Vector Integration Research Articles

Computational vectorelectrocardiography: comparison of representations according to McPhee-Parungao and Frank

Aim: to compare amplitude-temporal and vectorcardiographic (VCG) parameters calculated through most commonly used matrix transformations.Materials and methods. Preliminary literature search revealed Kors and inverse Dower transformation to be the most commonly used matrices for converting ECG‑12 into Frank VCG. Trunov-Aidu matrix appeared to be the only one for deriving VCG in the McFee-Parungao lead system.The study included 1250 ECGs of patients at the National Medical Research Center of Cardiology with various cardiovascular diseases: arterial hypertension, coronary heart disease, post-infarction cardiosclerosis, aortic stenosis. For each patient, using the above transformations, three VCGs with an intact and three VCGs with an inverted direction of the Z axis (according to Ozol) were obtained. The comparison was carried out based on the main amplitude-temporal indicators of P-QRS-T, as well as on VCG parameters: spatial QRS-T angle, QRS loop area, QRS integral vector, fractional integrals P and QRS. A total of 9 pairwise comparisons of 134 indicators were carried out for each synthesized VCGResults. The strongest (r > 0.9 or r < -0.9) significant (p < 0.001) linear correlation was found between the spatial metrics: P, QRS, T wave loop lengths, QRS loop area, QRS-T angle, ventricular gradient, and QRS shared integrals. Significant relationship between projection parameters and P-QRS-T amplitude and duration was observed in some cases. The largest number of correlations was noted between parameters calculated in McFee-Parungao and Frank lead system derived by Kors.Conclusions. Strong linear relationship was found between the VCG parameters determined through Kors, Dower and Trunov-Aidu matrix transformations, which indicates the equivalence of the results obtained through these matrices.

All-Analytic Statistical Modeling of Constellations in (Optical) Transmission Systems Driven by High-Speed Electronic Digital to Analog Converters Part I: DAC Mismatch Statistics, Metrics, Symmetries, Error Vector Magnitude

This two-part work develops a comprehensive toolbox for the statistical characterization of nonlinear distortions of DAC-generated signal constellations to be transmitted over communication links, be they electronic (wireline, wireless) or photonic, Mach–Zehnder modulator (MZM)-based optical interconnects in particular. The all-analytic toolbox developed here delivers closed-form expressions for the second-order statistics (means, variances) of all relevant constellation metrics of the DACs’ building blocks and of DAC-driven MZM-based optical transmitters, all the way to the slicer in the optical receivers over a linear channel with coherent detection. The key impairment targeted by the model is the random current mismatch of the ASIC devices implementing the DAC drivers. In particular the (skew-)centrosymmetry of the DAC metrics is formally derived and explored. A key applicative insight is that the conventional INL/DNL (Integral NonLinearity/Differential NonLinearity) constellation metrics, widely adopted in the electronic devices and circuits community, are not quite useful in the context of communication systems, since these metrics are ill-suited to predict communication link statistical performance. To rectify this deficiency of existing electronic DAC metrics, we introduce modified variants of the INL|DNL, namely the integral error vector (IEV) and the differential error vector (DEV) constellation metrics. The new IEV|DEV represent straightforward predictors of relevant communication-minded metrics: error vector magnitude (EVM) treated here in Part I, and Symbol/Bit Error-Rates (SER, BER) treated in the upcoming Part II of this paper.

Malnutrition in Amyotrophic Lateral Sclerosis: Insights from Morphofunctional Assessment and Global Leadership Initiative on Malnutrition Criteria.

Amyotrophic Lateral Sclerosis (ALS) is a progressive neurodegenerative disease frequently accompanied by malnutrition due to weight loss, increased energy expenditure, and muscle mass loss. This study aimed to evaluate morphofunctional assessment tools as predictors of malnutrition and to investigate their relationship with muscle status and disease severity in ALS patients. A cross-sectional study was conducted with 45 ALS patients at the San Cecilio University Hospital in Granada. Malnutrition was assessed using the Global Leadership Initiative on Malnutrition (GLIM) criteria. Morphofunctional assessment was performed using Bioimpedance Vectorial Analysis (BIVA), handgrip strength (HGS), and Short Physical Performance Battery (SPPB). Malnutrition prevalence was 38% according to GLIM criteria. Significant differences were observed between malnourished and non-malnourished groups in age (70 ± 9 vs. 62 ± 10 years, p = 0.01), sex (female prevalence: 58.8% vs. 25.0%, p = 0.02), dysphagia prevalence (83% vs. 29%, p < 0.001), PEG/PRG use (35.3% vs. 3.6%, p = 0.01), and ALSFRS-R scores (30 ± 12 vs. 34 ± 12, p = 0.02). Malnourished patients had lower values in anthropometric measurements, muscle mass obtained by BIVA, and phase angle (PA) (4.05 ± 0.8° vs. 5.09 ± 0.8°, p < 0.001). No significant differences were found in muscle strength or functional status. PA showed significant correlations with muscle strength (r = 0.52, p < 0.001) and muscle mass measures (r = 0.48, p < 0.001). Moreover, PA was associated with poorer disease progression and physical performance. In our sample, BIVA metrics such as PA (<4.3°), SPA (<-0.8), body cell mass (<9.2 kg/m), and extracellular water (>49.75%) were identified as malnutrition risk factors. The study underscores the critical importance of comprehensive morphofunctional assessment and the use of advanced diagnostic criteria, for early identification and intervention in malnutrition among people with ALS. Further research is warranted to validate these findings and develop targeted nutritional strategies into routine clinical practice.

Stabilizing massless fields with fluxes in Landau-Ginzburg models

Recent work on flux compactifications suggests that the tadpole constraint generically allows only a limited number of complex structure moduli to become massive, i.e., be stabilized at quadratic order in the spacetime superpotential. We study the effects of higher-order terms systematically around the Fermat point in the 19 Landau-Ginzburg model. This model lives at strong coupling and features no Kähler moduli. We show that indeed massless fields can be stabilized in this fashion. We observe that, depending on the flux, this mechanism is more effective when the number of initially massless fields is large. These findings are compatible with both the tadpole conjecture and the massless Minkowski conjecture. Along the way, we complete the classification of integral flux vectors with small tadpole contribution. Thereby we are closing in on a future complete understanding of all possible flux configurations in the 19 Landau-Ginzburg model.

Applying matrix diagonalisation in the classroom with GeoGebra: parametrising the intersection of a sphere and plane

In this paper, we explore how the typical second year undergraduate topic of matrix diagonalisation can be applied to solve a geometric problem which arises frequently in Vector Calculus: to find the curve of intersection of a plane and a surface. We use GeoGebra, which offers a cost-free and dynamic interface, to explore a specific variant of this problem, namely the parametrisation of the intersection of a plane and sphere. GeoGebra not only allows students to confirm their calculations, but it can also provide motivation to create connections between prior learning experiences and new knowledge.

A new synthetic biology system for investigating the biosynthesis of antibiotics and other secondary metabolites in streptomycetes

We have created a novel synthetic biology expression system allowing easy refactoring of biosynthetic gene clusters (BGCs) as monocistronic transcriptional units. The system is based on a set of plasmids containing a strong kasOp* promoter, RBS and terminators. It allows the cloning of biosynthetic genes into transcriptional units kasOp*-gene(s)-terminator flanked by several rare restriction cloning sites that can be sequentially combined into the artificial BGC in three compatible Streptomyces integration vectors. They allow a simultaneous integration of these BGCs at three different attB sites in the Streptomyces chromosome. The system was validated with biosynthetic genes from two known BGCs for aromatic polyketides landomycin and mithramycin.

Umbilical cord blood T cells can be isolated and enriched by CD62L selection for use in 'off the shelf' chimeric antigen receptor T-cell therapies to widen transplant options.

Umbilical cord blood (UCB) T cells exhibit distinct naive ontogenetic profiles and may be an attractive source of starting cells for the production of chimeric antigen receptor (CAR) T cells. Pre-selection of UCB-T cells on the basis of CD62L expression was investigated as part of a machine-based manufacturing process, incorporating lentiviral transduction, CRISPR-Cas9 editing, T-cell expansion and depletion of residual TCReeeT cells. This provided stringent mitigation against the risk of graft versus host disease (GVHD), and was combined with simultaneous knockout of CD52 to enable persistence of edited T cells in combination with preparative lymphodepletion using Alemtuzumab. Under compliant manufacturing conditions, two cell banks were generated with high levels of CAR19 expression and minimal carriage of TCReeeT cells. Sufficient cells were cryopreserved in dose-banded aliquots at the end of each campaign to treat dozens of potential recipients. Molecular characterisation captured vector integration sites and CRISPR editing signatures and functional studies, including in vivo potency studies in humanised mice, confirmed antileukaemic activity comparable to peripheral blood-derived universal CAR19 T cells. Machine manufactured UCB derived T cells banks offer an alternative to autologous cell therapies and could help widen access to CAR T cells.

An Integrated Framework for Landscape Indices’ Calculation with Raster–Vector Integration and Its Application Based on QGIS

Landscape-index calculation tools play a pivotal role in ecosystem studies and urban-planning research, enabling objective assessments of landscape patterns’ similarities and differences. However, the existing tools encounter limitations, such as the inability to visualize landscape indices spatially and the challenge of computing indices for both vector and raster data simultaneously. Based on the QGIS development platform, this study presents an innovative framework for landscape-index calculation that addresses these limitations. The framework seamlessly integrates both vector and raster data, comprising three main modules: data input, landscape-index calculation, and visualization. In the data-input module, the tool accommodates various data formats, including vector, raster, and tabular data. The landscape indices’ calculation module allows users to select indices at patch, class, and landscape scales. Notably, the framework provides a comprehensive set of 165 indices for vector data and 20 for raster data, empowering users to selectively calculate landscape indices for vector or raster data to their specific needs and leverage the strengths of each data type. Moreover, the landscape-index visualization module enhances spatial visualization capabilities, meeting user demands for an insightful analysis. By addressing these challenges and offering enhanced functionalities, this framework aims to advance landscape indices’ development and foster more comprehensive landscape analyses. And it presents a novel approach for landscape-index development.

Combating Malaria with Vaccines: Insights from the One Health Framework

Malaria remains a leading cause of morbidity and mortality worldwide, with significant efforts directed towards developing effective vaccines to curb its impact. The One Health concept, recognizing the interconnectedness of human, animal, and environmental health, offers a comprehensive approach to understanding and combating this disease. This review examines the development of malaria vaccine through the lens of the One Health framework, highlighting the integration of human, vector, and environmental factors in the fight against malaria. We discuss the current landscape of malaria vaccine development, including the deployment of the RTS,S/AS01 vaccine and the progress of other candidates such as the R21/Matrix-M and PfSPZ vaccine. The challenges posed by the complex lifecycle of the malaria parasite, its genetic diversity, and the environmental factors influencing transmission are explored. This review also discusses emerging technologies and innovations that could enhance vaccine efficacy and delivery. Additionally, we consider ethical, social, and economic factors critical to the successful implementation of vaccination programs. In concluding, this review underscores the importance of adopting a One Health approach to malaria vaccine development, advocating for integrated efforts to address the multifaceted challenges of malaria control and eradication.

The longitudinal kinetics of AAV5 vector integration profiles and evaluation of clonal expansion in mice

Adeno-associated virus (AAV)-based vectors are used clinically for gene transfer and persist as extrachromosomal episomes. A small fraction of vector genomes integrate into the host genome, but the theoretical risk of tumorigenesis depends on vector regulatory features. A mouse model was used to investigate integration profiles of an AAV serotype 5 (AAV5) vector produced using Sf and HEK293 cells that mimics key features of valoctocogene roxaparvovec (AAV5-hFVIII-SQ), a gene therapy for severe hemophilia A. The majority (95%) of vector genome reads were derived from episomes, and mean (± standard deviation) integration frequency was 2.70±1.26 and 1.79±0.86 integrations per 1000 cells for Sf- and HEK293-produced vector. Longitudinal integration analysis suggested integrations occur primarily within 1 week, at low frequency, and their abundance was stable over time. Integration profiles were polyclonal and randomly distributed. No major differences in integration profiles were observed for either vector production platform, and no integrations were associated with clonal expansion. Integrations were enriched near transcription start sites of genes highly expressed in the liver (P = 1x10−4) and less enriched for genes of lower expression. We found no evidence of tumorigenesis or fibrosis caused by the vector integrations.

ANALYSIS OF UKRAINE’S COMPETITIVENESS: PROBLEMS AND PROSPECTS OF EUROPEAN INTEGRATION

The article analyzes the competitiveness of Ukraine, identifies problems and outlines the prospects and consequences of the country’s European integration aspirations. A retrospective review of the development of the country’s economic model was conducted in order to evaluate the effectiveness of the implementation of reforms and identify errors that affected the place and role of the domestic economy in the world markets of goods and capital. This made it possible to single out certain comparative characteristics with the main theories of international trade and international investment. It was noted that unsuccessful attempts to quickly transform from a command-administrative economy to a mixed market system led to a loss of industrial potential and, accordingly, negatively affected the structure of foreign trade relations and the investment climate, which in turn led to a drop in the level of competitiveness of Ukraine. Along with this, the analysis of the key indicators of socio-economic development indicates certain positive changes in the period 2002-2012, which was reflected in the dynamics of GDP growth, an increase in incoming investment flows, stabilization of inflation at the targeted level and overall improved welfare of society. However, the uncertainty and constant change of the vector of economic integration together with the change of power led to the deterioration of the state’s economic condition and made sustainable economic growth impossible. The period of revival of business and investment activity in the post-Covid 2021 year was replaced by a deep crisis with the beginning of the war. At the same time, the aspiration of our state to join the European community nevertheless gave a powerful impetus to the implementation and implementation of innovative reforms, which made it possible to achieve certain success in the direction of digitalization, infrastructure development, and further implementation of educational, medical, and social reforms even during the conduct of military operations. Currently, on the way to European integration, Ukraine is overcoming the difficult path of transforming its economic system to the requirements and values of the EU. Our country, together with the European Union, needs to solve the issues of labor migration and refugees, the introduction of a duty-free regime for domestic goods, the creation of a safe investment climate, etc. And there is not always unity in the choice of tools for solving these issues in the EU countries. Ukraine needs to use its advantages in logistics, geographical location, labor and natural resources, develop an industrial direction, introduce modern technologies, improve its energy independence and take an active part in integration processes. Finding compromises and political will allow Ukraine to successfully reform the socio-economic model and become a full member of the EU.

Risk of Second Tumors and T-Cell Lymphoma after CAR T-Cell Therapy

BackgroundThe risk of second tumors after chimeric antigen receptor (CAR) T-cell therapy, especially the risk of T-cell neoplasms related to viral vector integration, is an emerging concern.MethodsWe reviewed our clinical experience with adoptive cellular CAR T-cell therapy at our institution since 2016 and ascertained the occurrence of second tumors. In one case of secondary T-cell lymphoma, a broad array of molecular, genetic, and cellular techniques were used to interrogate the tumor, the CAR T cells, and the normal hematopoietic cells in the patient.ResultsA total of 724 patients who had received T-cell therapies at our center were included in the study. A lethal T-cell lymphoma was identified in a patient who had received axicabtagene ciloleucel therapy for diffuse large B-cell lymphoma, and both lymphomas were deeply profiled. Each lymphoma had molecularly distinct immunophenotypes and genomic profiles, but both were positive for Epstein–Barr virus and were associated with DNMT3A and TET2 mutant clonal hematopoiesis. No evidence of oncogenic retroviral integration was found with the use of multiple techniques.ConclusionsOur results highlight the rarity of second tumors and provide a framework for defining clonal relationships and viral vector monitoring. (Funded by the National Cancer Institute and others.)

Update on Managing the Risks of Exposure to Lentiviral and Retroviral Vectors.

This paper aims to review the risks associated with using lentiviral and retroviral vectors in research and clinical settings and to propose an update to an effective treatment plan. Risks of exposure were evaluated based on vector design, safety features, viral tropism, transgene, and means and modes of transmission. These risks were weighed against the potential risks and benefits of current HIV medications. We recommend the following post-exposure prophylactic treatment for significant lentiviral vector exposures: 1) dolutegravir 50 mg. taken once a day for 7 days; and 2) tenofovir disoproxil fumarate 300 mg. taken once a day for 7 days (28 days of both medications for replication-competent vectors). Due to the highly efficient delivery of transgenes by modern lentiviral and retroviral vectors, post-exposure prophylaxis is indicated to prevent vector integration and oncogenic risks.

Modular, inducible, and titratable expression systems for Escherichia coli and Acinetobacter baumannii.

Gene expression systems that transcend species barriers are needed for cross-species analysis of gene function. In particular, expression systems that can be utilized in both model and pathogenic bacteria underpin comparative functional approaches that inform conserved and variable features of bacterial physiology. Here, we develop replicative and integrative vectors alongside a novel, IPTG-inducible promoter that can be used in the model bacterium Escherichia coli K-12 as well as strains of the antibiotic-resistant pathogen, Acinetobacter baumannii. We generate modular vectors that transfer by conjugation at high efficiency and either replicate or integrate into the genome, depending on design. Embedded in these vectors, we also developed a synthetic, IPTG-inducible promoter, P abstBR , that induces to a high level, but is less leaky than the commonly used trc promoter. We show that P abstBR is titratable at both the population and single cell level, regardless of species, highlighting the utility of our expression systems for cross-species functional studies. Finally, as a proof of principle, we use our integrating vector to develop a reporter for the E. coli envelope stress σ factor, RpoE, and deploy the reporter in E. coli and A. baumannii, finding that A. baumannii does not recognize RpoE-dependent promoters unless RpoE is heterologously expressed. We envision that these vector and promoter tools will be valuable for the community of researchers that study fundamental biology of E. coli and A. baumannii.

Problems and Opportunities in the use of Bioelectrical Impedance Analysis for Assessing Body Composition During Ketogenic Diets: A Scoping Review.

The use of bioelectrical impedance analysis (BIA) for monitoring body composition during the ketogenic diet has experienced a rapid surge. This scoping review aimed to assess the validity of procedures applying BIA in the ketogenic diet and to suggest best practices for optimizing its utilization. We conducted a systematic scoping review of peer-reviewed literature involving BIA for assessing body composition in individuals adhering to a ketogenic diet. Searches of international databases yielded 1609 unique records, 72 of which met the inclusion criteria and were reviewed. Thirty-five studies used foot-to-hand technology, 34 used standing position technology, while 3 did not declare the technology used. Raw bioelectrical parameters were reported in 21 studies. A total of 196 body mass components were estimated, but predictive equations were reported in only four cases. Most research on BIA during ketogenic diets did not report the equations used for predicting body composition, making it impossible to assess the validity of BIA outputs. Furthermore, the exceedingly low percentage of studies reporting and analyzing raw data makes it challenging to replicate methodologies in future studies, highlighting that BIA is not being utilized to its full potential. There is a need for more precise technology and device characteristics descriptions, full report of raw bioelectrical data, and predictive equations utilized. Moreover, evaluating raw data through vectorial analysis is strongly recommended. Eventually, we suggest best practices to enhance BIA outcomes during ketogenic diets.

Statistical analysis of gold production in South Africa using ARIMA, VAR and ARNN modelling techniques: Extrapolating future gold production, Resources–Reserves depletion, and Implication on South Africa's gold exploration

South African gold mining is one of the main contributors to the country's economic growth and employment creation. Assessment of future gold production is pivotal for positioning the country's supply security and contribution to the projected global demand. In this study, we modelled and forecasted South African and global gold production trends (1990–2022) using the Autoregressive Integrated Moving Average (ARIMA), Vector Autoregressive (VAR), and Autoregressive Neural Network (ARNN) techniques. The study also evaluated the impact of annual productions on the collated reserves (2008–2021) and the contribution of resource–reserve conversion in sustaining gold reserves within the South African goldfields. The ARIMA (1,1,0) model, based on root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE), outperformed both ARNN (1,1) and VAR (2) methods. The forecast of the ARIMA model showed an increase in South Africa's gold production, with a compounded annual growth rate (CAGR) of ∼0.6%. The model also predicted an increase in global gold production, with CAGR of ∼2.2%. The analyses of reserves–production trends showed that most South African mining companies have been depleting their gold reserves due to production and were minimally converting resources to reserves, averaging at ∼2%/year from 2017 till present. The minimal conversion may also reflect the challenging mining conditions (such as mining depths and underground flooding) and the mining industry's socio-political dynamics. We demonstrated that, if the resource–reserve conversion factor is maintained (at ∼2%/year and above), the forecasted production may sustain the current reserves (at > 2000 t Au excluding tailings) but deplete ∼27 % of the resources to reserves by 2040. However, if the conversion factor continues to decline (to <1 %), the forecasted gold production will reduce the reserves to < 500 t Au with ∼3% of the resources converted to reserves.

On the integration of $$L^0$$-Banach $$L^0$$-modules and its applications to vector calculus on $$\textsf{RCD}$$ spaces

AbstractA finite-dimensional $$\textsf{RCD}$$ RCD space can be foliated into sufficiently regular leaves, where a differential calculus can be performed. Two important examples are given by the measure-theoretic boundary of the superlevel set of a function of bounded variation and the needle decomposition associated to a Lipschitz function. The aim of this paper is to connect the vector calculus on the lower dimensional leaves with the one on the base space. In order to achieve this goal, we develop a general theory of integration of $$L^0$$ L 0 -Banach $$L^0$$ L 0 -modules of independent interest. Roughly speaking, we study how to ‘patch together’ vector fields defined on the leaves that are measurable with respect to the foliation parameter.

Metabolic engineering of Saccharomyces cerevisiae for the biosynthesis of a fungal pigment from the phytopathogenic fungus Cladosporium phlei

BackgroundCladosporium phlei is a phytopathogenic fungus that produces a pigment called phleichrome. This fungal perylenequinone plays an important role in the production of a photosensitizer that is a necessary component of photodynamic therapy. We applied synthetic biology to produce phleichrome using Saccharomyces cerevisiae.ResultsThe gene Cppks1, which encodes a non-reducing polyketide synthase (NR-PKS) responsible for the biosynthesis of phleichrome in C. phlei, was cloned into a yeast episomal vector and used to transform S. cerevisiae. In addition, a gene encoding a phosphopantetheinyl transferase (PPTase) of Aspergillus nidulans was cloned into a yeast integrative vector and also introduced into S. cerevisiae for the enzymatic activation of the protein product of Cppks1. Co-transformed yeasts were screened on a leucine/uracil-deficient selective medium and the presence of both integrative as well as episomal recombinant plasmids in the yeast were confirmed by colony PCR. The episomal vector for Cppks1 expression was so dramatically unstable during cultivation that most cells lost their episomal vector rapidly in nonselective media. This loss was also observed to a less degree in selective media. This data strongly suggests that the presence of the Cppks1 gene exerts a significant detrimental effect on the growth of transformed yeast cells and that selection pressure is required to maintain the Cppks1-expressing vector. The co-transformants on the selective medium showed the distinctive changes in pigmentation after a period of prolonged cultivation at 20 °C and 25 °C, but not at 30 °C. Furthermore, thin layer chromatography (TLC) revealed the presence of a spot corresponding with the purified phleichrome in the extract from the cells of the co-transformants. Liquid chromatography (LC/MS/MS) verified that the newly expressed pigment was indeed phleichrome.ConclusionOur results indicate that metabolic engineering by multiple gene expression is possible and capable of producing fungal pigment phleichrome in S. cerevisiae. This result adds to our understanding of the characteristics of fungal PKS genes, which exhibit complex structures and diverse biological activities.

Direct and Inverse Kinematics of a 3RRR Symmetric Planar Robot: An Alternative of Active Joints

Existing direct and inverse kinematic models of planar parallel robots assume that the robot’s active joints are all at the bases. However, this approach becomes excessively complex when modeling a planar parallel robot in which the active joints are within one single kinematic chain. To address this problem, our article unveils an alternative for a 3RRR symmetric planar robot modeling technique for the derivation of the robot workspace and the analysis of its direct and inverse kinematics. The workspace was defined using a system of inequalities, and the direct and inverse kinematics models were generated using vectorial analysis and an optimized geometrical approach, respectively. The resulting models are systematically presented and validated. Two final model renditions are delivered supplying a thorough equation analysis and an applicability discussion based on the importance of the robot’s mobile platform orientation. The advantages of this model are discussed in comparison to the traditional modeling approach: whereas conventional techniques require the solution of complex eighth-degree polynomials for the analysis of the active joint configuration of these robots, these models provide an efficient back-of-the-envelope analysis approach that requires the solution of a simple second-degree polynomial.

Recovering seldom-used theorems of vector calculus and their application to problems of electromagnetism

In this paper, we use differential forms to prove a number of theorems of integral vector calculus that are rarely found in textbooks. Two of them, as far as the author knows, have not been published before. Some possible applications to problems in physics are shared including a general approach for computing net forces and torques on current-carrying loops that yields insights that are not evident from the standard approach.