Partial Action Research Articles

Partial actions: what they are and why we care

We present a survey of recent developments in the theory of partial actions of groups and Hopf algebras.

Effects of electroacupuncture preconditioning on expression of aquaporin-1 and activity of protein kinase C in myocardium of rats with acute myocardial ischemia-reperfusion injury

To explore the partial action mechanism and the myocardial protective effect differences between electroacupuncture (EA) preconditioning at "Neiguan"(PC 6) and "Taiyuan"(LU 9) in rats with acute myocardial ischemia-reperfusion injury. Ninety-six Wistar rats were randomly assigned into a sham-operation group, a model group, a Neiguan group and a Taiyuan group, 24 rats in each one. The rats in the Neiguan group and Taiyuan group were treated with EA (2 Hz in frequency, 1 mA in intensity) at "Neiguan" (PC 6) and "Taiyuan" (LU 9) respectively, 20 min per treatment, once a day for consecutive 7 days. The rats in the sham-operation group and model group were treated with immobilization for the same time, and no EA was given. The model of myocardial ischemia-reperfusion injury was established in the model group, Neiguan group and Taiyuan group 24 h after the end of EA, while the rats in the sham-operation group were treated with sham operation (no ligation was made during surgery). The myocardial ischemic size, infarction size, activity of protein kinase C (PKC) and expression of aquaporin1 (AQP1) in each group were detected. Compared with sham-operation group, the myocardial ischemic size, infarction size, AQP1 expression and PKC activity in the model group were significantly increased (all P<0.01); compared with the model group and Taiyuan group, the myocardial ischemic size, infarction size, PKC activity and AQP1 expression were significantly decreased in the Neiguan group (P<0.01, P<0.05). By Pearson correlation analysis, the changes of AQP1 expression were positively correlated with those of PKC activity after EA preconditioning. EA preconditioning at "Neiguan" (PC 6) could significantly decrease myocardial AQP1 expression and PKC activity in rats with acute myocardial ischemia-reperfusion injuing, but the effect of EA preconditioning at "Taiyuan"(LU 9) is not obvious; its protective effect is likely to be achieved by inhibiting PKC activity and AQP1 expression.

National Blueprint for Biodefense, One Year Later: Taking Stock of Biosecurity Efforts and A Call to Action

In October 2015, a bipartisan study panel on biodefense, A National Blueprint for Biodefense made thirty-three recommendations to advance biopreparedness in the United States. A year later in December 2016, a report titled, The Biodefense Indicators: One Year Later, Events Outpacing Efforts to Defend the Nation (The “One Year Later Report”) provides compelling evidence that much work remains to be done. Within the thirty-three recommendations in the original National Blueprint for Biodefense, forty-six specific action items were designated for execution as a short-term action within a year or less. Among these, twenty-seven were not addressed by any action during the past year. Seventeen received partial action while only two of these were deemed completed. Continuing efforts to protect our populations from biological threats is imperative and warrant immediate constructive short-term action.

Partial group actions and partial Galois extensions

Let \(\alpha \) be a partial action of a group G on a ring S which has an enveloping action. Suppose that \((S,\alpha )\) is a partial Galois extension. We study partial Galois extensions inside \((S,\alpha )\). In particular, we derive some results on partial orbits and partial stabilizers and apply them to associate to each subgroup K of G certain partial Galois extensions inside \((S,\alpha )\) with partial actions of \(\alpha \) restricted to K.

A practical design of digital watermarking for video streaming services

A practical design of digital watermarking for video streaming services is proposed in this research. The information of a legitimate recipient is represented as a watermark, which is embedded in the video stream to serve as a cue to trace the recipient in case a clone of the video is illegally distributed. The watermark signals are designed to embed in some areas of video frames to benefit the video stream server, as the result of only partial actions required, including decoding, processing and re-encoding. The invariance of feature points and the self-similarity of hidden signals are further exploited to enable watermark detection without involving the original video. The watermark can decently survive transcoding processes and geometrical modifications of frames. The experimental results demonstrate the advantages of the proposed scheme in terms of watermark visibility, capacity and detection methodology.

Partial actions and KMS states on relative graph C⁎-algebras

The relative graph C⁎-algebras introduced by Muhly and Tomforde are generalizations of both graph algebras and their Toeplitz extensions. For an arbitrary graph E and a subset R of the set of regular vertices of E we show that the relative graph C⁎-algebra C⁎(E,R) is isomorphic to a partial crossed product for an action of the free group generated by the edge set on the relative boundary path space. Given a time evolution on C⁎(E,R) induced by a function on the edge set, we characterize the KMSβ states and ground states using an abstract result of Exel and Laca. Guided by their work on KMS states for Toeplitz–Cuntz–Krieger type algebras associated to infinite matrices, we obtain complete descriptions of the convex sets of KMS states of finite type and of KMS states of infinite type whose associated measures are supported on recurrent infinite paths. This allows us to give a complete concrete description of the convex set of all KMS states for a big class of graphs which includes all graphs with finitely many vertices.

Partial Actions on Categories

In this article, we introduce the definition of partial action of groups on R-semicategories, generalizing the similar notion of partial actions on categories. Our main result is Theorem 4.6 on the existence of an enveloping action for a partial action of a group on a small R-semi-category. We also define the notion of partial skew category, furthermore proving results similar to the ones in [7].

Globalization of partial actions of groupoids on nonunital rings

We prove a globalization theorem for a partial action of a groupoid on a [Formula: see text]-unital ring. We also construct a strict Morita context between the partial skew groupoid ring and the skew groupoid ring associated to the globalization.

GLOBALIZATION OF TWISTED PARTIAL HOPF ACTIONS

In this work, we review some properties of twisted partial actions of Hopf algebras on unital algebras and give necessary and sufficient conditions for a twisted partial action to have a globalization. We also elaborate a series of examples.

The structure of a partial Galois extension II

Let [Formula: see text] be a partial Galois extension where [Formula: see text] is a partial action of a finite group on a ring [Formula: see text] such that the associated ideals are generated by central idempotents. We determine the set of all Galois extensions in [Formula: see text], and give an orthogonality criterion for nonzero elements in the Boolean semigroup generated by those central idempotents. These results lead to a structure theorem for [Formula: see text].

Partial crossed products as equivalence relation algebras

For a free partial action of a group in a set we realize the associated partial skew group ring as an algebra of functions with finite support over an equivalence relation and we use this result to characterize the ideals in the partial skew group ring. This generalizes, to the purely algebraic setting, the known characterization of partial $C^*$-crossed products as groupoid $C^*$-algebras. For completeness we include a new proof of the $C^*$ result for free partial actions.

Supramenable groups and partial actions

We characterize supramenable groups in terms of the existence of invariant probability measures for partial actions on compact Hausdorff spaces and the existence of tracial states on partial crossed products. These characterizations show that, in general, one cannot decompose a partial crossed product of a $\text{C}^{\ast }$-algebra by a semidirect product of groups into two iterated partial crossed products. However, we give conditions which ensure that such decomposition is possible.

Norm Monitoring Under Partial Action Observability.

In the context of using norms for controlling multiagent systems, a vitally important question that has not yet been addressed in the literature is the development of mechanisms for monitoring norm compliance under partial action observability. This paper proposes the reconstruction of unobserved actions to tackle this problem. In particular, we formalize the problem of reconstructing unobserved actions, and propose an information model and algorithms for monitoring norms under partial action observability using two different processes for reconstructing unobserved actions. Our evaluation shows that reconstructing unobserved actions increases significantly the number of norm violations and fulfilments detected.

On partial H-radicals of Jacobson type

Let H be a Hopf algebra over a field \(\mathbbm {k}\). In this paper we present a general theory on partial H-radicals in the sense of Amitsur-Kurosh, for partial H-module algebras, as made in Fisher (J Algebra 34:217–231, 1975) and Sidorov (Algebra i Logika 28(6):705–721, 1989) for global actions, and study some partial H-radicals of Jacobson type. Among other results we discuss some questions posed by Fisher (1975) in the context of partial actions.

Partial Actions on Graphs

We define a partial action of a group on a graph and their partial orbits and stabilizers for partial graphs. Further some relations between partial orbits and stabilizers are proved. A relation between α-transitivity and β-transitivity of a partial graph is proved where α is a partial action of a group G on the set of vertices and β is a partial action of a group G on the edge set of the graph.

Maximality of dual coactions on sectional $C^{*}$-algebras of Fell bundles and applications

In this paper we give a simple proof of the maximality of dual coac- tions on full cross-sectional C � -algebras of Fell bundles over locally compact groups. This result was only known for discrete groups or for saturated (sep- arable) Fell bundles over locally compact groups. Our proof, which is derived as an application of the theory of universal generalised fixed-point algebras for weakly proper actions, is different from these previously known cases and works for general Fell bundles over locally compact groups. As applications we extend certain exotic crossed-product functors in the sense of Baum, Connes and Willett to the category of Fell bundles and the category of partial actions and we obtain results about the K-theory of (exotic) cross-sectional algebras of Fell-bundles over K-amenable groups. As a bonus, we give a characterisation of maximal coactions of discrete groups in terms of maximal tensor products.

Morita, Galois, and the trace map: a survey

Let A be a \({\mathcal {K}}\)-algebra and H a \({\mathcal {K}}\)-bialgebra (\({\mathcal {K}}\) being a field). Any action \(\beta \) of H on A gives rise to two new \({\mathcal {K}}\)-algebras, namely, the algebra \(A^\beta \) of the invariants of A under \(\beta \) and the smash product \(A\#_\beta H\), as well as a canonical Morita context connecting them. Such a context keeps a close relation with the notion of Galois extension. Indeed, in some cases where it makes sense the strictness of this context is equivalent to exactly say that A is a \(H^*\)-Galois extension of \(A^\beta \). In general, such an equivalence depends also on the surjectivity of a certain trace map from A to \(A^\beta \). This paper is a survey about the strictness of this context in the setting of partial actions of groups and of Hopf algebras.

Early detection of human actions—A hybrid approach

Early detection of human actions is essential in a wide spectrum of applications ranging from video surveillance to health-care. While human action recognition has been extensively studied, little attention is paid to the problem of detecting ongoing human action early, i.e. detecting an action as soon as it begins, but before it finishes. This study aims at training a detector to be capable of recognizing a human action when only partial action sample is seen. To do so, a hybrid technique is proposed in this work which combines the benefits of computer vision as well as fuzzy set theory based on the fuzzy Bandler and Kohout's sub-triangle product (BK subproduct). The novelty lies in the construction of a frame-by-frame membership function for each kind of possible movement. Detection is triggered when a pre-defined threshold is reached in a suitable way. Experimental results on a publicly available dataset demonstrate the benefits and effectiveness of the proposed method.

Morita equivalence of partial group actions and globalization

We consider a large class of partial actions of groups on rings, called regular, which contains all s-unital partial actions, as well as all partial actions on C∗-algebras. For them the notion of Morita equivalence is introduced, and it is shown that any regular partial action is Morita equivalent to a globalizable one, and the globalization is essentially unique. It is also proved that Morita equivalent s-unital partial actions on rings with orthogonal local units are stably isomorphic. In addition, we show that Morita equivalent s-unital partial actions on commutative rings must be isomorphic, and an analogous result for C∗-algebras is also established. Date: November 8, 2015. This work was partially supported by CNPq of Brazil (Proc. 305975/2013-7, Proc. 300362/20102), Fapesp of Brazil (Proc. Proc. 2009/52665-0), MINECO (Ministerio de Economia y Competitividad), (Fondo Europeo de Desarrollo Regional) project MTM2012-35240, Spain, and Fundacion Seneca of Murcia, Programa Hispano Brasileno de Cooperacion Universitaria PHB2012-0135, Spain. 2000 Mathematics Subject Classification: Primary 16S35; Secondary 16W22, 46L05.

Development of an automatic identification algorithm for antibiogram analysis

Routinely, diagnostic and microbiology laboratories perform antibiogram analysis which can present some difficulties leading to misreadings and intra and inter-reader deviations. An Automatic Identification Algorithm (AIA) has been proposed as a solution to overcome some issues associated with the disc diffusion method, which is the main goal of this work. AIA allows automatic scanning of inhibition zones obtained by antibiograms. More than 60 environmental isolates were tested using susceptibility tests which were performed for 12 different antibiotics for a total of 756 readings. Plate images were acquired and classified as standard or oddity. The inhibition zones were measured using the AIA and results were compared with reference method (human reading), using weighted kappa index and statistical analysis to evaluate, respectively, inter-reader agreement and correlation between AIA-based and human-based reading. Agreements were observed in 88% cases and 89% of the tests showed no difference or a <4mm difference between AIA and human analysis, exhibiting a correlation index of 0.85 for all images, 0.90 for standards and 0.80 for oddities with no significant difference between automatic and manual method. AIA resolved some reading problems such as overlapping inhibition zones, imperfect microorganism seeding, non-homogeneity of the circumference, partial action of the antimicrobial, and formation of a second halo of inhibition. Furthermore, AIA proved to overcome some of the limitations observed in other automatic methods. Therefore, AIA may be a practical tool for automated reading of antibiograms in diagnostic and microbiology laboratories.