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In this paper we present a novel numeral decomposer that is designed to revert Hurford's Packing Strategy. The Packing Strategy is a model on how numeral words are formed out of smaller numeral words by recursion. The decomposer does not simply check decimal digits but it also works for numerals formed on base 20 or any other base or even combinations of different bases. All assumptions that we use are justified with Hurford's Packing Strategy. The decomposer reads through the numeral. When it finds a sub-numeral, it checks arithmetic conditions to decide whether or not to unpack the sub-numeral. The goal is to unpack those numerals that can sensibly be substituted by similar numerals. E.g., in 'twenty-seven thousand and two hundred and six' it should unpack 'twenty-seven' and 'two hundred and six', as those could each be sensibly replaced by any numeral from 1 to 999. Our most used condition is: If S is a substitutable sub-numeral of a numeral N, then 2*value(S) < value(N). We have tested the decomposer on numeral systems in 254 different natural languages. We also developed a reinforcement learning algorithm based on the decomposer. Both algorithms' code and the results are open source on GitHub.

Artificial intelligence experienced a technological breakthrough in science, industry, and everyday life in the recent few decades. The advancements can be credited to the ever-increasing availability and miniaturization of computational resources that resulted in exponential data growth. However, because of the insufficient amount of data in some cases, employing machine learning in solving complex tasks is not straightforward or even possible. As a result, machine learning with small data experiences rising importance in data science and application in several fields. The authors focus on interpreting the general term of "small data" and their engineering and industrial application role. They give a brief overview of the most important industrial applications of machine learning and small data. Small data is defined in terms of various characteristics compared to big data, and a machine learning formalism was introduced. Five critical challenges of machine learning with small data in industrial applications are presented: unlabeled data, imbalanced data, missing data, insufficient data, and rare events. Based on those definitions, an overview of the considerations in domain representation and data acquisition is given along with a taxonomy of machine learning approaches in the context of small data.

In this paper we give instructions on how to write a minimalist grammar (MG). In order to present the instructions as an algorithm, we use a variant of context free grammars (CFG) as an input format. We can exclude overgeneration, if the CFG has no recursion, i.e. no non-terminal can (indirectly) derive to a right-hand side containing itself. The constructed MGs utilize licensors/-ees as a special way of exception handling. A CFG format for a derivation $A\_eats\_B\mapsto^* peter\_eats\_apples$, where $A$ and $B$ generate noun phrases, normally leads to overgeneration, e.\,g., $i\_eats\_apples$. In order to avoid overgeneration, a CFG would need many non-terminal symbols and rules, that mainly produce the same word, just to handle exceptions. In our MGs however, we can summarize CFG rules that produce the same word in one item and handle exceptions by a proper distribution of licensees/-ors. The difficulty with this technique is that in most generations the majority of licensees/-ors is not needed, but still has to be triggered somehow. We solve this problem with $\epsilon$-items called \emph{adapters}.

Speech-controlled user interfaces facilitate the operation of devices and household functions to laymen. State-of-the-art language technology scans the acoustically analyzed speech signal for relevant keywords that are subsequently inserted into semantic slots to interpret the user's intent. In order to develop proper cognitive information and communication technologies, simple slot-filling should be replaced by utterance meaning transducers (UMT) that are based on semantic parsers and a mental lexicon, comprising syntactic, phonetic and semantic features of the language under consideration. This lexicon must be acquired by a cognitive agent during interaction with its users. We outline a reinforcement learning algorithm for the acquisition of syntax and semantics of English utterances, based on minimalist grammar (MG), a recent computational implementation of generative linguistics. English declarative sentences are presented to the agent by a teacher in form of utterance meaning pairs (UMP) where the meanings are encoded as formulas of predicate logic. Since MG codifies universal linguistic competence through inference rules, thereby separating innate linguistic knowledge from the contingently acquired lexicon, our approach unifies generative grammar and reinforcement learning, hence potentially resolving the still pending Chomsky-Skinner controversy., Comment: 25 pages, 2 figures, 9 tables. arXiv admin note: text overlap with arXiv:1906.04447

Background / introduction. Vector symbolic architectures (VSA) are a viable approach for the hyperdimensional representation of symbolic data, such as documents, syntactic structures, or semantic frames. Methods. We present a rigorous mathematical framework for the representation of phrase structure trees and parse trees of context-free grammars (CFG) in Fock space, i.e. infinite-dimensional Hilbert space as being used in quantum field theory. We define a novel normal form for CFG by means of term algebras. Using a recently developed software toolbox, called FockBox, we construct Fock space representations for the trees built up by a CFG left-corner (LC) parser. Results. We prove a universal representation theorem for CFG term algebras in Fock space and illustrate our findings through a low-dimensional principal component projection of the LC parser states. Conclusions. Our approach could leverage the development of VSA for explainable artificial intelligence (XAI) by means of hyperdimensional deep neural computation. It could be of significance for the improvement of cognitive user interfaces and other applications of VSA in machine learning., Comment: 36 pages, 3 figures

Stochastic feed-in of fluctuating renewable energies is steadily increasing in modern electricity grids and this becomes an important risk factor for maintaining power grid stability. Here we study the impact of wind power feed-in on the short-term frequency fluctuations in power grids based on an IEEE test grid structure, the swing equation for the dynamics of voltage phase angles, and a series of measured wind speed data. External control measures are accounted for by adjusting the grid state to the average power feed-in on a time scale of one minute. The wind power is injected at a single node by replacing one of the conventional generator nodes in the test grid by a wind farm. We determine histograms of local frequencies for a large number of one-minute wind speed sequences taken from the measured data and for different injection nodes. These histograms exhibit a common type of shape, which can be described by a Gaussian distribution for small frequencies and a nearly exponentially decaying tail part. Non-Gaussian features become particularly pronounced for wind power injection at locations, which are weakly connected to the main grid structure. This effect is only present when taking into account the heterogeneities in transmission line and node properties of the grid, while it disappears upon homogenizing of these features. The standard deviation of the frequency fluctuations increases linearly with the average injected wind power., Comment: 9 pages, 7 figures

Speech-controlled user interfaces facilitate the operation of devices and household functions to laymen. State-of-the-art language technology scans the acoustically analyzed speech signal for relevant keywords that are subsequently inserted into semantic slots to interpret the user's intent. In order to develop proper cognitive information and communication technologies, simple slot-filling should be replaced by utterance meaning transducers (UMT) that are based on semantic parsers and a \emph{mental lexicon}, comprising syntactic, phonetic and semantic features of the language under consideration. This lexicon must be acquired by a cognitive agent during interaction with its users. We outline a reinforcement learning algorithm for the acquisition of the syntactic morphology and arithmetic semantics of English numerals, based on minimalist grammar (MG), a recent computational implementation of generative linguistics. Number words are presented to the agent by a teacher in form of utterance meaning pairs (UMP) where the meanings are encoded as arithmetic terms from a suitable term algebra. Since MG encodes universal linguistic competence through inference rules, thereby separating innate linguistic knowledge from the contingently acquired lexicon, our approach unifies generative grammar and reinforcement learning, hence potentially resolving the still pending Chomsky-Skinner controversy., Comment: 13 pages, 1 figure

In future power systems, electrical storage will be the key technology for balancing feed-in fluctuations. With increasing share of renewables and reduction of system inertia, the focus of research expands towards short-term grid dynamics and collective phenomena. Against this backdrop, Kuramoto-like power grids have been established as a sound mathematical modeling framework bridging between the simplified models from nonlinear dynamics and the more detailed models used in electrical engineering. However, they have a blind spot concerning grid components, which cannot be modeled by oscillator equations, and hence do not allow to investigate storage-related issues from scratch. We remove this shortcoming by bringing together Kuramoto-like and algebraic load-flow equations. This is a substantial extension of the current Kuramoto framework with arbitrary grid components. Based on this concept, we provide a solid starting point for the integration of flexible storage units enabling to address current problems like smart storage control, optimal siting and rough cost estimations. For demonstration purpose, we here consider a wind power application with realistic feed-in conditions. We show how to implement basic control strategies from electrical engineering, give insights into their potential with respect to frequency quality improvement and point out their limitations by maximum capacity and finite-time response., Comment: 12 pages, 6 figures

Non-linear equations describing the time evolution of frequencies and voltages in power grids exhibit fixed points of stable grid operation. The dynamical behaviour after perturbations around these fixed points can be used to characterise the stability of the grid. We investigate both probabilities of return to a fixed point and times needed for this return after perturbation of single nodes. Our analysis is based on an IEEE test grid and the second-order swing equations for voltage phase angles $\theta_j$ at nodes $j$ in the synchronous machine model. The perturbations cover all possible changes $\Delta\theta$ of voltage angles and a wide range of frequency deviations in a range $\Delta f=\pm1$~Hz around the common frequency $\omega=2\pi f=\dot\theta_j$ in a synchronous fixed point state. Extensive numerical calculations are carried out to determine, for all node pairs $(j,k)$, the return times $t_{jk}(\Delta\theta,\Delta \omega)$ of node $k$ after a perturbation of node $j$. We find that for strong perturbations of some nodes, the grid does not return to its synchronous state. If returning to the fixed point, the times needed for the return are strongly different for different disturbed nodes and can reach values up to 20 seconds and more. When homogenising transmission line and node properties, the grid always returns to a synchronous state for the considered perturbations, and the longest return times have a value of about 4 seconds for all nodes. The neglect of reactances between points of power generation (internal nodes) and injection (terminal nodes) leads to an underestimation of return probabilities., Comment: 19 pages, 9 figures