Academic literature on the topic 'Integer sequence generation'

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Journal articles on the topic "Integer sequence generation"

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Sabri, Ahmad, and Vincent Vajnovszki. "On the exhaustive generation of generalized ballot sequences in lexicographic and Gray code order." Pure Mathematics and Applications 28, no. 1 (2019): 109–19. http://dx.doi.org/10.1515/puma-2015-0035.

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Abstract A generalized (resp. p-ary) ballot sequence is a sequence over the set of non-negative integers (resp. integers less than p) where in any of its prefixes each positive integer i occurs at most as often as any integer less than i. We show that the Reected Gray Code order induces a cyclic 3-adjacent Gray code on both, the set of fixed length generalized ballot sequences and p-ary ballot sequences when p is even, that is, ordered list where consecutive sequences (regarding the list cyclically) differ in at most 3 adjacent positions. Non-trivial efficient generating algorithms for these ballot sequences, in lexicographic order and for the obtained Gray codes, are also presented.
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Massazza, Paolo. "A Dynamical System Approach to Polyominoes Generation*." Fundamenta Informaticae 180, no. 3 (2021): 251–73. http://dx.doi.org/10.3233/fi-2021-2040.

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We describe a method which exploits discrete dynamical systems to generate suitable classes of polyominoes. We apply the method to design an algorithm that uses O(n) space to generate in constant amortized time all polyominoes corresponding to hole-free partially directed animals consisting of n sites on the square grid. By implementing the algorithm in C++ we have obtained a new sequence that does not appear in the On-Line Encyclopedia of Integer Sequences.
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Lee, Suk-Hwan. "Reversible Data Hiding for DNA Sequence Using Multilevel Histogram Shifting." Security and Communication Networks 2018 (2018): 1–13. http://dx.doi.org/10.1155/2018/3530969.

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A large number of studies have examined DNA storage to achieve information hiding in DNA sequences with DNA computing technology. However, most data hiding methods are irreversible in that the original DNA sequence cannot be recovered from the watermarked DNA sequence. This study presents reversible data hiding methods based on multilevel histogram shifting to prevent biological mutations, preserve sequence length, increase watermark capacity, and facilitate blind detection/recovery. The main features of our method are as follows. First, we encode a sequence of nucleotide bases with four-character symbols into integer values using the numeric order. Second, we embed multiple bits in each integer value by multilevel histogram shifting of noncircular type (NHS) and circular type (CHS). Third, we prevent the generation of false start/stop codons by verifying whether a start/stop codon is included in an integer value or between adjacent integer values. The results of our experiments confirmed that the NHS- and CHS-based methods have higher watermark capacities than conventional methods in terms of supplementary data used for decoding. Moreover, unlike conventional methods, our methods do not generate false start/stop codons.
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Liu, Bo, Jiandong Liu, Shuhong Wang, Ming Zhong, Bo Li, and Yujie Liu. "HEVC Video Encryption Algorithm Based on Integer Dynamic Coupling Tent Mapping." Journal of Advanced Computational Intelligence and Intelligent Informatics 24, no. 3 (2020): 335–45. http://dx.doi.org/10.20965/jaciii.2020.p0335.

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A selective encryption algorithm is proposed to improve the efficiency of high efficiency video coding (HEVC) video encryption and ensure the security of HEVC videos. The algorithm adopts the integer dynamic coupling tent mapping optimization model as the pseudo-random sequence generator, and multi-core parallelization is used as the sequence generation mechanism. The binstrings during the process of context adaptive binary arithmetic coding are selected for encryption, which conforms to the features of invariable binstream and compatible format in terms of video encryption. Performance tests for six types of standard videos with different resolutions were performed. The results indicated that the encryption algorithm has a large key space and benefits from a high encryption effect.
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Wang, Qianxue, Simin Yu, Christophe Guyeux, Jacques M. Bahi, and Xiaole Fang. "Theoretical Design and Circuit Implementation of Integer Domain Chaotic Systems." International Journal of Bifurcation and Chaos 24, no. 10 (2014): 1450128. http://dx.doi.org/10.1142/s0218127414501284.

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In this paper, a new approach for constructing integer domain chaotic systems (IDCS) is proposed, and its chaotic behavior is mathematically proven according to Devaney's definition of chaos. Furthermore, an analog-digital hybrid circuit is also developed for realizing the designed basic IDCS. In the IDCS circuit design, chaos generation strategy is realized through a sample-hold circuit and a decoder circuit so as to convert the uniform noise signal into a random sequence, which plays a key role in circuit implementation. The experimental observations further validate the proposed systematic methodology for the first time.
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Hornfeck, Wolfgang. "Chiral spiral cyclic twins." Acta Crystallographica Section A Foundations and Advances 78, no. 1 (2022): 21–35. http://dx.doi.org/10.1107/s2053273321012237.

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A formula is presented for the generation of chiral m-fold multiply twinned two-dimensional point sets of even twin modulus m > 6 from an integer inclination sequence; in particular, it is discussed for the first three non-degenerate cases m = 8, 10, 12, which share a connection to the aperiodic crystallography of axial quasicrystals exhibiting octagonal, decagonal and dodecagonal long-range orientational order and symmetry.
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Pratihar, Sanjoy, and Partha Bhowmick. "On the Farey sequence and its augmentation for applications to image analysis." International Journal of Applied Mathematics and Computer Science 27, no. 3 (2017): 637–58. http://dx.doi.org/10.1515/amcs-2017-0045.

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AbstractWe introduce a novel concept of theaugmented Farey table(AFT). Its purpose is to store the ranks of fractions of aFarey sequencein an efficient manner so as to return therankof any query fraction in constant time. As a result, computations on the digital plane can be crafted down to simple integer operations; for example, the tasks like determining the extent of collinearity of integer points or of parallelism of straight lines—often required to solve many image-analytic problems—can be made fast and efficient through an appropriate AFT-based tool. We derive certain interesting characterizations of an AFT for its efficient generation. We also show how, for a fraction not present in a Farey sequence, the rank of thenearest fractionin that sequence can efficiently be obtained by theregula falsimethod from the AFT concerned. To assert its merit, we show its use in two applications—one in polygonal approximation of digital curves and the other in skew correction of engineering drawings in document images. Experimental results indicate the potential of the AFT in such image-analytic applications.
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Moftah, Khaled. "Block Format Solves the Collatz Conjecture." Journal of Advances in Mathematics and Computer Science 39, no. 4 (2024): 24–36. http://dx.doi.org/10.9734/jamcs/2024/v39i41880.

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Blocks are unit convergence between two consecutive odd numbers formed according to the three x plus one conjecture rules. The left odd number is the left hook, L, and the right odd number is the right hook, R. They include even numbers between their boundaries. They are divided into families (F1 = 5, 11, 17, … & F2 = 1, 7, 11, … & F3 = 3, 9, 15, …) and groups based on their group length (The number of the middle-even numbers between the two hooks). Blocks are taken individually and placed beside each other, similar to the domino tiles play, which, by their formulation, satisfies the conjecture rules. Formed chains reach number one in the convergence mode or continue generating odd positive numbers infinitely according to the generation mode. The final convergence to number one is reached because these blocks have all the positive integers included as left hooks (L1, L2, L3), and all the F1 and F2 odd positive numbers are included as right hooks (R1 and R2). Block rules mandate that a single left hook produces only one right hook. Accordingly, no looping or entanglement (Joining and consequent splitting) between chain branches would occur. Statistics show that R cannot increase infinitely. Repeated oscillation up and down without reaching number one would also violate the statistics. Statistics reveal that blocks of various lengths have a strict occurrence and repetition sequence along the positive integer series. Block lengths can extend infinitely, and each block length repeats its occurrence infinitely. In the generation mode, blocks are attached in reverse order to the conjecture/convergence rules. According to the rules, all positive integers can be generated starting from number one. Multiple sequences and clusters of specific block lengths occur according to specific rules and cannot continue infinitely.
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Andreani, Virgile, Eric J. South, and Mary J. Dunlop. "Generating information-dense promoter sequences with optimal string packing." PLOS Computational Biology 20, no. 7 (2024): e1012276. http://dx.doi.org/10.1371/journal.pcbi.1012276.

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Dense arrangements of binding sites within nucleotide sequences can collectively influence downstream transcription rates or initiate biomolecular interactions. For example, natural promoter regions can harbor many overlapping transcription factor binding sites that influence the rate of transcription initiation. Despite the prevalence of overlapping binding sites in nature, rapid design of nucleotide sequences with many overlapping sites remains a challenge. Here, we show that this is an NP-hard problem, coined here as the nucleotide String Packing Problem (SPP). We then introduce a computational technique that efficiently assembles sets of DNA-protein binding sites into dense, contiguous stretches of double-stranded DNA. For the efficient design of nucleotide sequences spanning hundreds of base pairs, we reduce the SPP to an Orienteering Problem with integer distances, and then leverage modern integer linear programming solvers. Our method optimally packs sets of 20–100 binding sites into dense nucleotide arrays of 50–300 base pairs in 0.05–10 seconds. Unlike approximation algorithms or meta-heuristics, our approach finds provably optimal solutions. We demonstrate how our method can generate large sets of diverse sequences suitable for library generation, where the frequency of binding site usage across the returned sequences can be controlled by modulating the objective function. As an example, we then show how adding additional constraints, like the inclusion of sequence elements with fixed positions, allows for the design of bacterial promoters. The nucleotide string packing approach we present can accelerate the design of sequences with complex DNA-protein interactions. When used in combination with synthesis and high-throughput screening, this design strategy could help interrogate how complex binding site arrangements impact either gene expression or biomolecular mechanisms in varied cellular contexts.
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Rawal, Shruti, and Indivar Gupta. "Solution of Large Sparse System of Linear Equations over GF(2) on a Multi Node Multi GPU Platform." Defence Science Journal 72, no. 6 (2022): 836–45. http://dx.doi.org/10.14429/dsj.72.17656.

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We provide an efficient multi-node, multi-GPU implementation of the Block Wiedemann Algorithm (BWA)to find the solution of a large sparse system of linear equations over GF(2). One of the important applications ofsolving such systems arises in most integer factorization algorithms like Number Field Sieve. In this paper, wedescribe how hybrid parallelization can be adapted to speed up the most time-consuming sequence generation stage of BWA. This stage involves generating a sequence of matrix-matrix products and matrix transpose-matrix products where the matrices are very large, highly sparse, and have entries over GF(2). We describe a GPU-accelerated parallel method for the computation of these matrix-matrix products using techniques like row-wise parallel distribution of the first matrix over multi-node multi-GPU platform using MPI and CUDA and word-wise XORing of rows of the second matrix. We also describe the hybrid parallelization of matrix transpose-matrix product computation, where we divide both the matrices row-wise into equal-sized blocks using MPI. Then after a GPU-accelerated matrix transpose-matrix product generation, we combine all those blocks using MPI_BXOR operation in MPI_Reduce to obtain the result. The performance of hybrid parallelization of the sequence generation step on a hybrid cluster using multiple GPUs has been compared with parallelization on only multiple MPI processors. We have used this hybrid parallel sequence generation tool for the benchmarking of an HPC cluster. Detailed timings of the complete solution of number field sieve matrices of RSA-130, RSA-140, and RSA-170 are also compared in this paper using up to 4 NVidia V100 GPUs of a DGX station. We got a speedup of 2.8 after parallelization on 4 V100 GPUs compared to that over 1 GPU.
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Dissertations / Theses on the topic "Integer sequence generation"

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Gupta, Kapil. "Combinatorial optimization and application to DNA sequence analysis." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26676.

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Thesis (Ph.D)--Industrial and Systems Engineering, Georgia Institute of Technology, 2009.<br>Committee Chair: Lee, Eva K.; Committee Member: Barnes, Earl; Committee Member: Fan, Yuhong; Committee Member: Johnson, Ellis; Committee Member: Yuan, Ming. Part of the SMARTech Electronic Thesis and Dissertation Collection.
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NOCENTINI, MASSIMO. "An algebraic and combinatorial study of some infinite sequences of numbers supported by symbolic and logic computation." Doctoral thesis, 2019. http://hdl.handle.net/2158/1217082.

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The subject of the thesis concerns the study of infinite sequences, in one or two dimensions, supporting the theoretical aspects with systems for symbolic and logic computation. In particular, in the thesis some sequences related to Riordan arrays are examined from both an algebraic and combinatorial points of view and also by using approaches usually applied in numerical analysis. Another part concerns sequences that enumerate particular combinatorial objects, such as trees, polyominoes, and lattice paths, generated by symbolic and certified computations; moreover, tiling problems and backtracking techniques are studied in depth and enumeration of recursive structures are also given. We propose a preliminary suite of tools to interact with the Online Encyclopedia of Integer Sequences, providing a crawling facility to download sequences recursively according to their cross references, pretty-printing them and, finally, drawing graphs representing their connections. In the context of automatic proof derivation, an extension to an automatic theorem prover is proposed to support the relational programming paradigm. This allows us to encode facts about combinatorial objects and to enumerate the corresponding languages by producing certified theorems at the same time. As a concrete illustration, we provide many chunks of code written using functional programming languages; our focus is to support theoretical derivations using sound, clear and elegant implementations to check their validity.
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Book chapters on the topic "Integer sequence generation"

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Thirumalai, Ashwath, and J. Ramanujam. "Fast address sequence generation for data-parallel programs using integer lattices." In Languages and Compilers for Parallel Computing. Springer Berlin Heidelberg, 1996. http://dx.doi.org/10.1007/bfb0014200.

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Stafford, Peter J. "Risk Oriented Earthquake Hazard Assessment: Influence of Spatial Discretisation and Non-ergodic Ground-Motion Models." In Springer Tracts in Civil Engineering. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-68813-4_8.

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AbstractThree important aspects of ground-motion modelling for regional or portfolio risk analyses are discussed. The first issue is the treatment of discretisation of continuous ground-motion fields for generating spatially correlated discrete fields. Shortcomings of the present approach in which correlation models based upon point estimates of ground motions are used to represent correlations within and between spatial regions are highlighted. It is shown that risk results will be dependent upon the chosen spatial resolution if the effects of discretisation are not adequately treated. Two aspects of non-ergodic groundmotion modelling are then discussed. Correlation models generally used within risk modelling are traditionally based upon very simple partitioning of ground-motion residuals. As regional risk analyses move to non-ergodic applications where systematic site effects are considered, these correlation models (both inter-period and spatial models) need to be revised. The nature of these revisions are shown herein. Finally, evidence for significantly reduced between-event variability within earthquake sequences is presented. The ability to progressively constrain location and sequence-dependent systematic offsets from ergodic models as earthquake sequences develop can have significant implications for aftershock risk assessments.
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Jain, Deepak, Ashwani kumar, and C. D. D Guruprakash. "IMPLEMENTATION OF AN EFFICIENT PSEUDORANDOM BIT GENERATION METHOD AND ITS VLSI ARCHITECTURE." In 9th National Conference & Exhibition on Emerging and Innovative Trends in Engineering Technology (NCEEITET). IARS' Press Australia, 2023. https://doi.org/10.62431/wr0x0956.

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Hence, data security has become a top priority. Cryptographic methods help resource-constrained smart devices encrypt and decrypt data. This protects data. PRBGs generate pseudo-random binary sequences from seeds. The cryptographic method's essential building element assures data secrecy. Academic research has used PRBG methods to generate pseudorandom bit sequences. Blum-Blum-Shub (BBS) PRBG is unexpected and cryptographically safe. BBS implementation requires huge integer modular multiplication. This makes the process computationally slow or costly. Han-Carlson adders and Montgomery modular multiplication are proposed for a low-latency BBS design. This will significantly reduce crucial route and computational delay. While improving the critical path, this technique has O(2n) clock delay due to recurrent calculation. This constraint necessitates research on a low hardware complexity coupled-LCG (CLCG) approach. CLCG uses a smaller region, reduced latency, and longer durations than BBS. Nevertheless, it fails the spectrum test, which can be rectified by dual-coupling four LCGs. The dual-CLCG approach requires inequality equations to obtain a valid one-bit random outcome. Inequality equations govern this procedure. Inequality equations slow the hardware implementation of the dual-CLCG approach for pseudorandom bit generation at every uniform clock rate. The thesis proposes a memory-based dual-CLCG architecture to solve this challenge. This architecture creates pseudorandom bits periodically. Its drawbacks include a high beginning clock delay, needless memory use, and a shorter sequence duration than other algorithms. This thesis presents two new PRBG algorithms and VLSI designs to solve these problems. These approaches create a pseudorandom bit every clock cycle with simple electronics. Both methods achieve the maximum length sequence and consistently pass all fifteen NIST benchmark tests. The recommended designs are built using Verilog HDL and prototyped using a commercial FPGA device in a lab. PRBG algorithms may assist produce pseudorandom bits in hardware security applications.
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"Integer arithmetic." In An introduction to Numerical Methods in C++, edited by B. H. Flowers. Oxford University PressOxford, 2000. http://dx.doi.org/10.1093/oso/9780198506935.003.0007.

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Abstract In this chapter we briefly study three branches of mathematics in which arithmetic is conducted mostly in terms of integers: prime number factorization, rational arithmetic, and the generation of sequences of numbers which for practical purposes, and in a sense to be investigated, may be regarded as random. In the next chapter we study the extent to which such sequences come up to expectations. We begin this chapter, however, by recalling some of the well-known properties of the prime numbers, the foundations of any theory of arithmetic.
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Zhang Yuhong and Chen Feng. "High Performance Sequence Mining Using Pairwise Statistical Significance." In Advances in Parallel Computing. IOS Press, 2013. https://doi.org/10.3233/978-1-61499-324-7-194.

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With the amount of sequence data deluge as a result of next generation sequencing, there comes the need to leverage the large-scale biological sequence data. Therefore, the role of high performance computational methods for mining interesting information solely from these sequence data becomes increasingly important. Almost every research issue in bioinformatics counts on the inter-relationship between sequences, structure and function. Although pairwise statistical significance (PSS) has been found to be capable of accurately mining related sequences (homologs), its estimation is both computationally and data intensive. To prevent it from being a performance bottleneck, high performance computation (HPC) approaches are used for accelerating the computation. In this chapter, we first present the algorithm of pairwise statistical significance estimation, then highlight the use of such HPC approaches for its acceleration employing multi-core CPU and many-core GPU, both of which enable significant performance improvement for pairwise statistical significance estimation (PSSE).
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Praveena, Hirald Dwaraka, Katta Sudha, Dr P. Geetha, and M. Venkatanaresh. "PERFORMANCE ANALYSIS OF WAVELET BASED OFDM IN LTE." In Futuristic Trends in Network & Communication Technologies Volume 2 Book 19. Iterative International Publishers, Selfypage Developers Pvt Ltd, 2023. http://dx.doi.org/10.58532/v2bs19p3ch3.

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Long term Evolution (LTE) is a noteworthy undertaking of third Generation Partnership Project, as a move from the third generation (3G) to the fourth generation(4G), has accomplished incredible limit and fast of cellular phone systems without uncertainty. Orthogonal Frequency Division Multiplexing (OFDM) is principal procedure utilized in fourth Generation Long Term Evolution (LTE). Inter Carrier Interference (ICI) and Inter Symbol Interference (ISI) are both problems occur in OFDM due to the loss of subcarrier orthogonality and to defeat this issue utilization of Cyclic Prefixing (CP) is required, which utilizes 20% of available data. usually, OFDM is executed utilizing FFT, then again OFDM can be implemented utilizing orthogonal wavelets. Regardless of the way that are execution of the OFDM structure absolutely a couple inconvenience. One of the genuine drawbacks is the high Peak to Average Power Ratio (PAPR) which realize broad measure of sub-transporters that make controls for possible applications. Partial Transmit Sequence and clipping are some PAPR diminish techniques that have been proposed to defeat this issue
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Çetinkaya, Arda, and Nurten Ayşe Akarsu. "Yeni Nesil Dna Dizileme Yöntemi İle Tüm Ekzom Ve Genom Dizileme." In Moleküler Biyoloji ve Genetik. Türkiye Bilimler Akademisi, 2023. http://dx.doi.org/10.53478/tuba.978-625-8352-48-1.ch07.

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Human reference genome, the most important outcome of the Human Genome Project, has led to revolutionary developments in many fields of human genetics including genetic diagnostics. However, human genome project was lacked in displaying inter-individual genomic variability. This vacuum was filled by widespread usage of second generation sequencing, also known as next-generation sequencing. Today, the vast information about human genome diversity obtained by such sequencing methods are accessible to clinicians and researchers through several databases. Second generation sequencing is a method involving the simultaneous sequencing of small DNA fragments in parallel, together with combination and analysis of the sequence information through bioinformatic tools. Currently, this method allows for sequencing of a whole human genome (WGS) in one single run. However, whole exome sequencing (WES) focusing on only protein/RNA coding exonic regions or other limited sequencing methods are in more common use. In this chapter, the principles making second generation sequencing technologies available, analysis of second generation sequencing, constraints and superiority of the technology will be explained. Additionally, the impact of second generation sequencing with a special focus on the field of medicine will be mentioned.
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Hoffman, P. N., and J. F. Humphreys. "Explicit Q-functions." In Projective Representations of the Symmetric Groups. Oxford University PressOxford, 1992. http://dx.doi.org/10.1093/oso/9780198535560.003.0009.

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Abstract More details concerning the Q-functions are given in this chapter. Motivated by Theorem 7.21, we first define a function Q a for each integer sequence α; but then immediately show that if α: is not a strict partition, then Q a is either zero or is a multiple of Q A for a certain γ in 𝒟. The Q a are needed in Chapter 10, but they also play a role in a Laurent identity, (9.5) here. This is a generating “expression” for the Q a. It could be re-interpreted as a raising operator formula, such as occurs in the theory of Schur functions, but we prefer to use the Laurent formulation. It leads to four more formulae for Q A.
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J. Miana, Pedro, and Natalia Romero. "Moments of Catalan Triangle Numbers." In Number Theory and Its Applications. IntechOpen, 2020. http://dx.doi.org/10.5772/intechopen.92046.

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In this chapter, we consider the Catalan numbers, C n = 1 n + 1 2 n n , and two of their generalizations, Catalan triangle numbers, B n , k and A n , k , for n , k ∈ N . They are combinatorial numbers and present interesting properties as recursive formulae, generating functions and combinatorial interpretations. We treat the moments of these Catalan triangle numbers, i.e., with the following sums: ∑ k = 1 n k m B n , k j , ∑ k = 1 n + 1 2 k − 1 m A n , k j , for j , n ∈ N and m ∈ N ∪ 0 . We present their closed expressions for some values of m and j . Alternating sums are also considered for particular powers. Other famous integer sequences are studied in Section 3, and its connection with Catalan triangle numbers are given in Section 4. Finally we conjecture some properties of divisibility of moments and alternating sums of powers in the last section.
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Diamantides, Marinos, and Anton Schütz. "The Transition from Secularism to Post-secularism." In Political Theology. Edinburgh University Press, 2017. http://dx.doi.org/10.3366/edinburgh/9780748697762.003.0007.

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Modernity has been forcing upon the entire world population a mercilessly uniform presto-accelerando tempo resulting in a de-regulated march towards ever more condensed rhythms of adaptation, competition, decision, transformation and, most decisively, self-transformation. It is a movement in which the adagio rhythm of human existence, understood as a matter of generations and inter-generational transmission, has been giving way to the feverish rattling of technogenous, e.g. micro-informatic-driven, innovations. In this chapter we first show how this process, far from stemming from a rupture with the medieval world, spans from origins in religious rituals and dogmas all the way to the moving target of secularization. In this regard we try to make graspable the differential social-cum-governmental techniques that set off, for a millennium and more, the Christian-cum-post-Christian West from the Byzantine East, and, specifically, the game of ‘hide and seek' forever underlying the relation between ‘glorious’ politics and oikonomia/management that was perfected in the Occident. We argue that this occidental-cum-universalist dualist machinery has, no doubt foreseeably, been fated to grind to a halt once the horizon of a boundlessly successful continuation of its ambitious logic elicited the first signs of its long-term un-sustainability, i.e. of its incapacity of providing endless further sequences of increase or escalation.
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Conference papers on the topic "Integer sequence generation"

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Svatoš, Martin, Peter Jung, Jan Tóth, Yuyi Wang, and Ondřej Kuželka. "On Discovering Interesting Combinatorial Integer Sequences." In Thirty-Second International Joint Conference on Artificial Intelligence {IJCAI-23}. International Joint Conferences on Artificial Intelligence Organization, 2023. http://dx.doi.org/10.24963/ijcai.2023/372.

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We study the problem of generating interesting integer sequences with a combinatorial interpretation. For this we introduce a two-step approach. In the first step, we generate first-order logic sentences which define some combinatorial objects, e.g., undirected graphs, permutations, matchings etc. In the second step, we use algorithms for lifted first-order model counting to generate integer sequences that count the objects encoded by the first-order logic formulas generated in the first step. For instance, if the first-order sentence defines permutations then the generated integer sequence is the sequence of factorial numbers n!. We demonstrate that our approach is able to generate interesting new sequences by showing that a non-negligible fraction of the automatically generated sequences can actually be found in the Online Encyclopaedia of Integer Sequences (OEIS) while generating many other similar sequences which are not present in OEIS and which are potentially interesting. A key technical contribution of our work is the method for generation of first-order logic sentences which is able to drastically prune the space of sentences by discarding large fraction of sentences which would lead to redundant integer sequences.
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Lee, Chong-Dao, and Yan-Haw Chen. "Fast Generation of Perfect Gaussian Integer Sequences of Primitive Length." In 2019 IEEE 4th International Conference on Signal and Image Processing (ICSIP). IEEE, 2019. http://dx.doi.org/10.1109/siprocess.2019.8868906.

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Koval, Aleksey. "Relationship between Lucas Sequences and Gaussian Integers in Cryptosystems." In 2015 12th International Conference on Information Technology - New Generations (ITNG). IEEE, 2015. http://dx.doi.org/10.1109/itng.2015.43.

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Makeev, Sergey Danilovich. "Hardly describable almost polynomial classes of requrrent sequences." In Academician O.B. Lupanov 14th International Scientific Seminar "Discrete Mathematics and Its Applications". Keldysh Institute of Applied Mathematics, 2022. http://dx.doi.org/10.20948/dms-2022-36.

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In this report, we will describe the problem of "hard to describe" classes return sequences, that is, such that the prediction behavior of such sequences is an algorithmically undecidable task. Integer classes will be considered sequences whose generating functions are composed compositions of polynomials (with integer coefficients) and some functions f. The main question under consideration is what should be this f, so that the resulting class is hard to describe. Such functions f we called border. Evidence will be presented that several wide families of functions are boundary. All this evidence stem from one "central" theorem, for proof of which Minsky machine simulations are used sequences, i.e. it is constructively proved that from the system functions "polynomials plus f" (for each of the considered f) it is possible to "build" a universal computing device.
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Osono, Gen, Shunsuke Araki, Takeru Miyazaki, Satoshi Uehara, and Ken'ichi Kakizaki. "A Study on Control Parameter and Output Sequence of the Logistic Map over Integers for Pseudorandom Number Generation." In 2021 IEEE International Conference on Consumer Electronics-Taiwan (ICCE-TW). IEEE, 2021. http://dx.doi.org/10.1109/icce-tw52618.2021.9603001.

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Ogawa, Yoshihiko, Tomohumi Takata, Takashi Iwai, Daichi Imamura, Katsuhiko Hiramatsu, and Kazuyuki Miya. "Pilot signal generation scheme using frequency dependent cyclic shift sequence for inter-cell interference mitigation." In 2009 IEEE Radio and Wireless Symposium (RWS). IEEE, 2009. http://dx.doi.org/10.1109/rws.2009.4957372.

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Li Junqing, He Long, and Wang Dong. "Rotor winding inter-turn fault analysis of doubly-fed induction generator based on negative sequence component." In 2013 International Conference on Electrical Machines and Systems (ICEMS). IEEE, 2013. http://dx.doi.org/10.1109/icems.2013.6713150.

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Naoki Kamikawa and Hiroshi Umeo. "Some algorithms for real-time generation of non-regular sequences on one-bit inter-cell-communication cellular automata." In SICE Annual Conference 2007. IEEE, 2007. http://dx.doi.org/10.1109/sice.2007.4421122.

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Chen, Wenqing, Jidong Tian, Caoyun Fan, Hao He, and Yaohui Jin. "Dependent Multi-Task Learning with Causal Intervention for Image Captioning." In Thirtieth International Joint Conference on Artificial Intelligence {IJCAI-21}. International Joint Conferences on Artificial Intelligence Organization, 2021. http://dx.doi.org/10.24963/ijcai.2021/312.

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Recent work for image captioning mainly followed an extract-then-generate paradigm, pre-extracting a sequence of object-based features and then formulating image captioning as a single sequence-to-sequence task. Although promising, we observed two problems in generated captions: 1) content inconsistency where models would generate contradicting facts; 2) not informative enough where models would miss parts of important information. From a causal perspective, the reason is that models have captured spurious statistical correlations between visual features and certain expressions (e.g., visual features of "long hair" and "woman"). In this paper, we propose a dependent multi-task learning framework with the causal intervention (DMTCI). Firstly, we involve an intermediate task, bag-of-categories generation, before the final task, image captioning. The intermediate task would help the model better understand the visual features and thus alleviate the content inconsistency problem. Secondly, we apply Pearl's do-calculus on the model, cutting off the link between the visual features and possible confounders and thus letting models focus on the causal visual features. Specifically, the high-frequency concept set is considered as the proxy confounders where the real confounders are inferred in the continuous space. Finally, we use a multi-agent reinforcement learning (MARL) strategy to enable end-to-end training and reduce the inter-task error accumulations. The extensive experiments show that our model outperforms the baseline models and achieves competitive performance with state-of-the-art models.
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Li, Shuai, Guangqing Zhang, Liye Zhang, Wenrui Wang, and Chunyang Zhao. "Effect of Alternate Fracturing on Rock Porosity and Permeability Near Hydraulic Fractures." In 57th U.S. Rock Mechanics/Geomechanics Symposium. ARMA, 2023. http://dx.doi.org/10.56952/arma-2023-0590.

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ABSTRACT Stimulated Reservoir Volume (SRV) fracturing of horizontal wells significantly increases oil and gas production by generating a large amount of high-permeability main and branch fractures. This study attempts to explores the effect of fracturing sequences on smaller-scale fractures (micro-fractures, pore scales). We carried out multi-stage sequential and alternate hydraulic fracturing experiments, respectively. The effect of fracturing sequence on porosity and permeability characteristics was quantitatively analyzed from the microscopic perspective through Nuclear Magnetic Resonance (NMR) technology. The results show that: (1) the fracture deflection angle of alternating fracturing is about 50% of that of sequential fracturing, and alternate fracturing can reduce inter-fracture interference and effectively control crack propagation morphology; (2) alternate fracturing can reduce horizontal stress difference, which is more conducive to the formation of complex microcracks than sequential fracturing; (3) compared with sequential fracturing, the porosity and permeability near the fracture of alternate fracturing increased by 14.2% and 126.7%, respectively. In conclusion, alternate fracturing has more advantages in increasing the production performance of horizontal wells than sequential fracturing. INTRODUCTION The volume fracture formed by multi-stage fracturing of horizontal wells has significantly increased oil and gas production. It is one of the key technologies for the efficient development of unconventional oil and gas reservoirs (Shelley et al., 2012; Shelley et al., 2010). The stimulated reservoir volume (SRV) fracturing system is generally considered to be formed by main fractures and branch fractures. Multiple hydraulic fractures formed by multi-stage fracturing of horizontal wells will interact with each other. The hydraulic pressure in the formed hydraulic fractures will change the stress field distribution around the hydraulic fractures, thus affecting the initiation, extension, and development of new hydraulic fractures formed around them, thus affecting the recovery and fracturing efficiency of horizontal wells. This phenomenon is usually called the "stress shadow effect" (Bunger et al., 2012; Daneshy et al., 2012; El Rabaa, 1989; Nagel and Sanchez-Nagel, 2011).
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Reports on the topic "Integer sequence generation"

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MR MSK Cartilage for Joint Disease, Consensus Profile. Chair Thomas Link and Xiaojuan Li. Radiological Society of North America (RSNA) / Quantitative Imaging Biomarkers Alliance (QIBA), 2021. http://dx.doi.org/10.1148/qiba/20210925.

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The goal of a QIBA Profile is to help achieve a useful level of performance for a given biomarker. The Claim (Section 2) describes the biomarker performance. The Activities (Section 3) contribute to generating the biomarker. Requirements are placed on the Actors that participate in those activities as necessary to achieve the Claim. Assessment Procedures (Section 4) for evaluating specific requirements are defined as needed. This QIBA Profile (MR-based cartilage compositional biomarkers (T1ρ, T2) ) addresses the application of T1ρ and T2 for the quantification of cartilage composition, which can be used as an imaging biomarker to diagnose, predict and monitor early osteoarthritis. It places requirements on Acquisition Devices, Technologists, MRI Physicists, Radiologists, Reconstruction Software and Image Analysis Tools involved in Subject Handling, Image Data Acquisition, Image Data Reconstruction, Image Quality Assurance (QA) and Image Analysis. The requirements are focused on achieving sufficient reproducibility and accuracy for measuring cartilage composition. The clinical performance target is to achieve a reproducibility of 4-5% for measurements of global cartilage composition with T2 and T1ρ relaxation time measurements and a 95% confidence level for a true/critical change in cartilage composition (least significant change) with a precision of 11-14% and 9-12% if only an increase is expected (claim is one-sided). The target applies to 3T MR scanners of one manufacturer with identical scan parameters across different sites. It does not apply to scanners from different manufacturers. This document is intended to help clinicians basing decisions on this biomarker, imaging staff generating this biomarker, vendor staff developing related products, purchasers of such products and investigators designing trials with imaging endpoints. Note that this document only states requirements to achieve the claim, not “requirements on standard of care.” Conformance to this Profile is secondary to properly caring for the patient. Summary for Clinical Trial Use The MR-based cartilage compositional biomarkers profile defines the behavioral performance levels and quality control specifications for T1ρ, T2 scans used in single- and multi-center clinical trials of osteoarthritis and other trials assessing cartilage composition longitudinally with a focus on therapies to treat degenerative joint disease. While the emphasis is on clinical trials, this process is also intended to be applied for clinical practice. The specific claims for accuracy are detailed below in the Claims. The specifications that must be met to achieve conformance with this Profile correspond to acceptable levels specified in the T1ρ, T2 Protocols. The aim of the QIBA Profile specifications is to minimize intra- and inter-subject, intra- and inter-platform, and interinstitutional variability of quantitative scan data due to factors other than the intervention under investigation. T1ρ and T2 studies performed according to the technical specifications of this QIBA Profile in clinical trials can provide quantitative data for single timepoint assessments (e.g. disease burden, investigation of predictive and/or prognostic biomarker(s)) and/or for multi-time-point comparative assessments (e.g., response assessment, investigation of predictive and/or prognostic biomarkers of treatment efficacy). A motivation for the development of this Profile is that while a typical MR T1ρ and T2 measurement may be stable over days or weeks, this stability cannot be expected over the time that it takes to complete a clinical trial. In addition, there are well known differences between scanners and the operation of the same type of scanner at different imaging sites. The intended audiences of this document include: Biopharmaceutical companies, rheumatologists and orthopedic surgeons, and clinical trial scientists designing trials with imaging endpoints. Clinical research professionals. Radiologists, technologists, physicists and administrators at healthcare institutions considering specifications for procuring new MRI equipment for cartilage measurements. Radiologists, technologists, and physicists designing T1ρ and T2 acquisition protocols. Radiologists, and other physicians making quantitative measurements from T1ρ and T2 sequence protocols. Regulators, rheumatologists, orthopedic surgeons, and others making decisions based on quantitative image measurements. Technical staff of software and device manufacturers who create products for this purpose. Note that specifications stated as 'requirements' in this document are only requirements to achieve the claim, not 'requirements on standard of care.' Specifically, meeting the goals of this Profile is secondary to properly caring for the patient.
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