Kinds Of Sequences Research Articles

An unbounded operator theory approach to lower frame and Riesz-Fischer sequences

Frames and orthonormal bases are important concepts in functional analysis and linear algebra. They are naturally linked to bounded operators. To describe unbounded operators those sequences might not be well suited. This has already been noted by von Neumann in the 1920ies. But modern frame theory also investigates other sequences, including those that are not naturally linked to bounded operators. The focus of this manuscript will be two such kind of sequences: lower frame and Riesz-Fischer sequences. We will discuss the inter-relation of those sequences. We will fill a hole existing in the literature regarding the classification of these sequences by their synthesis operator. We will use the idea of generalized frame operator and Gram matrix and extend it. We will use that to show properties for canonical duals for lower frame sequences, such as a minimality condition regarding its coefficients. We will also show that other results that are known for frames can be generalized to lower frame sequences. Finally, we show that the converse of a well-known result is true, i.e. that minimal lower frame sequences are equivalent to complete Riesz-Fischer sequences, without any further assumptions.To be able to tackle these tasks, we had to revisit the concept of invertibility (in particular for non-closed operators). In addition, we are able to define a particular adjoint, which is uniquely defined for any operator.

Effect of Tacticity Sequence of the Poly(N-isopropylacrylamide) Oligomer on Phase Transition Behavior in Aqueous Solution.

The tacticity of poly(N-isopropylacrylamide) (PNIPAM) has a strong impact on the lower critical solution temperature (LCST) in aqueous solution. The sequence of meso diads (m) and racemo diads (r) further contributes to such an effect. In this work, the phase transition behaviors of poly(N-isopropylacrylamide) pentamers with four kinds of sequences, i.e., rrmm, rmmr, mrrm, and rmrm, in water were studied applying replica exchange molecular dynamics with a modified OPLS/AA force field. The difference in local component concentration in the system was used as an order parameter to quantitatively describe the phase separation extent. It was found that the phase separation degree of rrmm and rmmr is higher than that of mrrm and rmrm at the same temperature. The LCSTs of rrmm and rmmr are lower than those of mrrm and rmrm. The radial distribution function and hydrogen bond analysis revealed that the average values of hydrogen bonds between pentamers for rrmm and rmmr are greater than those of mrrm and rmrm, whereas the average values of hydrogen bonds between pentamers and water for rrmm and rmmr are less than those of mrrm and rmrm. It was demonstrated that the isotactic triad (mm) plays an important role in the thermosensitive behaviors of the PNIPAM pentamer. The increase of isotactic triad (mm) content in the PNIPAM chain promotes the formation of intermolecular hydrogen bonds between amide and amide and leads to a higher aggregation of the pentamer with the sequence of rrmm or rmmr. Finally, the effect of the isotactic triad was qualitatively explained with the mean-field theory.

Dimensions of nonbinary antiprimitive BCH codes and some conjectures

Bose-Chaudhuri-Hocquenghem (BCH) codes have been intensively investigated. Even so, there is only a little known about primitive BCH codes, let alone non-primitive ones. In this paper, let q>2 be a prime power, the dimension of a family of non-primitive BCH codes of length n=qm+1 (also called antiprimitive) is studied. These codes are also linear codes with complementary duals (called LCD codes). Through some approaches such as iterative algorithm, partition and scaling, all coset leaders of Cx modulo n with q⌈m2⌉<x≤2q⌈m2⌉+2 are given for m≥4. And for odd m the first several largest coset leaders modulo n are determined. Furthermore, a new kind of sequences is introduced to determine the second largest coset leader modulo n with m even and q odd. Also, for even m some conjectures about the first several coset leaders modulo n are proposed, whose complete verification would wipe out the difficult problem to determine the first several coset leaders of antiprimitive BCH codes. After deriving the cardinalities of the coset leaders, we shall calculate exact dimensions of many antiprimitive LCD BCH codes.

О последовательности

The relevance of the study lies in the fact that for the first time attention is drawn to the sequence – the concept that is formed by the relation, more precisely, the location, of the preceding and subsequent. How the preceding and the following are arranged is a question that is answered in one way or another by the study of the sequence. This is the arrangement of numbers in the Fibonacci sequence or bases in DNA and RNA molecules, etc. The purpose of the article is to show how these categories “work” in different types of sequence. The relation of the preceding and the following has a universal character and covers history, art, philosophy, science, i.e. culture as a whole. In the article, the sequence is investigated primarily through the relation of the beginning to the final (subsequent). The concepts of “a priori” and “a posteriori”, primary, secondary, principle, antecedent, consequent, etc. are considered here. Following the principles is a person’s personality. Another step in sequence research is the causal relationship. The problem is “sharpened” in the case of induction in the meaning of the relation to the future (inducing the future). What follows the present? The research method is interdisciplinary analysis. This kind of sequence is considered as following a rule, where “rule” means both a logical rule and an ethical one, and specifically, rules-sequences in customs, rituals, cooking, language, microbiology, etc. as well as examples-mottos “Follow the White Rabbit!”, “Follow the money”, “Follow the instructions,” etc. There is a separate question about followers, pedigrees, heirs: Who is a follower of this or that person? If language is a sequence of signs, is a monkey capable of arbitrarily typing Shakespeare’s plays on a typewriter? Outside of the theory of probability, obviously not, because the monkey does not understand what he is doing. The analysis of the “last” as the limit of the sequence is proposed: there is a preceding, but there is no subsequent. Several types of sequence are distinguished here: “divergent sequence” – there is no limit to its construction; “convergent sequence” – there are limits to its construction; a sequence whose elements are determined by necessity; a sequence whose elements are freely chosen. Cosmic and individual eschatology are distinguished. The study comes to the conclusion: consistency is a universal phenomenon and concept, a means of producing culture, or following principles, rules, patterns, symbols and, most importantly, other people. Sequencing of organisms is a classic example of the discovery of a fundamental sequence and the prospects for its further research, including philosophical ones. Key words: sequence, preceding, following, followers, cause, effect, consequence, following, dynamic systems, location, last.

Large-scale chemical language representations capture molecular structure and properties

Models based on machine learning can enable accurate and fast molecular property predictions, which is of interest in drug discovery and material design. Various supervised machine learning models have demonstrated promising performance, but the vast chemical space and the limited availability of property labels make supervised learning challenging. Recently, unsupervised transformer-based language models pretrained on a large unlabelled corpus have produced state-of-the-art results in many downstream natural language processing tasks. Inspired by this development, we present molecular embeddings obtained by training an efficient transformer encoder model, MoLFormer, which uses rotary positional embeddings. This model employs a linear attention mechanism, coupled with highly distributed training, on SMILES sequences of 1.1 billion unlabelled molecules from the PubChem and ZINC datasets. We show that the learned molecular representation outperforms existing baselines, including supervised and self-supervised graph neural networks and language models, on several downstream tasks from ten benchmark datasets. They perform competitively on two others. Further analyses, specifically through the lens of attention, demonstrate that MoLFormer trained on chemical SMILES indeed learns the spatial relationships between atoms within a molecule. These results provide encouraging evidence that large-scale molecular language models can capture sufficient chemical and structural information to predict various distinct molecular properties, including quantum-chemical properties. Large language models have recently emerged with extraordinary capabilities, and these methods can be applied to model other kinds of sequence, such as string representations of molecules. Ross and colleagues have created a transformer-based model, trained on a large dataset of molecules, which provides good results on property prediction tasks.

Spatio-temporal analysis of East Asian seismic zones based on multifractal theory

Abstract In this article, the integrity of the seismic catalog obtained (1970–2014, M &gt; 2.8) was verified according to the Gutenberg–Richter relation, the appropriate minimum magnitude was determined, and the whole region was divided into five areas according to the geological structure background of the whole research object and the trend of the historical seismic zone. We applied multifractal analysis in each partition. The results showed that although in different geological backgrounds, before major earthquakes, the earthquake time series information dimension had different degrees of growth, and the parameter after the flame had different degrees of decline. To a certain extent, this reflected the seismic energy accumulation and release process. In addition, the variation of fractal parameters in scale-free regions of time series and spatial distribution series also indicated that these two kinds of sequences in different regions show the characteristics of a multifractal structure rather than a single and uniform fractal structure.

Hybrid offline and online task planning for service robot using object-level semantic map and probabilistic inference

To make service robots plan a whole task execution sequence and deal with task failure intelligently in the face of object occlusion and incomplete home environment information, a hybrid offline and online task planning strategy is proposed. We establish object-level semantic map and object location probabilistic relations between dynamic and static objects. Semantic mapping helps to obtain semantic locations of static objects, and the probabilistic relationship between dynamic and static objects can obtain semantic locations of dynamic objects through probabilistic reasoning. Probabilistic planning domain definition language (PPDDL) can generate offline action sequences, while partially observable Markov decision process (POMDP) can generate online action sequences. Therefore, a hybrid task planner that can receive semantic location information is constructed to generate offline and online action sequences, and realizes the dynamic switching of the two kinds of sequences through the designed planner switching mechanism. In order to improve the robustness and intelligence of robot task planning, a task replanning mechanism considering the position relationship between robot and candidate static objects is designed. Experimental results in real environment and simulation environment show that this approach can effectively increase the intelligence of task planning and improve the robustness and efficiency of robot task execution.

A study on I-deferred strongly Cesáro summable and μ-deferred i-statistical convergence for complex uncertain sequences

In this study, we introduce the five different types of I-deferred strongly Ces?ro summablity and ?-deferred I-statistical convergence (i.e., with respect to almost surely, uniformly almost surely, in measure, in distribution and in mean) of a complex uncertain sequence. We also introduce the spaces of such kind of sequences. Furthermore, some interesting properties of these definitions and inclusion relations between the spaces have been established under some conditions.

New Generalized Cyclotomic Quaternary Sequences with Large Linear Complexity and a Product of Two Primes Period

Linear complexity is an important criterion to characterize the unpredictability of pseudo-random sequences, and large linear complexity corresponds to high cryptographic strength. Pseudo-random Sequences with a large linear complexity property are of importance in many domains. In this paper, based on the theory of inverse Gray mapping, two classes of new generalized cyclotomic quaternary sequences with period pq are constructed, where pq is a product of two large distinct primes. In addition, we give the linear complexity over the residue class ring Z4 via the Hamming weights of their Fourier spectral sequence. The results show that these two kinds of sequences have large linear complexity.

Transient global amnesia: Signal alteration in 2D/3D T2-FLAIR sequences

PurposeTransient global amnesia (TGA) is one of the most enigmatic syndromes in clinical neurology. The detection rate of TGA lesions in 2D/3D FLAIR sequences has not been evaluated. MethodsA total of 201 patients (44 men and 157 women; mean age, 60.34 ± 9.23 years; range, 22–91 years) diagnosed with TGA, who underwent diffusion-weighted imaging (DWI; b = 1000 s/mm2, b = 2000 s/mm2, 4 mm) and/or 2D/3D-FLAIR sequences (4 mm, 0.9 mm; respectively) using 3-T MRI within 28 days after onset of TGA symptoms, were included in this single-center, retrospective, cross-sectional study. Hippocampal lesions were visually assessed in all sequences and detection rates were analyzed according to imaging timing (1 day, 2–4 days, 5–7 days, 8–11 days, and 12–28 days) and kinds of sequences. ResultsThe detection rates were highest 2–4 days after symptom onset in all sequences, and that was higher in order of b = 2000 (75.28% [67/89]), b = 1000 (63.92% [62/97]), 3D-FLAIR (59.38% [19/32]), and 2D-FLAIR (15.15% [15/99]). On FLAIR sequences, detectability was lower 5–7 days after onset than that 2–4 days after onset (2D-FLAIR, 15.15% [15/99] vs. 5.56% [1/18]; 3D-FLAIR, 59.38% [19/32] vs. 0.00% [0/1]). ConclusionFLAIR signal changes occur in approximately 60% of TGA patients 2–4 days after symptom onset, and decrease after 5 days. It is postulated that the pathophysiology of TGA might differ from common ischemic changes.

Multi-stream slowFast graph convolutional networks for skeleton-based action recognition

Recently, many efforts have been made to model spatial–temporal features from human skeleton for action recognition by using graph convolutional networks (GCN). Skeleton sequence can precisely represent human pose with a small number of joints while there is still a lot of redundancies across the skeleton sequence in the term of temporal dependency. In order to improve the effectiveness of spatial–temporal feature extraction from skeleton sequence, a SlowFast graph convolution network (SF-GCN) is proposed by implementing the architecture of SlowFast network, which is consisted of the Fast and Slow pathway, in the GCN model. The Fast pathway is a temporal attention embedded lightweight GCN for extracting the feature of fast temporal changes from the skeleton sequence with a high frame rate and fast refreshing speed. The Slow pathway is a spatial attention embedded GCN for extracting the feature of slow temporal changes from the skeleton sequence with a low frame rate and slow refreshing speed. The features of two pathways are fused by using lateral connection and weighted by using channel attention. Based on the aforementioned design, SF-GCN can achieve superior ability of feature extraction while the computational cost significantly drops. In addition to the coordinate information of joints, five high order sequences including edge, the spatial difference and temporal difference of joints and edges are induced to enhance the representation of human action. Six SF-GCNs are implemented for extracting spatial–temporal feature from six kinds of sequences and fused for skeleton-based action recognition, which is called multi-stream SlowFast graph convolutional networks (MSSF-GCN). Extensive experiments are conducted to evaluate the proposed method on three skeleton-based action recognition databases including NTU RGB + D, NTU RGB + D 120, and Skeleton-Kinetics. The results show that the proposed method is effective for skeleton-based action recognition and can achieve the recognition accuracy with an obvious advantage in comparison with the state-of-the-art.

Chess as Sequential Data in a Chess Match Outcome Prediction Using Deep Learning with Various Chessboard Representations

Moves made by chess players during the match are certainly some kind of sequence. In this work, we tried to answer the question if such data could be interpreted as sequential. To achieve that, a model build with LSTM layers only was designed. Results performed by the model are justifying that thesis. A novel model architecture was also proposed and trained on multiple data types—chess moves and chess game metadata. Its purpose was to perform as high classification accuracy as possible—we managed to achieve it with a result close to 69%. Moreover, we compared a couple of chessboard representation methods, more precisely a bitmap input and algebraic input, to check which one is more relevant for the neural networks training process. Contrary to what one might suppose, better scores were reached for bitmap input, which from the theoretical point of view carries out less information than algebraic input.

Multi-isotope approach (δ44/40Ca, δ88/86Sr and 87Sr/86Sr) provides insights into rhizolith formation mechanisms in terrestrial sediments of Nussloch (Germany)

Carbonates in loess-paleosol sequences are considered as a valuable paleoenvironmental proxy for climate change during the Quaternary period. In this study we propose a new dataset of δ44/40Ca, δ88/86Sr and 87Sr/86Sr to understand the formation of rhizoliths (roots encrusted with CaCO3) within these kinds of sequences from Nussloch region (Germany). Our results indicate that the leached fractions of rhizoliths (sampled at 3.25 m, 6.65 m, and 8.45 m depths and leached with HCl) have lower δ44/40Ca and δ88/86Sr, and higher 87Sr/86Sr isotopic values than the leached fractions of rhizosphere and root-free loess of the same stratigraphic levels. This suggests different mechanisms of carbonate formation and different sources of Sr and Ca. A three steps model of formation of rhizoliths from Nussloch has been proposed. First of all, the roots grow in an existent stratigraphic level and the biological activity associated with roots allows for the dissolution of carbonate and non-carbonate minerals. A part of the available Ca and Sr is taken up by roots, which absorb preferentially the light isotopes (e.g., 40Ca and 86Sr). A higher rate of water absorption by roots than nutrients, in association with CO2 released by biological respiration, allows to reach supersaturation with respect to CaCO3. The precipitation of rhizolith carbonate selects preferentially the light isotopes (e.g., 40Ca and 86Sr) leading to lower δ44/40Ca and δ88/86Sr isotope values than the ones recorded on the closest rhizosphere and loess. The higher 87Sr/86Sr signatures of rhizolith carbonates, which is not modified by root uptake or by precipitation processes, is the result of a mixture between 87Sr/86Sr signatures of carbonate and non-carbonate minerals digested around the roots. Nevertheless, grey zones remain, in this main hypothesis, about the very high contribution of residue materials to the isotopic signatures of rhizoliths. In this light, other mechanisms of downward transfer of Ca and Sr from upper stratigraphic level, that could imprint the leached fractions of rhizoliths, have been discussed.

Children’s working memory develops at similar rates for sequences differing in compressibility

Determining the causes of working memory maturation is a global issue in developmental cognitive psychology. The question has most often been addressed by manipulating stimulus types within participants. In the present experiment, we instead addressed this question by examining development in children’s working memory using a single stimulus type. Primary school children aged 6 to 10 years (total N = 256) participated in a task inspired by the game Simon®. Children saw sequences of colored squares presented one-at-a-time, and then attempted to reproduce the sequences in the correct order. Some sequences were simple and contained regularities that made them compressible, while other sequences were more complex and less compressible. We found that children’s memory for both kinds of sequences improved with age. However the ratio between children’s memory for simple and complex sequences did not substantially change with age. These findings suggest that storage capacity of working memory increases in middle childhood, but that children’s ability to optimize storage by compressing sequences remains stable across this age range.

Using filled prescription sequences to rank antidepressants according to their acceptability in the general population: The Constances cohort

Ranking antidepressants according to their acceptability (i.e. a combination of both efficacy and tolerability) in the general population may help choosing the best first-line medication. This study aimed to rank antidepressants according to the proportion of filled prescription sequences consistent with a continuation of the first treatment versus those consistent with a change. A first step was validating this measure as a proxy of acceptability by examining the association of these two kinds of sequences with levels of depressive symptoms. Among 64,467 individuals included in the French population-based Constances cohort, reimbursements of antidepressants from January 2009 to December 2015 were extracted from the French national health insurance system claims database. Depressive symptoms were measured at inclusion with the Center for Epidemiologic Studies-Depression scale (CES-D). Between January 2010 and December 2015, 6675 participants newly initiated an antidepressant (34.5% men, mean (SD) age: 48.3 (12.1) years). Among the subsample of participants included during the six-month period following treatment initiation, individuals with continuation sequences had lower levels of depressive symptoms than those with change sequences (mean (SE) CES-D score: 18.9 (0.8) versus 26.5 (2.1), p < 0.001). According to the continuation/change ratio observed over this six-month period in all participants, escitalopram ranked first, followed by sertraline, venlafaxine, citalopram, fluoxetine and paroxetine. In an independent replication sample representative of the French national population, the same six medications ranked first, with escitalopram remaining in first place. The proportion of filled prescription sequences consistent with a continuation versus a change of the first prescribed treatment may provide a widely available measure of antidepressant acceptability in community practice.

Varieties of Sobel sequences

In this paper I provide a unified analysis of a number of pragmatic anomalies that have been discussed in the literature. The paper’s main goal is to account for Sobel sequences of conditionals and sequences of disjunctive sentences, but I will also propose that this analysis can be extended to sequences of sentences with superlatives. The starting point is the observation that, while all these sequences are felicitous in one order, they are infelicitous when the order is reversed. Previous proposals have focussed on particular types of infelicitous sequences (e.g. von Fintel, in: Kenstowicz (ed) Ken Hale: A life in language, MIT Press, Cambridge, 2001; Moss in Nous 46:516–586, 2012; Lewis in Nous 52:481–507, 2018; a.o.), or a subset of all the phenomena cited above (e.g. Singh in On competition between only and exh, 2008b; Linguist Philos 31:245–260, 2008c; Dohrn, in: Pistoia-Reda, Domaneschi (eds) Linguistic and psycholinguistic approaches on implicatures and presuppositions. Palgrave McMillan, Basingstoke, 2017; a.o.). I propose that sequences of sentences belonging to the same structured set of alternatives T are subject to a Specificity Constraint (SC): sequences are acceptable if both alternatives are dominated by the same number of nodes in the structured set of alternatives T. Violations of SC can be avoided by strengthening the weaker alternative. However, covert strengthening violates an economy condition if the overtly stronger alternative is among those made salient by the preceding utterance in the sequence (if any). I propose that the set of alternatives made salient by an utterance of a sentence s consists of s’s sisters and mother in T. I will show that the strengthening mechanism varies depending on the kind of sequence we have.

Limiting Distributions for the Minimum-Maximum Models

We consider the extreme value problem of the minimum-maximum models for the independent and identically distributed random sequence and stationary random sequence, respectively. By invoking some probability formulas and Taylor’s expansions of the distribution functions, the limiting distributions for these two kinds of sequences are obtained. Moreover, convergence analysis is carried out for those extreme value distributions. Several numerical experiments are conducted to validate our theoretical results.

EAT-Rice: A predictive model for flanking gene expression of T-DNA insertion activation-tagged rice mutants by machine learning approaches.

T-DNA activation-tagging technology is widely used to study rice gene functions. When T-DNA inserts into genome, the flanking gene expression may be altered using CaMV 35S enhancer, but the affected genes still need to be validated by biological experiment. We have developed the EAT-Rice platform to predict the flanking gene expression of T-DNA insertion site in rice mutants. The three kinds of DNA sequences including UPS1K, DISTANCE, and MIDDLE were retrieved to encode and build a forecast model of two-layer machine learning. In the first-layer models, the features nucleotide context (N-gram), cis-regulatory elements (Motif), nucleotide physicochemical properties (NPC), and CG-island (CGI) were used to build SVM models by analysing the concealed information embedded within the three kinds of sequences. Logistic regression was used to estimate the probability of gene activation which as feature-encoding weighting within first-layer model. In the second-layer models, the NaiveBayesUpdateable algorithm was used to integrate these first layer-models, and the system performance was 88.33% on 5-fold cross-validation, and 79.17% on independent-testing finally. In the three kinds of sequences, the model constructed by Middle had the best contribution to the system for identifying the activated genes. The EAT-Rice system provided better performance and gene expression prediction at further distances when compared to the TRIM database. An online server based on EAT-rice is available at http://predictor.nchu.edu.tw/EAT-Rice.

Potential relations between post-spliced introns and mature mRNAs in the Caenorhabditis elegans genome

There are potential interactions between introns and their corresponding coding sequences (CDSs) in ribosomal protein genes that have been proposed by our group and the interactions are achieved by sequence matches between the two kinds of sequences. Here, the optimal matching relations between mature mRNAs and their corresponding introns in Caenorhabditis elegans (C.elegans) were investigated by improved Smith-Waterman local alignment software. Our results showed that the remarkably matched regions appear in the untranslated regions (UTRs) of mRNAs, especially in the 3′ UTR. The optimal matched segments (OMSs) are highly organized segments. In addition, the optimal matching relations were analysed between mature mRNAs and other introns. The matching strengths in the UTRs are clearly lower than those in their corresponding introns. Our studies indicate that there are potential interactions between mature mRNAs and their corresponding introns and the post-spliced introns should have other novel functions in the gene expression process.

Robust audio watermarking algorithm based on DWT using Fibonacci numbers

This paper presents a blind and robust audio watermarking algorithm developed based on Fibonacci numbers properties and the discrete wavelet transform (DWT) advantages. The method embeds watermark bits in the 6th level approximation subband of DWT at which there is less sensitivity of the human auditory system. The key idea is dividing the 6th level approximation coefficients into small frames and modifying their magnitude based on Fibonacci numbers and watermark bit values. The proposed watermarking method demonstrates a superior robustness against different common attacks (i.e., Gaussian noise addition, Low-pass filter, Resampling, Requantizing, MP3 compression, Amplitude scaling, Echo addition, Time shift, and Cropping). Compared to recently developed methods, the proposed algorithm is much more robust against the most common attacks with capacity as high as 686 bits per second. The results of PEAQ testing verify the quality of watermarked audio signal without significant perceptual distortion. The algorithm allows flexibility in audio watermark algorithm to achieve a balance between robustness and imperceptibility while the capacity is maintained constant by choosing various kinds of sequence.