The operator system of Toeplitz matrices

A recent paper of A. Connes and W.D. van Suijlekom [Comm. Math. Phys. 383 (2021), pp. 2021–2067] identifies the operator system of n × n n\times n Toeplitz matrices with the dual of the space of all trigonometric polynomials of degree less than n n . The present paper examines this identification in somewhat more detail by showing explicitly that the Connes–van Suijlekom isomorphism is a unital complete order isomorphism of operator systems. Applications include two special results in matrix analysis: (i) that every positive linear map of the n × n n\times n complex matrices is completely positive when restricted to the operator subsystem of Toeplitz matrices and (ii) that every linear unital isometry of the n × n n\times n Toeplitz matrices into the algebra of all n × n n\times n complex matrices is a unitary similarity transformation. An operator systems approach to Toeplitz matrices yields new insights into the positivity of block Toeplitz matrices, which are viewed herein as elements of tensor product spaces of an arbitrary operator system with the operator system of n × n n\times n complex Toeplitz matrices. In particular, it is shown that min and max positivity are distinct if the blocks themselves are Toeplitz matrices, and that the maximally entangled Toeplitz matrix ξ n \xi _n generates an extremal ray in the cone of all continuous n × n n\times n Toeplitz-matrix valued functions f f on the unit circle S 1 S^1 whose Fourier coefficients f ^ ( k ) \hat f(k) vanish for | k | ≥ n |k|\geq n . Lastly, it is noted that all positive Toeplitz matrices over nuclear C ∗ ^* -algebras are approximately separable.

Public Trust and Acceptance for Concepts of Remotely Operated Urban Air Mobility Transportation

There is building interest within industry and government to enable Urban Air Mobility (i.e., air-taxies). One concept envisions remotely piloted aircraft, yet it is unclear how this will impact public trust and acceptance. Method: Two hundred participants read vignettes describing remotely-piloted UAM operations and then responded to a series of questionnaires. The study employed a one-way between-subjects design manipulating five levels of Pilot-in-Command Distance: Onboard Pilot; Remote Control Pilot; Dedicated Remote Operator; Remote Operator; System Manager. Results: The Remote Control Pilot group indicated they would be less likely than the Onboard Pilot group to use UAM, based on the mediating effect of trust in the automation. The Remote Control Pilot and Remote Operator groups indicated they would be less likely to use UAM than the Onboard Pilot group, based on the mediating effect of trust in the remote pilot/operator. Conclusion: Trust in UAM automation and remote pilots/operators will likely affect public acceptance of UAM.

Characterization of ori and parS-like functions in secondary genome replicons in Deinococcus radiodurans

The mechanisms underlying multipartite genome maintenance and its functional significance in extraordinary radioresistance of Deinococcus radiodurans are not well understood. The sequences upstream to parAB operons in chrII (cisII) and MP (cisMP) could stabilize an otherwise, non-replicative colE1 plasmid, in D. radiodurans. DnaA and cognate ParB proteins bound specifically with cisII and cisMP elements. The ΔcisII and ΔcisMP cells showed the reduced copy number of cognate replicons and radioresistance as compared with wild type. Fluorescent reporter–operator system inserted in chrI, chrII, and MP in wild type and cisII mutants showed the presence of all three replicons in wild-type cells. Although chrI was present in all the ΔcisII and ΔcisMP cells, nearly half of these cells had chrII and MP, respectively, and the other half had the reduced number of foci representing these replications. These results suggested that cisII and cisMP elements contain both origin of replication and parS-like functions and the secondary genome replicons (chrII and MP) are maintained independent of chrI and have roles in radioresistance of D. radiodurans.

An Investigation of Speech Features, Plant System Alarms, and Operator–System Interaction for the Classification of Operator Cognitive Workload During Dynamic Work

Objective To investigate speech features, human–machine alarms, and operator–system interaction for the estimation of cognitive workload in full-scale realistic simulated scenarios. Background Theories and models of cognitive workload are critical for the design and evaluation of human–machine systems. Unfortunately, there are very few nonintrusive cognitive workload measures available for realistic dynamic human–machine interaction. Method The study was conducted in a full-scope control room research simulator of an advanced nuclear reactor. Six crews, each consisting of three operators, participated in 12 scenarios. The operators rated their workload every second minute. Machine learning algorithms were trained to estimate operators’ workload based on crew communication, operator–system interaction, and system alarms. Results Random Forest (RF) utilizing speech and system features achieved an accuracy of 67% on test data. Utilizing speech features only, the accuracy achieved was 63%. The most important speech features were pitch, amplitude, and articulation rate. A 61% accuracy was achieved when alarms and operator–system interaction features were used. The most important features were the number of alarms and amount of operator–system interaction. Accuracy for algorithms trained for each operator ranged from 39% to 98%, with an average of 72%. For a majority of analyses performed, RF and extreme gradient boosting (XGB) outperformed other algorithms. Conclusion The results demonstrate that the features investigated and machine learning models developed provide a potential for the dynamic nonintrusive measurement of cognitive workload. Application The approach presented can be developed for nonintrusive workload measurement in real-world human–machine applications, simulator-based training, and research.

Optimization of the triage nurse's time by decreasing time spent on non-nursing functions.

293 Background: Triage nurses are an essential part of the multidisciplinary management of the oncology patient. Because of the nature of their role, they spend a significant amount of time performing non-nursing functions, resulting in a delay in patient care and decreased job satisfaction. This study will examine whether implementing a central phone triage system and commensurate process improvements in a large oncology practice will decrease the amount of time that the triage nurses spend on non-nursing functions. Methods: Nine triage nurses at our practice participated in a survey to obtain baseline data. The survey focused on data regarding the non-nursing issues that are encountered during the work day. We then developed a survey for the nurses to determine how much time per 8-hour work day, was spent on the identified non-nursing functions. A new telephone operator system was evaluated for suitability and then implemented. With the new system, the central operator answers all phone calls coming into the practice, and directs them to appropriate department via a messaging system, thus eliminating phone calls to the triage nurses’ direct extensions. Two months after the implementation of this new system, we recollected data to measure the time spent on the previously identified non-nursing functions. A job satisfaction survey was collected pre- and post-study. Results: The initial data collected showed that triage nurses spent approximately 60 minutes per day on non-nursing functions. These functions included the following: the amount of time listening to and taking off patient messages, pre-cert issues, order clarifications and social work issues. The data collected after implementing a new telephone system showed that this time dropped to approximately 12 minutes per day, a 78% reduction in non-nursing calls received by nurses. Additionally, there was a 7% increase in the triage nurse job satisfaction. Conclusions: After implementing a new telephone operator system, the nurses at this large oncology practice were able to better optimize their time taking care of patient related nursing functions. This improved their work flow, increased their time performing direct patient care related functions, and increased their overall job satisfaction. During this process, we also learned the importance of taking triage nurses input to improve their job function. Further research is recommended to better define the role of the phone triage nurse with the multidisciplinary care team of complex hematology/oncology patients.

Strongly Peaking Representations and Compressions of Operator Systems

We use Arveson’s notion of strongly peaking representation to generalize uniqueness theorems for free spectrahedra and matrix convex sets that admit minimal presentations. A fully compressed separable operator system necessarily generates the $C^*$-envelope and is such that the identity is the direct sum of strongly peaking representations. In particular, a fully compressed presentation of a separable operator system is unique up to unitary equivalence. Under various additional assumptions, minimality conditions are sufficient to determine a separable operator system uniquely.

Operator System Structures and Extensions of Schur Multipliers

For a given C*-algebra $\mathcal{A}$, we establish the existence of maximal and minimal operator $\mathcal{A}$-system structures on an AOU $\mathcal{A}$-space. In the case $\mathcal{A}$ is a W*-algebra, we provide an abstract characterisation of dual operator $\mathcal{A}$-systems and study the maximal and minimal dual operator $\mathcal{A}$-system structures on a dual AOU $\mathcal{A}$-space. We introduce operator-valued Schur multipliers and provide a Grothendieck-type characterisation. We study the positive extension problem for a partially defined operator-valued Schur multiplier $\varphi $ and, under some richness conditions, characterise its affirmative solution in terms of the equality between the canonical and the maximal dual operator $\mathcal{A}$-system structures on an operator system naturally associated with the domain of $\varphi $.