esa-sceva/satcom-chunk-collection huggingface dataset:
# Determination of Nonlinear Creep Parameters for Hereditary Materials
## 5 Application of Proposed Algorithm and Methods  
### Material Nylon 6  
The works [5; 20] contain test results of material Nylon 6 at stresses 5, 10, and 15 MPa. The duration of the experiment was 100 h for all stresses. Values of creep strain for material Nylon 6 at specified stresses, obtained by processing of experimental results, are represented in Table 1.  
It has been also determined from the data of mentioned works that the instantaneous deformation curve of material Nylon 6 has been satisfactorily approximated by power function:  
\[\varepsilon_{0}^{m}\ =\ \left(\frac{\sigma}{19.0371}\right)^{1.3334} \tag{24}\]  
Approximation of creep strain values at minimum stress (\(\sigma\) = 5 MPa) using [PERSON]'s fractional exponential kernel gave the following values of creep parameters: \(\alpha\) = 0.85, \(\varepsilon_{0}\) = 0.1682, \(\beta\) = 0.18, and \(\lambda\) = 1.6682.  
Then the creep curve of material Nylon 6 at stress \(\sigma\) = 5 MPa will be described by equation  
\[\varepsilon_{m}(t)\ =\ \ 0.1682\ \left[1+1.6682\sum_{n\ =\ 0}^{\infty}\ \frac{(-0.18)^{n}t^{0.15(1+n)}}{\Gamma[0.15(1+n)+1]}\right]. \tag{25}\]  
From Equation (24) at \(\sigma\) = 5 MPa we find that \(\varepsilon_{0}^{m}\) = 0.1682%. Considering this fact, we determine the model rheological parameter:  
\[k_{m}(t)\ =\ \frac{\varepsilon_{m}(t)}{\varepsilon_{0}^{m}}\ =\ 1+1.6682\ \sum_{n\ =\ 0}^{\infty}\ \frac{(-0.18)^{n}t^{0.15(1+n)}}{\Gamma[0.15(1+n)+1]}. \tag{26}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \multirow{2}{*}{**Time \(t\), h**} & \multicolumn{2}{c}{**Strain \(\varepsilon_{E}\) (t), \%, at Stress \(\sigma\), MPa**} \\ \cline{2-4}  & **5** & **10** & **15** \\ \hline
0 & 0.1537 & 0.3873 & 0.6650 \\
1 & 0.4200 & 1.0585 & 1.8174 \\
20 & 0.5321 & 1.3408 & 2.3022 \\
40 & 0.5621 & 1.4164 & 2.4319 \\
60 & 0.5804 & 1.4624 & 2.5110 \\
80 & 0.5937 & 1.4961 & 2.5689 \\
100 & 0.6043 & 1.5229 & 2.6148 \\ \hline \end{tabular}
\end{table}
Table 1: Creep strain values of material Nylon 6.  
Now, one can calculate the value of creep strain at stresses 10 and 15 MPa under the formula (21). For these stresses, the values of instantaneous strain, obtained under formula (24), are equal to 0.4238% and 0.7277%, respectively.  
Experimental and calculated values of creep strain for material Nylon 6 at all three stresses are shown in Figure 4. As it is seen, convergence of calculated strains to experimental ones is good.
## 4 Problem Formulation  
The S-IoT uplink resource allocation algorithm needs to employ limited channel and power resources to guarantee IoT services' diverse QoS requirements and promote system performance on the following objectives. Terminal power efficiency needs to be optimizedto prolong the terminals' lifetime. Conversely, the algorithm intuitively needs to maximize the probability of successful data transmission from IoT terminals.  
The energy efficiency of terminal \(u_{k}\) is defined as:  
\[\mathrm{EE}_{k}^{t}=\frac{C_{k}^{t}}{p_{k,S}^{t}} \tag{8}\]  
where \(C_{k}^{t}\) represents the transmission capacity of terminal \(u_{k}\) in the \(t\)th time stick, which may fluctuate according to channel quality and co-channel interference of other recently allocated terminals \(p_{k}\) denotes the transmit power of terminal \(u_{k}\).  
For transmission success index, \(A_{k}^{t}\) indicates whether the data transmission request of \(u_{k}\) succeeds, which depends on whether the \(SINR\) exceeds the threshold.  
\[A_{k}^{t}=\left\{\begin{array}{ll}0,&if\quad SINR_{k}^{t}<\delta_{th}\\ 1,&if\quad SINR_{k}^{t}\geq\delta_{th}\end{array}\right. \tag{9}\]  
The optimization problem of the QoS-guaranteed uplink power and spectrum allocation for S-IoT terminals is formulated in Equation (10).  
\[\begin{array}{l}opt.\mathcal{P}_{1}=\max\sum\limits_{t=0}^{T-1}\sum\limits_{ k=1}^{K}A_{k}^{t}\\ \mathcal{P}_{2}=\max\sum\limits_{t=0}^{T-1}\sum\limits_{k=1}^{K}EE_{k}^{t}\\ s.t
# Investigation of Debonding Effect in Internal Replacement Pipe System Under Lateral Loading
## 3 Surface Preparation and Its Impact on Debonding  
This section examines the influence of adhesive strength on the performance of the IRP system. Different levels of adhesive strength achieved through various preparation techniques on the inner surface of the host pipe before bonding the IRP are investigated. The benchmark shear strength of the adhesive is 20 MPa (2.9 ksi) when the host pipe is freshly cleaned without any specific preparation [25]. In the case of unclean surfaces, the adhesive strength is reduced to 5 MPa (0.7 ksi), while ablated surfaces result in an increased adhesive strength of 40 MPa (5.8 ksi) [25].
# Exploring the Health Information Management System of Kuwait: Lessons and Opportunities
## 3 Results
### Policies and Procedures of the Medical Records Management Department  
Table 3 shows responses to questions on the policies and procedures of the medical records management system and the frequency of updating them. Moreover, we also asked the respondents whether their employees are aware of such policies and procedures, and what methods are used to keep the employees updated. Through the survey, we also inquired about how the employees become aware of their roles and responsibilities, and whether they are provided a copy of their roles and responsibilities. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{6}{c}{**Hospital Type**} \\ \cline{3-7}  & \multicolumn{1}{c}{**Government**} & \multicolumn{1}{c}{**Government**} & \multicolumn{1}{c}{**Government**} & \multicolumn{1}{c}{**Private**} & \multicolumn{1}{c}{**Oil Sector**} & \multicolumn{1}{c}{**Total**} \\ \multicolumn{1}{c}{**Records Management System**} & \multicolumn{1}{c}{**General**} & \multicolumn{1}{c}{**Tertiary**} & \multicolumn{1}{c}{**Hospitals**} & \multicolumn{1}{c}{**Hospital**} & \multicolumn{1}{c}{**Hospital**} & \multicolumn{1}{c}{**Total**} \\ \cline{3-7}  & \multicolumn{1}{c}{**n (\%)**} & \multicolumn{1}{c}{**n (\%)**} & \multicolumn{1}{c}{**n (\%)**} & \multicolumn{1}{c}{**n (\%)**} & \multicolumn{1}{c}{**n (\%)**} & \multicolumn{1}{c}{**n (\%)**} & \multicolumn{1}{c}{**n (\%)**} \\ \hline \multirow{3}{*}{Patient Records media} & Paper only & 0 (0.0) & 11 (57.9) & 2 (50.0) & 0 (0.0) & 13 (43.3) \\  & Paper \& Electronic & 6 (100.0) & 8 (42.1) & 2 (50.0) & 0 (0.0) & 16 (53.3) \\  & Paper, Electronic, \& DIMS & 0 (0.0) & 0 (0.0) & 0 (0.0) & 1 (100.0) & 1 (3.3) \\ \hline \multirow{3}{*}{Type of Records System Used} & Manual Record System & 0 (0.0) & 5 (26.3) & 1 (25.0) & 0 (0.0) & 6 (20.0) \\  & HIS & 0 (0.0) & 2 (10.5) & 0 (0.0) & 1 (100.0) & 3 (10.0) \\  & Hybrid (manual \& HIS) & 6 (100.0) & 12 (63.2) & 3 (75) & 0 (0.0) & 21 (70.0) \\ \hline \multirow{3}{*}{Filing System} & Serial & 0 (0.0) & 4 (21.1) & 2 (50.0) & 0 (0.0) & 6 (20.0) \\  & Terminal Digit & 6 (100.0) & 15 (78.9) & 2 (50.0) & 0 (0.0) & 23 (76.7) \\  & Other & 0 (0.0) & 0 (0.0) & 0 (0.0) & 1 (100.0) & 1 (3.3) \\ \hline \multirow{3}{*}{Patient records are kept in (multiple choice)} & Filing Room & 6 (100) & 16 (84.2) & 4 (100) & 0 (0.0) & 26 (86.7) \\  & Words & 0 (0.0) & 1 (5.3) & 0 (0.0) & 0 (0.0) & 1 (3.3) \\ \cline{1-1}  & Filing Room \& Words & 0 (0.0) & 3 (15.8) & 0 (0.0) & 0 (0.0) & 3 (10.0) \\ \cline{1-1}  & With patients & 1 (16.7) & 1 (5.3) & 0 (0.0) & 0 (0.0) & 2 (6.7) \\ \cline{1-1}  & Emergency room & 0 (0.0) & 1 (5.3) & 0 (0.0) & 0 (0.0) & 1 (3.3) \\ \cline{1-1}  & Other & 1 (16.7) & 1 (5.3) & 0 (0.0) & 1 (100.0) & 3 (10.0) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics of the Medical Records Management System in Kuwait.
## 2 Materials and Methods
### Data
#### 2.2.2 Wave Conditions  
Wave data were obtained from a datawell directional wave buoy located about 32 km NW of the study area, off the coast of Leixoes harbour (41\({}^{\circ}\)19.00\({}^{\prime}\) N, 008\({}^{\circ}\)59.00\({}^{\prime}\) W), at 83 m water depth (processed data supplied by the Portuguese Hydrographical Institute--IH; [[https://www.hidrografico.pt](https://www.hidrografico.pt)]([https://www.hidrografico.pt](https://www.hidrografico.pt)) (accessed on 15 March 2022)). Average significant heights (Hs) and wave peak directions for 3 h intervals were used (Figure 2). Wave roses were produced to show the wave direction distribution depending on the wave height (Figures 3-5), using 16 cardinal directions and frequencies for 3 significant-wave-height classes: above 4.5 m, between 3 m and 4.5 m, and above 4.5 m. These classes were based on the 85 th and 95 th percentiles of the mean significant wave heights (Hs) recorded during the study period, which were 3.1 m and 4.4 m, respectively. Three-hourly wave data were available for 89.5% of the total study period, with data missing for January 2010, January 2016, May and June 2018, and February 2019 due to equipment failure (mostly during winter) or maintenance (in spring/summer). Notice, that failures due to the damage or breakdown of the equipment during storm events meant that some data of extreme conditions, which are relevant for sediment transport, were missed.  
Figure 3: Distribution of 3-hourly wave directions for three significant-wave-height classes (**left plots**) and of hourly wind directions for three velocity classes (**right plots**) for the last decade and the two 5-year periods.  
Figure 2: Significant wave heights (Hs) measured at the Leixöes wave buoy and estimated wind velocities for the study area during the study period; survey dates are marked with red vertical lines.
## 2 Dynamic Model of Belt-Driven Electromechanical Spindle System
### Model of Belt Transmission  
Figure 4 shows a typical belt transmission system. To consider the effect of belt transverse vibration on the rotating motion of the belly, the belt was modelled as a translating string. This implies that, assuming a quasi-static stretch belt tension \(P_{1}\), \(P_{2}\) can be calculated by adopting both static and dynamic contributions as follows:  
\[\left\{\begin{array}{l}{{P_{1}}={P_{0}}+EA\left({u_{1,x_{1}}+\frac{1}{2}\int _{0}^{l}{w_{1,x_{1}}^{2}}{\rm{d}}x_{1}}\right)}\\ {{P_{2}}={P_{0}}+EA\left({u_{2,x_{2}}+\frac{1}{2}\int_{0}^{l}{w_{2,x_{2}}^{2}}{ \rm{d}}x_{2}}\right)}\end{array}\right. \tag{11}\]  
In Equation (11), the static axial tension \(P_{0}\) is assumed to remain constant for the translating belt. The second term is for the dynamic component due to belt transverse motions, and the comma preceding \(x\) or \(t\) refers to the partial differentiation from \(x\) or \(t\) with respect to the previous one. \(x_{1}\) and \(x_{2}\) represent the neutral-axis coordinates. \(t\) denotes the time. Transverse displacements \(w_{1}(x_{1},t)\) and \(w_{2}(x_{2},t)\) refer to the above and below belt spans, respectively, and longitudinal displacements \(u_{1}(x_{1},t)\) and \(u_{2}(x_{2},t)\) refer to the above and below belt spans, respectively. With the boundary conditions of the system,  
\[\begin{array}{l}{u_{1}}(0,t)={r_{1}}{\theta_{r}},{u_{1}}(l,t)={r_{2}}{\theta _{2}}\\ {u_{2}}(0,t)={r_{2}}{\theta_{s}},{u_{2}}(l,t)={r_{1}}{\theta_{r}}\\ {w_{1}}(0,t)=0,{w_{1}}(l,t)=0\\ {w_{2}}(0,t)=0,{w_{2}}(l,t)=0\\ {w_{1,\ x_{1}}}{\left(0,t\right)={w_{1,\ x_{1}}}{\left(1,t\right)}=1/{r_{1}}} \\ {w_{2,\ x_{2}}}{\left(0,t\right)={w_{2,\ x_{2}}}{\left(2,t\right)}=1/{r_{2}}} \end{array} \tag{12}\]  
Substituting Equation (11) into Equation (10) leads to the following equation:  
\[\left\{\begin{array}{l}{{P_{1}}={P_{0}}+{k_{b}}({r_{1}}{\theta_{r}}-{r_{2}}{ \theta_{s}})+\frac{1}{2}{k_{b}}\int_{0}^{l}{w_{1,x_{1}}^{2}}{\rm{d}}x_{1}}\\ {{P_{2}}={P_{0}}+{k_{b}}({r_{2}}{\theta_{s}}-{r_{1}}{\theta_{r}})+\frac{1}{2}{ k_{b}}\int_{0}^{l}{w_{2,x_{2}}^{2}}{\rm{d}}x_{2}}\end{array}\right. \tag{13}\]  
Figure 4: Two-pulley belt drive mechanical model.  
The viscoelastic belt dynamic equation is derived using [PERSON]'s second law:  
\[\left\{\begin{array}{l}\rho Aw_{1,t}+2\rho Aww_{1,x_{1}t}+\rho Av^{2}w_{1,x_{1}x _{1}}+c_{5}Aw_{1,t}-P_{1}w_{1,x_{1}x_{1}}=0\\ \rho Aw_{2,t}+2\rho Avw_{2,x_{2}t}+\rho Av^{2}w_{2,x_{2}x_{2}}+c_{5}Aw_{2,t}-P_ {2}w_{2,x_{2}x_{2}}=0\end{array}\right., \tag{14}\]  
where \(\rho\) is the belt density. For the transverse vibration of the translating belt, \(c_{5}\) is the viscous damping coefficient. The motion equation defines a nonlinear piecewise mixed discrete-continuous gyro system. Numerical solutions are considered in this study because it is impossible to solve Equation (14) analytically, especially when it includes various dynamic effects such as load oscillations and eccentricities.
## 4 Discussion
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline  & & _E. faecalis_ & _S. aureus_ & _S. epidermidis_ & _E. coli_ & _P. aeruginosa_ \\ \hline
**Mushroom Species** & **Extract** & **Rf Values** & **Rf Values** & **Rf Values** & **RF Values** & **Rf Values** \\ \hline  & EIOAc & 0.01, 0.03, 0.04, 0.08, & 0–0.05, 0.08, & 0.04, 0.05, 0.06, & & \\  & EIOAc & 0.15, 0.21, 0.30, 0.37, & 0.21–0.26, 0.30, & 0.41, 0.53, & 0.03, 0.44, & 0.45, 0.55, 0.63, \\  & 0.41, 0.53, 0.56, 0.62, & 0.48, 0.58, 0.64, & 0.58, 0.63, & 0.64, 0.74 & 0.71–0.74 \\ _Fomitopsis_ & & 0.66, 0.71, 0.82, 0.89 & 0.73, 0.75–0.79 & 0.73–0.76, 0.83 & & \\ _pinicola_ & & 0.31, 0.34, 0.38, 0.41, & 0.28–0.35, & 0.28, 0.33, 0.40, & 0.24, 0.27, 0.33, & 0.03, 0.08, 0.33–0.38, \\  & MeOH & 0.50, 0.56, 0.60, & 0.38, 0.45, & 0.53, 0.56, 0.70, & 0.39, 0.48, & 0.40–0.45, 0.46–0.49, \\  & 0.75, 0.81 & 0.60–0.73, 0.76 & 0.71–0.76, 0.80 & 0.57, 0.62 & 0.51, 0.54–0.58, 0.59, \\ \hline  & EIOAc & 0.19, 0.29, 0.58, & 0.28, 0.54, & & \\ _Ganoderma_ & & 0.82–0.86 & 0.76–0.81 & 0.75 & 0.72 & / \\ _applanatum_ & MeOH & 0–0.05 & 0.75–0.81, & 0 & 0.06, 0.23 & / \\  & & 0.85–0.90 & & & \\ \hline _Meripilus gigantus_ & EIOAc & 0.03, 0.08, 0.19, 0.45, & 0, 0.05, 0.55, 0.81 & 0.63, 0.74 & 0.03, 0.74 & / \\  & MeOH & / & / & 0 & 0 & / \\ \hline  & EIOAc & 0.03, 0.08, 0.18, 0.28, & & & \\ _Polyporus_ & EIOAc & 0.43–0.45, 0.60, 0.68, & 0.05, 0.68, 0.81 & 0.18, 0.25, & 0.03, 0.43, \\  & & 0.79–0.83 & & 0.43, 0.81 & 0.71–0.81 & / \\  & MeOH & 0.75, 0.78 & 0 & 0.11, 0.59 & / & / \\ \hline  & & 0.16, 0.43, & & & \\ _Tranetes versicolor_ & EIOAc & 0.28, 0.79–0.84 & 0.60–0.69, & 0.18, 0.21, & 0.31, 0.73–0.79 & / \\  & MeOH & / & 0.75–0.84 & 0.66, 0.81 & & \\ \hline  & & 0.18 & 0.24 & / & / \\ \end{tabular}
\end{table} 
Table 6: Antibacterial activity induced by Polyporales mushrooms against wild-type bacteria expressed as Rf values of inhibition bands.
## 3 Distributed Jamming System Model for LEO Constellation Downlink
### Jamming Evaluation Metrics
#### 3.1.4 Jamming Coverage Rate  
In practical distributed jamming optimization, the jamming coverage rate is typically measured using the ratio or multiplicity of coverage from the beams formed by jammersafter collaborative networking, targeting specific users in a given area. Therefore, in a specific jamming task, the jamming coverage rate can be expressed as follows:  
\[\eta=\frac{num(Users_{cover})}{num(Users)} \tag{9}\]  
where \(num(Users_{cover})\) is the total number of targets covered by all the jammers, and \(num(Users)\) is the total number of targets.
# Antenna Arrays for Line-of-Sight Massive MIMO: Half Wavelength Is Not Enough
## 4 Multi User Channel Matrix
With reference to the two extreme cases of \(d=\lambda/2\) and \(d=2\lambda\), let us now analyze the distribution of the singular values for \(K=50\). In Figures 8 and 9, we have the image map of the distribution of the singular values, as well as the plot of their average values. The larger spacing improves in particular the lower singular values, leading to a much more stable inversion. Figure 8: Singular values analysis for \(d=\lambda/2\) and \(K=50\). (**Left**) Image map of the distribution of each one of the 50 singular values; (**Right**) solid line, average singular values; dashed lines, average singular values \(\pm\) the standard deviation of the distribution. Figure 7: Distribution of the condition number as a function of the distance \(d\) for \(K=50\). Each column of the matrix in the image map is a histogram of the condition number. It has to be underlined that the results achieved in this paragraph hold also when we do not consider the normalization. Since we would just see a slightly larger spreading of the singular values for all of the considered cases, we do not report these results because of the limited space of the paper.
# Optical Boundaries for LED-Based Indoor Positioning System
###### Abstract  
Overlap of footprints of light emitting diodes (LEDs) increases the positioning accuracy of wearable LED indoor positioning systems (IPS) but such an approach assumes that the footprint boundaries are defined. In this work, we develop a mathematical model for defining the footprint boundaries of an LED in terms of a threshold angle instead of the conventional half or full angle. To show the effect of the threshold angle, we compare how overlaps and receiver tilts affect the performance of an LED-based IPS when the optical boundary is defined at the threshold angle and at the full angle. Using experimental measurements, simulations, and theoretical analysis, the effect of the defined threshold angle is estimated. The results show that the positional time when using the newly defined threshold angle is 12 times shorter than the time when the full angle is used. When the effect of tilt is considered, the threshold angle time is 22 times shorter than the full angle positioning time. Regarding accuracy, it is shown in this work that a positioning error as low as 230 mm can be obtained. Consequently, while the IPS gives a very low positioning error, a defined threshold angle reduces delays in an overlap-based LED IPS.  
Keywords:light emitting diodes; indoor localization; optical wireless communications; optical boundary; packet delivery ratio; infrared protocols; overlap +
Footnote †: journal:
# Target Localization Based on Bistatic T/R Pair Selection in GNSS-Based Multistatic Radar System
## 2 Target Localization Scheme with Multistatic Radar
### Positioning Performance Analysis  
When estimating the accuracy of target positioning value, it is obvious that the positioning performance is relevant to three factors, the multistatic geometry of the system, the positioning algorithm processing, as well as the BR measurement errors. In the multistatic radar system, when there is no positioning error, the intersection of ellipsoids corresponding to multiple BRs is a point where target is located. However, positioning errors commonly exist in the practical cases, with the intersection of multiple ellipsoids extended from a point to an area, and the target position could be any point in the area, as shown in Figure 2. Obviously, the larger the overlap area, the larger the positioning error.  
In the multistatic radar system, in order to achieve multistatic network information selection and optimize multistatic positioning, bistatic T/R pairs with good positioning performance can be selected according to certain criteria. For this purpose, this paper proposes two algorithms for the selection of external illuminators.
# Attack Classification Schema for Smart City WSNs
###### Abstract  
Urban areas around the world are populating their streets with wireless sensor networks (WSNs) in order to feed incipient smart city IT systems with metropolitan data. In the future smart cities, WSN technology will have a massive presence in the streets, and the operation of municipal services will be based to a great extent on data gathered with this technology. However, from an information security point of view, WSNs can have failures and can be the target of many different types of attacks. Therefore, this raises concerns about the reliability of this technology in a smart city context. Traditionally, security measures in WSNs have been proposed to protect specific protocols in an environment with total control of a single network. This approach is not valid for smart cities, as multiple external providers deploy a plethora of WSNs with different security requirements. Hence, a new security perspective needs to be adopted to protect WSNs in smart cities. Considering security issues related to the deployment of WSNs as a main data source in smart cities, in this article, we propose an intrusion detection framework and an attack classification schema to assist smart city administrators to delimit the most plausible attacks and to point out the components and providers affected by incidents. We demonstrate the use of the classification schema providing a proof of concept based on a simulated selective forwarding attack affecting a parking and a sound WSN.  
Keywords:anomaly detection; information security; intrusion detection; security information and event management; smart cities; wireless sensor networks +
Footnote †: journal: Sensors
# Entropy-Regularized Federated Optimization for Non-IID Data
## 7 Conclusions  
We introduce entropy-regularized federated optimization (ERFO), a lightweight client-side modification that augments each local objective with a single-scalar Shannon entropy penalty on the per-parameter update distribution, requiring no extra communication and integrating seamlessly into standard SGD. Our theoretical analysis shows that ERFO matches FedAvg's \(O(1/T)\) (linear under strong convexity) convergence rates--incurring only an \(O(\lambda)\) bias for fixed \(\lambda\) and converging exactly when \(\lambda_{t}\to 0\)--while driving the expected gradient norm to zero in non-convex settings (Appendix B). Empirically, across two disparate benchmarks, ERFO consistently improves overall accuracy (+1.6 pp on UNSW-NB15) and macro-F1 (up to +0.008) with smoother convergence and matches or exceeds FedAvg,FedProx, and SCAFFOLD on PneumoniaMNIST (90.3% accuracy and 0.878 macro-F1 over 50 runs), demonstrating robustness to \(\lambda\) in the \(5\times 10^{-4}\)-\(10^{-3}\) range. ERFO's gradient-only, model-agnostic design promises broad applicability to regression, reinforcement-learning, and other modalities; future work will explore adaptive \(\lambda\) schedules, hybrid personalization, and deeper theoretical analyses to further elucidate its empirical strengths.  
All code supporting the reported results is publicly available at [[https://github.com/koffka-lab/entropy-regularized-federated-optimization](https://github.com/koffka-lab/entropy-regularized-federated-optimization)]([https://github.com/koffka-lab/entropy-regularized-federated-optimization](https://github.com/koffka-lab/entropy-regularized-federated-optimization)) accessed on 14 July 2025.  
This research received no external funding.  
The UNSW-NB15 dataset can be obtained from the Australian Centre for Cyber Security ([[https://www.unsw.adfa.edu.au/unsw-canberra-cyber/cybersecurity/ADFA-NB15-Datasets/](https://www.unsw.adfa.edu.au/unsw-canberra-cyber/cybersecurity/ADFA-NB15-Datasets/)]([https://www.unsw.adfa.edu.au/unsw-canberra-cyber/cybersecurity/ADFA-NB15-Datasets/](https://www.unsw.adfa.edu.au/unsw-canberra-cyber/cybersecurity/ADFA-NB15-Datasets/)), accessed on 14 July 2025.); PneumoniaMNIST is part of MedMNIST v2 ([[https://medmnist.com/](https://medmnist.com/)]([https://medmnist.com/](https://medmnist.com/)) accessed on 14 July 2025). No new datasets were generated during the current study.  
The authors declare no conflicts of interest.