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This paper proposes a data preparation process for managing real-world kinematic data and detecting fishing vessels. The solution is a binary classification that classifies ship trajectories into either fishing or non-fishing ships. The data used are characterized by the typical problems found in classic data mining applications using real-world data, such as noise and inconsistencies. The two classes are also clearly unbalanced in the data, a problem which is addressed using algorithms that resample the instances. For classification, a series of features are extracted from spatiotemporal data that represent the trajectories of the ships, available from sequences of Automatic Identification System (AIS) reports. These features are proposed for the modelling of ship behavior but, because they do not contain context-related information, the classification can be applied in other scenarios. Experimentation shows that the proposed data preparation process is useful for the presented classification problem. In addition, positive results are obtained using minimal information., Comment: Sensors 2020

This paper develops a smooth model identification and self-learning strategy for dynamic systems taking into account possible parameter variations and uncertainties. We have tried to solve the problem such that the model follows the changes and variations in the system on a continuous and smooth surface. Running the model to adaptively gain the optimum values of the parameters on a smooth surface would facilitate further improvements in the application of other derivative based optimization control algorithms such as MPC or robust control algorithms to achieve a combined modeling-control scheme. Compared to the earlier works on the smooth fuzzy modeling structures, we could reach a desired trade-off between the model optimality and the computational load. The proposed method has been evaluated on a test problem as well as the non-linear dynamic of a chemical process.

Asymptotically log Fano pairs were introduced by Cheltsov and Rubinstein, generalising a definition of Maeda. They have received attention in the last decade within the theory of K-stability, as they approximate log Calabi Yau pairs while staying in the log Fano setting. In this note, written for the ZAG Proceedings, we summarise our talk on 1st September 2020 (Day of Knowledge) given on Zoom during the 24-hour ZAG Marathon. In the talk, we reported on joint work with P. Cascini and Y. Rubinstein, on the classification of the two-dimensional case, known as asymptotically log del Pezzo pairs., Comment: For publication on the ZAG seminar proceedings. 3 pages

We study the K-moduli of log del Pezzo pairs formed by a del Pezzo surface of degree $d$ and an anti-canonical divisor. These moduli spaces naturally depend on one parameter, providing a natural problem in variations of K-moduli spaces. For degrees 2, 3, 4, we establish an isomorphism between the K-moduli spaces and variations of Geometric Invariant Theory compactifications, which generalizes the isomorphisms in the absolute cases established by Odaka--Spotti--Sun and Mabuchi--Mukai., Comment: 41 pages, 6 tables. Comments are very welcome!

The integration of magnetic nanoparticles within fibrillar structures represents an interesting avenue for the remotely controlled release of therapeutic agents. This work presents a novel drug release platform based on electrospun magnetic fibers (EMFs) combining drugs, magnetic nanoparticles (MNPs) and mesoporous silica nanoparticles (MSNs) for controlled drug delivery via alternating magnetic fields (AMF). The platform was demonstrated to be versatile and effective for hydrophilic ketorolac (KET) and hydrophobic curcumin (CUR) encapsulation and the major response observed for AMF-triggered release was reached using drug-loaded MSNs within the fibers, providing fine control over drug release patterns. The EMFs exhibited excellent inductive heating capabilities, showing a temperature increase up to 8 {\deg}C within a 5 min AMF pulse. The system is shown to be promising for applications like transdermal pain management, oncological drug delivery, tissue engineering, and wound healing, enabling precise control over drug release in both spatial and temporal dimensions. The findings of this study offer valuable insights into the development of the next generation of smart drug delivery systems, based in multifunctional materials that can be remotely regulated and potentially revolutionize the field of nanomedicine.

We introduce a new subclass of Fano varieties (Casagrande-Druel varieties), that are $n$-dimensional varieties constructed from Fano double covers of dimension $n-1$. We conjecture that a Casagrande-Druel variety is K-polystable if the double cover and its base space are K-polystable. We prove this for smoothable Casagrande-Druel threefolds, and for Casagrande-Druel varieties constructed from double covers of $\mathbb{P}^{n-1}$ ramified over smooth hypersurfaces of degree $2d$ with $n>d>\frac{n}{2}>1$. As an application, we describe the connected components of the K-moduli space parametrizing smoothable K-polystable Fano threefolds in the families 3.9 and 4.2 in the Mori-Mukai classification., Comment: 58 pages

By identifying K-polystable limits in 4 specific deformations families of smooth Fano 3-folds, we complete the classification of one-dimensional components in the K-moduli space of smoothable Fano 3-folds., Comment: 30 pages

Acting as a goalkeeper in a video-game, a participant is asked to predict the successive choices of the penalty taker. The sequence of choices of the penalty taker is generated by a stochastic chain with memory of variable length. It has been conjectured that the probability distribution of the response times is a function of the specific sequence of past choices governing the algorithm used by the penalty taker to make his choice at each step. We found empirical evidence that besides this dependence, the distribution of the response times depends also on the success or failure of the previous prediction made by the participant. Moreover, we found statistical evidence that this dependence propagates up to two steps forward after the prediction failure.

We describe three algorithms to determine the stable, semistable, and torus-polystable loci of the GIT quotient of a projective variety by a reductive group. The algorithms are efficient when the group is semisimple. By using an implementation of our algorithms for simple groups, we provide several applications to the moduli theory of algebraic varieties, including the K-moduli of algebraic varieties, the moduli of algebraic curves and the Mukai models of the moduli space of curves for low genus. We also discuss a number of potential improvements and some natural open problems arising from this work., Comment: 32 pages, 3 figures. 1 table

We classify non-factorial nodal Fano threefolds with $1$ node and class group of rank $2$., Comment: 14 pages. Minor changes; improved exposition

This work reports on the synthesis and characterization of a new type of electrospun magnetic nanofibers (MNFs), and their application for degradation of organic pollutants using remote magnetic inductive heating. We describe a simple protocol combining a fast (app. 5 min) synthesis of MnFe\textsubscript{2}O\textsubscript{4} magnetic nanoparticles (MNPs) by sonochemical route, optimized for inductive heating, with their subsequent incorporation in electrospun MNFs composed of polyacrylonitrile (PAN) nanofibers. The resulting multifunctional MNFs (average diameter $\phi = 760 \pm 150$ nm) contain up to $\approx 30%$wt. of the MNPs. The composite showed superhydrophobic behaviour ($\theta_c = 165^\circ$) and a band gap value of 1.75 eV. We found that the presence of MNPs embedded into the polymeric nanofibers modify the exothermic and the glass transitions temperatures compared with pure PAN nanofibers, suggesting a strong attachment between MNPs and polymeric chains. The MNFs could be remotely activated by alternating magnetic fields (AMF, $f = 200-800$ kHz, $H_0 = 10-36$ kA/m) for accelerating the catalytic reactions of the organic dye methylene blue (MB). A remarkable stability of the MNFs against degradation under extreme pH conditions ($380%$ in the presence of hydrogen peroxide under AMFs, attributed to Fe\textsuperscript{2+}/\textsuperscript{3+} and Mn\textsuperscript{2+}/\textsuperscript{3+}/\textsuperscript{4+} active centers on the surface of the MNP/MNFs observed from XPS data. The capacity of these materials for magnetic remote activation appeals catalytic applications under conditions of darkness or restrained access, where no photocatalytic reactions can be achieved., Comment: 31 pages, 16 figures

In this article we address two related issues on the learning of probabilistic sequences of events. First, which features make the sequence of events generated by a stochastic chain more difficult to predict. Second, how to model the procedures employed by different learners to identify the structure of sequences of events. Playing the role of a goalkeeper in a video game, participants were told to predict step by step the successive directions -- left, center or right -- to which the penalty kicker would send the ball. The sequence of kicks was driven by a stochastic chain with memory of variable length. Results showed that at least three features play a role in the first issue: 1) the shape of the context tree summarizing the dependencies between present and past directions; 2) the entropy of the stochastic chain used to generate the sequences of events; 3) the existence or not of a deterministic periodic sequence underlying the sequences of events. Moreover, evidence suggests that best learners rely less on their own past choices to identify the structure of the sequences of events.

Comparative diagnostic in brain tumor evaluation makes possible to use the available information of a medical center to compare similar cases when a new patient is evaluated. By leveraging Artificial Intelligence models, the proposed system is able of retrieving the most similar cases of brain tumors for a given query. The primary objective is to enhance the diagnostic process by generating more accurate representations of medical images, with a particular focus on patient-specific normal features and pathologies. The proposed model uses Artificial Intelligence to detect patient features to recommend the most similar cases from a database. The system not only suggests similar cases but also balances the representation of healthy and abnormal features in its design. This not only encourages the generalization of its use but also aids clinicians in their decision-making processes. We conducted a comparative analysis of our approach in relation to similar studies. The proposed architecture obtains a Dice coefficient of 0.474 in both tumoral and healthy regions of the patients, which outperforms previous literature. Our proposed model excels at extracting and combining anatomical and pathological features from brain \glspl{mr}, achieving state-of-the-art results while relying on less expensive label information. This substantially reduces the overall cost of the training process. This paper provides substantial grounds for further exploration of the broader applicability and optimization of the proposed architecture to enhance clinical decision-making. The novel approach presented in this work marks a significant advancement in the field of medical diagnosis, particularly in the context of Artificial Intelligence-assisted image retrieval, and promises to reduce costs and improve the quality of patient care using Artificial Intelligence as a support tool instead of a black box system., Comment: 16 pages, 8 figures, 3 tables

In this short note we show the unboundedness of the dimension of the K-moduli space of $n$-dimensional Fano varieties, and that the dimension of the stack can also be unbounded while, simultaneously, the dimension of the corresponding coarse space remains bounded., Comment: 7 pages

In dimension two, we reduce the classification problem for asymptotically log Fano pairs to the problem of determining generality conditions on certain blow-ups. In any dimension, we prove the rationality of the body of ample angles of an asymptotically log Fano pair, i.e., these convex bodies are always rational polytopes., Comment: v2: Theorem 1.4 has been improved and now completely settles Problem 1.3; v3: final version to appear in Rendiconti del Circolo Matematico di Palermo

The 'moduli continuity method' permits an explicit algebraisation of the Gromov-Hausdorff compactification of K\"ahler-Einstein metrics on Fano manifolds in some fundamental examples. In this paper, we apply such method in the 'log setting' to describe explicitly some compact moduli spaces of K-polystable log Fano pairs. We focus on situations when the angle of singularities is perturbed in an interval sufficiently close to one, by considering constructions arising from Geometric Invariant Theory. More precisely, we discuss the cases of pairs given by cubic surfaces with anticanonical sections, and of projective space with non-Fano hypersurfaces, and we show ampleness of the CM line bundle on their good moduli space (in the sense of Alper). Finally, we introduce a conjecture relating K-stability (and degenerations) of log pairs formed by a fixed Fano variety and pluri-anticanonical sections to certain natural GIT quotients., Comment: 26 pages, 1 figure. Final version. To appear in J. Lond. Math. Soc

We consider projective rational strong Calabi dream surfaces: projective smooth rational surfaces which admit a constant scalar curvature K\"ahler metric for every K\"ahler class. We show that there are only two such rational surfaces, namely the projective plane and the quadric surface. In particular, we show that all rational surfaces other than those two admit a destabilising slope test configuration for some polarization, as introduced by Ross and Thomas. We further show that all Hirzebruch surfaces other than the quadric surface and all rational surfaces with Picard rank $3$ do not admit a constant scalar curvature K\"ahler metric in any K\"ahler class., Comment: 12 pages. v2: New introduction reflecting new notation on Calabi dream manifolds (implicitly considered in the 1st version) introduced by Chen and Cheng after this manuscript appeared on the ArXiv. All proofs remain the same. v3: final version. Accepted for publication in Math. Nachr

We study the moduli space of triples $(C, L_1, L_2)$ consisting of quartic curves $C$ and lines $L_1$ and $L_2$. Specifically, we construct and compactify the moduli space in two ways: via geometric invariant theory (GIT) and by using the period map of certain lattice polarized $K3$ surfaces. The GIT construction depends on two parameters $t_1$ and $t_2$ which correspond to the choice of a linearization. For $t_1=t_2=1$ we describe the GIT moduli explicitly and relate it to the construction via $K3$ surfaces., Comment: 28 pages, 2 figures. To appear in Eur. J. Math

We provide new examples of K-unstable polarized smooth del Pezzo surfaces using a flopped version first used by Cheltsov and Rubinstein of the test configurations introduced by Ross and Thomas. As an application, we provide new obstructions for the existence of constant scalar curvature Kahler metrics on polarized smooth del Pezzo surfaces., Comment: 102 pages, from which 64 pages are an appendix with symbolic computations. To appear in Trans. Amer. Math. Soc

The spontaneous emergence of vector vortex beams with non-uniform polarization distribution is reported in a vertical-cavity surface-emitting laser (VCSEL) with frequency-selective feedback. Antivortices with a hyperbolic polarization structure and radially polarized vortices are demonstrated. They exist close to and partially coexist with vortices with uniform and non-uniform polarization distributions characterized by four domains of pairwise orthogonal polarization. The spontaneous formation of these nontrivial structures in a simple, nearly isotropic VCSEL system is remarkable and the vector vortices are argued to have soliton-like properties.

In recent years governments have shown themselves willing to impose blackouts to shut off key communication infrastructure during times of civil strife, and to surveil citizen communications whenever possible. However, it is exactly during such strife that citizens need reliable and anonymous communications the most. In this paper, we present Rangzen, a system for anonymous broadcast messaging during network blackouts. Rangzen is distinctive in both aim and design. Our aim is to provide an anonymous, one-to-many messaging layer that requires only users' smartphones and can withstand network-level attacks. Our design is a delay-tolerant mesh network which deprioritizes adversarial messages by means of a social graph while preserving user anonymity. We built a complete implementation that runs on Android smartphones, present benchmarks of its performance and battery usage, and present simulation results suggesting Rangzen's efficacy at scale.

We consider the moduli space of log smooth pairs formed by a cubic surface and an anticanonical divisor. We describe all compactifications of this moduli space which are constructed using Geometric Invariant Theory and the anticanonical polarization. The construction depends on a weight on the divisor. For smaller weights the stable pairs consist of mildly singular surfaces and very singular divisors. Conversely, a larger weight allows more singular surfaces, but it restricts the singularities on the divisor. The one-dimensional space of stability conditions decomposes in a wall-chamber structure. We describe all the walls and relate their value to the worst singularities appearing in the compactification locus. Furthermore, we give a complete characterization of stable and polystable pairs in terms of their singularities for each of the compactifications considered., Comment: 23 pages, 2 figures, 4 tables. v3: Paper reorganised and shortened. Introduction improved. Same results. Final version. To appear in Rev. Mat. Complut

We give a simple sufficient condition for K-stability of polarized del Pezzo surfaces and for the existence of a constant scalar curvature Kahler metric in the Kahler class corresponding to the polarization., Comment: 1 Table, 20 pages. This article has been accepted for publication in IMRN, published by Oxford University Press

We study the GIT compactifications of pairs formed by a hypersurface and a hyperplane. We provide a general setting to characterize all polarizations which give rise to different GIT quotients. Furthermore, we describe a finite set of one-parameter subgroups sufficient to determine the stability of any GIT quotient. We characterize all maximal orbits of non stable and strictly semistable pairs, as well as minimal closed orbits of strictly semistable pairs. Our construction gives natural compactifications of the space of log smooth pairs for Fano and Calabi-Yau hypersurfaces., Comment: 13 pages.v3: Theorem 1.3 improved. Presentation improved. Final version. To appear in "Proceedings of the AMS"

In this article we prove two non-existence results for translating solitons of the mean curvature flow (translators for short) in $\mathbb{R}^{m+1}$. We also obtain an upper bound to the maximum height that a compact embedded translator in $\mathbb{R}^{3}$ can achieve. On the other hand, we study graphical perturbations of translators, showing that asymptotic graphical perturbations of a graph translator of revolution remain a hypersurface of revolution. Finally, we prove that compact translators that lie between two parallel planes inherit the symmetries of their boundaries curves., Comment: 20 pages, 3 figures

In this article we prove that a connected and properly embedded translating soliton in $\mathbb{R}^3$ with uniformly bounded genus on compact sets which is $C^1$-asymptotic to two planes outside a cylinder, either is flat or coincides with the grim reaper cylinder., Comment: 32 pages, 11 figures, original result improved, to appear in Journal f\"ur die reine und angewandte Mathematik

For every smooth del Pezzo surface $S$, smooth curve $C\in|-K_{S}|$ and $\beta\in(0,1]$, we compute the $\alpha$-invariant of Tian $\alpha(S,(1-\beta)C)$ and prove the existence of K\"ahler--Einstein metrics on $S$ with edge singularities along $C$ of angle $2\pi\beta$ for $\beta$ in certain interval. In particular we give lower bounds for the invariant $R(S,C)$, introduced by Donaldson as the supremum of all $\beta\in(0,1]$ for which such a metric exists., Comment: 21 pages

The global log canonical threshold (or Tian's alpha-invariant) plays an important role in the geometry of Fano varieties. Tian showed that Fano manifolds with big alpha-invariant can be equipped with a Kahler-Einstein metric. In recent years Donaldson drafted a programme to determine when a smooth Fano variety X admits a Kahler-Einstein metric. It was conjectured that the existence of such a metric is equivalent to X being K-stable, an algebraic-geometric property. A crucial step in Donaldson's programme consists on finding a Kahler-Einstein metric with edge singularities of small angle along a smooth anticanonical boundary. Jeffres, Mazzeo and Rubinstein showed that a dynamic version of the alpha-invariant could be used to find such metrics. The global log canonical threshold measures how anticanonical pairs fail to be log canonical. In this thesis we compute the global log canonical threshold of del Pezzo surfaces in various settings. We extend Cheltsov's computation of the global log canonical threshold of complex del Pezzo surfaces to non-singular del Pezzo surfaces over a ground field which is algebraically closed and has arbitrary characteristic. Then we study which anticanonical pairs fail to be log canonical, giving a classification of very singular anticanonical pairs for del Pezzo surfaces of small degree. We conjecture under which circumstances such a classification is plausible for an arbitrary Fano variety and derive consequences. As an application, we compute the dynamic alpha-invariant on smooth del Pezzo surfaces of small degree with any smooth elliptic curve as boundary. The main result of this thesis is a computation of the dynamic alpha-invariant on all smooth del Pezzo surfaces with boundary any smooth elliptic curve C. The values of the alpha-invariant depend on the choice of C. We apply our computation to find Kahler-Einstein metrics with edge singularities., Comment: PhD thesis. 179 pages, 2 figures, 18 tables

The global log canonical threshold of each non-singular complex del Pezzo surface was computed by Cheltsov. The proof used Koll\'ar-Shokurov's connectedness principle and other results relying on vanishing theorems of Kodaira type, not known to be true in finite characteristic. We compute the global log canonical threshold of non-singular del Pezzo surfaces over an algebraically closed field. We give algebraic proofs of results previously known only in characteristic $0$. Instead of using of the connectedness principle we introduce a new technique based on a classification of curves of low degree. As an application we conclude that non-singular del Pezzo surfaces in finite characteristic of degree lower or equal than $4$ are K-semistable., Comment: 21 pages. Thorough rewrite following referee's suggestions. To be published in Manuscripta Mathematica

We propose a new nonparametric test for the supposition of independence between two continuous random variables. The test is based on the size of the longest increasing subsequence of a random permutation. We identified the independence assumption between the two continuous variables with the space of permutation equipped with the uniform distribution and we show the exact distribution of the statistic. We calculate the distribution for several sample sizes. Through a simulation study we estimate the power of our test for diverse alternative hypothesis under the null hypothesis of independence., Comment: 22 pages, 13 figures

The starting point of this article is the question "How to retrieve fingerprints of rhythm in written texts?" We address this problem in the case of Brazilian and European Portuguese. These two dialects of Modern Portuguese share the same lexicon and most of the sentences they produce are superficially identical. Yet they are conjectured, on linguistic grounds, to implement different rhythms. We show that this linguistic question can be formulated as a problem of model selection in the class of variable length Markov chains. To carry on this approach, we compare texts from European and Brazilian Portuguese. These texts are previously encoded according to some basic rhythmic features of the sentences which can be automatically retrieved. This is an entirely new approach from the linguistic point of view. Our statistical contribution is the introduction of the smallest maximizer criterion which is a constant free procedure for model selection. As a by-product, this provides a solution for the problem of optimal choice of the penalty constant when using the BIC to select a variable length Markov chain. Besides proving the consistency of the smallest maximizer criterion when the sample size diverges, we also make a simulation study comparing our approach with both the standard BIC selection and the Peres-Shields order estimation. Applied to the linguistic sample constituted for our case study, the smallest maximizer criterion assigns different context-tree models to the two dialects of Portuguese. The features of the selected models are compatible with current conjectures discussed in the linguistic literature., Comment: Published in at http://dx.doi.org/10.1214/11-AOAS511 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org)

In this paper we present three different results dealing with the number of $(\leq k)$-facets of a set of points: 1. We give structural properties of sets in the plane that achieve the optimal lower bound $3\binom{k+2}{2}$ of $(\leq k)$-edges for a fixed $0\leq k\leq \lfloor n/3 \rfloor -1$; 2. We give a simple construction showing that the lower bound $3\binom{k+2}{2}+3\binom{k-\lfloor \frac{n}{3} \rfloor+2}{2}$ for the number of $(\leq k)$-edges of a planar point set appeared in [Aichholzer et al. New lower bounds for the number of ($\leq k$)-edges and the rectilinear crossing number of $K_n$. {\em Disc. Comput. Geom.} 38:1 (2007), 1--14] is optimal in the range $\lfloor n/3 \rfloor \leq k \leq \lfloor 5n/12 \rfloor -1$; 3. We show that for $k < \lfloor n/(d+1) \rfloor$ the number of $(\leq k)$-facets of a set of $n$ points in general position in $\mathbb{R}^d$ is at least $(d+1)\binom{k+d}{d}$, and that this bound is tight in the given range of $k$., Comment: 11 pages, 5 figures. Submitted to European Journal of Combinatorics. Changes: last result in the abstract generalized to $d$ dimensions, Section 4 simplified

We provide a new lower bound on the number of $(\leq k)$-edges of a set of $n$ points in the plane in general position. We show that for $0 \leq k \leq\lfloor\frac{n-2}{2}\rfloor$ the number of $(\leq k)$-edges is at least $$ E_k(S) \geq 3\binom{k+2}{2} + \sum_{j=\lfloor\frac{n}{3}\rfloor}^k (3j-n+3), $$ which, for $k\geq \lfloor\tfrac{n}{3}\rfloor$, improves the previous best lower bound in [J. Balogh, G. Salazar, Improved bounds for the number of ($\leq k$)-sets, convex quadrilaterals, and the rectilinear crossing number of $K_n$]. As a main consequence, we obtain a new lower bound on the rectilinear crossing number of the complete graph or, in other words, on the minimum number of convex quadrilaterals determined by $n$ points in the plane in general position. We show that the crossing number is at least $$ \Bigl({41/108}+\epsilon \Bigr) \binom{n}{4} + O(n^3) \geq 0.379631 \binom{n}{4} + O(n^3), $$ which improves the previous bound of $0.37533 \binom{n}{4} + O(n^3)$ in [J. Balogh, G. Salazar, Improved bounds for the number of ($\leq k$)-sets, convex quadrilaterals, and the rectilinear crossing number of $K_n$] and approaches the best known upper bound $0.38058\binom{n}{4}$ in [O. Aichholzer, H. Krasser, Abstract order type extension and new results on the rectilinear crossing number]., Comment: 14 pages, 4 figures, submitted to Discrete and Computational Geometry, fixed a gap in the proof of Theorem 10