EDBT 2026 Demo / reviewers in the wild / expert
Seong Ki Yoo
dblp:172/4416
· DBLP profile ↗
16ranked-venue papers
9as first author
4since 2021 · last 2025
0000-0001-5126-5090ORCID · verified
Domains — the database's venue-derived domains; a paper can count in several
Computer networks · 10 · 6 first-author · 3 since 2021Applied, interdisciplinary, general and emerging computing · 1
Expertise — from the expertise taxonomy: the topics of the expert's papers under the CCF categories. A weight counts papers with recency: 1 for a paper about the topic, 0.3 when the topic is its context, halved every five years.
| Computer networks
3 papers |
Physical-layer communications · 68% Cellular and mobile networks · 25% Wireless networking · 7% |
Topics — the 13 heaviest of 13, each with the papers that count most for it
| Topic | Weight | Papers | Last | Evidence papers |
|---|---|---|---|---|
Physical-layer communications
fading channels |
0.9 | 2 | 2021 | The κ-μ / Inverse Gamma and η-μ / Inverse Gamma Composite Fading Models: Fundamental Statistics and Empirical Validation · IEEE Trans. Commun. 2021 Entropy and Energy Detection-Based Spectrum Sensing Over ℱ-Composite Fading Channels · IEEE Trans. Commun. 2019 |
Physical-layer communications
channel modeling |
0.5 | 1 | 2021 | The κ-μ / Inverse Gamma and η-μ / Inverse Gamma Composite Fading Models: Fundamental Statistics and Empirical Validation · IEEE Trans. Commun. 2021 |
Physical-layer communications › fading channels › fading models
composite fading model |
0.5 | 1 | 2021 | The κ-μ / Inverse Gamma and η-μ / Inverse Gamma Composite Fading Models: Fundamental Statistics and Empirical Validation · IEEE Trans. Commun. 2021 |
Physical-layer communications › channel modeling › fading channel modeling
fading channel statistics |
0.5 | 1 | 2021 | The κ-μ / Inverse Gamma and η-μ / Inverse Gamma Composite Fading Models: Fundamental Statistics and Empirical Validation · IEEE Trans. Commun. 2021 |
Cellular and mobile networks
5g |
0.4 | 1 | 2020 | Indoor Millimeter-Wave Systems: Design and Performance Evaluation · Proc. IEEE 2020 |
Cellular and mobile networks
beam management |
0.4 | 1 | 2020 | Indoor Millimeter-Wave Systems: Design and Performance Evaluation · Proc. IEEE 2020 |
Cellular and mobile networks
radio access networks |
0.4 | 1 | 2020 | Indoor Millimeter-Wave Systems: Design and Performance Evaluation · Proc. IEEE 2020 |
Physical-layer communications › signal detection › noncoherent detection
energy detection |
0.4 | 1 | 2019 | Entropy and Energy Detection-Based Spectrum Sensing Over ℱ-Composite Fading Channels · IEEE Trans. Commun. 2019 |
Physical-layer communications › fading channels › fading models
generalized fading channel |
0.4 | 1 | 2019 | Entropy and Energy Detection-Based Spectrum Sensing Over ℱ-Composite Fading Channels · IEEE Trans. Commun. 2019 |
Wireless networking › cognitive radio
spectrum sensing |
0.4 | 1 | 2019 | Entropy and Energy Detection-Based Spectrum Sensing Over ℱ-Composite Fading Channels · IEEE Trans. Commun. 2019 |
Physical-layer communications › radio propagation › indoor radio propagation
indoor channel modeling |
0.1 | 1 | 2020 | Indoor Millimeter-Wave Systems: Design and Performance Evaluation · Proc. IEEE 2020 |
Physical-layer communications › channel modeling › propagation channel modeling
millimeter-wave channel modeling |
0.1 | 1 | 2020 | Indoor Millimeter-Wave Systems: Design and Performance Evaluation · Proc. IEEE 2020 |
Physical-layer communications
diversity combining |
0.1 | 1 | 2019 | Entropy and Energy Detection-Based Spectrum Sensing Over ℱ-Composite Fading Channels · IEEE Trans. Commun. 2019 |
Methods — techniques the papers use, named apart from their topics
moment generating function · 0.5goodness-of-fit analysis · 0.5performance evaluation · 0.4deployment planning · 0.4channel modeling · 0.4entropy analysis · 0.4ROC analysis · 0.4
| Year | Publication | Venue | Position |
|---|---|---|---|
| 2025 | Reinforcement Learning Based Whittle Index Policy for Scheduling Wireless SensorsabstractWireless Sensor nodes used in remote monitoring applications typically transmit data in a timely manner, often optimising for the Age of Information (AoI). However, this approach focuses solely on keeping updates at the sink fresh without considering the actual value of each update. This method is inefficient for sensor networks, which have limited resources. Transmitting data indiscriminately without evaluating its significance not only increases energy consumption but also raises storage requirements. To address this challenge, we propose a reinforcement learning-based scheduling strategy that prioritises sensor transmissions based on the Age of Incorrect Information (AoII) using an edge mining technique. This ensures that the most valuable updates are received while reducing energy consumption. We frame the scheduling problem as a Restless Multi-Armed Bandit (RMAB) and introduce a Whittle Index-based Q-learning (WIQL) policy to dynamically select the most informative sensors. Additionally, we employ an edge mining technique, where raw sensor data is processed locally before transmission, enhancing state estimation at the sink. Experimental results demonstrate that WIQL achieves near-optimal performance while significantly reducing the number of transmitted packets by up to $70 \%$. This reinforcement learning-based approach provides a scalable and adaptive solution for efficient data scheduling in resource-constrained WSNs. Sokipriala Jonah, Seong Ki Yoo, Saurav Sthapit |
ISCC | 2 |
| 2023 | On the Secrecy Capacity of $\mathcal{F}$ Composite Fading Channels with Multiple EavesdroppersabstractThis contribution quantifies the achievable physical layer security of wireless transmission over realistic composite fading conditions in the presence of multiple eavesdroppers (Eves). To this end, exact closed-form analytic expressions are derived for the achievable secure outage probability (SOP) and the probability of strictly positive secrecy capacity (SPSC) for the case of$\mathcal{F}$composite fading channels. The derived expressions are tractable and their validity is justified through comparisons with respective computer simulation results. In addition, they allow for the development of useful theoretical and practical insights on the effect of the presence of numerous eavesdroppers under different multipath fading and shadowing conditions, as these are encountered in realistic wireless communication scenarios. Seong Ki Yoo, Simon L. Cotton, Lei Zhang 0089, Jaeseung Song, Imran Shafique Ansari, Paschalis C. Sofotasios |
ICC | 1 |
| 2023 | Measurements Based Physical Layer Security in Device to Device mm-Wave CommunicationsabstractIn this contribution we evaluate the transmission of confidential information over ${\mathcal{F}}$ composite fading channels in the presence of an eavesdropper (Eve) who also experiences ${\mathcal{F}}$ composite fading. Upon obtaining tractable closed-form expressions for the secure outage probability and the probability of strictly positive secrecy capacity, we analyze extensively the achievable physical layer security performance in the context of mm-wave communications. This is realized with the aid of extensive measurement results from realistic communication scenarios, which show the behavior of composite ${\mathcal{F}}$ fading channels in device-to-device communication scenarios. The offered results provide meaningful insights of theoretical and practical importance that are expected to be useful in the design of mm-wave based communication systems. Seong Ki Yoo, Paschalis C. Sofotasios, Simon L. Cotton, Lei Zhang 0089, Jaeseung Song, Imran Shafique Ansari, Young Jin Chun |
VTC2023-Spring | 1 |
| 2021 | The κ-μ / Inverse Gamma and η-μ / Inverse Gamma Composite Fading Models: Fundamental Statistics and Empirical ValidationabstractThe$\kappa $-$\mu $/ inverse gamma and$\eta $-$\mu $/ inverse gamma composite fading models are presented and extensively investigated in this paper. We derive closed-form expressions for the fundamental statistics of the$\kappa $-$\mu $/ inverse gamma composite fading model, such as the probability density function (PDF), cumulative distribution function (CDF). Additionally, we solve the associated integral that is commonly used to obtain the moment generating function (MGF) of statistical distributions to provide an MGF-type function which is valid for performance analysis over the specified parameter space. Analytic expressions for the PDF, higher order moments and AF are also derived for the$\eta $-$\mu $/ inverse gamma composite fading model, while infinite series expressions are obtained for the corresponding CDF and MGF-type function. The suitability of the new models for characterizing composite fading channels is demonstrated through a series of extensive field measurements for wearable, cellular, and vehicular communications. For all of the measurements, two propagation geometry problems with special relevance to the two new composite fading models, namely the line-of-sight (LOS) and non-LOS (NLOS) channel conditions, are considered. It is found that both the$\kappa $-$\mu $/ inverse gamma and$\eta $-$\mu $/ inverse gamma composite fading models provide an excellent fit to fading conditions encountered in the field. The goodness-of-fit of these two composite fading models is also evaluated and compared using the resistor-average distance. As a result, it is shown that the$\kappa $-$\mu $/ inverse gamma composite fading model provides a better fit compared to the$\eta $-$\mu $/ inverse gamma composite fading model when strong dominant signal components exist. On the contrary, the$\eta $-$\mu $/ inverse gamma composite fading model outperforms the$\kappa $-$\mu $/ inverse gamma composite fading model when there is no strong dominant signal component and/or the parameter$\eta $is not equal to unity, indicating that the scattered wave power of the in-phase and quadrature components of each cluster of multipath are not identical. Seong Ki Yoo, Nidhi Simmons, Simon L. Cotton, Paschalis C. Sofotasios, Michail Matthaiou, Mikko Valkama, George K. Karagiannidis |
IEEE Trans. Commun. | 1 |
| 2020 | Indoor Millimeter-Wave Systems: Design and Performance EvaluationabstractIndoor areas, such as offices and shopping malls, are a natural environment for initial millimeter-wave (mmWave) deployments. Although we already have the technology that enables us to realize indoor mmWave deployments, there are many remaining challenges associated with system-level design and planning for such. The objective of this article is to bring together multiple strands of research to provide a comprehensive and integrated framework for the design and performance evaluation of indoor mmWave systems. This article introduces the framework with a status update on mmWave technology, including ongoing fifth generation (5G) wireless standardization efforts and then moves on to experimentally validated channel models that inform performance evaluation and deployment planning. Together these yield insights on indoor mmWave deployment strategies and system configurations, from feasible deployment densities to beam management strategies and necessary capacity extensions. Jacek Kibilda, Allen B. MacKenzie, Mohammad Abdel-Rahman, Seong Ki Yoo, Lorenzo Galati-Giordano, Simon L. Cotton, Nicola Marchetti, Walid Saad 0001, William G. Scanlon, Adrian García-Rodríguez, David López-Pérez, Holger Claussen 0001, Luiz A. DaSilva |
Proc. IEEE | 4 |
| 2019 | Effective Rate over F Composite Fading ChannelsabstractThe F composite fading model was recently proposed as an accurate and tractable statistical model for the characterization of the composite fading conditions encountered in realistic wireless communication scenarios. In the present contribution we capitalize on the distinct properties of this composite model to evaluate the achievable effective rate over F composite fading channels. To this end, we derive an exact closed-form expression for the effective rate, which is subsequently used as a benchmark for the derivation of tight upper and lower bounds, as well as of an accurate approximation. The derived analytic expressions are provided in closed-form and benefit from being tractable both analytically and numerically. This enables the development of meaningful insights on the effect of fading conditions and/or latency on the overall system performance. Also, it allows the accurate quantification of the signal to noise ratio required in target quality of service requirements under different composite fading conditions. Paschalis C. Sofotasios, Seong Ki Yoo, Simon L. Cotton, Sami Muhaidat, Francisco Javier López-Martínez, Juan Manuel Romero-Jerez, George K. Karagiannidis |
WCNC | 2 |
| 2019 | The Double Shadowed κ-µ Fading ModelabstractIn this paper, we introduce a new fading model which is capable of characterizing both the shadowing of the dominant component and composite shadowing which may exist in wireless channels. More precisely, this new model assumes a κ-μ envelope where the dominant component is fluctuated by a Nakagami-m random variable (RV) which is preceded (or succeeded) by a secondary round of shadowing brought about by an inverse Nakagami-m RV. We conveniently refer to this as the double shadowed κ-μ fading model. In this context, novel closed-form and analytical expressions are developed for a range of channel related statistics, such as the probability density function, cumulative distribution function, and moments. All of the derived expressions have been validated through Monte-Carlo simulations and reduction to a number of well-known special cases. It is worth highlighting that the proposed fading model offers remarkable flexibility as it includes the κ-μ, η-μ, Rician shadowed, double shadowed Rician, κ-μ shadowed, κ-μ/inverse gamma and η-μ/inverse gamma distributions as special cases. Nidhi Simmons, Carlos Rafael Nogueira da Silva, Simon L. Cotton, Paschalis C. Sofotasios, Seong Ki Yoo, Michel Daoud Yacoub |
WiMob | 5 |
| 2019 | Entropy and Energy Detection-Based Spectrum Sensing Over ℱ-Composite Fading ChannelsabstractIn this paper, we investigate the performance of energy detection-based spectrum sensing over F composite fading channels. To this end, an analytical expression for the average detection probability is first derived. This expression is then extended to account for collaborative spectrum sensing, square-law selection diversity reception, and noise power uncertainty. The corresponding receiver operating characteristics (ROC) are analyzed for different conditions of the average signal-to-noise ratio (SNR), noise power uncertainty, time-bandwidth product, multipath fading, shadowing, number of diversity branches, and number of collaborating users. It is shown that the energy detection performance is sensitive to the severity of the multipath fading and the amount of shadowing, whereby even small variations in either of these physical phenomena can significantly impact the detection probability. As a figure of merit to evaluate the detection performance, the area under the ROC curve (AUC) is derived and evaluated for different multipath fading and shadowing conditions. Closed-form expressions for the differential entropy and cross entropy are also formulated and assessed for different average SNR, multipath fading, and shadowing conditions. Then, the relationship between the differential entropy of F composite fading channels and the corresponding ROC/AUC is examined where it is shown that the average number of bits required for encoding a signal becomes small (i.e., low differential entropy) when the detection probability is high or when the AUC is large. The difference between composite fading and traditional small-scale fading is emphasized by comparing the cross entropy for Rayleigh and Nakagami-m fading. A validation of the analytical results is provided through a careful comparison with the results of some simulations. Seong Ki Yoo, Paschalis C. Sofotasios, Simon L. Cotton, Sami Muhaidat, Osamah S. Badarneh, George K. Karagiannidis |
IEEE Trans. Commun. | 1 |
| 2018 | Energy Detection-Based Spectrum Sensing over Fisher-Snedecor F Fading ChannelsabstractThis paper investigates the performance of energy detection-based spectrum sensing over Fisher-Snedecor F fading channels. To this end, an analytical expression for the corre- sponding average detection probability is firstly derived and then this is extended to account for collaborative spectrum sensing. The complementary receiver operating characteristics (ROC) are analyzed for different conditions of the average signal-to- noise ratio (SNR), time-bandwidth product, multipath fading, shadowing and number of collaborating users. It is shown that the energy detection performance is strongly linked to the severity of the multipath fading and amount of shadowing, whereby even small variations in either of these physical phenomena significantly impact the detection probability. Also, the versatile modeling capability of the Fisher-Snedecor F distribution is verified in the context of energy detection based spectrum sensing as it provides considerably more accurate characterization than the conventional Rayleigh fading model. To confirm the validity of the analytical results presented in this paper, we compare them with the results of some simulations. Seong Ki Yoo, Simon L. Cotton, Paschalis C. Sofotasios, Sami Muhaidat, Osamah S. Badarneh, George K. Karagiannidis |
GLOBECOM | 1 |
| 2018 | Ergodic Capacity Analysis of Wireless Transmission over Generalized Multipath/Shadowing ChannelsabstractNovel composite fading models were recently proposed based on inverse gamma distributed shadowing conditions. These models were extensively shown to provide remarkable modeling of the simultaneous occurrence of multipath fading and shadowing phenomena in emerging wireless scenarios such as cellular, off-body and vehicle-to-vehicle communications. Furthermore, the algebraic representation of these models is rather tractable, which renders them convenient to handle both analytically and numerically. Based on this, the present contribution analyzes the ergodic capacity over the recently proposed $\kappa-\mu$ / inverse gamma composite fading channels, which were shown to characterize excellently multipath fading and shadowing in line-of-sight communication scenarios, including realistic vehicular communications. Novel analytic expressions are derived which are subsequently used in the analysis of the corresponding system performance. In this context, the offered results are compared with respective results from cases assuming conventional fading conditions, which leads to the development of numerous insights on the effect of the multipath fading and shadowing severity on the achieved capacity levels. It is expected that these results will be useful in the design of timely and demanding wireless technologies such as wearable, cellular and inter-vehicular communications. Paschalis C. Sofotasios, Seong Ki Yoo, Sami Muhaidat, Simon L. Cotton, Michail Matthaiou, Mikko Valkama, George K. Karagiannidis |
VTC Spring | 2 |
| 2018 | Error analysis of wireless transmission over generalized multipath/shadowing channelsabstractThe η-μ / inverse gamma and κ-μ / inverse gamma distributions were recently introduced as particularly flexible and tractable composite fading models that provide accurate characterization of multipath and shadowing effects, which are encountered simultaneously during wireless transmission in emerging communication scenarios such as off-body, cellular and vehicular-to-vehicular communications. The present contribution analyzes the symbol error rate performance of digital communications over these fading channels. To this end, we derive novel analytic expressions for the symbol error rate of multiple amplitude based modulated systems under these fading conditions, which are subsequently used in the analysis of the corresponding system performance. In this context, numerous insights are developed on the effect of different fading conditions on the corresponding error rate, which are expected to be useful in the design of timely and demanding wireless technologies such as wearable, cellular and vehicular communication systems. Paschalis C. Sofotasios, Seong Ki Yoo, Sami Muhaidat, Simon L. Cotton, Michail Matthaiou, Mikko Valkama, George K. Karagiannidis |
WCNC | 2 |
| 2017 | A Comprehensive Analysis of 5G Heterogeneous Cellular Systems Operating Over κ-μ Shadowed Fading ChannelsabstractEmerging cellular technologies such as those proposed for use in 5G communications will accommodate a wide range of usage scenarios with diverse link requirements. This will necessitate operation over a versatile set of wireless channels ranging from indoor to outdoor, from line-of-sight (LOS) to non-LOS, and from circularly symmetric scattering to environments which promote the clustering of scattered multipath waves. Unfortunately, many of the conventional fading models lack the flexibility to account for such disparate signal propagation mechanisms. To bridge the gap between theory and practical channels, we consider κ-μ shadowed fading, which contains as special cases the majority of the linear fading models proposed in the open literature. In particular, we propose an analytic framework to evaluate the average of an arbitrary function of the signal-to-noise-plus-interference ratio (SINR) over κ-μ shadowed fading channels by using an orthogonal expansion with tools from stochastic geometry. Using the proposed method, we evaluate the spectral efficiency, moments of the SINR, and outage probability of a K-tier heterogeneous cellular network with K classes of base stations (BSs), differing in terms of the transmit power, BS density, shadowing, and fading characteristics. Building upon these results, we provide important new insights into the network performance of these emerging wireless applications while considering a diverse range of fading conditions and link qualities. Young Jin Chun, Simon L. Cotton, Harpreet S. Dhillon, Francisco Javier López-Martínez, José F. Paris, Seong Ki Yoo |
IEEE Trans. Wirel. Commun. | 6 |
| 2017 | An Experimental Evaluation of Switched Combining Based Macro-Diversity for Wearable Communications Operating in an Outdoor EnvironmentabstractThis paper investigates the potential improvement in signal reliability for outdoor wearable communications channels operating at 868 MHz using switched combining based macro-diversity. In this paper, a number of different macrodiversity configurations consisting of two and four base stations were considered to help mitigate the impact of body shadowing upon a wearable node, which was located on the central chest region of an adult male. During the field measurements, five different walking movements were performed, and then analyzed to investigate the efficacy of using macro-diversity. It was found that all of the considered switched combining schemes, including switch-and-stay combining, switch-and-examine combining (SEC) and SEC with post-examining selection (SECps) provided a worthwhile signal improvement when an appropriate switching threshold was adopted. The maximum diversity gain obtained in this paper was found to be 19.5 dB when using fourbase station SECps. The diversity gain, the number of path examinations, and the number of path switches between base stations for the switched combiner output varied according to the determined switching threshold, highlighting the importance of the selection of an appropriate threshold level. Furthermore, the performance/complexity tradeoff is demonstrated. Finally, the fading behavior at the output of the switched diversity combiners was then characterized using the diversity specific equations developed under the assumption of independent and non-identically distributed Nakagami-m fading channels. Over all of the measurement scenarios considered in this paper, the theoretical models provided an adequate fit to the fading observed at the output of the virtual switched combiner. Seong Ki Yoo, Simon L. Cotton, William G. Scanlon, Gareth A. Conway |
IEEE Trans. Wirel. Commun. | 1 |
| 2016 | Shadowed Fading in Indoor Off-Body Communication Channels: A Statistical Characterization Using the κ - μ /Gamma Composite Fading ModelabstractThis paper investigates the characteristics of the shadowed fading observed in off-body communications channels at 5.8 GHz. This is realized with the aid of the κ-μ/gamma composite fading model, which assumes that the transmitted signal undergoes κ-μ fading, which is subject to multiplicative shadowing. Based on this, the total power of the multipath components, including both the dominant and scattered components, is subject to non-negligible variations that follow the gamma distribution. For this model, we present an integral form of the probability density function (PDF) as well as important analytic expressions for the PDF, cumulative distribution function, moments, and moment generating function. In the case of indoor off-body communications, the corresponding measurements were carried out in the context of four explicit individual scenarios, namely: line of sight (LOS), non-LOS walking, rotational, and random movements. The measurements were repeated within three different indoor environments and considered three different hypothetical body worn node locations. With the aid of these results, the parameters for the κ-μ/gamma composite fading model were estimated and analyzed extensively. Interestingly, for the majority of the indoor environments and movement scenarios, the parameter estimates suggested that dominant signal components existed even when the direct signal path was obscured by the test subject's body. In addition, it is shown that the κ-μ/gamma composite fading model provides an adequate fit to the fading effects involved in off-body communications channels. Using the Kullback-Leibler divergence, we have also compared our results with another recently proposed shadowed fading model, namely, the κ-μ/lognormal LOS shadowed fading model. It was found that the κ-μ/gamma composite fading model provided a better fit for the majority of the scenarios considered in this paper. Seong Ki Yoo, Simon L. Cotton, Paschalis C. Sofotasios, Steven Freear |
IEEE Trans. Wirel. Commun. | 1 |
| 2015 | The K - μ / inverse gamma fading modelabstractStatistical distributions have been extensively used in modeling fading effects in conventional and modern wireless communications. In the present work, we propose a novel κ - μ composite shadowed fading model, which is based on the valid assumption that the mean signal power follows the inverse gamma distribution instead of the lognormal or commonly used gamma distributions. This distribution has a simple relationship with the gamma distribution, but most importantly, its semi heavy-tailed characteristics constitute it suitable for applications relating to modeling of shadowed fading. Furthermore, the derived probability density function of the κ - μ / inverse gamma composite distribution admits a rather simple algebraic representation that renders it convenient to handle both analytically and numerically. The validity and utility of this fading model are demonstrated by means of modeling the fading effects encountered in body centric communications channels, which have been known to be susceptible to the shadowing effect. To this end, extensive comparisons are provided between theoretical and respective real-time measurement results. It is shown that these comparisons exhibit accurate fitting of the new model for various measurement set ups that correspond to realistic communication scenarios. Seong Ki Yoo, Simon L. Cotton, Paschalis C. Sofotasios, Michail Matthaiou, Mikko Valkama, George K. Karagiannidis |
PIMRC | 1 |
| 2015 | The η - μ / inverse gamma composite fading modelabstractIn this paper we propose a new composite fading model which assumes that the mean signal power of an η — μ signal envelope follows an inverse gamma distribution. The inverse gamma distribution has a simple relationship with the gamma distribution and can be used to model shadowed fading due to its semi heavy-tailed characteristics. To demonstrate the utility of the new η — μ / inverse gamma composite fading model, we investigate the characteristics of the shadowed fading behavior observed in body centric communications channels which are known to be susceptible to shadowing effects, particularly generated by the human body. It is shown that the η — μ / inverse gamma composite fading model provided an excellent fit to the measurement data. Moreover, using Kullback-Leibler divergence, the η — μ / inverse gamma composite fading model was found to provide a better fit to the measured data than the k — μ / inverse gamma composite fading model, for the communication scenarios considered here. Seong Ki Yoo, Paschalis C. Sofotasios, Simon L. Cotton, Michail Matthaiou, Mikko Valkama, George K. Karagiannidis |
PIMRC | 1 |