Reinforcement learning using associative memory networks

It is shown that associative memory networks are capable of solving immediate and general reinforcement learning (RL) problems by combining techniques from associative neural networks and reinforcement learning and in particular Q-learning. The modified model is shown to outperform native RL techniques on a stochastic grid world task by developing correct policies. In addition, we formulated an analogous method to add feature extraction as dimensional reduction and eligibility traces as another mechanism to help solve the credit assignment problem. The network contrary to pure RL methods is based on associative memory principles such as distribution of information, pattern completion, Hebbian learning, and noise tolerance (limit cycles, one to many associations, chaos, etc). Because of this, it can be argued that the model possesses more cognitive explanative power than other RL or hybrid models. It may be an effective tool for bridging the gap between biological memory models and computational memory models.

Reinforcement learning using associative memory networks

It is shown that associative memory networks are capable of solving immediate and general reinforcement learning (RL) problems by combining techniques from associative neural networks and reinforcement learning and in particular Q-learning. The modified model is shown to outperform native RL techniques on a stochastic grid world task by developing correct policies. In addition, we formulated an analogous method to add feature extraction as dimensional reduction and eligibility traces as another mechanism to help solve the credit assignment problem. The network contrary to pure RL methods is based on associative memory principles such as distribution of information, pattern completion, Hebbian learning, and noise tolerance (limit cycles, one to many associations, chaos, etc). Because of this, it can be argued that the model possesses more cognitive explanative power than other RL or hybrid models. It may be an effective tool for bridging the gap between biological memory models and computational memory models.

On sparse interpolation of rational functions and gcds

In this note, we present a variant of a probabilistic algorithm by Cuyt and Lee for the sparse interpolation of multivariate rational functions. We also present an analogous method for the computation of sparse gcds.

Use of Grey Numbers for Evaluating a System's Performance Under Fuzzy Conditions

In the present research, a method using Grey Numbers as tools is developed for assessing a system's mean performance, which is useful when utilizing qualitative grades and not numerical scores for this purpose. Although this new method is proved to be equivalent with an analogous method using Triangular Fuzzy Numbers as tools developed in an earlier work, it reduces the required computational burden, since it requires the calculation of two components only (instead of three in the case of the Triangular Fuzzy Numbers) for obtaining the mean value of the Grey Numbers involved. Examples are also presented on student and athlete assessment illustrating the new method and showing that the system's quality performance, calculated by the traditional GPA index, may lead to different assessment conclusions.

Mining historical texts for diachronic spelling variants

The paper describes a method for finding diachronic spelling variants in a corpus that consists of historical and modern Polish texts. The procedure applies the Levenshtein distance and the similarity measure determined with a Word2vec model. The method was applied for both words and sub-word units. A sample of spelling variants was manually evaluated and compared against an existing morphological analyser for Polish historical texts. The resulting lists of spelling variants and spelling modernisation rules were used in a text modernisation tool and their contribution was evaluated. The paper also presents an analogous method for finding spelling variants that result from erroneous OCR. The obtained lists of OCR variants and rules may serve for the correction of OCR output.

Divide and conquer, just like Riemann sums in calculus

“Divide and conquer, just like Riemann sums in calculus” offers a basic introduction for how to estimate—with any desired non-zero margin of error—the area of an irregular shape. For an initial underestimate, readers are encouraged to draw a large rectangle that fits inside the irregular shape and then use the grade school formula to calculate the rectangle’s area: area equals length times width. To refine this underestimate, readers learn to draw multiple smaller rectangles inside the shape whose areas they also sum. An analogous method is provided for overestimates. The discussion concerning how to obtain underestimates or overestimates with any desired margin of error is illustrated with numerous hand-drawn sketches. Mathematics students and enthusiasts are encouraged to consider dividing and conquering in all challenges they face in mathematics or life. At the chapter’s end, readers may check their understanding by working on a problem. A solution is provided.

Integrating Allyl Electrophiles into Nickel-Catalyzed Conjunctive Cross-Coupling

Allylation and conjunctive cross-coupling represent two useful, yet largely distinct, reactivity paradigms in catalysis. The union of these two processes would offer exciting possibilities in organic synthesis but remains largely unknown. Herein, we report the use of allyl electrophiles in nickel-catalyzed conjunctive cross-coupling with a non-conjugated alkene and dimethylzinc. The transformation is enabled by weakly coordinating, monodentate azaheterocycle directing groups, that useful building blocks in synthesis, including saccharin, pyridones, pyrazoles, and triazoles. The reaction occurs under mild conditions and is compatible with a wide range of allyl electrophiles. High chemoselectivity through substrate directivity is demonstrated in the facile reactivity of the β-γ alkene of the starting material, while the ε-ζ alkene of the product is preserved. The generality of this approach is further illustrated through the development of analogous method with alkyne substrates. Mechanistic studies reveal the importance of the weakly coordinating directing group in dissociating to allow binding of the allyl moiety to facilitate C(sp³)–C(sp³) reductive elimination.

Integrating Allyl Electrophiles into Nickel-Catalyzed Conjunctive Cross-Coupling

Allylation and conjunctive cross-coupling represent two useful, yet largely distinct, reactivity paradigms in catalysis. The union of these two processes would offer exciting possibilities in organic synthesis but remains largely unknown. Herein, we report the use of allyl electrophiles in nickel-catalyzed conjunctive cross-coupling with a non-conjugated alkene and dimethylzinc. The transformation is enabled by weakly coordinating, monodentate azaheterocycle directing groups, that useful building blocks in synthesis, including saccharin, pyridones, pyrazoles, and triazoles. The reaction occurs under mild conditions and is compatible with a wide range of allyl electrophiles. High chemoselectivity through substrate directivity is demonstrated in the facile reactivity of the β-γ alkene of the starting material, while the ε-ζ alkene of the product is preserved. The generality of this approach is further illustrated through the development of analogous method with alkyne substrates. Mechanistic studies reveal the importance of the weakly coordinating directing group in dissociating to allow binding of the allyl moiety to facilitate C(sp³)–C(sp³) reductive elimination.

Notes on the correlation between sudden stratospheric warmings and solar activity

A correlation between solar activity and normalized occurrence rate of sudden stratospheric warmings (SSWs) has been found. As a proxy for solar activity, the 10.7 cm solar radio flux has been used. In order to find the correlation, we derived a normalized occurrence rate of major sudden stratospheric warmings (MSSWs) based on both the ERA-40/ERA-Interim dataset and NCEP data. Based on this distribution, we calculated the correlation coefficient, which amounts to 0.63, with a significance of 90.68 %, for ERA-40/ERA-Interim, and 0.55 for the NCEP–NCAR-I reanalysis, with a significance of 83.80 %. Additionally, we calculate correlation coefficients for Lyman-alpha flux and sunspot numbers with the analogous method for the same period.