Our results highlight the positive attitudes of inpatients and staff members toward ward cats and the potential of ward cats to enhance patient satisfaction. This influence might be mediated by factors such as the frequency of contact, the relationship between each patient and the cat, and each patient’s attitude toward cats in general.The aim of this study was to investigate inpatient and staff member attitudes toward and experiences with ward cats, and identify possible mechanisms for how cats affect patient satisfaction in a psychiatric clinic. Thirty-three inpatients diagnosed with depression or psychosis residing on wards with and without cats and 17 staff members working on wards with cats participated in semi-structured interviews using a cross-sectional study design. Data analysis included descriptive statistics and correlations. The results showed that 17 out of 19 inpatients and all the staff members liked having a cat on their ward. Further, 12 out of 14 inpatients on wards without cats would like having a cat on their ward. Inpatient perceptions of the cat’s impact on the ward atmosphere correlated significantly with their emotional relationship with the cat ( Patient satisfaction of inpatients with mental illness is an important factor in predicting functional and clinical outcomes . It is lA recent investigation found that psychiatric inpatients treated on wards with cats were more satisfied compared with patients on wards without cats . ResearcConcrete mechanisms explaining the effect of the presence of ward cats on patient satisfaction in our previous study  were uncThe aim of this study was to investigate inpatient attitudes toward and experiences with ward cats and identify possible mechanisms for how cats might affect patient satisfaction. We conducted semi-structured interviews with inpatients in psychiatric treatment on wards with cats and wards without cats. We additionally studied staff member perceptions on the effects of the cats.N = 20) or psychosis (N = 13) in four wards at the University Psychiatric Clinics (UPK) in Basel, Switzerland between July and August 2017. All the wards were acute psychiatric wards with an open-door policy; two were wards for inpatients with depression and two were wards for inpatients with psychosis, and each had one ward with and one ward without a cat. Patients were assigned to wards based on their mental health problems and were not given the choice of a ward with or without a cat. We also interviewed 17 staff members working on the two wards with cats. All the cats had lived on the wards for several years, with free choice daytime access to ward common rooms, patient rooms, or the clinic’s outdoor garden. At night, the cats remained in the ward common rooms. Inpatients were not permitted to close cats into their rooms at any time, and were advised to interact with the cats in the common rooms. Staff members were responsible for cat care, such as feeding, grooming, and veterinary checks.We interviewed all 33 inpatients with a diagnosis of depression .We interviewed inpatients and staff members after they agreed with the informed consent. The cantonal ethics committee  approved the study protocol, which was registered at The semi-structured interview targeted inpatient attitudes toward housing a cat on their ward, inpatient interactions with the cats, and inpatient general beliefs about the effects of a cat on atmosphere, social interactions, and their own well-being. We created similar interviews for inpatients on wards with and without cats and for staff members on wards with cats. The interview for inpatients on wards with cats contained 31 items: 11 rating questions, 13 polar questions, and 7 open questions see . We did The interview for inpatients on wards without cats contained 24 items: 8 rating questions, 9 polar questions, and 7 open questions. The first part of the interview was identical to the interview with inpatients on wards with cats. After that, inpatients on wards without cats were asked 14 cat-related questions. One question assessed if inpatients knew about the cats on other wards. Two items targeted the patient’s attitude about potentially housing cats on their ward. Two items asked inpatients about a cat’s potential impact on their ward, and one item asked about a cat’s potential impact on the patient. Two items assessed if inpatients would like to have a cat or other animal on their ward. Seven items investigated inpatient’s pet history, previous experiences with pets, whether they liked animals and cats, and if they had a cat hair allergy. The interview for staff members working on wards with cats contained 31 items: 12 rating questions, 16 polar questions, and 3 open questions. Similar to the interview conducted with inpatients, the first part of the interview assessed sociodemographic information, how long they had worked on the ward, their satisfaction with the ward, and what they perceived as important regarding ward atmosphere. After this, there were 26 cat-related items. Two items examined if the staff member knew that a cat lived on the ward and how often they saw the cat. One item asked if they thought the cat was affectionate. Three items assessed the staff member’s relationship to the cat. Three items asked the staff member about their attitude toward housing a cat on their ward. Two items assessed who was responsible for the cat, and if the cat required any additional effort by the staff member. One item asked staff members how the cat influenced their work satisfaction. Three items assessed how staff members perceived the cat’s impact on ward atmosphere. Four questions detected the staff member’s perception of the influence of the ward cat on inpatients. Seven items assessed staff member’s pet history, if they liked animals, and if they had a cat-hair allergy. The rating questions used a 6-stage Likert scale, with 1 indicating “no approval”, “negative”, “not at all”, or “never”; and 6 indicating “high approval”, “positive”, “very much”, or “very often”. For interpretation of results, we combined scores: 1 and 2 were considered as “no approval”, “negative” or “not at all”; 3 and 4 were considered as “medium”; and 5 and 6 were considered as “high approval”, “positive”, or “very much”. The statistical analyses were done without dichotomization. The question of ward cat impact on ward atmosphere in the interviews with inpatients on wards with cats had a reversed scale, which we recoded before data analysis. The polar questions (yes/no) explicitly examined inpatient opinions about suggested mechanisms. The interviews lasted approximately 15 minutes for each patient. We analyzed patient answers on the open questions with Mayring’s qualitative content analysis approach . First, We used descriptive statistics to describe the patient answers. Spearman’s correlation coefficients determined the relationship between different questions, since data were not normally distributed. We set the confidence interval at 95%. We used SPSS, Version 25 , for statistical analyses.Thirty-three inpatients  completed the interview, of whom 19 were on a ward with cats (9 inpatients with psychosis and 10 inpatients with depression) and 14 were on a ward without cats (4 inpatients with psychosis and 10 inpatients with depression). Seventeen staff members  participated in interviews, all of whom worked on wards with cats. z = −0.91, p = 0.362, d = 0.27).There was no difference between ward satisfaction between inpatients treated on wards with cats  compared to inpatients on wards without cats , and 9 of 19 inpatients said that cats had positive effects on their state of mind . Thirteen of 19 inpatients did not report any negative aspects when asked about these. The negative aspects of a cat included potential but not actual problems such as hygiene, allergies, cat welfare, and if someone did not like cats or was afraid of them. The rating questions revealed that 17 out of 19 inpatients reported positive feelings about the cat on their ward, whereas two reported neutral feelings, and no one reported negative feelings about the cat see . Seven or = 0.561, p = 0.015) and their attitude toward housing a cat on their ward . Moreover, inpatients believed that the cat’s impact on ward atmosphere was higher if they saw the cat more often , and if they liked cats more in general . However, the inpatient’s emotional relationship with the cat did not correlate with how often they saw the cat . Inpatient perception of the ward cat’s impact on ward atmosphere was significantly correlated with their emotional relationship with the cat  and their attitude toward housing a cat on their ward . However, having pets currently or in the past and growing up with animals did not correlate significantly with any ward cat-related item.The inpatient’s pet history correlated with some items. Their previous experiences with pets correlated significantly with their perceived closeness to the cat , and 7 inpatients believed that the cat might have a positive effect on their state of mind . The most often mentioned negative aspects of potentially housing a cat on a psychiatric ward targeted allergies (4 out of 14 inpatients) or hygiene (4 out of 14 inpatients). The results of the rating questions showed that 8 out of 14 inpatients believed a cat would help them feel more comfortable in the psychiatric clinic, whereas 6 inpatients believed the cat would have a medium impact. Further, nine inpatients thought that a cat would positively influence their satisfaction with their ward. Four inpatients thought that the cat would have a medium effect, and two thought that the cat would have a rather negative effect on their satisfaction with the ward see .Analysis of the polar questions revealed that 12 out of 14 inpatients treated on wards without cats stated that they would prefer to have a cat on their own ward.All the interviewed staff members working on wards with cats had positive feelings about the cat on their ward. Regarding the possible effects of the ward cat’s presence on inpatients, 16 of 16 staff members  believed the cat helped inpatients feel more comfortable and led to more conversation, both between inpatients and between inpatients and staff members. Further, 14 out of 17 staff members thought the cat had a positive impact on inpatient emotional well-being and the ward atmosphere, whereas 3 believed the cat had a neutral impact.Regarding the influence of the ward cat on staff members themselves, 14 out of 17 staff members stated the cat had a positive impact on their work satisfaction, 3 said that the cat had a neutral effect, and no one indicated a negative effect.The present study investigated inpatient and staff member attitudes toward and experiences with ward cats in a psychiatric setting to identify possible mechanisms on how cats affect patient satisfaction.The interview results revealed that the inpatients treated and staff members working on wards with cats and inpatients treated on wards without cats all had positive attitudes toward ward cats. All the inpatients who were treated on a ward with a cat listed positive aspects of housing a cat, while only 6 out of 19 could think of potential negative aspects. The majority of inpatients liked having a cat on their ward, with only one patient preferring to live on a ward without a cat. However, not all the inpatients believed that the cat had a positive impact on their emotional well-being or on factors related to patient satisfaction ,29,30,31Inpatient and staff member perception about the cat’s impact on ward atmosphere and on inpatient well-being were different. While patients did not perceive such an effect, staff members reported a positive influence of the cat on ward atmosphere and inpatient well-being. A possible explanation is that ward cats did not have a direct impact on inpatients, but worked as mediators by influencing staff members. Previous research reported beneficial effects of the presence of animals in health care centers ,14,32. SOur results suggest that the ward cat’s impact on inpatients depends on additional factors. The correlational analysis showed that inpatients on wards with a cat perceived the cat’s impact on ward atmosphere to be higher when they reported a stronger emotional relationship with the cat or saw the cat more often. The ward atmosphere is related to patient satisfaction ,29,30,31Our finding indicates that a relationship with a cat, which is defined as extent of emotional closeness and how often the patient saw the cat, is a prerequisite that influences patient satisfaction. It could be that relationship with a cat provides a direct source of comfort , which iSurprisingly, the intensity of the relationship with the cat did not correlate with how often the patient saw the cat, illustrating that this study is not sufficient to clarify which factor is more important. Correlations must be interpreted carefully, as the number of interviews was small, and no objective measurements were used. This study intended to generate hypotheses for mechanisms linking ward cats and patient satisfaction. Our results showed that all the inpatients on wards with cats noticed the cats and perceived them as integral to the ward. The majority of inpatients on wards without cats preferred having a ward cat. This outcome builds on our previous results, showing that patient satisfaction is higher on wards with a cat compared to wards without a cat. Future research should prospectively investigate the effect of ward cats on patient satisfaction. It would be valuable to combine patient self-reporting with patient and cat behavioral measurements, such as how often, how long, and how they interact. Individual cat personality is likely an important factor, and future work should identify whether specific characteristics are important to inpatients and staff members, incorporating a One Health approach .To make specific recommendations for clinics, more knowledge is needed about which types of inpatients might benefit from exposure to cats, and the extent of interaction and relationship necessary to improve patient satisfaction. Although we found inpatients were highly positive toward housing ward cats in general, this should always be addressed on an individual level. In our study, one inpatient on a ward with a cat preferred living on a ward without a cat, which should be respected regardless of the reported positive effects that animals might have on humans. Every healthcare center should have an animal-free ward, so patients can avoid contact when they are uncomfortable with animals.Positive feedback from inpatients and staff members supports the idea that cats enhance patient satisfaction in psychiatric clinics. However, perceptions of the two groups differed regarding the effects and impact of ward cats. Our correlational analysis indicated that the impact of ward cats on patient satisfaction could depend on how frequently the patients see the cat, how close the relationship is with the cat, and whether patients like cats. Further research should investigate these hypotheses in a larger sample to make recommendations on integrating cats in psychiatric clinic treatment settings to enhance inpatient satisfaction.


Virtual reality (VR) is emerging as one of key applications in future fifth-generation (5G) networks. Uploading VR video in 5G network is expected to boom in near future, as general consumers could generate high-quality VR videos with portable 360-degree cameras and are willing to share with others. Heterogeneous networks integrating with 5G cloud-radio access networks (H-CRAN) provides high transmission rate for VR video uploading. To address the motion characteristic of UE (User Equipments) and small cell feature of 5G H-CRAN, in this paper we proposed a content-sensing based resource allocation scheme for delay-sensitive VR video uploading in 5G H-CRAN, in which the source coding rate of uploading VR video is determined by the centralized RA scheduling. This scheme jointly optimizes g-NB group resource allocation, RHH/g-NB association, sub-channel assignment, power allocation, and tile encoding rate assignment as formulated in a mixed-integer nonlinear problem (MINLP). To solve the problem, a three stage algorithm is proposed. Dynamic g-NB group resource allocation is first performed according to the UE density of each group. Then, joint RRH/g-NB association, sub-channel allocation and power allocation is performed by an iterative process. Finally, encoding tile rate is assigned to optimize the target objective by adopting convex optimization toolbox. The simulation results show that our proposed algorithm ensures the total utility of system under the constraint of maximum transmission delay and power, which also with low complexity and faster convergence. In recent years, virtual reality (VR) technology has been rapidly commercialized, forming a $209 billion market by 2022 as predicted in . VR makeAs the popularity of the User-Generated Content (UGC) platforms increases , more people would like to generate VR videos themselves with portable 360-degree cameras  and share with others through UGC platform. Essentially, high-quality VR videos are produced and need to be uploaded to the UGC platform (uplink procedure); then, the UGC platform disseminates them to other VR viewers through applications like VR live broadcast (downlink procedure). These procedures, especially the uplink procedure, call for the use of 5G network as the strong support of mobility and collaboration. VR is predicted as the mass deployment of the 5G network [Optimization of VR video transmission is actively under explanation, but previous work mostly focused on the downlink procedure, and a common precondition of these studies is transcoding VR videos into multiple representations (bit rates) on the cloud server. Alface et al.  presente5G H-CRAN has been shown a promising solution for VR video transmission in the near future. Heterogeneous networks with massive densification of small cells and CRANs are combined in one network structure to improve spectral efficiency, resource management, and energy efficiency . HoweverThis paper addresses the VR video uploading problem in 5G network. Optimization for VR video uploading in 5G network is more challenging and demanded. First, it is not viable for a user terminal to create multiple representations due to the lack of computing and storage resources on board. Second, the uplink wireless bandwidth is more limited than the downlink in 5G network. Third, content-sensing based source coding is necessarily adopted due to the high data volume of 360 degree content. Fourth, moving feature of UE which calls dynamic association with corresponding RRH/g-NB. The last not the least, delay-sensitive of VR video needs to be well scheduled in the uplink procedure.Quite few studies VR video uploading over wireless network. However, RA for regular video uplink streaming over wireless network has been studied for different application types. Ragaleux et al.  presenteMotivated by the aforementioned challenges for VR video uploading over wireless network, RA for delay-sensitive VR videos uploading in 5G H-CRAN has been studied in this paper. As the storage resources on board and delay-sensitive character of VR video, tile-based source coding  is adoptNote that the problem is hardly solved in one shot by the optimization toolbox due to the problem consists of multiple stages in the VR video uploading process , a three stage algorithm is proposed to solve the problem efficiently in this paper. The total bandwidth is first allocated to g-NB groups according to the UE density of corresponding g-NB group, where frequency is reused at each RHH. Then RHH/g-NB association, sub-channel allocation and power allocation, and tile encoding rate assignment are jointly solved by decouple the problem into two sub-problem. First sub-problem can be described as allocate the optimal source coding rate for each tile under the constraint of maximum transition delay and upper bound of transmission rate, which is solved by optimization toolbox after the second sub-problem solved to obtain upper bound of transmission rate. While the second sub-problem can be expressed as find the optimization association, PA and SA to maximize the weighted sum-rate, which two step iterative algorithm is proposed to solve the sub-problem.The remainder of the paper is organized as follows. System model and saliency of tile-based VR video are introduced in The system considered in this work is depicted in I randomly User equipments (UEs) with 360-degree cameras which generate VR videos simultaneously, and need to upload them to the core network through 5G H-CRAN. Finally viewers experience the virtual reality in the HMDs by requesting the VR video contents through the UGC platform. Each VR video consists of multiple video chunks along the time which are denoted by Furthermore, consider g-th g-NB group is denoted by The RA scheduler is integrated with the BBU pool, and executes RA in the centralized approach. The available transmission bandwidth is subdivided into sub-channels, which are denoted by g-th g-NB group. On the other hand, UEs associated to a specific RRH within the coverage of the g-NB will share the m-th RRH/g-NB is expressed as followsTo enhance the spectral efficiency, all the  a time) . In addin to denote that the reused sub-channel at RRH/g-NB m belonging to the assigned sub-channels of g-th g-NB group.For the clarity of expression, we add upper index Tile based encoding is widely adopted in the adaptive VR video streaming. With the motion-constrained tile sets (MCTS) coding, which has been introduced with the High Efficiency Video Coding (HEVC) codec, A VR video is spatially split into rectangular, independently decodable, non-overlapping regions after Equirectangular Projection (ERP). MCTS introduces a bit-rate overhead due to losses in compression efficiency . HoweverSaliency can be predicted using models of visual features, such as color, intensity and object. ed video . Therefoed video  the viewU denotes the utility of the video, R denotes the video rate, and The QoE  metric for video networking quality evaluation is commonly used as Equation  defined z-th chunk can be defined as . Furthermore, for each tile, the saliency can also affect the perceived QoC. Inspired the QoE metric for downlink adaptive streaming, QoC metric for VR video uploading is introduced in this paper, which reflects the perceived quality of VR video after the source coding. Similarly, we defines the utility of one tile as , where wfined as , where Rcreasing . Note thThe symbols and notations used in the paper are summarized in Different density of UEs within each g-NB  and moving characteristic of UEs lead unstable topology of the system, which calls for a centralized RA scheduler to dynamically allocate the resource. Furthermore, tiles in the same VR video probably need different bit rate to achieve reasonable perceived quality, while the source coding rate for each tile is bounded by the maximum transmission delay and transmission rate of UE. Essentially, the content in different tile region should be taken into consideration during the RA.Motivated by this, we proposed a novel Content-Sensing RA scheme for VR video uploading in 5G H-CRAN, which is depicted as Each g-NB group is consisted by g-NB and RHHs under coverage of corresponding g-NB, which serve the UEs within the coverage of g-NB. Furthermore, all UEs report the channel quality to centralized RA scheduler through the g-NB , and associated to the corresponding RRH or g-NB according to the scheduling results.For the UE part, once the VR video is generated, the saliency detection is executed every RA round by the tile weight detection module. Then the weight for each tile region is then quantized into the range of the 5G Quality of Service (QoS) class identifier (5QI), which is expressed as . FinallyMeanwhile, the RA scheduler extracts the quantized weight for performing RA in our scheme instead of ensuring bearer traffic’s QoS. Finally, the encoder performs the tile-based encoding, while each tile is encoded at the target bit rate according to the RA results. After the multiplexing and modulation and coding, the encoded video signal then is transmit to the BBU pool for upper layer functions and baseband signal-processing through the corresponding RRH or g-NB.Note that RA scheduler integrated at the BBU pool play a key role in the proposed scheme. G-NB group RA, RHH/g-NB association, SA and PA, and tile encoding rate assignment are centralized determined by the scheduling results. In order to obtain a optimal solution for the RA scheduler, mathematical problem formulation and a three stage algorithm to solve the problem will be described in the following part.According the aforementioned analysis, the objective is to maximize the total QoC for VR uploading under constraints of resource, transmission delay of video chunk and UE power, while source coding rate for each tile is bounded by the maximum transmission delay and transmission rate of UE. Therefore, the transmission rate and transmission delay of UE is investigated in the following:i-th UE at z-th video chunk associated with m-th RRH on n-th sub-channel is calculated as follows [The signal to interference and noise ratio (SINR) for  follows .(8)γi,zi-th UE at z-th video chunk when associated with m-th RRH/g-NB can be written as followsn-th sub-channel on m-th RRH/g-NB assigned to i-th UE at z-th video chunk, and 0 otherwise. Note that a UE can be only associated with one RRH or g-NB at a certain time, the association can be changed as the motion of UEs. However the simplicity of system model and it is supposed that the association is unchanged during the period of each video chunk transmission.The achievable data-rate of i-th UE of z-th video chunk can be calculated asz-th video chunk of i-th UE, which can be written as i-th UE at z-th video chunk can be defined asThe transmission power for Thus the RA problem with the objective of total VR video utility maximization in the uplink of 5G H-CRAN subjected to the total resource constraint, maximum transmission delay of each video chunk and UE power constraint can be formulated as follows:The constraint C1 limits target source coding rate of each tile is selected in the set of pre-defined tile encoding rate. C2 indicates that transmission delay for each video chunk should be less than the maximum delay due to limitation of storage in board and timeliness of VR video. C3 represents maximum per UE transmit power constraint. The constraint C4 indicates a UE can be served by a single RRH or the g-NB. C5 is constraint to ensure that n-th sub-channel is only allocated to one UE when the UE associated with RRH or g-NB. The C5 and C6 limit allocation sub-channel to UEs is in the assigned sub-channels set of corresponding g-NB group. The resource constraints C7 and C8 indicate assigned sub-channels set to each g-NB group is disjointed and sum of these sets is under the total resource constraint, respectively.Note that OPT-1 is mixed-integer nonlinear problem (MINLP) , Howeversolution . TherefoIn this paper, we propose a three-stage optimization algorithm to solve the problem. The flow chat of proposed algorithm is shown as g-th g-NB group and total number of UE in the system.Note that total resource bandwidth is allocated to each g-NB group non-overlapping in order to mitigate the inter macro cell  interference and protection of control information signal. However the sub-channels assigned to each g-NB group, which not only can be reused by the g-NB, but also the RRHs within the coverage of the g-NB can be reused these sub-channels. And our strategy is to dynamically allocate the resource according to the requirement. Essentially, the g-NB group resource allocation which should be determined by the number of RRH and the UE transmission requirement in each g-NB group. For the simplicity, in our system, we assume the same density of RHH within each g-NB . Based on this assumption, the g-NB group RA is based on density of UEs within corresponding group, which can be expressed asOnce g-NB group resource allocation completed, the OPT-1 problem can be rewritten asi-th UE at z-th chunk.The OPT-2 can be described as joint RHH/g-NB association, SA, PA and source coding optimization problem. Notice that source coding rate of each tile is determined by tile weight  and upper bound of transmission rate of UEs. When transmission delay for each video chunk is fixed , it is obvious the objective function could get optimal value only if each UE reaches the maximum transmission rate. Consequently, The OPT-2 problem can be rewritten asz-th chunk of UE i. Note OPT-4 can be described as an Joint RRH/g-NB association, SA and PA problem and OPT-3 can be expressed as an tile encoding rate assignment problem under the constraint of upper bound transmission rate. And Stage 2 and Satge 3 of proposed algorithm solve the OPT-4 and OPT-3, respectively, which details are explained in the following part.Note that OPT-3 is an convex problem if the e system , upper bThe OPT-4 can be described as an weighted sum-rate maximization problem, and given the fixed association, the problem has be proven an NP-hard problem in ,27. FurtFor an initial RRH/g-NB association i and RRH m, and For initialization, we employed path-loss based association and uniform PA. More specifically, for RRH association, t iteration.So that for the fixed RRH/g-NB association and PA in each g-NB group, the achievable rate of each UE on each sub-channel is calculated iteratively and then the sub-channel is assigned to the UE which having highest weighted achievable rate on that sub-channel in each iteration. Finally, all the sub-channels are assigned to UEs according to the . where xIn this step, PA is performed more precisely after the SA. Note that the initial PA is performed in an uniformed way. However, after getting the sub-channels assigned to each UE nstraint . In addiThe IPA involves four phases to get optimality conditions. First, the inequality constraints are transformed into equality constraints by the addition of slack-variables to the former. Second, non-negativity situations are implicitly tackled by adding them to the objective function as logarithmic barrier terms. Third, the optimization problem with equality constraints is transformed into unconstrained optimization problem. Fourth, the perturbed Karush-Kuhn Tucker (KKT) first order optimality conditions are solved through the Newton method .i is set as While EPD allocates the maximum transmission power of UE equally distributed among the assigned sub-channels of UE. And the maximum transmission power of UE Note the EPD is also an alternative method with the simplicity and low complexity compared with the IPA. Consequently, the PA solution is updated as Since the initial association is based on path-loss, which may not be the optimal association. RRH/g-NB association optimization is performed in this step. After SA and PA, we try to optimize RRH/g-NB association with Due to sub-channels are reused at each RRH within corresponding g-NB group, RRH/g-NB association can be performed with given in . And theOne thing need to point out that method in  to solveConvergence of stage 2 is judged by comparing the previous iteration association with the current association. If the association is unchanged among all UEs, which indicates all UEs associate the optimal RRH/g-NB. Otherwise, the algorithm perform SA and PA again with current RRH/g-NB association , the similar problem has been studied in our previous work.N orthogonal sub-channels. ITU pedestrian B fast fading model and the COST231 Hata propagation model for micro-cell environment [There g-NB cell with 1 km radius is considered in the simulation, where two RRHs is uniformly distributed within g-NB cell. The users’ locations are randomly generated and UE follow a Poisson Point Process (PPP) with density ironment  are adopThe predefined minimum and maximum tile encoding rate is set Fixed g-NB group resource allocation (FGRA) + IPA power allocation (IPA) + Proposed RRH/g-NB association (PAS) + Tile rate assignment with CVX (TRAC): The group resource allocation in stage 1 is fixed, and will not change when the UE density in each group changed as the motion of UEs . And each group allocate the fixed resource to UEs of the group in a decentralized way. And PA and SA is performed according to IPA and PAS respectively. In stage 3, the tile rate assignment is according the solution of relaxed convex problem.Dynamic g-NB group resource allocation (DGRA) + IPA + PAS + TRAC: The group resource allocation is dynamically based on the UE density within each group. IPA and PAS is adopted in stage 2. And TRAC is performed in stage 3.DGRA + EPD + PAS + TRAC: DGRA and PAS is performed in stage 1 and stage 2, while the power allocation follows EPD scheme. And TRAC is performed in stage 3.DGRA + IPA + PAS + Tile rate assignment with global search (TRAGS): stage 1 and stage 2 adopt the DGRA, IPA and PAS, respectively. however the tile rate assignment in stage 3 using the global search to obtain the optimal solution.DGRA + IPA + association as in reference  (ASR) + DGRA + IPA + path-loss based association (PLAS) + TRAC: DGRA and IPA is adopted in stage 1 and stage 2, however g-NB association performed based on the path-loss . And TRAC is performed in stage 3.For performance comparison, different combination of schemes in each stage of algorithm is evaluated, which are summarized as follows:Note that fixed resource for each g-NB group performs the worst , since it lost adaptive resource allocation among the groups at centralized BUU pool. In addition, RRH/g-NB association based on reference   to obtain optimal solution. For simplicity, we ignore the complexity of the first stage, which is typically very fast. In addition, the complexity of tile encoding rate assignment is also not discussed, however, the CPU time of two different schemes is already given in Where the T is the necessary number of iteration to convergence. Note that stage 2 is most computational part of the algorithm, which is mainly consisted of three parts . Specifically, The SA complexity is order of number of sub-channels since all sub-channels are assigned to UE which having highest weighted achievable rate one by one; The complexity of PA with IPA and EPD is order of logarithm of number of sub-channels and order of number of sub-channels, respectively. For proposed association method , the complexity is order of number of UEs. The complexity of reference association method is order of number of RRHs power of number of UEs. while the path-loss based association can be performed at onetime.Overall, proposed DGRA + IPA + PAS + TRAC is an attractive combination for the solution algorithm with better achievable utility, faster converge and less executive time.In this paper, we studied delay-sensitive VR video uploading in 5G H-CRAN, and proposed an centralized scheme to allocate the resource based on content sensing, which is further formulated as a weighted utility optimization problem. A three stage algorithm is proposed to solve the MINLP problem. Dynamic g-NB group resource allocation is first performed according to the UE density of each group. In stage 2, joint RRH/g-NB association, sub-channel allocation and power allocation is performed by an iterative process.Finally, encoding tile rate is assigned to optimize the target objective with the help of convex optimization toolbox in stage 3. The simulation results show that the proposed algorithm with fast converge speed can achieve better utility , which is a promising solution for the MINLP problem.


Video gamers are a population at heightened risk of developing obesity due to the sedentary nature of gaming, increased energy intake, and the disruption caused to their sleep. This increases their risk of developing a number of noncommunicable diseases. To date, research seeking to improve health behaviors has focused on developing novel video games to promote behavior change. Although positive results have emerged from this research, large-scale success has been limited due to the lack of transferability to mainstream games and the focus on children and adolescents. The gaming community has a number of unique aspects, which have received comparatively less attention than the development of new video games.The purpose of this paper is to highlight under-researched areas that have the potential to encourage positive health behavior among this community.A narrative review of the lay and academic literature was conducted to provide context and support to our claims that further research could be beneficial in this area.Research has found that advertising can have implicit effects on an individual’s memories, which could influence later decisions. However, the effect of the exponential growth of in-game advertisements and the brand sponsorship of gaming events and professional gamers have not been explored in the gaming community. The possibility of using advertising techniques to encourage positive health behaviors within games or at these events has also not been explored. Research suggests that virtual communities can be effective at disseminating health information, but the efficacy of this needs to be explored using known community influencers within the gaming community.This paper has highlighted a number of potential avenues for the development of interventions within the gaming community. Further research must be conducted alongside game developers to ensure that any in-game developed interventions do not deter gameplay and gamers to ensure that potential approaches are acceptable. Obesity has become a major problem, with an estimated 1.9 billion adults worldwide classed as overweight or obese in 2014  and is tborderline impact for women) [Sedentary behavior is also implicated as an independent risk factor for a number of noncommunicable diseases . Epidemir women)  and prosr women)  cancer. r women) . Sedentar women) ,17. Reser women) -20, withr women) .r=−.92) [at-risk population that could benefit from targeted interventions.Video games have also been found to increase energy intake among healthy males. A randomized crossover study found that despite increased levels of energy expenditure while playing video games (mean energy increase compared with the rest state=89 kJ), this was counteracted by higher levels of energy intake after playing video games, resulting in an energy surplus of 335 kJ compared with those who rested for the same period . Furtherr=−.92) . Shorterr=−.92) . Those wThe majority of previous research involving gamers has focused solely on the potential for video games to be used as a medium for health behavior change, either by increasing the knowledge and awareness of health behaviors or by including physical activity within the game itself. A large body of research has explored the potential to develop games to improve health -27. A reThis paper aims to discuss the potential avenues for future research in this area, drawing on the attributes that are unique to the gaming community.snowball method was also employed, wherein references from relevant papers were reviewed to identify other relevant papers.This paper comprises a narrative literature review. It draws on lay literature to provide context and descriptive detail and academic literature to support the claims that further research could be beneficial in developing this area for health behavior change. This literature was identified through the following electronic databases: Web of Science, MEDLINE, Google, and Google Scholar. The following keywords were used in various combinations: “video games,” “gamers,” “professional gamers,” “gaming events,” “advertising,” “in-game advertisement,” “vloggers,” “forums,” “online communities,” “virtual communities,” “fast food,” and “marketing.” A gamers due to the lack of a universally accepted definition to objectively categorize these 2 groups [gaming community will be used to cover the areas in which gamers interact, such as video games, gaming events, online forums, and video blogs. Gamers are extremely heterogeneous, representing a range of demographic, social, and behavioral groups, and they span international and cultural divides. Understanding the heterogeneity of gamers and their behaviors and influences and subsequently targeting interventions or marketing would provide a rich avenue of research to pursue; however, this aspect is not explored in this review.This review will refer to both hardcore and casual gamers as 2 groups  and the Several aspects of gaming that could be utilized to engage gamers in health behavior change, including gaming environments, virtual communities, and community influencers, were identified. These features and their ability to be applied to health behavior change are described and discussed below.Companies use marketing to connect consumers with their products and services . There iResearch has found that IGAs have a strong effect on our implicit memory. For example, 1 study found that participants who played a Formula 1 video game scored significantly higher on a word-fragmentation task of brand names (that were shown in the video game) than those in a control condition . The autWendy’s (a burger chain operating primarily in North America) is set to have an IGA for their Baconactor  on billboards, bus shelters, and television screens within the virtual gaming systems of multiple games spanning Xbox, PlayStation 4, and personal computer platforms [In 2007, Ofcom, the communications regulator for the United Kingdom, introduced a ban on television advertisements of high fat, salt, or sugar (HFSS) food or drink products for children’s airtime to reduce the exposure of children aged less than 16 years to unhealthy foods . The efflatforms . Informalatforms . DynamicBanning HFSS advertisements in games may be more difficult than with television or the internet, as such a ban cannot be targeted at a certain age bracket and a blanket ban approach may be considered heavy-handed. This ban may also not be possible in certain countries that have laws guaranteeing freedom of speech, such as the United States. However, it may be possible for video games to be utilized in a different way to combat IGA of HFSS. If funds were available, charities  could consider counteradvertising and place their own IGA’s, which could target people directly with health-promoting messages or information. Within a collaborative context where charities and game developers share values on an approach, content of such premium games could be developed or adverts may be targeted toward health behavior change to influence implicit memory in gamers. This could be a viable alternative when regulation is not an option. Research has shown that gamers develop negative attitudes to advertisements that are intrusive and incongruent with the game, as it reduces their sense of realism ,52. TherBurger King teamed up with Sony Spain to offer the delivery of fast food to gamers who signed up to play with professional gamers online. After completing a game, the professional gamer would then take the order and it would be delivered to the gamer’s door [Call of Duty: Black Ops III, gaming prizes including Double XP could be won by buying special Mountain Dew and Doritos products [Sony can be targeted. In recent years, corporate social responsibility has become increasingly important to both the consumer and the company [Brands have diversified their promotional mix beyond advertisements to target the gamers in other unique ways. Viral marketing techniques utilize the internet and already established social networking services and sometimes community influencers to popularize a brand . Burger r’s door . Viral mr’s door . Brands products . Researcproducts . The use company . It can  company ,59. TherGaming events where gamers and developers gather to play, demonstrate, and discuss games are an extension of the gaming community. They offer additional opportunities for promoting health messages and engagement with audiences. A number of these events attract the video game community, such as comic book conventions, gaming festivals, and eSports tournaments. These typically feature high numbers of sponsors and promotions for energy drinks, fast food, and other high-calorie foods .Evil Geniuses [nudge toward healthy eating among this community [appetite for health marketing at these events and the methods to quantify the potential effects for the video game community.eSports are video gaming competitions involving mostly professional gamers that contend for prize money. These events are frequently broadcast on television and streamed live over the internet. The final for the League of Legends (a multiplayer online battle arena video game) 2015 World Championship drew a global audience of 36 million viewers , which wGeniuses . This suommunity . Initialinfluencers—individuals who have a greater amount of influence over members’ commitment [Among many communities, there are those who are considered mmitment . Professmmitment . These pmmitment . Celebrimmitment  and adulmmitment . This efmmitment ,71. Agaimmitment . Nonethespeed runs of people completing things in the fastest time [PewDiePie is the most popular vlogger on YouTube with over 54 million subscribers to his channel and was the first YouTube star to reach over 10 billion views; his popularity came from his commentary of video games [Water Campaign by encouraging subscribers to donate [Game-related video bloggers (vloggers) have become increasingly popular among gamers. These vloggers post videos of themselves playing games and giving commentary, glitches within games, reviews of games, formal walkthroughs of games, using video games to create films from the content, and est time . An indieo games ,74. PewDeo games . This ino donate , demonstinfluence among online communities is borne out in research, which suggests that these influencers provide an important role in the social discourse: encouraging discussion and interaction between members, arranging events, and keeping site content up-to-date [The effect of this -to-date . Zhang a-to-date  have sugThe aforementioned online social communities have developed in conjunction with many video games . IndividSecond Life has been studied as one of the most realistic and immersive virtual world’s available [massively multiplayer online role-playing games, such as World of Warcraft and Star Wars: The Old Republic, which offer less realistic worlds and are instead based on fantasy-oriented worlds. Gamers may interact with these games differently with regard to health matters, if at all. Gaining a greater understanding of how these communities approach both the social aspect of gaming and health issues may be important for the future development of interventions for this population.Research has also begun to investigate the ability of 3-dimensional virtual worlds to act as a more immersive form of online social support . Second vailable , where pvailable . The disvailable . HoweverThe exponential growth of gaming and its supporting online communities is a trend that continues to grow—followed by advertising investment—presenting an opportunity to engage with a key audience. The research outlined in this paper suggests that gamers are already exposed to advertisements that encourage unhealthy behavior both in games and at gaming events. There is, therefore, a need for policy and interventions to attempt to redress these effects and promote healthy behaviors among this group of individuals.There are points to consider when conducting further research that could have an influence on the development of interventions to influence health behavior change. First, in recent years, the gender gap in those that play video games has narrowed, with women making up over 40% of the gaming population in the United States and Europe ,91. Howeat-risk. However, there is currently no universal definition to objectively categorize the gamer type. A move toward better defining groups of gamers would enable studies to explore whether interventions should target differences in how these groups play games as well as the type of game and other behavioral factors. However, these issues were not explored and were beyond the scope of this review.Moreover, there should be more investigation about the distinction between hardcore and casual gamers and how future interventions could influence each group. Hardcore gamers have been described as those that dedicate a large portion of their leisure time to gaming in comparison with casual gamers , and so Furthermore, although we know that the IGA revenue has risen exponentially in the past decade , we do nIn summary, research to date has focused on the development of games specifically designed to change health, but more could be done to explore opportunities within existing online communities and virtual worlds and utilizing known influencers and methods of advertising to this group. Research in all these areas, conducted in a coordinated way with gamers, vloggers, and game developers, would offer any interventions their best chances of success.


Human action recognition (HAR) has emerged as a core research domain for video understanding and analysis, thus attracting many researchers. Although significant results have been achieved in simple scenarios, HAR is still a challenging task due to issues associated with view independence, occlusion and inter-class variation observed in realistic scenarios. In previous research efforts, the classical bag of visual words approach along with its variations has been widely used. In this paper, we propose a Dynamic Spatio-Temporal Bag of Expressions (D-STBoE) model for human action recognition without compromising the strengths of the classical bag of visual words approach. Expressions are formed based on the density of a spatio-temporal cube of a visual word. To handle inter-class variation, we use class-specific visual word representation for visual expression generation. In contrast to the Bag of Expressions (BoE) model, the formation of visual expressions is based on the density of spatio-temporal cubes built around each visual word, as constructing neighborhoods with a fixed number of neighbors could include non-relevant information making a visual expression less discriminative in scenarios with occlusion and changing viewpoints. Thus, the proposed approach makes the model more robust to occlusion and changing viewpoint challenges present in realistic scenarios. Furthermore, we train a multi-class Support Vector Machine (SVM) for classifying bag of expressions into action classes. Comprehensive experiments on four publicly available datasets: KTH, UCF Sports, UCF11 and UCF50 show that the proposed model outperforms existing state-of-the-art human action recognition methods in term of accuracy to 99.21%, 98.60%, 96.94 and 94.10%, respectively. During the last decade, human action recognition (HAR) has become a well-developing research area and has received substantial attention. It has been applied in a wide range of applications such as sports video analysis, content-based video retrieval, video surveillance, scene recognition, video annotation and human-computer interaction . In partState-of-the-art approaches have shown notable increases in performance in realistic and complex scenarios. However, there are still some unsolved issues such as background clutter, viewpoint variation, illumination change and class variability . RecentlHowever, since BoVW approaches only consider the frequency of each visual word and ignore the spatio-temporal relation among visual words, such representation is not able to exploit the contextual relationship between visual words. To overcome this drawback, we propose an extension of our previously proposed Bag of Expressions (BoE) model , which iBoth Kovashka et al.  and GilbConstructing neighborhoods with a specific number of neighbors, as in Reference , can redn, each neighboring STIP in the ST-cube is paired with a visual word to obtain n different visual expressions. This provides a local representation of visual expressions and enables some tolerance to viewpoint variation and occlusion.Kovashka et al.  were unaTo support view independence, we represent each action as a visual expression and, as in Reference , only thThe rest of the paper is organized as follows. We discuss related work in Bag of visual words (BoVW) along with its variations has become a popular approach for many visual interpretation tasks, including human action recognition. In BoVW, video representation is obtained using three steps: feature representation, dictionary learning and feature encoding. In such representation, performance is highly dependent on the discriminative power of each step. As work on action recognition using a BoVW approach is too broad to be covered here, we focus on the related approaches for feature representation and neighborhood features.Feature representation for video, including holistic and local representation approaches, have been reviewed in detail in survey papers such as Reference . HolistiLocal descriptors are then computed for these detected interest points. Local interest point descriptors can rely on 3D cuboid or trajectories. 3D HoG (Histogram of Gradients) , inspireAfter computing features, these are further transformed into visual words in a BoVW approach. Compared to text that is usually semi-structured, visual appearance is less structured and exhibits large variations when the same underlying visual pattern is present in varying illumination, different viewpoints and occluded environments. A possible solution to resolve the ambiguity of visual pattern representation is to consider its spatial-temporal context .k trajectories that are the possible candidates containing the object.Yuan et al.  introducFor video representation, Zhao et al.  used deeRahmani et al.  proposedWang et al.  trained Khan et al.  improvedMany researchers have extended the traditional 2D convolutional neural network to integrate temporal information. 3D CNN was proposed by Hara et al.  to incluSimonyan et al.  extendedFollowing the success of the two-stream architecture, Feichtenhofer et al.  extendedHara et al.  also utiIn this section, we present a dynamic spatio-temporal Bag of Expressions (D-STBoE) model for human action recognition. The proposed model recognizes human actions performed in complex scenarios by following the pipeline shown in m is a tunable sensitivity parameter and L is the first order spatio-temporal derivative and G is a Gaussian weighting function. As illustrated in V, the set of extracted spatio-temporal interest points are given by n is the total number of interest points detected for a video V. Clearly, the value of n varies for each video depending on the number of interest points detected by the 3D Harris corner detector.The feature detector aims to detect the distinctive locations of interest points which are used as a compact representation of the raw action video. Since in a video spatio-temporal interest points are considered to be both compact and salient for feature representation , 3D HarrV, the feature representations are denoted as Feature descriptors are used to describe the detected interest points. Since 3-Dimensional Scale Invariant Feature Transform (3D SIFT) , an extek groups [tm is the total number of videos for an action class, FP is a set of feature representation for the videos of an action class. We apply k-means clustering to obtain class-specific visual word representations, which correspond to the k cluster centers. They become the words of the class-specific dictionary, CDic.K-means clustering is a commonly used algorithm to automatically partition a dataset into k groups ,51. Let word dictionaries, the next step is to generate a concatenated visual expression dictionary containing C class-specific visual expression dictionaries, where C is the total number of unique action classes.After the generation of class-specific visual Constructing a neighborhood with visual words with a fixed number of neighbors  affects C class-specific visual expression dictionary.A bag of visual expressions is generated by incorporating a visual word’s neighborhood information present in the spatio-temporal cube, as described in the following sub-sections. After the construction of a spatio-temporal cube around a visual word and the calculation of the density of the respective ST-Cube, ‘Ccenter’ , in a dictionary CDic, a spatio-temporal cube (ST-C) is formed containing the spatio-temporal interest points around the cluster centers. As shown in P, where P is the set of interest points detected for an action class  is calculated in the spatio-temporal cube where ST-C density is defined as:Visual expressions are formed to incorporate the contextual spatio-temporal neighboring information of a visual word, by combining the visual words and their respective neighboring spatio-temporal interest points present in the spatio-temporal cube. Let The number of visual expressions formed against each visual word depends on its CEDic. In contrast to Reference [CEDic depends on the number of visual words, that is, k, obtained for each action class, the number of classes and spatio-temporal cube’s densities. As shown in k visual words for each CDic. Then, the class-specific visual expression dictionaries, CEDics, are generated for each action class. Note that the size of each CEDic varies as it is dependent on the size of each visual word’s ST-C density. Finally, these five CEDic are concatenated to obtain a visual expression dictionary, which is represented as EDic.Similarly to the approach used in Reference , after oeference , the sizV, let r is the corresponding VExp in EDic.The proposed model uses histogram encoding  for assiSince we use a multi-class support vector machine model for action recognition, we need to select both a kernel function and a multi-class model. We evaluated multi-class SVM models using three different kernel functions, that is, Gaussian kernel, linear kernel and polynomial kernel, which are defined, respectively, as:L binary learner and defined as:M is the coding design scheme matrix with elements l and C is the total number of unique action classes. Six different coding design metrics were considered for learning a binary learner:One vs. one: The multiclass model learns C(C − 1) binary learners. For this coding design matrix, one class is positive, another is negative and the rest is ignored.One vs. All: For each binary learner of a total C binary learners, one class is positive and the rest is negative.Ordinal: Matrix elements are assigned such that for the first binary learner the first class is positive and others are negative. For the second binary learner, the first two classes are positive and the rest are negative and so on. It has C − 1 binary learners.Binary Complete: The multi-class SVMs model learns Dense Random: Each element of the design matrix is assigned equal probability and has approximately Sparse Random: It assigns 1 or −1 to the class with 0.25 probability and 0 to class with 0.5 probability. It has approximately Multi-class SVMs models use different types of coding design schemes to learn . A videoThe dynamic spatio-temporal based Bag of Expressions (D-STBoE) method is summarized in Algorithm 1.Algorithm 1 D-STBoE algorithm for Human Action RecognitionRequire: Training video dataset C is the number of action classes,    Training labels     Testing video dataset 1:2:forz = 1:cdo3:for each video in do    4:FP        obtain feature representation 5:    do k-mean clustering to obtain 6:for each visual word do    7:fordo        8:           compute 9:        10:    11:for each video v in training set do12:EDic to get     feature encoding using 13:TrainC = TrainClassifier results in improved performance irrespectively of ST-Cube size. It also reveals that an increase in ST-Cube size tends to decrease performance after ST-Cube size = 5. Indeed, a larger size is likely to increase the number of non-relevant neighbors contributing to the visual expression formation, hence making it less discriminant. However, a smaller ST-Cube size may fail to integrate relevant neighbors, hence making the visual expression incomplete. Performance is even more dependent on the ’k’ parameter as an insufficient dictionary size leads to poorer accuracy. As our experiments show that up to k = 300 there is significant performance improvement, that value was selected. Similarly, an ST-Cube Size of 5 was chosen to produce optimal performance.We also evaluated the proposed D-STBoE model performance by varying ST-Cube size. (k) for k-means clustering leads to increased processing time.To analyze the computational complexity of the proposed method, we have evaluated the impact of the parameter that has the most significant contribution in terms of computational time. Following measurements of the average running time for the generation of a class-specific dictionary as described in In the next set of experiments, we evaluated the performance of different multi-class SVM models used for action recognition by testing three different kernel functions and six coding design matrices for the binary learner, as outlined in ’C’ class specific dictionaries versus one unsupervised dictionary. This section considers the contribution of each stage in the proposed model, as tested on the UCF Sports dataset. As presented in The trend line in However, this trend does not result in increased accuracy, as illustrated by The experiment section concludes with a comparison of the proposed model with state-of-the-art methods, including recent deep learning based methods. It should be noted that D-STBoE parameters were optimized for UCF Sports dataset as discussed in As shown in We compared the proposed model with the state of the art for the UCF11 and UCF50 datasets, with successful methods that have proven particularly suitable in dealing with the many practical problems represented in these realistic datasets. As shown in A particular strength of the proposed model is that it shows some degree of tolerance to occlusion and viewpoint variation. In this paper, a dynamic spatio-temporal Bag of Expressions model for human action recognition has been introduced. Not only does it preserve the inherent qualities of the classical BoVW approach but it also acquires contextual information that would be lost with a conventional formation of visual words representation. We proposed a new Bag of Expressions generation method based on the density of spatio-temporal cube of visual words. The new model addresses the inter-class variation challenge observed in realistic scenarios by using a class-specific representation for visual expression generation. Viewpoint variation and occlusion challenges are also partially addressed by considering the spatio-temporal relation of visual words representation. The model was tested on four publicly available datasets that is, KTH, UCF Sports, UCF11 and UCF50. D-STBoE consistently outperformed all state-of-the-art ’traditional’ methods while achieving competitive results when compared to deep learning approaches, which demonstrated best performance on two of the four datasets. In terms of practical deployment, D-STBoE could be a competitive solution compared to deep learning based systems, since, unlike them, it does not require a large dataset for training that is, D-STBoE is better suited for practical applications where availability of training data is usually limited.Future work will explore the potential advantage of using spatio-temporal cube’s density based neighborhood information for deep learning features and methods and also investigate exploiting spatio-temporal neighborhood information for action detection in even more realistic and complex scenarios.


This paper addresses approximately dual g-frames. First, we establish a connection between approximately dual g-frames and dual g-frames and obtain a characterization of approximately dual g-frames. Second, we give results on stability of approximately dual g-frames, which cover the results obtained by other authors. The notion of frame dates back to Gabor  1946) a946 a1] pH is a frame ifRecall that a sequence i et al.  first ini et al. , 23).Motivated by , in thisWe begin with some basic notions and results of g-frames. See , 17, 18 H and V, let V with J being a subset of integers H is denoted by H into δ is the Kronecker symbol. Then Given separable Hilbert spaces JVj (see ).H with respect to (w.r.t.) A, B are called the frame bounds. If only the right-hand inequality of .H w.r.t. Let H with their respective synthesis operators Let It is clear that the operator H w.r.t. Let This section focuses on the connection between approximately dual g-frames and dual g-frames and on a characterization of approximately dual g-frames.Letandbe two g-Bessel sequences forHw.r.t. Then the following are equivalent: (i)(ii)(iii)In case the equivalent conditions are satisfied, andare dual g-frames forHw.r.t. Letfor everyand letbe an o.n.b. forIfis defined bythenis a g-frame (g-Bessel sequence) forHif and only ifis a frame (Bessel sequence) forH.The following two theorems give a method to construct new dual g-frames  from given dual g-fromes.Letandbe dual g-frames forHw.r.t. and letandbe two bounded operators onHsuch thatThenandare dual g-frames  forHw.r.t. H, we see that By a standard argument, Letandbe dual g-frames forHw.r.t. and letTbe a unitary operator onH. Thenandare dual g-frames  forHw.r.t. Assume thatandare dual g-frames forHw.r.t. and letandalso be dual g-frames forHw.r.t. Then for anyandare dual g-frames forHw.r.t. H w.r.t. By a standard argument, H w.r.t. H w.r.t. Obviously, if Letandbe approximately dual g-frames forHw.r.t. with synthesis operatorsandrespectively. Thenis invertible; furthermore, the sequencesandare dual g-frames.H w.r.t. H. By Lemma Since For Theorem Letbe a g-frame forHw.r.t. with the synthesis operatorand frame boundsAandB. Thenis an approximately dual g-frame ofH w.r.t. Note that From Theorem Letbe a g-frame forHw.r.t. letbe its synthesis operator, and letbe an o.n.b. forThenandare approximately dual g-frames if and only ifwhereis a linear bounded operator such thatNecessity. Suppose H. Let H w.r.t. Next, we prove the converse. Suppose T is very important. The following lemma gives an explicit expression of T in Lemma From Lemma Letbe a g-frame forHw.r.t. with the synthesis operatorand the frame operatorThenif and only ifwhereIis the identity operator onandandare linear bounded operators satisfyingFirst, we suppose that Conversely, assume that Now, we turn to characterizing all approximately dual g-frames for a given g-frame.Letbe a sequence, and letbe a g-frame forHw.r.t. with the synthesis operatorand the frame operatorThenandare approximately dual g-frames if and only ifwhereandare linear bounded operators satisfyingI is the identity operator on H. Using the notations First, we assume that f. ThereforeH w.r.t. Now we prove the converse. Assume that  holds. FThe stability of frames is of great importance in frame theory, and it is studied widely by a lot of authors , 18). In. In18]).Letbe a g-frame forHw.r.t. with boundsAandB, andIfsatisfiesfor an arbitrary finite subsetandthenis a g-frame forHw.r.t. with boundsLetbe a g-frame forHw.r.t. Then forsatisfyingwe haveis a g-Bessel sequence with an upper boundBif and only ifwhereis an arbitrary finite subset ofJ.Letletbe a g-frame forHw.r.t. with boundsAandBand the synthesis operatorand letbe alternate dual forwith the upper boundCand the synthesis operatorAssume that there are constantsandsatisfyingwhereis an arbitrary finite subset ofJ, andIfthenandare approximately dual g-frames.H w.r.t. By Lemma ∈J. From  we haveFrom Theorem Letletbe a g-frame forHw.r.t. with boundsAandBand the synthesis operatorand letbe the canonical dual forwith the synthesis operatorSuppose that there are constantsandsuch thatwhereis an arbitrary finite subset ofJ, andIfthenandare approximately dual g-frames.H w.r.t. Note that Letand letbe a Parseval g-frame forHw.r.t. Assume that there are constantssuch thatfor an arbitrary finite subsetandIfthenandare approximately dual g-frames.Letbe a sequence, and letbe a g-frame forHw.r.t. Also, letbe an alternate dual forwith the upper boundC. If there exists a constantRsuch thatandthenandare approximately dual g-frames.Take Corollary Letbe a g-frame forHw.r.t. with synthesis operatorand boundsAandB. Assume thatfor alland there exist constantssuch thatfor an arbitrary finite subsetandIfandthenis a g-frame forHw.r.t. andandare approximately dual g-frames.We can prove the theorem by an argument similar to that of Theorem For a given frame, it is usually not easy to find a dual frame. The notion of approximately dual frames was introduced by Christensen in 2010. It is a generalization of dual frames. In this paper, on one hand, we obtain the link between approximately dual g-frames and dual g-frames and characterize approximately dual g-frames. On the other hand, we give stability results of approximately dual g-frames, which cover the results obtained by other authors.


Pelecanus occidentalis californicus) following oil contamination and rehabilitation to test for differences between previously oiled and rehabilitated (post-spill) and presumably uncontaminated pelicans. Post-spill pelicans released with either color leg bands alone, or bands plus harness-mounted satellite GPS tags, were relocated and visually assessed in the field at non-breeding communal roosts and compared to surrounding unmarked pelicans in the general population. Non-oiled pelicans bearing GPS tags were also included in the study. Post-spill pelicans lagged the general population in molt of ornamental yellow crown feathers but hind neck transition into white plumage was not significantly different. Both post-spill and non-oiled pelicans wearing GPS tags had lower gular redness scores than the unmarked, non-oiled population. Pre-breeding gular pouch redness of post-spill pelicans was more strongly influenced by wearing of a GPS tag than a history of oil contamination and rehabilitation. Gular pouch redness of post-spill pelicans in the first 18 months after release was positively correlated with long term survivorship. If gular pouch color is a condition-dependent sexual signal and overall health influences plumage molt progression, our results indicate that many post-spill pelicans marked with bands alone were in relatively good condition going into the next breeding season, but those released with electronic tags experienced additional stress due to wearing the equipment, introducing a confounding variable to the post-release study.Sublethal effects of oil spills may dampen seabird rehabilitation success due to lingering negative impacts of contamination and stress on reproduction and long-term survival. These effects can be difficult to measure while birds are in care as well as once birds are released. Expression of sexually selected traits that are sensitive to condition can provide information on physiological status of birds. We evaluated plumage molt and gular pouch skin color of California brown pelicans ( Wildlife exposed to petroleum products after spill incidents can be negatively affected in multiple ways. The primary acute impact to these animals is from external contamination by oil and subsequent hypothermia, increased metabolic effort, and emaciation –4. IngesResearchers have used a variety of techniques to track the fate of oiled seabirds following rehabilitation and release. These include quantifying band recoveries of live and dead birds, monitoring movement patterns with electronic tracking, and documenting reproductive success , 14–17. Pelecanus occidentalis) are a seabird commonly oiled following nearshore spills in the United States. Survival and dispersal of previously oiled and rehabilitated California brown pelicans  were examined in the early 1990’s by Anderson et al. [P.o. carolinensis) successfully breeding one year after oiling from the Deepwater Horizon spill. An increasing number of studies have demonstrated that seabird oil spill rehabilitation efforts can succeed in restoring birds to normal function, but further evidence is needed–specifically projects that extend beyond acute survival [Brown pelicans  during the breeding season has been related to a combination of carotenoids, hemoglobin, and increased blood flow [Both sexes of California brown pelicans (hereafter ‘pelicans’) develop a red gular pouch prior to the breeding season, when the dull grayish gular pouch blooms with redness proximally . The pouood flow . The speLarus michahellis) beaks was smaller in birds exposed to polyaromatic hydrocarbons compared to those that were not exposed. Similarly, the hue and brightness of skin colors of kittiwakes during the breeding season showed a negative relationship to endogenous pollution levels [Coloration has been found to indicate health and fitness in many species of birds , 43. Carn levels .We designed a study to test the null hypothesis that post-spill pelicans observed in the wild would not differ visually from conspecifics with respect to their outward physical appearance. Here, we provide a field-based comparison of molt progression in the head and neck, and expression of redness in the gular pouch between previously oiled/rehabilitated pelicans and the general, presumably never oiled, wild population. We further report on unexpected differences between post-spill pelicans bearing electronic tags versus post-spill birds released with only leg bands, and the relationship of gular color to known survival amongst rehabilitated birds.To further improve estimates of seabird recovery following oiling, the Oiled Wildlife Care Network (OWCN), a program led by the School of Veterinary Medicine at the University of California at Davis, initiated a study to track rehabilitated brown pelican movement patterns and survival following the May 2015 Refugio Beach Oil Spill near Santa Barbara California using Global Positioning Satellite platform transmitter terminal (GPS-PTT) tags . We deveThe Refugio Beach Oil Spill occurred on 19 May 2015, in Santa Barbara County, California, USA at 34.46° N, 120.09° W . The spiWork was completed in accordance with all appropriate State, Federal and university regulations and policies including the U.S. Geological Survey Bird Banding Laboratory with Federal Master Bander permit #23539, the U.S. Fish and Wildlife Service Scientific Collection Permit #MB191637-0, and the California Department of Fish and Wildlife Scientific Collection Permit #SC-003855. All procedures were conducted under University of California at Davis Institutional Animal Care and Use Committee Protocol #18823. Brown pelicans are protected under the Migratory Bird Treaty Act.Field reconnaissance was initiated approximately three months after release of the previously oiled birds. Data collection on plumage and color comparisons took place primarily from September 2015—March 2016. Field work occurred in seasonal sessions of 7–10 days and ranged along the coast from Grays Harbor, Washington, USA  to Ojo de Liebre, Baja California Sur, MX  previously oiled pelicans released with color band-only, 2) previously oiled pelicans with band plus GPS-PTT, and 3) non-oiled pelicans with band and GPS-PTT. Plumage aspect and soft-part color characteristics were based on classifications in Schreiber et al. .Molt phase and color assessments were limited to adult birds and focused on three distinct and readily visible body parts—the hind neck, the crown feathers, and the gular pouch. These features were visually scored using a combination of direct field observations and digital photographs. The hind neck and crown were categorized as either in a definitive plumage aspect or transitioning between states . An ordiSurveys of banded pelicans to document survival continued through the summer of 2018 and each post-spill bird was photographed. A separate analysis of post-spill survival of the Refugio incident pelicans, incorporating demographic and biomedical factors, is planned .Statistical analyses were conducted using R package v. 3.5.1(R Core Team 2018) . PelicanMost of the Refugio post-spill pelicans (79%) were re-sighted at least once following release. By September 2017, 220 sightings of 33 birds were documented . Frequent surveys of large communal roosts resulted in a greater number of visual encounters of target animals than did attempts to relocate electronically tagged pelicans based on GPS-PTT data feeds showing past positions. Sightings of the post-spill birds were most common in summer and fall  and relatively rare during late winter-spring  when pelMost visual sightings of post-spill birds occurred over 300 km north of the spill region in Central California . This waPlumage of post-spill band-only pelicans appeared normal with respect to waterproofing and overall integument condition , while four of the 12 pelicans seen wearing transmitters were observed shivering . Plumage disruption around the harness was generally visible around the ventral surface  and exceDuring the mid-September—December sampling period, nearly all non-oiled pelicans (98%) displayed solid yellow crown plumage . EmergenMost pelicans (93%) in the non-oiled general population had definitive basic white neck plumage during the sampling period , althougPelicans began to display red pouches at nonbreeding roosts by mid-September 2015, and red pouches were observed through March 2016. Expression of redness in the non-oiled/unmarked population was variable each month within the sampling period but scores tended to be highest in November-February . PreviouS = 0.796, p < 0.001). None of the birds with gular scores of zero (no redness in the pouch) were encountered >247 days post-release. Gular redness scores of zero were also associated with known mortality. Of four confirmed pelican mortalities in this study, three were seen alive in the field during the period of expected pouch redness, and all had a score of zero. Three of the pelican carcasses were GPS-PTT-bearing and found by searching in areas where electronic signals suggested lack of normal movement . The fourth carcass was from a color band-only bird and found incidentally by a member of the public.Sightings of banded birds through summer 2018 indicated high survival rates of the Refugio post-spill pelicans overall; at least 60% (25 of 42 pelicans) were alive one year after release and 43% (18 pelicans) were seen alive three years after the spill. Long-term survival of adult post-spill birds was positively correlated with the highest GRI score documented in the first 18 months after oil exposure  fitted with dummy transmitters attached with Teflon ribbon harness had lower body mass than controls without equipment. Fitted mallards also tended to avoid water, presumably due to greater energetic expenditure to thermoregulate in cold weather and compromised feather insulation caused by the equipment. In our study, one of the equipment-related stressors for pelicans was likely similar bodily heat loss due to plumage disruption around the chest harness and transmitter  apparently incurs oxidative costs for both sexes [If one assumes that the red gular pouch provides a positive measure of health in the California brown pelican, our results suggest that, although not equal to the general population, the post-spill birds released with only bands were in relatively good condition going into the first breeding season after the spill, that numerous complex interacting physiological mechanisms were functioning, and that many of these birds could afford the additional costs of color display , 69. Devth sexes . Perhapsth sexes –72. The th sexes  found thRelationships between body condition, integument color, and breeding success are relatively well-known for several seabird species but are not fully understood in the brown pelican. Investigation of the underlying mechanisms surrounding gular pouch color expression and how it relates to pelican fitness would increase the utility of using pouch color in future studies. In the sexually dimorphic great frigatebird, for example, the male displays a bright red inflated throat pouch during courtship that rapidly fades to orange at the onset of incubation. Astaxanthin, a carotenoid pigment, has been found in very high concentrations in the outer dermal layer of the pouch . The speTargeted field surveys with large sample sizes and from wide geographic ranges are also needed to better establish or update baseline patterns and variation in molt and seasonal color change for California brown pelicans. Schreiber et al.  noted thChronology and outcome of annual breeding effort can affect timing of avian molt , 38 but Despite the challenges, field tracking and visual assessment of plumage and gular pouch color of marked brown pelicans has good potential for future ecotoxicology and post-release studies. The expression of gular pouch redness likely plays a role in behavioral ecology at non-breeding communal roosts, as well as breeding colonies, and may provide a valuable window into many aspects of California brown pelican health and fitness. This study also serves as a reminder to use caution when interpreting data based on animals bearing a significant equipment burden and will hopefully help encourage development of improved remote tracking techniques for brown pelicans.S1 Fig(PPTX)Click here for additional data file.S2 Fig(PPTX)Click here for additional data file.S1 Datafile(CSV)Click here for additional data file.