing need for a comprehensive review covering the developments in quantifying these vital design factors. This paper presents a systematic review of the response factors used with linear analytical procedures recommended by modern building design provisions and the techniques employed in previous studies to evaluate these factors using SDOF and MDOF systems covering analytical, experimental and hybrid assessment approaches. Limitations and gaps identified from the previous studies indicated that most investigations focused on 2D analysis and regular low-rise buildings, while limited studies were directed to shear wall structures, considering mostly unidirectional seismic loading. This comparative review provides insights into previous studies’ methodologies and constraints and identifies the need for future research to calibrate seismic response factors to achieve more economical designs with consistent safety margins for different structural systems.

Evaluation of PTV margins with daily iterative online adaptive radiotherapy for postoperative treatment of endometrial and cervical cancer: a prospective single-arm phase 2 study

BackgroundTo determine the optimal planning target volume (PTV) margins for adequate coverage by daily iterative cone-beam computed tomography (iCBCT)-guided online adaptive radiotherapy (oART) in postoperative treatment of endometrial and cervical cancer and the benefit of reducing PTV margins.MethodsFifteen postoperative endometrial and cervical cancer patients treated with daily iCBCT-guided oART were enrolled in this prospective phase 2 study. Pre- and posttreatment iCBCT images of 125 fractions from 5 patients were obtained as a training cohort, and clinical target volumes (CTV) were contoured separately. Uniform three-dimensional expansions were applied to the PTVpre to assess the minimum margin required to encompass the CTVpost. The dosimetric advantages of the proposed online adaptive margins were compared with conventional margin plans (7–15 mm) using an oART emulator in another cohort of 125 iCBCT scans. A CTV-to-PTV expansion was verified on a validation cohort of 253 fractions from 10 patients, and further margin reduction and acute toxicity were studied.ResultsThe average time from pretreatment iCBCT to posttreatment iCBCT was 22 min. A uniform PTV margin of 5 mm could encompass nodal CTVpost in 100% of the fractions (175/175) and vaginal CTVpost in 98% of the fractions (172/175). The margin of 5 mm was verified in our validation cohort, and the nodal PTV margin could be further reduced to 4 mm if ≥ 95% CTV coverage was predicted to be achieved. The adapted plan with a 5 mm margin significantly improved pelvic organ-at-risk dosimetry compared with the conventional margin plan. Grade 3 toxicities were observed in only one patient with leukopenia, and no patients experienced acute urinary toxicity.ConclusionIn the postoperative treatment of endometrial and cervical cancer, oART could reduce PTV margins to 5 mm, which significantly decrease the dose to critical organs at risk and potentially lead to a lower incidence of acute toxicity.

Some Tsallis entropy measures in concomitants of generalized order statistics under iterated FGM bivariate distribution

&lt;p&gt;Shannon differential entropy is extensively applied in the literature as a measure of dispersion or uncertainty. Nonetheless, there are other measurements, such as the cumulative residual Tsallis entropy (CRTE), that reveal interesting effects in several fields. Motivated by this, we study and compute Tsallis measures for the concomitants of the generalized order statistics (CGOS) from the iterated Farlie-Gumbel-Morgenstern (IFGM) bivariate family. Some newly introduced information measures are also being considered for CGOS within the framework of the IFGM family, including Tsallis entropy, CRTE, and an alternative measure of CRTE of order $ \eta $. Applications of these results are given for order statistics and record values with uniform, exponential, and power marginals distributions. In addition, the empirical cumulative Tsallis entropy is suggested as a method to calculate the new information measure. Finally, a real-world data set has been analyzed for illustrative purposes, and the performance is quite satisfactory.&lt;/p&gt;

A novel rare variants association test for binary traits in family-based designs via copulas.

With the cost-effectiveness technology in whole-genome sequencing, more sophisticated statistical methods for testing genetic association with both rare and common variants are being investigated to identify the genetic variation between individuals. Several methods which group variants, also called gene-based approaches, are developed. For instance, advanced extensions of the sequence kernel association test, which is a widely used variant-set test, have been proposed for unrelated samples and extended for family data. Family data have been shown to be powerful when analyzing rare variants. However, most of such methods capture familial relatedness using a random effect component within the generalized linear mixed model framework. Therefore, there is a need to develop unified and flexible methods to study the association between a set of genetic variants and a trait, especially for a binary outcome. Copulas are multivariate distribution functions with uniform margins on the interval and they provide suitable models to capture familial dependence structure. In this work, we propose a flexible family-based association test for both rare and common variants in the presence of binary traits. The method, termed novel rare variant association test (NRVAT), uses a marginal logistic model and a Gaussian Copula. The latter is employed to model the dependence between relatives. An analytic score-type test is derived. Through simulations, we show that our method can achieve greater power than existing approaches. The proposed model is applied to investigate the association between schizophrenia and bipolar disorder in a family-based cohort consisting of 17 extended families from Eastern Quebec.

Comparative morphological analysis reveals a new record of &lt;i&gt;Boehmeria nakashimae&lt;/i&gt; (Urticaceae) in Korea

A newly recorded species, &lt;i&gt;Boehmeria nakashimae&lt;/i&gt; Yahara, is confirmed for the first time to be distributed on forest edges on Jejudo Island, Korea. This species is known to be endemic to northern Kyushu, Japan. It is characterized by ovate to broadly ovate, ellipticovate, or sub-orbicular middle leaf shapes, serrulate-dentate and uniform margins, 17–29 teeth on one side, a short caudate or narrowly acute apex, dense glomerules at fruiting, and densely strigillose on the stems, both surfaces of the leaves, the perianth of staminate flowers, and achenes. Therefore, it is given the new name ‘Je-ju-top-mo-si-pul’ in Korean based on its serrulate-dentate leaf margin and geographical distribution. A description, photographs, illustrations, and keys of related taxa in Korea are provided.

A new bivariate distribution with uniform marginals

Starting from three independent exponential random variables we have generated a bivariate random vector (U, V) having the marginal distributions as standard uniform. The joint distribution function and the survival function have been derived along with the moment generating function. We have also given an expression for the joint moment of order (r, s). The distributions of different functions of U and V have been derived. Different dependence measures between U and V have also been calculated. The reliability of the underlying stress-strength model has been obtained as an application of the distribution. A simulation exercise has been carried out to check for the goodness-of-fit of the model. We have also calculated the relative errors in different reliability measures under the assumption that the variables U and V are independent when actually they are not.

Evaluating the geometric and dosimetric impact of applying anisotropic CTV to PTV margins in image-guided post-prostatectomy radiation therapy.

Guidelines for clinical target volume (CTV) to planning target volume (PTV) margins in post-prostatectomy radiation therapy (PPRT) are varied and often not clearly defined. Assessment of appropriateness of margins is commonly measured on prevalence of geographic miss. Cone-beam CT (CBCT) images (n = 92) for 10 PPRT patients were incorporated to provide on-treatment information on the appropriateness of six different CTV expansion margins in terms of geographic miss and change in dose-volume statistics for CTV, rectum and bladder. Uniform margins included 10 mm, 5 mm, 10 mm + 5 mm posteriorly and 5 mm + 3 mm posteriorly. In addition, two anisotropic margins were evaluated by separating the superior and inferior portions of the CTV before expansion. Treatment plans were created for each PTV retrospectively. The frequency of geographic miss was the smallest for the large uniform expansions but resulted in the highest organ-at-risk (OAR) doses. Geographic miss in the smaller uniform and anisotropic PTVs was more prevalent but commonly to a small volume < 1% of CTV. When averaged over all CBCT fractions, V95% dose for all CTV margins remained > 99%. The anisotropic expansions generated smaller irradiated target volumes and consequently saw up to 7.3% reduction in bladder dose when compared with similar uniform expansion margins. Supplementing the incidence of geographic miss with dosimetric information on target coverage and OAR doses provides more informed assessment of the appropriateness of different CTV expansion margins. Our study extends the evaluation of anisotropic margins for PPRT.

Orthogonal Inductive Matrix Completion.

We propose orthogonal inductive matrix completion (OMIC), an interpretable approach to matrix completion based on a sum of multiple orthonormal side information terms, together with nuclear-norm regularization. The approach allows us to inject prior knowledge about the singular vectors of the ground-truth matrix. We optimize the approach by a provably converging algorithm, which optimizes all components of the model simultaneously. We study the generalization capabilities of our method in both the distribution-free setting and in the case where the sampling distribution admits uniform marginals, yielding learning guarantees that improve with the quality of the injected knowledge in both cases. As particular cases of our framework, we present models that can incorporate user and item biases or community information in a joint and additive fashion. We analyze the performance of OMIC on several synthetic and real datasets. On synthetic datasets with a sliding scale of user bias relevance, we show that OMIC better adapts to different regimes than other methods. On real-life datasets containing user/items recommendations and relevant side information, we find that OMIC surpasses the state of the art, with the added benefit of greater interpretability.

Measures of Extropy Based on Concomitants of Generalized Order Statistics under a General Framework from Iterated Morgenstern Family

In this work, we reveal some distributional characteristics of concomitants of generalized order statistics (GOS) with parameters that are pairwise different, arising from iterated Farlie–Gumbel–Morgenstern (IFGM) family of bivariate distributions. Additionally, the joint distribution and product moments of concomitants of GOS for this family are discussed. Moreover, some well-known information measures, i.e., extropy, cumulative residual extropy (CRJ), and negative cumulative extropy (NCJ), are derived. Applications of these results are given for order statistics, record values, and progressive type-II censored order statistics with uniform marginals distributions. Additionally, the issue of estimating the CRJ and NCJ is looked into, utilizing the empirical technique and the concomitant of GOS. Finally, bivariate real-world data sets have been analyzed for illustrative purposes, and the performance of the proposed method is quite satisfactory.

Radiotherapy for mediastinal lymphoma in breath hold using surface monitoring and nasal high flow oxygen: Clinical experiences and breath hold stability

PurposeIn this study we describe the clinical introduction and evaluation of radiotherapy in mediastinal lymphoma in breath hold using surface monitoring combined with nasal high flow therapy (NHFT) to prolong breath hold duration. Materials and methods11 Patients with mediastinal lymphoma were evaluated. 6 Patients received NHFT, 5 patients were treated in breath hold without NHFT. Breath hold stability as measured by a surface scanning system was evaluated, as well as internal movement based on cone beam computed tomography (CBCT) before and after treatment. Based on internal movement, margins were determined. In a parallel planning study we compared free breathing plans with breath hold plans using the determined margins. ResultsAverage inter breath hold stability was 0.6 mm for NHFT treatments, and 0.5 mm for non-NHFT treatments (p > 0.1). Intra breath hold stability was 0.8 vs. 0.6 mm (p > 0.1) on average. Using NHFT, average breath hold duration increased from 34 s to 60 s (p < 0.01). Residual CTV motion derived from CBCTs before and after each fraction was 2.0 mm for NHFT vs 2.2 mm for non-NHFT (p > 0.1). Combined with inter-fraction motion, a uniform mediastinal margin of 5 mm appears to be sufficient. In breath hold, mean lung dose is reduced by 2.6 Gy (p < 0.001), while mean heart dose is reduced by 2.0 Gy (p < 0.001). ConclusionTreatment of mediastinal lymphoma in breath hold is feasible and safe. The addition of NHFT approximately increases breath hold durations with a factor two while stability is maintained. By reducing breathing motion, margins can be decreased to 5 mm. A considerable dose reduction in heart, lungs, esophagus, and breasts can be achieved with this method.

Dosimetric benefit of a library of plans versus single-plan strategy for pre-operative gastric cancer radiotherapy

Background and purposeThe stomach experiences large volume and shape changes during pre-operative gastric radiotherapy. This study evaluates the dosimetric benefit for organs-at-risk (OARs) of a library of plans (LoP) compared to the traditional single-plan (SP) strategy. Materials and methodsTwelve patients who received SP CBCT-guided pre-operative gastric radiotherapy (45 Gy; 25 fractions) were included. Clinical target volume (CTV) consisted of CTVstomach (i.e., stomach + 10 mm uniform margin minus OARs) and CTVLN (i.e., regional lymph node stations). For LoP, five stomach volumes (approximately equidistant with fixed volumes) were created using a previously developed stomach deformation model (volume = 150–750 mL). Appropriate planning target volume (PTV) margins were calculated for CTVstomach (SP and LoP, separately) and CTVLN. Treatment plans were automatically generated/optimized and the best-fitting library plan was manually selected for each daily CBCT. OARs (i.e., liver, kidneys, heart, spleen, spinal canal) doses were accumulated and dose-volume histogram (DVH) parameters were evaluated. ResultsThe non-isotropic PTVstomach margins were significantly (p < 0.05) smaller for LoP than SP (median = 13.1 vs 19.8 mm). For each patient, the average PTV was smaller using a LoP (difference range 134–1151 mL). For all OARs except the kidneys, DVH parameters were significantly reduced using a LoP. Differences in mean dose (Dmean) for liver, heart and spleen ranged between −1.8 to 5.7 Gy. For LoP, a benefit of heart Dmean > 4 Gy and spleen Dmean > 2 Gy was found in 4 and 5 patients, respectively. ConclusionA LoP strategy for pre-operative gastric cancer reduced average PTV and reduced OAR dose compared to a SP strategy, thereby potentially reducing risks for radiation-induced toxicities.