Snake model-based lymphoma segmentation for sequential CT images j o u r n a l h o m e p a g e : w w w . i n t l . e l s e v i e r h e a l t h . c o m / j o u r n a l s / c m p b algorithm is produces good results. In addition, the proposed algorithm is fast with an average computing time 2.58 s. The proposed segmentation algorithm for lymph nodes is fast and can achieve high segmentation accuracy, which may be useful to automate the tracking and evaluation of cancer therapy. Computed tomography (CT) is commonly used for detection, diagnosis, and staging of cancers. Lymph node detection and segmentation is particularly important for cancer staging and treatment monitoring, as lymph nodes are commonly affected assessment such as RECIST (Response Evaluation Criteria in Solid Tumors) [1, 2] and IWC (International Workshop Criteria) [3] depend heavily on cancer lesion measurement. On the other hand, measuring cancer lesions is time-consuming and not coveted by radiologists, some of whom even contend should be the responsibility of oncologists [4, 5] . Though these measurements are crucial to clinical decision making, they are often not performed completely, and insufficient reporting of measurements is a common occurrence [6] . Approaches to improve quantitative imaging practices are needed, given their importance in cancer response assessment [4, 5] .. A particularly challenging aspect of quantitative imaging assessment is locating the previously reported lesions on follow-up imaging studies. An automated method to locate the corresponding lesions on follow-up studies and to segment them automatically could greatly improve not only the quality of quantitative imaging practice but also the efficiency of quantitative imaging assessment. In addition, automated methods could improve the ability of imaging to inform cancer care. Since lymph nodes are a frequent site of cancer lesions and account for many of the cases where multiple lesions need to be measured, our focus is automated assessment of cancer lesions in lymph nodes.. Automated segmentation of cancer lesions in lymph nodes is challenging. Lymph nodes are generally intermediate in signal intensity. Since parts of a lymph node boundary may be obscured due to partial volume effect, diffuse edges, sharing boundaries with surrounding tissues of similar intensities and potentially inhomogeneous density-values, it is difficult to reliably segment lymph nodes automatically. Rogowska et al. [7] evaluated five elementary segmentation techniques, such as watershed technique and thresholding, for lymph node segmentation and concluded that a high degree of model knowledge is needed for a reliable segmentation. One of the first attempts was a three-dimensional (3D) active surface approach by Honea and Snyder [8] , based on image gradients and shape constraints. Unfortunately, the approach was only evaluated on synthetic images, not clinical data. Dornheim et al. [9, 10] presented a stable 3D mass-spring model for lymph node segmentation in CT datasets. This model allowed for the first time to incorporate the three characteristic features of lymph nodes (gray value range, contour information and shape knowledge) into one single 3D model. The stable mass-spring model was extended by Dornheim et al. [11] for enlarged and mostly well separated necrotic lymph nodes. Due to the size preserving property, the performance of the mass spring model is highly affected by the size of the target structures. Thus, a size invariant mass spring model [12] was introduced to address the prior limitation. The fast marching technique [13] needed heavy user interaction (barriers, etc.). Maleike et al. [14] proposed a semi-automatic shape model guided deformable surface model for segmenting enlarged lymph nodes in CT images, which was integrated into an application together with a tool for manual correction of the segmentation. Barbu et al. [15] presented a learning-based method for the detection and segmentation of axillary lymph nodes. None of the aforementioned methods automatically segment lesions on longitudinal CT images, where the same lesions need to be consistently identified and segmented on each follow-up imaging study. Several lymph node segmentation methods for longitudinal CT images have been previously described. Yu et al. [16] presented an automatic tracking of lymph nodes in follow-up thoracic CT images, where the tracking performance of using affine and non-rigid registration was compared. The freeform deformation (FFD) is superior to give a better precision. Moltz et al. [17] presented a general framework for automatic detection of matching lesions in follow-up CT, which is not specialized for a certain lesion type and does not need any organ-specific registration or segmentation. Yan et al. presented a marker-controlled watershed algorithm to semiautomatically segment lymph nodes in sequential CT images [18] , where a lymph node was first identified by manually drawing a circle around it. Then, by incorporating information about the lymph node identified on the baseline scan with the matching result from the follow-up images, Yan et al. [19] developed a similar method to automatically determine the internal and external markers. Xu et al. [20] presented a method based on adaptive region-growing and clustering to automatically and reproducibly identify and segment abnormal lymph nodes in serial CT exams. Yu's method [16] and Moltz's framework [17] only provided the location of lesions, not the segmentation. The mark-controlled watershed algorithm [18] is semi-automatic, not automatic. The automatic method [19, 20] is time-consuming due to the non-rigid image registration.. This paper presents an automatic and fast lymph node segmentation algorithm for serial CT images. The candidate slices from follow up imaging studies, which contain the same lymph node in the baseline images, are selected by using an affine registration, maximizing the normalized mutual information (NMI) implemented in the 3D rigid registration tool of the Image Registration Toolkit (IRTK) 1 [21] . Then the slice, with minimum mean square error (MSE) between each of the registered candidate slices and the baseline scan, is taken as the corresponding slice in the follow up scan. The details of this registration-based approach have been previously described [20] . Fig. 1 shows the flowchart of the proposed algorithm, which we have initially developed in 2D. Based on the outline of lymph nodes created by radiologists in the baseline image, the automatic two-step registration in follow-up images is used to provide the initial evolving curve from the baseline image to locate and circumscribe the lesion in the followup images. Then, the initial evolving curve is refined with intensity and edge information to make the initial curve close to the boundaries of lymph nodes. Finally, the snake model is adopted to obtain the output result. Compared with our previous work [20] , the proposed algorithm mainly has two differences: (1) FFD was replaced with the two-step registration to improve the segmentation speed; (2) snake model was adopted, instead of region-growing and clustering, to obtain smooth segmentation results. This paper presents an automatic lymph node segmentation algorithm for longitudinal CT exams. Since the region of the human body in an image is very different from the background, a simple and robust coarse image registration is proposed based on the body detection. To deal with the change of the surrounding background, a template matching method with two different sizes is proposed to improve the coarse registration precision. The initial curve outlining the lymph node is refined based on image intensity and edge information to make the initial curve closely approximate the true lymph node boundaries. The final segmentation results are obtained by evolving the refined initial curve with the snake model. Experimental results demonstrate that our algorithm can successfully detect all of the 76 lymph nodes in the followup images and can achieve high segmentation accuracy; for example the average Hausdorff distance is 2.87 mm. The speed of the proposed algorithm is fast; the average computing time, including the image registration and segmentation, is 2.58 s.. Comparing to the state-of-art works, the main novelties of our work include: (1) two-step image registration is performed to quickly and effectively detect lymph nodes; (2) a snake model was adopted to achieve smooth and accuracy segmentation results. In the future, we will try to improve the proposed algorithm in three aspects: (1) adopt better image registration method to improve the accuracy of the initial evolving position; (2) adopt more flexible active contour model to obtain more accurate segmentation results; (3) set the parameters of our algorithm adaptively to make the algorithm more robust for different sets of images; (4) extend our algorithm from 2D to 3D; (5) Test and improve the system by using more data, and adapt it to be usable by medical experts.

O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Array regrouping and structure splitting using whole-program reference affinity While the memory of most machines is organized as a hierarchy, program data are laid out in a uniform address space. This paper defines a model of reference affinity, which measures how close a group of data are accessed together in a reference trace. It proves that the model gives a hierarchical partition of program data. At the top is the set of all data with the weakest affinity. At the bottom is each data element with the strongest affinity. Based on the theoretical model, the paper presents k-distance analysis, a practical test for the hierarchical affinity of source-level data. When used for array regrouping and structure splitting, k-distance analysis consistently outperforms data organizations given by the programmer, compiler analysis, frequency profiling, statistical clustering, and all other methods we have tried. All current PCs and workstations use cache blocks of at least 64 bytes, making the utilization an important problem. If only one word is useful in each cache block, a cache miss will not serve as a prefetch for other useful data. Furthermore, the program would waste up to 93% of memory transfer bandwidth and 93% of cache space, causing even more memory access.. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. To improve cache utilization we need to group related data into the same cache block. The question is how to define the relation. We believe that it should meet three requirements. First, it should be solely based on how data are accessed. For example in an access sequence "abab..ab", a and b are related and should be put in the same cache block, regardless how they are allocated and whether they are linked by pointers. Second, the relation must give a unique partition of data. Consider for example the access sequence "abab..ab...bcbc..bc". Since data a and c are not related, b cannot relate to both of them because it cannot stay in two locations in memory. Finally, the relation should be a scale. Different memory levels have blocks of increasing sizes, from a cache block to a memory page. The grouping of "most related" data into the smallest block should precede the grouping of "next related" data into larger blocks. In summary, the relation should give a unique and hierarchical organization of all program data.. In this paper, we define such a relation we call reference affinity, which measures how close a group of data are accessed together in an execution. Unlike most other program analysis, we measure the "togetherness" using the LRU stack distance, defined as the amount of data accessed between two memory references in an execution trace [28] . As a notion of locality, stack distance is bounded, even for long-running programs. The long stack distance often reveals long-range data access patterns that may otherwise hide behind complex control flows, indirect data access, or variations in coding and data allocation. We prove that the new definition gives a unique partition of program data for each distance k. When we decrease the value of k, the reference affinity gives a hierarchical decomposition and finds data sub-groups with closer affinity, much in the same way we sharpen the focus by reducing the radius of a circle.. Two earlier studies defined a reuse signature as a histogram of the reuse distance of all program data access [17, 36] . They showed that the reuse signature has a consistent pattern across all data inputs even for complex programs or regular programs after complex compiler optimizations. This suggests that we can analyze the reference affinity of the whole program by looking at its reuse signatures from training runs.. We present k-distance analysis, which simplifies the requirements of reference affinity into a set of necessary conditions about reuse signatures. The simplified conditions can then be checked efficiently for large, complex programs. The parameter k has an intuitive meaning-elements in the same group are almost always used within a distance of k data elements. The analysis handles sequential programs with arbitrarily complex control flows, indirect data access, and dynamic memory allocation. The analysis uses multiple training runs to take into account the variation caused by program inputs. In addition, we will use the analysis to find the worst reference affinity and measure the range of the impact from different data layouts.. Although reference affinity and k-distance analysis have strong properties, they are not optimal. We will formulate the problems in terms of partial and dynamic reference affinity and discuss their complexity. Our analysis checks the necessary rather than the sufficient conditions of reference affinity, so it may include data with false affinity. We will show that the probability of error is small and can be further reduced by strengthening the conditions. The rest of the paper is organized as follows. Section 2 defines the formal model of reference affinity and proves its properties. Section 3 presents k-distance analysis and a comparison with a number of other methods. Section 4 describes the compiler support for array regrouping and structure splitting. The last three sections present the experimental evaluation, related work, and conclusions. Reference affinity gives a unique and hierarchical partition of program data. The reference affinity among the source-level data can be tested by k-distance analysis. The result of k-distance analysis has an intuitive meaning. The elements of an affinity group must be accessed within a volume distance of at most k. Experiments show that the new method uncovers rich affinity relations among the data in complex programs. When used in array and structure reorganization, k-distance analysis outperforms all other methods with remarkable consistency. The close agreement between theoretical properties and experimental observations suggests that reference affinity is an effective way to bridge the gap between the memory hierarchy of a machine and the linear data layout of a program. This section discusses mainly the past work on data transformation. The discussion is more bibliographical than technical. The reader should refer Section 3.3 for a technical comparison.. Early compiler analysis identifies groups of data that are used together in loop nests. Thabit used the concept of pair-wise affinity Figure 9 : Reuse miss rate changes for Tomcatv he called reference proximity [38] . Wolf and Lam [29] and McKinley et al. [39] used reference groups. Thabit showed that the optimal data placement using the pair-wise affinity is NP-hard [38] . Kennedy and Kremer gave a general model that considered, among others, run-time data transformation. They showed that the problem is also NP-hard [24] . Ding and Kennedy used the results of Thabit and of Kennedy and Kremer to prove the complexity of the partial and dynamic reference affinity [14] . To reduce false sharing in multi-treaded programs, Anderson et al. [4] and Eggers and Jeremiassen [22] grouped data accessed by the same thread. Anderson et al. optimized a program for computation as well as data locality, but they did not combine different arrays. Eggers and Jeremiassen combined multiple arrays for thread locality, but their scheme may hurt cache locality if not all thread data are used at the same time.. For improving the cache performance, Ding and Kennedy grouped arrays that are always used together in a program [14] . They gave the optimal array layout for strict affinity. They later grouped arrays at multiple granularity [15] . An earlier version of this work defined hierarchical reference affinity and tested two programs using x-means and k-means clustering [42] .. Program profiling has long been used to measure the frequency of data access [25] . Seidl and Zorn grouped frequently accessed objects to improve virtual memory performance [35] . Using pairwise affinity, Calder et al. [7] and Chilimbi et al. [10] developed algorithms for hierarchical data placement in dynamic memory al- location. The locality model of Calder et al. was an extension of the temporal relation graph of Gloy and Smith, who considered reuse distance in estimating the affinity relation [19] . Chilimbi et al. split structure data in C and Java programs using pair-wise affinity [9] . Chilimbi later improved structure splitting using the frequency of data sub-streams called hot-streams [8] . Hot-streams combines dynamic affinity with frequency but does not yet give whole-program reference affinity. Access frequency and pair-wise affinity do not distinguish the time or the distance of data reuses. Petrank and Rawitz formalized this observation and proved a harsh bound: with only frequency or pair-wise information, no algorithm can guarantee a static data layout within a factor of k − 3 from the optimal solution, where k is proportional to the size of cache [33] .. Rabbah and Palem gave another method for structure splitting. It finds opportunities for complete splitting by calculating the neighbor affinity probability without constructing an explicit affinity graph [34] . The probability shows the quality of a given layout but does not suggest the best reorganization. Their splitting method is fully automatic as discussed in Section 4.. Reference affinity may change during a dynamic execution. Researchers have examined various methods for dynamic data reorganization [11, 13, 20, 30, 31, 37] . Ding and Kennedy found that consecutive packing (first-touch data ordering) best exploits reference affinity for programs with good temporal locality [13] , an observation later confirmed by Mellor-Crummey et al. [30] and Strout et al [37] . Ding and Kennedy considered the time distance of data reuses and used the information in group packing. They also gave a unified model in which consecutive packing and group packing became special cases. In principle, the model of reference affinity can be used at run time to analyze sub-parts of an execution. However, it must be very efficient to be cost effective. On-line affinity analysis is a subject of our on-going study.. Matson et al. first used reuse distance to measure the performance of virtual memory systems [28] . The recent uses include those of Zhou et al. [43] and Jiang and Zhang [23] , who studied file caching and showed a significant improvement for program, server, and database traces. At least five compiler groups have used reuse distance to analyze program locality [3, 5, 15, 26, 40] . Beyls and D'Hollander used per-reference distance pattern to annotate programs with cache hints and improved SPEC95 FP program performance by 7% on an Itanium processor [6] . Ding and Zhong analyzed large traces by reducing the analysis cost to near linear time. They found that reuse-distance histograms change in predictable patterns in many programs [17] . Zhong et al. used this result to predict cache miss rates across program inputs and cache configurations [41] .. Loop transformations have long been used to arrange stride-one access to maximize spatial reuse (see examples in [1, 18, 29] or a comprehensive text [2] ). Computation reodering is preferable because it makes no (negative) impact in other parts of a program. Still, this paper shows that using reference affinity, data transformation is beneficial for programs where loop transformations or other types of static techniques are inadequate because of the complex control flow and indirect data access. Test programs. Table 1 lists a set of 9 programs. The first four are array-based programs, including two from Spec95 suite and two dynamic programs originally from the Chaos group [12] for unstructured mesh and N-body simulation. The rest five programs use different tree structures including a splay tree for cache simulation, a quad-tree for image processing, and binary search trees for sorting and various other purposes. The cache simulator is part of the SimpleScalar tool set. The other four programs come from Olden benchmark set. We use different inputs for training and testing, as listed in the table. For a fair comparison, we only use one training input for each benchmark, despite that k-distance analysis can use multiple training runs.. We do not test more programs in part because our current compiler cannot safely split structures in all Olden programs, but also because the current set is statistically significant. All programs have at least 3 fields or arrays, five have 7 or more, and one program, Swim, has 14 arrays. A program with n arrays or structure fields has an exponential number (at least 2 n−2 and n i=0 i (n−i) to be exact) of possible data layouts. The possible layouts is 4 for n = 3, 210 for n = 7, and over 6 million for n = 14. Therefore, the probability for a single method to consistently pick the best layout for all programs among all tested choices and on all tested machines is effectively zero, unless the method is indeed the best.

B I O B O O O B I O O O O O O O O O O O O B O O O O O O O B O B O O B O B I O O O O O B O B O O O O O O O O O O O B O O O B O O B O O O O O O O O B O O O O O O O O O B O O O O O O O O O B O B O O B O B B O O O O O O B O O O B I O B O O B O O B O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O O O O O O O O O O B O O O B O O B O O O O O O O B I O O O O O B O B O O O O O O O O O O B O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O B O O O O O O O O O B O O O B O O O O O O O O O O O B O O O O O O B O O O O O O O O O O B O O B O O B O O O O O O O O O B I O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O B O O O B O O O O O O O O B I O O O O O O B O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O B O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O B O O B O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O O B I O O O O O O O O O B O O B I O O B O O O O O O O O O O O O O O O O O O B I O O O O O B O O O O O O O O O B I O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O B O B I O O O O O O O O B O O O O O O O O O O O O O O O O B I O B O O O O O O O O O O O O O B I O O O O O B O O B O B I O O O B O O O O O B O O O O B O O O O O O O O O B O O O O O O B O O O O O O O O O B O O O O O O B O O O O O O O O B O O B O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O O O O O B O O O O O B O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B B O O O O O O O O O O O O O B O O O O O B O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B I O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O B O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O B O O O O O O B O O O O O B O O O O O O O B O B I O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O B I O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O B I B O O O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O B O O O O B O B O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O B O O O O


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and

the

spatial

frequency

response

of

the

human

visual

system

(HVS).

The

saliency

computation

is

performed

in

a

statistical

way.

This

method

is

modeled

following

three

biologically

inspired

principles

and

compute

saliency

by

two

'scatter

matrices'

which

are

used

to

measure

the

variability

within

and

between

two

classes,

i.e.,

the

center

and

surrounding

regions,

respectively.

In

order

to

detect

multiple

salient

objects

of

different

sizes

in

a

scene,

the

saliency

of

a

pixel

is

estimated

via

its

saliency

support

region

which

is

defined

as

the

most

salient

region

centered

at

the

pixel.

Compliance

with

human

perceptual

characteristics

enables

the

proposed

method

to

detect

salient

objects

in

complex

scenes

and

predict

human

fixations.

Experimental

results

on

three

eye

tracking

datasets

verify

the

effectiveness

of

the

method

and

show

that

the

proposed

method

outperforms

the

state-of-the-art

methods

on

the

visual

saliency

detection

task.

Visual

saliency

is

a

state

or

quality

which

makes

an

item,

e.g.,

an

object

or

a

person,

prominent

from

its

surroundings.

Humans,

as

well

as

most

primates,

have

a

marvelous

ability

to

interpret

complex

scenes

and

pay

their

attention

to

the

salient

objects

or

regions

in

the

visual

environment

in

real

time.

Two

approaches

for

the

deployment

of

algorithm

based

on

visual

attention

have

been

proposed:

the

bottom-up

and

the

top-down

For

many

researches

in

physiology

neuropsychology

cognitive

science

and

computer

vision

it

is

essential

to

study

the

mechanisms

of

human

attention.

The

understanding

of

visual

attention

is

helpful

for

objectof-attention

image

segmentation

adaptive

coding

image

registration

video

analysis

and

perceptual

image/video

representation

Most

models

of

attention

are

bottom-up

and

biologically

inspired.

Typically,

these

models

posit

that

saliency

is

the

impetus

for

selective

vision.

Saliency

detection

can

be

performed

based

on

center-surround

contrast

information

theory

graph

model

common

similarity

or

learning

methods

The

bottom-up

saliency

detection

methods

can

be

broadly

classified

into

local

and

global

schemes.

The

local

contrast-based

methods

measure

the

visual

rarity

with

respect

to

the

local

neighborhoods

using

multi-scale

image

features

The

saliency

maps

generated

by

such

methods

usually

highlight

the

object

boundary.

Furthermore,

without

knowing

the

scale

of

the

salient

object,

the

local

methods

may

not

detect

the

salient

object

accurately.

On

the

contrary,

the

global

contrast-based

methods

measure

the

saliency

of

a

pixel

by

integrating

its

contrast

to

all

pixels

in

the

image

Generally,

the

global

methods

can

generate

saliency

maps

with

full

resolution

and

evenly

highlighted

salient

regions.

These

methods

can

achieve

good

accuracy

of

saliency

detection

in

a

scene

which

consists

of

a

single

salient

object

and

a

simple

background.

However,

it

is

hard

to

detect

salient

objects

from

complex

scenes

due

to

the

global

consideration.

As

shown

in

Figure

the

pen

container

is

the

most

salient

according

to

the

fixation

density

map

from

the

dataset

which

shows

the

region

attracting

the

attention

of

most

subjects.

The

saliency

map

in

Figure

highlights

the

object

boundary,

which

is

obtained

from

the

local

method

The

global

method

cannot

detect

the

container

because

the

color

of

the

container

is

similar

to

that

of

the

wall

and

its

contrast

to

all

the

pixels

of

the

image

is

low,

as

shown

in

Figure

(d)

Saliency

map

of

the

global

method

In

this

paper,

we

focus

on

a

bottom-up

model

of

saliency

detection,

which

is

widely

believed

to

be

closely

connected

to

the

ubiquity

of

attention

mechanisms

in

the

early

stages

of

biological

vision

In

neuroscience,

numerous

studies

show

that

the

neuronal

response

is

elevated

by

the

stimulus

within

the

classical

receptive

field

(the

center),

while

stimuli

presented

in

the

annular

window

surrounding

the

receptive

field

(the

surround)

inhibit

the

response

According

to

the

'center-surround'

mechanisms

and

the

spatial

frequency

response

of

the

human

visual

system

(HVS)

we

propose

a

saliency

model

based

on

the

following

principles

of

human

visual

attention:.

Appearance

distinctness

between

an

object

and

its

surroundings.

It

is

generally

considered

that

the

response

of

neurons

comes

from

the

contrast

of

the

center

region

and

the

surrounding

regions

For

a

pixel

p

which

is

inside

an

object,

the

pixel

is

salient

if

the

object

is

distinct

from

its

surroundings.

Unevenness

of

appearance

within

an

object

while

appearance

similarity

within

its

surrounding

region.

For

a

pixel

p

inside

a

region

(the

center),

the

pixel

is

salient

if

the

variability

of

the

region

is

not

too

low

since

some

intermediate

spatial

frequency

stimuli

may

evoke

a

peak

response

Meanwhile,

the

stimuli

from

the

surrounding

region

should

be

as

weak

as

possible

because

the

surround

is

antagonistic

to

the

center

and

a

stronger

response

will

be

evoked

without

the

surrounding

stimuli

So,

the

surrounding

region

should

have

low

variability.

Large

object

size.

According

to

the

neuropsychological

experiments,

attentive

response

increases

when

the

stimulus

size

is

large

and

the

object

is

attended

If

multiple

objects

have

the

same

distinctness

with

respect

to

their

surroundings,

humans

may

pay

attention

to

the

larger

object

first..

These

principles

reflect

the

common

human

characteristics

about

saliency

perception.

For

example,

according

to

the

visual

experiments,

the

spatial

frequency

response

of

the

HVS,

which

is

similar

to

the

response

of

a

bandpass

filter,

has

a

peak

response

at

about

to

cycles

per

degree

(cpd)

and

falls

off

at

about

cpd

As

shown

in

Figure

a

cluttered

image

is

hard

to

attract

people's

attention.

Principle

demands

HVS

to

be

sensitive

to

stimuli

from

the

center

and

not

at

the

surroundings

in

order

to

create

stronger

center-surround

contrast

and

make

the

object

attentive.

In

the

experiments,

we

find

that

each

of

the

principles

contributes

to

the

performance

of

the

saliency

detector.

Extending

our

previous

work

we

propose

a

novel

method

to

measure

visual

saliency

based

on

biologically

plausible

saliency

mechanisms

with

a

reasonable

mathematical

formulation.

We

define

the

saliency

of

an

image

region

in

a

statistical

way

by

means

of

the

scatter

matrix.

For

a

pixel

in

an

image,

the

center

region

and

the

surrounding

region

are

defined

as

the

regions

centered

at

the

pixel.

For

a

center

and

a

surrounding

region,

the

saliency

value

is

determined

by

two

scatter

matrices

of

the

visual

features.

The

first

is

the

'within-classes

scatter

matrix'

S

W

which

expresses

the

similarity

between

the

features

of

the

center

region

and

the

surrounding

region.

The

second

is

the

'between-classes

scatter

matrix'

S

B

which

describes

how

the

feature

statistics

in

the

center

region

diverge

from

those

in

the

surrounding

region.

For

a

pixel,

there

exist

many

concentric

regions

with

different

radii,

which

have

different

prominence

with

respect

to

their

surroundings.

In

order

to

detect

the

most

salient

objects

in

the

scenes,

the

saliency

support

region

of

a

pixel

is

explored,

which

is

the

most

salient

center

region

among

all

the

concentric

center

regions.

In

order

to

make

the

large

object

more

salient,

the

saliency

value

is

weighted

using

the

radius

of

the

saliency

support

region..

The

proposed

method

has

two

advantages.

First,

it

is

based

on

the

computational

architecture

of

human

visual

attention.

The

mechanism

of

the

method

is

consistent

with

human

perceptual

characteristics.

So,

the

method

has

a

good

performance

for

human

fixation

prediction.

Secondly,

the

proposed

method

searches

the

potential

saliency

support

regions

to

measure

the

saliency

of

multiple

objects

at

different

scales.

This

mechanism

enables

the

method

to

explore

various

salient

objects

adaptively.

It

is

effective

for

saliency

detection

in

complex

scenes.

The

proposed

method

is

evaluated

on

three

eye

tracking

datasets

which

comprise

natural

images

in

different

scenes

and

the

corresponding

human

fixation

data.

Compared

to

state-of-the-art

methods

and

the

human

fixation

data,

the

experimental

results

show

that

our

method

outperforms

all

other

methods

in

terms

of

receiver

operator

characteristic

(ROC)

area

metrics

for

the

human

fixation

prediction

task.

This

paper

is

organized

as

follows:

The

related

work

is

in

Section

Section

describes

the

proposed

method

for

saliency

detection.

The

experimental

results

are

provided

in

Section

to

verify

the

effectiveness

of

the

method.

Finally,

the

conclusion

is

drawn

in

Section

In

this

paper,

we

propose

a

novel

method

to

compute

visual

saliency

in

a

statistical

way.

According

to

three

principles

of

human

visual

attention,

we

use

the

withinclasses

scatter

matrix

and

the

between-classes

scatter

matrix

to

measure

the

similarity

and

distinctness

within

and

between

the

center

region

and

the

surrounding

region,

respectively.

Furthermore,

the

saliency

of

the

center

region

is

computed

by

the

two

scatter

matrices.

In

order

to

detect

the

salient

objects

with

different

sizes,

the

saliency

support

region

is

explored

and

the

saliency

value

of

the

center

pixel

of

the

region

is

obtained.

To

make

the

large

object

more

salient,

the

saliency

value

is

weighted

by

the

radius

of

the

saliency

support

region.

Experimental

results

are

obtained

by

applying

the

proposed

method

to

three

eye

tracking

datasets.

The

results

show

that

the

proposed

method

outperforms

the

state-of-the-art

methods

on

saliency

detection

in

complex

scenes

and

human

fixation

prediction.

In

our

model,

the

parameter

ω

c

is

designed

to

determine

the

region

of

which

frequency

will

be

assigned

a

high

saliency

value.

If

ω

c

is

set

to

and

the

regions

with

very

low

and

high

frequency

will

be

assigned

high

saliency

values,

respectively.

According

to

the

HVS

principles,

the

very

low

and

high

frequency

regions

may

weaken

the

response

of

the

HVS.

So,

an

inappropriate

value

of

ω

c

will

lead

to

the

wrong

detection,

i.e.,

the

ROC

area

may

be

small.

Figure

shows

the

relationship

between

the

ROC

area

and

the

weight

ω

c

in

on

the

three

datasets.

Generally,

when

the

weight

ω

c

is

bigger

than

the

ROC

area

decreases

as

the

weight

increases.

That

is

to

say,

the

salient

objects

are

not

necessarily

flat

according

to

the

evaluation

based

on

the

human

fixation

data.

On

the

contrary,

if

no

constraints

are

imposed

on

the

similarity

of

the

center

region,

i.e.,

ω

c

the

ROC

area

drops,

especially

on

the

BRUCE

dataset,

the

ROC

area

in

Figure

is

the

lowest

when

ω

c

That

is

to

say,

if

the

center

region

is

rather

cluttered,

it

may

not

attract

human

attention.

This

result

is

consistent

with

the

spatial

frequency

response

of

the

HVS

The

curves

in

Figure

are

similar

to

the

mirror

of

the

spatial

frequency

response

curve,

which

show

that

the

response

reaches

a

maximum

when

the

spatial

frequency

gets

an

intermediate

frequency,

ω

c

is

between

and

while

it

falls

off

rapidly

at

higher

frequency,

namely

ω

c

The

response

decreases

slowly

as

the

frequency

decreases

to

DC,

i.e.,

ω

c

from

the

intermediate

frequency.

It

is

worth

noting

that

our

model

is

biologically

plausible.

It

is

difficult

to

denote

the

spatial

frequency

by

specific

values

of

ω

c

The

performance

improvement

of

the

proposed

method

in

the

fixation

prediction

experiments

verifies

the

effectiveness

of

the

scatter

matrix-based

saliency

computation

and

the

saliency

support

region

exploration.

However,

since

we

use

the

pixel-wise

processing

manner

and

the

SSR

is

searched

for

every

processed

pixel,

the

method

is

computationally

expensive.

We

therefore

adopt

the

subsampling

method

to

reduce

the

cost.

The

average

running

time

on

the

BRUCE

dataset

to

generate

the

saliency

map

is

s

when

measured

on

an

Intel

CPU

with

RAM

in

Matlab

implementation.

In

the

future,

we

will

study

the

superpixel-based

processing

to

make

the

algorithm

more

efficient.

In

the

past

few

decades,

a

lot

of

bottom-up

saliency-driven

methods

have

been

proposed

in

cognitive

fields,

which

can

be

broadly

classified

as

biologically

inspired,

purely

computational,

or

an

integration

of

the

two

Many

attention

models

are

based

on

the

biologically

inspired

architecture

proposed

by

Koch

and

Ullman

which

is

motivated

from

Treisman

and

Gelade's

feature

integration

theory

(FIT)

This

structure

explains

the

human

visual

search

strategies,

i.e.,

the

visual

input

is

firstly

divided

into

several

feature

types

(e.g.,

intensity,

color,

or

orientation)

which

are

explored

concurrently,

and

then

the

conspicuities

of

the

features

are

combined

into

a

saliency

or

master

map

which

is

a

scalar,

twodimensional

map

providing

higher

intensities

for

the

most

prominent

areas..

According

to

this

biologically

plausible

architecture,

a

popular

bottom-up

attention

model

is

proposed

by

Itti

et

al.

In

Itti's

model,

three

multi-resolution

extracted

local

feature

contrasts,

i.e.,

luminance,

chrominance,

and

orientation,

are

mixed

to

produce

a

saliency

map.

Walther

and

Koch

extended

Itti's

model

to

infer

proto-object

regions

from

individual

contrast

maps

at

different

spatial

scales.

These

models

obtained

good

results

in

applications

from

computer

vision

to

robotics

In

the

last

decade,

many

purely

computational

methods

came

up

to

model

saliency

with

less

biological

motivation.

Ma

and

Zhang

proposed

a

fuzzy

growing

method

to

extract

salient

objects

based

on

local

contrast

analysis.

Achanta

et

al.

estimated

the

center-surround

contrast

by

using

a

frequency-tuned

technology.

In

order

to

solve

the

object

scale

problem,

Achanta

et

al.

extended

their

work

by

using

a

symmetric-surround

method

to

vary

the

bandwidth

of

the

center-surround

filtering

near

image

borders

Hu

et

al.

presented

a

composite

saliency

indicator

and

a

dynamic

weighting

strategy

to

estimate

saliency.

Hou

and

Zhang

extracted

the

saliency

map

from

the

spectral

residual

of

the

log-spectrum

of

an

image.

According

to

the

global

rarity

principle

of

saliency,

Zhai

and

Shah

and

Cheng

et

al.

used

the

histogrambased

method

to

detect

the

global

contrast

of

a

pixel

or

region.

By

filtering

color

values

and

position

values,

Perazzi

et

al.

computed

the

uniqueness

and

distribution

to

detect

salient

regions.

Recently,

based

on

a

graph-based

manifold

ranking

method,

Yang

et

al.

detected

saliency

of

the

image

elements

by

ranking

the

similarity

to

background

and

foreground

queries.

Li

et

al.

performed

saliency

detection

by

integrating

the

dense

and

sparse

reconstruction

errors

of

image

regions.

These

state-of-the-art

methods

can

extract

salient

regions

effectively..

Some

of

the

other

methods

model

saliency

based

on

both

of

the

biological

and

computational

models.

Harel

et

al.

used

Itti's

model

to

create

feature

maps,

which

are

integrated

into

activation

maps

by

using

a

graphbased

approach.

Finally,

saliency

maps

are

generated

by

a

Markovian

algorithm.

Bruce

and

Tsotsos

represented

the

probability

distribution

of

local

image

patches

by

using

the

independent

component

analysis

(ICA).

They

computed

the

self-information

of

image

regions

to

implement

a

neurally

plausible

circuit

that

closely

corresponds

to

visual

saliency.

Wang

et

al.

use

the

learned

sparse

codes

to

extract

some

sub-band

feature

maps

which

are

represented

by

a

random

walk-based

graph

model

to

simulate

the

information

transmission

among

the

neurons..

Besides

Bruce's

work,

some

other

saliency

detectors

also

established

models

based

on

information

theory.

Itti

and

Baldi

presented

a

Bayesian

definition

of

surprise

to

describe

saliency.

Gao

and

Vasconcelos

proposed

a

discriminant

saliency

detection

model

by

maximizing

the

mutual

information

of

the

center

and

surrounding

regions

in

an

image.

Klein

and

Frintrop

used

the

integral

histograms

to

estimate

the

distributions

of

the

center

and

surrounding

region

and

expressed

the

saliency

by

the

Kullback-Leibler

divergence

(KLD)

of

these

distributions..

Statistical

theory

has

also

gotten

into

the

field

of

saliency

detection.

Zhang

et

al.

computed

saliency

based

on

the

self-information

of

local

image

features

using

natural

image

statistics.

Also

using

natural

image

statistics,

Vigo

et

al.

detected

salient

edge

based

on

ICA..

We

implement

the

computation

of

saliency

based

on

the

statistics

of

local

image

regions.

Our

work

is

most

closely

related

to

the

within-classes

scatter

matrix

and

betweenclasses

scatter

matrix

in

Fisher's

linear

discriminant

analysis

(LDA)

which

is

commonly

used

for

dimensionality

reduction

before

later

classification

We

use

these

two

scatter

matrices

to

measure

the

variability

within/between

the

center

and

surrounding

regions

which

are

defined

in

Section

Furthermore,

we

compute

the

visual

saliency

based

on

principles

and

Some

methods

detect

saliency

at

a

single

spatial

scale

while

others

combine

feature

maps

at

multiple

scales

to

the

final

saliency

map

Without

knowing

the

scale

of

the

object,

these

methods

may

not

detect

the

most

salient

object

accurately.

The

proposed

method

finds

the

saliency

support

region

for

a

local

area

and

computes

the

saliency

of

this

region

with

respect

to

its

surroundings

to

detect

multiple

salient

objects

adaptively.

In

this

section,

we

apply

the

proposed

method

on

three

public

eye

tracking

datasets

(two

color

image

datasets

and

one

gray

image

dataset)

to

evaluate

the

performance

of

human

fixation

prediction.

These

datasets

comprise

natural

images,

containing

different

objects

and

scenes,

and

the

corresponding

human

fixations.

The

proposed

method

is

compared

with

the

state-of-the-art

bottomup

methods

based

on

a

well-known

validation

approach.

The

qualitative

and

quantitative

assessments

of

detection

results

are

reported.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Multilocus genetic models of handedness closely resemble single-locus models in explaining family data and are compatible with genome-wide association studies Right-and left-handedness run in families, show greater concordance in monozygotic than dizygotic twins, and are well described by single-locus Mendelian models. Here we summarize a large genome-wide association study (GWAS) that finds no significant associations with handedness and is consistent with a meta-analysis of GWASs. The GWAS had 99% power to detect a single locus using the conventional criterion of P < 5 × 10 Most models of the inheritance of handedness, from the early model of Ramaley 4 through to the models of McManus, 5 Annett, 6 and Klar, 7 describe a single locus with two or more alleles; fewer models specify two loci.8 For simplicity, this paper mainly considers the McManus DC model, which describes additive expression at a single locus with two alleles, D (Dextral) and C (Chance), and the three genotypes being DD, DC, and CC, although most of the conclusions broadly and similarly apply to other genetic models. In the DC model, the probabilities of left-handedness given the three genotypes, P(L|DD), P(L|DC), and P(L|CC), are 0%, 25%, and 50%. For a typical population rate of lefthandedness, P(L) = 10%, and for the frequency of the C allele, P(C) = 20%. The McManus model, as well as the Annett model, is successful in its predictions because the C allele (or Annett's RS-allele) produces randomness in the phenotypes. The phenotype of the CC genotype with its 50:50 mixture of right-and left-handedness does not indicate remaining genetic or environmental variance, but instead the phenotype itself is what can be called deep chance, corresponding to fluctuating asymmetry in biology; 9 in effect, ineradicable random biological noise. A good biological example of such a process in mice is the iv gene, 10 in which wild-type mice (+/+), as well as heterozygotes (iv/+), show situs solitus (ss), where the normal position of the heart is on the left, and the other viscera are in their usual

O O O O B O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O B O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Insights from pre-service teachers using science-based augmented reality Abstract This research examined the results of an exploratory case study on the use of the augmented reality (AR) platform Aurasma in the higher education science classroom. Thirty-one pre-service students, enrolled in an undergraduate science methodology course, participated in the study. Research methods included data collection of teaching reflections regarding pre-service teachers' experiences using the platform Aurasma for learning. Findings included student perceptions regarding the usability of AR in the classroom setting and insights into how the Aurasma platform facilitated inquiry and understanding of science concepts. An analysis of the data suggested that AR has the potential to positively impact classroom learning experiences including an increase in motivation and engagement, teacher enthusiasm, and the facilitation of a community of practice. However, the incorporation of AR into the classroom was not without challenges, highlighting the fact that AR may be time consuming, teachers may not have the skills needed to use such technology, or there may be a lack of infrastructure. Each topic is discussed and supported by relevant literature and excerpts from the student reflections. Recommendations are given for future classroom implementation.Keywords Augmented reality (AR) Á Science Á Pre-service teachers Á Visual literacy Á Virtual technology A New York Times (2013) editorial recently stated that today's students are simply not interested in science, technology, engineering, or math, recognized as STEM. According to Dejarnette (2012) , STEM programs have become a growing priority in American schools and efforts are continuing to introduce more STEM learning into existing P-12 curricula. Yet, the impact of high-stakes testing and issues related to teacher knowledge and staff development may hinder the process (Brophy 2008) . In Today's students live in a visual world constantly surrounded by images, media, and sound. It has been estimated that within the next 5 years (NMC 2012), AR technology will make it possible to connect science to the lived experiences of students growing up in a digital world. However, Kazlauskas and Robinson (2012) reported, ''The caricature of the 21st century student as an avid consumer of any and all technology does not necessarily transfer to the learning environment'' (p. 328). In order to keep up with the ever-changing pace, teachers need to have opportunities to learn and use these exciting and powerful tools. By preparing PSTs to increase student engagement, interest, and achievement through the use of emerging technologies such as AR, the hope is that future generations of students will understand STEM concepts and will pursue careers in a competitive, global work environment.. In the future, additional iterations of this study should go beyond just looking at engagement and motivation and measure additional learning outcomes on the specific concepts being addressed. Furthermore, it would be important to know whether the PSTs involved in this study continued to use AR over time and whether students' interests continued to be held with subsequent use. Also, the value of the PSTs in increasing the technological competency of the mentor teachers should be considered. According to Rogers and Knuth (2000) , mentor teachers must begin to view student teachers as a technology resource because of their familiarity and comfort level with the technology.. The research is unique because it looks at how AR can be used to promote engagement, motivation, and student learning from the multiple lenses of soon-to-be classroom teachers. This project, according to one PST, ''really pronounced the pros and cons of kids being so technologically advanced and how much effort is truly going to be needed to bridge the ever-growing gap between teachers and their kids!'' According to the results of this research, PSTs' reflections indicated that AR technology has the potential to impact learning experiences in elementary science education. Regardless of grade levels or science content, the use of AR increased student engagement, held student's attention longer than traditional teaching methods, and increased student questioning on scientific concepts. Cai et al. (2013) contended that the use of AR has the potential to result in more significant learning gains for lower-achieving students than for higher-achieving students. However, it is important to note that in this study, both regular and inclusion students were reported to have performed well on assessments after the use of AR supporting the notion that the use of AR has the potential to break down barriers and differentiate learning for all students regardless of background or disability.. According to Jukes et al. (2010) , there is a rapidly growing problem in education today. The problem is that modern students growing up in a digital world do not learn best from teachers using traditional methods of teaching. Educators must be willing to embrace technology in order to prepare our students for the twenty first century and beyond. In fact, research by Chai et al. (2010) emphasized that PSTs who have acquired higher levels of technology are more willing to use technology in the classroom. The International Society for Technology in Education (2008) standard specified that teachers are to advance student learning, creativity, and innovation using digital tools and resources. Yet, to use innovative technologies like AR in classrooms, it is important to recognize and find ways to overcome the challenges described in this study.. According to Pérez-López and Contero (2013) , one factor to consider when implementing any new technology is system usability. And, although the prospective teachers highlighted that fact that the Aurasma application was easy to use and effective in supporting the acquisition of scientific knowledge, some noted that there were still obstacles to learning the technology. Another challenge noted in this study was that teachers may be faced with a lack time of time or the motivation to learn new technology skills. These findings reinforce Ertmer and Ottenbreit-Leftwich's (2010) research that states ''although knowledge of technology is necessary, it is not enough if teachers do not also feel confident using that knowledge to facilitate student learning'' (p. 261). For those who did not grow up immersed in or feel confident in using technology, it is vital that support, time, and training be provided in order to integrate technology and pedagogy effectively into classrooms. Also, teacher preparation programs may want to consider the placement of PSTs into more technically advanced classrooms as some of the mentor teachers noted having limited time to teach science or integrate technology effectively.. Other limitations in this study involved the lack of hardware (iPads) and Internet (Wi-Fi) connectivity in classrooms to implement the Aurasma platform. When technology fails, it can shatter the confidence of the teacher who has invested time and energy into planning the AR activity. For those campuses who cannot afford to purchase individual iPads for students, it may be advantageous to team with other teachers and share devices. If Wi-Fi is scarce, one option would be to tether an iPad to an iPhone in order to get connectivity as needed. The consequence of not having the infrastructure in place will result in students who are not prepared for the world outside the classroom. Schools will need to make a significant investment in the resources (hardware and software) to meet the needs of the twenty first century learner.. Finally, this study indicates that reflection is a vital component to improving teacher practice. More than half of the PSTs implementing AR recognized ways to improve their future use of AR in the classroom. According to Subramaniam (2013) , ''A look into these practices through a study of the content of preservice teachers' reflections of their early field experiences provides teacher educators a lens into the varied practitioner expertise and practices that their preservice teachers experience, observe, and learn to ground their own future practice of teaching'' (p. 1854). In order to explore the dynamics of using AR for teaching and learning, an exploratory case study approach was conducted in an undergraduate science methods course in the College of Education, at one regional 4-year university. Olsson and Salo (2012) noted that because the field of AR is still emerging, an explorative approach is required. According to Yin (2003) , an exploratory case study involves examining situations in which the phenomenon being investigated has no clear, single set of outcomes. The case study, used as the research strategy, will allow a contribution to be made to the schools and universities interested in using AR and describe how to best support such emerging technologies in the classroom. Creswell (1998) noted that in order to build conceptual models for the future, a case study should provide a thorough description of the context, the processes observed, a discussion of the main findings, and the lessons to be learned.

O O B I O O O O O O O O O O O O O O O O O O O O B I I O O O O O O B O O O O O O O O B O O O O O O O O O O O O O O O B I O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B I I O B O B I O B I O B I O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Stochastic

parameter

search

for

events

Background:

With

recent

increase

in

affordability

and

accessibility

of

high-performance

computing

(HPC),

the

use

of

large

stochastic

models

has

become

increasingly

popular

for

its

ability

to

accurately

mimic

the

behavior

of

the

represented

biochemical

system.

One

important

application

of

such

models

is

to

predict

parameter

configurations

that

yield

an

event

of

scientific

significance.

Due

to

the

high

computational

requirements

of

Monte

Carlo

simulations

and

dimensionality

of

parameter

space,

brute

force

search

is

computationally

infeasible

for

most

large

models.

Results:

We

have

developed

a

novel

parameter

estimation

algorithm-Stochastic

Parameter

Search

for

Events

(SParSE)-that

automatically

computes

parameter

configurations

for

propagating

the

system

to

produce

an

event

of

interest

at

a

user-specified

success

rate

and

error

tolerance.

Our

method

is

highly

automated

and

parallelizable.

In

addition,

computational

complexity

does

not

scale

linearly

with

the

number

of

unknown

parameters;

all

reaction

rate

parameters

are

updated

concurrently

at

the

end

of

each

iteration

in

SParSE.

We

apply

SParSE

to

three

systems

of

increasing

complexity:

birth-death,

reversible

isomerization,

and

Susceptible-Infectious-Recovered-Susceptible

(SIRS)

disease

transmission.

Our

results

demonstrate

that

SParSE

substantially

accelerates

computation

of

the

parametric

solution

hyperplane

compared

to

uniform

random

search.

We

also

show

that

the

novel

heuristic

for

handling

over-perturbing

parameter

sets

enables

SParSE

to

compute

biasing

parameters

for

a

class

of

rare

events

that

is

not

amenable

to

current

algorithms

that

are

based

on

importance

sampling.

Conclusions:

SParSE

provides

a

novel,

efficient,

event-oriented

parameter

estimation

method

for

computing

parametric

configurations

that

can

be

readily

applied

to

any

stochastic

systems

obeying

chemical

master

equation

(CME).

Its

usability

and

utility

do

not

diminish

with

large

systems

as

the

algorithmic

complexity

for

a

given

system

is

independent

of

the

number

of

unknown

reaction

rate

parameters.

In

this

paper,

we

presented

SParSE-a

novel

stochastic

parameter

estimation

algorithm

for

events.

SParSE

contains

two

main

research

contributions.

First,

it

presents

a

novel

modification

of

the

multilevel

cross-entropy

method

that

concurrently

computes

multiple

intermediate

events

as

well

as

their

corresponding

biasing

parameters,

and

handles

over-perturbing

initial

reaction

rates

as

well

as

under-perturbing

ones.

Second,

it

uses

information

from

past

simulations

to

automatically

find

a

path

to

the

parametric

hyperplane

corresponding

to

the

target

event

with

user-specified

probability

and

absolute

error

tolerance..

By

introducing

a

novel

heuristic

for

handling

reaction

rates

that

over-perturb

the

system,

SParSE

can

handle

target

events

whose

probability

does

not

need

to

be

rare

with

respect

to

the

initial

reaction

rates

k

If

the

user

wishes

to

compute

the

probability

of

observing

P

E

with

respect

to

k

however,

it

can

be

done

by

simply

running

the

dwSSA

with

biasing

parameters

that

are

the

ratio

between

the

final

reaction

rates

k

from

SParSE

and

k

No

additional

multilevel

cross-entropy

simulations

are

required

by

the

dwSSA

to

determine

biasing

parameters

since

the

final

set

of

reaction

rates

computed

by

SParSE

contains

this

information.

For

this

reason,

SParSE

improves

upon

the

dwSSA

in

that

it

can

handle

an

additional

type

of

rare

event.

The

only

class

of

rare

events

whose

probability

dwSSA

can

estimate

is

the

one

that

is

seldom

reached

by

the

system

using

the

original

reaction

rates.

SParSE,

on

the

other

hand,

can

also

compute

the

probability

of

events

that

are

reached

too

often

with

respect

to

the

target

probability

using

the

original

reaction

rates.

Average

frequency

of

observing

such

target

event

with

k

would

be

much

higher

than

the

desired

frequency

(i.e.,

(P

E

P

E

N),

and

therefore

the

probability

of

observing

E

with

success

rate

P

E

P

E

and

reaction

rates

k

would

be

very.

small,

yet

its

biasing

parameters

are

uncomputable

with

the

dwSSA,

but

are

computable

with

SParSE..

It

is

important

to

note

that

the

computational

complexity

of

SParSE

is

independent

of

the

number

of

parameters

to

be

estimated.

Like

the

dwSSA

SParSE

utilizes

information-theoretic

concept

of

cross-entropy

to

concurrently

compute

biasing

parameters

for

all

reactions

in

the

system.

Moreover,

SParSE

avoids

serial

computation

of

biasing

parameters

for

multiple

intermediate

events

at

any

given

stage

of

multilevel

cross-entropy

method

by

introducing

a

clever

ordering

of

intermediate

events

and

data

management.

to

k

than

k

is.

Thus

intermediate

reaction

rates

near

k

can

be

used

to

improve

the

quality

of

interpolation

in

constructing

the

solution

hyperplane.

Another

computational

asset

of

SParSE

is

that

it

is

highly

parallelizable.

In

large

scale

application,

multiple

sets

of

initial

reaction

rates

can

be

dispatched

separately

since

each

set

finds

its

way

to

the

solution

hyperplane

independently

from

each

other.

In

smaller

scale,

SParSE

estimate

computation

or

an

ensemble

of

multilevel

cross-entropy

method

simulations

also

can

be

parallelized.

In

simulating

examples

presented

in

this

paper,

we

have

chosen

the

latter

method;

each

set

of

N

simulations

was

distributed

among

cores

using

the

Parallel

Computing

Toolbox™

in

Matlab.

Lastly,

a

single

SParSE

trajectory

from

the

multilevel

cross-entropy

method

without

any

biasing

(i.e.,γ

generates

the

same

number

of

uniform

random

numbers

as

the

SSA

does.

The

only

difference

is

that

SParSE

requires

additional

data

management

for

recording

biasing

parameter

information

(two

floating

point

numbers

for

each

reaction

which

is

used

in

the

next

round

of

multilevel

cross-entropy

method.

It

is

difficult

to

compare

the

exact

computational

cost

between

the

two

methods

when

SParSE

utilizes

γ

depending

on

the

amount

of

bias

applied

per

reaction,

the

number

of

random

numbers

generated

per

trajectory

will

differ

between

the

two

methods

even

if

the

same

reaction

rates

were

used.

For

the

exponential

interpolation

stage

in

SParSE,

SSA

is

used

to

computep

SParSE

thus

the

computational

cost

of

SParSE

and

SSA

trajectory

are

identical

for

a

given

set

of

reaction

rates..

One

of

the

inputs

required

by

SParSE

is

a

range

of

values

each

parameter

can

take.

There

is

no

theoretical

limit

on

the

parameter

range

SParSE

can

manage;

however,

it

is

required

for

the

following

practical

reasons.

First,

the

volume

of

the

solution

hyperplane

could

be

infinite

if

we

do

not

confine

parameter

ranges.

For

the

reversible

isomerization

process

presented

in

the

previous

section,

all

solution

hyperplanes

from

the

standard

test

scenarios

are

defined

by

the

ratio

between

the

two

reaction

rate

parameters;

infinitely

many

pairs

exist

that

keep

this

ratio

conserved.

In

addition,

a

range

is

required

to

sample

initial

reaction

rates.

If

a

user

wishes

to

use

a

distribution

other

than

the

uniform

distribution

to

generate

initial

reaction

rates,

different

statistics

(mean,

standard

deviation,

etc.)

may

be

needed..

We

remind

our

readers

that

although

parameter

ranges

are

used

to

constrain

the

position

of

initial

reaction

rates,

the

same

ranges

are

not

enforced

on

the

final

reaction

rates

on

the

solution

hyperplane.

The

main

reason

for

this

is

that

there

is

no

guarantee

the

solution

hyperplane

intersects

with

the

volume

defined

by

the

user-specified

parameter

ranges.

By

not

limiting

the

final

reaction

rates

to

reside

within

the

user-specified

region,

SParSE

is

able

to

find

a

set

of

reaction

rates

that

lie

on

the

solution

hyperplane

that

are

close

to

the

user-specified

parameter

ranges.

For

example,

in

Figure

white

dashed

lines

represent

parameter

ranges

specified

prior

to

the

simulation.

We

see

that

of

initial

sets

reached

the

solution

hyperplane

but

are

outside

this

region.

We

also

see

that

some

intermediate

reaction

rates

(white

squares)

escape

the

region

but

return

to

it

by

the

time

k

(red

square)

is

found.

For

most

practical

applications,

we

know

neither

the

curvature

of

the

solution

hyperplane

nor

the

existence

of

it

within

the

prescribed

parameter

ranges.

The

parameter

ranges

for

all

examples

in

this

paper

were

chosen

such

that

all

possible

values

in

are

captured

while

the

volume

of

a

solution

hyperplane

for

any

particular

P

E

is

well-defined

within

this

region.

Therefore

we

expect

the

computational

gain

from

employing

SParSE

over

SSA-URS

to

be

much

higher

for

an

arbitrary

problem

where

the

user

is

unable

to

provide

informative

parameter

ranges

for

the

target

event

of

interest

and

its

desired

probability.

Future

work

will

focus

on

two

main

areas

whose

improvement

will

substantially

benefit

the

algorithm.

First,

the

multilevel

cross-entropy

method

for

SParSE

can

improve

from

employing

an

adaptive

ρ(δ)

function,

whose

values

for

determining

intermediate

events

would

change

as

the

simulation

progresses.

While

SParSE

proved

to

be

computationally

efficient

for

all

three

examples

presented

in

this

paper,

their

results

demonstrated

that

the

same

ρ(δ)

function

can

produce

qualitatively

different

behavior

on

how

the

system

approaches

the

solution

hyperplane.

We

can

use

past

values

of

ρ(δ)

and

its

effect

onp

SParSE

to

estimate

the

speed

of

convergence

toward

the

solution

hyperplane.

This

can

potentially

reduce

the

number

of

multilevel

cross-entropy

method

iterations,

where

reduction

of

each

iteration

saves

N

simulations.

The

second

area

of

future

research

will

be

on

efficient

sampling

of

initial

reaction

rates.

Once

SParSE

finishes

simulating

first

sets

of

k

positions

of

resulting

k

may

be

far

away

from

each

other

and

thus

insufficient

to

construct

an

accurate

picture

of

the

solution

hyperplane.

Instead

of

randomly

sampling

the

next

set

of

initial

reaction

rates,

we

can

utilize

information

from

the

prior

ensemble

of

SParSE

simulations

to

improve

the

positioning

of

the

next

set

of

k

For

example,

we

can

construct

a

rough

interpolation

(e.g.,

linear

interpolation)

of

the

solution

hyperplane

using

k

s

from

the

first

ensemble,

and

sample

the

next

set

from

the

estimated

solution

hyperplane,

which

could

be

constrained

by

the

user-specified

parameter

ranges

if

necessary.

A

more

sophisticated

method

would

be

required

Stochastic

modeling

of

biochemical

and

ecological

systems

has

become

increasingly

popular

due

to

its

ability

to

represent

system

dynamics

correctly

at

a

detailed

level,

especially

when

species

are

present

at

low

population.

Deterministic

models,

on

the

other

hand,

are

easier

to

analyze,

yet

they

may

fail

to

capture

even

the

average

behavior

when

the

represented

system

exhibits

nonlinearity

or

is

near

extinction.

Recent

advancements

in

cloud

computing

platforms

and

GPU

computing

have

significantly

increased

the

affordability

of

computational

resources.

This

enables

development

and

use

of

stochastic

algorithms

that

would

have

been

deemed

computationally

infeasible

in

the

past.

However,

there

is

*Correspondence:

mroh@intven.com

Numerical

Methods,

Institute

for

Disease

Modeling,

Ave.

NE,

Bellevue,

USA

still

a

void

in

stochastic

methods

that

can

answer

scientifically

interesting

questions.

One

such

application

is

in

determining

reaction

rate

configurations

that

yield

an

event

of

interest

with

a

set

success

probability.

Most

parameter

estimation

algorithms

in

stochastic

chemical

kinetics

setting

take

time-series

data

as

an

input

and

compute

a

set

of

reaction

rate

parameters

that

most

closely

reproduce

the

data.

Methods

used

to

determine

these

reaction

rate

parameters

include

maximum

likelihood

ratio

gradient

decent

and

moment

closure

While

these

algorithms

are

useful

in

its

own

right,

scientists

are

often

interested

in

knowing

all

parameter

combinations

that

yield

a

specific

event

of

interest.

For

gene

regulatory

models,

knowledge

of

all

pathways

to

achieve

a

specific

event,

such

as

bistable

transition

of

lac

operon

in

E.

coli

may

be

used

to

guide

laboratory

experiments.

In

epidemiological

models,

all

intervention

parameter

combinations

that

achieve

eradication

can

be

combined

with

econometrics

in

computing

the

most

costeffective

strategy

for

eradicating

a

disease

To

authors'

knowledge,

no

algorithm

has

been

developed

in

stochastic

chemical

kinetics

setting

that

computes

such

parameter

combinations..

In

this

paper,

we

present

Stochastic

Parameter

Search

for

Events

(SParSE)

that

finds

a

parametric

hyperplane

of

reaction

rates

conferring

a

user-specified

event

with

prescribed

success

rate

and

error

tolerance.

Our

algorithm

is

robust

in

that

it

accurately

computes

the

solution

hyperplane

for

low

probability

events

as

well

as

high

probability

events.

It

is

also

trivial

to

parallelize

the

algorithm;

initial

parameter

sets

do

not

need

to

communicate

with

each

other

to

find

the

direction

to

the

unknown

solution

hyperplane.

Once

the

algorithm

finds

a

point

in

the

solution

hyperplane,

the

ratio

between

the

initial

and

final

rates

can

be

used

as

the

biasing

parameters

by

the

doubly

weighted

stochastic

simulation

algorithm

(dwSSA)

to

compute

the

probability

of

observing

the

target

event

with

its

success

rate

under

the

original

system

description.

This

allows

calculation

of

the

target

event

probabilities

under

the

original

parameters

as

a

powerful

side

benefit

of

the

algorithm.

Lastly,

the

SParSE

runtime

per

parameter

sample

is

of

the

same

order

as

that

of

the

stochastic

simulation

algorithm

(SSA),

i.e.,

the

algorithm

complexity

is

independent

of

the

number

of

unknown

parameters

for

a

given

system.

This

is

achieved

by

combining

a

novel

modification

of

dwSSA

Rubinstein's

cross-entropy

method

and

exponential

interpolation

of

biasing

parameters.

This

feature

provides

substantial

benefits

when

searching

multi-dimensional

parameter

space.

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Congruence distributivity implies bounded width We show that a constraint language with compatible Jónnson terms (or, equivalently, associated with an algebra generating a congruence distributive variety) defines a Constraint Satisfaction Problem solvable by the local consistency checking algorithm. The Constraint Satisfaction Problem (CSP) is one of few problems central to the development of theoretical computer science. An instance of CSP consists of variables and constraints and the aim is to determine whether variables can be evaluated in such a way that all the constraints are satisfied. CSP provides a common framework for many problems in various areas of computer science; some of the most interesting algorithmic questions in database theory [28] , machine vision recognition [23] , temporal and spatial reasoning [27] , technical design [25] , scheduling [22] , natural language comprehension [1] and programming language comprehension [24] are examples of constraint satisfaction problems.. The problem of solving CSP with arbitrary constraints is NP-complete, and therefore the research in this area is focused on solving CSP's with constraints taken from a fixed, finite set. More precisely, for any finite set of constraints (i.e. finitary relations) over a finite set we seek to determine the complexity of solving CSP restricted to instances with constraints coming exclusively from this set. The Dichotomy Conjecture of Feder and Vardi [15] postulates that every problem in such a family is NP-complete or solvable in polynomial time.. The Dichotomy Conjecture has proved to be a challenging question and the advances using standard methods were slow. A breakthrough in the development occurred when Jeavons, Cohen and Gyssens [18] announced an algebraic approach to the problem. Their work, refined later by Bulatov, Jeavons and Krokhin [9, 5] , showed that the complexity of any particular CSP is fully determined by a set of functions -polymorphisms of the constraints. This allowed a rephrasing of the problem in algebraic terms and provided tools necessary to deal with conjectures open for years (for example [2] ). More importantly, the algebraic approach allowed to conjecture a structure of problems solvable in polynomial time [9] and pointed out classes of problems that have to be characterized before the Dichotomy Conjecture can be attacked.. A positive verification of the Dichotomy Conjecture requires a construction of an algorithm (or a class of algorithms) unifying all known algorithms. A characterization of applicability classes of existing algorithms is crucial for constructing such a unification. In particular the class of problems of bounded width i.e. problems solvable by the widest known algorithm -the Local Consistency Checking algorithm has to be described. The only plausible conjecture on a structural characterization of this class was proposed by Larose and Zádori in [21] . They conjectured that a problem has bounded width if and only if the algebra associated with it (where operations of the algebra are polymorphisms of the constraints) generates a congruence meet semi-distributive variety.. A part of this conjecture that received most attention in the past years states that if the algebra associated with a set of constraints generates a congruence distributive variety then the CSP has bounded width. Considering such a class of algebras is a natural first step towards verifying the conjecture of Larose and Zádori. Algebras generating congruence distributive varieties are equivalently described as ones with a chain of Jónnson terms and the first attempts of an attack resulted in proving the conjecture for chains of three [20] and four [13] terms. We employ an approach, different from the one from [20] and [13] , based on the global behavior of the algorithm and prove bounded width for algebras with an arbitrary chain of Jónsson terms. We believe that the methods developed in this paper are crucial to a potential verification of the conjecture of Larose and Zádori.

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