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We extend a result on existence of Walrasian equilibria in He and Yannelis (Econ Theory 61:497–513, 2016) by replacing the compactness assumption on consumption sets made there by the standard assumption that these sets are closed and bounded from below. This provides a positive answer to a question explicitly raised in He and Yannelis (Econ Theory 61:497–513, 2016). Our new equilibrium existence theorem generalizes many results in the literature as we do not require any transitivity or completeness or continuity assumption on preferences, initial endowments need not be in the interior of the consumption sets, preferences may be interdependent and price-dependent, and no monotonicity or local non satiation is needed for any of the agents.

We study substitutive systems generated by nonprimitive substitutions and show that transitive subsystems of substitutive systems are substitutive. As an application we obtain a complete characterisation of the sets of words that can appear as common factors of two automatic sequences defined over multiplicatively independent bases. This generalises the famous theorem of Cobham.

The concept of a Sheffer operation known for Boolean algebras and orthomodular lattices is extended to arbitrary directed relational systems with involution. It is proved that to every such relational system, there can be assigned a Sheffer groupoid and also, conversely, every Sheffer groupoid induces a directed relational system with involution. Hence, investigations of these relational systems can be transformed to the treatment of special groupoids which form a variety of algebras. If the Sheffer operation is also commutative, then the induced binary relation is antisymmetric. Moreover, commutative Sheffer groupoids form a congruence distributive variety. We characterize symmetry, antisymmetry and transitivity of binary relations by identities and quasi-identities satisfied by an assigned Sheffer operation. The concepts of twist products of relational systems and of Kleene relational systems are introduced. We prove that every directed relational system can be embedded into a directed relational system with involution via the twist product construction. If the relation in question is even transitive, then the directed relational system can be embedded into a Kleene relational system. Any Sheffer operation assigned to a directed relational system $${\mathbf {A}}$$ A with involution induces a Sheffer operation assigned to the twist product of $${\mathbf {A}}$$ A .

In this paper, we first prove that the connected cubic edge-transitive bi-Cayley graphs over a generalized dihedral group have girth 6. Using this, a complete classification is given of these graphs.

This paper is a comparative study of the covert attitudinal meaning implicated in the transitivity system of Hanban’s and British Council’s 2017 annual reports. The dominant domain of inquiry is restricted to a comparison of entities that function as Agent and verbs that serve as Process in the clause. The analysis reveals that in organizational discourse material process is the primary subcategory of the transitivity system that invokes positive evaluation from putative readers and enacts self-identity and relations to the material world. Hanban constructs itself as an initiative and active participant in the global cultural events by adopting more processes that stress the ‘physical’ change it brings to the ecosocial world; however, the British Council portrays itself as an indispensable and significant contributor to the transformative shift of the world by deploying more processes that stress the ‘chemical’ change it makes to the ecosocial world. This study corroborates that material process verbs are scaled on a cline of invocation. Even the most seemingly ‘factual’ descriptive verb can invoke positive or negative evaluation of the appraised target in specific contexts. Moreover, the study cautions us against cultural stereotypes and biases towards discourse which is more conservative and constrained in terms of evaluative explicitness.

In this article, we investigate $2$-$(v,k,\lambda)$ designs with $\gcd(r,\lambda)=1$ admitting flag-transitive automorphism groups $G$. We prove that if $G$ is an almost simple group, then such a design belongs to one of the seven infinite families of $2$-designs or it is one of the eleven well-known examples. We describe all these examples of designs. We, in particular, prove that if $\mathcal{D}$ is a symmetric $(v,k,\lambda)$ design with $\gcd(k,\lambda)=1$ admitting a flag-transitive automorphism group $G$, then either $G\leq A\Gamma L_{1}(q)$ for some odd prime power $q$, or $\mathcal{D}$ is a projective space or the unique Hadamard design with parameters $(11,5,2)$., Comment: arXiv admin note: text overlap with arXiv:1904.10518

Let X be a C1+ vector field on a compact Riemannian manifold M with dimension d ≥ 3. Let Λ be a transitive singular hypebolic set with positive volume. We show that Λ = M and Λ is a uniformly hyperbolic set without singularities.

Some find it plausible that a sufficiently long duration of torture is worse than any duration of mild headaches. Similarly, it has been claimed that a million humans living great lives is better than any number of worm-like creatures feeling a few seconds of pleasure each. Some have related bad things to good things along the same lines. For example, one may hold that a future in which a sufficient number of beings experience a lifetime of torture is bad, regardless of what else that future contains, while minor bad things, such as slight unpleasantness, can always be counterbalanced by enough good things. Among the most common objections to such ideas are sequence arguments. But sequence arguments are usually formulated in classical logic. One might therefore wonder if they work if we instead adopt many-valued logic. I show that, in a common many-valued logical framework, the answer depends on which versions of transitivity are used as premises. We get valid sequence arguments if we grant any of several strong forms of transitivity of ‘is at least as bad as’ and a notion of completeness. Other, weaker forms of transitivity lead to invalid sequence arguments. The plausibility of the premises is largely set aside here, but I tentatively note that almost all of the forms of transitivity that lead to valid sequence arguments seem intuitively problematic. Still, a few moderately strong forms of transitivity that might be acceptable lead to valid sequence arguments, although weaker statements of the initial value claims avoid these arguments at least to some extent.

We present a number of alternative ways of handling transitive binary relations that commonly occur in first-order problems, in particular equivalence relations, total orders, and transitive relations in general. We show how such relations can be discovered syntactically in an input theory, and how they can be expressed in alternative ways. We experimentally evaluate different such ways on problems from the TPTP, using resolution-based reasoning tools as well as instance-based tools. Our conclusions are that (1) it is beneficial to consider different treatments of binary relations as a user, and that (2) reasoning tools could benefit from using a preprocessor or even built-in support for certain types of binary relations.

Enabling constraints are bottom up causes which create the possibility of the existence of a system. Disabling constraints reduce the degrees of freedom and narrow the choices of the system which are structural, functional, meaningful relations that assign executive roles to the component parts. In this paper, we discuss causality as enabling and disabling constraints in order to critique the absurdity of transitivity in causal relations. If downward causation is viewed as causation by constraints, we argue that it will not face the absurdity of self-causation which is incurred because of the transitivity principle. In the process of self-organization, organizationally new structures are created from the lower level subcomponents of the system. Such self-organizing systems can be broadly considered as sui-generis and transcend the transitivity principle by causally influencing its subcomponents. These higher level systemic constraints that causally influence the components in a self-organizing system without violating any physical laws via causal constraints are termed as Downward Causation.

The main result of this paper is that, if Γ is a finite connected 4-valent vertex- and edge-transitive graph, then either Γ is part of a well-understood family of graphs, or every non-identity automorphism of Γ fixes at most 1/3 of the vertices. As a corollary, we get a similar result for 3-valent vertex-transitive graphs.

Bale (2007) proposes that agentive intransitives differ semantically from agentive transitives, in that while the agent of a transitive is introduced by a functional projection and composes with its verb via Event Identification (Kratzer 1996), intransitives lexically encode their agent arguments and compose with them via Function Application. This is based on the availability of agentless repetitive presuppositions with again, with transitives permitting a repetitive presupposition excluding the agent while intransitives do not. In this paper, we challenge Bale’s claim and show that typically intransitive verbs like dance and bark, which do not usually allow agentless presuppositions, permit agentless presuppositions when they appear with an optional internal argument. To account for this, we propose that verbal roots possess an underspecified thematic role argument, along with individual and event arguments. Combined with a conservative syntax for introducing agents via VoiceP (Kratzer 1996), the analysis captures the dependence of agentless presuppositions on the presence of an internal argument without recourse to any distinction between transitive and intransitive eventive verb roots. The analysis contributes a new theory of roots lying between two theoretical poles, one that argues that roots take internal arguments (e.g., Harley 2014) and one that severs internal arguments syntactically and semantically from the verb (e.g., Schein 1993; Borer 2003, 2005).

We consider the class of partially hyperbolic diffeomorphisms $$f:M\rightarrow M$$ obtained as the discretization of topological Anosov flows. We show uniqueness of minimal unstable lamination for these systems provided that the underlying Anosov flow is transitive and not orbit equivalent to a suspension. As a consequence, uniqueness of quasi-attractor is obtained. If the underlying Anosov flow is not transitive we get an analogous finiteness result provided that the restriction of the flow to any of its attracting basic pieces is not a suspension. A similar uniqueness result is also obtained for certain one-dimensional center skew-products.

Let X be a normed linear space. We prove that if the norm on X is almost transitive and if there exists a unit vector u satisfying that, for each point y in the unit ball of X that is isosceles orthogonal to u, there always exists $$\alpha \in (0,1)$$ so that u is isosceles orthogonal to $$\alpha y$$ , then X is an inner product space.

Barrio et al. (Journal of Philosophical Logic, 49(1), 93–120, 2020) and Pailos (Review of Symbolic Logic, 2020(2), 249–268, 2020) develop an approach to define various metainferential hierarchies on strong Kleene models by transferring the idea of distinct standards for premises and conclusions from inferences to metainferences. In particular, they focus on a hierarchy named the $\mathbb {S}\mathbb {T}$ S T -hierarchy where the inferential logic at the bottom of the hierarchy is the non-transitive logic ST but where each subsequent metainferential logic ‘says’ about the former logic that it is transitive. While Barrio et al. (2020) suggests that this hierarchy is such that each subsequent level ‘in some intuitive sense, more classical than’ the previous level, Pailos (2020) proposes an extension of the hierarchy through which a ‘fully classical’ metainferential logic can be defined. Both Barrio et al. (2020) and Pailos (2020) explore the hierarchy in terms of semantic definitions and every proof proceeds by a rather cumbersome reasoning about those semantic definitions. The aim of this paper is to present and illustrate the virtues of a proof-theoretic tool for reasoning about the $\mathbb {S}\mathbb {T}$ S T -hierarchy and the other metainferential hierarchies definable on strong Kleene models. Using the tool, this paper argues that each level in the $\mathbb {S}\mathbb {T}$ S T -hierarchy is non-classical to an equal extent and that the ‘fully classical’ metainferential logic is actually just the original non-transitive logic ST ‘in disguise’. The paper concludes with some remarks about how the various results about the $\mathbb {S}\mathbb {T}$ S T -hierarchy could be seen as a guide to help us imagine what a non-transitive metalogic for ST would tell us about ST. In particular, it teaches us that ST is from the perspective of ST as metatheory not only non-transitive but also transitive.

This paper puts forward a systemic methodology to explore Critical Success Factors (CSFs). The common idea about ranking CSFs is to explore the relationship of ‘more important’, i.e. directly assessing whether success factor A is more important than factor B. This idea is prominent in the prevailing approaches, e.g. the qualitative inquiry, quantitative analysis, and multi-criteria decision making. Exploring CSFs from a different lens, this paper argues for systemic approaches, reckoning that manifold interrelationships could exist between system elements. Considering the manifold interrelationships, the proposed methodology contends that two opposite interrelationships could exist between CSFs—‘helping to achieve’ and ‘inhibiting to achieve’. The first step of assessing CSFs is to construct a digraph in a participatory way, showing the transitive ‘helping to achieve’ relationship between CSFs and obtain the ‘helping to achieve’ score for each element. The second step is to examine the inhibiting relationship through a pairwise comparison to obtain the ‘inhibiting to achieve’ score for each element. The third step is to combine the ‘helping to achieve score’ with ‘inhibiting to achieve’ score to obtain the net score for each success factor. This output aims to provide the relevant stakeholders with a more comprehensive spectrum in assessing CSFs to develop their organizations well.

In this paper we characterize hypercyclic translation operators on $$B_{0}(\mathcal {H})$$ , the space of all compact linear operators on a Hilbert space $$\mathcal {H}$$ . Also, we give some sufficient condition for a related cosine operator function to be chaotic or topologically transitive.

We prove that every transitive and non minimal semigroup with dense minimal points is sensitive. When the system is almost open, we obtain a generalization of this result., 5 pages, 1 figure

Does life-long literacy experience modulate syntactic priming in spoken language processing? Such a postulated influence is compatible with usage-based theories of language processing that propose that all linguistic skills are a function of accumulated experience with language across life. Here we investigated the effect of literacy experience on syntactic priming in Mandarin in sixty Chinese older adults from Hebei province. Thirty participants were completely illiterate and thirty were literate Mandarin speakers of similar age and socioeconomic background. We first observed usage differences: literates produced robustly more prepositional object (PO) constructions than illiterates. This replicates, with a different sample, language, and cultural background, previous findings that literacy experience affects (baseline) usage of PO and DO transitive alternates. We also observed robust syntactic priming for double-object (DO), but not prepositional-object (PO) dative alternations for both groups. The magnitude of this DO priming however was higher in literates than in illiterates. We also observed that cumulative adaptation in syntactic priming differed as a function of literacy. Cumulative syntactic priming in literates appears to be related mostly to comprehending others, whereas in illiterates it is also associated with repeating self-productions. Further research is needed to confirm this interpretation.

The efficiency of state-of-the-art algorithms for the dueling bandits problem is essentially due to a clever exploitation of (stochastic) transitivity properties of pairwise comparisons: If one arm is likely to beat a second one, which in turn is likely to beat a third one, then the first is also likely to beat the third one. By now, however, there is no way to test the validity of corresponding assumptions, although this would be a key prerequisite to guarantee the meaningfulness of the results produced by an algorithm. In this paper, we investigate the problem of testing different forms of stochastic transitivity in an online manner. We derive lower bounds on the expected sample complexity of any sequential hypothesis testing algorithm for various forms of stochastic transitivity, thereby providing additional motivation to focus on weak stochastic transitivity. To this end, we introduce an algorithmic framework for the dueling bandits problem, in which the statistical validity of weak stochastic transitivity can be tested, either actively or passively, based on a multiple binomial hypothesis test. Moreover, by exploiting a connection between weak stochastic transitivity and graph theory, we suggest an enhancement to further improve the efficiency of the testing algorithm. In the active setting, both variants achieve an expected sample complexity that is optimal up to a logarithmic factor.

A group G is an N-barely transitive group (NBT-group) if G acts on an infinite set transitively and faithfully and all proper normal subgroups of G have finite orbits. We investigate the main properties and structure of NBT-groups. We give some examples in non-perfect and perfect case. Also we show that there does not exist a locally soluble perfect cofinitary NBT-group.

Transitive proxy voting (or "liquid democracy") is a novel form of collective decision making, often framed as an attractive hybrid of direct and representative democracy. Although the ideas behind liquid democracy have garnered widespread support, there have been relatively few attempts to model it formally. This paper makes three main contributions. First, it proposes a new social choice-theoretic model of liquid democracy, which is distinguished by taking a richer formal perspective on the process by which a voter chooses a proxy. Second, it examines the model from an axiomatic perspective, proving (a) a proxy vote analogue of May's Theorem and (b) an impossibility result concerning monotonicity properties in a proxy vote setting. Third, it explores the topic of manipulation in transitive proxy votes. Two forms of manipulation specific to the proxy vote setting are defined, and it is shown that manipulation occurs in strictly more cases in proxy votes than in classical votes.

There is no known formula that counts the number of transitive relations on a set with n elements. In this paper, it is shown that no polynomial in n with integer coefficients can represent a formula for the number of transitive relations on a set with n elements. Several inequalities giving various useful recursions and lower bounds on the number of transitive relations on a set are also proved.

A Furstenberg family $$\mathcal{F}$$ is a collection of infinite subsets ofthe set of positive integers such that if $$A\subset B$$ and $$A\in \mathcal{F}$$ , then $$B\in \mathcal{F}$$ . For aFurstenberg family $$\mathcal{F}$$ , an operator $$T$$ on a topological vector space $$X$$ is said tobe $$\mathcal{F}$$ -transitive provided that for each non-empty open subsets $$U$$ , $$V$$ of $$X$$ the set $$\{n \in \mathbb{N}: T^n (U) \cap V \neq\emptyset\}$$ belongs to $$\mathcal{F}$$ . In this paper, we characterize the $$\mathcal{F}$$ -transitivityof composition operator $$C_\phi$$ on the space $$H(\Omega)$$ of holomorphic functionson a domain $$\Omega\subset \mathbb{C}$$ by providing a necessary and sufficient condition in terms ofthe symbol $$\phi$$ .

Eells and Sober proved in 1983 that screening off is a sufficient condition for the transitivity of probabilistic causality, and in 2003 Shogenji noted that the same goes for probabilistic support. We start this paper by conjecturing that Hans Reichenbach may have been aware of this fact. Then we consider the work of Suppes and Roche, who demonstrated in 1986 and 2012 respectively that screening off can be generalized, while still being sufficient for transitivity. We point out an interesting difference between Reichenbach’s screening off and the generalized version, which we illustrate with an example about haemophilia among the descendants of Queen Victoria. Finally, we embark on a further generalization: we develop a still weaker condition, one that can be made as weak as one wishes.

It is of much interest to derive the priority vector from a multiplicative reciprocal preference relation (MRPR) originating from the analytic hierarchy process. There exists a conflict between the prioritization methods and the transitivity property of the entries in inconsistent MRPRs. In this paper, we attempt to weaken the conflict and enhance the effectiveness of the prioritization methods. The main contribution is to introduce the concept of indirect weak transitivity standard of MRPRs. When an MRPR possesses indirect weak transitivity about an alternative, a consistent MRPR is constructed as a proxy of inconsistent ones. When an MRPR does not possess indirect weak transitivity about any alternative, an adjustment algorithm is proposed to produce a new MRPR with indirect weak transitivity about an alternative. Numerical results are reported to show the procedure of eliciting priorities from an MRPR with indirect weak transitivity. The observation reveals that the proposed indirect weak transitivity standard could be used to assist the decision-maker in determining the outcome with more rationality.

In this paper, we propose a novel data structure and the algorithms to build, update and perform range query operations of transitive function. The update and query operation takes O(log(n)) time, and the space required for operating data is also O(cn), where c=3 proving it to be efficient than other data structures such as segment tree and sparse table. Experimental analysis shows the statistical evidence of proposed algorithm and conclude that it provides a good trade-off between space and time complexity in comparison to existent methods.

This paper examines alternations in demonstrative ordering in Kikuyu, a Bantu language spoken primarily in Kenya. An interesting effect is found: direct objects may not have prenominal demonstratives in transitive constructions, but may have prenominal demonstratives in a number of ditransitive constructions. I argue that this alternation is tied to Case. It is shown that these alternations can be accounted for using a theory of dependent Case in which Case has a licensing function. In Kikuyu, direct objects and subjects are too distant in the structure for the former to be assigned Case, and therefore the N head of the direct object must be adjacent to the verbal complex at the surface in order to be licensed (Levin 2015). However, the presence of a medial argument allows direct objects to be assigned Case since the two are sufficiently local, thus obviating the requirement for N-V adjacency.

In this paper, the Transitivity Pursuit-Enhanced Object Migration Automata (TPEOMA) is used to capture the dependence of elements in a hierarchical Singly-Linked-Lists on Singly-Linked-Lists (SLLs-on-SLLs) “adaptive” data structure. In doing so, the TPEOMA-enhanced hierarchical SLLs-on-SLLs learns the probability distribution of elements in a Non-stationary Environment. In this framework, we divide the hierarchical Singly-Linked-Lists on Singly-Linked-Lists (SLLs-on-SLLs) into an outer and inner list context. The inner-list context is itself a SLLs containing sub-elements of the list, while the outer-list context contains these sublist partitions as its primitive elements. The elements belonging to a particular sublist partition are determined using the TPEOMA reinforcement learning scheme from the theory of Learning Automata. The idea of Transitivity builds on the Pursuit concept that injects a noise filter into the EOMA to filter divergent queries from the Environment, thereby increasing the likelihood of training the Automaton to approximate the “true” distribution of the Environment. The Transitivity phenomenon can infer “dependent” query pairs from non-accessed elements in the transitivity relation based on the statistical distribution of the queried elements. The TPEOMA-enhanced hierarchical SLLs-on-SLLs schemes results in superior performances to the MTF and TR schemes as well as to the EOMA-enhanced hierarchical SLLs-on-SLLs schemes in NSEs.

Noun incorporation is commonly thought to avoid the weak compositionality of compounds because it involves conjunction of an argument noun with the incorporating verb. However, it is weakly compositional in two ways. First, the noun’s entity argument needs to be bound or saturated, but previous accounts fail to adequately ensure that it is. Second, non-arguments are often incorporated in many languages, and their thematic role is available for contextual selection.We show that these two weaknesses are actually linked. We focus on the Kiowa language, which generally bars objects from incorporation but allows non-arguments. We show that a mediating relation is required to semantically link the noun to the verb. Absent a relation, the noun’s entity argument is not saturated, and the entire expression is uninterpretable. The mediating relation for non-objects also assigns it a thematic role instead of a postposition. Speakers can choose this role freely, subject to independent constraints from the pragmatics, syntax, and semantics.Objects in Kiowa are in fact allowed to incorporate in certain environments, but we show that these all independently involve a mediating relation. The mediating relation for objects quantifies over the noun and links the noun+verb construction to the rest of the clause. The head that introduces this relation re-categorizes the verb in the syntactic derivation. Essentially, we demonstrate two distinct mechanisms for noun incorporation.Having derived the distribution of Kiowa, we apply the same relations to derive constraints on English complex verbs and synthetic compounds, which exhibit most of the same constraints as Kiowa noun incorporation. We also look at languages with routine object incorporation, and show how the transitivity of the verb depends on whether the "Equation missing" head introducing the external argument assigns case to the re-categorized verb.

Research indicates that network structure affects the diffusion of a single behavior. However, in many social settings, two or more behaviors may compete for adoption, as in the case of religious competition, social movements and counter-movements, or conflicting rumors. Lessons from one-behavior diffusion cannot be easily applied because the outcome can take the form of one-behavior domination, two behaviors splitting the network, both behaviors occupying a small fraction of the network, or no diffusion. This article tests how three well-known factors of single-behavior diffusion—network transitivity, adoption threshold, and connectedness of early adopters—apply to scenarios of competitive diffusion. Results show that minor differences in initial adopter size tend to magnify, creating a significant “head-start advantage.” Nevertheless, the degree of this advantage depends on the interaction between network transitivity, adoption threshold, and connectedness of initial adopters. The article describes the conditions under which countervailing ties may (or may not) create inequality in behavioral diffusion.

This paper presents a generalization of Fine’s completeness theorem for transitive logics of finite width, and proves the Kripke completeness of transitive logics of finite “suc-eq-width”. The frame condition for each finite suc-eq-width axiom requires, in rooted transitive frames, a finite upper bound of cardinality for antichains of points with different proper successors. The paper also presents a generalization of Rybakov’s completeness theorem for transitive logics of prefinite width, and proves the Kripke completeness of transitive logics of prefinite “suc-eq-width”. The frame condition for each prefinite suc-eq-width axiom requires, in rooted transitive frames, a finite upper bound of cardinality for antichains of points that have a finite lower bound of depth and have different proper successors. We will construct continuums of transitive logics of finite suc-eq-width but not of finite width, and continuums of those of prefinite suc-eq-width but not of prefinite width. This shows that our new completeness results cover uncountably many more logics than Fine’s theorem and Rybakov’s theorem respectively.

In this paper, we give some sufficient and necessary conditions for discrete cosine operator functions on solid Banach function spaces to be chaotic or topologically transitive.

We introduce the concepts of S-sets and Q-sets for a flow (a group action on a compact metric space) and prove that a transitive flow is sensitive if and only if there exists an S-set with cardinality more than 2 and that each S-set of a transitive flow is a Q-set and the converse holds for minimal flows. Then according to cardinalities of S-sets, transitive flows are divided into several classes and some characterizations and relationships of different classes are given. This is a generalization of the $$\mathbb {Z}$$ -action of Ye and Zhang (Nonlinearity 21:1601–1620, 2008. https://doi.org/10.1088/0951-7715/21/7/012 ).

The relationship between a transitive GE-algebra and a belligerent GE-algebra (also, between an antisymmetric GE-algebra and a left exchangeable GE-algebra) is displayed. A condition for the trivial GE-filter to be a belligerent GE-filter is provided. The least GE-filter containing a given GE-filter and one element is formed. Conditions under which any set can be turned into a GE-filter are described. The notions of $$\odot $$ -GE-algebras and prominent GE-filters are introduced, and their properties are investigated. The relationship between a prominent GE-filter and a GE-filter are considered, and conditions for a GE-filter and the trivial GE-filter to be a prominent GE-filter are given. The conditions under which the upset of an element will be a prominent GE-filter are examined, and the extension property for the prominent GE-filter is established. The notion of GE-morphism is introduced, and the GE-morphism theorem is considered. Conditions for the kernel of a GE-morphism to be a belligerent GE-filter are provided, and the condition that if the kernel of a GE-morphism is a belligerent GE-filter, then the trivial GE-filter becomes a belligerent GE-filter is given. A condition for the kernel of a GE-morphism to be a belligerent GE-filter is discussed, and the vice versa is also considered.

We proposed a synonym search method to solve $$(A,B)\sim (C,D)$$ problem over time with a query by an example in a known domain for information in an unknown domain. It seems a natural relation that “Bush in the 2000s” is similar to “Reagan in the 1980s” because “Bush” and “Reagan” are the president of the USA in these decades. The abstraction is “A in B ” which is similar to “C in D.” We solve the $$(A,B)\sim (C,D)$$ problem over time by using transformation matrix word vectors over time in the Skip-gram model. The example of the $$(A,B)\sim (C,D)$$ problem is as below. For instance, the sentence “Bush in the 2000s” is similar to “X in the 1980s” is given. We search for the appropriate entity to X of the sentence. Therefore, we focus on the transitivity between the transformation matrix. Our approach is to convert the vector representation of “A ” in the model of the word embedding model of the “B ” to the vector representation of “X ” in the model of the word embedding model of the “D ” by getting the transformation matrix between word embedding models. We discuss the parameters of previous work and improve choosing words to make transformation matrix using co-occurrence cluster. Our aim is to search for synonyms in which there are more than the 1000 years of separation. However, there are a few common stable meaning words between the “2000s” and the “1000s.” Therefore, in the situation, there is difficulty to use co-occurrence cluster because the clusters of common words are more than 100,000. That is why, we use the transitive relation (2000s, X) $$\sim $$ (1500s, Y) , (1500s, Y) $$\sim $$ (1000s, Z) $$\Rightarrow $$ (2000s, X) $$\sim $$ (1000s, Z) (in the abstruction, the transitivity is $$x\sim y, y\sim z\Rightarrow x\sim z$$ ) to solve the $$(A,B)\sim (C,D)$$ problem over the 1000 years of separation. We had experiments as the demonstration to solve the $$(A,B)\sim (C,D)$$ problem and evaluate nDCG and MRR.

A long-standing charge of circularity against regularity accounts of laws has recently seen a surge of renewed interest. The difficulty is that we appeal to laws to explain their worldly instances, but if these laws are descriptions of regularities in the instances then they are explained by those very instances. By the transitivity of explanation, we reach an absurd conclusion: instances of the laws explain themselves. While drawing a distinction between metaphysical and scientific explanations merely modifies the challenge rather than resolving it, I argue that it does point us towards an attractive solution. According to Humeanism, the most prominent form of the regularity view, laws capture information about important patterns in the phenomena. By invoking laws in scientific explanations, Humeans are showing how a given explanandum is subsumed into a more general pattern. Doing so both undermines a principle of transitivity that plays a crucial role in the circularity argument and draws out a central feature of the Humean approach to scientific explanation.

In this paper, we give a characterisation for a class of edge-transitive Cayley graphs and provide a method for constructing edge-transitive graphs of valency 4 with arbitrarily large vertex stabiliser. In particular, in the last section, we obtain certain extensions of the results of Li et al. (Tetravalent edge-transitive Cayley graphs with odd number of vertices, J Comb Theory Ser B 96:164–181, 2006) on half-transitive graphs.

In this paper, we complete the classification of transitive ovoids of finite Hermitian polar spaces., Comment: 17 pages. To appear in Combinatorica

We study modules in which perspectivity of summands is transitive. Generalizing a 1977 result of Handelman and a 2014 result of Garg, Grover, and Khurana, we prove that for any ring R, perspectivity is transitive in $\mathbb {M}_{2}(R)$ if and only if R has stable range one. Also generalizing a 2019 result of Amini, Amini, and Momtahan we prove that a quasi-continuous module in which perspectivity is transitive is perspective.

For a completely distributive De Morgan algebra L, we develop a general framework of L-fuzzy rough sets. Said precisely, we introduce a pair of L-fuzzy approximation operators, called upper and lower L-fuzzifying approximation operators derived from general L-fuzzifying neighborhood systems. It is shown that the proposed approximation operators are a common extension of the L-fuzzifying approximation operators derived from L-fuzzy relations (INS 2019) and the approximation operators derived from general neighborhood systems (KBS 2014). Furthermore, we investigate the unary, serial, reflexive, transitive and symmetric conditions in general L-fuzzifying neighborhood systems, and then study the associated approximation operators from both a constructive method and an axiomatic method. Particularly, for transitivity (resp., symmetry), we give two interpretations, one is an appropriate generalization of transitivity (resp., symmetry) for L-fuzzy relations, and the other is a suitable extension of transitivity (resp., symmetry) for general neighborhood systems. In addition, for some special L-fuzzifying approximation operators, we use single axiom to characterize them, respectively. At last, the proposed approximation operators are applied in the research of incomplete information system, and a three-way decision model based on them is established. To exhibit the effectiveness of the model, a practical example is presented.

Emergence of equivalence relations among stimuli previously related by exclusion was assessed by using the blank-comparison-stimulus procedure throughout baseline and test trials, in order to avoid problems involved in testing emergent relations with either baseline or novel stimuli as S– comparisons. In Experiment 1, participants were exposed to pretraining phases in order to learn to respond to a blank comparison stimulus as the correct one when the other comparison stimuli were incorrect. Then, they learned a baseline of conditional relations for the emergence of stimulus Classes 1 and 2. Thereafter, they were exposed to exclusion trials, in which stimuli from the preexperimentally defined Class 3 were introduced as undefined stimuli, whereas baseline stimuli were defined. They were then presented with symmetry and transitivity trials for all three classes (Group 1), or only Class 3 (Group 2), in three-choice matching trials. Most participants in Group 2 related stimuli previously related by exclusion as if they were in an equivalence relation, but most participants in Group 1 did not. In Experiment 2, most participants of a single group (Group 3) showed emergence of equivalence by exclusion and transfer of stimuli functions when exposition to exclusion trials occurred after demonstration of equivalence of the baseline classes, and assessment of equivalence was conducted for the three classes in two-choice matching trials. Conditions under which the emergence of equivalence by exclusion occurs are discussed.

In this note we point out an error in a recent paper on flag-transitive block designs with gcd $$(r,\lambda )=1$$ , and we prove a result correcting the error.

This paper presents a study of a split absolutive-nominative agreement pattern in Gitksan (Tsimshianic) which co-occurs with ergative agreement. The split is conditioned on the basis of nominal type: alongside ergative agreement, a second type of agreement targets absolutives (S, O) when the subject is a participant or third-singular pronoun, or nominatives (S, A) when the subject is a full DP or third-plural pronoun. This results in what appears to be construction-dependent variation in the applicability of the Activity Condition, as some transitive subjects receive both ergative and nominative agreement. It is proposed that DP arguments and third-plural pronouns are able to receive multiple instances of agreement by virtue of bearing D-features; in contrast to the situation with typical pronouns, these D-features remain active for agreement even if prior ergative agreement has already deactivated the argument’s ϕ-features. Both ergative and nominative agreement may target a single argument because different groups of features are targeted during the two operations. The D-feature property is ultimately linked to a structural DP/non-DP distinction amongst arguments, providing some insight into the role of D in pronominal systems. This analysis, which crucially relies on an approach to activity that explicitly allows incremental deactivation of an argument, accounts for the empirical facts in Gitksan more readily than a purely morphological approach or an approach that considers distinctions between ϕ-features alone.

A digraph $$\overrightarrow {\rm{\Gamma}} $$ is said to be 1-transitive if its automorphism group acts transitively on the 1-arcs but not on the 2-arcs of $$\overrightarrow {\rm{\Gamma}} $$ . We give a tentatively complete classification of pentavalent strongly connected 1-transitive digraphs of order 2apbq, where p and q are two distinct odd primes, a ∈ {3,…, 8},b ∈ {1, …, 4}, whose automorphism groups are non-solvable. It is shown that such digraphs exist if and only if q = 3 or 13 and p ∈ {7, 11, 17, 19, 31, 41}.