Current Issue : October-December Volume : 2025 Issue Number : 4 Articles : 5 Articles
This article aims to limit the rule explosion problem affecting market basket analysis (MBA) algorithms. More specifically, it is shown how, if the minimum support threshold is not specified explicitly, but in terms of the number of items to consider, it is possible to compute an upper bound for the number of generated association rules. Moreover, if the results of previous analyses (with different thresholds) are available, this information can also be taken into account, hence refining the upper bound and also being able to compute lower bounds. The support determination technique is implemented as an extension to the Apriori algorithm but may be applied to any other MBA technique. Tests are executed on benchmarks and on a real problem provided by one of the major Italian supermarket chains, regarding more than 500, 000 transactions. Experiments show, on these benchmarks, that the rate of growth in the number of rules between tests with increasingly more permissive thresholds ranges, with the proposed method, is from 21.4 to 31.8, while it would range from 39.6 to 3994.3 if the traditional thresholding method were applied....
Dynamic mode decomposition with control (DMDc) is a widely used technique for analyzing dynamic systems influenced by external control inputs. It is a recent development and an extension of dynamic mode decomposition (DMD) tailored for input–output systems. In this work, we investigate and analyze an alternative approach for computing DMDc. Compared to the traditional formulation, the proposed method restructures the computation by decoupling the influence of the state and control components, allowing for a more modular and interpretable implementation. The algorithm avoids compound operator approximations typical of standard approaches, which makes it potentially more efficient in real-time applications or systems with streaming data. The new scheme aims to improve computational efficiency while maintaining the reliability and accuracy of the decomposition. We provide a theoretical proof that the dynamic modes produced by the proposed method are exact eigenvectors of the corresponding Koopman operator. Compared to the standard DMDc approach, the new algorithm is shown to be more efficient, requiring fewer calculations and less memory. Numerical examples are presented to demonstrate the theoretical results and illustrate potential applications of the modified approach. The results highlight the promise of this alternative formulation for advancing data-driven modeling and control in various engineering and scientific domains....
Despite its significance, hysteresis remains underrepresented in mainstream models of plasticity. In this work, we propose a novel framework that explicitly models hysteresis in simple one- and two-neuron models. Our models capture key feedbackdependent phenomena such as bistability, multistability, periodicity, quasi-periodicity, and chaos, offering a more accurate and general representation of neural adaptation. This opens the door to new insights in computational neuroscience and neuromorphic system design. Synaptic weights change in several contexts or mechanisms including, Bienenstock– Cooper–Munro (BCM) synaptic modification, where synaptic changes depend on the level of post-synaptic activity; homeostatic plasticity, where all of a neuron synapses simultaneously scale up or down to maintain stability; metaplasticity, or plasticity of plasticity; neuromodulation, where neurotransmitters influence synaptic weights; developmental processes, where synaptic connections are actively formed, pruned and refined; disease or injury; for example, neurological conditions can induce maladaptive synaptic changes; spike-time dependent plasticity (STDP), where changes depend on the precise timing of pre- and postsynaptic spikes; and structural plasticity, where changes in dendritic spines and axonal boutons can alter synaptic strength. The ability of synapses and neurons to change in response to activity is fundamental to learning, memory formation, and cognitive adaptation. This paper presents simple continuous and discrete neuro-modules with adapting feedback synapses which in turn are subject to feedback. The dynamics of continuous periodically driven Hopfield neural networks with adapting synapses have been investigated since the 1990s in terms of periodicity and chaotic behaviors. For the first time, one- and two-neuron models are considered as parameters are varied using a feedback mechanism which more accurately represents real-world simulation, as explained earlier. It is shown that these models are history dependent. A simple discrete two-neuron model with adapting feedback synapses is analyzed in terms of stability and bifurcation diagrams are plotted as parameters are increased and decreased. This work has the potential to improve learning algorithms, increase understanding of neural memory formation, and inform neuromorphic engineering research....
We show how the dynamics of inflation as represented by the Phillips curve follow from a response formalism suggested by Phillips and motivated by the Keynesian notion that it takes time for an economy to respond to an economic shock. The resulting expressions for the Phillips curve are isomorphic to those of anelasticity—a result that provides a straightforward and parsimonious approach to macroeconomic-model construction. Our approach unifies forms of the Phillips curve that are used to account for time dependence of the Phillips curve, expands the possible microeconomic explanations of this time dependence, and broadens the reach of this formalism in economics....
In this paper, we scrutinize a generalized (2+1)-dimensional nonlinear wave equation (NWE) which describes the waves propagation in plasma physics by utilizing Lie group analysis, Lie point symmetry are obtained and thereafter symmetry reductions are performed which lead to nonlinear ordinary differential equations (NODEs). These NODEs are then solved using various methods that includes the direct integration method. This then leads us to explicit exact solutions of NWE. Graphical representation of the achieved results is given to have a good understanding of the nature of solutions obtained. In conclusion, we construct conserved vectors of the NWE by invoking Ibragimov’s theorem....
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