al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT leve... more al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT levels and the development of pulmonary emphysema. An alAT gene is defined as "Null" when no alAT in serum is attributed to that alAT gene. Although all alAT Null genes have identical phenotypic consequences (i.e. no detectable alAT in the serum), different genotypic mechanisms can cause the Null state. This study defines the molecular basis for the alAT
† This paper is a corrected and clarified version of Curiel (2005), which itself is in the main a... more † This paper is a corrected and clarified version of Curiel (2005), which itself is in the main a distillation of the much lengthier, more detailed and more technical Curiel (2004). I make frequent reference to that paper throughout this one, primarily for the statement, elaboration and proof of technical results omitted here. ‡ I would like to thank someone for help with this paper, but I can't.
Every physical theory has (at least) two different forms of mathematical equations to represent i... more Every physical theory has (at least) two different forms of mathematical equations to represent its target systems: the dynamical (equations of motion) and the kinematical (kinematical constraints). Kinematical constraints are differentiated from equations of motion by the fact that their particular form is fixed once and for all, irrespective of the interactions the system enters into. By contrast, the particular form of a system's equations of motion depends essentially on the particular interaction the system enters into. All contemporary accounts of the structure and semantics of physical theory treat dynamics, i.e., the equations of motion, as the most important feature of a theory for the purposes of its philosophical analysis. I argue to the contrary that it is the kinematical constraints that determine the structure and empirical content of a physical theory in the most important ways: they function as necessary preconditions for the appropriate application of the theory; they differentiate types of physical systems; they are necessary for the equations of motion to be well posed or even just cogent; and they guide the experimentalist in the design of tools for measurement and observation. It is thus satisfaction of the kinematical constraints that renders meaning to those terms representing a system's physical quantities in the first place, even before one can ask whether or not the system satisfies the theory's equations of motion. † This paper has been submitted to Philosophy of Science, Mar. 2016. I thank Chris Pincock for detailed comments, insightful suggestions and hard questions on an earlier draft of a manuscript of which this paper is a fragment, and for many enjoyable, illuminating conversations about these things in general. I thank Adam Caulton, Bill Demopoulos, and Sebastian Lutz for enjoyable and helpful conversations on the structure and semantics of theories in general. Finally, I thank Howard Stein for many fruitful and delightful conversations over many years touching on all sorts of matters related to the issues I address here in particular, and, in general, for more than I can well say. This paper owes a clear and debt to several of his papers, especially Stein (1992, 1994, 2004).
I argue that, contrary to the standard view, one cannot understand the structure and nature of ou... more I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements) are modeled in theory. One upshot is that standard pictures of what a scientific theory can be are grossly inadequate. In particular, standard formulations assume, with no argument ever given, that it is possible to make a clean separation between, on the one hand, one part of the scientific knowledge a physical theory embodies, viz., that encoded in the pure mathematical formalism and, on the other, the remainder of that knowledge. The remainder includes at a minimum what is encoded in the practice of modeling particular systems, of performing experiments, of bringing the results of theory and experiment into mutually fruitful contact---in sum, real application of the theory in actual scientific practice. This assumption comes out most clearly i...
al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT leve... more al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT levels and the development of pulmonary emphysema. An alAT gene is defined as "Null" when no alAT in serum is attributed to that alAT gene. Although all alAT Null genes have identical phenotypic consequences (i.e. no detectable alAT in the serum), different genotypic mechanisms can cause the Null state. This study defines the molecular basis for the alAT gene Nullf,,,,, identified and cloned from genomic DNA of an individual with the NullNull phenotype and emphysema resulting from the heterozygous inheritance of the Nullm.,w, and Nullb.Iuigm genes. Sequencing of exons Ic-V and all exon-intron junctions of the Null",,Vt. gene demonstrated it was identical to the common normal Ml(Va1213) alAT gene except for the insertion of a single nucleotide within the coding region of exon V, causing a 3' frameshift with generation ofa premature stop signal. Family analysis using oligonu...
I sketch here the construction of Geroch (1969) (whose exposition I closely follow), which ground... more I sketch here the construction of Geroch (1969) (whose exposition I closely follow), which grounds the arguments of section 3 in Curiel (2016). (I simplify his construction in non-essential ways for our purposes, and gloss over unnecessary technicalities.) Consider a 1-parameter family of relativistic spacetimes, by which I mean a family {(Mλ, g(λ))}λ∈(0,1], where each (Mλ, g(λ)) is a relativistic spacetime with signature (+, −, −, −) for g(λ). (It will be clear in a moment why I work with the contravariant form of the metric tensor.) In particular, I do not assume that Mλ is diffeomorphic to Mλ′ for λ 6= λ′. The problem is to find a limit of this family, in some suitable sense, as λ → 0. To solve the problem in full generality, we will use a geometrical construction, gluing the manifolds Mλ of the family together to form a 5-dimensional manifold M, so that each Mλ is itself a 4-dimensional submanifold of M in such a way that the collection of all of them foliate M. λ becomes a scal...
arXiv: General Relativity and Quantum Cosmology, 2016
The standard argument for the uniqueness of the Einstein field equation is based on Lovelock'... more The standard argument for the uniqueness of the Einstein field equation is based on Lovelock's Theorem, the relevant statement of which is restricted to four dimensions. I prove a theorem similar to Lovelock's, with a physically modified assumption: that the geometric object representing curvature in the Einstein field equation ought to have the physical dimension of stress-energy. The theorem is stronger than Lovelock's in two ways: it holds in all dimensions, and so supports a generalized argument for uniqueness; it does not assume that the desired tensor depends on the metric only up second-order partial-derivatives, that condition being a consequence of the proof. This has consequences for understanding the nature of the cosmological constant and theories of higher-dimensional gravity. Another consequence of the theorem is that it makes precise the sense in which there can be no gravitational stress-energy tensor in general relativity. Along the way, I prove a result...
Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a fre... more Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a free scalar particle in R D are shown to be the result of summing over all dimensions D ′ ≥ D of R D ′ , each summand taken in the absence of quantum gravity.
The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting... more The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting of causal fermion systems. It is shown that for critical points of the causal action, the area change of two-dimensional surfaces under a Killing flow in null directions is proportional to the matter flux through these surfaces. This relation generalizes an equation in classical general relativity due to Ted Jacobson setting of causal fermion systems.
The analysis of theory-confirmation generally takes the form: show that a theory in conjunction w... more The analysis of theory-confirmation generally takes the form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theoryconfirmation this yields. The issue of confirmation for an entire framework (e.g., Newtonian mechanics en bloc, as opposed, say, to Newton's theory of gravitation) either does not arise, or is dismissed in so far as frameworks are thought not to be the kind of thing that admits scientific confirmation. I argue that there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. (In particular, Newtonian abduction is not inference to the best explanation, but rather is closer to Peirce's original idea of abduction.) I further argue that Newtonian abduction is at least as important a form of reasoning in science as the deductive form sketched above. The form is beautifully summed up by Maxwell (1876): "The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion." Contents 1 Types of Reasoning in Science 2 2 Frameworks 4 3 Abduction 7 4 Framework Confirmation 18 5 This Is True Confirmation 29 6 References 32 † I thank Bill Harper for many enjoyable and edifying discussions about Newton, scientific reasoning, and evidence, and for having written such a wonderful book (Harper 2011). I also thank him for detailed comments on an earlier draft of the paper, including catching an error in §3 in my discussion of Hall, Brown, and the precessions of Mercury and the Moon. I thank Tom Pashby for comments on an earlier draft, including interesting suggestions for elaboration in future work. I thank an anonymous referee for detailed criticisms and questions. I am grateful to Howard Stein as well, as always, for many illuminating and pleasurable conversations on all of these matters.
We study black holes produced via collapse of a spherically symmetric charged scalar field in asy... more We study black holes produced via collapse of a spherically symmetric charged scalar field in asymptotically flat space. We employ a late time expansion and argue that decaying fluxes of radiation through the event horizon imply that the black hole must contain a null singularity on the Cauchy horizon and a central spacelike singularity.
We numerically solve Einstein's equations coupled to a scalar field in the interior of Kerr black... more We numerically solve Einstein's equations coupled to a scalar field in the interior of Kerr black holes. We find shock waves form near the inner horizon. The shocks grow exponentially in amplitude and need not be axisymmetric. Observers who pass through the shocks experience exponentially large tidal forces and are accelerated exponentially close to the speed of light.
Although black holes are objects of central importance across many fields of physics, there is no... more Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason about them in radically different, and often conflicting, ways. All those ways, however, seem sound in the relevant contexts. After examining and comparing many of the definitions used in practice, I consider the problems that the lack of a universally accepted definition leads to, and discuss whether one is in fact needed for progress in the physics of black holes. I conclude that, within reasonable bounds, the profusion of different definitions is in fact a virtue, making the investigation of black holes possible and fruitful in all the many
I do not think the notion of rigidity in designation can be correct, at least not in any way that... more I do not think the notion of rigidity in designation can be correct, at least not in any way that can serve to ground a semantics that purports both to be fundamental in a semiotical sense and to respect the best science of the day. A careful examination of both the content and the character of our best scientific knowledge not only cannot support anything like what the notion of rigidity requires, but actually shows the notion to be, at bottom, incoherent. In particular, the scientific meaning of natural kind terms can be determined only within the context of a fixed scientific framework and not sub specie aeternitatis. Along the way, I provide grounds for the rejection of essentialist views of the ontology of natural kinds.
† This paper is a corrected and clarified version of Curiel (2005), which itself is in the main a... more † This paper is a corrected and clarified version of Curiel (2005), which itself is in the main a distillation of the much lengthier, more detailed and more technical Curiel (2004). I make frequent reference to that paper throughout this one, primarily for the statement, elaboration and proof of technical results omitted here. ‡ I would like to thank someone for help with this paper, but I can't.
Theoria an International Journal For Theory History and Foundations of Science, 2000
Those who make causality one of the original uralt elements in the universe or one of the fundame... more Those who make causality one of the original uralt elements in the universe or one of the fundamental categories of thought,-of whom you will find that I am not one,-have one very awkward fact to explain away. It is that men's conceptions of a Cause are in different stages of scientific culture entirely different and inconsistent. The great principle of causation which we are told, it is absolutely impossible not to believe, has been one proposition at one period of history and an entirely disparate one another and is still a third one for the modern physicist. The only thing about it which has stood, to use my friend Carus' word, a κτημα ἐς ἀεί,-semper eadem-is the name of it.
An energy condition, in the context of a wide class of spacetime theories (including general rela... more An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated.
al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT leve... more al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT levels and the development of pulmonary emphysema. An alAT gene is defined as "Null" when no alAT in serum is attributed to that alAT gene. Although all alAT Null genes have identical phenotypic consequences (i.e. no detectable alAT in the serum), different genotypic mechanisms can cause the Null state. This study defines the molecular basis for the alAT
† This paper is a corrected and clarified version of Curiel (2005), which itself is in the main a... more † This paper is a corrected and clarified version of Curiel (2005), which itself is in the main a distillation of the much lengthier, more detailed and more technical Curiel (2004). I make frequent reference to that paper throughout this one, primarily for the statement, elaboration and proof of technical results omitted here. ‡ I would like to thank someone for help with this paper, but I can't.
Every physical theory has (at least) two different forms of mathematical equations to represent i... more Every physical theory has (at least) two different forms of mathematical equations to represent its target systems: the dynamical (equations of motion) and the kinematical (kinematical constraints). Kinematical constraints are differentiated from equations of motion by the fact that their particular form is fixed once and for all, irrespective of the interactions the system enters into. By contrast, the particular form of a system's equations of motion depends essentially on the particular interaction the system enters into. All contemporary accounts of the structure and semantics of physical theory treat dynamics, i.e., the equations of motion, as the most important feature of a theory for the purposes of its philosophical analysis. I argue to the contrary that it is the kinematical constraints that determine the structure and empirical content of a physical theory in the most important ways: they function as necessary preconditions for the appropriate application of the theory; they differentiate types of physical systems; they are necessary for the equations of motion to be well posed or even just cogent; and they guide the experimentalist in the design of tools for measurement and observation. It is thus satisfaction of the kinematical constraints that renders meaning to those terms representing a system's physical quantities in the first place, even before one can ask whether or not the system satisfies the theory's equations of motion. † This paper has been submitted to Philosophy of Science, Mar. 2016. I thank Chris Pincock for detailed comments, insightful suggestions and hard questions on an earlier draft of a manuscript of which this paper is a fragment, and for many enjoyable, illuminating conversations about these things in general. I thank Adam Caulton, Bill Demopoulos, and Sebastian Lutz for enjoyable and helpful conversations on the structure and semantics of theories in general. Finally, I thank Howard Stein for many fruitful and delightful conversations over many years touching on all sorts of matters related to the issues I address here in particular, and, in general, for more than I can well say. This paper owes a clear and debt to several of his papers, especially Stein (1992, 1994, 2004).
I argue that, contrary to the standard view, one cannot understand the structure and nature of ou... more I argue that, contrary to the standard view, one cannot understand the structure and nature of our knowledge in physics without an analysis of the way that observers (and, more generally, measuring instruments and experimental arrangements) are modeled in theory. One upshot is that standard pictures of what a scientific theory can be are grossly inadequate. In particular, standard formulations assume, with no argument ever given, that it is possible to make a clean separation between, on the one hand, one part of the scientific knowledge a physical theory embodies, viz., that encoded in the pure mathematical formalism and, on the other, the remainder of that knowledge. The remainder includes at a minimum what is encoded in the practice of modeling particular systems, of performing experiments, of bringing the results of theory and experiment into mutually fruitful contact---in sum, real application of the theory in actual scientific practice. This assumption comes out most clearly i...
al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT leve... more al-Antitrypsin (alAT) deficiency is a hereditary disorder associated with reduced serum alAT levels and the development of pulmonary emphysema. An alAT gene is defined as "Null" when no alAT in serum is attributed to that alAT gene. Although all alAT Null genes have identical phenotypic consequences (i.e. no detectable alAT in the serum), different genotypic mechanisms can cause the Null state. This study defines the molecular basis for the alAT gene Nullf,,,,, identified and cloned from genomic DNA of an individual with the NullNull phenotype and emphysema resulting from the heterozygous inheritance of the Nullm.,w, and Nullb.Iuigm genes. Sequencing of exons Ic-V and all exon-intron junctions of the Null",,Vt. gene demonstrated it was identical to the common normal Ml(Va1213) alAT gene except for the insertion of a single nucleotide within the coding region of exon V, causing a 3' frameshift with generation ofa premature stop signal. Family analysis using oligonu...
I sketch here the construction of Geroch (1969) (whose exposition I closely follow), which ground... more I sketch here the construction of Geroch (1969) (whose exposition I closely follow), which grounds the arguments of section 3 in Curiel (2016). (I simplify his construction in non-essential ways for our purposes, and gloss over unnecessary technicalities.) Consider a 1-parameter family of relativistic spacetimes, by which I mean a family {(Mλ, g(λ))}λ∈(0,1], where each (Mλ, g(λ)) is a relativistic spacetime with signature (+, −, −, −) for g(λ). (It will be clear in a moment why I work with the contravariant form of the metric tensor.) In particular, I do not assume that Mλ is diffeomorphic to Mλ′ for λ 6= λ′. The problem is to find a limit of this family, in some suitable sense, as λ → 0. To solve the problem in full generality, we will use a geometrical construction, gluing the manifolds Mλ of the family together to form a 5-dimensional manifold M, so that each Mλ is itself a 4-dimensional submanifold of M in such a way that the collection of all of them foliate M. λ becomes a scal...
arXiv: General Relativity and Quantum Cosmology, 2016
The standard argument for the uniqueness of the Einstein field equation is based on Lovelock'... more The standard argument for the uniqueness of the Einstein field equation is based on Lovelock's Theorem, the relevant statement of which is restricted to four dimensions. I prove a theorem similar to Lovelock's, with a physically modified assumption: that the geometric object representing curvature in the Einstein field equation ought to have the physical dimension of stress-energy. The theorem is stronger than Lovelock's in two ways: it holds in all dimensions, and so supports a generalized argument for uniqueness; it does not assume that the desired tensor depends on the metric only up second-order partial-derivatives, that condition being a consequence of the proof. This has consequences for understanding the nature of the cosmological constant and theories of higher-dimensional gravity. Another consequence of the theorem is that it makes precise the sense in which there can be no gravitational stress-energy tensor in general relativity. Along the way, I prove a result...
Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a fre... more Quantum-gravity corrections (in the form of a minimal length) to the Feynman propagator for a free scalar particle in R D are shown to be the result of summing over all dimensions D ′ ≥ D of R D ′ , each summand taken in the absence of quantum gravity.
The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting... more The notions of two-dimensional area, Killing fields and matter flux are introduced in the setting of causal fermion systems. It is shown that for critical points of the causal action, the area change of two-dimensional surfaces under a Killing flow in null directions is proportional to the matter flux through these surfaces. This relation generalizes an equation in classical general relativity due to Ted Jacobson setting of causal fermion systems.
The analysis of theory-confirmation generally takes the form: show that a theory in conjunction w... more The analysis of theory-confirmation generally takes the form: show that a theory in conjunction with physical data and auxiliary hypotheses yield a prediction about phenomena; verify the prediction; provide a quantitative measure of the degree of theoryconfirmation this yields. The issue of confirmation for an entire framework (e.g., Newtonian mechanics en bloc, as opposed, say, to Newton's theory of gravitation) either does not arise, or is dismissed in so far as frameworks are thought not to be the kind of thing that admits scientific confirmation. I argue that there is another form of scientific reasoning that has not received philosophical attention, what I call Newtonian abduction, that does provide confirmation for frameworks as a whole, and does so in two novel ways. (In particular, Newtonian abduction is not inference to the best explanation, but rather is closer to Peirce's original idea of abduction.) I further argue that Newtonian abduction is at least as important a form of reasoning in science as the deductive form sketched above. The form is beautifully summed up by Maxwell (1876): "The true method of physical reasoning is to begin with the phenomena and to deduce the forces from them by a direct application of the equations of motion." Contents 1 Types of Reasoning in Science 2 2 Frameworks 4 3 Abduction 7 4 Framework Confirmation 18 5 This Is True Confirmation 29 6 References 32 † I thank Bill Harper for many enjoyable and edifying discussions about Newton, scientific reasoning, and evidence, and for having written such a wonderful book (Harper 2011). I also thank him for detailed comments on an earlier draft of the paper, including catching an error in §3 in my discussion of Hall, Brown, and the precessions of Mercury and the Moon. I thank Tom Pashby for comments on an earlier draft, including interesting suggestions for elaboration in future work. I thank an anonymous referee for detailed criticisms and questions. I am grateful to Howard Stein as well, as always, for many illuminating and pleasurable conversations on all of these matters.
We study black holes produced via collapse of a spherically symmetric charged scalar field in asy... more We study black holes produced via collapse of a spherically symmetric charged scalar field in asymptotically flat space. We employ a late time expansion and argue that decaying fluxes of radiation through the event horizon imply that the black hole must contain a null singularity on the Cauchy horizon and a central spacelike singularity.
We numerically solve Einstein's equations coupled to a scalar field in the interior of Kerr black... more We numerically solve Einstein's equations coupled to a scalar field in the interior of Kerr black holes. We find shock waves form near the inner horizon. The shocks grow exponentially in amplitude and need not be axisymmetric. Observers who pass through the shocks experience exponentially large tidal forces and are accelerated exponentially close to the speed of light.
Although black holes are objects of central importance across many fields of physics, there is no... more Although black holes are objects of central importance across many fields of physics, there is no agreed upon definition for them, a fact that does not seem to be widely recognized. Physicists in different fields conceive of and reason about them in radically different, and often conflicting, ways. All those ways, however, seem sound in the relevant contexts. After examining and comparing many of the definitions used in practice, I consider the problems that the lack of a universally accepted definition leads to, and discuss whether one is in fact needed for progress in the physics of black holes. I conclude that, within reasonable bounds, the profusion of different definitions is in fact a virtue, making the investigation of black holes possible and fruitful in all the many
I do not think the notion of rigidity in designation can be correct, at least not in any way that... more I do not think the notion of rigidity in designation can be correct, at least not in any way that can serve to ground a semantics that purports both to be fundamental in a semiotical sense and to respect the best science of the day. A careful examination of both the content and the character of our best scientific knowledge not only cannot support anything like what the notion of rigidity requires, but actually shows the notion to be, at bottom, incoherent. In particular, the scientific meaning of natural kind terms can be determined only within the context of a fixed scientific framework and not sub specie aeternitatis. Along the way, I provide grounds for the rejection of essentialist views of the ontology of natural kinds.
† This paper is a corrected and clarified version of Curiel (2005), which itself is in the main a... more † This paper is a corrected and clarified version of Curiel (2005), which itself is in the main a distillation of the much lengthier, more detailed and more technical Curiel (2004). I make frequent reference to that paper throughout this one, primarily for the statement, elaboration and proof of technical results omitted here. ‡ I would like to thank someone for help with this paper, but I can't.
Theoria an International Journal For Theory History and Foundations of Science, 2000
Those who make causality one of the original uralt elements in the universe or one of the fundame... more Those who make causality one of the original uralt elements in the universe or one of the fundamental categories of thought,-of whom you will find that I am not one,-have one very awkward fact to explain away. It is that men's conceptions of a Cause are in different stages of scientific culture entirely different and inconsistent. The great principle of causation which we are told, it is absolutely impossible not to believe, has been one proposition at one period of history and an entirely disparate one another and is still a third one for the modern physicist. The only thing about it which has stood, to use my friend Carus' word, a κτημα ἐς ἀεί,-semper eadem-is the name of it.
An energy condition, in the context of a wide class of spacetime theories (including general rela... more An energy condition, in the context of a wide class of spacetime theories (including general relativity), is, crudely speaking, a relation one demands the stress-energy tensor of matter satisfy in order to try to capture the idea that "energy should be positive". The remarkable fact I will discuss in this paper is that such simple, general, almost trivial seeming propositions have profound and far-reaching import for our understanding of the structure of relativistic spacetimes. It is therefore especially surprising when one also learns that we have no clear understanding of the nature of these conditions, what theoretical status they have with respect to fundamental physics, what epistemic status they may have, when we should and should not expect them to be satisfied, and even in many cases how they and their consequences should be interpreted physically. Or so I shall argue, by a detailed analysis of the technical and conceptual character of all the standard conditions used in physics today, including examination of their consequences and the circumstances in which they are believed to be violated.
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Papers by Erik Curiel