For that, a new procedure is designed in which thermal readout is obtained from the combination of in vivo transient thermometry measurements and in silico simulations. The synergy between in vivo and in silico measurements has made it possible to assess relevant numbers such as the efficiency of hyperthermia processes, the total heat energy deposited in the liver, and the relative contribution of Ag2S nanoparticles to liver heating. This work provides a new way for absolute thermal sensing of internal organs with potential application not only to hyperthermia processes but also to advanced diagnosis and therapy.Luminescent nano‐thermometry is a fast‐developing technique with great potential for in vivo sensing, diagnosis, and therapy. Unfortunately, it presents serious limitations. The luminescence generated by nanothermometers, from which thermal readout is obtained, is strongly distorted by the attenuation induced by tissues. Such distortions lead to low signal levels and entangle absolute and reliable thermal monitoring of internal organs. Overcoming both limitations requires the use of high‐brightness luminescent nanothermometers and adopting more complex approaches for temperature estimation. In this work, it is demonstrated how superbright Ag A new procedure for thermal readout is obtained from the combination of in vivo transient thermometry and in silico simulations. Quantities such as the efficiency of hyperthermia processes and the heat deposited in the liver are determined by a careful analysis. The results have potential applications not only in hyperthermia processes but also in advanced diagnosis and therapy. Since much is still left to understand about the thermal dynamics of organs during their natural functioning, the urgency of acquiring accurate internal thermal read‐outs seems to be more evident each day. One of the most complex and essential organs in vertebrates is the liver, which has a multifunctional role in maintaining body homeostasis. It performs essential processes including but not limited to complement system metabolism, energy storage in the form of the carbohydrate glycogen, blood detoxification of xenobiotics and endotoxins and nutrient digestion through bile production. Thus, the assessment of liver temperature would significantly contributes to the interpretation of its role in body's heat distribution and the effect of temperature in malfunctions such as hepatitis, hemochromatosis, steatosis and cirrhosis.The scientific research in the last decades has attested a widespread ambition on the achievement of minimally invasive in vivo thermal sensing. Contactless thermal sensing could be particularly beneficial for adjusting the delivered energy during the treatment of tumors using photothermal therapy. Such an adjustment, in turn, could result in a reduction of the operative trauma, pain, scarring, recovery time and/or the number of post‐surgical complications.1 The  Different strategies are continuously tested including active and passive microwave imaging, ultrasound imaging, magnetic resonance techniques and luminescence thermometry.  Despite the fierce competition, the latter has attracted a great deal of attention in the last years due to the implementation of innovative nanosized luminescent materials, the so‐called luminescent nanothermometers (LNThs). LNThs have been successfully employed to access to the thermal dynamics and loadings of cells, tissues and even organs such as brain. One of the most promising advance provided by LNThs was the remote evaluation of the health status of tissues as achieved by the combined use of luminescence‐based transient thermometry (TTh). This technique is based on a simple principle: when a tissue is subjected to a heating cycle, its temperature deviates from its basal  value to a maximum. Once the heating stimulus is off, the tissue starts thermal relaxation until it recovers its basal temperature. The profile of this thermal relaxation obeys to the Penne's bioheat equation and depends on the thermal and physical properties of the tissue. LNThs make possible non‐invasive measurement of cooling dynamics of the tissue. Any alteration in tissue properties caused by, for example, a pathological context, would alter the cooling profile provided by LNThs.Despite its critical importance, the contactless evaluation of the thermal dynamics of any internal organ still remains a challenging subject.5 Diff The major reason for this limitation is the non‐negligibility of the wavelength‐dependence of tissue‐induced attenuation. It has been shown that even in the biological windows , tissues cause relevant distortions in the emission spectra of LNThs. This, in turn, induces serious errors in the absolute measurement of temperature. In addition, the temperature dependence of the tissue‐induced attenuation also has a negative impact in the reliability of LNThs when operating at the level of internal organs. The temperature dependent optical properties of tissues lead to an alteration in the thermal sensitivity of LNThs in respect to that determined in an aqueous solution. This not only prevents inferring the absolute value of temperature in a deep organ but also the estimation of temperature variations inside of it.Although previous works have demonstrated that LNThs and TTh can detect incipient pathologies such as ischemia (in the paw's muscles of mice) and melanoma , recent results suggest that its applicability cannot be extended to the cases of more internal organs (up to 1–2 cm from the surface in murine models).22 The2S superdots produced by ultrafast photochemistry. Although the potential of Ag2S superdots for low dose in vivo imaging has been already demonstrated, this work constitutes their debut as thermal transducers and sensors at the in vivo level.Thus, given the recently reported drawbacks, two different strategies do exist to determine the liver thermal loading based on LNThs and TTh: i) the use of a thermometric parameter not affected by tissue induced distortions  or ii) to explore alternative methods for the proper interpretation of the cooling dynamics provided by LNTs without requiring the use of re‐calibration. In this work, we evaluate the second approach. We have combined in vivo experimental cooling profiles of mice liver with in silico simulations. Combination of in vivo and in silico data makes possible to determine the absolute liver temperature during a photothermal process. In vivo measurements were performed by using the state of the art in LNThs: we have used Aghemistry.26 Alt22.12S superdots. A complete description of their synthesis and characterization can be found elsewhere. These nanoparticles consist of Ag/Ag2S cores covered by an AgCl shell that reduces the surface‐related nonradiative decays and that increases their quantum yield up to 10%. Figure2S superdots. Here, we can observe that these nanoparticles exhibit an elliptical shape, with two well‐differentiated regions. EDS elemental mapping obtained from Figure  The Ag2S superdots exhibit a mean size of 13 nm as seen in Figure The optical agents used along this work were the recently fabricated Aglsewhere.26 The they present a thermally dependent broad emission centred at 1210 nm . Figure Iint. From the analysis of the experimental data, an intensity‐based relative thermal sensitivity of 3.9% °C–1 was estimated at 20 °C. This is, indeed, very similar to the intensity based thermal sensitivity reported for conventional Ag2S dots. At this stage, it is important to point out that, although the emitted intensity is not suited for absolute temperature estimations, it is still capable of providing some level of information about the time‐dependent part of the cooling dynamics. This, in turn, is sufficient for tissue diagnosis.Under 808 nm light excitation, the optimal wavelength for in vivo imaging experiments considering the minimization of heating effects, 29 the2S superdots as photothermal agents was demonstrated through an experiment in which a colloidal suspension of Ag2S superdots was illuminated with an 808 nm laser at different power densities, I. The temperature of the solution was then dynamically recorded by a thermographic camera  of superdots in PBS has been determined to be as low as 10%, indicating that the radiative decay rate is much smaller than the nonradiative ones. The heating efficiency of Ag2S NPs (ηh) is defined as the fraction of the absorbed energy that it is released in the form of heat (Section S1):λp = 808 nm and λf = 1200 nm are the excitation and averaged fluorescence wavelengths, respectively. Thus, according to Equation . The spot diameter was wide enough to illuminate the abdominal region corresponding to the anatomical location of the liver. The NIR fluorescence image of the mouse was recorded by a thermoelectrically cooled InGaAs camera . A temperature increment was then induced, and the steady state was achieved 5 min after illumination  so that no collateral damage could be induced in the surrounding organs. Its power, on the other hand, was correspondingly adjusted so that the light reaching the liver was enough to activate the nanoheaters inside of it , can be properly described by (Section S2):Tmax is the temperature increment induced in the heating cycle, τc is a parameter that depends primarily on the thermal properties of the tissues found between the skin and the internal organ, and β is a parameter that depends primarily on the location of the thermometer within the liver. Expression (2) is known as the stretched exponential function. Their main advantages over the use of a single‐exponential decay (as utilized in previous works) are: (i) it is more realistic as it considers that distinct layers of tissues will have different levels of importance in the heat distribution, and (ii) it can fit relaxation profiles obtained under various circumstances . Hence, as opposed to previous works, the characteristic relaxation time (τrelax) cannot be defined as the moment in which the normalized ΔTliver signal reduces from 1 to 1/e. Instead, according to literature, it has to be defined as the area below the normalized curve ).If the spectral distortions induced by the layers of tissue between the liver and the surface of the abdomen were negligible, the relation between the luminescence intensity and the temperature could be simply computed through the calibration included in Figure 24 To 2 ≈ 0.99). In addition, the fitting provides us a relaxation time for a healthy liver in absence of relevant thermal loading of 27 ± 3 s. This value is in excellent agreement with that provided by in silico simulations  a slightly higher power density than the one with no damaging heat and (ii) a mildly higher power density. Clear differences were observed. While the liver subjected to 300 mW cm−2 presented virtually the same τrelax as the one obtained under 200 mW cm−2, the liver subjected to 650 mW cm−2 showed slower cooling dynamics. Indeed, a characteristic relaxation time of τrelax = 42 s was found. In other words, the mild change in the excitation power caused an increment of approximately 45% in the liver relaxation time. The reason for this is found in the fact that a higher laser power density leads to an increment in the liver temperature. This, in turn, results in an observable change in the liver relaxation time. Therefore, τrelax emerges as a viable thermometric parameter for experiments. The link between τrelax and liver temperature could arise from the temperature dependence of tissue properties, and/or on the influence of starting temperature on the cooling dynamics. Given the right calibration, the value of τrelax could be inversed to provide the value of liver temperature increment (ΔTliver). Under such conditions, luminescence thermometry would then go back to its initially proposed potential.Figure τrelax with the liver temperature increment is not an easy task: τrelax depends on (i) the layers of tissue between the thermometers and the detection system and (ii) all the biological processes involving heat distribution (such as blood flow‐induced dissipation). To investigate the relation between τrelax and ΔTliver we performed numerical simulations of the heat diffusion in a computable phantom of a normal male mouse . As observed, though not linear, there is a unique correspondence between the numerically obtained τrelax and ΔTliver.Determining the dependence of τrelax. In the present case, we have tried to apply it for the determination of the thermal loading of the liver during a photothermal process as a function of laser power intensity. For doing so we have experimentally determined the variation of τrelax as a function of the heating laser power density. All the measurements were performed in the same experimental conditions set for Figure −2 the liver relaxation time remained virtually constant and close to the value reported in Figure −2 the liver cooling time was found to increase from 31 to 42 s; (iii) above 600 mW cm−2, the liver relaxation time remained constant at 43 s. To convert these relaxation times into temperature units, the data of Figure 2 W−1. This is significantly lower than the heating rate obtained for the colloidal suspension of Ag2S superdots in PBS –1, the Beer‐Lambert Law predicts that only 0.15% of the incident 808 nm radiation reaches the liver. This means, for instance, that for the maximum incident pump density used in this work (0.9 W cm−2) tissue extinction reduces the 808 nm laser power density reaching the liver down to 1.35·10–3 W cm−2. Assuming a spot diameter of 0.3 cm, the total laser power reaching the liver is estimated to be only 0.1 mW.The presence of the tissues between the liver and the detection system causes the excitation light to be attenuated. The tissue thickness between skin and liver has been estimated to be approximately 5 mm. Considering that the average extinction coefficient for murine skin tissues at 808 nm can be assumed to be 13 cmhe liver.39 Thiii)2S superdots.The actual concentration of nanoparticles in the liver differs from that of the injected solution due to the natural biodistribution of AgData of Figure −2) the total heating power provided to the liver is close to 0.09 mW. This is in a very good agreement with the 808 nm laser power experimentally determined to reach the liver . This, in turn, means that almost all the radiation reaching the liver is being absorbed and converted into heat. To have a general idea of the role played by Ag2S superdots in this conversion, a simple experiment was conceived. In it, an ex vivo liver of a mouse previously injected with the NPs was exposed to 808 nm illumination and its temperature achieved in the steady‐stated was compared with the one of an ex vivo liver of a mouse which had not been injected with Ag2S superdots. The results indicated that most of the absorption was caused by the tissue itself .While (i) causes a decrease in the delivered energy to the injected nanoparticles, (ii) implies on a reduced number of nanoheaters inside the organs. Both effects result in a reduction of the heat generated by the injected nanoparticles. With no surprise, accounting for them is not an easy task. But, once again, in silico simulations can shed some light. We have performed numerical simulations to register the in vivo liver temperature as a function of the heating power. Results are included in Figure  Similarly, one could apply such a concept to the thermal relaxation time and build a map (2D figure) that, by itself,would completely characterize the thermal dynamics of the internal organ. In other words, after analysing the set of figures obtained after the heating cycle, a new figure, whose pixels’ intensities would correspond to the local temperature, would be produced. To achieve this goal, a code was written and is described in Section S4. After repeating the process for the data obtained in the last experiment and applying a suitable pseudo‐colour scale, one will encounter the images included in Figure As the performed analysis was based on the acquisition of luminescence images at various times after the end of the heating cycle, the results here reported also present the potential of thermal imaging. After all, each pixel in the field of view can have its intensity evolution fitted to the stretched exponential. This function, in turn, is of particular interest from the computational point of view and finds applicability in areas such as fluorescence lifetime imaging (FLIM) where spatial discrimination of lifetimes is used to distinguish regions (or features) of a system.41 Sim2.3 Therefore, these parameters cannot account for the relaxation changes experimentally seen. On the other hand, looking into other relevant parameters, it is known that ω increases the heating time needed to produce some temperature elevation in organs, as well as decreases the initial time required to cool them down that leads in turn to a monotonic stretch towards thermal equilibrium. At the maximum temperatures achieved in our heating cycles and the corresponding exposure times, protein structural changes, hydrogen bonding breaking and some tissue retraction can take place. The occurrence of oedema is also possible due to vasodilatory pooling, and in fact some signs of it are observed in post‐mortem optical images from the illuminated liver (Section S5). In these conditions, the simulations suggest that blood perfusion becomes defective in certain liver portions and thermal relaxation proceeds differently. More precisely, the damping effect of ω during cooling is modified so that temperature decays more slowly at the beginning and then struggles to equilibrate. This, in turn, provides a justification, at the fundamental level, for the sensitivity of the technique.The results described in previous sections demonstrate the potential of TTh for contactless monitoring of the liver temperature after a heating cycle, but it provides no information about the nature of the heat‐induced modifications. To further understand it, one needs to take into account the equations describing the thermal dependence of the properties of tissues. On the one hand, it has been established that neither the thermal conductivity nor the heat capacity undergo noticeable changes within the considered temperature range for healthy liver.43 The32S superdots were capable of determining the thermal dynamics of a liver under in vivo conditions by highly penetrating transient thermometry. Additionally, when activating their light‐to‐heat conversion capability, we were able to observe variations in the characteristic relaxation time of the livers after intense heating cycles. Despite the attenuation of light into the surrounding tissues, these variations could be correlated with the temperature increment induced by Ag2S dots. After comparing the in vivo results with the heating efficiency of Ag2S superdots obtained under normal conditions, the potential of photothermal treatment was put into question. Numerical simulations involving the heat diffusion in mouse computable phantom determined that the increase in the relaxation time of a liver could be explained by the permanent change of blood perfusion after applying relatively long thermal gradients inside the organ. Thus, the present work provides a timely and novel kind of contribution in terms of the potential of NIR luminescent nanothermometers as tools for the control of thermal damage induced by optically activated nanoheaters.In summary, we have shown that luminescent nanothermometers can be used in small animal models to infer the temperature variations in an internal organ at the 2D level. In particular, infrared emitting Ag4 In order to mimic the in vivo setup as much as possible, the posture of the mouse virtual model has been adapted using a physics‐based poser engine included in the Sim4Life platform. The employed thermoregulation model is based on the Pennes bioheat equation (Eq. S1) containing a lumped term embodying ωb, ρb,  cb and Tb  to account for heat carried away by blood perfusion, or heat transfer rate term.Numerical simulations have been performed in a realistic computer mouse model using a transient solver that employs the finite‐difference time‐domain (FDTD) method, allowing for a better local resolution. The mouse model is available through the IT'IS FOUNDATION as part of the Virtual Family computational models.46 In Table  The width of the band considered here is 0.5 °C above and below the corresponding temperature limits.Also, in all the simulations the model has undergone a discretization into cubical voxels of the whole computational domain using a homogeneous grid with 0.3 mm x 0.3 mm x 0.3 mm resolution. The system has been evaluated for each tissue taking into account the corresponding tissue physical properties . The extent of this area is proportional to the volume of damaged tissue, which has been experimentally estimated to be 10%, helps in estimating the damage extension. In these conditions, blood perfusion becomes defective in wounded liver portions and thermal relaxation proceeds differently after PTT. More precisely, the damping effect of w during cooling is modified so that temperature decays slower at the beginning and then struggles to equilibrate. Due to this induced dysfunction, blood perfusion was assumed constant in all the simulations. Moreover, the observed variation against a piecewise linear approach (see section S3 in Supplementary Information) where the perfusion changes with the temperature, is less than 1% in the organ of interest.The possible extent of the temperature variation of the most relevant physical properties has been also considered in the simulations. On the one hand, it has been established that neither hy liver;43 thu for all tissues except the portion of liver radiated which corresponds to the 10% of the total organ volume and was assumed to have a reduced portion of water content in this area. This region was modelled as a shrunk sphere in the middle part of the liver. All tissues except the liver were set to the basal temperature seen in the in vivo experiments (34°C). The initial temperature for the liver and its radiated portion was determined calculating the absolute value for each ΔT shown in the graph. In the particular case of the data plotted in Figure  have been carried out, assuming a laser power high enough to produce an increment of the temperature in the liver of 6, 12, and 15°C  Ethics Committee, in compliance with the European Union directives 63/2010UE and Spanish regulation RD 53/2013. Experiments were designed in order to use the minimal amount of animals, in accordance with the 3Rs ethical principle. No randomization or blind studies were performed.−1 of 100% oxygen until loss of righting reflex was confirmed and breathing rhythm was significantly slowed. Anesthesia was maintained throughout the experiments by means of facemask inhalation of 1.5% isoflurane and core body temperature was kept at 36 ± 1°C, as measured with a rectal probe, using a heating pad. To have a higher temperature increment in the liver while keeping the safety conditions on laser power, the mouse core temperature was decreased down to 34 °C through the use of a heating pad set at 32 °C, and this was monitored with a rectal probe. After keeping this temperature constant for 5 min, we induced a heating cycle on the liver with a laser fiber coupled. Preliminary studies were performed to determine the optimal power densities that should be used to achieve a significant temperature. Once the steady state was achieved , the laser power then kept at the same value to ensure that the heat distribution was taking place in the organ for 5 min. After this, the laser power density was adjusted so that no additional heating was produced, and the thermal relaxation could be recorded. External temperature was monitored with an infrared thermographic camera.For this study, six CD1 female mice  bred at the animal facility at UAM were used. Mice were anesthetized prior to the imaging experiments in an induction chamber with a continuous flow of 4% isoflurane  in 0.5 mL minFive different mice have been used for the analysis of the average value of the characteristic relaxation time. The error was estimated through the calculation of the standard deviation of the mean. For the study of the dependence of the thermal relaxation time with the excitation power density, the sample size was reduced to one in order to minimize animal suffering. The error in their calculation, on the other hand, was computed through the error of the fitting function. The software utilized for analysis was OriginLab.The authors declare no conflict of interest.Supporting InformationClick here for additional data file.


Neglected sexual side effects (NSSE) are a group of less common sexual side effects that may present after Prostate Cancer (PCa) treatment. There is currently no valid and reliable tool to identify these side effects. A modified Delphi study is an effective way of developing the content of such a screening tool.A modified Delphi study was used to obtain consensus from a multi-disciplinary group of experts over 3 rounds during a 12 week period. Ten statements were presented containing 8 closed-ended statements on individual NSSEs, and 2 open-ended statements on psychosocial impact related to NSSE. Consensus was defined as a 75% strongly agree achievement on each statement, or the final statement evolution at the end of 3 rounds. Statement support in each round was determined by mean, standard deviation and range, after a numerical value was allocated to each statement during specific rounds. All three rounds were structured and suggestions and additions were incorporated in the statement evolution of the three rounds.Thirty-five participants were invited, and 27 completed Round 1 (RD 1), 23 participants completed RD2, and 20 participants completed RD3. All 3 rounds were completed in 12 weeks. Statement 1 , statement 2 (climacturia) and statement 3 (orgasm intensity) reached consensus after RD2, and statement 9  and statement 10 (experiences) were removed after RD3. Statement 4 (orgasmic pain), statement 5 (anejaculation), statement 6 (sensory disturbances), statement 7 (penile length shortening) and statement 8 (penile curvature) were finalised after the conclusion of RD3. Statements 1–3 were the most stable statements with the most support and least amount of disagreement. Statements 4–8 were less stable, but support for them improved over the 3 rounds. Statements 9–10 both had good stability, but the support indicated that they needed to be removed from the set of statements. Statement 5 had the poorest range due to an outlier opinion.Consensus was reached on the items making up the NSSE screening tool. Health care practitioners will be able to use this tool to identify the evidence of NSSE after PCa treatment. Further testing will be undertaken to confirm the reliability and validly of the tool.The online version contains supplementary material available at 10.1186/s12894-022-00982-0. Disability amongst men related to sexual dysfunction is high following their diagnosis and treatment for prostate cancer (PCa) , 2. The The less common symptoms of sexual dysfunction after PCa treatment may present in the form of a variety of complications that are collectively referred to as “Neglected Sexual Side Effects (NSSE)” , 13. TheA literature review indicated a few original publications on the NSSEs after PCa treatment, but only two publications address issues on how to assess the NSSEs , 14. BotThe aim of this study was to bring together a group of experts to develop an instrument that could be used as a self-administered clinical screening tool to identify NSSE 1–10 years after PCa treatment. A Delphi technique study provides such an opportunity where experts can give controlled feedback to develop a group opinion on a specific subject . The DelThe study explored the questions that should be included in a screening tool to investigate the NSSE after PCa and it sought gather consensus on the appropriate wording of statements from a group of experts to include in the NSSE screening tool.A modified Delphi study was performed according to the methodological criteria of Diamond et al. . The DelThe first round (RD 1) collected demographic information from the expert panel. All three rounds (RD1-3) presented a set of statements in the form of questions to be posed to a potential patient. The experts were asked to indicate how appropriate they thought the statement was by ranking it on a 5-point Likert scale  and they were asked to comment on each statement. This allowed for the identification of statements that were unclear or required additional attention. Once a participant submitted their survey answers, the study moderator was able to collate their information and code each participants’ data into an Excel spreadsheet. Participants who had not yet responded during each round were received two additional reminders to complete the round, and the Google form link was closed after three weeks. The research team discussed and implemented all the comments and suggestions and communicated the changes and the new version of the screening tool to the experts during subsequent rounds. The experts were thus asked to rank the appropriateness of a new set of statements in RD2 an RD3 according to the changes that the collective group of experts requested in the previous rounds.Quantitative and qualitative data was produced in all three rounds of this study. The quantitative data was represented by the percentage of participants choosing the “strongly agree option on the Likert scale, as we aimed to achieve a 75% approval rating in each round. In addition to this, RD 1 produced quantitative demographic data. The qualitative data was represented by the comments and the suggestions submitted by the experts in each round. A deductive approach was used to code the comments and suggestions (the perceptions of the participants) into a specific framework . This frWe identified a group of multi-disciplinary medical experts working in the field of prostate cancer and sexual medicine in South Africa. An additional international (Netherlands) expert  was identified from outside the setting due to the small number of appropriately qualified medical sexologists practicing in South Africa. In addition to working in the prostate cancer field, the overwhelming majority of the identified experts were either members of the South African Sexual Health Association or where affiliated to the Prostate Cancer Foundation of South Africa. Thirty-five potential participants were invited via email to participate in this study. This multi-disciplinary group consisted of urologists in the field of radical prostatectomies, urologists in the field of prostate radiation therapy, oncologists, medical sexologists, psycho-sexologists, psychologists, and pelvic health physiotherapists. There is no set participant number needed to conduct a Delphi study in the literature, but most Delphi studies usually use between 15 and 20 participants , 26.Consensus was predetermined as one of two scenarios. In scenario one consensus was defined as a 75% agreement/or disagreement amongst the participants on each questionnaire statement description on the final option of the 5-point Likert scale , in thisThe support of the statement between panellists in each round were determined by the mean, standard deviation and the range of each statement. A numerical value was matched with each Likert scale answer as follows: Strongly Agree = 1, Agree = 2, Disagree = 3 and Strongly Disagree = 5. The ideal mean would be 1, meaning that all the participants strongly agreed on a specific statement. A smaller standard deviation meant a bigger convergence towards strongly agree within a round, and a smaller range in each round meant a more unified opinion between experts within a round.The content covered in the questions circulated in RD 1 was derived from available literature on the NSSE after radiation therapy for PCa  and on NThe composition of the expert panelAgreement percentagesThe evolution of statementsThe support of statements by the expert panel.This section presents the results of the Delphi study and how consensus and stability evolved over the RD1-RD3 by looking at:Thirty-five participants were initially invited to participate in the study, and 27 responded and completed round one, 23 participants responded and completed round two, and 20 participants completed round three Fig. . The 3 rTable The ratio of male to female participants were equally split throughout the rounds. Two thirds of the participants had a minimum of 15 years’ or more experience in the field. The overwhelming majority of the participants were qualified at Masters level or PhD throughout the rounds . Most participants were practicing in the private sector (74%).The agreement for each statement for Rd1-3 is presented in Table Statement 1: Please refer to box 1.Round 1: The word “loss” and “arousal” was found to be problematic and replaced with “leaking” and “arousal (besides during an orgasm)”. A definition of arousal was suggested and included in round 2. Adjustments were proposed related to the Likert scale that was used, and the “never to always” scale was replaced with a “very rarely to very frequently” scale. One expert (a urologist) stated that this was not a side effect, especially not after brachytherapy.Round 2: It was suggested that “with or without a partner” and “with or without an erection” needed to be added to the definition of arousal. Consensus was reached.Statement 2: Please refer to box 2:Round 1: It was suggested that “with your orgasm” be replaced with “during an orgasm”, “loss” to be replaced with “leaking”. There was confusion between “orgasm” and “ejaculation”,Round 2: The experts asked that a statement needed to be added that an orgasm may occur with or without ejaculation. Consensus was reached.Statement 3: Please refer to box 3:Round 1: In relation to the wording some experts thought that the statement implied that an orgasm was already being achieved. The first part of this statement was subsequently changed to establish whether an orgasm was being achieved. Other suggestions required an amendment to the response on the Likert scale by changing the wording from a “decrease to increase scale to “much less to much more scale”.Round 2: It was suggested to swap the order of statement 2 and 3 to improve the flow of questioning. This was implemented in the final round. Consensus was reached.Statement 4: Please refer to box 4:Round 1: Suggestions were made to add a description of the area of symptoms, and to allow a way to quantify/measure the pain on a scale. This question was elaborated in round 2 to include frequency value to how often symptoms occur, a measuring capacity using the numeric pain rating scale (NPRS) and the allowance for descriptive words in the answers to allow for more detail on area of symptoms and descriptions of symptoms.Round 2: A suggestion was made to replace the NPRS with the visual analogue scale. This was rejected due to the fact that sizing of the scale may change on different screens/platforms losing its reliability.Round 3: A comment was made to simply state “Have you… instead of how often have you “. Another comment was made that the description of the patient’s pain would not be valuable, as it could not be used to distinguish different types of pain.Statement 5: Please refer to box 5:Round 1: The urologists on the panel expressed strong concern that this statement may be misleading to patients, as anejaculation is a given consequence for most post- prostatectomy patients. This was addressed in round 2, where the question was first asked whether ejaculation is able to occur. There were also concerns that some men may associate the ejaculation event as the actual orgasm event, and not be aware that an orgasm is possible without ejaculating.Round 2: A comment was once again made whether prostatectomy patients would get confused, as they will not be able to ejaculate after their treatment. It was thought that the question may confuse patients and that it may leave patients concerned that their surgery was performed poorly/incorrectly.Round 3: Suggestions were made to remove sections of the question. Some experts also expressed that it would be inappropriate to ask about a change in volume of ejaculate.Statement 6: Please refer to box 6:Round 1: A suggestion was made to include a section for other options that were not mentioned. The word “asleep” was queried, and suggested to be changed to “numb”, which was done.Round 2: A grammar comment was made relating to the Likert scale and implemented in round 3.Round 3: Suggestions were made to add the “how problematic” section to this question, similar to some of the other statement, and to remove the option to identify the type of sensation change that has occurred. These adjustments were made. Consensus was reached.Statement 7: Please refer to box 7:Round 1: Suggestions were made to remove the options of how much the decrease in size was estimated at, and to keep the question more general. There were suggestions to change the word “bothersome” which was done in round 2.Round 2: Some comments were made related to the impact of the penile shortening on self-confidence and self-image, but these were not considered for this questionnaire.Round 3: Suggestions were made to add a time scale and the partners’ perspective to the question. These suggestions were not considered as the partners perspective was already invited at the start of the questionnaire, and the time scale was already included for referencing purposes.Statement 8: Please refer to box 8:Round 1: A suggestion was made to change the phrase “different curvature” to “any new curvatures”, as some minor penile curves were deemed normal. One suggestion from a urologist was to remove this question as it was not a known consequence. The same suggestions that were made to change “bothersome” in statement 7 were again made, and changes were implemented in round 2.Round 2: A statement was made by a urologist that this question does not belong as it does not occur with cancer treatment. A comment was made to replace the word “curvature” with “change in shape.” This was not considered for the final round. Another comment suggested to include the word “bend” along with “curvature”, this was included in the final round.Round 3: Similar comments were made to statement 7 regarding the partners perspective and time scale. A urologist on the expert panel stated that this side effect was not a consequence of PCa treatment. There was also again a suggestion to include “shape” in this question. This was not included as shape was seen as a misleading inclusion as it could mean many different things.Statement 9: Please refer to box 9:Round 1: Suggestions were made to split the 2 questions completely. It was also suggested to include “intimacy” with the phrase. there were many positive comments regarding the fact that this was an open-ended question, and this would give context to the symptoms.Round 2: Most panellists agreed that this was an important question, but its appropriateness for inclusion in this quantitative questionnaire was questioned. Comparisons were made with other similar questionnaires that did not have open ended questions. This question was therefore completely removed from the questionnaire.Statement 10: Please refer to box 10:Round 1: It was suggested that the statement be split into two statements, or be rephrased as the question seemed a bit wordy.Round 2: As with statement 9, most panellist agreed that this was an important question, but its appropriateness for inclusion in this quantitative questionnaire was questioned. Comparisons were made with other similar questionnaires that did not have open ended questions. This question was therefore removed from the questionnaire.At the conclusion of the three rounds, a final screening tool was produced, and is outlined in Table The awareness of the NSSE after PCa is growing rapidly amongst health care practitioners, and with that preventative approaches are being targeted at an early stage after PCa treatment. There are currently no statistics on the prevalence rates of the NSSE after PCa on South African patients. There are however two landmark studies of the prevalence of NSSE after PCa treatment on Danish participants , 14. In A Delphi study provides an appropriate methodology to create content where there is a lack of information, incomplete knowledge or uncertainty regarding a specific topic , 30. ThiA Delphi technique study is defined by the quality and expertise of the panel of experts that participate in the study . Our expThree rounds of a Delphi technique study is considered optimal , and thiStability of consensus in this study was measured using agreement percentages and statement support parameters. Statement 2 was the most stable statement, as it had the smallest mean (1.40 and 1.09), smallest standard deviation (0.61 and 0.29) and the lowest range (1–2 and 1–2) between rounds. Statements 1 and 3 were also stable and were well supported by panellists with improvements made from round 1 to 2, and reaching consensus in round 2. While statements 4–8 all had increased in stability from round 1 to 2, they weakened from round 2 to 3 with regards to statement support from the panellists. Most comments and deliberations were made on these statements. Statements 4–8 all improved in their agreement over the 3 rounds. Statement 9 and 10 both had good stability but were removed after round 2.Statement 5 consistently had the poorest range of statement support due to an outlier opinion of one panellist. The urologists on the panel expressed concern about the definition and wording of statement 5 (round 1) that relates to “anejaculation”. They expressed the need for unambiguity in stating that anejaculation was a given consequence after a prostatectomy and not a side effect of PCa treatment. Similar outlier opinions were noted in round 3 of statement 8, weakening the statement support in round 3 for the statement. In statement 8, one expert (urologist), repeatedly requested the removal of the Peyronies disease/penile curvature statement and argued that the disease was not a known side effect after PCa treatment. Published literature relating to Peyronies disease, however showed the presence of an abnormal penile curvature in 10% of participants in a 2014 study . This stUltimately, the experts reached 75% agreement or disagreement on 4 of the statements, and a majority agreement as per scenario 2 was reached on 4 statements. Two statements were removed and the final screening tool consisting of 8 statements was created. The argument to remove two statements (open ended questions) was successfully made by the expert panel, and their suggestion was to include this in an expansion of the screening tool or as part of a follow up conversation that would be stimulated by the screening tool.All the experts were supportive of the development of a screening tool to screen for the NSSE’s following PCa diagnosis. The South African health care system allows for health care practitioners to work in the public sector and to spend a limited number of hours of Private remunerative work. Despite the fact that the South African health care system is still grossly inequitable, and due the severe shortages of health care personal, there is much enthusiasm to translate knowledge and interventions such as the development of a screening tool  for use in the public health sector.General suggestions included the desire for the questionnaire to remain brief and uncomplicated and this was implemented in the final questionnaire. Suggestions were made to remove the subjective options describing each of the side effects, and to focus on the impact it had on sexual activity, as was the case in the initial phrasing of statements 7 and 8. These were carefully considered and subsequently implemented. All the statements in round 1 ended with “during the last 3 months”. This phrase was removed from each individual statements in round 2 and included as an instruction for patients to “think about the last 3 months and compare that to the time before your prostate cancer treatment, and then answer the question”. The final screening tool produced is outlined in Table Continued commitment is required from participants who are being asked a similar question multiple times, and this may be a reason for the experts dropping out in subsequent rounds of the study. There is also no evidence of the reliability of Delphi studies if the same set of questions is presented to two different panels, and thus the success of a Delphi depends highly on the quality and experience of the expert panel. The study focuses on expected symptoms associated with current management modalities for Pea in South Africa.The findings are thus relevant to current contexts only. It will require updating with changes in treatment and would need to be tested in different populations.This study adds value in that it will assist health care practitioners to identify a variety of sexual dysfunction complications, collectively referred to as NSSE in men after PCa treatment. Currently these symptoms are often undiagnosed and remain untreated, especially in a low to middle income country such as South Africa. Consensus was reached on the statements making up the NSSE screening tool by a panel of experts. This screening tool may be applied on patients who have had treatment for early stage PCa that includes prostate surgery and prostate radiation therapies. This screening tool will need to undergo further psychometric testing to establish its validity and reliability.Additional file 1: Appendix 1. Original research statements.Additional file 2: Appendix 2. NSSE after PCa Screening Tool (Full Version).


The role of atmospheric parameters and aerosols in the transmission of COVID‐19 within tropical Africa, especially during the harmattan season, has been under‐investigated in published papers. The harmattan season within the West African region is associated with significant dust incursion from the Bodele depression and biomass burning. In this study, the correlation between atmospheric parameters (temperature and humidity) and aerosols with COVID‐19 cases and fatalities within seven locations in tropical Nigeria during the harmattan period was investigated. COVID‐19 infection cases were found to be significantly positively correlated with atmospheric parameters (temperature and humidity) in the southern part of the country while the number of fatalities showed weaker significant correlation with particulate matters only in three locations. The significant correlation values were found to be between 0.22 and 0.48 for particulate matter and −0.19 to −0.32 for atmospheric parameters. Although, temperature and humidity showed negative correlations in some locations, the impact is smaller compared to particulate matter. In December, COVID‐19 cases in all locations showed strong correlation with particulate matter except in Kano State. It is suggested that a reduction in atmospheric particulate matter can be used as a control measure for the spread of COVID‐19. The role of meteorological parameters and particulate matters in the number of COVID‐19 cases varies with location within NigeriaLocal climate affects the relationship between particulate matter and the number of infected personsThe role of socio‐economic, demographic, and environmental factors in the spread of COVID‐19 were discussed The impact of SARS‐CoV‐2 (COVID‐19) has been reported in global transportation  States from different regions within Nigeria. The demographic and geographic characteristics of the locations are shown in Table 3  were deployed during the fall of 2020. These stations provide a first order approximation of PM2.5 concentrations in locations throughout Nigeria. The stations are geographically located in the central and eastern parts of Nigeria. This data provides a means to evaluate the potential connections amongst of Particulate matter, temperature, relative humidity and COVID‐19 cases and fatalities in seven administrative states of Nigeria. The temporal evolution of COVID‐19 cases in the seven locations are shown in Figure 2.3The Spearman's correlation coefficient (r) is defined as:ρ within the range −1 ≤ ρ ≤ 1 is the Spearman's correlation coefficient, di the difference between the two ranks of each observation, and n is the number of observations. For comparison, the Pearson correlation was also considered. It is defined as:y¯ represent the mean value.The values of 3The temporal variation of COVID‐19 cases within the locations under consideration is shown in Figure Monthly correlation between COVID‐19 cases and selected parameters were considered and the results shown in Figure Spearman correlation between the selected predictors with the number of cases Table  and numb2 in the rural regions to 30, 658 km2 in the capital city. The location is subjected to regular dust intrusion from the Bodele depression during the harmattan season  and particulate matter  during the harmattan season in Nigeria could be attributed to a combination of socio‐economic, demographic, and environmental factors Table . In KebbThe correlation between the selected predictors and number of fatalities was also reported for Spearman Table  and Pearhttps://nigerianstat.gov.ng/download/952). Furthermore, the state has a doctor to population ratio of about 21,000, hence, the health care system is grossly inadequate for the location  as well as the country's capital (Abuja) could be attributed to the socio‐economic factors. The highly youthful and energetic within the densely populated State's capital is a contributing factor to the spread of the virus in the southern part of Nigeria . This will help in mitigating and controlling the spread of the virus within the general populace. In this study, we aim to determine the relationship between COVID‐19 and (a) atmospheric parameters ‐ temperature and humidity, and (b) particulate matters ‐ PM1.0, PM2.5, PM10.0, and visibility, in seven different locations within Nigeria. Results obtained showed that periods of high dust incursion into the country corresponds to the time frames of high number of COVID‐19 cases. Specific local climate such as topography and industrialization were found to contribute to the correlation values obtained on a monthly scale. Generally, during the harmattan season, significant positive correlation values were obtained between COVID‐19 cases and particulate matters in the southern part of the country including Abuja. The significant positive correlation between particulate matters and COVID‐19 cases and fatality will be useful in the control and mitigation of the pandemic spread within localities.The authors declare no conflicts of interest relevant to this study.


Our work is expected to be the first step toward an attentive architecture able to endorse scenarios in which the robots are perceived as social partners.Social robotics is an emerging field that is expected to grow rapidly in the near future. In fact, it is increasingly more frequent to have robots that operate in close proximity with humans or even collaborate with them in joint tasks. In this context, the investigation of how to endow a humanoid robot with social behavioral skills typical of human–human interactions is still an open problem. Among the countless social cues needed to establish a natural social attunement, this article reports our research toward the implementation of a mechanism for estimating the gaze direction, focusing in particular on mutual gaze as a fundamental social cue in face-to-face interactions. We propose a learning-based framework to automatically detect eye contact events in online interactions with human partners. The proposed solution achieved high performance both  Joint attention (or shared attention) is one of the most important mechanisms occurring in a non-verbal interaction between two or more individuals. It is achieved when individuals direct their gaze on the same object or event in the environment as a consequence of social gestures  . The abiIn this context, designing and building an attention architecture enabling joint attention between a human and an embodied artificial agent, such as iCub, has inspired many researchers from different fields, spanning from artificial intelligence to robotics and from neuro and cognitive science to social science . Inspireintentional stance as a strategy toward the robot like they do with other humans  is a neuropsychological test typically used to investigate attention orienting in response to a directional cue. In such a gaze-cueing task, the observer is typically asked to discriminate an object target  while looking at a directional cue  presented centrally, in between the locations of potential target presentation. The cue can be either valid or invalid, depending on whether it pointed to the target object or to a different direction.In their study, iCub was positioned between two lateral screens on which the target object was presented (in line with the Posner paradigm). iCub was used as the experimental apparatus both to establish a real-time eye contact with the human participant and to manipulate the directional gaze cue across the trials. The results revealed that the human reaction times depended on the combined effect of cue validity related to the iCub’s gaze direction and social aspect of mutual gaze. Another example can be found in Dataset collection for mutual gaze detection in frontal human–robot interaction. In the context of frontal tasks, the dataset collected is general enough to suit many different experimental scenarios. To the best of our knowledge, it is the first mutual-gaze dataset collected involving a humanoid robot.1. Designing, implementation, and training of a learning module based on the aforementioned dataset. Such a module is then embedded into the iCub’s framework and validated both in silico and in online scenarios. Furthermore, we compared our method with the solution proposed in 2. 3. As a case study, we select the experimental setup proposed in Some authors support the notion that a robot embodying artificial models capable of reproducing human skills is a unique and invaluable tool to explain human cognition . With thOur approach aims at reducing the amount of hardware equipment required by the robot to detect a mutual gaze with the human partner . The robot, indeed, relies only on the image frames captured by its eye-like cameras making the interaction as natural as possible. The algorithm developed in this work is an important building block for robotic setups that can be used to study human social cognition in naturalistic interactions.A total of 24 participants were recruited for data collection . All participants had normal or corrected normal vision (6 participants out 24 wore glasses) and provided written informed consent. The data collection was conducted at the Istituto Italiano di Tecnologia, Genoa, and it was approved by the Local Ethical Committee (Comitato Etico Regione Liguria).The humanoid robot iCub embeds two Dragonfly2 camerasParticipants were asked to sit in front of the iCub at a distance of around 1 m and to establish first mutual gaze and then averted gaze with the iCub’s eyes in order to acquire frames both in eye contact and in no eye contact condition. In the eye contact recording session, participants were also asked to look at the iCub’s eyes but moving first their torso and then their head . For eacw × h color image as input and produces the 2D locations  of anatomical keypoints for each person in the scene with the corresponding detection confidence level k as output. Relying on a multi-stage deep convolutional neural network, OpenPose can jointly detect body, face, hands, and foot keypoints reaching highly accurate and real-time performance, regardless of the number of people in the image.Once the dataset was collected, the vector feature was extracted from each image by means of OpenPosex, y, k) was taken for each point). Then, the detected keypoints were centered with respect to the head’s centroid, computed as the mean coordinates of all keypoints of the face, and normalized on the farthest point from the head’s centroid. The use of the face’s keypoints as a feature vector has the main advantage of making the classifier independent of the light conditions and the picture’s background.In our work, a subset of 19 face keypoints were considered , resulting in a vector of 57 elements  where r = 1 if a mutual gaze is detected (0 otherwise), while The resulting feature vector is finally used as input to the binary classifier. A support vector machine (SVM) with the RBF kernel was chosen to address this classification task. We compared the results produced by the SVM with a random forest classifier; the former was chosen because it reported the best performance in terms of accuracy and F1 scores. .The acquired dataset was augmented in order to be robust to the degenerative case in which OpenPose fails to detect the eyes’ boundaries and the pupils. To simulate such a condition, the coordinates of those keypoints in case of eye contact were set to zero, while the others  were left unchanged. Moreover, we applied a further augmentation by geometrically rotating the face’s keypoints, extracted by using OpenPose, to the left and right of a certain angle around the face’s centroid to cover a wider range of head rotations (not covered by the acquired samples). In detail, the facial keypoints were rotated to the left and right by an angle We handled the unbalanced dataset by properly weighing each class of classification. Such weights were chosen inversely proportional to class frequencies in the input data.Finally, OpenPose parameters were tuned in order to have the best performance for the considered dataset .k = 5 times in order to average the performance over different participant subsets and evaluate the statistical properties of the method. The performance was evaluated in terms of accuracy, precision, recall, and F1 scores reaching in all metrics values around 90%. Precisely we had accuracy = 0.91 ± 0.03, precision = 0.90 ± 0.08, recall = 0.89 ± 0.06, and F1-score = 0.89 ± 0.04.For the training of the classifier, the dataset was split into two subsets taking 19 out of 24 participants for the training set and the others 5 participants for the test set. The dataset was split ms. To this aim, we implemented a buffer of 3 elements at the inference time. The actual classifier result was selected through a majority rule evaluated on the buffer. The implementation of the buffer allowed us to reach even a higher level of accuracy. Specifically, the accuracy registered in the first three scenarios reached its maximum value—that is, 1.0—, whereas in the last one the accuracy was 0.93. Analyzing the last scenario, we found that the classifier made wrong predictions when the human’s torso reached the extreme angles of 90 (right) and −90 (left) while keeping the head straight toward the robot  no mutual gaze, 2) frontal mutual gaze, 3) human rotating the head to left/right while maintaining a mutual gaze with the robot, and 4) human rotating the torso while maintaining a mutual gaze with the robot. To avoid the flickering in the classifier predictions caused by the high video frame rates, we implemented a mechanism to propagate the predictions to those frames for which the classifier output is not available due to frame rate incompatibilities. The reason behind this is that, in practical settings, it is reasonable to assume coherent predictions in a time span of ∼ 100 In this section, the mutual gaze classifier is compared with the solution proposed in % of cases (probably due to the face masks), we used OpenPose for the bounding box detection. Such a bounding box was then used to crop the image sent as input to the convolution neural network. This was done to obtain a fair comparison between the two algorithms. The accuracy and F1 score were evaluated as metrics both on the test set and on the video streams.Proposed approach• Test set. Accuracy = 0.91 ± 0.03; F1 score = 0.89 ± 0.04.• Stream videos. Accuracy = 0.97; F1 score = 0.98.• +OpenPose• Test set. Accuracy = 0.76 ± 0.05; F1 score = 0.77 ± 0.06.• Stream videos. Accuracy = 0.89; F1 score = 0.82.• Because the training code of p-value t-test was performed to assess the statistical difference between the performance of the two approaches .Since data were normally distributed  is a method based on the coalitional game theory used to explain individually how each prediction is made by the learning algorithm. For each individual prediction, a value  is assigned to each feature as the measure of its impact on the model’s output. The final contribution for each feature is evaluated by averaging its SHAP values over a set of predictions .% percentage points. The analysis revealed that there is no feature that predominate the others, but all the elements of the feature vector make a comparable contribution to the prediction of the output. This was also confirmed by principal component analysis (PCA) reported in the In Next, we further validated our approach presented in The conclusions of • iCub starts with the head pointing down and with its eyes closed for 2 s;• it opens its eyes for 500 ms without moving the head;• iCub looks toward the participant’s eyes (eye contact) for 2.5 s;• iCub moves the head laterally toward one of the lateral screens, where the letter V or T appeared randomly either on the same screen where the robot is looking at  or on the opposite screen  for 200 ms; and• the participant was instructed to identify the target letter by pressing V or T on the keyboard while keeping a mutual gaze with the robot and without gazing at the screen.The experimental trial was designed as follows:To validate the classifier, we asked a total of 4 participants to carry out 8 blocks of 8 trials each. The experiments were controlled in order to have the ground truth for each block of trials. In detail, the participant was asked to maintain a mutual gaze with the robot in 5 blocks of trials and to always simulate a distracted participant in the other 4 blocks left . To assure the quality of the ground truth, the experimenter monitored online eye movements of the participants, and the trials were further checked offline before the analysis. Only one trial was discarded.As done before, the performance was evaluated in terms of accuracy, precision, recall, and F1 scores. We registered accuracy = 0.97, precision = 0.95, recall = 1.00, and F1 score = 0.97.In this research report, we presented our first results of an ongoing work aiming at developing a novel attentive architecture for the humanoid robot iCub. In this context, we focused on the social cue of the mutual gaze making iCub capable of recognizing eye contact events while interacting online with a human partner. We validated the proposed mutual gaze classifier both computationally and experimentally, showing high performance values. We also compared the proposed approach with the state-of-the-art method described in Improving and extending the mutual gaze scenario to a wider problem of the gaze estimation is a part of our current research. As a potential improvement, temporal information  from dynamic data, such as videos, could bring additional information to the system increasing performance and generalization capabilities. Furthermore, the implementation of an attention system with the ability to detect social cues is a fundamental step toward the realization of socially capable humanoid robots.


The voltage controlled magnetic anisotropy (VCMA) becomes a subject of major interest for spintronics due to its promising potential outcome: fast magnetization manipulation in magnetoresistive random access memories with enhanced storage density and very low power consumption. Using a macrospin approach, we carried out a thorough analysis of the role of the VCMA on the magnetization dynamics of nanostructures with out-of-plane magnetic anisotropy. Diagrams of the magnetization switching have been computed depending on the material and experiment parameters  thus allowing predictive sets of parameters for optimum switching experiments. Two characteristic times of the trajectory of the magnetization were analyzed analytically and numerically setting a lower limit for the duration of the pulses. An interesting switching regime has been identified where the precessional reversal of magnetization does not depend on the voltage pulse duration. This represents a promising path for the magnetization control by VCMA with enhanced versatility. In the last decade, magnetization manipulation by electric fields entered the race for energy efficient methods for information storage when the very first mentions of electric field manipulation of magnetization in ferromagnetic semiconductors and 3d metals opened this research direction5. It was shown experimentally that by using an electric field in order to control the magnetization dynamics, it is possible to achieve writing with only a few fJ/bit7. A wide series of theoretical and experimental studies have been dedicated to this subject, covering the topics of material optimization for enhanced voltage control of magnetic anisotropy (VCMA) as well as magnetization dynamics control9.In an era dominated by an increasing demand of information processing speed and efficient information storage, spintronics can offer novel solutions to circumvent some of the limitations presently reached by conventional microelectronics technologies10 and/or (ii) oxygen migration in the case of ionic mechanisms12. Another very likely source of electric-field control of the magnetization is the Rashba spin–orbit mechanism, where the underlayer in contact with the FM layer is a heavy metal (HM)13. In some cases, the HM/FM interface can have a greater contribution to the VCMA effect than the FM/Ox interface13. Many first principle studies have been dedicated to this topic, generally for systems composed of a heavy metal, a 3d ferromagnet and a dielectric, typically MgO17. Simultaneously, experimental evidence of voltage controlled magnetic anisotropy (VCMA) has emerged in a wide range of structures, and static and dynamic measurements have been performed in order to explore its limits18. However, from the micromagnetic and macrospin simulations point of view, this field is not explored enough and a deep understanding of the behavior of magnetization in this framework and of its governing parameters is still needed. Some studies on VCMA using the micromagnetic framework aim at explaining the magnetization reversal process under the influence of an electric field, with some design approaches being proposed21. A broad variety of macrospin studies exist, oriented towards the optimization of system operation through pulse shape23, thermal stability24 and towards decreasing of the write-error-rate (WER), some of which accompanied by experimental studies26. Other macrospin studies focus on the association between VCMA and spin transfer torque (STT) methods of magnetization manipulation27 or on the VCMA and a Rashba field which is used as an in-plane bias magnetic field25. A detailed fundamental study of the dynamics is dedicated to a design where an assisting magnetic field is absent28 and the switching relies purely on the fine tuning of the voltage pulse duration. However, a reliable fast switching process is conditioned by extremely short pulses of precise length. Therefore, we considered it appropriate to search for a less restrictive regime from an application point of view.The idea of voltage control of magnetization relies on the phenomenon of magnetic anisotropy modulation with an electric field. This effect can be due to several mechanisms: (i) charge depletion and accumulation at the ferromagnet(FM)/oxide(Ox) interface, in the case of purely electronic effectsIn this work, we carried out a thorough study of the precessional switching in the VCMA framework assisted by an external magnetic field, including the calculation of switching diagrams in the macrospin approximation, as such a detailed approach is still missing. We discuss the behavior of magnetization in response to simultaneously applied stimuli (voltage modulation of anisotropy and a magnetic field applied in plane). Therefore, we will not refer to a specific system, nor to a specific saturation magnetization value, anisotropy constant or field, but we will employ values that are close to those which are generally obtained in experimental systems and usually observed in simulations. The modelled system and the parameters used are described in the following sections. We will show that there is a recipe for reaching a regime where the switching probability is no longer sensitive to the electric field pulse duration, which is quite important from an application point of view. Also, we show that in the VCMA framework, a change of paradigm concerning the damping coefficient takes place: for spin transfer torque (STT) a small value is preferred, but in VCMA, this is no longer the case.t = 0.9 nm, saturation magnetization Ms = 1000 kA/m and an out-of-plane effective anisotropy field of µ0HK = 80 mT. These parameters are rather usual values for ferromagnetic thin films exhibiting perpendicular magnetic anisotropy (PMA)30 and particularly, they are typical for heavy-metal/ferromagnet/oxide systems most common in VCMA studies32. This model satisfies magnetic entities with lateral dimensions bellow the domain wall width, which in this case is around 72 nm.For the macrospin simulations, we considered a ferromagnetic disk of thickness Oz axis, parallel to the anisotropy field, HK. In order to trigger the magnetization switching driven by VCMA, an electric field is applied to reduce the energy barrier between the + Oz and  − Oz magnetization states, as well as a dynamic stimulus, such as a magnetic field applied in-plane, Hip, exerting a torque on the magnetization, responsible of a precessional motion31. In our simulations, we considered that the electric field is applied through a voltage pulse synchronized with an in-plane magnetic field pulse, applied independently with respect to the voltage pulse. The fact that the in-plane field Hip is applied simultaneously with the voltage pulse prevents additional initial precession around the effective anisotropy axis (issued from competition between the PMA and in-plane Hip) and lead to a final magnetization damped relaxation, after the precessional switch, towards -mz and not along the Hip-PMA effective quantization axis. This is schematically shown in Fig. Hip may have several origins, ranging from an applied DC field, exchange-bias or Rashba effect25, (a more detailed discussion of this aspect is available in the supplementary section). Such a field can be synchronized with the voltage pulse in such a manner that it would restore the effective field along the Oz direction after the pulse is cut, thus eliminating the concerns regarding a decrease of the thermal stability factor.At rest, the magnetization lies spontaneously along the p represents the modulation of the anisotropy field HK0, expressed as a percentage proportion of the anisotropy field HK = (1 − p)HK0. The amplitude of the magnetic field is µ0Hip = 32mT (~ 40% of HK0) while the duration of the pulse is varied at the nanosecond scale. The color code of the diagram Fig. Heff, which is the sum of HK and Hip and is controlled by the effective field orientation towards the Oz axis, as well as by the pulse duration.The response of the system excited by synchronous voltage and magnetic field pulses is summarized in the diagram shown in Fig. mentclass2pt{minimmentclass2pt{minimOz axis, around Heff, indicating a small reduction of the energy barrier. This behavior can be observed until the precession cone is tangent to the xOy plane, i.e. until a critical modulation of the anisotropy is reached. In region 2, although the switching does not occur, the reason behind this behavior is different. The magnetization requires a certain amount of time to reach the film plane, and this depends on Heff. However, no matter how we modulate the anisotropy, if the pulse length is not long enough, the precession is transferred too fast from Heff back to HK. The first blue stripe where the switching occurs for the first time is denoted in the diagram by region 3. This region contains a resonant switching regime, where an accurate pulse duration control is crucial for maximizing the switching probability. Figure Oz and  − Oz states. Related to this region, an analytical estimation of the minimum pulse length for which the magnetization crosses the xOy plane and relaxes in the  − Oz space is graphically represented by the thick orange line. This pulse duration is expressed as the sum of critical times τ1 and τ2 whose detailed expressions and significance are given in the Discussion section and does not account for damping. Region 4 depicts a situation where the pulse duration is long enough in order to allow the magnetization to relax on the -Oz direction and to go back to the initial state crossing the xOy plane twice. This behavior is limited in terms of pulse duration, longer pulses leading to a regime where the switching is again possible. This can be observed in region 5, where three successive reversals between + Oz to  − Oz end up with the magnetization along  − Oz direction. The diagram follows a pattern of resonant switching, alongside its superior harmonics, where the fastest switching takes place in region 1, for a pulse duration equal to a half of its precession period. Concerning the switching probability, it is clear that odd multiples of the half-precession period will favor the switching, while even multiples will place the magnetization back along the + Oz axis.In region 1, the magnetic anisotropy modulation is too small, and switching is not possible, regardless of pulse length. On the normalized energy surface, the minimum energy in the upper hemisphere is closer to the Hip and HK is large33. Figure p is remarked. The different representation of a switching diagram at fixed Tp, p and Hip, represented in Fig. Hip there is a critical modulation coefficient p below which there are no switching events.The position and width of the regular bands are affected both by the in-plane field amplitude and the damping parameter, as one can see on the diagrams from Fig. pc which appears to decrease linearly with Hip/Hk0 and vanishes if Hip becomes larger than half of the amplitude of the anisotropy field , the magnetization approaches the xOy plane, but it cannot touch the plane (mz ≠ 0), being pulled back to the effective field and finally relaxing towards + Oz once the pulses are stopped. If the modulation is equal to the critical value p = pc = 0.2150, the magnetization reaches a saddle-point with mx = 1 and mz = 0, which is the equivalent of the hard-plane orientation, then it successfully passes this point and relaxes towards the -Oz axis. This regime is maintained until p reaches the value of 0.2350, when the magnetization does not relax in the z < 0 space, but a second crossing of the hard plane occurs, so that the magnetization switches back to its initial state. One can notice the magnetization ringing to reach an equilibrium state, this feature being controlled both by the damping parameter and the MCA modulation coefficient, p.To get a deeper understanding of the linear dependence of the critical modulation on the in-plane magnetic field, one must analyze the trajectories described by the magnetization on the energy landscape in polar coordinates. Figure x-axis as shown in Fig. Based on the relation describing the free energy of the system see , it is s34, meaning that the energy of the initial state should be at least equal to that of the saddle point. The three cases presented in Fig. z-axis and thus the critical modulation The primary criterion to commute between the two minima is that the magnetization trajectory passes through the saddle pointHip value stays below a half of the anisotropy field HK0. The continuous line from Fig. Moreover, the critical modulation exists only if the p = 0.56 for which the pulse duration (Tp = 0.55 ns) is precisely equal to the lapse of time taken by the magnetization to go from + Oz to  − Oz. It is thus possible to achieve a sub-nanosecond switching (resonant switching) but within a very narrow range of MCA modulation. Otherwise, if the pulse has not this precise value , the magnetization rings for a long time to get to the equilibrium since the energy dissipation rate, proportional with the damping is very small. This drawback due to the ringing is obvious if we consider the zero-crossing time—τzc dependence on the MCA modulation  = 0, appears to be slightly dependent on the damping value and to decrease when the MCA modulation increases. For most of the MCA values, the zero-crossing time τzc, is short with respect to the overall switching time except at the optimal condition where the switching time is roughly twice the τzc. The ringing of the magnetization , we see that the trend seems to be completely opposite, as the damping pulls the magnetization harder towards the potential minimum, making it more difficult to reach close to the saddle point. This reveals the important ringing attenuation provided by α.From applicative point of view, tailoring the pulse duration in an accurate manner with 100 ps resolution is difficult. Thus, we find it more appealing to explore systems where this would cease to be a rigid constraint, even if this might lead to longer switching time than the resonant switching. Tailoring the switching time by damping constant seems to be a possible path, as indicated by the dynamics represented on energy surfaces in Fig. pc. Using the LLG equation (see Eq. (p = 1):This cut-through the region 1 of Fig. (see Eq.  Methods)p = 0.50 for different damping values reveal that an increased damping pulls the trajectory closer to the saddle point.The optimal condition to have the fastest magnetization switching corresponds to a pulse duration such as − Oz direction. This region property might be very useful in terms of switching reliability. Although it was shown that large damping values tend to increase the thermal fluctuations effect on the dynamics and thus the write-error-rate25, Matsumoto et al.36 showed that there is a minimum in the write-error-rate even at large damping values, following a stripe pattern that resembles the switching probability diagram  the damping in ferromagnetic heterostructures and/or increasing the value of the in-plane field used for magnetization precession. Another solution for efficient deterministic switching would be to operate the device in a parameter window corresponding to the curved (“elbow” like) region of the bands in the diagrams  is actively tuned and choosing materials with a high damping value could increase reliability. We show that there are two leading methods for switching optimization in this framework: one that follows the improvement of the switching time by forcing a faster relaxation in the opposite energy minimum, and one that offers a generous domain for pulse application, with the achievement of similar switching times, thus eliminating this constraint in applications. This combined with the simultaneous cutting of the in-plane magnetic field and voltage pulses, which restores the initial energy barrier between the + 0 the vacuum permeability. The electric field action on the magneto-crystalline anisotropy (MCA) is accounted by a modulation related to the relative reduction of anisotropy at a given applied electric field value (such as p can be translated as a percentage reduction of the effective anisotropy.The calculations have been performed using a home-made LLG macrospin code developed in C++ and parallelized for CPU computation facilities. In our simulations we have used a free energy of the system, given by:Supplementary Information.


The Covid-19 epidemic highlighted the significance of externalities: contacts with other people affect the chances of getting infected for our entire network. We study endogenous network formation where not only players or pairs but larger coalitions can, cooperatively change the network. We introduce a model for coalitional network stability for networks with widespread externalities. The network function form generalises the partition function form of cooperative games in allowing the network to be taken into account. The recursive core for network function form games generalises the recursive core for such environments. We present two simple examples to illustrate positive and negative externalities. The first is of a favour network and show that the core is nonempty when players must pay transfers to intermediaries; this simple setting also models economic situations such as airline networks. The second models social contacts during an epidemic and finds social bubbles as the solution. Networks are used to describe a wide class of social and economic situations. In a social network the nodes are individuals, and the edges or links may be trading possibilities  core. When some coalitions deviate from the current structure they can (i) arbitrarily restructure internal links, (ii) severe any outgoing links (iii) propose new outgoing links and (iv) allocate the value of the coalition among its members. The value of the coalition can only be determined once the entire graph is known so we determine the structure of the remaining, residual players.There are several possible approaches to take. By considering strong Nash equilibria  is simply the length m of the shortest path with We say that A new intention ent Fig. a.When 12¯ Fig. b.An existing link red Fig. c. In thiWe assume that the network is endogenous: players can build and destroy links Fig. . FollowiCoalitions can build or cancel any of the internal links among its members, destroy or propose outgoing links Fig. . A propoC embedded in partition We define the value of a coalition of players in a network by the network functionN, L, V) is a cooperative game in network form or simply a game.The triple  by Let us denote the set of outcomes in  has been defined for all games with N, V) by Q forming partition recursive coreC of  is the set of undominated outcomes. network players form, but the more general game requires some more complex notation and terminology. First we present this notation, as before, we define the way to derive a residual network game and finally present the recursive core for network games.R. Depending on the choice of players in R some of these existing, or proposed will be abandoned, some may be accepted or maintained. Likewise the consequence of having an outside link from R will depend on the interest at the other end in maintaining this connection. Since this interest is already known, knowing R. Indeed, given these decisions the problem the remaining players in R face is similar to the original game: it is also a game in network function form, just a little smaller one. In the following we define this residual game.Now assume that a coalition The residual game is a triple R of residual players. Internal links in Using our example network Fig. , we showPayoffs are the same as in the original game, and to determine these, we must recombine the residual configuration with that of k player games.Now we can define the recursive core for network function form games. The definition is analogous to that for partition function form games and is therefore recursive. First the core is defined for a trivial, single player game. Assuming the definition for all, at most Recursive core for network games) For a single-player game the recursive core is trivially defined. has been defined for all games with N, L, V).Now assume that the recursive core dominated if there exists a coalition Q forming partition for all outcomes we have recursive coreC of  is the set of undominated outcomes.We say that the outcome any  of the residual (core) outcomes. It is easy to verify that the optimistic recursive core is weakly contained in the pessimistic recursive core.In the terminology of Kóczy , this isN.Note that the elements of the core are always Pareto efficient: Pareto inefficient outcomes are dominated via a deviation of some partition of pairwise stability. A network is pairwise stable if (1) no unconnected pair benefits from linking up and (2) no player benefits from deleting an existing connection.In a seminal paper on network formation Jackson and Wolinsky  introducOur model differs in at least two aspects from pairwise stability. On the one hand, pairwise stability focuses on pairs, while we consider larger coalition, too. This would make our deviation concept more general and the set of stable configurations smaller. Pairwise stability, on the other hand, is a fundamentally noncooperative equilibrium concept as a slightly modified version is presented by Bloch and Jackson  makes itIn order to illustrate the differences, we present the following simple example with 4 nodes.connections game players benefit from being connected to each other. A connection may be direct or indirect, but indirect connections are less valuable. It is costly to be connected and the cost of the connection depends on the distance. We consider a game with four nodes, located at the corners of an elongated rectangle where connections are only possible on the sides. The short connections cost 8, long connections cost 16. The benefit of a direct connection is 4, an indirect one with a single stop is 3 and with two stops is 2  is not less than the benefits (4 for each of the connected nodes). If we would consider this to be a game of network formation, this would be the end of the story.ex ante payoff of 0.Suppose now that the two pairs of close nodes are connected and are considering to link up Fig a. Would status quo  with a player set N and a network function V. Time t is continuous, players can act at any time, but we assume that there is always an open time interval between two actions allowing players to intervene if necessary—this explicitly rules out two actions happening at the same time.Consider a game  events, represented by the sequence and the future.if i  at some time t, changing acceptance to rejection or vice versa, while the strategies can be quite different elsewhere.We rule out simultaneous deviations: For each deviation there exists Relevant subgame) The original game is relevant. Given a strategy s, a nontrivial subgame of a relevant subgame is relevant if it is played under i producing  if it does not depend on time but only on the current state summarised by A strategy How can a strategy be Markov and depend on history at the same time? History, while describes a series of events, is actually the current interpretation and strategies depend on this current interpretation.h by an arbitrary compatible alternative history h(s), with payoffs conditional on the current state s as given by Eq.  we haveFor a given network function form game  pointing to g to h instead. To be more precise: if there are such i that are not connected to h then the value of the network can be increased. We discuss 5 cases  of a triangle. Let f and g such non-connecting vertices of a triangle f and g have more secondary connections. While the direct connections h lose them, those in Select k be a leaf not connected to i, but to j. Since k is a leaf, j and k is moved to i and k. Since i is still a leaf we get Once we are done with the triangles, we have a node with many triangles attached to it, but for the rest, the graph is just like a tree. So let f, g are directly connected. Such connections are never needed to have each other as secondary connections as this works via the central player. Outer links are used to have the central player as a secondary connection. The added value of such a link is therefore f nor g is connected to other non-central players, the value is c these links are severed, for low values of c non-central players link up in pairs, and if n is even . At this point we are also very pragmatic and assume that it is only the number of contacts that matters.For a coalition Expression It is clear from looking at an individual’s payoff  to less its less formal versions. Our approach is motivated by New Zeeland’s social bubble approach that allows people to interact with a small group of family and friends while in lockdown. During the high alert phases of the epidemic the bubbles have been restricted to single households, but by mid April 2020, as the threat of infection diminished, citizens were allowed to expand their bubbles, “keep it exclusive, though and keep it small” (Prime Minister Jacinda Arden on 16 April)—very much in line with the core networks balancing the need to socialise with the infection risk.These examples have been chosen for their simplicity. There are also numerous other possible applications for this model. The balancing groups in electric power networks (Csercsik and Kóczy We may also think of road infrastructure planning where regions act as players (Wang and Zhang


This study assessed the level of satisfaction with the quality of nursing care among hospitalized older adults and the factors associated with it.This was a quantitative descriptive cross‐sectional survey.t test and one‐way ANOVA.We used a validated questionnaire to collect data from a convenience sample of 206 older adults from three government hospitals in Tamale, Ghana. Data were analysed using descriptive statistics, independent sample Most of the participants (72.3%) reported moderate levels of satisfaction with the quality of nursing care, while 23.8% reported high levels of satisfaction. The association between gender, religion and level of satisfaction with nursing care was not statistically significant. However, patients differed on levels of satisfaction based on healthcare facility: patients at the Tamale Central Hospital were more satisfied with the quality of nursing care than those at the Tamale Teaching Hospital. There is a need for capacity building and sensitization workshops on the rudiments of geriatric care for nurses in the metropolis to serve as an impetus for improvement in the quality of care. Patients who were unstable and those who were not in a position to give accurate responses were excluded from the study.3.4n is the sample size, N is the population size, and e is the margin of error. Given a total population of 421 patients with 0.05 margin of error, the sample size was calculated as follows:The sample size was determined using Yamane's formular Yamane, . This fo3.5We gathered data for the study using a structured questionnaire. The questionnaire comprised a demographic information section and the Patient Satisfaction with Nursing Care Quality Questionnaire (PSNCQQ), developed by Laschinger et al.  The PSNCA multi‐step forward‐backward translation of the questionnaire from the English language to Dagbani and back to the English language was undertaken by two professionals who are prolific speakers of both languages. The two professionals independently translated the original questionnaire from the English language to Dagbani. Following the initial translation, they met to discuss the translation process and produced a single copy of the translated questionnaire by consensus. A third professional who is a native speaker of Dagbani and also proficient with the English language was contacted to translate the Dagbani version of the questionnaire back to the English language.Content validity of the questionnaire was assessed with five experienced nurses using the Content Validity Index (CVI) .3.7t test to assess differences in the level of satisfaction with quality of nursing care between males and females. Lastly, we conducted a one‐way ANOVA to determine differences in the level of satisfaction with quality of nursing care based on religion, level of education and the admitting hospitals.We analysed the data using the Statistical Package for Social Sciences (SPSS) version 22 IBM, . We used3.8We obtained ethical clearance for the study. We also sought permission from the management of the participating hospitals before the data collection process began. Besides, we explained the purpose and potential benefits and risks for participating in the study to the participants in the English language or Dagbani  before the data collection. The participants were given a 24 hr period to consider their participation from the time they were approached to take part in the study. Participants who agreed to take part in the study were made to give their consent by signing the consent form. We also informed the participants that they could withdraw from the study at any time even after giving their consent and that refusal to participate in the study will not affect the quality of service they received from the hospitals.44.1Out of the total number of participants whom the questionnaires were administered to, 206 participants eventually completed the survey. The majority of the participants 128 (62.1%) were males, without formal education (54.9%), married 145 (70.4%) and belonging to the Islamic faith 160 (77.7%). Other characteristics of the participants are presented in Table 4.2A large majority of the participants 149 72.3%) reported moderate levels of satisfaction with the quality of nursing care received at the various hospitals. With satisfaction scores ranging from 22–110, the mean score was 74.126, with a standard deviation of 9.999. Participants’ levels of satisfaction with the quality of nursing care are presented in Table .3% reporWe also compared the level of participant satisfaction with the quality of nursing care across the three different hospitals. The findings are presented in Table 4.3t test was used. The test revealed that the difference in satisfaction scores between males and females was not statistically significant (t(197) = −0.918, p = .360). A one‐way ANOVA was also conducted to assess for differences in the level of satisfaction based on participants’ religion, level of education and admitting facility. The results showed that there were no statistically significant differences in the level of satisfaction of participants based on their religion  = 0.139, p = .870) and level of education  = 0.848, p = .535). However, the admitting facilities accounted for statistically significant differences in the level of satisfaction of participants  = 8.033, p = .001). A Tukey post hoc test revealed that the mean satisfaction score for participants admitted to the Tamale Central Hospital was statistically significantly higher  than those admitted to Tamale Teaching Hospital . The satisfaction scores for participants admitted to the Tamale West Hospital were not statistically different from the other facilities (p = .586). Further details of the one‐way ANOVA are presented in Table To determine factors influencing satisfaction with nursing care, we compared the level of satisfaction of participants using different demographic characteristics of the participants. To assess for differences in the level of satisfaction between males and females, the independent sample 5The findings of our study indicated that a greater percentage of the participants were moderately satisfied with the quality of nursing care at the various government hospitals in the Tamale metropolis. Only a smaller percentage of the participants reported high levels of satisfaction with the quality of nursing care. In tandem with our findings, previous studies have reported that the majority of hospitalized older adults are either dissatisfied or moderately satisfied with the quality of care rendered at hospitals (Ahmadabad et al., Regarding factors influencing satisfaction with the quality of nursing care, we found that gender, religion and educational attainment did not appear to influence participants’ level of satisfaction with nursing care. In conformity with our findings, several previous studies have reported no statistically significant difference in the levels of satisfaction with the quality of nursing care between older male and female patients (Kazerooni et al., However, we did find a statistically significant differences in participants’ level of satisfaction with the quality of nursing care based on the hospitals where they were admitted. This finding is incongruent with the findings of a similar study conducted in Makkah Al Mukramah, where there was no statistically significant difference in participants’ levels of satisfaction with quality nursing care among the three different hospitals involved in the study (El‐Nagger et al., 6Our findings revealed that the majority of older adults in the Tamale Metropolis are moderately satisfied with the quality of nursing care they receive at the various public hospitals in the metropolis with just a small proportion reporting high levels of satisfaction with nursing care. We also observed that hospitalized older adults at the Tamale Central Hospital are more satisfied with the quality of nursing care that those admitted at the Tamale Teaching Hospital. We conclude that besides the differences in the admitting facilities, other demographic characteristics such as gender and religion do not influence hospitalized older adults' levels of satisfaction with quality nursing care. There is a need for capacity building and sensitization workshops on the rudiments of geriatric care for nurses in the metropolis to enable them to improve on the quality of nursing care services for hospitalized older adults. The government of Ghana must introduce a specialist programme in geriatric nursing to equip nurses with the requisite knowledge and skill that will meet the multifaceted needs of hospitalized older adults.The authors declare no conflict of interest.The first author conceptualized the research topic and drafted the proposal for the project. He also wrote the discussion, conclusion and recommendations of the paper with support from the other authors. The second and fourth authors were responsible for the collection of the data for the project, while the third author assisted in the analysis of the data and writing of the report of the findings.