IA Scholar Query: Fork Algebras.
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Internet Archive Scholar query results feedeninfo@archive.orgThu, 29 Sep 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440The Geometry of the Bing Involution
https://scholar.archive.org/work/2madzpe3dfd4dmdk4b4efnli7a
In 1952 Bing published a wild (not topologically conjugate to smooth) involution I of the 3-sphere S^3. But exactly how wild is it, analytically? We prove that any involution I^h, topologically conjugate to I, must have a weakly exponential modulus of continuity. Specifically, there exists a constant c > 1.167 such that for a sequence of δs converging to zero, δ > 0, there are points x,y ∈ S^3 with dist(x,y) < δ, yet dist(I^h(x), I^h(y)) > ϵ, where δ^-1 = c^√(ϵ^-1), and dist is the usual Riemannian distance on S^3. In particular, I^h stretches distance much more than a Lipschitz function (δ^-1 = c^'ϵ^-1) or a Hölder function (δ^-1 = c^" (ϵ^-1)^p, 1 < p < ∞). Bing's original construction and known alternatives (see text) for I have a modulus of continuity δ^-1 > c √(2)^ϵ^-1, so the theorem is reasonably tight–we prove the modulus must be at least weakly exponential, whereas the truth may be exponential. Using the same technique we analyze a large class of "ramified" Bing involutions and show, as a scholium, that given any function f: ℝ^+ →ℝ^+, no matter how rapid its growth, we can find a corresponding involution J of the 3-sphere such that any topological conjugate J^h of J must have a modulus of continuity δ^-1(ϵ^-1) growing faster than f (near infinity). There is a literature on inherent differentiability (references in text) but as far as the authors know the subject of inherent modulus of continuity is new. Dedicated to R.H. Bing's life work on the 70th anniversary of his involution.Michael Freedman, Michael Starbirdwork_2madzpe3dfd4dmdk4b4efnli7aThu, 29 Sep 2022 00:00:00 GMTA High-Performance Design for Hierarchical Parallelism in the QMCPACK Monte Carlo code
https://scholar.archive.org/work/mn33v7onvfcq3jvhnlinaujr4m
We introduce a new high-performance design for parallelism within the Quantum Monte Carlo code QMCPACK. We demonstrate that the new design is better able to exploit the hierarchical parallelism of heterogeneous architectures compared to the previous GPU implementation. The new version is able to achieve higher GPU occupancy via the new concept of crowds of Monte Carlo walkers, and by enabling more host CPU threads to effectively offload to the GPU. The higher performance is expected to be achieved independent of the underlying hardware, significantly improving developer productivity and reducing code maintenance costs. Scientific productivity is also improved with full support for fallback to CPU execution when GPU implementations are not available or CPU execution is more optimal.Ye Luo, Peter Doak, Paul Kentwork_mn33v7onvfcq3jvhnlinaujr4mThu, 29 Sep 2022 00:00:00 GMTWeak heirs, coheirs and the Ellis semigroups
https://scholar.archive.org/work/tr7mf62veng6hgj4d3ijl62oga
Assume G≺ H are groups and A⊆ P(G), B⊆ P(H) are algebras of sets closed under left group translation. Under some additional assumptions we find algebraic connections between the Ellis [semi]groups of the G-flow S( A) and the H-flow S( B). We apply these results in the model theoretic context. Namely, assume G is a group definable in a model M and M≺^* N. Using weak heirs and weak coheirs we point out some algebraic connections between the Ellis semigroups S_ext,G(M) and S_ext,G(N). Assuming every minimal left ideal in S_ext,G(N) is a group we prove that the Ellis groups of S_ext,G(M) are isomorphic to closed subgroups of the Ellis groups of S_ext,G(N).Adam Malinowski, Ludomir Newelskiwork_tr7mf62veng6hgj4d3ijl62ogaThu, 29 Sep 2022 00:00:00 GMTOn NSOP_2 Theories
https://scholar.archive.org/work/ye23wvxiqbfwdkuqvlfglg5i24
Answering a question of Džamonja and Shelah, we show that every NSOP_2 theory is NSOP_1.Scott Mutchnikwork_ye23wvxiqbfwdkuqvlfglg5i24Wed, 28 Sep 2022 00:00:00 GMTRoadmap on Electronic Structure Codes in the Exascale Era
https://scholar.archive.org/work/72kg6tpwnncrxlfs77h32a3zde
Electronic structure calculations have been instrumental in providing many important insights into a range of physical and chemical properties of various molecular and solid-state systems. Their importance to various fields, including materials science, chemical sciences, computational chemistry and device physics, is underscored by the large fraction of available public supercomputing resources devoted to these calculations. As we enter the exascale era, exciting new opportunities to increase simulation numbers, sizes, and accuracies present themselves. In order to realize these promises, the community of electronic structure software developers will however first have to tackle a number of challenges pertaining to the efficient use of new architectures that will rely heavily on massive parallelism and hardware accelerators. This roadmap provides a broad overview of the state-of-the-art in electronic structure calculations and of the various new directions being pursued by the community. It covers 14 electronic structure codes, presenting their current status, their development priorities over the next five years, and their plans towards tackling the challenges and leveraging the opportunities presented by the advent of exascale computing.Vikram Gavini, Stefano Baroni, Volker Blum, David R. Bowler, Alexander Buccheri, James R. Chelikowsky, Sambit Das, William Dawson, Pietro Delugas, Mehmet Dogan, Claudia Draxl, Giulia Galli, Luigi Genovese, Paolo Giannozzi, Matteo Giantomassi, Xavier Gonze, Marco Govoni, Andris Gulans, François Gygi, John M. Herbert, Sebastian Kokott, Thomas D. Kühne, Kai-Hsin Liou, Tsuyoshi Miyazaki, Phani Motamarri, Ayako Nakata, John E. Pask, Christian Plessl, Laura E. Ratcliff, Ryan M. Richard, Mariana Rossi, Robert Schade, Matthias Scheffler, Ole Schütt, Phanish Suryanarayana, Marc Torrent, Lionel Truflandier, Theresa L. Windus, Qimen Xu, Victor W.-Z. Yu, Danny Perezwork_72kg6tpwnncrxlfs77h32a3zdeMon, 26 Sep 2022 00:00:00 GMTBayesian Modeling of Time-varying Parameters Using Regression Trees
https://scholar.archive.org/work/qlg2lermdfdbvhpx62765ti4le
In light of widespread evidence of parameter instability in macroeconomic models, many time-varying parameter (TVP) models have been proposed. This paper proposes a nonparametric TVP-VAR model using Bayesian Additive Regression Trees (BART). The novelty of this model arises from the law of motion driving the parameters being treated nonparametrically. This leads to great flexibility in the nature and extent of parameter change, both in the conditional mean and in the conditional variance. In contrast to other nonparametric and machine learning methods that are black box, inference using our model is straightforward because, in treating the parameters rather than the variables nonparametrically, the model remains conditionally linear in the mean. Parsimony is achieved through adopting nonparametric factor structures and use of shrinkage priors. In an application to US macroeconomic data, we illustrate the use of our model in tracking both the evolving nature of the Phillips curve and how the effects of business cycle shocks on inflationary measures vary nonlinearly with movements in uncertainty.Niko Hauzenberger, Florian Huber, Gary Koop, James Mitchellwork_qlg2lermdfdbvhpx62765ti4leSat, 24 Sep 2022 00:00:00 GMTConcurrent Graph Queries on the Lucata Pathfinder
https://scholar.archive.org/work/qzmymrz4abf2zg7unbkeorqrae
High-performance analysis of unstructured data like graphs now is critical for applications ranging from business intelligence to genome analysis. Towards this, data centers hold large graphs in memory to serve multiple concurrent queries from different users. Even a single analysis often explores multiple options. Current computing architectures often are not the most time- or energy-efficient solutions. The novel Lucata Pathfinder architecture tackles this problem, combining migratory threads for low-latency reading with memory-side processing for high-performance accumulation. One hundred to 750 concurrent breadth-first searches (BFS) all achieve end-to-end speed-ups of 81 to 97 RedisGraph running on a large Intel-based server, the Pathfinder achieves a 19× speed-up running 128 BFS queries concurrently. The Pathfinder also efficiently supports a mix of concurrent analyses, demonstrated with connected components and BFS.Emory Smith and Shannon Kuntz and Jason Riedy and Martin Deneroffwork_qzmymrz4abf2zg7unbkeorqraeFri, 23 Sep 2022 00:00:00 GMTSimplicity of the automorphism group of fields with operators
https://scholar.archive.org/work/jijeqrfdqvhw7dxpr23vlzqk5e
We adapt a proof of Lascar in order to show the simplicity of the group of automorphisms fixing pointwise all non-generic elements for a class of uncountable models of suitable theories of fields with operators.Thomas Blossier, Zoé Chatzidakis, Charlotte Hardouin, Amador Martin-Pizarrowork_jijeqrfdqvhw7dxpr23vlzqk5eThu, 22 Sep 2022 00:00:00 GMTThe Objective Function: Science and Society in the Age of Machine Intelligence
https://scholar.archive.org/work/2unyehnlczcpfnkcxvnjp6wxye
Machine intelligence, or the use of complex computational and statistical practices to make predictions and classifications based on data representations of phenomena, has been applied to domains as disparate as criminal justice, commerce, medicine, media and the arts, mechanical engineering, among others. How has machine intelligence become able to glide so freely across, and to make such waves for, these domains? In this dissertation, I take up that question by ethnographically engaging with how the authority of machine learning has been constructed such that it can influence so many domains, and I investigate what the consequences are of it being able to do so. By examining the workplace practices of the applied machine learning researchers who produce machine intelligence, those they work with, and the artifacts they produce. The dissertation begins by arguing that machine intelligence proceeds from a naive form of empiricism with ties to positivist intellectual traditions of the 17th and 18th centuries. This naive empiricism eschews other forms of knowledge and theory formation in order for applied machine learning researchers to enact data performances that bring objects of analysis into existence as entities capable of being subjected to machine intelligence. By data performances, I mean generative enactments which bring into existence that which machine intelligence purports to analyze or describe. The enactment of data performances is analyzed as an agential cut into a representational field that produces both stable claims about the world and the interpretive frame in which those claims can hold true. The dissertation also examines how machine intelligence depends upon a range of accommodations from other institutions and organizations, from data collection and processing to organizational commitments to support the work of applied machine learning researchers.Emanuel Mosswork_2unyehnlczcpfnkcxvnjp6wxyeWed, 21 Sep 2022 00:00:00 GMTProtocorks and monopole Floer homology
https://scholar.archive.org/work/hgvvbavqkrg2lbahqs2bzty2a4
We introduce and study a class of compact 4-manifolds with boundary that we call protocorks. Any exotic pair of simply connected closed 4-manifolds is related by a protocork twist, moreover, any cork is supported by a protocork. We prove a theorem on the relative Seiberg-Witten invariants of a protocork before and after twisting and a splitting theorem on the Floer homology of protocork boundaries. As a corollary we improve a theorem by Morgan and Szabó regarding the variation of Seiberg-Witten invariants with an upper bound which depends only on the topology of the data. Moreover we show that for any cork, only the reduced Floer homology of its boundary contributes to the variation of the Seiberg-Witten invariants after a cork twist.Roberto Laduwork_hgvvbavqkrg2lbahqs2bzty2a4Tue, 20 Sep 2022 00:00:00 GMTMolecular chirality and its monitoring by ultrafast X-ray pulses
https://scholar.archive.org/work/a7rrmyayfzd2lakhtbhz4kagcq
Major advances in X-ray sources including the development of circularly polarized and orbital angular momentum pulses make it possible to probe matter chirality at unprecedented energy regimes and with Angstr\"om and femtosecond spatiotemporal resolutions. We survey the theory of stationary and time-resolved nonlinear chiral measurements that can be carried out in the X-ray regime using tabletop X-ray sources or large scale (XFEL, synchrotron) facilities. A variety of possible signals and their information content are surveyed.Jeremy R. Rouxel, Shaul Mukamelwork_a7rrmyayfzd2lakhtbhz4kagcqMon, 19 Sep 2022 00:00:00 GMTSelection on treatment in the target population of generalizabillity and transportability analyses
https://scholar.archive.org/work/xnz5sbee5ng7nmu5sjeitrtxku
Investigators are increasingly using novel methods for extending (generalizing or transporting) causal inferences from a trial to a target population. In many generalizability and transportability analyses, the trial and the observational data from the target population are separately sampled, following a non-nested trial design. In practical implementations of this design, non-randomized individuals from the target population are often identified by conditioning on the use of a particular treatment, while individuals who used other candidate treatments for the same indication or individuals who did not use any treatment are excluded. In this paper, we argue that conditioning on treatment in the target population changes the estimand of generalizability and transportability analyses and potentially introduces serious bias in the estimation of causal estimands in the target population or the subset of the target population using a specific treatment. Furthermore, we argue that the naive application of marginalization-based or weighting-based standardization methods does not produce estimates of any reasonable causal estimand. We use causal graphs and counterfactual arguments to characterize the identification problems induced by conditioning on treatment in the target population and illustrate the problems using simulated data. We conclude by considering the implications of our findings for applied work.Yu-Han Chiu, Issa J. Dahabrehwork_xnz5sbee5ng7nmu5sjeitrtxkuMon, 19 Sep 2022 00:00:00 GMTPreservation of NATP
https://scholar.archive.org/work/p5apcz32r5hblhxnfmaqlbchh4
We prove several preservation theorems for NATP and furnish several examples of NATP. First, we prove preservation of NATP for the parametrization and sum of the theories of Fraïssé limits of Fraïssé classes satisfying strong amalgamation property. Second, we prove preservation of NATP for two kinds of dense/co-dense expansions, that is, the theories of lovely pairs and of H-structures for geometric theories and dense/co-dense expansion on vector spaces. Third, we prove preservation of NATP for the generic predicate expansion and the pair of an algebraically closed field and its distinguished subfield; for the latter, not only NATP, but also preservations of NTP_1 and NTP_2 are considered. Fourth, we present some proper examples of NATP using the results proved in this paper. Most of all, we show that the model companion of the theory of algebraically closed fields with circular orders (ACFO) is NATP.JinHoo Ahn, Joonhee Kim, Hyoyoon Lee, Junguk Leework_p5apcz32r5hblhxnfmaqlbchh4Mon, 19 Sep 2022 00:00:00 GMTEnvironmental governance investment and Air Quality: Based on China's provincial panel data
https://scholar.archive.org/work/ke52svia7zfh7hcdu2qbexcusq
Ambient air pollution is an important environmental problem that impacts the health and sustainable development of human beings. Many measures have been taken by governments to decrease air pollution. This paper focuses on whether government investment has a positive effect on air quality. Based on China's environmental statistics from 2003 to 2020, the Spatiotemporal Weighted Regression Model is used to observe the spatiotemporal correlation between environmental governance investment and air quality in different provinces in China, finding that there is a negative time-space correlation between environmental governance investment and air quality. In addition, environmental governance investment will not immediately improve air quality, and air pollution has the characteristics of spatial overflow that the pollution between regions affect each other. Then, to further research governments how to deal with environmental protection, configuration analysis has been used, and finds out four high-performance paths for environmental governance of China's provinces. At the end of this research, we put forward four suggestions for air protection. Firstly, government should formulate long-term air governance policies. Secondly, government environmental governance of air pollution should pay attention to the cooperativity of environmental governance between regions. Thirdly, the third sectors, companies and the public should be encouraged in air protection. Fourthly, government should build a whole-process air governance strategy.Zhendong Wu, Chengmeng Zhang, Yang Li, Chen Xu, Yang Wang, Gong Chenwork_ke52svia7zfh7hcdu2qbexcusqMon, 19 Sep 2022 00:00:00 GMTGl2 Foam Functoriality and Skein Positivity
https://scholar.archive.org/work/7652vo7rhvg67dt3uzkuzef3km
We prove full functoriality of Khovanov homology for tangled framed gl2 webs. We use this functoriality result to prove a strong positivity result for (orientable) surface skein algebras. The argument goes categorical and consists in proving that so-called linear complexes are stable under superposition.Hoel Queffelecwork_7652vo7rhvg67dt3uzkuzef3kmMon, 19 Sep 2022 00:00:00 GMTOn minimal flows and definable amenability in some distal NIP theories
https://scholar.archive.org/work/r7n6yx4wyzdajdgl3vwuae5la4
We study the definable topological dynamics (G(M), S_G(M)) of a definable group acting on its type space, where M is either an o-minimal structure or a p-adically closed field, and G a definable amenable group. We focus on the problem raised by Neweslki of whether weakly generic types coincide with almost periodic types, showing that the answer is positive when G has boundedly many global weakly generic types. We also give two "minimal counterexamples" where G has unboundedly many global weakly generic types, extending the main results of "On minimal flows, definably amenable groups, and o-minimality" to a more general context.Ningyuan Yao, Zhentao Zhangwork_r7n6yx4wyzdajdgl3vwuae5la4Sun, 18 Sep 2022 00:00:00 GMTPerformance Analysis of Reconfigurable Intelligent Surface Assisted Two-Way NOMA Networks
https://scholar.archive.org/work/qxjtlnywbvazbkb3wo6ravio7q
This paper investigates the performance of reconfigurable intelligent surface assisted two-way non-orthogonal multiple access (RIS-TW-NOMA) networks, where a pair of users exchange their information through a RIS. The influence of imperfect successive interference cancellation on RIS-TW-NOMA is taken into account. To evaluate the potential performance of RIS-TW-NOMA, we derive the exact and asymptotic expressions of outage probability and ergodic rate for a pair of users. Based on the analytical results, the diversity orders and high signal-to-noise ratio (SNR) slopes are obtained in the high SNR regime, which are closely related to the number of RIS elements. Additionally, we analyze the system throughput and energy efficiency of RIS-TW-NOMA networks in both delay-limited and delay-tolerant transmission modes. Numerical results indicate that: 1) The outage behaviors and ergodic rate of RIS-TW-NOMA are superior to that of RIS-TW-OMA and two-way relay OMA (TWR-OMA); 2) As the number of RIS elements increases, the RIS-TW-NOMA networks are capable of achieving the enhanced outage performance; and 3) By comparing with RIS-TW-OMA and TWR-OMA networks, the energy efficiency and system throughput of RIS-TW-NOMA has obvious advantages.Ziwei Liu, Xinwei Yue, Chao Zhang, Yuanwei Liu, Yuanyuan Yao, Yafei Wang, Zhiguo Dingwork_qxjtlnywbvazbkb3wo6ravio7qSun, 18 Sep 2022 00:00:00 GMTSymbolic Execution for Randomized Programs
https://scholar.archive.org/work/3bqd2dwsqrfm7ijqhmzzatn6vu
We propose a symbolic execution method for programs that can draw random samples. In contrast to existing work, our method can verify randomized programs with unknown inputs and can prove probabilistic properties that universally quantify over all possible inputs. Our technique augments standard symbolic execution with a new class of probabilistic symbolic variables, which represent the results of random draws, and computes symbolic expressions representing the probability of taking individual paths. We implement our method on top of the KLEE symbolic execution engine alongside multiple optimizations and use it to prove properties about probabilities and expected values for a range of challenging case studies written in C++, including Freivalds' algorithm, randomized quicksort, and a randomized property-testing algorithm for monotonicity. We evaluate our method against Psi, an exact probabilistic symbolic inference engine, and Storm, a probabilistic model checker, and show that our method significantly outperforms both tools.Zachary Susag, Sumit Lahiri, Justin Hsu, Subhajit Roywork_3bqd2dwsqrfm7ijqhmzzatn6vuFri, 16 Sep 2022 00:00:00 GMTSupernilpotent groups and 3-supernilpotent loops
https://scholar.archive.org/work/x3okwbm4wrbhhbs4rgjxid2iqe
We find a short equational basis for the variety of 3-supernilpotent loops. We also present a conceptually simple proof that k-nilpotence and k-supernilpotence are equivalent for groups. Connections between 3-supernilpotent loops, Moufang loops, code loops, automorphic loops and AIM loops are explored.David Stanovský, Petr Vojtěchovskýwork_x3okwbm4wrbhhbs4rgjxid2iqeFri, 16 Sep 2022 00:00:00 GMTLocality and error correction in quantum dynamics with measurement
https://scholar.archive.org/work/el2kgcz2qvhjjkiihua3w4olxa
The speed of light c sets a strict upper bound on the speed of information transfer in both classical and quantum systems. In nonrelativistic systems, the Lieb-Robinson Theorem imposes an emergent speed limit v ≪ c, establishing locality under unitary quantum dynamics and constraining the time needed to perform useful quantum tasks. We extend the Lieb-Robinson Theorem to quantum dynamics with measurements. In contrast to the general expectation that measurements can arbitrarily violate spatial locality, we find at most an (M + 1)-fold enhancement to the speed of quantum information v, provided the outcomes of M local measurements are known; this holds even when classical communication is instantaneous. Our bound is asymptotically optimal, and saturated by existing measurement-based protocols. We tightly constrain the resource requirements for quantum computation, error correction, teleportation, and generating entangled resource states (Bell, GHZ, W, and spin-squeezed states) from short-range entangled states. Our results impose limits on the use of measurements and active feedback to speed up quantum information processing, resolve fundamental questions about the nature of measurements in quantum dynamics, and constrain the scalability of a wide range of proposed quantum technologies.Aaron J. Friedman, Chao Yin, Yifan Hong, Andrew Lucaswork_el2kgcz2qvhjjkiihua3w4olxaFri, 16 Sep 2022 00:00:00 GMT