Academic literature on the topic 'Irreducible pattern'

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Journal articles on the topic "Irreducible pattern"

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Stuart, Jeffrey L., LeRoy Beasley, and Bryan Shader. "Irreducible, pattern k-potent ray pattern matrices." Linear Algebra and its Applications 346, no. 1-3 (2002): 261–71. http://dx.doi.org/10.1016/s0024-3795(01)00541-9.

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Li, Zhongshan, Frank J. Hall, and Jeffrey L. Stuart. "Irreducible powerful ray pattern matrices." Linear Algebra and its Applications 342, no. 1-3 (2002): 47–58. http://dx.doi.org/10.1016/s0024-3795(01)00436-0.

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Cavers, Michael, Jonathan Fischer, and Kevin N. Vander Meulen. "Spectral Properties of Sign Patterns." Electronic Journal of Linear Algebra 36, no. 36 (2020): 183–97. http://dx.doi.org/10.13001/ela.2020.5057.

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In this paper, an infinite family of irreducible sign patterns that are spectrally arbitrary, for which the nilpotent-Jacobian method does not apply, is given. It is demonstrated that it is possible for an irreducible sign pattern to be refined inertially arbitrary and not spectrally arbitrary. It is observed that not every nonzero spectrally arbitrary pattern has a signing which is spectrally arbitrary. It is also shown that every superpattern of the reducible pattern $\T_2 \oplus \T_2$ is spectrally arbitrary.
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Cho, Han Hyuk, Jong Sam Jeon, and Hwa Kyung Kim. "Periodic, irreducible, powerful ray pattern matrices." Linear Algebra and its Applications 404 (July 2005): 283–96. http://dx.doi.org/10.1016/j.laa.2005.02.019.

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Stuart, Jeffrey, Carolyn Eschenbach, and Steve Kirkland. "Irreducible sign k-potent sign pattern matrices." Linear Algebra and its Applications 294, no. 1-3 (1999): 85–92. http://dx.doi.org/10.1016/s0024-3795(99)00076-2.

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Le, Tung. "Supercharacters and pattern subgroups in the upper triangular groups." Proceedings of the Edinburgh Mathematical Society 56, no. 1 (2012): 177–86. http://dx.doi.org/10.1017/s0013091512000156.

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AbstractLet Un(q) denote the upper triangular group of degree n over the finite field $\mathbb{F}_q$ with q elements. It is known that irreducible constituents of supercharacters partition the set of all irreducible characters Irr(Un(q)). In this paper we present a correspondence between supercharacters and pattern subgroups of the form Uk(q) ∩ wUk(q), where w is a monomial matrix in GLk(q) for some k < n.
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SCHADEN, MARTIN. "IRREDUCIBLE SCALAR MANY-BODY CASIMIR ENERGIES: THEOREMS AND NUMERICAL STUDIES." International Journal of Modern Physics: Conference Series 14 (January 2012): 501–10. http://dx.doi.org/10.1142/s2010194512007635.

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We define irreducible N-body spectral functions and Casimir energies and consider a massless scalar quantum field interacting locally by positive potentials with classical objects. Irreducible N-body spectral functions in this case are shown to be conditional probabilities of random walks. The corresponding irreducible contributions to scalar many-body Casimir energies are finite and positive/negative for an odd/even number of objects. The force between any two finite objects separable by a plane is always attractive in this case. Analytical and numerical world-line results for the irreducible four-body Casimir energy of a scalar with Dirichlet boundary conditions on a tic-tac-toe pattern of lines are presented. Numerical results for the irreducible three-body Casimir energy of a massless scalar satisfying Dirichlet boundary conditions on three intersecting lines forming an isosceles triangle are also reported. In both cases the symmetric configuration (square and isosceles triangle) corresponds to the minimal irreducible contribution to the Casimir energy.
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Pelejo, Diane Christine, and Jean Leonardo Abagat. "On Sign Pattern Matrices that Allow or Require Algebraic Positivity." Electronic Journal of Linear Algebra 35 (February 1, 2019): 331–56. http://dx.doi.org/10.13001/1081-3810.3862.

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A square matrix M with real entries is algebraically positive (AP) if there exists a real polynomial p such that all entries of the matrix p(M) are positive. A square sign pattern matrix S allows algebraic positivity if there is an algebraically positive matrix M whose sign pattern is S. On the other hand, S requires algebraic positivity if matrix M, having sign pattern S, is algebraically positive. Motivated by open problems raised in a work of Kirkland, Qiao, and Zhan (2016) on AP matrices, all nonequivalent irreducible 3 by 3 sign pattern matrices are listed and classify into three groups (i) those that require AP, (ii) those that allow but not require AP, or (iii) those that do not allow AP. A necessary condition for an irreducible n by n sign pattern to allow algebraic positivity is also provided.
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Kagaris, Dimitri, Rajesh Aakuthota, and Anila Verma. "Maximum sequence test pattern generators with irreducible characteristic polynomials." Microprocessors and Microsystems 30, no. 2 (2006): 117–23. http://dx.doi.org/10.1016/j.micpro.2005.05.002.

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Piza-Davila, Ivan, Guillermo Sanchez-Diaz, Manuel S. Lazo-Cortes, and Cristina Noyola-Medrano. "Enhancing the Performance of YYC Algorithm Useful to Generate Irreducible Testors." International Journal of Pattern Recognition and Artificial Intelligence 32, no. 01 (2017): 1860001. http://dx.doi.org/10.1142/s0218001418600017.

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In pattern recognition, irreducible testors have been used for feature selection. A number of exhaustive algorithms that find irreducible testors have been reported in the literature. One of the latest and more efficient algorithms reported is YYC, an incremental algorithm that finds all the irreducible testors from a training matrix. Its efficiency relies on building a smaller number of feature combinations by finding compatible sets from the top of the matrix to the current row. Nevertheless, as the number of sets currently found grows, YYC execution becomes too slow. This work proposes two improvements of YYC algorithm, incorporated in a pre-processing phase; additionally, a parallel version is implemented. The paper presents some experimental results using synthetic and real data.
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Dissertations / Theses on the topic "Irreducible pattern"

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Kim, Paul J. "On the 4 by 4 Irreducible Sign Pattern Matrices that Require Four Distinct Eigenvalues." Digital Archive @ GSU, 2011. http://digitalarchive.gsu.edu/math_theses/101.

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A sign pattern matrix is a matrix whose entries are from the set {+,-,0}. For a real matrix B, sgn(B) is the sign pattern matrix obtained by replacing each positive(respectively, negative, zero) entry of B by + (respectively, -, 0). For a sign pattern matrix A, the sign pattern class of A, denoted Q(A), is defined as {B: sgn(B) = A}. An n by n sign pattern matrix A requires all distinct eigenvalues if every real matrix whose sign pattern is represented by A has n distinct eigenvalues. In this thesis, a number of sufficient and/or necessary conditions for a sign pattern to reuiqre all distinct eigenvalues are reviewed. In addition, for n=2 and 3, the n by n sign patterns that require all distinct eigenvalues are surveyed. We determine most of the 4 by 4 irreducible sign patterns that require four distinct eigenvalues.
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Books on the topic "Irreducible pattern"

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Wragg, Paul, and András Koltay, eds. Global Perspectives on Press Regulation. Hart Publishing, 2023. http://dx.doi.org/10.5040/9781509950379.

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In this ground-breaking two-volume set, world-leading experts produce a rich, authoritative depiction of the world’s press, its freedom and its limits. We want press freedom but we also want freedom from the press. A powerful press may expose a corrupt government or aid it. It may champion citizens or unfairly attack them. A vulnerable press may lack supporters and succumb to conformity. It may resist and overcome tyranny. According to common belief, press freedom involves social responsibilities to equip public debate and render government transparent. Is this attitude valid given that the press is usually a private, commercial actor? Globally, the health, authority and viability of the press varies dramatically. These patterns do not conform to traditional divisions between North and South, East and West. Instead, they are much more complex. How do we measure successful press regulation? What concessions can the state and/or society demand from the press? What constitutes the irreducible core of press freedom? The contributions in Volume 1 look at key jurisdictions in Europe, whereas Volume 2 goes beyond Europe to analyse the situation in key jurisdictions in Asia, Africa, the Americas and Oceania. Each volume can be used independently or as part of the complete set. This work will be incredibly valuable to policymakers and academics who seek to capture the global picture for the purposes of effecting change.
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Wragg, Paul, and András Koltay, eds. Global Perspectives on Press Regulation, Volume 2. Hart Publishing, 2024. http://dx.doi.org/10.5040/9781509950423.

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In this ground-breaking two-volume set, world-leading experts produce a rich, authoritative depiction of the world’s press, its freedom, and its limits. We want press freedom but we also want freedom from the press. A powerful press may expose corrupt government or aid it. It may champion citizens or unfairly attack them. A vulnerable press may lack supporters and succumb to conformity. It may resist, and overcome tyranny. According to common belief, press freedom involves social responsibilities to equip public debate and render government transparent. Is this attitude valid given that the press is usually a private, commercial actor? Globally, the health, authority, and viability of the press varies dramatically. These patterns do not conform to traditional divisions between North and South, East and West. Instead, they are much more complex. How do we measure successful press regulation? What concessions can the state and/or society demand of the press? What constitutes the irreducible core of press freedom? The contributions in Volume 1 look at key jurisdictions in Europe; whereas Volume 2 goes beyond Europe to analyse the situation in key jurisdictions in Asia, Africa, the Americas and Oceania. Each volume can be used independently or as part of the complete set. This work will be incredibly valuable to policy makers and academics who seek to capture the global picture for the purposes of effecting change. Volume 2: Asia, Africa, the Americas and Oceania
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Brunner, Ronald D., and Amanda H. Lynch. Adaptive Governance. Oxford University Press, 2017. http://dx.doi.org/10.1093/acrefore/9780190228620.013.601.

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Adaptive governance is defined by a focus on decentralized decision-making structures and procedurally rational policy, supported by intensive natural and social science. Decentralized decision-making structures allow a large, complex problem like global climate change to be factored into many smaller problems, each more tractable for policy and scientific purposes. Many smaller problems can be addressed separately and concurrently by smaller communities. Procedurally rational policy in each community is an adaptation to profound uncertainties, inherent in complex systems and cognitive constraints, that limit predictability. Hence planning to meet projected targets and timetables is secondary to continuing appraisal of incremental steps toward long-term goals: What has and hasn’t worked compared to a historical baseline, and why? Each step in such trial-and-error processes depends on politics to balance, if not integrate, the interests of multiple participants to advance their common interest—the point of governance in a free society. Intensive science recognizes that each community is unique because the interests, interactions, and environmental responses of its participants are multiple and coevolve. Hence, inquiry focuses on case studies of particular contexts considered comprehensively and in some detail.Varieties of adaptive governance emerged in response to the limitations of scientific management, the dominant pattern of governance in the 20th century. In scientific management, central authorities sought technically rational policies supported by predictive science to rise above politics and thereby realize policy goals more efficiently from the top down. This approach was manifest in the framing of climate change as an “irreducibly global” problem in the years around 1990. The Intergovernmental Panel on Climate Change (IPCC) was established to assess science for the Conference of the Parties (COP) to the U.N. Framework Convention on Climate Change (UNFCCC). The parties negotiated the Kyoto Protocol that attempted to prescribe legally binding targets and timetables for national reductions in greenhouse gas emissions. But progress under the protocol fell far short of realizing the ultimate objective in Article 1 of the UNFCCC, “stabilization of greenhouse gas concentrations in the atmosphere at a level that would prevent dangerous anthropogenic interference in the climate system.” As concentrations continued to increase, the COP recognized the limitations of this approach in Copenhagen in 2009 and authorized nationally determined contributions to greenhouse gas reductions in the Paris Agreement in 2015.Adaptive governance is a promising but underutilized approach to advancing common interests in response to climate impacts. The interests affected by climate, and their relative priorities, differ from one community to the next, but typically they include protecting life and limb, property and prosperity, other human artifacts, and ecosystem services, while minimizing costs. Adaptive governance is promising because some communities have made significant progress in reducing their losses and vulnerability to climate impacts in the course of advancing their common interests. In doing so, they provide field-tested models for similar communities to consider. Policies that have worked anywhere in a network tend to be diffused for possible adaptation elsewhere in that network. Policies that have worked consistently intensify and justify collective action from the bottom up to reallocate supporting resources from the top down. Researchers can help realize the potential of adaptive governance on larger scales by recognizing it as a complementary approach in climate policy—not a substitute for scientific management, the historical baseline.
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Book chapters on the topic "Irreducible pattern"

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Kärkkäinen, Juha, Dominik Kempa, and Marcin Piątkowski. "Tighter Bounds for the Sum of Irreducible LCP Values." In Combinatorial Pattern Matching. Springer International Publishing, 2015. http://dx.doi.org/10.1007/978-3-319-19929-0_27.

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Senko, Oleg, and Alexander Dokukin. "Multiple Regression Method Based on Unexpandable and Irreducible Convex Combinations." In Machine Learning and Data Mining in Pattern Recognition. Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-08979-9_4.

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Gruber, Judith, Michael Schüßler, and Ryszard Bobrowicz. "Introduction." In Pathways for Ecumenical and Interreligious Dialogue. Springer Nature Switzerland, 2024. http://dx.doi.org/10.1007/978-3-031-56019-4_1.

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AbstractOver the last few years, we have witnessed a surge in protest movements around the world. As planet Earth shows its vulnerability and a global pandemic has fundamentally recalibrated the textures of our individual and collective lives, a shared concern for survival triggers individuals and groups to contest the status quo and to call for alternative solutions to the pressing issues of our time. These problems confront us with irreducible complexity, and therefore trigger a wide variety of protest responses across the political spectrum, such as the global ‘Fridays for Future’ demonstrations, or the protests against coronavirus restrictions that have found strong support, particularly among the constituencies of right-wing, populist parties. Dissenting movements, thus, can take a range of forms. At their core, however, they share a common pattern, i.e. (1) they seek to manage the irreducible complexity of reality, (2) they make normative claims about what constitutes a good life, and (3) they offer visions of transformation and hope for a future. This is the stuff of theology, and, indeed, religious and theological messages are often explicitly present in protest movements. Yet, paradoxically, within religious communities, protest is often seen either as inherently intrinsic to, or simply antithetical to, religious loyalty (or ‘faithfulness’).
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Gallagher, Shaun. "The Nature of Patterns." In The Self and its Disorders. Oxford University PressOxford, 2024. http://dx.doi.org/10.1093/oso/9780198873068.003.0003.

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Abstract This chapter addresses some philosophical issues concerning the very concept of pattern. What does it mean to say that some grouping of things constitutes a pattern, or that a pattern constitutes a self? How is it possible to take a scientific approach to a heterogeneous collection of processes that includes bodily, experiential, affective, cognitive, social, cultural, narratival, and normative factors. Can such factors form a coherent phenomenon? The chapter develops the idea that we should think of a pattern as an irreducible dynamical gestalt where parts or processes are organized in nonlinear dynamical relations across a number of time scales rather than in a set of hierarchical levels. This solution builds on the work of Daniel Dennett, John Haugeland, and Scott Kelso and differs from both mechanistic and network theories.
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Silveira, José, and Patricia Rockman. "The Brain as a Complex Adaptive System." In Managing Uncertainty in Mental Health Care. Oxford University Press, 2021. http://dx.doi.org/10.1093/med/9780197509326.003.0002.

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This chapter introduces complexity and its contribution to objective uncertainty in mental health and addiction. The view of the brain as a complex adaptive system is discussed, and the conceptualization of the mind as emergent from the brain is introduced. Limits that complexity imposes on the accuracy of establishing causation, pattern recognition, and predictions—all three of which are fundamental to clinical practice and the research that informs it—are explained. The pragmatic utility of viewing the brain and mind through a lens of complex adaptive systems is discussed with emphasis on how it makes many sources of clinical uncertainty irreducible.
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De Dominicis L. "Sum frequency generation in chiral carbon nanotubes." In Atomic and Molecular Nonlinear Optics: Theory, Experiment and Computation. IOS Press, 2011. https://doi.org/10.3233/978-1-60750-742-0-118.

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The process of Sum Frequency Generation (SFG) in chiral Carbon Nanotubes (CNTs), with the exciting laser beams propagating along the CNT symmetry axis, is here investigated. First the general form of the first hyperpolarizability third rank tensor β for chiral CNTs is determined with group projector technique method applied to the Lnp22 line group describing their symmetry. For this purpose, the group natural factorization has been adopted and the associated irreducible representations, parameterized in terms of helical quantum numbers, then used to construct the group projector operator in the relevant vector space. The method demonstrates that second harmonic generation is symmetry forbidden in the collinear geometry while, conversely, SFG is symmetry allowed. Subsequently, the SFG far-field radiation pattern has been modelled with a calculation scheme derived from antenna's theory and already used for simulation of Rayleigh scattering from a CNT. The method has been overhauled for describing the here considered nonlinear optical interaction. The study of the role played by two induced counter-propagating current density retarded waves in shaping the radiation pattern is addressed and simulations are reported in the limit regimes of strong and weak attenuation.
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Hanna, Robert, and Michelle Maiese. "The Metaphysics of Agency III: Where the Action Is." In Embodied Minds in Action. Oxford University PressOxford, 2009. http://dx.doi.org/10.1093/oso/9780199230310.003.0009.

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Abstract In this chapter we complete our argument for the Essential Embodiment Theory of the mind–body relation, mental causation, and intentional action. In a wordbite, what we want to demonstrate is that essentially embodied minds are where the action is. In Section 8.1, we argue that the mental–physical property fusion relation at the basis of essentially embodied minds is best understood, in a neo-Aristotelian way, as a hylomorphic—i.e., a matter/form or stuffing/structure—relation of joint constitution, according to which a conscious, intentional mindƖ௦ is the irreducible and truly global intrinsic structure of a suitably neurobiologically complex living animal body. Now the Latin word for ‘mind’ or ‘soul’ is anima, and this beautifully captures the sense in which a conscious, intentional mindƖ௦ is that which animates a suitably neurobiologically complex living organismic body. To animate something in this sense is to channel its natural forces and causal powers by providing its otherwise unstable dynamic processes and disparate moving parts with an inherently dominating organization or pattern.
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McNally, Michael D. "Religion as Spirituality." In Defend the Sacred. Princeton University Press, 2020. http://dx.doi.org/10.23943/princeton/9780691190907.003.0003.

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This chapter considers the relative success of court decisions accommodating certain individual Native American inmates in their religious exercise in prisons, especially the sweat lodge. These cases reveal a pattern of what officials refer to as “Native American Spirituality.” In the prison cases, Native American Spirituality emerges as a term of art from corrections management, a line on the intake form for religious preference, and keyed to the language of the federal chaplaincy manual. Prison chaplaincy programs use it in an effort to articulate what's often exceptional and irreducibly diverse about Native religious traditions and to articulate what makes them so difficult to pin down. Especially insofar as the cases largely involve a triad of intertribal practices: sweat lodges, pipe ceremonies, and access to medicinal tobacco, sage, cedar, and sweetgrass.
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Connolly, Joy. "Cicero’s Orator." In The Oxford Handbook of Rhetoric and Political Theory. Oxford University Press, 2023. http://dx.doi.org/10.1093/oxfordhb/9780190220945.013.8.

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Abstract Contemporary political discourse enshrines concord as an ideal at the same time that it treats politics as a contest producing winners and losers. This chapter argues for a clearer normative account of the play of concord and discord in the republic that arises from the experience of oratory as a key element in citizens’ understanding of and engagement in politics. Cicero’s rhetorical dialogues and speeches show how the drive to achieve concordia or consensus thrives within a framing of politics as conflict free from physical violence. Cicero’s texts knit together productive instabilities even as the parts fail to cohere. His citizen is a virtuosic speaker actively mediating the collective will to harmony and acknowledged multiplicity—a person whose patterns of action and thought should have consequences for how we evaluate and design deliberative and judicial institutions. Drawing connections with the civic thinking of Hannah Arendt, this chapter shows that Cicero’s republican citizen is a paradoxical unity of multiple possibilities, habituated to and expressive of the irreducible plurality of the world.
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Scheman, Naomi. "Against Physicalism." In Feminist Philosophy of Mind. Oxford University PressNew York, 2022. http://dx.doi.org/10.1093/oso/9780190867614.003.0014.

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Abstract This chapter argues that one of the main reasons for the prominence of physicalism in the philosophy of mind is an unquestioning faith in individualism, which is the notion that mental events, states, and processes conceived as particulars in abstraction from social context constitute the foundation of any psychological explanation. Given this faith, the reasonableness of the physicalist project—where the mental is taken to supervene on the locally physical—seems irresistible. By contrast, this chapter brings to the fore the irreducibly social nature of our mental lives by acknowledging the role of social practices and their patterns of salience in shaping not only the meaning but even the identity of our beliefs, desires, and emotions. The chapter ultimately argues that physicalism is committed to an impossible metaphysics, since thinking of beliefs, desires, and emotions as real physical particulars evacuates their meaning and their very identity, which are partially crafted by social context.
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Conference papers on the topic "Irreducible pattern"

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Gonella, Stefano, and Massimo Ruzzene. "Homogenization of Vibrating Periodic Lattice Structures." In ASME 2005 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2005. http://dx.doi.org/10.1115/detc2005-84428.

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The paper describes a homogenization technique for periodic lattice structures. The analysis is performed by considering the irreducible unit cell as a building block that defines the periodic pattern. In particular, the continuum equivalent representation for the discrete structure is sought with the objective of retaining information regarding the local properties of the lattice, while condensing its global behavior into a set of differential equations. These equations can then be solved either analytically or numerically, thus providing a model which involves a significantly lower number of variables than those required for the detailed model of the assembly. The methodology is first tested by comparing the dispersion relations obtained through homogenization with those corresponding to the detailed model of the unit cells and then extended to the comparison of exact and approximate harmonic responses. This comparison is carried out for both one-dimensional and two-dimensional assemblies. The application to three-dimensional structures is not attempted in this work and will be approached in the future without the need for substantial conceptual changes in the theoretical procedure. Hence the presented technique is expected to be applicable to a wide range of periodic structures, with applications ranging from the design of structural elements of mechanical and aerospace interest to the optimization of smart materials with attractive mechanical, thermal or electrical properties.
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Alfonso, Carlos Esteban, Frédérique Fournier, and Victor Alcobia. "A Machine Learning Methodology for Rock-Typing Using Relative Permeability Curves." In SPE Annual Technical Conference and Exhibition. SPE, 2021. http://dx.doi.org/10.2118/205989-ms.

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Abstract The determination of the petrophysical rock-types often lacks the inclusion of measured multiphase flow properties as the relative permeability curves. This is either the consequence of a limited number of SCAL relative permeability experiments, or due to the difficulty of linking the relative permeability characteristics to standard rock-types stemming from porosity, permeability and capillary pressure. However, as soon as the number of relative permeability curves is significant, they can be processed under the machine learning methodology stated by this paper. The process leads to an automatic definition of relative permeability based rock-types, from a precise and objective characterization of the curve shapes, which would not be achieved with a manual process. It improves the characterization of petrophysical rock-types, prior to their use in static and dynamic modeling. The machine learning approach analyzes the shapes of curves for their automatic classification. It develops a pattern recognition process combining the use of principal component analysis with a non-supervised clustering scheme. Before this, the set of relative permeability curves are pre-processed (normalization with the integration of irreducible water and residual oil saturations for the SCAL relative permeability samples from an imbibition experiment) and integrated under fractional flow curves. Fractional flow curves proved to be an effective way to unify the relative permeability of the two fluid phases, in a unique curve that characterizes the specific poral efficiency displacement of this rock sample. The methodology has been tested in a real data set from a carbonate reservoir having a significant number of relative permeability curves available for the study, in addition to capillary pressure, porosity and permeability data. The results evidenced the successful grouping of the relative permeability samples, according to their fractional flow curves, which allowed the classification of the rocks from poor to best displacement efficiency. This demonstrates the feasibility of the machine learning process for defining automatically rock-types from relative permeability data. The fractional flow rock-types were compared to rock-types obtained from capillary pressure analysis. The results indicated a lack of correspondence between the two series of rock-types, which testifies the additional information brought by the relative permeability data in a rock-typing study. Our results also expose the importance of having good quality SCAL experiments, with an accurate characterization of the saturation end-points, which are used for the normalization of the curves, and a consistent sampling for both capillary pressure and relative permeability measurements.
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Farmanov, Ravan, Felix Feldmann, Eric Sonny Mathew, et al. "Application of Machine Learning for Estimating Petrophysical Properties of Carbonate Rocks Using NMR Core Measurements." In SPE Reservoir Characterisation and Simulation Conference and Exhibition. SPE, 2023. http://dx.doi.org/10.2118/212625-ms.

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Abstract Evaluation of petrophysical properties such as porosity, permeability, and irreducible water saturation is crucial for reservoir characterization to determine the hydrocarbon initially in place and further optimize hydrocarbon production. However, estimation of these parameters is challenging for carbonate rocks due to their heterogeneity. One of the ways to determine petrophysical properties is the use of nuclear magnetic resonance (NMR), which involves applying a magnetic field to the formation and detecting signals emitted from pore spaces. The main objective of this study is to develop an empirical correlation for porosity, permeability, and irreducible water saturation by comparing NMR and laboratory measurements for carbonate rocks in the Middle East. Furthermore, machine learning (ML) approach was applied to predict these petrophysical parameters utilizing NMR data. Different ML algorithms such as tree-based and neural networks were trained to estimate these petrophysical properties of carbonate rocks. The obtained results from ML algorithms were further compared with core measurements to ensure their accuracy. The results showed that the use of T2 spectrum as an input provided more accurate results than NMR features. It can be proven by observing the performance of deep neural networks algorithm, where the models showed R2 values of 0.87 and 0.74 for porosity prediction using T2 and features extraction approaches, respectively. The same behavior was followed for the permeability estimations as deep neural networks model scored R2 = 0.81 (T2 approach) and R2 = 0.74 (features extraction approach). Similarly, determination of irreducible water saturation was more accurate using T2 approach (R2 = 0.87), whereas features extraction technique also exhibited a decent performance (R2 = 0.71). Also, T2 approach is more convenient since it is more straightforward to generate T2 spectrum from NMR measurements and use it for the ML models. Furthermore, based on the machine learning approach, gradient boosting and deep neural networks models performed with higher accuracy than other algorithms. This can be attributed to their strong configuration, which is able to find patterns between input and output parameters. This study provides more insight into petrophysical properties determined from NMR measurements in carbonates using ML techniques. This is useful in better characterizing carbonate reservoirs in the Middle East through accurate estimations of hydrocarbon resources and related reserves.
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Shao, Wei, Gabriela Singer, Gabor Hursan, and Shouxiang Mark Ma. "NMR Fluid Substitution for Multimodal Carbonate Rocks." In 2023 SPWLA 64th Annual Symposium. Society of Petrophysicists and Well Log Analysts, 2023. http://dx.doi.org/10.30632/spwla-2023-0101.

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Nuclear magnetic resonance (NMR) petrophysical interpretation is largely based on the correlation between NMR relaxation time and formation pore-size distribution, assuming the reservoir is fully saturated by the wetting fluid within the logging tools’ sensitive volume. NMR fluid substitution (FS), a set of methods to eliminate the effect of nonwetting fluids from NMR data acquired in partially saturated rocks, has been developed and established for simple, mostly unimodal pore systems. This paper evaluates the effectiveness of existing FS methods in multimodal carbonate pore systems and proposes a new technique to overcome the limitations of prior approaches in these types of reservoirs. Existing FS methods are subdivided into two approaches, based on (1) the SDR and Coates permeability estimations or (2) the Brownstein equation and thin-film model. Historically, these methods were validated for mostly sandstones and only a limited number of carbonate samples. This work thoroughly evaluates the effectiveness of the existing FS methods using 20 carbonate samples with a multimodal pore system. The plugs were prepared to mimic hydrocarbon charge and drilling mud-filtrate invasion and measured by NMR at 100% water, irreducible water, and residual oil saturations. Four different existing FS methods were applied to partially water-saturated data to approximate T2 distributions at 100% water saturation, and each approximation was subsequently compared with actual measurements of the fully water-saturated samples. Finally, this paper also presents a new FS method for carbonate multimodal pore systems. The new technique consists of a nonlinear inversion method that uses the Looyestijn water saturation profile model to describe the process of hydrocarbon displacing water and an inversion process that minimizes the L2 or L1 distances between the modeled and observed T2 distributions. The inversion derives the T2 distributions at 100% water saturation and the Looyestijn water saturation profile parameters. Existing FS methods in complex carbonate rocks may not be able to reconstruct the details of the pore-size distribution that is required to evaluate its modality. Also, they tend to overestimate mesoporosities and underestimate macroporosity significantly. The new FS method, validated by 20 carbonate samples with a variety of pore-size distributions, yields satisfactory results both in terms of T2 distribution matching and pore typing. The new method eliminates false, hydrocarbon-related bimodality from NMR data in unimodal pore systems while it correctly retains the bimodal T2 distribution where the fully water-saturated NMR spectrum is bimodal. Compared with the existing FS methods, the new FS processing performs well for all carbonate pore-size distribution patterns. This method increases the accuracy of NMR-based pore size and rock-type evaluation in partially hydrocarbon-saturated, complex carbonate pore systems.
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