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In these notes, we describe the strategy for the derivation of the hydrodynamic limit for a family of long range interacting particle systems of exclusion type with symmetric rates. For $m \in \mathbb{N}:=\{1, 2, \ldots\}$ fixed, the hydrodynamic equation is $\partial_t \rho(t,u)= [-(-\Delta)^{\gamma /2} \rho^m](t,u) $. For $m=1$, this {is} the fractional equation, which is linear. On the other hand, for $m \geq 2$, this is the fractional porous medium equation (which is nonlinear), obtained by choosing a rate which depends on the number of particles next to the initial and final position of a jump., Comment: 27 pages, 1 figure

Reference Evapotranspiration (ET0) is a key parameter for designing smart irrigation scheduling, since it is related by a coefficient to the water needs of a crop. The United Nations Food and Agriculture Organization, proposed a standard method for ET0 computation (FAO56PM), based on the parameterization of the Penman-Monteith equation, that is widely adopted in the literature. To compute ET0 using the FAO56-PM method, four main weather parameters are needed: temperature, humidity, wind, and solar radiation (SR). One way to make daily ET0 estimations for future days is to use freely available weather forecast services (WFSs), where many meteorological parameters are estimated up to the next 15 days. A problem with this method is that currently, SR is not provided as a free forecast parameter on most of those online services or, normally, such forecasts present a financial cost penalty. For this reason, several ET0 estimation models using machine and deep learning were developed and presented in the literature, that use as input features a reduced set of carefully selected weather parameters, that are compatible with common freely available WFSs. However, most studies on this topic have only evaluated model performance using data from weather stations (WSs), without considering the effect of using weather forecast data. In this study, the performance of authors' previous models is evaluated when using weather forecast data from two online WFSs, in the following scenarios: (i) direct ET0 estimation by an ANN model, and (ii) estimate SR by ANN model, and then use that estimation for ET0 computation, using the FAO56-PM method. Employing data collected from two WFSs and a WS located in Vale do Lobo, Portugal, the latter approach achieved the best result, with a coefficient of determination (R2) ranging between 0.893 and 0.667, when considering forecasts up to 15 days., Comment: A partial version of the work submitted to ESRE/INTERNATIONAL CONFERENCE ON ENVIRONMENTAL SCIENCES AND RENEWABLE ENERGY

This paper investigates the correlation between magnetic resonance spectroscopic imaging (MRSI) and magnetic resonance fingerprinting (MRF) in glioma patients by comparing neuro-oncological markers obtained from MRSI to T1/T2 maps from MRF. Data from 12 consenting patients with gliomas were analyzed by defining hotspots for T1, T2 and various metabolic ratios, and comparing them using S{\o}rensen-Dice Similarity Coefficients (DSCs) and the distances between their centers of intensity (COIDs). Median DSCs between MRF and the tumor segmentation were 0.73 (T1) and 0.79 (T2). The DSCs between MRSI and MRF were highest for Gln/tNAA (T1: 0.75, T2: 0.80, tumor: 0.78), followed by Gly/tNAA (T1: 0.57, T2: 0.62, tumor: 0.54) and tCho/tNAA (T1: 0.61, T2: 0.58, tumor: 0.45). The median values in the tumor hotspot were T1=1724 ms, T2=86 ms, Gln/tNAA=0.61, Gly/tNAA=0.28, Ins/tNAA=1.15, and tCho/tNAA=0.48, and, in the peritumoral region, were T1=1756 ms, T2=102ms, Gln/tNAA=0.38, Gly/tNAA=0.20, Ins/tNAA=1.06, and tCho/tNAA=0.38, and, in the NAWM, were T1=950 ms, T2=43 ms, Gln/tNAA=0.16, Gly/tNAA=0.07, Ins/tNAA=0.54, and tCho/tNAA=0.20. The results of this study constitute the first comparison of 7T MRSI and 3T MRF, showing a good correspondence between these methods., Comment: Includes 3 tables, 6 figures, 3 supplementary tables, and 4 supplementary figures

We obtain the hydrodynamic limit of symmetric long-jumps exclusion in $\mathbb{Z}^d$ (for $d \geq 1$), where the jump rate is inversely proportional to a power of the jump's length with exponent $\gamma+1$, where $\gamma \geq 2$. Moreover, movements between $\mathbb{Z}^{d-1} \times \mathbb{Z}_{-}^{*}$ and $\mathbb{Z}^{d-1} \times \mathbb N$ are slowed down by a factor $\alpha n^{-\beta}$ (with $\alpha>0$ and $\beta\geq 0$). In the hydrodynamic limit we obtain the heat equation in $\mathbb{R}^d$ without boundary conditions or with Neumann boundary conditions, depending on the values of $\beta$ and $\gamma$. The (rather restrictive) condition in \cite{casodif} (for $d=1$) about the initial distribution satisfying an entropy bound with respect to a Bernoulli product measure with constant parameter is weakened or completely dropped., Comment: 42 pages, 1 figure

In this article we obtain the equilibrium fluctuations of a symmetric exclusion process in $\mathbb{Z}$ with long jumps. The transition probability of the jump from $x$ to $y$ is proportional to $|x-y|^{-\gamma-1}$. Here we restrict to the choice $\gamma \geq 2$ so that the system has a diffusive behavior. Moreover, when particles move between $\mathbb{Z}_{-}^{*}$ and $\mathbb N$, the jump rates are slowed down by a factor $\alpha n^{-\beta}$, where $\alpha>0$, $\beta\geq 0$ and $n$ is the scaling parameter. Depending on the values of $\beta$ and $\gamma$, we obtain several stochastic partial differential equations, corresponding to a heat equation without boundary conditions, or with Robin boundary conditions or Neumann boundary conditions.

Monitoring the behavior of automated real-time stream processing systems has become one of the most relevant problems in real world applications. Such systems have grown in complexity relying heavily on high dimensional input data, and data hungry Machine Learning (ML) algorithms. We propose a flexible system, Feature Monitoring (FM), that detects data drifts in such data sets, with a small and constant memory footprint and a small computational cost in streaming applications. The method is based on a multi-variate statistical test and is data driven by design (full reference distributions are estimated from the data). It monitors all features that are used by the system, while providing an interpretable features ranking whenever an alarm occurs (to aid in root cause analysis). The computational and memory lightness of the system results from the use of Exponential Moving Histograms. In our experimental study, we analyze the system's behavior with its parameters and, more importantly, show examples where it detects problems that are not directly related to a single feature. This illustrates how FM eliminates the need to add custom signals to detect specific types of problems and that monitoring the available space of features is often enough., Comment: 10 pages, 5 figures. AutoML, KDD22, August 14-17, 2022, Washington, DC, US

In this article we derive the fractional porous medium equation for any power of the fractional Laplacian as the hydrodynamic limit of a microscopic dynamics of random particles with long range interactions, but the jump rate highly depends on the occupancy near the sites where the interactions take place.

We analyse the hydrodynamical behavior of the long jumps symmetric exclusion process in the presence of a slow barrier. The jump rates are given by a symmetric transition probability $p(\cdot)$ with infinite variance. When jumps occur from $\mathbb{Z}_{-}^{*}$ to $\mathbb N$ the rates are slowed down by a factor $\alpha n^{-\beta}$ (with $\alpha>0$ and $\beta\geq 0$). We obtain several partial differential equations given in terms of the regional fractional Laplacian on $\mathbb R^*$ and with different boundary conditions. Surprisingly, in opposition to the diffusive regime, we get different regimes depending on whether $\alpha=1$ (all bonds with the same rate) or $\alpha\neq 1$.

In this article we analyse the hydrodynamical behavior of the symmetric exclusion process with long jumps and in the presence of a slow barrier. The jump rates for fast bonds are given by a transition probability $p(\cdot)$ which is symmetric and has finite variance, while for slow bonds the jump rates are given $p(\cdot)\alpha n^{-\beta}$ (with $\alpha>0$ and $\beta\geq 0$), and correspond to jumps from $\mathbb{Z}_{-}^{*}$ to $\mathbb N$. We prove that: if there is a fast bond from $\mathbb{Z}_{-}^{*}$ and $\mathbb N$, then the hydrodynamic limit is given by the heat equation with no boundary conditions; otherwise, it is given by the previous equation if $0\leq \beta<1$, but for $\beta\geq 1$ boundary conditions appear, namely, we get Robin (linear) boundary conditions if $\beta=1$ and Neumann boundary conditions if $\beta>1$.

Some mission critical systems, e.g., fraud detection, require accurate, real-time metrics over long time sliding windows on applications that demand high throughput and low latencies. As these applications need to run 'forever' and cope with large, spiky data loads, they further require to be run in a distributed setting. We are unaware of any streaming system that provides all those properties. Instead, existing systems take large simplifications, such as implementing sliding windows as a fixed set of overlapping windows, jeopardizing metric accuracy (violating regulatory rules) or latency (breaching service agreements). In this paper, we propose Railgun, a fault-tolerant, elastic, and distributed streaming system supporting real-time sliding windows for scenarios requiring high loads and millisecond-level latencies. We benchmarked an initial prototype of Railgun using real data, showing significant lower latency than Flink and low memory usage independent of window size. Further, we show that Railgun scales nearly linearly, respecting our msec-level latencies at high percentiles (<250ms @ 99.9%) even under a load of 1 million events per second., Comment: arXiv admin note: text overlap with arXiv:2009.00361

Some mission critical systems, such as fraud detection, require accurate, real-time metrics over long time windows on applications that demand high throughputs and low latencies. As these applications need to run "forever", cope with large and spiky data loads, they further require to be run in a distributed setting. Unsurprisingly, we are unaware of any distributed streaming system that provides all those properties. Instead, existing systems take large simplifications, such as implementing sliding windows as a fixed set of partially overlapping windows, jeopardizing metric accuracy (violating financial regulator rules) or latency (breaching service agreements). In this paper, we propose Railgun, a fault-tolerant, elastic, and distributed streaming system supporting real-time sliding windows for scenarios requiring high loads and millisecond-level latencies. We benchmarked an initial prototype of Railgun using real data, showing significant lower latency than Flink, and low memory usage, independent of window size., Comment: Previously submitted to CIDR 2021

We study the hydrodynamic limit for a model of symmetric exclusion processes with heavy-tailed long jumps and in contact with infinitely extended reservoirs. We show how the corresponding hydrodynamic equations are affected by the parameters defining the model. The hydrodynamic equations are characterized by a class of super-diffusive operators that are given by the regional fractional Laplacian with some additional reaction terms and various boundary conditions. This work solves some questions left open in \cite{BJGO2} about the same model.