Miracle-dz/UniFAR-FTUs huggingface dataset:
Nonnormal Small Jump Approximation of Infinitely Divisible Distributions

We study a type of nonnormal small jump approximation of infinitely divisible distributions. By incorporating compound Poisson, gamma, and normal distributions, the approximation has a higher order of cumulant matching than its normal counterpart, and, hence, in many cases a higher rate of approximation error decay as the cutoff for the jump size tends to 0. The parameters of the approximation are easy to fix, and its random sampling has the same order of computational complexity as the normal approximation. An error bound of the approximation in terms of the total variation distance is derived. Simulations empirically show that the nonnormal approximation can have a significantly smaller error than its normal counterpart.
The Bender-Dunne basis operators as Hilbert space operators

The Bender-Dunne basis operators, T−m,n=2−n∑k=0nnkqkp−mqn−k where q and p are the position and momentum operators, respectively, are formal integral operators in position representation in the entire real line R for positive integers n and m. We show, by explicit construction of a dense domain, that the operators T−m,n's are densely defined operators in the Hilbert space L2(R).
Identifying and Estimating Biases between XBT and Argo Observations Using Satellite Altimetry

Abstract A methodology is developed to identify and estimate systematic biases between expendable bathythermograph (XBT) and Argo observations using satellite altimetry. Pseudoclimatological fields of isotherm depth are computed by least squares adjustment of in situ XBT and Argo data to altimetry-derived sea height anomaly (SHA) data. In regions where the correlations between isotherm depth and SHA are high, this method reduces sampling biases in the in situ observations by taking advantage of the high temporal and spatial resolution of satellite observations. Temperature profiles from deep XBTs corrected for a bias identified and adopted during the 1990s are considered in this study. The analysis shows that the pseudoclimatological isotherm depths derived from these corrected XBTs are predominantly deeper than the Argo-derived estimates during the 2000–07 period. The XBT-minus-Argo differences increase with depth consistent with hypothesized problems in the XBT fall-rate equation. The depth-dependent XB.
On the index of meromorphic operator-valued functions and some applications

We revisit and connect several notions of algebraic multiplicities of zeros of analytic operator-valued functions and discuss the concept of the index of meromorphic operator-valued functions in complex, separable Hilbert spaces. Applications to abstract perturbation theory and associated Birman-Schwinger-type operators and to the operator-valued Weyl-Titchmarsh functions associated to closed extensions of dual pairs of closed operators are provided.
Global viscosity solutions of generalized Kahler-Ricci flow

We apply ideas from viscosity theory to establish the existence of a unique global weak solution to the generalized Kahler-Ricci flow in the setting of commuting complex structures. Our results are restricted to the case of a smooth manifold with smooth background data. We discuss the possibility of extending these results to more singular settings, pointing out a key error in the existing literature on viscosity solutions to complex Monge-Ampere equations/Kahler-Ricci flow.
Rate-constrained motion estimation

A theoretical frame work for rate-constrained motion estimation is introduced. The best trade- off between displacement vector rate and prediction error rate is shown to be the point were the partial derivatives of the multivariate distortion rate function are equal. Low bit-rate coders are severely rate-constrained, and coarser motion compensation is appropriate for lower bit- rates. A new region-based motion estimator builds a tree of nested regions from back to front, where each region is encoded by a closed B-spline contour. The rate-constraint is a natural termination criterion when building the region tree. Experimental results show that rate- constrained motion compensation is superior to a full-search block matching scheme when incorporated into a motion-compensating hybrid coding scheme, yielding up to 3 dB SNR improvement at 15 kbps.
A Weakly 1-Stable Limiting Distribution for the Number of Random Records and Cuttings in Split Trees

We study the number of random records in an arbitrary split tree (or equivalently, the number of random cuttings required to eliminate the tree). We show that a classical limit theorem for convergence of sums of triangular arrays to infinitely divisible distributions can be used to determine the distribution of this number. After normalization the distributions are shown to be asymptotically weakly 1-stable. This work is a generalization of our earlier results for the random binary search tree, which is one specific case of split trees. Other important examples of split trees include $m$-ary search trees, quadtrees, medians of $(2k+1)$-trees, simplex trees, tries and digital search trees.
A note on energy forms on fractal domains

J. Kigami has laid the foundations of what is now known as analysis on fractals, by allowing the construction of an operator of the same nature of the Laplacian, defined locally, on graphs having a fractal character. The Sierpinski gasket stands out of the best known example. It has, since then, been taken up, developed and popularized by R. S. Strichartz. The Laplacian is obtained through a weak formulation, obtained by means of Dirichlet forms, built by induction on a sequence of graphs that converges towards the considered domain. It is these Dirichlet forms that enable one to obtain energy forms on this domain. Yet, things are not that simple. If, for domains like the Sierpinski gasket, the Laplacian is obtained in a quite natural way, one must bear in mind that Dirichlet forms solely depend on the topology of the domain, and not of its geometry. Which means that, if one aims at building a Laplacian on a fractal domain, the topology of which is the same as, for instance, a line segment, one has to find a way of taking account a very specific geometry. We came across that problem in our work on the graph of the Weierstrass function The solution was thus to consider energy forms more sophisticated than classical ones, by means of normalization constants that could, not only bear the topology, but, also, the very specific geometry of, from now on, we will call W-curves. It is interesting to note that such problems do not seem to arise so much in the existing literature. We presently aim at investigating the links between energy forms and geometry. We have chosen to consider fractal curves, specifically, the Sierpi\'nski arrowhead curve, the limit of which is the Sierpinski gasket. Does one obtain the same Laplacian as for the triangle ? The question appears as worth to be investigated.
{\L}ojasiewicz-type inequalities with explicit exponents for the largest eigenvalue function of real symmetric polynomial matrices

Let $F(x) := (f_{ij}(x))_{i,j=1,\ldots,p},$ be a real symmetric polynomial matrix of order $p$ and let $f(x)$ be the largest eigenvalue function of the matrix $F(x). $ We denote by ${\partial}^\circ f(x)$ the Clarke subdifferential of $f$ at $x. $ In this paper, we first give the following {\em nonsmooth} version of \L ojasiewicz gradient inequality for the function $f$ with an explicit exponent: For any $\bar x\in \Bbb R^n$ there exist $c > 0$ and $\epsilon > 0$ such that we have for all $\|x - \bar{x}\| < \epsilon,$ \begin{equation*} \inf \{ \| w \| \ : \ w \in {\partial}^\circ f(x) \} \ \ge \ c\, |f(x) - f(\bar x)|^{1 - \frac{1}{\mathscr{R}(2n+p(n+1),d+3)}}, \end{equation*} where $d:=\max_{i,j = 1, \ldots, p}\deg f_{i j}$ and $\mathscr{R}$ is a function introduced by D'Acunto and Kurdyka: $\mathscr{R}(n, d) := d(3d - 3)^{n-1}$ if $d \ge 2$ and $\mathscr{R}(n, d) := 1$ if $d = 1. $ Then we establish error bounds with explicitly determined exponents, local and global, for the largest eigenvalue function $f(x)$ of the matrix $F(x)$.
Demographics, attitudes and emotions as predictors of support for bear management

Abstract Context. The Illinois Department of Natural Resources was mandated by legislation to develop management plans for American Black Bears and needed Illinois residents’ preferences for bear management strategies. Aims. The aim of this article was to examine how demographics, emotions and attitudes were related to support for three American black bear management strategies (active reintroduction, natural recolonisation, having breeding populations of black bears). Researchers have repeatedly suggested that these predictors are related to support for management actions. Methods. Data were obtained from a mail survey sent to two populations of stakeholder groups. A total of 896 agricultural producers completed the questionnaire (response rate = 36%); 904 hunters completed the questionnaire (response rate = 36%). Five demographic variables were used in the analyses: (1) agricultural producer; (2) hunter; (3) age; (4) sex; and (5) residence growing up. Positive and negative emotional dispositions were operationalised with eight items. General attitude toward bears was measured with four items. All three management questions were asked for ‘in Illinois’ and ‘in my county’. Reliability analyses supported combining the psychological variables into indices for each construct. Key results. Findings indicated that demographic and psychological characteristics are related to support for bear management strategies, but that these relationships are complex for a number of reasons. First, the regression beta coefficients for the demographic regression models were ‘minimal’ (M = 0.13), whereas the coefficients for psychological variables were ‘typical’ (M = 0.30). Second, not all of the demographic and psychological variables affected support for agency actions in the same way. Third, the average R2 for the three demographic models was only 16%, whereas the average R2 for the three psychological characteristics models was 53%. ConclusionsGiven the weak relationships between demographics and support for bear management, managers may not need to always target specific groups based on their demographics. Implications. Certain situations may warrant specific messages to target audiences; weak demographic relationships suggest that managers should be cautious when using these characteristics to target communication messages to specific groups.
Effect of loading orientation on plasticity in nano-laminated CoNiCrFeMn dual-phase high-entropy alloy: a molecular dynamics study

Dual-phase high-entropy alloys (DP-HEAs) have been proved to be a kind of promising materials that exhibit a combination of excellent strength and ductility. Previous studies have emphasized the effect of interface and phase volume fraction on mechanical performance in DP-HEAs. However, the deformation mechanisms such as interplays between dislocations and the constituent phases have not been fully understood. Particularly, the research concerning plastic anisotropy in DP-HEAs is still lacking. Here, molecular dynamics simulations are performed to probe the effect of loading orientation on plasticity in the nano-laminated face-centered cubic (FCC)/hexagonal close-packed (HCP) CoNiCrFeMn DP-HEA. Results reveal that a switch from strengthening to softening and back to strengthening is closely related to the activation of different slip systems when tailoring the inclination angles of the nanolaminates with respect to the tensile direction from 0° to 90°. Slip transfer across phase boundaries, phase transformation and the nucleation of shear bands dominate the plasticity in the samples with low, medium and high inclination angles, respectively. Furthermore, the evolution of microstructures, such as dislocations, stacking faults, and FCC/HCP phase are analyzed to study the underlying deformation mechanisms. These results can help understand the plastic anisotropy of DP-HEAs and design alloys with excellent mechanical properties for engineering applications.
Logarithmic conformal field theory: a lattice approach

Logarithmic conformal field theories (LCFT) play a key role, for instance, in the description of critical geometrical problems (percolation, self-avoiding walks, etc), or of critical points in several classes of disordered systems (transition between plateaux in the integer and spin quantum Hall effects). Much progress in their understanding has been obtained by studying algebraic features of their lattice regularizations. For reasons which are not entirely understood, the non-semi-simple associative algebras underlying these lattice models—such as the Temperley–Lieb algebra or the blob algebra—indeed exhibit, in finite size, properties that are in full correspondence with those of their continuum limits. This applies not only to the structure of indecomposable modules, but also to fusion rules, and provides an ‘experimental’ way of measuring couplings, such as the ‘number b’ quantifying the logarithmic coupling of the stress–energy tensor with its partner. Most results obtained so far have concerned boundary LCFTs and the associated indecomposability in the chiral sector. While the bulk case is considerably more involved (mixing in general left and right moving sectors), progress has also recently been made in this direction, uncovering fascinating structures. This study provides a short general review of our work in this area.
Categorical action of the extended braid group of affine type A

Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we identify the trigraded dimensions of the space of morphisms of this category with intersection numbers coming from the topological origin of the group.
The naming game on the complete graph

We consider a model of language development, known as the naming game, in which agents invent, share and then select descriptive words for a single object, in such a way as to promote local consensus. When formulated on a finite and connected graph, a global consensus eventually emerges in which all agents use a common unique word. Previous numerical studies of the model on the complete graph with $n$ agents suggest that when no words initially exist, the time to consensus is of order $n^{1/2}$, assuming each agent speaks at a constant rate. We show rigorously that the time to consensus is at least $n^{1/2-o(1)}$, and that it is at most constant times $\log n$ when only two words remain. In order to do so we develop sample path estimates for quasi-left continuous semimartingales with bounded jumps.
Computing higher rank primitive root densities

We extend the character sum method for the computation of densities in Artin primitive root problems developed by H. W. Lenstra and the authors to the situation of radical extensions of arbitrary rank. Our algebraic set-up identifies the key parameters of the situation at hand, and obviates the lengthy analytic multiplicative number theory arguments that used to go into the computation of actual densities. It yields a conceptual interpretation of the formulas obtained, and enables us to extend their range of application in a systematic way.
Algebraic Method in Tilings

In this paper we introduce a new algebraic method in tilings. Combining this method with Hilbert's Nullstellensatz we obtain a necessary condition for tiling $n$-space by translates of a cluster of cubes. Further, the polynomial method will enable us to show that if there exists a tiling of $n$-space by translates of a cluster $V$ of prime size then there is a lattice tiling by $V$ as well. Finally, we provide supporting evidence for a conjecture that each tiling by translates of a prime size cluster $V$ is lattice if $V$ generates $n$-space.
Definable coaisles over rings of weak global dimension at most one

In the setting of the unbounded derived category D(R) of a ring R of weak global dimension at most one we consider t-structures with a definable coaisle. The t-structures among these which are stable (that is, the t-structures which consist of a pair of triangulated subcategories) are precisely the ones associated to a smashing localization of the derived category. In this way, our present results generalize those of [B\v{S}17] to the non-stable case. As in the stable case [B\v{S}17], we confine for the most part to the commutative setting, and give a full classification of definable coaisles in the local case, that is, over valuation domains. It turns out that unlike in the stable case of smashing subcategories, the definable coaisles do not always arise from homological ring epimorphisms. We also consider a non-stable version of the telescope conjecture for t-structures and give a ring-theoretic characterization of the commutative rings of weak global dimension at most one for which it is satisfied.
A novel robust convolutional neural network for uniform resource locator classification from the view of cyber security

Uniform resource locator (URL)‐based cyber‐attacks form a major part of security threats in cyberspace. Even though the experience and awareness of the end‐users help them protect themselves from these attacks, a software‐based solution is necessary for comprehensive protection. To this end, a novel robust URL classification model based on convolutional neural network is proposed in this study. The proposed model classifies given URLs into five classes, namely, ( i$$ \mathrm{i} $$ ) benign$$ \mathrm{benign} $$ , ( ii$$ \mathrm{ii} $$ ) defacement$$ \mathrm{defacement} $$ , ( iii$$ \mathrm{iii} $$ ) phishing$$ \mathrm{phishing} $$ , ( iv$$ \mathrm{iv} $$ ) spam$$ \mathrm{spam} $$ , and ( v$$ \mathrm{v} $$ ) malware$$ \mathrm{malware} $$ . The proposed model was trained and evaluated on a gold standard URL dataset comprising of 36,707$$ \mathrm{36,707} $$ samples. According to the experimental result, the proposed model obtained an accuracy as high as 98.1%$$ 98.1\% $$ which outperformed the state‐of‐the‐art. Based on the same architecture, we proposed another classifier, a binary classifier that detects malicious URLs without dealing with their types. This binary classifier obtained an accuracy as high as 99.3%$$ 99.3\% $$ which outperformed the state‐of‐the‐art as well. The experimental result demonstrates the feasibility of the proposed solution.
Infrared frequencies and intensities for astrophysically important polycyclic aromatic hydrocarbon cations

Polycyclic aromatic hydrocarbons (PAHs) have been implicated as the carriers of the 'unidentified infrared' (UIR) emission bands observed from the interstellar medium. It has long been thought that these molecules, if present, probably exist as cations. In this paper we present infrared spectra of the cations of five moderate-sized PAHs. The PAH cations have been produced by low-energy electron impact and then trapped and stabilized in argon matrices at 12 K. To date, results have been obtained on naphthalene, anthracene, pyrene, perylene, and coronene. A common feature of the infrared spectra of all these cations is the very different intensity pattern of the ions compared to the neutral parents. Visible and (partial) infrared spectra of the coronene cation are also presented. It is shown that the out-of-plane CH bending mode shifts to a position very close to the UIR band at 11.3 microns. The astrophysical impact of these observations is discussed.
Phasor-Based Approach for Harmonic Assessment from Multiple Distributed Energy Resources

This paper analyzes impacts and interactions of harmonics from multiple sources, especially distributed energy resources, on distribution networks. We propose a new index, the Phasor Harmonic Index (PHI), that considers both harmonic source magnitude and phase angle, while other commonly used harmonic indices are based solely on magnitude of waveforms. The use of such an index becomes feasible and practical through emerging monitoring technologies like micro-Synchrophasors in distribution networks that help measure and visualize voltage and current phase angles along with their magnitudes. A very detailed model of a distribution network is also needed for the harmonic interaction assessment in this paper.
The Nascent Solar Wind: Origin and Acceleration

High-speed solar wind is known to originate in polar coronal holes, which, however, are made up of two components: bright, high-density regions known as "plumes" and dark, weakly emitting low-density regions known as "interplumes. " Recent space observations have shown that the width of UV lines is larger in interplume regions, while observations of the ratio of the O VI doublet lines at 1032 and 1037 Å, at 1.7 solar radii, suggest higher outflows in interplume regions than in plumes at that altitude. These results favor interplume regions as sources of the fast solar wind. The present work aims at investigating the outflow speed versus altitude properties of the O VI and H I ions, at heights below 2 solar radii, in both plumes and interplume regions. To this end, we examined Solar Ultraviolet Measurement of Emitted Radiation (SUMER) and Ultraviolet Coronagraph Spectrometer (UVCS) observations of a north polar coronal hole taken on 1996 June 3, over the altitude range between 1 and 2 solar radii, and through a Doppler dimming analysis of our data, we show that interplume areas may be really identified as sources of fast wind streams. The behavior of plumes, on the contrary, can be interpreted in terms of static structures embedded in the interplume ambient. We conclude by comparing our results with the predictions of theoretical models of the solar wind and giving an empirical estimate of the heating rate, per particle, for H I and O VI ions in interplume regions at 1.75 and 2.0 solar radii.
Characterization of the shape of a scattering obstacle using the spectral data of the far field operator

This paper is concerned with the inverse obstacle scattering problem for time harmonic plane waves. We derive a factorization of the far field operator F in the form and prove that the ranges of and G coincide. Then we give an explicit characterization of the scattering obstacle which uses only the spectral data of the far field operator F. This result is used to prove a convergence result for a recent numerical method proposed by Colton, Kirsch, Monk, Piana and Potthast. We illustrate this method by some numerical examples.
Solvable Leibniz algebra with non-Lie and non-split naturally graded filiform nilradical and its rigidity

The description of complex solvable Leibniz algebras whose nilradical is a naturally graded filiform algebra is already known. Unfortunately, a mistake was made in that description. Namely, in the case where the dimension of the solvable Leibniz algebra with nilradical $F_n^1$ is equal to $n+2$, it was asserted that there is no such algebra. However, it was possible for us to find a unique $(n+2)$-dimensional solvable Leibniz algebra with nilradical $F_n^1$. In addition, we establish the triviality of the second group of cohomology for this algebra with coefficients in itself, which implies its rigidity.