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Aspect-based sentiment analysis (ABSA) aims to predict sentiment orientations towards textual aspects by extracting insights from user comments. While pretrained large language models (LLMs) demonstrate proficiency in sentiment analysis, incorporating syntactic and semantic features into ABSA remains a challenge. Additionally, employing LLMs for sentiment analysis often requires significant computational resources, rendering them impractical for use by individuals or small-scale entities. To address this, we propose the semiotic signal integration network (SSIN), which effectively combines syntactic and semantic features. The core syncretic information network leverages isomorphism and syntax to enhance knowledge acquisition. The semantically guided syntactic attention module further enables integrated semiotic representations via sophisticated attention mechanisms. Experiments on the publicly available SemEval dataset show that SSIN performs better than existing state-of-the-art ABSA baselines and LLMs such as Llama and Alpaca with high accuracy and macro-F1 scores. Moreover, our model demonstrates exceptional interpretability and the ability to discern both positive and negative sentiments, which is vitally important for real-world applications such as social media monitoring, health care, and customer service. Code is available at https://github.com/AmbitYuki/SSIN. [ABSTRACT FROM AUTHOR]

Let p be a prime number and k = F ¯ p , the algebraic closure of the finite field F p of p elements. Let G be a connected reductive group defined over F p and B be a Borel subgroup of G (not necessarily defined over F p ). Let k H be the group algebra of a group H over k . We show that for each (one-dimensional) character θ of B (not necessarily rational), there is a unique (up to isomorphism) irreducible k G -module L (θ) containing θ as a k B -submodule, and moreover, L (θ) is isomorphic to a parabolic induction from a finite-dimensional irreducible k L -module for some Levi subgroup L of G . Thus, we have classified and constructed all (abstract) irreducible k G -modules with B -stable line (i.e. an one-dimensional k B -submodule). As a byproduct, we give a new proof of a result of Borel and Tits on the classification of finite-dimensional irreducible k G -modules. [ABSTRACT FROM AUTHOR]

We prove that the Drinfeld center Z (C) of a pivotal finite tensor category C comes with the structure of a ribbon Grothendieck–Verdier category in the sense of Boyarchenko–Drinfeld. Phrased operadically, this makes Z (C) into a cyclic algebra over the framed E 2 -operad. The underlying object of the dualizing object is the distinguished invertible object of C appearing in the well-known Radford isomorphism of Etingof–Nikshych–Ostrik. Up to equivalence, this is the unique ribbon Grothendieck–Verdier structure on Z (C) extending the canonical balanced braided structure that Z (C) already comes equipped with. The duality functor of this ribbon Grothendieck–Verdier structure coincides with the rigid duality if and only if C is spherical in the sense of Douglas–Schommer-Pries–Snyder. The main topological consequence of our algebraic result is that Z (C) gives rise to an ansular functor, in fact even a modular functor regardless of whether C is spherical or not. In order to prove the aforementioned uniqueness statement for the ribbon Grothendieck–Verdier structure, we derive a seven-term exact sequence characterizing the space of ribbon Grothendieck–Verdier structures on a balanced braided category. This sequence features the Picard group of the balanced version of the Müger center of the balanced braided category. [ABSTRACT FROM AUTHOR]

In this paper we study the set of MV-algebras with given prime spectrum and we introduce the class of spectral MV-algebras. An MV-algebra is spectral if it is generated by the union of all its prime ideals (or proper ideals, or principal ideals, or maximal ideals). Among spectral MV-algebras, special attention is devoted to bipartite MV-algebras. An MV-algebra is bipartite if it admits an homomorphism onto the MV-algebra of two elements. We prove that both bipartite MV-algebras and spectral MV-algebras can be finitely axiomatized in first order logic. We also prove that there is only, up to isomorphism, a set of MV-algebras with given prime spectrum. A further part of the paper is devoted to some relations between bipartite MV-algebras and their states. Recall that a state on an MV-algebra is a generalization of a probability measure on a Boolean algebra. Particular states are the states with Bayes' property. We show that an MV-algebra admits a state with the Bayes' property if and only if it is bipartite. [ABSTRACT FROM AUTHOR]

Reference placement is promising to handle the increasing complexity in printed circuit board (PCB) designs, which aims to find the isomorphism of the placed template in component combination to reuse the placement. In this paper, we convert the netlist information into a graph and then model the reference placement as a subgraph matching problem. Since the state-of-the-art subgraph matching methods usually recursively search the solutions and suffer from high time and memory consumption in large-scale designs, we develop a novel subgraph matching algorithm D2BS with diversity tolerance and improved backtracking to guarantee matching quality and efficiency. The D2BS algorithm is founded on a data structure called the candidate space (CS) structure. We build and filter the candidate set for each query node according to our designed features to construct the CS structure. During the CS optimization process, a graph diversity tolerance strategy is adopted to achieve efficient inexact matching. Then, hierarchical matching is developed to search the template embeddings in the CS structure guided by branch backtracking and matched-node snatching strategies. Based on the industrial PCB designs, experimental results show that D2BS outperforms the state-of-the-art subgraph matching method in matching accuracy and running time. [ABSTRACT FROM AUTHOR]

Consider a large labeled graph (network), denoted the target. Subgraph matching is the problem of finding all instances of a small subgraph, denoted the query, in the target graph. Unlike the majority of existing methods that are restricted to graphs with labels solely on vertices, our proposed approach, named can effectively handle graphs with labels on both vertices and edges. ntroduces an efficient new vertex/edge domain data structure filtering procedure to speed up subgraph queries. The procedure, called path-based reduction, filters initial domains by scanning them for paths up to a specified length that appear in the query graph. Additionally, ncorporates existing techniques like variable ordering and parent selection, as well as adapting the core search process, to take advantage of the information within edge domains. Experiments in real scenarios such as protein–protein interaction graphs, co-authorship networks, and email networks, show that s faster than state-of-the-art systems varying the number of distinct vertex labels over the whole target graph and query sizes. [ABSTRACT FROM AUTHOR]

In artificial intelligence problems, connected with the study of complex structured objects which are described in the terms of properties of their elements and relationships between these elements, it is convenient to use predicate calculus formulas, more precisely elementary conjunctions of atomic predicate formulas. In such a case, the problem of extraction common properties of objects arises. The common properties of complex structured objects are set by formulas with variables as arguments, which, up to the names of the arguments, coincide with the subformulas of the objects under study, that is, are isomorphic to these subformulas. Previously, the authors developed algorithms for checking such formulas for isomorphism, as well as for extraction the maximal common subformula of two elementary conjunctions of predicate formulas with a single predicate symbol. Two algorithms, the first of which solves this problem for elementary conjunctions containing two predicate symbols, and the second for an arbitrary number of predicate symbols are proposed in this paper using the last-mentioned algorithm. Estimates of the computational complexity of the presented algorithms are proved. The algorithm is implemented in Python. [ABSTRACT FROM AUTHOR]

In this study, we introduce the Sheffer stroke L-algebra and prove some fundamental theorems, propositions and lemmas of Sheffer Stroke L-algebras. The notions of filter and ultrafilter for Sheffer stroke L-algebra are studied. We give subalgebra and normal subset definitions of a Sheffer stroke L-algebras. Moreover, a homomorphism between Sheffer stroke L-algebras is introduced and isomorphism theorems are presented. Finally, we give three new algorithms for Sheffer stroke L-algebras. Thus, it is contributed to researchers on different application areas by presenting an algorithmic approach on this subject, for the first time in the literature. [ABSTRACT FROM AUTHOR]

In 1981, Gerhard Gierz and Jimmie Lawson gave a necessary condition for a complete lattice to be quasicontinuous using an equation. However, whether quasicontinuous lattices can be characterized by equations has remained unknown. In this paper, we give an equational characterization of quasicontinuous complete semilattices. Furthermore, we investigate congruences of quasicontinuous complete semilattices. We derive the first isomorphism theorem for quasicontinuous complete semilattices in the context of C-congruences. As a consequence, we show that the category of all continuous complete semilattices with maps preserving directed sups and nonempty infs is a reflective full subcategory of quasicontinuous complete semilattices. [ABSTRACT FROM AUTHOR]

Graph pattern matching is widely used in real-world applications, such as social network analysis. Since the traditional subgraph isomorphism is NP-complete and often too restrictive to catch sensible matches, relaxed graph pattern matching models are used. However, existing algorithms suffer from limited linear scalability and restricted degrees of parallelism. In this paper, we propose fast parallel algorithms, GPGS and GPDS, for graph simulation and dual simulation, respectively. They make most use of the GPU performance by adopting the edge-centric processing model. We perform parallel computations on the data graph edges to evaluate the matching constraints for each vertex allowing for fast and scalable algorithms. To the best of our knowledge, we present the first GPU-based algorithms for graph simulation and dual simulation. Extensive experiments on synthetic and real-world data graphs demonstrate that our algorithms significantly outperform existing methods, achieving up to 74.8 × acceleration for GPGS and up to 114.2 × acceleration for GPDS. [ABSTRACT FROM AUTHOR]

Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. We study their group structure for graphs obtained by attaching a cone vertex to a tree. For example, it is shown that the number of generators of the sandpile group is at most one less than the number of leaves in the tree. For trees on a fixed number of vertices, the paths and stars are shown to provide extreme behavior, not only for the number of generators, but also for the number of spanning trees, and for Tutte polynomial evaluations that count the recurrent sandpile configurations by their numbers of chips. [ABSTRACT FROM AUTHOR]

The article titled "Congruence-Simple Acts Over Completely Simple Semigroups" explores the characterization of simple and congruence-simple acts over a completely simple semigroup. The authors provide definitions and explanations of terms used in semigroup theory and act theory, and pay tribute to mathematician Aleksandr Vasilievich Mikhalev in the introduction. The text discusses congruences and associated subgroups, introducing lemmas and theorems to establish the relationship between congruences and subgroups. It also explores the properties of congruence-simple acts and provides a classification for different types of congruence-simple acts, with the goal of finding the maximal proper congruences of a given act. The authors declare no conflict of interest and acknowledge financial support for their research. [Extracted from the article]

In this paper, we investigate various elegant filters and congruences of the class of core regular double Stone algebras (briefly CRD-Stone algebras). We define and characterize the concepts of k-filters and principal k-filters of a core regular double Stone algebra with the core element k, as well as their algebraic structures. We also look at k- { ∗ } -congruences and principal k- { ∗ } -congruences of a CRD-Stone algebra L that are induced by k-filters and principal k-filters of L, respectively. We find an isomorphism between the lattice F k (L) of all k-filters of L (the lattice F k p (L) principal k-filters of L) and the lattice C o n k ∗ (L) of all k- { ∗ } -congruences on L (the lattice C o n k ∗ (L) of all principal k- { ∗ } -congruences) of a CRD-Stone algebra L. [ABSTRACT FROM AUTHOR]

The order type of a point set in R d maps each (d + 1) -tuple of points to its orientation (e.g., clockwise or counterclockwise in R 2 ). Two point sets X and Y have the same order type if there exists a bijection f from X to Y for which every (d + 1) -tuple (a 1 , a 2 , ... , a d + 1) of X and the corresponding tuple (f (a 1) , f (a 2) , ... , f (a d + 1)) in Y have the same orientation. In this paper we investigate the complexity of determining whether two point sets have the same order type. We provide an O (n d) algorithm for this task, thereby improving upon the O (n ⌊ 3 d / 2 ⌋) algorithm of Goodman and Pollack (SIAM J. Comput. 12(3):484–507, 1983). The algorithm uses only order type queries and also works for abstract order types (or acyclic oriented matroids). Our algorithm is optimal, both in the abstract setting and for realizable points sets if the algorithm only uses order type queries. [ABSTRACT FROM AUTHOR]

Let be a group, let be an isomorphism of onto a subgroup of , and let be a descending HNN-extension of corresponding to . The potency of is not inherited by even in the simplest case, when is an infinite cyclic group. We prove that if is a finitely generated torsion-free nilpotent group (a polycyclic group); then the index of in is finite and is -potent (virtually -potent), where is the set of all primes greater than . We also prove some generalizations of this assertion. Some of the results of this work on the potency of descending HNN-extensions are analogs of the well-known theorems on the residual finiteness of the HNN-extensions. [ABSTRACT FROM AUTHOR]

Due to the small size of uranium minerals, the occupations of U4+ and U6+, Th and Pb in uraninite is little studied. The coarse giant uraninite (CGU) from Miyi with size up to 1 cm is one of the best samples for studying uraninite mineralogical property. CGU mainly composed of UO2, ThO2, PbO, CaO. There are three forms of occurrence of U, namely UO2, UO3, and UO2+x; and impurity such as ThO2, PbO, CaO may entering the mineral lattice, which can affect mineral properties and facilitate the chemical reactions during mineralization and leaching processes. [ABSTRACT FROM AUTHOR]

We study zero-cycles in families of rationally connected varieties. We show that for a smooth projective scheme over a henselian discrete valuation ring the restriction of relative zero cycles to the special fiber induces an isomorphism on Chow groups if the special fiber is separably rationally connected. We further extend this result to certain higher Chow groups and develop conjectures in the non-smooth case. Our main results generalise a result of Kollár (Publ. Res. Inst. Math. Sci. 40(3):689–708, 2004). [ABSTRACT FROM AUTHOR]

Prior researches have highlighted challenges and variations arising from the requirements of research ethics committees and ethics governance systems across diverse research fields. This emphasizes the need to investigate how universities convey and implement research ethical practices. Research ethics plays a pivotal role in guiding the integration of ethical principles throughout all stages of research starting from its inception and planning to its completion and the dissemination of results. These practices encompass a range of considerations, reviews, guidelines, and processes aimed at safeguarding the rights, dignity, health, safety, and privacy of research participants. Using the content analysis technique, this paper aims to analyse research ethical practices information on universities' websites from three developed countries and developing countries respectively using the isomorphism conception. The findings suggest that the coercive, normative, and mimetic isomorphic pressures explain the research ethics governance practices. The ethical practices information was disclosed more on university websites of the developed countries. Suggestions to improve the university's research ethics governance system for the post-COVID-19 era were provided in the paper. [ABSTRACT FROM AUTHOR]

Let G be a connected graph with adjacency matrix A(G) and distance matrix D(G). Let dist (u , v) denote the distance between the pair of vertices u , v ∈ V (G) , then the transmission trs (u) of vertex u is defined as ∑ v ∈ V (G) dist (u , v) . Let trs (G) be the diagonal matrix whose diagonal elements are the transmissions of the vertices of G. And, let deg (G) be the diagonal matrix whose diagonal elements are the degrees of the vertices of G. In this paper we investigate the Smith normal form (SNF) and the spectrum of the matrices D + deg (G) : = deg (G) + D (G) , D deg (G) : = deg (G) - D (G) , A + trs (G) : = trs (G) + A (G) and A trs (G) : = trs (G) - A (G) . In particular, we explore how good the SNF and the spectrum of these matrices are for determining graphs up to isomorphism. We found that the SNF of A trs has an interesting behaviour when compared with other classical matrices. We note that the SNF of A trs can be used to compute the structure of the sandpile group of certain graphs. We compute the SNF of D + deg , D deg , A + trs and A trs for several graph families. We prove that the SNF of D + deg , D deg , A + trs and A trs determine complete graphs. Finally, we derive some results about the spectrum of D deg and A trs . [ABSTRACT FROM AUTHOR]

We classify all 2-term L ∞ -algebras up to isomorphism. We show that such L ∞ -algebras are classified by a Lie algebra, a vector space, a representation (all up to isomorphism) and a cohomology class of the corresponding Lie algebra cohomology. [ABSTRACT FROM AUTHOR]

Most of the bilingual lexicon induction (BLI) models learn a mapping function that can transfer word embedding (WE) spaces from one language to another. This usually relies on the isomorphism hypothesis, which posits that words in different languages share the same structures and relationships (i.e. similar in geometric structure). However, WE's isomorphism weakens substantially in distant language pairs, resulting in low accuracy of BLI. To address this problem, we propose a novel BLI method incorporating synonymous knowledge. The main idea is to stabilize the distance between words to optimize the monolingual WE space, yielding higher isomorphism. Specifically, we first induce monolingual synonym pairs from Wordnet and construct monolingual synonym lexicons. We then generate pseudo-sentences by substituting words in the training corpus with synonyms. Finally, the original sentences and pseudo-sentences are jointly used to generate monolingual WEs, enabling the word vectors of synonyms to be closer naturally. Comprehensive experiments on standard BLI datasets in diverse distant languages demonstrate that our method significantly outperforms the strong BLI systems in word translation. [ABSTRACT FROM AUTHOR]

Exact subgraph matching is fundamental to numerous graph data applications. The inherent NP-completeness of subgraph isomorphism poses significant challenges in developing efficient matching algorithms. Current methods show limited success, particularly in their filtering and verification stages. Selecting an optimal vertex-searching order can greatly improve a subgraph searching algorithm's effectiveness, yet a comprehensive theory for this selection is lacking. In this paper, we introduce the Multistage Graph Search Model (MGSM), a novel approach addressing this gap. MGSM provides insights for identifying the most efficient vertex-searching order and offers a systematic framework for evaluating existing algorithms. Using MGSM, we identify two main challenges in optimizing the search order and present a new matching algorithm "Tps" noted for its strategic vertex-searching order. Extensive experiments demonstrate the superior performance of Tps and its effectiveness and soundness in optimizing search orders. [ABSTRACT FROM AUTHOR]

In recent years, there has been a significant amount of work conducted in the field of Lattice Basis Reduction Techniques, which is one of the crucial areas of Lattice-based Cryptography. This field finds applications in the cryptanalysis of important problems, including SIS, LWE, the Lattice Isomorphism Problem, and more. Another critical role of Lattice reduction is in determining key sizes for various cryptosystems based on Lattices. Therefore, the study and development of Lattice basis reduction techniques are closely tied to the assessment of the Quantum resistance nature of Lattice-based Cryptosystems, making it valuable to investigate Lattice Reduction Techniques. Furthermore, when combined with other techniques, Lattice Reduction Techniques can yield excellent results. In this paper, we delve into various essential Lattice Reduction Techniques, such as LLL, BKZ, Generalized basis reduction in dimension 3, along with their improvements like DeepLLL, DeepBKZ, Self-dual DeepBKZ. We also explore other important techniques, including Hybrid Method, Cubification, LDSF, and recent developments. Additionally, we provide discussions on their comparisons, complexities, and improvements. [ABSTRACT FROM AUTHOR]

Impurity defects in sodium–gadolinium molybdate NaGd(MoO4)2 have been investigated by the method of interatomic potentials. The solution energies of tri-, di-, and monovalent impurities are estimated. The dependences of the solution energy on the impurity ionic radius are plotted. For heterovalent substitutions, the most energetically favorable mechanism of charge compensation is found, both due to intrinsic crystal defects and according to the conjugate isomorphism scheme. The positions of the most likely localization of defects are determined. The influence of the disordering of sodium and gadolinium ions on the positional differences in the energy of defects is estimated. A comparison of the solubility of impurities in NaGd(MoO4)2 and CaMoO4 (a compound isostructural to it) indicates that, although isovalent substitutions are energetically more favorable than heterovalent ones, the mechanism of conjugate isomorphism (providings electrical neutrality) can equalize these processes. [ABSTRACT FROM AUTHOR]

This paper introduces the concept of hesitant bipolar-valued fuzzy graph (HBVFG), which captures the two opposing perspectives, namely the positive and negative opinions. The novelty, importance and implications of this concept are illustrated by some results, examples, and graphical representations. There are, respectively, some theoretical terms of graphs such as partial directed hesitant bipolar-valued fuzzy subgraph (HBVFSG), directed HBVFSG, directed spanning HBVFSG, strong directed HBVFG and complete directed HBVFG which are introduced. The operations, such as Cartesian, direct, lexicographical, and strong products, are also defined between two HBVFGs with examples. The mapping relations, such as homomorphism, isomorphism, weak isomorphism, and co-weak isomorphism, are derived with an example. The applications of directed HBVFGs with algorithms for finding the optimal path in a network and the dominant node and influence of index with the self-persistence degree of a node in a social network are presented. For each problem, an algorithm is developed and its effectiveness is demonstrated by examples. The proposed concept is assessed in terms of theory and practice. The benefits of the proposed solution are highlighted and a clear comparison is made with the existing methods. [ABSTRACT FROM AUTHOR]

Impurity defects in sodium–gadolinium molybdate NaGd(MoO4)2 have been investigated by the method of interatomic potentials. The solution energies of tri-, di-, and monovalent impurities are estimated. The dependences of the solution energy on the impurity ionic radius are plotted. For heterovalent substitutions, the most energetically favorable mechanism of charge compensation is found, both due to intrinsic crystal defects and according to the conjugate isomorphism scheme. The positions of the most likely localization of defects are determined. The influence of the disordering of sodium and gadolinium ions on the positional differences in the energy of defects is estimated. A comparison of the solubility of impurities in NaGd(MoO4)2 and CaMoO4 (a compound isostructural to it) indicates that, although isovalent substitutions are energetically more favorable than heterovalent ones, the mechanism of conjugate isomorphism (providings electrical neutrality) can equalize these processes. [ABSTRACT FROM AUTHOR]

The Boolean map χ n : F 2 n → F 2 n , x ↦ y defined by y i = x i + (x i + 1 + 1) x i + 2 (where i ∈ Z / n Z ) is used in various permutations that are part of cryptographic schemes, e.g., Keccak-f (the SHA-3-permutation), ASCON (the winner of the NIST Lightweight competition), Xoodoo, Rasta and Subterranean (2.0). In this paper, we study various algebraic properties of this map. We consider χ n (through vectorial isomorphism) as a univariate polynomial. We show that it is a power function if and only if n = 1 , 3 . We furthermore compute bounds on the sparsity and degree of these univariate polynomials, and the number of different univariate representations. Secondly, we compute the number of monomials of given degree in the inverse of χ n (if it exists). This number coincides with binomial coefficients. Lastly, we consider χ n as a polynomial map, to study whether the same rule ( y i = x i + (x i + 1 + 1) x i + 2 ) gives a bijection on field extensions of F 2 . We show that this is not the case for extensions whose degree is divisible by two or three. Based on these results, we conjecture that this rule does not give a bijection on any extension field of F 2 . [ABSTRACT FROM AUTHOR]

We relate the Fukaya category of the symmetric power of a genus zero surface to deformed category O of a cyclic hypertoric variety by establishing an isomorphism between algebras defined by Ozsváth–Szabó in Heegaard–Floer theory and Braden–Licata–Proudfoot–Webster in hypertoric geometry. The proof extends work of Karp–Williams on sign variation and the combinatorics of the m = 1 amplituhedron. We then use the algebras associated to cyclic arrangements to construct categorical actions of gl (1 | 1) , and generalize our isomorphism to give a conjectural algebraic description of the Fukaya category of a complexified hyperplane complement. [ABSTRACT FROM AUTHOR]

Cominuscule flag varieties generalize Grassmannians to other Lie types. Schubert varieties in cominuscule flag varieties are indexed by posets of roots labeled long/short. These labeled posets generalize Young diagrams. We prove that Schubert varieties in potentially different cominuscule flag varieties are isomorphic as varieties if and only if their corresponding labeled posets are isomorphic, generalizing the classification of Grassmannian Schubert varieties using Young diagrams by the last two authors. Our proof is type-independent. [ABSTRACT FROM AUTHOR]

A cohesive power of a structure is an effective analog of the classical ultrapower of a structure. We start with a computable structure, and consider its effective power over a cohesive set of natural numbers. A cohesive set is an infinite set of natural numbers that is indecomposable with respect to computably enumerable sets. It plays the role of an ultrafilter, and the elements of a cohesive power are the equivalence classes of certain partial computable functions determined by the cohesive set. Thus, unlike many classical ultrapowers, a cohesive power is a countable structure. In this paper we focus on cohesive powers of graphs, equivalence structures, and computable structures with a single unary function satisfying various properties, which can also be viewed as directed graphs. For these computable structures, we investigate the isomorphism types of their cohesive powers, as well as the properties of cohesive powers when they are not isomorphic to the original structure. [ABSTRACT FROM AUTHOR]

In this paper we study essential hereditary undecidability. Theories with this property are a convenient tool to prove undecidability of other theories. The paper develops the basic facts concerning essentially hereditary undecidability and provides salient examples, like a construction of essentially hereditarily undecidable theories due to Hanf and an example of a rather natural essentially hereditarily undecidable theory strictly below R. We discuss the (non-)interaction of essential hereditary undecidability with recursive boolean isomorphism. We develop a reduction relation essential tolerance, or, in the converse direction, lax interpretability that interacts in a good way with essential hereditary undecidability. We introduce the class of Σ 1 0 -friendly theories and show that Σ 1 0 -friendliness is sufficient but not necessary for essential hereditary undecidability. Finally, we adapt an argument due to Pakhomov, Murwanashyaka and Visser to show that there is no interpretability minimal essentially hereditarily undecidable theory. [ABSTRACT FROM AUTHOR]

Starting from the problem of d-tensor isomorphism (d- TI ), we study the relation between various code equivalence problems in different metrics. In particular, we show a reduction from the sum-rank metric ( CE sr ) to the rank metric ( CE rk ). To obtain this result, we investigate reductions between tensor problems. We define the monomial isomorphism problem for d-tensors (d- TI ∗ ), where, given two d-tensors, we ask if there are d - 1 invertible matrices and a monomial matrix sending one tensor into the other. We link this problem to the well-studied d- TI and the TI -completeness of d- TI ∗ is shown. Due to this result, we obtain a reduction from CE sr to CE rk . In the literature, a similar result was known, but it needs an additional assumption on the automorphisms of matrix codes. Since many constructions based on the hardness of Code Equivalence problems are emerging in cryptography, we analyze how such reductions can be taken into account in the design of cryptosystems based on CE sr . [ABSTRACT FROM AUTHOR]

Stable laser resonators support three fundamental families of transverse modes: the Hermite, Laguerre, and Ince Gaussian modes. These modes are crucial for understanding complex resonators, beam propagation, and structured light. We experimentally observe a new family of fundamental laser modes in stable resonators: Boyer-Wolf Gaussian modes. By studying the isomorphism between laser cavities and quadratic Hamiltonians, we design a laser resonator equivalent to a quantum two-dimensional anisotropic harmonic oscillator with a 2:1 frequency ratio. The generated Boyer-Wolf Gaussian modes exhibit a parabolic structure and show remarkable agreement with our theoretical predictions. These modes are also eigenmodes of a 2:1 anisotropic gradient refractive index medium, suggesting their presence in any physical system with a 2:1 anisotropic quadratic potential. We identify a transition connecting Boyer-Wolf Gaussian modes to Weber nondiffractive parabolic beams. These new modes are foundational for structured light, and open exciting possibilities for applications in laser micromachining, particle micromanipulation, and optical communications. Lasers drive modern research and technology. The modes of laser resonators are crucial for understanding complex cavities, beam propagation, and structured light. Here, the authors experimentally observe a new family of fundamental laser modes with inherent parabolic symmetry: the Boyer-Wolf Gaussian modes. [ABSTRACT FROM AUTHOR]

In this work, we study the problem of partitioning a set of graphs into different groups such that the graphs in the same group are similar while the graphs in different groups are dissimilar. This problem was rarely studied previously, although there has been a lot of work on node clustering and graph classification. The problem is challenging because it is difficult to measure the similarity or distance between graphs. One feasible approach is using graph kernels to compute a similarity matrix for the graphs and then performing spectral clustering, but the effectiveness of existing graph kernels in measuring the similarity between graphs is very limited. To solve the problem, we propose a novel method called Deep Graph-Level Clustering (DGLC). DGLC utilizes a graph isomorphism network to learn graph-level representations by maximizing the mutual information between the representations of entire graphs and sub-structures, under the regularization of a clustering module that ensures discriminative representations via pseudo-labels. DGLC achieves graph-level representation learning and graph-level clustering in an end-to-end manner. The experimental results on six benchmark datasets of graphs show that our DGLC has state-of-the-art performance in comparison to many baselines. [ABSTRACT FROM AUTHOR]

This paper presents the conditions under which a coded digital communication system's performance may be improved using better signal sets design matched to groups. This improvement is directly related to the determination of the uniformization region of a hyperelliptic curve by using a Fuchsian differential equation and, consequently, the determination of the Fuchsian group and subgroup generators. The hyperelliptic curves of interest are given by y 2 = z n ± 1 , where n ∈ I N and n = 2 g + 1 or n = 2 g + 2 , and satisfy the following conditions: all the roots are distinct, they are symmetrically arranged (regular polygon) in the Poincaré disk, the juxtaposition of two such polygons gives the uniformization region. These conditions imply that the uniformization regions are regular polygons and that the associate Fuchsian group leads to regular tessellations from which arithmetic Fuchsian groups may be found. This work aims to answer and establish the conditions for the following questions: Can Fuchsian subgroups corresponding to two distinct hyperelliptic curves with the same degree and genus be isomorphic in D 2 as well as in H 2 ? What are the conditions under which an isometry acting on isomorphic Fuchsian subgroups in D 2 remain isomorphic in H 2 ? To show the isomorphism, we use the concept of conjugation. The first question's positive response is achieved for hyperelliptic curves given by y 2 = z n ± 1 . Finally, from the results established in D 2 and H 2 , if the Fuchsian subgroups are isomorphic by conjugation in D 2 , they remain isomorphic in H 2 by the action of an appropriate isometry as established in Theorem 3 and its generalization in Theorem 4. [ABSTRACT FROM AUTHOR]

In this paper, we establish a novel category of sequence spaces ℓ p q λ and ℓ ∞ q λ by utlizing q-analogue Λ q of Λ-matrix. Our investigation outlines several topological characteristics and inclusion results of these newly introduced sequence spaces, specifically identifying them as BK-spaces. Subsequently, we demonstrate that these novel sequence spaces are of nonabsolute type and establish their isometric isomorphism with ℓ p and ℓ ∞ . Moreover, we obtain the α-, β-, and γ-duals of these sequence spaces. We further characterize the class (ℓ p q λ , X) of matrices, where X is any of the spaces ℓ ∞ , c, or c 0 . Lastly, our study delves into the exploration of specific geometric properties exhibited by the space ℓ p q λ . [ABSTRACT FROM AUTHOR]

Recently, visual question answering (VQA) has gained considerable interest within the computer vision and natural language processing (NLP) research areas. The VQA task involves answering a question about an image, which requires both language and vision understanding. Effectively extracting visual representations from images, textual embedding from questions, and bridging the semantic disparity between image and question representations pose fundamental challenges in VQA. Lately, an increasing number of studies are focusing on utilizing graph neural networks (GNNs) to enhance the performance of VQA tasks. The ability to handle graph-structured data is a major advantage of GNNs for VQA tasks, which allows better representation of relationships between objects and regions in an image. These relationships include both spatial and semantic relationships. This paper systematically reviews various graph neural networks based studies for image-based VQA. Fifty-four related publications written between 2018—Jan. 2023 were carefully synthesized for this review. The review is structured into three perspectives: the various graph neural network techniques and models that have been applied for VQA, a comparison of the model's performance and existing challenges. After analyzing these papers, 45 different models were identified, grouped into four different GNN techniques. These are Graph Convolution Network (GCN), Graph Attention Network (GAT), Graph Isomorphism Network (GIN) and Graph Neural Network (GNN). Also, the performance of these models is compared based on accuracy, datasets, subtasks, feature representation and fusion techniques. Lastly, the study provided some possible suggestions to mitigate still existing challenges for future research in visual question answering. [ABSTRACT FROM AUTHOR]

The equivalence of the Haar system in a rearrangement invariant space on and a sequence of pairwise disjoint functions in some Lorentz space is known to imply that up to the equivalence of norms. We show that the same holds for the class of uniform disjointly homogeneous rearrangement invariant spaces and obtain a few consequences for the properties of isomorphic embeddings of such spaces. In particular, the space with is the only uniform -disjointly homogeneous rearrangement invariant space on with nontrivial Boyd indices which has two rearrangement invariant representations on the half-axis . [ABSTRACT FROM AUTHOR]

Inspired by locale theory, pointfree convex geometry was first proposed and studied by Yoshihiro Maruyama. In this paper, we shall continue to his work and investigate the related topics on pointfree convex spaces. Concretely, the following results are obtained: (1) A Hofmann–Lawson-like duality for pointfree convex spaces is established. (2) The M -injective objects in the category of S 0 -convex spaces are proved precisely to be sober convex spaces, where M is the class of strict maps of convex spaces; (3) A convex space X is sober iff there never exists a nontrivial identical embedding i : X ↪ Y such that its dualization is an isomorphism, and a convex space X is S D iff there never exists a nontrivial identical embedding k : Y ↪ X such that its dualization is an isomorphism. (4) A dual adjunction between the category CLat D of continuous lattices with continuous D-homomorphisms and the category CS D of S D -convex spaces with CP-maps is constructed, which can further induce a dual equivalence between CS D and a subcategory of CLat D ; (5) The relationship between the quotients of a continuous lattice L and the convex subspaces of cpt (L) is investigated and the collection Alg (Q (L)) of all algebraic quotients of L is proved to be an algebraic join-sub-complete lattice of Q (L) of all quotients of L, where cpt (L) denote the set of non-bottom compact elements of L. Furthermore, it is shown that Alg (Q (L)) is isomorphic to the collection Sob (P (cpt (L))) of all sober convex subspaces of cpt (L) ; (6) Several necessary and sufficient conditions for all convex subspaces of cpt (L) to be sober are presented. [ABSTRACT FROM AUTHOR]

Based on dynamic monitoring data on China's population, by using complex networks, spatial analysis and mathematical measurement, this study reveals the spatial characteristics and influencing factors of the network of flows of highly educated talents in the Yangtze River Delta region from the national and local perspectives. In the two perspectives, the network has strong isomorphism and certain differences. The in-flow of highly educated talents from cities with high administrative levels and more developed economies to Shanghai constitutes the core of the entire network. From a national perspective, highly educated talents tend to converge to the Yangtze River Delta region. From a local perspective, it was found that these talents cluster towards a limited number of cities in the region. From both perspectives, the flow network has developed into a "core-periphery" progressive hierarchical structure, with Shanghai becoming the sole core city. There is little difference in the influencing factors of talent mobility from both macro and meso perspectives. Highly educated talents would frequently flow between cities with strong economic development levels, and cities with high education level, scientific and technological level, complete infrastructure, and good aesthetics. However, geographical distance still plays a hindering role in the flow of highly educated talents, and factors such as cultural identity, institutional, and social modality differences among regions also have a certain effect on the flow of these talents. [ABSTRACT FROM AUTHOR]

Let Γ = PSL 2 (O) be a Bianchi group associated to one of the five Euclidean imaginary quadratic fields. We show that the space of weight k period polynomials for Γ is "dual" to the space of weight k modular symbols for Γ , reflecting the duality between the first and second cohomology groups of the arithmetic group Γ . Using this result, we describe the action of Hecke operators on the space of period polynomials for Γ via the Heilbronn matrices. As in the classical case, spaces of Bianchi period polynomials are related to parabolic cohomology of Bianchi groups, and in turn, via the Eichler–Shimura–Harder Isomorphism, to spaces of Bianchi modular forms. In the second part of the paper, we numerically investigate congruences between level 1 Bianchi eigenforms via computer programs which implement the above mentioned Hecke action on spaces of Bianchi period polynomials. Computations with the Hecke action are used to indicate moduli of congruences between the underlying Bianchi forms; we then prove the congruences using the period polynomials. From this we find congruences between genuine Bianchi modular forms and both a base-change Bianchi form and an Eisenstein series. We believe these congruences are the first of their kind in the literature. [ABSTRACT FROM AUTHOR]

In this paper we investigate locally free representations of a quiver Q over a commutative Frobenius algebra R by arithmetic Fourier transform. When the base field is finite we prove that the number of isomorphism classes of absolutely indecomposable locally free representations of fixed rank is independent of the orientation of Q. We also prove that the number of isomorphism classes of locally free absolutely indecomposable representations of the preprojective algebra of Q over R equals the number of isomorphism classes of locally free absolutely indecomposable representations of Q over R [ t ] / (t 2) . Using these results together with results of Geiss, Leclerc and Schröer we give, when k is algebraically closed, a classification of pairs (Q , R) such that the set of isomorphism classes of indecomposable locally free representations of Q over R is finite. Finally when the representation is free of rank 1 at each vertex of Q, we study the function that counts the number of isomorphism classes of absolutely indecomposable locally free representations of Q over the Frobenius algebra F q [ t ] / (t r) . We prove that they are polynomial in q and their generating function is rational and satisfies a functional equation. [ABSTRACT FROM AUTHOR]

This is the first of two papers dedicated to the detailed determination of the reduced C*-algebra of a connected, linear, real reductive group up to Morita equivalence, and a new and very explicit proof of the Connes–Kasparov conjecture for these groups using representation theory. In this part we shall give details of the C*-algebraic Morita equivalence and then explain how the Connes–Kasparov morphism in operator K-theory may be computed using what we call the Matching Theorem, which is a purely representation-theoretic result. We shall prove our Matching Theorem in the sequel, and indeed go further by giving a simple, direct construction of the components of the tempered dual that have non-trivial K-theory using David Vogan's approach to the classification of the tempered dual. [ABSTRACT FROM AUTHOR]

Mixing properties of solid solutions of the post-spinel phases with a composition of CaCr2O4–CaAl2O4, CaCr2O4–CaFe2O4, MgCr2O4–MgAl2O4, and MgCr2O4–MgFe2O4 in the temperature range of 1873–2223 K and at a pressure of 18–25 GPa were studied by the semi-empirical modeling. These PT parameters were used to estimate a formation energy of impurity defects of trivalent metal ions (aluminum and iron) in isomorphic sites. The study results: (1) the studied binary solid solutions are characterized by a complete miscibility; (2) the incorporation of Fe3+ impurity ion into the post-spinel phases of MgCr2O4 and CaCr2O4 is less favorable in terms of energy than that of Al3+ ions over the entire pressure and temperature range under study. The results obtained were used to interpret compositions of the post-spinel phases forming inclusions in lower mantle diamonds. [ABSTRACT FROM AUTHOR]

Two semigroups are lattice isomorphic if their subsemigroup lattices are isomorphic, and a class of semigroups is lattice closed if it contains every semigroup which is lattice isomorphic to some semigroup from that class. An orthodox semigroup is a regular semigroup whose idempotents form a subsemigroup. We prove that the class of all orthodox semigroups having no nontrivial finite subgroups is lattice closed. [ABSTRACT FROM AUTHOR]

The Lattice Isomorphism Problem (LIP) is the computational task of recovering, assuming it exists, an orthogonal linear transformation sending one lattice to another. For cryptographic purposes, the case of the trivial lattice Z n is of particular interest (Z LIP). Heuristic analysis suggests that the BKZ algorithm with blocksize β = n / 2 + o (n) solves such instances (Ducas, Postlethwaite, Pulles, van Woerden, ASIACRYPT 2022). In this work, I propose a provable version of this statement, namely, that Z LIP can indeed be solved by making polynomially many calls to a Shortest Vector Problem oracle in dimension at most n / 2 + 1 . [ABSTRACT FROM AUTHOR]

We prove that if two germs of plane curves (C, 0) and (C ′ , 0) with at least one singular branch are equivalent by a (real) smooth diffeomorphism, then C is complex isomorphic to C ′ or to C ′ ¯ . A similar result was shown by Ephraim for irreducible hypersurfaces before, but his proof is not constructive. Indeed, we show that the complex isomorphism is given by the Taylor series of the diffeomorphism. We also prove an analogous result for the case of non-irreducible hypersurfaces containing an irreducible component that is non-factorable. Moreover, we provide a general overview of the different classifications of plane curve singularities. [ABSTRACT FROM AUTHOR]

Given a lattice L in the plane, we define the affiliated deep hole lattice H(L) to be spanned by a shortest vector of L and a deep hole of L contained in the triangle with sides corresponding to the shortest basis vectors. We study the geometric and arithmetic properties of deep hole lattices. In particular we investigate conditions on L under which H(L) is well-rounded and prove that H(L) is defined over the same field as L. For the period lattice corresponding to an isomorphism class of elliptic curves, we produce a finite sequence of deep hole lattices ending with a well-rounded lattice which corresponds to a point on the boundary arc of the fundamental strip under the action of SL 2 (Z) on the upper halfplane. In the case of CM elliptic curves, we prove that all elliptic curves generated by this sequence are isogenous to each other and produce bounds on the degree of isogeny. Finally, we produce a counting estimate for the planar lattices with a prescribed deep hole lattice. [ABSTRACT FROM AUTHOR]

We consider the Lambek invariants in the context of semiexact and homological categories in the sense of Grandis. We generalize the Lambek isomorphism theorem to semiexact and homological categories. [ABSTRACT FROM AUTHOR]

We describe spaces that are dual to some subspaces of the space C∞(D) relative to the inductive limits, where inductive limits, where D ⊂ R p is a bounded convex domain. For any logarithmically convex space of positive numbers M = M k , k ∈ Z + p we introduce the normed space C D , M of functions f ∈ C ∞ D and prove that the Fourier-Laplace transform establishes a topological isomorphism between the strongly dual space and the projective limit of the normed spaces. [ABSTRACT FROM AUTHOR]