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Reciprocal feedback processes between experience and development are central to contemporary developmental theory. Autoregressive cross-lagged panel (ARCL) models represent a common analytic approach intended to test such dynamics. The authors demonstrate that—despite the ARCL model's intuitive appeal—it typically (a) fails to align with the theoretical processes that it is intended to test and (b) yields estimates that are difficult to interpret meaningfully. Specifically, using a Monte Carlo simulation and two empirical examples concerning the reciprocal relation between spanking and child aggression, it is shown that the cross-lagged estimates derived from the ARCL model reflect a weighted—and typically uninterpretable—amalgam of between- and within-person associations. The authors highlight one readily implemented respecification that better addresses these multiple levels of inference.

Let G be a nontrivial connected graph. We follow Chartrand, et al in [2] for the definiton of rainbow connection and strong rainbow connection number. For t ∊ N and t > 2, let {P(3,2)i|i ∊ {1, 2, ..., t}} is a finite collection of prism graph P3,2 that has a fixed vertex v called a terminal. The amalgamation of prism graph, Amal(P(3,2)i, v), is a graph formed by taking all the element of finite collection of prism graph P3,2 and identifying their terminal. This paper determines the rainbow connection and strong rainbow connection number from amalgamation of prism graph by a deductive reasoning method. The result are as follows: rc(Amal(P(3,2)i, v)) = 4 and src(Amal(P(3,2)i, v)) = max {4, t} for i ∊ {1, 2, ..., t}.

In this paper we give a constructive proof that the variety of Boolean algebras has the strong amalgamation property by describing constructively the strong amalgams in the variety. Then, capitalizing on this construction, we investigate several forms of amalgamation, such as the strong amalgamation property and Maksimova super-amalgamation for the varieties of regular double Stone algebras and centered regular double Stone algebras. In fact, we prove that the amalgamation property holds for the variety RDS. Then, we introduce the variety RDSk of centered regular double Stone algebras and prove that RDSk enjoys the strong amalgamation property. It is also proved that the varieties of Boolean algebras and centered regular double Stone algebras have the super-amalgamation property. We close the paper by providing a number of concrete examples and applications to illustrate the theory developed in the paper.

We give an abstract framework to transfer generalized amalgamation from a simple theory to another, and we apply it to theories of bounded PAC structures, of fields with operators and of lovely pairs. We show in particular that bounded pseudo-algebraically closed fields have generalized amalgamation, regardless of their imperfection degree.

The disjoint amalgamation property (DAP), which asserts that all spans of a class of models can be amalgamated with minimal intersection, is an important property in the context of abstract elementary classes, with connections to both Grossberg's question and Shelah's categoricity conjecture. We prove that, in a nice AEC \\(K\\) stable in \\( LS(K)\\) with a strong enough independence relation, all high cofinality \\(\\)-limit models are disjoint (non-forking) amalgamation bases. \\(Theorem.\\) Let \\(K\\) be an AEC stable in \\(\\), where \\(K_\\) has AP, JEP, and NMM, and let \\(K'\\) be some AC where \\(K_( ) K' K_\\). Suppose there is an independence relation on \\(K'\\) satisfying uniqueness, existence, non-forking amalgamation, \\(K_( )\\)-universal continuity* in \\(K_\\), and \\(( )\\)-local character. Assume \\(M_0, M_1, M_2 ın K_( )\\), and that \\(M_0 _K M_l\\) and \\(a_l ın M_l\\) for \\(l = 1, 2\\). Then there exist \\(N ın K_( )\\) and \\(f_l : M_l N\\) fixing \\(M_0\\) for \\(l = 1, 2\\) such that \\(gtp(f_l(a_l)/f_3-l[M_3-l], N)\\) does not fork over \\(M_0\\) and \\(f_1[M_1] f_2[M_2] = M_0\\). That is, our independence relation has disjoint non-forking amalgamation in \\(K_( )\\). In particular, every \\(M_0 ın K_( )\\) is a disjoint amalgamation base in \\(K_\\). The hypotheses on the independence relation can be weakened (closer to \\(\\)-non-splitting in \\(\\)-stable AECs) if we are willing to give up the `non-forking' conditions of the amalgamation.

We show two results on higher amalgamation in the theory \\(ACFA^+\\), the model companion of the theory of difference fields with an additive character (added as a continuous logic predicate) on the fixed field in characteristic 0. On one hand, we show that the non-trivial condition for 3-amalgamation established in a preceding paper is not sufficient for 4-amalgamation. On the other hand, we show that when working over substructures whose \\(L_\\)-reduct is a model of \\(ACFA\\), \\(n\\)-amalgamation holds for all \\(n 3\\).

We study the spectrum of limit models assuming the existence of a nicely behaved independence notion. Under reasonable assumptions, we show that all `long' limit models are isomorphic, and all `short' limit models are non-isomorphic. \\(Theorem.\\) Let \\(K\\) be a \\(_0\\)-tame abstract elementary class stable in \\( LS(K)\\) with amalgamation, joint embedding and no maximal models. Suppose there is an independence relation on the models of size \\(\\) that satisfies uniqueness, extension, non-forking amalgamation, universal continuity, and \\(( )\\)-local character in a minimal regular \\( < ^+\\). Suppose \\(_1, _2 < ^+\\) with \\(cf(_1) < cf(_2)\\). Then for any \\(N_1, N_2, M ın K_\\) where \\(N_l\\) is a \\(( _l)\\)-limit model over \\(M\\) for \\(l = 1, 2\\), \\[N_1 is isomorphic to N_2 over M ıff cf(_1) \\] Both implications in the conclusion have improvements. High cofinality limits are isomorphic without the \\(_0\\)-tameness assumption and assuming the independence relation is defined only on high cofinality limit models. Low cofinality limits are non-isomorphic without assuming non-forking amalgamation. We show how our results can be used to study limit models in both abstract settings and in natural examples of abstract elementary classes.

Given weakly exact tracial von Neumann algebras \\(M_1, M_2\\) with a common injective amalgam \\(B\\), we prove that the amalgamated free product \\(M_1*_BM_2\\) is biexact relative to \\(\\M_1,M_2\\\). In the case where \\( M_1 \\) and \\(M_2\\) are injective, we further show that \\(M_1*_BM_2\\) is biexact relative to the amalgam \\(B\\), and if \\(B\\) is mixing in each of \\(M_1\\) and \\(M_2\\), \\(M_1*_BM_2\\) itself is biexact. As applications, we derive structural decomposition results and subalgebra absorption theorems for amalgamated free product von Neumann algebras, extending those previously known in the group case.

We establish explicit expressions for the \\(K\\)-theory classes of higher Kazhdan projections for amalgamated product groups \\(Z_m*_Z_dZ_n\\). Our approach follows the methodology developed by Pooya and Wang for free product groups \\(Z_m*Z_n\\), and naturally generalizes their results on free products. As an application of the \\(K\\)-class expressions, we obtain non-vanishing results for delocalized \\(^2\\)-Betti numbers of \\(SL(2,Z)\\).

The Altaids accreted around, and grew southward, from the Siberian craton, but the time of final amalgamation of this orogen is still controversial. The Eastern Tianshan in the southernmost Altaids is characterized by multiple, late, accreted arcs and thus is an ideal tectonic environment to answer the time of final amalgamation of the Altaids. In this study we report the results of new field-based lithological mapping and structural analysis on the Kanguer mélange in the Eastern Tianshan, which is composed of blocks of basalt, chert, limestone, and other rocks within a strongly deformed and cleaved matrix of sandstone and schist. Our geochemical and isotopic data of basaltic blocks from several parts of the Kanguer mélange show they are relics of Normal-Mid-Ocean-Ridge (N-MORB)-type oceanic lithosphere, and U–Pb ages and Hf isotopes of detrital zircons from the matrix sandstones indicate they were derived only from the Dananhu arc to the north. Accordingly, our interpretation is that the Kanguer mélange was part of an accretionary complex that fringed the Dananhu arc, and therefore the subduction polarity of the Kanguer Ocean was to the north (present coordinates). The maximum depositional ages (MDAs) of our three sandstone samples (08K01, 08K02, and 08K03) from the mélange matrix were 234 ± 14 Ma, 242.5 ± 1.3 Ma, and 236 ± 2.0 Ma respectively, indicating that the Kanguer Ocean was still being subducted at ca. 234 Ma, and the accretion of the Kanguer mélange must have lasted until that time, when the accretionary complex was still located opposite to the Yamansu-CTS accretionary complex to the south. Thus, the final amalgamation of the Dananhu and Yanmansu-CTS arcs took place by the welding of two accretionary complexes in the late Middle Triassic (Ladinian) in this part of the southern Altaids. Integration with relevant amalgamation histories throughout the Tianshan indicates that the time of terminal amalgamation in the southern Altaids was probably in the Middle-Late Triassic, which is much younger than previously envisaged.