It has always been expected that robots can actively manipulate complex environments to fulfill human requirements. This process typically necessitates that the robot be equipped with the ability for embodied exploration and manipulation. To achieve this goal, in this paper, we propose to incorporate multi-source knowledge to enhance the ability of robotic embodied exploration and manipulation. Specifically, to eliminate the inherent biases in decision-making of large language models (LLMs), we introduce a multi-source knowledge fusion module to generate more reasonable exploration sequences. Notably, grasping detection plays a critical role in the process of robot manipulation. To achieve a better balance between the accuracy and efficiency of the grasping detection network, we design a two-branch feature fusion module with residual blocks to improve network performance. Conditioned on the aforementioned innovations, the robot is capable of actively exploring and manipulating in constrained environments to meet human requirements. Extensive experiments are conducted in both simulation and real-world environments. The results demonstrate the effectiveness and efficiency of our proposed framework.

In the second volume of his Systematic Theology, William Lane Craig raises a number of issues against the traditional doctrine of divine simplicity, along with several criticisms of Aquinas’s notion of existence. We can’t respond to all of his complaints here – but we can respond to what are, in our estimation, the most fundamental to his case.

Our focus will be on two of the main problems he presses against Aquinas’s view of existence: first, whether it makes sense to talk about existence itself as existing; and second, whether existence comes in degrees. These challenges are closely related – both, ultimately, concern the classical theist claim that God is identical to His own existence – and so our answers will be related as well.

We’ll conclude by raising a challenge for Craig.

The main objective of this article is to present a detailed structure of left nilpotent skew braces $B$ of class $2$, i.e. skew braces with $B^3 = 0$. We prove that if $B$ is of nilpotent type, then $B$ is centrally nilpotent. In fact, we show that $B$ is right nilpotent of class at most $2+mr$, i.e. $B^{(2+mr+1)} = 0$, where $m$ and $r$ are the nilpotency classes of the additive group of $B$ and $B^2$, respectively. If $B$ is of abelian type, then $B$ is actually right nilpotent of class $3$, i.e. $B^{(4)} = 0$, and this bound is the best possible.

Unpaid carers face significant financial risks, yet how caring shapes financial wellbeing (FWB) over time has been poorly understood. Drawing on qualitative research with fifty unpaid carers in Britain, purposively sampled across age, life stage, gender, caring intensity and socio-economic status, this paper applies and extends an ecological framework of FWB for the first time in a care context. It makes three contributions. First, it provides original empirical evidence showing that the financial consequences of caregiving are cumulative, uneven and experienced differently across the life course. Second, it develops a life course conceptualisation of carer FWB, highlighting dynamic interactions between individual circumstances, family situations and work, welfare and care systems. Third, it reframes policy debates by demonstrating how care costs are systematically individualised, making structural life stage sensitive interventions essential. Effective policy responses must therefore reflect carers’ differing needs across the life course and address cumulative financial risks. This includes support with saving and affordable housing for young adult carers; clearer pension information and protection from long term care related employment breaks in mid life; and more generous, flexible benefits and trusted care services. Our conceptualisation has international relevance in contexts where reliance on unpaid care is high, and formal support remains limited.

We introduce the concept of a restriction semigroupoid $\mathcal{S}$, which unifies the notion of restriction semigroups and restriction categories within a single structure. We prove a representation theorem, showing that every restriction semigroupoid can be embedded into a certain category of partial maps. Furthermore, we construct the Szendrei expansion $Sz(\mathcal{S})$ of $\mathcal{S}$ and establish that each premorphism between two restriction semigroupoids $\mathcal{S}$ and $\mathcal{T}$ is uniquely factorized by a morphism between the Szendrei expansion $Sz(\mathcal{S})$ and $\mathcal{T}$.

Let $T_m$ be a noncommutative Fourier multiplier. In recent work, Mei and Ricard introduced a noncommutative analogue of Cotlar's identity to prove that certain multipliers are bounded on the noncommutative $L_p$-spaces of a free group. Here, we study Cotlar-type identities in full generality, giving a closed characterization for them in terms of m:

$$\begin{align*}\big( m(g h) - m(g) \big) \, \big( m(g^{-1}) - m(h) \big) = 0, \; \forall g \in \mathrm{G}\setminus \{e\}, h \in \mathrm{G}. \end{align*}$$

$\mathbb{R}$

$\mathrm{G}$

$\widetilde{m}: X \to \mathbb{C}$

$X \setminus \{x_0\}$

$T_m$

$L_p$

$1 < p < \infty$

This result establishes a new connection between group actions on $\mathbb{R}$-trees and Fourier multipliers. This machinery allows us to simultaneously generalize the free group transforms of Mei and Ricard and the theory of Hilbert transforms in left-orderable groups, which follows from Arveson’s subdiagonal algebras. Using Bass-Serre theory, we construct new examples of Fourier multipliers on groups. These include new families such as Baumslag-Solitar groups. We also show that a natural Hilbert transform in $\mathrm {PSL}_2(\mathbb{C})$ satisfies Cotlar’s identity when restricted to the Bianchi group $\mathrm {PSL}_2(\mathbb{Z}[\sqrt{-1}])$.

In this paper, we obtain new lower bounds for the evolution of the radius of analyticity of solutions to two initial value problems (IVPs) with initial data belonging to the class of analytic functions $H^{\sigma,s}(\mathbb{R})$ defined via a hyperbolic cosine weight. First, we consider the IVP for the modified Korteweg–de Vries (mKdV) equation. For this problem, we prove that the evolution of the radius of analyticity $\sigma(T)$ of the solution admits an algebraic lower bound $cT^{-\frac 12}$ for some $c \gt 0$ and given arbitrarily large $T \gt 0$. Next, we analyse the IVP for the mKdV equation with generalized dispersion (mKdVm) and a damping term. For this problem, we guarantee the local well-posedness in $H^{\sigma,s}(\mathbb{R})$ and demonstrate that the local solution can be extended globally in time and admits constant lower bounds for the radius of analyticity $\sigma(t)$ as time goes to infinity. The outcome of this paper concerning the mKdV equation represents an improvement on that achieved by the authors’ previous work in [New lower bounds for the radius of analyticity for the mKdV equation and a system of mKdV-type equations. J. Evol. Equ. 24 (2024), no. 2, Art. 42]. As far as we know, the results for the mKdVm with damping are new.

This research investigates the impact of social media reviews on corporate environmental performance, with particular emphasis on the influence of reviewers’ professional expertise. We propose a two-stage social learning model to capture consumer product selection, the dissemination of reviews and firms’ decisions regarding environmental investments. Theoretically, our analysis demonstrates that social media reviews help bridge information gaps left by traditional product information sources and incentivize firms to enhance their environmental performance. Notably, reviews authored by professional reviewers have a more pronounced effect on motivating such investments. Empirically, we validate these theoretical insights using an eight-year dataset comprising daily observations from 125 publicly traded companies, which includes 294,727 expert reviews and 2,677,228 non-expert reviews sourced from online platforms. The empirical findings corroborate the theoretical predictions. Additionally, we observe that increased consistency and transparency in firms’ disclosed environmental values mitigate information asymmetry and reduce dependence on potentially biased expert evaluations.

Why did almost every Latin American state embrace the norm of Indigenous constitutional inclusion over the past five decades? Established sociological answers focus on the spread of global norms or on bottom-up pressure from social movements. However, these accounts are incomplete, overlooking the core political logic within the state that drives Indigenous inclusion – namely, legitimacy. In this article, I present a historical analysis of every instance of constitutional Indigenous inclusion in Latin America between 1970 and 2023, documenting significant variation in the timing (chronology) of norm adoption. In addition, I introduce a novel index of inclusion, shedding light on another significant source of variation: the degree of inclusion. Using comparative-historical analysis, I argue that these sources of variation largely reflect instances of legitimacy deficits: situations in which governments face pressure to demonstrate their legitimacy to specific legitimacy audiences. The cases analyzed show that policymakers enacted inclusionary policies in order to bolster state legitimacy in the eyes of domestic or international audiences and that domestic stakeholders generally achieved stronger forms of inclusion than international actors. Indigenous groups usually gained much less when governments pursued reforms mainly in order to appease eternal audiences.

This study explores the evolving discourse of Mongolian nationalism in online spaces, with specific attention to representations of Mongols beyond Mongolia’s borders. While the historically dominant, exclusive Khalkha-centric nationalist discourses continue to occupy a strong presence in cyberspace, Mongolian nationalist discourse has witnessed a shift toward a more inclusive, yet largely depoliticized, cultural Greater Mongol narrative. This narrative reimagines cross-border Mongols as members of a shared ethnic community. The research explores how the Mongolian state and Mongolian nationalist elites curate this cultural Greater Mongol discourse to position the Mongolian state as the historical and cultural center of the Mongol world. It contributes to a better understanding of the complex and dialectical transformations of nationalist discourses in contemporary Mongolian nation-building.

How does one’s community shape their racialized and political identity? Research studying group-based resources and political behavior focuses primarily on the overall size of a group. This study refines our understanding of how community context shapes Asian pan-ethnic identity by examining a second dimension of population: Asian national origin diversity. Using both existing and new survey data, I find that Asians living in more heterogeneous areas view Asian identity as less important and report lower levels of linked fate. I then examine variation in the role of physical and social resources across localities that differ in group size and diversity. Respondents in localities with larger Asian populations and lower levels of diversity are more likely to report higher levels of pan-Asian salience and availability of cultural resources. My analysis highlights the role of within-group diversity and the importance of community resources and institutions in cultivating connections between identity and politics.

Exposure to early life adversity (ELA) increases risk of poor mental health outcomes, including attention deficit/hyperactivity disorder (ADHD). In fact, ELA, especially in the form of “household ACEs” (e.g., socioeconomic disadvantage, incarceration of a caregiver), is among the most robust environmental predictors of a later ADHD diagnosis. Exposure to unpredictability is an understudied form of ELA that captures instability or inconsistency in routines, household experiences, and family relationships. The purpose of this study was to examine associations between unpredictability and ADHD symptoms in children and adolescents. Participants were drawn from two independent cohorts (Cohort 1: N = 99, Mage = 7.31 years [SD = 0.31]; Cohort 2: N = 217, Mage = 14.39 years [SD = 1.32]) participating in ongoing longitudinal studies of exposure to ELA. Unpredictability was measured by the Questionnaire of Unpredictability in Childhood, and ADHD symptoms were measured by the Child Behavior Checklist Attention Deficit/Hyperactivity Problems subscale, the Behavior Rating Inventory of Executive Function, and the Kiddie Schedules for Affective Disorders and Schizophrenia ADHD Screener. Childhood experiences of unpredictability were associated with ADHD symptoms in both cohorts and during childhood and adolescence. Further, associations were stronger in females than males. These findings show that unpredictability is a risk factor for ADHD which suggests that it should be explored as an early target for intervention to reduce the development of ADHD symptoms.

Roald Amundsen’s South Pole party is routinely depicted as an unusually harmonious and high-performing team. This article re-examines that assumption by returning to the only contemporary sources that intermittently record interpersonal strain during the Pole march: the diaries of Sverre Hassel and Olav Bjaaland. Using a deliberately narrow empirical base and a transparent inclusion procedure, the study restricts all claims about friction to what the diarists explicitly note. A minimal coding vocabulary—task, process/authority, and relationship/tone—serves as an organising device rather than an explanatory framework. Seventeen diary passages document irritation, disagreement, reprimand, sarcasm, or social sanction linked to identifiable expedition members. Read conservatively, the diaries neither support a counter-myth of dysfunction nor permit inferences about the prevalence or long-term significance of conflict. They do, however, make one conclusion difficult to avoid: the Pole march cannot responsibly be described as frictionless simply because it succeeded logistically or was later narrated smoothly. Instead, the diary evidence shows that operational excellence coexisted with domain-specific frictions—over judgement, rations, navigation, role allocation, and tent-life tone—and that authority and contradiction repeatedly appear as interactional fault lines. Cohesion, where it existed, was not the absence of strain but a condition under which strain could still be written down.

Given a (di)graph $H$, we say that a (di)graph $H^{\prime }$ is an $H$-subdivision if $H^{\prime }$ is obtained from $H$ by replacing one or more edges with internally vertex-disjoint paths. Pavez-Signé conjectured that for every $\varepsilon \gt 0$, there exists a constant $C_0\gt 0$ such that for every graph $H$ with $h$ edges and no isolated vertices, if $G$ is a graph on $n\geq C_0h$ vertices and minimum degree $\delta (G)\geq (1+\varepsilon )\frac {n}{2}$, then $G$ contains a spanning $H$-subdivision. This conjecture was later resolved by Lee [European J. Combin. 124 (2025), 104059]. In this paper, we strengthen Lee’s result. Specifically, we prove that for any digraph $D$ on $n\geq C_0h$ vertices, if the minimum semi-degree of $D$ is at least $\frac {n+h}{2}-1$, then $D$ contains a spanning $H$-subdivision. The lower bound on the minimum semi-degree is best possible. Furthermore, we show that there exist constants $C\gt 0$ and $\alpha , \beta \in (0, 1)$ such that for any integer partition $n=n_1+\cdots +n_m\geq Cm$ with $n_i\geq |V(H)|+3h$ for each $i$, and $\sum _{n_i\lt \alpha n}n_i\leq \beta n$, if a digraph of order $n\geq Cm$ has minimum semi-degree at least $\frac {n+m+h}{2}-1$, then it contains $m$ vertex-disjoint $H$-subdivisions whose orders are $n_1, \ldots , n_m$, respectively. The bound $\frac {n+m+h}{2}-1$ is also optimal. This work partly answers a conjecture of Lee [Combin. Probab. Comput. 34 (2025), 421–444] and generalises a recent result from the same paper.