IA Scholar Query: Shadowed Sets and Related Algebraic Structures.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgMon, 08 Aug 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Computing characteristic polynomials of hyperplane arrangements with symmetries
https://scholar.archive.org/work/flukl4df6zguxns3kio434di7a
We introduce a new algorithm computing the characteristic polynomials of hyperplane arrangements which exploits their underlying symmetry groups. Our algorithm counts the chambers of an arrangement as a byproduct of computing its characteristic polynomial. We showcase our julia implementation, based on OSCAR, on examples coming from hyperplane arrangements with applications to physics and computer science.Taylor Brysiewicz, Holger Eble, Lukas Kühnework_flukl4df6zguxns3kio434di7aMon, 08 Aug 2022 00:00:00 GMTSynthetic fibered (∞,1)-category theory
https://scholar.archive.org/work/5dh3q2p2drc3noltrbputvd5zq
We study cocartesian fibrations in the setting of the synthetic (∞,1)-category theory developed in the simplicial type theory introduced by Riehl and Shulman. Our development culminates in a Yoneda Lemma for cocartesian fibrations.Ulrik Buchholtz, Jonathan Weinbergerwork_5dh3q2p2drc3noltrbputvd5zqMon, 08 Aug 2022 00:00:00 GMTThe dual Lagrangian fibration of known hyper-Kähler manifolds
https://scholar.archive.org/work/5x3tu2263rbufijr262qsj2uxa
Given a Lagrangian fibration π : X →ℙ^n of a compact hyper-Kähler manifold of K3^[n], Kum_n, OG10 or OG6-type, we construct a natural compactification of its dual torus fibration. Specifically, this compactification is given by a quotient of X by certain automorphisms acting trivially on the second cohomology and respecting the Lagrangian fibration. It is a compact hyper-Kähler orbifold with identical period mapping behavior as X.Yoon-Joo Kimwork_5x3tu2263rbufijr262qsj2uxaMon, 08 Aug 2022 00:00:00 GMTFinite Semisimple Module 2-Categories
https://scholar.archive.org/work/gr4tgmr32rdadmhcizkfktojm4
Let ℭ be a multifusion 2-category. We show that every finite semisimple ℭ-module 2-category is canonically enriched over ℭ. Using this enrichment, we prove that every finite semisimple ℭ-module 2-category is equivalent to the 2-category of modules over an algebra in ℭ.Thibault D. Décoppetwork_gr4tgmr32rdadmhcizkfktojm4Mon, 08 Aug 2022 00:00:00 GMTTorus conformal blocks and Casimir equations in the necklace channel
https://scholar.archive.org/work/tey3dwp2obczhmsqv3r65bhzmm
We consider the conformal block decomposition in arbitrary exchange channels of a two-dimensional conformal field theory on a torus. The channels are described by diagrams built of a closed loop with external legs (a necklace sub-diagram) and trivalent vertices forming trivalent trees attached to the necklace. Then, the n-point torus conformal block in any channel can be obtained by acting with a number of OPE operators on the k-point torus block in the necklace channel at k=1,...,n. Focusing on the necklace channel, we go to the large-c regime, where the Virasoro algebra truncates to the sl(2, ℝ) subalgebra, and obtain the system of the Casimir equations for the respective k-point global conformal block. In the plane limit, when the torus modular parameter q→ 0, we explicitly find the Casimir equations on a plane which define the (k+2)-point global conformal block in the comb channel. Finally, we formulate the general scheme to find Casimir equations for global torus blocks in arbitrary channels.K.B. Alkalaev, Semyon Mandrygin, Mikhail Pavlovwork_tey3dwp2obczhmsqv3r65bhzmmSat, 06 Aug 2022 00:00:00 GMTTesting Symmergent gravity through the shadow image and weak field photon deflection by a rotating black hole using the M87^* and Sgr. A^* results
https://scholar.archive.org/work/ab3s36pu2bgj5dsa2fdzw5zbzy
Motivated by recent work on the Symmergent black hole [Phys. Dark Univ. 10.1016/j.dark.2021.100900, 2021], here we study spinning black holes in Symmergent gravity, with spin parameter a. The goal is to uncover the deviations caused by the Symmergent gravity parameters relative to the known Kerr solution. To this aim, we first investigate the deviations in the photon sphere and shadow size. The EHT data was used to find constraints to c_O that fit well in M87* within ±1σ than in Sgr. A*. We also found that depending on the sign of the quadratic curvature coefficient c_O, the increase in photon radius results in a decrease in shadow radius. Exploring the Symmergent effects on the geodesics of time-like particles, we find that these are more sensitive to the effects than null particles. To broaden the scope of the study, we also analyzed the weak field limit of the deflection angles, where we used the Gauss-Bonnet theorem with the consideration of the finite distance of the source and the receiver to the lensing object. We have shown how the Symmergent gravity parameter c_O, which is proportional to the number difference between fermions and bosons, affects the deflection angle. Remarkably, the distance of the receiver (or source) greatly affects the angle. Finally, we also analyze the Symmergent gravity effects on the rotating black hole as it acts as a particle accelerator.Reggie C. Pantig, Ali Övgün, Durmuş Demirwork_ab3s36pu2bgj5dsa2fdzw5zbzyFri, 05 Aug 2022 00:00:00 GMTOn the asymptotic expansion for the relative Reshetikhin-Turaev invariants of fundamental shadow link pairs
https://scholar.archive.org/work/jjyau7w4tzezjcgybdc7frwfqy
We verify the asymptotic expansion conjecture of the relative Reshetikhin-Turaev invariants proposed in for all pairs (M,L) satisfying the property that M∖ L is homeomorphic to some fundamental shadow link complement, with cone angles sufficiently small. In particular, the asymptotics of the invariants captures the complex volume and the twisted Reidemeister torsion of the manifold M∖ L associated with the hyperbolic cone structure determined by the sequence of colorings of the framed link L.Tushar Pandey, Ka Ho Wongwork_jjyau7w4tzezjcgybdc7frwfqyFri, 05 Aug 2022 00:00:00 GMTNovel architectures for noise-resilient superconducting qubits
https://scholar.archive.org/work/qcsw2hw5ofgmpp3g5avo2ybst4
Great interest revolves around the development of new strategies to efficiently store and manipulate quantum information in a robust and decoherence-free fashion. Several proposals have been put forward to encode information into qubits that are simultaneously insensitive to relaxation and to dephasing processes. Among all, given their versatility and high-degree of control, superconducting qubits have been largely investigated in this direction. Here, we present a survey on the basic concepts and ideas behind the implementation of novel superconducting circuits with intrinsic protection against decoherence at a hardware level. In particular, the main focus is on multi-mode superconducting circuits, the paradigmatic example being the so-called 0-π circuit. We report on their working principle and possible physical implementations based on conventional Josephson elements, presenting recent experimental realizations, discussing both fabrication methods and characterizations.Alessio Calzona, Matteo Carregawork_qcsw2hw5ofgmpp3g5avo2ybst4Thu, 04 Aug 2022 00:00:00 GMTNISQ: Error Correction, Mitigation, and Noise Simulation
https://scholar.archive.org/work/du5b73nopnc45mqa6uwevt6b2e
Error-correcting codes were invented to correct errors on noisy communication channels. Quantum error correction (QEC), however, may have a wider range of uses, including information transmission, quantum simulation/computation, and fault-tolerance. These invite us to rethink QEC, in particular, about the role that quantum physics plays in terms of encoding and decoding. The fact that many quantum algorithms, especially near-term hybrid quantum-classical algorithms, only use limited types of local measurements on quantum states, leads to various new techniques called Quantum Error Mitigation (QEM). This work examines the task of QEM from several perspectives. Using some intuitions built upon classical and quantum communication scenarios, we clarify some fundamental distinctions between QEC and QEM. We then discuss the implications of noise invertibility for QEM, and give an explicit construction called Drazin-inverse for non-invertible noise, which is trace preserving while the commonly-used Moore-Penrose pseudoinverse may not be. Finally, we study the consequences of having an imperfect knowledge about the noise, and derive conditions when noise can be reduced using QEM.Ningping Cao, Junan Lin, David Kribs, Yiu-Tung Poon, Bei Zeng, Raymond Laflammework_du5b73nopnc45mqa6uwevt6b2eThu, 04 Aug 2022 00:00:00 GMTCalogero-Moser spaces vs unipotent representations
https://scholar.archive.org/work/jmtyfwgcknd6ph3ms2ljroatdy
Lusztig's classification of unipotent representations of finite reductive groups depends only on the associated Weyl group W (endowed with its Frobenius automorphism). All the structural questions (families, Harish-Chandra series, partition into blocks...) have an answer in a combinatorics that can be entirely built directly from W. Over the years, we have noticed that the same combinatorics seems to be encoded in the Poisson geometry of a Calogero-Moser space associated with W (roughly speaking, families correspond to ℂ^×-fixed points, Harish-Chandra series correspond to symplectic leaves, blocks correspond to symplectic leaves in the fixed point subvariety under the action of a root of unity). The aim of this survey is to gather all these observations, state precise conjectures and provide general facts and examples supporting these conjectures.Cédric Bonnaféwork_jmtyfwgcknd6ph3ms2ljroatdyThu, 04 Aug 2022 00:00:00 GMTNoise Effects on Pade Approximants and Conformal Maps
https://scholar.archive.org/work/wyu4yxafxjei3knty2eh3ktqja
We analyze the properties of Pade and conformal map approximants for functions with branch points, in the situation where the expansion coefficients are only known with finite precision or are subject to noise. We prove that there is a universal scaling relation between the strength of the noise and the expansion order at which Pade or the conformal map breaks down. We illustrate this behavior with some physically relevant model test functions and with two non-trivial physical examples where the relevant Riemann surface has complicated structureOvidiu Costin, Gerald V. Dunne, Max Meynigwork_wyu4yxafxjei3knty2eh3ktqjaThu, 04 Aug 2022 00:00:00 GMTThe geometry of massive particle surfaces
https://scholar.archive.org/work/fg6vnqgsvrbd5dpx67pjugau6e
We propose a generalization of Claudel, Virbhadra, and Ellis photon surfaces to the case of massive charged particles, considering a timelike hypersurface such that any worldline of a particle with mass m, electric charge q and fixed total energy ℰ, initially touching it, will remain in this hypersurface forever. This definition does not directly appeal to the equations of motion, but instead make use of partially umbilic nature of the surface geometry. Such an approach should be especially useful in the case of non-integrable equations of motion. It may be applied in the theory of non-thin accretion discs, and also may serve a new tool for some general problems, such as uniqueness theorems, Penrose inequalities and hidden symmetries. The condition for the stability of the worldlines is derived, which reduces to differentiation along the flow of surfaces of a certain energy. We consider a number of examples of electrovacuum and dilaton solutions, find conditions for marginally stable orbits, regions of stable or unstable spherical orbits, stable and unstable photon surfaces, and solutions satisfying the no-force condition.Kirill Kobialko, Igor Bogush, Dmitri Gal'tsovwork_fg6vnqgsvrbd5dpx67pjugau6eThu, 04 Aug 2022 00:00:00 GMTAlmost Consistent Systems of Linear Equations
https://scholar.archive.org/work/4ktke6denbdqbmcnglhojd3t7e
Checking whether a system of linear equations is consistent is a basic computational problem with ubiquitous applications. When dealing with inconsistent systems, one may seek an assignment that minimizes the number of unsatisfied equations. This problem is NP-hard and UGC-hard to approximate within any constant even for two-variable equations over the two-element field. We study this problem from the point of view of parameterized complexity, with the parameter being the number of unsatisfied equations. We consider equations defined over Euclidean domains - a family of commutative rings that generalize finite and infinite fields including the rationals, the ring of integers, and many other structures. We show that if every equation contains at most two variables, the problem is fixed-parameter tractable. This generalizes many eminent graph separation problems such as Bipartization, Multiway Cut and Multicut parameterized by the size of the cutset. To complement this, we show that the problem is W[1]-hard when three or more variables are allowed in an equation, as well as for many commutative rings that are not Euclidean domains. On the technical side, we introduce the notion of important balanced subgraphs, generalizing important separators of Marx [Theor. Comput. Sci. 2006] to the setting of biased graphs. Furthermore, we use recent results on parameterized MinCSP [Kim et al., SODA 2021] to efficiently solve a generalization of Multicut with disjunctive cut requests.Konrad K. Dabrowski, Peter Jonsson, Sebastian Ordyniak, George Osipov, Magnus Wahlströmwork_4ktke6denbdqbmcnglhojd3t7eThu, 04 Aug 2022 00:00:00 GMTNeutrinos and their interactions with matter
https://scholar.archive.org/work/zmfdcvwljzaiffn7votpgfdxga
We have presented a review of the properties of neutrinos and their interactions with matter. The different (anti)neutrino processes like the quasielastic scattering, inelastic production of mesons and hyperons, and the deep inelastic scattering from the free nucleons are discussed and the results for the scattering cross sections are presented. The polarization observables for the leptons and hadrons produced in the final state, in the case of quasielastic scattering, are also studied. The importance of nuclear medium effects in the low, intermediate and high energy regions, in the above processes along with the processes of the coherent neutrino-nucleus scattering, coherent meson production, and trident production, have been highlighted. In some cases the results of the cross sections are also given and compared with the available experimental data as well as with the predictions in the different theoretical models. This study would be helpful in understanding the (anti)neutrino interaction cross section with matter in the few GeV energy region relevant to the next generation experiments like DUNE, Hyper-Kamiokande, and other experiments with accelerator and atmospheric neutrinos. We have emphasized the need of better theoretical models for some of these processes for studying the nuclear medium effects in nuclei.M. Sajjad Athar, A. Fatima, S. K. Singhwork_zmfdcvwljzaiffn7votpgfdxgaWed, 03 Aug 2022 00:00:00 GMTLearning quantum systems via out-of-time-order correlators
https://scholar.archive.org/work/vfmgwfe6r5fifkmn45ap52xbwe
Learning the properties of dynamical quantum systems underlies applications ranging from nuclear magnetic resonance spectroscopy to quantum device characterization. A central challenge in this pursuit is the learning of strongly-interacting systems, where conventional observables decay quickly in time and space, limiting the information that can be learned from their measurement. In this work, we introduce a new class of observables into the context of quantum learning -- the out-of-time-order correlator -- which we show can substantially improve the learnability of strongly-interacting systems by virtue of displaying informative physics at large times and distances. We identify two general scenarios in which out-of-time-order correlators provide a significant advantage for learning tasks in locally-interacting systems: (i) when experimental access to the system is spatially-restricted, for example via a single "probe" degree of freedom, and (ii) when one desires to characterize weak interactions whose strength is much less than the typical interaction strength. We numerically characterize these advantages across a variety of learning problems, and find that they are robust to both read-out error and decoherence. Finally, we introduce a binary classification task that can be accomplished in constant time with out-of-time-order measurements. In a companion paper, we prove that this task is exponentially hard with any adaptive learning protocol that only involves time-ordered operations.Thomas Schuster and Murphy Niu and Jordan Cotler and Thomas O'Brien and Jarrod R. McClean and Masoud Mohseniwork_vfmgwfe6r5fifkmn45ap52xbweWed, 03 Aug 2022 00:00:00 GMT"I would be afraid to be a bad CS teacher": Factors Influencing Participation in Pre-Service Secondary CS Teacher Education
https://scholar.archive.org/work/nio3ce7j4rbx7jupae3jw3u5jq
Objectives. Teachers are essential to making computing education available to students. A key place to sustainably prepare computer science (CS) teachers is in pre-service preparation programs, which are often required for certification in the United States. Prior work has examined many reasons that people choose to become teachers -or choose not to -but little prior work has examined factors that shape the pursuit of CS certifications in pre-service in particular. Participants. We recruited five teacher candidates who chose to pursue CS training in a new pre-service teacher preparation program in the United States and five candidates who expressed interest, but ultimately opted out. Method. We conducted semi-structured, remote interviews and performed a thematic analysis to inductively identify factors that influenced candidates' decisions. Findings. Candidates displayed many conceptions of justice that motivated them to teach CS, including repairing past wrongs in education, improving representation, and expanding literacy. Candidates reported many content knowledge and identity factors, including negative experiences in CS education, low CS self-efficacy, and a sense of not belonging or being respected in CS communities. Capacity for care as novice teachers was another factor: candidates feared not being able to care for students' needs while experiencing exhaustion from teaching and training during a pandemic, as well as the risks of added course preparation workload from being certified in multiple subject areas. Finally, candidates also considered opportunity costs like loss of income and job security as factors influencing their decisions. Conclusion. These factors highlight the importance of surfacing and dismantling implicit barriers, like injustice and inequity, and explicit barriers, like funding and overwork, so that future teachers feel confident in teaching CS and feel able to create equitable, inclusive environments for students to learn. CCS CONCEPTS • Social and professional topics → K-12 education.Jayne Everson, Amy J. Kowork_nio3ce7j4rbx7jupae3jw3u5jqWed, 03 Aug 2022 00:00:00 GMTJoint optimal beamforming and power control in cell-free massive MIMO
https://scholar.archive.org/work/5r5mnwnepna43khtq3c2zs5psa
We derive a fast and optimal algorithm for solving practical weighted max-min SINR problems in cell-free massive MIMO networks. For the first time, the optimization problem jointly covers long-term power control and distributed beamforming design under imperfect cooperation. In particular, we consider user-centric clusters of access points cooperating on the basis of possibly limited channel state information sharing. Our optimal algorithm merges powerful power control tools based on interference calculus with the recently developed team theoretic framework for distributed beamforming design. In addition, we propose a variation that shows faster convergence in practice.Lorenzo Miretti, Renato Luis Garrido Cavalcante, Slawomir Stanczakwork_5r5mnwnepna43khtq3c2zs5psaTue, 02 Aug 2022 00:00:00 GMTCelestial Mellin Amplitude
https://scholar.archive.org/work/cwtdid5hrreh7d46fdgsrdmcpy
Celestial holography provides a promising avenue to studying bulk scattering in flat spacetime from the perspective of boundary celestial conformal field theory (CCFT). A key ingredient in connecting the two sides is the celestial amplitude, which is given by the Mellin transform of momentum space scattering amplitude in energy. As such, celestial amplitudes can be identified with the correlation functions in celestial conformal field theory. In this paper, we introduce the further notion of celestial Mellin amplitude, which is given by the Mellin transform of celestial amplitude in coordinate. For technical reasons, we focus on the celestial Mellin amplitudes for scalar fields in three dimensional flat spacetime dual to 1D CCFT, and discuss the celestial Mellin block expansion. In particular, the poles of the celestial Mellin amplitude encode the scaling dimensions of the possible exchanged operators, while the residues there are related to the OPE coefficient squares in a linear and explicit way. We also compare the celestial Mellin amplitudes with the coefficient functions which can be obtained using inversion formulae. Finally, we make some comments about the possible generalizations of celestial Mellin amplitudes to higher dimensions.Hongliang Jiangwork_cwtdid5hrreh7d46fdgsrdmcpyTue, 02 Aug 2022 00:00:00 GMTTuning Co- and Contra-Variant Transforms: the Heisenberg Group Illustration
https://scholar.archive.org/work/pip4wrifyjbn5kwsftlhvv6qty
We discuss a fine tuning of the co- and contra-variant transforms through construction of specific fiducial and reconstructing vectors. The technique is illustrated on three different forms of induced representations of the Heisenberg group. The covariant transform provides intertwining operators between pairs of representations. In particular, we obtain the Zak transform as an induced covariant transform intertwining the Schrödinger representation on L_2(𝐑) and the lattice (nilmanifold) representation on L_2(𝐓^2). Induced covariant transforms in other pairs are Fock–Segal–Bargmann and theta transforms. Furthermore, we describe peelings which map the group-theoretical induced representations to convenient representation spaces of analytic functions. Finally, we provide a condition which can be imposed on the reconstructing vector in order to obtain an intertwining operator from the induced contravariant transform.Amerah A. Alameer, Vladimir V. Kisilwork_pip4wrifyjbn5kwsftlhvv6qtyTue, 02 Aug 2022 00:00:00 GMTNew examples of entangled states on ℂ^3 ⊗ℂ^3
https://scholar.archive.org/work/z55toe4vxbc33j6fn6erdgjncu
We build apon our previous work, the Buckley-method for simultaneous construction of families of positive maps on 3 × 3 self-adjoint matrices by prescribing a set of complex zeros to the associated forms. Positive maps that are not completely positive can be used to prove (witness) that certain mixed states are entangled. We obtain entanglement witnesses that are indecomposable and belong to extreme rays of the cone of positive maps. Consequently our semidefinite program returns new examples of entangled states whose entanglement cannot be certified by the transposition map nor by other well-known positive maps. The constructed states as well as the method of their construction offer some valuable insights for quantum information theory, in particular into the geometry of positive cones.Anita Buckleywork_z55toe4vxbc33j6fn6erdgjncuTue, 02 Aug 2022 00:00:00 GMT