esa-sceva/satcom-chunk-collection huggingface dataset:
# Equsum Partitions of Sets of Positive Integers +
## 1 Introduction
Given a finite set of positive integers \(V\subset\mathbb{Z}^{+}\), of cardinality \(|V|:=v\), let  
\[\mathcal{B}:=\{B_{i}|1\leq i\leq b\}\]  
be a partition of \(V\) into \(b\) nonempty subsets, called _blocks_, with \(1\leq b\leq v\). Thus,  
\[V=\cup_{1\leq i\leq b}B_{i}\,\qquad B_{i}\cap B_{j}=\varnothing\iff i\
eq j.\]  
For brevity, call \(\mathcal{B}\) a \(b\)-_partition_ of \(V\), and call \(b\) the _order_ of the partition. The partition \(\mathcal{B}\) is _proper_ when \(2\leq b<v\), and _trivial_ when \(b=1\) or \(b=v\). We consider the case when \(V\) has sum \(\Sigma V:=\Sigma[x:x\in V]\) which is a multiple of \(b\), say \(\Sigma V:=\ bs,\ s\ \in\ \mathbb{Z}^{+}\). A \(b\)-partition \(\mathcal{B}\) of \(V\) is _equisum_, with _block sum_\(s\), if each of its blocks has sum \(s\):  
\[\Sigma B_{i}:=\Sigma\{x:x\in B_{i}\}=s,\ \ 1\leq i\leq b.\]  
When does \(V\) have a proper equsum partition? Clearly, \(v\geq 3\) and \(2\leq b\leq\lceil v/2\rceil\) are necessary conditions, and these conditions are sharp. In the following sections, constructive algorithms will be used to show:  
1. If \(b,n\in\mathbb{Z}^{+},\ 2\leq b\leq\lceil n/2\rceil\) and \(b\leq 12\) or \(b\) is any prime-power \(p^{a}\), the initial interval of integers \([1,\ n]\) has an equisum \(b\)-partition if and only if \(\Sigma[1,\ n]\) is a multiple of \(b\). 2. No product of two odd prime-powers has an equisum 2-partition of its positive divisors; however, for any prime \(p\geq 3\) and \(a,\ m\in\mathbb{Z}^{+}\) with \(m\) odd, the set of all positive divisors of \(2^{a}p^{m}\) has an equisum 2-partition when \(2^{a+1}\geq\sigma(p^{m})\). Even perfect numbers are the \"boundary case\" of this result. 3. If the set of aliquot divisors of \(n\in\mathbb{Z}^{+}\) has an equisum 2-partition then \(n\) has at least two distinct prime factors. For any prime \(p\geq 3\) and \(a,\ m\in\mathbb{Z}^{+}\) with \(m\) odd, the set of aliquot divisors of \(2^{a}p^{m}\) has an equisum 2-partition if \(2^{a+1}\geq\sigma(p^{m})\). Again, even perfect numbers are the \"boundary case\" of this result. 4. If \(n\in\mathbb{Z}^{+}\) is odd, its set of aliquot divisors can have an equisum 2-partition only when \(n\) is a perfect square. Further, if \(n\) has exactly two distinct prime factors \(p,\ q\), they must either be twin primes or 3 and 7. The aliquot divisors always have an equisum 2-partition when \(\{p,\ q\}=\{3,\ 5\}\); this probably also holds when \(\{p,\ q\}=\{3,\ 7\}\). However, there may be only finitely many pairs \(\{p,\ q\}\) such that the aliquot divisors of \(n\) have such a partition. Some suggestive results are also obtained for initial intervals of the primes. For \(b\in\{2,\ 3,\ 4,\ 5,\ 6\}\), it is shown that the smallest feasible initial interval of primes with sum equal to a multiple of \(b\) does have an equisum \(b\)-partition. For \(b=2\), every odd-sized initial interval of primes \(p\leq 127\) does have an equisum 2-partition, and it is conjectured that this holds for every odd-sized initial interval of primes.
# Simultaneous Quantitation of Isoprenoid Pyrophosphates in Plasma and Cancer Cells Using LC-MS/MS
## Materials and Methods
### Charcoal-Stripped Plasma Preparation  
Activated charcoal was used to remove endogenous isoprenoids in the human plasma prior to preparation of standards. Briefly, charcoal suspension (12 mL) was prepared by mixing dextran-coated charcoal (0.66 g) in 100 mL of Dulbecco's Phosphate buffered saline (DPBS). The sample was centrifuged for 15 min (4000 g at 4\({}^{\circ}\)C) and the supernatant discarded. Plasma (6.0 mL) was then added to the charcoal pellet at 37 \(\pm\) 1 \({}^{\circ}\)C for two hours with continuous stirring, centrifuged at 13,000\(\times\)\(g\) for 15 min, and the supernatant collected. The process was repeated twice for maximal removal of endogenous IsoP. This stripped plasma was used to construct plasma calibration curves.
## 5 Discussion
### Overdispersion Analysis  
Dim OSL signals at high doses and low normalisation ratios in quartz grains have sometimes been correlated with a limited proportion of luminescence-sensitive traps and/or a low contribution from the fast component of the OSL signal [37,38]. At prolonged doses over time, this limitation can result in a natural OSL signal (\(L_{N}\)) of similar intensity to the natural OSL signal of the test dose (\(T_{N}\)), albeit within the recommended ratio (\(1/3L_{N}=T_{N}\)) [11,12]. Considering that the dose induced in the test dose represents 10% of the \(D_{e}\)[11,12], these low-sensitive quartz grains would not accurately reflect the real differences between signal and dose, which would result in a generalised reduction in the normalisation ratios (\(L_{N}/T_{N}\)). As the growth curve is constructed by plotting the normalised signal vs. dose-response, low normalisation ratios at increasing doses lead to a low slope of the linear segment of the dose-response curve. Interpolation of this normalised signal with errors in such low-slope curves can lead to high uncertainty of the \(D_{e}\) of individual aliquots [39,40]. When this occurs in most accepted aliquots (individual \(D_{e}\)s), it results in high variability between individual data, above what could be expected [37,38]. As a result, high \(OD\) values of the CAM could be obtained. This is the main reason for rejecting aliquots that interpolate above 200 Gy, taking this value as the saturation threshold [11], at which the estimates of the \(D_{e}\)s become unreliable [41], although the \(D_{e}\)s estimated by including these aliquots (>200 Gy) are similar [11]. On the other hand, the number of rejected aliquots in the recovery and recycling tests is very low and lower than those of aliquots with abnormal behaviour (aberrant growth curves) [11]. These characteristics of the OSL signal are coupled with rapid bleaching of the signal (see Section 5.1.1). Considering all these aspects and the low sensitivity and fast decay of the OSL signal, we used the early background (EBG) signal-integration method [13]. The EBG maximises the contribution of the fast component of the OSL signal [42], providing suitable dose-response curves for signal interpolation in cases of low OSL sensitivity [11] and low normalisation ratios with high error (between 10 and 20%). This error is due to intrinsic factors, such as counting statistics, reproducibility and luminescence sensitivity [37; 43]. When interpolating normalised signals with high error in the dose-response curves, a high error in the obtained \(D_{e}s\) is expected (in our samples, ranging between 5 and 20%), and the error increases with dose, so it is expected to be higher in older samples [44]. However, recovery tests (with an \(OD<5\%\)) evidenced that the \(D_{e}\) uncertainty due to intrinsic factors does not contribute substantially to the increase in \(OD\)[11], which has high values (>23%), with the exception of sample Mero-7 (13%). Thus, the analysis of other possible extrinsic factors, such as incomplete bleaching or beta microdosimetry, is necessary to check the most suitable age model.
# Orbit Decomposition Method for Rotordynamic Coefficients Identification of Annular Seals
## 5 Results and Discussion
### Whirl Amplitude Analysis  
For the orbit decomposition method, the influence of whirl amplitude is investigated by changing the major semiaxis \(a\). Five values of major semiaxis \(a\) are studied, corresponding to 0.1 \(C_{r}\), 0.2 \(C_{r}\), 0.3 \(C_{r}\), 0.4 \(C_{r}\), and 0.5 \(C_{r}\). For each major semiaxis \(a\), the minor semiaxis \(b\) is set to be 50% of the major semiaxis \(a\). The whirl frequency is 150 Hz.  
Figure 15 shows the variations in rotordynamic coefficients with whirl amplitude. It can be found that the effect of whirl amplitude on the rotordynamic coefficients is very small and can be ignored when \(a<0.2\)\(C_{r}\). This is because the rotor whirl is a small motion in this amplitude range. The rotordynamic system is linear, and the orbit decomposition method is valid to identify the rotordynamic coefficients. The rotordynamic coefficients are sensitive to the variation in whirl amplitude when \(a>0.2\)\(C_{r}\). This is because the nonlinear effect becomes important in this amplitude range. The accuracy of the orbit decomposition method decreases with the increasing whirl amplitude. Similar findings can be obtained at other frequencies.
# Usefulness of the Magnetodynamic Mallet in Tooth Extraction: A Case Series
###### Abstract  
Tooth extraction techniques have been refined over the years in order to be less traumatic and to better preserve alveolar bone. A recently introduced extraction method involves the use of the Magnetic Mallet(r), which allows clinicians to be more precise and perform extractions faster. Moreover, the instrument enables the procedure to be less traumatic for patients. The aim of the present study was to clinically evaluate whether extractions performed using the Magnetic Mallet(r) can lead to less buccolingual bone resorption. **Methods:** Between February 2023 and June 2023, nine patients with an average age of 62 years underwent 29 extractions using the Magnetic Mallet(r). Sectorial CBCTs were performed in order to measure buccolingual bone thickness at time 0 (T0, before extraction) and 3 months after extraction (T3M). All the extractions were performed by two different expert operators exclusively using the Magnetic Mallet(r). For statistical analysis, a two-sample \(t\)-test was performed to determine the difference between the measurements taken at T0 and those taken at T3M in the 29 dental elements and the difference in bone loss between the surgeries conducted by the two clinicians. **Results:** A total of 22 teeth were extracted in the upper jaw and 7 in the lower jaw. The average degree of mobility was 1. The average degree of force impressed by the instrument to extract the teeth was 2, while the average frequency of blows administered was 7. The average time taken for the extractions was 3\(\div\) min. After 3 months, the mean buccolingual bone resorption was 1.54 mm (SD: \(\pm\)). The difference in buccolingual bone thickness between T0 and T3 was significant at an alpha significance level of 0.01. No difference in bone resorption was found between the surgeries conducted by the two clinicians. **Conclusions:** The use of the Magnetic Mallet(r) results in bone loss in the buccolingual direction comparable with existing data in the literature on healing the post-extraction socket. This tool seems to be predictable in producing the same results between different operators.  
tooth extractions; magnetodynamic surgery; socket preservation; oral surgery; bone resorption A Case Series  
[PERSON]  
1 Division of Implant Prosthodomics, Department of Surgical Sciences (DISC), University of Genova,  
Largo R. Benzi 10, 16132 Genoa, Italy; [EMAIL_ADDRESS] (D.B.); [EMAIL_ADDRESS] (L.D.G.); [EMAIL_ADDRESS] (M.M.)  
2
# 3D Behavior Recognition Based on Multi-Modal Deep Space-Time Learning
## 4 Experimental Results
### Experimental Results on UTKinet-Action3D Dataset  
Firstly, we only apply 3D spatial-temporal convolutional neural networks to the depth map sequence. Unfortunately, the frame number of the videos in this dataset varies widely. For example, the seventh action \"push\" only contains 6 frames, while the fifth action \"handling\" contains about 100 frames. Therefore, after the normalization of the frame number to the same number, say 38, there will be a certain amount of information loss for the sequences with large number of frames. If only the 3D space-time convolutional neural network is applied to the depth map sequence or depth motion map, the classification accuracies are only 75.00% and 68.89% respectively. The classification accuracy of our proposed fusion based approach can achieve 97.29%. Although 3D skeleton manifold representation can get a satisfactory result, our method still makes some improvements over it, which shows the effectiveness of our fusion method.  
\begin{table}
\begin{tabular}{c c} \hline \hline
**Methods** & **Average Classification Accuracy** \\ \hline Ref. [6] & 82.22\% \\ Ref. [41] & 88.73\% \\ Ref. [45] & 93.09\% \\ Ref. [36] & 91.70\% \\ Ref. [46] & 90.53\% \\ Ref. [47] & 93.63\% \\ Our proposed method & **94.15\%** \\ \hline \hline \end{tabular}
\end{table}
Table 3: Comparisons of the average classification accuracy on MSR-Action3D dataset.  
Figure 6: Confusion matrix of our proposed method in UTD-MHAD dataset.  
The confusion matrix of our proposed method is shown in Figure 7. Our method can successfully identify most of the actions. The action \"throw\" has a relatively low recognition accuracy since the action is similar to other actions, and the motion information is not extracted completely.  
We compare the average classification accuracy of our method against other state-of-the-art methods. The comparison results are shown in Table 4. Our proposed method again achieves the highest classification accuracy.
## 2 Fundamentals
### Solution Space Management  
In product development, the solution space can be defined as the sum of all theoretically conceivable solution possibilities for a task [17]. Furthermore, the solution space can be described based on a set of degrees of freedom and their properties [18]. If the exemplary degree of freedom is the material choice for a part, then the associated properties could be alloy, steel, or magnesium. The set of properties of the degrees of freedom describes an alternative solution in the solution space [18]. Degrees of freedom differentiate between fixed and variable degrees of freedom. Fixed degrees of freedom are considered unchangeable, while variable degrees of freedom allow properties to vary within a certain range. For example, the inventory level can vary from 100 to 300 storage places [18]. To control the solution space, solution space management is necessary.  
[PERSON] [19] developed a process model for solution space management consisting of three steps. First, solution space structuring aims at defining sub-solution spaces for each sub-problem of the main solution space [18]. In product development, the solution space is constructed based on the functions of a product. Second, solution space planning involves developing a strategy for narrowing down the solution space [18]. Third, solution space control is used to iteratively control and steer the systematic reduction of the degrees of freedom by comparing the actual state with the target state [18].  
Solution space management originates from product development, but the concept has already been transferred to other domains, such as factory planning [20]. In the context of strategic network design and the planning approach shown in Figure 1, the solution space for a scenario encompasses all possible alternative network solutions. This means that fixed degrees of freedom are design parameters that are defined within a strategic structural scenario (e.g., plant locations), and variable degrees of freedom are design parameters influenced by operational decisions (e.g., inventory levels) concerning all possible combinations of design parameters.
# Novel Materials for Heavy Metal Removal in Capacitive Deionization
## 3 Materials for Heavy Metal Removing Using CDI
### Pure Carbon Materials
Based on the electroadsorption theory, the Helmholtz electrical double layer model is widely understood [98]. The initial CDI models for EDL structure models are the Helmholtz EDL model and the Gouy-Chapman-Stern (GCS) EDL model. An advanced equilibrium EDL structure model named the modified Donnan (mD) model can account for the macropores' confined nature in CDI electrodes [99]. In the mD model, micropores are seen to have a strongly overlapped double layer, so the classical Donnan notion of a uniform pore electrostatic potential can be used. In-depth research has found that a high ion adsorption capacity is closely related to the micropores rather than the mesopores [100; 101]. Thus, porous carbon is an attractive material for the electrochemical adsorption of HMs. In these micropores, typically, the Debye length \(\lambda\)D is of the order of, or larger than, the pore size. In micropores, when the R of the pores is smaller than the Debye length, an overlap of the electrical double layer is found. Hence, the electrical potential makes a distinct jump from a value on the surface outside the particles to another value in the micropores [80; 102]. Then, the concentration of counterions is significantly higher than that on the outside surface. Thus, the micropores (<2 nm) are highly effective in achieving high ion adsorption.
# Survey of Dense Video Captioning: Techniques, Resources, and Future Perspectives
## 3 Techniques for Dense Video Captioning
### Discussion-Encoder-Decoder Based APPROACH  
Encoder-decoder-based approaches for video captioning have significantly evolved, transitioning from simple CNN-RNN models to complex Transformer-based and modular frameworks. Attention mechanisms have been crucial for improving visual-textual alignment. Despite progress, challenges persist in generating diverse and accurate captions, capturing long-range dependencies, and incorporating external knowledge. Video captioning, vital for applications like video retrieval and human-computer interaction, has garnered attention.
## 2 Study Area and Data
### Conditioning Factors
#### 2.2.2 Hydrogeological Factors  
Hydrogeological factors, such as surface and groundwater level, movement and strength of the water in the region, and hydro-chemical and physical properties of groundwater, have a significant impact on the formation and development of sinkholes. Within the scope of this study, 14 factors related to groundwater level change and geochemical properties of groundwater, namely bicarbonate (DBC), carbonate (DCR), dissolved CO\({}_{2}\) (DDC), dissolved O\({}_{2}\) (DDO), conductivity (DCT), calcium (DCA), chloride (DCH), magnesium (DMG), pH (DPH), potassium (DPT), sodium (DSD), sulfate (DSU), and total ion exchange (DTI) were used. The formation and development of sinkholes related to the dissolution of rocks, surface or groundwater movement, and other geo-environmental conditions [52]. Monitoring the groundwater level and its chemical components are essential parameters for determining potential sinkhole areas, as it contains information about the dissolution rate of rocks and the location of aquifer compression areas [44]. Regarding hydrogeological factors that are mentioned above, geochemical analysis was carried out on water samples from both the wet and dry spells from 519 water wells distributed homogeneously in the study area; also, groundwater levels were measured in both spells. Surfaces for each parameter for both spells were created with the IDW interpolation method and the difference between the dry and wet spell was determined by subtracting the surfaces from each other. The hydrogeological maps obtained as a result of these processes are given in Figure 3.  
Figure 2: Geological and tectonic factors (**a**) LTG; (**b**) PTF.  
Figure 3: Hydrogeological factors: (**a**) GWL; (**b**) GWD; (**c**) DPT; (**d**) DSD; (**e**) DSU; (**f**) DMG; (**g**) DCA; (**h**) DCH; (**i**) DBC; (**j**) DTI; (**k**); DDC; (**l**) DDO; (**m**) DCT; (**n**) DPH.
# Finite Element Modeling of the Soil-Nailing Process in Nailed-Soil Slopes
## 6 Performance Comparison of FE and Laboratory Models of Nailed-Soil Slopes
### Vertical Settlement of the Foundation  
Figure 22 shows foundation vertical settlements (S/H, %) at different soil densities for both laboratory and FE models, (laboratory model results are drawn in solid lines, while the dotted lines represent the FE model results) [33]. It can be seen from the figure that the maximum footing settlement occurred at an overburden pressure of 30 kN/m\({}^{2}\). It can be observed from the graph that the FE models overestimate the footing settlements. The variation in observed and computed settlement ranges from 4.4% to 18.7 in the case of loose dense sand, whereas it ranges from 13.4% to 40.6% and from 0.4% to 35.0% in the cases of medium and dense sand, respectively.
# High-Throughput Line Buffer Microarchitecture for Arbitrary Sized Streaming Image Processing
## 4 Logic Implementation of D-SWIM
### Logic of Line Buffer  
Figure 9 shows the hardware composition of the Line Buffer (LB) and the related control signals from the Controller module. Each LB is composed of \(N_{bram}\) BRAMs and the associated control logic. According to the LB access pattern described in Section 3.3, the BRAM addressing pattern is sequential. Thus, we employed an AddrCounter module to each BRAM to manage the write address. The AddrCounter accepts the AddrInc and AddrRst signals from the Controller that determines whether to increase the address register by one or reset it to zero, respectively. The other signals related to the block store process, including WrMask, WrData, and WrEn, were generated by the Controller and directly connected to the BRAM primitives. Note that we annotate the width of each signal bus in the brace following the signal name in Figure 9.  
According to the line-rolling buffer access behavior, the read addresses of multiple LBs were synchronized to the write address of the LB which stores the input block. In the logic design, the WrAddr from AddrCounters were sent to a MUX, and the MUX selected the proper value as the RdAddr signal of all LBs under the control of the AddrSel signal.  
Figure 8: D-SWIM workflow with dynamic programming for arbitrary sized image processing.
# Optimal Siting and Sizing of FACTS in Distribution Networks Using the Black Widow Algorithm
###### Abstract  
The problem regarding the optimal placement and sizing of different FACTS (flexible alternating current transmission systems) in electrical distribution networks is addressed in this research by applying a master-slave optimization approach. The FACTS analyzed correspond to the unified power flow controller (UPFC), the thyristor-controlled shunt compensator (TCSC, also known as the _thyristor switched capacitor_, or TSC), and the static var compensator (SVC). The master stage is entrusted with defining the location and size of each FACTS device using hybrid discrete-continuous codification through the application of the black widow optimization (BWO) approach. The slave stage corresponds to the successive approximations power flow method based on the admittance grid formulation, which allows determining the expected costs of the energy losses for a one-year operation period. The numerical results in the IEEE 33-, 69-, and 85-bus grids demonstrate that the best FACTS device for locating in distribution networks is the SVC, given that, when compared to the UPFC and the TCSC, it allows for the best possible reduction in the equivalent annual investment and operating cost. A comparative analysis with the General Algebraic Modeling System software, with the aim to solve the exact mixed-integer nonlinear programming model, demonstrated the proposed BWO approach's effectiveness in determining the best location and size for the FACTS in radial distribution networks. Reductions of about 12.63% and 13.97% concerning the benchmark cases confirmed that the SVC is the best option for reactive power compensation in distribution grids.  
black widow optimizer (BWO); flexible alternating current transmission systems (FACTS); medium-voltage distribution networks; static var compensator (SVC); thyristor-controlled shunt compensator (TCSC); unified power flow controller (UPFC)