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Journal articles on the topic 'Alphabet arithmetic'
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1
Campbell, Jamie I. D., Yalin Chen, Kurtis Allen, and Leah Beech. "Transfer of training in alphabet arithmetic." Memory & Cognition 44, no. 8 (June 28, 2016): 1288–300. http://dx.doi.org/10.3758/s13421-016-0631-x.
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Perl, Y., and L. Gabriel. "Arithmetic interpolation search for alphabet tables." IEEE Transactions on Computers 41, no. 4 (April 1992): 493–99. http://dx.doi.org/10.1109/12.135562.
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Fias, Wim, Muhammet Ikbal Sahan, Daniel Ansari, and Ian M. Lyons. "From Counting to Retrieving: Neural Networks Underlying Alphabet Arithmetic Learning." Journal of Cognitive Neuroscience 34, no. 1 (December 1, 2021): 16–33. http://dx.doi.org/10.1162/jocn_a_01789.
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Abstract This fMRI study aimed at unraveling the neural basis of learning alphabet arithmetic facts, as a proxy of the transition from slow and effortful procedural counting-based processing to fast and effortless processing as it occurs in learning addition arithmetic facts. Neural changes were tracked while participants solved alphabet arithmetic problems in a verification task (e.g., F + 4 = J). Problems were repeated across four learning blocks. Two neural networks with opposed learning-related changes were identified. Activity in a network consisting of basal ganglia and parieto-frontal areas decreased with learning, which is in line with a reduction of the involvement of procedure-based processing. Conversely, activity in a network involving the left angular gyrus and, to a lesser extent, the hippocampus gradually increases with learning, evidencing the gradual involvement of retrieval-based processing. Connectivity analyses gave insight in the functional relationship between the two networks. Despite the opposing learning-related trajectories, it was found that both networks become more integrated. Taking alphabet arithmetic as a proxy for learning arithmetic, the present results have implications for current theories of learning arithmetic facts and can give direction to future developments.
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Biasizzo, Anton, Franc Novak, and Peter Korošec. "A Multi–Alphabet Arithmetic Coding Hardware Implementation for Small FPGA Devices." Journal of Electrical Engineering 64, no. 1 (January 1, 2013): 44–49. http://dx.doi.org/10.2478/jee-2013-0006.
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Arithmetic coding is a lossless compression algorithm with variable-length source coding. It is more flexible and efficient than the well-known Huffman coding. In this paper we present a non-adaptive FPGA implementation of a multi-alphabet arithmetic coding with separated statistical model of the data source. The alphabet of the data source is a 256-symbol ASCII character set and does not include the special end-of-file symbol. No context switching is used in the proposed design which gives maximal throughput without pipelining. We have synthesized the design for Xilinx FPGA devices and used their built-in hardware resources.
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Mahapatra, Sudipta, and Kuldeep Singh. "An FPGA-Based Implementation of Multi-Alphabet Arithmetic Coding." IEEE Transactions on Circuits and Systems I: Regular Papers 54, no. 8 (August 2007): 1678–86. http://dx.doi.org/10.1109/tcsi.2007.902527.
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Delaygue, É. "Arithmetic properties of Apéry-like numbers." Compositio Mathematica 154, no. 2 (October 20, 2017): 249–74. http://dx.doi.org/10.1112/s0010437x17007552.
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We provide lower bounds for$p$-adic valuations of multisums of factorial ratios which satisfy an Apéry-like recurrence relation: these include Apéry, Domb and Franel numbers, the numbers of abelian squares over a finite alphabet, and constant terms of powers of certain Laurent polynomials. In particular, we prove Beukers’ conjectures on the$p$-adic valuation of Apéry numbers. Furthermore, we give an effective criterion for a sequence of factorial ratios to satisfy the$p$-Lucas property for almost all primes$p$.
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Müller, Burkhard, and Jürgen Gehrke. "Acquisition and Use of Mental Operators: The Influence of Natural Order of Events." Experimental Psychology 51, no. 1 (January 2004): 33–44. http://dx.doi.org/10.1027/1618-3169.51.1.33.
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Abstract. The present article reports two experiments investigating the influence of natural order of events on the acquisition and use of knowledge about operations, in short mental operators. The principle of use specificity states that task performance depends directly on the similarity between acquisition context and the present situation. In contrast, the principle of natural order proposes that knowledge about operations can always be applied easier (faster) if reasoning follows the natural order of events. In Experiment 1, participants had to apply alphabet-arithmetic operators and LISP functions in a prognosis task (A + 2 = ?) or a retrognosis task (? - 2 = A). In alphabet-arithmetic, an advantage for the first kind of task at the beginning of training decreased with increasing practice. In LISP, however, a preference for this task (corresponding with a prospective knowledge use) emerged with increasing practice. In Experiment 2, arithmetic relations between digit pairs had to be induced. In a causal context condition, relations were described as input and output of electric circuits, in a neutral context the relations were described as arithmetic dependencies. A preference for the prognosis task was found for the causal context condition (corresponding with a prospective knowledge use) but not for the neutral one. The findings suggest that the natural order of events moderates the acquisition and use of mental operators. Further research is required to clarify the bases for this moderation.
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Natarajan, S., N. Ramadass, and Ramana Y. V. Rao. "State-based dynamic multi-alphabet arithmetic coding for image compression." Imaging Science Journal 57, no. 1 (February 2009): 30–36. http://dx.doi.org/10.1179/174313109x373648.
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Chen, Yalin, Alicia Orr, and Jamie I. D. Campbell. "What is learned in procedural learning? The case of alphabet arithmetic." Journal of Experimental Psychology: Learning, Memory, and Cognition 46, no. 6 (June 2020): 1165–77. http://dx.doi.org/10.1037/xlm0000775.
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Logan, Gordon D., and Stuart T. Klapp. "Automatizing alphabet arithmetic: I. Is extended practice necessary to produce automaticity?" Journal of Experimental Psychology: Learning, Memory, and Cognition 17, no. 2 (March 1991): 179–95. http://dx.doi.org/10.1037/0278-7393.17.2.179.
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Ryabko, B., and J. Rissanen. "Fast adaptive arithmetic code for large alphabet sources with asymmetrical distributions." IEEE Communications Letters 7, no. 1 (January 2003): 33–35. http://dx.doi.org/10.1109/lcomm.2002.807424.
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Klapp, Stuart T., Catherine A. Boches, Marilyn L. Trabert, and Gordon D. Logan. "Automatizing alphabet arithmetic: II. Are there practice effects after automaticity is achieved?" Journal of Experimental Psychology: Learning, Memory, and Cognition 17, no. 2 (March 1991): 196–209. http://dx.doi.org/10.1037/0278-7393.17.2.196.
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Koch, Iring, Wolfgang Prinz, and Alan Allport. "Involuntary retrieval in alphabet-arithmetic tasks: Task-mixing and task-switching costs." Psychological Research Psychologische Forschung 69, no. 4 (June 26, 2004): 252–61. http://dx.doi.org/10.1007/s00426-004-0180-y.
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Zbrodoff, N. Jane. "Effects of counting in alphabet arithmetic: Opportunistic stopping and priming of intermediate steps." Journal of Experimental Psychology: Learning, Memory, and Cognition 25, no. 2 (March 1999): 299–317. http://dx.doi.org/10.1037/0278-7393.25.2.299.
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Vogel, Stephan E., Trent Haigh, Gerrit Sommerauer, Melanie Spindler, Clemens Brunner, Ian M. Lyons, and Roland H. Grabner. "Processing the order of symbolic numbers: A reliable and unique predictor of arithmetic fluency." Journal of Numerical Cognition 3, no. 2 (December 22, 2017): 288–308. http://dx.doi.org/10.5964/jnc.v3i2.55.
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A small but growing body of evidence suggests a link between individual differences in processing the order of numerical symbols (e.g., deciding whether a set of digits is arranged in ascending/descending order or not) and arithmetic achievement. However, the reliability of behavioral correlates measuring symbolic and non-symbolic numerical order processing and their relationship to arithmetic abilities remain poorly understood. The present study aims to fill this knowledge gap by examining the behavioral correlates of numerical and non-numerical order processing and their unique associations with arithmetic fluency at two different time points within the same sample of individuals. Thirty-two right-handed adults performed three order judgment tasks consisting of symbolic numbers (i.e., digits), non-symbolic numbers (i.e., dots), and letters of the alphabet. Specifically, participants had to judge as accurately and as quickly as possible whether stimuli were ordered correctly (in ascending/descending order, e.g., 2-3-4; ●●●●-●●●-●●; B-C-D) or not (e.g., 4-5-3; ●●●●-●●●●●-●●●; D-E-C). Results of this study demonstrate that numerical order judgments are reliable measurements (i.e., high test-retest reliability), and that the observed relationship between symbolic number processing and arithmetic fluency accounts for a unique and reliable portion of variance over and above the non-symbolic number and the letter conditions. The differential association of symbolic and non-symbolic numbers with arithmetic support the view that processing the order of symbolic and non-symbolic numbers engages different cognitive mechanisms, and that the ability to process ordinal relationships of symbolic numbers is a reliable and unique predictor of arithmetic fluency.
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Jayavathi, S. D., A. Shenbagavalli, and B. Ganapathy Ram. "Efficient Hardware Architecture for Integer Implementation of Multi-Alphabet Arithmetic Coding for Data Mining." International Journal of Business Intelligence and Data Mining 12, no. 3/4 (2017): 1. http://dx.doi.org/10.1504/ijbidm.2017.10004685.
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Jayavathi, S. D., A. Shenbagavalli, and B. Ganapathy Ram. "Efficient hardware architecture for integer implementation of multi-alphabet arithmetic coding for data mining." International Journal of Business Intelligence and Data Mining 13, no. 1/2/3 (2018): 188. http://dx.doi.org/10.1504/ijbidm.2018.088432.
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Thevenot, Catherine, Jasinta D. M. Dewi, Jeanne Bagnoud, Kim Uittenhove, and Caroline Castel. "Scrutinizing patterns of solution times in alphabet-arithmetic tasks favors counting over retrieval models." Cognition 200 (July 2020): 104272. http://dx.doi.org/10.1016/j.cognition.2020.104272.
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TONIEN, DONGVU. "CANCELLATION LAW AND UNIQUE FACTORIZATION THEOREM FOR STRING OPERATIONS." Journal of Algebra and Its Applications 05, no. 02 (April 2006): 231–43. http://dx.doi.org/10.1142/s0219498806001739.
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Recently, Hoit introduced arithmetic on blocks, which extends the binary string operation by Jacobs and Keane. A string of elements from the Abelian additive group of residues modulo m, (Zm, ⊕), is called an m-block. The set of m-blocks together with Hoit's new product operation form an interesting algebraic structure where associative law and cancellation law hold. A weaker form of unique factorization and criteria for two indecomposable blocks to commute are also proved. In this paper, we extend Hoit's results by replacing the Abelian group (Zm, ⊕) by an arbitrary monoid (A, ◦). The set of strings built up from the alphabet A is denoted by String(A). We extend the operation ◦ on the alphabet set A to the string set String(A). We show that (String(A), ◦) is a monoid if and only if (A, ◦) is a monoid. When (A, ◦) is a group, we prove that stronger versions of a cancellation law and unique factorization hold for (String(A), ◦). A general criterion for two irreducible strings to commute is also presented.
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Ignatoski, Matea, Jonatan Lerga, Ljubiša Stanković, and Miloš Daković. "Comparison of Entropy and Dictionary Based Text Compression in English, German, French, Italian, Czech, Hungarian, Finnish, and Croatian." Mathematics 8, no. 7 (July 1, 2020): 1059. http://dx.doi.org/10.3390/math8071059.
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The rapid growth in the amount of data in the digital world leads to the need for data compression, and so forth, reducing the number of bits needed to represent a text file, an image, audio, or video content. Compressing data saves storage capacity and speeds up data transmission. In this paper, we focus on the text compression and provide a comparison of algorithms (in particular, entropy-based arithmetic and dictionary-based Lempel–Ziv–Welch (LZW) methods) for text compression in different languages (Croatian, Finnish, Hungarian, Czech, Italian, French, German, and English). The main goal is to answer a question: ”How does the language of a text affect the compression ratio?” The results indicated that the compression ratio is affected by the size of the language alphabet, and size or type of the text. For example, The European Green Deal was compressed by 75.79%, 76.17%, 77.33%, 76.84%, 73.25%, 74.63%, 75.14%, and 74.51% using the LZW algorithm, and by 72.54%, 71.47%, 72.87%, 73.43%, 69.62%, 69.94%, 72.42% and 72% using the arithmetic algorithm for the English, German, French, Italian, Czech, Hungarian, Finnish, and Croatian versions, respectively.
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St. John, Dennis. "Technology Tips: Exploring Hill Ciphers with Graphing Calculators." Mathematics Teacher 91, no. 3 (March 1998): 240–44. http://dx.doi.org/10.5951/mt.91.3.0240.
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Throughout history, coded messages have been used for various reasons. Today's students are fascinated by the secretive nature of these codes, and this fascination can lead them to explore the mathematics of cryptography. The simplest codes are called substitution ciphers. In these codes, each letter is replaced by another number or letter in the alphabet. These codes are easy to crack, or decode, because of the relative frequency of letters in messages. For example, e is the most often used letter in the English language; therefore, the substituted value for e is relatively easy to determine. One way to make substitution codes more difficult to crack is to group letters and then encode the groups of letters. A particular application of this strategy, one that combines matrix multiplication and modular arithmetic, is known as the Hill cipher (Anton and Rorres 1987). This article explains coding and decoding messages using Hill ciphers. These ciphers are an interesting example of an application of matrices called for in NCTM's Curriculum and Evaluation Standards for School Mathematics (NCTM 1989) for grades 9-12. A graphing calculator will facilitate the matrix and modular arithmetic used in the coding and decoding procedures.
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BORDIHN, HENNING, MARKUS HOLZER, and MARTIN KUTRIB. "UNSOLVABILITY LEVELS OF OPERATION PROBLEMS FOR SUBCLASSES OF CONTEXT-FREE LANGUAGES." International Journal of Foundations of Computer Science 16, no. 03 (June 2005): 423–40. http://dx.doi.org/10.1142/s0129054105003078.
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We investigate the operation problem for linear and deterministic context-free languages: Fix an operation on formal languages. Given linear (deterministic, respectively) context-free languages, is the application of this operation to the given languages still a linear (deterministic, respectively) context-free language? Besides the classical operations, for which the linear and deterministic context-free languages are not closed, we also consider the recently introduced root and power operation. We show non-semi-decidability, to be more precise, we show completeness for the second level of the arithmetic hierarchy for all of the aforementioned operations, except for the power operation, if the underlying alphabet contains at least two letters. The result for the power operation solves an open problem stated in Theoret. Comput. Sci.314 (2004) 445–449.
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Glazunova, Olga I. "On the Countable Meaning of the Glagolitic script." NSU Vestnik. Series: Linguistics and Intercultural Communication 18, no. 2 (2020): 46–61. http://dx.doi.org/10.25205/1818-7935-2020-18-2-46-61.
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Previous attempts to discover any links of the Glagolitic symbols with the Germanic runes, the Ethiopian, Coptic, Gothic, Arabic scripts, or with the Greek minuscule writing have not lead to any results. But at the same time, it is obvious that Glagolitic signs did not appear accidentally. There must be a certain initial meaning behind their schematic representation, and this meaning had a profound figurative cognitive and structural symbolic meaning for speakers. The author claims that the visual images of Glagolitic letters are directly related to the principles that guided the primitive artists when depicting reality. The article provides evidence that Glagolitic letters followed the logic of the development of social consciousness of that time, they reflected and transmitted the idea of Genus hominum. Primitive thinking was based on the associative connections between a sign, its meaning, and an associative representation of the role that this meaning played in the life of their tribe. The main task of these associative representations was to facilitate the process of perception and memorization of signs through their compliance with traditional cultural values of native speakers. The alphabet order of Glagolitic signs was interpreted in strict accordance with their numerical meaning. This order makes it possible to draw analogy between the form of the letters and the images of some ancient artifacts which had a special spiritual significance for the primitive man. The article claims that the first five Glagolitic signs contain figurative and cognitive ideas of the primitive man about himself, his family and ancestors: a man (1), a woman (2), their union (3), their house (4), and protection of the tribe (5). Structural and arithmetic correspondences of symbols played a significant role in the Glagolitic script as well. Unlike the Cyrillic alphabet, numerical values of the Glagolitic letters follow each other without any omission. This suggests that these letters were used first as numbers. There are also structural and schematic correspondences between Glagolitic symbols. Using various structural elements that the system assigned to them, it is possible to transform their graphic images into numbers “one”, “ten”, etc. This highlights the idea that initially the Glagolitic alphabet arose as a counting system and was adapted to write the sounds of speech later. For this reason Glagolitic letters received the same names as these in the Cyrillic alphabet, but they preserved the straight-through order of their numerical values.
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Tanaka, Yuu, and Kiyoshi Yamaoka. "Blink Activity and Task Difficulty." Perceptual and Motor Skills 77, no. 1 (August 1993): 55–66. http://dx.doi.org/10.2466/pms.1993.77.1.55.
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This study investigated the relationship between task difficulty and blink activity, which includes blink rate, blink amplitude, and blink duration. Two kinds of tasks established two levels of difficulty. In Exp. 1, a mental arithmetic task was used to examine the relationship. Analysis showed that blink rate for a difficult task was significantly higher than that for an easier one. In Exp. 2, a letter-search task (hiragana Japanese alphabet) was used while the other conditions were the same as those in Exp. 1; however, the results of this experiment were not influenced by the difficulty of the task. As results indicate that blink rate is related to not only difficulty but also the nature of the task, the nature of the task is probably dependent on a mechanism in information processing. The results for blink amplitude and blink duration showed no systematic change during either experiment.
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Bashkin, V. A. "On the Efficient Representation of an Unbounded Resource with the Aid of One-Counter Circuits." Modeling and Analysis of Information Systems 20, no. 2 (March 18, 2015): 139–56. http://dx.doi.org/10.18255/1818-1015-2013-2-139-156.
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A class of infinite-state automata with a simple periodic behaviour and a convenient graphical representation is studied. A positive one-counter circuit is defined as a strongly connected one-counter net (one-counter nondeterministic finite automata without zero-testing) with at least one positive cycle. It is shown that in a positive circuit an infinite part of a reachability set is an arithmetic progression; numerical properties of this progression are estimated. A specific graphical representation of circuits is presented. General one-counter nets are equivalent to Petri Nets with at most one unbounded place and to pushdown automata with a single-symbol stack alphabet. It is shown that an arbitrary one-counter net can be represented by a finite tree of circuits. A one-counter net is called sound, if a counter is used only for “infinite-state” (periodic) behaviour. It is shown that for an arbitrary one-counter net an equivalent sound net can be effectively constructed from the corresponding tree of circuits.
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Kirsanova, E. N., and M. G. Sadovsky. "Entropy Approach to Comparison of Images." Open Systems & Information Dynamics 08, no. 02 (June 2001): 183–99. http://dx.doi.org/10.1023/a:1011962818766.
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Basically new pattern recognition method is implemented to compare two (or several) digital images. The method has neither feature alphabet, nor pattern dictionary recovery stages. It compares input images due to a special object called palette built from fragments of images. The measures to estimate the distances between images are based on a determination of the specific entropy of the frequency dictionary of an image with respect to the palette; that latter presents the statistical ancestor of the group of the images under comparison. The palette is defined as the frequency dictionary with frequencies of the fragments equal to arithmetic mean of the frequencies of the same fragments from the images to be compared. Such definition yields a minimum of the sum of specific entropies of the compared images with respect to the palette. Some preliminary results in the application of the method in pattern recognition and synergistics problems are presented. The limitations and basic properties of the method are discussed.
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Lobovikov, Vladimir Olegovich. "A Logically Formalized Axiomatic Epistemology System Σ + C and Philosophical Grounding Mathematics as a Self-Sufficing System." Mathematics 9, no. 16 (August 5, 2021): 1859. http://dx.doi.org/10.3390/math9161859.
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The subject matter of this research is Kant’s apriorism underlying Hilbert’s formalism in the philosophical grounding of mathematics as a self-sufficing system. The research aim is the invention of such a logically formalized axiomatic epistemology system, in which it is possible to construct formal deductive inferences of formulae—modeling the formalism ideal of Hilbert—from the assumption of Kant’s apriorism in relation to mathematical knowledge. The research method is hypothetical–deductive (axiomatic). The research results and their scientific novelty are based on a logically formalized axiomatic system of epistemology called Σ + C, constructed here for the first time. In comparison with the already published formal epistemology systems Ξ and Σ, some of the axiom schemes here are generalized in Σ + C, and a new symbol is included in the object-language alphabet of Σ + C, namely, the symbol representing the perfection modality, C: “it is consistent that…”. The meaning of this modality is defined by the system of axiom schemes of Σ + C. A deductive proof of the consistency of Σ + C is submitted. For the first time, by means of Σ + C, it is deductively demonstrated that, from the conjunction of Σ + C and either the first or second version of Gödel’s theorem of incompleteness of a formal arithmetic system, the formal arithmetic investigated by Gödel is a representation of an empirical knowledge system. Thus, Kant’s view of mathematics as a self-sufficient, pure, a priori knowledge system is falsified.
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Müller, Burkhard, and Jürgen Gehrke. "Acquisition and Use of Mental Operators: Effects of Type of Practice." Experimental Psychology 49, no. 2 (April 2002): 141–52. http://dx.doi.org/10.1027//1618-3169.49.2.141.
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Abstract. Planning interactions with the physical world requires knowledge about operations; in short, mental operators. Abstractness of content and directionality of access are two important properties to characterize the representational units of this kind of knowledge. Combining these properties allows four classes of knowledge units to be distinguished that can be found in the literature: (a) rules, (b) mental models or schemata, (c) instances, and (d) episodes or chunks. The influence of practicing alphabet-arithmetic operators in a prognostic, diagnostic, or retrognostic way (A + 2 = ?, A? = C, or ? + 2 = C, respectively) on the use of that knowledge in a subsequent test was used to assess the importance of these dimensions. At the beginning, the retrognostic use of knowledge was worse than the prognostic use, although identical operations were involved (A + 2 = ? vs. ? - 2 = A). This disadvantage was reduced with increased practice. Test performance was best if the task and the letter pairs were the same as in the acquisition phase. Overall, the findings support theories proposing multiple representational units of mental operators. The disadvantage for the retrognosis task was recovered in the test phase, and may be evidence for the importance of the order of events independent of the order of experience.
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Robinson, Peter J., and Mee Aie Ha. "Instance Theory and Second Language Rule Learning under Explicit Conditions." Studies in Second Language Acquisition 15, no. 4 (December 1993): 413–38. http://dx.doi.org/10.1017/s0272263100012365.
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This study investigates the generalizability of claims by Logan (Klapp, Boches, Trabert, & Logan, 1991; Logan, 1985, 1988a, 1988b; Logan & Klapp, 1991) about the development of automaticity in the adult learning of alphabet arithmetic problems to the context of adult second language acquisition. Logan's proposal is that as individual solutions to problems accumulate in memory a transition in problem-solving procedures takes place. This transition involves the shift from an algorithm-based procedure for deducing correct solutions to direct retrieval of individual solutions or instances from memory. In the present study, second language learners of English were presented with a rule for understanding the morphological constraint on the dative alternation (Mazurkewich & White, 1984) and asked to judge the acceptability of 36 sentences presented in a training set. The sentences were controlled for frequency of presentation, one being presented eight times, one seven times, and so forth. When presented together with novel instances of the same type in a transfer set, reaction times to old instances were significantly faster. Reaction times to repetitions of the previously presented verbs in new frames and novel verbs in old frames were compared as a test of hypotheses about strategy switches in processing alternating and nonalternating verbs.
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Belarmino, Mary Jean T., and Victoria E. Tamban. "ILAW SA LILIM ANG PARA TEACHERS KONG NATAY: A PARENTS-INDUCED LEARNING TOWARDS ENHANCEMENT OF GRADE I PUPILS’ NUMERACY AND LITERACY SKILLS." International Journal of Theory and Application in Elementary and Secondary School Education 5, no. 1 (April 27, 2023): 23–32. http://dx.doi.org/10.31098/ijtaese.v5i1.1143.
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This study aimed to determine the effectiveness of parent-induced learning, namely "Ilaw Sa Lilim Ang Para teachers Kong Natay": an intervention program to enhance Grade I Pupils’ Numeracy and Literacy Skills. Through descriptive research design, the study involved 11 parents of those pupils who struggle with language literacy and numeracy who had voluntarily undergone online parental training for two weeks. Also, the statistical tools used in this study were mean, standard deviation, and dependent t-test. Through the mean scores in pre-test and post-test, the results showed that pupils scored in language literacy in terms of phonological awareness, alphabet knowledge, fluency, and reading comprehension. And in numeracy skills in terms of counting, basic arithmetic, number symbols, and recognizing symbols, all significantly improved their rating after the intervention program. The results also revealed a significant difference between the pre-test and post-test mean scores of Grade 1 Pupils in Language Literacy and Numeracy Skills indicating an improvement in their statistical value. Thus, the researcher recommends strengthening the communication link among the parents by tapping them to be actively involved in school and academic-related activities. Also, integrate the intervention program into the curriculum to consistently check and upgrade its needs and applicability, especially in the challenge of the new normal, by considering including it in any future training among the parents. Effective, practical, and feasible pedagogical skills that would meet the different learning styles and interests of the children so as to maintain their span of attention.
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Belousov, A. I., and R. S. Ismagilov. "On One Sufficient Condition for the Irregularity of Languages." Mathematics and Mathematical Modeling, no. 4 (October 23, 2018): 1–11. http://dx.doi.org/10.24108/mathm.0418.0000121.
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The article deals with a proof of one sufficient condition for the irregularity of languages. This condition is related to the properties of certain relations on the set of natural numbers, namely relations possessing the property, referred to as strong separability. In turn, this property is related to the possibility of decomposition of an arithmetic vector space into a direct sum of subspaces. We specify languages in some finite alphabet through the properties of a vector that shows the number of occurrences of each letter of the alphabet in the language words and is called the word distribution vector in the word. The main result of the paper is the proof of the theorem according to which a language given in such a way that the vector of distribution of letters in each word of the language belongs to a strongly separable relation on the set of natural numbers is not regular. Such an approach to the proof of irregularity is based on the Myhill-Nerode theorem known in the theory of formal languages, according to which the necessary and sufficient condition for the regularity of a language consists in the finiteness of the index of some equivalence relation defined by the language.The article gives a definition of a strongly separable relation on the set of natural numbers and examines examples of such relations. Also describes a construction covering a considerably wide class of strongly separable relations and connected with decomposition of the even-dimensional vector space into a direct sum of subspaces of the same dimension. Gives the proof of the lemma to assert an availability of an infinite sequence of vectors, any two terms of which are pairwise disjoint, i.e. one belongs to some strongly separable relation, and the other does not. Based on this lemma, there is a proof of the main theorem on the irregularity of a language defined by a strongly separable relation.This result sheds additional light on the effectiveness of regularity / irregularity analysis tools based on the Myhill-Neroud theorem. In addition, the proved theorem and analysis of some examples of strongly separable relations allows us to establish non-trivial connections between the theory of formal languages and the theory of linear spaces, which, as analysis of sources shows, is relevant.In terms of development of the obtained results, the problem of the general characteristic of strongly separable relations is of interest, as well as the analysis of other properties of numerical sets that are important from the point of view of regularity / irregularity analysis of languages.
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Kirova, Gabriela. "COMPARATIVE ANALYSIS OF THE GEOMETRICAL CONTENT IN THE NEW BULGARIAN TEXTBOOKS OF MATHEMATICS FOR THIRD GRADE." Knowledge International Journal 28, no. 3 (December 10, 2018): 991–96. http://dx.doi.org/10.35120/kij2803991g.
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Starting with 2018/2019 school year in Bulgaria, the math education in the third grade is implemented through new training kits. They were developed on the basis of the new third-grade mathematics curriculum, approved by Order No. РД 09-1093 / 25.01.2017 of the Minister of Education and Science, Annex No. 8, supplemented by Order No. РД 09-2555 / 15.06.2018 of the Minister of Education and Science. Training kits are approved by the Ministry of Education and Science and are 7 in total. Geometric learning content in new math textbooks is the second most important element after arithmetic content. It is combined with the arithmetic learning content, and by this the foundation of the successful study of geometry in the next school grades is laid. The new geometry knowledge that is included in the third grade curriculum is the following: straight line, curve, beam, angle, right angle, obtuse angle, acute angle, right triangle, acute triangle, obtuse triangle; naming geometric figures with Latin alphabet letters [11]78. It is important in a modern mathematics textbook to have a rich and varied geometric content. It is important that the new types of geometry tasks are introduced with rich visualization using a specific-inductive approach. The relative number of tasks of a given type is an important prerequisite for the successful formation and improvement of skills for solving geometric problems in pupils at the age of 9-10. This article will present a comparative analysis of the geometric content in the seven approved Bulgarian third-grade mathematics textbooks, which are used in the mass practice of this school year. For the purpose of the study, a classification of all types of tasks and exercises with geometric content has been developed. Then the tasks in the seven textbooks are systematized by the so chosen classification. The data are statistically processed taking into account the relative share of tasks of each type within a textbook, as well as a comparison between the relative shares of the geometric tasks in the different textbooks. The established differences in the number and relative share of different types of geometric tasks make it possible for the analyzed textbooks to be ranked. Such a study has not been published so far. It has a relation to the assessment of the quality of the textbooks offered. The conclusions formulated in this article can help primary teachers in their choice of textbooks to teach to their third grade students.
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Chen, Yalin, and Jamie I. D. Campbell. "Transfer of training in simple addition." Quarterly Journal of Experimental Psychology 71, no. 6 (January 1, 2018): 1312–23. http://dx.doi.org/10.1080/17470218.2017.1318295.
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In recent years, several researchers have proposed that skilled adults may solve single-digit addition problems (e.g., 3 + 1 = 4, 4 + 3 = 7) using a fast counting procedure. Practicing a procedure often leads to transfer of learning and faster performance of unpracticed items. Such transfer has been demonstrated using a counting-based alphabet arithmetic task (e.g., B + 4 = C D E F) that indicated robust generalization of practice (i.e., response time [RT] gains) when untrained transfer problems at test had been implicitly practiced (e.g., practice B + 3, test B + 2 or B + 1). Here, we constructed analogous simple addition problems (practice 4 + 3, test 4 + 2 or 4 + 1). In each of three experiments (total n = 108), participants received six practice blocks followed by two test blocks of new problems to examine generalization effects. Practice of addition identity rule problems (i.e., 0 + N = N) showed complete transfer of RT gains made during practice to unpracticed items at test. In contrast, the addition ties (2 + 2, 3 + 3, etc.) presented large RT costs for unpracticed problems at test, but sped up substantially in the second test block. This pattern is consistent with item-specific strengthening of associative memory. The critical items were small non-tie additions (sum ≤ 10) for which the test problems would be implicitly practiced if counting was employed during practice. In all three experiments (and collectively), there was no evidence of generalization for these items in the first test block, but there was robust speed up when the items were repeated in the second test block. Thus, there was no evidence of the generalization of practice that would be expected if counting procedures mediated our participants’ performance on small non-tie addition problems.
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Aswati, Muhammad Syafarudin, La Ode Ali Basri, and Ajeng Kusuma Wardani. "Public School in Watopute and the Dynamic Development, 1925-2021." Journal of Humanities and Social Sciences Studies 5, no. 6 (June 17, 2023): 98–105. http://dx.doi.org/10.32996/jhsss.2023.5.6.11.
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This research examines Watopute Grammar School and its development dynamics from 1925-2021. The specific aims of the study are (1) to explain the background to the founding of the school; (2) to describe the dynamics of the development of the school in the period of 1925-2021. This research uses the historical method, which consists of five stages of research, namely: (a) Selection of topics, (b) Heuristics, (c) Verification, (d) Interpretation, (e) Historiography. The results of this study show that, first, the establishment of the Watopute Grammar School in 1925 was due to the need for labor by the Dutch East Indies government to become administrative staff, forestry foremen, and teak processing factory workers. In addition, there was a mission from the Dutch East Indies government to improve the quality of human resources, especially the Muna nobilities, because they had an essential role in the area. Second is the dynamics of the development of the grammar school; During the Dutch East Indies era, the school was known as Volkshool. Teaching staff were brought in from Ambon and Manado, while students were from various districts in Muna. In the teaching and learning process at the school using simple facilities and infrastructure, the curriculum consists of alphabet, Indonesian, conversation, and arithmetic subjects. During the Japanese period, the Watopute Grammar School did not experience significant changes and only occurred in the field of curriculum. Japan uses a curriculum consisting of subjects, Japanese language, history, natural sciences, geography, regional languages, physical education, and Indonesian. After independence, Watopute Grammar School underwent a name change starting from SDN 5 Raha in 1946, the name changed to SDN 6 Kontunaga in 2001, and it became SDN 1 Watopute in 2014.
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BERGELSON, V., J. KUŁAGA-PRZYMUS, M. LEMAŃCZYK, and F. K. RICHTER. "Rationally almost periodic sequences, polynomial multiple recurrence and symbolic dynamics." Ergodic Theory and Dynamical Systems 39, no. 9 (January 18, 2018): 2332–83. http://dx.doi.org/10.1017/etds.2017.130.
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A set$R\subset \mathbb{N}$is calledrationalif it is well approximable by finite unions of arithmetic progressions, meaning that for every$\unicode[STIX]{x1D716}>0$there exists a set$B=\bigcup _{i=1}^{r}a_{i}\mathbb{N}+b_{i}$, where$a_{1},\ldots ,a_{r},b_{1},\ldots ,b_{r}\in \mathbb{N}$, such that$$\begin{eqnarray}\overline{d}(R\triangle B):=\limsup _{N\rightarrow \infty }\frac{|(R\triangle B)\cap \{1,\ldots ,N\}|}{N}<\unicode[STIX]{x1D716}.\end{eqnarray}$$Examples of rational sets include many classical sets of number-theoretical origin such as the set of squarefree numbers, the set of abundant numbers, or sets of the form$\unicode[STIX]{x1D6F7}_{x}:=\{n\in \mathbb{N}:\boldsymbol{\unicode[STIX]{x1D711}}(n)/n<x\}$, where$x\in [0,1]$and$\boldsymbol{\unicode[STIX]{x1D711}}$is Euler’s totient function. We investigate the combinatorial and dynamical properties of rational sets and obtain new results in ergodic Ramsey theory. Among other things, we show that if$R\subset \mathbb{N}$is a rational set with$\overline{d}(R)>0$, then the following are equivalent:(a)$R$is divisible, i.e. $\overline{d}(R\cap u\mathbb{N})>0$for all$u\in \mathbb{N}$;(b)$R$is an averaging set of polynomial single recurrence;(c)$R$is an averaging set of polynomial multiple recurrence.As an application, we show that if$R\subset \mathbb{N}$is rational and divisible, then for any set$E\subset \mathbb{N}$with$\overline{d}(E)>0$and any polynomials$p_{i}\in \mathbb{Q}[t]$,$i=1,\ldots ,\ell$, which satisfy$p_{i}(\mathbb{Z})\subset \mathbb{Z}$and$p_{i}(0)=0$for all$i\in \{1,\ldots ,\ell \}$, there exists$\unicode[STIX]{x1D6FD}>0$such that the set$$\begin{eqnarray}\{n\in R:\overline{d}(E\cap (E-p_{1}(n))\cap \cdots \cap (E-p_{\ell }(n)))>\unicode[STIX]{x1D6FD}\}\end{eqnarray}$$has positive lower density.Ramsey-theoretical applications naturally lead to problems in symbolic dynamics, which involverationally almost periodic sequences(sequences whose level-sets are rational). We prove that if${\mathcal{A}}$is a finite alphabet,$\unicode[STIX]{x1D702}\in {\mathcal{A}}^{\mathbb{N}}$is rationally almost periodic,$S$denotes the left-shift on${\mathcal{A}}^{\mathbb{Z}}$and$$\begin{eqnarray}X:=\{y\in {\mathcal{A}}^{\mathbb{Z}}:\text{each word appearing in}~y~\text{appears in}~\unicode[STIX]{x1D702}\},\end{eqnarray}$$then$\unicode[STIX]{x1D702}$is a generic point for an$S$-invariant probability measure$\unicode[STIX]{x1D708}$on$X$such that the measure-preserving system$(X,\unicode[STIX]{x1D708},S)$is ergodic and has rational discrete spectrum.
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Hague, Matthew, Artur Jeż, and Anthony W. Lin. "Parikh’s Theorem Made Symbolic." Proceedings of the ACM on Programming Languages 8, POPL (January 5, 2024): 1945–77. http://dx.doi.org/10.1145/3632907.
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Parikh’s Theorem is a fundamental result in automata theory with numerous applications in computer science. These include software verification (e.g. infinite-state verification, string constraints, and theory of arrays), verification of cryptographic protocols (e.g. using Horn clauses modulo equational theories) and database querying (e.g. evaluating path-queries in graph databases), among others. Parikh’s Theorem states that the letter-counting abstraction of a language recognized by finite automata or context-free grammars is definable in Linear Integer Arithmetic (a.k.a. Presburger Arithmetic). In fact, there is a linear-time algorithm computing existential Presburger formulas capturing such abstractions, which enables an efficient analysis via SMT-solvers. Unfortunately, real-world applications typically require large alphabets (e.g. Unicode, containing a million of characters) — which are well-known to be not amenable to explicit treatment of the alphabets — or even worse infinite alphabets. Symbolic automata have proven in the last decade to be an effective algorithmic framework for handling large finite or even infinite alphabets. A symbolic automaton employs an effective boolean algebra, which offers a symbolic representation of character sets (i.e. in terms of predicates) and often lends itself to an exponentially more succinct representation of a language. Instead of letter-counting, Parikh’s Theorem for symbolic automata amounts to counting the number of times different predicates are satisfied by an input sequence. Unfortunately, naively applying Parikh’s Theorem from classical automata theory to symbolic automata yields existential Presburger formulas of exponential size. In this paper, we provide a new construction for Parikh’s Theorem for symbolic automata and grammars, which avoids this exponential blowup: our algorithm computes an existential formula in polynomial-time over (quantifier-free) Presburger and the base theory. In fact, our algorithm extends to the model of parametric symbolic grammars, which are one of the most expressive models of languages over infinite alphabets. We have implemented our algorithm and show it can be used to solve string constraints that are difficult to solve by existing solvers.
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Yves Julien, Manifi Abouh Maxime, and Ethe Julia Ndibnu-Messina. "Vers quel modèle de traduction-terminologie en langues nationales à l’aune d’une éducation bi- plurilingue au Cameroun ?" Traduction et Langues 21, no. 1 (August 31, 2022): 137–56. http://dx.doi.org/10.52919/translang.v21i1.876.
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Towards what model of translation-terminology in national languages in the light of bi-plurilingual education in Cameroon?
Cameroon, a country characterised by obvious linguistic diversity, recognises the importance of education that is rooted in the culture of the pupils and develops professional or self-employment skills through bi-lingual education. However, the national languages of Cameroon do not have sufficiently elaborate metalanguages to fully convey all the knowledge related to school subjects such as grammar, arithmetic, geometry, etc. They therefore need to be developed and adapted to the needs of the students. They need to be equipped with adequate terminologies to meet the challenge of bi-plurilingual teaching (official languages and national languages), because the production of bi-plurilingual (Cameroonian languages and official languages: French and English) teaching manuals and metalinguistic tools (lexicons, dictionaries, etc.), among others, implies an intense activity of translation-terminology to express certain teaching contents. However, no standard theoretical-practical model has been adopted for translation- terminology involving these languages. This activity thus seems to be left to improvisation. Focusing on recent work in two terminology committees in Cameroon (the ELAN- Afrique committee and the one set up by the IFADEM-RETHE team in Cameroon in 2016), this article outlines some of the salient linguistic problems encountered in translation-terminology activities related to the elaboration of lexicons in national languages, in the perspective of bi-lingual education. These include problems relating to the order of priority in the choice of naming procedures, compliance with the rules of adaptation of borrowings, the length of lexicalised expressions, and the rate of translation of terms. With regard to the choice of naming procedures, certain notions were difficult to agree on and were sometimes the source of lengthy debates within the translation-terminology groups. For example, in view of the high level of abstraction of certain concepts, some members of the terminology committees proposed borrowing as a first recourse, while others, with a purist tendency, considered that procedures employing the internal resources of the target language should be preferred to borrowing, without taking into account the length of the lexemes that would be derived from them. As far as compliance with the rules of adaptation of borrowings is concerned, several terms are not morpho-phonologically adapted, contrary to what is recommended by the cultural approaches. Moreover, several graphemes and consonantal sequences not attested in the alphabet or in the morphophonology of certain languages have been disgracefully taken into account in lexicons. Furthermore, as regards the length of lexicalised expressions, several terms have been translated into excessively long syntagms, or even sentences, whereas several procedures could have allowed their lexicalisation in compliance with the principle of brevity dear to terminology. Finally, some terms, due to their high level of abstraction or technicality, remained untranslated. In addition, the study proposes some theoretical-practical issues in the perspective of a model of translation-terminology of school contents from the official languages into the national languages of Cameroon, by laying the groundwork for an extensive socio-cultural terminological approach that would not only preserve the identity needs of each local community (hence the socio-cultural component of the model), but would also take into account the linguistic and cultural diversity of Cameroon characterised by the other idioms that evolve in this territory with the cultures they convey (hence the extensive character of the model). It is a non-essentialist model in its socio-cultural dimension, which promotes the multidialectal and multilingual character of the territory in translation-terminology activities by encouraging and highlighting the lexical variations that could arise from the different linguistic variants within a single language, as well as the calques and borrowings between Cameroonian languages; this with a view to increasing the possibilities of terminological development.
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Barrouillet, Pierre, and Michel Fayol. "From algorithmic computing to direct retrieval: Evidence from number and alphabetic arithmetic in children and adults." Memory & Cognition 26, no. 2 (March 1998): 355–68. http://dx.doi.org/10.3758/bf03201146.
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Nadapdap, Tulus, Tulus ., and Opim Salim. "The Equation of the Set of Natural Numbers Just to Sum." International Journal of Research and Review 8, no. 5 (June 2, 2021): 379–88. http://dx.doi.org/10.52403/ijrr.20210547.
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Systems of equations of the form X = Y + Z and X = C, in which the unknowns are sets of integers,”+” denotes pairwise sum of sets S + T = m + n m S, n T , and C is an ultimately periodic constant. When restricted to sets of natural numbers, such equations can be equally seen as language equations over a one-letter alphabet with concatenation and regular constants, and it is shown that such systems are computationally universal, in the sense that for every recursive set S N there exists a system with a unique solution containing T with S = n 16n + 13 T. For systems over sets of all integers, both positive and negative, there is a similar construction of a system with a unique solution S = {n|16n ∈ T} representing any hyper-arithmetical set S ⊆ N. Keywords: Language equations, Natural numbers, Equations of natural number.
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Misra, Songhita, Joyeeta Singha, and R. H. Laskar. "Vision-based hand gesture recognition of alphabets, numbers, arithmetic operators and ASCII characters in order to develop a virtual text-entry interface system." Neural Computing and Applications 29, no. 8 (January 31, 2017): 117–35. http://dx.doi.org/10.1007/s00521-017-2838-6.
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Кожемякина, Н. В., and Н. Н. Пономаренко. "РЕКУРСИВНЕ ГРУПОВЕ КОДУВАННЯ З РЕКУРСИВНИМ ЧАСТОТНИМ МОДЕЛЮВАННЯМ." Radioelectronic and Computer Systems, no. 4 (June 17, 2016): 22–26. http://dx.doi.org/10.32620/reks.2016.4.02.
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Task of entropy group coding of data for reduce of its statistical redundancy on base of recursive group coding is considered. Recursive group coding provides effective coding of symbols of large alphabets. It is fast and in some cases more effective alternative of such methods as arithmetical coding and Huffman coding. However applications of recursive group coding are restricted by usage of statistical frequency modeling. For such modeling frequencies (or probabilities) of symbols are calculated for entire text as well as information about size sand contents of groups are stored in compressed file. In this work a modification of recursive group coding are proposed which is able effectively compress texts statistically heterogeneous by frequency characteristics. A model for synthesizing of test texts is considered. Also a new metric for estimates of uniformity of a given text is proposed. It is shown that for considered test texts the proposed modifications of recursive group coding provide up to 65% less compressed data size than conventional method.
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Jamaludin, Thandar Soe Sumaiyah, Mohd Said Nurumal, Masmunaa Hassan, Kyu Kyu Win, and Resti Yulianti Sutrisno. "Sustainable Education for Refugee Children: A Quasi-Experimental Study." Proceedings Series on Health & Medical Sciences 6 (January 17, 2025): 221–27. https://doi.org/10.30595/pshms.v6i.1427.
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Refugee children are unable to access formal education like public schools due to their status with no citizenship. According to sustainable development goals (SGDs), everyone should have equal access to formal education. Objective: This study aimed to evaluate the effectiveness of sustainable education programmes for refugee children. Method: An educational programme was provided to refugee children by using a quasi-experimental approach with 27 refugee children for a period of 1 year. The program consisted of teaching sessions in four subjects: Malay language, mathematics, Islamic lessons, and science. Pre- and post-program assessments were used to measure changes in the children’s learning outcomes. Significant improvements were observed across all subjects. Malay language competency increased, with 36% of younger children and 44% of older children able to vocalize more than five alphabets post-program. In mathematics, all children could count from 1-10 post-program, with 80% mastering basic arithmetic. Islamic knowledge also improved, with 90% of children able to recite Surah Al-Fatihah correctly. In science, 75% of children could identify body parts accurately. The results indicate that structured educational interventions can significantly enhance the learning outcomes of refugee children. Future programs should focus on sustaining these efforts through partnerships and improving teacher training.
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Antanavičius, Darius. "Chronograms and Chronostichs of the 1695 Kražiai Manuscript." Senoji Lietuvos literatūra 39 (May 22, 2015): 53–80. https://doi.org/10.51554/sll.2015.29083.
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Eight students of the Society of Jesus, who studied rhetoric at Kražiai College in 1694–1695, left a priceless fruit of their work – a 700-page manuscript book with an intricate baroque title, Fructus horni meditationis rhetoricae Crosis ab academicis Societatis fusi et in cornucopiam depositi, sive specimina profectus in utraque eloquentia rhetorum Crosensium Societatis Iesu anno M DC XCV sub reverendo patre Petro Puzyna professore dignissimo (Annual fruits of rhetorical meditation gathered and laid in a cornucopia in Kražiai by students of the Society of Jesus, or work samples in either rhetoric by students of the class of rhetoric at Kražiai College under the tutorship of Reverend Father Peter Puzyna, the most valuable professor of the year 1695), which is kept at Czartoryski Library in Cracow (manuscript 1866 IV). This paper focuses on the chronograms and chronostichs of the 1695 Kražiai manuscript.Up until now, literature has suggested only one way of composing and counting of chronograms and chronostichs, which is the arithmetical sum of the number-denoting letters of the Latin alphabet – M, D, C, L, V, and I, completely disregarding their sequence within the text. Most of the chronograms and chronostichs of the 1695 Kražiai manuscript do not comply with this principle. The aim of the paper is to introduce the cases detected and to determine their correct dating and the method of counting.Thirty chronograms and chronostichs were found in the 1695 Kražiai manuscript. In the paper, the original variants with the indication of their nature (chronostich or chronogram) and metre, with the calculation of their dates, and with their translations into Lithuanian are presented in sequential order.The different dates of these thirty chronograms and chronostichs that result from the application of the accepted method of their counting give cause for surprise: with 1715 as the dominating date, there are five instances of 1695, one of 1694, and even one of 1905 (!).What mystery hides behind 1715? If it is correct and corresponds to the authors’ line of thought, what could it mean and how could it be justified in the manuscript of 1695? Nothing definite can be said with regard to this question. Different consideration can take one as far as to cast doubts on the time of the production of the manuscript, to refute the students’ time in Kražiai in 1694–1695, to invent unverifiable theories of chronologically later ‘insertion’ of these chronograms and chronostichs, and the like.Next, the paper gives three samples of manuscript notes of the rhetoric course from the Manuscript Department of Vilnius University library on how this form of poetry used to be explained and how its composition was taught in the colleges of the Jesuit province of Lithuania in the late seventeenth century. These samples show that students were taught the elements of chronograms and their composition. It also becomes obvious that no other method of their composition and counting was referred to except the arithmetical sum of the number-denoting letters disregarding their sequence in the text. Thus the manuscript material of the rhetoric course does not offer any food for thought on how else the chronograms of the 1695 Kražiai manuscript could be counted, which means we have to do it ourselves.A closer look shows that there is a connection between the recurring 1715 and 1695, which is the even number 20. In our opinion, it is the key that could ‘unlock’ the chronograms and chronostichs analysed. We noticed that the operation of subtraction is sufficient to always turn 1715 to 1695. This can be illustrated by the example of the first chronogram, which is interlaced in the title of the manuscript: FrVCtVs hornI MeDItatIonIs rhetorICae. In order to make it more obvious, we are presenting the numbers in decreasing order: M+D+C+C=1700. We then add the first V to 1700, which results in 1705. We also add the second V and five I’s, and the result is 10. Finally, 1705–10=1695. Quod erat demonstrandum. Subtraction can be done in various ways, for example: 1700–10 (V+V or IIIII)+5 (V or IIIII)=1695, and the like.Through the application of subtraction, the seemingly illogical and strange date of 1715 turns into 1695 without any exceptions. The paper then proceeds to the counting of all chronograms. For the sake of clarity, the first method of subtraction is given.Conclusions. The method of chronogram composition and counting applied by the authors of the 1695 Kražiai manuscript has not been seen or used anywhere else. Therefore it is not clear whether it was a ‘one-off’ licentia poetica approved by the teacher in order to facilitate composition of chronograms for the students, or a search for new creative paths. Composition of six ‘regular’ chronograms, one of which is the so-called Cabbalah chronostich, raises no doubt as to the students’ talent and knowledge of mandatory rules. Hardly had such an ‘innovation’ a chance of spreading wider, for it would have been misunderstood and even treated as erroneous. We, too, were unable to explain, for quite a long time, why the counting resulted in the incomprehensible sum of ‘1715’. In this case we were much assisted by our awareness that the authors could only have the number ‘1695’ in their minds and not any other. Without such a key, a riddle like this might remain unsolved next time.
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Chouteau, Stéphanie, Benoît Lemaire, Catherine Thevenot, and Karine Mazens. "How learning material shapes learning strategies in an alphabet arithmetic task." Journal of Cognitive Psychology, February 10, 2025, 1–18. https://doi.org/10.1080/20445911.2025.2464600.
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Dewi, Jasinta DM, Jeanne Bagnoud, and Catherine Thevenot. "Do production and verification tasks in arithmetic rely on the same cognitive mechanisms? A test using alphabet arithmetic." Quarterly Journal of Experimental Psychology, June 4, 2021, 174702182110226. http://dx.doi.org/10.1177/17470218211022635.
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In this study, 17 adult participants were trained to solve alphabet–arithmetic problems using a production task (e.g., C + 3 = ?). The evolution of their performance across 12 practice sessions was compared with the results obtained in past studies using verification tasks (e.g., is C + 3 = F correct?). We show that, irrespective of the experimental paradigm used, there is no evidence for a shift from counting to retrieval during training. However, and again regardless of the paradigm, problems with the largest addend constitute an exception to the general pattern of results obtained. Contrary to other problems, their answers seem to be deliberately memorised by participants relatively early during training. All in all, we conclude that verification and production tasks lead to similar patterns of results, which can therefore both confidently be used to discuss current theories of learning. Still, deliberate memorization of problems with the largest addend appears earlier and more often in a production than a verification task. This last result is discussed in light of retrieval models.
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Sahan, Muhammet Ikbal, Ian Lyons, Daniel Ansari, and Wim Fias. "From counting to retrieving: The neural basis of learning alphabet-arithmetic problems." Frontiers in Neuroscience 13 (2019). http://dx.doi.org/10.3389/conf.fnins.2019.96.00083.
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"Supplemental Material for What Is Learned in Procedural Learning? The Case of Alphabet Arithmetic." Journal of Experimental Psychology: Learning, Memory, and Cognition, October 10, 2019. http://dx.doi.org/10.1037/xlm0000775.supp.
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"Implementation of Floating-Point Arithmetic Coding Using x86-64 AVX-256 Assembly Language." Engineering: Open Access 2, no. 3 (July 15, 2024): 01–18. http://dx.doi.org/10.33140/eoa.02.03.13.
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Bit manipulations, especially those executed on multiple strings in parallel, e.g., on Intel® processors equipped with Advanced Vector Extensions (AVX), can be a powerful way to speed up unoptimized high-level sequentially executed code. A case in point is made for floating-point arithmetic coding (FPAC), implemented herein as a non-adaptive, lossless data compression algorithm using x86 AVX-256 stand-alone assembly language under 64-bit MASM assembler in Visual Studio 2022. Apart from writing and reading bit strings to and from file, FPAC can become fully vectorized and be improved in performance (relative to unoptimized integer versions) by orders of magnitude by blocking short sequences of symbols and bypassing interval renormalization. For an alphabet size, up to 53—the limiting case made for 0.474MB Protein Data Bank entry 4HHB, referred to as oxygen transport file (OTF)—it can also strongly outperform a commercially available, unoptimized C++ Huffman encoder by over a factor of 10 and beat the decoder by roughly a factor of 2. Disadvantageous but necessary to this prescription of vectorizations is an additional compressed storage requirement of the length of the codeword (this binary integer is to encode a block of 5 symbols) in addition to the codeword itself; for size-5 blocks, this compromises the compression efficiency as follows: the average number of bits per symbol required to compress the input message is demonstrated to lie in the interval [H(S) + b, H(S) + 0.4 + b], where b = 1.0 for single-precision floating-point arithmetic coding (SPFPAC), b = 1.2 for a slower but more practical double-precision counterpart (DPFPAC), and H(S) is the Shannon entropy of symbol frequencies.
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Day, Joel, Vijay Ganesh, Nathan Grewal, Matthew Konefal, and Florin Manea. "A Closer Look at the Expressive Power of Logics Based on Word Equations." Theory of Computing Systems, December 11, 2023. http://dx.doi.org/10.1007/s00224-023-10154-8.
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AbstractWord equations are equations $$\alpha \doteq \beta $$ α ≐ β where $$\alpha $$ α and $$\beta $$ β are words consisting of letters from some alphabet $$\Sigma $$ Σ and variables from a set X. Recently, there has been substantial interest in the context of string solving in logics combining word equations with other kinds of constraints on words such as (regular) language membership (regular constraints) and arithmetic over string lengths (length constraints). We consider the expressive power of such logics by looking at the set of all values a single variable might take as part of a satisfying assignment for a given formula. Hence, each formula-variable pair defines a formal language, and each logic defines a class of formal languages. We consider logics arising from combining word equations with either length constraints, regular constraints, or both. We also consider word equations with visibly pushdown language membership constraints as a generalisation of the combination of regular and length constraints. We show that word equations with visibly pushdown membership constraints are sufficient to express all recursively enumerable languages and hence satisfiability is undecidable in this case. We then establish a strict hierarchy involving the other combinations. We also provide a complete characterisation of when a thin regular language is expressible by word equations (alone) and some further partial results for regular languages in the general case.
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Dewi, Jasinta D. M., and Catherine Thevenot. "Individual Differences in the Evolution of Counting." Experimental Psychology, June 13, 2022. http://dx.doi.org/10.1027/1618-3169/a000546.
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Abstract. The alphabet–arithmetic paradigm, in which adults are asked to add a numeral addend to a letter augend (e.g., D + 3 = G), was conceived to mimic the way children learn addition. Studies using this paradigm often conclude that procedural learning leads to the memorization of associations between operands and answers. However, as recently suggested, memorization might only be used by a minority of participants and only for problems with the largest addend. In the present paper, we aim at investigating these individual differences through transfer effects from trained problems to new ones. Participants were trained over 12 learning sessions, followed by 3 transfer sessions. A group of participants, that we called the nonbreakers, showed a linear function associating solution times and addends throughout the experiment. In this group, transfer was observed during the first transfer session, suggesting that a procedural strategy, transferable to new items, was still used at the end of training. In another group of participants, that we called the breakers, we observed a decrease in solution times for problems with the largest addend. In this group, transfer was only observed after two transfer sessions, suggesting that procedural strategies were not used as often in this group than in the other group. This was especially true for problems with the largest addend because transfer effects were stronger when they were excluded. Therefore, during learning and for breakers, the answers to problems with larger addends are retrieved first and, as for non-breakers, the answers to problems with very small operands remain computed.