4,537 research outputs found

    A Unifying Theory for Graph Transformation

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    The field of graph transformation studies the rule-based transformation of graphs. An important branch is the algebraic graph transformation tradition, in which approaches are defined and studied using the language of category theory. Most algebraic graph transformation approaches (such as DPO, SPO, SqPO, and AGREE) are opinionated about the local contexts that are allowed around matches for rules, and about how replacement in context should work exactly. The approaches also differ considerably in their underlying formal theories and their general expressiveness (e.g., not all frameworks allow duplication). This dissertation proposes an expressive algebraic graph transformation approach, called PBPO+, which is an adaptation of PBPO by Corradini et al. The central contribution is a proof that PBPO+ subsumes (under mild restrictions) DPO, SqPO, AGREE, and PBPO in the important categorical setting of quasitoposes. This result allows for a more unified study of graph transformation metatheory, methods, and tools. A concrete example of this is found in the second major contribution of this dissertation: a graph transformation termination method for PBPO+, based on decreasing interpretations, and defined for general categories. By applying the proposed encodings into PBPO+, this method can also be applied for DPO, SqPO, AGREE, and PBPO

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

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    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    An Inaugural, Qualitative Examination of the Relationships Between People With Gender Nonconforming Expression and Social Anxiety

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    The focus in this research was on the experience of social anxiety associated with people with gender nonconformity. The study involved consideration of the issues people with gender nonconformity face as well as the mental impact that often occurs as a result of the rejection of other people in their lives, including their family and friends, as well as how and in what ways gender nonconforming people are affected by negativity in their environment. Data related to the problems that develop with such people, in particular the impact of stigmatization, discrimination, and social anxiety on people with gender nonconformity were collected via interviews. The researcher collected both primary and secondary data for analysis via interviews and a literature review. It was hypothesized that gender nonconformity would have a strong relationship with social anxiety, with negative experiences playing the role of mediator. Results show people who are gender nonconforming face disapproval of their identity in some situations in their lives, which often has a negative impact on their mental health. Future research will be important to analyze the particular types of problems caused by such issues

    On Vector Spaces with Formal Infinite Sums

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    We discuss possible definitions of categories of vector spaces enriched with a notion of formal infinite linear combination in the likes of the formal infinite linear combinations one has in the context of generalized power series, we call these \textit{categories of reasonable strong vector spaces} (r.s.v.s.). We show that, in a precise sense, the more general possible definition for a strong vector space is that of a small Vect\mathrm{Vect}-enriched endofunctor of Vect\mathrm{Vect} that is right orthogonal, for every cardinal λ\lambda, to the cokernel of the canonical inclusion of the λ\lambda-th copower in the λ\lambda-th power of the identity functor: these form the objects for a universal r.s.v.s. we call ΣVect\Sigma\mathrm{Vect}. We relate this category to what could be understood to be the obvious category of strong vector spaces BΣVectB\Sigma\mathrm{Vect} and to the r.s.v.s. KTVectsK\mathrm{TVect}_s of separated linearly topologized spaces that are generated by linearly compact spaces. We study the number of iterations of the obvious approximate reflector on Ind-(Vectop)\mathrm{Ind}\text{-}(\mathrm{Vect}^{\mathrm{op}}) needed to construct the orthogonal reflector Ind-(Vectop)ΣVect\mathrm{Ind}\text{-}(\mathrm{Vect}^{\mathrm{op}}) \to \Sigma\mathrm{Vect} as it relates to the problem of constructing the smallest subspace of an XΣVectX \in \Sigma\mathrm{Vect} closed under taking infinite linear combinations containing a given linear subspace of HH of XX. Finally we show the natural monoidal closed structure on Ind-(Vectop)\mathrm{Ind}\text{-}(\mathrm{Vect}^{\mathrm{op}}) restricts naturally to ΣVect\Sigma\mathrm{Vect} and apply this to define an infinite-sum-sensitive notion of K\"ahler differentials for generalized power series. Most of the technical results apply to a more general class of orthogonal subcategories of Ind-(Vectop)\mathrm{Ind}\text{-}(\mathrm{Vect}^{\mathrm{op}}) and we work with that generality

    Charles Spurgeon and a Biblical View of Wealth

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    Charles Spurgeon preached wealth as a spiritual commodity based on his Christological exposition which countered the preaching of wealth as a divine right. Some people have come to view earthly wealth as a substance that comes as a result of obedience to God. There are also a number of people that believe that any biblical theology pertaining to wealth is amendable and see no lasting truth in the text. Spurgeon critiques these approaches. He saw earthly wealth primarily as a spiritual commodity and believed it to be a substance that should be utilized for the purpose of bringing glory to God. The researcher will present a study of what the Bible teaches with regards to wealth as perceived by Spurgeon by applying biblical theological categories and an analysis of wealth from its inception until the present day

    Deformation theory of G-valued pseudocharacters and symplectic determinant laws

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    We give an introduction to the theory of pseudorepresentations of Taylor, Rouquier, Chenevier and Lafforgue. We refer to Taylor’s and Rouquier’s pseudorepresentations as pseudocharacters. They are very closely related, the main difference being that Taylor’s pseudocharacters are defined for a group, where as Rouquier’s pseudocharacters are defined for algebras. Chenevier’s pseudorepresentations are so-called polynomial laws and will be called determinant laws. Lafforgue’s pseudorepresentations are a generalization of Taylor’s pseudocharacters to other reductive groups G, in that the corresponding notion of representation is that of a G-valued representation of a group. We refer to them as G-pseudocharacters. We survey the known comparison theorems, notably Emerson’s bijection between Chenevier’s determinant laws and Lafforgue’s GL(n)-pseudocharacters and the bijection with Taylor’s pseudocharacters away from small characteristics. We show, that duals of determinant laws exist and are compatible with duals of representations. Analogously, we obtain that tensor products of determinant laws exist and are compatible with tensor products of representations. Further the tensor product of Lafforgue’s pseudocharacters agrees with the tensor product of Taylor’s pseudocharacters. We generalize some of the results of [Che14] to general reductive groups, in particular we show that the (pseudo)deformation space of a continuous Lafforgue G-pseudocharacter of a topologically finitely generated profinite group Γ with values in a finite field (of characteristic p) is noetherian. We also show, that for specific groups G it is sufficient, that Γ satisfies Mazur’s condition Φ_p. One further goal of this thesis was to generalize parts of [BIP21] to other reductive groups. Let F/Qp be a finite extension. In order to carry this out for the symplectic groups Sp2d, we obtain a simple and concrete stratification of the special fiber of the pseudodeformation space of a residual G-pseudocharater of Gal(F) into obstructed subloci Xdec(Θ), Xpair(Θ), Xspcl(Θ) of dimension smaller than the expected dimension n(2n + 1)[F : Qp]. We also prove that Lafforgue’s G-pseudocharacters over algebraically closed fields for possibly nonconnected reductive groups G come from a semisimple representation. We introduce a formal scheme and a rigid analytic space of all G-pseudocharacters by a functorial description and show, building on our results of noetherianity of pseudodeformation spaces, that both are representable and admit a decomposition as a disjoint sum indexed by continuous pseudocharacters with values in a finite field up to conjugacy and Frobenius automorphisms. At last, in joint work with Mohamed Moakher, we give a new definition of determinant laws for symplectic groups, which is based on adding a ’Pfaffian polynomial law’ to a determinant law which is invariant under an involution. We prove the expected basic properties in that we show that symplectic determinant laws over algebraically closed fields are in bijection with conjugacy classes of semisimple representation and that Cayley-Hamilton lifts of absolutely irreducible symplectic determinant laws to henselian local rings are in bijection with conjugacy classes of representations. We also give a comparison map with Lafforgue’s pseudocharacters and show that it is an isomorphism over reduced rings

    The Picard index of a surface with torus action

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    We consider normal rational projective surfaces with torus action and provide a formula for their Picard index, that means the index of the Picard group inside the divisor class group. As an application, we classify the log del Pezzo surfaces with torus action of Picard number one up to Picard index 10,000.Comment: 28 pager, 3 figure

    Formal Verification of Verifiability in E-Voting Protocols

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    Election verifiability is one of the main security properties of e-voting protocols, referring to the ability of independent entities, such as voters or election observers, to validate the outcome of the voting process. It can be ensured by means of formal verification that applies mathematical logic to verify the considered protocols under well-defined assumptions, specifications, and corruption scenarios. Automated tools allow an efficient and accurate way to perform formal verification, enabling comprehensive analysis of all execution scenarios and eliminating the human errors in the manual verification. The existing formal verification frameworks that are suitable for automation are not general enough to cover a broad class of e-voting protocols. They do not cover revoting and cannot be tuned to weaker or stronger levels of security that may be achievable in practice. We therefore propose a general formal framework that allows automated verification of verifiability in e-voting protocols. Our framework is easily applicable to many protocols and corruption scenarios. It also allows refined specifications of election procedures, for example accounting for revote policies. We apply our framework to the analysis of several real-world case studies, where we capture both known and new attacks, and provide new security guarantees. First, we consider Helios, a prominent web-based e-voting protocol, which aims to provide end-to-end verifiability. It is however vulnerable to ballot stuffing when the voting server is corrupt. Second, we consider Belenios, which builds upon Helios and aims to achieve stronger verifiability, preventing ballot stuffing by splitting the trust between a registrar and the server. Both of these systems have been used in many real-world elections. Our third case study is Selene, which aims to simplify the individual verification procedure for voters, providing them with trackers for verifying their votes in the clear at the end of election. Finally, we consider the Estonian e-voting protocol, that has been deployed for national elections since 2005. The protocol has continuously evolved to offer better verifiability guarantees but has no formal analysis. We apply our framework to realistic models of all these protocols, deriving the first automated formal analysis in each case. As a result, we find several new attacks, improve the corresponding protocols to address their weakness, and prove that verifiability holds for the new versions

    Generalized logarithmic sheaf on smooth projective surfaces

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    We define the notion of generalized logarithmic sheaves on a smooth projective surface, associated to a pair consisting of a reduced curve and some fixed points on it. We then set up the study of the Torelli property in this setting, focusing mostly in the case of the blow-up of the projective plane on a reduced set of points and, in particular, in the case of the cubic surface. We also study the stability property of generalized logarithmic sheaves as well as carrying out the description of their moduli spaces.Comment: 39 pages. To appear in International Mathematics Research Notices. Comments are welcom
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