Relevant bibliographies by topics / Box polynomial

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  2. Dissertations / Theses
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Academic literature on the topic 'Box polynomial'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Box polynomial"

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Alamsyah, Alamsyah. "A Novel Construction of Perfect Strict Avalanche Criterion S-box using Simple Irreducible Polynomials." Scientific Journal of Informatics 7, no. 1 (May 30, 2020): 10–22. http://dx.doi.org/10.15294/sji.v7i1.24006.

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An irreducible polynomial is one of the main components in building an S-box with an algebraic technique approach. The selection of the precise irreducible polynomial will determine the quality of the S-box produced. One method for determining good S-box quality is strict avalanche criterion will be perfect if it has a value of 0.5. Unfortunately, in previous studies, the strict avalanche criterion value of the S-box produced still did not reach perfect value. In this paper, we will discuss S-box construction using selected irreducible polynomials. This selection is based on the number of elements of the least amount of irreducible polynomials that make it easier to construct S-box construction. There are 17 irreducible polynomials that meet these criteria. The strict avalanche criterion test results show that the irreducible polynomial p17(x) =x8 + x7 + x6 + x + 1 is the best with a perfect SAC value of 0.5. One indicator that a robust S-box is an ideal strict avalanche criterion value of 0.5
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Goodman, T. N. T., and S. L. Lee. "Homogeneous polynomial splines." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 117, no. 1-2 (1991): 89–102. http://dx.doi.org/10.1017/s0308210500027621.

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SynopsisWe construct functions which are piecewise homogeneous polynomials in the positive octant in three dimensions. These give a rich and elegant theory which combines properties of polynomial box splines see [6] and the references therein) with the explicit representation of simple exponential box splines [11], while enjoying complete symmetry in the three variables. By a linear transformation followed by a projection on suitable planes, one obtains piecewise polynomial functions of two variables on a mesh formed by three pencils of lines. The vertices of these pencils may be finite or one or two may be infinite, i.e. the corresponding pencils may comprise parallel lines. As a limiting case, all three vertices become infinite and one recovers polynomial box splines on a three-direction mesh.
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Encarnación, Mark J. "Black-box polynomial resultants." Information Processing Letters 61, no. 4 (February 1997): 201–4. http://dx.doi.org/10.1016/s0020-0190(97)00016-1.

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Mahmood, Shahid, Shabieh Farwa, Muhammad Rafiq, Syed Muhammad Jawwad Riaz, Tariq Shah, and Sajjad Shaukat Jamal. "To Study the Effect of the Generating Polynomial on the Quality of Nonlinear Components in Block Ciphers." Security and Communication Networks 2018 (2018): 1–8. http://dx.doi.org/10.1155/2018/5823230.

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Substitution box (S-box), being the only nonlinear component, contributes to the confusion creating capability of a cryptosystem. Keeping in view the predominant role of S-box, many design algorithms to synthesize cryptographically stronger S-boxes have gained pivotal attention. A quick review of these algorithms shows that all these ideas mainly concentrate on the choice of bijective Boolean functions, with nonobservance to the irreducible polynomial that generates the Galois field. In this paper, we propose that the selection of irreducible polynomial has a deep influence on the highly desirable features of an S-box such as nonlinearity, strict avalanche, bit independence, linear approximation probability, and differential approximation probability. We underpin our claim by investigating a detailed model, which deploys the same algorithm but different polynomials and produces unusual changes in the results regarding the performance parameters of S-box.
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Barlow, Angela T. "How Can a Box Help My Students with Multiplying Polynomials?" Mathematics Teaching in the Middle School 9, no. 9 (May 2004): 512–13. http://dx.doi.org/10.5951/mtms.9.9.0512.

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For most of my students, multiplying polynomials is not a difficult procedure to understand. Students quickly grasp the idea that each term in the first polynomial must be multiplied by each term in the second polynomial. The difficulty, however, lies in the organization of the product's terms for ease in combining like terms and in the accuracy of having multiplied all of the appropriate subproducts. The purpose of this article is to demonstrate how a box can help students with both of these aspects.
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Dokken, Tor, Tom Lyche, and Kjell Fredrik Pettersen. "Polynomial splines over locally refined box-partitions." Computer Aided Geometric Design 30, no. 3 (March 2013): 331–56. http://dx.doi.org/10.1016/j.cagd.2012.12.005.

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Zahid, Amjad, and Muhammad Arshad. "An Innovative Design of Substitution-Boxes Using Cubic Polynomial Mapping." Symmetry 11, no. 3 (March 25, 2019): 437. http://dx.doi.org/10.3390/sym11030437.

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In this paper, we propose to present a novel technique for designing cryptographically strong substitution-boxes using cubic polynomial mapping. The proposed cubic polynomial mapping is proficient to map the input sequence to a strong 8 × 8 S-box meeting the requirements of a bijective function. The use of cubic polynomial maintains the simplicity of S-box construction method and found consistent when compared with other existing S-box techniques used to construct S-boxes. An example proposed S-box is obtained which is analytically evaluated using standard performance criteria including nonlinearity, bijection, bit independence, strict avalanche effect, linear approximation probability, and differential uniformity. The performance results are equated with some recently scrutinized S-boxes to ascertain its cryptographic forte. The critical analyses endorse that the proposed S-box construction technique is considerably innovative and effective to generate cryptographic strong substitution-boxes.
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Sit, Atilla, Julie C. Mitchell, George N. Phillips, and Stephen J. Wright. "An Extension of 3D Zernike Moments for Shape Description and Retrieval of Maps Defined in Rectangular Solids." Computational and Mathematical Biophysics 1 (April 16, 2013): 75–89. http://dx.doi.org/10.2478/mlbmb-2013-0004.

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AbstractZernike polynomials have been widely used in the description and shape retrieval of 3D objects. These orthonormal polynomials allow for efficient description and reconstruction of objects that can be scaled to fit within the unit ball. However, maps defined within box-shaped regions ¶ for example, rectangular prisms or cubes ¶ are not well suited to representation by Zernike polynomials, because these functions are not orthogonal over such regions. In particular, the representations require many expansion terms to describe object features along the edges and corners of the region. We overcome this problem by applying a Gram-Schmidt process to re-orthogonalize the Zernike polynomials so that they recover the orthonormality property over a specified box-shaped domain. We compare the shape retrieval performance of these new polynomial bases to that of the classical Zernike unit-ball polynomials.
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Juma, Ali, Valentine Kabanets, Charles Rackoff, and Amir Shpilka. "The Black-Box Query Complexity of Polynomial Summation." computational complexity 18, no. 1 (April 2009): 59–79. http://dx.doi.org/10.1007/s00037-009-0263-7.

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Galatenko, Alexei V., Stepan A. Nersisyan, and Dmitriy N. Zhuk. "NP-Hardness of the Problem of Optimal Box Positioning." Mathematics 7, no. 8 (August 6, 2019): 711. http://dx.doi.org/10.3390/math7080711.

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We consider the problem of finding a position of a d-dimensional box with given edge lengths that maximizes the number of enclosed points of the given finite set P ⊂ R d , i.e., the problem of optimal box positioning. We prove that while this problem is polynomial for fixed values of d, it is NP-hard in the general case. The proof is based on a polynomial reduction technique applied to the considered problem and the 3-CNF satisfiability problem.
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Dissertations / Theses on the topic "Box polynomial"

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Ahmadi, Abhari Seyed Hamed. "Quantum Algorithms for: Quantum Phase Estimation, Approximation of the Tutte Polynomial and Black-box Structures." Doctoral diss., University of Central Florida, 2012. http://digital.library.ucf.edu/cdm/ref/collection/ETD/id/5096.

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In this dissertation, we investigate three different problems in the field of Quantum computation. First, we discuss the quantum complexity of evaluating the Tutte polynomial of a planar graph. Furthermore, we devise a new quantum algorithm for approximating the phase of a unitary matrix. Finally, we provide quantum tools that can be utilized to extract the structure of black-box modules and algebras. While quantum phase estimation (QPE) is at the core of many quantum algorithms known to date, its physical implementation (algorithms based on quantum Fourier transform (QFT)) is highly constrained by the requirement of high-precision controlled phase shift operators, which remain difficult to realize. In the second part of this dissertation, we introduce an alternative approach to approximately implement QPE with arbitrary constant-precision controlled phase shift operators. The new quantum algorithm bridges the gap between QPE algorithms based on QFT and Kitaev's original approach. For approximating the eigenphase precise to the nth bit, Kitaev's original approach does not require any controlled phase shift operator. In contrast, QPE algorithms based on QFT or approximate QFT require controlled phase shift operators with precision of at least Pi/2n. The new approach fills the gap and requires only arbitrary constant-precision controlled phase shift operators. From a physical implementation viewpoint, the new algorithm outperforms Kitaev's approach. The other problem we investigate relates to approximating the Tutte polynomial. We show that the problem of approximately evaluating the Tutte polynomial of triangular graphs at the points (q,1/q) of the Tutte plane is BQP-complete for (most) roots of unity q. We also consider circular graphs and show that the problem of approximately evaluating the Tutte polynomial of these graphs at a point is DQC1-complete and at some points is in BQP. To show that these problems can be solved by a quantum computer, we rely on the relation of the Tutte polynomial of a planar G graph with the Jones and HOMFLY polynomial of the alternating link D(G) given by the medial graph of G. In the case of our graphs the corresponding links are equal to the plat and trace closures of braids. It is known how to evaluate the Jones and HOMFLY polynomial for closures of braids. To establish the hardness results, we use the property that the images of the generators of the braid group under the irreducible Jones-Wenzl representations of the Hecke algebra have finite order. We show that for each braid we can efficiently construct a braid such that the evaluation of the Jones and HOMFLY polynomials of their closures at a fixed root of unity leads to the same value and that the closures of the resulting braid are alternating links. The final part of the dissertation focuses on finding the structure of a black-box module or algebra. Suppose we are given black-box access to a finite module M or algebra over a finite ring R and a list of generators for M and R. We show how to find a linear basis and structure constants for M in quantum poly (log|M|) time. This generalizes a recent quantum algorithm of Arvind et al. which finds a basis representation for rings. We then show that our algorithm is a useful primitive allowing quantum computer to determine the structure of a finite associative algebra as a direct sum of simple algebras. Moreover, it solves a wide variety of problems regarding finite modules and rings. Although our quantum algorithm is based on Abelian Fourier transforms, it solves problems regarding the multiplicative structure of modules and algebras, which need not be commutative. Examples include finding the intersection and quotient of two modules, finding the additive and multiplicative identities in a module, computing the order of an module, solving linear equations over modules, deciding whether an ideal is maximal, finding annihilators, and testing the injectivity and surjectivity of ring homomorphisms. These problems appear to be exponentially hard classically.
ID: 031001318; System requirements: World Wide Web browser and PDF reader.; Mode of access: World Wide Web.; Title from PDF title page (viewed March 27, 2013).; Thesis (Ph.D.)--University of Central Florida, 2012.; Includes bibliographical references (p. 82-86).
Ph.D.
Doctorate
Mathematics
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Mathematics
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Ambrose, Sophie. "Matrix groups : theory, algorithms and applications." University of Western Australia. School of Mathematics and Statistics, 2006. http://theses.library.uwa.edu.au/adt-WU2006.0112.

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[Abstract] This thesis is divided into two parts, both containing algorithms for dealing with matrices and matrix groups. Part I is concerned with individual matrices over an arbitrary field. Our algorithms make use of a sequence called the rank profile which is related to the linear dependence relations between the columns of a matrix. First we look at LSP decompositions of matrices as defined by Ibarra et al. in 1982. This decomposition is related to, and a little more general than, the LUP decomposition. The algorithm given by Ibarra et al. to compute an LSP decomposition was only defined for m?n matrices where m ≤ n and is claimed to have the same asymptotic cost as matrix multiplication. We prove that their cost analysis overlooked some aspects of the computation and present a new version of the algorithm which finds both an LSP decomposition and the rank profile of any matrix. The cost of our algorithm is the same as that claimed by Ibarra et al. when m ≤ n and has a similar cost when m > n. One of the steps in the Ibarra et al. algorithm is not completely explicit, so that any one of several choices can be made. Our algorithm is designed so that the particular choice made at this point allows for the simultaneous calculation of the rank profile. Next we study algorithms to find the characteristic polynomial of a square matrix. The current fastest algorithm to find the characteristic polynomial of a square matrix was developed by Keller-Gehrig in 1985. We present a new, simpler version of this algorithm with the same cost which makes the algorithm?s reliance on the rank profile explicit. In Part II we present generalised sifting, a scheme for creating Monte Carlo black box constructive group recognition algorithms. Generalised sifting is designed to facilitate computation in a known group, specifically re-writing arbitrary elements as words or straight-line programs in a standard generating set. It can also be used to create membership tests in black-box groups. Generalised sifting was inspired by the subgroup sifting techniques originally introduced by Sims in 1970 but uses a chain of subsets rather than subgroups. We break the problem down into a sequence of separately analysed and proven steps which sift down into each subset in turn ... All of the algorithms in Parts I and II are given with a theoretical proof and (where appropriate) complexity analysis. The LSP decomposition, characteristic polynomial and generalised sifting algorithms have all been implemented and tested in the computer algebra package GAP.
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Hedmark, Dustin g. "The Partition Lattice in Many Guises." UKnowledge, 2017. http://uknowledge.uky.edu/math_etds/48.

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This dissertation is divided into four chapters. In Chapter 2 the equivariant homology groups of upper order ideals in the partition lattice are computed. The homology groups of these filters are written in terms of border strip Specht modules as well as in terms of links in an associated complex in the lattice of compositions. The classification is used to reproduce topological calculations of many well-studied subcomplexes of the partition lattice, including the d-divisible partition lattice and the Frobenius complex. In Chapter 3 the box polynomial B_{m,n}(x) is defined in terms of all integer partitions that fit in an m by n box. The real roots of the box polynomial are completely characterized, and an asymptotically tight bound on the norms of the complex roots is also given. An equivalent definition of the box polynomial is given via applications of the finite difference operator Delta to the monomial x^{m+n}. The box polynomials are also used to find identities counting set partitions with all even or odd blocks, respectively. Chapter 4 extends results from Chapter 3 to give combinatorial proofs for the ordinary generating function for set partitions with all even or all odd block sizes, respectively. This is achieved by looking at a multivariable generating function analog of the Stirling numbers of the second kind using restricted growth words. Chapter 5 introduces a colored variant of the ordered partition lattice, denoted Q_n^{\alpha}, as well an associated complex known as the alpha-colored permutahedron, whose face poset is Q_n^\alpha. Connections between the Eulerian polynomials and Stirling numbers of the second kind are developed via the fibers of a map from Q_n^{\alpha} to the symmetric group on n-elements
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Gustafsson, Nils. "Box Polynomials of Lattice Simplices." Thesis, KTH, Matematik (Avd.), 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-228407.

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The box polynomial of a lattice simplex is a variant of the more well-known h∗-polynomial, where the open fundamental parallelepiped is considered instead of the half-open. Box polynomials are connected to h∗-polynomials by a theorem of Betke and McMullen from 1985. This theorem can be used to prove certain properties of h∗-polynomials, such as unimodality and symmetry. In this thesis, we investigate box polynomials of a certain family of simplices, called s-lecture hall simplices. The h∗-polynomials of these simplices are a generalization of Eulerian polynomials, and were proven to be real-rooted by Savage and Visontai in 2015. We use a modified version of their proof to prove that the box polynomials are also real-rooted, and show that they are a generalization of derangement polynomials. We then use these results to partially answer a conjecture by Brändén and Leander regarding unimodality of h∗-polynomials of s-lecture hall order polytopes.
Boxpolynomet av ett gittersimplex är en variant av det mer kända h∗-polynomet, där den öppna fundamentala parallelepipeden används istället för den halvöppna. Boxpolynom är kopplade till h∗-polynom tack vare en sats av Betke och McMullen från 1985. Denna sats kan användas för att bevisa vissa egenskaper hos h∗-polynom, som t.ex. unimodalitet och symmetri. I denna uppsats undersöker vi boxpolynomen hos en särskild familj av simplex, de så kallade s-hörssalssimplexen. För dessa simplex är h∗-polynomen en generalisering av de Eulerska polynomen, och visades ha endast reella rötter av Savage och Visontai 2015. Vi använder en modifierad version av deras bevis för att bevisa att även boxpolynomen bara har reella rötter, och att de är en generalisering av derangemangpoly-nom. Vi använder sedan dessa resultat för att delvis besvara en förmodan av Brändén och Leander angående unimodaliteten hos h∗-polynomen av s-hörsalsordningspolytoper.
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Said, Laila Refiana. "The influences of cognitive, experiential and habitual factors in online games playing." University of Western Australia. Faculty of Economics and Commerce, 2006. http://theses.library.uwa.edu.au/adt-WU2006.0100.

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[Truncated abstract] Online games are an exciting new trend in the consumption of entertainment and provide the opportunity to examine selected antecedents of online game-playing based on studying the cognitive, experiential and habitual factors. This study was divided into two parts. The first part analysed the structural relations among research variables that might explain online game-playing using the Structural Equation Modeling (SEM) techniques. These analyses were conducted on a final sample of 218 online gamers. Specific issues examined were: If the variables of Perceived Game Performance, Satisfaction, Hedonic Responses, Flow and Habit Strength influence the Intention to Replay an online game. The importance of factors such as Hedonic Responses and Flow on Satisfaction in online game play. In addition to the SEM, analyses of the participants? reported past playing behaviour were conducted to test whether past game play was simply a matter of random frequency of past behaviour, or followed the specific pattern of the Negative Binomial Distribution (NBD). … The playing-time distribution was not significantly different to the Gamma distribution, in which the largest number of gamers plays for a short time (light gamers) and only a few gamers account for a large proportion of playing time (heavy gamers). Therefore, the reported time play followed a simple and predictable NBD pattern (Chisquare=. 390; p>.05). This study contributes to knowledge in the immediate field of online games and to the wider body of literature on consumer research. The findings demonstrate that gamers tend to act habitually in their playing behaviour. These findings support the argument that past behaviour (habit) is a better explanation of future behaviour than possible cognitive and affective explanations, especially for the apparent routinesed behaviour pattern on online games. The pattern of online game-playing is consistent with the finding of the NBD pattern in television viewing, in which the generalisability of the NBD model has been found in stable environments of repetitive behaviour. This supports the application of the NBD to areas beyond those of patterns in gambling and the purchase of consumer items. The findings have implications both for managerial and public policy decision-making.
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Maeda, Kazuki. "Theory of Discrete and Ultradiscrete Integrable Finite Lattices Associated with Orthogonal Polynomials and Its Applications." 京都大学 (Kyoto University), 2014. http://hdl.handle.net/2433/188859.

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Νίκας, Ιωάννης. "Αριθμητική επίλυση μη γραμμικών παραμετρικών εξισώσεων και ολική βελτιστοποίηση με διαστηματική ανάλυση." Thesis, 2011. http://hdl.handle.net/10889/4919.

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Η παρούσα διδακτορική διατριβή πραγματεύεται το θέμα της αποδοτικής και με βεβαιότητα εύρεσης όλων των ριζών της παραμετρικής εξίσωσης f(x;[p]) = 0, μιας συνεχώς διαφορίσιμης συνάρτησης f με [p] ένα διάνυσμα που περιγράφει όλες τις παραμέτρους της παραμετρικής εξίσωσης και τυποποιούνται με τη μορφή διαστημάτων. Για την επίλυση αυτού του προβλήματος χρησιμοποιήθηκαν εργαλεία της Διαστηματικής Ανάλυσης. Το κίνητρο για την ερευνητική ενασχόληση με το παραπάνω πρόβλημα προέκυψε μέσα από ένα κλασικό πρόβλημα αριθμητικής ανάλυσης: την αριθμητική επίλυση συστημάτων πολυωνυμικών εξισώσεων μέσω διαστηματικής ανάλυσης. Πιο συγκεκριμένα, προτάθηκε μια ευρετική τεχνική αναδιάταξης του αρχικού πολυωνυμικού συστήματος που φαίνεται να βελτιώνει σημαντικά, κάθε φορά, τον χρησιμοποιούμενο επιλυτή. Η ανάπτυξη, καθώς και τα αποτελέσματα αυτής της εργασίας αποτυπώνονται στο Κεφάλαιο 2 της παρούσας διατριβής. Στο επόμενο Κεφάλαιο 3, προτείνεται μια μεθοδολογία για την αποδοτική και αξιόπιστη επίλυση μη-γραμμικών εξισώσεων με διαστηματικές παραμέτρους, δηλαδή την αποδοτική και αξιόπιστη επίλυση διαστηματικών εξισώσεων. Πρώτα, δίνεται μια νέα διατύπωση της Διαστηματικής Αριθμητικής και αποδεικνύεται η ισοδυναμία της με τον κλασσικό ορισμό. Στη συνέχεια, χρησιμοποιείται η νέα διατύπωση της Διαστηματικής Αριθμητικής ως θεωρητικό εργαλείο για την ανάπτυξη μιας επέκτασης της διαστηματικής μεθόδου Newton που δύναται να επιλύσει όχι μόνο κλασικές μη-παραμετρικές μη-γραμμικές εξισώσεις, αλλά και παραμετρικές (διαστηματικές) μη-γραμμικές εξισώσεις. Στο Κεφάλαιο 4 προτείνεται μια νέα προσέγγιση για την αριθμητική επίλυση του προβλήματος της Ολικής Βελτιστοποίησης με περιορισμούς διαστήματα, χρησιμοποιώντας τα αποτελέσματα του Κεφαλαίου 3. Το πρόβλημα της ολικής βελτιστοποίησης, ανάγεται σε πρόβλημα επίλυσης διαστηματικών εξισώσεων, και γίνεται εφικτή η επίλυσή του με τη βοήθεια των θεωρητικών αποτελεσμάτων και της αντίστοιχης μεθοδολογίας του Κεφαλαίου 3. Στο τελευταίο Κεφάλαιο δίνεται μια νέα αλγοριθμική προσέγγιση για το πρόβλημα της επίλυσης διαστηματικών πολυωνυμικών εξισώσεων. Η νέα αυτή προσέγγιση, βασίζεται και γενικεύει την εργασία των Hansen και Walster, οι οποίοι πρότειναν μια μέθοδο για την επίλυση διαστηματικών πολυωνυμικών εξισώσεων 2ου βαθμού.
In this dissertation the problem of finding reliably and with certainty all the zeros a pa-rameterized equation f(x;[p]) = 0, of a continuously differentiable function f is considered, where [p] is an interval vector describing all the parameters of the Equation, which are formed with interval numbers. For this kind of problem, methods of Interval Analysis are used. The incentive to this scientific research was emerged from a classic numerical analysis problem: the numerical solution of polynomial systems of equations using interval analysis. In particular, a heuristic reordering technique of the initial polynomial systems of equations is proposed. This approach seems to improve significantly the used solver. The proposed technique, as well as the results of this publication are presented in Chapter 2 of this dissertation. In the next Chapter 3, a methodology is proposed for solving reliably and efficiently parameterized (interval) equations. Firstly, a new formulation of interval arithmetic is given and the equivalence with the classic one is proved. Then, an extension of interval Newton method is proposed and developed, based on the new formulation of interval arithmetic. The new method is able to solve not only classic non-linear equations but, non-linear parameterized (interval) equation too. In Chapter 4 a new approach on solving the Box-Constrained Global Optimization problem is proposed, based on the results of Chapter 3. In details, the Box-Constrained Global Optimization problem is reduced to a problem of solving interval equations. The solution of this reduction is attainable through the methodology developed in Chapter 3. In the last Chapter of this dissertation a new algorithmic approach is given for the problem of solving reliably and with certainty an interval polynomial equation of degree $n$. This approach consists in a generalization of the work of Hansen and Walster. Hansen and Walster proposed a method for solving only quadratic interval polynomial equations
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Book chapters on the topic "Box polynomial"

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Buchheim, Christoph, and Claudia D’Ambrosio. "Box-Constrained Mixed-Integer Polynomial Optimization Using Separable Underestimators." In Integer Programming and Combinatorial Optimization, 198–209. Cham: Springer International Publishing, 2014. http://dx.doi.org/10.1007/978-3-319-07557-0_17.

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Jacquet, Stéphane, and Sylvain Hallé. "Reformulation of SAT into a Polynomial Box-Constrained Optimization Problem." In Lecture Notes in Computer Science, 387–94. Cham: Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-63461-2_21.

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Courtois, Nicolas T. "The Inverse S-Box, Non-linear Polynomial Relations and Cryptanalysis of Block Ciphers." In Advanced Encryption Standard – AES, 170–88. Berlin, Heidelberg: Springer Berlin Heidelberg, 2005. http://dx.doi.org/10.1007/11506447_15.

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Frosini, Lucia, and Giovanni Petrecca. "Black-Box Identification of the Electromagnetic Torque of Induction Motors: Polynomial and Neural Models." In Intelligent Problem Solving. Methodologies and Approaches, 741–48. Berlin, Heidelberg: Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/3-540-45049-1_90.

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Dinur, Itai, and Adi Shamir. "Cube Attacks on Tweakable Black Box Polynomials." In Advances in Cryptology - EUROCRYPT 2009, 278–99. Berlin, Heidelberg: Springer Berlin Heidelberg, 2009. http://dx.doi.org/10.1007/978-3-642-01001-9_16.

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Dey, Sankhanil, and Ranjan Ghosh. "4, 8, 32, 64 Bit Substitution Box Generation Using Irreducible or Reducible Polynomials Over Galois Field GF(Pq) for Smart Applications." In Security in Smart Cities: Models, Applications, and Challenges, 279–95. Cham: Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-030-01560-2_12.

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"Group Models of Artificial Polynomial and Trigonometric Higher Order Neural Networks." In Emerging Capabilities and Applications of Artificial Higher Order Neural Networks, 137–72. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-3563-9.ch003.

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Real-world financial data is often discontinuous and non-smooth. Neural network group models can perform this function with more accuracy. Both polynomial higher order neural network group (PHONNG) and trigonometric polynomial higher order neural network group (THONNG) models are studied in this chapter. These PHONNG and THONNG models are open box, convergent models capable of approximating any kind of piecewise continuous function, to any degree of accuracy. Moreover, they are capable of handling higher frequency, higher order nonlinear, and discontinuous data. Results confirm that PHONNG and THONNG group models converge without difficulty and are considerably more accurate (0.7542% - 1.0715%) than neural network models such as using polynomial higher order neural network (PHONN) and trigonometric polynomial higher order neural network (THONN) models.
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Zhang, Ming. "Artificial Polynomial and Trigonometric Higher Order Neural Network Group Models." In Artificial Higher Order Neural Networks for Modeling and Simulation, 78–102. IGI Global, 2013. http://dx.doi.org/10.4018/978-1-4666-2175-6.ch005.

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Real world financial data is often discontinuous and non-smooth. Accuracy will be a problem, if we attempt to use neural networks to simulate such functions. Neural network group models can perform this function with more accuracy. Both Polynomial Higher Order Neural Network Group (PHONNG) and Trigonometric polynomial Higher Order Neural Network Group (THONNG) models are studied in this chapter. These PHONNG and THONNG models are open box, convergent models capable of approximating any kind of piecewise continuous function to any degree of accuracy. Moreover, they are capable of handling higher frequency, higher order nonlinear, and discontinuous data. Results obtained using Polynomial Higher Order Neural Network Group and Trigonometric polynomial Higher Order Neural Network Group financial simulators are presented, which confirm that PHONNG and THONNG group models converge without difficulty, and are considerably more accurate (0.7542% - 1.0715%) than neural network models such as using Polynomial Higher Order Neural Network (PHONN) and Trigonometric polynomial Higher Order Neural Network (THONN) models.
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Zhang, Ming. "Cosine and Sigmoid Higher Order Neural Networks for Data Simulations." In Advances in Computational Intelligence and Robotics, 237–52. IGI Global, 2016. http://dx.doi.org/10.4018/978-1-5225-0063-6.ch010.

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New open box and nonlinear model of Cosine and Sigmoid Higher Order Neural Network (CS-HONN) is presented in this paper. A new learning algorithm for CS-HONN is also developed from this study. A time series data simulation and analysis system, CS-HONN Simulator, is built based on the CS-HONN models too. Test results show that average error of CS-HONN models are from 2.3436% to 4.6857%, and the average error of Polynomial Higher Order Neural Network (PHONN), Trigonometric Higher Order Neural Network (THONN), and Sigmoid polynomial Higher Order Neural Network (SPHONN) models are from 2.8128% to 4.9077%. It means that CS-HONN models are 0.1174% to 0.4917% better than PHONN, THONN, and SPHONN models.
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"Data Simulations Using Cosine and Sigmoid Higher Order Neural Networks." In Emerging Capabilities and Applications of Artificial Higher Order Neural Networks, 346–74. IGI Global, 2021. http://dx.doi.org/10.4018/978-1-7998-3563-9.ch008.

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A new open box and nonlinear model of cosine and sigmoid higher order neural network (CS-HONN) is presented in this chapter. A new learning algorithm for CS-HONN is also developed in this chapter. In addition, a time series data simulation and analysis system, CS-HONN simulator, is built based on the CS-HONN models. Test results show that the average error of CS-HONN models are from 2.3436% to 4.6857%, and the average error of polynomial higher order neural network (PHONN), trigonometric higher order neural network (THONN), and sigmoid polynomial higher order neural network (SPHONN) models range from 2.8128% to 4.9077%. This suggests that CS-HONN models are 0.1174% to 0.4917% better than PHONN, THONN, and SPHONN models.
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Conference papers on the topic "Box polynomial"

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Kadhim, Alaa F., and Zainab Ali Kamal. "Dynamic S-BOX base on primitive polynomial and chaos theory." In 2018 International Conference on Engineering Technology and their Applications (IICETA). IEEE, 2018. http://dx.doi.org/10.1109/iiceta.2018.8458093.

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Das, Indrajit, Subhrapratim Nath, Sanjoy Roy, and Subhash Mondal. "Random S-Box generation in AES by changing irreducible polynomial." In 2012 International Conference on Communications, Devices and Intelligent Systems (CODIS). IEEE, 2012. http://dx.doi.org/10.1109/codis.2012.6422263.

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Dumas, Jean-Guillaume, Clément Pernet, and B. David Saunders. "On finding multiplicities of characteristic polynomial factors of black-box matrices." In the 2009 international symposium. New York, New York, USA: ACM Press, 2009. http://dx.doi.org/10.1145/1576702.1576723.

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Elloumi, Sourour, Amelie Lambert, and Arnaud Lazare. "Semidefinite programming relaxations through quadratic reformulation for box-constrained polynomial optimization problems." In 2019 6th International Conference on Control, Decision and Information Technologies (CoDIT). IEEE, 2019. http://dx.doi.org/10.1109/codit.2019.8820690.

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Alamsyah, Agus Bejo, and Teguh Bharata Adji. "AES S-box construction using different irreducible polynomial and constant 8-bit vector." In 2017 IEEE Conference on Dependable and Secure Computing. IEEE, 2017. http://dx.doi.org/10.1109/desec.2017.8073857.

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Alamsyah. "Improving the Quality of AES S-box by Modifications Irreducible Polynomial and Affine Matrix." In 2020 Fifth International Conference on Informatics and Computing (ICIC). IEEE, 2020. http://dx.doi.org/10.1109/icic50835.2020.9288567.

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Karnin, Zohar S., and Amir Shpilka. "Black Box Polynomial Identity Testing of Generalized Depth-3 Arithmetic Circuits with Bounded Top Fan-In." In 2008 23rd Annual IEEE Conference on Computational Complexity. IEEE, 2008. http://dx.doi.org/10.1109/ccc.2008.15.

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Al-Janabi, Samaher, and Esraa Alwan. "Soft Mathematical System to Solve Black Box Problem through Development the FARB Based on Hyperbolic and Polynomial Functions." In 2017 10th International Conference on Developments in eSystems Engineering (DeSE). IEEE, 2017. http://dx.doi.org/10.1109/dese.2017.23.

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Carvalho de Castro, Henrique, and Bruno Henrique Groenner Barbosa. "Multi-gene Genetic Programming for Structure Selection of Polynomial NARMAX models." In Congresso Brasileiro de Automática - 2020. sbabra, 2020. http://dx.doi.org/10.48011/asba.v2i1.1384.

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In the area of black-box identication, NARMAX models are of great interest. The main diculty faced when working with such models is the selection of the correct structure to represent the underlying system in the data. Orthogonal Least Squares (OLS) methods are widely used for this task, however, there are systems with a high degree of non-linearity and long term dependencies, which makes the use of traditional OLS methods computationally impracticable. In this sense, this paper studies the use of Multi-Gene Genetic Programing (MGGP) together with the traditional OLS method to increase the search space and turn the structure selection practicable for average performance computer. It is shown that, in real-life problem data, the algorithm can nd better models than previous works' models. The MGGP found a model for a hydraulic pumping system with a better one-step-ahead prediction error (0:058 mlc2 against 0:070 mlc2) using PEM technique and better free-run simulation error (0:997 mlc2 against 1:120 mlc2) using SEM technique. The MGGP found a model with such a degree of non-linearity and maximum input-output lags that totalizes 142505 candidate terms for traditional OLS analysis, which is impracticable for average performance computers.
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Lee, Sang Hoon, and Wei Chen. "A Comparative Study of Uncertainty Propagation Methods for Black-Box Type Functions." In ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/detc2007-35533.

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It is an important step in deign under uncertainty to select an appropriate uncertainty propagation (UP) method considering the characteristics of the engineering systems at hand, the required level of UP associated with the probabilistic design scenario, and the required accuracy and efficiency levels. Many uncertainty propagation methods have been developed in various fields, however, there is a lack of good understanding of their relative merits. In this paper, a comparative study on the performances of several UP methods, including a few recent methods that have received growing attention, is performed. The full factorial numerical integration (FFNI), the univariate dimension reduction method (UDR), and the polynomial chaos expansion (PCE) are implemented and applied to several test problems with different settings of the performance nonlinearity, distribution types of input random variables, and the magnitude of input uncertainty. The performances of those methods are compared in moment estimation, tail probability calculation, and the probability density function (PDF) construction. It is found that the FFNI with the moment matching quadrature rule shows good accuracy but the computational cost becomes prohibitive as the number of input random variables increases. The accuracy and efficiency of the UDR method for moment estimations appear to be superior when there is no significant interaction effect in the performance function. Both FFNI and UDR are very robust against the non-normality of input variables. The PCE is implemented in combination with FFNI for coefficients estimation. The PCE method is shown to be a useful approach when a complete PDF description is desired. Inverse Rosenblatt transformation is used to treat non-normal inputs of PCE, however, it is shown that the transformation may result in the degradation of accuracy of PCE. It is also shown that in black-box type of system the performance and convergence of PCE highly depend on the method adopted to estimate its coefficients.
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Reports on the topic "Box polynomial"

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De Boor, Carl, Nira Dyn, and Amos Ron. On Two Polynomial Spaces Associated with a Box Spline. Fort Belvoir, VA: Defense Technical Information Center, April 1989. http://dx.doi.org/10.21236/ada210559.

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