Vector Integration Research Articles

A Sendai virus-based expression system directs efficient induction of chondrocytes by transcription factor-mediated reprogramming.

Cartilage rarely heals spontaneously once damaged. Osteoarthritis (OA) is the most common degenerative joint disease among the elderly; however, effective treatment for OA is currently lacking. Autologous chondrocyte implantation (ACI), an innovative regenerative technology involving the implantation of healthy chondrocytes, may restore damaged lesions. Chondrocytes for ACI may potentially be induced from differentiated somatic cells using retrovirus (RV)-mediated transduction of three reprogramming factors (SOX9, KLF4, and c-MYC). However, the efficiency of the current induction system needs to be improved and the safety issues arising from the genomic integration of the vector DNA have to be addressed. To solve these problems, we used an RNA vector, termed the replication-defective and persistent Sendai virus vector (SeVdp), to express reprogramming factors for chondrocyte induction. Our results showed that the SeVdp-based vector induced chondrocytes more efficiently than the RV vector, probably because of robust and rapid expression of the transgenes, without any apparent integration of the SeVdp vector. The induced chondrocytes formed cartilage-like tissues when injected subcutaneously into mice. Thus, the SeVdp-based system for inducing chondrocytes may act as a foundation for developing safer and more effective treatments for damaged cartilage.

Bounding Seed Loss from Isolated Habitat Patches

Dispersal of propagules (seeds, spores) from a geographically isolated habitat into an uninhabitable matrix can play a decisive role in driving population dynamics. ODE and integrodifference models of these dynamics commonly feature a “dispersal success” parameter representing the average proportion of dispersing propagules that remain in viable habitat. While dispersal success can be estimated by empirical measurements or by integration of dispersal kernels, one may lack resources for fieldwork or details on dispersal kernels for numerical computation. Here we derive simple upper bounds on the proportion of propagule loss—the complement of dispersal success—that require only habitat area, habitat perimeter, and the mean dispersal distance of a propagule. Using vector calculus in a probabilistic framework, we rigorously prove bounds for the cases of both symmetric and asymmetric dispersal. We compare the bounds to simulations of integral models for the population of Asclepias syriaca (common milkweed) at McKnight Prairie—a 14 hectare reserve surrounded by agricultural fields in Goodhue County, Minnesota—and identify conditions under which the bounds closely estimate propagule loss.

Improving the nutritional evaluation in head neck cancer patients using bioelectrical impedance analysis: Not only the phase angle matters.

Malnutrition and sarcopenia are highly prevalent in patients with head neck cancer (HNC). An accurate early diagnosis is necessary for starting nutritional support, as both are clearly associated with clinical outcomes and mortality. We aimed to evaluate the applicability and accuracy of body composition analysis using electrical bioimpedance vectorial analysis (BIVA) for diagnosing malnutrition and sarcopenia in patients with HNC cancer undergoing systemic treatment with chemotherapy or radiotherapy. Cross-sectional, observational study that included 509 HNC patients. A comprehensive nutritional evaluation that included BIVA was performed. The prevalence of malnutrition was higher in patients that received treatment with chemotherapy (59.2% vs. 40.8%, P<0.001); increased mortality was observed in malnourished patients (33.3% vs. 20.1%; P<0.001); ECOG status (1-4) was also worse in malnourished patients (59.2% vs. 22.8% P<0.001). Body cell mass (BCM) and fat mass were the most significantly associated parameters with malnutrition [OR 0.88 (0.84-0.93) and 0.98 (0.95-1.01), respectively]; BCM and fat free mass index (FFMI) were associated with several aspects including (1) the patient-generated subjective global assessment [OR 0.93 (0.84-0.98) and 0.86 (0.76-0.97), respectively], (2) the presence of sarcopenia [OR 0.81 (0.76-0.87) and 0.78 (0.66-0.92), respectively]. A BCM index (BCMI)<7.8 in combination with other parameters including FFMI and BCM accurately predicted patients with malnutrition [accuracy 95% CI: 0.803 (0.763-0.839); kappa index: 0.486; AUC: 0.618 (P<0.01)]. A BCMI cutoff of 7.6 was enough for identifying males with malnutrition (P<0.001), while it should be combined with other parameters in females. Body composition parameters determined by BIVA accurately identify patients with HNC and malnutrition. Phase angle, but other parameters including BCMI, FFMI and BCM provide significant information about nutritional status in patients with HNC.

Long-term lineage commitment in hematopoietic stem cell gene therapy.

Hematopoietic Stem Cell (HSC) gene therapy (GT) may provide lifelong reconstitution of the hematopoietic system with gene-corrected cells1. However, the effects of underlying genetic diseases, replication stress, and aging on hematopoietic reconstitution and lineage specification remain unclear. In this study, we analyzed hematopoietic reconstitution in 53 patients treated with lentiviral-HSC-GT for diverse conditions such as metachromatic leukodystrophy2,3 (MLD), Wiskott-Aldrich syndrome4,5 (WAS), and β-thalassemia6 (β-Thal) over a follow-up period of up to 8 years, using vector integration sites as markers of clonal identity. We found that long-term hematopoietic reconstitution was supported by 770 to 35,000 active HSCs. While 50% of transplanted clones demonstrated multilineage potential across all conditions, the remaining clones exhibited a disease-specific preferential lineage output and long-term commitment: myeloid for MLD, lymphoid for WAS, and erythroid for β-Thal, particularly in adult patients. Our results indicate that HSC clonogenic activity, lineage output, long-term lineage commitment, and rates of somatic mutations are influenced by the underlying disease, patient age at the time of therapy, the extent of genetic defect correction, and the hematopoietic stress imposed by the inherited disease. This suggests that HSCs adapt to the pathological condition during hematopoietic reconstitution.

Lentiviral Gene Therapy for Cerebral Adrenoleukodystrophy

BackgroundCerebral adrenoleukodystrophy is a severe form of X-linked adrenoleukodystrophy characterized by white-matter disease, loss of neurologic function, and early death. Elivaldogene autotemcel (eli-cel) gene therapy, which consists of autologous CD34+ cells transduced with Lenti-D lentiviral vector containing ABCD1 complementary DNA, is being tested in persons with cerebral adrenoleukodystrophy.MethodsIn a phase 2–3 study, we evaluated the efficacy and safety of eli-cel therapy in boys with early-stage cerebral adrenoleukodystrophy and evidence of active inflammation on magnetic resonance imaging (MRI). The primary efficacy end point was survival without any of six major functional disabilities at month 24. The secondary end points included overall survival at month 24 and the change from baseline to month 24 in the total neurologic function score.ResultsA total of 32 patients received eli-cel; 29 patients (91%) completed the 24-month study and are being monitored in the long-term follow-up study. At month 24, none of these 29 patients had major functional disabilities; overall survival was 94%. At the most recent assessment (median follow-up, 6 years), the neurologic function score was stable as compared with the baseline score in 30 of 32 patients (94%); 26 patients (81%) had no major functional disabilities. Four patients had adverse events that were directly related to eli-cel. Myelodysplastic syndrome (MDS) with excess blasts developed in 1 patient at month 92; the patient underwent allogeneic hematopoietic stem-cell transplantation and did not have MDS at the most recent follow-up.ConclusionsAt a median follow-up of 6 years after lentiviral gene therapy, most patients with early cerebral adrenoleukodystrophy and MRI abnormalities had no major functional disabilities. However, insertional oncogenesis is an ongoing risk associated with the integration of viral vectors. (Funded by Bluebird Bio; ALD-102 and LTF-304 ClinicalTrials.gov numbers NCT01896102 and NCT02698579, respectively.)

AAV-mediated genome editing is influenced by the formation of R-loops

Recombinant adeno-associated viral vectors (rAAV) hold an intrinsic ability to stimulate homologous recombination (AAV-HR) and are the most used in clinical settings for in vivo gene therapy. However, rAAVs also integrate throughout the genome. Here, we describe DNA-RNA immunoprecipitation sequencing (DRIP-seq) in murine HEPA1-6 hepatoma cells and whole murine liver to establish the similarities and differences in genomic R-loop formation in a transformed cell line and intact tissue. We show enhanced AAV-HR in mice upon genetic and pharmacological upregulation of R-loops. Selecting the highly expressed Albumin gene as a model locus for genome editing in both in vitro and in vivo experiments showed that the R-loop prone, 3’ end of Albumin was efficiently edited by AAV-HR, whereas the upstream R-loop-deficient region did not result in detectable vector integration. In addition, we found a positive correlation between previously reported off-target rAAV integration sites and R-loop enriched genomic regions. Thus, we conclude that high levels of R-loops, present in highly transcribed genes, may promote rAAV vector genome integration. These findings may shed light on potential mechanisms for improving the safety and efficacy of genome editing by modulating R-loops and may enhance our ability to predict regions most susceptible to off-target insertional mutagenesis by rAAV vectors.

Algebraic Complete Integrability of the $a_4^{(2)}$ Toda Lattice

The aim of this work is focused on the investigation of the algebraic complete integrability of the Toda lattice associated with the twisted affine Lie algebra $a_4^{(2)}$. First, we prove that the generic fiber of the momentum map for this system is an affine part of an abelian surface. Second, we show that the flows of integrable vector fields on this surface are linear. Finally, using the formal Laurent solutions of the system, we provide a detailed geometric description of these abelian surfaces and the divisor at infinity.

A project and lift approach for a 2-commodity flow relocation model in a time expanded network

We deal here with a general 2-commodity flow model over a time expanded network designed for the management of a shared mobility systems. The model involves an integral flow vector that represents carriers together with an integral flow vector that represents the items transported by those carriers. It simultaneously copes with temporal and resource issues, and is difficult to handle in the practice. So we propose here a Project and Lift approach to handle it. We start by projecting the time expanded network model on the original transit network to obtain a simpler two-commodity flow projected model. In order to make this projected model consistent with the original problem, we introduce some complex constraints, prove that these constraints can be separated in polynomial time and discuss the experimental behavior of the related Branch-and-Cut algorithm. Next, we introduce the Lift issue about the way one may turn an optimal solution of our projected model into a solution of the original problem. Finally, we thoroughly study a somewhat restrictive Strong Lift setting of this Lift issue, design and test an exact mixed integer programming Strong Lift model, and discuss some flexible alternative approaches.

Comparison and cross-validation of long-read and short-read target-enrichment sequencing methods for assessing AAV vector integration into host genome

Evaluation of host integration profiles by adeno-associated virus (AAV) is an important component of de-risking novel AAV gene therapies. Targeted enrichment sequencing (TES) is a cost-effective and comprehensive method for assessing integration. Most published TES datasets have been generated using short-read sequencing, which enables quantitation of integration sites (IS) and identifies patterns such as hotspots or clonal expansion. Characteristics such as IS length and recombination require longer reads to measure. The present study compared short-read to long-read TES using samples from monkeys treated with AAV, and used in vitro lentiviral-treated samples, a stable cell line and an engineered spike-in as controls. Both methods showed stochastic integration by both AAV and lentivirus, with most vector domains identified in IS. More IS were identified by short-read TES, as deeper coverage per base was achieved from a single sequencing run. AAV-treated samples showed minimal evidence of clonal expansion, in contrast to in vitro treated and stably transduced lentiviral cell line samples. Long-read TES revealed vector rearrangement in 4-40% of IS in AAV-treated animals. In summary, both methods yielded similar conclusions about relative numbers of IS and overall patterns. Long-read TES identified fewer IS, but enabled measurement of IS length and recombination patterns.

A new twist on torsion: A connection between vector calculus and mechanics of materials

In engineering education, the topic of torsion is taught in both calculus and mechanics of materials, but using different definitions. Apparently, a clear connection between these two concepts is not currently found in the literature. In this paper, for the case of a homogeneous linear-elastic cylindrical shaft subjected to external torques, mathematical expressions are derived for relating torsional stress, strain and angle of twist to the torsion of a curve as taught in calculus. A physical connection is also presented, in that the curve torsion resulting from the deformation of a longitudinal line close to the shaft axis is shown to be approximately equal to the mechanical twist per length in the shaft. Although some researchers have hinted at this connection, to our knowledge the full precise connection has not been previously established.

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. In this study, 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, PabstBR, that induces to a high level but is less leaky than the commonly used trc promoter. We show that PabstBR is titratable at both the population and single-cell levels, 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 who study the fundamental biology of E. coli and A. baumannii.IMPORTANCEAcinetobacter baumannii is a multidrug-resistant, hospital-acquired pathogen with the ability to cause severe infections. Understanding the unique biology of this non-model bacterium may lead to the discovery of new weaknesses that can be targeted to treat antibiotic-resistant infections. In this study, we provide expression tools that can be used to study the gene function in A. baumannii, including in drug-resistant clinical isolates. These tools are also compatible with the model bacterium, Escherichia coli, enabling cross-species comparisons of gene function. We anticipate that the use of these tools by the scientific community will accelerate our understanding of Acinetobacter biology.

Sendai virus-mediated RNA delivery restores fertility to congenital and chemotherapy-induced infertile female mice.

Current infertility treatment strategies focus on mature gametes, leaving a significant proportion of cases with gamete progenitors that stopped complete differentiation. On the other hand, recent advancements in next-generation sequencing have identified many candidate genes that may promote maturation of germ cells. Although gene therapy has shown success in mice, concerns about the integration of DNA vectors into oocytes hinder clinical applications. Here, we present the restoration of fertility in female mice through Sendai virus (SeV)-mediated RNA delivery. Ovaries lacking Kitl expression exhibit only primordial follicles due to impaired signaling to oocytes expressing the KIT tyrosine kinase. Despite SeVs being immunogenic and larger than the blood-follicle barrier, the administration of Kitl-expressing SeVs reinitiated oogenesis in genetically infertile mice that have only primordial follicles, resulting in the birth of normal offspring through natural mating. This virus also effectively addressed iatrogenic infertility induced by busulfan, a widely used cancer chemotherapy agent. Offspring born through SeV administration and natural mating displayed normal genomic imprinting patterns and fertility. Since SeVs pose no genotoxicity risk, the successful restoration of fertility by SeVs represents a promising approach for treating congenital infertility with somatic cell defects and protecting fertility of cancer patients who may become infertile due to loss of oocytes during cancer therapy.

Comparative analysis of surgically induced astigmatism following cataract surgery: influence of previous myopic correction and corneal parameters.

This retrospective study investigated the impact of corneal parameters on surgically induced astigmatism (SIA) in eyes with prior myopic correction undergoing cataract surgery. Department of Ophthalmology, San Marino Hospital, San Marino, Republic of San Marino. This case-control study analyzed existing data retrospectively, without randomization or masking. Eighty eyes divided in group 1 (40 eyes previous underwent refractive surgery for myopia) and group 2 ( 40 myopic eyes) that underwent cataract surgery with intraocular lens (IOL) implantation were included. SIA was calculated using values from the IOL Master Zeiss 700 and mean pupil power (MPP) derived from the CSO Sirius Topographer (based on 3mm pupil size) with vectorial analysis from doctor Hill software. No significant difference in SIA was observed between eyes with prior myopic photorefractive keratectomy and the control group (p > 0.05). SIA calculations using the IOL Master and CSO Sirius Tomographer yielded similar results. There was no significant correlation between SIA and axial length, corneal curvature, peripheral corneal thickness, or anterior chamber depth (p > 0.05). However, an inverse correlation was found between SIA and horizontal corneal diameter (p < 0.05). Corneal parameters, such as axial length, corneal curvature, peripheral corneal thickness, and anterior chamber depth, showed no significant influence on SIA. The inverse correlation between SIA and horizontal corneal diameter in study group suggests potential influence of white-to-white distance on SIA. These findings highlight the importance of considering corneal parameters for optimizing surgical outcomes.

The Role of International Cooperation in the Chinese Food Security Strategy

China's food security strategy is based on the principle of self-reliance. In the light of its historical experience, Beijing approaches the issue of attracting external resources in this area with caution. The integration of external vector into the national strategy has been gradual, from the assumption that external resources can be used in critical situations to a comprehensive vision of how they can contribute to domestic development. Along the way, China has progressively introduced measures to support domestic producers under the "bringing in" and "going out" policies and to promote international cooperation in food and agriculture. This was designed to reduce the pressure on domestic resources and contribute to the formation of a supportive external environment that favours the development of modern agriculture at home. As a result, there has been adopted the formula "utilising two markets, two resources": the external vector has become an important complementary element in ensuring food security. Along with its integration into the national strategy, there are trends towards systematising and scaling up. Under Xi Jinping's leadership, there has been strengthened interministerial coordination in planning the development of international cooperation in food and agriculture and expanded the tools used, from innovative formats for science and technology cooperation to more active participation in the global governance agenda on food security. In its efforts to shape a supportive external environment, China is endeavouring to take a proactive stance. This is reflected both in greater involvement in regional and international organisations on the food and agriculture agenda and in the promotion of its own initiatives.

Expanding the genetic toolbox for Neisseria meningitidis with efficient tools for unmarked gene editing, complementation, and labeling.

The efficient natural transformation of Neisseria meningitidis allows the rapid construction of bacterial mutants in which the genes of interest are interrupted or replaced by antibiotic-resistance cassettes. However, this proved to be a double-edged sword, i.e., although facilitating the genetic characterization of this important human pathogen, it has limited the development of strategies for constructing markerless mutants without antibiotic-resistance markers. In addition, efficient tools for complementation or labeling are also lacking in N. meningitidis. In this study, we significantly expand the meningococcal genetic toolbox by developing new and efficient tools for the construction of markerless mutants (using a dual counterselection strategy), genetic complementation (using integrative vectors), and cell labeling (using a self-labeling protein tag). This expanded toolbox paves the way for more in-depth genetic characterization of N. meningitidis and might also be useful in other Neisseria species.IMPORTANCENeisseria meningitidis and Neisseria gonorrhoeae are two important human pathogens. Research focusing on these bacteria requires genetic engineering, which is facilitated by their natural ability to undergo transformation. However, the ease of mutant engineering has led the Neisseria community to neglect the development of more sophisticated tools for gene editing, particularly for N. meningitidis. In this study, we have significantly expanded the meningococcal genetic toolbox by developing novel and efficient tools for markerless mutant construction, genetic complementation, and cell tagging. This expanded toolbox paves the way for more in-depth genetic characterization of N. meningitidis and might also be useful in other Neisseria species.

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 &gt; 0.9 or r &lt; -0.9) significant (p &lt; 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.