The Alignment of Agent-First Preferences with Visual Event Representations: Contrasting German and Arabic

How does non-linguistic, visual experience affect language production? A series of experiments addressed this question by examining linguistic and visual preferences for agent positions in transitive action scenarios. In Experiment 1, 30 native German speakers described event scenes where agents were positioned either to the right or to the left of patients. Produced utterances had longer speech onset times for scenes with right- rather than left-positioned agents, suggesting that the visual organization of events can affect sentence production. In Experiment 2 another cohort of 36 native German participants indicated their aesthetic preference for left- or right-positioned agents in mirrored scenes and displayed a preference for scenes with left-positioned agents. In Experiment 3, 37 Arabic native participants performed the same non-verbal task showing the reverse preference. Our findings demonstrate that non-linguistic visual preferences seem to affect sentence production, which in turn may rely on the writing system of a specific language.

Triangles in the suborbital graphs of the normalizer of $\Gamma_0(N)$

<p>In this paper, we investigate a suborbital graph for the normalizer of Γ_{0(<em>N</em>)} ∈ PSL(2;<em>R</em>), where <em>N</em> will be of the form 2⁴<em>p</em>² such that <em>p</em> &gt; 3 is a prime number. Then we give edge and circuit conditions on graphs arising from the non-transitive action of the normalizer.</p>

Affine cones over cubic surfaces are flexible in codimension one

Let Y be a smooth del Pezzo surface of degree 3 polarized by a very ample divisor that is not proportional to the anticanonical one. Then the affine cone over Y is flexible in codimension one. Equivalently, such a cone has an open subset with an infinitely transitive action of the special automorphism group on it.

ON COMPACT HOMOGENEOUS -MANIFOLDS

We prove that among all compact homogeneous spaces for an effective transitive action of a Lie group whose Levi subgroup has no compact simple factors, the seven-dimensional flat torus is the only one that admits an invariant torsion-free $\text{G}_{2(2)}$ -structure.

Suborbital graphs for a non-transitive action of the normalizer

In this paper, we investigate a suborbital graph for the normalizer of ?0(n) in PSL(2,R), where n will be of the form 32p2, p is a prime and p > 3. Then we give edge and circuit conditions on graphs arising from the non-transitive action of the normalizer.

On the involution fixity of exceptional groups of Lie type

The involution fixity [Formula: see text] of a permutation group [Formula: see text] of degree [Formula: see text] is the maximum number of fixed points of an involution. In this paper we study the involution fixity of primitive almost simple exceptional groups of Lie type. We show that if [Formula: see text] is the socle of such a group, then either [Formula: see text], or [Formula: see text] and [Formula: see text] is a Suzuki group in its natural [Formula: see text]-transitive action of degree [Formula: see text]. This bound is best possible and we present more detailed results for each family of exceptional groups, which allows us to determine the groups with [Formula: see text]. This extends recent work of Liebeck and Shalev, who established the bound [Formula: see text] for every almost simple primitive group of degree [Formula: see text] with socle [Formula: see text] (with a prescribed list of exceptions). Finally, by combining our results with the Lang–Weil estimates from algebraic geometry, we determine bounds on a natural analogue of involution fixity for primitive actions of exceptional algebraic groups over algebraically closed fields.

Evidence for the representation of movement kinematics in the discharge of F5 mirror neurons during the observation of transitive and intransitive actions

Mirror neurons (MirNs) are sensorimotor neurons that fire both when an animal performs a goal-directed action and when the same animal observes another agent performing the same or a similar transitive action. It has been claimed that the observation of intransitive actions does not activate MirNs in a monkey’s brain. Prompted by recent evidence indicating that the discharge of MirNs is modulated also by non-object-directed actions, we investigated thoroughly the efficacy of intransitive actions to trigger MirNs’ discharge. Using representational similarity analysis, we also studied whether the elements constituting the visual scene presented to the monkey during the observation of actions (both transitive and intransitive) are represented in the discharge of MirNs. For this purpose, the moving hand was modeled by its kinematics and the object by features of its geometry. We found that MirNs respond to the observation of both transitive and intransitive actions and that the discharge differences evoked by the observation of object- and non-object-directed actions are correlated more with the kinematic differences of these actions than with the differences of the objects’ features. These findings support the view that observed action kinematics contribute to action mirroring. NEW & NOTEWORTHY Mirror neurons in the monkey brain are thought to respond exclusively to the observation of object-directed actions. Here, we show that mirror neurons also respond to the observation of intransitive actions and that the kinematics of the observed movements are represented in their discharge. This finding supports the view that mirror neurons provide also a kinematics-based representation of actions.

Transitive action on finite points of a full shift and a finitary Ryan’s theorem

We show that on the four-symbol full shift, there is a finitely generated subgroup of the automorphism group whose action is (set-theoretically) transitive of all orders on the points of finite support, up to the necessary caveats due to shift-commutation. As a corollary, we obtain that there is a finite set of automorphisms whose centralizer is $\mathbb{Z}$ (the shift group), giving a finitary version of Ryan’s theorem (on the four-symbol full shift), suggesting an automorphism group invariant for mixing subshifts of finite type (SFTs). We show that any such set of automorphisms must generate an infinite group, and also show that there is also a group with this transitivity property that is a subgroup of the commutator subgroup and whose elements can be written as compositions of involutions. We ask many related questions and prove some easy transitivity results for the group of reversible Turing machines, topological full groups and Thompson’s $V$ .

The Toeplitz noncommutative solenoid and its Kubo–Martin–Schwinger states

We use Katsura’s topological graphs to define Toeplitz extensions of Latrémolière and Packer’s noncommutative-solenoid $C^{\ast }$-algebras. We identify a natural dynamics on each Toeplitz noncommutative solenoid and study the associated Kubo–Martin–Schwinger (KMS) states. Our main result shows that the space of extreme points of the KMS simplex of the Toeplitz noncommutative torus at a strictly positive inverse temperature is homeomorphic to a solenoid; indeed, there is an action of the solenoid group on the Toeplitz noncommutative solenoid that induces a free and transitive action on the extreme boundary of the KMS simplex. With the exception of the degenerate case of trivial rotations, at inverse temperature zero there is a unique KMS state, and only this one factors through Latrémolière and Packer’s noncommutative solenoid.