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This week HackerRank reported Java is now only the second most popular programming language, finally dropping behind JavaScript in the year 2018. Now longtime Slashdot reader shanen asks about the rumors that Java is dead  or is it? Can you convince me that Java isn't as dead as it seems? It's just playing dead and will spring to life? This week one Java news site argued that Javabased Minecraft has in fact "spawned a new generation of Java developers," citing an interview with Red Hat's JBoss Middleware CTO. (And he adds that "It's still the dominant programming language in the enterprise, so whether you're building enterprise clients, services or something in between, Java likely features in there somewhere.") Yet the original submission drew some interesting comments: "The licensing scheme for Java kills it..." "Java programs still are 'the alien on your desktop'. They suck in many ways. Users have learned to avoid them and install 'real programs' instead..." But what do Sl
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The FBI confiscated six drones in Atlanta for flying too close to the football stadium where the Super Bowl will be played Sunday, Reuters reports: Drone flight was prohibited on Saturday and from 10 a.m. until 5:30 p.m. EST on Sunday for one nautical mile (2 km) around the MercedesBenz Stadium and up to an altitude of 1,000 feet (305 meters), the Federal Aviation Administration said. The FAA will establish temporary flight restriction that prohibits drones within a 30nauticalmile radius of the stadium and up to 17,999 feet in altitude from 5:30 p.m. to 11:59 p.m. EST on Sunday, the agency said. .. Drones "are a big concern," said Nick Annan, Homeland Security Investigations special agent in charge. "There are a few other things that are in place to mitigate drones," he added without elaborating. Operators who send drones into restricted areas around the MercedesBenz Stadium could face more than $20,000 in civil penalties and criminal prosecution, according to the FAA. Drone pil
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An anonymous reader quotes TechCrunch: In September of last year, Elon Musk promised to make fixing service times a priority. On an earnings call, he outlined two ways they're working on it: more spare parts at service centers, and giving Tesla cars the ability to automatically get the process started by calling a tow truck as soon as it detects an issue. Said Elon on the call: The next thing we want to add is if a car detects something wrong  like a flat tire or a drive unit failure  that before the car has even come to a halt, there's a tow truck and service loaner on the way. False alarm? Don't want a tow truck to show up? You'll be able to cancel it through the indash display. Musk didn't provide a time frame for when this feature would become available.
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Longtime Slashdot reader darkwing_bmf writes: In an exclusive interview with Popular Mechanics, SpaceX founder Elon Musk explains why stainless steel is the best material to build rocket ships, beating carbon fiber in cost, durability and even weight. "As far as we know, this marks the first time the material has been used in spacecraft construction since some early, illfated attempts during the Atlas program in the late 1950s," reports Popular Mechanics. "It took me quite a bit of effort to convince the team to go in this direction..." Musk tells them. But among the other benefits "It has a high melting point. Much higher than aluminum, and although carbon fiber doesn't melt, the resin gets destroyed at a certain temperature... But steel, you can do 1500, 1600 degrees Fahrenheit."
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More than a year after Facebook commercially launched Express WiFi in five markets, it is ready to bring the connectivity service to the sixth: Ghana. From a report: In partnership with telecom operator Vodafone Ghana, Facebook today launched Express WiFi, part of Internet.org initiative, in the suburban communities of the Western African nation. The service, available locally in Nima, James Town, Kanda, Pig Farm, and Abossey Okine in the capital city Accra, will aim to offer "carriergrade WiFi" to people living in some remote communities that lack fiber optic cables. Ever since India booted Free Basics in early 2016, Facebook has seemingly grown cautious about its connectivity efforts. The company has stopped updating the social media page and press page of Internet.org. Last year, we learned that Facebook had quietly pulled Internet.org from a handful of emerging markets. In recent months, however, it has quietly expanded Internet.org to two new markets  Morocco (in North Afr
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An AIenhanced tool that suggests code snippets for Python developers in real time just raised $17 million in VC funding to expand its R&D team "with a focus on accelerating developer productivity." An anonymous reader quotes VentureBeat: "Our mission is to bring the latest advancements in AI and machine learning (ML) to make writing code fluid, effortless, and more enjoyable," explained [founder Adam] Smith. "Developers using Kite can focus their productive energy toward solving the next big technical challenges, instead of searching the web for code examples illustrating mundane and frequently repeated code patterns...." Instead of relying on the cloud to run its AI engine, Kite now runs locally on a user's computer, letting developers use it offline and without having to upload any code. (Kite still trains its machine learning models with thousands of publicly available code sources from highly rated developers.) Furthermore, running locally allows Kite to fully operate with
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We give two explicit sets of generators of the group of invertible regular functions over QQ on the modular curve Y1(N). The first set of generators is the most surprising. It is essentially the set of defining equations of Y1(k) for k<=N/2 when all these modular curves are simultaneously embedded into the affine plane, and this proves a conjecture of Maarten Derickx and Mark van Hoeij. This set of generators is an elliptic divisibility sequence in the sense that it satisfies the same recurrence relation as the elliptic division polynomials. The second set of generators is explicit in terms of classical analytic functions known as Siegel functions. This is both a generalization and a converse of a result of Yifan Yang. Our proof consists of two parts. First, we relate our two sets of generators. Second, we use qexpansions and Gauss' lemma for power series to prove that our functions generate the full group of modular functions. This second part shows how a proof of Kubert and Lang
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We discuss the extent to which solutions to onephase free boundary problems can be characterized according to their topological complexity. Our questions are motivated by fundamental work of Luis Caffarelli on free boundaries and by striking results of T. Colding and W. Minicozzi concerning finitely connected, embedded, minimal surfaces. We review our earlier work on the simplest case, onephase free boundaries in the plane in which the positive phase is simply connected. We also prove a new, purely topological, effective removable singularities theorem for free boundaries. At the same time, we formulate some open problems concerning the multiply connected case and make connections with the theory of minimal surfaces and semilinear variational problems.
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A consumer DNA testing company has given the FBI access to its two million
0202 MIT Technology 5671 
Antielementarity is a strong way of ensuring that a class of structures , in a given firstorder language, is not closed under elementary equivalence with respect to any infinitary language of the form $\mathscr{L}_{\infty\lambda}$. We prove that many naturally defined classes are antielementary, including the following: $\bullet$ the class of all lattices of finitely generated convex $\ell$subgroups of members of any class of $\ell$groups containing all Archimedean $\ell$groups; $\bullet$ the class of all semilattices of finitely generated $\ell$ideals of members of any nontrivial quasivariety of $\ell$groups; $\bullet$ the class of all Stone duals of spectra of MValgebrasthis yields a negative solution for the MVspectrum Problem; $\bullet$ the class of all semilattices of finitely generated twosided ideals of rings; $\bullet$ the class of all semilattices of finitely generated submodules of modules; $\bullet$ the class of all monoids encoding the nonstable K$_0$theory of
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Potential functions can be used as generating potentials of relevant geometric structures for a Riemannian manifold such as the Riemannian metric and affine connections. We study wether this procedure can also be applied to tensors of rank four and find a negative answer. We study this from the perspective of solving the inverse problem and also from an intrinsic point of view.
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This paper deals with singularities of genus 2 curves on a general (d_1,d_2)polarized abelian surface (S,L). In analogy with Chen's results concerning rational curves on K3 surfaces [Ch1,Ch2], it is natural to ask whether all such curves are nodal. We prove that this holds true if and only if d_2 is not divisible by 4. In the cases where d_2 is a multiple of 4, we exhibit genus 2 curves in L that have a triple, 4tuple or 6tuple point. We show that these are the only possible types of unnodal singularities of a genus 2 curve in L. Furthermore, with no assumption on d_1 and d_2, we prove the existence of at least a nodal curve in L. As a corollary, we obtain nonemptiness of all Severi varieties on general abelian surfaces and hence generalize [KLM, Thm 1.1] to nonprimitive polarizations.
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Fuglede's conjecture in $\mathbb{Z}_{p}^{d}$, $p$ a prime, says that a subset $E$ tiles $\mathbb{Z}_{p}^{d}$ by translation if and only if $E$ is spectral, meaning any complexvalued function $f$ on $E$ can be written as a linear combination of characters orthogonal with respect to $E$. We disprove Fuglede's conjecture in $\mathbb{Z}_p^4$ for all odd primes $p$, by using logHadamard matrices to exhibit spectral sets of size $2p$ which do not tile, extending the result of Aten et al. that the conjecture fails in $\mathbb{Z}_p^4$ for primes $p \equiv 3 \pmod 4$ and in $\mathbb{Z}_p^5$ for all odd primes $p$. We also prove the conjecture in $\mathbb{Z}_2^4$, resolving all cases of fourdimensional vector spaces over prime fields. We give an example showing that our simple proof method does not extend to higher dimensions. However, we include a link to a computer program which the authors have used to verify that, nevertheless, the conjecture holds in $\mathbb{Z}_2^5$ and $\mathbb{Z}_2^6$
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Let $U_1,U_2,\ldots$ be random points sampled uniformly and independently from the $d$dimensional upper halfsphere. We show that, as $n\to\infty$, the $f$vector of the $(d+1)$dimensional convex cone $C_n$ generated by $U_1,\ldots,U_n$ weakly converges to a certain limiting random vector, without any normalization. We also show convergence of all moments of the $f$vector of $C_n$ and identify the limiting constants for the expectations. We prove that the expected Grassmann angles of $C_n$ can be expressed through the expected $f$vector. This yields convergence of expected Grassmann angles and conic intrinsic volumes and answers thereby a question of B\'ar\'any, Hug, Reitzner and Schneider [Random points in halfspheres, Rand. Struct. Alg., 2017]. Our approach is based on the observation that the random cone $C_n$ weakly converges, after a suitable rescaling, to a random cone whose intersection with the tangent hyperplane of the halfsphere at its north pole is the convex hull of th
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Singular boundary value problems (SBVPs) arise in various fields of Mathematics, Engineering and Physics such as boundary layer theory, gas dynamics, nuclear physics, nonlinear optics, etc. The present monograph is devoted to systems of SBVPs for ordinary differential equations (ODEs). It presents existence theory for a variety of problems having unbounded nonlinearities in regions where their solutions are searched for. The main focus is to establish the existence of positive solutions. The results are based on regularization and sequential procedure. First chapter of this monograph describe the motivation for the study of SBVPs. It also include some available results from functional analysis and fixed point theory. The following chapters contain results from author's PhD thesis, National University of Sciences and Technology, Islamabad, Pakistan. These results provide the existence of positive solutions for a variety of systems of SBVPs having singularity with respect to independent
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Consider the minimization of a nonconvex differentiable function over a polyhedron. A popular primaldual firstorder method for this problem is to perform a gradient projection iteration for the augmented Lagrangian function and then update the dual multiplier vector using the constraint residual. However, numerical examples show that this approach can exhibit "oscillation" and may not converge. In this paper, we propose a proximal alternating direction method of multipliers for the multiblock version of this problem. A distinctive feature of this method is the introduction of a "smoothed" (i.e., exponentially weighted) sequence of primal iterates, and the inclusion, at each iteration, to the augmented Lagrangian function a quadratic proximal term centered at the current smoothed primal iterate. The resulting proximal augmented Lagrangian function is inexactly minimized (via a gradient projection step) at each iteration while the dual multiplier vector is updated using the residual o
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It is known that the following five counting problems lead to the same integer sequence~$f_t(n)$: the number of nonequivalent compact Huffman codes of length~$n$ over an alphabet of $t$ letters, the number of `nonequivalent' canonical rooted $t$ary trees (levelgreedy trees) with $n$~leaves, the number of `proper' words, the number of bounded degree sequences, and the number of ways of writing $1= \frac{1}{t^{x_1}}+ \dots + \frac{1}{t^{x_n}}$ with integers $0 \leq x_1 \leq x_2 \leq \dots \leq x_n$. In this work, we show that one can compute this sequence for \textbf{all} $n<N$ with essentially one power series division. In total we need at most $N^{1+\varepsilon}$ additions and multiplications of integers of $cN$ bits, $c<1$, or $N^{2+\varepsilon}$ bit operations, respectively. This improves an earlier bound by Even and Lempel who needed $O(N^3)$ operations in the integer ring or $O(N^4)$ bit operations, respectively.
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In this paper, we examine some properties of the fixed point set of a digitally continuous function. The digital setting requires new methods that are not analogous to those of classical topological fixed point theory, and we obtain results that often differ greatly from standard results in classical topology. We introduce several measures related to fixed points for continuous selfmaps on digital images, and study their properties. Perhaps the most important of these is the fixed point spectrum $F(X)$ of a digital image: that is, the set of all numbers that can appear as the number of fixed points for some continuous selfmap. We give a complete computation of $F(C_n)$ where $C_n$ is the digital cycle of $n$ points. For other digital images, we show that, if $X$ has at least 4 points, then $F(X)$ always contains the numbers 0, 1, 2, 3, and the cardinality of $X$. We give several examples, including $C_n$, in which $F(X)$ does not equal $\{0,1,\dots,\#X\}$. We examine how fixed point
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In this paper, a modified van der Pol oscillator equation is considered which appears in several heart action models. We study its global dynamics and verify many interesting bifurcations such as a Hopf bifurcation, a heteroclinic saddle connection, and a homoclinic saddle connection. Some of these bifurcations are detected by using Conley index methods. We demonstrate how the study of connection matrices and transition matrices shows how to select interesting parameter values for simulations.
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This paper introduces a hierarchical interpolative decomposition butterflyLU factorization (HIDBFLU) preconditioner for solving twodimensional electricfield integral equations (EFIEs) in electromagnetic scattering problems of perfect electrically conducting objects with open surfaces. HIDBFLU leverages the interpolative decomposition butterfly factorization (IDBF) to compress dense blocks of the discretized EFIE operator to expedite its application; this compressed operator also serves as an approximate LU factorization of the EFIE operator leading to an efficient preconditioner in iterative solvers. Both the memory requirement and computational cost of the HIDBFLU solver scale as $O(N\log^2 N)$ in one iteration; the total number of iterations required for a reasonably good accuracy scales as $O(1)$ to $O(\log^2N)$ in all of our numerical tests. The efficacy and accuracy of the proposed preconditioned iterative solver are demonstrated via its application to a broad range of sc
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Dimension profiles were introduced in [8,11] to give a formula for the boxcounting and packing dimensions of the orthogonal projections of a set $R^n$ onto almost all $m$dimensional subspaces. However, these definitions of dimension profiles are indirect and are hard to work with. Here we firstly give alternative definitions of dimension profiles in terms of capacities of $E$ with respect to certain kernels, which lead to the boxcounting and packing dimensions of projections fairly easily, including estimates on the size of the exceptional sets of subspaces where the dimension of projection is smaller the typical value. Secondly, we argue that with this approach projection results for different types of dimension may be thought of in a unified way. Thirdly, we use a Fourier transform method to obtain further inequalities on the size of the exceptional subspaces.
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We investigate the behavior of Boolean dimension with respect to components and blocks. To put our results in context, we note that for DushnikMiller dimension, we have that if $\dim(C)\le d$ for every component $C$ of a poset $P$, then $\dim(P)\le \max\{2,d\}$; also if $\dim(B)\le d$ for every block $B$ of a poset $P$, then $\dim(P)\le d+2$. By way of constrast, local dimension is well behaved with respect to components, but not for blocks: if $\text{ldim}(C)\le d$ for every component $C$ of a poset $P$, then $\text{ldim}(P)\le d+2$; however, for every $d\ge 4$, there exists a poset $P$ with $\text{ldim}(P)=d$ and $\dim(B)\le 3$ for every block $B$ of $P$. In this paper we show that Boolean dimension behaves like DushnikMiller dimension with respect to both components and blocks: if $\text{bdim}(C)\le d$ for every component $C$ of $P$, then $\text{bdim}(P)\le 2+d+4\cdot2^d$; also if $\text{bdim}(B)\le d$ for every block of $P$, then $\text{bdim}(P)\le 19+d+18\cdot 2^d$.
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We present a framework for characterizing injectivity of classes of maps (on cosets of a linear subspace) by injectivity of classes of matrices. Using our formalism, we characterize injectivity of several classes of maps, including generalized monomial and monotonic (not necessarily continuous) maps. In fact, monotonic maps are special cases of {\em componentwise affine} maps. Further, we study compositions of maps with a matrix and other composed maps, in particular, rational functions. Our framework covers classical injectivity criteria based on mean value theorems for vectorvalued maps and recent results obtained in the study of chemical reaction networks.
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Kontsevich and Manin gave a formula for the number $N_e$ of rational plane curves of degree $e$ through $3e1$ points in general position in the plane. When these $3e1$ points have coordinates in the rational numbers, the corresponding set of $N_e$ rational curves has a natural Galoismodule structure. We make some extremely preliminary investigations into this Galois module structure, and relate this to the deck transformations of the generic fibre of the product of the evaluation maps on the moduli space of maps. We then study the asymptotics of the number of rational points on hypersurfaces of low degree, and use this to generalise our results by replacing the projective plane by such a hypersurface.
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We present, to the best of the authors' knowledge, all known results for the crossing numbers of specific graphs and graph families. The results are separated into various categories; specifically, results for general graph families, results for graphs arising from various graph products, and results for recursive graph constructions.
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For a lowmobile Poisson bipolar network and under lineofsight/nonlineofsight (LOS/NLOS) pathloss model, we study repetitive retransmissions (RR) and blocked incremental redundancy (BIR). We consider spatiallycoded multipleinput multipleoutput (MIMO) zeroforcing beamforming (ZFBF) multiplexing system, whereby the packet success reception is determined based on the aggregate data rate across spatial dimensions of the MIMO system. Characterization of retransmission performance in this lowmobile configuration is practically important, but inherently complex due to a substantial rate correlation across retransmissions and intractability of evaluating the probability density function (pdf) of aggregate data rate. Adopting tools of stochastic geometry, we firstly characterize the rate correlation coefficient (RCC) for both schemes. Our results show that, compared to RR scheme, BIR scheme has higher RCC while its coverage probability is substantially larger. We demonstrate that t
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Detecting the components common or correlated across multiple data sets is challenging due to a large number of possible correlation structures among the components. Even more challenging is to determine the precise structure of these correlations. Traditional work has focused on determining only the model order, i.e., the dimension of the correlated subspace, a number that depends on how the modelorder problem is defined. Moreover, identifying the model order is often not enough to understand the relationship among the components in different data sets. We aim at solving the complete modelselection problem, i.e., determining which components are correlated across which data sets. We prove that the eigenvalues and eigenvectors of the normalized covariance matrix of the composite data vector, under certain conditions, completely characterize the underlying correlation structure. We use these results to solve the modelselection problem by employing bootstrapbased hypothesis testing.
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This paper studies curves on quartic K3 surfaces, or more generally K3 surfaces which are complete intersection in weighted projective spaces. A folklore conjecture concerning rational curves on K3 surfaces states that all K3 surfaces contain infinite number of irreducible rational curves. It is known that all K3 surfaces, except those contained in the countable union of hypersurfaces in the moduli space of K3 surfaces satisfy this property. In this paper we present a new approach for constructing curves on varieties which admit nice degenerations. We apply this technique to the above problem and prove that there is a Zariski open dense subset in the moduli space of quartic K3 surfaces whose members satisfy the conjecture. Various other curves of positive genus can be also constructed.
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We initiate the study of Boolean function analysis on highdimensional expanders. We give a randomwalk based definition of high dimensional expansion, which coincides with the earlier definition in terms of twosided link expanders. Using this definition, we describe an analogue of the Fourier expansion and the Fourier levels of the Boolean hypercube for simplicial complexes. Our analogue is a decomposition into approximate eigenspaces of random walks associated with the simplicial complexes. We then use this decomposition to extend the FriedgutKalaiNaor theorem to highdimensional expanders. Our results demonstrate that a highdimensional expander can sometimes serve as a sparse model for the Boolean slice or hypercube, and quite possibly additional results from Boolean function analysis can be carried over to this sparse model. Therefore, this model can be viewed as a derandomization of the Boolean slice, containing only $X(k1)=O(n)$ points in contrast to $\binom{n}{k}$ points
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Given two $\left( n+1\right) \times\left( n+1\right)$matrices $A$ and $B$ over a commutative ring, and some $k\in\left\{ 0,1,\ldots,n\right\}$, we consider the $\dbinom{n}{k}\times\dbinom{n}{k}$matrix $W$ whose entries are $\left( k+1\right) \times\left( k+1\right)$minors of $A$ multiplied by corresponding $\left( k+1\right) \times\left( k+1\right)$minors of $B$. Here we require the minors to use the last row and the last column (which is why we obtain an $\dbinom{n}{k}\times\dbinom{n}{k}$matrix, not a $\dbinom{n+1}{k+1}\times\dbinom{n+1}{k+1}$matrix). We prove that the determinant $\det W$ is a multiple of $\det A$ if the $\left( n+1,n+1\right)$th entry of $B$ is $0$. Furthermore, if the $\left( n+1,n+1\right)$th entries of both $A$ and $B$ are $0$, then $\det W$ is a multiple of $\left( \det A\right) \left( \det B\right)$. This extends a previous result of Olver and the author ( arXiv:1802.02900 ).
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Using dual perturbation theory in a nonsunreflexive context, we establish a correspondence between 1. a class of nonlinear abstract delay differential equations (DDEs) with unbounded linear part and an unknown taking values in an arbitrary Banach space and 2. a class of abstract weak* integral equations of convolution type involving the sunstar adjoint of a translationlike strongly continuous semigroup. For this purpose we also characterize the sun dual of the underlying state space. More generally we consider bounded linear perturbations of an arbitrary strongly continuous semigroup and we comment on some implications for the particular case of abstract DDEs.
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The presented splitting lemma extends the techniques of Gromov and Forstneri\v{c} to glue local sections of a given analytic sheaf, a key step in the proof of all Oka principles. The novelty on which the proof depends is a lifting lemma for transition maps of coherent sheaves, which yields a reduction of the proof to the work of Forstneri\v{c}. As applications we get shortcuts in the proofs of Forster and Ramspott's Oka principle for admissible pairs and of the interpolation property of sections of elliptic submersions, an extension of Gromov's results obtained by Forstneri\v{c} and Prezelj.
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Inspired by a PDEODE system of aggregation developed in the biomathematical literature, an interacting particle system representing aggregation at the level of individuals is investigated. It is proved that the empirical density of the individual converges to solution of the PDEODE system.
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Caching the content closer to the user equipments (UEs) in heterogenous cellular networks (HetNets) improves userperceived QualityofService (QoS) while lowering the operators backhaul usage/costs. Nevertheless, under the current networking strategy that promotes aggressive densification, it is unclear whether cacheenabled HetNets preserve the claimed costeffectiveness and the potential benefits. This is due to 1) the collective cost of caching which may inevitably exceed the expensive cost of backhaul in a dense HetNet, and 2) the excessive interference which affects the signal reception irrespective of content placement. We analyze these significant, yet overlooked, issues, showing that while densification reduces backhaul load and increases spectral efficiency in cacheenabled dense networks, it simultaneously reduces cachehit probability and increases the network cost. We then introduce a caching efficiency metric, area spectral efficiency per unit spent cost, and find it enou
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Let $K$ be a Henselian, nontrivially valued field with separated analytic structure. We prove the existence of definable retractions onto an arbitrary closed definable subset of $K^{n}$. Hence directly follow definable nonArchimedean versions of the extension theorems by TietzeUrysohn and Dugundji. This generalizes our previous paper dealing with complete nonArchimedean fields with separated power series and remains true for Henselian valued fields with strictly convergent analytic structure, because every such a structure can be extended in a definitional way to a separated analytic structure. Our proof uses a variant of the one from that paper, based on canonical resolution of singularities, and a modeltheoretic compactness argument.
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In this note, we extend work of Farkas and Rim\'anyi on applying quadric rank loci to finding divisors of small slope on the moduli space of curves by instead considering all divisorial conditions on the hypersurfaces of a fixed degree containing a projective curve. This gives rise to a large family of virtual divisors on $\overline{\mathcal{M}_g}$. We determine explicitly which of these divisors are candidate counterexamples to the Slope Conjecture. The potential counterexamples exist on $\overline{\mathcal{M}_g}$, where the set of possible values of $g\in \{1,\ldots,N\}$ has density $\Omega(\log(N)^{0.087})$ for $N>>0$. Furthermore, no divisorial condition defined using hypersurfaces of degree greater than 2 give counterexamples to the Slope Conjecture, and every divisor in our family has slope at least $6+\frac{8}{g+1}$.
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We investigate the effect of surface tension on the linear RayleighTaylor (RT) instability in stratified incompressible viscous fluids with or without (interface) surface tension. The existence of linear RT instability solutions with largest growth rate $\Lambda$ is proved under the instability condition (i.e., the surface tension coefficient $\vartheta$ is less than a threshold $\vartheta_{\mm{c}}$) by modified variational method of PDEs. Moreover we find a new upper bound for $\Lambda$. In particular, we observe from the upper bound that $\Lambda$ decreasingly converges to zero, as $\vartheta$ goes from zero to the threshold $\vartheta_{\mm{c}}$. The convergence behavior of $\Lambda$ mathematically verifies the classical RT instability experiment that the instability growth is limited by surface tension during the linear stage.
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Let $(\bf U, \bf U^\imath)$ be a quasisplit quantum symmetric pair of arbitrary KacMoody type, where "quasisplit" means the corresponding Satake diagram contains no black node. We give a presentation of the $\imath$quantum group $\bf U^\imath$ with explicit $\imath$Serre relations. The verification of new $\imath$Serre relations is reduced to some new qbinomial identities. Consequently, $\bf U^\imath$ is shown to admit a bar involution under suitable conditions on the parameters.
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Calabi observed that there is a natural correspondence between the solutions of the minimal surface equation in $\mathbb{R}^3$ with those of the maximal spacelike surface equation in $\mathbb{L}^3$. We are going to show how this correspondence can be extended to the family of $\varphi $minimal graphs in $\mathbb{R}^3 $ when the function $\varphi$ is invariant under a twoparametric group of translations. We give also applications in the study and description of new examples.
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We prove that the KLR algebra associated with the cyclic quiver of length $e$ is a subquotient of the KLR algebra associated with the cyclic quiver of length $e+1$. We also give a geometric interpretation of this fact. This result has an important application in the theory of categorical representations. We prove that a category with an action of $\widetilde{\mathfrak{sl}}_{e+1}$ contains a subcategory with an action of $\widetilde{\mathfrak{sl}}_{e}$. We also give generalizations of these results to more general quivers and Lie types.
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Recently, in the paper \cite{CJKM1} we suggested the two conjectures about the diameter of iodecomposable Riordan graphs of the Bell type. In this paper, we give a counterexample for the first conjecture. Then we prove that the first conjecture is true for the graphs of some particular size and propose a new conjecture. Finally, we show that the second conjecture is true for some special iodecomposable Riordan graphs.
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Unmanned aerial vehicles (UAVs) have recently found abundant applications in the public and civil domains. To ensure reliable control and navigation, connecting UAVs to controllers via existing cellular network infrastructure, i.e., ground base stations (GBSs), has been proposed as a promising solution. Nevertheless, it is highly challenging to characterize the communication performance of cellularconnected UAVs, due to their unique propagation conditions. This paper proposes a tractable framework for the coverage analysis of cellularconnected UAV networks, which consists of a new blockage model and an effective approach to handle general fading channels. In particular, a lineofsight (LoS) ball model is proposed to capture the probabilistic propagation in UAV communication systems, and a tractable expression is derived for the Laplace transform of the aggregate interference with general Nakagami fading. This framework leads to a tractable expression for the coverage probability, wh
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Our aim is to study the existence and uniqueness of the $L^{p}$  variational solution, with $p>1,$ of the following multivalued backward stochastic differential equation with $p$integrable data: \[ \left\{ \begin{align*} &dY_{t}+\partial_{y}\Psi\left( t,Y_{t}\right) dQ_{t} \ni H\left( t,Y_{t},Z_{t}\right) dQ_{t}Z_{t}dB_{t},\;t\in\left[ 0,T\right] ,\\ &Y_{T} =\eta, \end{align*} \right. \] where $Q$ is a progresivelly measurable increasing continuous stochastic process and $\partial_{y}\Psi$ is the subdifferential of the convex lower semicontinuous function $y\mapsto\Psi(t,y)$. In the framework $p\geq2$ of Maticiuc, R\u{a}\c{s}canu from [Bernoulli, 2015], the strong solution found it there is the unique variational solution, via the uniqueness property proved in the present article.
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Presented is a method to compute certain classes of HamiltonJacobi equations that result from optimal control and trajectory generation problems with time delays. Many robotic control and trajectory problems have limited information of the operating environment a priori and must continually perform online trajectory optimization in real time after collecting measurements. The sensing and optimization can induce a significant time delay, and must be accounted for when computing the trajectory. This paper utilizes the generalized Hopf formula, which avoids the use of grids and numerical gradients that is typical of other methods for computing solutions to the HamiltonJacobi equation, which suffer exponential dimensional scaling. We present as an example a robot that incrementally predicts a communication channel from measurements as it travels. As part of this example, we introduce a seemingly new generalization of a nonparametric formulation of robotic communication channel estimatio
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Let $\text{Mod}(S_g)$ be the mapping class group of the closed orientable surface $S_g$ of genus $g\geq 2$. In this paper, we derive necessary and sufficient conditions for two finiteorder mapping classes to have commuting conjugates in $\text{Mod}(S_g)$. As an application of this result, we show that any finiteorder mapping class, whose corresponding orbifold is not a sphere, has a conjugate that lifts under any finitesheeted cover of $S_g$. Furthermore, we show that any torsion element in the centralizer of an irreducible finite order mapping class is of order at most $2$. We also obtain conditions for the primitivity of a finiteorder mapping class. Finally, we describe a procedure for determining the explicit hyperbolic structures that realize twogenerator finite abelian groups of $\text{Mod}(S_g)$ as isometry groups.
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Derived equivalences of twisted K3 surfaces induce twisted Hodge isometries between them; that is, isomorphisms of their cohomologies which respect certain natural lattice structures and Hodge structures. We prove a criterion for when a given Hodge isometry arises in this way. In particular, we describe the image of the representation which associates to any autoequivalence of a twisted K3 surface its realization in cohomology: this image is a subgroup of index one or two in the group of all Hodge isometries of the twisted K3 surface. We show that both indices can occur.
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In this work we consider the following class of fractional $p\&q$ Laplacian problems \begin{equation*} (\Delta)_{p}^{s}u+ (\Delta)_{q}^{s}u + V(\varepsilon x) (u^{p2}u + u^{q2}u)= f(u) \mbox{ in } \mathbb{R}^{N}, \end{equation*} where $\varepsilon>0$ is a parameter, $s\in (0, 1)$, $1< p<q<\frac{N}{s}$, $(\Delta)^{s}_{t}$, with $t\in \{p,q\}$, is the fractional $t$Laplacian operator, $V:\mathbb{R}^{N}\rightarrow \mathbb{R}$ is a continuous potential and $f:\mathbb{R}\rightarrow \mathbb{R}$ is a $\mathcal{C}^{1}$function with subcritical growth. Applying minimax theorems and the LjusternikSchnirelmann theory, we investigate the existence, multiplicity and concentration of nontrivial solutions provided that $\varepsilon$ is sufficiently small.
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Apple has now shut down Google’s ability to distribute its internal iOS apps, following a similar shutdown that was issued to Facebook earlier this week. A person familiar with the situation tells The Verge that early versions of Google Maps, Hangouts, Gmail, and other prerelease beta apps have stopped working today, alongside employeeonly apps like a Gbus app for transportation and Google’s internal cafe app. “We’re working with Apple to fix a temporary disruption to some of our corporate iOS apps, which we expect will be resolved soon,” says a Google spokesperson in a statement to The Verge. Apple has not yet commented on the situation. There are two sides to this story. One the one hand, I’m glad Apple is taking measures and revoking some of these companies’ developer rights. These kinds of privacyinvading apps are a terrible idea, even if people get paid for them, and no platform should allow them. On the other hand, though, I would much rather have such tactics be w
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We show that if $M$ is a subRiemannian manifold and $N$ is a Carnot group such that the nilpotentization of $M$ at almost every point is isomorphic to $N$, then there are subsets of $N$ of positive measure that embed into $M$ by bilipschitz maps. Furthermore, $M$ is countably $N$rectifiable, i.e., all of $M$ except for a null set can be covered by countably many such maps.
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Nonnegative matrix factorization (NMF) is a linear dimensionality reduction technique for analyzing nonnegative data. A key aspect of NMF is the choice of the objective function that depends on the noise model (or statistics of the noise) assumed on the data. In many applications, the noise model is unknown and difficult to estimate. In this paper, we define a multiobjective NMF (MONMF) problem, where several objectives are combined within the same NMF model. We propose to use Lagrange duality to judiciously optimize for a set of weights to be used within the framework of the weightedsum approach, that is, we minimize a single objective function which is a weighted sum of the all objective functions. We design a simple algorithm using multiplicative updates to minimize this weighted sum. We show how this can be used to find distributionally robust NMF (DRNMF) solutions, that is, solutions that minimize the largest error among all objectives. We illustrate the effectiveness of this
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A nested Schur complement solver is proposed for iterative solution of linear systems arising in exponential and implicit time integration of the Maxwell equations with perfectly matched layer (PML) nonreflecting boundary conditions. These linear systems are the socalled double saddle point systems whose structure is handled by the Schur complement solver in a nested, twolevel fashion. The solver is demonstrated to have a meshindependent convergence at the outer level, whereas the inner level system is of elliptic type and thus can be treated efficiently by a variety of solvers.
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We introduce the $2$nodal spherical deformation of certain singular fibers of genus $2$ fibrations, and use such deformations to construct various examples of simply connected minimal symplectic $4$manifolds with small topology. More specifically, we construct new exotic minimal symplectic $4$manifolds homeomorphic but not diffeomorphic to ${\mathbb{CP}}^{2}\#6({\overline{\mathbb{CP}}^{2}})$, ${\mathbb{CP}}^{2}\#7({\overline{\mathbb{CP}}^{2}})$, and $3{\mathbb{CP}}^{2}\#k({\overline{\mathbb{CP}}^{2}})$ for $k=16, 17, 18, 19$ using combinations of such deformations, symplectic blowups, and (generalized) rational blowdown surgery. We also discuss generalizing our constructions to higher genus fibrations using $g$nodal spherical deformations of certain singular fibers of genus $g \geq 3$ fibrations.
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In this paper we study axially symmetric solutions of AllenCahn equation with finite Morse index. It is shown that there does not exist such a solution in dimensions between $4$ and $10$. In dimension $3$, we prove that these solutions have finitely many ends. Furthermore, the solution has exactly two ends if its Morse index equals $1$.
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We establish the rectifiability of measures satisfying a linear PDE constraint. The obtained rectifiability dimensions are optimal for many usual PDE operators, including all firstorder systems and all secondorder scalar operators. In particular, our general theorem provides a new proof of the rectifiability results for functions of bounded variations (BV) and functions of bounded deformation (BD). For divergencefree tensors we obtain refinements and new proofs of several known results on the rectifiability of varifolds and defect measures.
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Thomassen formulated the following conjecture: Every $3$connected cubic graph has a redblue vertex coloring such that the blue subgraph has maximum degree $1$ (that is, it consists of a matching and some isolated vertices) and the red subgraph has minimum degree at least $1$ and contains no $3$edge path. We prove the conjecture for Generalized Petersen graphs. We indicate that a coloring with the same properties might exist for any subcubic graph. We confirm this statement for all subcubic trees.
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