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BackgroundObjectiveCase DescriptionOutcomesConclusionBody lateropulsion (BL) is a phenomenon in which the body involuntarily falls to one side; however, its detailed postural control characteristics remain unclear.This case report aimed to measure the surface electromyography (EMG) of the lower limbs while standing in a patient with severe BL on the affected side due to pontine infarction and to investigate the characteristics of postural control.We evaluated a patient with severe BL due to pontine infarction at two-time points, 6 and 20 days after onset, to assess static standing balance under open and closed eye conditions and measure the center of pressure (COP) and lower extremity EMG during these tasks.There were minimal changes in COP position and total locus length during the eyes closed condition compared to the eyes open condition. However, the head and trunk to the non-BL side of the tilt and bilateral medial hamstring muscle activity tended to be higher when the eyes were closed. At the final evaluation, head and trunk tilt and EMG changes were reduced during the eyes-closed condition compared to the eyes-open condition. The initial postural response was considered to reflect a compensatory postural strategy for BL, characterized by the body involuntarily tilting to one side.The change in posture over time may indicate a reduction in the compensatory postural response as the condition improves. In this case, characteristic postural findings were identified through EMG measurements, suggesting the possibility of future studies involving multiple cases. [ABSTRACT FROM AUTHOR]

We study when the Picard group of smooth surfaces of degree |$d\geq 5$| in |$\mathbb{P}^{3}$| acquires extra classes. In particular we show that the so-called exceptional components of the Noether–Lefschetz locus are not Zariski dense. This answers a 1991 question of C. Voisin. We also obtain similar results for the Noether–Lefschetz locus for suitable |$(Y,L)$|⁠ , where |$Y$| is a smooth projective three-fold and |$L$| a very ample line bundle. Both results are applications of the Zilber–Pink viewpoint recently developed by the authors for arbitrary (polarized, integral) variations of Hodge structures. [ABSTRACT FROM AUTHOR]

Mirror symmetry for higher genus curves is usually formulated and studied in terms of Landau–Ginzburg models; however the critical locus of the superpotential is arguably of greater intrinsic relevance to mirror symmetry than the whole Landau–Ginzburg model. Accordingly, we propose a new approach to the A-model of the mirror, viewed as a trivalent configuration of rational curves together with some extra data at the nodal points. In this context, we introduce a version of Lagrangian Floer theory and the Fukaya category for trivalent graphs, and show that homological mirror symmetry holds, namely, that the Fukaya category of a trivalent configuration of rational curves is equivalent to the derived category of a non-Archimedean generalized Tate curve. To illustrate the concrete nature of this equivalence, we show how explicit formulas for theta functions and for the canonical map of the curve arise naturally under mirror symmetry. [ABSTRACT FROM AUTHOR]

We describe the Loewner chains of the real locus of a class of real rational functions whose critical points are on the real line. Our main result is that the poles of the rational function lead to explicit formulas for the dynamical system that governs the driving functions. Our formulas give a simple method for mapping the class of rational functions into solutions to a non-trivial system of quadratic equations, and for directly showing that the curves in the real locus satisfy geometric commutation. These results are entirely self-contained and have no reliance on probabilistic objects, but make use of an integral of motion for the Loewner chain that is motivated by ideas from conformal field theory. We also show that the dynamics of the driving functions are a special case of the Calogero–Moser integrable system, restricted to a particular submanifold of phase space carved out by the Lax matrix. Our approach complements a recent result of Peltola and Wang, who showed that the real locus is the deterministic κ → 0 limit of the multiple SLE (κ) curves. [ABSTRACT FROM AUTHOR]

Diplocarpon coronariae is a fungal pathogen that is prevalent in low-input apple production. Over the past 15 years, it has become increasingly distributed in Europe. However, comprehensive insights into its biology and pathogenicity remain limited. One particular aspect is the rarity of the sexual morph of this pathogen, a phenomenon hitherto unobserved in Europe. Diplocarpon coronariae reproduces through a heterothallic mating system requiring at least two different mating types for sexual reproduction. Genes determining the mating types are located on the mating-type locus. In this study, D. coronariae strain DC1_JKI from Dresden, Germany, was sequenced and used to unravel the structure of the mating type locus. Using short-read and long-read sequencing methods, the first gapless and near-complete telomere-to-telomere genome assembly of D. coronariae was achieved. The assembled genome spans 51.2 Mbp and comprises 21 chromosome-scale contigs of high completeness. The generated genome sequence was used to in silico elucidate the structure of the mating-type locus, identified as MAT1-2. Furthermore, an examination of MAT1-1 and MAT1-2 frequency across a diverse set of samples sourced from Europe and Asia revealed the exclusive presence of MAT1-2 in European samples, whereas both MAT loci were present in Asian counterparts. Our findings suggest an explanation for the absence of the sexual morph, potentially linked to the absence of the second mating idiomorph of D. coronariae in European apple orchards. [ABSTRACT FROM AUTHOR]

We compute the dimension of certain components of the family of smooth determinantal degree d$d$ surfaces in P3${\mathbb {P}}^3$, and show that each of them is the closure of a component of the Noether–Lefschetz locus NL(d)$NL(d)$. Our computations exhibit that smooth determinantal surfaces in P3${\mathbb {P}}^3$ of degree 4 form a divisor in |OP3(4)|$|\mathcal {O}_{{\mathbb {P}}^3}(4)|$ with five irreducible components. We will compute the degrees of each of these components: 320,2508,136512,38475$320,2508,136512,38475$, and 320112$\hskip.001pt 320112$. [ABSTRACT FROM AUTHOR]

Hammer throwing is a motorically demanding sport in which the execution of the movement significantly influences the result, that is the throwing distance. There are many approaches for supporting technical training that are based on measurement technology and image capturing. The accelerations and locus curves of the athlete and hammer are recorded and compared. In this article, these methods are supplemented by a multi‐body simulation (MBS) of the hammer throw. The kinematics of the hand movement is described using a parameterized synthetic trajectory. Scalar parameters in the approach allow the trajectory to be modified. With a MBS model of the wire cable and the hammer, the movement of the hammer can be determined by numerical time integration from the hand's trajectory. As a result the final throwing distance after free flight phase can be analyzed. Due to the complex spatial motion of the hammer during the acceleration phase only heuristic methods can be used to optimize the maximum throwing distance. In a final step the optimized movement can be used to improve the athlete's training. [ABSTRACT FROM AUTHOR]

The Artin stack ℳ n of zero-dimensional sheaves of length n on 3 carries two natural d-critical structures in the sense of Joyce. One comes from its description as a quotient stack [ crit (f n) / GL n ] , another comes from derived deformation theory of sheaves. We show that these d-critical structures agree. We use this result to prove the analogous statement for the Quot scheme of points Quot 3 ( ⊕ r , n) = crit (f r , n) , which is a global critical locus for every r > 0 , and also carries a derived-in-flavor d-critical structure besides the one induced by the potential f r , n . Again, we show these two d-critical structures agree. Moreover, we prove that they locally model the d-critical structure on Quot X (F , n) , where F is a locally free sheaf of rank r on a projective Calabi–Yau 3 -fold X. Finally, we prove that the perfect obstruction theory on Hilb n 3 = crit (f 1 , n) induced by the Atiyah class of the universal ideal agrees with the critical obstruction theory induced by the Hessian of the potential f 1 , n . [ABSTRACT FROM AUTHOR]

Premise: Target sequence capture (Hyb‐Seq) is a cost‐effective sequencing strategy that employs RNA probes to enrich for specific genomic sequences. By targeting conserved low‐copy orthologs, Hyb‐Seq enables efficient phylogenomic investigations. Here, we present Asparagaceae1726—a Hyb‐Seq probe set targeting 1726 low‐copy nuclear genes for phylogenomics in the angiosperm family Asparagaceae—which will aid the often‐challenging delineation and resolution of evolutionary relationships within Asparagaceae. Methods: Here we describe and validate the Asparagaceae1726 probe set (https://github.com/bentzpc/Asparagaceae1726) in six of the seven subfamilies of Asparagaceae. We perform phylogenomic analyses with these 1726 loci and evaluate how inclusion of paralogs and bycatch plastome sequences can enhance phylogenomic inference with target‐enriched data sets. Results: We recovered at least 82% of target orthologs from all sampled taxa, and phylogenomic analyses resulted in strong support for all subfamilial relationships. Additionally, topology and branch support were congruent between analyses with and without inclusion of target paralogs, suggesting that paralogs had limited effect on phylogenomic inference. Discussion: Asparagaceae1726 is effective across the family and enables the generation of robust data sets for phylogenomics of any Asparagaceae taxon. Asparagaceae1726 establishes a standardized set of loci for phylogenomic analysis in Asparagaceae, which we hope will be widely used for extensible and reproducible investigations of diversification in the family. [ABSTRACT FROM AUTHOR]

The collocation boundary element method, as developed and taught in the traditional books, suffers from severe inconsistencies, partly responsible for the method's lack of clarity and broader applicability (not to mention the uncontrollable proliferation of misleading alternatives that only add to more confusion). This has been recently corrected, as summarized in this review paper, in which we report the proposition of a convergence theorem for the general, just consistent, three-dimensional isoparametric formulation of potential and elasticity problems (https://doi.org/10.1016/j.enganabound.2023.01.017), and also introduce the not interchangeable concepts of nodes and loci, for boundary displacements and tractions in elasticity, respectively, as well as of points, for domain sources. We have implemented, for both two-dimensional potential and elasticity problems, real-variable (https://doi.org/10.1016/j.enganabound.2023.01.015, https://doi.org/10.1016/j.enganabound.2023.03.026) and—still better—complex-variable (https://doi.org/10.1016/j.enganabound.2023.04.024) codes for generally high-order, curved elements, which effortlessly enable evaluations with numerical precision that is only machine-limited and only resorts to the problem's mathematics—plus Gauss–Legendre quadrature of all integrals' regular parts. (Ad hoc mechanical interpretations, "regularizations," interval subdivisions, special quadrature formulas, or variable transformations are neither strictly speaking correct nor generally applicable nor required.) Despite the singular kernels that enter diverse forms of Somigliana's identity (as for evaluating stress results at a domain point), problem-unrelated singularities do not come up in a mathematically consistent formulation and implementation: singularities are just man-made. A few examples of highly challenging topological issues are presented. We show that fracture mechanics problems may be dealt with seamlessly, and we manage to objectively assess a problem's topological consistency, precision, accuracy, and round-off errors related to a given mesh discretization and software-conditioned computational digits. [ABSTRACT FROM AUTHOR]

We compare two partitions of real bitangents to smooth plane quartics into sets of 4: one coming from the closures of connected components of the avoidance locus and another coming from tropical geometry. When both are defined, we use the Tarski principle for real closed fields in combination with the topology of real plane quartics and the tropical geometry of bitangents and theta characteristics to show that they coincide. [ABSTRACT FROM AUTHOR]

We give a characterization of rational points lying on the Noether-Lefschetz locus of moduli spaces of K3 surfaces by studying their lifting properties under some natural coverings of the ambient space. We then prove that the Bombieri-Lang conjecture implies non-density statements for the rational points in the Noether-Lefschetz locus, as predicted by a conjecture of Shafarevich. [ABSTRACT FROM AUTHOR]

Early Modern Italian manuals for memorization present memory as deeply embodied, especially through the memory palace technique. Here, physical sensation, emotion, navigational skills, and personal experience, are all functional to intellectual learning. This article individuates these embodied tools through the analysis of three memorization manuals from 16th century Italy – a time, place, and religious context, in which the body could still be involved in mnemnonics: Dolce’s Dialogo del modo di accrescere e conservar la memoria (1562), Della Porta’s L’Arte del Ricordare (1566), and Gesualdo’s Plutosofia (1592). In these manuals, it is especially the loci, the architectures of the memory palace, which show sensory participation. Fundamental for place-navigation skills, these embodied techniques are a theoretical challenge for the manuals’ authors, tied to the period’s view of memory as a fundamentally abstract process. Their various approaches are reviewed, and organized along a spectrum, from claiming to denying the contribution of the described practices to a theory of memory and knowledge. [ABSTRACT FROM AUTHOR]

Clubroot disease caused by Plasmodiophora brassicae is becoming a serious threat to rapeseed (Brassica napus) production worldwide. Breeding resistant varieties using CR (clubroot resistance) loci is the most promising solution. Using marker‐assisted selection and speed‐breeding technologies, we generated Brassica napus materials in homozygous or heterozygous states using CRA3.7, CRA08.1, and CRA3.2 loci in the elite parental line of the Zhongshuang11 background. We developed three elite lines with two CR loci in different combinations and one line with three CR loci at the homozygous state. In our study, we used six different clubroot strains (Xinmin, Lincang, Yuxi, Chengdu, Chongqing, and Jixi) which are categorized into three groups based on our screening results. The newly pyramided lines with two or more CR loci displayed better disease resistance than the parental lines carrying single CR loci. There is an obvious gene dosage effect between CR loci and disease resistance levels. For example, pyramided lines with triple CR loci in the homozygous state showed superior resistance for all pathogens tested. Moreover, CR loci in the homozygous state are better on disease resistance than the heterozygous state. More importantly, no negative effect was observed on agronomic traits for the presence of multiple CR loci in the same background. Overall, these data suggest that the pyramiding of triple clubroot resistance loci conferred superior resistance with no negative effects on agronomic traits in Brassica napus. [ABSTRACT FROM AUTHOR]

Given k points (xi, yi) ∈ ℙ2 × ℙ2, we characterize rank deficiency of the k × 9 matrix Zk with rows x i ⊤ ⊗ y i ⊤ in terms of the geometry of the point configurations {xi} and {yi}. In this paper we present results for k ≤ 6. For k ≤ 5, the geometry of the rank-drop locus is characterized by cross-ratios and basic (projective) geometry of point configurations. For the case k = 6 the rank-drop locus is captured by the classical theory of cubic surfaces. The results for k = 7, 8 and 9 are presented in the sequel [7] to this paper. [ABSTRACT FROM AUTHOR]

Hybrid genotypes can provide significant yield gains over conventional inbred varieties due to heterosis or hybrid vigor. However, hybrids can also display unintended negative attributes or phenotypes such as extreme pathogen susceptibility. The necrotrophic pathogen Pyrenophora teres f. maculata (Ptm) causes spot form net blotch, which has caused significant yield losses to barley worldwide. Here, we report on a non-transgressive hybrid susceptibility locus in barley identified between the three parental lines CI5791, Tifang and Golden Promise that are resistant to Ptm isolate 13IM.3. However, F2 progeny from CI5791 × Tifang and CI5791 × Golden Promise crosses exhibited extreme susceptibility. The susceptible phenotype segregated in a ratio of 1 resistant:1 susceptible representing a genetic segregation ratio of 1 parental (res):2 heterozygous (sus):1 parental (res) suggesting a single hybrid susceptibility locus. Genetic mapping using a total of 715 CI5791 × Tifang F2 individuals (1430 recombinant gametes) and 149 targeted SNPs delimited the hybrid susceptibility locus designated Susceptibility to Pyrenophora teres 2 (Spt2) to an ~ 198 kb region on chromosome 5H of the Morex V3 reference assembly. This single locus was independently mapped with 83 CI5791 × Golden Promise F2 individuals (166 recombinant gametes) and 180 genome wide SNPs that colocalized to the same Spt2 locus. The CI5791 genome was sequenced using PacBio Continuous Long Read technology and comparative analysis between CI5791 and the publicly available Golden Promise genome assembly determined that the delimited region contained a single high confidence Spt2 candidate gene predicted to encode a pentatricopeptide repeat-containing protein. [ABSTRACT FROM AUTHOR]

Conditionally on the Tate–Shafarevich and Bloch–Kato Conjectures, we give an explicit upper bound on the size of the |$p$| -adic Chabauty–Kim locus, and hence on the number of rational points, of a smooth projective curve |$X/{\mathbb{Q}}$| of genus |$g\geq 2$| in terms of |$p$|⁠ , |$g$|⁠ , the Mordell–Weil rank |$r$| of its Jacobian, and the reduction types of |$X$| at bad primes. This is achieved using the effective Chabauty–Kim method, generalizing bounds found by Coleman and Balakrishnan–Dogra using the abelian and quadratic Chabauty methods. [ABSTRACT FROM AUTHOR]

Motivated by the classical Rodrigues' formula, we study below the root asymptotic of the polynomial sequence R [ α n ] , n , P (z) = d [ α n ] P n (z) d z [ α n ] , n = 0 , 1 , ⋯ where P(z) is a fixed univariate polynomial, α is a fixed positive number smaller than deg P , and [ α n ] stands for the integer part of α n . Our description of this asymptotic is expressed in terms of an explicit harmonic function uniquely determined by the plane rational curve emerging from the application of the saddle point method to the integral representation of the latter polynomials using Cauchy's formula for higher derivatives. As a consequence of our method, we conclude that this curve is birationally equivalent to the zero locus of the bivariate algebraic equation satisfied by the Cauchy transform of the asymptotic root-counting measure for the latter polynomial sequence. We show that this harmonic function is also associated with an abelian differential having only purely imaginary periods and the latter plane curve belongs to the class of Boutroux curves initially introduced in Bertola (Anal Math Phys 1: 167–211, 2011), Bertola and Mo (Adv Math 220(1): 154–218, 2009). As an additional relevant piece of information, we derive a linear ordinary differential equation satisfied by { R [ α n ] , n , P (z) } as well as higher derivatives of powers of more general functions. [ABSTRACT FROM AUTHOR]

We construct a sequence of explicit blow-ups and blow-downs on an irreducible compact Hermitian symmetric spaces |$X$| which transforms it into a projective space of the same dimension. Moreover, this resolves a birational map given by Landsberg and Manivel. Centers of the blow-ups for |$X$| are constructed by loci of chains of minimal rational curves and centers of the blow-ups for the projective space are constructed from the variety of minimal rational tangents of |$X$| and its higher secant varieties. The result was known in the special case where |$X$| is of rank 2 and could be found in Zak's monograph "Tangents and secants of algebraic varieties." [ABSTRACT FROM AUTHOR]

Over the moduli space of pointed smooth algebraic curves, the projectivized k th Hodge bundle is the space of k -canonical divisors. The incidence loci are defined by requiring the k -canonical divisors to have prescribed multiplicities at the marked points. We compute the classes of the closure of the incidence loci in the projectivized k th Hodge bundle over the moduli space of curves with rational tails. The classes are expressed as a linear combination of tautological classes indexed by decorated stable graphs with coefficients enumerating appropriate weightings. As a consequence, we obtain an explicit expression for some relations in tautological rings of moduli of curves with rational tails. [ABSTRACT FROM AUTHOR]

The genetic dissection of reproductive barriers between diverging lineages provides enticing clues into the origin of species. One strategy uses linkage analysis in experimental crosses to identify genomic locations involved in phenotypes that mediate reproductive isolation. A second framework searches for genomic regions that show reduced rates of exchange across natural hybrid zones. It is often assumed that these approaches will point to the same loci, but this assumption is rarely tested. In this perspective, we discuss the factors that determine whether loci connected to postzygotic reproductive barriers in the laboratory are inferred to reduce gene flow in nature. We synthesize data on the genetics of postzygotic isolation in house mice, one of the most intensively studied systems in speciation genetics. In a rare empirical comparison, we measure the correspondence of loci tied to postzygotic barriers via genetic mapping in the laboratory and loci at which gene flow is inhibited across a natural hybrid zone. We find no evidence that the two sets of loci overlap beyond what is expected by chance. In light of these results, we recommend avenues for empirical and theoretical research to resolve the potential incongruence between the two predominant strategies for understanding the genetics of speciation. [ABSTRACT FROM AUTHOR]

In this paper, we analyze the Hessian locus associated to a general cubic hypersurface, by describing its singular locus and its desingularization for every dimension. The strategy is based on strong connections between the Hessian and the quadrics defined as partial derivatives of the cubic polynomial. In particular, we focus our attention on the singularities of the Hessian hypersurface associated to the general cubic four-fold. It turns out to be a minimal surface of general type: its analysis is developed by exploiting the nature of this surface as a degeneracy locus of a symmetric vector bundle map and by describing an unramified double cover, which is constructed in a more general setting. [ABSTRACT FROM AUTHOR]

Varicose vein disease (VVD) is a common health problem worldwide. Microfibril-associated protein 5 (MFAP5) is one of the potential key players in its pathogenesis. Our previous microarray analysis revealed the cg06256735 and cg15815843 loci in the regulatory regions of the MFAP5 gene as hypomethylated in varicose veins which correlated with its up-regulation. The aim of this work was to validate preliminary microarray data, estimate the level of 5-hydroxymethylcytosine (5hmC) at these loci, and determine the methylation status of one of them in different layers of the venous wall. For this, methyl- and hydroxymethyl-sensitive restriction techniques were used followed by real-time PCR and droplet digital PCR, correspondingly, as well as bisulfite pyrosequencing of +/- oxidized DNA. Our microarray data on hypomethylation at the cg06256735 and cg15815843 loci in whole varicose vein segments were confirmed and it was also demonstrated that the level of 5hmC at these loci is increased in VVD. Specifically, among other layers of the venous wall, tunica (t.) intima is the main contributor to hypomethylation at the cg06256735 locus in varicose veins. Thus, it was shown that hypomethylation at the cg06256735 and cg15815843 loci takes place in VVD, with evidence to suggest that it happens through their active demethylation leading to up-regulation of the MFAP5 gene, and t. intima is most involved in this biochemical process. [ABSTRACT FROM AUTHOR]

Considering a non-Hermitian version of p-wave Kitaev chain in the presence of additional second nearest neighbour tunnelling, we study dynamical quantum phase transition (DQPT) which accounts for the vanishing Loschmidt amplitude. The locus of the Fisher's zero traces a continuous path on the complex time plane for the Hermitian case while it becomes discontinuous for non-Hermitian cases. This further leads to the half-unit jumps in the winding number characterizing a dynamical topological aspect of DQPT for non-Hermitian Hamiltonian. Uncovering the interplay between non-Hermiticity and long-range tunnelling, we find these features to be universally present irrespective of the additional second nearest neighbour tunnelling terms as long as non-Hermiticity is preserved. The upper panel depicts the discontinuity in Fisher's zeros exactly on the imaginary axis. The lower panel demonstrates the half-qunatized jumps in the dynamical winding number corresponding to such discontinuous jump. [ABSTRACT FROM AUTHOR]

The Hilbert scheme Hilb n ℂ 3 of n points on ℂ 3 can be expressed as the critical locus of a regular function on a smooth variety . Recent development in birational geometry suggests a study of singularities of the pair (, Hilb n ℂ 3) using jet schemes. In this paper, we use a comparison between Hilb n ℂ 3 and the scheme C 3 , n of three commuting n × n matrices to estimate the log canonical threshold of (, Hilb n ℂ 3). As a consequence, we see that although both dim and dim Hilb n ℂ 3 have asymptotic growth O (n 2) , the largest multiplicity of any points on Hilb n ℂ 3 has at most linear growth O (n). [ABSTRACT FROM AUTHOR]

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We discuss various applications of a uniform vanishing result for the graded components of the finite length Koszul module associated to a subspace K ⊆ ⋀ 2 V , where V is a vector space. Previously Koszul modules of finite length have been used to give a proof of Green's Conjecture on syzygies of generic canonical curves. We now give applications to effective stabilization of cohomology of thickenings of algebraic varieties, divisors on moduli spaces of curves, enumerative geometry of curves on K3 surfaces and to skew-symmetric degeneracy loci. We also show that the instability of sufficiently positive rank 2 vector bundles on curves is governed by resonance and give a splitting criterion. [ABSTRACT FROM AUTHOR]

This paper is a continuation of our paper entitled "Symmedian locus Configuration, Part I ". Assume that C is a circle with center O and radius r. Fix a point H with r < OH < 3r. For the (C,H) -locus, there exists a unique (C,H) -locus satisfying the properties: (1)OH and OH are in opposite direction, (2) the (C,H) - and (C,H) -loci have the same symmedian circle, i.e. CH = CH, and (3) C ∩ CH ∩ C = {P,Q}. We also define the concept of a degenerate triangle inscribed in a circle and show that its orthocenter and symmedian point are well-defined. The above intersection points P and Q turn out to be the symmedian points of two pairs of degenerate triangles, one pair from the (C,H) -locus and the other from the (C,H) -locus. [ABSTRACT FROM AUTHOR]

One of the geometric figures that has symmetry properties is the Cassini oval. The Cassini oval is a curve defined as the locus of points in the plane such that the product of the distances to two fixed points is constant. Cassini ovals are named after the astronomer Giovanni Domenico Cassini, who studied them in 1680. Today, the geometric properties of Cassini ovals are used in many fields: analytical geometry, nuclear physics, radiolocation, and industrial applications. The bistatic radar uses Cassini ovals to detect various targets in radiolocation. Until now, there have been no studies on the clustering capabilities of Cassini ovals. As a novelty, it is hypothesized that clustering possibilities could be used for Cassini ovals. In this article, a study of the capabilities of Cassini ovals in radiolocation was carried out, and their suitability for clustering purposes was shown. [ABSTRACT FROM AUTHOR]

Any triangle in an isotropic plane has a circumcircle u and incircle i. It turns out that there are infinitely many triangles with the same circumcircle u and incircle i. This one-parameter family of triangles is called a poristic system of triangles. We study the trace of the centroid, the Feuerbach point, the symmedian point, the Gergonne point, the Steiner point and the Brocard points for such a system of triangles. We also study the traces of some further points associated with the triangles of the poristic family, and we prove that the vertices of the contact triangle, tangential triangle and anticomplementary triangle move on circles while the initial triangle traverses the poristic family. [ABSTRACT FROM AUTHOR]

In this paper, we show that the conjectural mod p local Langlands correspondence can be realized in the mod p cohomology of the Lubin–Tate towers. The proof utilizes a well-known conjecture of Buzzard–Diamond–Jarvis [8, Conjecture 4.9], a study of completed cohomology of the ordinary and supersingular locus of the Shimura curves for a totally real field F and of mod l (≠ p) local Langlands correspondence as given by Emerton–Helm [20]. In the case of modular curves, a similar theorem was obtained by Chojecki [13]. [ABSTRACT FROM AUTHOR]

Complex-balanced mass-action systems are some of the most important types of mathematical models of reaction networks, due to their widespread use in applications, as well as their remarkable stability properties. We study the set of positive parameter values (i.e., reaction rate constants) of a reaction network G that, according to mass-action kinetics, generate dynamical systems that can be realized as complex-balanced systems, possibly by using a different graph G ′ . This set of parameter values is called the disguised toric locus of G. The R -disguised toric locus of G is defined analogously, except that the parameter values are allowed to take on any real values. We prove that the disguised toric locus of G is path-connected, and the R -disguised toric locus of G is also path-connected. We also show that the closure of the disguised toric locus of a reaction network contains the union of the disguised toric loci of all its subnetworks. [ABSTRACT FROM AUTHOR]

We compare the performance of two systems, ChatGPT 3.5 and GeoGebra 5, in a restricted, but quite relevant, benchmark from the realm of classical geometry: the determination of geometric loci, focusing, in particular, on the computation of envelopes of families of plane curves. In order to study the loci calculation abilities of ChatGPT, we begin by entering an informal description of a geometric construction involving a locus or an envelope and then we ask ChatGPT to compute its equation. The chatbot fails in most situations, showing that it is not mature enough to deal with the subject. Then, the same constructions are also approached through the automated reasoning tools implemented in the dynamic geometry program, GeoGebra Discovery, which successfully resolves most of them. Furthermore, although ChatGPT is able to write general computer code, it cannot currently output that of GeoGebra. Thus, we consider describing a simple method for ChatGPT to generate GeoGebra constructions. Finally, in case GeoGebra fails, or gives an incorrect solution, we refer to the need for improved computer algebra algorithms to solve the loci/envelope constructions. Other than exhibiting the current problematic performance of the involved programs in this geometric context, our comparison aims to show the relevance and benefits of analyzing the interaction between them. [ABSTRACT FROM AUTHOR]

For a general cubic four-fold |$X\subset {\mathbb {P}}^5$| with Fano scheme of lines |$F$|⁠ , we prove a number of properties of the universal family of lines |$I\to F$| and various subloci. We first describe the moduli and ramification theory of the genus four fibration |$p:I\to X$| and explore its relation to a birational model of |$F$| in |$I$|⁠. The main part of the paper is devoted to describing the locus |$V\subset F$| of triple lines, i.e. the fixed locus of the Voisin map |$\phi :F\dashrightarrow F$|⁠ , in particular proving it is an irreducible projective singular surface of class |$21\textrm {c}_2({\mathcal {U}}_F)$| and detailing its intersection with the locus |$S$| of second type lines. A consequence of the analysis of the singularities of |$V$| is a geometric proof of the fact that if |$X$| is very general, then the number of singular (necessarily 1-nodal) rational curves in |$F$| of primitive class is 3780. [ABSTRACT FROM AUTHOR]

Premise: A family‐specific probe set for sunflowers, Compositae‐1061, enables family‐wide phylogenomic studies and investigations at lower taxonomic levels, but may lack resolution at genus to species levels, especially in groups complicated by polyploidy and hybridization. Methods: We developed a Hyb‐Seq probe set, Compositae‐ParaLoss‐1272, that targets orthologous loci in Asteraceae. We tested its efficiency across the family by simulating target enrichment sequencing in silico. Additionally, we tested its effectiveness at lower taxonomic levels in the historically complex genus Packera. We performed Hyb‐Seq with Compositae‐ParaLoss‐1272 for 19 Packera taxa that were previously studied using Compositae‐1061. The resulting sequences from each probe set, plus a combination of both, were used to generate phylogenies, compare topologies, and assess node support. Results: We report that Compositae‐ParaLoss‐1272 captured loci across all tested Asteraceae members, had less gene tree discordance, and retained longer loci than Compositae‐1061. Most notably, Compositae‐ParaLoss‐1272 recovered substantially fewer paralogous sequences than Compositae‐1061, with only ~5% of the recovered loci reporting as paralogous, compared to ~59% with Compositae‐1061. Discussion: Given the complexity of plant evolutionary histories, assigning orthology for phylogenomic analyses will continue to be challenging. However, we anticipate Compositae‐ParaLoss‐1272 will provide improved resolution and utility for studies of complex groups and lower taxonomic levels in the sunflower family. [ABSTRACT FROM AUTHOR]

We study two quite different types of Terracini loci for the order d-Veronese embedding of an n-dimensional projective space: the minimal one and the primitive one (defined in this paper). The main result is that if n = 4 , d ≥ 19 and x ≤ 2 d , no subset with x points is a minimal Terracini set. We give examples that show that the result is sharp. We raise several open questions. [ABSTRACT FROM AUTHOR]

For an algebraic K3 surface with complex multiplication (CM), algebraic fibres of the associated twistor space away from the equator are again of CM type. In this paper, we show that algebraic fibres corresponding to points at the same altitude of the twistor base ${S^2} \simeq \mathbb{P}_\mathbb{C}^1$ share the same CM endomorphism field. Moreover, we determine all the admissible Picard numbers of the twistor fibres. [ABSTRACT FROM AUTHOR]

Assessing donor/recipient HLA compatibility at the eplet level requires second field DNA typings but these are not always available. These can be estimated from lower‐resolution data either manually or with computational tools currently relying, at best, on data containing typing ambiguities. We gathered NGS typing data from 61,393 individuals in 17 French laboratories, for loci A, B, and C (100% of typings), DRB1 and DQB1 (95.5%), DQA1 (39.6%), DRB3/4/5, DPB1, and DPA1 (10.5%). We developed HaploSFHI, a modified iterative maximum likelihood algorithm, to impute second field HLA typings from low‐ or intermediate‐resolution ones. Compared with the reference tools HaploStats, HLA‐EMMA, and HLA‐Upgrade, HaploSFHI provided more accurate predictions across all loci on two French test sets and four European‐independent test sets. Only HaploSFHI could impute DQA1, and solely HaploSFHI and HaploStats provided DRB3/4/5 imputations. The improved performance of HaploSFHI was due to our local and nonambiguous data. We provided explanations for the most common imputation errors and pinpointed the variability of a low number of low‐resolution haplotypes. We thus provided guidance to select individuals for whom sequencing would optimize incompatibility assessment and cost‐effectiveness of HLA typing, considering not only well‐imputed second field typing(s) but also well‐imputed eplets. [ABSTRACT FROM AUTHOR]

Photovoltaic system applications require to use a solar panel, a power converter, and a load. When voltage reduction from a panel to a battery is necessary, a buck converter is usually proposed. In the specialized literature, there are a wide variety of controllers oriented to commercial panels; However, even though measuring the energy extraction of a solar panel is the main indicator, there are other metrics such as switching effort that also affect the overall performance of the PV system. The main contribution of this work is the design of two digital controllers for photovoltaic energy extraction: a servo system controller with integrator and a PI controller based on root locus techniques considering an MPPT algorithm and system perturbations to demonstrate the reliability and efficiency of the controllers under different system scenarios. [ABSTRACT FROM AUTHOR]

Female participation in society is marked by constant demands for rights and equity in the social sphere, whether in the public or private sphere. Therefore, it becomes imperative to [re]think the places they occupy, as well as the way they have been represented for a long time. Therefore, this article aims to analyze the role of the character Agatha Bell in the short story “The Matchmakers”, written by Chimamanda Nigozi Adichie, which makes up the collection of short narratives The Thing Around Your Neck (2017). To this end, we used the theoretical contributions of Bonnici (2004), Cooper (2007), Vergès (2020), Spivak (1997), Pinto (2007), Davis (2016), Ribeiro (2018) and Cardoso (2022). Therefore, qualitative and descriptive research of a documentary and bibliographic nature was used to construct theoretical discussions and analyze the corpus. The studies developed here point to the need to no longer accept socially conventional female roles based on essentialist precepts, as well as the relationship between gender, class and race should not be used as a category to delegate a female inferiority locus. [ABSTRACT FROM AUTHOR]

The axon initial segment (AIS) is a critical locus of control of action potential (AP) generation and neuronal information synthesis. Concussive traumatic brain injury gives rise to diffuse axotomy, and the majority of neocortical axonal injury arises at the AIS. Consequently, concussive traumatic brain injury might profoundly disrupt the functional specialization of this region. To investigate this hypothesis, one and two days after mild central fluid percussion injury in Thy1-YFP-H mice, we recorded high-resolution APs from axotomized and adjacent intact layer 5 pyramidal neurons and applied a second derivative (2o) analysis to measure the AIS- and soma-regional contributions to the AP upstroke. All layer 5 pyramidal neurons recorded from sham animals manifested two stark 2o peaks separated by a negative intervening slope. In contrast, within injured mice, we discovered a subset of axotomized layer 5 pyramidal neurons in which the AIS-regional 2o peak was abolished, a functional perturbation associated with diminished excitability, axonal sprouting and distention of the AIS as assessed by staining for ankyrin-G. Our analysis revealed an additional subpopulation of both axotomized and intact layer 5 pyramidal neurons that manifested a melding together of the AIS- and soma-regional 2o peaks, suggesting a more subtle aberration of sodium channel function and/or translocation of the AIS initiation zone closer to the soma. When these experiments were repeated in animals in which cyclophilin-D was knocked out, these effects were ameliorated, suggesting that trauma-induced AIS functional perturbation is associated with mitochondrial calcium dysregulation. [ABSTRACT FROM AUTHOR]

This article argues that in Alsea ([aes]; Penutian/isolate; dormant; Oregon Coast) the main event line (mel) of narratives is reliably signaled by a particular combination of clause-initial particles, functioning as discourse markers, and not by a specific set of verb forms, the means usually identified and discussed in the literature as a cue for the mel status of a clause. The strength of the link between this combination of discourse markers and the mel, then, represents a cross-linguistic situation that seems rare. Alsea has a rich system of discourse markers and a rich system of verbal affixes, with over 20 potentially co-occurring markers in each. The relative wealth of these discourse markers and their potential combinations make an intricate system of signaling the syntactic, semantic, and pragmatic relationship between clauses and their immediate environment, essentially signaling their discourse status. One combination of markers has the function of signaling the mel. Alsea verbal affixes, on the other hand, play a major role in event semantics and aspectual construal, but a minor one in discourse structuring. This allows for seemingly paradoxical uses of irrealis or imperfective verb forms on the mel of narratives, where the later coerces the event into specific types of bounded and realis readings. [ABSTRACT FROM AUTHOR]

We consider the loci of curves of genus 2 and 3 admitting a |$d$| -to-1 map to a genus 1 curve. After compactifying these loci via admissible covers, we obtain formulas for their Chow classes, recovering results of Faber–Pagani and van Zelm when |$d=2$|⁠. The answers exhibit quasimodularity properties similar to those in the Gromov–Witten theory of a fixed genus 1 curve; we conjecture that the quasimodularity persists in higher genus and indicate a number of possible variants. [ABSTRACT FROM AUTHOR]

Multilocus variable number tandem repeat analysis (MLVA) utilizes short DNA repeat polymorphism in genomes, which is termed variable number tandem repeat (VNTR), to differentiate closely related organisms. One research challenge is to find an optimal set of VNTR to distinguish different members accurately. An intuitive method is to use an exhaustive search method. However, this method is not an efficient way to find optimal solutions from a dataset comprising many attributes (loci) due to the curse of dimensionality. In this study, metaheuristic methods are proposed to find an optimal set of loci combination. Basic genetic algorithm (BGA) and modified genetic algorithm (MGA) were proposed in our previous work for this purpose. However, they require prior knowledge from an experienced user to specify the minimum number of loci for achieving good results. To impose no such expertise requirement for parameter setting, a GA with Duplicates (GAD), which allows the inclusion of duplicated loci in a chromosome (potential solution) during the search process, is developed. The study also investigates the search performance of a hybrid metaheuristic method, namely quantum-inspired differential evolution (QDE). Hunter-Gaston Discriminatory Index (HGDI) is used to indicate the discriminatory power of a loci combination. Two Mycobacterium tuberculosis MLVA datasets obtained from a public portal and a local laboratory respectively, are used. The results obtained by using exhaustive search and metaheuristic methods are first compared, followed by a performance comparison among BGA, MGA, GAD, and QDE by a statistical approach. The best-performing GA method (i.e., GAD) and QDE are selected for a performance comparison with several recent metaheuristic methods using both MLVA datasets by a statistical approach. The statistical results show that both GAD and QDE could achieve higher HGDI than the recent methods using a small but informative set of loci combination. [ABSTRACT FROM AUTHOR]

The moduli space of holomorphic differentials on curves of genus g admits a natural action of the group . The study of orbits of this action and their closures has attracted the interest of a wide range of researchers in the last few decades. In the 2000s, C. McMullen described an infinite family of orbifolds that are closures of such orbits in the space of holomorphic differentials on curves of genus 2. In spaces of holomorphic differentials on curves of higher genera, well-known examples of orbifolds that are unions of -orbit closures are Prym eigenform loci. They are nonempty for surfaces of genus at most 5. This paper presents the first nontrivial calculations of the number of connected components in Prym eigenform loci for surfaces of maximum possible genus. [ABSTRACT FROM AUTHOR]

Polynomial system solving arises in many application areas to model non-linear geometric properties. In such settings, polynomial systems may come with degeneration which the end-user wants to exclude from the solution set. The nondegenerate locus of a polynomial system is the set of points where the codimension of the solution set matches the number of equations. Computing the nondegenerate locus is classically done through ideal-theoretic operations in commutative algebra such as saturation ideals or equidimensional decompositions to extract the component of maximal codimension. By exploiting the algebraic features of signature-based Gröbner basis algorithms we design an algorithm which computes a Gröbner basis of the equations describing the closure of the nondegenerate locus of a polynomial system, without computing first a Gröbner basis for the whole polynomial system. [ABSTRACT FROM AUTHOR]

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We give a concise summary on the technical history of visualizing implicit locus equations in the widely used dynamic geometry system GeoGebra. We mainly focus on the “draggable locus” equation, introduced in GeoGebra 5 (2014), and the dynamic envelopes. We discuss how user interface improvements (the Locus Equation and Envelope tools in GeoGebra Discovery), backend updates (the Giac subsystem) and algebraic experiments (to automatically exclude degeneracy) lead to easy study of caustics of a circle or a parabola in the classroom. [ABSTRACT FROM AUTHOR]

A finite length graded R -module M has the Weak Lefschetz Property if there is a linear form ℓ in R such that the multiplication map × ℓ : M i → M i + 1 has maximal rank. The set of linear forms with this property form a Zariski-open set and its complement is called the non-Lefschetz locus. The main result is to give a complete proof for the theorem stated in [1] that for any general complete intersection I in R [ x 1 , x 2 , x 3 , x 4 ] the non-Lefschetz locus has expected codimension. [ABSTRACT FROM AUTHOR]

The first phylogenomic study using a custom target capture bait panel within the Isonandreae tribe in Sapotaceae is presented. The combination of taxon-specific and universal loci from the Angiosperms353 probe set achieved high species resolution within the genus Palaquium and provides the first phylogenomic insights into Malesian representatives of Sapotaceae, where relationships between taxa often remain poorly understood. The results highlight that generic and some species circumscriptions require further investigation and possible revision: Aulandra longifolia is found to be nested in Palaquium , and P. rostratum within P. microphyllum. Population structure analysis produced limited resolution between and within species, but the bait set was able to recover parameters that are potentially useful in population genomic studies. [ABSTRACT FROM AUTHOR]