This study delves into the foundational aspects of electrocardiographic (ECG) lead systems, specifically focusing on Einthoven’s Triangle and Wilson’s Central Terminal. We introduce the innovative concept of a Precordial Central Terminal, a strategic arrangement of thoracic electrodes that establishes two Einthoven’s triangles within the horizontal plane, in accordance with physical-mathematical principles. Furthermore, we meticulously scrutinize Goldberger’s contributions to the field of ECG, particularly augmented leads, which shed light on the development of our theory. Additionally, we propose the implementation of a novel standardized electrocardiograph, characterized by its use of exclusively “precordial” electrodes, yet capable of providing a comprehensive three-dimensional perspective of cardiac electrical activity. By amalgamating theoretical underpinnings with empirical experimentation, our study lays the groundwork for future investigations, including the experimental validation of our innovative Precordial Terminal. This validation holds the promise of yielding substantial advancements in the realm of clinical electrocardiography.

We explore the concept of Euclidean locality within treonic topological spaces. Our study establishes a foundational theoretical framework, elucidating the properties of continuity, homeomorphisms, and compactness in these spaces. We assess the Euclidean locality of treonic spaces through the analysis of specific homeomorphisms, which enables us to define manifolds in treonic spaces and extend recent research on Bermejo Algebras. For the first time, we characterize treonic manifolds by incorporating the property of Euclidean locality alongside previously studied properties such as Hausdorff spaces and second countable spaces. Our findings advance the understanding of the topological and geometric properties of treonic spaces, providing significant insights for advanced mathematical research.

Bermejo Algebras, which consist of Algebra B and Treon Algebra, are non-associative and unital algebraic structures that introduce new complex entities. Recently, a Hausdorff space associated with the space where these algebras act was defined. We constructed a second-countable treon space utilizing a novel metric derived from these algebras. We defined topological spaces and established a metric to prove the second-countable property within Bermejo Algebras. Our findings contribute to the construction of manifolds in treon spaces by defining a countable base using the density of rationals in the real numbers.

We conducted a topological analysis of the novel, non-associative, and unital algebraic structure known as Bermejo Algebras, developed by Alejandro Bermejo, which includes the Algebra B and Treon Algebra. This algebras can define Lie and Malcev algebras when their product operations are derived from the Bermejo Algebras product. Central to this study are treons, complex entities that arise as isomorphisms of Algebra B when the field is real. We define the vector spaces associated with Bermejo Algebras to establish equivalence classes and a quotient topology, resulting in Hausdorff spaces that do not depend on traditional norms, inner products, or metrics. Our findings lay the groundwork for constructing new types of differential manifolds, opening new avenues for advanced mathematical research.

We explored an extension of the Cauchy-Riemann equations to the algebra of treons, recently described by Alejandro Bermejo, whose elements are ordered 3-tuples. We leveraged the isomorphism between the algebra of treons and algebra B, and deduced the Cauchy-Riemann equations for the algebra of treons, establishing the necessary conditions for analyticity in this algebraic structure. This work significantly broadened our horizons in complex analysis and introduced new possibilities for applications across various fields of advanced mathematics.

We present an exploration of algebra B, a recently published unital and non-associative algebra. Unique complex entities emerged from this algebra, distinct from both quaternion and complex number systems, which we termed treons. We defined the treonic number system and established an isomorphism between this system and the real vector space. Our findings revealed that the treonic representation maintained structural integrity under the defined operations. Based on this foundation, we proceed to determine Euler identity for algebra B within the treonic system. By presenting the fundamental definitions and properties of algebra B, we derived a generalized version of Euler identity applicable within this algebra. This formula revealed the emergence of hyperbolic trigonometric entities, extending the applicability of Euler identity beyond traditional complex numbers. Our results provide a theoretical foundation for a deeper understanding of the properties and behaviors of complex entities within this expanded algebraic framework, thus enabling new theoretical developments and practical applications in the realms of advanced mathematics and theoretical physics.

We introduce a novel algebraic structure, termed algebra B, which generalizes Lie algebras through the definition of a non-associative and unital algebra. We demonstrate that algebra B retains essential properties such as bilinearity and antisymmetry, and satisfies both the Jacobi and Malcev identities; this occurs when the product operations of Lie and Malcev algebras are derived from the product operation defined in our algebra. By examining the connections between algebra B, Malcev algebras, and Lie algebras, we establish that algebra B effectively generalizes these structures. Furthermore, we show that algebra B can generate complex entities with a novel structure distinct from those currently known. Our findings lay the groundwork for future investigations into the practical applications and further theoretical development of this new algebraic framework.

Brugada Syndrome is a cardiac channelopathy closely related to lethal arrhythmias and sudden death in people without underlying structural pathology. The diagnosis is usually assumed with electrocardiographic patterns strictly limited to the right precordial leads, V1 or V2; but this is not so at all. In our article, we describe the clinical case of a patient with a novel and different electrocardiographic presentation: the typical diagnostic pattern was presented in a lower lead of the electrocardiogram, and next to it, another pattern was presented in a contiguous lead. In addition, we propose the possible association of a structural pathology (non-compaction cardiomyopathy) with Brugada Syndrome, since both share a possible common genetic origin in the SCN5A gene.

Coronavirus Disease-2019 (COVID-19) is an infectious disease caused by the Severe Acute Respiratory Syndrome Coronavirus 2 (SARS-CoV-2). There is sufficient experimental evidence to confirm that SARS-CoV-2 infection produces states of ciliary and flagellar dysfunction. However, these studies are unable to explain the observed effects molecularly, because they lack a sufficient understanding of the interaction between human proteins and virus proteins. Using the physical-chemical study of the human interactome in interaction with the SARS-CoV-2 proteome, we found evidence of interactions to explain the experimental effects from a molecular perspective. We found that ten viral proteins interact with key components in the maintenance of the molecular structure of axoneme. Additionally, we evaluated the pulmonary and extrapulmonary pathogenesis of COVID-19 from the point of view of ciliary dysfunction, and warned about other possible complications such as episodes of transient infertility that, due to the limitations of our work, would need verification.

Glycosylation, the most significant modification of proteins, plays an essential role in cellular processes. Congenital disorders of glycosylation (CDG) are multisystemic diseases resulting from mutations affecting glycosylation steps. Diagnosis of CDG relies on biochemical assays, such as isoelectric focusing. Despite its significance, CDG cases remain unreported in Cuba due to the lack of implemented diagnostic methods. This study aimed to evaluate transferrin glycoforms for diagnosing congenital N-glycosylation defects. We conducted a cross-sectional descriptive study using serum samples from 17 patients stored at the National Center for Medical Genetics of Cuba for suspected CDG. Results revealed abnormal glycosylation patterns in 7 patients, suggesting congenital N-glycosylation defects. We conclude that the implementation of transferrin glycoform analysis could pioneer a preliminary diagnosis of CDG in Cuba.

We present a case report of a young patient with pectus carinatum who experienced a small right apex pneumothorax and exhibited Brugada patterns on electrocardiogram tracing. This is the first clinical case reporting Brugada pattern presentation in both a patient with pectus carinatum and a small pneumothorax. We conducted a clinical, anatomical, and electrocardiographic analysis to explore a physiopathological explanation for these findings, considering our patient had no history or clinical signs of Brugada Syndrome. We conclude that: 1. Pectus carinatum may create a window that facilitates the less resistive measurement of cardiac action potentials; 2. Small pneumothoraces can induce modifications in the cardiac electrical signal detected by surface electrodes, and pectus carinatum could unmask these modifications; and 3. Surface electrodes may measure subepicardial potentials that include and are modified by adjacent pericardial tissues, potentially resulting in alterations in transmural potential differences, thus producing fictitious Brugada patterns. Similarly, there is a possibility that the right ventricular outflow tract may be included within the subendocardial potentials.

We document for the first time epsilon waves on the electrocardiogram of a patient with Dravet syndrome (DS) who does not exhibit structural cardiac pathology. DS, a severe form of pediatric epilepsy, involves mutations in the SCN1A gene, which disrupt sodium ion flow and increase the risk of sudden unexpected death in epilepsy. The epsilon waves, typically associated with arrhythmogenic right ventricular dysplasia, may also suggest a link between neuronal and cardiac dysfunctions. In our case, the epsilon waves appear to originate from abnormalities in sodium channels rather than structural changes in the myocardium. This finding underscores the importance of assessing both neurological and cardiac manifestations in patients with severe epilepsy, opening new avenues for the research and treatment of these interactions in DS.