IA Scholar Query: Three Mutually Orthogonal Idempotent Latin Squares of Order 18.
https://scholar.archive.org/
Internet Archive Scholar query results feedeninfo@archive.orgTue, 15 Nov 2022 00:00:00 GMTfatcat-scholarhttps://scholar.archive.org/help1440Dimensional reduction of the Dirac theory
https://scholar.archive.org/work/swvhbpl3ibgnlm23bkiwxebpdi
We perform a reduction from three to two spatial dimensions of the physics of a spin-1/2 fermion coupled to the electromagnetic field, by applying Hadamard's method of descent. We consider first the free case, in which motion is determined by the Dirac equation, and then the coupling with a dynamical electromagnetic field, governed by the Dirac-Maxwell equations. We find that invariance along one spatial direction splits the free Dirac equation in two decoupled theories. On the other hand, a dimensional reduction in the presence of an electromagnetic field provides a more complicated theory in 2+1 dimensions, in which the method of descent is extended by using the covariant derivative. Equations simplify, but decoupling between different physical sectors occurs only if specific classes of solutions are considered.Giuliano Angelone, Elisa Ercolessi, Paolo Facchi, Davide Lonigro, Rocco Maggi, Giuseppe Marmo, Saverio Pascazio, Francesco V. Pepework_swvhbpl3ibgnlm23bkiwxebpdiTue, 15 Nov 2022 00:00:00 GMTRelative Entropy for Fermionic Quantum Field Theory
https://scholar.archive.org/work/heyzl3fldnai5m5zncy4pkfyaq
We study the relative entropy, in the sense of Araki, for the representation of a self-dual CAR algebra 𝔄_SDC(ℋ,Γ). We notice, for a specific choice of f ∈ℋ, that the associated element in 𝔄_SDC(ℋ,Γ) is unitary. As a consequence, we explicitly compute the relative entropy between a quasifree state over 𝔄_SDC(ℋ,Γ) and an excitation of it with respect to the abovely mentioned unitary element. The generality of the approach, allows us to consider ℋ as the Hilbert space of solutions of the classical Dirac equation over globally hyperbolic spacetimes, making our result, a computation of relative entropy for a Fermionic Quantum Field Theory. Our result extends those of Longo and Casini et al. for the relative entropy between a quasifree state and a coherent excitation for a free Scalar Quantum Field Theory, to the case of fermions. As a first application, we computed such a relative entropy for a Majorana field on an ultrastatic spacetime.Stefano Galandawork_heyzl3fldnai5m5zncy4pkfyaqTue, 18 Oct 2022 00:00:00 GMTBayesian Fixed-domain Asymptotics for Covariance Parameters in a Gaussian Process Model
https://scholar.archive.org/work/wi3m43pzn5fblhvut64pnxrdy4
Gaussian process models typically contain finite dimensional parameters in the covariance function that need to be estimated from the data. We study the Bayesian fixed-domain asymptotics for the covariance parameters in a universal kriging model with an isotropic Matern covariance function, which has many applications in spatial statistics. We show that when the dimension of domain is less than or equal to three, the joint posterior distribution of the microergodic parameter and the range parameter can be factored independently into the product of their marginal posteriors under fixed-domain asymptotics. The posterior of the microergodic parameter is asymptotically close in total variation distance to a normal distribution with shrinking variance, while the posterior distribution of the range parameter does not converge to any point mass distribution in general. Our theory allows an unbounded prior support for the range parameter and flexible designs of sampling points. We further study the asymptotic efficiency and convergence rates in posterior prediction for the Bayesian kriging predictor with covariance parameters randomly drawn from their posterior distribution. In the special case of one-dimensional Ornstein-Uhlenbeck process, we derive explicitly the limiting posterior of the range parameter and the posterior convergence rate for asymptotic efficiency in posterior prediction. We verify these asymptotic results in numerical experiments.Cheng Liwork_wi3m43pzn5fblhvut64pnxrdy4Sun, 25 Sep 2022 00:00:00 GMTData Fusion: Theory, Methods, and Applications
https://scholar.archive.org/work/ntcpnuxe4zd3do75kjdnhn6j6a
A proper fusion of complex data is of interest to many researchers in diverse fields, including computational statistics, computational geometry, bioinformatics, machine learning, pattern recognition, quality management, engineering, statistics, finance, economics, etc. It plays a crucial role in: synthetic description of data processes or whole domains, creation of rule bases for approximate reasoning tasks, reaching consensus and selection of the optimal strategy in decision support systems, imputation of missing values, data deduplication and consolidation, record linkage across heterogeneous databases, and clustering. This open-access research monograph integrates the spread-out results from different domains using the methodology of the well-established classical aggregation framework, introduces researchers and practitioners to Aggregation 2.0, as well as points out the challenges and interesting directions for further research.Marek Gagolewskiwork_ntcpnuxe4zd3do75kjdnhn6j6aTue, 02 Aug 2022 00:00:00 GMTPauli component erasing operations
https://scholar.archive.org/work/bqnrtwpxszettbljxl2aqidudy
Decoherence of quantum systems is described by quantum channels. However, a complete understanding of such channels, specially in the multi-particle setting, is still an ongoing difficult task. We propose the family of quantum maps that preserve or completely erase the components of a multi-qubit system in the basis of Pauli strings, which we call Pauli component erasing (PCE) maps. For the corresponding channels, it is shown that the preserved components can be interpreted as a finite vector subspace, from which we derive several properties and complete the characterization. Moreover, we show that the obtained family of channels form a semigroup and derive its generators. We use this simple structure to determine physical implementations and connect the obtained family of channels with Markovian processes.Jose Alfredo de Leon, Alejandro Fonseca, Francois Leyvraz, David Davalos, Carlos Pinedawork_bqnrtwpxszettbljxl2aqidudyThu, 12 May 2022 00:00:00 GMTOn the spectrum and linear programming bound for hypergraphs
https://scholar.archive.org/work/o24mflld3fhfbe4fzuol2l6vwi
The spectrum of a graph is closely related to many graph parameters. In particular, the spectral gap of a regular graph which is the difference between its valency and second eigenvalue, is widely seen an algebraic measure of connectivity and plays a key role in the theory of expander graphs. In this paper, we extend previous work done for graphs and bipartite graphs and present a linear programming method for obtaining an upper bound on the order of a regular uniform hypergraph with prescribed distinct eigenvalues. Furthermore, we obtain a general upper bound on the order of a regular uniform hypergraph whose second eigenvalue is bounded by a given value. Our results improve and extend previous work done by Feng–Li (1996) on Alon–Boppana theorems for regular hypergraphs and by Dinitz–Schapira–Shahaf (2020) on the Moore or degree-diameter problem. We also determine the largest order of an r-regular u-uniform hypergraph with second eigenvalue at most θ for several parameters (r,u,θ). In particular, orthogonal arrays give the structure of the largest hypergraphs with second eigenvalue at most 1 for every sufficiently large r. Moreover, we show that a generalized Moore geometry has the largest spectral gap among all hypergraphs of that order and degree.Sebastian M. Cioabă, Jack H. Koolen, Masato Mimura, Hiroshi Nozaki, Takayuki Okudawork_o24mflld3fhfbe4fzuol2l6vwiMon, 07 Mar 2022 00:00:00 GMTEnumeration of Maximal Cycles Generated by Orthogonal Cellular Automata
https://scholar.archive.org/work/5gebfs6bvrh65c4pyn2tavlkla
Cellular Automata (CA) are an interesting computational model for designing Pseudorandom Number Generators (PRNG), due to the complex dynamical behavior they can exhibit depending on the underlying local rule. Most of the CA-based PRNGs proposed in the literature, however, suffer from poor diffusion since a change in a single cell can propagate only within its neighborhood during a single time step. This might pose a problem especially when such PRNGs are used for cryptographic purposes. In this paper, we consider an alternative approach to generate pseudorandom sequences through orthogonal CA (OCA), which guarantees a better amount of diffusion. After defining the related PRNG, we perform an empirical investigation of the maximal cycles in OCA pairs up to diameter d=8. Next, we focus on OCA induced by linear rules, giving a characterization of their cycle structure based on the rational canonical form of the associated Sylvester matrix. Finally, we devise an algorithm to enumerate all linear OCA pairs characterized by a single maximal cycle, and apply it up to diameter d=16 and d=13 for OCA respectively over the binary and ternary alphabets.Luca Mariotwork_5gebfs6bvrh65c4pyn2tavlklaSat, 05 Mar 2022 00:00:00 GMTKite-group divisible packings and coverings with any minimum leave and minimum excess
https://scholar.archive.org/work/tgo3hoiq3rbqbfn2uhi5vvvmlm
<p style='text-indent:20px;'>Following Hu, Chang and Feng's work [Graphs Combin., 2016], we further subdivide the possible types of minimum leaves and minimum excesses for maximum group divisible packings and minimum group divisible coverings with kites. We show that a maximum group divisible packing and a minimum group divisible covering with kites for any given type of minimum leave and minimum excess exist, respectively.</p>Yuxing Yang, Yanxun Chang, Lidong Wangwork_tgo3hoiq3rbqbfn2uhi5vvvmlmConstructing $(3, b)$-Sudoku pair Latin squares
https://scholar.archive.org/work/cfmmlg5zvfbrriinubbm5ahdsq
An (a, b)-Sudoku pair Latin square is a Latin square that is simultaneously an (a, b)-Sudoku Latin square and a (b, a)-Sudoku Latin square. While (a, b)-Sudoku Latin squares are known to exist for any positive integers a and b, the pairs {a, b} for which an (a, b)-Sudoku pair Latin square exists are largely unknown. In this article we establish the existence of (a, b)-Sudoku pair Latin squares for an infinite collection of pairs (a, b). Our results show that a (3, b)-Sudoku pair Latin square can be constructed for any positive integer b.Braxton Carrigan, David Diaz, James M. Hammer, John Lorch, Robert Lorchwork_cfmmlg5zvfbrriinubbm5ahdsq