We introduce a definition for the total graph of a gain graph (Γ,ψ) on a group G by using G-phases, which are a generalization of the notion of orientation to gain graphs. Our construction is ...well-defined in the sense that gain graphs that are switching isomorphic have switching isomorphic total graphs. In particular, the switching equivalence class of the total graph does not depend on the particular choice of the G-phase associated with ψ. More precisely, we consider the left-right multiplication action of G on the space of all G-phases, proving that its orbits consist of sets of G-phases inducing the same switching equivalence class of gain functions on Γ or, equivalently, on its total graphs. Moreover, we prove that the stabilizers of this action are isomorphic to the centralizers of the sets of gains of closed walks in the associated gain graphs. Our construction is consistent with the existing notions of total graph for signed graphs and, in analogy with the signed case, we are able to explicitly compute the spectrum of the total graph of a regular gain graph over an arbitrary group G, where the spectrum is defined by means of a unitary representation of the gain group G.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
In this letter, we suggest a local covariant action for a gauge field theory of fermionic Continuous-Spin Particles (CSPs). The action is invariant under gauge transformations without any constraint ...on both the gauge field and the gauge transformation parameter. The Fang–Fronsdal equations for a tower of massless fields with all half-integer spins arise as a particular limit of the equation of motion of fermionic CSPs.
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GEOZS, IJS, IMTLJ, KILJ, KISLJ, NLZOH, NUK, OILJ, PNG, SAZU, SBCE, SBJE, UILJ, UL, UM, UPCLJ, UPUK, ZAGLJ, ZRSKP
A potential limitation of a motor imagery (MI) based brain-computer interface (BCI) is that it usually requires a relatively long time to record sufficient electroencephalogram (EEG) data for robust ...classifier training. The calibration burden during data acquisition phase will most probably cause a subject to be reluctant to use a BCI system. To alleviate this issue, we propose a novel sparse group representation model (SGRM) for improving the efficiency of MI-based BCI by exploiting the intersubject information. Specifically, preceded by feature extraction using common spatial pattern, a composite dictionary matrix is constructed with training samples from both the target subject and other subjects. By explicitly exploiting within-group sparse and group-wise sparse constraints, the most compact representation of a test sample of the target subject is then estimated as a linear combination of columns in the dictionary matrix. Classification is implemented by calculating the class-specific representation residual based on the significant training samples corresponding to the nonzero representation coefficients. Accordingly, the proposed SGRM method effectively reduces the required training samples from the target subject due to auxiliary data available from other subjects. With two public EEG data sets, extensive experimental comparisons are carried out between SGRM and other state-of-the-art approaches. Superior classification performance of our method using 40 trials of the target subject for model calibration (Averaged accuracy = 78.2%, Kappa = 0.57 and Averaged accuracy = 77.7%, Kappa = 0.55 for the two data sets, respectively) indicates its promising potential for improving the practicality of MI-based BCI.
Efficient Multi Port-Based Teleportation Schemes Studzinski, Michal; Mozrzymas, Marek; Kopszak, Piotr ...
IEEE transactions on information theory,
2022-Dec., 2022-12-00, Volume:
68, Issue:
12
Journal Article
Peer reviewed
Open access
In this manuscript we analyse generalised port-based teleportation (PBT) schemes, allowing for transmitting more than one unknown quantum state (or a composite quantum state) in one go, where the ...state ends up in several ports at Bob's side. We investigate the efficiency of our scheme discussing both deterministic and probabilistic case, where parties share maximally entangled states. It turns out that the new scheme gives better performance than various variants of the optimal PBT protocol used for the same task. All the results are presented in group-theoretic manner depending on such quantities like dimensions and multiplicities of irreducible representations in the Schur-Weyl duality. The presented analysis was possible by considering the algebra of permutation operators acting on <inline-formula> <tex-math notation="LaTeX">n </tex-math></inline-formula> systems distorted by the action of partial transposition acting on more than one subsystem. Considering its action on the <inline-formula> <tex-math notation="LaTeX">n- </tex-math></inline-formula>fold tensor product of the Hilbert space with finite dimension, we present construction of the respective irreducible matrix representations, which are in fact matrix irreducible representations of the Walled Brauer Algebra. I turns out that the introduced formalism, and symmetries beneath it, appears in many aspects of theoretical physics and mathematics - theory of anti ferromagnetism, aspects of gravity theory or in the problem of designing quantum circuits for special task like for example inverting an unknown unitary.
Permutation invariant Gaussian two-matrix models Barnes, George; Padellaro, Adrian; Ramgoolam, Sanjaye
Journal of physics. A, Mathematical and theoretical,
04/2022, Volume:
55, Issue:
14
Journal Article
Peer reviewed
Open access
Abstract
We construct the general permutation invariant Gaussian two-matrix model for matrices of arbitrary size
D
. The parameters of the model are given in terms of variables defined using the ...representation theory of the symmetric group
S
D
. A correspondence is established between the permutation invariant polynomial functions of the matrix variables (the observables of the model) and directed colored graphs, which sheds light on stability properties in the large
D
counting of these invariants. A refined counting of the graphs is given in terms of double cosets involving permutation groups defined by the local structure of the graphs. Linear and quadratic observables are transformed to an
S
D
representation theoretic basis and are used to define the convergent Gaussian measure. The perturbative rules for the computation of expectation values of graph-basis observables of any degree are given in terms of the representation theoretic parameters. Explicit results for a number of observables of degree up to four are given along with a Sage programme that computes general expectation values.
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