Multireference Stochastic Coupled Cluster.

We describe a modification of the stochastic coupled cluster algorithm that allows the use of multiple reference determinants. By considering the secondary references as excitations of the primary reference and using them to change the acceptance criteria for selection and spawning, we obtain a simple form of stochastic multireference coupled cluster which preserves the appealing aspects of the single-reference approach. The method is able to successfully describe strongly correlated molecular systems using few references and low cluster truncation levels, showing promise as a tool to tackle strong correlation in more general systems. Moreover, it allows simple and comprehensive control of the included references and excitors thereof, and this flexibility can be taken advantage of to gain insight into some of the inner workings of established electronic structure methods

Diagrammatic Coupled Cluster Monte Carlo.

We propose a modified coupled cluster Monte Carlo algorithm that stochastically samples connected terms within the truncated Baker-Campbell-Hausdorff expansion of the similarity-transformed Hamiltonian by construction of coupled cluster diagrams on the fly. Our new approach-diagCCMC-allows propagation to be performed using only the connected components of the similarity-transformed Hamiltonian, greatly reducing the memory cost associated with the stochastic solution of the coupled cluster equations. We show that for perfectly local, noninteracting systems diagCCMC is able to represent the coupled cluster wavefunction with a memory cost that scales linearly with system size. The favorable memory cost is observed with the only assumption of fixed stochastic granularity and is valid for arbitrary levels of coupled cluster theory. Significant reduction in memory cost is also shown to smoothly appear with dissociation of a finite chain of helium atoms. This approach is also shown not to break down in the presence of strong correlation through the example of a stretched nitrogen molecule. Our novel methodology moves the theoretical basis of coupled cluster Monte Carlo closer to deterministic approaches.Sims Fun

Mathematical modeling of the metastatic process

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.Comment: 24 pages, 6 figures, Revie

Ultrashort Echo Time Imaging of the Osteochondral Junction in Subjects with Knee Osteoarthritis and Age-matched Healthy Volunteers

SYNOPSIS We describe in vivo translation of ultrashort TE (UTE) imaging of the osteochondral junction (OCJ) at the knee in 9 subjects with osteoarthritis (OA) and 4 age-matched healthy volunteers. The OCJ plays an important role in onset and progression of OA. Our study demonstrates that UTE imaging of the OCJ is repeatable and demonstrates OCJ defects in OA subjects but not in healthy volunteers. Areas of OCJ damage commonly co-locate to other osteochondral pathology (bone marrow lesions and cartilage defects). UTE imaging of the OCJ may be a helpful tool for assessing OCJ damage in clinical studies of OA. INTRODUCTION Disruption of the osteochondral junction (OCJ) is thought to play an important role in the onset and progression of osteoarthritis (OA). Using conventional MR imaging, direct visualisation of the OCJ is not possible due to inherent short T1 and T2 relaxation times of the OCJ tissues. However, by achieving echo times (TEs) of < 1 ms, ultrashort echo time (UTE) MR imaging allows direct visualisation of the OCJ. The normal OCJ appears as an area of linear high signal intensity (SI) on UTE images at the bone-cartilage interface. In OA it has been shown that this area of linear high SI can become thinned or absent, compatible with histological findings of OCJ defects(1, 2). These findings have been described in a number of cadaveric MR studies, but there are limited in vivo data available(3-5). The aims of this study were to compare the in vivo appearance of the OCJ on UTE MR imaging between subjects with knee OA and age-matched healthy volunteers, to determine the relationship between OCJ defects and other osteochondral pathology, and to assess test-retest repeatability. METHODS We imaged 9 participants with mild-moderate knee osteoarthritis, characterised by radiographs with medial tibiofemoral compartment predominant disease and Kellgren-Lawrence grades 2-3, and 4 age-matched healthy volunteers. Participants were imaged at baseline and 1 month. MR studies were performed on a 3T system (GE 750, GE Healthcare). The MR protocol consisted of standard clinical sequences (coronal and sagittal intermediate-weighted fat-saturated fast spin echo (FSE) sequences plus a coronal T1-weighted FSE sequence) and a sagittal dual-echo UTE gradient echo sequence acquired using a 3D cones trajectory (research prototype; repetition time 15 ms, TE 0.03/4.5 ms, flip angle 13o, field-of-view 18 x 18 cm, matrix 430 x 430, slice thickness 2 mm, number of averages 1, acquisition time ~ 7.5 minutes). To increase conspicuity of short T2 tissues, we performed weighted digital image subtraction of the longer TE (4.5 ms) from the shorter TE images (0.03 ms)(6). The presence or absence of characteristic linear high SI at the OCJ was scored in 12 regions for each knee, corresponding to tibiofemoral subdivisions commonly used for semi-quantitative scoring. The presence of bone marrow lesions (BML) or cartilage defects in the same regions was also recorded. Assessment was performed by a single musculoskeletal radiologist with 5 years' experience in OA research, blinded to group assignment. We used descriptive statistics to compare the number of regions with OCJ defects in subjects with OA and healthy volunteers, and to assess the frequency with which OCJ defects co-located with BMLs or cartilage defects. Test-retest repeatability was evaluated using kappa statistics. RESULTS Participant characteristics are displayed in table 1. Six out of 9 OA participants (67%) had an OCJ defect in at least one region compared to 0 out of 4 controls (0%). The most commonly involved region was the central medial tibia (4 participants). OCJ defects commonly co-located to BMLs (7 out of 10 OCJ defects, 70%) and cartilage defects (6 out of 10 OCJ defects, 60%). Results are displayed in table 2. Sample images are displayed in figures 1 - 3. The kappa value for test-retest repeatability of OCJ assessment using UTE was 0.83 (95% confidence interval 0.64 to 1). DISCUSSION The appearances of OCJ defects in subjects with OA in vivo are in keeping with abnormalities predicted by cadaveric MR and histology studies(1, 3). The biological plausibility of the findings is enhanced by the frequency of co-location of OCJ damage to other osteochondral pathology (BMLs and cartilage defects). Our findings demonstrate in vivo translation of UTE imaging of the OCJ, and suggest that this is a useful tool for future studies of OA onset and progression. This may include predicting response to intervention, as equine studies have demonstrated that the presence or absence of OCJ damage is an important predictor of response to treatment of cartilage defects(7). Our results demonstrate that UTE imaging of the OCJ is repeatable with kappa values in keeping with 'near-perfect' test-retest repeatability for qualitative assessment(8). Previous in vivo studies have not used age-matched control subjects, therefore it has been unclear whether areas of OCJ damage are related to OA or normal ageing(4). The normal appearance of the OCJ in age-matched control subjects in this study suggests that the OCJ defects are not part of normal ageing, although at present the number of healthy volunteers imaged is small. CONCLUSION In vivo UTE MR imaging of the OCJ is repeatable and demonstrates OCJ defects in subjects with OA. OCJ defects commonly co-locate with other osteochondral pathology