Obligations of Trust for Privacy and Confidentiality in Distributed Transactions Purpose -This paper describes a bilateral symmetric approach to authorization, privacy protection and obligation enforcement in distributed transactions. We introduce the concept of the Obligation of Trust (OoT) protocol as a privacy assurance and authorization mechanism that is built upon the XACML standard. The OoT allows two communicating parties to dynamically exchange their privacy and authorization requirements and capabilities, which we term a Notification of Obligation (NoB), as well as their commitments to fulfilling each others requirements, which we term Signed Acceptance of Obligations (SAO). We describe some applicability of these concepts and show how they can be integrated into distributed authorization systems for stricter privacy and confidentiality control.Design/Methodology/Approach -Existing access control and privacy protection systems are typically unilateral and provider-centric, in that the enterprise service provider assigns the access rights, makes the access control decisions, and determines the privacy policy. There is no negotiation between the client and the service provider about which access control or privacy policy to use. We adopt a symmetric, more user-centric approach to privacy protection and authorization, which treats the client and service provider as peers, in which both can stipulate their requirements and capabilities, and hence negotiate terms which are equally acceptable to both parties.Findings -We demonstrate how the Obligation of Trust protocol can be used in a number of different scenarios to improve upon the mechanisms that are currently available today.Practical Implications -This approach will serve to increase trust in distributed transactions since each communicating party receives a difficult to repudiate digitally signed Acceptance of Obligations, in a standard language (XACML), which can be automatically enforced by their respective computing machinery.Originality/Value -This paper adds to current research in trust negotiation, privacy protection and authorization by combining all three together into one set of standardized protocols. Furthermore, by providing hard to repudiate Signed Acceptance of Obligations messages, this strengthens the legal case of the injured party should a dispute arise. Trends in emerging access management systems raise an interesting paradox. On the one hand, service providers' applications require identity/attribute related information in order to validate a user's request. On the other hand, users may not wish to disclose their information or attributes to a remote Service Provider (SP) without determining in advance whether the service provider can be trusted to comply with their privacy preferences. Conventionally, privacy is often considered from the users' perspective, just as access control is considered from the SP's standpoint. That is, the user is concerned about the confidentiality of their personal identifying information (PII), and the resource provider is concerned about the confidentiality and integrity of the resource information. These assumptions have resulted in unilateral asymmetric approaches. Yet the user's PII may become the SP's resource once it has been transferred, and the SP may also have sensitive attributes such as membership certificates of consortia, or trust relationships with third parties (TTPs) or policies of various kinds that a resource user may demand to see before releasing their PII. This suggests a symmetrical approach may be more appropriate, and has led to the research topic called trust negotiation where each party's attributes are released incrementally to the other, as trust is established between them (Bertino et al. 2004) .. Often, confidentiality is used as a substitute for privacy but they are not identical. It is important to accurately differentiate between them in order to identify the associated challenges and risks. Simply put, whilst confidentiality is the process of making sure that only the right ('legitimate') party gets access to information, privacy ensures that this legitimate party treats the information in the right way and only uses it for the purposes for which it is intended. Privacy is governed by factors such as legislation, laws, guidelines and principles that cut across national borders (OECD, 2000) . This paper describes one concrete approach to enhancing privacy assurance, by permitting the bilateral exchange of privacy Requirements and the Capabilities to satisfy them. The OoT mechanism provides technical solutions to support possible social/judicial solutions for security assurance in distributed open systems. This mechanism demonstrates a secure way of using P3P and other policies in WS-XACML which provides a framework for the dynamic exchange of requirements and capabilities, meaning that this framework can support the P3P platform with minimal effort. Our solution demonstrates significant improvement in the provision of privacy in distributed transactions where technically "difficult-to-repudiate" services are vital.

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


Modeling and emergence of flapping flight of butterfly based on experimental measurements The objective of this paper is to clarify the principle of stabilization in flapping-of-wings flight of a butterfly, which is rhythmic and cyclic motion. For this purpose, a dynamics model of a butterfly is derived by Lagrange's method, where the butterfly is considered as a rigid multi-body system. For the aerodynamic forces, a panel method is applied. Validity of the mathematical models is shown by agreement of the numerical result with the measured data. Then, periodic orbits of flapping-of-wings flights are searched in order to fly the butterfly models. Almost periodic orbits are obtained, but the model in the searched flapping-of-wings flight is unstable. This research, then, studies how the wake-induced flow and the flexibly torsional wings effect on the flight stability. Numerical simulations demonstrate that both the wake-induced flow and the flexible torsion reduces the flight instability. Because the obtained periodic flapping-of-wings flight is unstable, a feedback control system is designed, and a stable flight is realized. Butterflies can maintain desired flapping-of-wings flights against environmental uncertainties and variations, e.g. gust, weight gain or loss, etc., using their adaptation-capability. Such an adaptive function is considered to emerge from the interaction of the nervous system, body, and environment. We call the adaptive motor function "Mobiligence.". The flapping flight of butterfly is an example of Mobiligence in which the environment is the generated flowfield. Actually, it essentially has the same structure with other Mobiligence subjects, e.g., to emerge the flapping flight from the interaction of the nervous system, body, and environment. From the viewpoint, this study discusses the principle to emerge the stable flapping flight of butterfly, which is rhythmical periodic motion.. There are many unknown points for the stable flight, e.g. "how the butterfly moves," "how the control is realized," etc. Concretely, this study investigates the following two issues by the biological analysis through experimental observations of living butterflies and by the systems engineering or synthetic approach. This paper summarizes a part of study results obtained by a research project based on this approach. References [1, 2, 3, 4, 5, 6, 7, 8] reports some studies in detail.. An experimental system with a low-speed wind tunnel is constructed to measure the motion and aerodynamic forces of actual butterflies quantitatively. A 3D mathematical model is constructed by using a panel method for aerodynamics formulation in order to analyze the stability of free-flying butterflies and so on. Its validity and accuracy are examined by comparing with the obtained experimental data. A periodic trajectory of flapping-ofwings flight is searched in order to fly the constructed butterfly model. Using the constructed numerical simulator and the obtained periodic trajectory, it is shown that the free-vortices in the wakes provides a type of stabilization effect. In addition, wing torsion caused by structural flexibility is also introduced to the model and its effect on the flapping-of-wings flight is examined. But the obtained trajectory is still unstable, and the butterfly model goes down after a few flapping periods. Therefore, a feedback control system is discussed to realize a stable flight. A designed controller stabilizes the flapping-of-wings flight, where the fully nonlinear model is controlled by a sampled-data linear controller.. The rest of this paper is organized as follows. Section 2 organizes flapping mechanism of butterfly using anatomical observation and knowledge of mus-culoskeltal system. Section 3 shows observation experiments and measured results. Section 4 explains modeling of butterfly, in which a butterfly is considered as a rigid multi-body system, and aerodynamic forces are formulated by a panel method. Its numerical results are compared with the measured data, and their good agreement justifies the validity and accuracy of the mathematical model. In section 5, a periodic trajectory of flapping-of-wings flight is searched by using the constructed numerical simulator, and an almost periodic trajectory is obtained. Wing torsion caused by structural flexibility is also introduced to the model and its effect on the flapping-of-wings flight is examined. Numerical simulations show the extension of the flying period considering them. Meanings of this stabilization effect is discussed, which can be considered as a common principle of mobiligence. Because the obtained periodic flapping-of-wings flight is unstable, a feedback control system is designed in section 6, and a stable flight is realized. Finally, concluding remarks are given in section 7. Fig. 1 schematically illustrates a flapping mechanism of insects that is powered by indirect muscles [9] . The wings are connected to the thorax by lever mechanisms, where the wings have been evolved from exoskeleton. The end of the wing link is connected by a hinge with the lateral suctum in the thorax. The wing link is also connected by another hinge near the previous hinge with the thoral wall in the thorax. When the suctum lifts up, the principle of leverage moves the wing down. The horizontal muscles known as dorsal longitudinal muscles tends to contract and increase the curvature of the suctum to which the muscles are connected to the rear and the front. There are vertical muscles known as the dorsoventral muscles running from the roof of the thorax to the floor. Contraction of the dorsoventral muscles pulls the suctum down. While relaxation of the dorsoventral muscles results in the dorsal longitudinal muscles' contraction and the suctum's lifting up. This flapping mechanism can be considered as almost one degree-of-freedom vibrating mechanism. A butterfly contracts the dorsoventral muscles periodically to vibrate the mechanism for flapping of the wings. According to experimental observation in latter section, each butterfly has an almost constant flapping eigenfrequency. It may be because to vibrate sympathetically at eigenfrequency of the mechanism realizes efficient flapping motion [10] . As suggested in the anatomical observation below, the other direct muscles may add slight motions, which are in the extent of modification to the basic vibration. This study has analyzed the mechanism to emerge the flapping flight of butterfly considering the generated free vortices in the environment. First, flapping mechanism of butterfly has been organized by using anatomical observation and knowledge of musculoskeltal system to know the available motion of living butterflies. The experimental system with a low-speed wind tunnel has been constructed, and the motion and aerodynamic forces of actual butterflies have been measured quantitatively. Then the 3D mathematical model has been constructed. Its validity and accuracy have been examined by comparing with the obtained experimental data. Moreover, a periodic flapping flight has been realized by using the obtained model. It has clarified that the free-vortices in the wakes induced by flapping and the wing torsion caused by structural flexibility effect on the stability of flapping flight. They have been considered as the implicit controls that have been the common principle of mobiligence. But the obtained trajectory has been still unstable. The feedback control as an explicit control has been designed and the stable flight has been realized. For more realistic control reflecting biological knowledge will be our future subject.

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


Modelling homeorhesis by ordinary differential equations Homeorhesis is a necessary feature of any living system. If a system does not perform homeorhesis, it is nonliving. The present work develops the sufficient conditions for the ODE model to describe homeorhesis and suggests the structure of the model. The proposed homeorhesis model is fairly general. It treats homeorhesis as piecewise homeostasis. The model can be specified in different ways depending on specific system and specific purposes of this analysis. An example of the specification is the PhasTraM model, the homeorhesis-aware nonlinear reaction-diffusion model for hyperplastic oncogeny in the previous works of the author. The qualitative agreement of the developed homeorhesis model with the living-system experimental results is noted. The work also shows that the basic mathematical models (such as the active-particle generalized kinetic theory) are substantially more important for the living-matter studies than in the case of nonliving matter. A few directions for future research are suggested as well. Advanced generalized-kinetic-theory (GKT) models for biological systems are developed for populations of active (or living) particles [1] - [5] . They are described with both the stochastic variables common in kinetic theory (such as the time, the particle random location and velocity) and the stochastic variables related to the internal state of an active particle. Evolution of this state represents biological, ecological, or social properties of the particle behavior. Paper [6] analyzes a number of the well-known statistical-mechanics approaches and shows that the active-particle GKT (APGKT) is the only treatment capable of modelling living systems. The significance of the notion of an active particle in kinetic models is given in work [2] . This notion draws attention to the features which distinguishes living matter from nonliving matter. They are discussed by many authors (e.g., [7] - [15] , [1] - [3] , [6] , [16] - [19] ). Note that book [11] considers many differences between living and nonliving matters, and the limitations of the modelling approaches developed for nonliving matter. A further insight in mathematics for living systems is presented in [20] . Work [6] mainly focuses on the comparison of a few theoretical mechanics treatments in terms of the key living-matter properties formulated in [15] .. One of the distinguishing features of living systems is homeorhesis. It is, loosely speaking, a peculiar qualitative and quantitative insensitivity of a living system to the exogenous signals acting on it. The notion of homeostasis was introduced by W. B. Cannon in 1926 who discussed the phenomenon in detail later [7] . Homeorhesis introduced by C. H. Waddington [8, p. 32 ] generalizes homeostasis and is well known in biology [8] , [9] , [12] . It is an inherent part of mathematical models for oncogeny (2.1) for which the following assumption holds. Vector is the internal state of the system, vector is the value of the -dependent exogenous signals acting on the system, and is the exogenous-signal -vector-function. The exogenous signals are characteristics of the surrounding of the system but are not its parts (cf., [6, Remark A.2] ). (The term 'exogenous' means 'coming from outside the system'.) As is mentioned in Section 1, the internal state represents biological, ecological, or social properties, depending on the system.. Function of is such that . The symbol ( ) denotes the set of the functions which have values in ( ) and are defined, uniformly bounded, and piecewise continuous (piecewise continuously differentiable) on .. For every fixed , every solution of ODE (2.1) is defined on . More specifically, for every and , this ODE with initial condition has the unique solution (obviously, piecewise continuously differentiable in ), and this solution is defined on . If ODE (2.1) has a solution which is determined solely by function , we denote it with .. A mode of the system under consideration is described with an appropriate individual solution of ODE (2.1). In order to be fully applicable, this description must be valid on any time interval in with no exception, including neighborhoods of points and . Since the state of the system is practically meaningful only if it is finite at any moment, no matter if the moment is within or beyond the mentioned neighborhoods, the system mode should be modelled with a solution which is uniformly bounded in on the entire time axis , i.e. with a solution in set (described in Assumption 2.1).. The previous treatment [6, Appendix] assumes that ODE (2.1) at any has the unique solution in . The present section formulates the corresponding sufficient conditions and does not involve the mentioned assumption. The formulation is based on a much weaker requirement, namely Assumption 2.3, preceded by Assumption 2.2, and is presented in Theorem 2.1. Note that solution takes a special part in the present work. This is indicated by the subsequent assumptions and theorems. For the sake of brevity, all of the expressions and statements below which include are assumed to hold for all with the exception of the cases when the other is explicitly noted. This is a linear matrix ODE for matrix . Assumption (2) allows to use solution in the limit case when . One can also make sure that matrix is applicable in this limit case. Indeed, assumption (1) indicates that the Cauchy matrix for ODE (2.11) is . The latter tends to zero when because of Remark 2.1. This proves assertion (1) .. Assertion (1) enables one to apply (2.4) in assumption (3) that, together with assumption (1) results in assertion (2) . Assertion (3) follows from notation (2.6) and the facts that:. • function is continuous in (see assumption (1)) • and all of the variables of function on the right-hand side of (2.6) are uniformly bounded in on that follows from relations and prescribed by assumption (1).. Let us prove assertion (4 Passing in (2.13) to the limit when , involving Remark 2.1 and assumption (4) in the resulting equality, and applying assertion (2), one obtains that the limit in assertion (4) is a solution of integral equation (2.5) . This, in view of assumption (5), implies both the uniqueness in assertion (4) and relation (2.7). This proves assertion (4) .. The inequality in assertion (5) follows from assumption (1) and assertion (3) . This inequality and the fact that (see assumption (1)) indicate that function is uniformly bounded on , i.e.. . This proves assertion (5). Assertion (5) implies that is a solution of ODE (2.1) in set . By virtue of Remark 2.1 (applicable because of assumption (1)), the mentioned solution is unique in and can be denoted with . The latter feature is expressed by means of (2.8). This proves assertion (6) and completes the proof of the theorem.. The analysis in [6, Appendix] and (2.1) as the unperturbed and perturbed equations, respectively. Theorem 2.1 assumes that (2.14) has the only solution which is uniformly bounded in time on the entire time axis and formulates the sufficient conditions for (2.1) to also have the unique uniformly bounded on solution. Allowing for the fact that both ODEs (2.14) and (2.1) are generally nonlinear, one can regard Theorem 2.1 as a result contributing to theory of globally bounded solutions of nonlinear dynamical systems. Theorem 2.1 is also the very one which assures the homeorhesis-enabling Theorem 3.1 (see below). Distinguishing features of these theorems are further discussed in Remark 3.3.. Also note that Theorem 2.1 does not require function in (2.1) to be differentiable in . This differentiability is not employed in the present work either. Homeorhesis is a necessary feature of any living system. This issues is still somewhat underestimated in modelling. For instance, the most common models in population dynamics, i.e. nonconstant timeperiodic solutions of autonomous ODEs, do not include homeorhesis and, thus, are inapplicable to living populations.. The analysis in Sections 2-4 results in a version of the sufficient conditions for homeorhesis and structure (4.1)-(4.7) for the corresponding ODE model. Since these conditions are sufficient rather than necessary, they present a hypothesis. It needs to be verified. As is shown below, certain qualitative aspects of the proposed model agree with experimentally obtained behaviors of living systems.. The proposed model (4.1)-(4.7) which includes homeorhesis can be reduced to an autonomous ODE in a very particular case. Firstly, one skips the model relations (4.2)-(4.7) and, secondly, replaces with an appropriate time-independent vector, for instance, (see (3.9)). As a result, ODE (4.1) is simplified to . This equation is autonomous if and only if is independent of . However, if it is autonomous, it, according to the present approach, can not have solutions which are nonconstant periodic in (see Remark 2.2). In other words, the time behavior of any system performing homeorhesis, including any living system, can not be nonconstant periodic in . This purely theoretical result is confirmed by numerous experimental data, for instance, the data of works in medical research on heart, one of the examples of an autonomous living subsystem. To mention a few, we note [29, the left column on p. 208], [23, the right column on p. 282], [30] . The experimental results in this area are not accounted in recent theoretical works which still attribute the time-periodicity to living populations (e.g., [31] ).. Moreover, it has been proven by experiments that, if the time-varying state of a living system, certainly nonperiodic, performs an evolution to the periodic shape, then this tendency is an important indicator of one or another dangerous disease (capable of transforming hosts from the living to nonliving state). For instance, paper [30] considers the heart-rate variability (HRV) which is a straightforward measure of the nonperiodicity, and shows that the risk of mortality after acute myocardial infarction is 5.3 times higher in the group of patients with less than 50 ms HRV compared to the patient group with more than 100 ms HRV.. There is no indication either that the state of a living system can be nonconstant time-periodic in the general, non-autonomous case. This is also indicated, for instance, by the non-autonomous-ODE analysis of population dynamics in [32] . We also stress that, no matter whether a system is autonomous or non-autonomous, the periodicity of its state means that the knowledge of the dynamics during any one period provides complete information on the system in the future, in particular, in the next period. To the best of our knowledge, a living system which allows the latter predictability has never been discovered yet.. The above well-established nonperiodicity is an inherent property of living matter. It is the second indicator of that the autonomous-ODE-based periodicity is inapplicable to living system, e.g., populati-ons (the first indicator is, as is noted before, the lack of homeorhesis in these models). The difficulties with application of the nonliving-system models to living systems are not over here. In particular, the nonperiodicity enables one to properly formulate applicability of the entire approaches to living-matter problems. An example is described below.. Some statistical institutions (e.g., selected higher-education units) encourage the purely statistical approach (PSA), i.e. a vision of statistics as the tool set capable of unquestionable solving any applied problem solely by means of measurement data, without application of continuous space-time dynamic, stochastic or kinetic models. The question is if PSA is relevant to living matter. One can investigate this question in the following way.. As is well known, statistical analysis of a stochastic process is based on an averaging of a large number of the process sample functions obtained on the same time interval. Since it is usually technologically difficult to measure different samples on the same interval simultaneously, the samples are measured on a series of the consecutive time intervals of the same length. The necessary conditions of applicability of this approach include the following requirements:. • for arbitrary fixed numbers and , , there exist sequence where , , such that the probability distributions of the stochastic process on all intervals are identical • and every of these intervals contains at least sample points where is the order of the process.. Regarding the second condition, we note that the literature does not include any technique able to determine the order of a stochastic process solely within the PSA frames. The problem of the order determination is also complicated by the fact that may be very high in the case of a living system. Indeed, even if the living system is described with such a simple model as a system of Itô's stochastic differential equations in Euclidean space, the order of every scalar entry of any of its solution is where, according to [15, p. C49 ] (see also [6, Section 1]), can be of a few thousands. The first condition can hold if the aforementioned probability distribution is periodic in time and the precise value of the period is known. In this case, it is sufficient to set all the parameters , , to be divisible by the period of the distribution. However, the problem is that, as is discussed above, determinate characteristics of the distribution (e.g., expectation) can not be nonconstant time-periodic in the case of a living system. Thus, the first condition can not be valid if the system is living.. Summing up the discussion, we note that the properties of living matter do not allow to meet the above two requirements. Therefore, statistically meaningful sets of the sample functions for the stochastic process representing the state of a living system can not be obtained experimentally. This means that the input data for PSA are unavailable. For this very reason, PSA is inapplicable to living matter.. Remark 5.1. In the living-system studies, the only way to obtain statistically meaningful sets of the stochastic-process sample functions for the system state is numerical simulation of the corresponding stochastic time-continuous dynamical models. This emphasizes the paramount importance of the mathematical modelling for research in living matter, first of all, the basic models such the generalized kinetics for active particles, or APGKT (see Section 1) into which model (4.1)-(4.7) can be incorporated.. For the reason of the above impossibility to provide PSA with the input data, PSA may suggest to use Bayesian paradigm or its empirical version (a concise and highly focused review of A.N. Shiryaev on both can be found in [33, pp. 350-352] ). Bayesian approach to statistical problems is based on the assumption that one can assign a definite probability distribution to any parameter in the problem. This alternative, however, has its own disadvantages: the necessity of postulating both the existence of an a priori distribution of the unknown parameter and the precise form of this distribution. To what extent these difficulties facilitate PSA to solve problems in living systems is not formulated in PSA.. The above discussion indicates the following.. Remark 5.2. Validation and calibration of mathematical models for living systems (both comprehensive descriptions such as the active-particle generalized kinetics (see Section 1) or particular models such as the proposed homeorhesis model (4.1)-(4.7)) are substantially different from the analogous activities for nonliving systems. It may be helpful to subdivide the validation into the qualitative and quantitative stages, considering the latter in conjunction with the calibration. The qualitative validation would provide a qualitative compliance of the models with the described living-matter phenomena on the basis of the directly available, unprocessed measurement results.. The personnel processing the measured data for the subsequent quantitative validation and calibration may not be aware of the distinguishing properties of living matter or may not have the techniques other than those used in the case of nonliving matter. Automatic acceptance of the outcomes of such processing may lead to misleading, irrelevant conclusions on the model. In fact, the model developers should always make sure that the conditions of the experiments and the assumptions of the experimental-data processing are explicitly formulated and correspond to the system which the model is developed for. The greater responsibility of the developers for the selection of the measurements and data indicates an entirely new role of mathematical model-ling, the role which is not an issue if the studied systems are nonliving.. Some abnormalities in living systems (e.g., diseases) present homeorhetic dysfunctions (e.g., cancer). These dysfunctions may be caused by various reasons, for instance, systemic stressors. In terms of the developed model, homeorhetic dysfunctions can be taken into account by means of the system states which are similar to the creode but different from it, thereby presenting alternatives to it, say, the counter-creodes. The picture may be the following.. The creode and each of the counter-creodes has respective attraction domain. These attraction domains are separated from each other by unstable manifolds. When the actual-mode trajectory is in one of these domains, the unstable manifolds serving as the boundary of this domain, can vary much faster than the trajectory, and can even intersect it, thereby placing it in a neighboring attraction domain and forcing it to converge to the creode-type trajectory for which the latter domain is the attraction one. This convergence holds until the related unstable manifolds, in the way similar to the above, places the actual-mode trajectory in the attraction domain of another creode-type trajectory. Then the actual mode converges to the latter. And so forth. Note that the acts of the aforementioned intersections corresponds to what is in biology termed thresholds. Also note that instabilities (or positive feedbacks) are well known not only in biological systems but also in ecosystems (e.g., [11, p. 174

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


Typing linear algebra: A biproduct-oriented approach Interested in formalizing the generation of fast running code for linear algebra applications, the authors show how an index-free, calculational approach to matrix algebra can be developed by regarding matrices as morphisms of a category with biproducts. This shifts the traditional view of matrices as indexed structures to a type-level perspective analogous to that of the pointfree algebra of programming. The derivation of fusion, cancellation and abide laws from the biproduct equations makes it easy to calculate algorithms implementing matrix multiplication, the central operation of matrix algebra, ranging from its divide-and-conquer version to its vectorization implementation.From errant attempts to learn how particular products and coproducts emerge from biproducts, not only blocked matrix algebra is rediscovered but also a way of extending other operations (e.g. Gaussian elimination) blockwise, in a calculational style, is found.The prospect of building biproduct-based type checkers for computer algebra systems such as MATLAB™ is also considered.Keywords: Linear algebra, categories of matrices, algebra of programming In a recent article [2] , David Parnas questions the traditional use of formal methods in software development, which he regards unfit for the software industry. At the core of Parnas objections lies the contrast between the current ad-hoc (re)invention of cumbersome mathematical notation, often a burden to use, and elegant (thus useful) concepts which are neglected, often for cultural or (lack of) background reasons.. The question is: what is it that tells "good" and "bad" methods apart? As Parnas writes, there is a disturbing gap between software development and traditional engineering disciplines. In such disciplines one finds a successful, well-established mathematical background essentially made of calculus, vector spaces, linear algebra and probability theory. This raises another question: can one hope to share such a successful tradition in the computing field, or is this definitely a different kind of science, hostage of formal logics and set theory?. There are signs of change in such direction already, as interest in the application of linear algebra techniques to computing seems to be growing, driven by disparate research interests briefly reviewed below.. Gunther Schmidt, for instance, makes extensive use of matrix notation, concepts and operations in his recent book on relational mathematics [3] . This pays tribute to binary relations being just Boolean matrices. Of historical relevance, explained in [4] , is the fact of one of the first known definitions of relational composition, due to Charles Peirce , being essentially what we understand today as matrix multiplication.. In the area of process semantics, Bloom et al [5] have developed a categorical, machines as matrices approach to concurrency 2 ; Trčka [7] presents a unifying matrix approach to the notions of strong, weak and branching bisimulation ranging from labeled transition systems to Markov reward chains; and Kleene coalgebra is going quantitative [8] .. The "quantum inspiration" is also pushing computing towards linear algebra foundations. Focussing on quantum programming and semantics of probabilistic programs, Sernadas et al [9] adopt linear algebra techniques by regarding probabilistic programs as linear transformations over suitable vector spaces. Natural language semantics, too, is going vectorial, as nicely captured by the aphorism nouns are vectors, adjectives are matrices [10] . In this field of "quantum linguistics", Coecke et al [11] have developed a compositional model of meaning in which the grammatical structure of sentences is expressed in the category of finite dimensional vector spaces. Unrelated to quantum linguistics but related to knowledge discovery, the authors of the current paper show in [12] how to implement data mining operations solely based on linear algebra operations. And more examples of the adoption of linear algebra background in computing could be mentioned. In this paper we have exploited the formalization of matrices as categorial morphisms (arrows) in a way which relates categories of matrices to relation algebra and program calculation. Matrix multiplication is dealt with in detail, in an elegant, calculational style whereby its divide-and-conquer, triple-nested-loop and vectorized implementations are derived.. The notion of a categorial biproduct is at the heart of the whole approach. Using categories of matrices and their biproducts we have developed the algebra of matrixblock operations and shown how biproducts scale up so as to be fit for particular applications of linear algebra such as Gaussian elimination, for instance.. We have also shown how matrix-categorial biproducts shed light into the essence of an important data transformation -vectorization -indispensable to the efficient implementation of linear algebra packages in parallel machines. Our calculations in this respect have shown how polymorphic standard matrices such as eg. the commutation matrix are, making dimension polymorphism an essential part of the game, far beyond the loose "valid only for matrices of the same order" [33] attitude found in the literature. We have prototyped our constructs and diagrams in MATLAB™ all the way through, and this indeed showed how tedious and error-prone it is to keep track of matrix dimensions in complex expressions. It would be much nicer to write eg. eye instead of eye(n), for some hand-computed n and let MATLAB infer which n accommodate the formula we are writing.. The prospect of building biproduct-based type checkers for computer algebra systems such as MATLAB is therefore within reach. This seems to be already the approach in Cryptol [46] , a Haskell based DSL for cryptography, where array dimensions are inferred using a strong type-system based on Hindley-Milner style polymorphism extended with arithmetic size constraints.. In retrospect, we believe to have contributed to a better understanding of the blocked nature of linear algebra notation, which is perhaps its main advantage -the tremendous improvement in concision which Backhouse stresses in the quotation which opens the paper -and which can be further extended thanks to the (still to be exploited) algebra of biproducts. This raises the issue of matrix polymorphism and enriches our understanding that matrix dimensions are more than just numbers: they are types in the whole sense of the word. Thus the matrix concept spruces up, raising from the untyped number-container view ("rectangles of numbers") to the typed hom-set view in a category. Perhaps Sir Arthur Eddington (1882 Eddington ( -1944 A comprehensive calculational approach to linear algebra algorithm specification, transformation and generation is still missing. However, the successes reported by the engineering field in automatic library generation are a good cue to the feasibility of such a research plan. We intend to contribute to this field of research in several directions.. SPIRAL. The background of our project is the formalization of OL, the Operator Language of [14, 16] , in matrix-categorial biproduct terms. In the current paper we have stepped forward in this direction (as compared to [21] , for instance) in developing a categorial approach to vectorization, but much more work is still needed to achieve a complete account of the refinement steps implicit in all OL-operator breakdown rules. SPIRAL's row-major vectorized representation calls for further work in adapting our results to such a variant of vectorization.. Kleene algebras of matrices. Thus far we have assumed matrices to take their elements from an algebraic field K. The matrix concept, however, extends to other, less rich algebraic structures, typically involving semirings instead of rings, for instance. Fascinating work in this wider setting shows how, by Kleene algebra, some graph algorithms are unified into Gaussian elimination, for instance [1] . We would thus like to study the impact of such a relaxation on our biproduct approach to the same algorithm.. Khatri-Rao product generalization of relational forks. The monoidal structure provided by the tensor product defined in Section 7 is the key concept to generalize, to arbitrary matrices, the relational (direct) product presented in [3, 26] .. It turns out that the fork operation of relation algebras [26] is nothing but the operator known in the linear algebra community as the Khatri-Rao product [48] . The standard definition offers this product as a (column-wise) variant of Kronecker product. To emphasise the connection to relation algebra, our definition is closer to that of a fork [26] : given matrices m n . where A * B is the Hadamard (element-wise) product and matrices m m × k. o o are known as projections. To define these we rely on row vectors wholly filled up with 1s, denoted by symbol "!" 14 :. Khatri-Rao product is associative and its unit is !, that is, ! ▽ A = A = A ▽ ! hold. The close link between the Khatri-Rao and Kronecker products can be appreciated by expressing the latter in terms of the former,. meaning that Khatri-Rao can be used as alternative to Kronecker in formulating concepts such as, for instance, vectorization [3] . A thorough comparison of both approaches in the setting of arbitrary matrices is a topic for future work [34] . Curiously enough, the monadic flavour of vectorization can already be savored in version (96) of MMM, suggesting such an implementation as analogue to composition in the "brother" Kleisli category:. F B Categories of matrices can be traced back to the works of MacLane and Birkhoff [20, 24] , with focus on either illustrating additive categories or establishing a relationship between linear transformations and matrices. Biproducts have been extensively studied in algebra and category theory. In [24] , the same authors find applications of biproducts to the study of additive Abelian groups and modules. A relationship between biproducts and matrices can also be found in [24] , but it is nevertheless in [20] that the hint which triggered the current paper can be found explicit (recall Section 4). However, no effort on exploiting biproducts calculationally is present, let alone algorithm derivation. To the best of the authors' knowledge, the current paper presents the first effort to put biproducts in the place they deserve in matrix algebra.. Bloom et al [5] define a generic notion of machine and give their semantics in terms of categories of matrices, under special (blocked) composition schemes. They make implicit use of what we have identified as the standard biproduct (enabling blocked matrix algebra) to formalize column and row-wise matrix join and fusion, but the emphasis is on iteration theories which matricial theories are a particular case of.. Other categorial approaches to linear algebra include relative monads [43] , whereby the category of finite-dimensional vector spaces arises as a kind of Kleisli category. Efforts by the mathematics of program construction community in the derivation of matrix algorithms include the study of two-dimensional pattern matching [44] .. Reference [5] is related to Kleene algebras of matrices [45] . An account of the work on calculational, index-free reasoning about regular and Kleene algebras of matrices can be found in [1] . The close relationship between categories of matrices and relations is implicit in the allegorial setting of Freyd andŠčedrov [19] : essentially, matrices whose data values are taken from locales (eg. the Boolean algebra of truth values) are the morphisms of the corresponding allegory (eg. that of binary relations). Bird and de Moor [18] follow [19] . Schmidt [3] dwells on the same relation-matrix binomial relationship too, but from a different, set-theoretical angle. He nevertheless pushes it quite far, eg. by developing a theory of vectorization in relation algebra. Relational biproducts play no explicit role in either [3] , [19] or [18] .

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 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 B I B I I 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 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 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 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 B I 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 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 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 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 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 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 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 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 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 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 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 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


Joint latent topic models for text and citations In this work, we address the problem of joint modeling of text and citations in the topic modeling framework. We present two different models called the Pairwise-Link-LDA and the Link-PLSA-LDA models.The Pairwise-Link-LDA model combines the ideas of LDA [4] and Mixed Membership Block Stochastic Models [1] and allows modeling arbitrary link structure. However, the model is computationally expensive, since it involves modeling the presence or absence of a citation (link) between every pair of documents. The second model solves this problem by assuming that the link structure is a bipartite graph. As the name indicates, Link-PLSA-LDA model combines the LDA and PLSA models into a single graphical model.Our experiments on a subset of Citeseer data show that both these models are able to predict unseen data better than the baseline model of Erosheva and Lafferty [8] , by capturing the notion of topical similarity between the contents of the cited and citing documents. Our experiments on two different data sets on the link prediction task show that the Link-PLSA-LDA model performs the best on the citation prediction task, while also remaining highly scalable. In addition, we also present some interesting visualizations generated by each of the models. Proliferation of large electronic document collections such as the web, news articles, blogs and scientific literature in the recent past has posed several new, interesting challenges to researchers in the data mining community. In particular, there is an increasing need for automatic techniques to visualize, analyze and mine these document collections. In the recent past, latent topic modeling has become very popular as a completely unsupervised technique for topic discovery in large document collections. These models, such as PLSA [9] and LDA [4] , exploit co-occurrence patterns of words in documents to unearth semantically meaningful probabilistic clusters of words called topics. These models also assign a probabilistic membership to documents in the latent topicspace, allowing us to view and process the documents in this lower-dimensional space.. Most of the models in this framework such as Dynamic topic models [5, 15] , Pachinko Allocation [11] , Correlated Topic Model [3] , etc., model various aspects of document collections such as time, hierarchy of topics, correlations between topics respectively. However, all the above mentioned models ignore a rich feature that contains valuable information, namely, the citation or hyperlink structure. It is a known fact in information retrieval that a citation between two documents not only indicates topical similarity of the two documents but also authoritativeness of the cited document [10] . This idea has been exploited by algorithms such as PageRank [16] which are now de facto techniques in search engine technology.. In our work, we aim at addressing the problem of jointly modeling text and citations in the topic modeling framework. Our hope is that explicit modeling of citations captures the topicality of documents in the collection better, and thereby improves the predictive power of these models.. The rest of the paper is organized as follows. In section 2, we discuss some of the past work done on joint models of topics and citations in the framework of latent topic models. We introduce two new models in section 3 and their corresponding learning and inference techniques using variational approximations. In section 4, we describe the data sets, the tasks and evaluation we used for our experiments. Section 5 reports and analyzes the results of our experiments. We conclude the discussion in section 6 with a few remarks on directions for future work.. Note that in the rest of the paper, we use the terms 'citation', 'hyperlink' and 'link' interchangeably. Likewise, note that the term 'citing' is synonymous to 'linking' and so is In this paper, we presented two novel topic models for joint modeling of links and text. We introduce the Pairwise Link-LDA for the first time, but limited preliminary results for Link-PLSA-LDA were presented recently in [14] . This work focused only on the single domain of blog data, and compared the Link-PLSA-LDA model to only the Link-LDA baseline. In this paper, we extend this work by performing more rigorous experiments on an additional data set and also by comparing the model to Pairwise Link-LDA , a new truly generative model for text citations.. Although the Pairwise Link-LDA is more expressive than Link-PLSA-LDA in terms of modeling arbitrary link structure, our experiments on Citeseer data and blog data show that the Link-PLSA-LDA model outperforms the former on both log-likelihood and link prediction. We believe the superior performance of the multinomial based Link-PLSA-LDA model compared to the multiple Bernoulli based Pairwise Link-LDA model has interesting parallels with the experience of Multinomial vs. Bernoulli distributions for text classification. It has been observed by McCallum et al [13] that modeling a document in terms of words that occur in the document using a multinomial distribution rather than in terms of presence and absence of all the words in the vocabulary using a multiple Bernoullis yields superior performance. One of the reasons for this behavior could be because features that are present are much more important than features that are absent. The same reasoning could be extended to the behavior of the two models in the present context. Our hypothesis is that the Pairwise Link-LDA model suffers to due to significant expenditure of modeling effort on citations that are absent.. Apart from its superior performance, another attractive feature of the Link-PLSA-LDA model is its relative scalability to large document collections in comparison to the Pairwise Link-LDA model. To demonstrate its scalability, in figure 9 , we plotted the average variational EM iteration (outer loop) run time for each model, as a function of number of topics. The measurements were made on a standard Linux machine with Intel Pentium III 0.7 GHz processor and 4GB memory. Clearly, there is a huge gap in computational time between Pairwise Link-LDA and the other two models. The run times of Link-PLSA-LDA and Link-LDA are comparable, but the former is the faster. The main reason for the prohibitive costs of the Pairwise Link-LDA model is that its computational complexity is quadratic in both the number of documents as well as number of topics. On the other hand, Link-PLSA-LDA and Link-LDA models are both linear in the number of documents and number of topics, making them more scalable. Despite the superior performance and scalability of the Link-PLSA-LDA model, we believe the Pairwise Link-LDA model is still very desirable owing to its superior semantics. Its generative process not only captures arbitrary link structure, but allows us to generate new cited as well as citing documents. Hence it may be more attractive in situations where capturing the true link structure is more important.. As part of our future work, we will try to build more tractable approximations to the Pairwise Link-LDA model. non-scalability and restrictive assumptions respectively.

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


Mining specifications of malicious behavior Malware detectors require a specification of malicious behavior. Typically, these specifications are manually constructed by investigating known malware. We present an automatic technique to overcome this laborious manual process. Our technique derives such a specification by comparing the execution behavior of a known malware against the execution behaviors of a set of benign programs. In other words, we mine the malicious behavior present in a known malware that is not present in a set of benign programs. The output of our algorithm can be used by malware detectors to detect malware variants. Since our algorithm provides a succinct description of malicious behavior present in a malware, it can also be used by security analysts for understanding the malware. We have implemented a prototype based on our algorithm and tested it on several malware programs. Experimental results obtained from our prototype indicate that our algorithm is effective in extracting malicious behaviors that can be used to detect malware variants. Malicious software (malware) is code that achieves the harmful intent of an attacker. Typical examples include viruses, worms, trojans, and spyware. Although the history of malware reaches back more than two decades, the advent of large-scale computer worm epidemics and waves of email viruses have elevated the problem to a major security threat. Recently, this threat has also acquired an economic dimension as attackers benefit financially from compromised machines (e.g., by selling hosts as email relays to spammers).. Historically, detection tools such as virus scanners have performed poorly, particularly when facing previously unknown malware programs or novel variants of existing ones. The fundamental cause is the disconnect between the malware specification used for detection and the actual malware behavior (which is the attacker's goal). Certain malicious behavior desired by an attacker (e.g., virus self replication through mass-mailing) can be realized in many different ways. However, current detectors focus only on the specific characteristics of individual malware instances, e.g., on the presence of particular instruction sequences. Therefore, they fail to detect different manifestations of the same malicious behavior. Attackers are quick to exploit this weakness by using program obfuscation techniques such as polymorphism and metamorphism [19, 22, 25, 29] . Recent research results have highlighted how shortcomings in both network-based and host-based detection techniques can be effectively exploited by attackers to evade detection [6, 14] .. Advanced detection techniques such as semantics-aware malware detection [7, 16] and malicious-code model checking [12] counter the obfuscation techniques of attackers by using higher-level specifications of malicious behavior. Instead of focusing on individual characteristics of particular malware instances, these detectors specify general behavior exhibited by an entire family of malicious code. Examples of such specifications include self-unpacking and selfpropagation via email. The power of these approaches resides in the use of high-level specifications that abstract details specific to a malware instance. Thus, obfuscation transformations, which preserve the behavior of the malware but may change its form, are no longer effective techniques for evading detection. Unfortunately, the high-level specifications of malicious behavior used by these advanced malware detectors are currently manually developed. Creating specifications manually is a time-consuming task that requires expert knowledge, which reduces the appeal and deployment of these new detection techniques. To address this limitation, this paper introduces a technique to automatically derive specifications of malicious behavior from a given malware sample. Such a specification can then be used by a malware detector, allowing for the creation of an end-to-end tool-chain to update malware detectors when a new malware appears. Since our technique provides a succinct description of the malicious intent of a malware, it can also be used by security analysts for malware understanding.. We cast malicious-specification mining as the problem of finding differences between a malware sample and a set of benign programs. This approach supports the requirement that the specification of malicious behavior must capture aspects that are specific to the malware and absent from any benign programs. The software-engineering research community has put a lot of effort in analyzing commonalities and differences between programs and many techniques for clone detection [3, 11, 13, 30] and program differencing [2, 9, 10, 17] have been proposed. The differencing techniques are closest to our goal of mining specifications of malicious behavior, but they fall short because they generally require access to source code and because they produce differences between low-level elements of the program (e.g., individual statements) or between structural elements (e.g., type hierarchy, procedures). Since we do not have the malware source code and since the malware writer controls the structure of the program, mining malicious specifications requires a new approach.. Our mining technique takes into account an adversarial setting in which the malware writer tries to make his software hard to analyze and detect. We define a new graph representation of program behavior and a mining algorithm that constructs a malicious specification. The representation explicitly captures the system calls made by the program and summarizes all other program code, because system calls are the primary interaction with the operating system. Our algorithm infers the system-call graphs from execution traces, then derives a specification by computing the minimal differences between the system-call graphs of malicious and benign programs. This paper makes the following contributions:. • A language for specifying malicious behavior in terms of dependences between system calls (Section 3).. • An algorithm, called MiniMal 1 that mines specifications of malicious behavior from dependence graphs (Section 4).. • An experimental evaluation that shows that specifications extracted MiniMal are qualitatively equivalent to those manually developed by Symantec's expert virus analysts and can be used with a malware detector to identify subsequent malware variants (Section 5). The goal of our specification language is to describe malicious behavior. In general, the behavior of a program can be described as its observable effect on the execution environment. Depending on what is considered the program's environment, behavior can be specified at different levels of granularity.. One approach is to define behavior as the effect of a sequence of instructions on the state of a process. For this 1 MiniMal is a technique for mining minimally mal icious behavior. call R e g C l o s e K e y Figure 1 : Bagle.J code fragment performing registry cleanup, one of its "administrative" tasks.. purpose, the state of a process is defined as the content of the memory address space. The effect on this state are modifications to the contents of the address space. Another approach to specify program behavior is to view the running program as a black-box and only focus on its interaction with the operating system. In this case, a particularly convenient interface to monitor is the set of operating system calls that this process invokes. Every action that involves communication with the process' environment (e.g., accessing the file system, sending a packet over the network, or launching another program) requires the process to make use of an appropriate operating system service. For this work, we choose the second approach and use system calls as the basic building blocks of our specification language. We only consider the actions of the program at the operating system interface, thus making our technique robust to any code-obfuscation techniques employed by malware authors. The end result is a specification of malicious behavior that captures the intent of the malware writer in terms of its effect on the host operating system. Such a specification can then be used to detect the original malware as well as obfuscated variants that exhibit the same system-call footprint.. At a high level, the mining algorithm works in three steps: Algorithm MiniMal We will walk through the application of the mining algorithm on the email worm Bagle.J, the tenth variant in a long line of malware known as the Bagle malware family. According to the Symantec Security Response [24] , Bagle.J exhibits the following high-level functionality:. • It spreads through email, sending copies of itself using a built-in SMTP engine.. • It opens a backdoor on the infected system, allowing the attacker to access and control the victim system remotely.. • It self-propagates through several file-sharing networks (Kazaa and iMesh).. • It performs multiple "administrative" tasks that include. R e g D e l e t e V a l u e A ( 0 x0007FFC4 , " ssate.exe " ) == 0 We introduced a language for specifying malicious behavior and an algorithm for mining such specifications (mal-specs) from dynamic traces of malware samples and benign programs. Our prototype, MiniMal, infers malspecs by differencing the dependence graphs of a malware sample and of multiple benign programs. Experimental results showed that the malspecs mined by our algorithm compare favorably with behavioral specifications manually constructed by human experts. Malspecs can also be used to detect multiple malware variants.. The current work computed the behavioral difference as a subgraph of the malicious dependence graph, without taking into account the constraints of any similar benign subgraph. One possibility is to define the difference to consider both the malicious constraints and the (negation of) benign constraints -we plan to explore this in future research.. The choice of test programs is an important element of our mining approach. For malicious program we would like to know whether certain classes of malware are more amenable to mining. For benign programs we want to ensure that a broad selection of behaviors are represented in the test set. Thus a goal for future work is to determine the impact the choice of test programs has on the quality of the mined malspecs. A related problem is the incompleteness of the dependence graph built from a finite set of execution traces. Combining dynamic and static analysis could provide techniques to derive a better dependence graph. The evaluation showed that our malspec-mining algorithm was successful in identifying behaviors unique to malware samples. It did so without any a priori security policy that defined malicious or benign behaviors. Furthermore, these malspecs could then be used to provide forward detection of later malware variants.. There were several aspects to address when considering the validity of our experiments. The most important one was the internal validity, i.e., the factors that could influence the observed behavior of the test programs (both benign and malicious). We considered two sources of threats to internal validity: (1) impact of execution monitoring, and (2) relevance of execution traces. The execution monitor simply collected system-call traces for a fixed time period. Since the monitored program could not observe the execution monitor, which was present only in protected kernel space, we expected the monitored program to execute normally, without biasing our results.. The threat of execution relevance arose from differences between our "emulated Internet" environment and the real Internet. If the malware attempted, for example, to download additional components or commands from a remote server, it would fail without executing any malicious behaviors. Similarly, the malware might not execute any malicious behaviors during the monitoring period if it was timedependent. In such cases, MiniMal would not discover any differences between malicious and benign programs. We operated under the assumption that most malware tries to execute in as many environments as possible. In future, we will explore ways to eliminate this assumption, for example by allowing limited interaction with the Internet and by analyzing multiple execution paths [20] .. A second aspect was that of external validity, the lack of which could limit our ability to generalize our malspecmining technique to other classes of malicious programs. While our experiments focused on mass-mailing worms, the technique was general enough to apply to any class of malware behaviors. In particular, we note that the variants in our test set exhibited behaviors above and beyond those traditionally characteristic of a mass-mailing worm.. Finally, the third aspect of concern was that of construct validity. This relates to how expressive the malspec language is and how powerful the dependence graph construction is. We discussed the malspec language in Section 3. As noted in the results above, the dependence inference failed when the information flow between system-call arguments was complex. We plan to address this limitation in future work, possibly using dynamic information-flow tracing. There is a large body of work in the area of learning program features and program understanding using dynamic traces. We focus on two areas most related to our work, specification mining for software engineering and specification mining for software security.. Mining of specifications has received considerable attention for a variety of program-related aspects, including APIusage and general programming rules [1, 18, 27] . In contrast, we mine specifications of malicious behavior, with no a priori definition of "malicious," by comparing malicious and benign programs. Clone-detection techniques compare programs [3, 11, 13, 30] , but they target similarities, not distinctions, between and within programs. Programdifferencing techniques have goals similar to ours, but are limited to distinctions at the statement level or at the structural level [2, 9, 10, 17] . The execution-history matching introduced by Zhang and Gupta [30] is closest to our technique in that it analyzes dynamic data-dependence graphs, albeit with the goal of finding similar programs. Executionhistory matching also operates at the instruction level and requires precise information about data and control dependences, and thus it is not directly applicable to our problem.. In computer security, the area of host-based intrusion detection has applied specification mining techniques to derive models of program behavior, which can be used to contain execution. These program models of "good" behavior can be derived through static analysis [8] or learned from dynamic traces [23] . Recent work has looked at the use of constraints over system-call arguments for host-based intrusion detection. Kruegel et al. proposed a system for learning models for the string values of individual system-call arguments without taking into account dependences between system calls [15] . Their models could be used as local constraints in the malspecs we extract. Bhatkar et al. introduced a technique for deriving a dataflow model to be used for intrusion detection [4] . They derived both local constraints and dependences for system-call arguments, using a fine-grained set of relations over strings (e.g., isWithinDir, hasExtension, hasSameDirAs). These types of constraints fit into our malspec language and we will research extending our dependence-graph construction to discover such string constraints.

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


Efficient parallel resolution of the simplified transport equations in mixed-dual formulation A reactivity computation consists of computing the highest eigenvalue of a generalized eigenvalue problem, for which an inverse power algorithm is commonly used. Very fine modelizations are difficult to treat for our sequential solver, based on the simplified transport equations, in terms of memory consumption and computational time.A first implementation of a Lagrangian based domain decomposition method brings to a poor parallel efficiency because of an increase in the power iterations [1] . In order to obtain a high parallel efficiency, we improve the parallelization scheme by changing the location of the loop over the subdomains in the overall algorithm and by benefiting from the characteristics of the RaviartThomas finite element. The new parallel algorithm still allows us to locally adapt the numerical scheme (mesh, finite element order). However, it can be significantly optimized for the matching grid case. The good behavior of the new parallelization scheme is demonstrated for the matching grid case on several hundreds of nodes for computations based on a pin-by-pin discretization. The operation of a PWR-based 1 nuclear plant requires its fuel to be changed every 18 months. This must be done while ensuring the safety and the productivity of the plant in service. More precisely, in our context, EDF uses the numerical simulation of the neutron transport inside a nuclear reactor. Hence, EDF has developed a fast sequential solver [2] based on the simplified transport equations [3, 4] 2 . The mid-term goal is to run efficiently large scale simulations 3 based on the simplified transport equations. In this context, the sequential algorithm suffers of two limitations. On the one hand, we are not able to run efficiently large scale computations due to memory consumption and/or computational time. On the other hand, it is necessary to refine a large part of the mesh when a better numerical approximation is needed in a local part of the reactor core. So, to tackle these problems, in [5, 1] we adapted a non overlapping domain decomposition method based on Lagrange multipliers to the simplified transport equations. In order to get the most generic algorithm, an approach with multigroup solver was chosen. As this approach leads to a significant increase in the number of power iterations, a good scalability could not be obtained. In the present article, we obtain a very good parallel efficiency while improving the parallelization scheme of Lagrangian domain decomposition method applied to the sequential power algorithm made of four nested loops. First, we change the location of the loop over the subdomains to obtain the same number 1 Pressurized Water Reactor. 2 These equations are called SPn. 3 Like pin-by-pin discretization of SP3/SP5 equations with 26 energy groups.. of power iterations as the sequential algorithm. Secondly, we benefit from the characteristics of the Raviart-Thomas finite element to optimize the implementation of the new parallel algorithm.. In section 2, the diffusion equation and the sequential algorithm based on the same algorithm as used by the Minos solver [6, 7] , are presented. As the domain decomposition strategy proposed in this paper is performed at the level of one diffusion system, the presentation is performed on the diffusion equation instead of SPn equations. Then in section 3, after an overview of previous works on the parallelization of the sequential algorithm, the Lagrange multipliers domain decomposition method and our new parallel algorithm are introduced. In section 4, the characteristics of Raviart-Thomas finite elements are used in the case of matching grids to get an efficient parallel implementation. Finally, in section 5, numerical results on the IAEA-3D benchmark and on data from real core computations are provided and analyzed; compared to the previous approach described in [1] , the performance improvement factor is between 5 and 20, depending on the test case. Let us reconsider the algorithm of the previous approach [5, 1] . Compared to the sequential monodomain algorithm, a new loop is added to solve the saddle point system induced by domain decomposition (see Algorithm 3). This loop was put between the power algorithm and the loop over the energy groups. As the inner loops (iterative algorithms in each subdomains) are fixed point algorithms with only one iteration, we also used a fixed point method to solve the saddle point system (Uzawa-MR algorithm was chosen). The previous approach was more generic than the new one, but the increase in the number of outer iterations for real industrial cases was not satisfying.. In the new approach, as in the previous one, one loop is added to Algorithm 4 to get convergence of the iterative algorithm used to solve the interface systems. In our new approach the domain decomposition loop is under the alternate direction computations and use the solver in each spatial direction. Hence we can benefit from a direct solver in each subdomain. In the following, we consider a fixed number i of iterations: the algorithm is called PCGi. In the same way as the sequential monodomain solver, the iteration loop of the outer algorithm is used to get convergence. The new approach enables some new implementation optimizations which are described in the following section.. The both approachs are compared in the manuscrit [? ] of the PhD which is at the origin of this article. The proposed domain decomposition method in the difficult context of an approximate resolution of the linear system at each inverse power iteration reveals very reliable and efficient on SP1/SP3 pin-by-pin computation coming from the IAEA benchmark and from industrial cases. The method satisfies two criteria: memory requirement and parallel efficiency. Compared to [1] , the parallel efficiency is improved by a factor 20. The method is as least as efficient as the result obtained in [14] and avoids the difficulties resulting from:. • the choice of the Robin transfer coefficient;. • the introduction of an additional approximation and a small overlap due to the Robin transfer conditions with a mixed dual formulation.. As the numerical behavior of the method is very satisfactory with a large number of subdomains, a next step will be a hybrid implementation (shared and distributed memory). Such an implementation will enable us to use more efficiently a multi-core architecture. This step is needed to get an efficient non-matching grid implementation, since for non-matching grids more flexibility is required to balance the load between the nodes.. Hardware accelerators such as Graphic Processor Units suffer from insufficient memory size but can be very relevant in terms of computational time. In [22] , the authors obtained a speed-up of 30 for the monodomain solver. So, it seems natural to use the domain decomposition algorithm on a GPU cluster in order to take advantage of GPU acceleration without memory limitation. The next step is the integration of this parallel algorithm in the industrial platform. Hence it will be possible to perform studies with a large number of groups and with pin-by-pin discretizations.

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


Efficient Exact Evaluation of Signs of Determinants This paper presents a theoretical and experimental study on two different methods to evaluate the sign of a determinant with integer entries. The first one is a method based on the Gram-Schmidt orthogonalization process which has been proposed by Clarkson [Cl]. We review his algorithm and propose a variant of his method, for which we give a complete analysis. The second method is an extension to n × n determinants of the ABDPY method [ABD + 2] which works only for 2 × 2 and 3 × 3 determinants. Both methods compute the sign of an n × n determinant whose entries are integers on b bits, by using exact arithmetic on only b + O(n) bits. Furthermore, both methods are adaptive, dealing quickly with easy cases and resorting to full-length computation only for null determinants.

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