This paper is based on a talk given at the 14-th International Workshop on Differential Geometry and Its Applications, hosted by the Petroleum Gas University from Ploiesti, between July 9-th and July 11-th, 2019. After presenting some historical facts, we will consider some geometry problems related to unification approaches. Jordan algebras and Lie algebras are the main non-associative structures. Attempts to unify non-associative algebras and associative algebras led to UJLA structures. Another algebraic structure which unifies non-associative algebras and associative algebras is the Yang-Baxter equation. We will review topics relared to the Yang-Baxter equation and Yang-Baxter systems, with the goal to unify constructions from Differential Geometry.

The study of dog point following has been increasingly popular, at least partially due to the initial claims that dogs outperform apes and the suggestion that our domestication process caused dogs to have a biological capacity to communicate with humans. We take the view that dog pointing is more complicated than was initially reported, and in this study, we explore several potential variables that may make a difference. Our variables include point type (ipsilateral (same-side) vs contralateral (cross-body) points), position (standing vs seated), and distance (proximal vs distal). We find that most dogs follow ipsilateral points while less than half of the dogs in our sample follow contralateral points, and that position and distance also affect dogs’ success. We suggest that dogs acquire ipsilateral points via associative mechanisms, but that contralateral points require the dogs to understand the humans’ communicative intent.

A statistical analysis of semantic memory should reflect the complex, multifactorial structure of the relations among its items. Still, a dominant paradigm in the study of semantic memory has been the idea that the mental representation of concepts is structured along a simple branching tree spanned by superordinate and subordinate categories. We propose a generative model of item representation with correlations that overcomes the limitations of a tree structure. The items are generated through "factors" that represent semantic features or real-world attributes. The correlation between items has its source in the extent to which items share such factors and the strength of such factors: if many factors are balanced, correlations are overall low; whereas if a few factors dominate, they become strong. Our model allows for correlations that are neither trivial nor hierarchical, but may reproduce the general spectrum of correlations present in a data-set of nouns. We provide an estimate of the number of concepts that can be stored and retrieved by a large-scale cortical network, the Potts network, which is perhaps approximately 10⁷ with human cortical parameters. When this storage capacity is exceeded, however, retrieval fails completely only for balanced factors; above a critical degree of imbalance, a phase transition leads to a regime where the network still extracts considerable information about the cued item, even if not recovering its detailed representation: partial categorization seems to emerge spontaneously as a consequence of the dominance of particular factors, rather than being imposed ad hoc. We argue this to be a relevant model of semantic memory resilience in Tulving’s remember/know paradigms.

This paper is a continuation of previous papers on unification theories publishes in AXIOMS. We present results about the (modified) Yang-Baxter equation, Euler’s formula, dual numbers, coalgebra structures, non-associative structures, differential geometry, and (mean) inequalities. We will also attempt to relate our discussion to some Brain Studies and Machine Learnig.

We consider several unification problems in mathematics. We refer to transcendental numbers. Also, we present some ways to unify the main non-associative algebras (Lie algebras and Jordan algebras) and associative algebras.

Humans learn from a lot of information sources to make decisions. Once this information is learned in the brain, spatio-temporal associations are made, connecting all these sources (variables) in space and time represented as brain connectivity. In reality, to make a decision, we usually have only part of the infor-mation, either as a limited number of variables, or limited time to make the decision, or both. The brain functions as spatio-temporal associative memory. Inspired by the ability of the human brain, a brain-inspired spatio-temporal associative memory was proposed earlier, that utilizes the NeuCube brain-inspired spiking neural network framework. Here we apply the STAM framework to develop STAM for neuroimaging data, on the cases of EEG and fMRI, resulting in STAM-EEG and STAM-fMRI. The paper shows that once a NeuCube STAM classification model is trained on a complete spatio-temporal EEG or fMRI data, it can be recalled using only part of the time series, or/and only part of the used variables. We evaluate accordingly the temporal association accuracy and spatial association accuracy. This is a pilot study that opens the field for the development of multimodal classification systems on other multimodal neuroimaging data, such as the also shown longitudinal MRI data, trained on complete data, but recalled on partial data collected across different settings, in different labs and clinics, that may vary in terms of variables, time of data collection, and other parameters. The proposed methods will allow also for brain diagnostic/prognostic marker discovery using spatio-temporal neuroimaging data.

The voice contains elementary social communication cues, conveying speech, as well as paralinguistic information pertaining to the emotional state and the identity of the speaker. In contrast to vocal-speech and vocal-emotion processing, voice-identity processing has been less explored. This seems surprising, given the day-to-day significance of person recognition by voice. A valuable approach to unravel how voice-identity processing is accomplished is to investigate people who have a selective deficit in recognising voices. Such a deficit has been termed phonagnosia. In the present chapter, we provide a systematic overview of studies on phonagnosia and how they relate to current neurocognitive models of person recognition. We review studies that have characterised people who suffer from phonagnosia following brain damage (i.e. acquired phonagnosia) and also studies, which have examined phonagnosia cases without apparent brain lesion (i.e. developmental phonagnosia). Based on the reviewed literature, we emphasise the need for a careful behavioural characterisation of phonagnosia cases by taking into consideration the multistage nature of voice-identity processing and the resulting behavioural phonagnosia subtypes.

The development of synthetic biology has enabled us to make massive progress on biotechnology and to approach research questions from a brand new perspective. In particular, the design and study of gene regulatory networks in vitro, in vivo and in silico, have played an increasingly indispensable role in understanding and controlling biological phenomena. Among them, it is of great interest to understand how associative learning is formed at the molecular circuit level. Noticeably, mathematical models have been increasingly used to predict the behaviors of molecular circuits. The Fernando’s model, which is thought to be one of the first works in this line of research using the Hill equation, attempted to design a synthetic circuit that mimics Hebbian learning in the neural network architecture. In this article, we carry out in-depth computational analysis of the model and demonstrate that the reinforcement effect can be achieved by choosing the proper parameter values. We also construct a novel circuit that can demonstrate forced dissociation, which was not observed in the Fernando’s model. Our work can be readily used as reference for synthetic biologists who consider implementing the circuits of this kind in biological systems.

In manual maintenance inspections of large-scaled photovoltaic (PV) or rooftop PV systems, several days are required to survey the entire PV field. To improve reliability and shorten the amount of time involved, this study proposes an electrical examination based method for locating multiple faults in the PV array. The maximum power point tracking (MPPT) algorithm is used to estimate the maximum power of each PV panel; this is then compared with metering the output power of PV array. Power degradation indexes are parameterized to quantify the degradation between maximum power and metered output power. Bidirectional hetero-associative memory (BHAM) networks are then used to locate multiple faults within the entire PV field. For a rooftop PV system with two strings, as seen in Figure 1, experimental results demonstrate that the proposed model has computational efficiency for real-time applications and that its algorithm is easily implemented in a mobile intelligent vehicle.

Paired associative stimulation (PAS) is a non-invasive brain stimulation technique that modulates synaptic plasticity in the human motor cortex (M1). Since previous studies have primarily used motor evoked potentials (MEPs) as outcome measure, cortical correlates of PAS-induced plasticity remain unknown. Therefore, the aim of this observational study was to investigate cortical correlates of a standard PAS induced plasticity in the primary motor cortex by using a combined TMS-EEG approach in a cohort of eighteen healthy subjects. In addition to the expected long-lasting facilitatory modulation of MEPs amplitude, PAS intervention also induced a significant increase in transcranial magnetic stimulation evoked potentials (TEPs) P30 and P60 amplitude. No significant correlation between the magnitude of PAS-induced changes in TEP components and MEP amplitude were observed. However, the linear regression analysis revealed that the combined changes in P30 and P60 component amplitudes significantly predicted the MEP facilitation after PAS. The findings of our study offer novel insight into the neurophysiological changes associated with PAS-induced plasticity at M1 cortical level and suggest a complex relationship between TEPs and MEPs changes following PAS.