High order cumulant tensors carry information about statistics of non-normally distributed multivariate data. In this work we present a new efficient algorithm for calculation of cumulants of arbitrary order in a sliding window for data streams. To present an application of the algorithm, we propose a measure of non-normality of data stream based on tensor norms of high order cumulant tensors. We show how to detect the transition from Gaussian distributed data to non-Gaussian ones in a~data stream. In order to achieve high implementation efficiency of operations on super-symmetric tensors, such as cumulant tensors, we employ the block structure to store and calculate only one hyper-pyramid part of such tensors.

}, keywords = {data streaming, High order cumulants, non-normally distributed data, time-series statistics}, doi = {10.2478/amcs-2019-0015}, author = {Krzysztof Domino and Piotr Gawron} } @article {2557, title = {Efficient computation of higher order cumulant tensors}, journal = {SIAM J. SCI. COMPUT.}, volume = {40}, year = {2018}, pages = {A1610}, chapter = {A1590}, abstract = {In this paper, we introduce a novel algorithm for calculating arbitrary order

cumulants of multidimensional data. Since the d{\textquoteright}th order

cumulant can be presented in the form of an d-dimensional tensor, the

algorithm is presented using tensor operations. The algorithm provided in the

paper takes advantage of super-symmetry of cumulant and moment tensors.

We show that the proposed algorithm considerably reduces the computational

complexity and the computational memory requirement of cumulant calculation as

compared with existing algorithms. For the sizes of interest, the

reduction is of the order of d! compared to the naive algorithm.

In this work, we extend the idea of quantum Markov chains (Gudder in J Math Phys 49(7):072105 [3]) in order to propose quantum hidden Markov models (QHMMs). For that, we use the notions of transition operation matrices and vector states, which are an extension of classical stochastic matrices and probability distributions. Our main result is the Mealy QHMM formulation and proofs of algorithms needed for application of this model: Forward for general case and Vitterbi for a restricted class of QHMMs. We show the relations of the proposed model to other quantum HMM propositions and present an example of application.

}, issn = {1573-1332}, doi = {10.1007/s11128-017-1544-8}, url = {http://dx.doi.org/10.1007/s11128-017-1544-8}, author = {Micha{\l} Cholewa and Piotr Gawron and Przemys{\l}aw G{\l}omb and Dariusz Kurzyk} } @article {2409, title = {Relativistic Quantum Pseudo-telepathy}, journal = {Acta Physica Polonica B}, volume = {47}, year = {2016}, pages = {1147}, issn = {0587-4254, 1509-5770}, doi = {10.5506/APhysPolB.47.1147}, author = {Piotr Gawron and {\L}ukasz Pawela} } @book {2491, title = {Rewolucja stanu - fantastyczne wprowadzenie do informatyki kwantowej}, year = {2016}, pages = {128}, publisher = {IITiS PAN}, organization = {IITiS PAN}, address = {Gliwice}, abstract = {{\'S}wiat, jaki znamy {\textendash} {\'s}wiat wolnych sieci informacyjnych, {\'s}wiat swobodnej wymiany wiedzy i do{\'s}wiadcze{\'n} {\textendash} sko{\'n}czy{\l} si{\k e} nieodwo{\l}alnie. Wolny dost{\k e}p do wiedzy okaza{\l} si{\k e} szkodliw{\k a} ide{\k a}, a najbardziej skorzystali na nim zbrodniarze, tw{\'o}rcy broni biologicznej, kt{\'o}ra nieomal zmiot{\l}a cywilizacj{\k e} z powierzchni ziemi. Zdziesi{\k a}tkowana przez terror, wojny i epidemi{\k e} ludzko{\'s}{\'c} powoli odradza si{\k e} pod czujnym okiem Cerbera. Jego agenci maj{\k a} jeden cel: nie dopu{\'s}ci{\'c}, aby wiedza sta{\l}a si{\k e} zn{\'o}w powszechnie dost{\k e}pna.

Jednak wszechobecna cenzura rodzi bunt.

Niekt{\'o}rzy s{\k a} nawet gotowi gin{\k a}{\'c} {\textendash} i zabija{\'c} {\textendash} za wolny dost{\k e}p do informacji. I najwyra{\'z}niej czuj{\k a} si{\k e} do{\'s}{\'c} pewnie, by rzuci{\'c} Cerberowi wyzwanie {\textendash} bo czym innym mo{\.z}e by{\'c} zamach na wysokiego dygnitarza organizacji w jej g{\l}{\'o}wnej kwaterze? Teraz Cerber musi u{\.z}y{\'c} wszystkich dost{\k e}pnych {\'s}rodk{\'o}w, by znale{\'z}{\'c} zleceniodawc{\'o}w napastnika. Niestety, jego as atutowy, kwantowa hakerka Eve, w{\l}a{\'s}nie zasiada na {\l}awie oskar{\.z}onych pod zarzutem zdrady na rzecz grupy terrorystycznej ALICE...

}, issn = {9788392605416}, url = {https://depot.ceon.pl/handle/123456789/16807}, author = {Piotr Gawron and Micha{\l} Cholewa and Katarzyna Kara} } @article {iitisid_0681, title = {Generalized open quantum walks on Apollonian networks}, journal = {PLoS ONE}, volume = {10}, number = {7}, year = {2015}, note = {arXiv:1407.1184}, pages = {e0130967}, author = {{\L}ukasz Pawela and Piotr Gawron and J.A. Miszczak and Przemys{\l}aw Sadowski} } @article {iitisid_0720, title = {Quantum image classification using principal component analysis}, journal = {Theoretical and Applied Informatics}, volume = {27}, year = {2015}, chapter = {1}, issn = {1896-5334}, doi = {10.20904/271001}, url = {http://dx.doi.org/10.20904/271001}, author = {Mateusz Ostaszewski and Przemys{\l}aw Sadowski and Piotr Gawron} } @article {iitisid_0686, title = {Real numerical shadow and generalized B-splines}, journal = {Linear Algebra and its Applications}, volume = {479}, year = {2015}, note = {arXiv:1409.4941}, pages = {12{\textendash}51}, abstract = {arXiv:1409.4941

}, doi = {10.1016/j.laa.2015.03.029}, url = {https://doi.org/10.1016/j.laa.2015.03.029}, author = {Charles F. Dunkl and Piotr Gawron and {\L}ukasz Pawela and Zbigniew Pucha{\l}a and Karol {\.Z}yczkowski} } @article {2424, title = {Wybory samorz{\k a}dowe 2014 w poszukiwaniu anomalii statystycznych}, journal = {Electoral Studies}, volume = {30}, year = {2015}, pages = {534{\textendash}545}, author = {Piotr Gawron and {\L}ukasz Pawela and Zbigniew Pucha{\l}a and Szklarski, Jacek and Karol {\.Z}yczkowski} } @article {iitisid_0771, title = {Approximation of separable numerical range using simulated annealing}, journal = {Theoretical and Applied Informatics}, volume = {26}, number = {3,4}, year = {2014}, pages = {151{\textendash}160}, author = {Piotr Gawron and Przemys{\l}aw Sadowski} } @article {iitisid_0619, title = {Decoherence effects in the quantum qubit flip game using Markovian approximation}, journal = {Quantum Information Processing}, volume = {13}, number = {665-682}, year = {2014}, note = {arXiv:1306.5957}, chapter = {665}, doi = {10.1007/s11128-013-0681-y}, author = {Piotr Gawron and Dariusz Kurzyk and {\L}ukasz Pawela} } @article {iitisid_0674, title = {Dimensionality reduction of dynamic animations using HO-SVD}, journal = {Lecture Notes in Artificial Intelligence}, volume = {8467}, year = {2014}, pages = {757{\textendash}768}, issn = {0302-9743}, author = {Micha{\l} Romaszewski and Piotr Gawron and Sebastian Opozda} } @conference {iitisid_0687, title = {Natural hand gestures for human identification in a Human-Computer Interface}, booktitle = {Image Processing Theory Tools and Applications (IPTA), 2014 4th International Conference on}, year = {2014}, month = {10}, pages = {404{\textendash}409}, publisher = {IEEE}, organization = {IEEE}, author = {Micha{\l} Romaszewski and Przemys{\l}aw G{\l}omb and Piotr Gawron}, editor = {Khalifa Djemal} } @article {iitisid_0634, title = {Numerical range for random matrices}, journal = {Journal of Mathematical Analysis and Applications}, volume = {418}, number = {1}, year = {2014}, note = {arXiv:1309.6203}, pages = {516}, author = {Beno{\^\i}t Collins and Piotr Gawron and Alexander E. Litvak and Karol {\.Z}yczkowski} } @article {iitisid_0595, title = {Analysis of patent activity in the field of quantum information processing}, journal = {International Journal of Quantum Information}, volume = {11}, number = {1}, year = {2013}, note = {arXiv:1212.2439}, pages = {1350007}, issn = {0219-7499}, author = {Ryszard Winiarczyk and Piotr Gawron and J.A. Miszczak and {\L}ukasz Pawela and Zbigniew Pucha{\l}a} } @article {iitisid_0638, title = {Compression of animated 3D models using HO-SVD}, journal = {arXiv:1310.1240}, year = {2013}, note = {arXiv:1310.1240}, author = {Micha{\l} Romaszewski and Piotr Gawron and Sebastian Opozda} } @article {iitisid_0719, title = {Dimensionality Reduction of Dynamic Mesh Animations Using HO-SVD}, journal = {Journal of Artificial Intelligence and Soft Computing Research}, volume = {3}, number = {4}, year = {2013}, note = {DOI 10.2478/jaiscr-2014-0020}, pages = {277{\textendash}289}, issn = {2083-2567}, author = {Micha{\l} Romaszewski and Piotr Gawron and Sebastian Opozda} } @article {iitisid_0590, title = {Enhancing pseudo-telepathy in the Magic Square game}, journal = {PLOS ONE}, volume = {8}, year = {2013}, note = {arXiv:1211.1213}, pages = {e64694}, author = {{\L}ukasz Pawela and Piotr Gawron and Zbigniew Pucha{\l}a and Jan S{\l}adkowski} } @article {iitisid_0586, title = {A model for quantum queue}, journal = {International Journal of Quantum Information}, volume = {11}, number = {2}, year = {2013}, note = {arXiv:1210.8339}, pages = {1350023}, issn = {0219-7499}, author = {Piotr Gawron and Dariusz Kurzyk and Zbigniew Pucha{\l}a} } @article {iitisid_0515, title = {Noise effects in the quantum search algorithm from the viewpoint of computational complexity}, journal = {International Journal of Applied Mathematics and Computer Science}, volume = {22}, number = {2}, year = {2012}, note = {arXiv:1108.1915}, pages = {493{\textendash}499}, abstract = {We analyse the resilience of the quantum search algorithm in the presence of quantum noise modelled as trace preserving completely positive maps. We study the influence of noise on computational complexity of the quantum search algorithm. We show that only for small amounts of noise the quantum search algorithm is still more efficient than any classical algorithm.}, author = {Piotr Gawron and Jerzy Klamka and Ryszard Winiarczyk} } @article {iitisid_0513, title = {Qubit flip game on a Heisenberg spin chain}, journal = {Quantum Information Processing}, volume = {11}, number = {6}, year = {2012}, note = {arXiv:1108.0642}, pages = {1571{\textendash}1583}, abstract = {We study a quantum version of a penny flip game played using control parameters of the Hamiltonian in the Heisenberg model. Moreover, we extend this game by introducing auxiliary spins which can be used to alter the behaviour of the system. We show that a player aware of the complex structure of the system used to implement the game can use this knowledge to gain higher mean payoff.}, author = {J.A. Miszczak and Piotr Gawron and Zbigniew Pucha{\l}a} } @article {iitisid_0536, title = {Restricted numerical shadow and geometry of quantum entanglement}, journal = {J. Phys. A: Math. Theor.}, volume = {45}, year = {2012}, note = {arXiv:1201.2524}, pages = {415309}, abstract = {The restricted numerical range W\_R(A) of an operator A acting on a D-dimensional Hilbert space is defined as a set of all possible expectation values of this operator among pure states which belong to a certain subset R of the of set of pure quantum states of dimension D. One considers for instance the set of real states, or in the case of composite spaces, the set of product states and the set of maximally entangled states. Combining the operator theory with a probabilistic approach we introduce the restricted numerical shadow of A {\textendash} a normalized probability distribution on the complex plane supported in W\_R(A). Its value at point z in C is equal to the probability that the expectation value is equal to z, where |psi> represents a random quantum state in subset R distributed according to the natural measure on this set, induced by the unitarily invariant Fubini{\textendash}Study measure. Studying restricted shadows of operators of a fixed size D=N\_A N\_B we analyse the geometry of sets of separable and maximally entangled states of the N\_A x N\_B composite quantum system. Investigating trajectories formed by evolving quantum states projected into the plane of the shadow we study the dynamics of quantum entanglement. A similar analysis extended for operators on D=2^3 dimensional Hilbert space allows us to investigate the structure of the orbits of GHZ and W quantum states of a three{\textendash}qubit system.}, author = {Zbigniew Pucha{\l}a and J.A. Miszczak and Piotr Gawron and Charles F. Dunkl and J.A. Holbrook and Karol {\.Z}yczkowski} } @inbook {iitisid_0512, title = {Eigengestures for natural human computer interface}, booktitle = {Man-Machine Interactions 2}, year = {2011}, note = {arXiv:1105.1293}, pages = {49{\textendash}56}, publisher = {Springer}, organization = {Springer}, address = {Berlin / Heidelberg}, abstract = {We present the application of Principal Component Analysis for data acquired during the design of a natural gesture interface. We investigate the concept of an eigengesture for motion capture hand gesture data and present the visualisation of principal components obtained in the course of conducted experiments. We also show the influence of dimensionality reduction on reconstructed gesture data quality.}, isbn = {978-3-642-23168-1}, author = {Piotr Gawron and Przemys{\l}aw G{\l}omb and J.A. Miszczak and Zbigniew Pucha{\l}a}, editor = {Tadeusz Czach{\'o}rski and Stanis{\l}aw Kozielski and Urszula Sta{\'n}czyk} } @article {iitisid_0466, title = {Experimentally feasible measures of distance between quantum operations}, journal = {Quantum Information Processing}, volume = {10}, number = {1}, year = {2011}, note = {arXiv:0911.0567 IF=2.085(2010);}, pages = {1{\textendash}12}, abstract = {We present two measures of distance between quantum processes which can be measured directly in laboratory without resorting to process tomography. The measures are based on the superfidelity, introduced recently to provide an upper bound for quantum fidelity. We show that the introduced measures partially fulfill the requirements for distance measure between quantum processes. We also argue that they can be especially useful as diagnostic measures to get preliminary knowledge about imperfections in an experimental setup. In particular we provide quantum circuit which can be used to measure the superfidelity between quantum processes. We also provide a physical interpretation of the introduced metrics based on the continuity of channel capacity.}, issn = {1570-0755}, author = {Zbigniew Pucha{\l}a and J.A. Miszczak and Piotr Gawron and B. Gardas} } @article {iitisid_0509, title = {Numerical shadow and geometry of quantum states}, journal = {J. Phys. A: Math. Theor.}, volume = {44}, number = {33}, year = {2011}, note = {arXiv:1104.2760 IF=1.641(2010);}, pages = {335301}, abstract = {The totality of normalised density matrices of order N forms a convex set Q\_N in R^(N^2-1). Working with the flat geometry induced by the Hilbert-Schmidt distance we consider images of orthogonal projections of Q\_N onto a two-plane and show that they are similar to the numerical ranges of matrices of order N. For a matrix A of a order N one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini-Study measure on the complex projective manifold CP^(N-1). We define generalized, mixed-states shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein.}, issn = {1751-8113}, author = {Charles F. Dunkl and Piotr Gawron and J.A. Holbrook and J.A. Miszczak and Zbigniew Pucha{\l}a and Karol {\.Z}yczkowski} } @article {iitisid_0504, title = {Numerical shadows: measures and densities on the numerical range}, journal = {Linear Algebra Appl.}, volume = {434}, year = {2011}, note = {arXiv:1010.4189 IF=1.005(2010);}, pages = {2042{\textendash}2080}, abstract = {For any operator M acting on an N-dimensional Hilbert space H\_N we introduce its numerical shadow, which is a probability measure on the complex plane supported by the numerical range of M. The shadow of M at point z is defined as the probability that the inner product (Mu,u) is equal to z, where u stands for a random complex vector from H\_N, satisfying ||u||=1. In the case of N=2 the numerical shadow of a non-normal operator can be interpreted as a shadow of a hollow sphere projected on a plane. A similar interpretation is provided also for higher dimensions. For a hermitian M its numerical shadow forms a probability distribution on the real axis which is shown to be a one dimensional B-spline. In the case of a normal M the numerical shadow corresponds to a shadow of a transparent solid simplex in R^{N-1} onto the complex plane. Numerical shadow is found explicitly for Jordan matrices J\_N, direct sums of matrices and in all cases where the shadow is rotation invariant. Results concerning the moments of shadow measures play an important role. A general technique to study numerical shadow via the Cartesian decomposition is described, and a link of the numerical shadow of an operator to its higher-rank numerical range is emphasized.}, issn = {0024-3795}, author = {Charles F. Dunkl and Piotr Gawron and J.A. Holbrook and Zbigniew Pucha{\l}a and Karol {\.Z}yczkowski} } @article {iitisid_0473, title = {Product numerical range in a space with tensor product structure}, journal = {Linear Algebra Appl.}, volume = {434}, number = {1}, year = {2011}, note = {arXiv:1008.3482 IF=1.005(2010);}, pages = {327{\textendash}342}, abstract = {We study operators acting on a tensor product Hilbert space and investigate their product numerical range, product numerical radius and separable numerical range. Concrete bounds for the product numerical range for Hermitian operators are derived. Product numerical range of a non-Hermitian operator forms a subset of the standard numerical range containing the barycenter of the spectrum. While the latter set is convex, the product range needs not to be convex nor simply connected. The product numerical range of a tensor product is equal to the Minkowski product of numerical ranges of individual factors.}, issn = {0024-3795}, author = {Zbigniew Pucha{\l}a and Piotr Gawron and J.A. Miszczak and {\L}. Skowronek and Man-Duen Choi and Karol {\.Z}yczkowski} } @booklet {iitisid_0519, title = {Towards a natural gesture interface: LDA-based gesture separability}, year = {2011}, note = {arXiv:1109.5034}, url = {https://arxiv.org/abs/1109.5034}, author = {Micha{\l} Romaszewski and Piotr Gawron and Przemys{\l}aw G{\l}omb} } @article {iitisid_0458, title = {Extending scientific computing system with structural quantum programming capabilities}, journal = {Bulletin of the Polish Academy of Sciences - Technical Sciences}, volume = {58}, number = {1}, year = {2010}, note = {arXiv:1006.1549}, pages = {77{\textendash}88}, issn = {0239-7528}, author = {Piotr Gawron and Jerzy Klamka and J.A. Miszczak and Ryszard Winiarczyk} } @article {iitisid_0457, title = {Noisy quantum Monty Hall game}, journal = {Fluctuation and Noise Letters}, volume = {9}, number = {1}, year = {2010}, note = {arXiv:0907.1381}, pages = {9{\textendash}18}, issn = {0219-4775}, author = {Piotr Gawron} } @article {iitisid_0476, title = {Restricted numerical range: A versatile tool in the theory of quantum information}, journal = {J. Math. Phys.}, volume = {51}, number = {10}, year = {2010}, note = {arXiv:0905.3646 IF=1.291(2010);}, pages = {102204}, issn = {00222488}, author = {Piotr Gawron and Zbigniew Pucha{\l}a and J.A. Miszczak and {\L}. Skowronek and Karol {\.Z}yczkowski} } @article {iitisid_0401, title = {Noise Effects in Quantum Magic Squares Game}, journal = {International Journal of Quantum Information}, volume = {06}, number = {Supp}, year = {2008}, note = {arXiv:0801.4848}, pages = {667}, issn = {0219-7499}, author = {Piotr Gawron and J.A. Miszczak and Jan S{\l}adkowski} } @article {iitisid_0395, title = {Kompilator j{\k e}zyka QCL QCL2QML}, journal = {Studia Informatica}, volume = {28}, number = {4}, year = {2007}, pages = {5{\textendash}18}, author = {Ryszard Winiarczyk and Piotr Gawron and J.A. Miszczak} } @article {iitisid_0036, title = {Numerical simulations of mixed state quantum computation}, journal = {International Journal of Quantum Information}, volume = {3}, number = {1}, year = {2005}, author = {Piotr Gawron and J.A. Miszczak} } @article {iitisid_0049, title = {Quantum Implementation of Parrondo Paradox}, journal = {Fluctuation and Noise Letters}, volume = {5}, number = {4}, year = {2005}, note = {arXiv:quant-ph/0502185}, pages = {L471{\textendash}L478}, abstract = {We propose a quantum implementation of a capital-dependent Parrondo{\textquoteright}s paradox that uses O(log2(n)) qubits, where n is the number of Parrondo games. We present its implementation in the quantum computer language (QCL) and show simulation results.}, author = {Piotr Gawron and J.A. Miszczak} } @inbook {iitisid_0162, title = {Wysokowydajne sieci komputerowe}, year = {2005}, publisher = {WK{\L}}, organization = {WK{\L}}, chapter = {Symulacje gier kwantowych}, author = {Piotr Gawron and J.A. Miszczak}, editor = {Andrzej Grzywak and Andrzej Kwiecie{\'n}} } @article {iitisid_0059, title = {Symulacja komputer{\'o}w kwantowych}, journal = {Studia Informatica}, volume = {23}, number = {2A(48)}, year = {2002}, pages = {105{\textendash}112}, author = {Ryszard Winiarczyk and Piotr Gawron} }