Recurrent Sequences Research Articles

Prediction of Evolution Behaviors of Transportation Hubs Based on Spatiotemporal Neural Network

With the deterioration of the transportation ecosystem and traffic congestion, traffic graph representations become more complex and lack intelligibility. The deep learning method provides a new way for traffic prediction by mining the spatiotemporal relations of historical states in traffic network. Recurrent neural networks based on gate control can avoid the gradient vanishing and graph convolutional networks provide theoretical support for spatial feature extraction of traffic graph. However, in the prediction of traffic evolution behaviors, the statuses of units and groups distributed in the traffic network have strong and continuous spatiotemporal correlations. Modeling only based on the temporal or spatial perspective usually lacks comprehensiveness and semantic relevance which results in poor prediction performance. In this paper, we propose a spatiotemporal hierarchical propagation graph convolutional network(SHPGCN) to get the whole spatiotemporal evolution features of traffic graph, which can be used to predict the propagation effects and state changes of traffic flow. Considered the inadequacy of graph convolution in the learning of hierarchical features, we construct a low-dimensional propagation graph representation that projects complex node relationships into first-order neighborhoods to capture dynamic changes at different spatial and temporal scales. The SHPGCN uses graph convolution to encode the traffic propagation features and embeds them into a bidirectional recurrent sequence for traffic prediction. The experiment results show that SHPGCN can provide good prediction accuracy and robustness for the traffic evolution behaviors.

Ruin probability for finite negative binomial mixture claims via recurrence sequences

A new procedure to find the ultimate ruin probability in a discrete-time risk model is presented for claims with a mixture of m negative binomial distributions. The method involves the theory of linear recurrence sequences. It requires to find the zeroes of an m degree polynomial and the solution of a system of m linear equations. Numerical results and plots are provided as examples.

A comparative study of the phrase frames used in the essays of native and nonnative English students

A phrase frame (i.e., p-frame) is a type of recurrent discontinuous multiword sequence. So far, many studies have investigated the p-frames used in written texts in various genres, disciplines, and registers. However, few previous p-frame studies have attempted a comparative analysis of the p-frames used by native and nonnative English students. This scarcity prevents us from obtaining a full understanding of phraseological competence development in nonnative English learners. Using a corpus-driven approach, the current study identified and compared the 5-word p-frames used by native and nonnative English students in their college essays. The results showed no statistically significant difference between these two groups with respect to the types and tokens of p-frames used in their essays. However, significant intergroup differences could be observed when the predictability, variability, structural characteristics, and discourse functions of the identified p-frames were considered. These findings on the use of p-frames by native and nonnative English students could complement the comparative studies of recurrent continuous multiword sequences and thus advance our understanding of phraseological competence development in nonnative English learners.

Capturing Sequences of Learners' Self-Regulatory Interactions With Instructional Material During Game-Based Learning Using Auto-Recurrence Quantification Analysis.

Undergraduate students (N = 82) learned about microbiology with Crystal Island, a game-based learning environment (GBLE), which required participants to interact with instructional materials (i.e., books and research articles, non-player character [NPC] dialogue, posters) spread throughout the game. Participants were randomly assigned to one of two conditions: full agency, where they had complete control over their actions, and partial agency, where they were required to complete an ordered play-through of Crystal Island. As participants learned with Crystal Island, log-file and eye-tracking time series data were collected to pinpoint instances when participants interacted with instructional materials. Hierarchical linear growth models indicated relationships between eye gaze dwell time and (1) the type of representation a learner gathered information from (i.e., large sections of text, poster, or dialogue); (2) the ability of the learner to distinguish relevant from irrelevant information; (3) learning gains; and (4) agency. Auto-recurrence quantification analysis (aRQA) revealed the degree to which repetitive sequences of interactions with instructional material were random or predictable. Through hierarchical modeling, analyses suggested that greater dwell times and learning gains were associated with more predictable sequences of interaction with instructional materials. Results from hierarchical clustering found that participants with restricted agency and more recurrent action sequences had greater learning gains. Implications are provided for how learning unfolds over learners' time in game using a non-linear dynamical systems analysis and the extent to which it can be supported within GBLEs to design advanced learning technologies to scaffold self-regulation during game play.

Linear recurrent cryptography: Golden-like cryptography for higher order linear recurrences

We develop matrix cryptography based on linear recurrent sequences of any order that allows securing encryption against brute force and chosen plaintext attacks. In particular, we solve the problem of generalizing error detection and correction algorithms of golden cryptography previously known only for recurrences of a special form. They are based on proving the checking relations (inequalities satisfied by the ciphertext) under the condition that the analog of the golden Q-matrix has the strong Perron–Frobenius property. These algorithms are proved to be especially efficient when the characteristic polynomial of the recurrence is a Pisot polynomial. Finally, we outline algorithms for generating recurrences that satisfy our conditions.

A corpus-pragmatics approach to evaluation in professor reviews

AbstractThis study takes a corpus pragmatics approach to investigate the use of evaluative language in professor reviews, focusing on how review writers express evaluation through recurrent four-word sequences and the pragmatic functions of these sequences in positive and negative reviews on the website,RateMyProfessors.com. Based on an analysis of a 2.9-million-word corpus of free text comments, the findings indicate that positive reviews used more 4-grams, and more varied types, than negative ones. The 4-word sequences were found to carry out four pragmatic functions: attitudinal evaluation, reader engagement, referential expression, and discourse organization. While a similar distribution of the main functional categories was observed among the top 100 4-grams in both review types, with evaluative clusters being most predominant, distinctive intra-genre variations were found in the ways review writers employed different functional sub-categories. For example, positive reviews relied heavily on hedged suggestion 4-grams to engage readers, whereas negative reviews used directive 4-grams for the same purpose. These findings suggest the important role of multi-word sequences in the understanding of evaluative resources in professor reviews of different valence types.

A polynomial variant of diophantine triples in linear recurrences

Let (G_n)_{n=0}^{infty } be a polynomial power sum, i.e. a simple linear recurrence sequence of complex polynomials with power sum representation G_n = f_1alpha _1^n + cdots + f_kalpha _k^n and polynomial characteristic roots alpha _1,ldots ,alpha _k . For a fixed polynomial p, we consider sets left{ a,b,c right} consisting of three non-zero polynomials such that ab+p, ac+p, bc+p are elements of (G_n)_{n=0}^{infty } . We will prove that under a suitable dominant root condition there are only finitely many such sets if neither f_1 nor f_1 alpha _1 is a perfect square.

Linear recurrence sequence associated to rays of negatively extended Pascal triangle

We consider the extension of generalized arithmetic triangle to negative values of rows and we describe the recurrence relation associated to the sum of diagonal elements laying along finite rays. We also give the corresponding generating function. We conclude by an application to Fibonacci numbers and Morgan-Voyce polynomials with negative subscripts.

Evaluation of residual stresses in additively produced thermoelastic cylinder. Part I. Thermal fields

The study is aimed at mathematical modeling of non-stationary temperature and stress-strain fields in growing thermoelastic cylinder, which growth is due to the layer-by-layer sintering over its lateral surface. This modeling makes it possible to estimate the reciprocal impact of non-stationary temperature fields, stress-strain state and the scenario of the additive process even in manufacturing of more complicated shapes. The problem is considered in the framework of the theory of thermal stresses with non-linear radiative boundary condition. A distinctive feature of modeling is that the material composition of the body changes over time. Therefore, the mathematical model is represented by the recurrent sequence of initial boundary value problems, formulated for each step of the additive process in different domains with respect to the increments of thermal and stress fields. The domains constitute nested sequence of regions and, together with the sequence of the moments of layer sintering, define the scenario of additive process. Initial values for a step are taken to be equal to the corresponding values at the final moment of previous step. The solution for each step is represented in the form of decomposition over eigenfunctions of differential operator, generated by boundary value problem on this step. Computational modeling of various sintering modes has been carried out. A classification of thermomechanical additive processes, based on the relationship between the characteristic time of the process and the time of thermal relaxation of the attached layer is given. Special attention is paid to non-uniform volume heating, which can be obtained by skin effect during high-frequency induction. Computational simulations based on obtained analytical solution show that auxiliary inductive heating makes it possible to substantially reduce the non-uniformity of the temperature field and thus to reduce the temperature stresses caused by it.

Graphs containing finite induced paths of unbounded length

The age $\mathcal{A}(G)$ of a graph $G$ (undirected and without loops) is the collection of finite induced subgraphs of $G$, considered up to isomorphy and ordered by embeddability. It is well-quasi-ordered (wqo) for this order if it contains no infinite antichain. A graph is \emph{path-minimal} if it contains finite induced paths of unbounded length and every induced subgraph $G'$ with this property embeds $G$. We construct $2^{\aleph_0}$ path-minimal graphs whose ages are pairwise incomparable with set inclusion and which are wqo. Our construction is based on uniformly recurrent sequences and lexicographical sums of labelled graphs.

Identities relating six members of the Fibonacci family of sequences

In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences. These identities are obtained as special cases of formulas relating two linear combinations of products of three generalized Fibonacci or Lucas sequences. The latter formulas are in turn obtained from a more general generating function result for the product of three terms coming from second-order linearly recurrent sequences with arbitrary initial values. We employ algebraic arguments to establish our results, making use of the Binet-like formulas of the underlying sequences. Among the sequences for which the aforementioned identities are found include the Fibonacci, Pell, Jacobsthal and Mersenne numbers, along with their associated Lucas companion sequences.

Ultimate periodicity problem for linear numeration systems

We address the following decision problem. Given a numeration system U and a U-recognizable set [Formula: see text], i.e. the set of its greedy U-representations is recognized by a finite automaton, decide whether or not X is ultimately periodic. We prove that this problem is decidable for a large class of numeration systems built on linear recurrence sequences. Based on arithmetical considerations about the recurrence equation and on p-adic methods, the DFA given as input provides a bound on the admissible periods to test.

Terms of recurrence sequences in the solution sets of generalized Pell equations

In this paper, we completely describe those recurrence sequences which have infinitely many terms in the solution sets of generalized Pell equations. Further, we give an upper bound for the number of such terms when there are only finitely many of them.

Exponential sums in prime fields for modular forms

The main objective of this article is to study the exponential sums associated to Fourier coefficients of modular forms supported at numbers having a fixed set of prime factors. This is achieved by establishing an improvement on Shparlinski’s bound for exponential sums attached to certain linear recurrence sequences over finite fields.

O-Minimal Invariants for Discrete-Time Dynamical Systems

Termination analysis of linear loops plays a key rôle in several areas of computer science, including program verification and abstract interpretation. Already for the simplest variants of linear loops the question of termination relates to deep open problems in number theory, such as the decidability of the Skolem and Positivity Problems for linear recurrence sequences, or equivalently reachability questions for discrete-time linear dynamical systems. In this article, we introduce the class of o-minimal invariants , which is broader than any previously considered, and study the decidability of the existence and algorithmic synthesis of such invariants as certificates of non-termination for linear loops equipped with a large class of halting conditions. We establish two main decidability results, one of them conditional on Schanuel’s conjecture is transcendental number theory.

Clonotype pattern in T-cell lymphomas map the cell of origin to immature lymphoid precursors

AbstractMature T-cell lymphomas (TCLs) are rare, clinically heterogeneous hematologic cancers with high medical need. TCLs have an inferior prognosis which is attributed to poor understanding of their pathogenesis. On the basis of phenotypic similarities between normal and neoplastic lymphocytes, it has been assumed that TCLs develop in the periphery, directly from various subtypes of normal T cells. To address the debated question of the cell of origin in TCLs, we attempted to identify the highly variable complementarity-determining regions (CDRs) of T-cell receptors (TCRs) to trace the clonal history of the T cells. We have collected previously published whole-genome, whole-exome, and whole-transcriptome sequencing data from 574 patients with TCL. TCR clonotypes were identified by de novo assembly of CDR3 regions of TCRα, TCRβ, and TCRγ. We have found that the vast majority of TCLs are clonotypically oligoclonal, although the pattern of oligoclonality varied. Anaplastic large-cell lymphoma was the most diverse comprising multiple clonotypes of TCRα, TCRβ, and TCRγ, whereas adult TCL or leukemia and peripheral TCLs often showed monoclonality for TCRβ and TCRγ but had diverse TCRα clonotypes. These patterns of rearrangements indicated that TCLs are initiated at the level of the lymphoid precursor. In keeping with this hypothesis, TCR rearrangements in TCLs resembled the pattern seen in the human thymus, which showed biased usage of V (variable) and J (joining) segments of high combinatorial probability resulting in recurrent public CDR3 sequences shared across unrelated patients and different clinical TCL entities. Clonotypically diverse initiating cells may seed target tissues that are then responsible for disease relapses after therapy.

Recurrent Multinomial Models for Categorical Sequences

This paper presents a model of recurrent multinomial sequences. Though there exists a quite considerable literature on modeling autocorrelation in numerical data and sequences of categorical outcomes, there is currently no systematic method of modeling patterns of recurrence in categorical sequences. This paper develops a means of discovering recurrent patterns by employing a more restrictive Markov assumption. The resulting model, which I call the recurrent multinomial model, provides a parsimonious representation of recurrent sequences, enabling the investigation of recurrences on longer time scales than existing models. The utility of recurrent multinomial models is demonstrated by applying them to the case of conversational turn-taking in meetings of the Federal Open Market Committee (FOMC). Analyses are effectively able to discover norms around turn-reclaiming, participation, and suppression and to evaluate how these norms vary throughout the course of the meeting.

Are the Catalan Numbers a Linear Recurrence Sequence?

We answer the question in the title in the negative by providing four proofs.

Recurrent numerical sequences: theory and applications

Recurrent numerical sequences: theory and applications

Fibonacci–Lucas–Pell–Jacobsthal relations

In this paper, we prove several identities involving linear combinations of convolutions of the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes of second-order linearly recurrent sequences with constant coefficients. As a consequence, we obtain as special cases many identities relating exactly four sequences amongst the Fibonacci, Lucas, Pell, Pell–Lucas, Jacobsthal, and Jacobsthal–Lucas number sequences. We make use of algebraic arguments to establish our results, frequently employing the Binet-like formulas and generating functions of the corresponding sequences. Finally, our identities above may be extended so that they include only terms whose subscripts belong to a given arithmetic progression of the non-negative integers.