Outer Action Research Articles

A Character of Righteous Integrity in Light of God’s Reign: The Spirituality of Jesus According to Matthew

This essay examines Matthew’s depiction of both the spirituality demonstrated by Jesus’ actions and words (his own spirituality) and the spirituality he preaches (prescribes/expects of others). Key Matthean themes interweave in this topic. Jesus’ own spirituality and that which he expects of his followers are shaped most profoundly by the apocalyptic expectation of the imminent Reign of God. All practices and attitudes must be aligned with this coming reality. Because of this, the key mark of a true disciple or righteous person is integrity—the congruence of one’s inner character and outer actions, of one’s professed commitments and one’s behaviors. In this, Jesus is the paragon of integrity: everything he does is in alignment with the character of the coming Reign and God’s will. His actions are always a manifestation of his inner character as God’s son and messianic agent within God’s emerging Reign. Those who, like Jesus, manifest a character that is aligned with the realities of the coming age are called righteous and, at the judgment, are allowed to experience God’s Reign. Their attitudes and behaviors have shown that their inner character is in alignment with the character of the Reign of God. By contrast, the scribes and Pharisees are continually upbraided for their hypocrisy and warned that this will cause them to be barred from the Reign. Thus, the spirituality of Jesus in Matthew can be summed up as “spiritual integrity” (which is “righteousness”) shaped by the character of the imminent Reign of God. Jesus exemplifies this and calls his followers to demonstrate their character with integrity as well.

Application of locally regularized extremal shift to the problem of realization of a prescribed motion

Abstract A controlled system of differential equations under the action of an unknown disturbance is considered. The problem discussed in the paper consists in constructing algorithms for forming a control that provides the realization of a prescribed motion for any admissible disturbance. Namely these algorithms should provide the closeness in the metric of the space of differentiable functions of a phase trajectory of a given controlled system and some etalon trajectory of an analogous system functioning when any outer actions are absent. As the space of admissible disturbances, we take the space of measurable square integrable (with respect to the Euclidean norm) functions. The cases of inaccurate measurements of phase trajectories of both systems at all times and at discrete times are under study. Two computer oriented algorithms for solving the problem are designed. The algorithms are based on the (well-known in the theory of guaranteed control) method of extremal shift. In the process, its local (at each time of control correction) regularization is performed by the method of smoothing functional (the Tikhonov method). In addition, estimates for algorithm’s convergence rate are presented.

Properly outer and strictly outer actions of finite groups on prime C*-algebras

An action of a compact, in particular finite group on a C*-algebra is called properly outer if no automorphism of the group that is distinct from identity is implemented by a unitary element of the algebra of local multipliers of the C*-algebra. In this paper, I define the notion of strictly outer action (similar to the definition for von Neumann factors in [S. Vaes, The unitary implementation of a locally compact group action, J. Funct. Anal. 180 (2001) 426–480]) and prove that for finite groups and prime C*-algebras, it is equivalent to the proper outerness of the action. For finite abelian groups this is equivalent to other relevant properties of the action.

Dynamical comparison and [formula omitted]-stability for crossed products of simple C⁎-algebras

We establish Z-stability for crossed products of outer actions of amenable groups on Z-stable C⁎-algebras under a mild technical assumption which we call McDuff property with respect to invariant traces. We obtain such result using a weak form of dynamical comparison, which we verify in great generality. We complement our results by proving that McDuffness with respect to invariant traces is automatic in many cases of interest. This is the case, for instance, for every action of an amenable group G on a classifiable C⁎-algebra A whose trace space T(A) is a Bauer simplex with finite dimensional boundary ∂eT(A), and such that the induced action G↷∂eT(A) is free. If G=Zd and the action G↷∂eT(A) is free and minimal, then we obtain McDuffness with respect to invariant traces, and thus Z-stability of the corresponding crossed product, also in case ∂eT(A) has infinite covering dimension.

Core-shell cisplatin/SiO2 nanocapsules combined with PTC-209 overcome chemotherapy–Acquired and intrinsic resistance in hepatocellular carcinoma

The primary cause of cisplatin resistance in liver cancer is reduced intracellular drug accumulation and altered DNA repair/apoptosis signaling. Existing strategies to reverse cisplatin resistance have limited efficacy, as they target individual factors. This study proposes a drug delivery system consisting of a cisplatin core, a silica shell with a tetra-sulfide bond, and a PEG-coated surface (Core/shell-PGCN). The system is designed to consume glutathione (GSH) and reduce cisplatin excretion from cells, thereby overcoming acquired cisplatin resistance. In addition, Core/shell-PGCN incorporates PTC-209 (Core/shell-PGCN@PTC-209), a Bmi1 inhibitor that suppresses liver cancer stem cells (CSC), to mitigate DNA repair/apoptosis signaling and reverse intrinsic cisplatin resistance. In vivo and in vitro results demonstrate that Core/shell-PGCN@PTC-209 can comprehensively regulate GSH and CSC, reverse intrinsic and acquired cisplatin resistance, and enhance the efficacy of cisplatin in treating liver cancer. This "inner cultivation, outer action" approach may offer a new strategy for reversing cisplatin resistance in liver cancer. Statement of significanceCisplatin resistance is widely observed in liver cancer (HCC) chemotherapy, with two mechanisms identified: acquired and intrinsic. Most strategies aimed at overcoming cisplatin resistance focus on a single perspective. This study introduces a core-shell drug delivery system (DDS) combined with HCC stem cell inhibitors, which can effectively address cisplatin resistance in HCC by targeting both acquisition and internality. Specifically, the core-shell drug delivery system can impede cisplatin efflux by neutralizing the acquired resistance factor (GSH), thus overcoming acquired resistance. Additionally, HCC stem cell inhibitors can reverse intrinsic resistance by inhibiting HCC stem cells. Therefore, this study contributes to the application of DDS in combating drug resistance in HCC and enhances its potential for clinical implementation.

Equivariant Kirchberg-Phillips type absorption for the Razak-Jacelon algebra

Let A and B be simple separable nuclear monotracial C⁎-algebras, and let α and β be strongly outer actions of a countable discrete amenable group Γ on A and B, respectively. In this paper, we show that α⊗idW on A⊗W and β⊗idW on B⊗W are cocycle conjugate where W is the Razak-Jacelon algebra. Also, we characterize such actions by using the fixed point subalgebras of Kirchberg's central sequence C⁎-algebras.

Spectral gap and strict outerness for actions of locally compact groups on full factors

We prove that an outer action of a locally compact group G on a full factor M is automatically strictly outer, meaning that the relative commutant of M in the crossed product is trivial. If moreover the image of G in the outer automorphism group Out M is closed, we prove that the crossed product remains full. We obtain this result by proving that the inclusion of M in the crossed product automatically has a spectral gap property. Such results had only been proven for actions of discrete groups and for actions of compact groups, by using quite different methods in both cases. Even for the canonical free Bogoljubov actions on free group factors or free Araki–Woods factors, these results are new.

MAESTRO-X: Distributed Orchestration of Rotary-Wing UAV-Relay Swarms

This work details a scalable framework to orchestrate a swarm of rotary-wing UAVs serving as cellular relays to facilitate beyond line-of-sight connectivity and traffic offloading for ground users. First, a Multiscale Adaptive Energyconscious Scheduling and TRajectory Optimization (MAESTRO) framework is developed for a single UAV. Aiming to minimize the time-averaged latency to serve user requests, subject to an average UAV power constraint, it is shown that the optimization problem can be cast as a semi-Markov decision process, and exhibits a multiscale structure: outer actions on radial wait velocities and terminal service positions minimize the longterm delay-power trade-off, optimized via value iteration; given these outer actions, inner actions on angular wait velocities and service trajectories minimize a short-term delay-energy cost; finally, rate adaptation is embedded along the trajectory to leverage air-to-ground channel propagation conditions. A novel hierarchical competitive swarm optimization scheme is developed in the inner optimization, to devise high-resolution trajectories via iterative pair-wise updates. Next, MAESTRO is eXtended to UAV swarms (MAESTRO-X) via scalable policy replication, enabled by a decentralized command-and-control network augmented with: (1) spread maximization to proactively position UAVs to serve future requests; (2) consensus-driven conflict resolution to orchestrate scheduling decisions based on delay-energy costs including queuing dynamics; (3) adaptive frequency reuse to improve spectrum utilization across the network; and (4) a piggybacking mechanism allowing UAVs to serve multiple ground users simultaneously. Numerical evaluations show that, for user requests of 10 Mbits, generated according to a Poisson arrival process with rate 0.2 req/min/UAV, single-agent MAESTRO offers 3.8× faster service than a high-altitude platform and 29% faster than a static UAV deployment; moreover, for a swarm of 3 UAV-relays, MAESTRO-X delivers data payloads 4.7× faster than a successive convex approximation scheme; and remarkably, a single UAV optimized via MAESTRO outclasses 3 UAVs optimized via a deep-Q network by 38%.

Group-theoreticity of numerical invariants and distinguished subgroups of configuration space groups

Let $\Sigma$ be a set of prime numbers which is either of cardinality one or equal to the set of all prime numbers. In this paper, we prove that various objects that arise from the geometry of the configuration space of a hyperbolic curve over an algebraically closed field of characteristic zero may be reconstructed group-theoretically from the pro-$\Sigma$ fundamental group of the configuration space. Let $X$ be a hyperbolic curve of type $(g,r)$ over a field $k$ of characteristic zero. Thus, $X$ is obtained by removing from a proper smooth curve of genus $g$ over $k$ a closed subscheme [i.e., the "divisor of cusps"] of $X$ whose structure morphism to Spec$(k)$ is finite étale of degree $r$; $2g-2+r>0$. Write $X_n$ for the $n$-th configuration space associated to $X$, i.e., the complement of the various diagonal divisors in the fiber product over $k$ of $n$ copies of $X$. Then, when $k$ is algebraically closed, we show that the triple $(n,g,r)$ and the generalized fiber subgroups—i.e., the subgroups that arise from the various natural morphisms $X_n \to X_m$ $[m$ < $n]$, which we refer to as generalized projection morphisms—of the pro-$\Sigma$ fundamental group $\Pi_n$ of $X_n$ may be reconstructed group-theoretically from $\Pi_n$ whenever $n \geq 2$. This result generalizes results obtained previously by the first and third authors and A. Tamagawa to the case of arbitrary hyperbolic curves [i.e., without restrictions on $(g,r)$]. As an application, in the case where $(g,r)= (0,3)$ and $n \geq 2$, we conclude that there exists a direct product decomposition Out$(\Pi_n) = {\mathrm{GT}^{\Sigma}} \times \mathfrak{S}_{n + 3}$ —where we write "Out$(-)$" for the group of outer automorphisms [i.e., without any auxiliary restrictions!] of the profinite group in parentheses and ${\mathrm{GT}^{\Sigma}}$ (respectively, $\mathfrak{S}_{n + 3}$) for the pro-$\Sigma$ Grothendieck-Teichmüller group (respectively, symmetric group on $n + 3$ letters). This direct product decomposition may be applied to obtain a simplified purely group-theoretic equivalent definition—i.e., as the centralizer in ${\rm Out}(\Pi_n)$ of the union of the centers of the open subgroups of ${\rm Out}(\Pi_n)$—of ${\mathrm{GT}^{\Sigma}}$. One of the key notions underlying the theory of the present paper is the notion of a pro-$\Sigma$ log-full subgroup—which may be regarded as a sort of higher-dimensional analogue of the notion of a pro-$\Sigma$ cuspidal inertia subgroup of a surface group—of $\Pi_n$. In the final section of the present paper, we show that, when $X$ and $k$ satisfy certain conditions concerning "weights", the pro-$l$ log-full subgroups may be reconstructed group-theoretically from the natural outer action of the absolute Galois group of $k$ on the geometric pro-$l$ fundamental group of $X_n$.

The Novels by T. Hardy “Tess of the D’urbervilles” and “Loose” by Panas Myrnyi: Peculiarities of Stylistic Narration

The peculiarities of stylistic narration of the novels by T. Hardy and Panas Myrnyi are considered in the article. We defined that historical and typological principles, being theoretically “disclosed”, have already contributed to defining a significant number of peculiarities of historical and literary development under any national conditions. All this, on the whole, gives the possibility to all-round studying the artistic culture. We found out that using cultural data in the linguistic creation of the text is one way to acquire the style mastership. The purpose of the article is to explore the peculiarities of the stylistic narration in the novels by T. Hardy and Panas Myrnyi. The research subject is socio-psychological novels by T. Hardy and Panas Myrnyi. The methods such as historical-typological, historical-genetic, and historical-functional were used to achieve the goal. We underlined the fact that the prose of the mentioned authors is characterised by using different forms of narration: inner monologues and dialogues, recollections, letters and narrative elements. It contributed to the lyricism of the novel genre and sophistication of the composition of the novels, which let to transfer the plan of solving problems from the outer actions to the inner psychological plan.

Classification of outer actions of discrete amenable groupoids on injective factors

We classify outer actions (or $\mathscr{G}$-kernels) of discrete amenable groupoids on injective factors. Our method based on unified approach for classification of discrete amenable groups actions, and cohomology reduction theorem of discrete amenable equivalence relations. We do not use Katayama–Takesaki type resolution group approach.

Adaptive Power Control Based on Double-layer Q-learning Algorithm for Multi-parallel Power Conversion Systems in Energy Storage Station

An energy storage station (ESS) usually includes multiple battery systems under parallel operation. In each battery system, a power conversion system (PCS) is used to connect the power system with the battery pack. When allocating the ESS power to multi-parallel PCSs in situations with fluctuating operation, the existing power control methods for parallel PCSs have difficulty in achieving the optimal efficiency during a long-term time period. In addition, existing Q-learning algorithms for adaptive power allocation suffer from the curse of dimensionality. To overcome these challenges, an adaptive power control method based on the double-layer Q-learning algorithm for <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> parallel PCSs of the ESS is proposed in this paper. First, a selection method for the power allocation coefficient is developed to avoid repeated actions. Then, the outer action space is divided into <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$n$</tex> +1 power allocation modes according to the power allocation characteristics of the optimal operation efficiency. The inner layer uses an actor neural network to determine the optimal action strategy of power allocations in the non-steady state. Compared with existing power control methods, the proposed method achieves better performance for both static and dynamic operation efficiency optimization. The proposed method optimizes the overall operation efficiency of PCSs effectively under the fluctuating power outputs of the ESS.

Numerical investigation on crack propagation and coalescence induced by dual-borehole blasting

Dynamic directional fracture of dual-borehole blasting is very vital to the rock fragmentation and final contour of some projects, such as the tunnel and slope. In this paper, a rock-like material, polymethyl methacrylate (PMMA), is utilized to explore the effects of borehole distance d, delayed time td, and guide hole type on crack propagation behavior under dual-borehole blasting through numerical simulations. To improve the deficiency of constitutive model and the post-failure response of brittle material and reduce the mesh dependency, a coupling scheme of Johnson-Holmquist (JH-2) model, failure criterion, and crack softening failure model is adopted here. First, the crack propagation results of single-borehole blasting well reproduced inner and outer actions of blasting, which proved the reliability of this scheme. For the dual-borehole blasting, it was found that the increase of borehole distance indeed penalized the crack coalescence and the length of crack produced at the common guide hole. Compared with the common guide hole, the grooved guide hole at d = 30 cm contributes more crack coalescences, which is independent of the delayed time; at d = 40 cm, the longer cracks are produced at grooved guide hole than common one and the crack coalescence is related to the delayed time. The grooved guide hole was more conducive to the coalescence and lengthening of crack. More importantly, the crack coalescence manner showed mutual, direct, and indirect ones, and two manners could coexist in one model. In addition, guide hole also could enrich the crack coalescence manner. Lastly, the crack stagger depends on the change of tensile stress at one crack tip into the compressive one at another one; the crack coalescence indicates tensile stress fields of two crack tips have no mutual influence.

Group amenability and actions on [formula omitted]-stable C*-algebras

We study strongly outer actions of discrete groups on C*-algebras in relation to (non)amenability. In contrast to related results for amenable groups, where uniqueness of strongly outer actions on the Jiang-Su algebra is expected, we show that uniqueness fails for all nonamenable groups, and that the failure is drastic. Our main result implies that if G contains a copy of F2, then there exist uncountably many, non-cocycle conjugate strongly outer actions of G on any tracial, unital, separable C*-algebra that absorbs tensorially the Jiang-Su algebra. Similar conclusions hold for outer actions on McDuff II1 factors. We moreover show that G is amenable if and only if the Bernoulli shift on any finite strongly self-absorbing C*-algebra absorbs the trivial action on the Jiang-Su algebra. Our methods are inspired by Jones' work [27], and consist in a careful study of weak containment for the Koopman representations of certain generalized Bernoulli actions.

Equivariant property (SI) revisited

We revisit Matui-Sato's notion of property (SI) for C*-algebras and C*-dynamics. More specifically, we generalize the known framework to the case of C*-algebras with possibly unbounded traces. The novelty of this approach lies in the equivariant context, where none of the previous work allows one to (directly) apply such methods to actions of amenable groups on highly non-unital C*-algebras, in particular to establish equivariant Jiang-Su stability. Our main result is an extension of an observation by Sato: For any countable amenable group $\Gamma$ and any non-elementary separable simple nuclear C*-algebra $A$ with strict comparison, every $\Gamma$-action on $A$ has equivariant property (SI). A more general statement involving relative property (SI) for inclusions into ultraproducts is proved as well. As a consequence we show that if $A$ also has finitely many rays of extremal traces, then every $\Gamma$-action on $A$ is equivariantly Jiang-Su stable. We moreover provide applications of the main result to the context of strongly outer actions, such as a generalization of Nawata's classification of strongly outer automorphisms on the (stabilized) Razak-Jacelon algebra.

Equivariant -absorption theorem for exact groups

We show that, up to strong cocycle conjugacy, every countable exact group admits a unique equivariantly$\mathcal {O}_{2}$-absorbing, pointwise outer action on the Cuntz algebra$\mathcal {O}_{2}$with the quasi-central approximation property (QAP). In particular, we establish the equivariant analogue of the Kirchberg$\mathcal {O}_{2}$-absorption theorem for these groups.

Double Affine Hecke Algebras and Congruence Groups

The most general construction of double affine Artin groups (DAAG) and Hecke algebras (DAHA) associates such objects to pairs of compatible reductive group data. We show that DAAG/DAHA always admit a faithful action by automorphisms of a finite index subgroup of the Artin group of type $A_{2}$, which descends to a faithful outer action of a congruence subgroup of $SL(2,\mathbb{Z})$ or $PSL(2,\mathbb{Z})$. This was previously known only in some special cases and, to the best of our knowledge, not even conjectured to hold in full generality. The structural intricacies of DAAG/DAHA are captured by the underlying semisimple data and, to a large extent, by adjoint data; we prove our main result by reduction to the adjoint case. Adjoint DAAG/DAHA correspond in a natural way to affine Lie algebras, or more precisely to their affinized Weyl groups, which are the semi-direct products $W\ltimes Q^{\vee}$ of the Weyl group $W$ with the coroot lattice $Q^{\vee}$. We now describe our results for the adjoint case in greater detail. We first give a new Coxeter-type presentation for adjoint DAAG as quotients of the Coxeter braid groups associated to certain crystallographic diagrams that we call double affine Coxeter diagrams. As a consequence we show that the rank two Artin groups of type $A_{2},B_{2},G_{2}$ act by automorphisms on the adjoint DAAG/DAHA associated to affine Lie algebras of twist $r=1,2,3$, respectively. This extends a fundamental result of Cherednik for $r=1$. We show further that the above rank two Artin group action descends to an outer action of congruence subgroup $\Gamma_{1}(r)$. In particular $\Gamma_{1}( r) $ acts naturally on the set of isomorphism classes of representations of an adjoint DAAG/DAHA of twist type $r$, giving rise to a projective representation of $\Gamma_{1}( r) $ on the space of a $\Gamma_{1}( r) $-stable representation.

Full Factors and Co-amenable Inclusions

We show that if M is a full factor and $$N \subset M$$ is a co-amenable subfactor with expectation, then N is also full. This answers a question of Popa from 1986. We also generalize a theorem of Tomatsu by showing that if M is a full factor and $$\sigma :G \curvearrowright M$$ is an outer action of a compact group G, then $$\sigma $$ is automatically minimal and $$M^G$$ is a full factor which has w-spectral gap in M. Finally, in the appendix, we give a proof of the fact that several natural notions of co-amenability for an inclusion $$N\subset M$$ of von Neumann algebras are equivalent, thus closing the cycle of implications given in Anantharaman-Delaroche’s paper in 1995.

ISOTOPY AND HOMEOMORPHISM OF CLOSED SURFACE BRAIDS

AbstractThe closure of a braid in a closed orientable surface Ʃ is a link in Ʃ ×S1. We classify such closed surface braids up to isotopy and homeomorphism (with a small indeterminacy for isotopy of closed sphere braids), algebraically in terms of the surface braid group. We find that in positive genus, braids close to isotopic links if and only if they are conjugate, and close to homeomorphic links if and only if they are in the same orbit of the outer action of the mapping class group on the surface braid group modulo its centre.

Rohlin Actions of Finite Groups on the Razak–Jacelon Algebra

AbstractLet $A$ be a simple separable nuclear C$^*$-algebra with a unique tracial state and no unbounded traces, and let $\alpha $ be a strongly outer action of a finite group $G$ on $A$. In this paper, we show that $\alpha \otimes \textrm{id}$ on $A\otimes \mathcal{W}$ has the Rohlin property where $\mathcal{W}$ is the Razak–Jacelon algebra. Combing this result with the recent classification results and our previous result, we see that such actions are unique up to conjugacy.