Intersection Matrix Research Articles

Glimmers from the axiverse

We study axion-photon couplings in compactifications of type IIB string theory. We find that these couplings are systematically suppressed compared to the inverse axion periodicity, as a result of two effects. First, couplings to the QED theta angle are suppressed for axion mass eigenstates that are light compared to the mass scale set by stringy instantons on the cycle supporting QED. Second, in compactifications with many axions the intersection matrix is sparse, making kinetic mixing weak. We study the resulting phenomenology in an ensemble of 200,000 toy models constructed from the Kreuzer-Skarke database up to the maximum Hodge number h1,1 = 491. We examine freeze-in production and decay of thermal axions, birefringence of the cosmic microwave background, X-ray spectrum oscillations, and constraints on the QCD axion from supernovae. We conclude that compactifications in this corner of the landscape involve many invisible axions, as well as a handful that may be detectable via photon couplings.

Intelligent Extraction of Multi-style and Multi-template Title Block Information Based on Fuzzy Matching

ABSTRACT Title blocks are crucial primary data on drawings necessary for the operation of modern manufacturing enterprises. However, their uniform export poses a challenge due to the heterogeneity across multiple sources and the variety of export templates. Therefore, this paper proposes an intelligent extraction method for title block information (TBI) based on fuzzy matching. This method evaluates the geometrical composition of the title block, the logical relationship between information cells, and the diversification of the title block. It establishes a weighted intersection point matrix for the title block as the topological structure model. The fuzzy matching, based on the intersection matrix points, disregards the variations in the size and position of the title block and focuses only on the style that impacts the extraction of information. The matched title blocks are categorized, and the base table of each type determines the information distribution of the title block. A hash table is then created between the description cell and the value cell of information to accumulate the TBI. The method is integrated into the AutoCAD software and presented with an interactive program interface. Finally, an example is presented to further demonstrate the stability, reliability, and efficiency of the method and the system.

Some results on characters of a class of P-polynomial table algebras

In this paper, we study the character values of homogeneous monotonic P-polynomial table algebras with finite dimension d ≥ 5. To this end, we obtain a trigonometric polynomial to calculate the eigenvalues of the first intersection matrix of these table algebras using the z-transform. Finally by applying some methods for tridiagonal matrices, the character values of these table algebras are given in terms of Chebyshev polynomials.

A quantitative fuzzy-valued intersection matrix for obtaining fuzzy relationships between vague spatial objects

Topological relation between geographical objects is one of the key components of the Geographical Information System (GIS). Considering the objects to be exact with sharp boundaries, four intersection, and nine intersection matrices initiated the study of calculating the topological relations. Due to the extensive existence of vague spatial phenomenons, the study of uncertainty object modeling has grown rapidly. Parallelly, the relationship calculating tools have been upgraded to handle vague concepts. The fuzzy 9-intersection matrix and Egg-Yolk methods are popular tools. Although the geographical objects are uncertain, surprisingly, most of these tools generate certain relations between them. The qualitative nature of these tools overlooks the essence of their uncertainty. We propose a quantitative fuzzy-valued 9-intersection matrix to overcome these drawbacks to obtain a fuzzy relationship between uncertain geographical objects. Then two new similarity computation techniques are introduced to calculate the membership grade between the proposed matrix and the known crisp matrices. These similarity computations allow two spatial objects to have partial membership against the eight established topological relations. The quantitative calculations indicate the strength of the relationship. The superiority of the proposed model is exhibited through comparative studies. Further, certain linguistic variables are linked to the evaluated membership grades to generate an immediate association with the known crisp relations. Examples are provided to demonstrate the applicability and efficacy of this association.

DETECTION OF VOID NUCLEATION, COALESCENCE AND COLLAPSE IN ATOMISTIC SIMULATIONS

Extraction of required information from atomic configurations is crucial for efficient use of molecular dynamics (MD) simulations, and automating this process allows the collection of statistical data to develop and validate physical models and data-driven approaches. Here we update the previously developed pore searching algorithm to automatically detect the events of void nucleation, collapse and coalescence by comparing pairs of atomic configurations. We calculate an intersection matrix, which shows common regions between voids of current and previous time frames, and analysis of this intersection matrix gives a numerical criterion for determination of the considered events. The updated algorithm is verified in the case of small MD system and further used to analyze a large MD system with many hundreds of voids. The predominance of void collapse is confirmed in the case of uniform triaxial tension of solid aluminum, while void coalescence instead of collapse is detected in the case of a more complex loading with axial compression and lateral tension. This dependence of the predominant mechanism on the loading path correlates with previous finite element analysis in the literature. Another interesting finding is a continuing nucleation and collapse of voids far beyond the fracture beginning at a level of negative pressure much lower than the spall strength, which can be attributed to a developed defect structure of material produced by plastic growth of voids.

Discriminant groups of wild cyclic quotient singularities

Let p be prime. We describe explicitly the resolution of singularities of several families of wild Z/pZ-quotient singularities in dimension two, including families that generalize the quotient singularities of type E_6, E_7, and E_8 from p=2 to arbitrary characteristics. We prove that for odd primes, any power of p can appear as the determinant of the intersection matrix of a wild Z/pZ-quotient singularity. We also provide evidence towards the conjecture that in this situation one may choose the wild action to be ramified precisely at the origin.

Normal surface singularities with an integral homology sphere link related to space monomial curves with a plane semigroup

In this article, we consider an infinite family of normal surface singularities with an integral homology sphere link which is related to the family of space monomial curves with a plane semigroup. These monomial curves appear as the special fibers of equisingular families of curves whose generic fibers are a complex plane branch, and the related surface singularities appear in a proof of the monodromy conjecture for these curves. To investigate whether the link of a normal surface singularity is an integral homology sphere, one can use a characterization that depends on the determinant of the intersection matrix of a (partial) resolution. To study our family, we apply this characterization with a partial toric resolution of our singularities constructed as a sequence of weighted blow-ups.

Circulant almost cross intersecting families

Let ℱ and G be two t-uniform families of subsets over [k] = {1, 2, ..., k}, where |ℱ| = |G|, and let C be the adjacency matrix of the bipartite graph whose vertices are the subsets in ℱ and G, where there is an edge between A ∈ ℱ and B ∈ G if and only if A ∩ B ≠ ∅. The pair (ℱ,G) is q-almost cross intersecting if every row and column of C has exactly q zeros. We further restrict our attention to q-almost cross intersecting pairs that have a circulant intersection matrix Cp, q, determined by a column vector with p > 0 ones followed by q > 0 zeros. This family of matrices includes the identity matrix in one extreme, and the adjacency matrix of the bipartite crown graph in the other extreme. We give constructions of pairs (ℱ,G) whose intersection matrix is Cp, q, for a wide range of values of the parameters p and q, and in some cases also prove matching upper bounds. Specifically, we prove results for the following values of the parameters: (1) 1 ≤ p ≤ 2t − 1 and 1 ≤ q ≤ k − 2t + 1. (2) 2t ≤ p ≤ t2 and any q > 0, where k ≥ p + q. (3) p that is exponential in t, for large enough k. Using the first result we show that if k ≥ 4t − 3 then C2t − 1, k − 2t + 1 is a maximal isolation submatrix of size k × k in the 0, 1-matrix Ak, t, whose rows and columns are labeled by all subsets of size t of [k], and there is a one in the entry on row x and column y if and only if subsets x, y intersect.

Representing 3D Topological Adjacencies between Volumes Using a 36-Intersection Model

Topological properties of objects should be maintained and preserved to concisely represent objects. However, the implementation of 2D topological rules requires the decomposition of 3D objects into lower dimensions to determine topological relationships. This results in 2D topological relationships although the connected objects are in 3D. Hence, accurate representation of 3D connectivity in 3D models is limited. 3D topological rules can be implemented to include topological connectivity in 3D space. This paper implemented an extension of the 27-Intersection Model (27-IM) called the 36-Intersection Model (36-IM) to represent 3D topological adjacencies of two objects in 3D space. This resulted in a 12 × 3 intersection matrix or 36-IM that represented the intersections in terms of dimension and number of separations. Six cases were tested, consisting of “meets”, “disjoint” “intersects at a line”, “intersects at a point”, “contains”, and “overlaps”. The resulting 36-IM matrices provided an accurate representation of how the objects in 3D space were related and their dimension of intersections. The formalisms of the 36-IM matrices were also interoperable which allowed the interpretation of 36-IM using the 9IM and DE-9IM to determine general topological relationships. By examining the intersection of interiors, boundaries and exteriors of 3D objects without object decomposition, 3D topological relationships can be determined as well as the dimension and manner of intersection.

Maruyoshi-Song flows and defect groups of {mathrm{D}}_{mathrm{p}}^{mathrm{b}} (G) theories

We study the defect groups of {D}_p^b (G) theories using geometric engineering and BPS quivers. In the simple case when b = h∨(G), we use the BPS quivers of the theory to see that the defect group is compatible with a known Maruyoshi-Song flow. To extend to the case where b ≠ h∨(G), we use a similar Maruyoshi-Song flow to conjecture that the defect groups of {D}_p^b (G) theories are given by those of G(b)[k] theories. In the cases of G = An, E6, E8 we cross check our result by calculating the BPS quivers of the G(b)[k] theories and looking at the cokernel of their intersection matrix.

Morphological Analysis of general system–environment complexes: Representation and application

AbstractSystems and their environments must be understood in an integrated manner because any changes in the systems will affect their environments and vice versa in the ubiquitous open systems. Existing studies classify systems based on the diversity of their interactions and the systems' responses to changes in their environments. However, the uses of such classifications are limited. We attempt to address this limitation by using morphological analysis (MA) to identify, represent and characterise the general system–environment complex (SEC) and its components. The latter, called ‘dimensions’, and their respective manifestations, termed ‘variants’, are integrated into the MA representation to enable a holistic understanding of SECs in terms of six dimensions and 101 variants. The resultant representation and characterisation will help researchers identify potential research opportunities, demonstrated through the construction of a variants intersection matrix, and help develop practical principles for system design and evaluation.

Convergence of the mirror to a rational elliptic surface

The construction introduced by Gross, Hacking and Keel allows one to construct a formal mirror family to a pair $(S,D)$ where $S$ is a smooth rational projective surface and $D$ a certain type of Weil divisor supporting an ample or anti-ample class. In that paper they proved two convergence results. Firstly that if the intersection matrix of $D$ is not negative semi-definite then the family they construct lifts to an algebraic family. Secondly they prove that if the intersection matrix is negative definite then their construction lifts along certain analytic strata on the base, and then over a formal neighbourhood of this. In the original version of that paper they claimed that if the intersection matrix were negative semi-definite then family in fact extends over an analytic neighbourhood of the origin but gave an incorrect proof. In this paper we correct this error. We explain how the general Gross-Siebert program can be used to reduce construction of the mirror to such a surface to calculating certain relative Gromov-Witten invariants. We then relate these invariants to the invariants of a new space where we can find explicit formulae for the invariants. From this we deduce analytic convergence of the mirror family, at least when the original surface has an $I_4$ fibre.

From Simultaneous Localization and Mapping to Collaborative Localization for Intelligent Vehicles

This paper describes a new method for real-time collaborative localization for intelligent vehicles based on a combination of an extension of simultaneous localization and mapping and track-to-track fusion methods. This strategy aims to overcome the shortcomings of the embedded proprioceptive sensors and solve the localization issues in a cluster of intelligent vehicles, which are equipped with low-cost navigation systems (global position systems, rangefinders, and vehicle to vehicle communication means) in an unknown environment. The strategy improves the vehicles’ localization accuracy and tracks a cluster of vehicles for advanced driver assistance systems and vehicles self-driving. For real-time purposes, the computational complexity of standard solutions, which are based on Kalman filter derivatives, is transformed, herein, from cubic to quadratic with respect to the state vector of the cluster. Furthermore, the correlated data is another challenge that needs to be solved in cooperative localization scenarios. To this end, two independent, local and global, fusion nodes are associated with each vehicle. The local node exploits multiple forms of the extended Kalman filter and its dual extended information filter to estimate the vehicles’ state, information vectors, covariance and information matrices in the moments and information forms, respectively. Then, the vehicles broadcast the result of their respective local fusion node to cluster. The information is used to solve the second problem, which is a track-to-track fusion on distributed architectures, with two methods: covariance intersection and information matrix fusion in the global fusion node. The simulation and the experimental results of the proposed methods, on distributed architectures, are compared to the optimal solution of centralized data fusion, and to the traditional SLAM method in terms of root mean square errors and consistency.

Half-hypermultiplets and incomplete/complete resolutions in F-theory

We consider resolutions of codimension-two enhanced singularities from SO(12) to E7 and from E7 to E8 in six-dimensional F-theory, where a half-hypermultiplet arises for generic complex structures achieving them. The exceptional fibers at the enhanced point exhibit different structures depending on how the colliding 7-brane approaches the stack of gauge 7-branes, as previously observed by Morrison and Taylor in the case of the enhancement from SU(6) to E6. When the colliding brane approaches them as O(s), where s is the coordinate of the base space along the gauge 7-branes, the resolution process ends up with fewer exceptional fibers than naively expected from the Kodaira classification, with a non-Dynkin intersection matrix including half-integral intersection numbers. We confirm that the exceptional fibers at the enhanced point form extremal rays of the cone of the positive weights of the relevant pseudo-real representation, explaining why a half-hypermultiplet arises there. By altering the ordering of the singularities blown up in the process, we obtain, for both SO(12) → E7 and E7 → E8, the intersection diagram on every other row of the corresponding box graphs. We present detailed derivations of the intersection diagrams of the exceptional fibers at the singularity enhanced points by examining how an exceptional curve is lifted up on the chart arising due to the subsequent blowing-up process. When the colliding brane approaches the stack of branes as O(s2), we obtain additional conifold singularity at the enhanced point, which completes the full Dynkin diagram of the enhanced group as was found previously.

Gas distribution mapping for indoor environments based on laser absorption spectroscopy: Development of an improved tomographic algorithm

Gas distribution mapping (GDM) is an important technology for the study of indoor environment, which can be used to evaluate the efficiency of environmental control system and identify pollutant sources. Most recent studies have implemented GDM through contact sensors or a sensor network, which is difficult to calibrate all the sensors and cover the whole space. In this study, we introduced the non-contact tunable diode laser absorption spectroscopy (TDLAS) technology for GDM in the indoor environment. An improved tomographic algorithm, namely Least Square with Tikhonov Regularization (LSTR), was proposed and compared with two available tomographic algorithms using four validated computational fluid dynamics (CFD) simulations. We also analyzed the effects of the laser emitter placements and optical path densities on the concentration field reconstruction quantitatively. The results showed that the LSTR method could reduce the average relative root mean square error (RRMSE) of tomography by 52%, and the laser emitter at the long edge middle (LEM) can achieve better tomographic performance. The degree of the concentration dispersion from the source would mainly impact the tomographic results: when the sector dispersion (SD) value of concentration distribution was about 2.3 times larger, the average RRMSE value would be decreased by about 40%. The intersection matrix with a higher path density achieved a more accurately reconstructed map due to its lower condition number. In addition, the optical path density was suggested to twice the number of grid cells considering the trade-off between scanning time and accuracy.

A unified viewpoint for upper bounds for the number of points of curves over finite fields via euclidean geometry and semi-definite symmetric Toeplitz matrices

We provide an infinite sequence of upper bounds for the number of rational points of absolutely irreducible smooth projective curves X X over a finite field, starting from the Weil classical bound, continuing to the Ihara bound, passing through infinitely many n n -th order Weil bounds, and ending asymptotically at the Drinfeld-Vlăduţ bound. We relate this set of bounds to those of Oesterlé, proving that these are inverse functions in some sense. We explain how the Riemann hypothesis for the curve X X can be merely seen as a euclidean property coming from the Toeplitz shape of some intersection matrix on the surface X × X X\times X together with the general theory of symmetric Toeplitz matrices. We also give some interpretation for the defect of asymptotically exact towers. This is achieved by pushing further the classical Weil proof in terms of euclidean relationships between classes in the euclidean part F X \mathcal {F}_X of the numerical group Num ⁡ ( X × X ) \operatorname {Num}(X\times X) generated by classes of graphs of iterations of the Frobenius morphism. The noteworthy Toeplitz shape of their intersection matrix takes a central place by implying a very strong cyclic structure on F X \mathcal {F}_X .

The Boolean rank of the uniform intersection matrix and a family of its submatrices

We study the Boolean rank of two families of binary matrices. The first is the binary matrix Ak,t that represents the adjacency matrix of the intersection bipartite graph of all subsets of size t of {1,2,...,k}. We prove that its Boolean rank is k for every k≥2t.The second family is the family Us,m of submatrices of Ak,t that is defined as Us,m=(Jm⊗Is)+(I¯m⊗Js), where Is is the identity matrix, Js is the all-ones matrix, s=k−2t+2 and m=(2t−2t−1). We prove that the Boolean rank of Us,m is also k for the following values of t and s: for s=2 and any t≥2, that is k=2t; for t=3 and any s≥2; and for any t≥2 and s>2t−2, that is k>4t−4.

Total separable closure and contractions

We show that on integral normal separated schemes whose function field is separably closed, for each pair of points the intersection of the resulting local schemes is local. This extends a result of Artin from rings to schemes. The argument relies on the existence of certain modifications in inverse limits. As an application, we show that Čech cohomology coincides with sheaf cohomology for the Nisnevich topology. Along the way, we generalize the characterization of contractible curves on surfaces by negative-definiteness of the intersection matrix to higher dimensions, using bigness of invertible sheaves on non-reduced schemes.

Qualitative topological relations between interval type‐2 fuzzy spatial objects

AbstractThe topological relations between fuzzy objects are crucial in geographical spatial analysis. A qualitative topological relationship analysis method for interval type‐2 fuzzy spatial objects (IT2 FSOs) is proposed in this article. Similarities between the interval type‐2 fuzzy topological relation matrices and the corresponding crisp topological relation matrices are calculated using Jaccard's similarity measure and sorted to identify the two major relations. Next, the proximity degrees and quantifiers that correspond to these two major relations can be determined. Thus, two methods can be used to describe the relation between two IT2 FSOs; the method proposed in this article conforms to human cognitive habits and meets the requirements of a variety of applications in geographical information systems (GIS). Users can select different boundary definitions, intersection matrix types, and calculation functions for each cell in the intersection matrix, as well as different description methods according to the requirements of different GIS applications.

Wild quotients of products of curves

Let k be an algebraically closed field of characteristic $$p>0$$ . Let and be two smooth proper connected curves, each endowed with an automorphism $$\sigma _i:B_i \rightarrow B_i$$ of order p. Let , and let $$\sigma :Y \rightarrow Y$$ be the automorphism . We show that the graph of the resolution of any singularity of is a star-shaped graph with three terminal chains when $$B_2$$ is an ordinary curve of positive genus. The intersection matrix N of the resolution satisfies , and can be completely determined when $$B_1$$ is also ordinary, or when $$\sigma _1$$ has a unique fixed point. The singularity is rational. Wild -quotient singularities of surfaces are expected to have resolution graphs which are trees, with associated intersection matrices N satisfying for some $$r\geqslant 0$$ . We show, for any $$s>0$$ coprime to p, the existence of resolution graphs with one node, $$s+2$$ terminal chains, and with intersection matrix N satisfying .