140 research outputs found

    LIPIcs, Volume 251, ITCS 2023, Complete Volume

    Get PDF
    LIPIcs, Volume 251, ITCS 2023, Complete Volum

    Degree Spectra, and Relative Acceptability of Notations

    Get PDF

    A Note on a Question of Sacks: It is Harder to Embed Height Three Partial Orders than Height Two Partial Orders

    Full text link
    A long-standing conjecture of Sacks states that it is provable in ZFC that every locally countable partial order of size continuum embeds into the Turing degrees. We show that this holds for partial orders of height two, but provide evidence that it is hard to extend this result even to partial orders of height three. In particular, we show that the result for height two partial orders holds both in certain extensions of ZF with only limited forms of choice and in the Borel setting (where the partial orders and embeddings are required to be Borel measurable), but that the analogous result for height three partial orders fails in both of these settings. We also formulate a general obstacle to embedding partial orders into the Turing degrees, which explains why our particular proof for height two partial orders cannot be extended to height three partial orders, even in ZFC. We finish by discussing how our results connect to the theory of countable Borel equivalence relations.Comment: 19 page

    Kolmogorov Complexity Characterizes Statistical Zero Knowledge

    Get PDF
    We show that a decidable promise problem has a non-interactive statistical zero-knowledge proof system if and only if it is randomly reducible via an honest polynomial-time reduction to a promise problem for Kolmogorov-random strings, with a superlogarithmic additive approximation term. This extends recent work by Saks and Santhanam (CCC 2022). We build on this to give new characterizations of Statistical Zero Knowledge SZK, as well as the related classes NISZK_L and SZK_L

    Semidistrim Lattices

    Get PDF
    We introduce semidistrim lattices, a simultaneous generalization of semidistributive and trim lattices that preserves many of their common properties. We prove that the elements of a semidistrim lattice correspond to the independent sets in an associated graph called the Galois graph, that products and intervals of semidistrim lattices are semidistrim and that the order complex of a semidistrim lattice is either contractible or homotopy equivalent to a sphere

    Exploring Conformational Landscapes and Cryptic Binding Pockets in Distinct Functional States of the SARS-CoV-2 Omicron BA.1 and BA.2 Trimers: Mutation-Induced Modulation of Protein Dynamics and Network-Guided Prediction of Variant-Specific Allosteric Binding Sites

    Get PDF
    A significant body of experimental structures of SARS-CoV-2 spike trimers for the BA.1 and BA.2 variants revealed a considerable plasticity of the spike protein and the emergence of druggable binding pockets. Understanding the interplay of conformational dynamics changes induced by the Omicron variants and the identification of cryptic dynamic binding pockets in the S protein is of paramount importance as exploring broad-spectrum antiviral agents to combat the emerging variants is imperative. In the current study, we explore conformational landscapes and characterize the universe of binding pockets in multiple open and closed functional spike states of the BA.1 and BA.2 Omicron variants. By using a combination of atomistic simulations, a dynamics network analysis, and an allostery-guided network screening of binding pockets in the conformational ensembles of the BA.1 and BA.2 spike conformations, we identified all experimentally known allosteric sites and discovered significant variant-specific differences in the distribution of binding sites in the BA.1 and BA.2 trimers. This study provided a structural characterization of the predicted cryptic pockets and captured the experimentally known allosteric sites, revealing the critical role of conformational plasticity in modulating the distribution and cross-talk between functional binding sites. We found that mutational and dynamic changes in the BA.1 variant can induce the remodeling and stabilization of a known druggable pocket in the N-terminal domain, while this pocket is drastically altered and may no longer be available for ligand binding in the BA.2 variant. Our results predicted the experimentally known allosteric site in the receptor-binding domain that remains stable and ranks as the most favorable site in the conformational ensembles of the BA.2 variant but could become fragmented and less probable in BA.1 conformations. We also uncovered several cryptic pockets formed at the inter-domain and inter-protomer interface, including functional regions of the S2 subunit and stem helix region, which are consistent with the known role of pocket residues in modulating conformational transitions and antibody recognition. The results of this study are particularly significant for understanding the dynamic and network features of the universe of available binding pockets in spike proteins, as well as the effects of the Omicron-variant-specific modulation of preferential druggable pockets. The exploration of predicted druggable sites can present a new and previously underappreciated opportunity for therapeutic interventions for Omicron variants through the conformation-selective and variant-specific targeting of functional sites involved in allosteric changes

    Algebraic Reasoning and Conceptual Understanding: A Mixed Methods Comparison of In-Person and Virtual Classroom Strategies

    Get PDF
    Algebraic reasoning is the beginning school of thought to critical thinking. Employers are looking for this 21st century skill. The purpose of this research was to investigate equity in mathematics education using the NCTM Teaching and Learnings Beliefs Survey. Four area were studied: the number of years in education, the degree earned, the grade level taught in education, and the number of years in an educator’s teaching position. A mixed methods inventory was used. Most results were not rejected in this study. Two statements in the survey warranted a discussion. Recommendations were made for further research

    Water Resources Allocation and Agriculture

    Get PDF
    The book brings together a range of leading scholars and practitioners to compile an international account of water allocation policies supporting a transition to sustainable water use in regions where agriculture is the dominant water use. In Section 1, the collection canvasses five key cross-cutting issues shaping the challenge of sustainable water allocation policy, such as legal and economic perspectives, the role of politics, the setting of environmental flows, and the importance of indigenous rights. Section 2 presents 13 national, state and transboundary case studies of water allocation policy, covering cases from Europe, the Americas, Central Asia, the Middle East and the Pacific region. These case studies highlight novel and innovative elements of water allocation regimes, which respond to the cross-cutting issues addressed in Section 1, as well as local challenges and social and environmental imperatives. The book provides a comprehensive account of water allocation in a range of international settings and provides a reference point for practitioners and scholars worldwide wishing to draw on the latest advances on how to design and implement sustainable water allocation systems
    • …
    corecore