esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 Parallelisation of DEM
### DEM Algorithm
#### 2.1.1 Calculate Contact Forces  
A contact pair list between connected particles (also particle-wall) is updated prior to the essential calculation of the contact forces, which will be detailed in the following section. Assume Particle \(i\) is in contact with Particle \(j\) with a distance \(d_{ij}\). The overlap between the two particles will be (Figure 1)  
\[U_{ij}=(R_{i}+R_{j}-d_{ij})/2 \tag{1}\]  
The normal direction from Particle \(i\) to \(j\) is:  
\[n_{ij}=(X_{j}-X_{i})/d_{ij} \tag{2}\]  
The normal force imposed on Particle \(i\) from Particle \(j\) is:  
\[F_{ij}^{\rm n}=-K^{\rm n}U_{ij}n_{ij} \tag{3}\]  
where \(K^{\rm n}\) is the normal stiffness at contact. Calculation of the shear force is more complicated. The relative velocity of Particle \(j\) to Particle \(i\) is:  
\[\Delta V_{ij}=\left(V_{j}-\omega_{j}\times n_{ij}\right)-\left(V_{i}+\omega_{ i}\times n_{ij}\right) \tag{4}\]  
Then the shear component of the relative velocity can be derived as:  
\[\Delta V_{ij}^{\rm s}=\Delta V_{ij}-\left(\Delta V_{ij}\cdot n_{ij}\right)n_{ij} \tag{5}\]  
The corresponding shear force occurring over an incremental step of \(\Delta t\) is:  
\[\Delta F_{ij}^{\rm s}=K^{\rm s}\Delta V_{ij}^{\rm s}\Delta t \tag{6}\]  
Figure 1: Overlap between particles.  
where \(K^{\text{s}}\) is the shear stiffness at contact. The new shear contact force is calculated by summing the old shear force \(F^{\text{s}}_{ij,\text{old}}\) at the start of the timestep by considering the transition of the contact plane [53; 54].  
\[F^{\text{s}}_{ij}=\left\{F^{\text{s}}_{ij}\right\}_{\text{rot,2}}+\Delta F^{ \text{s}}_{ij} \tag{7}\]  
\[\left\{F^{\text{s}}_{ij}\right\}_{\text{rot,1}}=F^{\text{s}}_{ij,\text{old}}- F^{\text{s}}_{ij,\text{old}}\times n^{\text{old}}_{ij}\times n_{ij} \tag{8}\]  
\[\left\{F^{\text{s}}_{ij}\right\}_{\text{rot,2}}=\left\{F^{\text{s}}_{ij} \right\}_{\text{rot,1}}-\left\{F^{\text{s}}_{ij}\right\}_{\text{rot,1}}\times \left[\frac{1}{2}(\omega_{i}+\omega_{j})\cdot n_{ij}\right]n_{ij}\Delta t \tag{9}\]  
where \(n^{\text{old}}_{ij}\) is the old normal direction from Particle \(i\) to Particle \(j\) at the previous incremental step. The widely used slip model is adopted to allow for mutual slip between particles by limiting the shear force values. The frictional force is adjusted by:  
\[F^{\text{s}}_{ij}=F^{\text{s}}_{ij}\frac{\text{min}\left(\mu\left|F^{\text{n} }_{ij}\right|,\left|F^{\text{s}}_{ij}\right|\right)}{\left|F^{\text{s}}_{ij} \right|} \tag{10}\]  
Then the total force at Particle \(i\) from Particle \(j\) is:  
\[F_{ij}=F^{\text{n}}_{ij}+F^{\text{s}}_{ij} \tag{11}\]  
and the moment is:  
\[M_{ij}=n_{ij}\times F^{\text{s}}_{ij} \tag{12}\]
# Boundary SPH for Robust Particle-Mesh Interaction in Three Dimensions
###### Abstract  
This paper introduces an algorithm to tackle the boundary condition (BC) problem, which has long persisted in the numerical and computational treatment of smoothed particle hydrodynamics (SPH). Central to the BC problem is a need for an effective method to reconcile a numerical representation of particles with 2D or 3D geometry. We describe and evaluate an algorithmic solution--boundary SPH (BSPH)--drawn from a novel twist on the mesh-based boundary method, allowing SPH particles to interact (directly and implicitly) with either convex or concave 3D meshes. The method draws inspiration from existing works in graphics, particularly discrete signed distance fields, to determine whether particles are intersecting or submerged with mesh triangles. We evaluate the efficacy of BSPH through application to several simulation environments of varying mesh complexity, showing practical real-time implementation in _Unity3D_ and its high-level shader language (HLSL), which we test in the parallelization of particle operations. To examine robustness, we portray slip and no-slip conditions in simulation, and we separately evaluate convex and concave meshes. To demonstrate empirical utility, we show pressure gradients as measured in simulated still water tank implementations of hydrodynamics. Our results identify that BSPH, despite producing irregular pressure values among particles close to the boundary manifolds of the meshes, successfully prevents particles from intersecting or submerging into the boundary manifold. Average FPS calculations for each simulation scenario show that the mesh boundary method can still be used effectively with simple simulation scenarios. We additionally point the reader to future works that could investigate the effect of simulation parameters and scene complexity on simulation performance, resolve abnormal pressure values along the mesh boundary, and test the method's robustness on a wider variety of simulation environments.  
computational fluid dynamics; smoothed particle hydrodynamics; boundary condition; mesh; signed distance fields; Voronoi regions; simulation Article
# CUDA and OpenMp Implementation of Boolean Matrix Product with Applications in Visual SLAM
## 3 Review of the Transformation  
In what follows, we introduce a set of transformations defined by [1], on the Euclidean distance matrix \(A\), that improves the hierarchical structure of dissimilarity space. These transformations are in the form of powers of Euclidean distance matrices over a lattice structure.  
Let \(\mathbb{M}(\mathbb{L})\) be a set of square matrices over a distributive lattice \(L\), then for any \(A_{1},A_{2},A_{3}\in\mathbb{M}(\mathbb{L})\).  
\(A_{1}*A_{2}\) is defined as:  
\[\bigvee_{l=1}^{n}(a_{il}\wedge b_{lj})\quad for\ 1\leq i,j\leq n \tag{2}\]  
The \(\bigvee\) and \(\bigwedge\) operators are defined as follows:  
\[\bigvee_{l=1}^{n}(X_{1},X_{2},\ldots,X_{n})=min\{X_{1},X_{2},\ldots,X_{n}\} \tag{3}\]  
\[\bigwedge_{l=1}^{n}(X_{1},X_{2},\ldots,X_{n})=max\{X_{1},X_{2},\ldots,X_{n}\} \tag{4}\]  
Let the identity element be:  
\[I_{n}=(\delta_{ij})\begin{cases}1&\text{i = j}\\ 0&\text{i \
eq j}\end{cases} \tag{5}\]  
Then from the definition of \(\bigvee\) and \(\bigwedge\) :  
\[\begin{cases}A_{1}*(A_{2}*A_{3})=(A_{1}*A_{2})*A_{3}\\ A_{1}*I=I*A_{n}\\ A^{i+1}{=}A^{i}*A\end{cases} \tag{6}\]  
**Remark 1**.: _For all \(A\in\mathbb{M}(\mathbb{L})\), the sequence \(A^{1},A^{2},\dots,A^{n},\dots\) is ultimately periodic, because it contains a finite number of distinct matrices. This sequence forms a cyclic group in terms of multiplication [1]._  
The relation \(\leq\) between any two matrices \(A^{1}\), \(A^{2}\) from set \(\{A^{1},A^{2},...,A^{n}\}\) is defined as follows:  
\[A^{1},A^{2}\iff[A]_{ij}\geq[A^{2}]_{ij}\quad\forall i,j\in[1\dots n] \tag{7}\]  
**Theorem 1**.: _Let \(A\in M_{n}\), with the property \(A\leq A^{2}\), then \(A\) converges to \(A^{k(A)}\) with \(k(A)\leq n\)._  
For proof, see Theorem 5.1 in [1].
## 4 Taxonomy of Cooperation in UASNs
### Reputation-Based Cooperation
#### 4.1.1 Direct Reputation (First-Hand)  
A direct reputation (first-hand) is a system in which a particular node observes the behavior of other nodes, and based on the observed reputation, the node calculates the reputation value of other nodes and store it in the reputation table. The node punishes the nodes with low reputation value (below the threshold) that are detected by isolating them from the network and not using them for information exchange based on a particular reputation system [52]. In [53,54], authors allow a particular node (ender) to select the relay node that has high reputation as the next-hop in order to route the packet to the target node to achieve maximum cooperation and reliability. In OCEN [53] they do not accept (second-hand) indirect reputation observation forms of information, but rather they use a direct observation to achieve a secure cooperation. In [55] authors introduced the idea of expanding the node behavior observation scope to more than one hop.
## 1 Introduction
The use of an intrinsic model that takes into account the mechanical properties of the surrounding rock is necessary. Currently, the mechanical parameters of the rock mass are determined by inverse analysis based on monitoring information from the project site [24]. The inversion analysis is mainly based on displacement data, whereas the whole deformation of the surrounding rock in mountain tunnels is difficult to obtain. Since the deformation of tunnel excavation is affected by a variety of factors, the accuracy of the numerical calculations is strongly dependent on the parameter values of the intrinsic model and the time-consuming calculations. Artificial intelligence models based on computer arithmetic and algorithmic models have been widely used to solve problems such as deformation prediction in tunnel construction due to their flexibility and accessibility. Artificial neural networks (ANNs) can solve the problem of approximating nonlinear arbitrary functions [25; 26]. ANNs are used for deformation prediction during tunnel excavation [27; 28]. Hyperparameters in intelligent prediction models are an important factor in determining the accuracy of the model. To improve the model prediction accuracy, optimization algorithms are used for hyper-parameter optimization, such as particle swarm optimization [29], Fruit Fly Optimization Algorithm [30], Grey Wolf Optimizer [31], Whale Optimization Algorithm [32], etc. However, there are many factors affecting the deformation of the surrounding rock in underground caverns, such as geological conditions, excavation sequence, and tectonic ground stress. These factors exhibit complex characteristics of nonlinearity, spatial variability, and uncertainty. It is important to consider parameter characteristics and physical mechanisms comprehensively in AI prediction models. With these factors in mind, there is a need to propose a model that takes into account the characteristics and physical meaning of the data to provide better deformation predictions. According to the statistical analysis of on-site construction data, the structural deformation influencing factors of large-section tunnel construction by drill and blast method are classified and coded with the excavation footage for processing. In this paper, a model for predicting structural deformation based on feature extraction of multi-source data is proposed. The efficiency and accuracy of the proposed model are verified by the tunnel construction and monitoring data from the Capital Ring Expressway. Multiple algorithms are compared to verify the superiority of the proposed method in prediction accuracy. The influence of input parameters on the performance of the prediction models is analyzed. It provides a model to predict tunnel structure deformation.
# Research Status and Progress of All-Position Narrow-Gap GMAW for Pipelines
## 1 Introduction  
Oil and gas pipelines bear the responsibility of transporting oil and gas resources, serving as a bridge that connects supply and demand. Accelerating the construction of oil and gas pipelines is critical support for the high-quality development of the industry but also an effective aid to steady economic growth. Due to the constraints of on-site construction conditions, all-position welding methods are predominantly used in pipeline construction at present [1, 2], involving manual or semi-automatic welding, which has relatively low efficiency. Compared with the traditional welding methods, narrow-gap welding reduces the level cross-sectional area, transforming the previously required large-angle, multi-layer, multi-pass welding process into multi-layer, single-pass welding process. This not only reduces the material consumption and improves the welding efficiency but also decreases heat input and thermal deformation, making it suitable for all-position welding. As a result, this method has been widely used in the on-site construction of long-distance oil and gas pipelines.  
All-position narrow-gap gas metal arc welding (GMAW) is prone to the following defects during the construction process: (1) Due to the small bevel angle, the arc does not sufficiently heat the side wall, which is prone to side wall unfused defects; (2) In non-flat welding positions, the influence of gravity can cause the middle of the weld seam to bulge,making it difficult for the arc to heat the concave areas where the groove side walls meet the previous weld pass during subsequent layer welding. This can easily generating porosity and interlayer lack of fusion defects.  
In response to the aforementioned issues, summarizing the droplet transition behavior, arc morphology, and molten pool behavior under different positions in narrow-gap GMAW, analyzing strategies such as optimizing welding process parameters and improving welding methods, as well as the future technological development trends, holds significant guiding implications for the technical development of all-position welding in pipelines.
## 4 Platform Development  
This section of the manuscript is dedicated to the discussion of the software and hardware tools that were used to develop the proposed application and discuss the development workflow. The AR scenes were created using the CAD files of the equipment. Next, in order to develop the interfaces required for the application, the MS(r) Visual Studio Community 2017 (Version 15.9.43, Microsoft, Redmond, WA, United States) IDE (Integrated Development Environment) has been utilized. As regards the development of the AR module and its functionalities, the Unity 3 DTM (version 2018.4.36f1, Unity Technologies, San Francisco, CA, USA) game engine was used in conjunction with the Vuforia plugin. For enabling the build/publishing of the mobile application in Android-based devices, JDK (Java Development Kit) was also implemented in Unity 3 DTM (Java version 1.8.0_333-b02, Open JDK 1.8.0_152, Oracle Corporation, Austin, TX, USA). Regarding the development of the scripts, C# was used for the scripts related to the operation of the mobile application. As regards the communication of the clients (i.e., mobile application instances) with the server (i.e., Cloud platform), PHP (Hypertext Preprocessor) was utilized. Essentially, PHP is used in order to interface the mobile application with the Cloud platform. Although the proposed application is aimed at mobile devices, it can be implemented on other types of hardware (for example, HMDs) as long as they host a camera and a display. The proposed framework also requires a Cloud Database, supporting the File Transfer Protocol (FTP) and SQL (Structured Query Language) databases. For the development of the Cloud platform, phpMyAdmin (version 5.2.0) was used, which is a PHP-based free software tool providing functionalities for handling the administration of MySQL and MariaDB. In addition, the MySQL (version 8.0, Oracle Corporation, Austin, TX, USA) open-source database management system was also implemented. In order to host the Cloud platform, the MS(r) Azure was implemented. It is stressed that MS(r) Azure according to the official site is defined as a \"_cloud computing service for application management_\" [65]. In terms of hardware, an Android-based tablet PC and a Smart phone were used to implement the proposed system, which is connected to the databases and hosts the user interface. For the development and the management of the mobile application and the Cloud platform, a desktop PC was used, equipped with an Intel Core i7--8750 CPU, 16 GB RAM, and NVIDIA GeForce GTX 1060 GPU (8 GB dedicated RAM). Finally, a network connection, either local or global, is required for communication between the two parties. A collection of the AR user interfaces of the developed application is presented in Figure 4.
# Sesame Plant Disease Classification Using Deep Convolution Neural Networks
## 4 Model Evaluation and Discussion
### Performance of Proposed Model Trained with Augmented Images
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline
**Epoch** & **Iteration** & **Time Elapsed** & \begin{tabular}{l} **Mini-Batch** \\ **Accuracy** \\ \end{tabular} & \begin{tabular}{l} **Validation** \\ **Accuracy** \\ \end{tabular} & \
\begin{tabular}{l} **Mini-Batch** \\ **Loss** \\ \end{tabular} &
\begin{tabular}{l} **Validation** \\ **Loss** \\ \end{tabular} \\ \hline \(1\) & \(1\) & 0:00:28 & 38.00\% & 56.67\% & 1.9619 & 1.1099 \\ \hline \(4\) & 30 & 0:02:53 & 86.00\% & 86.67\% & 0.3858 & 0.3753 \\ \hline \(7\) & 50 & 0:04:10 & 74.00\% & 84.44\% & 0.7992 & 0.433 \\ \hline \(8\) & 60 & 0:04:52 & 90.00\% & 86.67\% & 0.4536 & 0.3306 \\ \hline \(12\) & 90 & 0:06:51 & 92.00\% & 86.67\% & 0.138 & 0.3306 \\ \hline \(13\) & 100 & 0:07:29 & 74.00\% & 84.44\% & 1.0104 & 0.3789 \\ \hline \(15\) & 120 & 0:08:47 & 90.00\% & 91.11\% & 0.2837 & 0.2539 \\ \hline \(19\) & 150 & 0:10:47 & 74.00\% & 86.67\% & 0.1437 & 0.2942 \\ \hline \(23\) & 180 & 0:12:39 & 92.00\% & 88.89\% & 0.2929 & 0.229 \\ \hline \(25\) & 200 & 0:14:40 & 92.00\% & 90.00\% & 0.2897 & 0.2327 \\ \hline \(27\) & 210 & 0:16:43 & 94.00\% & 90.00\% & 0.145 & 0.2327 \\ \hline \(30\) & 240 & 0:16:43 & 96.00\% & 94.44\% & 0.1825 & 0.1961 \\ \hline \(32\) & 250 & 0:18:13 & 92.00\% & 94.44\% & 0.1825 & 0.1961 \\ \hline \(34\) & 270 & 0:18:49 & 92.00\% & 93.33\% & 0.1449 & 0.2185 \\ \hline \(38\) & 300 & 0:21:13 & 98.00\% & 92.22\% & 0.0466 & 0.209 \\ \hline \(40\) & 320 & 0:23:13 & 98.00\% & 92.22\% & 0.0466 & 0.209 \\ \hline \multicolumn{7}{l}{Test accuracy 0.9667} \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Testing accuracy of augmented images.
# Measurement-Device-Independent Two-Party Cryptography with Error Estimation
## 2 Preliminaries
### Entropy Qualities  
Here, we present some crucial entropy qualities for our security proof. Bulleted lists look like this:  
**Definition 1** (Shannon entropy).: \(P(X)\) _is the probability distribution function of a random variable \(X\). The entropy \(H(X)\) is defined as:_  
\[\mathrm{H}(X)=-\sum_{X}\mathrm{P}(x)\mathrm{log}_{2}\mathrm{P}(x).\]  
As same as Ref. [2; 19], we define guessing probability:  
\[\mathrm{P}_{\mathrm{guess}}(X|\mathrm{E})=\max_{M_{x}}\sum_{X}\mathrm{P}_{X} (x)\mathrm{Tr}(M_{x}\rho_{E}^{x}),\]where \(\mathrm{p}_{\mathrm{guess}}(\mathrm{X}|\mathrm{E})\) is the probability of guessing \(X\) when given register \(E\), and its maximization is over all positive operate-valued measurements (POVMs) \(|M_{x}|\) acting on register \(E\). Then we can easily get that the conditional min-entropy of \(X\) given \(E\) is:  
\[\mathrm{H}_{\mathrm{min}}(\mathrm{X}|\mathrm{E})=-\mathrm{log}_{2}\mathrm{P} _{\mathrm{guess}}(\mathrm{X}|\mathrm{E}),\]  
and also the definition of conditional smooth min-entropy is:  
\[\mathrm{H}_{\mathrm{min}}{}^{\varepsilon}(X|Y)=\max_{\mathcal{E}}\mathrm{H}_{ \mathrm{min}}(X\mathcal{E}|Y),\]  
where for any event \(\mathcal{E}\), we have:  
\[\mathrm{P}_{\mathrm{guess}}(X\mathcal{E}|Y)=\sum_{y}\mathrm{P}_{Y}(y)\max_{x} \mathrm{P}_{X\mathcal{E}|Y}(x|y).\]  
Next, we discuss min-entropy-splitting lemma used in Ref. [2; 17] for the security proof of 1-2 ROT and WSE protocol.  
**Lemma 1** (Entropy splitting [2; 17]).: _Let \(\varepsilon\geq 0\), and \(X_{1},X_{2},\ldots,X_{m}\) and \(Z\) are random variables subjected to \(\mathrm{H}_{\mathrm{min}}^{\varepsilon}(X_{i}X_{j}|Z)\geq\alpha\)\((i\
eq j)\). There exists a random variable \(V\subseteq\{1,\ldots,m\}\) such that for any independent random variable \(W\subseteq\{1,\ldots,m\}\) with \(H_{\mathrm{min}}(W)\geq 1\),_  
\[\mathrm{H}_{\mathrm{min}}^{2m\varepsilon}(X_{W}|VWZ,V\
eq W)\geq\frac{\alpha}{ 2}-\mathrm{log}_{2}(m)-1.\]  
**Lemma 2** (Min-entropy splitting [2; 17]).: _Let \(\varepsilon\geq 0\), and \(X_{0}\), \(X_{1}\), and \(Z\) are random variables subjected to \(\mathrm{H}_{\mathrm{min}}^{\varepsilon}\geq\alpha\). Then there exists a random variable \(D\in\{0,1\}\), such that:_  
\[\mathrm{H}_{\mathrm{min}}^{\varepsilon}(X_{D}|DZ)\geq\frac{\alpha}{2}-1.\]  
Finally, we introduce quantum uncertainty relation as the core of security proof for our redesigned protocol.  
**Theorem 1** (Quantum uncertainty relation [24]).: _Suppose \(Q\) is an arbitrary fixed \(n\)-qubit state, and \(\theta\) is a random basis (\(\theta\in_{R}\{0,1\}\)), and \(X\in_{R}\{0,1\}^{n}\) is a random variable for the outcome of measuring \(Q\) in basis \(\theta^{n}\), then it has \(\delta>0\), and the conditional smooth min-entropy has a lower bound such that:_  
\[\mathrm{H}_{\mathrm{min}}^{\varepsilon}(X|\theta^{n})\geq(\frac{1}{2}-2 \delta)n.\]  
_Here,_  
\[\varepsilon=2\mathrm{exp}\left(-\frac{(\frac{\delta}{4})^{2}}{32(2+log_{2} \frac{4}{\delta})^{2}}\right).\]
## 2 Study Area and Data
### Data Sets  
In this study, the PS-InSAR analysis utilizes Sentinel-1 SAR data provided by the European Space Agency (ESA). The Sentinel-1 SAR operates at C-band frequencies, and Sentinel-1A consists of four modes of operation: SM, IW, EW, and WV, including interferometric wide-field (IWF) modes with a resolution of 5 m \(\times\) 20 m and an amplitude of 250 km. mode with a revisit period of 12 days. A total of 90 single-view complex (SLC) images acquired from ascending orbits in interferometric wide-field (IW) mode were used in this study. The study area has an incidence angle of approximately 38.96\({}^{\circ}\), a distance-directional resolution of 2.32 m, and an azimuthal resolution of 13.91 m. These images cover a time span from 14 July 2019 to 12 June 2022, with a temporal resolution of 12 days, and the data were obtained from the Alaska Aeronautical Communications Agency. The DEM is the U.S. Shuttle Endeavour's radar topography mapping SRTM (Shuttle Radar Topography Mission (SRTM)) data, providing elevation information at a spatial resolution of 30 m. Precision orbit files were obtained from the ESA Copernicus Program data distribution site.  
In order to analyze the causes of urban deformation anomalies, we reviewed the \"Environmental Geological Survey and Evaluation of Major Cities in Henan Province-Zhengzhou City Summary Report\" and drew a sketch map of the distribution of undesirable geotechnical bodies in Zhengzhou City (Figure 1b). The rainfall data were obtained from the NOAA Global Environment website, the subway construction information was obtained from the Zhengzhou Municipal Bureau of Statistics, and the land cover type data were obtained from the global land use cover data produced by ESRI based on the Sentinel-2 data using the deep learning method. The 2019 housing vector boundaries of Zhengzhou City were obtained from web sharing and checked for accuracy to be used for the research in this paper. Optical images obtained using Google Earth and street photos of June 2021 provided by Baidu Maps were used to study the changes in urban construction.
# K2S Challenge: From Undersampled K-Space to Automatic Segmentation
## 2 Materials and Methods
### Overview of Top Submission Methodologies
#### 2.5.2 UglyBarnacle (Skolkovo Institute of Science and Technology, Moscow, Russia)  
UglyBarnacle's submission differed from other top submission methodologies by leveraging CS as opposed to DL for reconstruction. An initial reconstruction pipeline accepted as input the 18-channel, 256 \(\times\) 256 \(\times\) 200 8\(\times\) undersampled k-space array, performing a CS reconstruction with a combined L\({}_{1}\)-wavelet and total variation (TV) regularization function, imposing 3 times the weight on TV as opposed to L\({}_{1}\)-wavelet. The CS reconstruction was solved as an optimization problem: the goal was to find the undersampled part of the k-space that minimized the target value function (weighted sum of L\({}_{1}\)-wavelet and TV of volumetric image). The optimization problem was solved using the Adam optimization algorithm over 50 iterations for each scan. Reconstructed images were fed to an architecture similar to V-Net for tissue segmentation. The segmentation network was implemented in 3D, with the following feature map depths at V-Net stages: 16, 32, 64, 128, 256. Max-pooling was used to compress the representation of feature maps in the encoder, and upsampling to increase resolution in the decoder, with skip connections transferring information from the encoder to corresponding parts of the decoder. The network output was fed through two final convolutions (one with a feature map depth of 7 and the last with a depth of 1) to yield predicted segmentations.