Optimal diagonal-norm SBP operators Optimal boundary closures are derived for first derivative, finite difference operators of order 2, 4, 6 and 8. The closures are based on a diagonal-norm summation-by-parts (SBP) framework, thereby guaranteeing linear stability on piecewise curvilinear multi-block grids and entropy stability for nonlinear equations that support a convex extension. The new closures are developed by enriching conventional approaches with additional boundary closure stencils and non-equidistant grid distributions at the domain boundaries. Greatly improved accuracy is achieved near the boundaries, as compared with traditional diagonal norm operators of the same order. The superior accuracy of the new optimal diagonal-norm SBP operators is demonstrated for linear hyperbolic systems in one dimension and for the nonlinear compressible Euler equations in two dimensions. Wave-propagation problems frequently require farfield boundaries to be positioned many wavelengths away from the disturbance source. Efficient simulation of these problems requires numerical techniques capable of accurately propagating disturbances over long distances. It is well know that high-order finite difference methods (HOFDMs) are ideally suited for problems of this type. (See the pioneering paper by Kreiss and Oliger [22] .) Not all high-order spatial operators are applicable, however. For example, schemes that are G-K-S stable [13] , while being convergent to the true solution as ∆x → 0, may experience nonphysical solution growth in time [5] , thereby limiting their efficiency for longtime simulations. Thus, it is imperative to use HOFDMs that do not allow nonphysical solution growth in time-a property termed "strict stability" [12] . Deriving a strictly stable, accurate, and conservative HOFDM is a significant challenge that has received considerable past attention. (For examples, see [24, 41, 38, 1, 3, 15, 39, 14] .). A robust and well-proven high-order finite difference methodology that ensures the strict stability of time-dependent partial differential equations (PDEs) is the summation-by-parts-simultaneous approximation term (SBP-SAT) method. The SBP-SAT method combines semi-discrete operators that satisfy a summation-by-parts (SBP) formula [20] , with physical boundary conditions implemented using the simultaneous approximation term (SAT) method [5] . Examples of the SBP-SAT approach can be found in [33, 34, 35, 28, 30, 31, 36, 27, 43, 23, 9, 29, 17, 16, 19] .. An added benefit of the SBP-SAT method is that it naturally extends to multi-block geometries while retaining the essential single-block properties: strict stability, accuracy, and conservation [6] . Thus, problems involving complex domains or non-smooth geometries are easily amenable to the approach. References [27, 30, 18] report applications of the SBP-SAT method to problems involving nontrivial geometries.. A wide variety of numerical methods may be expressed as summation-byparts operators; examples include finite-difference operators, spectral collocation [8, 7] , and some finite-volume methods [45] . Herein we focus exclusively on finite difference operators. Finite-difference operators may be further categorized by the structure of their norm: a) diagonal, b) diagonal interior with block boundary closures, c) fully banded. The early papers [21, 40] report first derivative SBP operators up to 6th order, based on diagonal-norms and block-norms, while in [4] a 4th order accurate first derivative Padé type banded SBP operator is derived. The SBP framework may also be used to develop second-derivative operators. In [28] diagonal-and block-norm SBP operators up to 8th order were derived for both the first and second deriva-tives.. Matrix structural constraints required by all SBP operators preclude uniform spatial accuracy for diagonal norm finite-difference operators [21] . Indeed, a 2pth order diagonal-norm SBP operator may be closed at the boundaries with at most pth order accurate biased stencils. For first order hyperbolic problems, this implies a suboptimal convergence rate (i.e., global convergence) of (p + 1)th order when using a 2pth order interior operator. By comparision, a block norm SBP operator with an identical interior stencil may be closed at the boundaries with (2p − 1)th order accurate stencils, thereby yielding optimal 2pth order convergence. Similarly, strongly parabolic problems and second order hyperbolic problems convergence at a rate of (p + 2)th order using a 2pth order diagonal-norm SBP operator. (See [11, 46] for more information on the accuracy of finite difference approximations.). At first glance, it would appear that block norm or banded SBP operators would be preferred for simulations with stringent accuracy requirements. It is well known, however, that block-norm SBP operators may exhibit instabilities when applied to problems mapped onto curvilinear grids [42] , while diagonal norm operators remain stable. The same instability mechanism exists on Cartesian grids for second order systems with variable coefficients [32] .. Furthermore, recent developments appearing in reference [10] provide a general procedure for developing entropy consistent and entropy stable SBP schemes for systems of equations that support a convex extension (e.g., the entropy in the compressible Navier-Stokes equations). This procedure is only valid, however, for diagonal norm SBP spatial operators. For these reasons diagonal-norm operators have gained more interest in practical applications.. State-of-the-art diagonal norm finite-difference operators approach a point of dimenishing return with 8th order interior operators and 4th order boundary closures [28, 30] , thereby achieving 5th order convergence (for first order hyperbolic systems and incompletely parabolic systems) on curvilinear grids. An optimized 10th order diagonal-norm SBP operator appears in [9] , but exhibits large negative eigenvalues that separate from the cluster, leading to very small time-steps for explicit time-stepping methods.. Herein, diagonal-norm SBP finite difference operators are derived with highly optimized boundary closures. Although the resulting operators are formally 5th-order accurate (for the 8th order case), the leading order error constants are reduced by several orders of magnitude. Thus, very accurate simulations can be performed on relatively coarse meshes. The optimized boundary operators utilize additional unknowns in the SBP boundary closures, as well as a non-equidistant point distribution at the first three bound-ary points in the domain. The superior accuracy properties of the newly derived diagonal-norm SBP operators are demonstrated for linear hyperbolic problems in 1-D and the compressible Euler equations in 2-D, where the computational domain consists of two curvilinear grids.. In Section 2 the SBP-SAT method is introduced in one spatial dimension. In Section 3 the accuracy and stability properties of the newly developed SBP operators are verified by performing 1-D numerical simulations. Verification of accuracy and stability by numerical studies of the 2-D problem is performed in Section 4. Section 5 summarizes the work. The SBP operators are presented in Appendix. The main focus has been to construct new diagonal-norm SBP operators with optimal accuracy properties, to combine truly high-order accuracy and stability on curvilinear multi-block grids. This is achieved by introducing more boundary stencils and (or) allowing the grid-points to be non-equidistant Table 8 : Maximal time step with no grid stretching (l = 0) and with l = 2 in (14), relative the time-step for the 2nd order scheme on a non-stretched grid. Determined experimentally on an 81 × 41 grid. Table 9 : log(l 2 −errors) and convergence rates using the traditional diagonalnorm operators with grid stretching l = 2. N x and N y denote the number of grid points in the x and y directions, respectively, in each subdomain. Table 10 : log(l 2 − errors) and convergence rates using the optimal diagonalnorm operators with grid stretching l = 2. N x and N y denote the number of grid points in the x and y directions, respectively, in each subdomain.. close to the boundaries. The boundary and interface conditions are treated with the SAT technique. We study both first and second order hyperbolic problems on piecewise curvilinear multi-block grids. Numerical computations in 1-D and 2-D corroborate the stability-and accuracy-properties and also show that the numerical schemes built on optimal diagonal-norm SBP operators are superior to the corresponding traditional diagonal-norm SBP operators. For the second order wave equation we obtain super-convergence, and also for the 2-D Euler vortex problem the new optimal SBP operators yield higher than expected order of convergence.. It is likely that further improvements in accuracy could have been achieved for the optimal 6th and 8th order cases by allowing for more than 3 "free" locations of the boundary points in the minimisation. However, due to a limitation in Maple we where forced to limit the number to 3. With other minimisation routines this limitation might be lifted. The 8th order case could potentially allow for 7 free boundary points.. In a coming study we will investigate the efficiency of using the new diagonal-norm SBP operators in a more complex 3-D setting, with focus on second order hyperbolic systems and hyperbolic-parabolic systems.

O O O O O O O O O O O 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 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 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 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 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 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 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 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 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 B 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 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


ON PARIKH MATRICES, AMBIGUITY, AND PRINTS In the algebraic study of words and languages it is often convenient to analyze words as numerical quantities. One such now-famous example is the study of words by using their attached Parikh mapping (or vector). However, the Parikh vector abstracts away too much of the structure of the word. Parikh matrices were introduced as a means to obtain more than just the number of occurrences of single letters. When studying properties of words, an important property is that a word is uniquely determined by the number of occurrences of certain predetermined subwords. In the context of Parikh matrices, the problem is translated in finding which words are completely characterized by their associated Parikh matrix. This paper links this problem with that of the print of a word, i.e. the word obtained by considering consecutive occurrences of the same letter as only one letter. We obtain results regarding finiteness and contextfreeness of such classes of words. The Parikh matrix mapping was introduced by Mateescu et al. in [8] as a mapping from words to algebraic structures (matrices) in the spirit of the classical Parikh mapping which associates vectors to words. By using matrices instead of vectors more information about the word is preserved and numerical facts such as the number of occurrences of certain subwords in a word can be elegantly computed (by matrix multiplication). Because of the ease in dealing with subword occurrences, some interesting problems were discovered and solved using this tool in fields like combinatorics on words (see [5, 12] and the references there) and theory of codes [3] .. An interesting question in studying numerical properties of words is whether a word is completely determined by the number of occurrences of some of its subwords. The subwords used by the Parikh matrix do not always do this, so the notion of M-ambiguity was introduced in [7] . Although several papers are dealing with this notion and important properties of M-ambiguous and Munambiguous words have been discovered [13, 14, 2] , a complete characterization is not yet available.. In [14] the print of a word was introduced, noticing that for alphabets of size two and three, the M-unambiguity of a word implies the M-unambiguity of its print. This paper tries to advance towards a characterization of M-unambiguous words by investigating the connection between prints and M-ambiguity. Two main contributions are made in this direction: 1. We show that M-unambiguous prints have bounded length for a given alphabet;. 2. We show that the language of M-unambiguous words can be context free only if the language of its prints is finite.. The remainder of this paper is structured as follows. Section 2 recalls some basic notions and results regarding Parikh matrices and their characterization. Section 3 recalls the notion of M-ambiguity and relates it to its print for alphabets of size less than 4. Section 4 introduces parameterized ambiguity and proves the main result of the paper. Section 5 applies that to proving a necessary condition for context-freeness of the language of M-unambiguous words and the finiteness of the set of M-unambiguous prints for any given alphabet. Section 6 concludes the paper.

O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 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 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 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O


Inferring microbial interaction network from microbiome data using RMN algorithm Background: Microbial interactions are ubiquitous in nature. Recently, many similarity-based approaches have been developed to study the interaction in microbial ecosystems. These approaches can only explain the non-directional interactions yet a more complete view on how microbes regulate each other remains elusive. In addition, the strength of microbial interactions is difficult to be quantified by only using correlation analysis. Results: In this study, a rule-based microbial network (RMN) algorithm, which integrates regulatory OTU-triplet model with parametric weighting function, is being developed to construct microbial regulatory networks. The RMN algorithm not only can extrapolate the cooperative and competitive relationships between microbes, but also can infer the direction of such interactions. In addition, RMN algorithm can theoretically characterize the regulatory relationship composed of microbial pairs with low correlation coefficient in microbial networks. Our results suggested that Bifidobacterium, Streptococcus, Clostridium XI, and Bacteroides are essential for causing abundance changes of Veillonella in gut microbiome. Furthermore, we inferred some possible microbial interactions, including the competitive relationship between Veillonella and Bacteroides, and the cooperative relationship between Veillonella and Clostridium XI. Conclusions: The RMN algorithm provides the reconstruction of gut microbe networks, and can shed light on the dynamical interactions of microbes in the infant intestinal tract. In this paper we presented RMN algorithm, a rule-based algorithm using the OTU-triplet model with parametric weighting function, to construct microbial regulatory networks. RMN algorithm can theoretically extract directional interactions to delineate the cooperative and competitive relationships between microbes from highthroughput sequencing time series data. The efficiency estimation shows the high performance of RMN algorithm on simulated data with three latent factors and different noise levels. We also applied our framework to identify new relationships in infant gut samples. RMN algorithm is both computationally feasible and capable of detecting biologically significant progresses embedded in a microbial community. Although simple pairwise relationship has been used to describe complex forms of microbial interactions, advanced techniques are still required to infer complex microbial networks. Recent studies show that the cooperative and competitive relationships between microbes coexist in complicated ecological communities [8, 22, 23] . In addition, triplet relation, like activatorrepressor-target pattern, has been adopted to construct gene regulatory network form time course gene expression data [24] . Basing on such a rationale, we developed RMN algorithm to describe the relationship among every triplet of microbe as the cooperator-competitortarget. RMN algorithm is used to search for triplet relations of OTUs where the abundances of the target Fig. 6 The reconstruction of microbial regulatory networks in infant intestinal tract. Here, the competitive and cooperatively relationships are defined as ┤and →, individually should be high while that for the cooperator is high and that for the competitor is low (conversely, the abundances of the target should be low while that for the cooperator is low and that for the competitor is high). Our evaluation results suggest RMN algorithm has high performance when subjected to simulated data with different levels of noise (see Figs. 4 and 5) . As presented in the results, our algorithm has characterized well-known and possible microbial interactions from time series microbiome data of infant gut samples (see Fig. 6 ).. In summary, networks reconstructed by using simple similarity-based method often fail to capture the complex topology of a real system, and such networks may be full of false positive links. Furthermore, biologically significant relationships are often difficult to be identified from such networks. Our RMN algorithm can produce low false positive links even for highly noisy data (see Fig. 5(a) ). Moreover, RMN algorithm is designed to explore complex networks consisted of non-linear, decentralized and directed interactions among microbes. However, having said all these, the drawback of RMN algorithm is that it may not be able to detect simple linear correlation between two OTUs. Another potential concern is that we tested our method using a simulated data with the Tanh functions, the circularity in the model construction and validation can cause bias on our results. Overall, RMN algorithm can theoretically predict microbial interactions from low correlation data (see Tables 1 and 2 ). Our method should be a promising starting step to identify novel microbial interactions that normally cannot be found by using similarity-based methods. Therefore, by integrating similarity-based methods and our RMN algorithm, one can potentially gain a more accurate picture of microbial interactions towards a better understanding of microbial dynamics. Microbes are the most abundant and diverse organisms on earth and their interactions are crucial in understanding both the ecology and the evolution of microorganisms. Microbial interactions, including mutualism, competition, parasitism and commensalism, are difficult to quantify as the underlying processes usually cannot be observed directly and are often too complex for laboratory experiments [1] . However, recent advances in high-throughput sequencing technology have made large scale surveys of microbial communities feasible. Metagenomic studies and network-based approaches have yield detailed information on the composition of microbial communities, which in turn pave the way to study the structure of microbial ecosystems and their dynamics [2] [3] [4] .. Elucidating competitive and cooperative relationship is a challenge in generating a microbial interaction network because of the direction of such interactions [5] . Competition and cooperation are the two most studied microbial interactions in the recent times with the former dominating the latter in various microbial communities [6] [7] [8] [9] . Recent studies have also shown that competitive interactions can drive the evolution of cooperation in microbial ecosystems [9] . Therefore, identifying competitive and cooperative relationships between microbes is profound importance; however, the directional nature of such interactions also poses as a difficult challenge in network construction.. There are several approaches in constructing a microbial network. One commonly used method is the similaritybased network construction where the co-occurrences of two species over multiple time-series samples are measured to infer their interaction [2, 3, [10] [11] [12] . In such networks, nodes correspond to organisms and an edge between two nodes represents the significant relationship of two taxa across a set of time series samples. Although other derived approaches [13] [14] [15] can identify the pairwise relationships between microbes by using correlation estimation, they do not identify the nature and the strength of these relationships [1] . In general, these methods cannot capture the complexity of microbial interactions and cannot elucidate how microbes regulate each other.. To model complex relationships (one species influencing multiple others), methods employing mathematical and statistical models have been developed recently. For example, the generalized Lotka-Volterra framework was used to model the dynamics of microbial populations in order to estimate parameters governing species-species interactions [16] [17] [18] . Moreover, other studies have used nonparametric regression models to infer the dynamic relationships between three microbial populations [19, 20] . These regression models use smooth functions to describe microbial relationships and estimate their relative effects. Because these regression analyses do not use a priori knowledge to build dynamic microbial interactions, the prediction from those models often lack biological explanations, especially when the microbial community under examination is a complex one [21] . Therefore, how to construct a meaningful microbial interaction network remains a challenge in microbial ecology.. Due to the importance of competitive and cooperative relationships between microbes in complex ecological communities [8, 22, 23] , an inference model for constructing microbial regulatory network should consider these interactions simultaneously. However, all of the studies mentioned above do not incorporate these features into their construction of regulatory networks. Association rule mining can be a promising way to infer complex relationships. A rule-based method, named smooth response surface (SRS) algorithm, was developed to construct complex regulatory networks [24] . Basing on a piecewise linear-quadratic polynomial, the SRS algorithm uses a three-dimensional model surface (3D-MS) to successfully infer the relationships between the target, activator, and repressor nodes.. In this paper, we adopt a similar rationale as the SRS algorithm to detect the cooperative and competitive relationships between microbes for constructing microbial regulatory networks. Our new methodology, named the rule-based microbial network (RMN) algorithm, is an advanced version of the rule-based approach. We used Tanh functions for modeling nonlinear responses as regulatory effects of microbes. To our understanding, Tanh functions have been used to model nonlinear responses in some microbial studies, such as dose influences of pathogens [25] , regulatory effects of microbes [26] , influences of microbial compositions (phospholipids fatty acids) [27] . The RMN algorithm uses a nonlinear regulatory OTU-triplet (NRO) model to capture cooperative and competitive relationships and consequently infers the directional interaction between microbes. We applied our new approach to simulated data and showed that the RMN algorithm was capable to reconstruct microbial regulatory networks. Furthermore, we used Koenig' data (2011) to construct the interaction network for the microbial community in infant gut [28] ; and our results suggest that Bifidobacterium, Streptococcus, Clostridium XI, and Bacteroides play essential roles in regulating the abundance of Veillonella in an infant gut microbiome.

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


Wiener-based ICI cancellation schemes for OFDM systems over fading channels Abstract. The subcarriers of orthogonal frequency division multiplexing (OFDM) systems may fail to keep orthogonal to each other under timevarying channels. The loss of orthogonality among the subcarriers will degrade the system performace, and this effect is named intercarrier interference (ICI). In this paper, a Wiener-based successive interference cancellation (SIC) scheme is proposed to detect the OFDM signals. It provides good ICI cancellation performance; however, it suffers large computation complexity. Therefore, a modified Wienerbased SIC scheme is further proposed to reduce the computation complexity. Simulation results show the performance of the Wienerbased SIC scheme is better than those of zero forcing, zero forcing plus SIC and original Wiener-based schemes. Furthermore, with the modified Wiener-based SIC scheme, the performance is still better than the others. Although the performace of the modified Wiener-based SIC scheme suffers little degradation compared to Wiener-based SIC scheme, the computation complexity can be dramatically reduced. Orthogonal frequency division multiplexing (OFDM) has been applied in many digital transmission systems, such as digital audio broadcasting (DAB) system, digital video broadcasting terrestrial TV (DVB-T) system, asymmetric digital subscriber line (ADSL), IEEE 802.11a/g wireless local area network (WLAN), IEEE 802.16 worldwide interoperability for microwave access (WiMax) systems, and ultra-wideband (UWB) systems [1] [2] [3] [4] [5] [6] . It can also be Since the transmission environment is time-varying; therefore, the phase, attenuation, delay and Doppler shift of the signal are random variables.. For a time-varying multipath channel, the impulse response could be expressed as: . where the amplitude of h l (t) is modeled as Rayleigh distribution with the maximum Doppler shift f d , and it denotes the channel impulse response as lth delay path at the time t. According to (1) the time delay and the attenuation are function of time. The Fig. 3 shows the time-varying channel. In the mobile radio channels, the Rayleigh distribution is commonly used to describe the statistical time-varying channel. It is well known the envelope of sum of two quadrature Gaussian noise signals obeying a Rayleigh distribution. Fig. 4 shows a Rayleigh distributed signal envelope as a function of time. As shown in Fig. 5 , consider a mobile moving at a constant velocity v, along a path with length d between point X and Y, it receives signal from a remote source S. The difference in path lengths traveled by the signal wave from source S to the mobile at point X and Y is Δl= dcosθ= vΔtcosθ, where Δt is the time required for the mobile to travel from X and Y, and the angles θ are assumed to be the same at points X and Y since the source is assumed to be very far away from the mobile. Therefore, the phase change in the received signal due to the difference in path lengths is. and the apparent change in frequency, or Doppler shift is given by f m , where. where c is velocity of light and f c is carrier frequency. The Doppler shift f d could be maximized when cosθ is equal to 1.. The time-varying channel is expressed in (1) , and the time-varying path gain h l (t) is generally represented by a Rayleigh random process. For the classical Doppler spectrum [12] , the spectral density of h l (t) is 2 , if. where f d is the maximum Doppler frequency. Therefore, if the channel is time-varying, the ICI would be occurred.. In the orthogonal frequency division multiplexing (OFDM) system, the transmission bandwidth is divided into many narrow subchannels, and they are transmitted in parallel. Because the bandwidth of subchannel is very narrow, channel response could be seen constant. In contrast to time domain, the symbol duration increases, such that the intersymbol interference (ISI) would be happened. If the guard interval is greater than the maximum delay path, the ISI will be removed. This is the reason why OFDM could against the frequency selective fading. Increase in the symbol duration makes it much more vulnerable to time selective fading due to the Doppler spread effect.. The output of IFFT (inverse fast Fourier transform) in OFDM system could be expressed as:. The transmitted signal could be represented as:. where the interval -T g ≦ t <0 is the guard interval for opposing to the intersymbol interference (ISI).. Then the received signal r(t) could be obtained as: . where f c is the carrier frequency. The signal in the output of down converter is . where Δf is the carrier frequency offset. After passing through the lowpass filter, the signal could be obtained as:. Sampling the received signal y(t) with the rate N/T and removing the portion of cyclic prefix, the received signal could be obtained as y(n)=y(T/N), n =0, 1, 2,…, N-1, within one symbol interval. The received signal could be rewritten as:. where |τ l+1 -τ l | is assumed equal to T/N, and the normalized frequency offset is represented as ε=Δf×T=Δf / f in which T is the symbol duration, and f is the subcarrier spacing.. The FFT of y(n) could be expressed as: . h n x n l e w n e h n X k e e w n e N h n. where the ICI term is defined as:. According to the (12), it is clear that if there is no frequency offset, ε=0, and the channel is stationary, h l (n)=h l , then the ICI= h(k)δ(m-k), there will be no intercarrier interference. If there is no frequency offset, ε=0, due to the time-varying channel fading characteristic of the mobile channel, ICI would exist in OFDM systems for the mobile application. In contrarily, the channel is stationary but the frequency offset is not equal to zero, ICI would still exist in OFDM systems.. In this paper we focus on the time-varying channel fading characteristic of the mobile channel, so we set frequency offset ε equal to zero. In timevarying channels, the ICI term is defined as:. where H l (m-k) is the ICI effect of the k-th subcarrier to the m-th subcarrier. Then output of FFT (fast Fourier transform) is also written as:. where the first term is the desired signal and the second term is the ICI component.. For a time-varying fading channel, the channel variations would lead to the loss of orthogonality between subcarriers, hence the ICI effect could be occurred. The ICI effect in OFDM systems would result in an error floor. In next section, we would propose a scheme to suppress ICI. A refined SIC detection for OFDM systems under Rayleigh fading channels has been presented. The performance for a low SINR subcarrier can be significantly improved due to ICI reduction scheme. According to the simulation results, SIC detection is very suitable for high fading rate mobile communications, such as the high-speed rail communication systems. The algorithm and the BER performance for the Wiener-based SIC scheme have been presented. According to the simulation results, we could clearly realize the performance of the Wiener-based SIC scheme is better than the ZF-SIC scheme's. Because the detection scheme may have noise enhancement in ZF-SIC scheme, the performance would be degraded. Although the Wienerbased SIC scheme has better performance, it has high computation complexity. In order to reduce the computation complexity for the Wienerbased SIC scheme, the modified Wiener-based SIC scheme is proposed.. According to the analysis, the computation complexity of the modified Wiener-based SIC scheme with q = 8 is 15% of the original Wiener-based SIC scheme. According to complexity analysis and simulation results, the performance with a large q is better than the performance with a small q, but the computation complexity is higher. Hence, this is a trade-off problem between the system performance and the computation complexity.. The schemes studied in this paper require perfect channel state information. To obtain a precision channel state information becomes an important issue worthy of further studying. Besides, due to the population of MIMO-OFDM technology, applying the proposed scheme to MIMO-OFDM systems is also worthy to investigate.

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


Large-time behaviour of solutions to the equations of one-dimensional nonlinear thermoviscoelasticity with memory This paper is concerned with the large-time behaviour of globally defined smooth solutions of the initial-boundary value problem for the one-dimensional nonlinear thermoviscoelasticity system with memory. In this paper we consider the system of one-dimensional nonlinear thermoviscoelasticity,. 2). which is the Lagrangian description of the balance laws of momentum and energy of one-dimensional materials with reference density ρ 0 = 1. To the system is added a heat flux following the second law of thermodynamics expressed through the Clausius-Duhem inequality. (1.4). In the above equations, u, v, e, σ , η, θ and q denote specific volume (deformation gradient), velocity, internal energy, stress, specific entropy, temperature and heat flux, respectively. The quantities e, σ , η, and q are given by so-called constitutive relations for the thermoviscoelasticity material considered. The functions u, θ, and e take only positive values. We will assume here that the boundary points of the material are stress-free and thermally insulated, that is, σ (0, t) = σ (1, t) = 0 t > 0, (1.5) q(0, t) = q(1, t) = 0 t > 0.. (1.6). The prescribed initial values for u, v, and θ are:. u(x, 0) = u 0 (x), x ∈ [0, 1], (1.7) v(x, 0) = v 0 (x), x ∈ [0, 1], (1.8) θ (x, 0) = θ 0 (x), x ∈ [0, 1].. (1.9). Without loss of generality, by superimposing a trivial rigid motion, we normalize the initial velocity so that . where c v and k are positive constants, f (u) is twice continuously differentiable for u > 0,. There, the authors assumed the viscosityμ(u) to be uniformly positive, that iŝ. Moreover, they obtained the following asymptotic behaviour for the smooth solutions globally defined {u(x, t), v(x, t), θ (x, t)}:. (III) There exists a family of probability measure {ν x } x∈[0,1] on R (depending measurable on x) with supp. In this work we will extend these results for materials with memory, i.e., will consider a material with the following constitutive relations. where. Furthermore, we assume that the initial data are compatible with the boundary conditions. The paper is organized as follows. In Section 2, we comment the existence of global smooth solutions. In Section 3, we present some technical lemmas, and finally in Section 4, we give the proof of the main result.

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 B I 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 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


The oscillation of partial difference equations with continuous arguments Abstract--For the partial difference equationsA(x -a, y) -F A(x, y -b) -A(x, y) + P(x, y)A(x + T, y + a) = 0 andwe shall obtain sufficient conditions for the oscillation of all solutions of these equations. (~) Partial difference equations are difference equations that involve functions of two or more independent variables [1, 2] . Partial difference equations have been posed from various practical problems [1, 3, 4] and in the approximation of solutions of partial differential equations by finite difference methods [1, 5, 6] .. From the 1980s, the oscillation of solutions of partial differential equations with delay has been investigated by many authors (see [7] ). Tramov [8] , Kreith and Ladas [9] , Mishev and Bainov [10] started to consider the oscillation for elliptic, parabolic, and hyperbolic partial difference equations with delay, respectively. The partial difference equations with delay can be regarded as discrete analogues of partial differential equations with delay [1, 8, 11] . Recently, the qualitative analysis of partial difference equations has received much attention, see [1, 7, [11] [12] [13] [14] [15] [16] [17] [18] [19] .. In this paper, we shall first consider the linear partial difference equation with continuous arguments A solution A(x, y) of (1.1) is said to be eventually positive if A(x, y) > 0 for all large x and y. It is said to be oscillatory if it is neither eventually positive nor eventually negative.. In Section 2, we shall obtain sufficient conditions for all solutions of (1.1) to be oscillatory. In Section 3, we shall consider the oscillations of a class of nonlinear partial difference equations.

O B 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 B 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 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 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 B I I 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 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 B I I


A variant of the parallel model for sample surveys with sensitive characteristics A new non-randomized response (NRR) model (called a variant of the parallel model) is proposed. The survey design and corresponding statistical inferences including likelihood-based methods, Bayesian methods and bootstrap methods are provided. Theoretical and numerical comparisons showed that the proposed variant of the parallel model over-performs two existing NRR crosswise and triangular models for most of the possible parameter ranges. An outline for handling the possible non-compliance behavior in the proposed model is provided. An illustrative example from an existing survey on 'sexual practices' in San Francisco, Las Vegas and Portland is used to demonstrate the proposed statistical analysis methods. Two real surveys on the cheating behavior in examinations at the University of Hong Kong are conducted and are used to illustrate the proposed design and analysis methods. Consider a target population which can be divided into two mutually exclusive groups: one with a sensitive attribute and the other without. Statistically, let Y be a sensitive binary variable, {Y = 1} denote the population group that has the sensitive attribute and {Y = 0} denote the complementary group. Usually, a well-designed survey is conducted for collecting sensitive data, which are used to estimate the proportion (denoted by π = Pr(Y = 1)) of persons with the sensitive characteristic. Several techniques are developed to encourage truthful responses while protecting the privacy of respondents (or minimizing the interviewee's feeling of jeopardy). The first one is the randomized response technique dents' sensitive answers (Takahasi and Sakasegawa, 1977; Tian et al., 2007b Tian et al., , 2011 Yu et al., 2008; Tan et al., 2009; Tang et al., 2009) . Like the UCT, the NRR designs don't require any randomizing devices.. One basic distinction between a randomized response model and a non-randomized response model is that the former usually requires a randomization device such as a coin or a die which is related to a random variable without reproducibility, while the latter requires an independent non-sensitive variate such as birth date combined with the sensitive response variable to form an incomplete contingency table, resulting in a reproducibility. That is, the same respondent may yield different answers depending on the outcome of the randomization device in repeated experiments (e.g., repeatedly flip a coin). For example, in the unrelated question design with a coin as the randomization device, if the outcome is head, the first question is answered; if the outcome is tail, the second question is answered. Suppose that the result of the first (second) flip is a tail (head), the answer is a 'yes' ('no'). As a result, interviewers do not know which answer should be collected.. It is not true that any randomized response model can be easily transformed to a nonrandomized response model. Up to now, only the Warner model and the unrelated question model were successfully transformed to the non-randomized crosswise model (Yu et al., 2008 ) and the non-randomized parallel model (Tian, 2012) , respectively. Next, although some randomized response models can be transformed to non-randomized versions, the resulting statistical analysis methods are totaly different. For example, for the randomized unrelated question model with an unknown θ = Pr(U = 1), two independent samples of sizes n 1 and n 2 and two randomization devices are required, while for its non-randomized version, i.e., the proposed variant of the parallel model in this paper, only one sample is needed without using any randomization devices and the corresponding statistical analysis methods are developed based on a trinomial distribution with two complete observations and one incomplete observation. The second example is as follows. To assess the association of two sensitive questions with binary outcomes, a randomized response model in general requires two randomization devices (Christofides, 2005) , while in the non-randomized hidden sensitivity model (Tian et al., 2007b) , respondents only need to answer a non-sensitive ques-tion instead of the original two sensitive questions and the corresponding analysis methods are developed based on an incomplete 4 × 4 contingency table. Finally, for other randomized response models (e.g., Kuk, 1990) , the corresponding non-randomized partners are not yet available up to now.. Recently, Tian (2012) proposed a new NRR model, called the parallel model, to estimate the unknown proportion, π = Pr(Y = 1), of individuals with a sensitive characteristic.. By introducing two non-sensitive dichotomous variates U and W such that Y , U and W are mutually independent, Tian (2012) developed a general framework of design and analysis for the NRR parallel model. Theoretical comparison showed that the parallel model over-performs two existing NRR crosswise and triangular models for most of the possible parameter ranges. It was noted that all these findings are based on the assumption of known proportions θ = Pr(U = 1) and p = Pr(W = 1). However, in survey practice, it is usually difficult to choose an appropriate non-sensitive dichotomous variate U with known θ = Pr(U = 1). Even such a binary variable U can be found and a constant θ 0 is assumed to be equal to the true value of the θ, how to test the hypothesis H 0 : θ = θ 0 is still not available for the parallel design. The main goal of this paper is to propose a variant of the parallel model with unknown θ = Pr(U = 1).. The rest of the paper is organized as follows. In Section 2, we propose the survey design for the variant of the parallel model, and discuss the estimation of the parameters, relative efficiency and the degree of privacy protection. In Section 3, three asymptotic confidence intervals (CIs) and the exact CI of π are derived. In addition, a modified maximum likelihood estimate (MLE) of π is provided and the corresponding asymptotic property is investigated.. Statistical inferences on θ and two bootstrap CIs of the parameters are given in Sections 4 and 5, respectively. Bayesian inferences are discussed in Section 6. Comparisons with the NRR crosswise and triangular models are conducted theoretically and numerically in Section 7. An outline for handling the possible non-compliance behavior in the proposed model is presented in Section 8. In Section 9, an illustrative example from an existing survey on 'sexual practices' in San Francisco, Las Vegas and Portland is used to demonstrate the proposed statistical analysis methods. Two real surveys on the cheating behavior in examinations at the University of Hong Kong are conducted and are used to illustrate the proposed design and analysis methods. A discussion is given in Section 10. The exact inversion Bayesian formulae (IBF) sampling is provided in Appendix A. Suppose that U and W are two non-sensitive dichotomous variates, and Y , U and W are mutually independent with unknown θ = Pr(U = 1) and known p = Pr(W = 1). For example, we may define U = 1 if the respondent lives in Hong Kong Island (or likes watching football/soccer on TV, or likes fishing/singing/shopping/traveling, or is educated above the level of high school) and U = 0 otherwise. Similarly, we could define W = 1 if the last digit of the respondent's ID/cell phone number is odd (or the respondent's birthday is in the second half of a year/month) and W = 0 otherwise. Hence, it is reasonable to assume that. The interviewer may design the questionnaire in the format as shown at the left-hand side of Table 1 and ask the interviewee to truthfully put a tick in the circle if he/she belongs to {U = 0, W = 0} or put a tick in the triangle if he/she belongs to {Y = 0, W = 1} or put a tick in the upper square if he/she belongs to {U = 1, W = 0} ∪ {Y = 1, W = 1}. Note that all {W = 0}, {W = 1}, {U = 0}, {U = 1} and {Y = 0} are non-sensitive classes, thus {U = 1, W = 0} ∪ {Y = 1, W = 1} is also a non-sensitive subclass. Therefore, whether the interviewee belongs to the sensitive class {Y = 1, W = 1} is not on record. Since θ is unknown, we call this a variant of the parallel model. The corresponding cell probabilities are displayed at the right-hand side of Table 1 . Since the three binary variables U, Y and W are independent, the joint probability is the product of two corresponding marginal probabilities. Table 1 . The survey design for the variant of parallel model with unknown θ = Pr(U = 1). Note:. • Please truthfully put a tick in the circle if you belong to {U = 0, W = 0} or put a tick in the triangle if you belong to {Y = 0, W = 1} or put a tick in the upper square if you belong to {U = 1, W = 0} ∪ {Y = 1, W = 1}.. • For those respondents not completely understanding the questionnaire shown in Table 1 , investigators can formulate the questionnaire of the variant of the parallel model as follows:. Let Y = 1 if a respondent is a drug user and Y = 0 otherwise.. (1) If your birthday is in the first half of a year (i.e., W = 0), please answer '0' (i.e., U = 0), or '2' (i.e., U = 1) to the question: Do you like shopping?. (2) If your birthday is in the second half of a year (i.e., W = 1), please answer '1' (i.e., Y = 0), or '2' (i.e., Y = 1) to the question: Are you a drug user?. Answering '0' is equivalent to putting a tick in the circle in Table 1 , answering '1' is equivalent to putting a tick in the triangle in Table 1 and answering '2' is equivalent to putting a tick in the upper square in Table 1 . The paper presents a new development for the parallel model originally proposed by Tian Table 3 and Table 4 . A possible reason for these conclusions is that the variant of the parallel design can gather exact information (instead of mixing information) for two cells (i.e., the circle and the triangle in Table 1 ) because of the introduction of an additional non-sensitive binary variate U when comparing with the crosswise and triangular models. Finally, we provide a simple way to handle the possible non-compliance behavior in the proposed model.. One referee pointed out that from the analysis viewpoint (rather than the design viewpoint), the proposed model in this paper is a member of the family of multinomial processing tree models (see, e.g., Erdfelder et al., 2009 ). Hu and Batchelder (1994) obtained point estimates of parameters by using the EM algorithm and the corresponding standard errors from the Fisher information matrix in multinomial processing tree models. However, we noted that the resulting interval estimates (based on derivatives from Hu and Batchelder, 1994) in the form of point estimate plus/minus 1.96 times standard error may be beyond the unit interval [0, 1] when the true value of the proportion with the sensitive characteristic is close to zero or one. In fact, in Section 6.2 of this paper we have given the EM algorithm to calculate the posterior modes which are identical to the MLEs of the corresponding parameters π and θ if two independent uniform priors are adopted. In addition, our bootstrap CIs for π and θ in the form of (5.3) are always within the unit interval [0, 1] . the probability mass function, i.e., f (z k |Y obs ) = Pr{Z = z k |Y obs }. Therefore, it suffices to find ω k = f (z k |Y obs ) for k = 1, . . . , K. For any (π 0 , θ 0 ) ∈ S (π,θ|Y obs ) , let q k (π 0 , θ 0 ) = Pr{Z = z k |Y obs , π 0 , θ 0 } f (π 0 , θ 0 |Y obs , z k ) , k = 1, . . . , K. (A.2). From the sampling-wise IBF (A.1), we immediately obtain. , k = 1, . . . , K. (A.3) and {ω k } K k=1 are independent of π 0 and θ 0 . Thus, it is easy to sample from f (Z|Y obs ) since it is a discrete distribution with probability ω k on z k for k = 1, . . . , K. We summarize the algorithm as follows. The exact ibf sampling:. Step 1. Identify S (Z|Y obs ) = S (Z|Y obs ,π,θ) = {z 1 , . . . , z K } from f (Z|Y obs,π,θ ) and calculate {ω k } K k=1 according to (A.2) and (A.3).. Step 2. Generate i.i.d. samples {Z (l) } L l=1 of Z from the probability mass function f (Z|Y obs ) with probabilities {ω k } K k=1 on {z k } K k=1 .. Step 3. Generate (π (l) , θ (l) ) ∼ f (π, θ|Y obs , Z (l) ) for l = 1, . . . , L, then {π (l) , θ (l) } L l=1 are i.i.d. samples from the observed posterior distribution f (π, θ|Y obs ).

O O O B I I 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 B I 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 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 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 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 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 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 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 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 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 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 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 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


On the infeasibility of modeling polymorphic shellcode Re-thinking the role of learning in intrusion detection systems Abstract Current trends demonstrate an increasing use of polymorphism by attackers to disguise their exploits. The ability for malicious code to be easily, and automatically, transformed into semantically equivalent variants frustrates attempts to construct simple, easily verifiable representations for use in security sensors. In this paper, we present a quantitative analysis of the strengths and limitations of shellcode polymorphism, and describe the impact that these techniques have in the context of learning-based IDS systems. Our examination focuses on dual problems: shellcode encryption-based evasion methods and targeted "blending" attacks. Both techniques are currently being used in the wild, allowing real exploits to evade IDS sensors. This paper provides metrics to measure the effectiveness of modern polymorphic engines and provide insights into their designs. We describe methods to evade statistics-based IDS sensors and present suggestions on how to defend against them. Our experimental results illustrate that the challenge of modeling self-modifying shellcode by signature-based methods, and certain classes of statistical models, is likely an intractable problem. Code injection attacks, and their counter-measures, remain important research topics within the security community. Attacks such as buffer overflow and heap corruption exploit vulnerabilities in the way certain software handles input data, to inject foreign code into the execution context of target applications. At the memory layer, the injected code is composed of machine instructions known as "shellcode", whose etymology originates from their use in spawning command shells on the target. Until recent years, one of the most relied-upon methods to detect such attacks have been network layer signature matching, where specialized monitors issued alerts for suspicious strings observed within network traffic. Recently, however, standard practice in the attacker community have evolved to incorporate sophisticated obfuscation techniques which aim to render these detection schemes obsolete. The new paradigm, known as "polymorphic shellcode," utilizes self-modifying code that is delivered to the target in an encrypted form and performs dynamic self-decryption upon execution, revealing the actual attack code at the last moment. Evasion tactics against statistical sensors have also begun appearing, such as purposely skewing the distribution of bytes within shellcode-such methods represent the beginnings of a new challenge of targeted blending attacks.. In a previous paper, we examined the difficulty of modeling polymorphic shellcode from a machine learning perspective with experiments using real world obfuscation engines (Song et al. 2007 ). While emerging trends in polymorphic shellcode design include elements of both code obfuscation and targeted blending, our previous paper focused primarily on the former technique and had only briefly mentioned the latter. In this longer paper, we expand on our earlier work to provide a more comprehensive exploration of the problem of shellcode detection. This paper provides an examination of machine learning-based blending attacks which, given the current trends, we expect adversaries to utilize in the near future. This paper analyzes the complexity of these two problems, discuss their implications and presents evidence that signature-based modeling and certain statistical approaches are not likely to remain as practical solutions in the long term.. Organization This paper is organized as follows: Sect. 2 describes shellcode and polymorphism in detail. Section 3 discusses related works in this area. Code obfuscation techniques and our methods for measuring the strengths of polymorphic engines are presented in Sect. 4 while Sect. 5 covers the fusion of code obfuscation and simple targeted blending attacks. Section 6 presents our methodology for advanced higher order blending attacks. Section 7 explores the theoretical boundaries of shellcode polymorphism. We present our conclusions in Sect. 8. This paper studies these dual evasion tactics, of self-cipher-based obfuscation and targeted blending attacks, and metrics are proposed to quantify the effectiveness of these obfuscations. Our attention is focused on analyzing the decoder portion of the shellcode, since this is the most constrained portion of the attack. Other than the higher order bits of the return address zone, this is the only section that cannot be trivially disguised, since it must hold executable machine code. At the same time we also study the challenge of making shellcode appear similar to normal traffic, in order to evade certain classes of statistical anomaly detection-based sensors. Our results show the difficulties we face when designing detectors given modern obfuscation techniques. We proposed metrics which can measure the strengths of these engines and have shown how targeted higher order blending attacks are possible, in an effort to forecast future threats. We explained how signature-based modeling can work in some cases, and confirmed that the long-term viability of such approaches is consistent with the long held, intuitive, belief that polymorphism will eventually defeat these methodologies.. We argue that while signature-based methods may work in the short term, evidence suggests that they cannot generalize to protect against future attacks. Similarly, feature-counting based statistical models also suffer from equally troubling deficiencies. In our discussion on blending, we assumed that we had access to labeled samples-in practice this is a luxury that is not always available, at least not for the defender. In contrast, the attacker can generate perfectly labeled data by querying the target host for positive samples, as we did in our experiments to find the normal traffic pattern.. Given these properties, any generative approach to modeling malicious code would appear to be threatened. At the same time, we must always keep in mind the stringent falsepositive requirements that constrain all anomaly-detection sensors, and that we must expect the attackers to exploit this requirement. The strategy of modeling malicious content forces us to try to keep up with the adversary, and if polymorphic code is really distributed in the manner that our study indicates, then we might never achieve a generalizable defense by continuously refining a single representation of what the attackers may do. A positive-security model, one that focus on normal content, might be a more reliable solution. Though it was the virus writers who first introduced self-decryption and self-unpackingbased polymorphism as simple, yet effective, ways of evading signature-based AV scanners, it did not take long before shellcode writers adopted this technique. Recently, polymorphism has become a standard tool for web-based attacks as well, where exploits are delivered in the form of interpreted code such as Javascript or PHP. The MPack (Panda Labs 2007) toolkit, currently being traded in the malware underground and responsible for tens of thousands of recent website compromises, obfuscates Javascript attacks with several layers of self-encryption and randomization. The Metasploit team, already famous for their shellcode exploit engines, has announced the release of their "eVade o'Matic Module (VoMM)," a polymorphism engine for Javascript based exploits.. Countering such polymorphic attacks is a difficult problem. Researchers have proposed a variety of defenses against polymorphic shellcode, from artificial diversity of the address space (Bhatkar et al. 2003) or instruction set (Kc et al. 2003; Barrantes et al. 2003) to compiler-added integrity checking of the stack (Cowan et al. 1998; Etoh 2000) or heap variables and "safer" versions of library functions (Baratloo et al. 2000) . Other systems explore the use of tainted dataflow analysis to prevent the use of untrusted network or file input (Costa et al. 2005; as part of the instruction stream. A large number of schemes propose capturing a representation of the exploit to create a signature for use in detecting and filtering future versions of the attack. Signature generation methods are based on a number of content modeling strategies, including simple string-based signature matching techniques like those used in Snort Development Team (2009). Many signature generation schemes focus on detection heuristics such as traffic characteristics (Singh et al. 2004; Kim and Karp 2004 ) (e.g., frequency of various packet types) or identification of the NOP sled (Toth and Kruegel 2002) , while others derive a signature from the actual exploit code (Liang and Sekar 2005; Locasto et al. 2005) or statistical measures of packet content (Wang and Stolfo 2004; Wang et al. 2005; , including content captured by honeypots (Yegneswaran et al. 2005 ).

O 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 O O O O O O O O O O O O O O O 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 B 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 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 O O O O O O O O O O O O O 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 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 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 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 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 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 O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O 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 O B O O O O O O O O O O B O O O O O O O O B B O O O O O O O O O O O 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 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 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 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 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 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 B O 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 O O O O O O O O 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 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


What lies beneath?: Knowledge infrastructures in the subseafloor biosphere and beyond We present preliminary findings from a threeyear research project comprised of longitudinal qualitative case studies of data practices in four large, distributed, highly multidisciplinary scientific collaborations. This project follows a 2 × 2 research design: two of the collaborations are big science while two are little science, two have completed data collection activities while two are ramping up data collection. This paper is centered on one of these collaborations, a project bringing together scientists to study subseafloor microbial life. This collaboration is little science, characterized by small teams, using small amounts of data, to address specific questions. Our case study employs participant observation in a laboratory, interviews (n = 49 to date) with scientists in the collaboration, and document analysis. We present a data workflow that is typical for many of the scientists working in the observed laboratory. In particular, we show that, although this workflow results in datasets apparently similar in form, nevertheless a large degree of heterogeneity exists across scientists in this laboratory in terms of the methods they employ to produce these datasets-even between scientists working on adjacent benches. To date, most studies of data in little science focus on heterogeneity in terms of the types of data produced: this paper adds another dimension of heterogeneity to existing knowledge about data in little science. This additional dimension makes more complex the task of management and curation of data for subsequent reuse. Furthermore, the nature of the factors that contribute to heterogeneity of methods suggest that this dimension of Long predicted by the science community [30] , both Nature and Science have now heralded the opportunities and challenges presented by the scientific data deluge [19, 20] . Universities themselves are assessing their rights, roles, and responsibilities for managing and for exploiting data from their researchers [4] .. In addition to the sheer size of data generated, the heterogeneity of datasets is also increasing, even within individual domains. Scientific collaboration is becoming a more multidisciplinary, distributed endeavor [15] . As a result, approaches from multiple epistemological or social perspectives may be combined in the production of a dataset, and conversely a single dataset may be used in multiple contexts, crossing epistemological, cultural and social boundaries.. Contemporary digital scholarship is thus a rapidly changing and expanding undertaking. However, today's scientific methods and organization of collaborative work often do not scale well to today's volumes or diversity of data generated; qualitatively different approaches to scientific inquiry are required. As data are combined from multiple sources and are mined for new interpretations, the challenges of data management and curation multiply. Modern sensor networks, satellites, telescopes, and laboratory instruments can collect vastly more data, at far faster rates and far greater variety, than ever before. Scientists rely on their instruments, algorithms, and collaborators to clean, verify, visualize, and inter-pret their data. Much can go wrong in the many steps involved in the design and deployment of instruments, collection and cleaning of data, and in the analysis and reporting of results. Data and responsibility pass through many hands, often over the course of many years, in the life cycles of collaborative data-driven science.. Scientific data management requires deep expertise in scientific theory, method, instrumentation, and interpretation. Skill sets are complex and are divided differently in each field and specialty. Each step in data handling requires knowledge and judgment of the steps that went before. Necessary details of data provenance often go undocumented, leaving researchers in the position of making multiparty inferences with insufficient information [42] . Minute differences in calibration, miniscule artifacts in a data stream, and other perturbations may be spotted by those closest to the research design-but these factors decrease in visibility the farther the interpreter lies from the source of the data.. The pressure from funding agencies such as the National Science Foundation (NSF) and the National Institute of Health (NIH) to share research data highlights the complexity of data-driven science. "Data" is a contested notion. Furthermore, competing views exist of research, innovation, and scholarship, disparate incentives for collecting and releasing data, the economics and intellectual property of research products, and public policy-and the requisite technical and human infrastructure. However, relatively few studies document consistent data release. Sharing research data is thus a conundrum-"an intricate and difficult problem" [11] .. Research in both data-intensive big science, where data products are large in volume but typically homogeneous, such as astronomy projects centered on the building and operation of massive-scale instruments, and in little science, where data products are small in size but large in number, such as sensor network applications in ecology, marine biology, environmental engineering, and seismology, reveals a critical lack of infrastructure to support these new forms of scholarship. The promise of technology-enabled, datadriven digital scholarship in science is predicated upon available systems, services, tools, content, policies, practices, and human resources to discover, mine, and use research products, as well as to create those products in forms that are useful to others. Not only is this infrastructure not yet in place, it. is not yet clear what should be built or how to build it [10, 25] .. However, this problem is becoming better recognized, as is the fact that sociotechnical research approaches can produce critical insights that inform the design, policy, and human resource requirements for scientific information infrastructure [25] . This paper presents preliminary findings from a three-year study of such infrastructures. The Transformation of Knowledge, Culture, and Practice in Data-Driven Science: A Knowledge Infrastructures Perspective (henceforth known as the Knowledge Infrastructures project) involves longitudinal qualitative case studies of four large, distributed, multidisciplinary scientific collaborations. Two of these collaborations could be considered as big science, whereas the other two involve multiple research teams performing little science. Furthermore, two of these collaborations have been in the process of ramping down data collection and active research, while the two others are ramping up their activities. Beyond the preliminary results in this paper, the Knowledge Infrastructures project will continue to analyze these four distinct collaborations.. Here, we present an agenda for researching knowledge infrastructures, defined as "robust networks of people, artifacts, and institutions that generate, share, and maintain specific knowledge about the human and natural worlds" [23, p. 17] , through motivating and presenting the research questions that guide our Knowledge Infrastructures project team. Then, we present the methodologies of the Knowledge Infrastructures project, introduce the four case studies, and explain how our approach to research will make significant contributions in pursuing the research agenda. To demonstrate these contributions, we present preliminary findings from one of the case studies, a multidisciplinary, multi-institutional collaboration that involves studying microbial life beneath the seafloor. In particular, we explore and account for the diversity of practices in producing datasets that we observed across scientists, even in the same laboratory. To date, research on data practices has focused on heterogeneity of data types produced in a research setting; by contrast, here we demonstrate that for a single data type, there can be significant heterogeneity in how such datasets are produced even in the same research setting. This heterogeneity can multiply significantly the challenges involved in data management and curation. Scientists across a wide range of scientific disciplines are being confronted by the challenges of managing volumes of data increasing in both scale and diversity. To exploit the potential of digital scholarship to its fullest, it is vital to study existing data practices to inform the development of research infrastructures.. The Knowledge Infrastructures project presented in this paper has already made significant progress toward understanding data practices, and will continue to fill existing gaps in the literature. To date, studies have focused on heterogeneity in terms of the types of datasets being produced. In this paper, however, we find that even within a single workflow in a single laboratory, the practices, methods, and techniques used in the production of datasets can be highly heterogeneous, with many implications for data storage, curation, integration with other sources of data, and potential data sharing and reuse. In Subsect. 3.3, we present examples of heterogeneity observed in data production practices in our case study of C-DEBI, with scientists in the same laboratory and even working on adjacent benches using a diversity of approaches to accomplish similar tasks and produce datasets similar in form and intent. Indeed, the heterogeneity presented above is only a fraction of the total heterogeneity that we have observed. For example, scientists perform analysis of sequences using a disparate range of tools and software including commercially available and open-source software, and sequence databases.. Heterogeneity of data practices has long been regarded as a hallmark of little science [46] . To date, this heterogeneity has been understood in terms of the types of dataset produced [13, 46] . The analysis presented in Subsect. 3.3 introduces heterogeneity along another dimension, namely scientists using a diversity of practices to produce datasets similar in purpose and form.. As discussed above, our CENS research demonstrates that decisions made at each stage of the data life cycle have a cumulative effect on data [53] . In the case of the subseafloor biosphere, decisions regarding the choice of methods can have a significant impact on the results of scientific analyses, with important implications for the reuse of datasets. For example, the quantification of global subseafloor biomass is foundational to the study of the subseafloor biosphere, and attempts to quantify this biomass involve aggregating datasets from a wide range of studies [33] . However, a recent meta-analysis of studies of subseafloor life found that the method employed to quantify biomass can have a major impact on the results [40] , with significant implications for the quantification of global biomass.. Furthermore, the ability of a scientist to assess the integrity and trustworthiness of a dataset tends to be enhanced when the scientist has greater knowledge about the factors-both social and technical-involved in the different stages of the dataset's production and curation [54] . Our CENS findings show that the production and use of multiple types of datasets significantly complicate these issues. Different people from different disciplinary backgrounds are involved in the production of different datasets, using different methods for producing these data. The task of tracking, documenting, and maintaining access to all of the datasets in a single workflow becomes extremely complicated. Adding another dimension of heterogeneity as described in Subsect. 3.3 can only complicate this task further. We are conducting a longitudinal ethnographic case study of C-DEBI. An ethnographic study involves a range of qualitative research methods to provide a thorough account of the organization under study [28] . Our methods include interviews, participant observation, online ethnography, and document analysis. Drawing on data from a range of sources allows for triangulation [43] . The content of texts (including interview transcripts, reports, and ethnographic notes) is highly contingent, rather than simply reflecting an underlying reality. Triangulation involves the crosschecking of data from different sources produced in different contexts, which helps to ensure that conclusions drawn from the data are not biased by the context in which the data are produced.

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