5,146 research outputs found
A Canonical Locally Named Representation of Binding
No full textThis paper is about completely formal representation of languages with binding. We have previously written about a representation following an approach going back to Frege, based on first-order syntax using distinct syntactic classes for locally bound variables vs. global or free variables (Sato and Pollack, J Symb Comput 45:598–616, 2010). The present paper differs from our previous work by being more abstract. Whereas we previously gave a particular concrete function for canonically choosing the names of binders, here we characterize abstractly the properties required of such a choice function to guarantee canonical representation, and focus on the metatheory of the representation, proving that it is in substitution preserving isomorphism with the nominal Isabelle representation of pure lambda terms. This metatheory is formalized in Isabelle/HOL. The final section outlines a formalization in Matita of a challenging language with multiple binding and simultaneous substitution. The Isabelle and Matita proof files are available online
ON IWASAWA THEORY OF ELLIPTIC CURVES OVER Q AT PRIMES OF SUPERSINGULAR REDUCTION OVER Z_p-EXTENSIONS OF NUMBER FIELDS
No full textIn this paper, we make a study of the Iwasawa theory of an elliptic curve at a supersingular prime p along an arbitrary Z(p)-extension of a number field K in the case when p splits completely in K. Generalizing work of Kobayashi and Perrin-Riou , we define restricted Selmer groups and lambda(+/-), mu(+/-)-invariants; we then derive asymptotic formulas describing the growth of the Selmer group in terms of these invariants. To be able to work with non-cyclotomic Z(p)-extensions, a new local result is proven that gives a complete description of the formal group of an elliptic curve at a supersingular prime along any ramified Z(p)-extension of Q(p)
A Computational Model of Symbiotic Composition in Evolutionary Transitions
Get PDFSeveral of the major transitions in evolutionary history, such as the symbiogenic origin of eukaryotes from prokaryotes, share the feature that existing entities became the components of composite entities at a higher level of organisation. This composition of pre-adapted extant entities into a new whole is a fundamentally different source of variation from the gradual accumulation of small random variations, and it has some interesting consequences for issues of evolvability. Intuitively, the pre-adaptation of sets of features in reproductively independent specialists suggests a form of ‘divide and conquer’ decomposition of the adaptive domain. Moreover, the compositions resulting from one level may become the components for compositions at the next level, thus scaling-up the variation mechanism. In this paper, we explore and develop these concepts using a simple abstract model of symbiotic composition to examine its impact on evolvability. To exemplify the adaptive capacity of the composition model, we employ a scale-invariant fitness landscape exhibiting significant ruggedness at all scales. Whilst innovation by mutation and by conventional evolutionary algorithms becomes increasingly more difficult as evolution continues in this landscape, innovation by composition is not impeded as it discovers and assembles component entities through successive hierarchical levels
A complex analogue of the Goodman-Pollack-Wenger theorem
Get PDFA \textit{-transversal} to family of sets in is a
-dimensional affine subspace that intersects each set of the family. In 1957
Hadwiger provided a necessary and sufficient condition for a family of pairwise
disjoint, planar convex sets to have a -transversal. After a series of three
papers among the authors Goodman, Pollack, and Wenger from 1988 to 1990,
Hadwiger's Theorem was extended to necessary and sufficient conditions for
-transversals to finite families of convex sets in with
no disjointness condition on the family of sets. We prove an analogue of the
Goodman-Pollack-Wenger theorem in the complex setting.Comment: Correction: A complex Goodman-Pollack-Wenger theorem is proven as in
the main theorem of the first version. It does not imply a corresponding
result for real transversals as initially state
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Hit By a Horse
Get PDFThe document "Hit By a Horse" by Robert Pollack recounts a personal experience in which the author was struck by a horse-drawn carriage in New York City. Pollack uses this incident to explore broader themes of morality, human behavior, and the distinction between ignorance and evil. He contrasts the indifference of bystanders with the kindness of his wife and the emergency room staff, suggesting that moral choices are not determined by education or knowledge but are instead independent and intrinsic decisions. Pollack reflects on the necessity of addressing moral questions within the intersection of science and religion, emphasizing that understanding what is right and good remains a crucial, albeit data-resistant, aspect of human life. He concludes by linking this personal reflection to the mission of the Center for the Study of Science and Religion (CSSR), advocating for the importance of integrating moral inquiry into scientific and educational endeavors
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Biohazards in biological research: proceedings
No full textThe 1973 publication "Biohazards in Biological Research," edited by S. Hellman, M. Oxman, and R. Pollack, focuses on the risks and safety concerns associated with biological research. In his comments, Robert Pollack addresses the need for improved safety protocols and stricter controls in laboratories working with potentially hazardous biological agents. He emphasizes the uneven standards in the certification and handling of biological materials, such as primary monkey cells and hybrid viruses, and the inconsistencies in the availability of certified, safe biological products like poliovaccine. Pollack calls for immediate action to implement safer practices, particularly in laboratories that handle dangerous viruses, cells, or animals. He also highlights the necessity for central certification of virus seed stocks and suggests that governmental and private research agencies must provide the necessary funds to ensure safety in research. Pollack warns that without adequate funding and safety measures, research may either continue with unnecessary risks or be halted entirely. Additionally, he stresses the importance of conducting prospective studies on the incidence of disease, including cancers, in laboratory workers to assess the potential harm of the agents being studied
Uncertainty principles connected with the Mobius inversion formula
Get PDFWe say that two arithmetic functions and form a \emph{M\"{o}bius pair} if for all natural numbers . In that case, can be expressed in terms of by the familiar M\"{o}bius inversion formula of elementary number theory. In a previous paper, the first-named author showed that if the members and of a M\"{o}bius pair are both finitely supported, then both functions vanish identically. Here we prove two significantly stronger versions of this uncertainty principle. A corollary of our results is that in a nonzero M\"{o}bius pair, one cannot have both $\sum_{f(n) \neq 0}\frac{1}{n
RG 9015-001-001 Frank R. Zebley Collection, Along the Brandywine Photograph Collection
No full textPollack Mill on Beaver Cree
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On the Fourier-Jacobi Expansion of Quaternionic Modular Forms on Spin(8)
Get PDFIn this dissertation, we study a class of non-holomorphic, cohomological automorphic functions on the split, simply connected, spin group G=Spin(4,4). Following ideas of Gross-Wallach, Gan-Gross-Savin, M. Weissman, and A. Pollack, we term these automorphic functions quaternionic modular forms on G, and analyze a theory of scalar-valued Fourier coefficients associated to them. Our results build parallels between the theory of quaternionic modular forms on G, and the arithmetically rich theory of genus two Siegel modular forms. The main result states that a level one quaternionic modular form on G is determined by its primitive Fourier coefficients. As an input to this result, we develop a theory of Fourier-Jacobi expansions for quaternionic modular forms, in which the non-degenerate coefficients are themselves genus two Siegel modular forms. Our primary application strengthens earlier joint work of the author with J. Johnson-Leung, I. Negrini, M. Roy, and A. Pollack. More precisely, in this dissertation we show that the level one quaternionic modular forms on SO(4,4) that arise as theta lifts from Sp(4) admit an elementary Fourier coefficient theoretic characterization, which is akin to a characterization of the classical Saito-Kurokawa subspace proven by D. Zagier
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