Miracle-dz/UniFAR-FTUs huggingface dataset:
Sul limite delle soluzioni di problemi di Cauchy relativi all'equazione del calore

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Quantifying and Visualizing the Sharpness of Attraction Basins in Neural Network Error Landscapes

Algorithms used to train neural networks (NNs) converge in valleylike parts of the loss landscape. The point of convergence is considered a flat minimum when the valley is wide, and a sharp minimum when the valley is narrow. It has been hypothesized that flat minima in wide valleys generalize better than sharp minima in narrow valleys, but this has not been shown to hold in general. Theoretical studies propose conflicting ideas about the relevance, shape, and definition of sharp and flat minima. This study proposes a method for sampling the neighborhood around local minima of NN error landscapes. Using this method, we define two metrics to quantify the sharpness of minima as well as a 2-dimensional visualization for approximating the structure of the basins of attraction. We then conduct experiments to verify or refute the correlation between the sharpness of a valley around a local minimum and the ability of the NN to generalize well at that minimum. Results provide no evidence to support this correlation.
Multi-Step-Ahead Web Service QoS Time Series Forecasting: A Multi-Predictor-Based Genetic Programming Approach

Previously, in a GECCO 2022 Hot-off-the-Press paper [1], we presented a comprehensive survey of the modeling and prediction of Web service (WS) quality of service (QoS) time series [2]. Based on the exhaustive investigation in [2], this research subject has already been deeply and widely studied for over a decade; for the one-step-ahead version of this problem, which can be considered its most primitive problem form, overall, our proposed and developed genetic programming (GP)-based solution outperforms competitors in terms of both modeling and forecasting accuracy, according to our ongoing study, which has been reported in [3] [4] [5]. Nevertheless, as argued in [6], for the long-term use and rental of cloud-based WSs, multi-step-ahead QoS time series prediction of these services is needed. Thus, the authors employed and revised the two most widely used single-predictor-based time series methods, namely, autoregressive integrated moving average (ARIMA) models and exponential smoothing (ES), to address this latest version of the problem. For this multi-step-ahead variant of the problem, in Y. Y. Fanjiang, Y. Syu and W. L. Huang, "Time Series QoS Forecasting for Web Services Using Multi-Predictor-based Genetic Programming", IEEE Transactions on Services Computing (TSC), Vol. 15, P.P. 1423--1435, 2022, we devise and employ a multipredictor-based approach to genetic programming. First, due to its superiority in our past work for the basic (i.e., one-step-ahead) version of the problem, we investigate the performance of GP on this newly emerged (multi-step-ahead) form of the problem. Second, instead of using a single model for predictions regarding multiple future time points, which is the method commonly adopted in prior research [2], we evolve and apply a dedicated GP-generated predictor for each targeted future time point and its projection. Furthermore, two different strategies for the consumed predictor inputs are tested to determine their differences and influence on accuracy so that a better strategy can be empirically determined. In addition, we propose in the reported paper [7] two disparate techniques to further enhance the resulting performance of our multi-predictor-based GP method. As in our previous GECCO Hot-off-the-Press paper [1], this abstract paper presents to the GECCO community a verified application of GP on a more difficult and challenging type of WS QoS time series forecasting. Our purpose is to enable the GECCO community to use this application of GP, to try to improve GP to obtain more accurate and better results, and to investigate other potential evolutionary paradigms and techniques for this issue.
Polarimetric characteristics of melting hail at S and C bands

Polarimetric method for hail detection is based on the assumption that differential reflectivity ZDR of hail is low due to almost random orientation of hailstones, and the combination of low ZDR and high reflectivity factor Z points to the presence of hail (Bringi and Chandrasekar 2001). Limited validation studies (e,g., Heinselman and Ryzhkov 2006; Depue et al. 2007) have demonstrated good overall skills of the method at S band. However, several practically important issues regarding detection of hail and determination of its size at different radar wavelengths remain to be resolved. These include (1) Estimation of maximal hail size. The most recent version of hydrometeor classification algorithm (HCA) for polarimetrically upgraded WSR-88D radars implies detection of “rain mixed with hail” (Park et al. 2009) and does not distinguish between large and small hail. (2) Separation of hail and rain in the mixture. Hail is commonly mixed with rain below the freezing level. Larger hailstones with original sizes exceeding 20 – 30 mm do not entirely melt on the way to the ground and their polarimetric signatures may be overwhelmed by the ones caused by rain originating from smaller size hailstones and graupel. This also necessitates taking into account the height of the radar sampling volume with respect to the freezing level. (3) Adaptation of the hail detection procedure originally developed and validated at S band for the use at shorter radar wavelengths. There is growing evidence that intrinsic ZDR of hail/rain mixture (after correction for differential attenuation) at C band is noticeably higher than the one at S band (Ryzhkov et al. 2007). (4) Anomalously high attenuation / differential attenuation frequently reported at C band and their possible relation to the presence of hail (e.g., Tabary et al. 2008). Such differential attenuation in “hotspots” is difficult to correct and it has very strong impact on the magnitude of ZDR and reliability of hail detection at C band. This study is an attempt to develop possible approaches to address these four issues and to interpret observed polarimetric signatures of hail at S and C bands by examining two microphysical models of melting hail.
Sn nanothreads in GaAs: experiment and simulation

The gated GaAs structures like the field-effect transistor with the array of the Sn nanothreads was fabricated via delta-doping of vicinal GaAs surface by Sn atoms with a subsequent regrowth. That results in the formation of the chains of Sn atoms at the terrace edges. Two device models were developed. The quantum model accounts for the quantization of the electron energy spectrum in the self-consistent two-dimensional electric potential, herewith the electron density distribution in nanothread arrays for different gate voltages is calculated. The classical model ignores the quantization and electrons are distributed in space according to 3D density of states and Fermi-Dirac statistics. It turned out that qualitatively both models demonstrate similar behavior, nevertheless, the classical one is in better quantitative agreement with experimental data. Plausibly, the quantization could be ignored because Sn atoms are randomly placed along the thread axis. The terahertz hot-electron bolometers (HEBs) could be based on the structure under consideration.
Multi-Objective Evolutionary Search of Compact Convolutional Neural Networks with Training-Free Estimation

With the increasing demand of deploying convolutional neural networks (CNNs) on resource-constrained devices, designing high-performance and lightweight architectures has become a main challenge for neural architecture search (NAS). This paper develops an evolutionary multi-objective optimization framework to explore CNNs with different compactness in a flexible way. A multi-scale convolutional module is developed to enhance the feature learning capability. To further improve the architecture search efficiency, a low-cost metric based on neural tangent kernel is leveraged to estimate the trainability of CNNs instead of performing an expensive training process. Experiments are carried out on CIFAR-10 and CIFAR-100, to verify the effectiveness of the proposed method. Compared with the state-of-the-art algorithms, the proposed method discovers architectures with a smaller number of parameters and competitive classification performance using only up to 0.2 GPU days, showing a better trade-off between accuracy and model complexity.
Replicable Self-Documenting Experiments with Arbitrary Search Spaces and Algorithms

We introduce moptipy, a toolbox for implementing, experimenting with, and applying optimization algorithms. It features mechanisms for executing fully reproducible experiments. Our seeding procedure for random number generators makes our experiments deterministic. Our system creates self-documenting log files that store the algorithm setup, the system configuration, the random seed, the final solutions, and the progress of the optimization algorithm over time. The parallelization and distribution of experiments works on most operating systems and requires no additional synchronization, inter-process-communication, or libraries. moptipy supports both single- and multi-objective optimization with arbitrary search spaces. Time measurements and computational budgets can be based both on wall clock time and objective function evaluations. moptipy is also an educational platform with comprehensive documentation and an accompanying free electronic book introducing the basic concepts of metaheuristics, discussing the implemented algorithms, and showing their performance on basis of actual experimental results.
On the Influence of Multiplication Operators on the Ill-posedness of Inverse Problems

In this thesis we deal with the degree of ill-posedness of linear operator equations Bx = y in Hilbert spaces X =Y = L2(0,1), where B may be decomposed into a compact linear integral operator J with a well-known decay rate of singular values and a multiplication operator M. This case occurs for example for nonlinear operator equations F(x) = y, where F = N ◦J. Then the local degree of ill-posedness is investigated via the Frechet derivative in x0 ∈ D(F) which has the form F ′(x0) = M ◦ J providing the situation described above. If the multiplier function has got zeroes, the determination of the local degree of ill-posedness is not trivial. We are going to investigate this situation, provide analytical tools as well as their limitations. By using several numerical approaches for computing the singular values of F ′(x0) we find that the degree of ill-posedness does not change through those multiplication operators. We even provide a conjecture, verified by several numerical studies, how these multiplication operators influence the singular values of F ′(x0) = M ◦ J. Finally we analyze the influence of those multiplication operators on the opportunities of Tikhonov regularization and corresponding convergence rates. In this context we also provide a short summary on the relationship between nonlinear problems and their linearizations. Zusammenfassung Diese Arbeit beschaftigt sich mit dem Grad der Inkorrektheit linearer Operatorgleichungen der Form Bx = y in Hilbertraumen X = Y = L2(0,1), wobei B als Komposition eines vollstetigen linearen Integraloperators J mit bekannter Abklingrate der Singularwerte und eines Multiplikationsoperators M dargestellt werden kann. Dieser Fall tritt beispielsweise bei nichtlinearen Operatorgleichungen F(x) = y, wobei F = N ◦ J. Dann wird der lokale Inkorrektheitsgrad uber die Frechet-Ableitung in x0 ∈ D(F) bestimmt, welche mit F ′(x0) = M ◦ J die oben beschriebene Form hat. Falls die Multiplikatorfunktion Nullstellen hat, ist die Bestimmung des lokalen Grades der Inkorrektheit nicht einfach. Moglichkeiten und Grenzen der Analyis fur diese Situation werden betrachtet. Unterschiedliche numerische Ansatze fur die Bestimmung der Singularwerte von F ′(x0) liefern das Ergebnis, dass der Grad der Inkorrektheit durch die Multiplikatorfunktionen nicht beeinflusst wird. Es wird sogar ein Zusammenhang gefunden, wie diese Multiplikationsoperatoren die Singularwerte von F ′(x0) = M ◦ J beeinflussen. Schlieslich werden noch die Moglichkeiten der Tikhonov Regularisierung unter Einfluss der Multiplikationsoperatoren untersucht. In diesem Zusammenhang wird auch eine kurze Zusammenfassung zur Beziehung von nichtlinearen Problemen und ihren Linearisierungen gegeben.
Evolutionary Computation for Feature Selection and Feature Construction

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from Permissions@acm.org. GECCO '23 Companion, July 15–19, 2023, Lisbon, Portugal © 2023 Copyright is held by the owner/author(s). Publication rights licensed to ACM. ACM ISBN 979-8-4007-0120-7/23/07. $15.00 https://doi.org/10.1145/3583133.3595050. v Bing Xue is is currently a Professor of Artificial Intelligence, and Deputy Head of School in the School of Engineering and Computer Science at Victoria University of Wellington. She has over 300 papers published in fully refereed international journals and conferences and her research focuses mainly on evolutionary computation, machine learning, classification, symbolic regression, feature selection, evolving deep NNs, image analysis, transfer learning, multi-objective machine learning. Dr Xue is currently the Chair of IEEE CIS Evolutionary Computation Technical Committee and Editor of IEEE CIS Newsletter. She has also served as associate editor of several international journals, such as IEEE CIM, IEEE TEVC and ACM TELO. She is also a Fellow of Engineering New Zealand.
Axisymmetric flow in a cylindrical tank over a rotating bottom. Part II. Deformation of the water surface and experimental verification of the theory

The theory of axisymmetric flow in a cylindrical container with a rotating bottom, as described in Part I, is validated against the results of previous and our own laboratory experiments. First, deformation of the water surface is derived using the velocity distribution of the axisymmetric flow obtained by the theory. The form of the water surface is classified into three regimes, and the rotation rates of the transitions between these regimes are determined. The parameters predicted from this theory are compared with the results measured in laboratory experiments and also with data from previous experimental studies. The theory predicts the experimental data well, but a slight difference was found in the narrow region close to the side wall. Corrections estimated by considering the fluid behavior around the side wall boundary layer successfully explain most of the discrepancies. This theory appears to predict the results of the laboratory experiments very well, much better than a theory using an assumption of quadratic drag as a model of turbulent boundary layers.
Analytic model of a resistive magnetohydrodynamic shock without Hall effect

An analytic model of a stationary hypersonic magnetohydrodynamic (MHD) shock with an externally applied magnetic field is proposed. Basically, original jump conditions at a plane oblique shock, analogous to the Rankine–Hugoniot formulae, with a moderately resistive air plasma downstream are derived. Viscous, thermal and Hall effects are neglected, but the plasma dissociation behind the shock causing a jump of isentropic exponent is also a major input of the model. Then, a shock-fitting procedure with ambient atmospheric conditions is worked out by the coupling of these MHD jumps with thermodynamic correlations and an electric conductivity model. For an application to atmospheric entry problems, the flow behind an axisymmetric blunt-body shock is modelled with a stream function satisfying these MHD jump conditions as boundary conditions. An important feature put into evidence is a similarity rule involving the hypersonic parameter $M_{1}\cos \unicode[STIX]{x1D712}_{1}$ , which shows an aerodynamic correspondence between the upstream Mach number $M_{1}$ and the velocity angle $\unicode[STIX]{x1D712}_{1}$ . It also emerges that curvature effects become important past $30^{\circ }$ and the assumption of a spherical shock also becomes untenable past $50^{\circ }$ ; therefore, we limit the model of shock thickness used in the MHD fitting to $\unicode[STIX]{x1D712}_{1}<50^{\circ }$ .
Simulation of synthetic aperture radar imaging of dynamic wakes of submerged body

Simulation of the wakes excited by a submerged body in high-resolution synthetic aperture radar (SAR) imaging is presented. The hydrodynamic model consists of two sets of ocean dynamics closely relevant to SAR imaging, namely time evolution of the wake and wind waves, and orbital motion of Bragg waves riding on them. For the wake, the orbital motion is reconstructed through a least square-based solution from the known elevation map. Time domain backscattering from the electrically very large ocean scenario is computed by a quasi-stationary algorithm, in which a physical optics phase correction of the two-scale model is proposed to take account the Doppler effects caused by wave orbital motions. SAR images of the wake are simulated as a function of the size, speed and depth of the submerged body, in which a range of wake features are observed, such as azimuth displacement, velocity bunching and smearing. This work might provide insights into the feasibility of using a SAR sensor to detect the wakes of a submerged body.
Assessment of the pseudo-tracking approach for the calculation of material acceleration and pressure fields from time-resolved PIV: part II. Spatio-temporal filtering

The present study characterises the spatio-temporal filtering associated with pseudo-tracking. A combined theoretical and numerical assessment is performed that uses the relatively simple flow case of a two-dimensional Taylor vortex as analytical test case. An additional experimental assessment considers the more complex flow of a low-speed axisymmetric base flow, for which time-resolved tomographic PIV measurements and microphone measurements were obtained. The results of these assessments show how filtering along Lagrangian tracks leads to amplitude modulation of flow structures. A cut-off track length and spatial resolution are specified to support future applications of the pseudo-tracking approach. The experimental results show a fair agreement between PIV and microphone pressure data in terms of fluctuation levels and pressure frequency spectra. The coherence and correlation between microphone and PIV pressure measurements were found to be substantial and almost independent of the track length, indicating that the low-frequency behaviour of the flow could be reproduced regardless of the track length. It is suggested that a spectral analysis can be used inform the selection of a suitable track length and to estimate the local error margin of reconstructed pressure values.
Design and Analysis of Replication Studies

Issues surrounding the importance and interpretation of replication research have generated considerable debate and controversy in recent years. Some of the controversy can be attributed to imprecise and inadequate specifications of the statistical criteria needed to assess replication and nonreplication. Two types of statistical replication evidence and four types of statistical nonreplication evidence are described. In addition, three types of inconclusive statistical replication evidence are described. An important benefit of a replication study is the ability to combine an effect-size estimate from the original study with an effect-size estimate from the follow-up study to obtain a more precise and generalizable effect-size estimate. The sample size in the follow-up study is an important design consideration, and some methods for determining the follow-up sample size requirements are discussed. R functions are provided that can be used to analyze results from a replication study. R functions to determine the appropriate sample size in the follow-up study also are provided.
An Inverse Optimal Stopping Problem for Diffusion Processes

Let $X$ be a one-dimensional diffusion and let $g\colon[0,T]\times\mathbb{R}\to\mathbb{R}$ be a payoff function depending on time and the value of $X$. The paper analyzes the inverse optimal stopping problem of finding a time-dependent function $\pi:[0,T]\to\mathbb{R}$ such that a given stopping time $\tau^{\star}$ is a solution of the stopping problem $\sup_{\tau}\mathbb{E}\left[g(\tau,X_{\tau})+\pi(\tau)\right]\,. $ Under regularity and monotonicity conditions, there exists a solution $\pi$ if and only if $\tau^{\star}$ is the first time when $X$ exceeds a time-dependent barrier $b$, i.e. $\tau^{\star}=\inf\left\{ t\ge0\,|\,X_{t}\ge b(t)\right\} \,. $ We prove uniqueness of the solution $\pi$ and derive a closed form representation. The representation is based on an auxiliary process which is a version of the original diffusion $X$ reflected at $b$ towards the continuation region. The results lead to a new integral equation characterizing the stopping boundary $b$ of the stopping problem $\sup_{\tau}\mathbb{E}\left[g(\tau,X_{\tau})\right]$.
Subcritical Destabilization of African Easterly Waves by Saharan Mineral Dust

AbstractA theoretical framework is presented that exposes the radiative–dynamical relationships that govern the subcritical destabilization of African easterly waves (AEWs) by Saharan mineral dust (SMD) aerosols. The framework is built on coupled equations for quasigeostrophic potential vorticity (PV), temperature, and SMD mixing ratio. A perturbation analysis yields, for a subcritical, but otherwise arbitrary, zonal-mean background state, analytical expressions for the growth rate and frequency of the AEWs. The expressions are functions of the domain-averaged wave activity, which is generated by the direct radiative effects of the SMD. The wave activity is primarily modulated by the Doppler-shifted phase speed and the background gradients in PV and SMD.Using an idealized version of the Weather Research and Forecasting (WRF) Model coupled to an interactive dust model, a linear analysis shows that, for a subcritical African easterly jet (AEJ) and a background SMD distribution that are consistent with obser.
Seasonal Cycle in German Daily Precipitation Extremes

The seasonal cycle of extreme precipitation in Germany is investigated by fitting statistical models to monthly maxima of daily precipitation sums for 2,865 rain gauges. The basis is a non-stationary generalized extreme value (GEV) distribution variation of location and scale parameters. The negative log-likelihood serves as the forecast error for a cross validation to select adequate orders of the harmonic functions for each station. For nearly all gauges considered, the seasonal model is more appropriate to estimate return levels on a monthly scale than a stationary GEV used for individual months. The 100-year return-levels show the influence of cyclones in the western, and convective events in the eastern part of Germany. In addition to resolving the seasonality, we use a simulation study to show that annual return levels can be estimated more precisely from a monthly-resolved seasonal model than from a stationary model based on annual maxima.